base pressure redistribution - teng
TRANSCRIPT
per cent of the applied contact pressure. These lines of equal pressure arebulb shaped and consequently are called pressure bulbs. The most commonlyused pressure bulb is the one for 0.2q because in practical cases any stressless than 0.2q is often of little consequence. For circular and square footingsthe pressure bulb is about 1.5B wide and 1.5B deep, B being the width ofthe footing.
The computation of vertical pressure by tl:J.eBoussinesq's equation is alaborious procedure and suitable only for research works. In practice agraphical solution by the Newmark influence chart, Fig. 6-11, is used. Thesolution is simple, expeditious and can be best illustrated by an example. In
this example it is desired to determine the vert-ical pressure at a depth of 10 ft below point xdue to a uniform contact pressure q = 4500 psffrom a footing shown in Fig. 6-12. The firststep is to draw a plan of the footing and the.location of point x on a transparent paper insuch a scale that the distance AB shown onthe influence chart is equal to the depth 10 ft.Then place the plan on top of the influencechart, so that point x lies at the origin of thechart, and count the number of influence areasoccupied by the footing. An influence area isan individual area bounded by two adjacentstraight lines and two adjacent arcs. The vert-ical pressure at a depth of 10ft below point xis equal to the number of influence areas (78)
times the intensity of footing pressure (4500) times the influence valve (0.001)which equals 350 psf.
Both the Boussinesq's equation and the Newmark influence chart areintended for the case of surface loading. If they are used for computingstresses in the soil due to a deep foundation, the computed stress would begreater than the actual value.
6.8 Settlement of Footings
Footings on granular soils will not suffer detrimental settlement if tpesmaller value of the two allowable pressures given by Eqs. (6-1) and (6-2) isused. Footings on stiff clay, hard clay, and other firm soils generally requireno settlement analysis if the design provides a minimum factor of safety of 3.Soft clay, compressible silt, and other weak soils will settle even undermoderate pressure, and therefore settlement analysis is necessary.
The total settlement of a footing on clay may be considered to consist ofthree parts (Skempton and Bjerrum, 1957): -
.-'
--.128 SPREAD FOOTINGS'
B' x 6' footino
/Point Kof
Fig.6-12 Example illustrating theuse of the Newmark influencechart.
..;<1-".-:'
CHAP. 6 "'"SEC.6-8 SETILEMENT OF FOOTINGS 129
S = s, + Sc + S$
where S = total settlement,
S, = immediateelastic settlement,
Sc = settlementdue to consolidationof clay,
S$= settlementdue to secondaryconsolidationof clay.
(6-6)
1. lmmediate settlement. Immediately upon application of load on thefooting, elastic compression of the underlying soil takes place causing asettlement of the footing. This amount can be computed by elastic theory.However, it is usually very small and can be neglected for all practicalpurposes.
1.21
1.0'
~ 0.81Z =thickness of clay layeri3 = widthof continuousfooting
""0.2tL- -' - - ~ Continuous'footing- Circular footing
o (,2
Pore pressurecoefficient
Fig. 6-13 Coefficient f3for computing consolid-ation settlement. FromSkempton and Bjerrum.
~oJ!'"
~;g.g ~~ .~..~~~ a~ ~;g~ ~9~~~ §~ ~~~ ~u
J ~ 8o !!o
2. Settlement due to consolidation. The settlement caused by consolidationis due to the slow extrusion of water from the pores of the fine particles ofclay. The amount of final consoli~ation settlement Sc can be calculated bythe following equation:
Sc = SofJ (6-7)
wherep = the coefficient depending on the geometry of the footing and theloading history of the clay. Values of fJ are shown in Fig. 6-13.
- ..
130 SPREAD FOOTINGS CHAP. 6SEC. 6-9 ECCENTRIC LOADING 131
So = settlement calculated by Terzaghi theory of consolidation;
= m. iJpH
Cc H I Po + iJp'= - Og101 + eo Po
where m. = coefficient of volume compressibility of the clay. This value isdeterminedby consolidationtest. .
Jp = vertical stress due to load on footing.
H = thickness of the compressible clay. The clay thickness should bedivided into several layers to obtain reasonably accuratesettlement of a thick layer.
Cc = compression index, also determined by consolidation test.
Po = vertical effective pressure due to soil overburden.
The computation of settlement due to consolidation is illustrated in thedesign example, sheet 2 DE 6.
