Thursday, November 29, 2012


1. Pier of any length and size can be constructed at the site
2. Construction equipment is normally mobile and construction can proceed rapidly
3. Inspection of drilled holes is possible because of the larger diameter of the shafts
4. Very large loads can be carried by a single drilled pier foundation thus eliminating the necessity of a pile cap
5. The drilled pier is applicable to a wide variety of soil conditions
6. Changes can be made in the design criteria during the progress of a job
7. Ground vibration that is normally associated with driven piles is absent in drilled pier construction
8. Bearing capacity can be increased by underreaming the bottom (in non-caving materials)
Installation of drilled piers needs a careful supervision and quality control of all the materials used in the construction
2. The method is cumbersome. It needs sufficient storage space for all the materials used in the construction
3. The advantage of increased bearing capacity due to compaction in granular soil that could be obtained in driven piles is not there in drilled pier construction
4. Construction of drilled piers at places where there is a heavy current of ground water flow due to artesian pressure is very difficult


Drilled piers may be described under four types. All four types are similar in construction technique, but differ in their design assumptions and in the mechanism of load transfer to the surrounding earth mass. These types are illustrated in Figure 17.1.

Straight-shaft end-bearing piers develop their support from end-bearing on strong soil, "hardpan" or rock.

The overlying soil is assumed to contribute nothing to the support of the load imposed on the pier (Fig. 17.1 (a)).

Straight-shaft side wall friction piers pass through overburden soils that are assumed to carry none of the load, and penetrate far enough into an assigned bearing stratum to develop design load capacity by side wall friction between the pier and bearing stratum (Fig. 17.1(b)).

Combination of straight shaft side wall friction and end bearing piers are of the same construction as the two mentioned above, but with both side wall friction and end bearing assigned a role in carrying the design load. When carried into rock, this pier may be referred to as a socketed pier or a "drilled pier with rock socket" (Fig. 17.1(c)).

Belled or under reamed piers are piers with a bottom bell or underream (Fig. 17.1(d)). A greater percentage of the imposed load on the pier top is assumed to be carried by the base.

Figure 17.1 Types of drilled piers and underream shapes (Woodward et al., 1972)


Drilled pier foundations, the subject matter of this chapter, belong to the same category as pile foundations. Because piers and piles serve the same purpose, no sharp deviations can be made between the two. The distinctions are based on the method of installation. A pile is installed by driving, a pier by excavating. Thus, a foundation unit installed in a drill-hole may also be called a bored cast-in-situ concrete pile. Here, distinction is made between a small diameter pile and a large diameter pile. A pile, cast-in-situ, with a diameter less than 0.75 m (or 2.5 ft) is sometimes called a small diameter pile. A pile greater than this size is called a large diameter bored-cast-in-situ pile.

The latter definition is used in most non-American countries whereas in the USA, such large- diameter bored piles are called drilled piers, drilled shafts, and sometimes drilled caissons.


General Considerations
The earlier sections dealt with the behavior of long vertical piles. The author has so far not come across any rational approach for predicting the behavior of batter piles subjected to lateral loads. He has been working on this problem for a long time (Murthy, 1965). Based on the work done by the author and others, a method for predicting the behavior of long batter piles subjected to lateral load has now been developed.

Model Tests on Piles in Sand (Murthy, 1965)
A series of seven instrumented model piles were tested in sand with batters varying from 0 to ±45°.

Aluminum alloy tubings of 0.75 in outside diameter and 30 in long were used for the tests. Electrical resistance gauges were used to measure the flexural strains at intervals along the piles at different load levels. The maximum load applied was 20 Ibs. The pile had a flexural rigidity El = 5.14 x 10^4 lb-in^2

The tests were conducted in dry sand, having a unit weight of 98 lb/ft^3 and angle of friction Ø equal to 40°. Two series of tests were conducted-one series with loads horizontal and the other with loads normal to the axis of the pile. The batters used were 0°, ± 15°, ±30° and ±45°. Pile movements at ground level were measured with sensitive dial gauges. Flexural strains were converted to moments.

Successive integration gave slopes and deflections and successive differentiations gave shears and soil reactions respectively. A very high degree of accuracy was maintained throughout the tests.

Based on the test results a relationship was established between the nh^b values of batter piles and n°h.

Figure 16.20 Effect of batter on nh^b / n°h and n (after Murthy, 1 965)

values of vertical piles. Fig. 16.20 gives this relationship between nh^b / n° and the angle of batter β . It is clear from this figure that the ratio increases from a minimum of 0.1 for a positive 30° batter pile to a maximum of 2.2 for a negative 30° batter pile. The values obtained by Kubo (1965) are also shown in this figure. There is close agreement between the two.

The other important factor in the prediction is the value of n in Eq. (16.8a). The values obtained from the experimental test results are also given in Fig. 16.20. The values of n are equal to unity for vertical and negative batter piles and increase linearly for positive batter piles up to a maximum of 2.0 at + 30° batter.

