gint technical bulletin: equations used in lab testing · scenario 4: casagrande liquid limit, with...

gINT Technical Bulletin: Equations Used in Lab Testing gINT Technical Bulletin: Equations Used in Lab Testing ....................................................... 1

Water Content / Density............................................................................................ 1 Void Ratio and Saturation Calculations....................................................................... 3

Atterberg Analysis ................................................................................................... 5 Sieve Analysis......................................................................................................... 7 Hydrometer Analysis ............................................................................................... 12 Fine Specific Gravity ............................................................................................... 15 Compaction .......................................................................................................... 17

Optional Calculation of Maximum Dry Density and Optimum Moisture Content ..................... 19 Unconfined Compression .......................................................................................... 21 Consolidation ........................................................................................................ 25 Direct Shear ......................................................................................................... 25 Falling Head Permeability ......................................................................................... 26

Appendix A -- Scenarios using Wet Specimens in Sieve Analysis ............................................29 Scenario 5: Wet specimen, no split, incremental weighing.................................................. 29 Scenario 6: Wet specimen, split sieve........................................................................... 30 Scenario 7: Wet specimen, coarse fraction sieved wet....................................................... 32

EQUATIONS USED IN LAB TESTING

Water Content / Density

(per ASTM D2216)

Water Content Calculations

There are three ways to calculate Water_Content:

• From WC_Wt_Wet, WC_Wt_Dry and WC_Wt_Tare as follows:

(WC_Wt_Wet - WC_Wt_Dry) Water_Content =

(WC_Wt_Dry - WC_Wt_Tare)

Example:

Entered Calculated

WC_Wt_Wet WC_Wt_Dry WC_Wt_Tare Water_Content

95.3 80 20.2 25.59%

• From Wet_Density and Dry_Density as follows:

(Wet_Density - Dry_Density) Water_Content =

Dry_Density

Example:

Entered Calculated

Wet_Density Dry_Density Water_Content

133.2 115.424 15.40%

• From Dry_Density and source fields for Wet_Density (Diameter, Height, Wt_Spec_Tare, and Wt_Tare)

(see Wet_Density calculations, below)

gINT Software, Inc. www. gintsoftware.com

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Wet Density Calculations

Wet_Density (also known as total unit weight or wet unit weight) can be calculated in either of two ways:

• From Diameter, Height, Wt_Spec_Tare, Wt_Tare and Water_Unit_Wt as follows:

(Wt_Spec_Tare - Wt_Tare) x Water_Unit_Wt Wet_Density =

volume

where: volume (cu cm) = (Height x .01) x Water_Unit_Wt x (π x ((Diameter x 0.1)/2)2

or volume (cu ft) = (Height / 304.8) x Water_Unit_Wt x (π x ( (Diameter /(2 x 304.8) )2

Cubic cm example:

Entered Calculated

Diameter (mm)

Height (mm)

Wt_Spec_ Tare (g)

Wt_ Tare (g)

area sq cm

volume cu cm

Water_ Unit_Wt

Wet_ Density

50.8 152.4 655.7 0 20.2683 308.8889 62.42796 132.52

Cubic ft example:

Entered Calculated

Diameter (mm)

Height (mm)

Wt_Spec_ Tare (g)

Wt_ Tare(g)

net wt spec lbs

area sq ft volume cu ft

Water_ Unit_Wt

Wet_ Density

50.8 152.4 655.7 0 1.445571 0.021817 0.010908 1 132.52

• From Water_Content and Dry_Density as follows:

Wet_Density = (Water_Content + 1) x Dry_Density

Example:

Entered Calculated

Dry_Density Water_Content Wet_Density

101.26 23.98% 125.54


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Dry Density Calculations

Dry_Density (also known as dry unit weight) can be calculated from the following:

• From Water_Content and Wet_Density as follows:

Wet_Density Dry_Density =

(Water_Content + 1)

Example:

Entered Calculated

Water_Content Wet_Density Dry_Density

31.32% 119.5 90.999

• From Water_Content and Wet_Density’s source fields (Diameter, Height, Wt_Spec_Tare, and Wt_Tare)

(see “Wet Density Calculations,” above)

• From Wet_Density and Water_Content’s source fields (WC_Wt_Wet, WC_Wt_Dry and WC_Wt_Tare)

(see “Water Content Calculations,” above)

Void Ratio and Saturation Calculations

Void Ratio and Saturation % are calculated values displayed in reports, primarily the LAB SUMMARY graphic table. They are calculated via the Rep_Void_Ratio and Rep_Saturation user system data items respectively, and are derived from the Water_Content and Dry_Density values in the current WC DENSITY record, as well as Water_Unit_Wt in PROJECT (to establish the units for densities) and Specific_Gravity in LAB SPECIMEN.

Note: If there is no Specific_Gravity value in the parent LAB SPECIMEN record, Void Ratio and Saturation % are not calculated. Also, note that if Dry_Density is missing from the WC DENSITY record, the Dry_Density field in UNCONF COMPRESS, then CONSOLIDATION, then DIRECT SHEAR is accessed until a value is found (refer to the Rep_Dry_Density user system data item in the library for details).


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Void Ratio is calculated as follows:

Specific_Gravity Void Ratio =

(Dry_Density / Water_Unit_Wt) - 1

Example:

Entered Calculated

Dry_ Density

Specific_ Gravity

Water_ Unit_Wt

Void Ratio

108 2.65 62.42796 0.532

Saturation % is calculated as follows:

Specific_Gravity x Water_Content Saturation % =

Void Ratio

Example:

Entered Calculated

Water_ Content

Specific_ Gravity

Void Ratio

Saturation %

17.89% 2.65 0.532 89.13


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Atterberg Analysis

Atterberg indices and soil classification are covered in ASTM D2487.