(6-8)
(3-4)
where q = contact pressure at a given point (x, y);, Q = vertical load ;
A = area of footing;
x and y = coordinates of the point at which the contact pressure iscalculated;
Mx, My = load Q multiplied by eccentricity parallel to x and y axes,respectively;
Ix, Iy = moment of inertia of the footing area about the x and y axes,respectively.
Equation (6-9) is valid when one of the following conditions exists:
(a) The footing is symmetrical about x and y axes.
(b) The footing is symmetrical about x axis and ey = O.
(c) The footing is symmetrical about y axis and ex = O.
For rectangular footings, Eq. (6-9) may be written in a simpler form:
3. Settlement due to secondary consolidation. When an undisturbed soilsample is tested in the consolidometer (Oi' oedometer) the rate of volumedecrease checks very closely with the theory. However, when the sample isone hundred per cent consolidated (according to the theory of consolidation)the volume decrease does not stop according to the theory, but instead thesample continues to compress at a reduced and rather constant rate. Theamount of consolidation that can be computed by the theory is calledprimary consolidation; whereas the slow consolidation that takes placeafterwards is called secondary consolidation, Sec. 3-5.
q = Q (1 :f: 6~ :I::~ )A L B (6-9a)
6-9 Eccentric Loading
Eccentric loading may result from a load applied off the center of thefooting or from a concentric load plus a bending moment. For the purpose ofdetermining the pressure under the footing the moment may be removed byshifting the vertical load to a fictitious location with an eccentricitye = momentJverticalload. In the analysis of an eccentrically loaded footingtwo separate problems are confronted: .
1. For the purpose of structural design, the pressure against the bottom ofthe footing, commonly called contact pressure, is assumed to have a planardistribution. When the load is applied within the kern of the footing area,common flexural formulae ar?"applicable. . .
Q :I:: Mx Myq=- -x+-yA Iy Ix
(6-9)
When ex, ey or eb' el exceed a certain limit, Eq. (6-9) or (6-9a) gives anegative value of q which indicates tension between the soil and bottom offooting. Unless the footing is weighted down by surcharge loads, the soilcannot be relied upon for bonding to the footing and offering tensile resis-tance. Therefore, the flexural formulae Eq. (6-9) and (6-9a) are applicableonly when the load is applied within a limited area which is known as thekern and is shown shaded in Fig. 6-14(a). The proc;:~g,urefor determinationof soil pressure when the load is applied outside the kern is simple in principlebut laborious. Cases for rectangular and Circillar footings have been workedout andlni'kerns are shown by shaded areas in Fig. 6-14 [(a) and (c)]. Forfootings of other shapes, the graphical method of successivetrials is probablythe simplest for practical 'solutions (Roark, 1954).
The graphical method, similar to any other method, is based on theassumption that the pressure varies linearly with the distance to the neutralaxis from zero at the neutral axis to a maximum at the most remote point andon the requirement of statical equilibrium that the resultant of the soilpressure should lie on the line of action of the applied load Q. The procedureis as follows. Draw a trial neutral axis N-N, Fig. 6-14(b) and a line abperpendicular to N-N, starting from point b which is most remote. The areabetween point band N-N is under compression while the area on the otherside of N-N is unstressed. The intensity of stress at a given point varies in simpleproportion with its perpendicular distance from N-N. The compression areais divided into several narrow strips of uniform width dy, running parallel to
'"' .
132 SPREAD FOOTINGS
B ---,
r
CHAP. 6
For II:!; % q=i(1:!:61J
For II> % q"",,=H3:~6,J
q i .. 0 at a distance ofmn 3(f-e} from
edge of footing
L
1/'i-e
(a) Rectangular footing, load onone of the center lines of footing.
wV
~qmo'
Fore:$i~4 q =~[1:!:4fJ
}
, .A =1T,2
qmo,=k%Fore>14
Nqb
(b) General procedure.
~
tl,:(
k values are tabulated below /
'I, = 0.25 0.30 0.35 0040 0045 0.50 0.55 0.60 0.6~ 0.70 0.75 0.80 0.90k =2.00 2.20 2.43 2.70 3.10 3.55 4.22 4.92 5.90 7.20 9.20 13.0 80.0
i
(c) Circul~r footing.
Fig. 6-14 Pressure distribution used for stcuctural design of eccentrically loaded footings.
-'- .
