Foundation

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Settlement of Foundations Introduction The total settlement of a foundation can be divided into three components: The immediate settlement Δ which takes place due to elastic deformation of soil without change in water content. The consolidation settlement ΔH which takes place in clayey soil mainly due to the expulsion of the pore water in the soil.

Secondary (creep) settlement ΔS which takes place over long periods due to viscous resistance of soil under constant compression. 2

Methods of calculation of settlement of foundations  Methods using elastic theory for all types of soils.  By Teng's formula based on SPT values for granular soils.  Meyerhof's formula based on SPT values for granular soils.

 De Beer's method based on SCPT values for granular soils.  Schmertmann's method based on SCPT values for granular soils.  Terzaghi's consolidation theory for clays.  Equivalent raft approach for pile group in clays.

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Elastic Settlement of Footings Elastic or immediate settlement of rectangular flexible shallow footings is given by

Where, q B H Es Iw

= = = = =

Intensity of pressure least lateral dimension = width Poisson’s ratio modulus of elasticity of soil assumed to be constant with depth Influence factor depending on shape of footing and its rigidity as given in Table below.

The settlement of a rigid plate on a semi-infinite homogeneous elastic medium has been worked out by complex calculations involving distribution of pressures and is

where IR = 0.82 for a square plate

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Settlement of Foundation on Cohesionless Soil The SPT corrected values at foundation level Nh at depth 1.5 B(N2) and at depth 2B(N3) are used as follows to find the average value of A' to be used in the assessment of settlements and bearing capacity:

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Terzaghi and Peck's Correlation From Terzaghi and Peck's correlation of settlement with SPT values, Teng proposed the following expression for the load for a given settlement of a footing of breadth B in a sand deposit with SPT value of N

where q is in kN/m and B in meters Meyerhof in 1965 proposed the following:

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Meyerhof's Formula Based on SPT Values for Cohesionless Soils

•noted that the Terzaghi and Peck's correction overestimates the actual settlement considerably. •proposed the following formula based on SPT tests for settlement in mm for q in kN/m2 and B in meters

Estimation of Total Settlement of Foundations on Cohesive Soils

In the case of cohesive soils, the total settlement can be expressed as follows: where, Δ = immediate settlement ΔH = consolidation settlement ΔS = creep or secondary consolidation settlement

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Estimation of Differential Settlement

Terzaghi recommends the following relation for probable differential settlement for footing foundations in buildings.

Thus for a maximum settlement of 1 inch in footings, the expected differential settlement will be 3/4 inch Raft foundations The differential settlement of practical rafts will not be more than 50% of the differential settlement calculated for footings. Hence the differential settlement in rafts can be calculated as follows:

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Settlement of a Group of Piles Used as Foundation (Deep Foundations)  difficult to calculate accurately the settlement of a group of piles from the load settlement data of a single pile.  Generally, the settlement for a group of piles will be more than that for a single pile carrying the same load per pile. Approximate evaluation of settlement of a group of piles in sand from tests on single piles In sands, data from a single pile test may be used for the approximate settlement of a group of piles by using the formula recommended by Skempton in 1953. Taking Sg for group settlement and Si for single pile settlement,

Where, B is the width of pile group (centre to centre of piles) in meters 9

Meyerhof (1959) also has given the following similar formula for the estimation of a settlement of a group of piles from results of test on a single pile.

Where, s = ratio of pile spacing to pile diameter r = number of rows in the pile group In general, the settlement of a pile group in sand will be much more than that of a single pile under the same load. Settlement of Pier Foundations •The effect of the depth of foundation on settlement of piers is relatively small compared to its ultimate bearing capacity. •Allowable settlement will control the safe load on pier foundations. •Terzaghi suggests that the settlement of pier foundations in sand at any depth will not be less than about one half the settlement of an equally loaded area of footing at shallow depth. settlement of pier = 1/2 x (settlement of footing at shallow depth)