Scenario 1: Liquid Limit and Plastic Limit Values Directly Entered

This is the simplest case. You can directly enter Liquid_Limit and Plastic_Limit values in the parent ATTERBERG table, and these will be used in reporting if nothing is entered in the lower grid. However, if data is entered in child ATTB READINGS records from which parent Liquid_Limit or Plastic_Limit values can be calculated, the calculated parent values will overwrite the entered parent values on saving.

Scenario 2: Plastic Limit Calculation from ATTB READINGS Data

The ATTB READINGS records that are used for plastic limit calculation are those that do not contain Number_Blows, Cone_Pen_Initial, and Cone_Pen_Final values. They contain Water_Content values, either directly entered, or computed from the WC_Wt_Wet, WC_Wt_Dry, and WC_Wt_Tare values in the same ATTB READINGS record. Multiple readings records can be entered, but a single record is acceptable.

The Plastic_Limit value in the parent ATTERBERG record is computed as the average of the Water_Content values in the child plastic limit ATTB READINGS records.

• Plastic_Limit = AVG1..n[ Water_Content(n) ]

where: (WC_Wt_Wet - WC_Wt_Dry)

Water_Content =


or: Water_Content is directly entered

Example:

Entered in ATTB READINGS

Calculated in ATTB

READINGS

Calculated in ATTERBERG (upper grid)

WC_Wt_Wet (g)

WC_Wt_Dry (g)

WC_Wt_Tare (g)

Water_Content (%)

Plastic Limit

18.16 17.38 14.56 27.65957

17.08 16.44 14.21 28.69955

17.98 16.88 13.06 28.79581

28.3849

Scenario 3: Casagrande Liquid Limit, with Single-Point Reading

If only one reading exists, the ASTM D4318 one point method is used. The requirement for the one-point method is that Number_Blows be between 20 and 30. The calculation uses the following equation:


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Number_Blows Liquid_Limit = Water_Content x ( 25 ) 0.121

where: (WC_Wt_Wet - WC_Wt_Dry)

Water_Content =


or: Water_Content is directly entered

Example:

Entered in ATTB READINGS Calculated in ATTERBERG

Water_Content Number_Blows n/25 ** 0.121 Liquid_Limit

59.62963 24 0.96 0.99507272 59.33582

Scenario 4: Casagrande Liquid Limit, with Two-Point Readings

If two readings are used, liquid limit values are computed for each reading using the one-point method, then the two one-point values are averaged. As with the one-point method, Number_Blows values must be between 20 and 30.

Example:

Entered in ATTB READINGS Calculated in ATTB READINGS

Calculated in

ATTERBERG

Water_Content Number_Blows n/25 ** 0.121 Liquid_Limit

(lower grid) Liquid_Limit (upper grid)

59.62963 24 0.96 0.99507272 59.33582

60.42618 27 1.08 1.00935578 60.99151

60.16367

Scenario 5: Casagrande Liquid Limit, with Multi-Point (3 or More) Readings

If three or more readings are obtained, a best fit line through a graph of the logarithm of blows vs. arithmetic water contents is used and the Liquid_Limit is defined as the water content at 25 blows on this best fit line.

Scenario 6: Cone Penetrometer Liquid Limit

You must have a minimum of three readings. Each ATTB READINGS record must have a Water_Content value (or values in WC_Wt_Wet, WC_Wt_Dry, and WC_Wt_Tare), as well as Cone_Pen_Initial and Cone_Pen_Final values.

Computation of Liquid_Limit is achieved by calculating a best fit line through a graph of arithmetic penetration vs. arithmetic water contents, and the Liquid_Limit is defined as the Water_Content at 20 mm penetration on this best fit line.


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Sieve Analysis

Various data entry scenarios are possible, depending on your needs. The most common ones, unsplit sieve and split sieve without moisture calculations, are described below (in addition to the non-calculated scenario, direct entry of Percent_Finer values). More complicated scenarios involving wet specimens are described in “Appendix A -- Scenarios using Wet Specimens in Sieve Analysis” on page 29.

Scenario 1: Percent Finer values directly entered

If the Percent Finer (Percent_Finer) values are directly entered into the SV READINGS grid, nothing is required in the parent record except Depth, and no calculations are performed.

Scenario 2: Dry total weight supplied, no split, incremental weighing

Incremental weighing records the weight retained on each sieve individually. Values are required in Wt_Total_Spec, Wt_Sieving_Tare_Coarse, and Weighing_Method in the parent SIEVE record and Soil+Tare values in the relevant child SV READINGS records. When you save, Percent_Finer is calculated for each SV READINGS record with a Soil+Tare (called Soil_Tare in the database) value, and the Wt_Passing_Split_Sieve in the parent SIEVE record is also calculated.

The following calculations are used for incremental weighing in unsplit sieving:

• Wt_Passing_Split_Sieve = Wt_Total_Spec x Percent_Finer(nfinal)

• Percent_Finer(n) = SUMn+1..nfinal[ percent(n) ]

where: percent(n) = [ Soil_Tare(n)— Wt_Sieving_Tare_Coarse ] / Wt_Total_Spec


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Example:

We are doing an incremental calculation, no split, no moisture content, with the following values:

Entered in SIEVE Record

Wt_Total_Spec Wt_Sieving_ Tare_Coarse

128.3 20.8

The resulting Wt_Passing_Split_Sieve is 10.2, and the Percent_Finer values are as shown in the right column of the table.

