computerized analysis of stress-strain consolidation data
TRANSCRIPT
CALVIN G. GRAYSON
SECRETARY
MEMO TO:
SUBJECT:
G. F. Kemper
COMMONWEALTH OF KENTUCKY DEPARTMENT OF TRANSPORTATION
Division of Hesearch 533 South Limestone Lexington, KY 40508
March 30, 1977
State Highway Engineer Chainnan, Research Committee
JULIAN M. CARROLL
GovERNOR
H.2.79
Research Report No. 468, "Computerized Analysis of Stress-Strain Consolidation Data," KYHPR-75-74; HPR-PL-1(12), Part II
The report enclosed completes a task or pl!ase of work which may be appreciated by persons involved in consolidation testing of soils or, more specifically, analysis of the data from consolidation tests. The difficulty of determining the preconsolidated condition of a soil has been an enduring one. Any errors affect estimates of foundation settlement. The computer program is readily implementable, and the report may properly be called an "Implementation Package."
gd Enclosure cc's: Research Committee
Respectfully
?U' �Y.��·-j J as. H. Havens Director of Research
T ec:hnical keport Documentation Page 1. Report No. 2. Government Accession No. 3. Recipient's Cotolog No.
4. Title and Subtitle s. Report Dote
Computerized Analysis of Stress-Strain Consolidation Data March 1977
6. Performing Organization Code
8. Performing Organization Report No. 7. Author( s)
E. Gregory McNulty 468
9, Performing Organization Nome and Address Pivision of Research
10. Work Unit No. (TRAIS)
Kentucky Bureau of Highways 11. Controct or Grant No. 533 S. Limestone Street Lexington, Kentucky 40508 KYHPR-76-74
13. Type of Report and Period Covered
12. Sponsoring Agency Nome and Address
Interim
14. Sponsoring Agency Code
15. Supplementary Notes
Prepared in cooperation with the US Department of Transportation, Federal Highway Administration Study Title: Controlled Rate of Strain and Controlled Gradient Consolidation Testing
16. Abstract
A computerized, mathematical algorithm is described and presented for analyzing the semilogarithmic stress-strain (time-independent) properties of standard, controlled-gradient, and controlled-rate-of-strain
consolidation tests. This algorithm is an automation of manual graphical procedures currently used in engineering practice to obtain stress-strain information necessary for use in time-independent settlement analysis. The Casagrande and Schmertmann constructions are analytically represented to determine the preconsolidation stress and the in situ, compressibility coefficients of compression and expansion. Values for each of these parameters range between a probable and minimum value. The point of maximum curvature is determined for the Casagrande construction by use of the mathematical definition of the radius of curvature or by the analytical representation of a· newly proposed graphical approach. The location of the point of maximum curvature has been found to depend on the arithmetic scale factors used for the horizontal and vertical directions in the semilogadthmic representation of the consolidation curves. The mathematical algorithm is written in Fortran N for use with the IBM 370/165 computer and the Calcomp 663 drum plotter. The computer program has proven effective in the reduction and analysis of stress-strain data from more than 40 controlled and 30 standard consolidation tests.
17. Key Words 18. Distribution Stc:�tement Computer Controlled Gradient Consolidation Graphical Constructions Laboratory Tests Stress-Strain Standard Test Constant Rate of Strain
19. Security CIOssif. (of this report) 20, Security Cla55if, (of this pc:�ge) 21• No. of Pc:�ges 22. Price
Form DOT F 1700.7 18-721 Reproduction of completed page authorized
Research Report 468
COMPUTERIZED ANALYSIS OF STRESS-STRAIN CONSOLIDATION DATA
Interim Report KYHPR-75-74; HPR-PL-1(12), Part II
by
E. Gregory McNulty Research Engineer Assistant
Division of Research Bureau of Highways
DEPARTMENT OF TRANSPORTATION Commonwealth of Kentucky
in cooperation with Federal Highway Administration
U. S. DEPARTMENT OF TRANSPORTATION
The contents of this report reflect the views
of the author who Is responsible for the
facts and the accuracy of the data presented herein.
The contents do not necessarily reflect the official
views or policies of the Federal Highway Administration
or the Kentucky Bureau of H lghways,
This report does not constitute a standard,
specification, or regulation.
March 1977
INTRODUCTION
BACKGROUND The problem of settlement has long been a concern
to civil e<>gineers. The Leaning Tower of Pisa remains a monumental reminder. Before Ka{l Terzaghi disclosed the mechanics of the settlement process in Erabaumechanik in 1925, only parts of the process had been understood .. no one had put it all together. Terzaghi described in an analytical fashion the process associated with the compression of a mass of discrete irregular particles into a denser material. This process became known. as consolidation. The test developed by Terzaghi to study the characteristics of the consolidation process consisted of encasing a cylindrical specimen of particulate material in a ring to prevent lateral deformations, bounding the top and bottom of the specimen with porous s'tones to permit the escape of water from the soli specimen, and applying a vertical pressure to the sample. Deformations of the sample were measured and plotted as a function of stress. Because deformation is permitted only in the vertical direction, this test is commonly referred to today as the one-dimensional consolidation test. Test data have been studied using semilogarithmic graphical representations of the stress-deformation (time-independent) characteristics of the data. Such a representation yields the stress history and compressibility of the material. Knowledge of these material characteristics is of great practical value in the prediction of settlement associated with loadings where the effects of immediate settlement and lateral consolidation may be neglected.
The principle event in the stress history of a soil is tlllit of the maximum, past, vertical pressure, the largest stress experienced by the material in its natural, subsurface environment. It is usually the result of loads imposed by past or present overlying materials and( or) the result of dessication. Today, the maximum, past, vertical pressure is referred to as the "preconsolidation stress." In 1936, Arthur Casagrande (1) devised an empirical, graphical procedure to determine the preconsolidation presssure from the semilogarithmic representation of time-independent, laboratory consolidation data. This method has come to be known as the "Casagrande construction." Figure 1 (2) illustrates the essential characteristics of this well known procedure.
Before 1955, the compressibility characteristics of particulate materials were expressed as the aritlunetic
slopes of the line representations of the semilogarithmic, laboratory consolidation curves. However, these lines did not account for the effects of disturbance on the consolidation curves. In 1955, Schmertmann ( 3) developed a procedure which accounted for the effect of sample distrubance and estimated in situ compressibility characteristics Figure 2 ( 4) shows the essential characteristics of the Schmertmann procedure.
Analyses of time-independent, one-dimensional consolidation data by empirical, graphical techniques such as the Casagrande and Schmertmann constructions have several drawbacks in their practical applications. Graphical procedures require a certain amount of time and effort from competent personnel oftentimes require subjective judgements which are somewhat susceptible to various graphical or computational errors. Results of a survey conducted by Sallfors ( 5) of 28 geotechnical engineers emphasized these difficulties. Figure 3 shows the scatter among engineers asked to determine the preconsolidation pressure of a given set of time-independent consolidation data. Values reported ranged from about 47 to 73 kilopascals. At the SO-percent confidence interval, the values ranged from approximately 55 to 65 kilopascals. Twenty of the 28 values fell in that range. The results show not only the difficulty in determining the preconsolidation pressure but also reflect the fact that different methods were used. Sallfors' survey, while not directly pertinent to the graphical procedures under discl.lSSion, again suggests there is a need for some means to alleviate the problems associated with the analysis of time independent consolidation data. · According to the Geodex Information Source (1973), the only published attempt involving a computer analysis of time-independent consolidation data is that of Schiffman ( 6). As documented in 1973, the program developed by Schiffman does not consider the graphical procedures discussed above and considers only data obtained from the standard, laboratory consolidation test. In essence, his program determines the coefficients for onewdimensional compression and expansion by calculating the arithmetic slope between consecutive data points on the void ratio-logarithm of effective-stress consolidation curves. The effect of specimen disturbance is not accounted for in the determination of the compression coefficients.
Figure 1.
2
Casagrande Construction for the Determination of the Preconsolidation Pressure (after Ladd, 1968).
. ..
·tPRECONSOL.IDAT ON PRE.SSURE)
.!:"---........,.,.. 1-10 R I :tON TAL. . ... . . .
... -..... ·SECTOR
EXPANSION OR CURVE.
Figure 2.
(PROBABl-11:. FROM CASAGRANDE COINSl�RUC'flriNJ
Reconstruction of in situ Compression Curves Using Schmertmann 's Construction (after Ladd, 1968).
3
Figure 3. Distribution of Evaluated Preconsolidation Pressures (80-percent confidence interval) (after Sallfors, 1975).
In May 1975, the Kentucky Department of Transportation's Division of Research began the development of a computer program which would completely reduce, analyze, and plot data obtained from three types of laboratory consolidation tests. The material presented herein is a detailed description of the computer program which was achieved during an ensuing year of research and development. Included are coding instructions and examples of input and output. The computer program contains several innovative features which provide for the mathematical application of the Casagrande and Schmertmann constructions and the determination of the preconsolidation pressure and in situ coefficients of compressibility. The program also provides for complete reduction and plotting of the time-independent consolidation data obtained from three laboratory tests: standard, controlled-gradient, and
4
controlled-rate-of-strain. A discussion of the latter two has been presented elsewhere (7, 8, 9). The following discussion also includes a description of the algorithm used to study the time-independent consolidation data, the use of the algorithm for determining the point of maximum curvature and the preconsolidation pressure, a new procedure for determining maximum curvature and preconsolidation pressure, and the computer program capabilities and limitations. The computer program in APPENDIX A does not consider time-dependent (compression as a function of time) data obtained from the various consolidation tests. Future efforts will be devoted to plotting and analyzing time-dependent consolidation data and to determining coefficients of consolidation, Cv. This second phase will be in a future report.
ALGORITHM FOR TIME-INDEPENDENT, LABORATORY, CONSOLIDATION TEST DATA
The algorithm presented herein is a means of automating the current, manual, graphical procedures to analyze the time-independent, laboratory consolidation data. Four main points will be discussed in the description of this algorithm: the type of numerical analysis employed, the reasons for choosing this type of numerical analysis, a brief description of the analytical procedures, and a general description of how they are used to automate the Casagrande and Schmertmann graphical constructions with respect to the semilog, time�independent, one-dimensional consolidation data.
TYPE OF NUMERICAL ANALYSIS The central element of the algorithm is the use of
analytical curve-fitting procedures to represent the standard, graphical, semilog representation of test data. An ordinary ]east-squares polynomial ( 10) is used to represent the compression curve characteristics; a linear, least-squares representation is used for the rebound or expansion data. It is important to understand that these two functions are applied to the logarithms, base ten, of the abscissae. In other words, the raw data points which originally span logarithmic cycles are now reduced to a common, narrow, arithmetic range of values.
CRITERIA FOR SELECTION OF ORDINARY POLYNOMIAL
Three criteria were considered in selecting ordinary polynominals: functional shape, functional simplicity, and analytical accuracy. Any analytical fnnction which is used for curve fitting must satisfy the all-important criteria of functional shape or form. Implied in this statement is the requirement that the function have the flexibility to accurately duplicate the wide range of shapes or forms to be expected from a given set of data. The ordinary polynomial satisfies all of these requirements amazingly well. Other types of functional fits have been investigated. Exponential and logarithmic ftu1ctions are not satisfactory because their seemingly appropriate shapes are too extreme and inflexible to provide an accurate estimate of the point of maximum curvature and linear portion of virgin compression. In contrast, rational functions based on Chebyshev (Tchebycheff) polynomials are much better for fitting curves than exponential or logarithmic functions. However, these types of rational functions still have the general characteristic of being too inflexible to satisfactorily describe some of the finer, yet essential! shape characteristics. Example fits of the rational function to data are given in Figure 4. It is obvious
from the figure that there are significant variations between rational functions of different orders. In contrast, the ordinary polynomials shown in Figure 5 do not vary significantly in their fit to the same data points shown in Figure 4. In view of this comparison, the shape of the ordinary polynominal has less dependence on the functional order used. This is very important from the standpoint of reducing the subjectivity involved in the choice of an appropriate order of the curve-fitting function.
The choice of any curve-fitting function should take into account the difficulty of manipulating the analytical expression. Differentiation and the use of related analytical expressions may become cumbersome for many types of functions. Exponential and logarithmic functions are especially cumbersome in a general operational sense because their related analytical operations are wholly dependent on the particular fnnctional expression at hand. In other words, these types of functions are usually not derived from any particular recurrence relationship which can be used to obtain greater flexibility in functional shape. On the other hand, rational and polynomial functions do have desirable recurrence relationships. From the standpoint of mathematical manipulations, the ordinary polynomial is the most desirable of these functions because its recurrence relationships provide simpler analytical expressions. This fact is especially true from the standpoint of differentiation and generation of the functional expressions. The expressional forms of these two functions easily demonstrate this fact . The ordinary polynomial has the form
1
where p(x) is the given polynomial with terms having constant coefficients c for the abscissa terms x with integer powers n. The rational function using the ratio of two Chebyshev polynomials, Tn+1(x) and Tm+1 (x), has the form
u(x)/v(x) = Tn+ 1 (x)/Tm+ 1 (x) =
n
L (2x(Tn(x)) - Tn_ 1 (x)) / n== 1
n L (2x(Tm(x)) - Tm_1 (x))
n== 1
5
where T0(x); I, T1(x); x, T2(x); 2x2 - I, and n and m are the degrees of the Chebyshev polynomials in the numerator and denominator, respectively. Derivatives are easily obtained on the ordinary polynomial using the product rule of differentiation,
d(p(x))/dx ; ncxCn-l), 3
on the quantity
involve a nontrivial consideration of its individual terms which have the somewhat peculiar recurrence relation shown in Equation 2. These derivatives are obtained using the quotient rule of differentiation,
d(u(x))/v(x))/dx ; (v(du/dx) - u(dv/dx))/v2, 5
which in this case is nontrivial. In view of these differences in simplicity and the indications of fit found in Figures 4 and 5, the benefits gained using a rational
p(x);cxn. 4 function as opposed to an ordinary polynomial would be questionable at best.
In contrast, derivatives of the rational function will
Figure 4.
6
Examples of Curve Fits by Rational Functions Having the Form u(x)/v(x), where u(x) and v(x) are Chebyshev Polynomials Having Orders k and m, respectively.
Figure 5. Examples of Curve Fits by Ordinary Polynomials p(x) Having Different Orders n.
The final reason for choosing the ordinary polynomial as the curve-fitting function is the accuracy which can be obtained in the first and second derivatives of the analytical expression. This is due more to the functional characteristic than to a shape characteristic. As pointed out in the discussion of functional shape, the ordinary polynomial usually will provide a very good fit of the semilog representation of compression data. Consequently, differentiation based on the mathematical definitions of Equations 3 or 5 will yield accurate estimates of the first and second derivaties. When a finite
difference approach is used as a check on the derivatives of the generated ordinary polynomial (Equation 3), the same results can be obtained if the increments are sufficiently small. The derivatives obtained by the two mathematical definitions will be legitimate if the polynomial curve provides a good representation of the data. In contrast, as the functional representation of the data becomes less accurate (as in the cases of rational functions and low degree polynomials), the legitimacy of the first· and higher-order derivatives becomes increasingly questionable.
7
ANALYTICAL PROCEDURES Tilis algorithm employs a variety of analytical
procedures to represent the geometrical characteristics of the semilog, stress-deformation, consolidation curves. To begin with, the equation of the fitted ordinary polynomial is used to evaluate ordinate values at various abscissa locations on the curve. Slopes at these abscissa locations are determined using Equation 3. It should be noted that the rebound data are fitted only with a straight line. These analytically determined slopes are used with associated abscissa and ordinate values to produce equations of straight lines. Another geometrical quantity represented by analytical procedures is the radius of curvature. After the mathematical definition of Equation 3 is applied twice to evaluate the second derivative, the radius of curvature can be analytically
determined at various abscissa locations through the use of the following mathematical definition:
6
where R ·is the radius of curvature. The point of maximum curvature is given by the minimum value of the radius, 'R'. Another means of determining the point of maximum curvature is by approximating other geometrical characteristics of the curve. A combination of the procedures which set up equations of straight lines form the basis of this new method to determine the point of maximum curvature. A more complete discussion of this method follows in the section entitled "Graphical Method to Select Point of Maximum Curvature".
AUTOMATION OF THE CASAGRANDE AND SCHMERTMANN CONSTRUCTIONS
The analytical procedures described in the preceeding section form the basis for the mathematical representation of the two most widely used methods in the analysis of time·independent settlement. In review, the Casagrande construction is used by this aigorithm to estimate the probable preconsolidation pressure, and the Schmertmann construction is employed to account for the effects of disturbance on the compressibility of the specimen. Steps in the two empirical constructions are described here to illustrate the various analytical procedures.
The first step in the Casagrande construction is the selection of the point of maximum curvature on the polynominal representation of the compression data. In the manual application of this step, a subjective decision is made on the basis of the appearance of the curve. In the analytical application of this step, the point of maximum curvature may be selected by one of two possible methods. One method employs the
8
mathematical definition of the radius of curvature given in Equation 6 and is called the Analytical Method. The other is the newly developed Graphical Method, and the pictorial characteristics of the compression curve are used to choose the point of maximum curvature. This method is discussed further in the section entitled "Graphical Method to Select Point of Maximum Curvature 11• After the point of maximum curvature has been selected, lines horizontal and tangential to the fitted polynominal are mathematically determined at this point as shown by lines A and B, respectively, in Figure 6. The angle between these two lines is then bisected and mathematically represented by another line as shown by line C in Figure 6. The final step in the Casagrande construction comes in the selection of the line representation of the virgin compression curve. The polynomial representation of the compression curve is analyzed for a representative slope and suitable intercept, as shown by line D in Figure 6. The preconsolidation pressure, P 0(PROBABLE), is then determined at the intersection point of lines D and C, as shown in Figure 6, by taking the antilog of the abscissa at that point.
Following the Casagrande construction, the Schmertmann construction employs similar procedures to estimate . the in situ compressibility characteristics implied by th� geometrical nature of the consolidation curves. The mathematical steps exactly parallel those in the manual construction. In situ compressibility characte-ristics of the compression curve are approximated by two straight lines. First, the initial portion of the compression curve is represented by a line going through the in situ state of stress and strain having the slope of the rebound curve, line E in Figure 6. Finally, the in situ, virgin compression curve is represented by a line going from the end point of line
F at the preconsolidation pressure to the point where the virgin curve, line D, intersects the ordinate value of strain at 42 percent of the initial void ratio. This is line G in Figure 6.
A m1mmurn preconsolidation pressure, P c(MINIMUM), is shown in Figure 6. This lower limit of preconsolidation pressure is determined in accordance with a procedure reviewed and modified by Schmertmann (4). This minimum preconsolidation pressure is found simply by extending the virgin curve represented by line D in Figure 6 until it intersects either the £v = 0 line or the in situ recompression curve represented by line F.
Figure 6. Combined Use of the Casagrande and Schmertmonn Constrnctions.
GRAPHICAL METHOD TO SELECT POINT OF MAXIMUM CURVATURE
Equation 6 can not be used successfully on curves having ill-defmed curvature. The conceptual basis of this graphical method is the idealization of the recompression and virgin compression curves as straight line segments which have a transitional curve between them. Several assumptions are made. The first is that the recompression curve has the same slope as the rebound curve. Note that the Schmertmann construction employs a similar assumption. Second, the transitional curve between the two straight-line segments is to be smooth. evenly distributed, and have its point of maximum curvature at the center of its variance from the straight-line segments. An analogous situation can be found with the spiral highway curve and the principle, there, of gradual transition. Finally, the center point of the transitional curve is found by bisecting the interior angle formed by the intersection of the line representations of the recompression and virgin portions of the compression curves to obtain the point of maximum curvature as shown in Figure 7.
The implementation of this graphical method follows procedures outlined below. Consult Figure 7 for each of the following steps:
I. A line with the slope of the rebound curve is placed tangent to the recompression curve. If it is impossible to locate a tangent with this slope on the recompression curve, the line is arbitrarily drawn through the recompression curve at some point -
preferably the earliest possible point on the curve which is free from any irregular effects possibly produced during initial loading.
2. The virign compression curve is then represented by a line having the slope of its straight portion.
3. Extend the tangent of the recompression curve and the straight-line representation of the virgin compression curve until they intersect.
4. Bisect the interior angle formed by the intersection of these two lines.
5. Extend the angle bisector until it intersects the compression curve . This point of intersection is selected as the point of maximum curvature.
9
Figure 7. Graphical Procedure to Select Point of Maximnm Curvatnre.
Most consolidation (compression) curves will not rigorously follow the assumption that their points of maximum curvature will be located at the center of their transitional curves. If the point of maximum curvature can be chosen accurately by visual inspection, it may be located slightly before or after the
· graphically
selected point, aud its location depends entirely on the characteristic shape of the time-independent compression curve. Nevertheless, this graphical approach is a more rational procedure to the determination of the point of maximum curvature on curves having ill-defined curvature thau the traditional method of selecting this point by visual inspection. This method also provides more consistent results with curves having
ill-defined curvature. In adddition, it is obvious from the nature of the Casagraude construction that the selection of the point of maximum curvature is less critical to the determined value of the preconsolidation stress than the selection of the virgin compression curve. And since this graphical approach determines the midpoint of the rauge of the possible points of maximum curvature, it is a reasonably good
1 0
I) INITIAL TANGENT LINE
3) INTERIOR ANGLE
VIRGIN •• COMPRESSION . . CURVE ... ..
approximation to the midpoint of the range of possible values for the preconso!idation stress as determined by the Casagraude construction. Consequently, even though Casagrande does not use the construction which bears his name ( 11 ), the graphical approach to the selection of the point of maximum curvature is in keeping with his statement that the preconsolidation pressure should always be considered in terms of a rauge of values (12).
INFLUENCE OF POLYNOMIAL DEGREE ON ANALYSIS
The polynomial degree has been found to have a rauge of effects on three particular considerations: the shape of the fitted curve, the selected point of maximum curvature, and the values of the preconsolidation pressure and compression ratio. Similarly, since the effects of polynomial degree are largely dependent on the size of the data set being fitted, the three preceding points must be considered in terms of standard consolidation data versus controlled consolidation data.
EFFECT OF POLYNOMIAL DEGREE ON THE SHAPE OF FITTED POLYNOMIAL CURVE
For controlled test data, the polynominal degree has been found to have a small effect on the polynominal curve's shape for two reasons. First, the large number of data points involved in the controlled consolidation test usually gives a well-defmed curve which can be easily duplicated by high-degree polynomials. Secondly, since the large number of data points allows the use of higher degree polynomials, the undulatory characteristics of low-degree polynomials cited by Hastings (13) are automatically avoided.
In contrast, consolidation curves derived from standard tests do not have the benefit of a large number of data points. The scarcity of data points introduces a reasonable amount of ambiguity into the shape of the curve. This ambiguity appears in the analysis of these standard compression curves irrespective of any curve-fitting process which is used, manual or analytical. Because of this ambiguity, a certain amount of variation
in the shape of the compression curve results for polynomials of different degrees.
In addition, the small number of data points from the standard test limits the curve-fitting procedure to use of low-degree polynomials which have a certain undulatory characteristic. These shape characteristics of low-degree polynomials can sometimes introduce frustrating variations into the curve. These variations usually arise in cases where the curves assumes an almost horizontal character in the initial portion followed by a sharp angular break into the virgin compression portion. As Hastings (13) points out, the low-degree polynomials cannot turn sharply and go as straight as it is sometimes required by curves like the ones shown in Figure 8 (14). Figure 9 shows the best possible, low-degree polynomial fit on Crawford's "End of Primary11 curve of Figure 8. From this figure, one can get an idea of the shape limitations of low-degree polynomials.
Figure 8. Crawford's 1964 Illustration of the Influences of Secondary Compression on the Preconsolidation Pressure.
1 1
Figure 9. Best Low-Degree Polynomial Fit on Crawford's "End of Primary Curve" in Figure 8.
EFFECT OF POLYNOMIAL DEGREE ON THE SELECTION OF POINT OF MAXIMUM CURVATURE
The point of maximum curvature can be selected either by the Analytical or Graphical Methods discussed
earlier in the section entitled rr Algorithm for Time-Independent, Laboratory, Consolidation Test Data11• As far as the controlled test data curves are concerned, both the Analytical and Graphical Methods give very consistent choices for the point of maximum curvature for polynomials of degree nine or greater when these twp methods are considered separately. Figures 10 and I I, which will be discussed in greater detail later
12
in this section, show that a n acceptable consistency is obtained within each method to select a point 9f maximum curvature for polynomials of degree six or greater. Consistency occurs in each of these two methods after the sixth degree; there are two reasons: the shape of the well-defined compression curves are accurately duplicated with higher degree polynomials, and the undulatory characteristics more often found in low-degree polynomials are avoided, particularly in the initial portions of the compression curve and area of maximum curvature.
Figure 10. Preconsolidation Stress Plotted as a Function of Polynomial Degree of the Analytical and Graphical Methods to Select a Point of Maximum Curvature, Controlled-Gradient Test 13.
Figure 11. Compression Ratio Plotted as a Fnnction of Polynomial Degree for the Analytical and Graphical Methods to Select a Point of Maximum Curvature, Controlled-Gradient Test 13.
13
In contrast, the effect of changing polynominal degree on the selection of the point of maximum curvature from polynomial fits of standard consolidation data is significantly greater. The number of data points involved restricts one to the use of low-degree polynomials on data groups that already admit a reasonable amount of ambiguity into their curve representations. Hence, given the undulatory characteristics of low-degree polynomials and the ambiguities inherent from few data points, selection of the point of maximum curvature can be affected in three ways: by localized undulations in the initial portion of the compression curve representations, by changes in the location of the point of maximum curvature with different polynomial degrees, and by special problems caused by a nonexistent or ambiguously defmed point of maximum curvature. For the Analytical Method, the presence of localized irregularities in the initial portion of the polynomial representation of the compression curve can cause an erroneous point of maximum curvature to be chosen. Secondly, changes in the polynomial degree used in fitting a group of standard data can shift the point of maximum curvature from one location to another because of the ambiguities possible when fitting a few data points and the undulatory nature of low-degree polynomials. An example of the effects of the undulatory nature of low-degree polynomials on the selection of the point of maximum curvature can be realized through a comparison of the analyzed consolidation curves of Standard Test 24 in Figures 12a and 12b with Figure 12c. Thirdly, special problems occur when the Analytical Method is used on a polynomial representation of a set of consolidation data lacking a distinct and unique point of maximum curvature. In other words, the curve may lack a unique point of maximum curvature due to the nature of the data or because of the poor representation afforded by the low-degree polynomial. An excellent example of the nature of the data contributing to the ill-defined point of maximum curvature is shown in Figure 13 of Standard Test 12. Even though the third, fourth, fifth, and even sixth degree polynomials provide excellent representations of the data, the small differences in shape between these polynomials overshadow the ambiguous information furnished by the data points concerning the point of maximum curvature and give rise to significant differences in the location of the point of maximum curvature.
14
In contrast to the selection of the point of maximum curvature by the Analytical Method, the Graphical Method is influenced differently with varying amounts of significance for the three problems discussed above with respect to standard data. It may be helpful here for the reader to re-acquaint himself with the earlier description of the Graphical Method, with special attention to Figure 7, in the section entitled "Graphical Method to Determine Point of Maximum Curvature". As for the first problem, localized irregularities in the initial portion of the polynomial for the initial compression curve can disturb the Graphical Method by causing slight displacements or offsets up or down in the initial tangent line shown in Part I of Figure 7. An actual example of an upward displacement of this tangent line can be seen in the sixth degree polynomial fit on Standard Test 24 in Figure 19c. This upward displacement of the initial tangent line causes the angle bisector of Part 4 of Figure 7 to intersect the. compression curve at a point further back up the curve. A downward displacement of the intitial tangent line will cause the point of maximum curvature to be located at a point further down on the compression curve. As for the second problem, the location chosen by the Graphical Method as the point of maximum curvature is largely unaffected by small changes in the shape of the fitted curve in the general area of the point of maximum curvature With changing polynomial degree. In other words, the point chosen remains essentially. the same with changing polynomial degree. Basically, this fact comes about because the point selected by the Graphical Method is determined mostly by the interior angle formed by the intersection of the straight-line representations of the recompression and virgin compression curves shown in Figure 7. Hence, the Graphical Method is largely unaffected by changes in the characteristics of the fitted polynomial between the straight-line representations of the recompression and virgin compression curves.
Finally, the special problems encountered by the Analytical Method with an ill-defined point of maximum curvature are largely avoided by the use of the Graphical Method. When the data are responsible_ for these problems, as in the case in Figure 13 for Standard Test 12, the Graphical Method becomes more consistent and gives just as reasonable results by pictorially taking the midpoint of the range of possibilities for the point of maximum curvature, as shown in Figure 14.
..... CJ1 -
Figure 12.
Standard Test 24, Analytical Method Used to Detennine the Point of Maximum Curvature: (a) 4th-Degree Fit; (b) 5th-Degree Fit; (c) 6th-Degree Fit .
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Figure 13. Standard Test 12, Analytical Method Used to Determine a Point of Maximnm Curvature: (a) 3rd-Degree Fit; (b) 4th-Degree Fit; (c) 5th-Degree Fit; (d) 6th-Degree Fit.
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to Determine a Point of (b) 4th-Degree Fit; (c)
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INFLUENCE OF POLYNOMIAL DEGREE ON THE VALUES OF THE PRECONSOLIDATION STRESS AND COMPRESSION RATIO
Variations caused by polynomial degree in the sha.pe of the fitted curve and selected point of maximum curvature affect the values of preconsolidation stress, PC' and the compression ratio, CR. Many observations to be made herein have already been mentioned. For controlled test data, the large number of data points allows the use of higher degree polynomials which give consistent results for the preconsolidation stress and compression ratio after the sixth degree. This consistency prlmarily reflects a lack of change in the shape of the fitted curve with increasing degree. Figures I 0 and 11 demonstrate this point for the values of preconsolidation stress and compression ratio, respectively. The most represr.ntative values for these two parameters are usually obtained when the highest polynomial degree of 11 is use.d; but of course, the polynomial representation of a compression curve must be smooth and well defined by sufficient data points from a controlled consolidation test. The obvious trend of lower values for P c and CR in Figures I 0 and I I for the Analytical Method is due only to the character of the data and its fitted polynomial but not because the Graphical Method always gives a trend of higher values for P c and CR. !n other words, for differently shaped compression curves, the Graphical Method could give a trend of lower values for P c and CR.
In contrast, since the standard test data allow greater variation in the shape of the fitted polynomial and the selected point of maximum curvature with changing polynominal degree, the values of preconsolidation stress and compression ratio consequentially show less consistency with changing polynomial degree. However, fair consistency in the determination of P c and CR is retained for certain polynomial degrees within each of the two methods to select a point of maximum curvature. In Figures 15 and 16 for Standard Test 24, good consistency is obtained by the fourth and fifth degree polynomials. In Figures 17 and 18 for Standard Test 12, satisfactory consistency is obtained in the third, fourth. and fifth degree polynomials. Note that in both sets of figures for Standard Tests 12 and 24, this consistency brealcs down at the sixth degree. At the sixth degree, this breakdown in consistency can be expected since there is no least-squares smoothing afforded by the fitting polynomial when the polynomial degree is equal to the number of data points minus one.
Changes in the shape of the fitted polynomial with changing polynomial degree, particularly in the initial portion of compression data curve, are primarily responsible for the sudden changes in the determined
18
values of P c and CR. In Figures I 5 and 16 for the use of the Analytical Method on the data of Standard Test 24, the change in the shape of the fitted polynomial at the sixth degree occurs because the few data points in the initial portion of the compression curve cannot prevent the polynomial from curving in this region. Curving of the polynomial in the initial data causes the point of maximum curvature to move further down the curve and thereby cause an increase in P c and CR shown at point C in Figures IS and 16, respectively. This effect can be seen by comparing the analyzed consolidation curves for the fourth, fifth, and sixth degree polynomials in Figures 12a, b, and c, respectively. In contrast, the curving of the. sixth degree polynomial in the initial data of the compression curve of Standard Test 24 produces an opposite effect on the determined values of P c and CR when the Graphical Method is used. This undulation in the fitted curve causes an upward displacement of the initial tangent found by the Graphical Method The effect of this undulation can be noted by comparing the analyzed consolidation curves for the fourth, fifth, and sixth degree polynomials in Figures 19a, b, and c. In Figure 19c the upward displacement of the initial tangent mo'tes the selected point of maximum curvature back up the compression curve with a consequential reduction of P c and CR at point E' in Figures I 5 and 16, respectively.
The effect of changes in the shape of the fitted polynomial at the sixth degree is quite different for the data of Standard Test 12. Here again there is no least-squares smoothing at the sixth degree. For the Analytical Method's determination of P c and CR for standard test 24, there was an increase in their values at the sixth degree, as shown in Figures 17 and 18 and point C. However, for Standard Test 12, the values of P cand CR show instead a decrease at the sixth degree. This change in the values of P c and CR for Standard Test 12 is also caused by a small shape aberration of the sixth degree polynomial fit in the initial data points of the compression curve. The decrease of the values of P c and CR occurs because the point of maximum curvature is moved back up the curve instead of down the curve, as in the case of the previously discussed example of Standard Test 24. The backward shift of the point of maximum curvature can be easily seen by comparing the analyzed consolidation curves of Standard Test 12 for the third, fourth, fifth, and sixth degree polynomials in Figure 13 a, b, c, and d, respectively. As for the effect of this sixth degree polynomial shape aberration on the values of P c and CR determined with the use of the Graphical Method to select the point of maximum curvature, there is not as large a change as accompanied the previously discussed example of Standard Test 24 of the preceeding discussion concerning the Analytical Method and
Figure 15. Preconsolidation Stress Plotted as a Function of Polynomial Degree for the Analytical and Graphical Methods to Select a Point of Maximum Curvature, Standard Test 24 .
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19
Figure 16. Compression Ratio Plotted as a Function of Polynomial Degree for the Analytical and Graphical Methods of Selecting a Point of Maximum Curvature, Standard Test 24.
20
Figure 17.
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Preconsolidation Stress Plotted as a Function of Polynomnal Degree on Compression Data which Lack a Well-Defined Point of Maximnm Clll'V"ture, Standard Test 12.
Figure 18.
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Compression Ratio Plotted as a Function of Polynomial Degree on Compression Data which Lack a Well-Defined Point of Maximum Curvature, Standard Test 12.
21
.., ..,
Figure 19.
·standard Test 24, Graphical Metholi' Used to select the Point of Maximnm Curvatnre: (a) 4th-Degree Fit; (b) 5th-Degree Fit; (c) 6th-Degree Fit.
Standard Test 12. Hence, values of P c and CR for the sixth degree Graphical Method's determination remain fairly consistent with respect to the other degrees as shown in Figures 1 7 and 1 8 for Standard Test 12. In spite of the excellent polynomial representations of the data furnished by all degrees of three or greater on the data of Standard Test 12, the scatter obtained in the values of P c and CR when the Analytical Method is used illustrates the difficulties involved with selecting the point of maximum curvature on data which ambiguously define curvature. Whether the data from Standard Test 1 2 are accurate or not is not an issue here. Instead, the problem of selecting the point of maximum curvature on certain types of curves illustrates some basic limitations inherent in the use of empirical, graphical procedures to determine properties of stress-strain consolidation data. Sometimes, use of empirical, graphical procedures may raise some questions in their applicability to the analysis of certain types of data. With this in mind, the use of the Graphical Method as opposed to the Analytical Method to determine the point of maximum curvature on the data curves from Standard Test 12 gives just as reasonable choices for this geometrical- quantity and, in addition, much more consistent values of P c and CR. This can be seen by inspection of the analyzed consolidation curves for the third, fourth, fifth, and sixth degree polynomial fits in Figures 14a, b, c, and d, respectively.
SUMMARY Changing the degree of the polynomial has a greater
effect on the shapes of the curves fitted to standard data than on those fitted to controlled consolidation data. Usually, the best curve representation of the data will be obtained when the highest polynomial degree that provides some least-squares smoothing is used. However, there is one situation where any polynomial representation may not be adequate for either standard or controlled compression data curves. In Figure 8, there are curve shapes which are difficult to produce through the use of ordinary polynomials, particularly low-degree polynomials. This difficulty results because it is hard for polynomials to make sharp turns or to go straight horizontally for any great distance, especially when there are few data points to sufficiently constrain the polynomial fit as in the case of Figure 9. Secondly, changing polynomial degree does change the location for the point of maximum curvature. At low-degree polynomial fits, changes in the polynomial degree can adversely affect both the Analytical and Graphical Methods to select the point of maximum curvature because of possible undulations in the fitted curve in the initial portions of the data and region of maximum curvature. When the curvature of the fitted curve is ambiguously defined, despite an excellent polynomial
representation of the data at most degrees, the Graphical Method to select the point of maximum curvature will be less susceptible to small variations in the fitted curve than the Analytical Method. And, considering the broad spectrum of shapes possible with most stress-strain consolidation data, the Graphical Method will give more
consistent results with changing polynomial degree. It is important to compare qualitatively the
influences of polynomial degree with other external difficulties which can affect the analysis of consolidation test data irrespective of the procedures which are used. It will be shown herein that the variations incurred with different degree polynomials are usually less than the variations caused by effects external to the analysis of the data itself. For standard data, there are two significant sources of variations which can have a larger influence on the analysis than changing the polynomial degree. A very important factor is specimen disturbance, which can have a very appreciable influence on the values of P c and CR and far outweigh any variations incurred by the curve-fitting functions. Also, such factors as load-increment ratio and load-increment duration can affect the determined values for P c and( or) CR much more than changing polynomial degree, especially when data on highly sensitive clays are considered. (Crawford ( 14) showed in Figure 8 the extreme but valid case of a 50-percent reduction in the value for P c for incremental loading programs of different durations.) In addition, Sallfors ( 3) pointed out that it is possible to represent the compression data with a number of different curves when there are only six or seven data points. This last type of variation accounts for most discrepancies between the values of P c and CR for different degree polynomials. Hence, these variations in the shape of the fitted curve are just as much a result of the limitations imposed by .standard consolidation tests as from the use of different polynomial degrees. For the controlled consolidation tests, this problem of choosing the appropriate curve representation of the compression data is greatly alleviated by the greater amount of . data involved. However, this type of consolidation data can be influenced by some other factors external to the analysis. For instance, the effect of specimen disturbance is just as significant for the controlled consolidation tests as it is for the standard test. In addition, there are the special effects caused by pore pressure lag and strain rate which can change the nature of the compression curves and the determined values for P c and CR. These special effects are generally far more significant than those incurred through the use of different polynomial degrees. In summary, variations incurred with the use of different degree polynomials are usually less than the inaccuracies incurred by such things as sample disturbance, few data points, loading procedures, and measurement of pore pressures.
23
THE COMPUTER PROGRAM In contrast, controlled consolidation dat� are defined by a similar but less order-bound criterion.
The computer program, CASAGR-0, analyzes the Compression data still must be entered first and in order time-independent, one-dimensional strain consolidation of increasing effective stress. The difference is that small, ,c;lata associated with consolidation tests. The program '1 local decreases in the values of effective stress in _dl;'ltermines the preconsolidation stress and the in situ compression data will not cause the computer program compressibility characteristics. The results derived from to treat all subsequent data points as rebound data. As this program are used in. the time-independent, long as localized decreases are not greater than 0.7 tons one-dimensional strain analysis of settlement. The main per square foot (67 kPa), the computer program ·will characteristics of the program to be discussed herein continue to treat all subsequent data as compression include a description of its methods of solution, data. When this amount of change occurs, all subsequent capabilities and limitations, data inputs, program data points are treated as rebound points in the options, program output, flow-chart outline, and sample curve-fitting process. Finally, the data point which runs. provokes this decrease in effective stress is dropped from
METHOD OF SOLUTION The computer program employs a numerical
curve-fitting procedure with a least-squares ordinary polynomial to facilitate the analytical application of the Casagrande (I) and Schmertmarm ( 3) constructions. Several procedures have been developed and incorporated into the program to carry out the analytical application of these constructions. The poirrts to be discussed herein are the application of the curve-fitting procedure, a criterion for distinguishing between compression and rebound data, the selection of the point of maximum curvature, the selection of the virgin compression curve , and constants built into the program.
Application of the Curve-Fitting Procedure -- The compression and rebound curves are separated and fitted by two different polynomial functions. The compression data are fitted by a user-specified, least-squares polynomial. The rebound data are fitted by a least-squares straight line. These two functional representations provide the basis for the approach proposed in the section entitled "Algorithm to Study Time-Independent Laboratory Consolidation Test Data."
Criteria for Distinguishing between Compression and Rebound Data Curves - This criterion is predicated on the fact that compression data are read into the computer in an order such that the values of effective stress are increasing. Once this compression data have been read in, they are followed by the rebound data distinguished from compression data on the basis that there is a decrease in the value of effective stress. This criterion for distinguishing between compression and rebound data is applied differently to the data obtained from different types of consolidation tests. For standard consolidation test data, the computer program distinguishes between compression and rebound data when it encounters a data point having an effective stress less than the one previous to it. When this occurs, the computer program treats all subsequent data points as rebound data.
24
the analysis entirely to avoid any effects it may have on the polynomial representation of the compression date.
Selection of the Point of Maximum Curvature -
The Casagrande point of maximum curvature is determined by the computer program by two methods, both of which have previously been described. The Analytical Method uses the mathematical definition of the radius of curvature given in Equation 6 to find the point of maximum curvature. The location of the point depends primarily on the arithmetic ratio of the scale factors. Hence, with a different ratio for the horizontal to vertical scale factors, the point of maximum curvature will be located at a different abscissa location on a given curve. The ratio of the horizontal to vertical scale factors must be multiplied times the first and second derivatives before Equation 6 can be used to select the point of maximum curvature based on the pictorial characteristics of the fitted curve. To find the point of maximum curvature, the Analytical Method tests for a minimum value for the radius of curvature within a 90-percent mid portion of the search area as defmed by the user-specified, abscissa search boundaries. If a discrete minimum value for the radius of curvature is not found within this 90-percent interval, the minimum value of the radius is not considered to be unique. In such a case, the computer program will default to select the point at which the second derivative is a maximum as the point of maximum curvature.