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ALLOWABLE DIFFERENTIAL SETTLEMENTS deflection ratio (Δ/L) angular distortion (h/L) where L is the length over which the differential settlement is measured IS 1904 (1986) Code of practice for design of foundation in soils general requirements gives guidelines for limiting angular distortion in building designs. According to Skempton and McDonald, it is the angular distortion h/L that is more important than the total differential settlement. IS 1904 allows a maximum settlement of not more than the following for individual footings: 65 mm on clay and 40 mm on sand. For rafts, the values are 65 to 100 mm for clays and 45 to 65 mm for sand. The permissible values for differential settlement are 40 mm for clay and 25 mm for sand. The permissible angular distortion in framed structures should be only 1/500 to 1/1000 depending on their use and importance. Angular distortions of more than 1/150 produce 11 considerable cracking in brick and panel walls

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Methods to Reduce Settlement in Buildings Reduce the load on the soil by removing soil and adopting basement floor (i.e. adopt a floating or compensated foundation)

Reduce the load on soil by using lighter building materials like ribbed floors, light weight wall panels. Adopt a pile foundation properly designed to reduce settlement. Adopt pre-loading of the site to attain necessary pre-consolidation stage by heaping of sand and also by providing sand drains for quick dissipation of pressure. Extend construction period to reduce damage on building. Design the structure so that the differential settlement is small. This is achieved by providing rigidity to the structure so that the whole structure settles uniformly this will even out the settlement. Prevent lateral strain in soft clays (if they are present underneath the foundation) by providing lateral confinement by suitable constructions like sheet pile walls. Provide construction joints and time schedule for the construction of various parts to take care of settlements. Provide jacking arrangements under columns so that the settlements can be adjusted by 13 jacking and providing additional extensions to the column to the foundation.

General Requirements of Shallow and Deep Foundations Foundations with depth/breadth ratio equal to or less than one are normally called shallow foundations. Those with this ratio greater than 5 are considered as deep foundations.

The intermediate types are said to be moderately deep. Spread footings can be classified as: Simple (square, circular or rectangular) footings with flat or sloping top surface Strip footings Combined footings (rectangular, trapezoidal, or other shapes) Strap footings (balanced base type and cantilever type) 14

DEPTH OF FOUNDATIONS The minimum depth of foundations prescribed by IS 1904 is 0.5 m. Generally, a minimum depth of 1 m is adopted for foundations. In clayey soils and especially in case of expansive clays, the depth should be below a level where there is no variation of moisture with change of seasons. As the external walls have to act as a protection against insects and rodents, the depth should be sufficient so as to prevent their access through burrows made under the foundation.

Constructing a new footing near the footing of an old building. Minimum horizontal distance between the two footings should not be less than the width of the larger footings to avoid damage to the existing structure. If the distance is limited, the principle of 2 horizontal to 1 vertical dispersion should be used so that the foundation of the old building is not very much affected by the new construction. 15

Footings on surface rocks and sloping rock faces In places where solid rock is available near the ground level (less than 90 cm in depth), the rock should be chipped and the concrete of the foundation should be properly keyed into the rock. In places where the rock surface is on a shallow slope, it is advisable to provide dowel rods 16 mm dia dowelled to a minimum depth of 225 mm at a spacing of not more than 1 metre and adequately grouted. In such places, we can also bench the rock surface to provide a better key to the foundation.

Standard Practice of Laying Footing Foundation of Buildings •If the foundation soil is clayey, it is preferable to have a 150 mm to 300 mm thick hardcore or sand filling, greater thickness is to be provided for the more clayey soil. •Over this, a block of 1:2:6 lime, brick jelly concrete (preferred for clay soils) or plain cement concrete 1:4:8 with large size (50 mm) aggregate is laid. •The thickness of this layer should be 150 to 450 mm depending on the site, Construction of brickwork or reinforced concrete footing is commenced only after this levelling course has properly set. 16

•Brick walls using 9 inch bricks (bricks are still manufactured to this size) and stepped footings can be built over plain cement concrete using 21/4 inches offset, each successive course being one half brick that is, 41/2 inches larger in width. •Each course consists of 2 or 3 brickwork in height. For such walls, reinforced concrete foundations are not needed. The standard details of foundation used in India for load bearing footings are shown:

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Safe Bearing Capacity for Simple Cases The safe bearing capacity of soils can be taken from those specified in code of practices under the following conditions:

The soil is uniform to a depth at least three times the footing width. The resultant of external forces passes through the middle third of the footing area.