Entered in SV READINGS Calculated

Sieve Size Soil_Tare Wt_Sieving_ Tare_Coarse

net soil wt percent(n)

Percent_ Finer

Wt_Passing_ Split_Sieve

#4 20.8 20.8 0 0.00% 100.00%

#8 33.6 20.8 12.8 9.98% 90.02%

#16 46.5 20.8 25.7 20.03% 69.99%

#30 52.9 20.8 32.1 25.02% 44.97%

#50 46.5 20.8 25.7 20.03% 24.94%

#100 33.6 20.8 12.8 9.98% 14.96%

#200 29.8 20.8 9 7.01% 7.95%

total_sieved 118.1 7.95%

Wt_Total_Spec 128.3 7.95%

Wt_Passing_Split_Sieve 10.2 7.95% 10.2

Note that in this scenario (and all the subsequent ones), the assumption is that all of your sieves are the same weight, and a single tare value can be entered in the parent record (in Wt_Sieving_Tare_Coarse when there is no split, or separately in Wt_Sieving_Tare_Coarse and Wt_Sieving_Tare_Fine when split). This is the default setup for sieve analysis in gINT. However if you need to specify different tare weights for the various sieves, this can be done—see “Error! Reference source not found.” on page Error! Bookmark not defined..

Scenario 3: Dry total weight supplied, no split, cumulative weighing

Cumulative weighing sums the weights of all soil retained on each sieve and those coarser. The same set of fields is required for cumulative weighing (with dry weights and no split) as for incremental: namely Wt_Total_Spec, Wt_Sieving_Tare_Coarse, and Weighing_Method in the parent SIEVE record and Soil+Tare values in the relevant child SV READINGS records. Percent_Finer is calculated for each SV READINGS record with a Soil+Tare value. Also, the Wt_Passing_Split_Sieve in the parent SIEVE record is calculated.


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The following calculations are used for cumulative weighing (dry weights, no split):


• Percent_Finer(n) = 1 — percent(nfinal)


Example:

We are doing a cumulative calculation, no split, no moisture content, with the following settings:


Wt_Total_ Spec

Wt_Sieving_ Tare_Coarse

61.78 20.2

The resulting Wt_Passing_Split_Sieve is 52.94, and the Percent_Finer values are as shown in the second column from the right in the table.

Entered in SV READINGS Calculated

Sieve Size Soil_Tare


net soil wt

percent(n) Percent_ Finer

Wt_Passing_ Split_Sieve

#20 20.2 20.2 0 0.00% 100.00%

#30 22.45 20.2 2.25 3.64% 96.36%

#50 24.07 20.2 3.87 6.26% 93.74%

#100 25.65 20.2 5.45 8.82% 91.18%

#200 29.04 20.2 8.84 14.31% 85.69%

total_sieved 8.84

Wt_Total_Spec 61.78

Wt_Passing_Split_Sieve 52.94 52.94


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Scenario 4: Dry total weight supplied, split sieving, incremental weighing

You can split the test specimen into coarse and fine fractions. This is commonly done when the soil has a large gravel fraction. The entire coarse fraction, and a portion of the fine fraction, are sieved. That is, the total sample is sieved through successive sieves until the one designated as the “split sieve” is used (designated in gINT using Size_Split_Sieve, entered in mm). The fraction passing this sieve is not passed through subsequent sieves in its entirety. Instead, a much smaller fraction called the “fines fraction”, designated in gINT as Wt_Fines_Tested, is removed and sieved through the fine sieves.

Data entry is required in the following fields in the SIEVE parent record for split sieving (using dry weights): Wt_Total_Spec, Wt_Fines_Tested, Size_Split_Sieve, Weighing_Method, Wt_Sieving_Tare_Coarse, and Wt_Sieving_Tare_Fine. Dry weights are entered in the Soil_Tare field in child SV READINGS records. Percent_Finer values are calculated in the child records, and Wt_Passing_Split_Sieve is calculated in the parent.

The following calculations are used for split sieving using dry weights (incremental method):




for coarse fractions;

and: [ Soil_Tare(n)— Wt_Sieving_Tare_Fine ] x Wt_Passing_Split_Sieve

percent(n) =

Wt_Fines_Tested x Wt_Total_Spec

for fine fractions.


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Example:

We are doing a split sieve calculation, dry weights only, incremental method, with the following:


Wt_Total_ Spec

Wt_Fines_ Tested

Size_Split_ Sieve


Wt_Sieving_ Tare_Fine

502.6 170 4.75 28.3 18.4

The resulting Wt_Passing_Split_Sieve is 261.2, and the Percent_Finer values are as shown in the right column of the table.

Entered in SV READINGS Entered in SIEVE Calculated

Sieve Size Soil

_Tare

Wt_ Sieving_

Tare_ Coarse

Wt_ Sieving_

Tare_ Fine

net soil wt percent(n)

Percent_Finer

% of tot fines

3" 28.3 28.3 0.00 0.00% 100.00%

1-1/2" 67.6 28.3 39.30 7.82% 92.18%

3/4" 67.9 28.3 39.60 7.88% 84.30%

3/8" 123.4 28.3 95.10 18.92% 65.38%

#4 (4.75) 95.7 28.3 67.40 13.41% 51.97%

#8 50.8 18.4 32.40 9.90% 42.06% 19.06%

#16 40.2 18.4 21.80 6.66% 35.40% 12.82%

#30 35.2 18.4 16.80 5.14% 30.26% 9.88%

#50 31.8 18.4 13.40 4.10% 26.17% 7.88%

#100 25.9 18.4 7.50 2.29% 23.88% 4.41%

#200 22.6 18.4 4.20 1.28% 22.59% 2.47%

coarse sieved 241.40

Wt_Total_Spec 502.6

Wt_Passing_Split_Sieve

261.20 22.59%


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Hydrometer Analysis

Percent Finer

Percent finer for each readings row is calculated by first correcting the hydrometer reading: by deducting the composite correction, then by multiplying the result by a specific gravity correction factor. The corrected hydrometer reading is divided by the weight of soil represented by the soil in the hydrometer (weight of soil in hydrometer / percent of original specimen). In other words, since the soil in the hydrometer test is a fraction of the original specimen (the percent passing the finest sieve, such as #40 or #200), this soil’s mass is converted from its mass in the hydrometer to its extrapolated mass in the total specimen. The corrected hydrometer reading is then divided by this value to obtain the percent finer for the reading.

