B.E. FIFTH SEMESTER · 2019. 5. 26. · 9) Net safe bearing capacity (q ns):-The net safe bearing capacity is the net ultimate bearing capacity divided by a factor of safety F 10)

ANJUMAN COLLEGE OF ENGINEERING & TECHNOLOGY

MANGALWARI BAZAAR ROAD, SADAR, NAGPUR - 440001.

DEPARTMENT OF CIVIL ENGINEERING

Prof. Rashmi G. Bade, Department of Civil Engineering, Geotechnical Engineering – II 1

Geotechnical Engineering – II

B.E. FIFTH SEMESTER





UNIT – V

SHALLOW FOUNDATIONS:

Bearing capacity of soils : Terzagi‟s theory , its validity and limitations , bearing capacity factors ,

types of shear failure in foundation soil , effect of water table on bearing capacity factors , types of

shear failure in foundation soil , effect of water table on bearing capacity , correction factors for

shape and depth of footings. Bearing capacity estimation from N-value , factors affecting bearing

capacity , presumptive bearing capacity.

Settlement of shallow foundation : causes of settlement , elastic and consolidation settlement ,

differential settlement , control of excessive settlement. Proportioning the footing for equal

settlement . Plate load test : Procedure , interpretation for bearing capacity and settlement prediction.

(8)





INRODUCTION

It is the customary practice to regard a foundation as shallow if the depth of the foundation is less

than or equal to the width of the foundation. A foundation is an integral part of a structure. The

stability of a structure depends upon the stability of the supporting soil. Two important factors that

are to be considered are:-

1. The foundation must be stable against shear failure of the supporting soil.

2. The foundation must not settle beyond a tolerable limit to avoid damage to the structure.

Figure.1 Types of shallow foundations: (a) plain concrete foundation, (b) stepped reinforced

concrete foundation, (c) reinforced concrete rectangular foundation, and (d) reinforced concrete wall

foundation.

DEFINITIONS

1) Footing:- A footing is a portion of the foundation of a structure that transmits loads directly

to the soil.

2) Foundation: - A foundation is that part of he structure which is in direct contact with and

transmits loads to the ground.

3) Foundation soil: - It is the upper part of the earth mass carrying the load of the structure.





4) Bearing capacity: - The supporting power of a soil or rock is referred to as its bearing

capacity.

5) Gross pressure intensity (q):- The gross pressure intensity q is the total pressure at the base

of the footing due to the weight of the superstructure, self-weight of the footing and the

weight of the earth fill, if any.

6) Net pressure intensity (qn):- It is defined as the excess pressure, or the difference in

intensities of the gross pressure after the construction of the structure and the original

overburden pressure. Thus, if D is the depth of the footing

7) Ultimate bearing capacity (qf):- The ultimate bearing capacity is defined as the minimum

gross pressure intensity at the base of the foundation at which the soil fails in shear.

8) Net ultimate nearing capacity (qnf):- It is minimum net pressure intensity causing shear

failure of soil. The ultimate bearing capacity qf and the net ultimate capacity are evidently

connected by the following relation:

Where, σ is the effective surcharge at the base level of the foundation.

9) Net safe bearing capacity (qns):- The net safe bearing capacity is the net ultimate bearing

capacity divided by a factor of safety F

10) Safe bearing capacity (qs):- The maximum pressure which the soil can carry safely without

risk of shear failure is called the safe bearing capacity.

11) Allowable bearing capacity or pressure (qa):- It is the net loading intensity at which

neither the soil fails in shear nor there is excessive settlement detrimental to the structure.

BEARING CAPACITY OF SOILS: Terzagi’s theory, its validity and limitations

Terzaghi (1943) used the same form of equation as proposed by Prandtl (1921) and extended

his theory to take into account the weight of soil and the effect of soil above the base of the

foundation on the bearing capacity of soil. Terzaghi made the following assumptions for developing

an equation for determining qu for a c-Ф soil.