In the case of batter piles the loads and deflections are considered normal to the pile axis for the purpose of analysis. The corresponding loads and deflections in the horizontal direction may be written as

where Pt and yg , are normal to the pile axis; Pt(Hor) and yg (Hor) are the corresponding horizontal components.


The prediction of the various curves depends primarily on the single parameter nh. If it is possible to obtain the value of nh ndependently for each stage of loading Pt the p-y curves at different depths along the pile can be constructed as follows:

1. Determine the value of nh for a particular stage of loading Pt.
2. Compute T from Eq. (16.14a) for the linear variation of Es with depth.
3. Compute y at specific depths x = x1, x = x2, etc. along the pile by making use of Eq. (16.9), where A and B parameters can be obtained from Table 16.2 for various depth coefficients Z.
4. Compute p by making use of Eq. (16.13), since T is known, for each of the depths x = x1
x = x2, etc.
5. Since the values of p and y are known at each of the depths x1, x2 etc., one point on the p-y curve at each of these depths is also known.
6. Repeat steps 1 through 5 for different stages of loading and obtain the values of p and y for each stage of loading and plot to determine p-y curves at each depth.

The individual p-y curves obtained by the above procedure at depths x1, x2, etc. can be plotted on a common pair of axes to give a family of curves for the selected depths below the surface. The p-y curve shown in Fig. 16.2b is strongly non-linear and this curve can be predicted only if the values of nh are known for each stage of loading. Further, the curve can be extended until the soil reaction, pu, reaches an ultimate value, pu, at any specific depth x below the ground surface.

If nh values are not known to start with at different stages of loading, the above method cannot be followed.

Supposing p-y curves can be constructed by some other independent method, then p-y curves are the starting points to obtain the curves of deflection, slope, moment and shear. This means we are proceeding in the reverse direction in the above method. The methods of constructing p-y curves and predicting the non-linear behavior of laterally loaded piles are beyond the scope of this book. This method has been dealt with in detail by Reese (1985).

  Figure 16.2 (b) characteristic shape of a p-y curve

Table 16.2 The A and B coefficients as obtained by Reese and Matlock (1956) for long vertical piles on the assumption Es = nhx


Matlock and Reese (1960) have given equations for the determination of y, S, M, V, and p at any point x along the pile based on dimensional analysis. The equations are

where T is the relative stiffness factor expressed as

In Eqs (16.9) through (16.13), A and B are the sets of non-dimensional coefficients whose values are given in Table 16.2. The principle of superposition for the deflection of a laterally loaded pile is shown in Fig. 16.4. The A and B coefficients are given as a function of the depth coefficient, Z, expressed as

The A and B coefficients tend to zero when the depth coefficient Z is equal to or greater than 5 or otherwise the length of the pile is more than 5T. Such piles are called long or flexible piles. The length of a pile loses its significance beyond 5T.
Normally we need deflection and slope at ground level. The corresponding equations for these may be expressed as

Figure 16.4 Principle of superposition for the deflection of laterally loaded piles

yg for fixed head is

Table 16.2 The A and B coefficients as obtained by Reese and Matlock (1956) for long vertical piles on the assumption Es = nhx


As stated earlier, the problem of the laterally loaded pile is similar to the beam-on-elastic foundation problem. The interaction between the soil and the pile or the beam must be treated quantitatively in the problem solution. The two conditions that must be satisfied for a rational analysis of the problem are,

1. Each element of the structure must be in equilibrium and
2. Compatibility must be maintained between the superstructure, the foundation and the supporting soil.

If the assumption is made that the structure can be maintained by selecting appropriate boundary conditions at the top of the pile, the remaining problem is to obtain a solution that insures equilibrium and compatibility of each element of the pile, taking into account the soil response along the pile. Such a solution can be made by solving the differential equation that describes the pile behavior.

The Differential Equation of the Elastic Curve
The standard differential equations for slope, moment, shear and soil reaction for a beam on an elastic foundation are equally applicable to laterally loaded piles.

The deflection of a point on the elastic curve of a pile is given by y. The x-axis is along the pile axis and deflection is measured normal to the pile-axis.

The relationships between y, slope, moment, shear and soil reaction at any point on the deflected pile may be written as follows.

deflection of the pile = y

where El is the flexural rigidity of the pile material.

The soil reaction p at any point at a distance x along the axis of the pile may be expressed as

where y is the deflection at point x, and Es is the soil modulus. Eqs (16.4) and (16.5) when combined

which is called the differential equation for the elastic curve with zero axial load.

The key to the solution of laterally loaded pile problems lies in the determination of the value of the modulus of subgrade reaction (soil modulus) with respect to depth along the pile.