SEC. 6-9 ECCENTRIC LOADING 133
0.5
0.1 I 10.2 0.3 .p.4
Valuesof etlL =longitudinal eccentricity/length of footingSolid curves give values of K
Ma~imum pressure Pma." K~Q/ BL
Q= concentrated load on footing
0.5
[f$fca: I
B eb mo,e p" Q
I """ 8L(1+6ez/L+6~
)
~L~' B
Casem P
~ ~D 1m";. D",LU+2R+3R2)
~ t ~1 4(t+R+R2)1- eb - e =-..!f. A= MU+R+R2+R3)
I t 4U+R+R2)I--L--J R=N/MP" 60
~G """ LM(1+R+R2)P"""
r- G H Case IVB ebL "e ~
L IP ..~L I . mo, 8GH
Case D
~ """
~ eb PII\CII-KQ/BLB ';'et
~ '.J I x and y fromchart~~(d) Rectangular footing, double eccentricity.
'0...
?;':Q
Nt--JC '1 I 1..
I"g
....'0'..
.. ...2
~--
134 SPREAD FOOTINGS CHAP. 6
N-N. The unit pressure acting on this strip is equal to (Y/ X)qb, where qbis theunit pressure at point b, and the total pressure is equal to (Y/ X)qbldy. Thetotal pressure may be represented by the shaded strip with a length of (Y/ X)l.This shaded strip, if under a uniform pressure qb, carries the same load asthe whole strip under the actual pressure (Y/ X)qb' Therefore, it may becalled a transformed strip. All the transformed strips form a transformedarea. If the location of the trial neutral axis N-N is correct, the centroid ofthe transformed area will coincide with the point of action of the load Q.For practical purposes, the centroid or center of gravity of the transformedarea may be determined by cutting out a cardboard of the same shape andbalancing the board on a pencil point. The cardboard will balance only whenit is supported on the center of gravity. Severa.!such trials will enable theengineer to approach the'correct location of the neutral axis.
2. For determination of ultimate or allowable bearing capacity of aneccentrically loaded footing, the concept of useful width has been introduced.By this concept, the portion of the footing which is symmetrical about theload is considered useful and the other portion is simply assumed superfluousfor the convenience of computation. If the eccentricities are e, and eb, asshown in Fig. 6-15, the useful widths are B - 2eb and L - 2e/, the equiv-alent area (B - 2eb)(L - 2e,) is considered as subjected to a central loadfor determination of bearing capacity. .
eb f-lb
2u.2c:~u".....II:
LLL~:~ Eccentricity ratio e/B
fig. 6-'5 Useful widths for deter-mination of bearing capacity of .
eccentrically loaded footing oncohesivesoils. .
fig. 6-16 Bearing capacity ofeccentrically loaded footing. AfterAREA.
The concept above simply means that the bearing capacity of a footingoel..cc;lseslinearly with the eccentricity of load, as is shown by a straight linein Fig. 6-16. In cohesive soils, this linear relationship prevails, but in granularsoils,however,the reductionisparabolicra~herthan linear,(Meyerhof,1953).
....
-1
r
-~-
SEC. 6-10 INCLINED LOAD 135
Therefore, the reduction factor shown in Fig. 6-16 should be used for designpurposes: First the bearing capacity of the footing is determined on the basisthat the load is applied at the centroid of the footing. Then, this bearingcapacity is corrected by multiplying with the factor shown in Fig. 6-16.
6-10 InclinedLoad
The conventionalmethod of stability analysis of footings subjectedtoinclined loads is as follows: the inclinedload Q is resolvedinto a verticalcomponent Qv and a horizontal component QH' The stability of the footingagainst ultimate failure under.the vertical load is treated by the same principlesfor footings subjected to vertical Joad only, and the effect of the horizontalcomponent is ignored. Then, the stability of the footing against the horizontalforce is analysed by calculating the factor of safety against sliding which isdefined as the ratio between the total horizontal resistance and the horizontalforce. The total horizontal resistance in general consists of a passive resis-tance of soil, Pp,and a frictional resistance R, Fig. 6-17. The value of Ppcan be
.., 2cr-
H
l pp~"",D;"'-"."'~' :~:::~::'.~ ::. ~I-ppH j R=?~..~)-
N = total vertical force acting on thebase of footing
Foetor of safety against sliding = Pp -;: + R
lP___ _
-! 2c T yH I+- f?;:c ~ footing area
Granular soils Cohesive soils
The values above may be used in small jobs. Backfill must be well compacted to insure the designpassive pressure
fig. 6-'7 Conventional method of analysis of footings subjected toinclined loads.
determined by the principles discussed in Chapter 4. However, for smallerprojects, conservative values such as those shown in the figure may be used.It should be emphasized that high values of passive earth pressure Ppmay notbe realized in granular soils unless it is backfilled and wellcompacted in layers.
