Integral equation method for interaction effect of stress of vertically loaded pile groups considering consolidation

The interaction effect of stress is obtained for two vertically loaded piles which are of equal or different pile lengths embedded in the homogeneous poroelastic saturated soils governed by the Biot’s theory. The pile-soil system is decomposed into an extended soil and two fictitious piles, and the compatibility condition between the axial strain of the fictitious piles and the extended soil is established. This approach yields the governing Fredholm integral equations of the second kind, and the basic unknowns of the axial force and settlement along the pile shaft are calculated. For the piles with the same length, the additional force along the pile shaft can be observed at 20%~80% depth of pile length due to the adjacent pile and decreases with the pile spacing. Extending two-pile model into pile group analysis, pile group effect will lead to the differences in load at the pile heads. The consolidation effect can alter the distribution of axial stress along the pile shafts. The loadings acting on the corner piles decrease. For the piles with different dimensions, the interactions among long and short piles are different, and the additional axial force along the long pile is greater than that along the short one. The combination of long and short piles is applied to the optimization of pile groups. The results show that adjusting the pile length within a pile group can reduce the differential pile-head loadings without increasing the total pile length and pile-head settlement.