CHAPTER 13 SHALLOW FOUNDATION II: SAFE BEARING PRESSURE AND SETTLEMENT CALCULATION
13.1
INTRODUCTION
Allowable and Safe Bearing Pressures
The methods of calculating the ultimate bearing capacity of soil have been discussed at length in Chapter 12. The theories used in that chapter are based on shear failure criteria. They do not indicate the settlement that a footing may undergo under the ultimate loading conditions. From the known ultimate bearing capacity obtained from any one of the theories, the allowable bearing pressure can be obtained by applying a suitable factor of safety to the ultimate value. When we design a foundation, we must see that the structure is safe on two counts. They are, 1. The supporting soil should be safe from shear failure due to the loads imposed on it by the superstructure, 2. The settlement of the foundation should be within permissible limits. Hence, we have to deal with two types of bearing pressures. They are, 1. A pressure that is safe from shear failure criteria, 2. A pressure that is safe from settlement criteria. For the sake of convenience, let us call the first the allowable bearing pressure and the second the safe bearing pressure. In all our design, we use only the net bearing pressure and as such we call qna the net allowable bearing pressure and qs the net safe bearing pressure. In designing a foundation, we use 545
546
Chapter 13
the least of the two bearing pressures. In Chapter 12 we learnt that qna is obtained by applying a suitable factor of safety (normally 3) to the net ultimate bearing capacity of soil. In this chapter we will learn how to obtain qs. Even without knowing the values of qna and qs, it is possible to say from experience which of the two values should be used in design based upon the composition and density of soil and the size of the footing. The composition and density of the soil and the size of the footing decide the relative values of qna and qs. The ultimate bearing capacity of footings on sand increases with an increase in the width, and in the same way the settlement of the footing increases with increases in the width. In other words for a given settlement 5p the corresponding unit soil pressure decreases with an increase in the width of the footing. It is therefore, essential to consider that settlement will be the criterion for the design of footings in sand beyond a particular size. Experimental evidence indicates that for footings smaller than about 1.20 m, the allowable bearing pressure q is the criterion for the design of footings, whereas settlement is the criterion for footings greater than 1.2 m width. The bearing capacity of footings on clay is independent of the size of the footings and as such the unit bearing pressure remains theoretically constant in a particular environment. However, the settlement of the footing increases with an increase in the size. It is essential to take into consideration both the shear failure and the settlement criteria together to decide the safe bearing pressure. However, footings on stiff clay, hard clay, and other firm soils generally require no settlement analysis if the design provides a minimum factor of safety of 3 on the net ultimate bearing capacity of the soil. Soft clay, compressible silt, and other weak soils will settle even under moderate pressure and therefore settlement analysis is necessary. Effect of Settlement on the Structure If the structure as a whole settles uniformly into the ground there will not be any detrimental effect on the structure as such. The only effect it can have is on the service lines, such as water and sanitary pipe connections, telephone and electric cables etc. which can break if the settlement is considerable. Such uniform settlement is possible only if the subsoil is homogeneous and the load distribution is uniform. Buildings in Mexico City have undergone settlements as large as 2 m. However, the differential settlement if it exceeds the permissible limits will have a devastating effect on the structure. According to experience, the differential settlement between parts of a structure may not exceed 75 percent of the normal absolute settlement. The various ways by which differential settlements may occur in a structure are shown in Fig. 13.1. Table 13.1 gives the absolute and permissible differential settlements for various types of structures. Foundation settlements must be estimated with great care for buildings, bridges, towers, power plants and similar high cost structures. The settlements for structures such as fills, earthdams, levees, etc. can be estimated with a greater margin of error. Approaches for Determining the Net Safe Bearing Pressure Three approaches may be considered for determining the net safe bearing pressure of soil. They are, 1. Field plate load tests, 2. Charts, 3. Empirical equations.
Shallow Foundation II: Safe Bearing Pressure and Settlement Calculation
547
Original position of column base
Differential settlement
t ^— Relative rotation, /?
(a)
-Wall or panel •
Tension cracks
T
H
H
Tension cracks —'
I "— Relative deflection, A ^ Relative sag Deflection ratio = A/L
„ , ,. , Relative hog
(b)
Relative rotation, (c)
Figure 13.1
Definitions of differential settlement for framed and load-bearing wall structures (after Burland and Wroth, 1974)
Table 13.1 a Maximum settlements and differential settlements of buildings in cm. (After McDonald and Skempton, 1955) SI. no.
Criterion
Isolated foundations
Raft
1/300
1/300
Clays
4-5
4.5
Sands
3-25
3.25
Clays
7.5
10.0
Sands
5.0
6.25
1.