The second method to determine the point of maximum curvature is the Graphical Method. Procedures for this method have already been described in detail in the section entitled "A Graphical Method to Select Point of Maximum Curvature". The computer program uses the Graphical Method in several steps. First, the program searches between the user-specified boundaries for a point on the compression curve having the same slope as the line representation of the rebound curve. If this point is found, the line representation of the initial portion of the compression curve will be drawn through this point. If this point is not found, the
computer program defaults and uses the first search boundary as the point through which to draw the line representation of the initial recompression curve. Note that this line will have the slope of the rebound curve line representation. Next, the pictorial appearance of the interior angle formed by the intersection of the line representations of the initial compression and virgin compression curves is bisected. Note that the pictorial appearance of this interior angle is directly related to the scale factors in the horizontal and vertical directions. Finally, having bisected this interior angle, the intersection of the angle bisector line with the compression curve is determined by comparing the incrementally generated ordinates of the angle bisector line and the polynomial representation of the compression curve. The ordinate values are computed at incrementally generated abscissae which are increasing in magnitude. When the ordinate of the angle bisector is greater than that of the compression polynomial, the point of intersection has been passed. The determination of the intersection point is refmed by several iterations using .the same procedure. This intersection is the graphically selected point of maximum curvature.
Selection of the Virgin Compression Cnrve ·· The selection of an appropriate straight-line representation of the virgin compression curve uses the concept of percent difference. The percent-difference criterion is a procedure which is used to find that portion of the compression curve on which the slope is relatively constant. If the slope is relatively constant, the percent difference between slopes of consecutively generated search points will be very small and that portion of the curve will be nearly a straight line. In the use of this concept, the computer program incorporates the additional requirement that the straight-line representation of the virgin compression curve be selected at the point having the largest slope of those points whose slopes have passed the percent-differrence criterion. However, the percent�difference criterion will not always be satisfied. Hence, some kind of backup criterion is needed. The criterion to be outlined herein depends on the type of test data being analyzed. For controlled data, the computer program uses a simple default procedure when the percent-difference criterion is not satisfied. If the criterion is not satisfied for controlled data, the program selects the point at which the maximum slope occurs. This point and the slope of the curve at this point will be used to construct the straight-line representation of the virgin compression curve.
In the case of standard data when the percent-difference criterion is not satisfied, the procedures are slightly more complicated than those used on controlled data. When the percent-difference
criterion is not satisfied on standard data, the representation of the virgin compression curve will be selected on the basis of the two procedures illustrated in. Figures 20 and 2 1 . In the case of a compression curve similar to the one in Figure 20, the line representation of the virgin compression curve will be selected at the point of maximum slope. In the case of a compression curve similar to the one in Figure 2 1 , a much different procedure will be used because use of the tangent to the compression curve at its maximum slope would lead to a very unconservative estimate of the preconsolidation stress. Also, use of a line through the last two compression points as the representation of the virgin compression curve can be inappropriate because the next to last point may not be on the straight-line portion of the virgin compression range, as indicated by the trend of compression points in Figure 2 1 . Hence, some median is needed between these two possible extremes. A way to obtain this median is simply to select a line having a slope averaged from the two extremes just discussed and going through the last compression curve point. This line is shown as a dashed line in Figure 21 .
Constant Values Built Into Program -· Several constant values are built into the computer program for use in various steps of the analysis. There are constants for the Schmertmann construction and for matching of increasing dial readings with downward deflection (decreasing specimen length). For the Schmertmann construction, the computer program takes the intersection of the line representation of the in situ compression curve with the line representation of the laboratory virgin compression cutve as occurring at 42 percent of the initial void ratio, as suggested by Schmertmann (3).
Next, the program is set up to accept increasing dial readings of standard and controlled-rate-of-strain data as indicating downward deflection (decrease in specimen length). This has been accomplished by setting the variable name '!DIAL' equal to '+I' during the data reduction for these two test types. Similarly, controlled-gradient data reduction is handled in much the same way with the exception that '!DIAL' is set equal to ' -1 ' when this type of data is being considered. The reason for this is that the dial gauge used for the controlled-gradient test apparatus has increasing dial readings indicating specimen lengthening:
SAMPLE HEIGHT = IN!. HEIGHT - !DIAL *(DIAL RDG. - ZERO RDG.).
25
Figure 21.
26
Figure 20. Standard Data for which the Line Representation of the Virgin Compression Curve Is Selected at Location of .Maximum Slope.
Standard Data for which the Line Representation of the Virgin Curve Is Selected by Averaging Slopes of Two Lines: One Tangent to the Curve at Its Maximum Slope and the Other Going through the Last Two Points.
By inspection of Equation 7, one can easily see that the use of this kind of procedure avoids the necessity of having different deformation equations for different types of dial gauges. The advantage of this scheme readily becomes apparent when dial gauge equipment varies within a laboratory for a given type of consolidation test. Finally, the user has the ability of overriding these built-in relationships through an option that changes the sign of the value for !DIAL in Equation 7.
PROGRAM CAPABILITIES Ranges of Assigned Values - Quantities involved
in the computer program which require certain. limitations on the range of input values fall into three basic categories: array storage space, effective stress values, and polynomial degree specification. First, the amount of array storage space limits the amount of data which can be considered at any given time. These arrays• have been set up to hrutute a maximum of 300 compression data values and 100 rebound data values. Next, the effective stress values are limited to stresses greater than or equal to 0.1 ton per square foot (9.6 kPa). Any data having a value of effective stress Jess than 0.1 ton per square foot (9.6 kPa) will be changed to 0.1 ton per square foot (9.6 kPa). Ail for the polynomial degree specification, the program is limited in two ways, one internal and one external. Internally, the program can not handle any polynomial degree greater than 1 1 . Externally, the user must make sure that the polynomial degree is not larger than the number of data points being fitted minus one. Otherwise, the user will receive an error message from the curve-fitting subroutine in the . program.
· Limitations on the Fonnulation of a Test Problem - Two points must be made herein to defme what constitutes a test problem. First, a given set of consolidation test data must have both compression and rebound data as shown in Figure 22. Otherwise, the program carmot analyze a data set which consists ouly of compression curve data as shown in Figure 23. Secondly, the program is set up to handle only one load cycle at a time. A load cycle consists of loading (compression) and uuloading (rebound) as shown in Figure 22. The single load cycle illustrated in Figure 22 is considered by the computer program as one problem. Hence, the three load cycles displayed in Fi,gure 24 will be considered as three separate problems by the computer program.
In considering the family of curves in Figure 24 as three separate problems, confusion will arise in the analysis if the initial void ratio, e0, is not changed for load cycles two and three. First and foremost, the use of Schmertmann's construction in the later load cycles with . the original initial void ratio will lead to unjustifiably large increases in the in situ compressibility, as shown by curve A in Figure 25. In addition, since the initial void ratio is not scaled by the computer in relation to the rest of the data before it is plotted, the output will become disturbed when the computer attempts to plot the determined position of the initial void ratio outside the limits of the plot page in the vertical direction. Hence;· it is necessary in the analysis of load cycles two and . three in Figure 24 to use different values for the initial void ratio. For load cycle two, it is suggested_ that the fmal void ratio for load cycle one, efl, be used as the initial void ratio. For load cycle three, it is suggested that the fmal void ratio for the load cycle two, ef2, be used as the initial void ratio. Following this procedure, a more reasonable determination of the in situ compressibility can be made, as shown by curve B in Figure 25. The reader should be well aware that these. problems concern both the void ratio and vertical strain deformation analyses. Results of each deformation analysis is intimately involved Wltn the value of tne initial void ratio. However; one should also realize that the vertical strain results lend readily to the comparison of the compressibility characteristics of soils having different initial void ratios. This enables a settlement analysis without knowledge of the in situ void ratios on layers of otherwise homogeneous materials which have the same compressibility characteristics.
DATA INPUTS The data are input from punched cards using the
format shown on the coding sheet forms in Figure 26a, b, and c in APPENDIX A. Detailed instructions are also contained in APPENDIX A along with a description of the job control cards.
27
Figure 22.
28
Both Compression and Rebound Data necessary for Computer. Program; Single Load Cycle Shown.
Figure 23. Compression Data only, Not Sufficient for Computer Program.
Figure 25.
Figure 24.
Use of e0 instead of ef as the Initial Void Ratio on Later Load Cycles Leads to Unjustifiably Large Increases in Compressibility Coefficients. This Is Shown by a Comparison of In Sitn Curves A and B.
Three Load Cycles.
29
PROGRAM OPTIONS There are several run options available to the user
of the computer. program, CASAGR-0. All options are user specified. The user specifies the type of consolidation data being analyzed, the type of deformation analyses to be performed, and the method to select the point of maximum curvature. No debugging options are provided since the normal output of the program provides sufficient information for debugging.
Type of Consolidation Test - The user may specify analysis on data from three different types of consolidation tests. These are the standard, controlled-gradient, and controlled-rate-of-strain consolidation tests.
Deformation Analyses The user may obtain results in terms of a void ratio and( or) vertical strain. Both yield essentially the same determination of the preconsolidation pressure. Also, the program enables the user to use deformation data from dial gauges with different calibration factors and directions of dial gauge movement.
Methods to Select Point of Maximum Curvature -
The user can choose either the Analytical or Graphlcal Method to select the point of maximum curvature. Details of these two methods have already been discussed. In review, the Graphlcal Method generally is less susceptible to anomalies caused by undulations in fitted compression curves and by irregularities in the data. The Analytical Method is better suited to consolidation curves which have relatively well-defined and undisturbed points of maximum curvature.
OUTPUT Printed Output - All input information and final
results are printed to facilitate checking results. The user has the option of specifying whether or not the calculated radii from the analytical determination of the point of maximum curvature should be printed.
Plotted Output -- An example of plotted output is referred to in the discussion of the sample run in APPENDIX B. The plots produced by the computer program show data points, fitted curves, numerical results, and all the steps involved in the graphical analyses. The plot information is stored on 800-bytes-per-inch magnetic tape used in conjunction with the Calcomp 663 drum plotter.
30
I.
2.
3.
4.
5.
6.
7.
REFERENCES
Casagrande, A.; Preconsolidation
The Detennination of the Load and Its Practical
Significance, Proceedings, First International Conference on Soil Mechanics and Foundation Engineering, Cambridge, MA, Vol 3, 1936, pp. 60-64.
Ladd, C. C.; Strength and Deformation Properties for Analyses of Embankments on Soft Clay, Woodward-Clyde & Associates, Clifton, NJ, December 1968.
Schmertmann, J. H.; The Undisturbed Consolidation Behavior of Clay, Transactions, ASCE Vol 120, Paper No. 2775, 1955, pp. 1201-1227.
Christian, J. T.; Lysmer, J.; and Reti, A. G.; Engineering Computer Program Document Standard, Journal of the Soil Mechanics and Foundations Division, ASCE, Vol 99, SM3, March 1973, pp. 249-266.
Sallfors, G.;Preconsolidation Pressure of Soft, High Plastic Clays, thesis presented to Chalmers University of Technology, Goteborg, Sweden, in partial fulfillment of the requirements for the Degree of Doctor of Phllosophy, October 1975.
Schlffman, R. L.; Calculation of Compression lndices for Laboratory Void Ratio-Effective Stress Curves, University of Colorado, Boulder, CO, April 1972.
Gorman C. T.; Constant-Rate-of-Strain and Controlled-Gradient Consolidation Testing, Division of Research, Kentucky Bureau of Highways, May 1976.
8. Lowe III, J.; Jonas, E.; and Obrcian, V.; Controlled Gradient Consolidation Test, Jonrnal of the Soil Mechanics and Foundations Division, ASCE, Vol 95, No. SMI, Paper No. 6327, January 1969, pp. 77-97.
9. Smith, E.; and Wahls, H. E.; Consolidation under Constant Rate of Strain, Journal of the Soil Mechanics and Foundations Division, ASCE, Vol 95, No. SM2, Paper No. 6452, March 1969, pp. 319-539.
10. Thrailkill, L.; Allen, K.; and Taylor, W.; N�erical Analysis Library for University of Kentucky 370, University of Kentucky, Lexington, KY, December 1970, pp. 70-7 1 .
I I . Casagrande, A.; as Discusser at Large, ASCE Specialty Conference on Settlement, Evanston, IL, June 16-19, 1964.
12. Casagrande, A.; personal communication with E. G. McNulty, Harvard University, August 18, 1975.
13. Hastings, C.; Woodward, J. T.; and Wong, J. P., Jr.; Approximations for Digital Computers, Princeton University Press, Princeton, New Jersey, 1955.
14. Crawford, C. B.; Interpretation of the Consolidation Test, Journal of the Soil Mechanics and Foundations Division, ASCE, Vo/ 90, No. SM5, September 1964.
31
APPENDIX A
PROGRAM INPUT INSTRUCTIONS
CASAGR·O
TIME-INDEPENDENT CONSOLIDATION
TEST DATA ANALYSIS
PROGRAM CODING SHEET
Number of problems, columns 1-2, right justified.
I� NOPROB is greater than one, all of the remaining cards must be repeated for each problem.
For NPLOTS place a '1 ' in column 2.
IPRINT · output option .for, the Analytical method to determine the pOint of maximum curvature. CODE '0' · Calculated radii printed out
'I' . Calculated radii not printed out
NDEG . Degree of polynomial used in curve fitting.
RUNTYP .
ZDEPTH
KRAD
KIND
SECOND
IIDIAL
Type of consolidation test In COL. 13: CODE 'o' . standard data
'1 ' . controlled gradient data '2' . controlled rate of strain data
Approximate field depth from which sample was recovered, in feet.
Option for method to select point of maximum curvature. In COL. 31 a blank or '0' causes the Graphical method to be used.
a '2' causes the Analytical method to be used.
Type of deformation analysis. In COL. 33 '0' is for both void ratip and strain analyses.
'1 ' is for void ratio analysis only. '2' is for strain analysis only.
Stress at start of secondary compression (controlled tests only). If left blank, SECOND has default value of 31.2 Tsf.
Option to override the assumed dial reading-versus-deflection relationship �pecified by computer program for each type of consolidation test. In COLS. 50 a blank or '0' changes none of the assumed relationships.
'1 ' will specify that increasing dial readings indicate
BOUND!
specimen shortening. . 49-50 '-1' will specify that increasing dial readings indicate
specimen lengthening.
BOUND2 BOUND3
14 15 16 17 18 19 zo 2 1 22 23 24 25 26 27 28
BOUND!, BOUND2 . search boundaries for selection of point of maximum curvature using Analytical or Graphical methods.
BOUND3, BOUND4 . search boundaries for selection of the line representation of the virgin compression curve.
BOUND4
A-1
::---""
CASAGR - 0 LABORATORY CONSOLIDATION TEST DATA
SAMPLE AND TEST DESCRIPTION TO BE USED AS PLOT TITLE ( B C D )
, I 1 1 , ' ' ' SAMPLE NO.
'·· j_ ��_j_�___l_____L_.L� L J.. __ J.. I
TEST HOLE NO. (HOL)f}SAM)
LocATioN ! Loc> I \\ I ���in I /,"' OPERATOR (OPR)
f I DATE (OAT) I SAMPLE DESCRIPTON (DES)
1 l � l l i � I 5 I G I 7 L L l J t ..L..L..L_l_i_.....LJ. [ I_.L� ..L. i_..l_ _.._l_L�_l__.J_J _ _ i ...l_____j_.�..L���
SP GR. I (SPG) IN!. WET I (WTIW)
SPECIMEN FIN. WET I (WTFW)
WEIGHTS FIN. DRY (WTFD)
CALIBRATION FACTORS
DEFLECTION RDGS.
IN!. I (DEFJ) FIN. (DEFF)
DEFLECTION I I PORE PRESS (DCF) LOAD (LCF) ( PCF)
DIAM. SAMPLE BLANK ; default
to 2.5"-(DIA)
BACK PRESS.
(BP)
ZERO READINGS DE FL. I LOAD I p P.
(DEFZ) (WRZ) (PPZ)
J ' L j_J I '-'�..L. '------l
WATER
Can No.
Wt can + wet soil
Wt. can + dry soil
Wt. of can
Wt. of water
Wt. dry soil
Mois. cont.
L__j __ i_l.J__J__j_ _ _L��_L��L.J������-'
(b)
--CONTENT DATA
INITIAL FINAL ..
IN!. SAMPLE HEIGHT (SAMPHI)
BLANK= default to 111
(zz(z3(z4(zs(z6(nlza(z9\3o\ NOTE: P P. ZERO READING should be taken after B. P. application.
t N ?'
?;
I 8
CASAGR - 0 LABORATORY CONSOLIDATION TEST DATA
CONTROLLED GRADIENT OR CONTROLLED RATE OF STRAIN CONSOLIDATION TEST
DATA FORMAT
LABORATORY READINGS
TIME
I DEFL.
I P. P. I LOAD I TR ( ) DEFR ( ) PPR { ) jWRD ( )
fiT� "5 6 ,Z 8 9 101 1 12 ;"3�ififiT/iev9 TIME I DEFL.
I P. p I LOAD I
TR { ) DEFR { ) PPR { ) WRD { 1
0.��-�-��.t.� L�., �-�f.....·�-f-.-
��L �L .. C J-.-L� f...-..-�� -��1-L.>-LL ���f-.-1-..1.......1...- .... l-1..-L.L
�-.-'-'- �.L '-� � 1--o� . ..'-'.� .L�I-c-,�1-c ��-�L� ·�f-.�J-- _l • ....l-..L.....I-+���-c�c+"-1
... L .... l .... ...l..... ...J .... .l • ...L..L ��-L��,-+� �J .•. ·LL·' ' �--l.��� �-.J,_j__ .....J.-J...[ _ _..J .•• f--...-.c. .... l .... +��4�
Figure 26. (Continued)
I 2 3 4 5 6 7 8 9 10 II 12 13 14 IS 16 17 18 19
LAST CARD OF DATA BLANK
'
STANDARD CONSOLIDATION
TEST DATA FORMAT
(c)
EFf!: STRESS P I I
(TSF)
DIAL RDG. E { ) (IN)
I � 3 4 5 6 7 8 9 10 II 12 13 14 I S 16 171819 2
LAST CARD OF DATA BLANK
A-3
C ASAGR-0
INPUT INSTRUCTIONS FOR
TIME-INDEPENDENT LABORATORY CONSOLIDATION DATA ANALYSIS
COLUMNS NAME FORMAT I . NUMBER OF PROBLEMS CARD
1-2 NOPROB !2
2. OUTPUT OPTION CARD 1· 2 NPLOTS I2
3·4 !PRINT I2
3. DESCRIPTION OF ANALYSIS CARD 1-3 NDEG I3
1 3
Note:
A-4
RUNTYP II
Repeat cards 2 through 1 0 for each additional problem.
REMARKS
This card defines the number of problem sets to be solved. The number of problems equals the number of stress-strain axes which will be used tn plotttng the data. If card number two has NPLOTS equal to one, the number of problems will simply be the number of consolidation tests to be analyzed.
For NPLOTS, place a ' I ' in column 2. This parameter is used only in program version CASAGR-I.
Output option for the Analytical Method's determination of the potnt of maximum curvature (see CARD 3). A '0' or blank in columns 3·4 will cause the calculated radii of curvature at the generated incremental search abscissae to be printed out. A '1' in column four will elimtnate this printed output.
These columns specify the degree of the ordtnary, least -squares polynomial to be used in fitttng the consolidation compression curve. The maximum possible degree is I I . Use the highest possible degree in most cases. For cases having few or scattered data points, a lower·degree polynomial must be used. A low polynomial degree of four or five generally provides a good fit.
For data sets having less than 12 points, the maximum polynomial degree which can be used is equal to the number of data points minus I . However, the best polynomial representation of the data will usually be obtained when the highest polynomial that provides some least-squares smoothing is used (number of data points minus 2). If this degree polynomial is found to provide an undulating representation of the data, the user can use a lowermdegree polynomial in another computer run.
Place tn column 13 a '0' for standard consolidation data reduction, ' I ' for controlled-gradient consolidation data
reduction, or '2' for controlled�rate-of-strain consolidation data
reduction.
2 1-30 ZDEPTH
3 1 KRAD
33 KIND
36-40 SECOND
49-50 IIDIAL
F lO.O
1 1
11
FS.O
12
Place in columns 2 1 -30 the approximate depth in decimal feet at which the sample was recovered in the field. This depth is used to calculate the approximate overburden pressure in tons per square foot from the wet unit weight of the laboratory test specimen. The calculation of this overburden pressure does not take into account the effects of the water table or layers of different materials. The user may compensate for these situations by using a depth which will produce the desired effective stress for a given wet unit weight of the specimen. The following relationship is used to calculate the overburden stress: Overburden stress � (DEPTH (ft)) * (! ton/2000 lbf)
* (Wet Unit weight (grams)) I (453.6 grams/lbf) * (1728 in3jft3)/(lab sample volume (in3)).
This parameter determines the method used to select the point of maximum curvature in Casagrande's construction. A '2' placed in column 3 1 causes the program to use the Analytical Method shown in Figure 2_7a. A blank in column 3 1 will cause the program to employ the Graphical Method to determine the point of maximum curvature as shown in Figure 27b. The Graphical Method is well suited to handling anomalies in data, illudefined points of maximum curvature, and undulations in the fitted curve.
Option for type of deformation analysis in terms of void ratio and( or) vertical strain. A ' I ' placed in column 33 specifies that the analysis be performed in terms of void ratio. A '2' placed in column 33 specifies that the analysis be performed in terms of vertical strain. If a '0' or a blank is in column 33, the deformation analysis is performed in terms of both void ratio and vertical strain.
This parameter is used to remove the secondary compression points shown in Figure 28. This is done specifying the stress in Tsf at which secondary compression begins in controlled consolidation tests. If columns 32-40 are left blank, the program will default to a value of 3 1 .2 Tsf. Note that this parameter is not used in the analysis of the standard consolidation test data.
Option to override the assumed dial reading-versus-deflection relationships found in the computer program for each type of consolidation test. A ' I ' in column 50 will specify that increasing dial readings indicate specimen shortening. A '�1 ' in columns 49-50 will specify that increasing dial readings indicate specimen lengthening. If columns 49-50 are left blank or filled with zeros, the program will default to use the dial reading-versus-deflection relationships specified in
A-5
4. SEARCH BOUNDARY CARD 1-10 BOUND! FIO.O
l l-20 BOUND2 FIO.O
21-30 BOUND3 FIO.O
3 1 -40 BOUND4 FIO.O
A-6
the program. The program assumes, unless the above override option is used, that increasing dial readings indicate specimen shortening for standard and controlled-rate-of-strain test data. For controlled-gradient test data, the program assumes that increasing dial readings indicate specimen lengthening.
Stress search boundaries used for fmding the point of maximum curvature by either the Analytical or Graphical Methods. These boundaries are especially useful in choosing the representative portions of the curve and avoiding the localized effects of poor data and undulations in the fitted curve. These kind of choices are not possible when the user lacks knowledge of data1s appearance during the first computer run. In the first run of t{le data, the user can make rough estimates for these search boundaries. A list of suggested values for BOUND I and BOUND2 is provided at the conclusion of these remarks. These values will usually provide acceptable results in the absence of disruptive anomalies in the data.
When these boundaries are used in conjunction with the Analytical Method shown in Figure 29, the user must have them span the expected range of locations for the point of maximum curvature. In contrast, these boundaries are used by the Graphical Method to locate a tangent to the consolidation compression curve having the same slope as the rebound curve shown in Figure 30.
BOUND! is the most important search boundary for the graphical method. BOUND2 is of no consequence if it is located well into the steep portion of the compression curve. If a tangent to the consolidation compression curve cannot be found between BOUND I and BOUND2, the line having the slope 'E' of the rebound curve is drawn through the compression curve at BOUND 1 as shown in Figure 3 1 .
SPECIMEN CHARACTER
Very soft
Very stiff
SUGGESTED PRELIMINARY VALUES FOR BOUNDI AND BOUND2
ANALYTICAL GRAPHICAL
BOUND! BOUND2 BOUND! BOUND2
(tsf) (tsf)
0.5 4.0 0.5 16.0
0.5 8.0 0.5 16.0
TI1ese stress search boundaries are used to select the straight-line portion of the virgin compression curve shown in Figure 32. BOUND4 is the most important of these two search boundaries. BOUND4 usually is taken as the last or nearly last value of effective stress, but never greater than the last value of effective Stress. BOUND3 is of no consequence if it is before the
5. PLOT TITLE CARD 1-80 BCD 20A4
6. PRINTOUT DATA CARD l-16 LOC 4A4
17-18 HOL 12
]9-21 SAM A3
22-25 TES 14
26-�9 OPR f\.4
30-41 DAT 3A4
42-57 DES 4A4
7. IN):TIAL SOIL PROPERTIES CARD 1-5 SPG F5.2
6-12 WTIW F7.2
13-19 WTFW F7.2
20-26 WTFD F7.2
27-31 DEFI FS,2
3V6 DEFf F5.2
straight-line portion of the virgin compression curve. If the need arises, these search boundaries may be used to select a more representative portion of the virgin compression curve data.
Alphanumeric information which will serve as the plot title and description of the test. The test description should include test type and series number, borehole location and number, sample number, and any other information pertinent to the data and testing procedures.
General name of site from which sample was taken.
Borehole number entered as a right justified integer.
Alphanumeric identification of the sample.
Test number in a particular consolidation testing program.
Initials of the consolidation test operator.
Alphanumeric identification of testing period.
Alphanumeric information concerning material characteristics of sample.
Specific gravity of solids for the specimen.
Initial wet weight, in grams, of specimen.
Final wet weight, in grams, of specimen at end of test.
Final d1y weight, in grams, of specimen after dessication.
Dial reading just before start of test.
Dial reading at conclusion of consolidation test.
8, CALIBRATION FACTORS AND SAMPLE DIAMETER CARD 1-10 DCF F l O.O Defiection calibration factor expressed with a decimal
(inch/division).
1 1 -20 LCF
21 -30 PCF
31-40 DIA
F IO.O
FIO.O
FlO.O
Load calibration factor expressed with a decimal (lbs/division).
Pore-pressure calibration factor expressed with a decimal (psi/division).
Diameter of sample in inches. If these columns are left blank, a default value of 2.5 r r ... , used.
A-7
9. ZERO INFORMATION CARD 1-5 BP FS.l
6-10 DEFZ F5.2
1 1-14 WRZ F4.0
15-18 PPZ F4.0
21-30 SAM PHI F 10.0
Back pressure reading (psi).
Dial reading taken when sample is at its initial height.
Load reading corresponding to zero applied load.
Pore-pressure reading taken after application of back pressure and before loading of specimen.
Height of sample in inches after placement in consolidation ring and placement of end platens, or previously measured height. lf left blank, a default value of 1" is assumed.
l OA. CONTROLLED-GRADIENT OR CONTROLLED-RATE-OF-STRAIN CONSOLIDATION DATA FORMAT 1-4 TR( ) F4.0 Time reading.
5-9 DEFR( ) F5.2
10- 1 3 PPR( ) F4.0
14-17 WRD( ) F4.0
(Add an additional card for each test reading)
lOB. STANDARD CONSOLIDATION TEST DATA FORMAT 1-10 P( ) FlO.O
1 1 -20
(Add an additional card for each data point)
A-8
E( ) FlO.O
Defection reading; increasing for controlled-rate-of-strain and decreasing for controlled-gradient tests.
Pore-pressure reading.
Load reading.
NOTE: Consolidation compression points must be read in with the effective stress increasing. A drop in effective stress of greater than 0.7 tsf will cause the computer to treat all subsequent readings as rebound-expansion data.
Place in these first ten columns the effective stress in tons per square foot applied for a given load increment. Express the stress as a decimal number. Any stress less than 0.1 tsf will be automatically changed to 0.1 tsf.
Dial reading at 100-percent primary consolidation for effective stress shown in columns 1-10. Dial readings should increase with increasing deflection and describe the change in inches in the specimen height. All dial readings must be expressed with a decimal.
NOTE: Standard consolidation test data cards must start with compression data points and increasing effective stress. Rebound or expansion curve data cards follow the last compression data point in order of decreasing effective stress.
EFFECTIVE STRESS ORDER (tsf)
0.25 0.50 1 .0
I I . END OF DATA SET CARD 1-80 BLANK F IO.O
32.0 1 .0 0.5 0.25
This is the last card to be enclosed with each particular set of test data. The entire card is blank and signals to the program the end of the current set of test data.
A-9
JOB CONTROL CARDS
The following groups of job control cards apply when the University of Kentucky's IBM 370 at McVey Hall is used. These cards describe the JCL necessary for a source deck run, object deck run, source deck run with production of an object deck, and a source or object deck run in which the plot output is suppressed.
A standard JOB card which includes the waste paper option is the following:
//P74EGM JOB(l009,5 1001,1 , , ,W), MCNULTY,MSGLEVEL= l , REGION=268K
FOR RUN WITH SOURCE DECK
j /standard JOB card //P74EGM EXEC FORTGCLP //FORT.SYSIN DD *
FORTRAN SOURCE DECK
/* I /GO.SYS!N DD *
DATA
;•
To produce an object deck from a source deck run, change the second JCL card to the following:
//P74EGM EXEC FORTGCLP ,PARM.FORT=DECK
NOTE: See Figure 33
A-lO
FOR RUN WITH OBJECT DECK
//standard JOB card //P74EGM EXEC FORTGLP I /LKED.SYSIN DD •
FORTRAN Object Deck
/* I /GO.SYSIN DD •
DATA
/*
To run either source or object deck versions of programs without production of plotted output, add the following card before the I /GO.SYSIN DD • card:
//GO.PLOTTAPE DD DUMMY
PLOT OUTPUT NOTATION
l)EG Degree of polynomial fit PO In situ vertical streS& EO In situ void ratio or vertical strain PC Vertical presonsolication stress, P c EC Vertical preconsolidation strain OCR Overconsolidation ratio CC Compression coefficient, Cc (void-ratio
lll\alysis) CS Expansion coefficient, Cs (void-ratio analysis) CR Compression coefficient for strain analysis,
usually referred to as the compression ratio SR Expansion coefficient for strain analysis,
usually referred to as the swell ratio
TEST DESIGNATIONS
STD Standard consolidation CG Controlled-gradient consolidation CRS Controlled-rate-of-strain consolidation
A-U
Figure 27. Two Methods to Select the Point of Maximum Curvature.
..
A·l2
lOGA RITHMIC SCALE • oy•
SELECTED POINT / OF MAXIMUM CURVATURE
,.£;/ J
LOGARITHMIC SCALE • 0V 1
- - /\ �; \
SELECTED POINT I � OF MAXIMUM CURVE
ANALY T ICAL ME THOD KRAD = 2
GRAPHICAL METHOD KRAD Jl 2
2
VERTICAL EFFECTIVE STRESS , OV'' (LOG SCALE)
4 6 8 10° 2 4 6 8 101 2 4 6 8 102
I I I I I I I
STRESS VALUE AT START OF
SECONDARY COMPRESSION I I I I I I I I I I
REMOVED SECONDARY COMPRESSION
�DATA POINTS
Figure 28. Procedure for Removing Secondary Compression Effects of Controlled Data on Curve-Fitting Process.
A-13
..
LOGAR I T H M I C SCALE , cry•
BOUND I BOUND 2 I
I I I I ....--r- SE LECTED POINT � ! OF MAXIMUM CURVAT URE y'! <.. I
I I I
Figure 29. Search Boundaries for the Analytical Determination of the Point of Maximum Curvature.
A-14
r
LOGARITHt.41Cf �(fAL.E . ov I BOI,JNO I
I
SE LE�TEO POINT OF / M A XIMUM CURVATURE
�� ' . '
I
Figure 30. Search Boundaries for the Graphical Method to Select the Point of Maximum Curvature. BOUND2 Is Located in Straight Portion of Virgin Compression Curve.
Figure 3 ! . Special-Case Use of BOUND! by the Graphical Method as a default Location for the Initial Tangent Line when the Initial Portion of the Compression Curve Has a Slope Greater than E.
..
A-16
'·
LOGA R I T H M I C SCA L E , a; 8
BOUND I
-
------------�
LOGAR I T HMIC SCALE , cr;•
BOUND 3 BOUND 4
Figure 32. Use of Search Boundaries to Select Straight Portion of Virgin
Compression Curve.
I
A-17
Figure 33. Approximate Computer Processing Time versus Number of Problems for Source aud Object Deck Program Versions.
2 0
1 8
1 6
.... 1 2 (/)
c (f) z 0 0 z 0 0 Ll.l 1 0 (.) ILl (/) Cf) ..... Ll.l II
:IE ILl -8 �
1- 1-
z z :;::) 0 n:: !;j: 6 _j
____-·
a.. :IE 0
____-· (.)
4
____-·
- - - - - - -- ·
2
0 2 3 4
NUMBER OF PROBLEMS
A-18
SOURCE DECK
OBJECT DECK
Al'PENDIX B
SAMPLE PROBLEM
NDEG
CASAGR-0
TIME-INDEPENDENT CONSOLIDATION
TEST DATA ANALYSIS
PROGRAM CODING SHEET
Number of problems, columns 1-2, right justified.
lf NOPROB is greater than one, all of the remaining citrds must be repeated for each problem.
For NPLOTS place a '1' in column 2.
!PRINT - output option _for. the Analytical method to determine the pOint of maximum curvature. CODE '0' - Calculated radii printed out
'1 ' - Calculated radii not printed out
_ Degree of polynomial used in curve fitting.
RUNTYP _ Type of consolidation test
ZDEPTH
KRAD
In COL. 13: CODE '0' standard data ' 1 ' - controlled gradient data '2' - controlled rate of strain data
Approximate field d!lpth from which sample was re!lovered, in feet.
Option for method to select point of maximum curvature. In COL. 31 a blank or '0' causes the Graphical method to be used.
a '2' causes the Analytical method to be used.
KIND Type of deformation analysis.
SECOND
II DIAL
In COL. 33 '0' is for both void ratio and strain analyses. ' 1 ' is for void ratio analysis only. '2' is for strain analysis only.
Stmss at start of secondary compression (controlled tests only). If left blank, SECOND has default value of 31.2 Tsf.
Option to override the assumed dial reading-versus-deflection relationship specified by computer program for each type of consolidation test. In COLS. 50 a blank or '0' changes none of the assumed relationships.
BOUND!
' 1 ' will specify that increasing dial readings indicate specimen shortening.
49-50 ' .J' will specify that increasing dial readings indicate specimen lengthening.
BOUND2 BOUND3
1 2 3 4 5 6 7 8 9 IQ II 12 13 14 15 16 !7 18 19 2.0 2 1 22 23 24 25 26 27 28
.1 o a 1 00 :1. 0 . oo
BOUNDI, BOUND2 . search boundanes for selection of point o f maximum curvature using Analytical or Graphical methods.
BOUND3, BOUND4 - scard1 boundaries for selection of the line representation of the virgin compression curve.
BOUND4
B-1
\ll I»
CASAGR - 0 LABORATORY CONSOLIDATION TEST DATA
SAMPLE AND TEST DESCRIPTION TO BE USED AS PLOT TITLE (BCD)
r ' l .�;-;;-- �
l.F.S,--Z;'_ ' · - , __ _1 ' ___ i__, SAMPLE NO.
HOLE NO. (HOL)I)SAM) OPERATOR (OPR) TEST � ��.c:
L;..::O.c:
C,ATION (LOCI I i\ I ���S ) I f I DATE (OAT) I SAMPLE DESCRIPTON (DES)
; • 1 � ' 0 . 7 , � S 110- n 12 rl 14 . I� r;G '' -'8 IS 20-zl � � ll :l"4 �� 16 11 28 ' 2� 30!1': l2 ll 1H,l� lGI )7 l8'l� 40 ., 42:43:44!4�14&!47 148 49'50, 5 1 1 12 5] S4!5�!5G �7
1 I j_ [ _ ; �'----"· j -'-----.l_J.__j __ _L_L-:...__ .L ,i__( ___ _,_ _j __ ...L
M,II{O)( CiL"'Y ' I
SP GR. \ (SPG)
INI . WET I ( W T I W )
SPECIMEN FIN. WET I (WTFW)
WEIGHTS
FIN. DRY (WTFD)
DEFLECTION RDGS.
INI. I IDEFI) FIN. (DEFF)
CALI BRATION FACTORS DIAM. SAMPLE.
DEFLECTION I I PORE PRESS I BLANK " default (DCF) LOAD (LCF) ( P C F ) to 2.5" (DIA)
�-�- . . ' �-.:._-� 8 I iO ' •I ll '' :0 ·0 I I,
IB I� 20 lr 12 <J 114 l!i 2(; U1l6 �� 30 )r l.' ll_..::��,4Q� 10. o3 'l.')? t- O'lQ_ , . _ _ .·Jk<e,;. 7
BACK PRESS
(BPI
ZERO READINGS DEFL. I LOAD I (DEFZ) ( W R Z I
p . O l t 3 . ,0
INI. SAMPLE HEIGHT (SAM PHil
BLAN K = default to 1"
WATER CONTENT DATA INITIAL FINAL
Can No.
Wt. can + wet soil
Wt. con + dry soil '
Wt of can
Wt. of water
Wt. dry soil
Mois. cont.
NOTE� P P. ZERO READING should be taken after B. P application.
CASAGR - 0 LABORATORY CONSOLIOATION TEST DATA
CONTROLLED GRADIENT OR CONTROLLED RATE OF STRAIN CONSOLIDATION TEST
DATA FORMAT
LABORATORY READINGS
TIME
I DEFL
I p P. 1 LOAD _I
TR I ) DEFR l l PPR I ) �RD q TIME I DEFL. _).�1 P. P. I LOAD � TR I ) DEFR I" PPR I ) WRD I
I 2 3 4 5 6 7 B 9 10 II 12 I 3 14 15 IG I 7 1 8 19 I 2 3 4 5 6 7 8 9 10 II 12 13 1 4 1 5 1 6 I 7 18 I
tl / .... . . &. 9<::1· .9.0J 3 . .5 / 3 . . 2� .99S 95-t ��.<l f..,f!, 1!.£ 9'-« .9a2 3.? /3 • . 22 99.'1 95.S
.3 J.9. • .s:S . 99:' 9n.� 1-C 13 . .JP. 1aoc. 9M •
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STANDARD CONSOLIDATION
TEST DATA FORMAT
EF� STRESS P ( )
(TSF)
DIAL ROG. E ( ) (IN)
1 2 5 4 5 6 7 8 9 10 II 12 ll 14 15 15 ll' 1111 I
LAST CARD OF DATA BLANK
B-3
CASAGR - 0 LABORATORY CONSOI_IDATION TEST DATA
CONTROLLED GRADIENT OR CONTROLLED RATE OF STRAIN CONSOLIDATION TEST
DATA FORMAT
LABORATO�Y READINGS
T I M E l l1EFL. -1 P. p I LOAD ! TR I I DEFR I I PPR I lr-'iRD q TIME I DEFL. ) II P. P. I LOAD
� TR I I DEFR I l PPR I ) WRD I •I� ' 6 r e 9 10 ,; ·� ·� •4 ·� 1£ i ? IB 19 ' ' ' 5 6 7 8 9 10 II 12 13 14 15 16 17 IB 19
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LAST CARD OF DATA BLANK
B-4
STANDARD CONSOLIDATION
TEST DATA FORMAT
EF� STRESS P I l
DIAL RDG.
IT SF) 1 2 3 4 5 6 7 6 9 10
E ( l (IN)
II I� 13 1 4 1 5 1 1; 1' 1' 1 8 1 11 2
LAST CARD OF DATA BLANK
CASAGR - 0 LABORATORY CONSOLIDATION TEST DATA
CONTROLLED GRADIENT OR CONTROLLED RATE OF STRAIN CONSOLIDATION TEST
DATA FORMAT
LABORATORY READINGS
TIME
I DEFL.
I P. p I LOAD I T R I I DEFR I I PPR I l r." RD q
' 2 � 4 � "' 7 8 3 10 " 12 13 14 1�·16 1 7 1 8 19
�13.Q u.. 15:.0 /0/ 2. 1.23'7 1.U. t. L,§:e. /,CJJ 2 I 2. 4 3 .�,� .£/LfL7 I.Q/2. / 2,4,9 35'S IJ. . • � !ta./J. 1.2.5:4
lt>.J.5 �L.:t;l (pl.� 12::f:'i _/,'?,?.3 uha� l_pl 7£.·
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TIME I DEFL. I P. p I LOAD I TR I I DEFR I I PPR ( I WRD q I 2 3 4 s l6 71e 9 IQ II i2 1 3 14 1 5 1 6 1 7 18 19
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STANDARD CONSOLIDATION
TEST DATA FORMAT
EF� STRESS p ( )
(TSF)
DIAL RDG. E ( l (IN)
1 2 � 4 5 6 7 6 !1 10 II 12 ll 1 4 1 5 1 6 1 1 1 8 1 9 2
LAST CARD OF DATA BLANK
B-5
CASAGR - 0 LABORATORY CONSOLIDATION TEST DATA
CONTROLLED GRADIENT OR CONTROLLED RATE OF STRAIN CONSOLIDATION TEST
DATA FORMAT
LABORATORY READINGS
TIME I
DEFL.
I P. p I LOAD I
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B-6
TIME I DEFL. I P. p I LOAD I TR ( I DEFR ( l PPR I ) WRD q I 2 � 4 � G 7' 8 9 iO IE 12 13 14 15 16 I 7 18 19
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:l.Sf£1 '"' 61'1 99� I 3.9-B l28fS /,(), ""'9 -��"-' /335 lz�otl '._(/,, 6,9 99� l/.�_;>3
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LAST CARD OF DATA BLANK
STANDARD CONSOLIDATION
TEST DATA FORMAT
EFF STRESS P ( )
(TSF)
DIAL RDG. E I l (IN)
I 2 ! 4 S 6 1 ll 9 10 II 12 13 14 IS 16 IT 18 I. 2
��
LAST CARD OF DATA BLANK
CASAGR - 0 LABORATORY CONSOLIDATION TEST DATA
CONTROLLED GRADIENT OR CONTROLLED RATE OF STRAIN CONSOLIDATION TEST
DATA FORMAT
LABORATORY READINGS
TIME I DEFL. I P. P. I LOAD I TR ( ) DEFR I ) PPR I ) WRD q I 2 3 4 5 6 1 6 9 IQ II 12 13 14 15 16 17 IB 19
I:'! r/lt l<> • • aa .�82 /.0� 1::?/.Z� 'Ja .8.9 ,'/82 109-f" 3 l4o /,I'J . 1!9 98.2 /o3? � 15"."5 /,0, • . 9tJ .915'2 /03 la1:u lO ·.�C '182 1.0.30 �1 9,C /0.- .9.1 '18.2 O,l.,? 132(:),$ 'to . . Y.l 98;. /.02"' 3,2,2,() lo.- .9.l -�8 /OJ..' l>Z35 1 0. ,.92 9.8> /011 l3z.s:: /0 .9.3 '1!1,2 /0/.9 3 270 10 . 9.3 9fl2 ltll.Jr l 7 ?0o '''' -!?.9 .�2 l!oo.l 3.32:l ltJ.. 9/i .9.8 11.003 tH:c I.C/.9,9 9� 'iUi
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STANDARD CONSOLIDATION
TEST DATA FORMAT
EF� STRESS P I )
DIAL RDG.