Pp psf Coel. ofType of Soil dry or Friction,
submerged moist f
Sand and/or grovel 210 350 0.55with less than 5% silt
Sand and/or grovel :80 250 0.45with 5% or more silt
Sill or soils containing 120 150 0.35more than 30% silt
Cohesive UnitType of Soil Strength Weight, (
c=psf pcfVery soft 200 110
cloy
Soft cloy 400 120
Medium,stiff, and 600 125hard cloy
1134 SPREAD FOOTINGS CHAP. 6
N-N. The unit pressure acting on this strip is equal to (Y/ X)qb, where qbis theunit pressure at point b, and the total pressure is equal to (Y/ X)qbldy. Thetotal pressure may be represented by the shaded strip with a length of (Y/ X)l.This shaded strip, if under a uniform pressure qb' carries the same load asthe whole strip under the actual pressure (Y/ X)qb' Therefore, it may becalled a transformed strip. All the transformed strips form a transformedarea. If the location of the trial neutral axis N-N is correct, the centroid ofthe transformed area will coincide with the point of action of the load Q.For practical purposes, the centroid or center of gravity of the transformedarea may be determined by cutting out a cardboard of the same shape andbalancing the board on a pencil point. The cardboard will balance only whenit is supported on the center of gravity. Several such trials will enable theengineer to approach the .correct location of the' neutral axis.
2. For determination of ultimate or allowable bearing capacity of aneccentricalIy loaded footing, the concept of useful width has been introduced.By this concept, the portion of the footing which is symmetrical about theload is considered useful and the other portion is simply assumed superfluousfor the convenience of computation. If the eccentricities are e/ and eb' asshown in Fig. 6-15, the useful widths are B - 2eband L - 2e" the equiv-alent area (B - 2eb)(L - 2e/) is considered as subjected to a central loadfor determination of bearing capacity.
Fig.6-15 Useful widths for deter-mination of bearing capacity of .
eccentrically loaded footing oncohesivesoils.
c:~u'"..,..0::
Eccentricity ratio e/B
Fig. 6-16 Bearing capacity ofeccentrically loaded footing. AfterAREA.
The concept above simply means that the bearing capacity of a footingoel.reJses linearly with the eccentricity of load, as is shown by a straight linein Fig. 6-16. In cohesive soils, this linear relationship prevails, but in granularsoils,however,the reductionisparabolicra~herthan linear,(Meyerhof,1953).
.,\,
-1
- - ._,~.
SEC.6-10 INCLINEDLOAD 135
Therefore, the reduction factor shown in Fig. 6-16 should be used for designpurposes: First the bearing capacity of the footing is determined on the basisthat the load is applied at the centroid of the footing. Then, this bearingcapacity is corrected by multiplying with the factor shown in Fig. 6-16.
6-10 Inclined Load
The conventional method of stability analysis of footings subjected toinclined loads is as folIows: the inclined load Q is resolved into a verticalcomponent Q. and a horizontal component QH' The stability of the footingagainst ultimate failure under the vertical load is treated by the same principlesfor footings subjected to vertical :oad only, and the effect of the horizontalcomponent is ignored. Then, the stability of the footing against the horizontalforce is analysed by calculating the factor of safety against sliding which isdefined as the ratio between the total horizontal resistance and the horizontalforce. The total horizontal resistance in general consists of a passive resis-tance of soil, Pp,and a frictional resistance R, Fig. 6-17. The value of Ppcan be
2cr-
H
1 Pp~:..:.:: :..":~p ., :o':.~'~.:':..." ~I-ppH-j R=.,~. '-1,oh'-
N = total vertical force acting on thebase of footing
Factor of safety against sliding = Pp-:;+R
lP--I 2~ 1" i:' I-- fi';: C x looting area
Granular soils Cohesive soils
The values above may be used in small jobs. Backfill must be well compacted to insure the designpassive pressure
r
Fig. 6-17 Conventional method of analysis of footings subjected toinclined loads.
determined by the principles discussed in Chapter 4. However, for smalIerprojects, conservative values such as those shown in the figure may be used.It should be emphasized that high values of passive earth pressure Ppmay notbe realized in granular soils unless it is backfilIed and welIcompacted in layers.