Most of the external forces are not dynamic in nature. The ground water level is at a depth of at least equal to the footing width in granular soils and twice the width in cohesive soils. If the bottom of the footing is at least 2.0 m below the ground level, then only the allowable bearing capacity should be increased by the weight of the soil between the footing bottom and the surface as any subsequent excavation near the footing will reduce the bearing capacity. 18

Types of shallow and deep foundations and their uses Isolated footings These are used for column loadings and can be of brick work, mass concrete or reinforced concrete. It is ideal when column load is axial and not very large compared to the bearing capacity of the soil. Strip footings These are generally used for wall footings where the loading is not very large. The width of footing is to be based on the bearing capacity or the thumb rule that it should be not less than three times thickness of wall or two times thickness of wall plus 30 cm. Combined footings When two adjacent columns of different loads have to be accommodated together, we use a combined footing. Balanced footings or cantilever footings These are commonly used when one column which exist too near the property line 19 has to be balanced by an adjacent column.

Raft foundation These are used when the foundation soil offers poor bearing capacity and particularly when it has weak patches. With isolated footings, they come too close to each other and differential settlements tend to be very large. Pile foundation When the top strata is very poor and reasonably good soil strata exist below the top soil, a pile foundation becomes more reliable and economic than others.  Also in certain situations where settlements cannot be tolerated, we have to use piles.  For large rigid frame structures like tall buildings, chimneys and where settlements are dangerous and very high lateral loads are to be transmitted through the foundations, pile foundations are the obvious choice. Piled raft When the bearing capacity of a raft is satisfactory but the settlement is not satisfactory, a combination of raft on piles will provide the advantages of both, rafts and piles. As a means of reducing settlements, piles are called upon only to take a small percentage 20 of the load and the rest is designed to be carried by the raft.

Compensated or floating foundations The method used in this type is to excavate considerable amount of soil, as nearly equal to the weight of the building as possible, from the bottom of the structure and build basement floors, so that the load carried by the soil is considerably reduced. Pier or well foundations Large diameter piles, piers, and deep-well foundations are usually used for bridges and other structures to carry heavy loads. Deep-well foundations are specially useful for bridges across large rivers with deep scouring of the river bed.

Major factors affecting Bearing Capacity  Size of the foundation  Shape of the foundation  Depth of the foundation  Inclination of the load  Inclination of the foundation base  Inclination of the ground Position of ground water table 21

Effect of Size of Foundation

Nc, Nq and Nγ are called Terzaghi's bearing capacity factors. The first term represents the contribution of cohesion, the second the contribution due to surcharge of unit weight γ0 and the third, the contribution by the shear strength of soil below foundation level with friction and self-weight γ0 of soil below the foundation level. In 1940 Schultze extended the bearing capacity theory to a rectangular foundation B x L by introducing shape factors as follows:

Effect of Shape, Depth and Inclination of Load on Bearing Capacity of Footings Shape In a long strip footing the shear planes develop only along the width of the foundation. In a rectangular footing, shear planes may develop along breadth and length, thus mobilizing a larger soil mass than in a strip footing. Thus the shape of22 the footing affects its bearing capacity.

Foundation depth With increasing depth the bearing capacity increases not only because of the overburden pressure but also due to the failure pattern of deep foundations. The effect of overburden is the main consideration in deciding the depth of shallow foundation. Inclination of the load The bearing capacity decreases rapidly with larger inclination of the load from the vertical and this reduction is more pronounced for horizontal bases than for inclined bases so that with inclined loads there is some advantage in adopting inclined bases. IS CODE RECOMMENDATIONS Both Hansen and Meyerhof have given their equations for the various effects given above. Based on these values, IS 6403-1981 has recommended the following equations for the calculation of the ultimate bearing capacity of shallow footings.