IT SF) E I I (IN)
1 2 3 4 5 6 7 1l !HO II 12 11 1 � 1 5 1 6 1 7 18 11 2
LAST CARD OF DATA BLANK
B-7
C O N T R C L L E S G R A D I ENT C O N S O L I D A T i n � T E S T C A T A R E D U C T I O N
C G- 1 3 E L I Z A B E T H T O W N H - 3 S - 2 8 2 . 5 P S I
T E S T N O . 1 3
L OC A T I O N E L I Z A B E T H T O - N
C A T E 3 / 3 1 - 4 / 1 0 / 7 5
S C I L T Y P E - R E D S A N D Y C L A Y
B A C K P R E S S U R E 1 0 . 0 0 P S I
H O L E N O . 3
S AM P L E � D . 2 8
O P E RA T OR C T G
I N I T I A L F I N AL
2 3 . 4 %
0 . 6 2
• A T E R C O N T E N T
V O I D R A T I O
D E G . O F S A T U R A T I O N
2 6 .. 7 %
o . ao
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D E G R E E P O L Y N O M I A L = 1 1
1 0 2 . 3 %
P T . C F M A X . C L R V A T U R E S E L E C T ED R Y T H E A N A L Y T I C A L M E T H O D
S E A R C H B O U N DA R I E S F O R P T . O F M A X . C U R V A T U R E : 1 . 00 T S F 1 3 . 00 T S F
S E A R C H B O U N D A R I E S F O R V I RG I N C O M P R E S S I O N C U R V E : 1 0 . 0 0 T S F 2 il o G O T S F
D E P T H F O R I N S I T U S T R E S S C A L C U L A T I O N : 1 1 . 00 F E E T S E C O N D A R Y C O M P R E S S I O N A T 3 l o 2 0 T S F
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I N S I T U V E R T I C A L S T R E S S = 0 . 6 5 3 T S F I N I T I A L V O I D R A T I O I EO I 0. 7 9 9.
R A N G E S O F S T R E S S- V O I D R A T I O S E T T L E M E N T P A R A M E T E R S
P RO B A B L E
V E R T I C A L P R E C C NS O L I Q A T I UN S T R E S S • • • • • • • • • • • • • • 1 . 5 4 5 T SF
P R E C O N SO L I D A T I O N S T A T E � S V O I D R A T I C . .. . . . .. . . . . . . . . . . 0 . 7 6 4
O V E R C O N S O L I D A T I O N R A T I O I OC R ! · · · · � · � · · · · · · · · · · · · · · 1 4 . 6 1 3
S h E L L E X P A N S I O N I N D E X I C S ) • • • • • • • • • • • • • • • • • • • • • • • • - 0 . 0 3 0
B-8
M I N I MU M
8 . 1 L 2 T S F
0 . 7 6 6
1 2 . 4 1 1
- 0 . 2 7 9
>:: S T R A P < A r'>; A L Y S I .S :;:
* * * ¥ * * * * *� �- * ** * * * * * * * * * (• ¢ ¢ ( ¥�-�� * * * * * * * * * ** �' * * * * * * * * * * * * *
I � S I T U V E R T I C A L S T R � S S = O . b S 3 T S F I N I T I A L V O I D R A T I O I E1 l G e 79 9
R A N G E S O F S T R E S S - S T R A I � S E T T L E M F � T P A R A M E T ER S
P R 1 B A d L i:
V E R T I C A L P R EC O �S O L I D A T I O N S T R E S S • • • • • • • • • • • • • •
P R E C C � SG L I D A T I O N S T A T E ' S V E R T I C A L S T R A I N • • • • • • • • • •
O V E RC C N S O L I D A T I J �J R A T I O ( OC � l • • .. . . .. . . . . .. . . .. . .. .. . . .. .. 1 4 . 4 5 4
C C� P R E S S J C N R A T I O ! C R I • • • • • • • • ., • • • • • • • • • • • • • • • • • • • - 0 . 1 6 1
S h E L L R A T I O ( S R J • • o • o • • • • • o • • • • • • • • • • • • • • • o • • • • • • • - O o 0 l 7
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T I 1'-1 E C E F L . R C G . P o P e R LJ G . L C .A O K D G ..
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1 0 0 .. 1 2 . 6 6 l C 1 4 e l :J '5 lt . 1 0 5 . 1 2 . 6 5 1 0 1 3 • 1 u S 6 . 1 1 0 .. 1 2 .. b 2 1 0 1 3 • l J 6 2 .. l l s .. 1 2. .. 6 1 1C 1 3 .. l u 6 3 . 1 2 :; .. 1 2 .. 5 13 1 0 1 2 0 1 0 6 6 . U G . 1 2 .. 5 6 1 0 1 2 . 1 0 7 2 . 1 4 � .. 1 2 . 5 3 1 0 l 1 • 1 U 7 4 . 1 5 C . 1 2 .. 5 l l G l 1 • 1 0 7 9 . 1 5 ,:; . • 1 2 . 4 9 1 0 1 1 . 1 U P 1 . 1 s �) " 1 2 • ,, 7 1 (1 1 l .. 1 0 � 3 . 1 7 S . 1 2 . 4 5 1 c l 1 .. 1 u R 5 . 1 d 5 .. l 2 .. -'t3 1 r 1 1 .. 1 0 ·9 � . 1 9 5 . 1 2 . 4 l 1 C l 0 . 1 U 9 1 ., 2 0 5 . 1. 2 . 3 9 1 G 1 C .. 1 U 9 5 o 2 2 ':> .. 1 2 . 3 6 1 () 1 c 0 1 1 0 0 . 2 3 5 o 1 2 . 3 3 1 r, l c .. 1 [ () 3 . 2 4 5 . 1 2 . 3 1 1 :n c . 1 1 0 6 . 2-� �) .. l i. 0 2 p 1 ' \ 1 c 0 1 1 l 1 . 2 3 0 . 1 2 . 2 5 t r: l C . 1 1 1 6 . 2 9 5 . l 2 . 2 2 u: 1 G o 1 1 1 ') . 3 1 0 . 1 2 . 1 q 1 n 1 c .. 1 1 2 4 . 3 2 5 . 1 2 . 1 7 1 c l c . 1 1 2 >5 . 3 4 0 .. l 2 e l �; 1 ° 1 C .. 1 1 3 1 . 3 5 5 .. 1 2 . 1 2 l(Jl 0 . l 1 3 5 0
d . L ;� T S F
0 . J 1 8 1 2 . .. t 1 "1 - 0 . 1 '1 5
B-9
3 7 0 . 1 2 . l 0 l c l 0 . 1 1 3 9 . 3 ) 0 , 1 2 . 0 7 1 0 l c . 1 1 4 3 . 4 1 0 . 1 2 . 0 4 l 0 l l . 1 1 4 8 . 4 3 0 . l Z . J l l C' l l . l 1 5 2 . 44 ? . l l o 9 9 1 0 1 1 . l l 5 6 . 4 b 0 . 1 1 . 9 7 l c l l . 1 1 5 9 . 4 H o 1 1 . 9 6 1 0 l l . 1 1 6 l .. 5 J 8 . 1 1 . 1 1 1 C l l . 1 1 6 9 . 54 6 . 1 1 . 3 7 1 0 1 1 . 1 1 7 8 . 5 8 4 . 1 1 . 8 2 1 0 1 1 . 1 1 8 6 . 6 2 l • 1 1 . 7 8 1 0 l l . 1 1 9 3 . 6 5 4 . 1 1 . 7 3 1 0 1 1 . 1 2 0 0 . 6 9 7 . 1 1 . 7 0 1 0 l 2 . 1 2 0 7 . 7 3 4 . 1 1 . 6 6 l 0 1 2 . 1 2 1 4 . 7 7 2 . l l o 6 3 1 0 1 2 . 1 2 2 0 . A l O . 1 1 . 6 0 l 0 1 2 . 1 2 2 6 . a 4 e . l l . 5 6 1 0 1 2 . 1 2 3 1 . e o � e ll . 5 3 1 0 1 2 . 1 2 3 7 . 9 2 2 . 1 1 . 5 0 1 c 1 2 . 1 2 4 3 , 9 6 0 . 1 1 . 4 7 1 1' 1 2 . 1 2 4 9 . 9 9 8 . 1 l o 4 4 1 0 1 2 . 1 2 5 4 ,
1 0 3 5 . 1 1 . 4 1 1 0 1 2 . 1 2 5 9 . 1 0 7 3 . 1 1 . 3 9 1 0 1 2 . 1 2 0 4 .. 1 1 1 1 . l l o 3 7 1 0 1 2 . 1 2 6 9 . 1 1 4 E , 1 1 . 3 4 1 r 1 2 . 1 2 7 4 . 1 1 8 6 . 1 1 . 3 2 l 0 1 2 . 1 2 g c , 1 2 2 4 . 1 1 . 3 0 l 0 1 2 . 1 2 8 5 . 1 2 6 2 . l l o 2 8 1 0 L 2 . l 2 9 C . 1 2 9 9 . 1 1 . 2 6 1 :1 1 2 , 1 2 9 5 . 1 3 3 7 . 1 1 o 2 3 1 r 1 2 . 1 3 0 l . 1 3 7 5 . 1 1 o 2 1 1 0 1 3 . l 3 f1 7 . 1 4 0 0 . 1 1 . 2 0 1 0 1 3 . 1 3 0 9 . 1 4 2 0 . 1 1 o l q 1 0 1 3 . 1 3 1 2 . 1 4 4 0 . 1 1 . 1 8 1 0 1 3 . 1 3 1 5 . 1 4 7 5 . l l o 1 5 1 0 1 3 . 1 3 1 9 . 1 4 9 0 . 1 1 . 1 5 1 0 1 4 . 1 3 2 1 . 1 5 0 0 . 1 1 . 1 4 1 0 1 4 . 1 3 2 2 . 1 5 1 5 . l l . 1 3 1 0 1 4 . 1 3 2 4 . 1 5 3 5 . l l o 1 2 1 0 1 4 . 1 3 2 7 . 1 5 6 0 . 1 1 . 1 1 1 C 1 4 . 1 3 3 0 . � 5 8 5 . 1 1 . 0 9 1 0 1 4 . 1 3 3 4 . 1 6 1 0 . 1 1 . o e 1 0 1 4 . 1 3 3 8 . 1 6 3 0 . 1 1 . 0 7 1 0 1 4 . 1 3 4 0 . 1 6 6 0 . 1 1 . 0 5 1 0 1 4 . 1 3 4 4 . 1 6 3 5 . 1 1 . 0 4 l C' l 4 . 1 J lt 7 o l 7 2 0 . 1 1 . 0 1 t rl 1 6 . 1 3 6 l o l 7 3 0 . 1 1 o 0 0 U' 1 1 , 1 3 6 3 . l 8 2 0 . 1 0 . 9 5 1 0 1 6 . 1 3 6 b o lfl7 0 . 1 0 . 9 2 1 0 1 6 . 1 3 s c . 1 9 0 0 . 1 0 . 9 0 1 0 1 6 . 1 3 8 b . 1 9 3 7 . 1 o . 8 8 1 0 1 6 . 1 3 " 0 . 1 9 7 5 . 1 0 . 8 6 1 0 1 6 . 1 3 9 4 . 2 0 1 3 . 1 0 . 8 4 1 0 1 6 . 1 4 0 1 . 2 0 5 0 . 1 0 . 8 2 l 0 1 6 . 1 4 1 4 . 2 0 8 8 . 1 0 . 7 9 1 0 1 7 . 1 4 2 0 . 2 0 8 8 . 1 o . 7 7 l 0 1 7 . 1 4 ? 3 . 2 0 8 8 . 1 0 . 7 5 1 0 1 7 . 1 4 2 7 . 2 O d 8 , l o . 7 3 1 0 1 6 . 1 4 2 8 o 2 0 S E . l :.:;· 0 7 2 1 0 1 5 . 1 4 2 '! . 2 C b 8 . 1 0 . 7 2 1 1) l 4 • 1 4 2 9 . 2 0 8 8 . 1 o . 71 1 0 1 3 . 1 4 ? Y .. 2 O d 8 . 1 0 . 7 0 l n 1 1 • 1 4 3 c . 2 C b e . l C �a 7 0 [ () LJ 'l . 1 4 3 C .
B-10
2 0 8 8 . 1 0 o 6 9 1 0 0 3 . 1 <t 3 C . 2 0 8 8 . 1 0 . 6 9 1 0 0 7 . 1 4 3 0 . 2 0 8 8 . 1 0 . 6 8 1 0 0 6 . 1 4 3 0 . 2 0 8 8 . 1 0 . b 8 1 0 0 5 . 1 4 3 0 . 2 0 8 8 . 1 0 . 6 8 1 0 0 4 . 1 4 3 0 . 2 0 8 e . 1 0 . 6 8 1 0 0 3 . 1 4 3 0 . 2 0 8 8 . 1 0 . 6 8 1 0 0 2 . 1 4 3 0 . 2 0 8 8 . 1 0 . 6 7 1 0 0 2 . 1 4 3 0 . 2 0 8 s . 1 0 . 6 7 1 0 0 2 . 1 4 3 0 . 2 0 8 8 . 1 0 o 6 7 1 0 0 1 . 1 4 3 0 . 2 0 8 8 . 1 0 . 6 7 1 0 0 1 . 1 4 3 0 . 2 0 8 8 . 1 0 o 6 7 1 0 0 1 . 1 4 3 0 . 2 0 8 8 . 1 0 . 6 7 1 0 0 1 . 1 4 3 0 . 2 8 6 0 . 1 0 . 6 7 1 0 0 1 o 1 4 1 9 . 2 8 6 5 . 1 0 . 6 7 1 0 0 1 . 1 4 0 9 . 2 8 7 5 . 1 0 . 6 8 1 0 0 0 . 1 3 8 5 . 2 8 8 0 . 1 0 . 6 8 1 0 0 0 . 1 3 7 5 . 2 8 8 5 . 1 0 . 6 8 1 0 0 0 . 1 3 6 0 . 2 8 9 0 . 1 0 . 6 8 9 9 9 . 1 3 4 8 . 2 8 9 5 . 1 0 . 6 9 9 9 9 . 1 3 3 5 . 2 9 0 0 . 1 0 . 6 9 9 9 8 . 1 3 2 3 . 2 9 0 5 . 1 0 . 7 0 9 9 8 . 1 3 0 9 . 2 9 1 0 . 1 0 . 7 0 9 9 8 . 1 2 9 3 . 2 9 1 5 . 1 0 . 7 0 9 9 7 . 1 2 8 2 . 2 9 2 0 . 1 0 . 7 l 9 9 7 . 1 2 7 1 . 2 9 2 5 . 1 0 . 7 1 9 9 6 . 1 2 5 9 . 2 9 3 0 . 1 0 . 7 2 9 9 6 . 1 2 4 6 . 2 9 3 5 . 1 0 . 7 2 9 9 5 . 1 2 3 5 . 2 94 0 o 1 o . 7 3 9 9 5 . 1 2 2 0 . 2 94 5 . 1 o . 7 3 9 9 4 . 1 2 0 8 , 2 9 5 0 . 1 0 . 7 4 9 9 3 . 1 1 9 5 . 2 9 5 5 . 1 0 . 7 5 9 9 2 . 1 1 8 3 0 2 96 0 . 1 0 . 7 6 9 9 1 . 1 1 6 8 . 2 96 5 . 1 0 . 7 7 9 9 0 . 1 1 5 5 . 2 9 7 0 . 1 0 . 7 8 9 8 9 . 1 1 4 4 . 2 9 7 5 . 1 0 . 7 8 9 8 9 . 1 1 3 3 . 2 9 8 0 . 1 0 o 7 9 9 8 8 . 1 1 1 8 . 2 9 8 5 . 1 0 . 8 0 9 87 . 1 1 1 3 . 2 9 9 0 . 1 0 . 8 1 9 8 7 . 1 1 0 7 . 2 9 9 5 . 1 0 . 8 1 9 8 6 . 1 1 0 2 . 3 00 0 . 1 0 . 8 2 9 8 6 . 1 0 9 6 . 3 00 5 . 1 o . 8 2 9 8 5 . 1 0 8 9 . 3 0 1 5 . 1 0 . 8 3 9 8 5 . 1 0 8 3 . 3 02 5 . 1 0 • 8 4 9 8 4 . 1 0 7 8 . 3 0 4 0 . 1 0 . 8 5 9 8 3 . 1 0 7 0 . 3 0 5 5 . 1 0 . 8 6 9 8 3 . 1 0 6 3 . 3 0 7 0 . 1 0 o 8 7 9 8 3 . 1 0 5 6 . 3 0 9 0 . 1 0 . 8 7 9 8 2 . 1 0 5 0 . 3 10 5 . 1 0 . 8 8 9 8 2 . 1 0 4 3 . 3 1 2 5 . 1 0 . 8 9 9 8 2 . 1 0 4 0 . 3 1 4 0 . 1 0 . 8 9 9 8 2 . 1 0 3 7 . 3 1 5 5 . 1 0 . 9 0 9 8 2 . 1 0 3 3 . 3 1 7 0 . 1 0 . 9 0 9 8 2 . 1 0 3 0 . 3 1 9 0 . 1 o . 9 1 9 8 2 . 1 0 2 7 . 3 2 0 5 . 1 0 o 9 1 9 8 2 . 1 0 2 4 . 3 2 2 0 . 1 0 . 9 2 9 8 2 . 1 0 2 0 . 3 2 3 5 . 1 0 . 9 2 9 8 2 . 1 0 1 7 . 3 2 5 5 . l 0 o 9 3 9 8 2 . 1 0 1 4 . 3 2 "/ 0 . 1 0 . 9 3 9 8 2 . t o t o . 3 2 8 5 . 1 0 . 9 4 9 8 2 . 1 0 0 7 . 3 3 2 5 . 1 0 . 9 5 9 8 1 . 1 0 0 3 . 4 44 0 . 1 0 . 99 9 9 3 . 9 9 5 .
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1 0 . 2 5 0 4 1 0 . 7 2 6 74 0 . 0 4 0 0 0 1 3 0 . 0 0 0 0 0 1 0 . 3 7 8 3 8 0 . 7 2 4 6 7 0 . 0 4 1 1 5 1 4 5 . 0 0 0 0 0 1 0 . 6 7 8 3 3 o . 7 2 3 2 8 0 . 0 4 1 9 2 1 50 . o o o o o 1 0 . 7 9 8 3 3 0 . 7 2 1 9 0 0 . 0 4 2 6 9 1 5 5 . 0 0 0 0 0 1 0 . 9 1 8 2 9 o . 7 2 0 5 2 0 . 0 4 3 4 6 1 6 5 . 0 0 0 0 0 1 1 . 0 3 8 2 7 0 . 7 1 9 1 3 0 . 0 4 4 2 3 1 7 5 . 00 0 0 0 1 1 . 2 1 8 2 7 0 . 7 1 7 7 5 0 . 0 4 5 0 0 1 8 5 . 0 0 0 0 0 1 1 . 4 0 6 2 3 0 . 7 1 6 37 0 . 0 4 5 7 7 1 9 5 . 00 0 0 0 1 1 . 6 4 6 1 9 0 . 7 1 4 9 8 0 . 0 4 6 5 4 2 0 5 . 00 0 0 0 1 1 . 9 4 6 1 4 o . 7 l 2 9 1 0 . 0 4 7 6 9 2 2 5 . 0 0 0 0 0 1 2 . 1 2 6 1 3 0 . 7 1 0 8 3 0 . 0 4 8 8 5 2 3 5 . 0 0 0 0 0 1 2 . 3 0 6 1 0 o . 7 0 9 4 5 0 . 0 4 9 6 2 2 4 5 . 00 0 0 0 1 2 . 6 0 6 0 3 o . 7 0 7 3 7 0 . 0 5 0 7 7 2 6 5 . 0 0 0 0 0 1 2 . 90 6 0 1 0 . 7 0 5 3 0 0 . 0 5 1 9 2 2 8 0 . 0 0 0 0 0 1 3 . 0 8 5 9 7 0 . 7 0 3 2 2 0 . 0 5 3 0 8 2 9 5 . 0 0 0 0 0 1 3 . 3 8 5 9 4 0 . 7 0 1 1 5 0 . 0 5 4 2 3 3 1 0 . 0 0 0 0 0
B- 12
1 3 . 6 2 5 9 0 0 . 6 9 9 7 6 0 . 0 5 5 0 0 3 2 5 . 00 0 0 0 1 3 . 8 0 5 8 5 0 . 6 9 8 3 8 0 . 0 5 5 7 7 3 40 . oo o o o 1 4 . 0 4 5 6 1 0 . 69 6 3 0 0 . 0 5 6 9 2 3 5 5 . o o o o o 1 4 . 2 8 5 7 9 0 . 6 9 4 9 2 0 . 0 57 6 9 3 70 . 00 0 0 0 1 4 . 5 2 5 76 0 . 6 9 2 8 4 0 . 0 5 8 8 5 3 9 0 . 00 0 0 0 1 4 . 8 1 7 7 1 0 . 6 9 0 7 7 0 . 06 0 00 4 1 0 . 0 0 0 0 0 1 5 . 0 5 7 6 8 0 . 6 8 8 6 9 0 . 0 6 1 1 5 4 3 0 . 00 0 0 0 1 5 . 2 9 7 6 5 0 . 6 8 7 3 1 0 . 0 6 1 9 2 4 4 5 . 00 0 0 0 1 5 . 4 7 7 6 1 0 . 6 8 5 9 3 0 . 0 6 2 6 9 4 6 0 . 00 0 0 0 1 5 . 5 9 7 5 7 0 . 68 5 24 O o 06 3 0 8 4 7 1 . 0 0 0 0 0 1 6 . 0 7 7 5 0 0 . 6 8 1 7 8 0 . 06 5 0 0 5 0 8 . 0 0 0 0 0 1 6 . 6 1 7 3 9 0 . 6 7 9 0 1 0 . 0 6 6 5 4 5 4 6 . 00 0 0 0 1 7 . 0 9 7 3 2 0 . 67 5 5 5 0 . 0 6 8 46 5 8 4 . 00 0 0 0 1 7 . 5 1 7 2 6 0 . 6 7 2 7 8 0 . 0 7 0 0 0 6 2 1 . 00 0 0 0 1 7 . 9 3 7 1 9 0 . 66 9 3 2 0 . 0 7 1 9 2 6 5 9 . 00 0 0 0 1 8 . 3 4 9 1 2 0 . 66 7 2 5 0 . 0 7 3 0 8 6 9 7 . 00 0 0 0 1 8 . 7 6 9 0 9 0 . 66 4 4 8 0 . 0 7 4 62 7 3 4 . 0 0 0 0 0 1 9 . 1 2 9 00 0 . 66 2 4 1 0 . 0 7 5 77 7 7 2 . 00 0 0 0 1 9 . 4 8 8 9 8 0 . 66 0 33 0 . 0 7 6 9 2 8 1 0 . 00 0 0 0 1 9 . 7 8 8 9 1 0 . 65 7 5 6 0 . 0 7 8 46 8 4 8 . 00 0 0 0 2 0 . 1 4 8 8 6 0 . 6 5 5 4 9 0 . 0 7 9 6 2 8 8 5 . 0 0 0 0 0 2 0 . 5 0 8 7 9 0 . 6 5 3 4 1 0 . 0 80 7 7 9 2 2 . 00 0 0 0 2 0 . 8 6 8 7 7 0 . 6 5 1 34 0 . 0 8 1 9 2 9 6 0 . 0 0 0 0 0 2 1 . 1 6 8 7 3 0 . 64 9 2 6 0 . 0 8 3 0 8 9 9 8 . 00 0 0 0 2 1 . 4 6 8 6 7 0 . 6 4 7 1 9 0 . 0 8 4 2 3 1 0 3 5 . 0 0 0 0 0 2 1 . 76 8 6 0 0 . 6 4 5 8 0 o . o 8 5 0 0 1 0 7 3 . o o o o o 2 2 . 06 8 5 9 0 . 6 4 4 4 2 0 . 0 8 5 7 7 1 1 1 1 . oo o o o 2 2 . 3 6 8 5 0 0 . 6 4 2 3 4 0 . 0 86 9 2 1 1 4 8 . 0 0 0 0 0 2 2 . 72 84 7 0 . 64 0 9 6 0 . 0 8 7 69 1 1 8 6 . 00 0 0 0 2 3 . 02 8 4 4 0 . 63 9 5 8 0 . 0 8 8 4 6 1 2 2 4 . 00 0 0 0 2 3 . 3 2 8 3 7 0 . 63 8 1 9 O o 0 89 2 3 1 2 6 2 . 00 0 0 0 2 3 . 6 2 8 3 3 0 . 63 6 8 1 0 . 0 9 0 0 0 1 2 9 9 . 00 0 0 0 2 3 . 9 8 8 2 8 0 . 6 3 4 1 3 0 . 0 9 1 1 5 1 3 3 7 . 00 0 0 0 2 4 . 3 4 0 2 4 0 . 6 3 3 3 5 0 . 0 9 1 9 2 1 3 7 5 . 00 0 0 0 2 4 . 4 6 0 2 1 0 . 6 3 2 6 6 0 . 0 9 2 3 1 1 40 0 . 00 0 0 0 2 4 . 64 0 2 1 0 . 63 1 9 7 0 . 0 9 2 6 9 1 4 2 0 . 00 0 0 0 2 4 . 82 0 1 8 0 . 6 3 1 2 7 0 . 0 9 3 0 8 1 44 0 . 0 0 0 0 0 2 5 . 0 6 0 1 0 0 . 62 9 2 0 0 . 0 9 4 2 3 1 47 5 . 00 0 0 0 2 5 . 1 7 2 0 6 0 . 6 2 9 2 0 0 . 0 9 4 2 3 1 4 9 0 . 00 0 0 0 2 5 . 2 3 2 0 6 0 . 62 8 5 1 0 . 0 9 4 6 2 1 5 0 0 . 00 0 0 0 2 5 . 3 5 2 0 8 0 . 6 2 7 8 2 0 . 0 9 5 00 1 5 1 5 . 0 0 0 0 0 2 5 . 5 3 2 03 0 . 62 7 1 2 0 . 0 9 5 3 8 1 5 3 5 . oo o co 2 5 . 7 1 2 0 2 0 . 6 2 6 4 3 0 . 0 9 5 77 1 5 6 0 . 00 0 0 0 2 5 . 9 5 1 9 7 0 . 6 2 5 0 5 0 . 0 9 6 5 4 1 5 8 5 . 00 0 0 0 2 6 . 1 9 1 9 6 0 . 6 2 4 3 6 0 . 0 96 9 2 1 6 1 0 . 00 0 0 0 2 6 . 3 1 1 92 0 . 6 2 3 66 0 . 0 9 7 3 1 1 6 3 0 . oo o o o 2 6 . 5 5 1 8 6 0 . 6 2 2 2 8 0 . 0 9 8 0 8 1 66 0 . 00 0 0 0 2 6 . 7 3 1 8 7 0 . 62 1 5 9 0 . 0 9 8 4 6 1 68 5 . 0 0 0 0 0 2 7 . 5 5 5 7 4 0 . 6 1 9 5 1 0 . 0 9 9 6 2 1 7 20 . 0 0 0 0 0 2 7 . 6 6 7 74 0 . 6 1 8 8 2 0 . 1 00 00 1 7 3 0 . 00 0 0 0 2 7 . 8 5 5 6 8 0 . 6 1 5 3 6 O o l 0 1 9 2 1 8 2 0 . 00 0 0 0 2 8 . 6 9 5 5 9 0 . 6 1 3 2 9 0 . 1 0 3 0 8 1 8 7 0 . 00 0 0 0 2 9 . 1 7 5 4 9 0 . 6 1 1 9 0 0 . 1 0 3 8 5 1 90 0 . 00 0 0 0 2 9 . 2 9 5 4 7 0 . 6 1 0 5 2 0 . 1 0 4 6 2 1 93 7 . 00 0 0 0 2 9 . 5 3 5 4 5 0 . 60 9 1 4 0 . 1 0 5 38 1 9 7 5 . oo o oo 2 9 . 9 5 5 3 7 0 . 60 7 7 5 0 . 1 0 6 1 5 2 0 1 3 . 0 0 0 0 0 3 0 . 7 3 5 2 3 0 . 60 6 3 7 0 . 1 0 6 9 2 2 0 5 0 . 0 0 0 0 0 3 1 . 0 8 7 1 7 0 . 60 4 2 9 0 . 1 0 8 0 8 2 0 8 8 . 00 0 0 0 3 1 . 0 8 7 1 7 0 . 6 0 4 2 9 0 . 1 0 8 0 8 2 0 8 8 . 00 0 0 0 3 1 . 0 8 7 1 7 0 . 60 4 2 9 0 . 1 0 8 0 8 2 0 8 8 . 00 0 0 0 3 1 . 0 8 7 1 7 0 . 60 4 2 9 0 . 1 0 8 0 8 2 0 8 8 . 00 0 0 0 3 1 . 0 8 7 1 7 0 . 60 4 2 9 0 . 1 0 8 0 8 2 0 8 8 . 00 0 0 0 3 1 . 0 8 7 1 7 0 . 6 0 4 2 9 0 . 1 0 8 0 8 2 0 8 8 . 00 0 0 0
B-13
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0 . 60 4 2 9 0 . 60 4 2 9 0 . 60 4 2 9 0 . 6 0 4 2 9 0 . 60 4 2 9 0 .. 6 0 4 2 9 0 . 60 4 2 9 0 . 60 4 2 9 0 . 60 4 2 9 0 . 60 4 2 9 0 . 60 4 2 9 0 . 60 4 2 9 0 . 60 4 2 9 0 . 60 4 2 9 0 . 6 0 4 2 9 0 . 60 4 2 9 0 . 5 9 5 9 9 0 . 59 5 9 9 0 . 5 9 6 6 8 0 . 59 66 8 0 . 5 9 6 6 8 0 . 5 9 6 6 8 0 . 5 9 7 3 8 0 . 5 9 7 3 8 0 . 5 9 8 0 7 0 . 5 9 807 0 . 5 9 807 0 . 5 9 8 7 6 0 . 59 8 7 6 0 .. 5 9 9 4 5 o .. s 9 q 4 5 0 . 60 0 1 4 0 .. 6 0 0 1 4 0 . 6 0 0 8 4 0 .. 60 1 ':) 3 0 . 6 0 2 2 2 0 .. 60 2 9 1 0 .. 60 3 6 0 0 . 60 36 0 0 . 60 4 2 9 0 ,. 6 () 4 9 9 o .. & u s &r. 0 .. 6 0 5 6 8 0 . 6 0 6 3 7 0 . 6 0 6 3 7 0 . 60 7 0 6 0 . 60 7 7 5 0 . 6 0 8 4 5 0 . 6 0 9 1 4 0 . 60 9 8 3 0 .. 6 0 9 8 3 0 . 6 1 0 5 2 0 . 6 1 1 2 1 0 . 6 ! l 2 1 0 . 6 1 1 9 0 0 . 6 1 1 9 0 0 . 6 1 2 60 0 . 6 1. 2 6 0 0 . 6 1 3 2 9 O e 6 l 3 2 9 C . 6 1 3 9 R (1 .. 6 1 3 -:l A 0 .. 6 1 467
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C G - 1 3 E L I Z A B E T H T O W N H - 3 5 - 2 6 2 . 5 P S I
L O G ( V E R T I C A L E F F . S T R E S S , T S F l
3 4 5 6 7 8 9 ,! 0° 2 3 4 5 6 7 8 9 .1 0' 2 3 4 s 6 7 8 9 .1 o'
DEG • 1 I
PO • 0 . 653 T S F E O • 0 . 79B7
RANGE OF VALUES
PROBABLE - M I N I MUM
PC 9 . 44 T S F - B . l l TSF
EC 0 . 0 1 9 1 - O . O I B I
OCR 1 4 . 5 - 1 2 . 4
CR - 0 . 1 6 1 - - 0 . 1 55
SR - 0 . 0 1 65
C G - 1 3 E L I Z A B E T H T O W N H - 3 S - 2 B 2 . 5 PS I
L O G ( V E R T I C A L E F F . S T R E S S , T S F J
�} o-• 2 3 y 5 6 7 8 9 l o' 2 3 4 5 6 7 8 9 ,1 01 2 3 4 5 6 7 8 9 ,\ o'
0
0 "'
DEG • 1 1 0
PO • 0 . 653 T S F EO • 0 . 7987
<D r--
RANGE OF VALUES 0
PROBABLE - M l N l M U M
PC 9 . 55 T S F - 8 . 1 1 TSF
ru r--
EC 0 . 764 - 0 . 7 6 6 0
w - OCR 1 4 . 6 - 1 2 . 4
0 �"'
<D cc · 0 . 2 9 1 - - 0 . 279
>-- • a:o cs - 0 . 0297 a: 0 � o =' >�
0
0 <D
0
<D "'
0
N
t;o "'
,.... 0
....
APPENDIX C
COMPUTER SYSTEM DESCRIPTION
Computer Manufacturer Model number Word length
Core access speed Virtual storage
Peripheral Equipment Line printers
Card readers Card punch Magnetic tape drives
Plotters
COMPUTER SYSTEM DESCRIPTION
IBM System/370 Model 165 II Single Precision · 4 bytes, 32 bits Double Precision · 8 bytes, 64 bits 700 nano seconds 16 mega bytes (maximum)
IBM/32 1 1 Chain Printers IBM/2821-5 1/0 Control Unit IBM/3505 Card Reader IBM/029 Card Key Punch IBM Tape Unit 2401 processes tapes at 75 inches/second Uses 800 bytes per inch density magnetic tape Processes 60,000 bytes/second Uses either 9 or 7 track tapes Calcomp 663 Digital Incremental Drum Plotter
Source Program's Storage Requirements Total storage requirements of program around 268k
MAIN 42556 ANARAD 44760 GRARAD 4490 CASPLT 1 5 308 CONSGRA 5858 FLSQFY 958 FGEFYT 1 904 FCODA 928 Plot buffer · up to 74k
C. I
APPENDIX D
FLOW CHART
D-1
D-2
Continuo lo
read dolo
" comprenlon data
No
Haa affective siren dttrtaud more than 0.7 T1f botwnn con"cutlve
data polnh '
'"
"' I ( '"' re��.�ato J
Has effective strua decreaud
between con18cutlve data polnto
'
'"
'"
'"' ol
data
SEMI- LOGARITHMIC STRESS -DEFORMATION ANALYSIS
II a void ratio analy1i1 I• to be done, 11 lo done flrot. Any
vertical otrain analytlt 11 dou ucond.
'" Slandord data
'
"
..
Ccntlnu& "
read data "
comproulon datil
No
I "" I " jv.rll��������oln I
CALL FLSQFY "
Ill tptclllod ltatl oquore& pat)rnamlal to tha semi-log
repn"ntotlon of comprluion dolo
,, __________________ <( >-------------------"'
Select tine ,
location of mox•mum slope
Compute
Select line ot
location of lorgnt slope
po .. lng % dill
criteria
roclil of curvature ,
geoerotod abociuo betwoen
oeorch boundoriea
'"
Select tine at I aeolian
of largnt olo�o pa�ein�
% d1ll cr<ter�a
Select line ;oing through 1011 compreuion cur.o point having stope
determined from the overage of two linn'
one tangent to comprtnlon curve at ito maximum slopt end ona going through the loot two
point•
"
D-3
'"
"'
D-4
,, there n point
of maximum curvature in 90% midportlon
Gf search
"' Default to uu
location "
ma�lmum valuo '"
"'
Default 111 uu flr1t uarch
boundary Ill point lhrouph which lint
hav•ng &lopt of oxpaneion- rebound
cur•• 1011! be drown
Biooct interior angle formed ��"rdi'i!����r an
°J curv:1'ff�� ���r:::�l�rlon
nccnd derivative .. chosen point "
ma•imum curvature
APPLY THE CASAGRANDE CONSTRUCTION TO DETERMINE THE
PRECONSOLIOATION PRESSURE
APPLY THE SCHMERTMANN CONSTRUCTION TO DETERMINE THE COMPRESSI81LITY
COEFFICIENTS FOR INSITU VIRGIN COMPRESSION
Find inteructioo "
angle bl11cto.r tine with
comprenion curve J)Oiynemial repre11nlotion
Return "
main
"'
Printout '"
data and ro•ull• pertinent to thi�
current deformation onalf!is
>------------- '"
D-5
APPENDIX E
CASAGR-0 COMPUTER PROGRAM
c
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c
c
c
c
c
c
* ** * * * * * * * ** * * * * ** * * * * * * **** * * * * * * * * * * * * * * * * * *
!,:
C A S A G R - 0 ::;:
1 S T V E R S I ON , M A Y 1 9 7 6 *
U P D A T E S , V E R S I ON S : N C N E ,,
*
* * * * ** * * * * * * * * * * ** * * * * * * * * * * * * * * * * * * * * * * * * * * * *
*
* C O � P U T E R A P P L I C AT IO N
O F T H E
C A S AG R A N D E A N D S C H M E R T � A N N
C O N S T R U C T I O N S *
B Y
;',:
E D �U N D G R E G O R Y M C N U L T Y
*
* ** * * * * * * * * * * * * * ** * * * * * * * * * * * * * * * * * * * * * * * * * * * *
T H I S C O M P U T E R P R O G R A M E MP L O Y S A M A T H E MA T I C A L A LGOR I TH M T O A N A L Y Z E T H E S E M I - L O G A R I T H M I C R E P RE S E � T A T I O N O F T H E T I ME I ND E P E N D E N T S T R E S S
D E F ORMA T I O N C UR V E S F O R T H E C O N V E N T I O N AL , C O N T RO L L E D G R A D I EN T ,
A N D C O N T R O L L E D R A T E O F S TR A I � C O NS O L I DA T I O N T E S T S , T H E C A S AG R A N D E A N U S C H M E R T M A N N C O N S TR UC T I ON S A R E
E M P L O Y E D T O D E T E R � I N E T H E P R E C CNS D L I DA T I O N P R E S SU R E AND T H E C O E F F I C I E N T S D F C OM PR E S S I B I L I T Y F O R T H E C OMP R E S S I O N A N D E X P A N S I O N - R E B O U N D D A T A C U R v E S ,
*
*
*
*
* * * * * * ** * * ** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
0 0 1 0 0 0 2 0 0 03 0
0 04 0
0 0 5 0 0 0 6 0
0 0 7 0 0 0 8 0
0 0 9 0 0 1 0 0
0 1 1 0 0 1 2 0
O l3 0 0 14 0 0 1 5 0 0 1 60
0 17 0 0 1 8 0 0 1 90
0 2 0 0 0 2 1 0 0 2 2 0 0 2 3 0 0 2 4 0
0 2 50 0 260 0 2 7 0
0 2 8 0
0 2 90 0 3 0 0
0 3 1 0
0 32 0
0 3 3 0
0 3 4 0
0 35 0
0 360 0 37 0 0 38 0 0 390 0 4 0 0 0 4 1 0 0 4 2 0 0 4 3 0 0 4 4 0 0 4 5 0 0 4 6 0 0 4 7 0 0 4 8 0 0 4 9 0
E-1
c
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E-2
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
TH I S P RO G R A • I S • R I T T E N I N F OR T R AN I V A N D P R O D UC E S PLCT
T E D O U T P U T U S I NG THE I BM 3 7 0 / 1 65 I I AND C A LC C M P 6 6 3 DRUM P L O TT E R .
TH I S P R C G R A � W A S D E V E L O P E D BY
T H E K E N T U C K Y D E P A R T M E N T O F T R A N S P O R T A T I ON
6 UR E A U CF H I G H w A Y S
D I V I S I ON O F R E S E A RC H
SDJLS S E C T I ON
5 3 3 S . L I ME ST O N E S T .
L E X I NG T O N , K EN T U C K Y
4 0 5 0 8
P H . 6 0 6 2 54 - 4 4 7 5 E X T 2 8
* * * * � � * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * � * * * * * * * * * * * * * * * * * * * * * * * * **
A V A I L A B I L I TY O F T H F P RO G R A M ' S C A R D D ECK A �O / O R L I S T I NG � I L L
B E C ON S I D E R E D 0� T H E � E R J T S O F E A C H I N D I V I DU A L I N CU ! R Y . T H E U S E R
I S T O T A L L Y R E S P C N S I B L E F O R T H E R E S U L T S D ER I V E D F R O M TH I S
P R OG R A �· ' S U S E .
T H I S P R O G R A M H A S T H E C A P AB I L I T Y O F E M P L O Y I N G A VO I D R AT I O
AN D / O R V E R T I C A L S T R A I N D E F O R MA T I ON A N A LY S I S . A L S D o T H E P R O G R A M
P R OV I D E S F O R T H E S P E C I F IC A T I O N O F C A L I B R A I ON F A C T O R S C C M �O � L Y U S E D
A N D A M E A N S O F � A T C H I N G A D I A L G A UG E ' S I NC R E A S I NG D I AL R E A D I NG S W I TH I NC R E A S I NG D O w N W A R D D E F L E C T I O N .
T H E P R O G R AM A L S O O E T ER � I N E S T H E I N I T I A L A N D F IN A L T E S T
P R O PE R T I E S O F T � E C O N S O L I DA T I O N T E S T S P EC I M E � .
T H E M E TH O D O F A N A L Y S I S I S B A S E D O N A L E A S T SQUA R E S C U R V E
F I TT I N G S C H E M E B Y O R D I N A R Y P D L Y NO � I A L S . T H E C CM P R E S S I CN C U R V E
D A T A I S F I TT E D � I TH A U S ER S P E C I F I E D P O L YN O M I A L O F U P T O T H E
E L E VE N T H D EG R E E . TH E E X P A N S I ON - R E B O U N D C U R V E D A T A I S F I T T E D
W I TH A L E A S T S Q U AR E S S T R A I GH T L I N E . U S I NG T H E M AT H E M A T I C A L
C H A R A C T E R I S T I C S O F T H E S E T hO F U NC T I ON S , T H E C A S A G R A N D E A N D
S C H M E R T M A N N C O N S T R UC T I ON S A R E E M P L O Y E D .
T H E P O I N T O F M A X I M U M C U R V A T U R E F CR C A S A GR A N D E ' S C O N S T R UC T I O N
M A Y B E D E T E R M I N E D B Y T h O C O M P L E T E L Y D I F F E R E N T M ET H OD S • T H E
A N A L Y T I C A L M E TH C O U S E S T H E M A T H E M A T I C A L OE F I � I T I ON O F T H E RA Q I I I S
O F C UR V A T U R E T O S E L E C T T H E PO I NT O F M A X I MUM C U R V A T U R E . T H E
G R A P H I C A L M E T HOD I S A � E W L Y P R OP O S E D M E T HO D h � I C H U S E S T H E
G E O M E T R I C A L C H A R A C T E R I S T I C S O F T H E C O N SC L ! D A T I CN C U R V E S T O
S E L E C T T H E P O I N T O F MA X I M U M C uR V A T U R E .