Fig. 16.2(a) shows a vertical pile subjected to a lateral load at ground level. The deflected position of the pile and the corresponding soil reaction curve are also shown in the same figure. The soil modulus Es at any point x below the surface along the pile as per Eq. (16.5) is

Figure 16.2 The concept of (p-y) curves: (a) a laterally loaded pile, (b) characteristic
shape of a p-y curve, and (c) the form of variation of Es with depth

As the load Pt at the top of the pile increases the deflection y and the corresponding soil reaction p increase. A relationship between p and y at any depth x may be established as shown in Fig. 16.2(b). It can be seen that the curve is strongly non-linear, changing from an initial tangent modulus Esi to an ultimate resistance pμ. ES is not a constant and changes with deflection.

There are many factors that influence the value of Es such as the pile width d, the flexural stiffness El, the magnitude of loading Pt and the soil properties.

The variation of Es with depth for any particular load level may be expressed as

in which nh is termed the coefficient of soil modulus variation. The value of the power n depends upon the type of soil and the batter of the pile. Typical curves for the form of variation of Es with depth for values of n equal to 1/2, 1, and 2 are given 16.2(c). The most useful form of variation of Es is the linear relationship expressed as

which is normally used by investigators for vertical piles.

Table 16.1 Typical values of n, for cohesive soils (Taken from Poulos and Davis, 1980)

Table 16.1 gives some typical values for cohesive soils for nh and Fig. 16.3 gives the relationship between nh and the relative density of sand (Reese, 1975).

Figure 16.3 Variation of nh with relative density (Reese, 1975)

WINKLER'S HYPOTHESIS: Solutions for Laterally Loaded Piles.

Most of the theoretical solutions for laterally loaded piles involve the concept of modulus of subgrade reaction or otherwise termed as soil modulus which is based on Winkler's assumption that a soil medium may be approximated by a series of closely spaced independent elastic springs.

Fig. 16.1(b) shows a loaded beam resting on a elastic foundation. The reaction at any point on the base of the beam is actually a function of every point along the beam since soil material exhibits varying degrees of continuity. The beam shown in Fig. 16.1(b) can be replaced by a beam in Fig. 16.1(c). In this figure the beam rests on a bed of elastic springs wherein each spring is independent of the other. According to Winkler's hypothesis, the reaction at any point on the base of the beam in Fig. 16.1(c) depends only on the deflection at that point. Vesic (1961) has shown that the error inherent in Winkler's hypothesis is not significant.

The problem of a laterally loaded pile embedded in soil is closely related to the beam on an elastic foundation. A beam can be loaded at one or more points along its length, whereas in the case of piles the external loads and moments are applied at or above the ground surface only.

The nature of a laterally loaded pile-soil system is illustrated in Fig. 16.1(d) for a vertical pile.

The same principle applies to batter piles. A series of nonlinear springs represents the force-deformation characteristics of the soil. The springs attached to the blocks of different sizes indicate reaction increasing with deflection and then reaching a yield point, or a limiting value that depends on depth; the taper on the springs indicates a nonlinear variation of load with deflection. The gap between the pile and the springs indicates the molding away of the soil by repeated loadings and the increasing stiffness of the soil is shown by shortening of the springs as the depth below the surface increases.

Figure 16.1 (a) Batter piles, (b, c) Winkler's hypothesis and (d) the concept of
laterally loaded pile-soil system


When a soil of low bearing capacity extends to a considerable depth, piles are generally used to transmit vertical and lateral loads to the surrounding soil media. Piles that are used under tall chimneys, television towers, high rise buildings, high retaining walls, offshore structures, etc. are normally subjected to high lateral loads. These piles or pile groups should resist not only vertical movements but also lateral movements. The requirements for a satisfactory foundation are,

1. The vertical settlement or the horizontal movement should not exceed an acceptable
maximum value,
2. There must not be failure by yield of the surrounding soil or the pile material.

Vertical piles are used in foundations to take normally vertical loads and small lateral loads.

When the horizontal load per pile exceeds the value suitable for vertical piles, batter piles are used in combination with vertical piles. Batter piles are also called inclined piles or raker piles. The degree of batter, is the angle made by the pile with the vertical, may up to 30°. If the lateral load acts on the pile in the direction of batter, it is called an in-batter or negative batter pile. If the lateral load acts in the direction opposite to that of the batter, it is called an out-batter or positive batter pile.

Fig. 16.1a shows the two types of batter piles.

Extensive theoretical and experimental investigation has been conducted on single vertical piles subjected to lateral loads by many investigators. Generalized solutions for laterally loaded vertical piles are given by Matlock and Reese (1960). The effect of vertical loads in addition to lateral loads has been evaluated by Davisson (1960) in terms of non-dimensional parameters. Broms (1964a, 1964b) and Poulos and Davis (1980) have given different approaches for solving laterally loaded pile problems. Brom's method is ingenious and is based primarily on the use of limiting values of soil resistance. The method of Poulos and Davis is based on the theory of elasticity.

The finite difference method of solving the differential equation for a laterally loaded pile is very much in use where computer facilities are available. Reese et al., (1974) and Matlock (1970) have developed the concept of (p-y) curves for solving laterally loaded pile problems. This method is quite popular in the USA and in some other countries.