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where, B c q0 γ0 γ1

= width of foundation = undrained cohesion of soil = effective overburden pressure at foundation level = D = effective unit weight of soil above foundation level = effective unit weight of soil below foundation level

Nc, Nq and Nγ are the bearing capacity factors sc, sq and sγ are shape factors dc, dq and dγ are depth factors ic iq and iγ are inclination factors which depend on inclination α of load to the vertical W’ is a factor for effect of water table which is 1 if water table is at a depth B below the foundation level and linearly varies to 0.5 if it is at the base of foundation. According to IS 6403 the value of Nc, Nq and Nγ is to be taken as those derived by Vesic. They may be also calculated from the following equations (Vesic's equations).

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The values of these modifying factors as recommended in IS 6403-1981

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Effect of Footings on Sloping Ground For a gradually sloping ground, the bearing capacity for a depth equal to that of the centre of gravity of the foundation can be used for design. When the footing is very near to the edge of a steep slope, it is better to make a stability analysis of the slope to determine the safety conditions taking into account the variation of the water level also. 26

Effect of Shape of Base of Foundation In cohesionless soils, the bearing capacity is greater under concave foundation (looking from below) than under convex shapes. The increase can be as much as 20% depending on the relative density of the soil and curvature of the foundation. General Equations for Bearing Capacity Meyerhof's method is more popular in North America and Hansen's factors in European countries IS 6403 recommendation (Hansen's values) can be safely used for all practical designs. The following procedures can be used for calculation of bearing capacity of footings:

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Uses of piles To carry loads which are too heavy to be supported by a shallow foundation and are to be transferred to deeper, stronger and less compressible strata or over a larger depth of the foundation soil.

To carry part of the load to deeper soil for reducing the settlement as in piled raft foundations. To carry horizontal loads as in bridge abutments or retaining walls and also to increase the stability of tall buildings. To withstand uplift forces in foundations as in expansive soils and floating foundations. To avoid loss of support by scour as in bridges. To produce large differential settlement in situations where there are large variations of column loads. To compact foundation material such as loose sands. 28

Types of Piles On the basis of their size (diameter) Piles larger than 600 mm in diameter are called large diameter piles. Sizes 300 to 600 mm are called normal or small diameter piles.  Piles of 150 to 250 mm in diameter are called mini piles while those below 150 mm diameter are classified as micro piles. On the basis of the method of installation driven cast in-situ bored cast in-situ precast driven precast piles driven in pre-bored holes

On their action (that is, the purpose they are intended to serve) Displacement piles (driven piles) Non-displacement piles (bored piles) Small displacement piles (driven steel H pile)

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Codes on Piles The specification for the four types of commonly used concrete piles are covered by Indian Standard IS 2911 (Second revision) under the following heads: Driven cast in-place (displacement) piles—Section 1 Bored cast in-situ (non-displacement) piles—Section 2 Pre-cast driven (displacement) piles—Section 3 Pre-cast piles driven in pre-bored (non-displacement) piles—Section 4. In addition, the following Indian Standards also pertain to pile design and construction: IS 2911 Part II—Timber piles IS 2911 Part III—Under reamed piles IS 2911 Part IV—Load tests on piles. Factors affecting Choice of Type of Pile Disturbance of nearby old structures: Vibrations are caused during pile driving. Length and size of pile: Precast R.C driven piles are small in size and are usually of length up to 16 m and size less than 550 mm. Bored piles can be taken very deep provided they are reasonably large. They can also be of large diameters. 30

Time taken for piling: Driven precast and cast in-situ piles, can be more quickly executed than bored cast in-place piles. However if ground heave is expected, driven cast in-place piles will pose problems involving the integrity of the pile. Loss of bearing at pile tip: In bored cast in-place piles, the success in washing the base of the pile depends on the availability of good equipment, workmen and experienced contractors. Surface water currents: In sandy areas near large water bodies subsurface flow channels may exist. In such cases, the concrete in cast in-place piles can be washed out before it sets, thus causing local weakness.