D A T A P O I NT S , F I TT E D C U R V E S , A N D T H E I NT E R M E D I A T E
C O N S T R U C T I O N S I � V O L V E D I N T H E C A S A G R A N D E A �D S CH M E R T M A � N
P R O C E DU R E S A R E S H O � N I N T H E P L O T T E D O U T P U T A L O N G W I TH T H E
F I N A L ?. E S U L T S .
0 5 0 0 0 '> 1 0
0 5 2 0
0 5 3 0
0 54 0
0 5 5 0
0 5 6 0
0 5 7 0
0 5 8 0
0 59 0
0 6 0 0
0 6 1 0
0 6 2 0
0 6 3 0
0 6 4 0
0 6 5 0
0 6 6 0 0 6 7 0
0 6 8 0
0 6 0 0
0 700
0 7 1 0
0 7 2 0
0 7 1 0
0 74 0
0 7 5 0
0 760
0 77 0
0 7 8 0
0 79 0
0 8 00
0 8 1 0
O b 2 0 0 8 3 0
0 84 0
0 8 5 0 0 8 6 0
0 8 7 0
0 8 8 0
0 8 9 0
0 900
0 9 1 0
0 92 0
0 93 D
0 9 4 0
0 9 5 0
0 960
0 9 7 0
0 9 8 0
0 99 0
1 000
1 0 1 0
I 0 20
1 03 0
1 04 0
1 0 5 0
1 0 60
l 0 7 V
l 0 8 0
t oo n
c * * * * * * * * * * * * ** * *�** ********************************** ********** *** c
C T HE P R O G R A � U S E S T H E F O L L O W I N G S U B R OU T I N E S A N D C O M P U T E R
C S U PP L I E D B U F F ER S : c C 1 . M A I N P R O G R A M
c
C 2 . S U B R O U T I N E C O N G R A - I N P U T A N D R ED U C T I O N O F
C C O N T R O L L E D C O N S O L I D AT I O N
C D A T A . c
C 3 . S U BR OU T I N E F L S Q F Y - L EA S T S Q U AR E S C U R V E C F I T T I N G BY O R D I N A R Y
C P O L Y NO M I A L S .
c
C 4 . S U B R O U T I NE G R A R A D - G RA P H I C A L M E T HO D T O C D ET E R M I N E P C I �T O F M A X C C UR V A T U R E . c C 5 . S U B R OU T I N E A N A R A D - ANA L Y T I C A L M E T H O D T C C D E T E R M I N E P O I � T O F M A X
C C UR V A T U R E .
c
C 6 . S U B R OU T I N E C A S P L T - P L O T T I N G OF R E S U L T S
c
C 7 . S U B R O U T I N E P L O T S - S E T S U P P L O T L I B R A R Y
C B U F F E R F O R I BM 3 7 0 / I 6 5 I I C C O M PU T E R .
c
C B . P L O T L I BR A R Y S U B R O U T I N E S : A X I S
C D A S H LN C L I NE
C LOGA X S C N U M B E R C P L O T
C SC A L E C S Y MB O L c
C 9 . L I BR A R Y F U NC T I O N S : A B S
C A T A N
C A S I N C D S Q R T
C S I N
C T A N
c
c * * * * * * * * * * * * * * * * ** * * * * * * * * * * * * * ************ *********************** c
C P O S S I B L E D I F F I CU L T I E S W I T H R E S U L T S :
c
C I I I F U N D U L A T I ON S P R E S E N T I N F I TT E D C U RV E ; c
C P O S S I BL E C A U S E S : - LOW D E G R E E P O L Y N O M I A L L I M I TA T I O N D U E
C T O F E W D A T A P O I N T S . I F TH I S I S
C T H E C A S E , T H E O N L Y P O S S I B L E COUR S E
C OF A C T I O N I S T O T R Y A L O W E R
C D E G R E E P O L Y N OM I A L .
c
C H A R C TO F I T D A T A , E I TH E R S C A T T E R E D C D A T A O R S H A P E C H A R AC T E R I S T I C S O F D AT A
C T OQ E X T R E M E T C R E F I TT E D BY A P O L Y NO M I A L .
1 1 00
I 1 1 0
1 1 2 0
1 13 0
1 1 40
1 1 5 0
1 1 60
1 I 7 0
I l 8 0
I 1 9 0 I Z OO
1 2 I O
1 2 2 0
1 23 0
1 24 0
1 2 5 0
1 260
1 2 7 0
1 28 0
1 29 0
1 300
1 3 1 0
1 32 0
1 33 0
1 340
1 35 0
1 360
1 37 0
1 38 0
1 39 0
1 400 1 4 1 0
1 4 2 0
1 4 3 0
1 44 0
1 4 5 0
I 460
1 4 7 0
1 4 8 0
I 4 9 0
I 500
1 5 1 0
1 5 2 0
1 5 3 0
1 54 0
1 5 5 0
1 5 60
1 57 0
I 5 8 0
1 5 9 0
1 600
1 6 1 0
1 6 2 0
1 6 3 0
I 640
1 6 50
1 660
1 67 0
I 6B O
I 69 0
c C - T O O L O � A D E G R E f P D L Y NO � I A L , U S E H I G H E S T C P O S S I B L e D E G R E E .
c C 2 1 I F P n i N T O F � ' X ! M U � C UR V AT U R E D O E S � O T E X I S T • H E N A N A L Y T I C A L C M E T rl O D I S U S E D ; c C P O S S I BL E C A U S E S : - S E A R C H B OUND A R I E S N E E D T C dE C H A NG E D . c C - P O I N T OF M A X C UR V A T UR E N CT � E L L E N O U GH C O E F I � E D T O BE A � ' A L Y T I C AL L Y D E T ER M I N E D . c C - S I M P L Y C O E S N C T E X I S T . C P O S S I BL E S O L U T I O N I S TO U S E G R A P h i C A L
C M E T H O D .
c c • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •
c c c c c
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ** * * * * * * * * * * * ** * * * * * * * * * * * * * * * * * *
c V A R I A d L E D E F I N I T I ON S
c c c
* ** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
C A c c c
H O R I Z O N T A L P E N P O S I T I O N A T W h i C H L E TT E A ' A ' I S P L O T TE D . V A R I A B L E I S C O M P U T E D I N SU BR OU T I N E C A S P L T .
T H I S
c c
A L P h A ! I
c C A R c c C A Y c c c 8
c c c 8 (
c c c
S C R A T C H A R R A Y F O R S U B R OU T I N E F L SQ F Y .
A R E A O F T E S T S P EC I �E N I N I N CH E S .
S E E C E P T A .
HOR I Z O N T A L P E N P O S I T I O N A T WH I C H L E T T E R ' B ' I S P L O T T E D .
I N C R E M E N T A L A B S C I S S A E G E N E R A T E D O N T H E F I T T � D P C L Y N CM I A L I N S E A R C H I NG F O R T H E V I RG I N C O� P RE S S I DN C UR V E .
c c
P O D 2 0 A 4
c c c c c c c c c c c c
P L O T T I TL E A � D C O M P U T E R P R I N T O U T H E A D I � G .
F E T A l l
SC R A T C H A R R A Y F O R S U P R OU T I N E F L SQ F Y .
B I S E C T ! I
P I G
S T O R A G E L J C A T I O N O F G E N E R A T E D I NC R E M E N T A L O R D I N AT E S U S E D I N P L O T T I NG T H E L I NF R E P R E S E N T I � G T H E A N G L E d i S EC T C R U S E D I N T H E
G R A P H I C A L � E T H C D T O S E L EC T T H E P O I N T O F " A X I M U M C UR V A T UR E .
T H E S E L E C T E D S L O P E F O R T H E L I NE R E P R E S F N T A T I O� C F T H E V I R G I N C O M P R E S S I OI''-1 C UR V E ..
E-4
1 7 00
1 7 1 D
1 7 20
1 73 0
1 740
1 7 5 0
1 76 0
1 77 0
1 78 0
1 79 0
1 8 00
1 8 1 0
1 8 2 0
1 83 0
1 84 0
1 8 5 0
1 86 0
1 8 70
1 8 8 0
1 89 0
1 9 0 0
1 9 1 0
1 9 2 0
1 93 0
1 94 D
1 95 0
1 96 0
1 97 0
1 98 0
1 99 0
2 0DO
2 0 ! 0
2 D 2 0
2 0 3 0
2 04 0
2 0 5 0
2 0 6 0
2 07 0
2 0 8 0
2 09 0
2 1 DO
2 1 1 0
2 1 2 0
2 1 3 0
2 1 40
2 1 5 0
2 1 60
2 1 7 0
2 1 9 0
2 1 9 0
2 2 DO
2 2 1 0
2 2 2 D
2 2 3 0
2 24 0
2 2 5 0
2 2 60
2 2 7 0
2 2·�0
2 2 9 0
c C R O U N C
C T E � P O R A R Y S T O R A G E L OC A T I O� F O R B O U N D ! I N S UB R OU T I N E G R A R A D .
c c B O U N O l , 8 1
C B O U N0 2 , 8 2
C B O U ND 3 , 8 3
C BOUN04 , B 4 C B O U ND S , B 5 C B O U N D 6 , 86
C B O U N D A R I E S 1 AND 2 A R E A B S C I S S A S E A R C H B O U N DA R I E S F C R P O I N T O F
C M A X I M U M C U R V A T U R E . B O U ND A R I E S 3 A N D 4 A R E A B S C I S S A S E AR C H B O U N D -
C A R I E S r O R T H E S E L E C T I O N OF L I NE R E P R E S E NT A T I O N OF T H E V I R G I N C OM-
e P R E S S I ON C U R V E . B O U N D A K I E S 5 A ND 6 ARE G E N ER A L L Y U S E D A S
T E � PO R A R Y S TO RA G E L OC A T I ON S F O R B O U N D ! A N D BOUN02 I N S U B R OU T I N E
A N A R A D .
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E Q U A T I O N I S U S E D T O C O M P U T E T H E S L O P E A T E A CH O F T H E G E N E R A T E D
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C C O E F F I C I E N T VAR I A B L E U S E D F O R S E TT I NG U P A L L P O L Y NO M I A L E QU A T I O N S .
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P R E S S I O N D A T A ' S F I T T E D P O L Y N O M I A L ·
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C C E P T B
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C C E P TC
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c c c c c c c c c c c
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V E R T I C A L I N T E R C e P T S A T T � E Z ER O A B S C I S S A F O R L l � E S A , g , B I S C EC T , ( , C t E , F , G , A � D T A N G E N R E S P E C T I V E L Y .
C H E C K U S E � T O C H E C < I F P E RC E N T D I F F E R E N C E C R I T E R I A F O R S L O P E C CN S T A N C Y � A S B E E N S A T I S F I E D . I F C H E C K I S � O T S • T E O U A L T O O N E , T H E P E R C E N T D I F F E R E NC E C R I T E R I A H A S N O T B E E N SA T I S F I E D A N D T H E � A X I MU M S L O P E F O U� C I S U S E r .
C C R
c C O � P R E S S I O N R A T I O . c c c c c c c s c c
� ! N l �U �' V A L U E O F C OMP R E S S l O t' R A T I O OR C C � P R E S S ! ON I ND E X t I . E .
T H E S L O P E O F L A B O R A T O R Y V I R G I N C U RV E , L I N E O I .
S W E L L - E X P A N S ! O N - R E B J U N O C O E F F I C I EN T .
c c
C S E VT t I
c D UMMY V A R I A B L E U S E D P R I MA R I L Y F O R S T O R A G E O F V O I D R A T I O S GF C O M P R E S S I ON C UR V E D A T A P O I NT S P R I O R TJ O U T P U T .
c c c c c
C S E V T E t I D U � � y V A R I A B L E U S E D P R I MA � ! L Y F G R S TO R A G E OF VO l � R A T I O S CF R E P C U N O- E X P A � S ! O N D A T A P O I N T S P R I OR T J C U T P J T .
C UR V E t I c c C O M P U T E D O R D I N A T E S A T T H E G E � E R A T E D A BS C I S S A
C O M P R E S S I O N C UR V E ' S F I T T E D P O L Y � DM I A L . L O C A T I CN S A L O N G T H E
c c
C UR V F T t I c c C O� P U T E O O R D I � A T E S
P L O T T I N G P U R P O S E S . O F T H E F I T T E J P O L Y NO M I A L W H I C H A R E U S E D F O R
c c c e x c c c C C Y c c c 0 c c c
H O R I Z O N T A L P E N PO S I T I O N AT WH I C H T H E L E T T E R ' C ' I S P L O T T E D .
V A R I A B L E I S C C � PU T E O I N S J P R C U T ! N E C A S P L T .
V E R T I C A L I N T E � C E P T O F L I N E ' C ' A T T H E Z E R O A BS C I S S A .
H D R I Z O � T A L P E N P O S I T I O N A T WH I C H T H E L E T T E R ' 0 ' I S P LO T T E D .
V A R I A B L E I S C O M P U T E D I N S U P R CUT I N E C A S P L T .
D A S H { I
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C P R I NC I P L E S C R A T CH A K R A Y U S E D F D K P L O T T I NG PUR P O S E S . 3 5 0 0
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c 3 5 4 0
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C F I N A L D E F L E C T I O N R E A D I N G T A K E N A T E ND O F T E ST . 3 560
c 3 57 0
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c 3 6 00
C O E F R I I 3 6 1 0
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C SC L I D A T I ON T E S T S . 3 6 3 0
c 3 6 4 0
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C C O N S O L I O A T I O� T E S T S . 3 6 7 0
c 3 68 0
C D E F Z 3 6 9 0
C D I A L R E A D I N G T A K E N W H E N S A � P L E I S A T I T S I N I T I A L H E I G H T . 3 700
c 3 7 1 0
C D E L L O G 3 720
C P O R T I O N OF LOG C Y C L E P E R I N C H O F P LOT P A P ER . I N P L CT T I NG SUB- 3 73 0
C P R O G R A M C A S P L T o D E L L O G I S S E T E QU A L T O 0 . 3 0 0 F O R T H R E E LOG C YC L E S 3 7 4 0
C O V E R T E N I N C H E S OF P A P E R . 3 7 50
c 3 7 6 0
C D E L T A 3 77 0
C I N C R E M E N T T O B E U SE D I N G E N E RA T I ON OF E V E � L Y S PA C E D V A L U E S O F A 3 7 8 0
C G I V E N P A R A ME T E R . 3 7 9 0
c 3 8 00
C D E S 4 A 4 3 8 1 0 C S A M P L E D E S C R I P T I ON . 3 8 2 0 c 3 8 3 0
C D F L I I I 3 8 4 0
C C A L C U L A T E D D E F L EC T I ON I N I N C H E S FOR C ON T R O L L E D C O N S G L I D � T I O N T E S T 3 8 5 0
C C O M P R E S S I O N D A T A . 3 8 6 0
c 3 8 7 0
C D F L I E I I 3 8 B O
C C A L C U L A T E D D E F L EC T I ON I N I N C H E S FOR C J N T R O L L E D C O N S C L I D AT I ON T E ST 3 8 9 0
C E X P A N S I O N - R E BOUND D A T A . 3 900
c 3 9 1 0
C D I A 3 92 0
C D I A M E T E R O F C O N SO L I D AT I ON T E S T S P EC I � EN I N I N C H E S . 3 93 0
c 3 9 4 0
C O I F F 3 9 5 0
C P E R C ENT D I F F E R E NC E B E T W E E N C O N S E C U T I V E S L J P E S 0� T H E C O M P R E S S I ON 3 96 0
C D A T A ' S P C L Y N C M I A L R E P R E S E� T A T I O N o 3 97 0
c 3 9 8 0
C D I F F , O I F F l 3 99 0
C D I F F ER E NC E I � E F F E C T I V E S T R E S S B ET W E E N C O N S E C UT I VE C O N T R OL L E D 4 000
C C O N S C L I OA T I ON T E S T C CH PR E 5 S I CN D A T A P O I N T S . 4 0 1 0
c 4 02 0
C D Y 4 0 3 0
C S E E C E P T D 4 0 4 0
c 4 0 5 0
C E I I 4 0 60
C V A R I A B L E � H I C rl S T O R E S D I AL R E A D I NG S , VO I D R A T I O S , A �O V E RT I C A L 4 07 0
C S T R A I N OF C O� P R E S S I ON D A T A P C I N T S A T VA R I O U S T I M E S D U R I NG T H E 4 0 8 0
C P R O G R A � ' S E X E C U T I ON . 4 0 9 0
E-7
c
C EC
C VO I C R A T I O OR V E • T I C A L S T R A I N A T T H E PR EC O N SC L I C A T I GN S T A T E A S
C I O E A L I Z E J E Y T H E S C rl • E R T •A � N C O N S T R uC T I ON .
c
C E C " I N
c O R D I N A T E V A L u E O F V O I D R A T I O 00 VE R T I C A L S T R A I N A T T H E
� I N I " U M P R E C G N S O L I D A T I ON S T A T E . c
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c
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E E I
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V A R I A B L E � H I C H S T OR E S D I AL R E A D I N G S , VG I O R A T I O S , A ND V E R T I C AL
S TR A I N O F E X P A N S I O N - R E B O U N D DA T A P O I N T S A T V A R I C U S T I • E s DUR I N G
D R Q G R A � ' S � X E C U T I O N .
V O I D R A T I O F C R F I R S T D A T A P O I N T O N S T AN D A RD T E S T ' S E X P A N S I ON
R E P CU N O C UR V E .
C F I N A L V O I D R A T I O .
c
C E I
c
c
C E O
c
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I N I T I A L V O I D RA T I O .
I N I T I A L V O I D R A T I O .
c
c
F A C T OR
c
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T H E C O R R E C T I C N N E E D E D
M J D I F Y T H E A P P E A R AN C E
T O T A K E I N T O A C CO U N T T H E SC A L E F A CT CR S T H A T
O F A N GL E S C N T H E P L O T OU T PU T .
c
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T H E I N I T I A L S T A RT I N G E X PON E Nt O F T E N F O C • WH I C H T H E L O G A X I S � I LL
B E D R A WN I N P L O T T I N G S Ub P R O G R A M C A S P L T . I I . E . , F I R LGG I S • �U A L
T O - 1 . 0 1
V E R T I C A L I N T E R C E P T O F L I N E ' F ' A T T H E I E R O A B S C I S S A .
V E R T I C A L I N T E R C E P T OF L I N E ' G ' A T T H E I ER Q A BS C I S S A .
H E I GHT OF S P E C I M E N FOR C O N T R O L L E D C O • P R E S S I C N D A T A . S TG R A G E
VA R I A B L E F O R I N PUT D I A L R E A D I NG S F O R S T AN D A R D T E S T C C � P R E S S I O N
D A T A .
C H E I I
C H E I G H T C F S P E C I M E N F O R C ON TR OL L E D E X P A� S I O N - R E B OU N O D A T A . STOR AG E
C V AR I A B L E F O R I N P U T D I A L R E A D I N G S O F S T A ND A R D T E S T E XP AN S I ON -
( R E R C U N D D A T A .
c
C l-I I
C I N I T I A L H E I G H T O F S P EC I M E N A T S T A R T C F T E S T .
c
C H O L I 2
C BOR E H O L E N U � 3 E R .
c
C H S
C HE I GH T C F S OL I D S .
E-8
4 1 00
4 1 1 0
4 1 20
4 1 3 0
4 1 4 0
4 1 5 0
4 1 60
4 1 7 0
4 1 8 0
4 1 9 0
4 2 0 0
4 2 1 0 4 2 2 0
4 2 3 0
4 2 4 0
4 2 5 0
4 2 6 0
4 2 7 0
4 2 8 0
4 2 9 0
4 3 0 0
4 3 1 0
4 32 0
4 33 0
4 340
4 3 50
4 3 6 0
4 3 7 0
4 3 f:.l. O
4 3 9 0
4 4 0 0
4 4 1 0
4 4 2 0
4 4 3 0
4440
4 4 5 0
4 4 6 0
4 4 7 0
4 4 8 0
4490
4 5 0 0
4 5 1 0
4 5 2 0
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4 54 0
4 5 5 0
4 5 6 0
4 5 7 0
4 5 8 0
4 5 9 0
4 6DO
4 6 1 0
4 6 2 0
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4 6 4 0
4 6 5 0
4 660
4 6 7 0
4 6 8 0
4 6 9 0
c C H V c l � I T ! A L H E I GH T O F V O I D S . c c c c c c c c c c c c c c c
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D O L C O P P A R A M E T E R .
A R R A Y L OC A T I O N F O R T H E A BS C I SS A V A L U E C O R R E S P ON D I NG L OC A T I O N O F T H E L AR G E S T R A D I U S O F C URVA T U R E .
T O T H E
! C H E C K T H I S V A R I A B L E I S S E T E QU A L T O O N E I N S U BRO U T I NE A N A R A D � H E N A D I S C R E T E L O C A L I Z ED P O I N T O F M A X ! � U M C U R V A T U R E H A S B E E N F O U � D . I F A D I SC R E T E P O I N T O F M A X I M U � C U R V A T U R E H A S � C T B E E N F O U N D , ! CH EC K H A S A V A L U E C F Z E RO A N D T H I S C AU S E S A D E F A U L T T C S E L E C T T H E P O I N T W H E R E T H E S E C O N D D ER I VA T I VE I S A M A X I M U M .
C I OE RV 2 C A R R A Y L OC A T I O N F O R T H E A BS C I S S A V A L U E W I T H T H E L A R G E S T V A L U E O F C T H E S E C O N D D E R I V A T I V E . c c c c c c c c c c c c c c c c
! D I A L V A R I A B L E T O S P E C I F Y W H E T H E R D I A L R E A D I N G S I NC R E A S E CR D E C R E A S E W I T H I N CR E A S I N G D O W N W A R D D E F L EC T I O N . ! D I A L E Q U A L S + 1 F C R D I A L R E A D I N G S W H I C H I NC R E A S E W I T H I N CR E A S I N G D O W N W A R D D E F L E C T I ON . ! D I AL E Q U A L S - 1 F O R D I A L R E A D I N G S W H I C H D E C R E A S E W I TH I NC R E A S I N G O O W � W A R J D E F L E C T I ON .
! ! D I A L
I M I N
O P T I ON V A R I A B L E W H I C H C A N P E U S E D T O O V E RR I D E P ROGR AM ' S B U I L T I N V A L U E S F O R ! D I A L .
A R R A Y L OC A T I ON C U R V A T U R E .
F O R THE A BS C I S S A V A L U E O F T H E P O I NT O F � AX J MU M
C I N c c c c c c c c c c c c c c c c c c c c c c
C O M P U T E R ! � P U T U T I L I T Y D E V I C E N U M B E R F O R R E A D S T A T E � E N T S .
I N UM DUMMY A RG U M E N T I N S U B RO U T I N E L O C A T I O N F O R T H E G R A P H I C A L L Y
G R A R A D T H A T A S S I GN C O R R E C T A R R A Y S E L E C T E D P G I � T O F M A X I M U � C U R V AT U R E .
l O U T C O • P U T E R O U T P U T U T I L I T Y D E V I C E N U M B E R F CR W R I T E S T A T E � E NT S .
! P R I N T O P T I ON P A R AM E T E R F O R R E DUC I NG T H E A M O U N T S E L E C T I N G T H E P O I N T OF M AX I M U M C U R V A T U R E
O F O U T P U T P R O D U C E D I � B Y T H E A N A L Y T I CA L M E T H O D .
I S T R D O O R I F
I VO I D DO O R I F
L O O P P A R A M E T ER W H I C H I S M A N I P U L A T E D T O G I V E E I T H E R A VO I D RA T I O V ER T I C AL S T R A I N A N A L Y S I S . I F K I N D E �U A L S 1 o J S T R E Q U A L S 1 . K I N O E Q U A L S 2 , I ST R E Q U A L S 2 .
L C O P P A R A M E T E R WH I C H I S M A N I P U L A T E D T O G I V E E I TH E R V E R T I C A L S TR A I N A N A L Y S I S . I F K I N O E QU A L S l o ! V O I D K J N C E Q UA L S 2 , ! V O I D E Q U A L S 2 .
A V O I D R A T I O D Q U A L S 1 .
4 7 0 0 4 7 ! 0 4 7 2 0 4 7 3 0 4 740 4 7 5 0 4 760 4 7 7 0 4 7 8 0 4 7 9 0 4 8 0 0 4 8 1 0 4 8 2 0 4 8 3 0 4 8 4 0 4 8 5 0 4 8 6 0 4 8 7 0 4 8 8 0 4 8 9 0 4 9 00 4 9 1 0 4 9 2 0 4 9 3 0 4 9 4 0 4 9 5 0 4 9 6 0 4 9 7 0 1t 9 P O 4 99 0 5 000 5 0 1 0 5 0 2 0 5 0 3 0 5 04 0 5 05 0 5 060 � 070 5 0 8 0 5 09 0 5 1 00 5 ! 1 0 5 1 2 0 5 ! 3 0 5 14 0 5 1 5 0 5 1 6 0 5 ! 7 0 5 1 8 0 5 1 9 0 5 2 00 5 2 ! 0 5 2 2 0 5 2 3 0 5 24 0 5 25 0 5 2 6 0 5 27 0 5 2 8 0 5 29 0
E-9
c c J
C C O L C J P P A R A � E T E R &
c C J P R I N T
C O P T I ON P A R A � E T F R F O R O U T P U T Wrl i C H I S P 0 E S � N T L Y N O T U S E D .
c C K I N O
C O P T I O � V A R I A B L E F O R S P E C I F Y I NG � I T H E R V C I D R A T I C OR V E R T I C A L
C S T R A I N A N A LY S I S .
c ' C K K
c OJ L CG P P A R A � E T E R F O R D I S T I NG U I SH I N G
V E R T I C A L S TR A I N � O D E S O F A N A L Y S I S a
o � T W E E N V O I D R AT I O A N D
c c c c c c c c c c c c c c c
K R A D
O P T I ON P A R A M E T E R F O R S E L E C T I O N O F D E S I R ED M E T H O D T O S E L E C T P O I N T
O F � A X I M U M C � R V A T UR E . I F K R A D I S N O T E Q U A L T Q ' 2 ' • P RO G R A M
D E F A U L T S T O U S E T H E G R A P H I C A L � E THDO TO S E L E C T T H E P O I N T OF
K S L O P E
P A P A � E T E R U S E D I N T E L L I � G T rl E P RO G R A M H O W T H E V I R G I � C U R V E L I N E
P E P R E S E N T A T I C N o A S S E L E C T E D F O R S T A N D A R D C O � S O L I O A T I ON D A T A .
I F K S L O P E I S N O T E C tJ A L T O ' 0 ' , T H E L I NE W A S S E L EC T E D O N T H E B A S I S
O F A N A V E R A G E S L O P E B E T h E E N T HE T A N G E NT O F M A X I MU M S L O P E A N D A
L I N E G O I N G T � R0 0 G H T H E L A S T T o O C O M P R E S S I O N D A T A P O I NT S .
C L
c O U � � y P A R A M � T E R P R � S E N T L Y N O T U S E D .
c c c c c c c c c c c c c c c c c c c c c c c c c c c
L C F R E A L
L E � G T H C AL I B R A T I O N F A C T O R �
L I � E A I R e A L
l ! N E B I R e A L
L I N E C I R E A L
L I N E D ! R E A L
l ! N E E I R E A L
L I N E F I R E A L
L I N E G I I R F A L
R E A L V A R I A • L E S wH I C H A R E U S ED I N S U B R D U T I � E C A S P L T T O S T C R E T H E
I N C R E M E N T A L L Y G E N E R A T E D O R D I N A T E S V A L UE S U S E D I N P L C T T I �G L I N E S A ,
g , c , ., • • G ..
L I �I E A - � 0 R I Z O N T A L
L I � E B - T AN G E N T T O
C UR V A T U R E .
L I N E T H R O U G H P O I N T O F � A X I M U � C U RV A T U R E .
C CM P � E S S I CN C U R V E A T P O I � T O F M A X I � U �
L I N E C -
l l i\J E O -
L ! N E E -
L I N E
L I N E
L I N E
3 I S E C T 1 NG A N G L E B E T W E E N L I N E S ' A t A � D ' B ' .
R E P R E S E N T A T I O N OF V I R G I N C C 0 P R E S S I ON C U R V E .
R E PR E S E N T A T I O N C F E X P A N S I O N- R E B O U N D C U R V E .
L I �: E F - L I N E I N S C H M E R T M A N� ' S C O N S T RUC T I O � 0 S ED T O R F P R E S EN T
I N I T I A L C O M P R E S S I ON C U R V E . I T H A S T H E S L O P E O F L l � E E A � O G O E S
T H P C U G H T H E P O I N T H A V I N G I T S A B SC I S S A A T T H E ! N S I T U V E R T I C A L
S T R E S S A N O OR D I N A T E A T T H E I N I T I A L VO I D R A T I O O R V E R T I C A L S T R A I N .
L I N EG - L I � E D E R I VE D F R C M S C H ME R T �A N N ' S C O � S T R U C T I O N A S R E P
R E S EN T A T I O N CF T H E ! N S I T U V I R G I N C O M P R " S S ! O� C UR V E .
C L L
c OU L C O P P AR A '' E T E R U S E D I N D O I NG T H E S P < C I F I ED N U MB E R OR P RO B L E � S .
c
E-10
5 300
5 3 1 0
5 3 2 0
5 3 3 0
5 3 4 0
5 3 5 0
5 3 6 0
5 3 7 0
5 3 A O
5 3 9 0
5 4 0 0
5 4 1 0
5 4 2 0
5 4 3 0
5 4 4 0
5 4 5 0
5 4 6 0
5 4 7 0
5 4 9 0
5 4 9 0
5 5 0 0
5 5 1 0
5 5 2 0
5 5 3 0
5 54 0
5 5 5 0
5 5 6 0
5 5 7 0
5 5 8 0
5 5 9 0
5 6 DO
5 6 1 0
5 6 2 0
5 6 3 0
5 64 0
5 6 5 0
5 6 6 0
5 6 7 0
5 6 8 0
5 6 9 0
5 7 0 0
5 7 1 0
') 7 2 0
5 7 3 0
� 7 4 0
5 7 5 0
5 760
5 7 7 0
5 7 8 0
5 7 0 0
5 8 0 0
5 8 1 0
5 8 2 0
5 8 3 0
5 8 4 0
5 8 5 0
5 8 6 0
5 8 7 0
5 8 8 0
5 89 0
C L O C I I 4 A 4
C G E N E R A L L O C A T I O N OR N A M E O F S I T E F R O M W H I C H S A M P L E W A S T A K E N .
c c c c c c c c
tv\DC
M O E
W A T F I V E P AR A M E T ER T H A T R E P R E S E N T S T H E C CM P R E S S I ON C U R V E ' S N U M B E R
O F D A T A P O I N T S , P L U S T H E D E G R E E O F P O L Y N OM I AL , A N D P L U S O N E .
S A M E A S M DC , B U T F O R E X P A N S I ON - R E B O U N D C U R V E D A T A .
C N C
c c c c c c c c c c c c c c c c c
N O C
N D E
N D E G
NU M B E R O F C OM P R E S S I ON C U R V E D A T A P O I NT S ,
W AT F I V E P AR A M E T E R W H I C H S P EC I F I E S T H E N U M B E R O F P O L Y NO M I AL CO
E F F I C I E N T S N E E DE D FOR THE P O L YN O M I A L F I T T E D T H R OU G H THE C O M
P R E S S I ON C U R V E D A T A .
S A M E A S N O C BUT F O R E X P AN S I ON - R E B O U N D C U R V E D A T A .
D EG R E E P O L V N CM I AL F O R C OM P R E S S I ON C U R V E ,
N D E G E
E Q U A L S
D A T A .
O N E A N D I S D E G R E E P O LYNOM I AL FOR E X P A N S I ON - R E BO U N D C U R V E
C N E
c c c c c c c
N U M B E R O F E X P AN S I ON-RE B O U N D D A T A PO I NT S .
N O P R O B
T H E N U M B E R O F P R O B L E M S E T S T O B E S O L V E D . I N P R O G R A M V E R S I O N
C A S AG R- I , T H I S Q U AN T I T Y I S S Y N O M O U S W I T H T H E N U M B E R O F S T R E S S
S T R A I N A X E S h H I C H W I L L BE U S E D I N T H E P L O T T I NG OF T H E D A T A .
C N P L C T S C I N P R O G R A M V E R S I ON C A S A G R- 0 , N P L O T S I S A D U M M Y I NP U T P L A C E H O L D E R .
c c c
I N T H E P R O G R A M V E R S I O N C A S A G R- I , T H I S Q UA � T I T Y I S T H E N U M B E R O F
P L O T S T O A P P EA R U N O N E S E T O F S TR E S S - S T RA I N A X E S .
C N U M P T C
c c
N U M B E R OF C OM P R E S S I ON C U R V E D A T A P O I N T S .
C N U M P T E
c c
N U M B E R O F E X P AN S I ON - R E B O U N D C UR V E D A T A P O I N T S .
C O RC M I N
C M I N I M U M P O S S I B L E O V E R C O N SO L I D A T I ON RA T I G ,
c c c c c c c c c c c
C P R I I A4
I N I T I A L S OF T E S T O P E RA T O R .
O R O I N A
P I I
V A R I AB L E U S E D I N P L OT T I NG
T H E R E DUC E D S T A N D A R D T E ST
S U B RO U T I N E C A S P L T T O C H A N G E L I N E S W H I L E
D A T A I S B E I NG P L O T T E D I N T A B U L A R F O R � .
E F F EC T I V E S TR E S S O F C O P PR E S S I O N D AT A P O I NT S .
5 900
5 9 1 0
5 9 2 0
5 9 3 0
5 94 0
5 9 50
5 96 0
5 97 0
5 9 8 0
5 99 0
6 000
6 0 1 0
6 0 2 0
6 03 0
6 04 0
6 0 5 0
6 060
6070
6 0 8 0
6 09 0
6 1 00
6 1 1 0
6 1 20
6 1 3 0
6 14 0
6 1 50
6 1 60
6 17 0
6 1 8 0
6 1 90
6 200
6 2 1 0
6 2 20
6 23 0
6 24 0
6 2 5 0
6 2 60
6 27 0
6 2 8 0
6 2 9 0
6 300
6 3 1 0
6 3 2 0
6 3 3 0
6 34 0
6 3 5 0
6 360
6 3 7 0
6 3 8 0
6 3 9 0
6 4 0 0
6 4 1 0
6 4 2 0
6 4 3 0
6440
6 4 5 0
6 4 6 0
6 4 7 0
6 4 8 0
6 4 9 0
E-l l
C P C
C P R F C O N S G L I C A T I DN P R E S S U R E .
c
C P C F
C P R E S S U R E C A L I B R A T I ON F A C TO R I P S I / D I V I .
c
C P D U '-lM Y ( I C O U � M Y V A R I A B L E F O R P L O T T I N G T H E T A 3 L E O F E F F E C T I V E S T R E S S V A L U E S .
c
C P E l C E F F EC T I VE S TR E S S o • E X P A N S I ON - R E BO U N D D A T A P O I N T S .
c
C P I
c 3 . 1 4 1 5 q z
c
C P I N ST U
C O V E R B U R D E N P R E S SU R E .
c
C P O l I , P O V E , P D V E R
C I S E E P I N S T U I
c
C P P P I I C P O R E P R E S S U R E I N P S I F O R C OM P R E S S I ON D A T A .
c
C P P P E I I C P O R E P R E S S U R E I N P S I F O R E X PA N S l GN- R E B O U N C O A T A e
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
P P R I I
P O R E P R E S S UR E R E A D I NG F O R C O • P R E S S I ON D A T A .
P P R E I I P O R E P R E S S UR E R E A D I N G F O R E X P A N S I O N - R E 8 0 U � D D A T A .
P P T I I P O R E P R E S S U R E I N T S F F O R C OM P RE S S I O N D A T A .
P P T E I I
P P Z
P O R E P R E S S U R E I N T S F F O R E X P A N S I O N- R E B O U N D D A T A .
P O R E P R E S S UR E R E A D I NG T A K E N A F T E R B A C K P R E S S U R E A P P L I C A T I ON A � D
B E F C R E L O A D I �G O F S P E C I M E N .
P RE C O N
P R E C O N S O L I D A T I ON P R E S S U R E .
P RE M I N
M I N I MU M P O S S I B L E P R E OC O N SO L I D A T I ON S T RE S S D E T E R M I N E D B Y E X T E N D I NG
T H E L A B O R A T O R Y V I RG I N S LO P E U N T I L I T I � T E R S EC T S E I T H E R T H E I N I T I A L
T H E I N I T I A L VO I D R A T I O O R Z E R O S T R A I N L I N E CR L I N E A R
R E P R E S E N T A T I ON O F R E C O � PR � S S I Q � C L� V E ( L I � E F ) .
R A O I I C A L C U L A T E D R A D I U S OP C UR V A T U R E .
R A O M I N
M I N I �U � P A D I � S O F C U R V A T UR E .
R A D M X
A B S C I S S A A T P O I N T O F T � E M I N I M U M R A D I U S O F C U R V A T U R E l l . E . , P O I N T
E-12
6 5 0 0
6 S 1 0
6 5 2 0
6 5 1 0
6 5 4 0
6 5 5 0
6 5 60
6 5 7 D
6 5 8 0
6 5 9 0
6 6 0 D
6 6 1 0
6 6 2 0
6 6 3 0
6 6 4 0
6 6 5 0
6 6 6 0
6 6 7 0
6 6 8 0
6 6 9 0
6 7 D D
6 7 1 0
6 7 2 0
6 7 3 0
6 74 0
6 7 'i 0
6 7 6 0
6 7 7 D
6 7 8 0
6 7 9 D
6 8 0 0
6 B 1 D
6 8 2 0
6 8 3 D
6 8 4 0
6 8 5 0
6 8 6 0
6 8 7 0
6 8 8 D
6 8 9 0
6 9 0 0
6 9 1 0
6 92 0
6 9 1 0
6 94 0
6 9 5 0
6 9 6 0
6 9 7 0
6 9 8 0
6 9 9 0
7 0 DO
7 0 1 0
7 0 2 0
7 0 3 0
7 D 4 0
7 0 5 0
7 0 6 0
7 0 7 0
7 0 8 0
7 0 9 0
c
c
c
c
c
c
c
c
OF M A X I MU M C U R V A T U R E I .
R U N T Y P I N T E G E R
S I I
T Y P E O F
C O D E Q :
C O D E 1 : C O D E 2 :
C O N S GL I O AT I ON D A T A :
- S T A N D A R D
- C O � T R O L L E D G R A D I E NT
- C O N T R O L L E D R A T E O F S T R A I �
c
c S C R A T C H A R R A Y F OR S u B R O U T I N E F L SQ F Y ,
c
S A M A 3 c
c I DE N T I F I C A T I O N OF S A � P L E .
c
c
c I N I T I A L H E I G H T OF S A M P L E I N I NC H E S .
c
C S B
c
c
c s c
c
c
c s o
c
c
C S E
c
c
S E E S L O P E S
S E E S L O P EC
S E E S L O P E D
S E E S L O P E E
S E C O N D c
c
c
S T R E S S I N T S F
C O �I SC L I D A T I Oti
AT W H I C H S E C O N D A R Y C OMPK" S S I O N B E G I N S I N C O N T R O L L E D
T E S T D A T A .
c
S E V T I I c
c V E R T I C A L E F F EC T I V E S T R E S S F O R C O� PR E S S I CN D A T A P O I N T S .
c
S EV T E I I c
c V E R T I C A L E F F E C T I V E S TR E S S F O R E X P AN S !ON - R E B CU N O D A T A P O I N T S .
c
C S F
c
c
S E E S L O P E F
C S F A C I N T E G E R
C A R R A Y L OC A T ! G N O F
S F A C = N U M P T C + 2 c
c
S F A C U R I N T E G E R
T H E COM P R E SS I ON D A T A ' S S C A L E F A C T OR S .
c
c
c
A R R A Y LOC A T I O � F O R T H E
I N P L O T T I �G T H E F I T T E D
SC A L E F A C TO R F O R V A R I A B L E S W H I C H A R F U S E D
P O L Y N OM I AL C U R VE S F A C U R = 1 0 1 + 2 . c
c
c
S F A E I N T E G E R
c
c
C S G
c
c
A R R A Y LOC A T I ON FOR
S A F E = N U M P T E + 2
S E E S L O P E G
s e e. s o 1 1
T H E E X P A N S I O N - R E BOUND D A T A ' S S C A L E F AC TO R S .
c
c S C R A TC H A R R A Y U S f O BY S U B�OU T I � E F L SQ F Y .
c
7 1 00 7 l l u 7 1 2 0 7 1 3 0 7 14 0 7 1 5 0 7 1 60 7 1 7 0 7 1 80 7 1 9 0 7 2 00 7 2 1 0 7 2 2 0 7 2 3 0 7 240 7 2 50 7 2 60 7 2 7 0 7 2 8 0 7 2 9 0 7 300 7 3 1 0 7 3 2 0 7 3 3 0 7 340 7 3 '5 0 7360 7 37 0 7 3 � 0 7 3 90 7400 7 4 1 0 7 4 2 0 7 4 3 0 744Q 7 4 5 0 7460 7 4 7 0 7 4 8 0 7490 7 5 00 7 5 1 0 7 5 2 0 7 5 3 0 7 540 7 5 50
7 5 60 7 5 7 0 7 5 ·q 0
7 5 9 0 7 600 7 6 1 0 7 6 2 0 7 6 3 0 7 640 7 6'5 0 7 6 60 7 6 7 0 7 6 8 0 7 6 9 0
E-13
C S I
C I N I T I AL D E G R E E OF S A T U R A T ! O� .
c
C S L O P [! !
C S L C P E O F A N G L E B I S E C T O R L I N E U S E D 9 Y T H E GR A P H I C A L M E T H O D T O
C D E T E R M I N E P O I � T OF � A X I MU � C U R V A T U R E ,
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
S L O P E
S L O P E O F L I N E
C O N S OL I D A T I O N
G O I N G T H R OU G H L A S T T W O P O I N T S OF T H E S T A N D A R D T E S T ' S
C O M P R E S S I ON C UR VE .
S L O P E 1 1 I
F I R S T D E R I V A T I V E O R S L O P E A T G E N E R A T E D A B > C I S S A V A L U E S A L O N G T H E
C O � P R E S S I O N D A T A ' S F I T T E D P OL Y � O • I A L C U R V E .
S L O P E 2 1 I S E C C N D D E R I V A T I V E A T G E N E R A T E D A B S C I SSA V A L U E S
P R E S S I O N D A T A ' S F I T T E D P O L YNOM I A L C U e VE .
S L O P EB
S L O P E O F L I N E S .
S L O P E C
S L O P E O F L I N E C •
S L O P E D
S L O P E O F L I N E D .
S L O P E E
S L O P E O F L I N E E .