Pp psi Coel. ofType of Soil dry or Friction,
submerged moist tSand and/or gravel 210 350 0.55
with less than 5% silt
Sand and/or gravel !80 250 0.45with 5% or mare silt
Silt or soils containing 120 150 0.35more than 30% silt
Cohesive UnitType of Soil Strength Weight, r
c=psf pcfVery soft 200 110
clay
Soft clay 400 120
Medium,stiff, and 600 125hard clay
SPREAD FOOTINGS CHAP. 6
tf
0° 5° 10° 15° 20° 25° 30° 35° 40° 45°300200
1001
~.c 50'0co
~.. 20
i7
~..
0,
~I-B: J
(Area=A)
0,+NhOh I~ =Nec+Nq)'D+ zN,yB
0h cannot exceed Q,tan 1>
c " cohesion
</>"angle of internalfriction'h
.0.3 0.4 0.5 0.6 0.7 o.e 0.9 1.0
tan </>
FI,.6-18 General formula for bearing 'capacity of continuous footingsubjected to inclined load. After N. Janbu.
r::ffr-' Q ~ Q
DaD1-- r 4.:
!-B-I B'Y~!!!- Rq fl-R q a:B-1 B-1q " ultimate (or allowable) bearing capacity of horizontal footing
under vertical load
RI " reduction factor, see charts below
co'50.4"'0i£
0.2
o o 20 40 60 eo 90InclinationaO of load to vertical
"inclinationof foundationtohorizontal
After G. G. Meyerhof
(b)
From AREA
(a)
Fig. 6-19 Bearing capacity of footing subjected to inclined load: (a)horizontal foundation; (b) inclined foundation (after G. G. Meyerhofand AREA). .
1
SEC. 6-12 UPUFT OF FOOTINGS 137
Research in soil mechanics has extended the bearing capacity theory intothe case of inclined loading (Meyerhof, 1953; Janbu, 1957). Janbu's analysisis a direct extension of Terzaghi theory with a factor Nh in addition to theTerzaghi bearing capacity factors Ne, Ny, and'Nq.
1Q + NhQh - N c + N YD + - NyyB- e q 2A (6-10)
The notations and values of Ne, Nq, Ny, and Nh are shown in Fig. 6-18.Meyerhof has calculated ultimate bearing capacity of footings subjected to
inclined loading and published the results in graphical form. They have beenconstructed in convenient charts shown in Fig. 6-19. The load is assumed toapply vertically and the bearing capacity is determined by the normal pro-cedure. Then it is corrected by the factor Ri shown in Fig. 6-19.
6-11 Footingson Slopes
The bearingcapacityof footingson slopingground maybe determinedbythe followingequation (Meyerhof,1957):
q = cNcq+ tYBNyq . (6-11)
The values of the bearing capacity factors Neqand Nyqfor continuous footingsare shown in Fig. 6-20. These factors vary with the slope of the ground, therelative position of the footing and the angle of internal friction of the soil.
Before construction of footings on sloping ground, the stability of the slopeitself must be investigated. Footings should not be constructed on slopeswhich are unstable. They should also be avoided on slopes where slow creepof the superficial material takes place. The stability of a stable slope may beendangered by the addition of footings.
6-12 Uplift of Footings
The resistance of a footing against uplift is derived from the weight of thefooting and the weight of soil above it. For soil below ground water level thesubmerged weight should be used.
As a footing is being uplifted, a prism of soil is carried by the footing,Fig. 6-21(a). The shape of the prism depends upon the characteristics of soilabove the footing. Due to lack of conclusive data, no rational design ruleshave been developed. However, conventional method assuming a 60 degreeprism, Fig. 6-21(a) may lead to unsafe results. For footings subjected to asmall uplift, the method shown in Fig. 6-21(b) may be used. If a large numberof footings are subjected to high uplift forces, some model tests or full-sizedfield pull-out tests may be economically justified.
r ~
138 SPREAD FOOTINGS
Both cases:
q =cNcq+O.5yB N1'IStability foetor:
N. = yH/cc = cohesionr = unit weight of soil
Linear interpretation forintermediate depths:
D/B =0; solid linesD/B =I; dash lines
caseftD .