Angular distortion
2.
Greatest differential settlements
3.
Maximum Settlements
548
Chapter 13 Table 13.1b
Permissible settlements (1955, U.S.S.R. Building Code)
Sl.no. Type of building 1.
Average settlement (cm)
Building with plain brickwalls on continuous and separate foundations with wall length L to wall height H
LJH>2.5
7.5
LIH 5
0.0005L
0.0007L
3.
Water towers, silos etc.
0.004L
0.004L
4.
Slope of crane way as well as track 0.003L
0.003L
for bridge crane track
where, L = distance between two columns or parts of structure that settle different amounts, H = Height of wall.
13.2
FIELD PLATE LOAD TESTS
The plate load test is a semi-direct method to estimate the allowable bearing pressure of soil to induce a given amount of settlement. Plates, round or square, varying in size, from 30 to 60 cm and thickness of about 2.5 cm are employed for the test. The load on the plate is applied by making use of a hydraulic jack. The reaction of the jack load is taken by a cross beam or a steel truss anchored suitably at both the ends. The settlement of the plate is measured by a set of three dial gauges of sensitivity 0.02 mm placed 120° apart. The dial gauges are fixed to independent supports which remain undisturbed during the test. Figure 13.2a shows the arrangement for a plate load test. The method of performing the test is essentially as follows: 1. Excavate a pit of size not less than 4 to 5 times the size of the plate. The bottom of the pit should coincide with the level of the foundation. 2. If the water table is above the level of the foundation, pump out the water carefully and keep it at the level of the foundation. 3. A suitable size of plate is selected for the test. Normally a plate of size 30 cm is used in sandy soils and a larger size in clay soils. The ground should be levelled and the plate should be seated over the ground.
Shallow Foundation II: Safe Bearing Pressure and Settlement Calculation
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Top plan Figure 13.2a
Plate load test arrangement
A seating load of about 70 gm/cm2 is first applied and released after some time. A higher load is next placed on the plate and settlements are recorded by means of the dial gauges. Observations on every load increment shall be taken until the rate of settlement is less than 0.25 mm per hour. Load increments shall be approximately one-fifth of the estimated safe bearing capacity of the soil. The average of the settlements recorded by 2 or 3 dial gauges shall be taken as the settlement of the plate for each of the load increments. 5. The test should continue until a total settlement of 2.5 cm or the settlement at which the soil fails, whichever is earlier, is obtained. After the load is released, the elastic rebound of the soil should be recorded.
4.
From the test results, a load-settlement curve should be plotted as shown in Fig. 13.2b. The allowable pressure on a prototype foundation for an assumed settlement may be found by making use of the following equations suggested by Terzaghi and Peck (1948) for square footings in granular soils.
550
Chapter 13 Plate bearing pressure in kg/cm2 or T/m2 i \ qa = Net allowable pressure
Figure 13.2b
Load-settlement curve of a plate-load test
B Sf =S x —-
(IS.lb)
where
5, = permissible settlement of foundation in mm, S - settlement of plate in mm, B = size of foundation in meters, b = size of plate in meters. For a plate 1 ft square, Eq. (13.la) may be expressed as
iJ fr — 0p
(13.2)
in which S, and 5 are expressed in inches and B in feet. The permissible settlement 5, for a prototype foundation should be known. Normally a settlement of 2.5 cm is recommended. In Eqs (13.la) or (13.2) the values of 5, and b are known. The unknowns are 5 and B. The value of S for any assumed size B may be found from the equation. Using the plate load settlement curve Fig. 13.3 the value of the bearing pressure corresponding to the computed value of 5 is found. This bearing pressure is the safe bearing pressure for a given permissible settlement 5~ The principal shortcoming of this approach is the unreliability of the extrapolation of Eqs (13. la) or (13.2). Since a load test is of short duration, consolidation settlements cannot be predicted. The test gives the value of immediate settlement only. If the underlying soil is sandy in nature immediate settlement may be taken as the total settlement. If the soil is a clayey type, the immediate settlement is only a fraction of the total settlement. Load tests, therefore, do not have much significance in clayey soils to determine allowable pressure on the basis of a settlement criterion.