S L O P E F
S L O P E O F L I N E F o
S L O P E G
S L O P E O F L I N E G .
A L mJ G T H E COM-
C S L O P E M
C A V E R A G E O F T h O L I NE S , O N E T A N GE N T T O T H E C U R V E AT I T S M A X I MU M
C S L O P E A N D T H E O T� E R GO I NG T H R O U G H T H E S TA N D A R D C OM P R E S S I ON
C C U R V E ' S L A S T T W O D A T A P O I N T S .
c
C S P G
C S P E C I F I C G R A V I TY O F SO L I D S .
c
C S R
c
c
S W E L L R A T I O .
c
c
S T A R E I NT E G E R
c
c
c
c
A R R A Y L OC A T I O N OF T H E S T A R T I N G V A L U E T H A T W I L L B E U S E D I N P L OT T I NG
T H E A B S C I S S A A N D O R D I N A T E P O S I T I ON S OF T H E E X P A N S I O N- R E B OU N D
C U R V E ' S D A T A P O I N T S .
S T A R E = N U � P T E + 1
c
c
S TA R T I NT E G E R
c
c
c
c
E-14
A R R A Y LOC A T I ON OF THE S TA R T I NG V A L U E T H A T W I L L B E U S E D IN P LOT T I NG
T H E A B S C I S S A A N D O R D I N A T E P O S I T I ON S OF T H E C O � P R E S S I O N C U RV E ' S
D A T A P O I N T S .
S T A R T = N U M P T C + 1
7 700
7 1 l 0
7 7 2 0
7 7 3 0
7 74 0
7 7 5 0
7 76 0
7 7 7 D
7 7 8 0
7 79 0
7 8 00
7 8 ! 0
7 8 2 D
7 83 0
7 8 4 0
7 8 5 0
7 860
7 8 7 0
7 8 8 0
7 8 9 0
7 900
7 9 1 D
7 9 2 0
7 93 0
7 94 0
7 95 D
7 96 0
7 97 0
7 9 8 0
7 99 0
8 0 0 D
8 0 1 0
8 0 2 0
8 0 3 0
8 04 0
8 D 5 0
8 D6D
8 D 7 0
8 D B O
8 D 9 D
8 1 0 0
8 l l D
8 1 20
8 1 3 0
8 1 4 0
8 1 5 0
8 1 6 0
8 1 7 D
8 1 8 0
8 1 9 0
8 2 D O
82 1 0
8 2 2 0
8 2 3 0
8 2 4 0
8 2 5 0
8 26 0
8 2 7 0
B 2 8 D
8 2 9 0
C S T A R X I r\T EG E R
C A R R A Y L OC A T I O N O F T H E S T AR T I NG V A L U E T H A T W I L L BE U S E D I N P L OT T I N G
C T H E A B S C I S S A A N D O R D I � A TE P O S I T I ON S CF T H E G E NE R A T E D S E G M E N T S O F
C T H E P O L Y NO � I AL C U R V E .
C S T A R X = l Q l + l
c C S T R I I C V E q T I C A L S T R A I N A R R A Y F O R C O � PR E S S I ON C A T A PO I N T S .
c C S T R E I I
C V E R T I C A L S T R A I N A R R A Y O F T H � E X P A NS I CN- R E H O U N D D A T I P O I �T S .
(
C S T V T I I C TO T A L V E R T I C A L S T R E S S A R R A Y F O R C O M P R E S S I O N C A T A P O I N T S . c C S T V T E I I C T O T A L V E R T I C A L S T R E S S A R R A Y FOR E X P A N S ! C N - R EBOUND D A T A P O I N T S .
c C T l C T I • E A T h H I C h C O� P R E S S ! O� D A T A P O I N T •A S A C Q U I R ED D U R I N G C O N -
e T R C L L E O C C N S C L I O A T ! DN T E S T .
(
C T A N G E N ! I C S T O R A G E L JC A T I O N O F T H E G E N E R AT E D I NC R E • E N T AL O R D I N A T E S U S E D I N C P L O T T I N G T HE L I N E T A N G E N T T O T H � C O M P R e S S I O N C UR V E AT T H E PO I N T
C I X T A N , Y T AN I .
c (
(
(
(
T E l I
T ! �· E A T WH I C r
C O � S O L ! D A T I O�
E X P AN S ! O� - R E B O U N C C A T A P O I N T � A S A C QU I R E D D U R I NG T E S T .
(
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THE VO I D R A T I J A T T H E P R EC ON SO L I D A T ! ON
S C H M E R T • A � N ' S C O N S TRUC T I ON .
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A R R A Y 1 � N H I C rl T H E w E I G H T S 0 � I � C I V I QUA L C A T A
F O R S U E S E QU E� T U S E d Y S U BR Ou T I N E F L SO F Y . I L L
T O H A V E E W U A L W E I GHT S ! I . E . , o l I • 1 . 0 1 .
F I N A L W A T E R C J N T E NT .
I N I T I A L W A T E R C O N T E N T .
P O I N T S A R E P L A C E D
D A T A PO I N T S A R E M A D E
A 3 0 0 B 3 1 0 8 3 2 0 8 3 3 0 8 3 4 0 8 3 5 0 8 3 60 8 3 7 0 8 3 8 0 8 3 9 0 8 4 0 0 8 4 1 0 8 4 2 0 8 4 3 0 8 4 4 0 8 4 5 0 8 4 6 0 8 4 7 0 8 4 R O 8 4 9 0 8 5 00 8 5 1 0 8 5 2 0 8 5 3 0 8 5 4 0 8 5 5 0 8 5 6 0 8 5 7 0 8 5 8 0 8 5 9 0 8 6 0 0 8 6 1 0 8 6 2 0 8 6 3 0 8 64 0 8 6 5 0 8 6 6 0 8 6 7 0 8 6 8 0 8 6 9 0 8 70 0 8 7 ! 0 8 7 2 0 8 7 3 0 8 7 4 0 8 7 5 0
8 7 60 8 77 0 8 7 8 0 8 7 9 0 8 8 0 0 8 8 1 0 8 8 2 0 8 8 3 0 8 8 4 0 8 8 5 0 8 8 6 0 8 8 7 0 8 8 8 0 8 8 9 0
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L D A O R E A D I N G C O R R E S P O N D I NG T C Z � R O A P P L ! F D L O A D .
F I N A L D R Y WE I G � T O < C J � S O L ! J A T I C N S P EC I � E � .
c r � A L W ET W E I G � T O F C O N S OL 1 8 A T I ON S P EC T � E � .
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I N T E R S E C T I ON • ET • E E N T H E G R AP H I C A L L I N E A N D T H E V I R � I N C OM P R E S S I O � L I � E .
C X B
c c
A B S C I S S A T � � C U G H W H I C H T H E L I NE R E P R E S E N T I O N O F V I R G I N C U R V E A I LL
B E C R A W N ( I . E . , L I N t: C I .. c c c c c c c c c c c c
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S A M E A S X B .
x e � x e =::x !=l
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c X R 9 x e ::= =:'9
C X � 1 0 � X 3 ''"'' 1 0
C X B l l = X R ':":' l l
C T H E S E V A R I A B L E S S E T UP P D L YNCM I A L T E R M S F R O M T H E A B SC I S S A V A L U E
C O F A P O I NT 0� R E P R E S E N T A T I V E P O R T I O N O F V I R G I N C O � P R E S S I CN C U R V E .
C T H E S E T E R M S h i L L S E P A I R ED W I TH A P P R C P A I A T E C O E F F I C I E N T S TO
C C O M P U T E A N O R O I NA T I E V A L U E A T A P J I N T Q N T � � R F P R E S E NT A T I VE
C P O R T I O N OF V I R G I � C O � P R E S S I O� C UR VE , c C X S
C A B S C I S S A O F T H E P O I N T O F MA X I MU M C U RV A T U R E . c c c c c c c c
X S 1
X S 2
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E- 16
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X S ''"'' 5 = X S '"'' 6
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C X S l O = X S ''"'' l 0
C X S l l = X S ''"'' l l
C T H E S E V A R I A B L E S S E T UP TH E P O L Y N OM I A L T E P � S F R O M T H E A 9 S C I S S A
C V A L U E O F T H E P O I N T O F � A X I � U � C U R V A T U R E . T H E S E T E R M S W I L L B E
C P A I R E D W I T H T H E A P P R O P R I A T E � O E F F I C I E N T S T O C O � PU T E T H E O R D I N A T E
C O F T H E S E L E C T E D P O I N T O F M A X I MU M C U R V A T U O E ,
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C S A M E A S X S .
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C U R V E A � D I S O E T E R • I N E D gy S U U R CU T I N E G R A R A D .
c
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A B S C I S S A
O R C I NA T E
O F T H E P O I NT O F I N T E R S E C T I O N � E T o E E N L I N E ' D ' A N D T H E
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C X l l { , ) = X ( , ) ::::;: 1 1
C T H E S E V A R I A B L E S S E T U P
C A B S C I S S A E S O T H A T T H E Y
C E F F I C I E N T S .
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C o u • • Y S CR A TC H A R R A Y .
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M AY B E P A I R E D W I TH T H E I R R E S P EC T I V E C O -
O R D I N A T E V A L U E S C F T H E A �G L E B I S E C T O R
G R A R A O .
c
c C R D I N A T E O F T H E P O I N T O F M A X I M U M C U R V A T UR E .
c C Y T A N
C O R D I NA T E O F
C C O M PR E S S I O N
T H E P O I NT O F T A N G E N C Y ON T H E I N I T I A L P O R T I O � OF T H E
C U R V E A N D I S D E T E R M I N E D BY SUB R OU T I N E G R A R A D .
c
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E QU A L S 0 . 42 ':' E O .
Z D E PT H
A P P R O X I MA T E F I E L D D E P T H A T W H I C H S A M P L E W A S R E C O V E R E D .
Z E R O
D I A L R E A D I N G C O R R E S P O N D I NG
R E B O U N D C U R V E . T C F I R S T D A T A P O I NT O N T H E E X P AN S I ON -
* ** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ** * * ** * * * * * * * * * * * * * * * * * * * * * * * * * *
9 5 0 0
9 5 1 0
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9 5 3 0
9 540
q :; 5 o
9 5 6 0
9 57 0
9 5 B O
9 5 9 0
9 6 0 0
9 6 1 0
9 6 2 0
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9 64 0
9 6 50
9 66 0
9 6 7 0
9 6 8 0
9 6 9 0
9 7 0 0
9 7 1 0
9 72 0
9 7 3 0
9 740
9 7 50
9 760
9 7 7 0
9 7 8 0
9 79 0
9 8 0 0
9 8 1 0
9 8 20
9 8 3 0
9 84 0
9 8 5 0
9 8 6 0
9 8 7 0
9 8 8 0
9 8 9 0
9 9 0 0
9 9 1 0
9 9 2 0
9 9 3 D
9 940
9 9 5 0
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9 9 7 0
9 9 8 0
9 99 0
0 0 1 0
0 0 2 0
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0 04 0
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E-1 7
c c
c
C O M � O N / B L O K I / P l 3 0 3 l o E I 30 3 1 , P E i l 0 3 l o EE i l 0 3 l , C C i l 0 3 l
D O U B L E P R E C I S I O N C C
C O M � O � / B L O K 2 / C E P T A o S L O P E B , C E P T B , S L O P c C , C E P T C o S L O P E D , C E P T D ,
l S L D P E E , C E P T E , S L O P E F , C E P T F , S L O P E G , C E P T G , aOUN O l , B O UN O Z , b O U N0 3 , B O U N D 4
2 t B O U N 0 5 , 80 U NC & t NU M P T C , N U � P T E , P I N S T U , X S L P 2 , P C , E C t E O , C C R , CC l t C S 9 C R ,
3 S R o N D E G o i N o ! C U T , I D I A L
C O � M ON / B L O K 3 / P D V E o P R E C ON o P R E � I N , V O ! D C o E C M I N , O C R M I N o C R M I N
C O M � ON / B L O K 4 I T R I 3 0 3 l , T R E I 1 0 3 l , D E F R 1 3 0 3 l , D E F R E 1 1 0 3 l , P P R I 3 0 3 l , 1 P P R E I l 0 3 l , WR D I 3 0 3 l , WR D E I l U 3 I , L , S T V T I 3 0 :i I , 2 S T V l E I l 0 3 l , P P P I 3 0 3 I , P P P E I 1 0 3 I , P P T I 3 0 3 l , PP T E I I 0 3 l ,
3 C S E V T I 3 0 3 l o C S E V T E I 1 0 3 l o O FL I I 3 0 3 l o D F L ! E i l 0 3 l 0 S T R I 3 0 3 l o
4 S T R E i l 0 3 l , H i 3 0 3 l o H E I I J 3 1 o O C F , L C F , P C F
C O Mr O N / E L O K 5 / LOC I 4 l o H CL o S A M o T E S o O PR I 1 1 o D A T 1 3 l o 0 E S I 4 l o BC D I 2 0 l ,
1 K K o R U N T Y P
C O M � O N / B L O K 6 / S P G , � T I W , W T F � , � T F O , O E F I , O E F F 9 B P t D E F Z , W R Z 9 P P Z 9 H S t H i t
l H V , S I , E I , E F , S F t � I , W F t S E C O N O , A R
C O M M O N / B L O K R / � A 0 1 ! 0 3 l o R A D M ! � o R A O M X o ! M ! N 0 ! P R ! N T o J P R I N T 0 K I N O
C O M � ON / B L 0 r( 9 / X l 1 0 3 , 4 l o S L 'J P E 1 1 1 0 3 1 o S L O P E 2 1 10 3 1
C O M I'-'. 0 1\J X U L C 3 t 4 l , X 2 ( 1 0 3 , 4 ) , X _ H l 0 3 , 4 l t X 4 ( 1 J 3 , 4 l t X 5 1 1 0 3 9 4 ) ,
l X 6 ( l 0 3 , 4 ) , X 7 { 1 0 3 t 4 l t X 8 1 1 0 3 , 4 l , X 9 ( 1 0 3 , 4 l , X l 0 1 1 0 3 , 4 l t X l l l l Q 3 , 4
2 )
D O U B L E P R E C I S I ON 1< 1 3 0 3 J 0 C I 1 2 1 0 A L P h A I 3 1 4 l o b E T A I 3 1 4 l o S I 3 1 4 l o
1 SG M S Q I 3 1 4 l o P R I 3 1 4 l o P 0 1 3 1 4 J o B I 3 1 4 1 o Y I 1 0 3 , 4 1
R E A L L C F
I N T E G E R R U N T Y P , T E S , HO L
I N T E G E R S T A R T 0 S F A C
O I � E N S I C N C A T A I 1 0 2 4 l
C A L L P L O T S I C A T A o 4 0 9 6 l
C A L L P L O T ( Q ., Q , - 1 1 .. , - 3 )
C A L L P L O T ( Q ,. -J , l ., 0 , - 3 )
C I N P U T A N D OU T P U T U T I L I T Y O E V I C E C O D E N U M B E R S .
c I N = 5
I O U T = 6
c K K = 1
C N O P R 0 9 - N U M B E R OF P R O B L E M S T O B E A N A L Y Z E D
R E A D I ! N o l O O O l N O P R O S
1 0 0 0 F O R M A T I 2 ! 2 l
D O 4 00 l l = l 9 � 0 P R O cl
C N P L C T S I S E Q U A L T O O N E A L W A Y S F O R T H I S P R O G R A M V E R S I O N .
C ! P R I NT - O U T P U T O P T I O N F O R C A L C U L A T E D R A D I I F R O M S U B A � AR A D .
c
R E A D I ! N o 1 0 0 0 l N P L O T S , ! P R I N T
I F I N P L O T S . t: Q , O I N P L O T S = 1
C R E A D D A T A F O R C O M P R E S S I O N C U R V E S .
C N D E G = P O L Y N O M I A L D E G R E E
C R U N T Y P = T Y P E O F C O N S J L I O A T I O N T E S T D A T A
C Z D E P T H = D E P T H F O R C A L C U L A T I O N O F I N S I T U S T R E S S B A S E D O h S P E C ! • E N
C w E T UN I T W E I G H T .
C ! N S E 0 1 •' C L L O W I � G I N C O L , 3 1 F O R R A D I U S M E T H O D
C G R h F H ! C A L R A D I U S M E T H O � - S E T K R A D = O
C A N A L Y T I C A L R A O I J S M E T H O D - S E T K R A 0 = 2
c
C K I N D - O P T I O N V A R I A B E F O R S P E C I F Y I � G E I T H E R A V C ! O R A T ! C CR C V E R T I C A L S TR A I N A N A L Y S I S . P L A C E I N C O L . 3 3 O h E O F T H E
C F O L L O h ! N G V A L U E S F O R ' K I N D '
E-18
0 l l O
0 1 2 0
0 1 3 0
0 1 4 0
0 1 5 0
0 1 6 0
0 1 7 0
0 1 8 0
0 1 9 0
D 2 DO
0 2 1 D
0 2 2 0
0 2 3 0
0 2 4 0
0 2 5 0
0 2 6 D
0 2 7 0
0 2 8 0
0 2 9 0
0 3 0 0
0 3 1 0
0 3 2 0
0 3 3 0
0 3 4 D
0 3 5 0
0 3 6 0
0 3 7 0
0 3 8 0
0 3 9 0
0 4 0 0
0 4 1 0
D 4 2 0
0 4 3 0
0 44 0
0 4 5 0
0 4 6 0
0 4 7 0
0 4 8 0
0 4 9 0
D 5 0 0
0 5 1 0
0 5 2 0
0 5 3 0
0 5 4 0
0 5 5 0
0 560
D 5 7 0
0 5 p [; 0 ' / 0 6 0 J 0 6 1 0
0 6 2 0
0 6 3 0
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0 6 7 0
O b P ·)
() 6 0 l)
0 7 0 0
c c c c c c c c c c c c
1 0 1 0
c c c c c c c c c c c
c c :;: ;;:
c c
c c c
c c c c c c
1 0 2 0 c c c
c c c c
1 0 3 0 c c c c
K I N Q ; C , O D E S B O T H V O I D P- A T I O AND V E R T I C A L S T R A I N A N A L Y S E S , K ! N O ; J , O � L Y VO I D R A T I O A N AL Y S I S P E R F O R � E D , K J N Q ; 2 , O � L Y V E R T I C A L S T R A I N A N A LY S I S P E R F O R � E O .
S E C O N D - P R E SS U R E A T W H I C H S E C O N D A R Y C O MP R E S S I O N OCCUR S ,
! ! D I AL - O P T I ON V AR I AB L E T O O V E R R I D E P R OG R A M ' S B U I L T- I N V A L U E S F O R ! D I A L . ! ! D I AL M U S T B E M A D E E Q U A L T O E I T H E R ' • 1 ' O R ' - 1 ' T O O V E R R I D E B U I L T - I N V A L U E S O F ! D I A L . S EE D E SC R I PT I O N O F ! D I A L B E L O W .
R EA D I HI . 1 0 1 0 I N O E G , R U N T Y P , Z O E P T H , K R A O , K ! N O , S E C O N D , I 1 0 ! A L F O R M A T I 2 ( ! 3 , 7 X l t F l O .. O , I l , l X , I l , 2 X , F 5 o O t 8 X , I t. ) I F I S E C O N O . L T . 0 . 00 1 1 S E C O N Q ; 3 1 . 2
! D I A L I S U S E D T O M A T C H D I A L G A U G E R E A D I � G � W I T � D E F L EC T I ON . N O T E : I NC R E A S I N G D E F L E C T I O N I S S P EC I • E � S H O R T E N I N G . ! D I A L I S E Q U A L T O + 1 W H E N D I AL R E A D I NG S I N C R E A S E W I TH D E F L E C T I O N . ! D I A L I S E Q U A L T O - 1 W H E N D I AL R E A D I � G S O E C R E A S � W I TH D E F LE C T I O N . I F T H E R E L A T I ON SH I P 8 E T oE E N D I A L R E A D ! � G A N D D E F L E C T I O N I S C H A N G E D F O R A P A R T I CU L A R T E S T T Y P E o T H E T E S T ' S R E S P EC T I V E A RG U M E N T F O R ! D I A L W I L L B E S E T E Q U A L T O T � E V A L U E O • ! ! D I A L .
S T D . D I A L R O G S . I NC R E A S I N � W I T H ! NC � E A S ! �G D E F L EC T I CN I DE F ! -O E F Z I . I F ! R U N TY P . E Q . O I ! D I AL ; + 1
C O N T R O L . G R AD . D I A L R D G S . D E C RE A S I N G �/ ! �C R . D E F L o I O E F Z - D E F I I , I F I RU N TY P . E C . 1 1 ! D I AL ; - 1
C O N T RO L . R A T E C F S TR A I N R D G S . ! NC R . h / ! N C R . O E F L . I D E F ! - DE F Z I . I F ! R U N T Y P . EQ . 2 1 ! D I A L = + 1
C H E C K I N G I F P RO G R A M I S T O O V E RR I D E BU I L T - I N V A L U E O F ! D I A L . I F ! l ! D ! AL . N E . O I I D I AL ; J J O I A L
R E A D I N S E A R C H B O U N D A R I E S F O R S E L E C T I O N O F P O I N T OF M A X I MU M C U R V A T U R E A N D L I N E R E P R E S EN T A T I O N O F V I R G I N C O M P R E S S I O N C U R V E ,
R E A D I I �i , 1 0 2 0 ) B O U N O L , B D U NO Z , BO U N 0 3 , B D U N 04 F O R t<A T I 4 F 1 0 • 0 I
T H E F O L L O W I N G A R G U � E N T S A R E T H E D I A M E T E R A N D A R E A O F T H E S A M P L E B E I N G S P E ! C I F I E D I N I N C H E S A N D I NC H E S S � U A R E O . D ! A = 2 , 5 0 A R = 4 . 9 0 8 7
R E A O P L O T T I T L E
R E A D I I N , 1 0 3 C I BC D F O R. 1� A T ( 2 0 A 4 )
R E A D L O C A T I O � , H DL E o S A M P L E , T E S T , O P E R A T O R , D A T E A N D S A M P L E D E S CR I P T I O N .
0 7 1 0 0 7 20 0 7 3 0 0 74 0 0 7 5 0 0 7 6 0 0 77 0 0 78 0 0 79 0 0 8 0 0 0 8 1 0 0 8 2 0 0 8 3 0 0 84 0 0 8 5 0 0 8 6 0 C 8 7 0 0 8 8 0 0 8 9 0 0 9 00 0 9 1 0 0 9 2 0 0 9 3 0 0 94 0 0 9 5 0 0 9 6 0 0 9 7 0 0 9 8 0 0 9 9 0 1 000 1 0 1 0 1 0 20 1 03 0 1 04 0 1 0 5 0 1 06 0 1 07 0 l OB O
1 09 0 1 1 00 I 1 1 0 1 1 2 0 1 13 0 1 1 4 0 1 1 5 0 1 1 6 0
1 1 7 0 1 1 8 0 1 1 9 0 1 2 00 1 2 1 0 1 22 0 I 2 3 0 1 240 1 2 5 0 1 26 0 1 27 0 1 2 8 0 1 29 0 1 3 00
E-19
c R E A U I I /'J , 1 040 1 LOC , H D L t S M1 t T E S t DP R , D A T , O E S
! C 4 0 F O R M A T 1 4 A 4 t ! 2 t A 3 , I 4 t A4 9 3 A 4 t 4 A4 1 c c C R E A Q S P EC I F I C GRA V I T Y , I N I T I AL � E T h E I G H T , F I N A L W E T W E I G H T , C F I N A L D R Y W E i u � T , I N I T I A L D E F L E C T I O N • A ND F I N A L D E F LE C T I CN .
c
1 0 50 c
C E A D I I N , L 05 C J S P G , wT I W , W T F rl t W T FO , O E F l t D E F F F O R � A T ( F 5 . 2 o 3 F 7 . 2 o 2 F 5 . 2 1
c c c c c c c c
c
c c
D E F L . C A L . F A C T O R - D C F I I N C H / C J V I L O A D C A L . F A C T O R - L C F I L o S / D I V I P R E S S U R E C A L . F A C T O R - P C F I P S I / D I V I O i l - D I AM E T E R OF S O I L S A � P L E I I NC H E S I R E A D I N C A L I BR A T I ON F A C T C R S F O R D E F L E C T I O � , L O A D o P R E S S UR E o A N D D I AM E T E R O F S O I L S P E C I � E N I F I T I S N O T E Q U A L T O 2 . 5 • .
R E A D t i N , l 06 C I DC F , LC F , PC F , O I A 1 06 0 F O P � A T 1 4 F 1 0 . 2 1
I F ! D I A . L T . 0 . 0 0 1 I D I A = 2 . • 5 A R= I 3 5 5 . / 1 1 3 . 1 0 ( D I A / 2 . 0 I 00 2
C R E A D B A C K P R E S S U R E , Z ER O D E F L E C T I ON , Z E RO L C A D o Z ER C P O R E o A N D C I N I T I A L H E I Gh T O F S A M P L E I F NOT E Q U A L T C O N E I N C H .
c
c
c
R E A D l i N t l 0 7 C J 2P , O E F Z , kR Z t P P Z 9 S A M P H I 1 0 7 0 F O R M A T I F5 . 1 o f 5 , 2 , 2 F 4 . 0 , 2X o F 1 0 . 0 I
I F ! S A M PH I . L T . D . 00 1 1 S A M P H I = 1 . 00 0
C C O � P U T E I N I T I A L A N D F I N A L S O I L PRO P E R T I E S
c
c c c c
c c
c c c
E-20
H S = � T F O/ I S P G O A R 0 1 6 . 3 8 7 1 1 H I = S A M PH I - I D I A L''' i I D E F I - D E F Z I ''' 0 C F I H V = H I - H S S I = I WT I �- � T F C I * ! OO . / I H V * AR 0 1 6 . 3 8 7 l l E l = H V / H S E D = E I E F = I H V - ! 0 I A L '' I O E F F - O E F I I ''' D C F I / H S S F = I W T F � - W T F C I O J OO . / I I H V - l D I AL O ( D E F F - D E F I I O OC F I O A R 0 1 6 . 3 87 l l W l = I W T I � - � T F C I / WT F 0 0 1 0 0 W F = C W T F w- W T F C I / W T F OO ! O O P I N S T U = I W T I W0 1 7 2 8 0 Z O E P T H I / I A R * H I 0 45 3 o 6 0 2 0 0 0 . 0 I
C O N T R O L L E D T E S T D A T A I N P UT A N D R E D U C T I O N .
* * ** * * * * * * ** * * * * * * * * * I F 1 P. U N T Y P . E Q . 1 1 C A L L C CNG R A I F C R U N T Y P . E C . Z I C A L L C O NG R A * * * * * * * * * * * * * * * * * * * * *
I F I R U N T Y P . EC . l I GO T CJ 5 0 I F ( RU N T Y P ., E Q . Z l GC r J 5 0
S T A N D A R D T E S T D A T A I N P U T
1 3 1 0 1 3 2 0 1 33 0 1 340 1 3 5 0 1 36 0 1 37 0 1 3 8 0 1 39 0 1 40 0 1 4 1 0 1 4 2 0 1 4 3 0 1 440 1 45 0 1 4 6 0 1 4 7 0 1 4B O 1 4 9 0 ! 5 0 0 1 5 1 0 1 5 2 0 1 5 3 0 1 54 0 1 5 5 0 ! 56 0 1 57 0 1 5 8 0 1 59 0 1 60 0 1 6 1 0 1 62 0 1 63 0 1 64 0 1 6 5 0 1 6 60 1 6 70 1 68 0 1 6 9 0 1 70 0 1 7 1 0 1 7 2 0 1 7 3 0 l 7 4 0 1 7 5 0 1 7 6 0 1 77 0 1 7 8 0 1 79 0 1 8 0 0 1 8 1 0 1 6 2 0 1 8 3 0 1 84 0 1 8 5 0 1 <l 6 0 1 8 7 0 1 8 8 0 1 8 9 0 1 9 0 0
c 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
C S T A ND A R D T E S T D I A L K E A D ! N G S A R E B E I NG P L A C E D I N P R O P E R A R R A Y
C L O C A T I O N S .
D O ! 0 I = ! , 2 0
c
C C O M P R E S S I ON C UR V E D I AL R E A D I NG S .
c
K E A O I I N , t 02 C J P I I J , E I I I
S T R I I J = C I I I
!-! { I I = E: { I J I F ( I . f (.;· . L J CJ TC 1 0
C H A S E F F E C T I V E S T R E S S D E CR E A S E D B E T . E E N C O � S EC U T I V E D A T A P O I � T S ?
C I F S C , C ON S I D E R A L L S U B S E Q U E NT D A T A AS E X P A N S I O N - R E BOUND D A T A .
c
c
I F I P I I J . L T , P I I - 1 1 1 G O T O 2 0
1 0 C O N T I N U E
2 0 C O N T I N U E
N U � P T C = I - l
D O 3 0 I = 3 r 2 0
C R E A D I N R E BOLN C - E X P A N S I ON D A T A
C D I A L R E A D I N G S A R E B E I N G P L A C E D I N P R O P E R A R R A Y LOC A T I ON S .
c
c
c
R E A D I I N d 0 2 C J P E I I J , E E I I I
S T R E I I I = E E I I I
H E I I I = E E I ! I
P E I I J = P I N U � PT C I
E E i l i = E I N U � P T C I
S T R E I ! I = E I NU � P T C I
H E i l i = E I N U M P T C J
Z ER C = E E I l l
P E 1 2 1 = P I NU M P T C + l J
E E 1 2 J = E I NU M P T C + l l
S T R E 1 2 l = E I NU M P T C + l l
H E 1 2 1 = E I N U M P TC + ! J
I F I P E I ] J , L J, Q , OO ! I G \J T O 4 0
3 0 C O N T I N U E
4 0 C O N T I NU E
N U r-' P T E = I - 1
5 0 C O N T I N U E
I F I R U N T Y P . E C , O I W R I T E I I O U T o l 0 8 0 1
I F I R U N T Y P . E G . l I I> R I T E I I D U T , ! 0 9 C J
I F i R U N T Y P . c Q , Z J IJR ! T E I I O U T o l l OO I
W R I T E ! I OU T . I 2 1 0 1 B C D
� R I T E ( l OU T t l l l O l T E S t HO l t L OC , S A � t D A T , O P R
>!R I T E I I OU T o l l 2 0 1 O E S , B P
W R I T E C I O U T , l l 3 0 ) W I 9 W F 9 E l 9 E F , S I 9 S F
I F I BO U NO l . E W . D . O I B O U N D l =O . l
J F I B O U N O Z . E J , Q , O J B O U N C 2 =0 o l
I F I B C U N 0 3 . E J . O , O i B O U N 0 3 = 0 o l
I F I 8C UND4 . E Q . O . O I B O U � D 4 = 0 . l
I F I P I N S TU . EJ , O . O i P I N S T U = O . l
B O U N D l = A L Q G ! O I 5 0 U N D l l
B O U � 02 = AL O G ! C I P O U N 0 2 1
B O U ND 3 = A L O G ! O I BO U N D 3 1
B O U , D 4 = A L O G ! O I B O U N D 4 l
P I N S T U= AL Q G l O C P I N S T U l
I F C R UN T Y P . E .: .. O l S E C Q,"..JD 9 9 9 9 9
1 9 1 0
1 92 0
1 93 0
1 940
1 9 50
1 96 0
1 97 0
1 98 0
1 99 0
2 000
2 0 1 0
2 0 2 0
2 0 3 0
2 040
2 050
2 06 0
2 0 7 0
? O P O
2 090
Z ! Oll
2 ! 1 0
2 1 20
2 ! 3 0
2 1 40
2 1 5 0
2 1 60
2 ! 7 0
2 ! 8 0
2 !9 0
2 2 0 0
2 2 1 0
2 2 20
2 2 3 0
2 24 0
2 2 5 0
2 2 6 0
2 2 7 0
2 2 8 0
2 29 0 z 1no 2 3 1 0
2 3 2 0
2 3 3 0
2 34 0
2 3 5 0
2 3 60
2 370
2 3 8 0
2 3 9 0
2 4 00
2 4 1 0
2 4 2 0
2 4 3 0
2 4 40
2 4 5 0
2 4 60
2 4 7 0
2 4 P U
2 4 90
2 5 00
E-21
c
c
c c c c
c c
c c c
c
c
B l = t o . ::":' eou� c t
8 2 = 1 0 . ''"'' 8 U U N C 2
R 3 = 1 0 , ''"'' 80 U � C 3
R 4 = 1 0 . ''"'' B0U,jC4
I F t K K A C . E Q ., 2 l f.JR I T E ( T OU T , 1 1 40 1 � D E G , B l , p, z , B 3 , 8 4 . Z D E P ,T H , S E C ONU
I F 1 K i< A O . N f' , 2 1 •R I T E ! I O U T , l l 5 0 1 N O E G , B l , B Z , B 3 , P 4 o l D E P T H , S E C O N D
DO 6 0 I = l , N U ,V, p T C
W I l l = l . O
6 0 C O N T I NU E
* * * * * * * * * * * * * * * * * * * ** * * * * * * * * * * * * ** * * * * *�'* * * * * * * * *
S F M I - L O G A R ! T H Y I C S T R E S S D E F O R M A T I ON A NA L Y S I S •
* * * * * * * * * * * * * * ** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
V J I O RA T I O A � O S T R A I N A N A L Y S I S CF C O � S O L I O A T I U� � A T A T O E E
P E R F O R M E D I F S P EC I F I E D P � E V I CU S L Y B Y US E R ,
I V C I D = l
I S T K = 2
I F I K ! N C . E Q . ! J ! VO I D = ! I F I K I N D . E Q . l l ! S TR = l
I F t K I N O . E Q . 2 l I V O I D = 2
I F I K I N O . EQ , 2 1 ! ST R = 2
DO 3 9 0 K K = I V C I D . I S T R
C R E D U C E D E F O R M A T I ON D A T A ,
c C C O M P R E S S I O N C A T A P O I N T S .
DO 1 00 ! = l , NU ,� P TC
I F I RU N TY P . E C . ! I GO T U 8 0
I F I R UN TY P . E C . 2 1 G O T J 8 0
I F t KK .. E O . Z l G O T � 7 0
E i I I = E O - ! O I A L ''' i E I I 1 - C E F ! I / H S
7 0 C ON T I N U E
I F I KK . E O . l l G O T O 3 0
C C O N V E N T I ON A L O E F L E C T I J N R E A D I N G S A � E ! N C � E A S ! N G .
E I I I = I 0 I A L ,,, I o T R I I 1 - D E F I I ''' DC F I H I
c
C P U R P O S E S . C V A L U E S C F V E RT I C A L S T R A I � A � E � A D E N E G A T I V E FOR C UR V E F I T T I N G
E I I J = - E i l l
GJ TC 9 0
8 0 ( Q j\i l i � U E I F t KK . t: IJ o l ) ;:; c T O '1 0
C V A L U E S C F V E R T l C A L S T R A I N A R E � A D E N EG � T I V E FOR C U � V E F I T T I �G
C P U R P C S F S ..
c c
E l l l � - S T � I I J
90 C O N T I � U C
I F I KK . EQ . l l C S E V T I I I = E I I J
I F I P I I J . L E , C , l l P I I I = O . l
P l l i " A L OC ! O I F I I I I
C NOW C A L L I N G F L S J F Y F O R N U M E R I C A L
C A N A L Y S I S b Y L E A S T S Q U A R E S C U R V E
E-22
2 5 1 0
z 5 2 0
2 5 3 0
2 540
2 5 5 0
2 5 6 0
2 5 7 0
2 5 8 0
2 5 9 0
2 6 00
2 6 1 0
2 6 2 0
2 6 3 0
2 64()
2 6 5 0
2 660
2 6 7 0
2 6 8 0
2 b 9 0
2 7 0 0
2 7 1 0
2 7 2 0
2 7 3 0
2 740
2 7 5 0
2 760
2 77 0
2 78 0
2 79 0
2 8 00
2 8 1 0
2 8 2 0
2 8 3 0
2 840
2 8 '50
2 8 60
2 87 0
2 88 0
2 8 9 0
2 900
2 9 1 0
2 92 0
2 9) 0
2 94 0
2 9 5 0
2 960
2 97 0
2 9 8 0
2 9Q O
3 000
3 0 1 0
3 02 0
3 0 3 0
3 0 4 0
3 0 5 0
3 060
3 07 0
3 0 8 0
3 0 9 0
3 1 00
c c c c c c
F I T T I NG TU O E T A I N P O L Y N O M I A L C G f FF I C I E'l T S .
� U S T I � I T I A L I Z E V A LJ E � F OR C O EF F I C E l � T S T O A VO I D U N J E F I N E D V A R I A L & E E R R O R U V - J U P O N R E T U R N F O R M S U 8 R U U � T I N E F L SOF Y .
3 1 I O 3 1 2 0 3 ! 3 0
3 1 4 0
3 1 50
3 1 6 0
D O 1 1 0 I o 1 , 1 2 3 1 7 0 C I I I o Q , Q 3 1 • 0
1 1 0 C ON T I N U E 3 1 90
c 3 2 0 0
N D C o N D F G + 1 3 2 1 0
M D C o N D E G + N UM P T C + 1 3 2 2 0 c 3 2 3 0
c 3 2 4 0
C F I T S P E C I F I E D L E A S T S Q U A R E S P O L Y N O M I A L TO S E M I - L OG R E P R E S E N T A T I ON 3 2 5 0
C O F C O M P R E S S I GN D A T A . 3 260
c 3 2 7 0 C A L L F L S QF Y t �O E G , N U M P T C , P , E , W , C , A L PH A t 2 E T A , S t S G M S Q , p� , P C , N D C , MD C I 3 2 A O
c 3 2 9 0
c 3 300
DO 1 20 J o 1 , 1 2 3 3 1 0
C C I I I o C I I I 3 3 2 0 1 20 C O N T I NU E 3 3 3 0
c 3 340
c 3 3 5 0
C R E B O U N D- E X P A N S I ON D A T A PO I N T S . 3 3 6 0
c 3 3 7 0
C F I N D T H E S LO P E OF T H E S .E L L- R E C OM P R E S S I CN C U R V E 3 3 8 0
C A N D C A L L I T S L O P E E . 3 3 9 0
c 3 4 0 0
D O 1 30 I o 1 , N U M P T E 3 4 1 0
W l l l 0 1 o 0 3 4 2 0
1 3 0 C O N T I NU E 3 4 3 0
c 3440
c 3 4 5 0
c c
D O 1 7 0 I o 1 , NU M P T E 3 4 6 0 I F I RU N T Y P . E Q . l l GO T O 1 50 3 4 7 0
I F I RU N T Y P . E Q . 2 1 GO T O 1 50 3 4 8 0
I F I KK . E Q . 2 1 G O T O 1 4 0 3 49 0
E E O o E I N U M P T C I 3 5 00
E E I I I o E EO - I D I A L* I E E I I I - Z E R O 1 /H S 3 5 1 0 C S E V T E I I I o E E I I I 3 5 2 0
G O T G 1 6 0 3 5 3 0
1 4 0 C ON T I N U E 3 54 0
E E I I I = I 0 I A L ''' i S T R E I I 1 -0 E F I I ''' J C F I H I 3 5 50
E E I I I o - E E I I I 3 5 6 0 G J TO 1 60 3 5 7 0
1 5C C O� T I � U i' I F I KK . E Q . l l C S EV T E I I I o E E I I I I F I KK . EG . 2 1 E E I I I = - S T R E I I I
1 bC C J N T I � � E I F t P E t i J .. L t: . O .. l ) P E t i i = O . l P E I I I o A L Q G 1 0 1 P E I I I I
1 7 0 C O �: T I N U E
C C A L L I NG F L S � F Y T O O BT . I N L I NE AR C O E F F ! C E ! � T S .
3 5 80
3 590
3600
3 6 1 0
3 6 20
3 6 3 0
3 6 4 0
3 6 5 0
3 6 60
3 6 7 0
3 6 8 0
3 6 9 0
3 7 0 0
c N D F G E o 1 N D t o 2
E-23
c c c
c c c
c c c c c c c c c
c
c c c
c
c
c
f'-� O E :;:; /\JUM P T E + Z
F I T L E A S T S J U AR E S S T R A I GHT L I N E T O E X P A N S I O N R E BOUN D D A T A .
C A L L � L SQ F Y I � D E G E , N U � P T E , P E , E E , w , C , A L P H A , cl f T A , S , SG M S Q , P R , PO , N O E , M D l E I
L I N E E :;:; ( ( l l + C ! 2 J * X P
S L O P E E = C I Z I
C E P T E = C I 1 1
F I N D S L O P E O F V I R G I N C OM P R E S S I O N C U RV E .
* * * * * * * * * ** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
O S E L E C T S TR A I GHT L I N E R E P R E S E N T A T I O N O F V I R G I N C O M P R E S S I O� C U R V E O
* ** * * * * * * * * * * * * ** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
C H E C K = O . O
X B ! G = O . O
B I G = O . O
D E L T A = I B O U N D 4 - B O U N D 3 1 / l OO .