~
..&
CHAP. 6
600
500~ "
" .,~
400 '\ ,,
~''r;::
6-13 StructuralDesignof Footings
In practiceall individualand wall footingsate designedon the assumptionthat the distributionof the soil pressure against the bottom of the footing isstraight-line or planar. When the load is applied at the centroid of the
j1
-
SEC. 6-13 STRUCTURAL DESIGN 0'F Foo11NGS 139
footing area, the unit pressure is equal to the total load divided by thefooting area. In case of eccentric load, the pressure may be calculated by theprocedure described in Sec. 6-9.
--j;
Plitlcapacity= W+ F
F F=Pof (granular soils)= cA (cohesive soils)
W = weight of soil plus footingF = friction or cohesion
''':'':'9 Varies with type and. characteristics of soil.
Conventional assumption of6 .. 60. may be unsafe insome cases
(b)
Po = total horiz. earth pressure atrest acting on the entirevertical surface
= 0.4 x unit wt of soilf = coeff. of friction
= 0.35 - 0.55c = cohesion = 200-600P"A = total vertical surface above
perimeter of footing
FI,; 6-21 Uplift capacity of footing: (a) probable uplift capacity; (b)minimum theoretical uplift.
(0)
By far the majority of footings are constructed of concrete, and .the designof such footings should follow the concrete codes.* The design criteria usedin the current American practice are shown in Fig. 6-22.
If a pedestal is so proportioned that its height is at least equal to twice itswidth beyond the face of column, Fig. 6-23, the critical sections for computingbending, bond, and shear stresses are as shown in Fig. 6-22, and there is noneed to analyse the stresses in the pedestal. For pedestals having smallerdepth/width ratio, the stresses in the pedestal must be ana lysed. The analysisma.y be made on the assumption that the bond stress along the entire em-bedment of dowels below the top of the pedestal is uniformly distributed.Based on this assumption, the total stress acting on the bottom of the pedestalis equal to the total stress in the concrete of the column plus the amount ofstress in the column vertical reinforcement transmitted through bond withinthe depth of the pedestal. Fig. 6-23 illustrates .the stresses acting on eachelement of the footing.
The members in a steel grillage are designed as cantilever beams subjectedto uniformly distributed soil pressure.
* American Concrete Institute, American Association of State Highway Officials,American Railroad Engineers Association, Canadian National Code, British Code ofPractice, or the local building codes.
SPREAD FOOTINGS
Total pressureacting on this
area is resistedby section b-b
b~
Bose It
CHAP. 6
b"4
Masonry wall
a
(0)
~t" "3 clear
(b)
Fig. 6-22 Criteria for design of concrete footings: (a) critical section(a-a) and load area for computing bond and bending stresses; (b) criticalsection (b-b)and load area for computing shear stress. "
Fi:=total stress onconcrete in thecolumn
T1Lp L
~F
!:eF=Fc+F'LFs = total stress in vertical bars
of the column
Lp =height at pedestalL =length of bar embeddment
fir. 6.23 Stresses in pedestaled footings.
+
\,
I
A
r
SEC. 6-14 FIXITY OF COLUMN BASE AND ROTATION OF FOOTING 141
6-/4 Fixity of Column Base and Rotation of Footing
The engineer is sometimes confronted with the question of whether thecolumn bases should be fixed or free to rotate. At other times he is compelledto design the footings for a central load and a moment, and for a limitedamount of rotation. Therefore an understanding of the rotation characteris-tics of the column base and the footing is essential.
When the lower end of a column is subjected to a bendin~ m~~.~!!h thejoint between the column and the footing must be strong-enough to transferthe stresses. In the case of concrete columns, this can be readily done byembedding the dowels in the footing, and the column may be considered fullyfixed to the footing. The lower end of steel ~olumns may.J?~Lfix,~.Q.J9-1be.footings by meanu)Lanchor bolts. Wfieilihe 'anchor:bQit~ ~~e.r~ql,l
-7~
SPREAD FOOTINGS CHAP.6 SEC. 6-15 CONSTRUCTION 143
following analysis. The toe of the footing will probably not settle more thanthe amount 81which is the average settlement if the entire footing is subjectedto the maximum toe pressure; the heel of the footing probably not more thanthe amount 82 which is the average settlement if the entire footing is sub-jected to the minimum pressure at the heel. The maximum and minimumpressures are computed on the assumption of straight line or planar distribu-tion. The probable amount of rotation, therefore, is equal to or less than(81 - 8.;) divided by the width (or length) of the footing.
must be simple and expeditious. The soil conditions should be inspectedafter the excavation but before concreting. For clays or clayey soils, soilsamples may be taken by a,hand aug~.!:.orshovei, and the approximate strengthmaybe determined'by a simple portable unconfined compression tester or by apocket siie penetrometer. In most cases, the shear strength can be estimatedby the simple thumb test described in Table 1-2, Sec. I-8A.
