When the loads imposed at the foundation level are not capable of being balanced by a single pile, a set of piles is installed in order to constitute a pile group. The piles are connected at the top by a very rigid element, the pile cap, which has the function of distributing the loads imposed by the structure over the different piles.
Considering the generalized loading system shown in Figure 7.28, composed of vertical and horizontal forces, as well as moments acting in both directions, it is common practice to develop the analysis of the axial and lateral pile response by an uncoupled approach, i.e.,
Figure 7.28 Determination of axial force on piles from a group.
assuming that the pile-soil interaction mechanisms are independent of the loading direction (axial or lateral). As can be understood, since the piles are spaced apart, the moments arising from the structure are balanced by the generation of increments (positive and negative) to the axial force applied to each of the piles. Therefore, the axial force on each pile is given by:
where N, is the axial force in pile i, Mx, My are the moments and V the vertical force at the center of gravity at the base of the pile cap, and x, and y, are the coordinates of the center of gravity of the cross section of pile i.
When the pile group is subjected to horizontal loads, the distribution of the loads by the different piles is not uniform and it is a consequence of the pile-soil-pile interaction mechanism that will be analysed in Section 7.7.3.
Due to the development of a complex mechanism of load transfer, the response of a pile group can be quite different from that of a single isolated pile, giving rise to the so-called group effect. In following sections, this will be analyzed in detail.
Group effect in axially loaded piles
The interaction between piles belonging to a group and the surrounding soil is complex and the group bearing capacity can be different from the sum of the bearing capacity of the individual piles. Figure 7.29 presents a schematic representation of the increase of the soil loading due to the overlapping of soil stresses induced by each individual pile. As suggested in the same figure, the settlement of a pile group is also larger than the settlement of a single pile subjected to the same axial force as one of the piles from the group, since the volume of soil subjected to large stress increments is also larger.
The pile group bearing capacity, Rcg, is given by:
where Eg is the group efficiency factor, n is the number of piles of the group and Rc is the axial bearing capacity of a single isolated pile.
Figure 7.29 Heavily stressed zones near single piles and pile groups (Tomlinson and Woodward, 2007).
The group efficiency factor can be lower or greater than 1, depending on several issues, namely (Coduto, 2001):
i) the number, length, diameter, arrangement, and spacing of piles;
ii) the relative contributions of shaft and base resistances to the ultimate bearing capacity;
iii) the sequence of pile installation, mainly in the case of displacement piles;
iv) the soil type;
v) the interaction, if any, between the pile cap and the soil;
vi) the direction of the applied load (tension or compression).
The relative lack of experimental data available makes it difficult to validate theoretical models for the estimation of the group efficiency factor.1 Despite that, there are some main trends that can be readily discerned:
i) the group efficiency of displacement piles in loose sand is usually greater than 1 (Lo, 1967; Vesic, 1969). This is explained by the higher normal effective stress on the shaft and by the greater compaction of the soil around the piles driven in a group (Fleming et al., 2009);
ii) the group efficiency of displacement piles installed in clayey soils is generally lower than 1 due to soil remolding; another aspect that deserves attention is the time dependence of the group bearing capacity (see Section 7.3.2);
iii) for non-displacement piles, there are even fewer experimental data; accordingly to some authors (Das, 2004; Reese et ah, 2005), the group efficiency of bored piles should be slightly lower than 1 for pile spacing less than 3B.
For close-spaced pile groups, an alternative failure mechanism can develop, as shown in Figure 7.30. The bearing capacity of the pile group is given by the sum of the lateral resistances along the block perimeter, with the base resistance being computed by taking into account the area corresponding to the base of the block. It should be noticed that this failure mechanism only governs the group bearing capacity when dealing with close-spaced pile groups installed in clay under undrained conditions. Therefore, the block bearing capacity can be estimated as follows:
Figure 7.30 Failure modes in pile groups: a) isolated single pile failure; b) block-failure (adapted from Reese et al., 2005).
Experimental data is scarce because the required loads for pile groups are extremely high, making the testing difficult and expensive. Alternatively, small-scale centrifuge tests have provided useful insights about the topic.
where D is the pile length, LB and BB are the horizontal cross-sectional dimensions of the block, cld is the value of the undrained shear strength along the pile shaft, and cu2 is the undrained shear strength at the base of the block.
The bearing factor, N', is given by:
Obviously, if two distinct failure mechanisms are admissible, the group bearing capacity corresponds to the lowest value from Equations 7.82 and 7.83.
The following guidelines, presented by Hannigan et al. (2016) for driven piles, may be used for design purposes.
For driven piles in cohesionless soils:
i) For piles spaced more than three diameters apart and not underlain by a weak deposit, assume Eg= 1.
ii) Jetting or pre-drilling to pile installation should be avoided, since it can result in group efficiencies less than 1.
For driven piles in cohesive soils:
i) When cu< 95 kPa and without pile cap resting on the ground, for pile spacing, s, equal to 2.5B, use £s=0.65; for s>6B use E =1; linear interpolation should be used for intermediate center-to-center pile spacing.
ii) When cu< 95 kPa, but with the pile cap in firm contact with the ground, Eg= 1 may be used if s>3B.
iii) If c„>95 kPa, Eg=l may be used if s>3B.
iv) In any case, the pile group bearing capacity is the lesser value obtained from Equation 7.82 and the block failure capacity is given by Equation 7.83.
As already mentioned, experimental results for non-displacement piles are even rarer than for driven pile groups. The following guidelines were presented by Loehr et al. (2011):
For bored piles in cohesionless soils:
The pile group bearing capacity can be estimated from Equation 7.82, and group efficiency factor should be selected as follows:
i) for s = 2.5B, take Eg=0.65;
ii) for s>4B, assume Eg= 1;
iii) linear interpolation may be applied for intermediate spacings.
The guidelines expressed above are applicable regardless of the contact conditions between the pile cap and the ground.
For bored piles in cohesive soils:
The guidelines presented above for groups of driven piles installed in cohesive soils are also applicable for bored piles.