Shallow Foundation II: Safe Bearing Pressure and Settlement Calculation
Pistp inaH Flate load test
TLoadA qn per unit•* area ^ca
/
551
Foundation of building
I lJJJJlLLiJ \y/////////////////^^^^ Stiff clay
Pressure bulbs
Figure 13.2c
Soft clay
Plate load test on non-homogeneous soil
Plate load tests should be used with caution and the present practice is not to rely too much on this test. If the soil is not homogeneous to a great depth, plate load tests give very misleading results. Assume, as shown in Fig. 13.2c, two layers of soil. The top layer is stiff clay whereas the bottom layer is soft clay. The load test conducted near the surface of the ground measures the characteristics of the stiff clay but does not indicate the nature of the soft clay soil which is below. The actual foundation of a building however has a bulb of pressure which extends to a great depth into the poor soil which is highly compressible. Here the soil tested by the plate load test gives results which are highly on the unsafe side. A plate load test is not recommended in soils which are not homogeneous at least to a depth equal to \l/2 to 2 times the width of the prototype foundation. Plate load tests should not be relied on to determine the ultimate bearing capacity of sandy soils as the scale effect gives very misleading results. However, when the tests are carried on clay soils, the ultimate bearing capacity as determined by the test may be taken as equal to that of the foundation since the bearing capacity of clay is essentially independent of the footing size. Housel's (1929) Method of Determining Safe Bearing Pressure from Settlement Consideration The method suggested by Housel for determining the safe bearing pressure on settlement consideration is based on the following formula
O ^ = Ap m + Pp n
C13 3) \±~>.~> j
where Q = load applied on a given plate, A = contact area of plate, P = perimeter of plate, m = a constant corresponding to the bearing pressure, n - another constant corresponding to perimeter shear. Objective To determine the load (Xand the size of a foundation for a permissible settlement 5-.. Housel suggests two plate load tests with plates of different sizes, say Bl x B^ and B2 x B2 for this purpose.
552
Chapter 13
Procedure 1 . Two plate load tests are to be conducted at the foundation level of the prototype as per the procedure explained earlier. 2. Draw the load-settlement curves for each of the plate load tests. 3. Select the permissible settlement S,. for the foundation. 4. Determine the loads Q{ and Q2 from each of the curves for the given permissible settlement sf Now we may write the following equations Q\=mAP\+npP\
(13.4a)
for plate load test 1 . Q2=mAp2+nPp2
(13.4b)
for plate load test 2. The unknown values of m and n can be found by solving the above Eqs. (13.4a) and (13. 5b). The equation for a prototype foundation may be written as Qf=mAf+nPf
(13.5)
where A, = area of the foundation, />,= perimeter of the foundation. When A, and P,are known, the size of the foundation can be determined. Example 13.1 A plate load test using a plate of size 30 x 30 cm was carried out at the level of a prototype foundation. The soil at the site was cohesionless with the water table at great depth. The plate settled by 10 mm at a load intensity of 160 kN/m2. Determine the settlement of a square footing of size 2 x 2 m under the same load intensity. Solution The settlement of the foundation 5,,may be determined from Eq. (13. la).
=3a24mm Example 13.2 For Ex. 13.1 estimate the load intensity if the permissible settlement of the prototype foundation is limited to 40 mm. Solution In Ex. 13. 1, a load intensity of 160 kN/m2 induces a settlement of 30.24 mm. If we assume that the load-settlement is linear within a small range, we may write
Shallow Foundation II: Safe Bearing Pressure and Settlement Calculation
553
where, q{ = 160 kN/m2, S^ = 30.24 mm, S^ = 40 mm. Substituting the known values 40 q2 = 160 x —— = 211.64 kN/m 2
Example 13.3 Two plate load tests were conducted at the level of a prototype foundation in cohesionless soil close to each other. The following data are given: Size of plate 0.3 x 0.3 m 0.6 x 0.6 m
Load applied 30 kN 90 kN
Settlement recorded 25 mm 25 mm
If a footing is to carry a load of 1000 kN, determine the required size of the footing for the same settlement of 25 mm. Solution Use Eq. (13.3). For the two plate load tests we may write:
PLTl: Apl = 0.3 x 0.3 = 0.09m2 ; Ppl = 0.3 x 4 = 1.2m; Ql = 30 kN PLT2: Ap2 =0.6x0.6 = 0.36m2; Pp2 = 0.6 x 4 = 2.4m; Q2 = 90 kN Now we have 30 = 0.09m + 1.2n 90 = 0.36m + 2.4n On solving the equations we have m = 166.67, and n = 12.5 For prototype foundation, we may write Qf = 1 66.67 Af+ 12.5 Pf Assume the size of the footing as B x B, we have Af = B2, Pf = 4B, and Qf = 1000 kN
Substituting we have 1000 =166.67fl2 +505 or B2 +0.35-6 = 0 The solution gives B = 2.3 m. The size of the footing = 2.3 x 2.3 m.