However, the work on batter piles is limited as compared to vertical piles. Three series of tests on single 'in' and 'out' batter piles subjected to lateral loads have been reported by Matsuo (1939).

They were run at three scales. The small and medium scale tests were conducted using timber piles embedded in sand in the laboratory under controlled density conditions. Loos and Breth (1949) reported a few model tests in dry sand on vertical and batter piles. Model tests to determine the effect of batter on pile load capacity have been reported by Tschebotarioff (1953), Yoshimi (1964), and Awad and Petrasovits (1968). The effect of batter on deflections has been investigated by Kubo (1965) and Awad and Petrasovits (1968) for model piles in sand.

Full-scale field tests on single vertical and batter piles, and also groups of piles, have been made from time to time by many investigators in the past. The field test values have been used mostly to check the theories formulated for the behavior of vertical piles only. Murthy and Subba Rao (1995) made use of field and laboratory data and developed a new approach for solving the laterally loaded pile problem.

Reliable experimental data on batter piles are rather scarce compared to that of vertical piles.

Though Kubo (1965) used instrumented model piles to study the deflection behavior of batter piles, his investigation in this field was quite limited. The work of Awad and Petrasovits (1968) was based on non-instrumented piles and as such does not throw much light on the behavior of batter piles.

The author (Murthy, 1965) conducted a comprehensive series of model tests on instrumented piles embedded in dry sand. The batter used by the author varied from -45° to +45°. A part of the author's study on the behavior of batter piles, based on his own research work, has been included in this blog.

Figure 16.1 (a) Batter piles

Wednesday, November 28, 2012


The uplift capacity of a pile group, when the vertical piles are arranged in a closely spaced groups may not be equal to the sum of the uplift resistances of the individual piles. This is because, at ultimate load conditions, the block of soil enclosed by the pile group gets lifted. The manner in which the load is transferred from the pile to the soil is quite complex. A simplified way of calculating the uplift capacity of a pile group embedded in cohesionless soil is shown in Fig. 15.33(a). A spread of load of 1 Horiz : 4 Vert from the pile group base to the ground surface may be taken as the volume of the soil to be lifted by the pile group (Tomlinson, 1977).

For simplicity in calculation, the weight of the pile embedded in the ground is assumed to be equal to that of the volume of soil it displaces. If the pile group is partly or fully submerged, the submerged weight of soil below the water table has to be taken.

In the case of cohesive soil, the uplift resistance of the block of soil in undrained shear enclosed by the pile group given in Fig. 15.33(b) has to be considered. The equation for the total uplift capacity Pgu of the group may be expressed by

Figure 15.33 Uplift capacity of a pile group

A factor of safety of 2 may be used in both cases of piles in sand and clay.

The uplift efficiency Egu of a group of piles may be expressed as

The efficiency Egu varies with the method of installation of the piles, length and spacing and the type of soil. 

The available data indicate that Egu increases with the spacing of piles. Meyerhof and
Adams (1968) presented some data on uplift efficiency of groups of two and four model circular footings in clay. The results indicate that the uplift efficiency increases with the spacing of the footings or bases and as the depth of embedment decreases, but decreases as the number of footings or bases in the group increases. 

How far the footings would represent the piles is a debatable point.
For uplift loading on pile groups in sand, there appears to be little data from full scale field tests.


Figure 15.32(a) shows a single pile and (b) a group of piles passing through a recently constructed cohesive soil fill. The soil below the fill had completely consolidated under its overburden pressure.

When the fill starts consolidating under its own overburden pressure, it develops a drag on the surface of the pile. This drag on the surface of the pile is called 'negative friction'. Negative friction may develop if the fill material is loose cohesionless soil. Negative friction can also occur when fill is placed over peat or a soft clay stratum as shown in Fig. 15.32c. The superimposed loading on such compressible stratum causes heavy settlement of the fill with consequent drag on piles.

Negative friction may develop by lowering the ground water which increases the effective stress causing consolidation of the soil with resultant settlement and friction forces being developed on the pile.

Negative friction must be allowed when considering the factor of safety on the ultimate carrying capacity of a pile. The factor of safety, Fs, where negative friction is likely to occur may be written as

Figure 15.32 Negative friction on piles

Computation of Negative Friction on a Single Pile
The magnitude of negative friction Fn for a single pile in a fill may be taken as (Fig. 15.32(a)).

(a) For cohesive soils

(b) For cohesionless soils

Negative Friction on Pile Groups
When a group of piles passes through a compressible fill, the negative friction, Fn , on the group may be found by any of the following methods [Fig. 15.32b].

Equation (15.82) gives the negative friction forces of the group as equal to the sum of the
friction forces of all the single piles.

Eq. (15.83) assumes the possibility of block shear failure along the perimeter of the group which includes the volume of the soil γLnA8 enclosed in the group. The maximum value obtained from Eqs (15.82) or (15.83) should be used in the design.