• spec_grav_correction from Specific_Gravity

spec_grav_correction = 1 + (0.2 x (2.65 — Specific_Gravity))

(see Day p. 59, equation 4.3)

Example:

Entered in HYDROMETER Record

Calculated

Specific_ Gravity spec. gravity correction

2.75 0.98

2.67 0.996

• Percent_Finer from Hydrometer_Reading, composite_correction and spec_grav_correction

corrected_hydr_reading x Percent_Of_Total Percent_Finer =

Wt_Dry_Specimen

(see Day p. 59, equation 4.4)

where: corrected_hydr_reading = (Hydrometer_Reading — composite_correction) x spec_grav_correction


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Example:

Entered in HYDROMETER Record

Wt_Dry_ Specimen

Percent_Of_ Total

Specific_ Gravity

Test_ Temperature

_Units

Calibration_ Slope

Calibration_ Intercept

52.5 75.35 2.67 C -0.3816289 13.15383

Entered in HYD READINGS Calculated

Time Hydrometer_ Reading

Temperature composite correction

reading less CC

spec. gravity correction

Percent_ Finer

2 39.8 22 4.76 35.04 0.996 50.09

5 37.9 22 4.76 33.14 0.996 47.38

15 34.1 22 4.76 29.34 0.996 41.94

30 33 22.1 4.72 28.28 0.996 40.43

60 31.1 22.3 4.64 26.46 0.996 37.82

240 27 23.5 4.19 22.81 0.996 32.61

1440 21.9 22.1 4.72 17.18 0.996 24.56

Particle Size

Particle size for each readings row is computed from the effective depth of the hydrometer, and the time in minutes, using Stoke’s law. Effective depth is the distance from the surface of the solution to the level at which the density of solution is being measured by the hydrometer. Stoke’s law takes the square root of the ratio of effective depth to time, and multiplies it by a soil viscosity correction factor to derive the particle size in mm.

• effective_depth, from Hydrometer_Reading

Hydrometer_Readingeffective_depth = 16.3 x ( 1 —

100 )

(see Day, p.60, equation 4.7)

Example:


Time Hydrometer_ Reading effective_depth

2 39.8 9.8126

5 37.9 10.1223

15 34.1 10.7417


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• viscosity_correction, from Temperature and Specific_Gravity

(13 + (0.15 x (24.0 - Temperature)) + (4 x (2.65 - Specific_Gravity))) viscosity_correction =

1000

(See Day, p. 60, equation 14.6)

Example:

Entered in HYDROMETER

Entered in HYD READINGS

Calculated

Specific_ Gravity Temperature viscosity correction factor

2.67 22.1 0.013205

2.67 22.3 0.013175

• Particle_Size, from Time, effective_depth, and viscosity_correction

effective_depth 0.05 Particle_Size = viscosity_correction x ( Time )

(see Day, p. 60, equation 4.5)

Example:


Time Hydrometer_Reading

Temp-erature

viscosity correction factor

effective depth Particle_ Size

2 39.8 22 0.01322 9.8126 0.029283

5 37.9 22 0.01322 10.1223 0.01881

15 34.1 22 0.01322 10.7417 0.011187


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Fine Specific Gravity

The only meaningful scenario is the one in which the Specific_Gravity in the parent FINE SG record is computed by calculating the individual Specific_Gravity values in the child FINE SG READINGS records from weight and temperature values, then averaged to create the value in the parent.

• FINE SG READINGS Specific_Gravity from Wt_Bottle_Water, Wt_Bottle_Water_Soil, Wt_Dry_Soil_Tare, Wt_Tare and Temperature:

dry_mass x temp_correction_factor Specific_Gravity =

dry mass — (Wt_Bottle_Water_Soil — Wt_Bottle_Water)

(see Day, p 36. equation 3.5)

where dry_mass = (Wt_Dry_Soil_Tare — Wt_Tare)

and temp_correction_factor is a lookup from the following table (from ASTM D854):

Temp, oC temp_ correction_

factor

16 1.0007

18 1.0004

20 1.0000

22 0.9996

24 0.9991

26 0.9986

28 0.9980

30 0.9974


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Example:

Entered in FINE SG

Depth (ft)

Readings Temperature

Units

1 C

Entered in FINE SG READINGS Calculated

Wt_ Bottle_ Water

Wt_ Bottle_ Water_

Soil

Wt_Dry_ Soil_Tare

Wt_Tare Temper-ature

Net Wt. Soil

temp_ correction_

factor

Corrected Dry Mass

Specific_ Gravity

500 600 160.64 0 19 160.64 1.0000 160.64 2.649077

550 655 178.5 10 22 168.5 0.9996 168.43 2.652482

500 600 160.64 0 18 160.64 1.0004 160.70 2.650136

550 655 178.5 10 21 168.5 1.0000 168.50 2.653543


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Compaction


Water_Content can be calculated from the following:

• From WC_Wt_Wet, WC_Wt_Dry and WC_Wt_Tare as follows:

(WC_Wt_Wet - WC_Wt_Dry) Water_Content =


Example:

Entered in COMP READINGS Calculated

WC_Wt_Wet WC_Wt_Dry WC_Wt_Tare Water_Content

70.2 65.4 4.7 7.91%

• From Wet_Density and Dry_Density as follows:

(Wet_Density - Dry_Density) Water_Content =

Dry_Density

Example:

Entered in COMP READINGS

Calculated

Wet_Density Dry_Density Water_Content

123.36 114.31 7.91%

• From Dry_Density and source fields for Wet_Density (Wt_Soil_Mold, Mold_Weight and Mold_Volume)

(see “Wet_Density Calculations,” below)


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Wet Density Calculations

Wet_Density (also known as total unit weight or wet unit weight) can be calculated from the following:

• From Wt_Soil_Mold, Mold_Weight and Mold_Volume as follows:

Wt_Soil_Mold - Mold_Weight Wet_Density =

Mold_Volume

Example:


Entered in COMPACTION Calculated

Wt_Soil_Mold Mold_Weight Mold_Volume Volume Units Wet_Density

9.312 5.2 0.0333333 ft 123.36

• From Water_Content and Dry_Density as follows:

Wet_Density = (Water_Content + 1) x Dry_Density

Example:


Calculated

Dry_Density Water_Content Wet_Density

114.32 7.91% 123.36


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Dry Density Calculations

Dry_Density (also known as dry unit weight) can be calculated from the following:

• From Water_Content and Wet_Density as follows:

Wet_Density Dry_Density =

(Water_Content + 1)

Example:

Entered in COMP READINGS Calculated

Water_Content Wet_Density Dry_Density

31.32% 119.5 90.999

• From Water_Content and Wet_Density’s source fields (Wt_Soil_Mold, Mold_Weight and Mold_Volume)

(see “Wet Density Calculations,” above)

• From Wet_Density and Water_Content’s source fields (WC_Wt_Wet, WC_Wt_Dry and WC_Wt_Tare)

(see “Water Content Calculations,” above)

Optional Calculation of Maximum Dry Density and Optimum Moisture Content

By default, Max_Dry_Density and Opt_Moisture_Content (Optimium Water Content) fields in the COMPACTION table are not calculated by gINT from the data in the COMP READINGS table. This is because the computation methodology for these values is subject to user discretion, and gINT typically does not interpret data. However, you can add a checkbox field to COMPACTION that will cause the values entered in these two fields are to be calculated automatically when unchecked, using the cubic spline interpolation method of curve fitting. When checked, the default behavior is performed, namely, any values directly entered in these two fields is left intact following saves.

To set up optional calculation of Max_Dry_Density and Opt_Moisture_Content using cubic spline curve fitting, add the following field to the COMPACTION table in DATA DESIGN:

Name Type

Do Not Calc Max Opt Boolean

Be sure to create the field name exactly as written above.

After creating this field in DATA DESIGN, automatic calculation will occur in INPUT for COMPACTION rows that have this field unchecked. If the field doesn't exist, or it exists and is checked, the program will not perform the calculation, allowing you to insert whatever values you wish.


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Disclaimer: Soil testing results, especially compaction tests, are open to interpretation. The automatic calculation methodology in gINT, if you activate it, may not be correct in the judgment of persons reviewing the work. It is your responsibility to double-check the results and make adjustments if you deem them necessary.

The calculation uses the Cubic Spline vs. Independent Axis (unadjusted) curve fitting method. Therefore, at least three points are required. If the fit fails for any reason, a message box will appear informing you that it could be not done. Note that this algorithm bases its results only on the data in the COMP READINGS table, and there is no accounting for rock correction or additional plot points that you may have added.

Note also that the calculated results using this method may or may not match the curve-fitting algorithm used to generate the curve(s) in the COMPACTION and COMPACTION (MULTIPLE CURVES) graphs in your library. Lab testing libraries created by gINT Software will typically specify this method, which appears as the ‘Cubic Spline vs Ind (unadjusted)’ selection in the Graph Line Option property of the Data Representation tab in the report properties for the graph in REPORT DESIGN. However, you may find it worthwhile to verify that this method is indeed specified in the report designs for your graphs, and change it if it isn’t.


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Unconfined Compression

Strain (UNC READINGS)

During the shearing of the soil specimen, the height deflection of the compressing platen is recorded for each reading. The observed value of height deflection of the compressing platen is recorded as Deflection_Reading, in units specified in Deflection_Units in the parent record. In the first UNC READINGS row, this value is assumed to be the starting value of the gauge, and later UNC READINGS rows deduct the initial value from their own deflection readings when Strain is computed.

If the Deflection_Units are inches, Deflection_Reading values are converted to mm before calculating, since Height is in mm. Also, since Strain is expressed as a percentage, the system must multiply the ratio by 100.

• Strain from Deflection_Reading and Height

( Deflection_Reading(n) — Deflection_Reading(1) ) x units_conversion x 100 Strain(n) =

Height

where units_conversion = 1 if Deflection_Units = mm units_conversion = 2.65 if Deflection_Units = inches

Example:

Entered in UNC READINGS Calculated

Deflection_ Reading (in)

Deflection Reading

(mm) Strain ratio

Strain %

0.2 5.08 0.000000 0.0000

0.22 5.588 0.003333 0.3333

0.24 6.096 0.006667 0.6667

0.26 6.604 0.010000 1.0000

0.29 7.366 0.015000 1.5000

0.32 8.128 0.020000 2.0000

0.361 9.1694 0.026833 2.6833


21


Stress (UNC READINGS) -- single load ring

• Stress from Load_Reading, Strain, Slope_Initial and Diameter (single load ring)

( Load_Reading(n) — Load_Reading(1) ) x Slope_Initial x π x (Diameter/2)2 Stress(n) =

1 — Strain/100

Example:

Entered in UNCONF COMPR Calculated

Slope_Initial Deflection_Units Stress_Area Diameter Height area, sq

mm area, sq ft

0.29843 I Ft 63.5 152.4 3166.922 0.03409


Load_ Reading

Deflection Reading

Strain %

Load_Reading less initial

load, less

initial Stress

100 0.2 0.00000 0 0.000 0.000

276 0.22 0.33333 176 52.524 1535.669

409 0.24 0.66667 309 92.215 2687.129

482 0.26 1.00000 382 114.000 3310.805

512 0.29 1.50000 412 122.953 3552.782

540 0.32 2.00000 440 131.309 3774.973

566 0.361 2.68333 466 139.068 3970.162


22


Stress (UNC READINGS) -- dual load ring

• Stress for ( Load_Reading(n) — Load_Reading(1) ) ≤ Slope_Break

As long as the stress for a reading is below the Slope_Break value, the calculations are the same as for a single load ring.