B i l i = B O U N D 3
DO Z O O J = 1 . t 0 1
B 1 = 8 1 J I
B Z = B I J I '''5 1 J I
B 3 = B I J I O B I J I OB I J I
B4= B I J I * B I J I O B I J I O B I J I
B 5 = B I J I O B I J I O B I J I OB I J I O B I J I
8 6 = E I J I * B I J I O B I J I OB I J I O B I J I O B I J I
B 7 = 2 1 J J O B I J I * B I J I O B I J I O B I J I OB I J I * B I J I
B B = B I J I * B I J I O B I J I * B I J I OB I J I O B I J I O B I J I O S I J I
B 9 = B I J I * P I J I O B i J I O B I J I 08 1 J I 08 1 J I O B I J I O B I J I O B I J I
B 1 D = B I J I O B I J I OB I J I O B I J I O B I J I O B I J I OB I J I O B I J I O B I J I O S I J I
S LC P E ! I J I = C C I Z I • Z O C I 3 1 * B l
! 50 C I 6 1 *B4 • 6* C I 7 I 0 8 5
2 9 '''( 1 1 0 1 "' 8 8 + l 0 ''' C I 1 l 1 '' 5 9
I F I J . E Q . l l GO TO 1 9 0
+ 3 * C I 4 l * B 2 + 4 * C 1 5 l * B 3 +
+ 7 *C I 8 l *B6 + d *C I 9 l *B 7
+ ! PC 1 1 2 1 '''8 1 0
O I F F = A B S I I S L G P !:: l l J I - S L O PE 1 1 J - l l 1 /S L O P E I I J I I
I F I O I F F . L E . 0 . 0 0 0 1 9 1 C H E C K = 1 . 0
I F I D I F F . L E . C . 0 00 1 9 1 GO T G 1 8 0
I F I I R U N T Y P . E Q . 2 1 . A N D o i O I F F . L E . O . O C 2 5 1 1 C h E C K = l
I F I I R U NT Y P . E Q . Z I . A N O . I D I F F . L E . O . OO Z 5 1 1 GO TO ! 90
G O TO 1 9 0
1 8 0 I F I A P S I S L O P E I I J I I . G T . AP S I S I G I I X 8 I G = 8 1 J I
I F I A B S I SL O P E 1 1 J I I . G T . A B S I B I G I I B I G = S L O P E 1 1 J I
1 9 0 C O N T I N U E
3 { J + l J :;:; E ( J ) + :; E L T .A
Z O O Cll�. T I N U E
I F I CH E C K . G T . G . 5 0 1 G O T O 2 3 0
D O 2 2 0 ! = I d O l
•
E-24
3 7 1 0
3 7 20
3 73 0
3 740
3 7 5 0
3 760
3 77 0
3 780
3 7 9 0
3 o Oo
3 ti l 0
3 8 2 0
3 8 3 0
3 840
3 8 5 0
3 86 0
3 8 7 0
3 8 8 0
3 8 9 0
3 9 00
3 91 u 3 9 2 0
3 9 3 0
3 9 4 0
3 9 5 0·
3 960
3 9 7 0
3 98 0
3 99 0
4 0 0 0
4 0 1 0
4 0 2 0
4 0 3 0
4 0 4 0
4 0 5 0
4 0 6 0
4 0 7 0
4 0 A O
4 0 9 0
4 1 00
4 1 1 0
4 1 20
4 ! 3 0
4 1 4 0
4 1 50
4 1 6 0
4 1 7 0
4 1 8 0
4 1 9 0
4 2 00
4 2 1 0
4 2 2 0
4 2 3 0
4 240
4 2 5 0
4 2 6 0
4 2 7 0
4 2 8 0
4 2 9 0
4 3 0 0
c
c c c c c c c
c c c c c c c c
( c c c c c c c c
I F I A B S ! S L O P f l ! I I I o G E . A 6 S I B ! G I I G O TO 2 1 0
G O T C 2 2 0
2 1 0 <' I G = - A � S I S LO P E ! I I I I
X S I G = B i l l
2 2 0 C O N T I " U E
G O T O 2 4 0
2 3 0 C O '! T I N U E
2 4 0 C O ' H I N U E X B = X B I G
X B l :;;; X B
X 8 2 � X t P:' X B
X B 3 = X !l ''' X P ''' X B
X 6 4 = X cF X E ''' X B ''' X B
X B S = X S * X P* X B * X B * X B
X B 6 = X B O X B O X B O X R O X 5 0 X B
X B 7 = X B * X B * X B * X R * X 3 * X B * X B
X 5 8 = X � * X9 * X B* X B * X B * X B * X B * X B
X B 9 = X b * X B* X B * X P* X B * X B * X B* X B* X a
X 8 1 C = X B * X B* X E * X B* X R * X B * X B * X B * X B * X B
X 0 1 1 = X P O X B O X E O X B* X B O X 5 0 X BO X BO X B O X B O X B
C A L C U L A T E A L I N E ' 0 ' R E P R E S E NT I NG T H E
S T � A I G H T P O R T I O N O F V I R G I N C C M P R E S S I GN C U R V E .
Y B I G = C C I 1 1 + C C I Z I O X B 1 + C ! 3 I O X B2 + C I 4 1 0 X b 3 +C ! 5 I OX B4 + 1 C l 6 l * X B 5 + C l 7 l * X B 6 + C ( A l * X B 7 + C l 9 l * X 8 8 +
2 C I 1 0 I O X B 9 + C I 1 1 I O X B 1 0 + C I 1 2 1 * X B 1 l
F O R S T A N D A R D T E S T D A T A Ui\: L Y ! ! ! ! !
I F • A X I M U M S L O P E T A NG E � T I S B E T w E EN L A S T T W C C O M P RE S S I O N C U R V E
P O I NT S A N D H A S A G R E A T E R S L O P E T H AN A L I N E G O I N G T H R O U G H LA S T T W O
C O � P R E S S I O N C UR V E P O I N T S , T A K E T H E A V � R A G E S L O P E O F T H E T W O
A N D D R A W T H E L I N E T H R O U G H T H E L A S T C C MP R E S S I C N C U R V E P O I N T .
K S L G P E " O
I F I R U N T Y P . N E . O I G O T O 2 5 J
I F I Y G I G . G T . E I N U M P T C - 1 I I G O T O 2 5 0
S L O P E = I E I N U M P T C I - E ! � U M P TC - 1 1 1 / I P I NU M P T C I - P I N U M P T C - 1 1 1
I F I A B S I S L O P E I . LT . A B S I B I G I I S L O P E M= S L O P E- A B S I S L C P E- B I G I / 2
I F t A e. S ( SL O P E I .. L T . A B S l B I G i l K S L C P E = 9 9 9
2 5 0 CJN T I N U E
S L O P E D= B I G
I F I K S L C P E . E Q . 9 9 9 1 S L O P E D= S LO P E M
I F I K S L O P E . E Q . 9 9 9 1 Y B I G = E ! NIJ M P T C I I F I K S LO P E . E C . 9 9 9 1 X B I G = P I N U ii P T C J
C E P TO = Y B I G- S L O P E O O I X B I G I
L I N E O = S L O P E O O X + C E P T D
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
o C A L L U S ER S P E C I F I E D M E T H O D T G S E L E C T P O I N T O F M A X I MU M C UR V A T U R E *
* * ** * * * * * * ** * * ** * * ** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
T E S T I N G N O W F O R P O I N T O F M A X I M U M
4 3 1 0
4 3 2 0
4 3 3 0
4 3 4 0
4 3 5 0
4 3 6 0
4 3 7 0
4 3 9 0
4 3 9 0
4 4 00
4 4 1 0
4 4 2 0
4 4 3 0
4440
4 4 5 0
4 4 6 0
4470
448 0
4 4 9 0
4 5 0 0
4 5 1 0
4 5 2 0
4 5 3 0
4 5 4 0
4 5 5 0
4 56 0
4 5 7 0
4 5 8 0
4 5 9 0
4 6 0 0
4 6 1 0
4 6 2 0
4 6 3 0
4 6 4 0
4 6 5 0
4 6 6 0
4 6 7 0
4 6 8 0
4 6 9 0
4 7 0 0
4 7 1 0
4 7 2 0
4 7 3 0
4 74 0
4 7 5 0
4 7 6 0
4 7 7 0
4 7 8 0
4 7 9 0
4 S O O
4 8 1 0
4 8 2 0
4 8 3 0
4 8 4 0
4 8 5 0
4 8 6 0
4 8 7 0
4 8 8 0
4 8 9 0
4 90 0
E-25
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
C UR V A T UR E B E T � E E N X V A L U E S O F B OU N D ! A N D B O U N DZ .
* ** * * * * * * * * * * * * * * * * * *
I F I KR A D . E Q . Z I C A L L A N A R A D
I F I KR A D . N E . Z I C A L L G R A R A D
* * * * * * * * * ** * * * * * * * * * *
X S = R A D M X
X S L P Z = R A C M X
X Z Z = R A DM X
D E T E R M I N E ORD I N AT E V A L U E A T P O I N T O F MA X I MU M C U RV A T U R E .
X S l • X S
X S Z = X S '''XS
X S 3 = X 5 ''' X 5 ''' X S
X 5 4 = X S ''' X 5 ''' X 5''' X S
X S 5 = x s o x so x so x s o x s
X S 6 = x s o x s • x s o x s o x s o x s
X S 7 = x s o x so x so x s o x s o x s o x s
x s s = x s o x s o x s o x s o x s o x so x s o x s
X S 9 = x s o x s o x s o x s o x s o x s o x s o x s o x s
X S I C = x s o x s o x s o x so x s o x s o x s o x s o x s o x s
x s t t = x s o x s o x s o x s o x s o x s o x so x so x s o x s o x s
Y S L P Z = C C i l i + C C I Z I O X S l + C I 3 I O X S 2 + C I 4 J O X S 3 + C I 5 I OX S4
l + C i t i * X S 5 + C I 7 1 0 X S 6 + C 1 8 I O X S 7 + C I 9 I O X S 8
Z + C i l 0 1 ''' X S 9 + C t l l i ''' X S l •J + C i l Z I ''' X S l l
* * * * * * * * * * * * * * * * * * * * * * t,:
C A S A G R A N D E ' S C ON S TRUC T I O N
� * * * * � * * * * * * * * * * * * * * * *
C A L C U L A T E A H O R I Z O N T A L L I N E C A L L E D ' A ' T H R O U G H
I X S L P Z , Y S L P Z i o PO I N T O F M A X C UR V A T U R E .
C E P T A = Y SL P Z
L I N E A = Y S L P Z
C A L C U L A T E A L I N E T A N G E N T T O C U R V E A T
I X S L P Z o Y S L P Z l o P C I N T O F � A X C U R V A T UR E ,
A N D C A L L I T L I N E ' B ' •
S L O P F B = CC I 2 1 + 2 0C i l i O X S 1 + 3 0 C I 4 1 0 X S 2 + 40C I 5 I O X S 3 + 5 0C I 6 1 0 X S4 +
l 60C I 7 I O X S 5 + 7 0 C I B I O X S 6 + 80 C I 9 1 0 X S 7 + 9 0C I I O I O X S 8 +
l l 0 ''' C i l l i ''' X S 9 + l l '''C i l 2 1 '' X 5 1 0
C E P T P= Y S L P 2- S L O Pf B * I X S L P 2 1
4 9 1 0
4 9 2 0
4 9 3 0
4 94 0
4 9 5 0
4 96 0
4 9 7 0
4 9P O
4 9 9 0
5 00 0
5 0 1 0
5 0 2 0
5 03 0
5 04 0
5 05 0
5 06 0
5 01 0
5 0 R O
5 0 9 0
5 1 0 0
<; 1 1 0
5 1 2 0
5 1 3 0
5 1 4 0
5 1 5 0
5 1 6 0
5 1 7 0
5 ! 8 0
5 1 90
5 z oo
5 2 1 0
5 2 2 0
5 2 3 0
5 24 0
5 2 50
5 2 60
5 27 0
5 2 B O
5 2 9 0
5 3 00
5 3 1 0
5 3 2 0
5 3 3 0
5 34 0
5 3 '3 0
5 3 60
5 370
5 3 8 0
5 3 9 0
5 4 0 0
5 4 1 0
5 4 2 0
5 4 3 0
5 44 0
5 4 5 0
5 4 60
5 4 7 0
5 4 8 0
5 4 9 0
5 500
c
c
c
c
c
c
c
c c
c
c
c
c
c
c
c
c
c
c
c
c
L I N E R = 5 L O P E B0 K P + C E P T R
B I S � C T D I F F E R E N C E S I N S L O P E B E T w E E N
L I N E • A ' A N D L I N E ' b ' A N D C AL C U L A T f
L I � E ' C ' T H k C U G H P O I N T O F M A X C UR V A TU R E .
S L Q P E C = S L O P E E / 2
C E P T C = Y S L P 2 - 5 L O P EC O I X S L P 2 1
L I N EC = S LC P E C O X P +C E P TC
F I N D I � T E R S E C T I ON OF L I N E S ' D ' A N D ' C ' T O G E T
T H E V A L U E F O R P R E C O N SO L I D A T ! ON P R E S SU R E ,
P C = I C E P T C - C E P T C I / I S LO P E U - S L OP E C I
* � ¢ � * * * * * * * * * * * * * *
o S C H � E R TM ANN ' S C O N S T R U C T I O N
* * * * * * * * * * * * * * * * * *
C C O M P U T E A L I N E ' f ' T H A T H A S A S L O P E O F
C ' S L C P E E ' A N D G O E S T H R O U G H I N T I A L P R E S S U R E
C A N D I N I T I A L V O I D RA T I O OR Z f R O P E R C E NT S T R A I N .
c
c
I F ( KK .. E Q . 2 ) UO T O 2 60
C E P T F = E O - S L O P E E O I P I N ST U I
GO T C 2 7 0
2 6 0 C E P T F = - S L OP E E O P I N S T U
2 7 0 C O N T I N U E
S L O P E F = S L J P Ec F
C L I N E F = S LO P E E O X P + C E P T F
c
C C OM P U T E P R E C C N S O L I D A T I ON V O I D R A T I O CR P R E C C N S O L I D A T I O N V E R T I C A L
C S T R A I N T O D E F I N E I N S I T U P R E C O N S O L I D A T I O � S T A T E .
c
E C = S L O P E E O P C + C E P T F
c
C NO W C C � P U T E A L I N E ' G ' THA T W I L L R E P R E S EN T
C T R U E V I R G I N C O� PR E S S I O N L I N E .
c
c
c
c
c
c
c
c
c
Y V I R G I = 0 . 42 H O
I F I KK . E Q , 1 1 G O T O 2 8 0
Y V I R G I = - I E O - C . 4 2 0 E O I / 1 1 + EO I
2 8 0 C ON T I N U e
X V I RG I = I Y V I R G I- C E P T O I / S L D P E D
S L O P E G = I Y V I RG I - E C I / I X V I RG I - P C I
C E P T G = E C- S L O P E GO P C
L I N E G = S L O P E G * X P + C E P TG
O U T PU T O V E R C J N S O L I DA T I ON R A T I O A N D P R E C O � S C L I D A T I O N V E R T I C A L
E F F EC T I V E P R E S S U R E W I T H E I T H E R T H E VO I D R A T I O D R V A LU E C F S T R A I N .
5 5 1 0
5 5 2 0
5 5 j Q 5 54 0
5 5 5 0
5 5 60
5 5 7 0
5 5 8 0
5 5 9 0
5 600
5 6 1 0
5 6 2 0
5 6 3 0
5 640
5 6 5 0
5 6 6 0
5 67 0
5 68 0
5 69 0
5 700
5 7 1 0
5 7 2 0
5 73 0
5 740
5 750
5 7 6 0
5 77 0
5 7 8 0
5 7 9 0
< B OO
5 8 1 0
5 8 2 0
5 8 3 0
5 84 0
5 8 5 0
5 8 60
5 8 7 0
5 88 0
5 89 0
5 9 00
5 9 1 0
5 92 0
5 9 3 0
5 94 0
5 9 5 0
5 9 6 0
5 97 0
5 9 8 0
5 99 0
6 00 0
6 0 1 0
6 0 2 0
6 0 "3 0
6 04 0
6 0 5 0
6 060
6 0 7 0
6 0 8 0
6 0 9 0
6 1 00
E-27
c
c
c
POV E � 1 0 • ''"'' P I N S TU
P R E C C N � 1 0 . 0'-"'' P C
C C l � S L O P E G
c s � S L O P E E
V O I O C = E C
CC R � P R E C O N / P C V E
I F I KK . E Q . l l C R = C C I
I F I KK . E Q . l l S R = C S
I F I KK . E O . l l C R M I N = S L O P E D
P C " I N= i C E P T D -C E P T F I / I S L O P E F - S L O P E D I
E C " I N = S LO P E E O P C M I N • C E P T F
I F I KK . EQ . t . A N O . E C " I N . G T . E C I P C M I N= I C E P T D- E C I / 1 - S L O P E O I
I F I KK . E Q . l . A N O . E C M I N . G T . E O I E C M I N= E D
I F I KK . E C . 2 . A N C . E C � I N . G T . O I P C � I N =- C E P T D / S L D P E D
I F I KK ., EQ .. 2 ., Ar-.JO .. E C fJ I N . G T . O l E C � I N= O . O
P R E M I N = l O , oo p c " I N
OC R M I N= P R E " I N / P O V E
I F I KK . EQ . 2 1 C R = C C I
I F I KK . E Q . 2 1 S R = C S
I F I KK , E 0 , 2 1 C R M I N= S L O P E D
C C AL L P L OT T I N G S U B R OU T I NE C A S P L T
c
c 0 00 0 * 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
c
C A L L C A S P L T
c
c 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
c
c
P I N S TU = l QO O P I N S TU
DO 2 9 0 I = l , NU M P T C
P ( I l = l 0 o 0 ''"'' P ( I I
2 9 0 C ON T I N U E
D O 3 0 0 I = 1 , NU M P T E
P E l I 1 � 1 0 o 0 ''"'' P E I I I
3 0 0 C O N T I N U E
1 0 8 0 F O R " A T l ' l ' o / / 1 4 X o " S T A N D A R D C O N S OL I D A T I ON T E S T ' / 2 0 X o
l D U C T I O N ' / / 1
' D A T A R E
1 0 90 F O R M A T l ' l ' , / / 1 4X , ' C O N T R O L L E D G R A D I E N T C O � S CL I DA T I O N T E S T ' / 2 5 X ,
! D A T A R E O U C T J C N ' // 1
1 1 0 0 F O R M A T l ' l ' , / / 1 4 X , ' C O N T R O L L E O R A T E O F S TR A I N C O N SO L I D A T I ON T E S T '
l / 2 8 X , ' D A T A R E DUC T J ON ' // 1
1 1 1 0 F O R M A T 1 1 H 0 , 9 X , ' T E S T � O . ' t l 4 t l 9 X t ' HO L � N O . ' t 1 2 / 1 H0 , 9 X t ' L O C A T I C N 1 l t 4 A 4 t b X t ' S A M P L E N O . ' t A 3 / l �0 , 9 X t ' DA T E ' t 3 A 4 t l 4 X t ' O P E R AT O R ' t A 4 l
1 1 2 0 F O R M A T ( l H O , S X , ' S O I L T Y P E - ' t 4 A 4 / l H0 , 9 X t 1 BA C K P R E S S U R E 1 t F 6 e 2 t l X ,
l ' P S I ' // / t l H0 , 3 4 X t ' I N I T I AL ' , 9 X , ' F I N A L ' I
1 1 3 0 F O R M A T l l H 0 , 9 X , ' WA TE R C O N T E N T • t l 4 X t F4 o l t ' % ' t l O X , F 4 . l t ' % 1 / l H O t 9 X t ' V
l C I D R A T I O ' t l 7 X , F4 , 2 t l l X t F4 . 2 / l H O t 9 X t ' DE G e O F S A TU R A T I ON ' , S X , F S . l t '
2 �· ' t 9 X , F 5 . l t ' % ' )
1 1 40 F O R � A T i l H 0 / / /2 5 X , ' D EGR E E P O L Y N O M I AL = ' o 1 2 / 1 H C , 5 X ,
l ' P T . O F � A X . C UR V A T U R E S E L E C T E D B Y T H E A N AL Y T I C A L M E T HO D ' / l H O ,
2 5 X o ' S E A R C H B G U N D A R I E S F O R P T . O F MA X . C UR V A T U R E : • ,
A 2 X t F 5 . 2 t ' T S F ' , 2 X , F 5 e 2 t ' T S F '
3 / l H O , S X t ' S E A � C H B O U NJ A R I E S F O R V I RG I � C C M P R E S S I CN C U R V E : ' , F 6 e 2 t ' T
4 S F ' , 2X , F 5 . 2 t 1 T S F ' / l h0 , 5 X , ' D E P T H F OR I N S I T U S TR ES S C A L C U L A T I ON : • ,
5 2 X t F 5 . 2 t ' F E E T ' , 4 X , ' S E C O N D A R Y C C � P R E S S I G!I..: A T ' , l X ,
6 F 5 .. 2 , ' T S F ' l
E-28
6 1 1 0 6 1 2 0
6 1 3 0
6 1 4 0
6 1 5 0
6 1 6 0
6 17 0
6 1 9 0
6 1 9 0
6 2 DO
6 2 1 0
6 2 2 0
6 2 3 0
6 24 D
6 2 5 0
6 2 6 0
6 2 7 D
6 2 8 0
6 2 9 0
6 3 0 0
6 3 1 0
6 3 2 0
6 3 3 0
6 34 0
6 3 5 0
6 36 0
6 3 7 0
6 3 B D
6 39 0
6 4 0 0
6 4 1 0
6 4 2 0
6 4 3 0
6 4 4 0
6 4 5 0
6 4 6 0
6 4 7 0
6 4 8 0
6 4 9 0
6 5 0 0
6 5 1 0
6 5 2 0
' 6 5 3 0
6 54 0
6 5 5 0
6 5 60
6 5 7 0
6 5 8 0
6 5 9 D
6 6 0 0
6 6 1 0
6 6 2 0
6 6 3 0
6 64 0
6 6 :: 0
6 6 6 0
6 6 7 0
6 6 8 (J
6 6 9 D
6 7 0 0
l 1 5C F OR � A T ( l fi0 / / / 2 5 X . ' D EG R F E ? OL Y NO M I AL = ' t l 2 / 1 H0 , 5 X ,
l ' P T . O F M A X a C UR V A T U R E S E L F C T E D E Y T H E G R A P H I C A L M E THO D ' / lH Q , 2 5 X , ' S E A R C H � C U N O A R I E S F Q R I N I T I A L T A N G � NT : ' , 2 X t F 5 a 2 t ' T S F • , z X , F 5 e 2 3 1 ' T SF ' / 1 H 0 , 5 X t ' S E A R. C H t3 0 U N J A R I E S F O R V I R G i l� C O M P R E S S I O t\ C U t<. V E : • ,
A Z X , F 5 a 2 t ' T S F ' , z X , F 5 . 2 4 t ' T S F ' / l H O , S X , ' D E P T H F O R I N S I T U S T R E S S C A L C U L A T I ON : • ,
5 2 X t F 5 a 2 , � F E E T ' , 4 X t ' S E COND A R Y C GM P R E S S I ON A T ' , l X t 6 F 5 . 2 t ' T S F ' l
I F I K I N O . N E . 2 . M>O . K K . E 0 , 1 . A ND . K R A O . N E . Z I _, K I T E I I clU T , l l B D I I F ! K I N O a E C a 2 e A ND . K K . E C a 2 a A ND . K R A O . N E . 2 J WR I T E t i OU T t l l B C J I F I KK . EC . l l W R I T E I I O U T , 1 1 9 0 l I F { KK a EC . Z J W R I T E ( I J UT ·tl .Z O O J
I F I KK . E Q . l l � R I T E I I OUT o 1 2 2 0 1 P I N S T U o EO o P R E C CN , P R E M I N o VO I DC o EC M I N o 1 C t R 9 0 C R M I N 9 C R , C R M I N 9 S R
I F I KK . E 0 . 2 1 V C I D C � - V O I D C I F I KK . E0 . 2 l E C M I N � - E C M I N I F I KK . E O . Z l • R I T E I I OU T , 1 2 3 0 1 P I N S T U , !O , P R E C CN o PR E M I N o V C I D C , EC M I N o
l CC R , OC R M I N t CR , C R M I N , S R F I KK . E Q . 2 l \/O I OC �-VO I DC I F I KK . E 0 . 2 l E C M I N � - E C M I N I F I RU N T Y P , i' C , O l GO T O 34Ll
I F I I K K . E Q , 1 l , A ND . I K I N O , c � , O I I GO TO 3 3 0 W R I T E ( 1 00 T , l l 6 0 )
1 1 6 0 F J R � A T ( 1 H l , 2 9 X , ' I N PU T D A T A 1 // 1 H0 , 9 X , ' T I � E ' , 3 X t ' D E F L . R O G . ' - t 9 X , • P .
l P e R C G . 1 , 4 X t ' L 0 A D R OG . ' / l H J CJ 3 1 J I = l , �U M P T C \'R I T E I I O U T , l 1 7 0 1 Ti< l ! l , D E F f< l I l , p pe i i l o i>R D I I l
1 1 7 0 FOR � A T t l ii , g x , F 5 o C t 5 X t F 6 . 2 t lO X , F S . O , l O X . F 5 . 0 J 3 1 C C O� T I N U E
DO 3 2 0 I = l , � L M P T E �; R I T F ( I OU T , l l 7 0 ) T K E t i J , O E FR E t i l t P P R E t i l , W KD E t l l
3 2 0 C D "-n i r� u E
I> R I T E I I O U T , 1 1 8 0 l
1 1 8 0 != O R "'\ A T ( ' l ' l
3 3 0 C O N T I N U E
1 1 90 F O R " A T 1 1 X I I 1 X o
1 0 0 0 0 0 0 0 0 0 0 00 0 0 0
2
� � � � � �* * * ** * * * * * * * * * * ** * * * * * * ** * * * * * * * * **
3 VO I D RA T ! J A � A L Y S I S 4 1 X t '
5 ,,, I I L X ' ' s • • • • • - · · · · · • • • • • • •
1 20 0 F O R M A T ( l X / / l X · I
l :;: :;: .,,., ;;: ::;::;: :,'.: :;: ;' :;: :;: :;: :;: :,': z 3 S T R A P J
4 1 X ' I .,.
5 * ' I l X t '
6 ''"'"'"' . . . ''"'"'' . . .
3 4 0 CJN T I I< U E 1 2 1 0 F O R � A T ( l 6 X , 2 0 A 4 / l
I l
I I l X ' I ,., I I 1 X ' '
' I I
1 2 2 0 F O R M A T ! l H J / l X • ' I N S I T U V E R T I C A L S T R � S S = 1 , F 6 m 3 t 1 T S F ' t 9 X ,
! ' I N I T I A L V O I C R A T I O ! EO J = ' t Fb a 3 / / l H O , l OX t ' R A N G E S O F S T R E S S - ' , Z ' V O I D R A T I O S E T T L E �EN f P A R A M f T E R S ' / l HO , S QX , ' P R D B A B L E ' ,
' I
, I
3 ' M I N I M UM ' / l rl C , ' V E R T I C A L P R E C O N S C L I D A T I O N S T � E S S • • • • • • m a • • a • a • ' t 4 F 8 . 3 , ' T S F - ' , F 8 . 3 9 ' T S F ' / l H O , 3 5H PR EC O N SO L I O A T I CN S T A T E ' S V C I O 5 R A T I O 9 1 6 ( ' a ' l , f 8 ., 3 9 2 X t ' - 1 , F � . 3 / 1 H0 9 ' 0 V 'C R C O I\ S C L I D A T I ClN ' , 6 ' R A T I O f O C R J ' , Z l ( ' ,. ' l , F B a 3 , 2 X , ' - ' , F 8 .. 3 / l H C , ' C C"1 PR E S S I C� ' • 7 ' I N D E X ( CC J ' , 2 8 ( ' . ' ) , � e . 3 , 2 X , ' - ' , F 8 ., 3 / 1HO , ' S W E LL B F. X P A N S I ON I N C E X ! C S J ' • 2 4 ( ' • ' l , F s ,. 3 , 2 X/ / )
6 7 1 0 6 7 2 0
6 73 0
6 74 0
6 7 5 0
6 7 6 0
6 7 7 0
6 7 8 0
6 7 9 0
6 8 0 0
A 8 1 0
6 8 2 0
6 8 3 0
6 84 0
6 8 5 0
6 86 0
6 8 7 0
6 8 8 0
6 89 0
6 9 0 0 6 9 1 0
6 92 0
6 9 3 0
6 9 4 0
6 95 0 6 9 6 0
6 9 7 0 6 9 8 0
6 99 0
7 0 0 0
7 0 1 0 7 02 0
7 03 0
7 04 0 7 05 0
7 0 6 0
7 07 0 7 0 8 0
7 0 9 0
7 1 00 7 1 1 0
7 1 20
7 1 3 0
7 1 4 0
7 1 5 0
7 1 6 0
7 1 7 0
7 1. 8 0
7 19 0 7 2 0 0
7 2 1 0
7 2 2 0
7 2 3 0
7 2 4 0
7 2 5 0
7 2 6 0
7 2 7 0
7 2 8 0
7 2 9U 7 300
E-29
c
1 23 0 FOR M AT ( l H O , J ! X , • I N S I T U V E R T I C A L S TR E S S = ' 0 F 6 . 3 o ' T S F ' 9 9 X 0 ! ' I N I T I A L V D I C R AT I O ! EO ! = ' , F6 . 3 I I 1 HO . I 3X o ' R A N G E S O F S T R E S S- S TR A I N
2 S E T T L E M E N T P A R AM E T E R S ' I 1 H C , 5 0 X o ' PR O B A 8 L E M I N ! MUM ' I l H O ,
3 ' V E R T I C A L P R E C O N S O L I D A T l ON S T R E S S • • • • • • • • • • • • • • ' � F 8 a 3 v ' T S F - ' v 4 F 8 , 3 , ' T S F ' I l H 0 , 4 1 H P R E C O N S O L I DA T I D N S TA T E ' S V E R T I C A L S T R A I N , ! 0 ( '
5 . ' l v F 8 .. 3 t 2 X v ' - ' v F 8 . 3/ l H C t ' 0 V E R C O N S O L I DA T I O N R A T I O ( GC R l 1 9 2 1 ( 1 a 1 1 9 6 F .:3 a 3 t 2 X v ' - ' v F 8 a 3 / l H 0 v ' C OM PR E SS I CN R AT I O ( ( R I 1 ., 7 2 8 1 ' . ' h F 8 .. 3 v 2 X v ' - ' • F 8 . 3 / l H O v ' S w E L L R A T I O ( SR I ' •
8 3 4 1 ' . ' l , F 8 a 3 t 2 X / / / l I F ( ( K I N D . E Q , Q ) , A N D , ( K K , E J o l l l G O T O 3 8 0 I F ( K I N D . E Q , Q , A N D . R U NT Y P . E Q , D , A ND . K R A D , E Q , 2 ) G O T O 3 5 0
I F ! K I N O , E Q , O , A N D , R J NT Y P . E Q , O ) I> R I T E ! ! O UT o l l B O I 3 50 C O N T I N U E
I F ! ! K K . E J , 2 l . AN D . ! R U N T Y P . N E . D l l �IR I T E ( ! U UT o 1 2 5 0 l
I F ( ( K K , E Q . 2 l , A NO , ( R U N T Y P . E Q , Q ) l W R I T E ! I O U T o 1 2 4 0 l
I F ( ( K K , F Q . 1 I , A N D . ( R U N T Y P . N E , 0 l • A N D , ( K I NO . � E , 0 l l wR I T E ( I OUT . t 2 5 D l I F ( ! K K . E Q . l i . A ND . l R U N T Y P . E Q . O l . AN O . ( K I ND . N E . O l l >W I T E ( I a UT . t 2 4 0 l
1 2 4 0 F O R M A T t B X , ' E F F . V E R T . ' t 9 X , ' VO I D R A T IO ' t 9 X , ' VE R T . S T R A I N ' / l l H 0 ' 8 X ' I s T R E s s ' ' 3 4 X ' f ( I N I [ N ) 1 ' l 3 )( ' I 0 I A L R 0 G " ' / 1 11 0 ' 8 X ' ' ( T s F ) t I I I
1 2 5 0 F O R M A T I B X , ' E F F e V E R T . • , 9 X , ' VO I D R A T I O ' t 9 X t ' VE R T . S T R A I N ' /
l l H0 , 8 X , ' S T R E S S ' t 3 4 X t ' I I N/ I N 1 ' , 1 3 X t ' T I ME I � I N l ' / l H 0 , 8 X , ' ( T S F l ' / / 1 DO 3 6 0 I = l o NU M P TC
I F ! NU � P T C , GT . ! D I E ! I I = - E ! I l
I F ! ! K I N O . E Q . 1 l , AN D . ! RU N T Y P . EQ . O l I w R I T E ! I O U T o 1 2 7 D l P ! I l o C S E V T { I ) , H ! I
1 I
I F ( ( K I N 0 . E Q . 1 l , A N D . ( R J N TY P , i< E . 0 l l WR I T E ( I auT , 1 2 7 0 l P ( I l , C S E V T ( I l , T R ( 1 I l
I F ( I K I N D . E Q . 2 l . AN O . I RU N T Y P . E Q , O l I W R I T E ! I aU T , ! 2 8 0 l P ( I l 0 E ( I ) , H ! I l
I F ( ( K I N O . E Q . 2 l , A N D , ( R U N T Y P . N E , 0 l l W R I T E ( ! O U T . 1 2 80 l P ( I l , E ( I l , T R ( I l I F ! K I N D . N E . O ) GO T O 3 6 0
I F ( RU N TY P . EQ , O I W R I T E ! I D U T o 1 2 6 0 1 P U l , C S E VT ! I ) , E ( I l , H ! I l
I F ( RU N T Y P . N E . O l W R I T E ! IO U T o l 2 6 0 1 P ! I l 0 C S E VT ! I I o E I ! l , T R ! I l
1 2 6 0 F O R � A T ( ! H , 5 X , 6 ( F 1 0 . 5 o l 0 X l l 1 2 70 F O R � A T 1 1 H , 5 X , 2 ! F 1 0 . 5 . t 0 X ) , 2 0 X o F 1 0 . 5 1
1 2 8 0 FOR " A T ! l H , 5 X , F 1 0 . 5 , 3 0 X o Z ( F l 0 . 5 o l D X l )
3 6 0 C ON T I NU E D O 3 7 0 I = ! , N U M P T E I F ! NU M P T C . G T . t O I E E l i l = -H ! I l
I F ! ! K I N O . E Q . 1 l . A N Q , ( RU N T Y P . E Q . O l ) WR I T E ! I OU T . t 2 7 0 l P E l i l , C S E V T E ! I ) ,
1 H E ( I l I F ( ( K I N O . E Q , 1 l , A N D . I R U N T Y P . N E , 0 l l W R I T E ( ! O U T , 1 2 7 0 l P E ( I I , C S E V T E ( 1 I ,
! T R E ! I l
I F ( ( K I N O . E Q , 2 I • A N D , I R U N T Y P , E Q , 0 l l W R I T E ( I O U T . 1 2 8 0 l P E I I l , E E ( I l , H E { 1 l
I F I ( K I N 0 . E Q , 2 l • A N D . ( R U N T Y P , N E , 0 l I WR I T E ( I au T , 1 2 8 0 l P E ( I I , E E ( I ) ,
1 T R E I I I
I F ( K ! r, O . N E . C l GO TO 3 7 0
I F ! RU N T Y P . E Q , O I W R I T E ! I O U T o 1 2 6 0 l P E ! I l , C S E V T E ! I l o E E ! I l , HE l i l
I F ( R U N T Y P . I, E . O l >< R I T E I I O U T . t 2 6 D l P E ! I l , C S E V T E ! I l o E E ! I J , TR E I I l
3 7 0 C O N T I N u E
3 8 0 C o N T I NU E
C I F T H E P T , O F • A X . C U R V A T U R E H A S G R E A T E R A B SC I S S A V A L U E T H A N T H E
C P R E C O N S D L ! D A T ! O N S T R E S S AY C A S A G R AN D E ' S C O N S T RUCT I O N , T H E PKDC E D U R
C H A S F A I L E D .
c
I F ! PC . L T . X SL P 2 1 W R I T E ! I O U T , l 2 9 0 1
1 2 90 F O R M A T ( ! X I /I 1 X o ' 0 0 0 0 A T T E N T I ON o o o o A � AL Y T ! C A L P RO C E D U R E � I T H
! C A S A G R A N D E C O N S T R , H A S F A I L E D . C H E C K D A T A A N D A S S U M P TI O N S ! ! ! '"'' A 2 ''"'" I I I I
P I N S T U = A L O G 1 C ! P I N S T O I
E-30
7 3 1 0 7 3 2 0 7 330
7 34 0
7 35 0
7 3 6 0
7 37 0 7 3 B O
7 39 0 7 400 7 4 1 0
7 4 2 0 7 4 3 0 7 4 4 0
7 4 5 0
7 4 6 0 7 4 7 0
7 4 R O 7 4 9 0
7 5 0 0
7 5 1 0 7 5 2 0
7 5 30
7 54 0 7 5 5 0
7 56 0
7 5 7 0 7 5 8 0
7 5 9 0 7 6 0 0
7 6 1 0
7 6 2 0
7 6 3 0 7 64 0 7 6 5 0
7 660
7 o 7 0
7 6 8 0
7 69 0
7 7 0 0 7 7 1 0
7 7 2 0
7 7 3 0
7 740
7 7 5 0
7 760
7 7 7 0
7 7 8 0
7 79 0
7 8 0 0
7 8 1 0
7 8 2 0
7 8 3 0
7 840 7 8 50
7 8 60
7'870
7 8 R J 7 8 9 0
7 9 0 0
3 9 0 C O N T I NU E 7 9 1 0
W i< ! Tf I I OU T . l 3 00 1 OC F , L C F , P C F 7 9 2 0
1 3 0 0 F � R '' A T I I HJ , S X , ' A D D I T I JN A L I N P U T O A T A ' // 6X , ' C A L ! B R A T ! O N F A C T OR S : ' / 7 9 3 0
l 6 X t ' D E F L E C T I C � = ' , F 8 o 5 t 5 X , ' L0AO = • , F � . � 9 5 X , 1 P R E S SU� E = ' , F 8 . 5 l 7 94 0
W R I T f t i O U T , l 3 1 0 l O E F Z , �R Z , ? P l 7 9 5 0
1 3 1 0 F O R 1"1- A T t l H 0 t 5 X t ' E OU I P "'. E N T Z E R O R t: A D I I\JG S : ' /6 X t ' D E F L E C T I O N = • , 7 960
1 F 8 . 3 t 5 X , ' L U A C = 1 , f 8 , 3 , 5 X , ' P O R E P R E S S U R = = 1 t f 8 , 4 1 7 9 7 0
W R I T E I I O U T , 1 J Z O I D I A , S A M P H ! 7 9 8 0
1 3 2 0 F O R f}, AT i lHO , S X , ' iJ I. AM E T E R O F S P EC I M EN = • , F6 . 3 t ' I NC H E S • , s x , 7 9 9 0
1 ' I N I T I A L H E I G H T O F S A M P L E = • , F 6 . 3 , ' I NC H E S ' I 8 000
400 C O� T I NU E B O l O
W R I T E 1 ! 0 U T , 1 1 BO I g o z o
C A L L P L OT 1 1 5 . 0 , 0 . 0 , - 3 1 8 0 3 0
C A L L P L O T I O . C , Q , Q , 9 9 9 1 8 04 0
S T O P 8 0 5 0
E N D 8 060
S U P R OU T ! N E C CN G R A C O NG 0 0 1 0
C C ONG0 0 2 0
C T H I S S U B R O U T I N E R E A D S A N D R E D J C E S T H E T E S T D A T A FOR T H E C CN T R G L L E DC ONG0 0 3 0
C G R A D I E N T A N J R A T E O F S T R A I N C U N S C L I D A T I ON T E S T S . C O N G 0 0 4 0
C C ON G 0 0 5 0
c c c c c
1 00 0 c c c
C J •�ON / B L O K l / S E V T 1 3 0 3 1 , E i 30 3 1 o S E V T E 1 ! 03 1 o E E I 1 0 3 1 , C I 1 0 3 1 C GN G 0 0 6 0
D O U E L E P RE C I S I ON C C ON G 0 0 7 0
C J � � G N / B L O K Z / C E P T A o S L DP E B o C E P T e , SL O P EC , C E P TC , SL O P E O o CE P T U o C ONGO O B O
1 S L C P E E o C E P T E o S L O P E F , C E P T F o S L O P E G o C E P TG , 80uND 1 o 8 0 U ND 2 , 8 0 U N D 3 , B O U N 0 4 C ONG0 0 9 0
z � B O U N 0 5 , BO U ND 6 t NU M P T C , N U � P T E i P I N S T U , X S L P2 t P C t E C , EJ t DC R t CC l , C S r C R t C O�GO i O O
3 S R , ND E G , I N , I CU T , ! D I AL C ON G 0 1 1 0
C O � M C N / B L O K e / T R I 3 0 3 1 o TR E I 1 0 3 1 , D E F R I 30 3 1 o D E F RE 1 1 0 3 1 o P P R I 3 0 3 1 , C O N G 0 1 2 0
1 • P R E I 1 0 3 1 , WR D I 30 3 1 , •R D E I 1 0 3 1 o L o S T V T I 3 U 3 1 o C ON G 0 1 3 0
Z S T V T E 1 1 03 1 , P P P I 3 0 3 1 , P P P E I 1 0 3 1 o P P T I 3 03 1 o PP T E 1 1 0 3 1 o C ON G C 1 4 0
3 C S E V T i 3 0 3 I , C S E V T E I I 0 3 I , D F L I 1 3 0 3 I , O F L l E I 1 0 3 I , S T R 1 3 0 3 I , C ONGO 1 5 0
4 S T R E I 1 0 3 1 , H I 3 0 3 1 , H E i l 0 3 1 o O C F , L C F , P C F C ON G 0 1 6 0
C O t-'- � C N / B L C I( ': / L OC I 4 1 9 H CL , S A � , T E S , O PR i l l t D A T 1 .3 l 9 D E S I 4 1 t 8C 0 ( 2 0 1 t C O N G 0 1 7 0
l K K , RU � T Y P C ONGO l � O
C J � � O � / B L O K 6 / SP G , wT I W , WT F W , � T F D t D E F J , C E F F t B P t OE F Z , W R Z , P P Z , H S t H i t C J NG 0 1 90
l HV , S I , E l t E F , S F , W i t W f , S f C ON n , A R C ON G 0 2 00
D I � E � S I O� T t 50 J l , T � f 5 0 3 l C ONG0 2 1 0
R E A L L C F C ONGO Z Z D
I N T E G ER R U N T Y P C ON G 0 2 3 0
C CN G 0 2 4 0
R E A � I � C � � T R J L L E D T E S T C O M PR E S S I 0N D A T A -- T I M E , O E F L F C T I O � t C ONGQ 2 5 U
P O R E P P E S S U� � , A N D L O AC . C ONG0 2 6 0
00 3 0 I = l , 3 0 C
R E A D f i N t l CO C l T R I I J , O E FR. I I I , ? P R I I l t 'n iHl l l l t l
F O R � A T I F 4 . 0 , F 5 . 2 , 2 F4 . 0 , I Z I
C O• P U T F I L L C U T P U T
T I I I = T O I I I - TR I 1 I • 1 • J
S T V T I I I = I I W � C I I I - ,;R Z I ''' L C C<• 1 4 4 . 0 I / I 2 000 • u•:• AR I P P P I l I = I I P P R I I I - P P Z I •:• p C F I
P P T I I I = P P P I I I '' 0 , 0 7 2
S E V T l I I = S T V T I I I - I 0 • 6666 7'''P P T I I I I
C S E V T I ! I = S E VT I I I C·F L I I I I = I D I A L * I O E F R I ! I - D E F I ) ':• O C F
S T R I I I = OF L I I I I / H l
H I T I = H ! -r· F L ! I I I E I I I = I H V - O F L l l I I I / H S
C O NG0 2 7 0
C ON G 0 2 � 0
C ONG0 2 9 0
C ONGO 3 0 0
C CN G 0 3 10
C ONG0 3 2 0
CONG0 3 3 0
C ON G 0 3 4 0
C ONG0 3 5 0
C ONGO 3 6 0
C ON G 0 3 7 0
C ONG0 3H Q
C ON G 0 3 9 0
C GN G 0 4 0 J
C G NG Q 4 1 0
C GN G 0 4 2 0
C C/I.J G 0 4 3 0
C O N G 0 4 4 'J
E-31
c
c c c c
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c
I F I SE V T I I I . G T . S E C O ·� O I T R I I I = T R I I - 1 1 I F I S E V T I I I . G E . S E C O N O I S T R I I I = S T R I I - 1 1 I F I S E V T I I I . G E . S E C O N D I E I I I = E I I - 1 1 I F I S E V T I I l .. G E . S EC Ol"D l S EV T I I J ::;; S E VT f i - l l I F I K>< . E� . t l C S E V T I I I = E I I I MU S T O E T E R � I � E • H E N E X P AN S I ON PO I N T S S T A R T . I F f i ., E Q ., l ) G G T O 2_ 0
H A S E F F EC T I V E S T R E S S J E C RE A S E D M C R E T H A N 0 . 7 T S F B E TW E E � C O � S E C U T I V E C A T A P O I N T S ? I F S O o C O N S I D E R A L L S U B S E Q U E N T D A T A A S E X P AN S I ON- R E BQ UNO D A T A . I F I S E V T I 1 I • G T . 1 • 0 I G O T 0 1 0 D I F F = S E VT I I I - S E VT I I - 1 1 I F I I .. E Q . 2 J G C T O 1 0 J I F F l = S E V T I 1 - 1 1 - S IO V T I I - 2 1
1 0 C O N T I N U E I F I S E V T I I I . L T . I S E V T I I - 1 1 - 0 . 7 1 1 G O T O 4 0 I F I S E V T i i i . L T . O . l l S E V T I I I = 0 . 1
C O N T I N U E T O R E A D C O M P R E S S I ON DA T A . 2 0 C O N T I N U E 3 0 C O N T I N U E
4 0 C O N T I NU E
C ON G 0 4 5 0 C ON G 0 4 6 0 C O I\J G 0 4 l' O C O N G 0 4 8 0 C ON G 0 4 9 0 C UNGQ 500 C G N G0 5 l 0 C ON G 0 5 2 0 C O N G 0 5 1 0 C UNG0 5 4 0 C ONG0 5 5 0 C ONG0 5 6 0 C ONGO 5 7 0 C ON G 0 5 B O C ONG0 5 9 0 C ON G 0 6 0 0 C ONG0 6 l 0 C ON G 0 6 2 0 C ON G 0 6 3 0 C GNG0 640 C ON G 0 6 5 0 C ON G 0 6 6 0 C ON G 0 6 7 0
c ''"'"'' I GN C R I N G L A S T PO I N T I S E C CN O A R Y C C M P R E S S I O � P R O B A BL Y ! F I T T E D C U R V E 3 E N D I N G B A C K T R Y I N G T O F I T I T . N U � P T C = I - l
T O A VO I D C ON G 0 6 8 0 C ONG0 6 9 0 C ONGO 7 0 0 C ONG 0 7 l 0 C O N G 0 7 2 0 C O NG 0 7 3 0
c
c ''"'"'' T H I S P O I N T H A S N O W B E E N M A D E I N V I S I BL E T O A N A L Y S I S . c c c c c
c c c
c c c
R E A D I N C O N T R O L L E D T E S T E X P A N S ! O N - R E 5 0 U N � D A T A -
P O R E P R E S S U R E , A N D L O A D .