When the fill is underlain by a compressible stratum as shown in Fig. 15.32(c), the total negative friction may be found as follows:

The maximum value of the negative friction obtained from Eqs. (15.84) or (15.85) should be used for the design of pile groups.


The total settlements of pile groups may be calculated by making use of consolidation settlement equations.

The problem involves evaluating the increase in stress Δp beneath a pile group when the group is subjected to a vertical load Qg . The computation of stresses depends on the type of soil through which the pile passes. The methods of computing the stresses are explained below:

Figure 15.31 Settlement of pile groups in clay soils

1. The soil in the first group given in Fig. 15.31 (a) is homogeneous clay. The load Qg is assumed to act on a fictitious footing at a depth 2/3L from the surface and distributed over the sectional area of the group. The load on the pile group acting at this level is assumed to spread out at a 2 Vert : 1 Horiz slope.

2. In the second group given in (b) of the figure, the pile passes through a very weak layer of depth L1 and the lower portion of length L2 is embedded in a strong layer. In this case, the load Q is assumed to act at a depth equal to 2/3 L2 below the surface of the strong layer and Q8 spreads at a 2 : 1 slope as before.

3. In the third case shown in (c) of the figure, the piles are point bearing piles. The load in this case is assumed to act at the level of the firm stratum and spreads out at a 2 : 1 slope.


Driven piles. If piles are driven into loose sands and gravel, the soil around the piles to a radius of at least three times the pile diameter is compacted. When piles are driven in a group at close spacing, the soil around and between them becomes highly compacted. When the group is loaded, the piles and the soil between them move together as a unit. Thus, the pile group acts as a pier foundation having a base area equal to the gross plan area contained by the piles. The efficiency of the pile group will be greater than unity as explained earlier. It is normally assumed that the efficiency falls to unity when the spacing is increased to five or six diameters. Since present knowledge is not sufficient to evaluate the efficiency for different spacing of piles, it is conservative to assume an efficiency factor of unity for all practical purposes. We may, therefore, write

where n - the number of piles in the group.

The procedure explained above is not applicable if the pile tips rest on compressible soil such as silts or clays. When the pile tips rest on compressible soils, the stresses transferred to the compressible soils from the pile group might result in over-stressing or extensive consolidation. The carrying capacity of pile groups under these conditions is governed by the shear strength and compressibility of the soil, rather than by the 'efficiency'' of the group within the sand or gravel stratum.

Bored Pile Groups In Sand And Gravel
Bored piles are cast-in-situ concrete piles. The method of installation involves

1. Boring a hole of the required diameter and depth,
2. Pouring in concrete.

There will always be a general loosening of the soil during boring and then too when the boring has to be done below the water table. Though bentonite slurry (sometimes called as drilling mud) is used for stabilizing the sides and bottom of the bores, loosening of the soil cannot be avoided. Cleaning of the bottom of the bore hole prior to concreting is always a problem which will never be achieved quite satisfactorily. Since bored piles do not compact the soil between the piles, the efficiency factor will never be greater than unity. However, for all practical purposes, the efficiency may be taken as unity.

Figure 15.27 Block failure of a pile group in clay soil

Pile Groups In Cohesive Soils
The effect of driving piles into cohesive soils (clays and silts) is very different from that of cohesionless soils. It has already been explained that when piles are driven into clay soils, particularly when the soil is soft and sensitive, there will be considerable remolding of the soil. Besides there will be heaving of the soil between the piles since compaction during driving cannot be achieved in soils of such low permeability. There is every possibility of lifting of the pile during this process of heaving of the soil. Bored piles are, therefore, preferred to driven piles in cohesive soils. In case driven piles are to be used, the following steps should be favored:
1. Piles should be spaced at greater distances apart.
2. Piles should be driven from the center of the group towards the edges, and
3. The rate of driving of each pile should be adjusted as to minimize the development of pore water pressure.
Experimental results have indicated that when a pile group installed in cohesive soils is loaded, it may fail by any one of the following ways:
1. May fail as a block (called block failure).
2. Individual piles in the group may fail.

When piles are spaced at closer intervals, the soil contained between the piles move downward with the piles and at failure, piles and soil move together to give the typical 'block failure'. Normally this type of failure occurs when piles are placed within 2 to 3 pile diameters. For wider spacings, the piles fail individually. The efficiency ratio is less than unity at closer spacings and may reach unity at a spacing of about 8 diameters. 

The equation for block failure may be written as (Fig. 15.27).

The bearing capacity of a pile group on the basis of individual pile failure may be written as

The bearing capacity of a pile group is normally taken as the smaller of the two given by Eqs. (15.70) and (15.71).


The spacing of piles is usually predetermined by practical and economical considerations. The design of a pile foundation subjected to vertical loads consists of

1. The determination of the ultimate load bearing capacity of the group Qgu.
2. Determination of the settlement of the group, S , under an allowable load Qga

The ultimate load of the group is generally different from the sum of the ultimate loads of individual piles Qu.