( Load_Reading(n) — Load_Reading(1) ) x Slope_Initial x π x (Diameter/2)2 Stress(n) =

1 — Strain/100

• Stress for ( Load_Reading(n) — Load_Reading(1) ) > Slope_Break

If the stress for a reading exceeds the Slope_Break, the Slope_2ndary field is brought into the stress calculation.

[( Load_Reading(n) — Load_Reading(1) ) x Slope_2ndary + intcpt_2nd] x π x (Diameter/2)2 Stress(n) =

1 — Strain/100

where intcpt_2nd = Slope_Break x (Slope_Initial — Slope_2ndary)

Example:

Entered in UNCONF COMPR

Slope_Initial Slope_Break Slope_2ndary Deflection_Units Stress_Area Diameter Height

0.29843 382 0.75229 I Ft 63.5 152.4


Load_ Reading Strain Load_Reading less initial load

area, sq mm

area, sq ft Stress

100 0.00000 0 0 3166.92 0.03409 0.000

276 0.33333 176 52.52368 3166.92 0.03409 1535.669

409 0.66667 309 92.21487 3166.92 0.03409 2687.129

482 1.00000 382 114.00026 3166.92 0.03409 3310.805

512 1.50000 412 136.56896 3166.92 0.03409 3946.216

540 2.00000 440 157.63308 3166.92 0.03409 4531.751

566 2.68333 466 177.19262 3166.92 0.03409 5058.543


23


Strain and Stress with Seating Correction

With a non-zero Seating_Correction value, the Seating_Correction is deducted from each Strain value.

( Deflection_Reading(n) — Deflection_Reading(1) ) x units_conversion x 100 Strain(n) =

Height — Seating_

Correction

Note that this also changes the calculated Stress values, since Strain is used in obtaining the corrected area from the measured area.

Example (same as single-ring Stress above, but with Seating_Correction = 0.2:

Entered in UNCONF COMPR Calculated

Slope_Initial Deflection_ Units

Stress_ Area

Seating_ Correction Diameter Height

area, sq mm

area, sq ft

0.29843 I Ft 0.2 63.5 152.4 3166.922 0.03409


Load_ Reading Strain, no correction

Strain with

correction Load_Reading

less initial load Stress

100 0.00000 0.00000 0 0.000 0.000

276 0.33333 0.13333 176 52.524 1538.751

409 0.66667 0.46667 309 92.215 2692.540

482 1.00000 0.80000 382 114.000 3317.494

512 1.50000 1.30000 412 122.953 3559.995

540 2.00000 1.80000 440 131.309 3782.677

566 2.68333 2.48333 466 139.068 3978.321


24


Consolidation

• Strain from Cumulative_Deflection and Height

Cumulative_Deflection(n) x units_conversion x 100 Strain(n) =

Height

where units_conversion = 1 if Deflection_Units = mm units_conversion = 2.65 if Deflection_Units = inches

Example:

Entered in CONSOLIDATION

Deflection_Units Diameter Height

I 63.5 25.4

Entered in CONSOL READINGS Calculated

Stress Cummulative_

Deflection Deflection Readg mm

Strain Ratio Strain %

150 0.0017 0.04318 0.0017 0.17

300 0.0029 0.07366 0.0029 0.29

550 0.005 0.127 0.005 0.5

1100 0.012 0.3048 0.012 1.2

2200 0.0291 0.73914 0.0291 2.91

300 0.0121 0.30734 0.0121 1.21

2200 0.0309 0.78486 0.0309 3.09

4400 0.0663 1.68402 0.0663 6.63

8800 0.1427 3.62458 0.1427 14.27

2200 0.1245 3.1623 0.1245 12.45

300 0.0938 2.38252 0.0938 9.38

150 0.073 1.8542 0.073 7.3

Direct Shear

Calculated Cohesion and Calculated Friction Angle are calculated as the intercept and slope (respectively) of the best fit line between the (Normal Stress, Failure Stress) coordinate pairs in the readings records. Calculation of this line and its resulting intercept and slope are beyond the scope of this manual.


25


Falling Head Permeability


Refer to “Water Content / Density” on page 1—the calculations are the same.