Difficulty in pulling out casing: In pure sand deposits while using driven cast in-place piles it will be difficult to pull out the casing after concreting. Defects like necking occur in such cases. Quality of concrete and its capacity to withstand deterioration: In bad environmental conditions with chlorides and sulphates precast driven piles are superior to cast inplace concrete which needs very good care and supervision in its placement. The dumping of concrete especially in driven cast in piles from large height and with the pile reinforcement in place, segregation of concrete cannot be avoided. It discourage the use of driven cast in-situ piles. 31

Probability of negative skin friction: It is claimed that this can be reduced in precast piles by bituminous coatings. However because of larger disturbances produced while driving, driven piles produce more negative friction. Possibility of pile damage during driving: If the driving is hard, precast driven piles tend to get damaged in the body due to driving stresses and at head due to inadequacy of equipment or lack of strength at the top. Possibility of socketing: For bearing piles in weathered rock, bored cast in-place piles are ideal and, if necessary, socketing of piles can also be carried out. This will increase pile capacity considerably in soft and weathered rock formations. When good rock is available at reasonable depths, bored piles taken to rock present the best solution. Load Carrying Capacity The static method based on soil properties for all types of piles. The dynamic method using pile-driving formulae based on the resistance observed in the field in driving the piles for driven piles. The wave equation method for driven piles. (Both the theoretical method and case method using field values are used.) IS 2911 incorporates only the first two methods

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Effective Length Point Of Inflection If the pile is projecting free above the ground level, the following criteria can be used to fund the point of inflection or contraflexure to find effective length [IS 2911 part I/sec 1 1999 clause 6.5.1]: If the ground is firm, the depth of PI is taken as 1/10 the projecting pile length or lm subject to a minimum of 3D (B.S. Code CP 2004 recommends it as 1.5 m).

If the top embedded stratum is soft below 0.1 kg/cm2 in undrained shear strength, the depth of point of inflection is to be taken as one-half the, depth of penetration but not more than 10D or 3 m, whichever is less. If the stratum is liquid, mud is to be treated as water. If the top end is fixed, both in position and in direction, the upper point of inflection may be taken as one-fourth the exposed length below the top of the pile. 33

METHOD 1—STATIC FORMULA (FOR PILES IN GRANULAR SOILS) The ultimate bearing capacity, Qu of piles in granular soils is given in IS 2911 by the following formula: Qu = End bearing resistance + skin friction resistance

where AP D γ Ny Nq PD K1 PD1 δ As

= cross-sectional area of the pile = stem diameter of pile = unit weight of soil = bearing capacity factor taken for general shear = berezantsev's bearing capacity factor = effective overburden pressure = coefficient of earth pressure = effective overburden pressure of corresponding layer = angle of wall friction usually taken as 3/4ϕ of soil = surface area of pile.

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The first term and the last term are usually small and can be neglected in the above equation. Hence, Equation modifies as,

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Structural Capacity of Piles The working load on the pile should not exceed its structural capacity given by the following formula: Qst = (0.25fck)Ac where, fck = cube strength of concrete Ac = area of cross section of concrete pile METHOD 1—STATIC FORMULA (FOR COHESIVE SOILS) The ultimate bearing capacity, Qu of piles in cohesive soils is given by the following formula (IS 2911 part 1 Sec. 3): Qu = end bearing resistance Qp + skin friction resistance Qs

where Nc cp αi

= bearing capacity factor in clays which is taken as 9 = average cohesion at pile toe = adhesion factor

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ci Asi αi ci

= average cohesion of the ith layer on the side of the pile = surface area of pile stem in the ith layer. = adhesion between shaft of pile and clay.

Method 1: From empirical value of α The values of α recommended by IS 2911 Part I Section 3 Clause B2 for driven piles for various soils are given in table

Method 2: From field c/σv values (IS 2911 Part 1 Sec. 2 Bored piles). •For normally consolidated clays, the value of c/σv can be assumed to range from 0.2 to 0.3, so that (c/σv)1/2 can be assumed to have a mean value of 0.5 •If the value of c/σv (=ψ) is greater than 0.5, the clay can be assumed to be overconsolidated.