The factor
is called group efficiency which depends on parameters such as type of soil in which the piles are embedded, method of installation of piles i.e. either driven or cast-in-situ piles, and spacing of piles.

There is no acceptable "efficiency formula" for group bearing capacity. There are a few formulae such as the Converse-Labarre formula that are sometimes used by engineers. These formulae are empirical and give efficiency factors less than unity. But when piles are installed in sand, efficiency factors greater than unity can be obtained as shown by Vesic (1967) by his experimental investigation on groups of piles in sand. There is not sufficient experimental evidence to determine group efficiency for piles embedded in clay soils.

Efficiency of Pile Groups in Sand
Vesic (1967) carried out tests on 4 and 9 pile groups driven into sand under controlled conditions.

Piles with spacings 2, 3,4, and 6 times the diameter were used in the tests. The tests were conducted in homogeneous, medium dense sand. His findings are given in Fig. 15.26. The figure gives the following:

1. The efficiencies of 4 and 9 pile groups when the pile caps do not rest on the surface.
2. The efficiencies of 4 and 9 pile groups when the pile caps rest on the surface.
3. The skin efficiency of 4 and 9 pile groups.
4. The average point efficiency of all the pile groups.

Figure 15.26 Efficiency of pile groups in sand (Vesic, 1967)

It may be mentioned here that a pile group with the pile cap resting on the surface takes more load than one with free standing piles above the surface. In the former case, a part of the load is taken by the soil directly under the cap and the rest is taken by the piles. The pile cap behaves the same way as a shallow foundation of the same size. Though the percentage of load taken by the group is quite considerable, building codes have not so far considered the contribution made by the cap.

It may be seen from the Fig. 15.26 that the overall efficiency of a four pile group with a cap resting on the surface increases to a maximum of about 1.7 at pile spacings of 3 to 4 pile diameters, becoming somewhat lower with a further increase in spacing. A sizable part of the increased bearing capacity comes from the caps. If the loads transmitted by the caps are reduced, the group efficiency drops to a maximum of about 1.3.

Very similar results are indicated from tests with 9 pile groups. Since the tests in this case were carried out only up to a spacing of 3 pile diameters, the full picture of the curve is not available. However, it may be seen that the contribution of the cap for the bearing capacity is relatively smaller.

Vesic measured the skin loads of all the piles. The skin efficiencies for both the 4 and 9-pile groups indicate an increasing trend. For the 4-pile group the efficiency increases from about 1.8 at 2 pile diameters to a maximum of about 3 at 5 pile diameters and beyond. In contrast to this, the average point load efficiency for the groups is about 1.01. Vesic showed for the first time that the increasing bearing capacity of a pile group for piles driven in sand comes primarily from an increase in skin loads. The point loads seem to be virtually unaffected by group action.

Pile Group Efficiency Equation
There are many pile group equations. These equations are to be used very cautiously, and may in many cases be no better than a good guess. The Converse-Labarre Formula is one of the most widely used group-efficiency equations which is expressed as


Very rarely are structures founded on single piles. Normally, there will be a minimum of three piles
under a column or a foundation element because of alignment problems and inadvertent
eccentricities. The spacing of piles in a group depends upon many factors such as

1. overlapping of stresses of adjacent piles,
2. cost of foundation,
3. efficiency of the pile group.

The pressure isobars of a single pile with load Q acting on the top are shown in Fig. 15.24(a).

When piles are placed in a group, there is a possibility the pressure isobars of adjacent piles will overlap each other as shown in Fig. 15.24(b). The soil is highly stressed in the zones of overlapping of pressures. With sufficient overlap, either the soil will fail or the pile group will settle excessively since the combined pressure bulb extends to a considerable depth below the base of the piles. It is possible to avoid overlap by installing the piles further apart as shown in Fig. 15.24(c). Large spacings are not recommended sometimes, since this would result in a larger pile cap which would increase the cost of the foundation.

The spacing of piles depends upon the method of installing the piles and the type of soil. The piles can be driven piles or cast-in-situ piles. When the piles are driven there will be greater overlapping of stresses due to the displacement of soil. If the displacement of soil compacts the soil in between the piles as in the case of loose sandy soils, the piles may be placed at closer intervals.

Figure 15.24 Pressure isobars of (a) single pile, (b) group of piles, closely spaced,
and (c) group of piles with piles far apart.

But if the piles are driven into saturated clay or silty soils, the displaced soil will not compact the soil between the piles. As a result the soil between the piles may move upwards and in this process lift the pile cap. Greater spacing between piles is required in soils of this type to avoid lifting of piles. When piles are cast-in-situ, the soils adjacent to the piles are not stressed to that extent and as such smaller spacings are permitted.

Generally, the spacing for point bearing piles, such as piles founded on rock, can be much less than for friction piles since the high-point-bearing stresses and the superposition effect of overlap of the point stresses will most likely not overstress the underlying material nor cause excessive settlements.