(1) The soil is semi-infinite, homogeneous and isotropic,

(2) the problem is two-dimensional,

(3) the base of the footing is rough,

(4) the failure is by general shear,

(5) the load is vertical and symmetrical,

(6) the ground surface is horizontal,

(7) the overburden pressure at foundation level is equivalent to a surcharge load q'0 = γDf where γ is

the effective unit weight of soil, and D the depth of foundation less than the width B of the

foundation,





(8) the principle of superposition is valid, and

(9) Coulomb's law is strictly valid, that is, σ = c + σ tan Ф.

Limitations:-

(1) As the soil compresses, Ф changes, slight downward movement of footing may not develop

the plastic zones.

(2) Error due to separate calculation of three component of Pp, and then their addition, although

their critical surfaces are not identical, is small and on the safe side.

(3) Error due to assumption that failure zones do not extend above horizontal plane through the

base of footing, increase with the depth of foundation, and hence the theory is suitable for

shallow foundation only.

Mechanism of Failure

The shapes of the failure surfaces under ultimate loading conditions are given in Fig. 2. The zones of

plastic equilibrium represented in this figure by the area gedcf may be subdivided into

1. Zone I of elastic equilibrium

2. Zones II of radial shear state

3. Zones III of Rankine passive state

When load qu per unit area acting on the base of the footing of width B with a rough

base is transmitted into the soil, the tendency of the soil located within zone I is to spread but this is

counteracted by friction and adhesion between the soil and the base of the footing. Due to the

existence of this resistance against lateral spreading, the soil located immediately beneath the base

remains permanently in a state of elastic equilibrium, and the soil located within this central Zone I

behaves as if it were a part of the footing and sinks with the footing under the superimposed load.

The depth of this wedge shaped body of soil abc remains practically unchanged, yet the footing

sinks. This process is only conceivable if the soil located just below point c moves vertically

downwards. This type of movement requires that the surface of sliding cd (Fig. 2) through point c

should start from a vertical tangent. The boundary be of the zone of radial shear bed (Zone II) is also

the surface of sliding. As per the theory of plasticity, the potential surfaces of sliding in an ideal

plastic material intersect each other in every point of the zone of plastic equilibrium at an angle (90°

- 0). Therefore the boundary be must rise at an angle Ф to the horizontal provided the friction and

adhesion between the soil and the base of the footing suffice to prevent a sliding motion at the base.

Figure. 2 General shear failure surface as assumed by Terzaghi for a strip footing.





The sinking of Zone I creates two zones of plastic equilibrium, II and III, on either side of the

footing. Zone II is the radial shear zone whose remote boundaries bd and a/meet the horizontal

surface at angles (45° - Ф/2), whereas Zone III is a passive Rankine zone. The boundaries de and fg

of these zones are straight lines and they meet the surface at angles of (45° - Ф/2). The curved parts

cd and cf in Zone II are parts of logarithmic spirals whose centers are located at b and a respectively.

TYPES OF SHEAR FAILURE

1) GENERAL SHEAR FAILURE: -

Fig.a shows a strip footing resting on the surface of a dense sand or a stiff clay. The figure

also shows the load settlement curve for the footing, where ‘q’ is the load per unit area and

‘s’ is the settlement. At a certain load intensity equal to qu, the settlement increases suddenly.

A shear failure occurs in the soil at that load and the failure surfaces extend to the ground

surface. This type of failure is known as general shear failure. A heave on the sides is always

observed in general shear failure.

2) LOCAL SHEAR FAILURE: -

Fig.b shows a strip footing resting on a medium dense sand or on a clay of medium

consistency. The figure also shows the load – settlement curve. When the load is equal to a

certain value . The foundation movement is accompanied by sudden jerks. The failure

surfaces gradually extend outwards from the foundation, as shown. However, a considerable

movement of the foundation is required for the failure surfaces to extend to the ground

surface (shown dotted). The load at which this happens is equal to qu, beyond this point, an

increase of load is accompanied by a large increase in settlement. This type of failure is

known as local shear failure. A heave is observed only when there is substantial vertical

settlement.