Permeability, with Constant Temperature less than or equal 20° C

Σ(1 to n)Permeabilityn Permeabilityavg =

n

where:

Burette_Area x (Height + Chg_in_Ht) Headinit Permeabilityn =

sample_area x Timen x Ln(

Headn ) x temp_correction

sample area = π x (Diameter/2)2

1301 ( 998.333 + (8.1855 x (Tempn-20))+ (0.00585 x (Tempn-20)2)

) — 1.30233 temp _correction =

10

(Tempn values are in °C)

Example:

Entered in FALL HEAD K Calculated

K_Units_ Factor

Initial_ Head

Burette_ Area mm2

Diameter mm

sample area mm2

K_ Calculated

1 52.4 125 61.72 2991.863 3.22E-04

Entered in FHK READINGS Calculated

Time (min)

Head (mm) Temp

temp correction permeability

corrected permeability

K x units factor

35 51.8 18 1.053263291 3.53E-04 3.72E-04 3.72E-04

140 50.2 18 1.053263291 3.29E-04 3.46E-04 3.46E-04

220 49.4 18 1.053263291 2.88E-04 3.03E-04 3.03E-04

350 47.4 18 1.053263291 3.08E-04 3.24E-04 3.24E-04

500 45.7 18 1.053263291 2.94E-04 3.09E-04 3.09E-04

1385 37.3 18 1.053263291 2.64E-04 2.78E-04 2.78E-04


26


Permeability, with Constant Temperature greater than 20° C


n

where:



Headn ) x temp_correction


1.372 x (20 - Tempn) — 0.001053 x (Tempn - 20)2 ( Tempn + 105

) temp _correction = 1.002 x 10


Example:


K_Units_ Factor

Initial_ Head

Burette_ Area mm2

Diameter mm

sample area mm2

K_ Calculated

1 52.4 125 61.72 2991.863 2.79E-04


Time (min)

Head (mm) Temp



K x units factor

35 51.8 24 0.90822715 3.53E-04 3.21E-04 3.21E-04

140 50.2 24 0.90822715 3.29E-04 2.99E-04 2.99E-04

220 49.4 24 0.90822715 2.88E-04 2.61E-04 2.61E-04

350 47.4 24 0.90822715 3.08E-04 2.79E-04 2.79E-04

500 45.7 24 0.90822715 2.94E-04 2.67E-04 2.67E-04

1385 37.3 24 0.90822715 2.64E-04 2.39E-04 2.39E-04


27



28

Permeability, with Variable Temperature during the Test


n

where:



Headn ) x temp_correctionn


1301

= ( 998.333 + (8.1855 x (WtAvTempn-20))+ (0.00585 x (WtAvTempn-20)2) ) — 1.30233

temp _correctionn (for Tempn <=20) 10

1.372 x (20 - WtAvTempn) — 0.001053 x (WtAvTempn - 20)2

= ( WtAvTempn + 105 ) temp

_correctionn (for Tempn >20) 1.002 x 10

Σ(1 to n)[(Timen — Timen-1) x Tempn] WtAvTempn =

Timen


Example:


K_Units_ Factor

Initial_ Head

Burette_ Area mm2

Diameter mm

sample area mm2

K_ Calculated

1 52.4 125 61.72 2991.863 3.11E-04


Time (min)

Head (mm) Temp

Temperature Weighted



K x units factor

35 51.8 18 18 1.05326329 3.53E-04 3.72E-04 3.72E-04

140 50.2 19 18.75 1.02708855 3.29E-04 3.38E-04 3.38E-04

220 49.4 20 19.2045 1.00194155 2.88E-04 2.88E-04 2.88E-04

350 47.4 21 19.8714 0.97717079 3.08E-04 3.01E-04 3.01E-04

500 45.7 22 20.51 0.95329707 2.94E-04 2.80E-04 2.80E-04

1385 37.3 21 20.8231 0.97717079 2.64E-04 2.58E-04 2.58E-04


Appendix A -- Scenarios using Wet Specimens in Sieve Analysis The Sieve Analysis section of this user guide explains the data entry and calculations for four scenarios involving only the entry of dry total weights. However, the software also supports calculations that compensate for moisture content. This can be performed for an unsplit specimen, for the coarse fraction of a split specimen but not the fine, or both the coarse and fine fractions of a split specimen. Also, in the circumstance where the coarse fraction is sieved wet and wet weights are supplied in the child SV READINGS records, gINT can compensate for this.

Scenario 5: Wet specimen, no split, incremental weighing

To utilize a wet total weight in an unsplit specimen requires the use of three additional fields: WC_Wt_Wet_Coarse (Water Content Coarse Wet Wt+Tare), WC_Wt_Dry_Coarse (Water Content Coarse Dry Wt+Tare), and WC_Wt_Tare_Coarse (Water Content Coarse Wt Tare). The principle is that some portion of the soil sample is set aside for moisture content testing. The weighing dish is weighed to establish the tare value, and the moist sample on the dish is weighed to establish the wet weight with tare. The sample is heated to vaporize the moisture, and it is re-weighed. The difference between the wet and dry weights is the weight of the moisture lost, and the ratio of the lost moisture to the weight of the dry sample is the moisture content percentage (saved in the parent record as Water_Content_Coarse). This percentage can then be used to convert dry Soil_Tare weights into equivalent wet weights for calculation of Percent_Finer values.

Note that for unsplit samples, the “coarse” moisture content fields are used, and the “fine” are ignored. Also note that the assumption in this scenario is that the specimen is dried before sieving, so all Soil_Tare values are dry weights.

The following calculations are used for wet total weight with no split:

• Water_Content_Coarse = wt_water / wt_dry_soil

where: wt_water = WC_Wt_Wet_Coarse — WC_Wt_Dry_Coarse

wt_dry_soil = WC_Wt_Dry_Coarse — WC_Wt_Tare_Coarse



where: [ Soil_Tare(n)— Wt_Sieving_Tare_Coarse ] x (1 + Water_Content_Coarse)

percent(n) =

Wt_Total_Spec

Example:

We are doing an incremental calculation, no split, with moisture content, with:

ο Wt_Total_Spec = 1504

ο Wt_Sieving_Tare_Coarse = 18.4


29


ο WC_Wt_Wet_Coarse = 129

ο WC_Wt_Dry_Coarse = 100

ο WC_Wt_Tare_Coarse = 16.1

ο Soil_Tare values as shown in the second column of the table below.