The minimum allowable spacing of piles is usually stipulated in building codes. The spacings for straight uniform diameter piles may vary from 2 to 6 times the diameter of the shaft. For friction piles, the minimum spacing recommended is 3d where d is the diameter of the pile. For end bearing piles passing through relatively compressible strata, the spacing of piles shall not be less than 2.5d.
For end bearing piles passing through compressible strata and resting in stiff clay, the spacing may be increased to 3.5d. For compaction piles, the spacing may be Id. Typical arrangements of piles in groups are shown in Fig. 15.25.

Figure 15.25 Typical arrangements of piles in groups


Piles are also used to resist uplift loads. Piles used for this purpose are called tension piles, uplift piles or anchor piles. Uplift forces are developed due to hydrostatic pressure or overturning moments as shown in Fig. 15.22.

Figure 15.22 shows a straight edged pile subjected to uplift force. The equation for the uplift force Pul  may be written as

Uplift Resistance of Pile in Clay
For piles embedded in clay, Eq. (15.65) may written as

Figure 15.23 gives the relationship between a and cu based on pull out test results as collected by Sowa (1970). As per Sowa, the values of ca agree reasonably well with the values for piles subjected to compression loadings.

Figure 15.22 Single pile subjected to uplift

Figure 15.23 Relationship between adhesion factor α and undrained shear strength cu (Source: Poulos and Davis, 1980)

Uplift Resistance of Pile in Sand
Adequate confirmatory data are not available for evaluating the uplift resistance of piles embedded in cohesionless soils. Ireland (1957) reports that the average skin friction for piles under compression loading and uplift loading are equal, but data collected by Sowa (1970) and Downs and Chieurzzi (1966) indicate lower values for upward loading as compared to downward loading especially for cast-in-situ piles. Poulos and Davis (1980) suggest that the skin friction of upward loading may be taken as two-thirds of the calculated shaft resistance for downward loading.
A safety factor of 3 is normally assumed for calculating the safe uplift load for both piles in clay and sand.


Piles are at times required to be driven through weak layers of soil until the tips meet a hard strata for bearing. If the bearing strata happens to be rock, the piles are to be driven to refusal in order to obtain the maximum carrying capacity from the piles. If the rock is strong at its surface, the pile will refuse further driving at a negligible penetration. In such cases the carrying capacity of the piles is governed by the strength of the pile shaft regarded as a column as shown in Fig. 15.6(a). If the soil mass through which the piles are driven happens to be stiff clays or sands, the piles can be regarded as being supported on all sides from buckling as a strut. In such cases, the carrying capacity of a pile is calculated from the safe load on the material of the pile at the point of minimum cross-section. In practice, it is necessary to limit the safe load on piles regarded as short columns because of the likely deviations from the vertical and the possibility of damage to the pile during driving.

If piles are driven to weak rocks, working loads as determined by the available stress on the material of the pile shaft may not be possible. In such cases the frictional resistance developed over the penetration into the rock and the end bearing resistance are required to be calculated. Tomlinson (1986) suggests an equation for computing the end bearing resistance of piles resting on rocky strata as

Boring of a hole in rocky strata for constructing bored piles may weaken the bearing strata of
some types of rock. In such cases low values of skin friction should be used and normally may not
be more than 20 kN/m2 (Tomlinson, 1986) when the boring is through friable chalk or mud stone.

In the case of moderately weak to strong rocks where it is possible to obtain core samples for unconfmed compression tests, the end bearing resistance can be calculated by making use of Eq. (15.64).

Pile Driving Equipment for Driven and Driven Cast-in-situ Piles.

Pile driving equipment contains three parts. They are

1. A pile frame,
2. Piling winch,
3. Impact hammers.

Pile Frame
Pile driving equipment is required for driven piles or driven cast-in-situ piles. The driving pile frame must be such that it can be mounted on a standard tracked crane base machine for mobility on land sites or on framed bases for mounting on stagings or pontoons in offshore construction. Fig.15.3 gives a typical pile frame for both onshore and offshore construction. Both the types must be capable of full rotation and backward or forward raking. All types of frames consist essentially of leaders, which are a pair of steel members extending for the full height of the frame and which guide the hammer and pile as it is driven into the ground. Where long piles have to be driven the leaders can be extended at the top by a telescopic boom.

The base frame may be mounted on swivel wheels fitted with self-contained jacking screws for leveling the frame or it may be carried on steel rollers. The rollers run on steel girders or long timbers and the frame is moved along by winching from a deadman set on the roller track, or by turning the rollers by a tommy-bar placed in holes at the ends of the rollers. Movements parallel to the rollers are achieved by winding in a wire rope terminating in hooks on the ends of rollers; the frame then skids in either direction along the rollers. It is important to ensure that the pile frame remains in its correct position throughout the driving of a pile.

Piling Winches
Piling winches are mounted on the base. Winches may be powered by steam, diesel or gasoline engines, or electric motors. Steam-powered winches are commonly used where steam is used for the piling hammer. Diesel or gasoline engines, or electric motors (rarely) are used in conjunction with drop hammers or where compressed air is used to operate the hammers.