For sand or gravel, some simple penetration tests may be used for com-parison of soil density at various locations. The penetration test may besimply the counting of blows required to drive a certain size reinforcing rodwith a specific weight dropping a given height. (For example i in. diain roddriven by a 7 lb hammer falling 18 in.). Such tests should be,made first atlocations where the soil density (and consequently the bearing capacity) is
, known from the soil borings or tests, and the results should be used as abasis for comparison. If further tests made at any other footing locationsencounter smaller resistance, the adequacy of the soil for sustaining thedesign pressure must be carefully investigated by more accurate tests or loadbearing t:sts.
6-15 Construction
Footings are the simplest type of foundation in so far as the constructionprocedure is concerned. In addition to the normal exercise of precautionthere are relatively few points that require special attention, namely: theinspection of subsoil conditions, the relative depth of footings, and the de-watering of the excavation when necessary.
The construction of footings for buildings is usually started after thegeneral grading work is completed at which time the ground is leveled to an-elevation at, or 6 in. below; the bottom of the lowest floor slab. ,!~en the-a~~!is excavated by simple or power operated hand tools. The bottom of theexcavation is ,carefully excavated to the required depih, the form work forthe sides of footing is placed and held by stakes, and the reinforcemeni -isplaced on cement block supports (and high chairs if top bars are used)~Before placing the concret;:, anchor bolts or column dowels must be accuratelysecured on the form work. Short and straight dowels of small diameter may'be placed by hand immediately after the concrete is poured. The form workfor the sides may not be necessary and the ~oncrete may be poured againstthe vertical sides of the excavation if the soil does not slough in.
A. Inspection of subsoil conditions. Natural soil deposits are seldom trulyuniform. An apparently uniform soil stratum often contains pockets orlenses of material having somewhat different engineering properties. It isimpractical and almost impossible to ascertain the soil condition under eachfooting by ordinary soil boring program. Therefore, it is the responsibilityof the engineer to evaluate the average soil condition based on the soil boringresults, and often he has to make conservative generalizations. Before thefoundation is finally constructed, he must check the actual conditions in thefield. If the soil conditions at certain footin 10 II.!' are not as good as he
i!~~~U.W~~, the footing m'ust e either lowered to a stratum having s~fficicjCbearing power or enlarged to reduce the pressure to suit the bearing.cap.!lciJyof the soil. The choice between these two methods depends upon the relativeeconomy, the time, or other factors involved.
'The method for checking the soil conditions at the footing excavations
B. Relative depth of footings. Any adjacent footings should not be con-structed at such different levels that the construction of the lower footingwould. disturb the soil supporting the upper footing, and that the pressurefrom the upper footing would n<?tintroduce undue additional stress to thesoil under the lower footing. This difficulty is generally avoided by keepingthe difference in footing elevations not greater than one-half the clear distancebetween the footings. For this reason it is always a good practice to constructthe lower footings first, and when necessary to construct the lower fo<;>tingata greater depth than contemplated, the elevation of the upper footing can beadjusted accordingly.
Sometimes the adjacent footings must be constructed at largely differentlevels, for example, when a new basement is constructed adjacent to footingsunder an existing first floor. Sheeting may be used to retain the adjacentground when excavation is made. ,
The problem of footings at two different levels is illustrated in Fig. 6-24where a wall footing at the first floor adjoins a basement wall. It is the com-monpractice to l0wer the first floor footing in gradual steps down to thelevel of the basement footing as shown in Fig. 6-24(a). By so doing thenatural state of the subsoil is considered unaltered. An al~ernativemethod isshown in Fig. 6-24(b). In order to construct the basement, an excavationlarger than the basement floor must be made. After the basement wall ismatured, the overexcavated area is backfilled with suitable soil. If theoriginal soil is sand or gravel, and the backfill consists of the same materialwhich is compacted in layers (6 to 9 in.) to a density equal to or greater thanthat of the original soil, the footing at the first floor may'be supported on the
144 SPREAD FOOTINGS CHAP. 6
"-Wall-.. "--Wall......