3) PUNCHING SHEAR FAILURE: -

Fig.c shows a strip footing resting on a loose sand or soft clay. In this case, the failure

surfaces do not extend up to the ground surface. There are jerks in foundation at a load of

. The footing fails at a load qu at which stage the load – settlement curve becomes steep

and practically linear. This type of failure is called the punching shear failure. No heave is

observed. There is only vertical movement of footing.





Figure. 3 Types of shear failure.

EFFECT OF WATER TABLE ON BEARING CAPACITY

When the water table is above the base of the footing, the

submerged weight γ’ should be used for the soil below the water table for computing the effective

pressure or the surcharge. When the water table is located somewhat below the base of the footing,

the elastic wedge is partly of moist soil and partly of submerged soil and a suitable reduction factor

should be used with the wedge term ½ γBNγ, since it uses effective unit weight.

CASE I : - Water table located above the base of footing





The effective surcharge is reduced as the effective weight below the water table is equal to the

submerged unit.

q = Dw γ + a γ’

where Dw = Depth of water table below the ground surface,

a = height of water table below the base of footing.

= Df – Dw

q = Dw γ + (Df – Dw) γ’

= γ’ Df + (γ – γ’) Dw

Therefore, ultimate bearing capacity is given by

CASE II : - Water table located at a depth ‘b’ below base

If the water table is located at the level of the base of footing or below it, the surcharge term

is not affected. However, the unit weight is modified as,

where b = depth of water table below the base,

B = base width of the footing.

Therefore,

When b = 0, i.e. W/T at the base,

When b = B, i.e. W/T at depth B below the base.





Hence, when the ground water table is located at a depth ‘b’ equal to or greater than B there

is no effect on the ultimate bearing capacity.

For intermediate positions, linear interpolation of reduction be made. For any position of the

water table equations are as below: -

Here, Rw1 and Rw2 are water reduction factors.

When water is much below or at greater depth, then no effect of water table is to be

considered.

SKEMPTON’S ANALYSIS FOR COHESIVE SOILS

Skemton (1951) showed that the bearing capacity factor Nc in Terzaghi’s equation tends to

increase with depth for a cohesive soil (Фu = 0, c = cu). Fig.4 shows the variation of Nc with Df/B

ratio for strip and circular (or square) footings. For a strip footing, the value of Nc is equal to 5.14 for

the surface footing and has a maximum value of 7.50 and Df / B ratio ≥ 4.50.

For square and circular footings, the value of Nc is equal to 6.2 for the surface footing. The

maximum value of about 9.0 is attained for Df / B ratio equal to or greater than 4.50. The curve for

square and circular footings can also be used for rectangular footings using the following relation.

Alternatively, the curve for the strip can be used, making use of the following relation.

The following approximately relations can be used for the determination of Nc for different Df /B

ratios.

(a) Df/B < 2.50

(b) Df/B ≥ 2.50

Ultimate Bearing capacity

For Фu = 0, Nq = 1.0 and Nγ = 0.0





Therefore,

The net ultimate bearing capacity becomes

This is used for the determination of the net ultimate bearing capacity of footings on cohesive

soils, taking Nc value given by Skempton. It may be mentioned that Terzaghi’s value of Nc is

applicable only for shallow footings (Df < B), whereas Skempton’s value can be used for all values

of Df/B ratio.

Figure.4 Skempton’s chart.

SETTLEMENT OF FOUNDATION

(a) Settlement under loads

Foundation settlement under loads can be classified into 3 types.

(1) Immediate or elastic settlement (Si): - Immediate or elastic settlement takes place

during or immediately after the construction of the structure. It is also known as the

distortion settlement as it is due to distortions (and not the volume change) within the

foundation soil. Although the settlement is not truly elastic, it is computed using elastic

theory, especially for cohesive soils.

(2) Consolidation settlement (Sc): - This component of the settlement occurs due to gradual

expulsion of water from the voids of the soil. This component is determined using

Terzaghi’s theory of consolidation.