554
13.3
Chapter 13
EFFECT OF SIZE OF FOOTINGS ON SETTLEMENT
Figure 13.3a gives typical load-settlement relationships for footings of different widths on the surface of a homogeneous sand deposit. It can be seen that the ultimate bearing capacities of the footings per unit area increase with the increase in the widths of the footings. However, for a given settlement 5, such as 25 mm, the soil pressure is greater for a footing of intermediate width Bb than for a large footing with BC. The pressures corresponding to the three widths intermediate, large and narrow, are indicated by points b, c and a respectively. The same data is used to plot Fig. 13.3b which shows the pressure per unit area corresponding to a given settlement 5j, as a function of the width of the footing. The soil pressure for settlement Sl increases for increasing width of the footing, if the footings are relatively small, reaches a maximum at an intermediate width, and then decreases gradually with increasing width. Although the relation shown in Fig. 13.3b is generally valid for the behavior of footings on sand, it is influenced by several factors including the relative density of sand, the depth at which the foundation is established, and the position of the water table. Furthermore, the shape of the curve suggests that for narrow footings small variations in the actual pressure, Fig. 13.3a, may lead to large variation in settlement and in some instances to settlements so large that the movement would be considered a bearing capacity failure. On the other hand, a small change in pressure on a wide footing has little influence on settlements as small as S { , and besides, the value of ql corresponding to Sj is far below that which produces a bearing capacity failure of the wide footing. For all practical purposes, the actual curve given in Fig. 13.3b can be replaced by an equivalent curve omn where om is the inclined part and mn the horizontal part. The horizontal portion of the curve indicates that the soil pressure corresponding to a settlement S{ is independent of the size of the footing. The inclined portion om indicates the pressure increasing with width for the same given settlement S{ up to the point m on the curve which is the limit for a bearing capacity Soil pressure, q
(a)
Given settlement, S\
Narrow footing
(b)
Width of footing, B
Figure 13.3
Load-settlement curves for footings of different sizes (Peck et al., 1974)
Shallow Foundation II: Safe Bearing Pressure and Settlement Calculation
555
failure. This means that the footings up to size Bl in Fig. 13. 3b should be checked for bearing capacity failure also while selecting a safe bearing pressure by settlement consideration. The position of the broken lines omn differs for different sand densities or in other words for different SPT N values. The soil pressure that produces a given settlement Sl on loose sand is obviously smaller than the soil pressure that produces the same settlement on a dense sand. Since N- value increases with density of sand, qs therefore increases with an increase in the value of N. 13.4
DESIGN CHARTS FROM SPT VALUES FOR FOOTINGS ON SAND
The methods suggested by Terzaghi et al., (1996) for estimating settlements and bearing pressures of footings founded on sand from SPT values are based on the findings of Burland and Burbidge (1985). The SPT values used are corrected to a standard energy ratio. The usual symbol Ncor is used in all the cases as the corrected value. Formulas for Settlement Calculations The following formulas were developed for computing settlements for square footings. For normally consolidated soils and gravels (13.6) cor
For preconsolidated sand and gravels for qs>pc
Sc=B°."-(qs-0.67pc)
(13.7a)
cor
—!± NIA cor
(I3.7b)
If the footing is established at a depth below the ground surface, the removal of the soil above the base level makes the sand below the base preconsolidated by excavation. Recompression is assumed for bearing pressures up to preconstruction effective vertical stress q'o at the base of the foundation. Thus, for sands normally consolidated with respect to the original ground surface and for values of qs greater than q'o, we have, for qs>q'0
Sc = B0'75-—(qs-Q.61q'0)
(13 8a)
™ cor
for qsq'o,
qs =16Q+Q.61q'o
(13.14a)
for qs1.2m
(13.17a) (13.17b)
DJ
An approximate formula for all widths qs=2.7qcRw2kPa where qc is the cone point resistance in kg/cm2 and qs in kPa. The above equations have been developed for a settlement of 25 mm.
(13.17c)
560
Chapter 13
Meyerhof (1956) developed his equations based on the relationship qc = 4Ncor kg/cm2 for penetration resistance in sand where Ncor is the corrected SPT value. Example 13.6 Refer to Example 13.4 and compute qs by modified (a) Teng's method, and (b) Meyerhof 's method. Solution
(a) Teng's equation (modified) — Eq. (13.16a)
if D ' where Rw2 = - ^1 +- j = 0.5 since Dw2 = 0
F,d, = \+—£- = 1 + B 4
=1.5