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On the basis of the assumption, the following α values are recommended by IS 2911 (Sec. 2)

For bored piles the value of α as obtained above is to be multiplied by 0.8. CAPACITY OF PILES IN c-ϕ SOILS BY STATIC FORMULA Method 1: If the soil has small value of Φ treat it as a purely cohesive soil. Similarly if the cohesion is small and Φ is large than treat the soil as being cohesionless. Method 2: Where the soil has large values of both c and Φ (as for a true c - Φ soil), we should use the conservative Terzaghi's bearing capacity factors to determine the load carrying capacity. This formula is expressed as follows.

where, Nc,Nq,Nγ = Terzaghi's bearing capacity factors σvbσv = Effective overburden pressure of base and pile shaft, irrespective of the critical depth.

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FACTOR OF SAFETY FOR STATIC FORMULA BASED ON SOIL PROPERTIES The factor of safety to be used in the static formula should depend on: Reliability of soil parameters used for calculations The manner in which load is transferred to the soil The importance of the structure Allowable total and differential settlement tolerated by the structure.

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METHOD 2—MEYERHOF'S FORMULA FOR DRIVEN PILES IN SAND BASED ON SPT VALUES Meyerhof s formula is given in IS 2911 for driven piles in sands. In 1959, Meyerhof proposed the following formula for the ultimate bearing capacity of driven piles in cohesionless soils.

Meyerhof's Approach Extended to Clay Assume SPT value N as a measure of the consistency of clays and thus indirectly its cohesion values as c = N/20 kg/cm2 or N/2 t/m2. Using the relationship 1 kg/cm2 = 10 t/m2,

where Ap and As are in m2

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METHOD 3 —LOAD CARRYING CAPACITY FROM STATIC CONE PENETRATION TESTS Static cone penetration test is a miniature pile test to failure. IS 2911 recommends this method when static cone resistance data is available, for the full depth of the soil profile.

The end bearing and side friction are calculated separately as follows. Unit end bearing: The ultimate end bearing resistance qu according to IS 2911 can be taken as

where, qc0 = average SCPT value for 2D below pile toe qc1 = minimum SCPT value for 2D below pile toe qc2 = average of the envelope of minimum SCPT value over 8D above the toe of the pile

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IS2911 specification for detaining ultimate base resistance of piles in sand from static cone penetration test

Ultimate skin friction resistance: The approximate values of side friction can be got from Table.

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Ultimate load carrying capacity: The sum of the ultimate end bearing and skin friction values gives us the ultimate capacity of the pile. CAPACITY OF PILES FOUNDED ON SOLID ROCK The bearing capacity of piles founded on rock also depends on the type of rock met with at the tip of the pile and also the method of installation of the piles at its base. Rocks are classified as solid or weathered depending on core recovery while drilling. Steel H piles are generally recommended for piles driven to refusal on rock. If the rock is irregular, the piles are fitted with a rock point to enable the pile to 'wedge' itself to the rock. Driven Piles Resting on Rock When driving piles to good rock, it is the general practice to provide the piles with special shoes and drive the piles to refusal. In such cases the pile capacity is taken as its structural capacity considering it as a concrete column .

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Tomlinson recommends the strength of piles driven into soft rock to be estimated from the following equation derived along the lines of finding the minimum depth of foundation by Rankine's theory.

where, quc NΦ Φ

= uniaxial compression strength of rock = tan2 (45 + Φ /2) = friction value.

It is taken as 30 to 40° for high friction rocks like basalt and granites, 25-35° for medium friction rock such as sandstone, and 20-25 for low friction, rocks, e.g., as mica schist. Strength of Socketed Piles by Cole and Stroud Approach Total bearing resistance= (end bearing resistance) + (socket bond strength between rock and pile)

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where, cu = shear strength of rock below base of pile NC = bearing capacity factor D = diameter of pile α = reduction factor τa = average shear strength of socketed length L = length of socket FS = factor of safety (recommended = 3) ατu = adhesion for which the lesser value of 0.05 times cylinder strength of concrete and 0.05 times unconfined compression strength of rock has been recommended.

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