The resulting Wt_Passing_Split_Sieve is 241.78, the Water_Content_Coarse is 34.56%, and the Percent_Finer values are as shown in the right column of the table.

Soil_Tare (entered)

Wt_Sieving_ Tare_Coarse (entered)

net dry soil wt (calc) add wc

net wet soil wt (calc)

percent(n) (calc)

Percent_ Finer (calc)

#4 220 18.4 201.6 69.68 271.28 18.04% 81.96%

#30 225 18.4 206.6 71.41 278.01 18.48% 63.48%

#50 225 18.4 206.6 71.41 278.01 18.48% 44.99%

#100 230 18.4 211.6 73.14 284.74 18.93% 26.06%

#200 130 18.4 111.6 38.57 150.17 9.99% 16.08%

total sieved 938.00 1262.22

total specimen 1504 0.00 1504.00

wt passing split sieve

241.78 16.08%

Scenario 6: Wet specimen, split sieve

To utilize a wet split specimen requires the use of six additional fields (beyond the ones necessary for a dry split specimen):

• WC_Wt_Wet_Coarse (Water Content Coarse Wet Wt+Tare)

• WC_Wt_Dry_Coarse (Water Content Coarse Dry Wt+Tare)

• WC_Wt_Tare_Coarse (Water Content Coarse Wt Tare)

• WC_Wt_Wet_Fine (Water Content Fine Wet Wt+Tare)

• WC_Wt_Dry_Fine (Water Content Fine Dry Wt+Tare)

• WC_Wt_Tare_Fine (Water Content Fine Wt Tare)

The assumption in this scenario is that the specimen is dried before sieving, so all Soil_Tare values are dry weights.


30


The following calculations are used for wet total weight with split sieving:

• Water_Content_Coarse = wt_water / wt_dry_soil

where: wt_water = WC_Wt_Wet_Coarse — WC_Wt_Dry_Coarse

wt_dry_soil = WC_Wt_Dry_Coarse — WC_Wt_Tare_Coarse

• Water_Content_Fine = wt_water / wt_dry_soil

where: wt_water = WC_Wt_Wet_Fine — WC_Wt_Dry_Fine

wt_dry_soil = WC_Wt_Dry_Fine — WC_Wt_Tare_Fine


• Wt_Passing_Split_Sieve = Wt_Total_Spec — coarse_sieved

where: coarse_sieved = SUMcoarse1..coarseN[ Soil_Tare(n) — Wt_Sieving_Tare_Coarse ]


where: [ Soil_Tare(n)— Wt_Sieving_Tare_Coarse ] x (1 + Water_Content_Coarse)

percent(n) =

Wt_Total_Spec

for coarse fractions;

and: percent(n) =

[ Soil_Tare(n)— Wt_Sieving_Tare_Fine ] x Wt_Passing_Split_Sieve x (1 + Water_Content_Fine)

Wt_Fines_Tested x Wt_Total_Spec

for fine fractions.

Example:

We are doing an incremental calculation, split sieving, with moisture content, with:

ο Wt_Total_Spec = 5201.4

ο Wt_Fines_Tested = 175

ο Size_Split_Sieve = 4.75

ο Wt_Sieving_Tare_Coarse = 28.3

ο Wt_Sieving_Tare_Fine = 18.4

ο WC_Wt_Wet_Coarse = 520.3

ο WC_Wt_Dry_Coarse = 495.8

ο WC_Wt_Tare_Coarse = 14.8

ο WC_Wt_Wet_Fine = 122.6

ο WC_Wt_Dry_Fine = 106.9

ο WC_Wt_Tare_Fine = 13.8


31



32

ο Soil_Tare values as shown in the second column of the table below.

The resulting Wt_Passing_Split_Sieve is 4805.2, the Water_Content_Coarse is 5.09%, the Water_Content_Fine is 16.86%, and the Percent_Finer values are as shown in the right column of the table.

Soil_Tare (entered)

Wt_Sieving_ Tare_Coarse (entered)

net dry soil wt (calc) add wc

net wet soil wt (calc)

percent(n) (calc)

Percent_ Finer (calc)

3" 28.3 28.3 0 0.00 0.00 0.00% 100.00%

1-1/2" 128.4 28.3 100.1 5.10 105.20 2.02% 97.98%

3/4" 142.7 28.3 114.4 5.83 120.23 2.31% 95.67%

3/8" 123.4 28.3 95.1 4.84 99.94 1.92% 93.74%

#4 95.7 28.3 67.4 3.43 70.83 1.36% 92.38%

#8 50.8 18.4 32.4 5.46 37.86 19.99% 72.39%

#16 40.2 18.4 21.8 3.68 25.48 13.45% 58.95%

#30 35.2 18.4 16.8 2.83 19.63 10.36% 48.58%

#50 31.8 18.4 13.4 2.26 15.66 8.27% 40.31%

#100 25.9 18.4 7.5 1.26 8.76 4.63% 35.69%

#200 22.6 18.4 4.2 0.71 4.91 2.59% 33.10%

total sieved 377.00 396.20

total specimen 5201.4

wt passing splt sv 4805.20 33.10%

Scenario 7: Wet specimen, coarse fraction sieved wet

If you sieve the coarse fraction wet, you can have gINT adjust the wet weights you enter so that the final calculations for Wt_Passing_Split_Sieve and the Percent_Finer values are corrected for the moisture content. To accomplish this, check the Coarse_Sieved_Wet checkbox in the parent record. Normally this box is unchecked. Note that gINT assumes that the fine fraction is always sieved dry, so wet sieving of the dry fraction is not offered as an option.

An example and equations are not provided here for this option.

gint technical bulletin: equations used in lab testing · scenario 4: casagrande liquid limit, with...

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