(3) Secondary Consolidation Settlement (Ss): - This component of the settlement is due to

secondary consolidation. This settlement occurs after completion of the primary





consolidation. It can be determined form the coefficient of secondary consolidation. The

secondary consolidation is not significant for inorganic clays and silty soils.

The total settlement (s) is given by

s = si + sc + sr

(b) Settlement due to other causes

In addition to settlement under loads, the settlement may also occur to a number of other

causes.

1) Underground erosion: - Underground erosion may cause formation of cavities in the

subsoil which when collapse cause settlement.

2) Structural collapse of soil: - Structural collapse of some soils, such as saline, non-

cohesive soils, gypsum, silts and clays and loess, may occur due to dissolution of

materials responsible for intergranular bond of grains.

3) Thermal changes: - Temperature change cause shrinkage in expansive soils due to which

settlement occurs.

4) Frost heave: - Frost heave occurs if the structure is not founded below the depth of frost

penetration.

5) Vibration and Shocks: - Vibrations and shock cause large settlements, especially in

loose, cohesionless soils.

6) Mining subsidence: - Subsidence of ground may occur due to removal of minerals and

other materials from mines below.

7) Land slides: - If land slides occur on unstable slopes, there may be serious settlement

problems.

8) Creep: - The settlement may also occur due to creep on clay slopes.

9) Changes in the vicinity: - If there are changes due to construction of a new building near

the existing foundation, the settlement may occur due to increase in the stresses.

Suitable measures are taken to reduce the settlements due to all above causes.

BEARING CAPACITY OF SQUARE AND CIRCULAR FOOTING

Based on experimental results, Terzaghi gave the following equations for the ultimate bearing

capacity for square and circular shallow footings.

(a) Square Footing: -

where ‘B’ is the dimension of each side of footing.

(b) Circular Footing: -

where ‘B’ is the dimension of each side of footing.

The bearing capacity factors Nc, Nq and Nγ are the same as that for the strip footing.





IMMEDIATE SETTLEMENT OF COHESIONLESS SOILS

As cohesionless soils do not follow Hooke’s law, immediate settlements are computed using

a semi – empirical approach proposed by Schmertmann and Hartman (1978).

where, C1 = correction factor for the depth of foundation embedment =

C2 = correction factor for creep in soils [ = 1 + 0.2 log10 (time in years/0.1].

q = pressure at the level of the foundation, q = surcharge (= γ Df),

Es = modulus of elasticity, Iz = strain influence factor.

The value of the strain-influence factor Iz varies linearly for a square or circular foundation.

The value of Iz at depth z = 0, 0.5 B and 2B are respectively equal to 0.1, 0.5 and 0.0. For rectangular

foundations, with L/B ratio, between 1.0 and 10.0, interpolation can be made.

The value of Es can be determined from the standard penetration number (N) using the

following equations given by Schmertmann (1970).

Es = 766N (kN/m2)

Alternatively, it can be estimated from the static cone penetration resistance (qc) as

Es = 2 qc.

Procedure: - For computation of the immediate settlement, the soil layer is divided into several

layers of thickness Δz, upto a depth z = 2B, in case of square footings and z = 4B, in case of

rectangular footings. The immediate settlement of each layer is computed using equation of si, taking

corresponding values of Es and Iz. The required immediate is equal to the sum of the settlements of

all individual small layers.





ACCURACY OF FOUNDATION SETTLEMENT PREDICTION

The prediction of the foundation settlements prediction:-

1) The soil deposits are sudden isotropic and linearly elastic. The deposits are generally non-

homogeneous.

2) It is not possible to estimate the increase in stresses caused by loads. The Boussinesq solution

gives only approximate results.

3) For estimation of the settlement due to consolidation, it is not possible to locate exactly the

drainage faces.

4) For computation of immediate settlements, it is not possible to estimate the correct value of

the modulus of elasticity.

5) The rigidity of the foundation is usually neglected and the pressure distribution is assumed to

be uniform.