Impact Hammers
The impact energy for driving piles may be obtained by any one of the following types of hammers.

They are

1. Drop hammers,
2. Single-acting steam hammers,
3. Double-acting steam hammers,
4. Diesel hammer,
5. Vibratory hammer.

Figure 15.3 Pile driving equipment and vibratory pile driver

Drop hammers are at present used for small jobs. The weight is raised and allowed to fall freely on the top of the pile. The impact drives the pile into the ground.
In the case of a single-acting steam hammer steam or air raises the moveable part of the hammer which then drops by gravity alone. The blows in this case are much more rapidly delivered than for a drop hammer. The weights of hammers vary from about 1500 to 10,000 kg with the length of stroke being about 90 cm. In general the ratio of ram weight to pile weight may vary from 0.5 to 1.0.

In the case of a double-acting hammer steam or air is used to raise the moveable part of the hammer and also to impart additional energy during the down stroke. The downward acceleration of the ram owing to gravity is increased by the acceleration due to steam pressure. The weights of hammers vary from about 350 to 2500 kg. The length of stroke varies from about 20 to 90 cm. The rate of driving ranges from 300 blows per minute for the light types, to 100 blows per minute for the heaviest types.

Diesel or internal combustion hammers utilize diesel-fuel explosions to provide the impact energy to the pile. Diesel hammers have considerable advantage over steam hammers because they are lighter, more mobile and use a smaller amount of fuel. The weight of the hammer varies from about 1000 to 2500 kg.

The advantage of the power-hammer type of driving is that the blows fall in rapid succession (50 to 150 blows per minute) keeping the pile in continuous motion. Since the pile is continuously moving, the effects of the blows tend to convert to pressure rather than impact, thus reducing damage to the pile.

The vibration method of driving piles is now coming into prominence. Driving is quiet and does not generate local vibrations. Vibration driving utilizes a variable speed oscillator attached to the top of the pile (Fig. 15.3(b)). It consists of two counter rotating eccentric weights which are in phase twice per cycle (180° apart) in the vertical direction. This introduces vibration through the pile which can be made to coincide with the resonant frequency of the pile. As a result, a push-pull effect is created at the pile tip which breaks up the soil structure allowing easy pile penetration into the ground with a relatively small driving effort. Pile driving by the vibration method is quite common in Russia.

Jetting Piles
Water jetting may be used to aid the penetration of a pile into dense sand or dense sandy gravel. Jetting is ineffective in firm to stiff clays or any soil containing much coarse to stiff cobbles or boulders.

Where jetting is required for pile penetration a stream of water is discharged near the pile point or along the sides of the pile through a pipe 5 to 7.5 cm in diameter. An adequate quantity of water is essential for jetting. Suitable quantities of water for jetting a 250 to 350 mm pile are

A pressure of at least 5 kg/cm^2  or more is required.


The method of installing a pile at a site depends upon the type of pile. The equipment required for this
purpose varies. The following types of piles are normally considered for the purpose of installation

1. Driven piles
The piles that come under this category are,

a. Timber piles,
b. Steel piles, H-section and pipe piles,
c. Precast concrete or prestressed concrete piles, either solid or hollow sections.

2. Driven cast-in-situ piles
This involves driving of a steel tube to the required depth with the end closed by a detachable conical tip.

The tube is next concreted and the shell is simultaneously withdrawn. In some cases the
shell will not be withdrawn.

3. Bored cast-in-situ piles
Boring is done either by auguring or by percussion drilling. After boring is completed, the bore is concreted with or without reinforcement.

⇒ Pile Driving Equipment for Driven and Driven Cast-in-situ Piles 


The major uses of piles are:

1. To carry vertical compression load.
2. To resist uplift load.
3. To resist horizontal or inclined loads.

Normally vertical piles are used to carry vertical compression loads coming from superstructures such as buildings, bridges etc. The piles are used in groups joined together by pile caps. The loads carried by the piles are transferred to the adjacent soil. If all the loads coming on the tops of piles are transferred to the tips, such piles are called end-bearing or point-bearing piles.

However, if all the load is transferred to the soil along the length of the pile such piles are called friction piles. If, in the course of driving a pile into granular soils, the soil around the pile gets compacted, such piles are called compaction piles. Fig. 15.2(a) shows piles used for the foundation of a multistoried building to carry loads from the superstructure.

Piles are also used to resist uplift loads. Piles used for this purpose are called tension piles or uplift piles or anchor piles. Uplift loads are developed due to hydrostatic pressure or overturning movement as shown in Fig. 15.2(a).

Piles are also used to resist horizontal or inclined forces. Batter piles are normally used to resist large horizontal loads. Fig. 15.2(b) shows the use of piles to resist lateral loads.

Figure 15.2(a) Principles of floating foundation; and a typical rigid raft foundation
Figure 15.2(b) Piles used to resist lateral loads