(a) (b)
Fir. 6-24 Wall footings at different levels.
backfill. If there is any doubt of the bearing capacity of the backfill, thewall footing should be stepped down as shown in fig. 6-24(a) or else the wallitself should be designed to span between the basement wall and a point onthe original ground at several feet from the excavation line.
C. Dewatering. The excavation should be kept dry during the constructionperiod because free water is objectionable for several reasons. In clay orclayey soils, free water tends to soften the upper portion of the soil andcauses settlement of footings. The soil conditions under water cannot bereadily inspected. Excavation in water is expensive and not satisfactory.Furthermore, the quality of concrete placed in water is questionable, particu-larly when the water is not stagnant.
To avoid the difficulties mentioned above, excavations below groundwater level are kept dry by various methods discussed in Chapter 5.
6-16 Design Example
On sheet 1, Plate DE 6, the column loads, walls loads, floor loads, andpertinent soil data are shown. On the right-hand side of the soil profile,results of the standard penetration tests are shown for the granular soils, andthe unconfined compression strength qu' natural void ratio eo,and compres-sion index Cc for the soft clay are also indicated.- The water level was 25 ftbelow the finished grade.
The first step was to determine the bearing capacity of the upper sandlayer. The N value was adjusted in accordance with Eq. (2-1). Because theadjusted value exceeds 2 times the test value (N') a reduction factor of 2 wasused. This gives N = 28.
The stress on the layer of loose sand was analysed by the approximatemethod discussed in Sec. 6-7.
The total settlement of the footings consisted of three components, namelythe settlement due to each of the three layers of soil above the hardpan. Thehardpan itself contributes practically no settlement, as indicated by the localexperience. The bedrock lies immediately under the hardpan.
II;
..-j
SEC. 6-16 DESIGN EXAMPLE 145
According to Eq. (6-2) the medium-dense sand layer will settle 1 in. at apressure q2 = 8600 Ib per sq ft. Since an allowable value of 5000 Ib per sqft was used in design, the approximate settlement is equal to 5000/8600 =0.58 in. The same procedure is used for settlemenl calculation for the loosesand layer. The consolidation settlement of the soft clay was computed byEq. (3-4), with the values of eoand Cc determined by laboratory tests.
144 SPREAD FOOTINGS CHAP. 6
~WolI-.. ~-WolI......
(0) (b)
FI,. 6-24 Wall footings at different levels.
backfill. If there is any doubt of the bearing capacity of the backfill, thewall footing should be stepped down as shown in fig. 6-24(a) or else the wallitself should be designed to span between the basement wall and a point onthe original ground at several feet from the excavation line.
C. Dewatering. The excavation should be kept dry during the constructionperiod because free water is objectionable for several reasons. In clay orclayey soils, free water tends to soften the upper portion of the soil andcauses settlement of footings. The soil conditions under water cannot bereadily inspected. Excavation in water is expensive and not satisfactory.Furthermore, the quality of concrete placed in water is questionable, particu-larly when the water is not stagnant.
To avoid the difficulties mentioned above, excavations below groundwater level are kept dry by various methods discussed in Chapter 5.
6-16 Design Example
On sheet 1, Plate DE 6, the column loads, walls loads, floor loads, andpertinent soil data are shown. On the right-hand side of the soil profile,results of the standard penetration tests are shown for the granular soils, andthe unconfined compression strength qu' natural void ratio eo,and compres-sion index Cc for the soft clay are also indicated.- The water level was 25 ftbelow the finished grade.
The first step was to determine the bearing capacity of the upper sandlayer. The N value was adjusted in accordance with Eq. (2-1). Because theadjusted value exceeds 2 times the test value (N') a reduction factor of 2 wasused. This gives N = 28.
The stress on the layer of loose sand was analysed by the approximatemethod discussed in Sec. 6-7.
The total settlement of the footings consisted of three components, namelythe settlement due to each of the three layers of soil above the hardpan. Thehardpan itself contributes practically no settlement, as indicated by the localexperience. The bedrock lies immediately under the hardpan.
III: ..I~
..j
.'
SEC. 6-16 DESIGN EXAMPLE 14S
According to Eq. (6-2) the medium-dense sand layer will settle 1 in. at apressure q2 = 8600 lb per sq ft. Since an allowable value of 5000 lb per sqft was used in design, the approximate settlement is equal to 5000/8600 =0.58 in. The same procedure is used for settlemeni calculation for the loosesand layer. The consolidation settlement of the soft clay was computed byEq. (3-4), with the values of eoand Cc determined by laboratory tests.