6) It is difficult to obtain undisturbed samples of cohesionless soils. The semi-empirical

methods do not give accurate results.

7) Settlements may occur due to causes other than that due to loads. It is not possible to estimate

these settlements accurately.

Despite all the above reasons, the settlements in most cases can be estimated to an

accuracy of about 25 to 30%, which is good enough seeing the complexity of the problem.

ALLOWABLE SOIL PRESSURE FOR OHESIONLESS SOILS

The allowable soil pressure (qna) of a shallow foundation is limited either by the net safe

bearing capacity (qns) or the safe settlement pressure (qnρ). The design of shallow foundation on

cohesionless soils is generally governed by the safe settlement pressure, as the net safe bearing

capacity for footings of usual size is quite high. However, in the case of narrow footings on water-

logged sands, the net safe bearing capacity may be the controlling criterion for the design.

It is the normal practice for the design of footings of usual size to use empirical methods

based on N-values for the determination of the allowable soil pressure for cohesionless soils. The

plate load tests are also used in the case of soils having small boulders and stones which obstruct the

standard penetration test. The methods using the standard penetration test are preferred to plate load

tests for homogeneous soils, as these are more economical.

Footings on granular soils are generally designed using the following empirical relationships

for the allowable soil pressure.

1) Peck Method

Terzaghi and Peck (1967) gave charts for the safe bearing pressures inducing a total

settlement of 25mm and a differential settlement of 19 mm for different sizes of footing. Peck et al

(1974) revised the Terzaghi and Peck curves to take into consideration the later research, and gave

the following equation for the safe settlement pressure.

where qnρ = safe settlement pressure (kN/m2),

N = average SPT number, corrected for overburden pressure and dilatancy,

s = settlement (mm),





Cw = water table correction factor.

2) Teng’s Equation

Teng (1962) expressed the charts given by Terzaghi and Peck (1948) in the form of

the following formulas. Allowance was made for an increase in pressure with depth by

introducing a depth factor.

For a settlement of 25 mm,

where qnρ = safe settlement pressure (kN/m2), N = SPT number, B = width of footing (m),

Wγ = water table correction factor,

Rd = depth correction factor =

The above equation can be written in general form as

where s = tolerable settlement (mm).

3) Meyerhof’s equation

Meyerhof proposed equations which are slightly different from Teng’s equations.

According to him, for a settlement of 25 mm,

and

where all the terms are the same as in Teng’s equation, except Rd, which is given by

4) Bowle’s equation

Bowles (1977) suggested that the net allowable pressure given by Meyerhof’s equation can

be safely increased by 50%. Thus, for a settlement of 25 mm,

and

5) IS : 6403 – 1971 equation

IS : 6403 – 1971 gives the following equation, which is similar to Teng’s equation. For a

settlement of 40 mm,





The depth factor is not considered.

Fig.5 gives the allowable soil pressure for a settlement of 40 mm.

PLATE LOAD TEST

Plate load test is a field test to determine the ultimate bearing capacity of soil, and the

probable settlement under a given loading. The test essentially consists in loading a rigid plate at the

foundation level, and determining the settlements corresponding to each load increment. The

ultimate bearing capacity is then taken as the load at which the plate starts sinking at a rapid rate. The

method assumes that down to the depth of influence of stresses, the soil strata is reasonably uniform.

The bearing plate is square, of minimum recommended size 30 cm square and maximum size

75 cm square. The plate is machined on sides and edges, and should have a thickness sufficient to

withstand effectively and bending stresses that would be caused by maximum anticipated load. The

thickness of steel plate should not be less than 25 mm.

The test pit width is made five times the width of the plate Bp. At the centre of the pit, a small

square hole is dug whose size is equal to the size of the plate and the bottom level of which

correspond to the level of the actual foundation. The depth Dp of the hole should be such that

The loading to the test plate may be applied with the help of a hydraulic jack. The reaction of

the hydraulic jack may be bores by either of the following two methods:

a) Gravity loading platform method.

b) Reaction truss method.