D O 5 0 ! :; 1 , 1 0 3 R E A D I I N . t O O C I TR E I I I o D E F R E I I I o P P RE I H o • R D E I I I o L
C ONGO 7 4 0 T I M E o O E F L EC T ! ON o C ON G 0 7 5 0
C ONG0 7 60 C ON G O 7 7 0 C ONGO 7 8 0 C ONGO 7 9 0
H A S A B L A N K C A R D B E E N E NC O U N T E R E D ? M O R E D A T A .
I f N O T , C ON T I N U E T O L OOK F O R C ONGO B O O C u NG O B l O C ON G 0 8 2 0 C ON G 0 8 3 0 C ON G 0 8 4 0 C O N G 0 8 50 C ON G 0 8 6 0 C ON G 0 8 7 0 C ON G 0 8 8 0 C O N G 0 8 9 0 C O N G 0 9 0 0 C ON G 0 9 l 0 C ON G 0 9 2 0 C ONGO 9 3 0 C ON G 0 94 0 C ONGO 9 5 0 C ON G 0 9 6 0 C ON G 0 9 7 0 C ON G 0 9 B O C ON G 0 9 9 0 C O N G I OOO C O NG l 0 1 0 G R A R O O ! O G R A R 0 0 2 0 G R AR 0 0 3 0
I F I T R E I I I . U . O I GO T O 6 0 T E I I I = T R E I I I - T R E I 1 I + ! . 0
T E I I I = T R E I I I - T R I 1 1 • l . O T RE I I I = T E I I I
S T V T E I I I = I I W R D E I I I - W RZ I •:•L C F " 1 44 o 0 1 / 1 2 0 0 0 . 0 <• A R I P P P E I I I = I I P P R E I 1 1 - P P Z I •> P C F I P P T E I l i = P P P E I J ) •:• 0 . 0 7 2 N U � P T E= I S E V T E I I I = S T V T E I I I - I 0 • 6 6 6 6 7 •:• P P T E I I I I C S E V T E I I I = S E V T E I I I D F L I E I I I = I D I A U I O E F R E I I 1 -D E F ! i " DC F S T R E I I I = DF L ! E i l i / H l H E I I I = H I - D F L I E I I I E E I I I = I rl V- D F L I F I I I I I H S I F I KK . E Q . 1 1 C S E V T E I I I = E E I I I
5 0 C O N T I N U E 6 0 C O N T I N U E
R E T U R N E N D
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E-32
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* G R A P � I C A L r E T HCJ D *
S U � R O U T I N E G R A R A O
C R AR 0 0 4 0 G R A R 0 0 5 0
G R AR 0 06 0
G R A R 0 0 7 0
G R A R O O e O
T H I S V E K S I ON E M P L O Y S M C NUL T Y ' S C O N S T R UC T I O � T O D E T E RM I N E G R AR 0 090
THE P O I N T O F M A X I M U M C U R V A T U R E . G R AR 0 1 00
C O �� ON / S L O K l / P I 3 0 3 1 0 F i 30 3 l o P E I 1 0 3 1 , EE I 1 0 3 1 o C i l 0 3 1 G R ARO l l O
OOU E L E P R E C I S I O � C G R A R 0 1 2 0
C O � � O N / B L O K 2/ C E P T A , S L OP E B . C E P T B , S L O P E C , C E P T C t S L O P E O , C E P T O, G R AR 0 i 3 0
l $ L C P � E , C f P T � t S L O P E F t C E P T F , S LO P E G t C E P T G t 8 0 U � 0 1 , B G U N0 2 t B OUNQ 3 , B O U N D 4 G R AR0 1 4 0
2 t BO U ND 5 , BO U N C b , �U M P T C , N U � P T E t P I N S TU , X S L P 2 , P C , E C , EO t CC R , CC l , C S , C R 9 G R AR O l S O
3 SR , N D E G , I N , I CU T , I O I A L G R AR0 1 60
C J M tJ O N / C L C K 5 / L OC ( 4 ) , HO L t S M' , T E S , O P R ( l ) , Q A T ! 3 1 t O E S t 4 l , BC O I Z O I t G R AR0 1 7 0
1 K K 9 R U N T Y P G R ARO i B O
C O ��CN / P L O K 8 / � A O t l 0 3 l , R A D M I N t R A D � X , I � I N , I PR I N T , J P R I N T , K I N D G R AR0 1 90
C O M M O � / P L CJ K 9 / X l l 0 3 o 4 1 o S L O P E 1 1 1 0 3 1 o S L C P E 2 ( 1 0 3 1 G � A R 0 2 0 0
C O M f'.I· O N X l ( l 0 3 , 4 l , X 2 t l 0 3 , <'t l t X 3 l l 0 3 , 4 l t X4 1 1 03 t 4 l t X 5 ( 10 3 t 4 l t G R AR 0 2 1 0
l X 6 ( l 0 3 t 4 J , X7 ( 1 03 , 4 l , X d t l 0 3 , 4 1 , X 9 ( 1 0 3 , 4 1 , X l 0 ( 1 0 3 t 4 l t X l l l l 0 3 , 4GR AR0 2 2 0
2 1 G R AR 0 2 3 0
C O M � O N / P I S E C / XT AM o Y T A N o C E P T AN , X A N G L E o S L � P B I , C E P T B I G R A R 0 24 0 I N T E G E R RUN T Y P G R A R 0 2 5 0 I NT E G E R S T A R T , S F AC G R A R 0 2 6 0
D I � E NS I ON C U R V E I ! O l i , Y L ! N tc i ! O l l G R AR 0 2 7 0
P O U N D I S U S E D A S T E M P O R A R Y S T O R A G E LOC A T I O N F O R BUUND 1 .
B O U N D = BOU N 0 1
RO U N D 5 = BO U N D 2
G R AR 0 2 8 0
G R A R 0 2 9 0
G R AR 0 3 0 0
G R A R0 3 1 0
G R A � 0 3 2 0
E O U N D 6 I S S E T E J U A L TO Q , J S O T H A T P L O T T I � G S U B R O U T I N E C A S P L T W I L L G R A R 0 3 3 0
U S E A P P R O P R I A T E S T A T M E N T S W H I C H W I L L P L G T • C N U L T Y ' S C O N T R U C T I ON , G R A R 0 3 4 0
B O U N D 6 = 0 . 0 G R A R 0 3 5 0
I � I N = 7
R A D � I N = l OO .
R A D M X = O . O
F I N D A U N E T A N G E N T TO I N I T I A L C C M P K E S S I O � C U R V E H A V I N G S L O P E O F
E X P A N S I ON - R E B O U N D C U R V E .
DO 3 0 J = 1 , 3
O E L T A = A B S I P O U N 0 2- B O U N D 1 1 / 1 0 0 . 0
R A D � I N = 1 0 0 . 0
D C 1 0 I = l , l O l
X l 1 o J I = BO U N D 1
X 2 ( I t J l = X I I , J l :;: X I I , J 1
X 3 1 I t J l = X ( I , J l * X I I , J l * X ! I , J l
X 4 1 I , J J ::: X ( I , J ) =:= x ( l t J J =:= x t I t J J =:= x t I , J )
X 5 1 I , J J = X I I , J J ::= x t I t J I .O:= X t I , J ) ::: x t I , J ) =::x t i , J I
X b I I , J ) = X I I t J l :;: X ( I , J l =:: X I I , J ) ':=X I I 9 J I >:: X I I , J l :;: X I I , J J
X 7 t i , J J = X t r , J J =:= x t r , J J =:= x i r , J J =:= x t r , J J O:= X t r , J J =:= x t r , J J •:=x t r , J 1
X S I I o J I = X I I , J I ''' X i I • J I ''' X I I o J i ''' X i I o J I ''' X I I o J I <' X I l o J i <' X I I , J ) <' X I I , J J
X 9 ( r , J I = X t I , J l :;: X ( I t J I :;: X I I 9 J l ,;, X I I • J J :;: X I I 9 J l :;: X I I , J ) :::X ( I , J l :;: X I I , J l
1 ':'X I I o J I
X 1 C I I , J l = X I I t J 1 :;: X I I , J l ::: X I I , J l :;: X ( I , J J =:= X I I , J 1 :;: X I I 9 J l :;: X I I , J 1 ::: X I I , J l
S L C P E l i i i = C I Z J + 2 '''C i 3 i "' X 1 1 I . J I + 3 '''C i 4 1 ''' X 2 1 l o J I + 4'''C i 5 i <' X 3 i l o J I +
G R AR0 3 6 0
G R A R 0 3 7 0
G R A R 0 3 f. O
G R A R 0 3 9 0
G R A � 0 4 0 0
G R A R 0 4 1 0
G ?. A R 0 4 2 0
G R AR 0 4 3 0
G RA R 0 4 4 0
G R A R 0 4 5 0
G R A R 0 4 6 0
G R A R 0 4 7 0
G R A R 0 4 8 0
G R A R 0 4 9 0
G R A R O S O O
G R ARO 5 1 0
G R A R 0 5 2 0
G R A R 0 5 3 0
G R A R 0 5 4 0
G R A R 0 5 5 0
G R A R 0 5 6 0
G R A R 0 5 7 0
G R A R o s g o
G R A R 0 5 9 0
G R A R 0 6 0 0
G R A R0 6 1 0
G R A R 0 6 2 0
G R A R 0 6 3 0
E-33
c
c
c
c
c
c
c
c
c
c
c
c c
c
c
c
c
c c c
E-34
K 5 ':'( ( 6 1 ''' X 4 ( I , J I • 6 ''- C l 7 1 <' X 5 ( ! , J I • 7 ''' C l B I "' X o l i , J .I + 8 ':'( ( 9 1 <' X 7 t i , J I •
K 9 '''( ( 1 0 P X 8 ( I , J I • 1 0 '''( ( 1 l i ''' X 9 ( I , J I < l l "' C l 1 2 1 '''X 1 U l I , J I
T RY I �G T O F I �O T A N G E N T TO C U R V E W I T H > L C P E G F R E BO U � D- E X P A N S I O N
C U R V E .
I F l S L O P E 1 l i i . L T . S L OP E E I G O T O 2 0
1 0 X ( I + l , J ) = X I I 1 J ) + D E L T A
Z O C ON T I NU E
I F ( J , E Q , 1 1 G O T O 4 0
B D U N O Z = X l I , J I
B O U N D 1 = X l i - 1 , J I
3 0 C ON T I N U E
J = 3
X B = X l i , J I
40 C O N T I N U E
I F A T A N G E N T T D I N l T I A L C � �P R E S S I O � C U� V F I S N O T F G U N D , D E F A U L T
T O U S E F I R S T S E A R C h P O U ND A R Y ( P O U N D L J A S A � SC I S SA V A L U E C N
C O M P R E S S ! O ' C UO V E T H R O U G H WH I C H L I N E H A V I � G T H E S L J P E W I L L B E S R A. h N ..
I F ( I , E Q , 1 I X B = 6 G U N D
X T A N -= X B
X B 1 = X ll
X 8 2 = X B '!' X R
X B 3 = X � ':' X 8':' X 8
X 3 4 = X 8 ''X P ''' X B ''' X B
X G 5 = X B * X B * X B * X B * X B
X B 6 = X B O X BO X B O X 8 0 X B O X B
X B 7 = X B * X F O X 8 0 X 8 0 X B O X B O X B
X d B = X B * X B * X B * X B * X B * X B * X B * X B
X b 9 = XB * X B * X B * X B * X B * X B * X B * X B * X 3
X 3 1 C = X B * X t3 * X B * X B * X B * X d * X B* X B* X P * X B
X B l L = X B * X B * X P * X B * X B * X B * X B * X B * X B * X B * X E
Y T A � = C l 1 1 + C ( Z I * X B 1 + C ( 3 I O X B Z + C l 4 I O X B 3 • C l 5 I O X 84
1 C l 6 l * X 8 5 + C ( 7 l * X B 6 + C ( 8 J * X 8 7 + C l 9 l * X � 8 +
2 C ( 1 C H X B 9 + C ( l l i "' X tl 1 0 + C ( l Z I '''X B 1 1
C E P T A N = Y T A� - S L O P E E O X B
T A! 1 G E t'H L L \; E H A S 5 E t: N D E F I N E D .
F I N O I � T E � S E C T I O�i W I TH L I NE ' 0 ' ( V I KG I N C OM P R E S S I O� L I N E J .
X A N G L E = l C E P T A N- C E P TO I / l S L O P E D- S L O P E E I
Y A \ G L � = S L J P E E * X A N G L � +C E P T A N
P I = .:3 '1 5 . / l l 3 e
S F ft. C = N L!'� P T C + 2
I F ( K i<.. . E Q .. I J E ( S F AC J = J . Q4
I f ( KK . iC C , Z I t l S F AC I = O . O Z
D E L T A = E l l l - � l N U i� P T C J
I f l t<.K . C:O .. L . fi � D . A t3 S ( D E L T A J . GT .. 0 . 3 2 J E l S F AC J = O . O B
I F ( K, . i:C' . Z . A N D . A B S t n E L T A ) . G T , O . l 6 1 E l S F A C I = 0 . 0 4 r . . !_ 1 __ .) , � • { r:: , 0 . :1 , \ U \\ 1) .,.. ( , 1 1 P ( S F AC I = 0 , 3 0 C J
F A C T O R = P l S F A C I / E l S F AC I
G R A R 0 6 4 0
G R AR 0 6 5 0
G K A R 0 6 6 0
G R AR 0 6 7 0
G R A R 0 6 8 0
G R A R 0 6QO
G R A R O 700
G R A R 0 7 1 0
G R AR 0 7 Z O
G R A R O 7 3 0
G k A R 0 7 4 0
G i{ AR 0 7 5 0
G R A R 0 7 6 0
G R AR 0 7 7 0
G F( AR 0 7 8 0
G R A R 0 7 9 0
G K A R 0 8 0 0
G R A R O d 1 0
G R AR 0 8 2 0
G R A R 0 8 3 0
G R ARO 8 4 0
G R AR 0 8 5 0
G R A R 0 tl 6 0
G R. A R 0 8 7 0
G R AR 0 8 8 0
G R A R 0 8 9 0
G R A R 0 900
G R A R 0 9 1 0
G R A R 0 9 Z O
G R AR 0 9 3 0
G R A R0 94 0
G R A R 0 9 5 0
G R A R 0 9 6 0
G R A R 0 9 7 0
G R A R 0 9 9 0
G R A R 0 9 9 0
G R AR l 0 0 0
G R A R 1 0 1 0
· c R A R 1 0 2 0
G R AR 1 03 0
G R AR 1 0 4 0
G R A R 1 0 5 0
G R A R 1 0 6 J
G R A R l 0 7 0
G R AR I C B O
G K AR 1 09 0
G R AR 1 1 0 0
G R A R l l l J
G R A R 1 1 Z O
G R AR 1 1 3v
G R A R 1 1 4 0
G R A.R. l l 5 0
G R AR l l 6 0
G R A R 1 1 7 0
G R A R 1 1 8 0
G R A R 1 1 90
G i{ A R 1 Z O O
G R AR 1 2 1 0
G � ,\ � 1 2 ? 0
C R AR 1 2 3 0
G RA R I Z4 0
C G R AR ! Z 5 0 C B I S EC T P I C T O R I A L R E P R E S E NT A T I O N O F I N T E R I O R A N G L E F CR � E D G R AR 1 26 0 C BY I N T E R S E C T I J N O F I N I T I AL T A N G E N T A N D V I � G I N C C � P R E S S J ON G R aR l 2 7 0 C C U � V E L I N E � E P R E S E� T A T I ON . G R A R I Z S O
S L D P B I = T A N I P I - A B S I A f A N I S L U P E D O F A C T O R I I - A B S I A B S I AT AN I S L O P E EO G R A R I Z 9 0 l F A C T O R I I - A B S I A T AN I S L O P E D ''F A C T O R I I + P I I /2 . 0 I G R Atl.l 300
C G R AR I 3 \ 0 S L O P B I = S L O P B I / F A C T O R G R A R l 3 ZO C E P T B I = Y A N G L E- S LD P B I O X A N G L E G R A R l 3 3 0
C L I N E O F A N G L E B I S E C T O R H A S B E E N D E F I N E D . G R A R l 340 BOUN D ! = BOUND G R A R l 3 5 0 B O U N O Z = P I N U M P T C I G R A R l 360
C G R AR 1 37 0 C F I N D I � T E R S E C T I O N O F A N G L E B I S E C TOR L I N E W I TH C C M P R E S S I ON C U R V E ' S G R A R ! 3 8 0
C P O L Y N O � I A L R E P R E S E N TA T I ON . G R A R l 39 0
D O 7 0 J = l o 3 G R A R 1 4 0 0 D E L T A = A B S I B O U N D Z- B O U ND l l / l O O . O G ' A R l 4 l O 0 0 5 0 I = l o l O l G R AR l 4 2 0 X l l o J I = BOUNO l G R A R ! 4 3 0 X l ( I , J l = X ( I , J J =:= l . O G R A R 1 440 X 2 ( I , J J ::: X ( I , J I =:= x t i , J l G R A R 1 4 5 0
X 3 ( I , J l = X t J , J J =:= x t I . J J :::X ( I , J l [, R A R 1 4 6 0
X 4 1 l • J l = X ( I , J ) ':' X I l t J l =:= X t I , J ) t.= X t I t J I r, R AR 1 47 0
X 5 1 I , J J ::: X ( I , J ) =:= x t J , J ) =:. x t I , J ) ::: x t l t J H= X ( I , J ) G R A K 1 4 8 0
X 6 I I , J l = X ( I , J l ::: X { I , J J :;: X ( I , J l :;: X { I t J H= X t I , J J :;: X I I t J J G R AR 1 4 9 0 X 7 ( I , J l ::: X ( I , J l :;: X I � , J J :;: X I I , J l :;: X ( I , J I :;: X ( I t J l ,;, X ( I t J H= X ( I , J I G R AR 1 5 00
X 8 I I , J I =X I I , J I ''' X I I , J I '' X I I o J I"' X I I 0 J I ''' X I I o J I ' 'X I l o J I ''' X I I , J I ''' X I l , J I G R AR l 5 1 0 X 9 1 I , J I = X I I o J I ''' X I I • J I '' X I I o J I ''' X I I o J I "'X I I , J I ''' X I I , J I '''X I I , J I ''' X I I o J I G R AR l 5 2 0
F X I I o J I G R .A R ! 5 3 0
X l 0 ( I , J J = X ( J , J ) =:= x t I , J ) t.• X ( ! , J ) =:= X ( I , J J :::x t I , J ) =!= X ( I , J ) •:• X I l t J J ::: X ( J , J J G R A R 1 540 ! "' X I I o J I "' X I I , J I G R A R l 5 5 0
X l l i i o J I = X I I o J I O X ( I o J I O X I I o J I O X ( I , J I O X I I o J I O X I I o J I O X I I o J I O X I I o J I G R A R l 5 6 0
t =:= X t i . J J =:= X ( I , J J =:= X I I t J I G R AR 1 57 0
C G R AR 1 5 8 0 C G R A R l 5 9 0
C G R A R ! 600
C UR V E I I I = C i l I • C I Z I '''X l l I o J I + C l 3 i ':' X 2 1 l o J I + C 1 4 1 '' X 3 1 l o J l + G R AR l 6 l O ! C I 5 1 0 X 4 1 I , J I + C I 6 1 * X 5 1 I , J I + C I 7 1 * X 6 1 I o J I + C I 8 I O X 7 1 l o J I + G R A R l 6 2 0 2C i 9 1 ''' X 8 1 I o J I + C i l O I "' X 9 1 I o J I + C l l l i ''' X l O i l o J I + C l l 2 1 '' X l l i i o J I G R A R 1 6 3 0
C G R A R 1 6 4 0 Y L ! N E' I I I = S L0 ° cJ P X I I o J I + C E P T B I G R A R ! 6 5 0
C G R A R 1 660 I NU • = J G R A R l 6 7 0
C G R A R ! 6 8 0 C F I N D I N G T HE I N T E R S E C T I O N O F A N G L E R I S EC TO R w i T H C O� P R E S S I O N C UR V E G R A R l 6 9 0 C P Y C CM P A R I NG O R D I NA T E S O F C O O P R E S S I ON C U R V E ' S P O L Y N C M I A L A N D G R A R ! 700 C A N G L E B I S EC TO R L I N E W I T H I N C R EA S I NG A B S C I S S A V A LU E S . I � T E A S E C T I ON G R AR 1 7 1 D C I S F O U N D � H E � T H E O R D I N A T E V A L U E OF T H E A N G L E B I S EC T OR L I NE I S G R A R 1 7 2 0 C G R E A T E g T H A N T H E C O R R E S P ON D I N G CR D I NA I E V A L U E O F T H E C OMP RE S S I O N G R A R 1 7 3 0 C C U R V E P O L YNOV I A L . G R A R 1 74 0 C P O I N T O F I N T E R S EC T I ON I S G R A P H I C A L L Y S E L E C T E D P C I NT OF MA X I MU M G R AR 1 7 5 0 C C UR V A T U R E . G R A R l 7 60 C G R A R l 7 7 0
I F I Y L ! N E I I I . G T . C UR V F I I I I GO T O 60 G R AR 1 7 8 0 C G R A R 1 7 9 0
X ( I + l , J l = X I I , J l + D E L T A C. R A R 1 800 50 C O N T I NU E G R AR l 8 1 0 6 0 C O � T I NU E G R AR l 8 2 0
I F I I . L E . l l GO TO 7 0 G R A R l 8 3 0 B O U � D Z = X ( I , J J G R A R l d 4 0
E-35
c
B O U � D l = X I I - l , J I 7 0 C O N T I N U E
I F ( I . �� E .. l ) J = 3
I F I I I 'I UM . !' J . t i . A ND . I I . L E . l l l J = l
I F I I I NU � . E il . Z i o M D . I ! . L E . ! I I J = Z
I F I I P, U M . ' � . 3 I o A N D . I I . L E . l l l J = 3
P O U ND l = B O U N O e O U i\j O Z = D D U N D 5
C T H E G R A P H I C A L L Y S E L E C T E D P O I N T O F M A X . C U R V A T UR E .
G R A R I 8 50 G R A R I 3 6 0
G R A R I 8 7 0
G R A R l 8 8 0
r. R A K l d9 0
G R A R l 9DO G R A R I 9 l 0 G R A R l 92 D G R A R l 9 3 D
G R AR l 94 D
G R A R \ 9 5 0
G R A R \ 9 6 0
C R A R 1 97 0
G R AR I 980
A N A R O OO l A N A RO O l O A N A R 0 0 2 0
A N AR 0 0 3 0
A N AR 0 0 4 0
A N A R 0 0 5 0
c
c c c c c
R A 0l'-1 X = X ( l , J )
R E T U R N E N D
S U 2 R O U T I N E A � A R A D
* * �'** * * * * * * * * * * * * * * * *
0 A N A L Y T I C A L M E TH O D o * * * * * * * * * * * * * * * * * * * * *
C A N A R 0 0 6 0
C A N AR 0 0 6 l
C T H I S V E R S I ON E M PL O Y S T H E M A TH E M A T I C A L D E F I N I T I O � O F T H E A N AR 0 0 6 2
C R A C I U S O F C U R V A TU R E I N S E A R C H I N G F O R T H E P O I N T O F M A X I 0UM A N A R 0 0 6 3
C C UR V A T U R E . A N A R 0 0 6 4
C A N AR 0 0 7 0 C T H E P I C TO R I A L L OC A T I O N O F T H E P O I N T O F M A X I M U M C U R V A T U R E D E P E N D S A N AR 0 0 8 0
C P R I 0 A R I L Y ON T H E A R I TH � E T I C R A T I O O F T H E S C A L E F AC TO R S U S E D I N A N A R 0 0 9 0
C T H E H O R I Z O N TA L A N D I E R T I C A L D I R EC T I ON S . H E NC E , W I T H A D I F F E R EN T A N A R D l O O
C R A T I O F O R T H E H O R I Z O N T A L T O V ER T I C A L S C A L E F A C T O R S , T H E P O I NT O F A N AR O l l O C • A X l " U � C U R V A T U R E W I L L B E L OC A T E D A T A D I F F E R E N T A B S C I S S A L OC A T I ON A N AR D 1 20
C ON A G I V E N C L R V E o T H E R AT I O OF T H E HOR I ZO N T A L T O V E R T I C A L S C A L E A N AR 0 1 3 0
C F A C T O R S � U S T H E M U L T I P L I ED T I M E S T H E F I R S T A N D S E C O N D D E R I V A T I V E S A N AR 0 1 4 0
C B E F O R E T H E � A T H EM A T I C A L D E F I N I T I O N 0' T H E P O I N T O F M A X I MU M C U R - A N A R O l 5 0
C V A T U R E C A N BE U S E D T C S E L E C T T H E P O I NT O F �AX I MUM C UR VA T U R E B A S E D A N AR0 1 6 0
C ON T H E P I C T OR I A L C H A R A C T E R I S T I C S O F T H E F I T T E D C U R V E . A N AR 0 1 7 0
C A N A R D l 8 0
R E A L O S O S Q R T A N A R 0 1 9 0
C O M M O N / B L O K l / P I 3 0 3 1 , E i 3 0 3 1 , P E i l 0 3 ! , EE i l 0 3 1 o C C i l 0 3 1 A N A R O Z D O
D O U B L E P R E C I S I O N C C A N A R0 2 1 0
C O M M O N / B L O K 2 / C E P T A , S L OP E B , C E P T B , S LO P E C o C E PT C , S L O P E D , C E P T O , A N A R 0 2 2 0
l S L O P E E , C E P T E , S L O P E F , C E P T F , S LO P E G , C E P T G , E O U N Q l t B O U N D 2 t B O U N 0 3 , BO U N 0 4 A N A R 0 2 3 0
z , B O U N D 5 , BO U N C & , NU M P TC , NU � P T E , P I N S T U , X S L P 2 , PC , E C , EO , CC R , CC 1 , C S , C R , A N AR 0 2 4 0
3 S R , N D E G , I N , I CU T t i D I A L A � AR 0 2 5 0
C O �� O N / B L G K 5 / L OC 1 4 1 , H OL , S M1 , T E S , O P R i l i , D A T I 3 1 • D E S 1 4 1 , BC D I 2 0 1 , A N AR D 2 6 0
l K K , R U N T Y P A N A R 0 2 7 0
C O � � O N / � L O K B / R A 0 ( 1 0 3 ) , R A C M I N , R A D MX , I M I N t i P R I N T , J P R I � T , K I N D A � AR 0 2 8 0
D O U B L E P R E C I S I ON C l l Z I , X I l 0 3 , 4 1 . S L OP E I I I J 3 J A I' A R 0 2 9 0
D I � E N S I O N S LC P E 2 1 l 0 3 1 A N A R 0 3 0 0
D O U B L E P R E C I S I O N X 1 1 1 0 3 , 4 1 t X 2 t l 0 3 , 4 1 , X 3 ( 1 03 , 4 l t X4 t l Q 3 , 4 ) , A t� AR 0 3 1 0
1 X 5 1 1 0 3 , 4 1 9 X 6 ( 1 0 3 t 4 l , X 7 1 10 3 , 4 ) 9 X 8 1 1 0 3 9 4 J , X9 ( 1 0 3 , 4 ) , X l 0 1 1 0 3 9 4 l , t.. N A R 0 3 2 0
KX l l l l U 3 , 4 l A N AR 0 3 3 0
D O 1 0 I = 1 , ! 2 A N AR 0 3 4 0
C l I 1 = 0 . 0 A N A R 0 3 50
C I I I = C C I I I A N AR0 3 6 0
! D C O N T I NU E A N A R 0 3 7 0
C A N ARC 3 8 0
B O U N C S = BOUNO ! A N A R 0 3 9 0
B O U N D 6 = 8 0 U � D 2 A N A R 0 4 0 0
C A N A R0 4 1 0
E-36
c c c
c
c c c
c c c
O E R I V Z = O . O ! M I N � ? I D E R V2 = 7 R AD B I G = O . O I C H E C K � O J = 1
I F I KK . EQ . l l E I NU M P TC + Z I =0 . 04 I F I KK . E Q . Z I E I NU M P TC + 2 I �O . O Z D E L T A= E i l i - E I N U M P T C I I F I KK . E Q . l . A N D . A B S I O E L T A I . G T . D . 3 2 1 E I N U � P T C + Z I � 0 . 0 8 I F I KK . EQ . Z . AN O . A B S I O E L TA I . GT . O . l 6 1 E I N U M P T C + Z I = 0 . 0 4 C A L L S C A L E I E , S . O , NU M P T C , 1 1 F AC TOR = O o 3 0 0 0 / E I N U � P TC + 2 1
C O � P U T E R A D I I O F C U R V A T U R E A T G E NE R A T E D A B S C I S S A B E T W E E � S E A R C H B O U N D A R I E S . DO 4 0 J � l , Z I F I I P R ! N T . E C . O I WR I T E I ! O U T , ! 0 3 0 1 I F I I I P R I N T . EQ . t i . A N D . I J . E Q . 2 1 1 W R I T E I I CU T , l 0 3 0 1 O E L I A = A B S I B O U N D Z - � O U ND 1 1 / 1 0 0 . 0 R A D M I N� t oo . o D O 3 0 I = 1 o ! C l X I l , J I � BO U N D l
X l l l o J I � X t I , J I "t . O X 2 I I , J I � X I I , J I ,,, X I l , J I X 3 I I , J I � X I I , J I <• X I I , J I ,,, X I I , J I X 4 1 I , J I � X t I o J i <• X t ! , J ) <:• X ( I , J I ''' X I l o J I X 5 1 h J I � X t I , J ) •:• x t [ , J ) •> X t I , J ) •:• x t I o J I <• X t I , j ) X 6 1 I , J I = X I I , J ) •:• x t I , J I '' X I I , J I ''' X I I o J ) •:•x t l o J ) •:•x t I , J I X 7 1 I . J l � X ( I , J ) ::' X I I , J ) ': =X t i , J J >!= X ( I , J H= X I I , J ) ::< X ( I , J ) O:: X ( I , J ) X B t i , J I = X t ! , J ) O X ( I o J I O X ( I , J ) O X ( ] , J ) O X ( I , J i O X ( I , J ) O X ( ! , J I O X ( I , J I X 9 I I , J I � X I I , J I ''' X I I , J I ''' X I I , J I '' X I I , J I <• X I I , J I ,,, X I I , J I '''X I I , J I '' X I l , J I
l ':: X ( I , J ) X 1 0 1 I o J I = X I ! , J ) •:• X t ! , J I ''' X I ! , J I '' X I I , J ) •:• X I I , J H• X I I , J i <• X t I o J ) •:•X ( ! , J I
l ''' X I I , J ) <• X t I o J I
S L O P E I I I I = C I Z I + Z , •:• C t 3 i" X l i ! , J I + 3 , •:•C I 4 1 '' X Z I ! , J I + 4 . •:•C i 5 l "'X 3 ( 1 , J I + K 5 • ''' C I 6 I ''' X 4 I l , J I + 6 • ''' C I 7 H• X 5 I I , J I • 7 . ''' C I 8 I •:•x 6 I I , J I + 8 • ''' C I 9 I ''' X 7 I I , J I + K 9 •:•C t l O J •:• X B I I o J I + l O<•C t l l i ''' X 9 1 I , J I + l l" C I l Z I •:• X l O I I o J I
A N AR 0 4 2 0 A N A R 0 4 3 0 A N AR 0 4 4 0 A ,\I A R 0 4 50 A N AR 0 4 6 0 M A R 0 4 7 0 A N AR 0 4 8 0 A I< AR 0 4 9 0 A N AR0 5 0 0 A N A RO S ! O A N ARO S Z O A N ARO 5 3 0 A N A R 0 5 4 0 A N A R 0 5 5 0 A N A R 0 5 6 0 A N AR0 5 7 0 A N AR 0 5 8 0 A N AR O 5 9 0 A N AR 0 6 0 0 A N AR 0 6 1 0 A N A R 0 6 2 0 A .� A R 0 6 3 0 A N AR 0 64 0 A N AR 0 6 5 0 A N AR0 6 6 0 A N A R 0 o 7 0 A N A R 0 6 8 0 A N AR 0 6 9 0 A N AR O 7 0 0 A N AR 0 7 1 0 A N A R 0 7 2 0 A N A R O 7 3 0 A N A R 0 7 4 0 ACJARO 7 5 0 A N A R 0 7 6 0 A N A R 0 77 0 A N AR 0 7 8 0 A N A R 0 7 9 0 A � A R O B O O A N AR0 8 1 0 A N A R 0 8 Z O A N A R O d 3 0 A N A R 0 84 0 A N AR 0 8 5 0 A N A R 0 8 60
S L O P F Z I I I = 2 0C I 3 1 + 6 0 C I 4 I O X ! I I o J I + l Z OC I 5 1 0X z t l o J I + ZO O C ( 6 1 0 X 3 1 l o J I A N AR 0 8 7 0 l + 3 0 ':'( ( 7 l ,;, X 4 ( I , J l + 4 2 ;;:( I 8 l :;: X 5 ( I , J l + 56 O:=C ( 9 I ::: X 6 ( I , J } A N ARO BR 0 2 + 7 Z •:•c t 1 0 P X 7 1 I . J I + 9 Q•:•c t I l l ''' X8 1 I , J I + l l Q •:• c t l 2 i <• X 9 t i , J I A N AR 0 8 9 0
C A N A R 0 9 0 0 S L O P E l i ! I = S L C P E l l ! ) •:• F A C T O R A N A R 0 9 l 0 S L O P E Z I I I = S L C! P E Z I I I •:• F A C T O R A N A RO 9 2 0
C T H I S N E XT F JU A T ! O N I S U S E D TC C AL C U L A T E A � AR 0 9 3 0 C T H E � ! N I �U M R A D I U S O F C U R V A T U R E . A N A R 0 94 0 C T H E S E R A D I I A R E T H E N C OM P A R E D T O O U T A I N T H E A N A R 0 9 5 0 C S M A L L E S T O N E P R E S E N T . A N A R 0 9 6 0
C A N A R 0 9 7 0
R A 0 I I I = 0 S Q R. T I I 1 + S L 0 P E l I I i':' S L O P E 1 I I I I ''' I l + S L 0 P E l I I I ''' S L O P E I I I I )':< I l + A I' A R O 98 0
1 S L O P E l I I I ''' S L C P E l l I I I I I S L O P f Z I I I A N A R O 99 0 I F I I P R ! N T . E Q . D I " R I T E I I OU T . IO O O I I , X ( I , J I , R A D I I I , S LD P E Z I I I A N AR l OO O
1 0 0 0 F O R � A T l l X , I 3 , Z X , ' X z ' , G l 5 . 5 , 5 X , ' RA D -= ' , G l 5 . 5 , 5 X , ' S L O P t= Z -= ' , F l 0 . 5 ) A :'Il A R 1 0 1 0
E-37
c
c
! F I A B S I R A O I ! I I . G E . A B S I P ADB ! G I I R A O B ! G = R AD I ! I ! F I A B S I R A O I I I I . G E . A B S I R A DB ! G I I ! B I G = ! ! F I A R S I R A O I ! I I , GE , A il S I R AD<O ! G I I X B I G = X I l o J I I F I A B S I SL O P E 2 1 I I I . G T . A B S I D E R I V2 1 1 I b E R V 2 = I I F I A R S I S L O P E 2 1 ! 1 I . G f . A B S I D E R I V2 1 1 D E R I V 2= S L CP E 2 1 l l I F I I . E Q o l l G O T O 3 0 I F I A B S I R A D I ! I I . G T . A B S I R A O I I - 1 1 1 1 GQ T O 2 0 G O T O 3 0
2 0 C O � T I N U E I F l l . E J . 2 1 G O T O 3 0 I F I A B S I R A D M I N I . L E . A B S I R AD I I - 1 1 I I G O TO 3 0 I F I A B S I R A D I I - 2 1 1 . L E . AB S I R AD I I - 1 1 1 1 G O TO 3 0 I C � E C K = 1 I �, I N = I - 1 I F I I M I N . L E . S I GO T O 3 0 I F I J !A J N . G E . 9 6 I G O T O 3 0 R A D � I N = R A O I I - 1 I R A C M X = X I I - 1 , J I
3 0 X ( I + l , J } � X ( l , J J +D E L T A I F I I M I N . E 0 . 7 1 G O T O 4 0 I F I I M I N . E Q , 1 1 G O T O 4 0 I F I I fH N . E Q , 1 0 1 l G O T O 40 B O U N Q 1 = X I I n �- 1 , J I B O U N D2 -= X ( I M I /'I. + l , J J
40 C O N T I N U E J = 2
C I S T H E R E A D I S C R E T E P O I N T O F M A X I MU M C U R V A T U R E I N 9 0 1 M ! O PO R T ! O N
A N A R 1 0 2 0 A N A R 1 0 3 0 A N AR 1 04 0 A N A R 1 050 A N A R 1 060 A N AR 1 07 0 A N A R 1 0 8 0 A N A R 1 090 A N A R l l O O A N AR 1 l l 0 A N AR 1 1 20 A N A R 1 ! 3 0 A N A R 1 1 4 0 A .� A R 1 1 50 A N AR I 1 6 0 A N A R 1 1 7 0 A N A R l U l O A N A R 1 1 9 0 A N A R I 2 0 0 A N AR 1 2 ! 0 A N AR 1 2 2 0 A N A R 1 2 3 0 A N A R 1 240 A N A R 1 2 5 0 A N A R 1 2 60 A N A R 1 2 7 0 A N A R 1 2 B O A N A R 1 2 9 0 A N A R 1 3 0 0 A N A R 1 3 I O A N A R 1 32 0 A N AR 1 3 3 0 A N A R 1 3 4 0 A N A R 1 3 5 0 A N A R I 3 6 0 A N A R 1 3 7 0 A N A R I 3 8 0 A � AR l 3 9 0
C O F S E A R C H B O U N D A R I E S ? I F T H E R E I S N O T , D E F AU L T T O U S E L O C A T I O N C O F T H E M A X I MU M V A L U E F O R T H E S E C O N D D E R I VA T I V E A S C H O S E N PO I NT C O F M A X I MU M C UR V A T UR E ,
I F I I C HE C K . E Q . O I I M I N= ! D E RV 2 I F I I C H E C K . E Q . O I R A D f•IX = X I I �· I N , J I I F I ! M I N . L E o 6 1 R A O M X = X I I D E R V 2 , J I I F I I ·" I N . G E . 94 1 R A D M X = X I ! D E R V 2 , J I I F I I P R I NT . EQ . O I W R I T E I ! OU T . I O ! O I X I ! M I '� • J I o i M I N , D ER ! V2 , I O E R V 2
1 0 1 0 F O R M A T f S X , ' X� I N = ' , F l 0 . 5 , 5 X , ' I � I N = ' , I 3 , 9 X , ' D E R I V2 = ' , F l 0 . 5 , 5X t K ' I OE R V Z � · , ! 3 ) A N A R 1 400
I F I I C H E CK . E Q , Q f W R I T E I I OU T , I O Z O I A N AR 1 4 1 0 ! F I I M ! N . L E . 6 1 W R i f E I ! G U T o l O Z O I A N A R I 4 2 0 I F I I M I N . G E . 9 4 I W R I T E I I 0 U T , 1 0 2 0 I A N AR I 4 3 0
I 0 2 0 F D R M A T I ' O ' , S X , ' * * W A R N I N GOO : P T . M A X , C U R V A T U R E N O T � ! T H I N 9 0 1 ' A N AR 1 4 4 0 ! , ' M l D P D R T ! DN O F B O U N D ! AND BOU N 0 2 . ' / 1 H0 , 5 X o ' LO C A T ! O N O F M A X I M U M ' A N A R I 4 5 0 2 , • S E C D N D D E R I V A T I V E T A K E N A S D E F A U L T F O R P T . O F M A X , C U R V AT U R E ' / / I A N A R 1 460
I F I I C H E C K . EO . O I W R ! T E I I OU f o l 0 3 0 1 A N A R 1 47 0 I F I I C H E CK , N E . Q , A N O . ! P R I NT . E Q . O I W R I T E I ! CU T o l 03 0 1 A N A R 1 4 8 0
1 0 3 0 F O R M A T 1 ' 1 ' 1 A N AR 1 49 0
B O U N D I = BO U N 0 5 A N A R 1 5 0 0
BOU� C 2 = B O U N 0 6 A N AR 1 5 1 0 C A N AR 1 5 2 0 C B O U N D 6 I S S E T E W U A L T O 9 9 9 S O T H A T P LO T T I NG S U B R OU T I N E A N A R 1 5 3 0 C C A S P L T W I L L S K I P A R G U M E N T S R E L A T I NG T O T � E G R A P H I C A L A N AR 1 54J C M E T H O D . A N A R 1 5 5 0
B O U N D 6 = 9 9 9 . 0 A N A R 1 5 6 0 C A N A R I 5 7 0
R E T U R N A N A R 1 5 R O E N D A N A R I 5 9 0
c 0 00 0 0 0 1 0 c o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o 0 0 0 0 0 020
E-38
c c c c c c c c c c c c c c
o L E A S T S Q UA R E S CRO ! �A R Y P O L Y N O M I A L C U R V E F I T T I NG S U BRDUT ! N E . o * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ('( '** * * * * * * * * * * * * * * * * * * * * *
i\JU :-I A L I 5
U N I V E R S I T Y O F K � N TUC K Y
'� C V E Y H A L L
L E X I N� T O N , K F � T U C K Y
0 0 0 0 0 0 3 0
0 0 0 0 0 04 0
0 0 0 0 0 0 5 0
0 0 0 0 0 0 6 0
0 0 0 0 0 0 7 0
O O OOOQ ·q Q 0 0 0 0 0 0 9 0
0 0 00 0 1 00
O O O U O l l O
0 0 0 0 0 1 2 0
0 0 000 1 3 0
0 0 0 0 0 1 4 0
0 0 00 0 1 S O
O O OU0 1 6 0
S U B � OU T I N E F L S Q FY ( N , M , X , Y , W , C , A L P h A , B E T A , S t SG MS C t P� , pQ , � l , MN l l O O OO C 1 7 0
I M P L I C I T � E A L O B I A- H o U- � o Z I 0 0 0 0 0 1 8 0
D I �E N S ! OI� C l l> 1 1 o AL PH A I �N 1 1 o BE T A 1 '1 � 1 l o :. 1 1; N 1 1 o SG � SQ I M � l l o PR I MN 1 1 o P0 1 0 0 000 1 9 J
$ M N l l o w i i; I , X I '' I o Y I .� I 0 0 00 0 2 00
G A VO A = l .