In the case of gravity loading method, a platform is constructed over a vertical column resting

on the plate, and the loading is done with the help of sand bags, stones or concrete blocks.

When load is applied to the plate, it sinks or settles. The settlement of the plate is measured

with the help of sensitive dial gauges. For square plate, two dial gauges are used. The dial gauges are





mounted on independently supported datum bar. As the plate settles, the ram of the dial guage moves

down and settlement is reconsidered. The load is indicated on the load – guage of the hydraulic jack.

(a) (b)

Figure.5 (a) Trial pit, b) Plate load test: Reaction by Gravity loading.

Test Procedure

1) The plate is firmly seated in the hole, and if the ground is slightly uneven, a thin layer of sand

is spread underneath the plate. Indian Standard (IS : 1888 – 1962) recommends a seating load

of 70 g/cm2 which is related before the actual testis started.

2) The load is applied with the help of a hydraulic jack (preferably with the remote control

pumping unit), in convenient increments, say of about one-fifth of the expected safe bearing

capacity or one-tenth of the ultimate bearing capacity.





3) Settlement of the plate is observed by 2 dial gauges fixed at diametrically opposite ends, with

sensitivity of 0.02 mm.

4) Settlement should be observed for each increment of load after an interval of 1, 4, 10, 20, 40

and 60 minutes and thereafter at hourly intervals until the rate of settlement becomes less

than about 0.02 mm per hour. After this, the next load increment is applied. The maximum

load that is to be applied corresponds to 1 ½ times the estimated ultimate load or to 3 times

the proposed allowable bearing pressure.

5) The water table has a marked influence on the bearing capacity of sandy or gravelly soil. If

the water table is already above the level of the footing, it should be lowered by pumping and

the bearing plate seated after the water table has been lowered just below the footing level.

6) Even if the water table is located above 1 m below the base level of the footing the load test

should be made at the level of the water table itself.

7) The load intensity and settlement observations of the plate load test are plotted. Curve I

corresponds to general shear failure, and II corresponds to local shear failure. Curve III is a

typical of dense cohesionless soils which do not show any marked sign of shear failure under

the loading intensities of the test. IS: 1888 – 1962 recommends a log – log plot giving straight

lines the intersection of which may be considered the yield value of the soil. In order to

determine the safe bearing capacity it would be normally sufficient to use a factor of safety of

2 or 2.5 on ultimate bearing capacity.

Figure.6 Load settlement curves.

Limitation of the plate load test

The plate load test has the following limitations:

1) Size effect: - The results of the plate load test reflect the strength and the settlement

characteristics of the soil within the pressure bulbs. As the pressure bulb depends upon the

size of the loaded area, it is much deeper for the actual foundation as compared to that of the

plate. The plate load test does not truly represent the actual conditions if the soil is not

homogeneous and isotropic to a large depth.

2) Scale effect: - The ultimate bearing capacity of saturated clays is independent of the size of

the plate but for cohesionless soils, it increases with the size of the plate. To reduce scale

effect, it is desirable to repeat the plate load test with plates of two or three different sizes and





extrapolate the bearing capacity for the actual foundation and take the average of the values

obtained.

3) Time effect: - A plate load test is essentially a test of short duration. For clayey soils, it does

not give the ultimate settlement. The load-settlement curve is not truly representative.

4) Interpretation of failure load: - The failure load is not well-defined, except in the case of a

general shear failure. An error of personal interpretation may be involved in other types of

failure.

5) Reaction load: - It is not practicable to provide a reaction of more than 250kN. Hence, the

test on a plate of size larger than 0.6 m width is difficult.

6) Water table: - The level of the water table affects the bearing capacity of the sandy soils. If

the water table is above the level of the footing, it has to be lowered by pumping before

placing the plate. The test should be performed at the water table level if it is within about 1m

below the footing.

Documents

B.E. FIFTH SEMESTER · 2019. 5. 26. · 9) Net safe bearing capacity (q ns):-The net safe bearing capacity is the net ultimate bearing capacity divided by a factor of safety F 10)