.\lO = O
C A L L F GE F Y T I N , N O t X t Y t � t d f T A , S , S G � S Q , AL P H A , D R , PO , � , M� l l
C A L L F C O D A I N t C t P O , P K t A L P H A t 9 E T A , G A � J A , S , N + l )
R ET U R N
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S U E R OU T I N E F C O O A I N , C , P � , P R , A L P H A , d E T A t G A M C A t S t N N J
I M P L I C I T R � A L *B I A- H , U- h , Z J
0 I /'-' E N S I O�J C ( 1\-'l J , A L P d A ( 1\Jf-J I , P t.: T A ( N N I � P /1-' ( "J �\ l , P R ( N!\l J � S I 1\.f\1 I 1\i l = f\j -t- 1
00 1 0 I B ; 1 o N 1
C l T � J = O .
P M I I i? I = O .
1 0 P R I 1 � 1 ;:: Q ., P R i l l ; ! ,
C l l i ; S I 1 1
00 2 0 1 = 1 , 1\.J
T 2 = C .
1\i l = I + l
�J J 2 0 I B = l , \J l T 1 ; I T 2 - .A L P H A I I I '''P R I I B I - B E T A I I I '' P � I I a I I I G M D A T 2 ; PR I f B I P M I ! R I ; P R I ! B I
P R I [ R. I ; T 1
Z D C l I 2 1 o C I I 3 1 • T P S 1 ! > 1 1
R E T U R N
E � O
S U 8 R OU T I N E F G E F Y T ( N , NO t X t Y t W t B E TA t S t SG M SQ , A L P H A , P R t FO , M , N l l
I M P L I C I T R f A L * B I A- H , Q- k , l l
D I /1-'E N S I ON X l f!I J t Y I 1"1 l , B E T A I N I l t A l,. PHA I N i l , 5 ( 1\ I J , S G M S � I N I J , PR. ( M J ,
$ P () ( ,'-l ) , VJ ( M )
! COO F O R M A T 1 3 2 H T H E R E I S AN E R R O R I N Y O U R D A T A l
I F I N - i�O - l"i l 1 0 , 3 0 , 2 0
1 0 I F I � -��0 ) 2 0 , 30 , 3 0
2 0 P R I N T 1 0 0 0
G U T C 2 1 0
3 0 B E T A I N O • L J = O ..
D S Q ; O .
W P P = O .
L X A C T = Cl
I F I �- N 0 - � + 1 1 50 , 4 0 , 4 0
4 0 L X A C T ; 1
0 0 0 0 0 2 ! 0
0 0 0 0 0 2 2 0
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0 0 00 0 2 6 0
O O OO O U ! U 0 00 0 0 0 2 0
0 0 0 0 0 0 3 0
0 0 0 0 0 04 0
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0 0 0 0 0 0 6 0
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0 0 0 0 0 1 2 0
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0 0 0 0 0 1 60
0 0 0 0 0 1 7 0
0 0 00 0 1 8 0
0 0 0 0 0 1 9 0
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0 0 0 0 0 04 0
0 0 00 0 0 5 0
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c o ouo l 4 l)
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E-39
c
c
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c
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50 DO 8 0 J = l , �
P R I J J o 1 ,
P O I J I " O •
6 0 W P P = W P P + \-i ( J J
I F I L X A C T I 8 0 o 7 0 o 8 0
7 0 D S Q " O S Q + W I J J O Y I J I O Y I J J
a o C O N T I N U E
N O t\ = NO + l
NN " N + 1
DiJ 2 0 0 I = N O N , NN
L R F CD0-:::: 1"1,- I + N O
W Y P = O .
W X P P " D •
D O 1 20 J " 1 o M
T E M P " w i J I "' P R I J I
I F ( I -NN l 90 , 1 G O , 1 00
90 W X P P " W X P P + T E M P O X I J J O P R I J I
1 0 0 ! F I L R E E O O J 1 2 0 , 1 1 0 o 1 1 0
1 1 0 � Y P " W Y P • T E M PO Y I J J
1 2 0 C O N T I N U E
I F I L R E E OC I 1 4 0 o 1 3 0 , l 3 0
1 3 0 S i l J o W Y P / W P P
1 4 0 I F I L X A C T J 1 6 0 , 1 5 0 , 1 6 0
1 50 O S C " O S Q- S I I I ''' S I ! i "' W P P
B R = L R E F. QC'
S G � S Q I I i " D S O / B R
G J T C 1 7 0
1 6 0 S G t' S Q i l i " G •
1 7 0 ! F I I -N M I 1 8 0 , 2 0 0 , 2 0 0
1 8 0 A L P rl A i l i " o X P P / W P P
1 9 0
2 0 0
2 1 0
W P P C = W P P
W P P " O •
D O 1 9 0 J = l , i-'1
T E M P " I X I J J - A L P H A I ! I i ''' P R i J J - B E T A i l i '''PC I J I W P P = W P P + W ( J J * T E � P * * 2 P O I J I " P R I J I
P R I J I " TEf:p
B E T A I I • 1 1 " W PP / W P P O
C O N T I N U E
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* * * * * * ** * * * * * * * * * * * * * * *
S U B � CU T ! N E C A S P L T
T � I S S U B R OU T I N E P L O T S T H E R E S U L T S O F T H E A N A L Y T I C A L A P P L I
C AT I O N S O F T r l E � OI U L T Y , C A S A GR A N D E , A N D S C H M E R T MA N N C O N
S T R U C T I O N S .
0 0 000 1 6 0
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0 0 0 0 0 3 7 0
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O O OO O <t 60
O O OOO't70
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- C A SP 0 09 0
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C A S P 0 1 7 0
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E-40
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2 B 5 , 8 CUN06 , �C , N E , P O V t R , X S L P 2 , PC , EC , E O , OC R , ( C l , C S , C R , S R , N OE G t i N
3 t i CU T , I D I A L
C O �' � O N I 8 L O K 3 / P O , P R E C O N , P R E � I N , V O I O"C , E C M Hl o O C R � I N , C R � I � C O M M O N / B L O K o· / L OC I 4 1 o H OL o S A M , T E S o O PR I 1 1 o O A T I 3 ) o O E S I 4 1 o BC D I 2 0 1 o
1 K K 9 R U ;\I T Y P
C O � P C N / B L O K 8 / R AD I 1 0 3 I , R A D M I N o R A O � X o i M I N 0 I PR I N T • J P R I N T , K I N 0
C O M� D N / 9 I S E C / X T A N o Y T A N o C E P T A N o X AN G L E o SL U P 9 I o C E P T B I
D I M E N S I ON D A T A I 1 D 2 4 1 o X I 1 0 3 1 o C U R V F T 1 1 0 3 1
0 I �·E N S I O N � O V E R 1 3 I , V O I D t O I 3 1 , DA SH 1 1 3 1 , D A S H Y I L ) I 0 P D U �, M Y I 1 D 3 1
R E A L L I N E A 1 1 0 3 I , L l N E B I 1 0 3 I , L l N E C 1 1 0 3 1 , L 1 N E D I 1 0 3 1 , L I N E E 1 1 0 3 I ,
1 L ! N E F 1 1 03 1 o L I N E G I 1 0 3 1 D I � E N S I O N T A N G E N I 1 0 3 1 o 8 I S E CT I 1 3 1
I N T E G E R S T A R T , S F A C
I N T E G E R S T AR E , S F A E o S T A R X o S F AC U R
I N T E G ER R U N T Y P
C A L L S C A L E I E , B . O o N C o 1 1
B O V E R I 1 1 = P O V E R
V O I J E O I l l = E O
I F I KK . EO . Z I VO ! D ED i l i = O . O
D A S H Y I ! I = P C O S O + O Y
V O l D P C = D A S HY I 1 1
S E T T I N G U P S T A R T I N G A N D S C A L E F A � T O R P O S I T I CN S
F O R E A C H D F T H E R E S P EC T I Vf P L U T V A R I A B L E S .
S T A R. T = I\fC +- 1
S T A R E = N E + l
S T A R X = l O l + l
S F A C = N C + 2
S F A E= N E + Z
S F A C U R = 1 0 1 + 2
P I S T A R T I =- 1 . 00 0
P E I S T A R E I = P I S T A R T I
I F I KK . E Q . Z I E I S T AP T I = O . O
E E I S T A R E I = E I S T A R T I
X I S TA R X I = P I S T A R T I
C U R V FT I S T AR X I = E I S T A R T I
L I N E A I S T A R X I = E I S T AR T I
L I N E B I S TA R X I = E I S T AR T I
L I N E C I S T A R X I = E I S T AR T I
L I N E D I S TA R X I = E I ST AR T I
L I N E E I S T A R X I = E I S T AR T I
L I N E F I S T A R X I = E I ST AR T I
L I N E G I S T A R X I = E I S T AR T I
B O V E R I Z I = P I S T AR T I
V O ! D EO I Z I = E I S T Ak T I
D A S H I 1 2 1 = P I ST AR T I
D A S H Y I ! Z I = E I S T A R T I
T A N G E N I S T A R X I = E I S T A R T I
S ! S E C T I 1 2 1 = E I S T A R T I
P I S F AC I = 0 . 3 J C J
P E I S F A E I = P I S F A C I
E E I S F A E I = E I S F AC I
X I S F A C UR I = P I S F A C I
C U R V F T I S F A C UR I = E I S F A C I
C A S P O Z ! O
C A S P 0 2 2 0
C A S P 0 2 3 0 C A S P D 2 4 0
C A SP 0 2 5 0
C A S P 0 2 6 0
C A S P 0 27 0
C A S P 0 2 8 J
C A S P O Z 9 0
C A S P 0 300
C A S P 0 3 1 0 C A S P 0 3 2 0
C A S P 0 3 3 0
C A SP 0 34 0
C A S P 0 3 5 0
C A S P O 360
C A S P 0 3' 0
C A S P 0 3 8 0
C A S P 0 39 0
C A S P 0 4 00
C A S P 0 4 1 0
C A S P 0 4 2 0
C A SP 0 4 3 0
C A S P 0 4 4 D
C A SP 0 4 5 0
C A S P 0 4 6 0
C A S P 0 4 7 0
C A S P 0 4P O
C A S P0 4 90
C A S P D 5 00
C A S P0 5 1 0
c A SP 0 5 2 0
": A S P0 5 3 0
C A SP 0 5 4 0
C A S P 0 5 5 0
C A S P 0 5 60
C A S P 0 5 7 0
C A S P 0 5 8 0
C A S P O 5 9 0 C A S P0 60 0
C A S P 0 6 ! 0
C A SP 0 6 20
C A SP 0 6 3 0
C A S P 0 640
C A S P 0 6 5U
C A S P 0 6 6 U
C A SP D 67 0
C A S P 0 6 8 0
C A SP O o 9 0
C A S P 0 7 0 0
C A SP 0 7 1 0
C A S P 0 7 ? 0
C .\ S P O 7 3 0
C A S P 0 740
C A S P 0 7 5 0
C A SP 0 7 6 0
C A 5 P 0 7 7 0
C A S P 0 78 0
C A S P 0 7 9 0
E-41
L I N E A I S F A C U R I = E I SF A C I C A S P O B O O L ! N E 2 1 S F AC U R I = E I SF A C I C A S P O a 1 o L I N E C I S F A C UR I = E I SF A C I C A S P O B 2 0 L I N E D I S F A C UR I = E I SF A C I C A S P 0 8 3 0 L I � E 0 1 S F A CUR I = E I S F A C I C A SP 0 8 4 ()/
L I � E F ! S F A C UR I = E I S F A C I C A S P 0 8 5 0 L I � E G I S F A C U R I = E I SF A C I C A S P 0 8 6 0 POV E R 1 3 1 = P I S F A C I C A SP 0 8 7 0 VO I O EO I 3 1 = F I S F A C I C A S P 0 8 R O D A S H I 1 3 1 = P I S F A C I C A S P 0 8 9 0 D A S HY I 1 3 1 = E I SF A C I C A S P 0 900 T A N G E N I S F AC U R I = E I S F AC I C A S P 0 9 1 0 B I S E C f l l 3 1 = E I S FAC I C A S P 0 9 2 0
C C A SP 0 9 3 0 F I R LOG = - 1 . 00 0 C A SP 0 94 0 D E L LO G = 0 . 3 00 0 0 C A S P 0 95 0 C A L L L D G A X S I G , 0 , 8 . 0 o ' L 0 G I V E R T I C A L E F F . S T R E S S , T S F I ' o 3 l o 1 0 . 0 1 0 o O o C A SP 0 9 6 0
1 - l . C OD o O o 3 00 0 0 1 C A S P 0 97 0 I F I KK . E Q . Z l G O T O 1 0 C A S P0 9 8 0 C A L L A X I S I O . O , O , O , ' V O I D R A T I O I E I ' o l 4 , R , OO o 9 0 . 0 , E I S TA R T i o E I S F AC I I C A S P 0 9 9 0 G O T O 2 0 C A S P 1 0DO
C C A SP 1 0 1 0 1 0 C ON T I NU E C A S P 1 0 2 0
C A L L P L O T ( Q , Q , B . O o- 3 1 C A S P 1 03 U C A L L A X I S I O . O o O o O o ' V E R T I C A L S T R A I N I I � / I � I ' o - 2 3 o 8 . 0 o 2 7 0 . Q , Q , Q C A S P 1 04 0
1 , E I S F A C I l C A S P 1 0 5 D 2 0 C ON T I N U E C A SP 1 060
C C A SP 1 07 0 C G E N E R A T E T H E P L O T S C A S P 1 0 8 0 C C A S P 1 0 9 0 C C A S P 1 1 0 0 C C OM P R E S S I ON C UR V E . J = 1 . ONL Y S Y M B O L S F O R E A C H P C ! N T P R O D U C E D . C A SP 1 1 1 0
C A L L L I N E I P , E , N C , 1 , - l , l l C A S P 1 1 2 Q C A L L L I N E I P E o E E , N E o 1 o - 1 o 1 l C A S P 1 1 3 0
C E X P A N S I ON C U R V E , J ; ! , O N L Y S Y M B O L S F O R E A C H P O I N T P R O D U C E D . C A S P 1 1 4 0 C C A S P 1 ! 5 0 C C A S P 1 1 60
X I 1 1 = P I 1 1 C A S P 1 1 7 0 D E L T A = I P I NC I - P i l l l / 1 00 C A S P 1 1 8 J D O 3 0 1 = 2 , 1 0 1 C A S P 1 1 9 0
3 0 X I I I = X I I - l i + D E L TA C A S P I 2 00
00 40 I = 1 , 1 0 1 C A SP 1 2 1 0 C C A S P 1 2 2 0
X 1= X I I I C A S P 1 2 3 0 X Z = X I I I *X I I I C A SP 1 240 X 3 = X I I I "<X I I I '''X I I I C A S P 1 2 5 0 X 4 = X I I I <'X I I l <' X I l i '> X ! I l C A S P 1 2 6 0 X 5= X I I i <' X I I I "'X I I i '''X I I I '''X I I I C A S P 1 2"! 0 X 6 ; X I I I ''X I I I ''' X I I l ''' X I I I ''X I I I ''' X I I I C A S P 1 2 ·q 0 X 7 = X I I I '' X I I I o X I I I '' X I I I ''X I I I ,,, X I I l ,, X I ! I C A S P I 2 9 0 X 8 = X I I I ''' X I I I "X I I )': < X I I I ''' X I I I ,,, X I I I ''' X I I I ,,, X I I I C A S P 1 3 DO X 9= X I ! I ''X I I I '' X I I I '' X I I I ''X I ! I ''' X I I l '''X I I I ''' X I I I ''' X I I I C A S P l 3 1 U X 1 0 = X I I I '' X I I I ''X I I I ''X I I I oX I I I ,,, X I I I ,,, X I I I '' X I I I <• X I I P X I I I C A S P 1 3 2 D
X 1 1 ; X I I I '' X I I I ''X I I I ''' X I I I ''' X I I I ''' X I I PX I I I ''' X I I i "' X I I I '' X I I I ''' X I I I C A S P 1 3 3 0 C U R V FT I I J ; ( ( 1 1 + C I Z I O X 1 + C I 3 1 0 X 2 + C 1 4 1 0X J + C I 5 I O X 4 + C I 6 1 0 X 5 C A S P 1 3 4 0
1 +C I 7 1 0 X 6 + C I B I *X 7 • C I 9 I O X 8 + C I ! O I O X 9 + C l 1 l i * X l 0 + C I 1 2 I O X 1 1 C A S P 1 3 5 0 C C A S P 1 3 6 0
40 C ON T I NU E C A S P 1 3 7 0 C C A S P 1 3 8 0 C F I T T E D C U R V E , J = O . O N L Y A L I N E P L O T P R O D U C E D , NO S Y M B OL S . C A S P 1 3 9 0
E-42
c C N O W P L O TT I N G E X P A N S I ON P R E B O� N D C U R V E L I N E A E P R E S E N T AT I O � . c
c
c c c c c
X l l i =P E i l l D E L T A = I PE I N E I - P t l l l 1 / ! 0 0 D O 5 0 1 = 2 , 1 0 1 X i i i = X I I - l i + D E L TA
5 0 C ON T I NU E D O 6 0 I = l , ! O l L ! N E E I I I = S E •:•x I I I •· E Y
6 0 C O N T I � U E
C A L L L I N E ( X , L I N E E 9 1 0 l t l t 0 t 0 1
I F ( 8G U N 0 6 . G T . 99 8 ) GO T O 1 1 0
... ... ::: :;: :;: :;< :;: ::: ... :::: ... :;: ::: ::: f.:
... " C N U L T Y • s G R A P H I c AI. C O N S T R U C ... ... ::;: .. .. �· " .. ... .. . . >:: ... >:• X I I I = X T A N- 0 . 1 D E L T A = A B S I X A N G L E - X 1 1 1 1 / 1 0 0 , 0 9 0 7 0 I = 2 o l 0 1 X I I I = X I I - 1 1 + D E L TA
7 0 C O N T I NU E D O 3 0 1 = 1 , 1 0 1
T AN G E N I I I = S E * X I I I + C E P T A N 8 0 C O N T I N U E
::;:
C A L L L I N E ( X , T A N G EN t l O l t l t O t O l D A S H I 1 1 = X S L P 2- 0 , 0 5 D E L T A= A B S I X A N G L E - D A S H I 1 I 1 / 1 0 . 0 DO 9 0 I =2 , 1 1 D A S H ! I I = D A S H I I - 1 1 + DE L T A
9 0 C ON T I N U E D O 1 00 1 = 1 . 1 1
::::
T >;:
B I S E C T I I I � SLCP H I •:• D A S H I I I +C E P T B I ! D O C O � T I NU E
c
[ c
C A L L D A S H L N I O A SH , B ! S E C T o 1 1 , p
1 1 0 C J � T I N U E
c • • •• • • • • • • • • • • • • • • •• • • • • • c C C A S AG R A N D E ' S C O N S T R UC T I ON c c * * * * * * * * * * * * * * * * * * * * * * * * * c
c
X I 1 1 = X S L P 2 D E L T A = A B S t P C + O o 0 5 - x S L P 2 1 / 1 0 0 D O 1 2 0 I -; 2 t l O l X I I I � X I I - l i + C E L TA
1 20 C O N T I NU E
D O 1 3 0 1 � 1 o 1 0 1 l I N E A ( I l = A Y + C • 0':' X ( I l
1 3 0 C ll � T I N U E C A L L L I �E I X , L I N E A , L J l t l t O t O I A = 1 X I l 0 1 1 - X I l 0 2 1 1 / X I 1 0 3 1 + 0 . 1
t,: {: :::: * ... 1!: >::
I ON TO D E T E R M I ::;: t,: .. .. ... :;: :;:-
L I ': E A I l O l l = i L I N E A i 1 0 1 1 - L ! N E A i l 0 2 ) 1 / L ! Nf A I 1 0 3 1
.;: t,: :;: :;: :;: ...
N E P T • O F M A X :;: ;;: ... t,: . .. ...
1,:
•
. ..
C A S P 1 400 C .A S P 1 4 1 0 C A S P 1 4 2 0 C A S P l 4 3 0 C A SP 1 440 C A S P 1 4 5 0 C A SP 1 46 0 C A S P l 47 0 C A S P 1 48 0 C A SP l 4 90 C A S P 1 5 0 0 C A S P l 5 1 0 C A SP l 5 2 0 C A S P 1 5 3 0 C A S P 1 5 4 0 C A S P 1 5 5 0 C A S P 1 5 6 0
''' '' '' C A S P 1 5 7 0 C u R v . •:•C A S P l 5 B O =:: =:: ':' C A S P 1 5 9 0
C A S P l 600 C A SP 1 6 l 0 C A S P 1 62 0 C A S P 1 63 0 C A S P 1 64 0 C A SP l 65 0 C A SP 1 660 C A S P 1 67 0 C A S P I 6 8 0 C A S P 1 6 9 0 C A S P 1 700 C A SP 1 7 1 0 C A S P 1 7 2 0 C A SP 1 7 3 0 C A S P 1 740 C A S P l 7 5 0 C A S P 1 7 6 0 C A S P ! 7 7 0 C A S P I 7 8 0 C A S P 1 7 9 0 C A S P 1 8 0 0 C A S P 1 8 1 0
C A S P 1 8 2 0 C A S P 1 8 3 0 C A S P l 840 C A S P 1 5 5 0 C A S P ! 8 6 0 C A S P ! B 7 0 C A S P 1 8 8 0 C A SP 1 89 0 C A S P ! 900 C A SP 1 9 l 0 C A S P 1 9 2 0 C A S P 1 9 3 0 C A SP 1 940 C A SP 1 9 5 0 C A S P 1 960 C A S P 1 97 0 C A S P 1 9 8 0 C A SP 1 990
E-43
c C A L L S Y � 8 0 L ( A , L I NE A I 1 0 l l t 0 e l 4 t 1 A ' t 0 e 0 t l I
c C L I N E T A N G E N T T O C UR V E A T P O I N T O F M A X C u R V A TU R E . c
c
c
D O 1 4 0 I = 1 d 0 l L I N E B I I l = 5 8 ''' X I I l + B Y
1 40 C ON T I NUE C A L L L I N E I X ,l i N E B , l O l t l t O t O I
8 = I X I ! O l J - X I l 0 2 l l i X ! l 0 3 } + 0 . 1 0
L I N ES I l 0 l l = I L l N E B I I 0 I I - L l N E B I 1 0 2 l l I L 1 NE 8 1 l 0 3 l C A L L S YM 80 L { 8 , L I N EB 1 1 0 l l t 0 e l 4 t ' B ' t O e O t l l
C B I S E C T L I N E S ' A ' A N O ' 8 1 • c
c c c
DO ! 50 I = l o ! O l
L I N E C I I l = S C<'X I I l + C Y
1 50 C O N T I N U E C A L L L I N E I X t L I NEC , l O l , l , O , O I
C X = I X I 1 0 l i - X I !0 2 l l i X 1 1 0 3 1 + 0 . 1 0
L I N E C I l C I I = I L I N E C 1 1 0 I I - L l N E C I 1 0 2 l l I L 1 NE C I 1 0 3 1 C A L L S YMPO L I C X , L I NE C I 1 0 l l t 0 e l 4 t ' C ' t 0 • 0 t l l
C P R O J E C T L I N E ' 0 ' B A C K F Rat� S T R A I G H T P O R T I ON
C O F V I R G I N C O M P R E S S I ON C UR V E T O G E T AN I NT ER S E C T I O N C W I T H L I N E ' C ' T O S H O W T H E P R E C O N S D L I D A T I O N P R E S SURE . c
c
c c c
X ( 1 1 = X A N G L E I F ! BO U N 06 . G T . 9 9 B J X ! 1 l = PC
D E L T A= I P I NC l - X I l l l / 1 00 o O D O 1 6 0 1=2 . 1 0 1 X I I I = X I I - l i + C E L T A
1 6 0 C O N T I N U E
D O 1 7 0 I = 1 . t 0 1 L I N E 0 I I I = S 0'' X I I l + D Y
1 70 C ON T I NU E C A L L L I N E ( X , L TN E D t l O l , t , O , O I
X I 1 I : I X I l l - X I 1 0 2 I I I X I l 0 3 I L I N E D 1 1 l = I L I N E D i l l - L ! NE D I 1 0 2 l l i L ! NE D ! 10 3 l + 0 . 1 C A L L S YM B D L I X I l l , L I N ED ( l } , O . l 4 t ' D ' r O • O t l l
c • • • • • • • • • • • • • • • • • • • • • • • • • • c C S C H M ER T M A N N ' S C O N S T R UC T I ON c c • • • • • • • • • • • • • • • • • • • • • • • • • • c C P L O T O V E R B U R D E N P R E S S U R E I BO V E R , V O I D EO l .
C A L L L I N E I B O V E R , VO I O E O t l t l t - 1 9 0 1 c C P L O T P R E C O N SG L I D A T I CN C O M P R E S S I ON C UR V E ' F ' . c
E-44
X I l l =3 0 V E R I 1 l
O E L T A = I P C - B O V E R ! l l 1 1 1 0 0
C A S P Z O O O C A SP Z C l O
C A S P 2 0 2 0
C A S P 2 0 3 0 C A S P 2 04 0
C A S P 2 0 5 0 C A S P Z 06J C A S P2 07 0 C A SP 2 08 0 C A S P 2 09 0 C A SP Z ! O O
C A S P 2 1 1 0 C A SP 2 l 20 C A S P 2 1 3 0 C A S P 2 1 4 0 C A S P 2 1 5 0 C A SP 2 1 6 0
C A S P 2 l 7 0 C A S P2 l 8 0 C A S P 2 1 9 0
C A S P 2 2 00
C A S P 2 2 1 0 C A SP 2 2 2 0
C A S P 2 23 0
C A SP 2 2 4 0
C A S P 2 2 5 0 C A S P 2 2 6 0 C A S P 2 27 0 C A S P 2 28 0
C A S P 2 29 0 C A S P 2 300 C A S P 2 3 l 0
C A S P 2 3 2 0 C A S P 2 330 C A S P 2 340
C A S P Z 3 5 0
C A S P 2 360 C A SP 2 3 7 0 C A S P Z 3 8 0 C A S P 2 3 9 0 C A S P 2 400 C A S P 2 4 1 0 C A SP 2 4 2 0 C A S P 2 4 3 ll
C A S P 2 44 0 C A S P 2 4 5 0 C A S P 2 460
C A S P 2 4 7 0 C A S P 2 4 8 0
C A S P 2 4 9 0 C A S P 2 5 0 0 C A S P 2 5 1 0 C A S P 2 52 0
C A S P 2 5 3 0 C A S P 2 54 0 C A S P 2 5 5 0 C A S P 2 5 6 0
C A S P Z 5 7 0 C A S P 2 5 8 0 C A S P 2 5 9 0
c
c c
00 1 8 J I = Z , l C l X I ! I = X I I - 1 1 + r E L H
1 80 CO� T I N L f
OJ 1 9 0 l = l . t G l l I N E F ( I ) = S F ,;, X ( I J + F Y
1 9 0 C O N T I NU E
C P L O T T H E S TE P S E M P L O Y E D I N T H E D E T E R � I N A T I O N O F A M I N I � UM
C P R E C O N S O L I DA T I O� P R e S S U R E . C A S H { l l = A L OG 1 0 1 PR E M I � I
C A S H ! l l l = X A. N G L E
I F I BJ U N � 6 . GT . 9 98 1 D A S H I \ t i = P c D E L T A = I O A S H i l l i -D A S H I \ 1 1 / t O . OO OJ 2 0 0 ! = 2 , 1 1
.
D A S H I I I = D A S H I I - l l + D E L T A 2 0 0 C ON T I NU E
DO 2 1 0 I = t . t 1
D A S H Y I I I = S Q<:< C A S H I I I + O Y 2 1 0 C ON T I N U E
C A L L O A SH L N I C A S H , Q A S H Y , 1 1 o l l D A S H Y i l l = E C. � I N
D A S h I ! I = A L O G 1 0 I P � E n N I D E L T A = I VO I DE O I 1 1 - E C M I N I / l J . O
I F I A B S I O E L T A I . LT . O . QJ C C t . A N D . K K . E Q • 1 1 O E L T A = D o GO l � I F I Ab S I D E L T A I . L T . O . O G O O l . AI;O . K K . EQ , z l D E L T A = O . C 0 0 7 5 I F I EC M I N . E W . VO I D E0 1 1 1 1 D E L T A = - D E L T A D O 2 2 0 I = 2 d l
D A S H ! I I = A L O G l J I PR E " I N I
O A S H Y I I I = D A S H Y i l - l l + D E L T A 2 2 0 C O N T I NU E
C A L L D A S� L N I C A SH , QA SH Y o l 1 0 1 1 C P L O T T R U E V I R G I � C OM P R E S S I C � L I N E ' G ' • c
c c
X l l i = P C D E L T A = I P I N C I • . 1 3- P C I * S G / L I � E G I 1 0 3 1 B 5 = E C + O E L T A
C C H E C K I N G A R GU � E N T S TC M A K • S U R E L I N E G I S N O T D R A W N TOG F A R .
c
c
I F I A3 S i B 5 J , G T . d . O I D E L T A = 8 . 0 - A B S I E C I
D E L T A= A B S I I O E L T A '''L l N EG I 1 0 J I I / S G I / l 0 0 o J
D O 2 3 0 1 = 2. , 1 0 1
X i l i = X I I - l i + C E L T A 2 3 C C ON T I N U E
D O 2 4 0 ! = 1 , 1 0 1 L l >; E G I I I = S G''' X I I I + G Y
2 4 0 C O "l ! N U E C A L L L I � f l X t L I N EG , I O l , l , Q , Q ) D E L T A = A B S I V O l uE 0 1 1 1 - V J I D P C 1 / 1 0
D A S H i l i = P C D A S H Y I 1 1 = V O I C P C 0 0 2 5 0 I =2 o l 1 D A S H I I I = P C
D A S H Y I I I = O A S H Y I I - 1 1 + D E L T A 2 5 0 C ON T I NU E
C A S P 2 60U C A S P 2 6 1 0
C A S P 2 6 2 Q
C A S P 2 6 3 0
C A S P 2 b 4J
C A S P 2 6 5 U C A S P 2 660 C A S P 2 6 7 0
C A S P 2 6 8 0 C A S P 2 6 9 0 C A S P 2 7 0 0
C A S ? 2 7 lll C A SP 2 7 2 :J
C A S P 2 7 3 J
C A S P 2 740 C A S P 2 7 5 0 C A S P 2 76 0
C A S P 2 77 0 C A S P 2 7 8 0 C A S? 2 7 9 0
C A S P 2 o 0 0
C A SP 2 8 1 0 C A SP 2 5 2 0 C A S P 2 8 3 0
C A S? 2 8 4 0 C A S P 2 8 5 0 C A S P ? 8 6 0
C A SP 2 8 7 0 C A S P 2 8El0 C A S P 2 8 9 0
C A SP Z 9 0 0 C A S P 2 9 1 0 C A S P 2 92 0 C A S P 2 91 0 C A SP ? 94 0
C A S P 2 95 0 C A S P 2 9 6 0 C A S P 2 9 7 0 C A S P 2 9 8 0 C A SP 2 99 0 C A S P 3 0 0 0
C A SP 3 0 1 0
C A SP 3 0 2 0
C A SP 3 03 0
C A S P 3 0 4 0 C A SP 3 0 50
C A S P 3 0 60
C A S P 3 0 7 0
C A S P 3 0 g 0 C A SP 3 09 0 C A S ? 3 !0 0
C A SP 3 1 1 0 C A SP 3 1 2 0
( A SP 3 l 3 0
C A S P 3 1 4 0 C A SP 3 1 5 0 C A S P 3 1 6 0 C A S P 3 1 7 0 C A S P 3 1 2 0
C A S P 3 l g 0
E-45
C A L L D A SH L N I D A S H o D A S H Y o l l o l l C A S P 3 ZOO I F I KK . EO . Z I C A LL P L O T ( 0 , 0 , - 8 . 0 ,- 3 1 C A S P 3 Z l 0
C A L L S Y � B D L 1 2 . 5 , 9 , Q , O , l 4 o B CO o O • O o!O I C A SP 3 22 0
F P N = N D E G + O . O l C A SP 3 2 3 0
C A L L N U M B E R l l Q . , 7 . 0 , 0 . l O , F PN , O . O , - l J C A SP 3 2 4 0
C A L L S Y M BO L f 9 .. 4 , 7 .. 0 , 0 . l 0 t ' D E G = ' , Q ., 0 , 6 1 C A SP 3 2 5 0 C A L L S YJ\1f;.Q L ( 9 . 4 , 6 .. 5 , 0 . 1 0 , ' PO ::: ' ., o .. O , S l C A S P 3 2 6 0 C A L L N U M B E R ( 9 . 9 , o .. S , O . l O t P O , Q ., Q , 3 J C A S P 3 2 7 0
C A L L S Y M B O L { L 0 . 5 , 6 . 5 , 0 e l 0 t ' T S F ' , O . O t 3 1 C A SP 3 2 8 0
C A L L S YM B O L ( l t .. 3 , 6 .. 5 , 0 ., 1 0 t ' EO = • , Q ., Q , S I C A S P 3 2 9 0
C A L L N U M P E R l l l . 8 , 6 . 5 , 0 . l O o E O , O . O o 4 1 C A S P 3 30 0
C A L L S Y M B O L ( [ Q . 3 , 6 . 0 , 0 . l0 o � R A N G E O F VA L U E S ' , Q , O o l 5 1 C A SP 3 3 l 0
C A L L S Y � B O L C l O . l t 5 e 7 5 , C e l 0 , 9 PR O BA B L E - M I N I �U M ' , O e 0 t l 8 1 C A S P 3 32 0
C A L L S Y "1 B O L ( 9 .. 4 , 5 o 4 r 0 e l 0 , ' PC T S F - T SF 1 , 0 e 0 , 2 7 ) C A S P 3 3 3 0
C A L L N U M B E R I l 0 . , 5 . 4 o O o l 0 o PR EC D N o O . O o Z I C A SP 3 34 0
C A L L N U,� 5 E R l l l . 2 o 5 . 4 o O o l O o P R E n N , O , O o 2 1 C A S P 3 3 5 0
C A L L S Y � P O L ( 9 ., 4 , S . O , O . L O , ' E C • , o ., 0 , 2 7 1 C A S P 3 3 6 0
I F I KK . EO . Z J V O I D C = - VO I OC C A S P 3 37 0
I F I KK . EO , I J C A L L N U M 9 E R l l 0 . 4 o 5 . 0 o O o lC o V O I DC o O • O o 3 1 C A S P 3 38 0
I F I KK . E Q . 2 1 C A LL N U M b E R l l 0 . 3 o 5 . 0 o O . l O o V O I OC o O • O o 4 1 C A S P 3 390 IF I KK . E Q , 2 ) V O I OC = -VO I DC C A S P 3 4 00 I F I KK . E Q . 2 J E C M I N= - E C M J N C A S P 3 4 1 0
I F ( KK .. E Q .. l ) C A LL N U �<1 0 E R I l l .. Z t 5 .. 0 , 0 . l O , EC M I N t O • O t 3 1 C A SP 3 42 0
I F { KK .. E 0 .. 2 l C A LL N U� S E R l l l .. 2 t 5 o O t O o l O , EC � I N 9 Q ., Q , 4 ) C A S P 3 4 3 0
I F I KK . E Q , 2 1 E C M I N= - E C M I N C A S P 3 4 4 0
C A L L S YfiBOL I 9 , 4 , 4 . 6 , Q , l O o ' OC i< ' , Q , Q o 2 1 l C A SP 34 5 0
C A L L N U M B E R l l C . 5 o 4 . 6 o O . l O o OC R o O . O o l l C A S P 3 46 0
C A L L N U M B E � l l l o 2 o 4 . 6 , 0 . lO o OC R M I N 0 0 . 0 0 l l C A S P 3 470
I F I KK . EQ , Z I GO TO 2 60 C A S P 3 4R O
C A L L S Y M B O L l 9 . 4 o 4 o 2 , Q , l 0 o ' CC ' 9 0 . 0 0 2 7 1 C A S P 3 49 0
C A L L S YM B O L ( 9 . 4 o 3 . 8 , Q , l 0 o ' C S ' o 0 • 0 o 2 l C A S P 3 5 0 0
2 6 0 C O N T I N U E C A SP 3 5 1 0
I F I KK . E Q , l J G O T O n o C A SP 3 5 20 C A L L S YM B O L ( 9 ., 4 ., 4 .. 2 , 0 . 1 0 , ' C R 1 , 0 ., 0 , 2 7 1 C A S P 3 5 3 0
C A L L S Yiv\ BO L 1 9 .. 4 , 3 .. a , o .. l D t ' SR ' , Q ,. 0 , 2 1 C A S P 3 54 0
2 7 0 C O N T I N U E C A S P 3 5 50
C A L L N U M B E R l l 0 . 3 o 4 • 2 o O . l O o CR ; 0 . 0 0 3 1 C A S P 3 5 6 0
C A L L N U M B E R l l l • 2 o 4 • 2 o O . lO o C R M I N o D • O o 3 l C A S P 3 5 7 J
C A L L N U M B E R l l Q . 2 , 3 , 8 o O . l O o SR , O . O o 4 1 C A SP 3 5R O
l F I NC . G T . l O I G O T O 3 2 0 C A S P 3 5 9 0
I F I KK . E Q , Z I G O T O 2 8 0 C A S P 3 6 0 0
C A L L S Y,� B O L I 9 , 4 , 3 . s , o . 1 0 , ' E F F , S TR. E S S V O I D R A T I O I E I ' , O . O o 3 0 I C A S P 3 6 1 0
I F I KK . EQ . l l G O T O 2 9 0 C A S P 3 6 2 0 2 8 0 C O N T I N U E C A S P 3 6 3 0
C A L L S n B D L l 9 . 4 o 3 . 3 , Q , l O , ' E F F . S T R E S S V E R T . S T R A I N ' o O . O o 27 J C A SP 3 6 4 0
2 9 0 C O N T I N U E C A S P 3 6 5 0
0 RO I N A = 3 . 0 C A SP 3 6 60
DO 3 0 0 I = l o �C C A S P 3 67 0
P OU M M Y I I I = l 0 . 0 ''"''P I I I C A S P 3 6 � 0
C A L L N UM P ER ( 9 , 7 o OR O I NA , O . l 0 o P D U M MY I I I o O . O o 3 1 C A S P 3 69 0
I F I KK . EQ . 2 1 E I I I = - E I I I C A S P 3 7 DO
C A L L N U M B E R l l l . 3 o O i< D I N A o O • l 0 o E I I I o 0 • 0 o 4 l C A S P 3 7 l 0
O R D I N A = OR O I �A- 0 . 2 C A S P 3 7 2 0
3 0 D C O N T I N U E C A SP 3 73 D
E-46
DO 3 1 0 J = l o N E C A S P 3 740
P D UM � Y I J J = l O . O ** P E I J I C A SP 3 7 5 0
C A L L N U M 9 E R 1 9 . 7 o OR D I N A o O . l O o P D U M MY I J I 0 0 , Q , 3 1 C A S P 3 760 I F I KK . E Q , 2 1 E I' I J I = - E E I J I C A SP 3 77 0 C A L L N UM B E R l l l . 3 o ORO I N A , O . l 0 0 E E I J I 0 0 , 0 0 4 1 C A S P 3 7 8 0
O R D I N A = OR O I N A - 0 , 2 C A SP 3 7 9 0
3 1 0 C O"! T l NU E 3 2 0 C O N T I N U E
C A L L P L OT I 1 5 , Q , Q , Q , - 3 J
R E T U R N E N D
C A S P 3 8 00 C A S P 3 B l 0
C A S P 3 8 2 0
C A S P 3 8 3 0 C A SP 3 d 4 u
