The Vertical Behaviors of Dissimilar Pile Composite Foundations over Inclined Bedrock

Abstract

Pile composite foundations (PCFs) have been commonly applied in reinforcement engineering to adjust the vertical stiffness of foundations, due to the displacement control design criteria for foundations. PCFs that have dissimilar pile lengths, located over inclined bedrock, have shown significantly different vertical behaviors from PCFs with equal pile lengths, placed over a semi-infinite medium. However, the vertical behaviors of dissimilar PCFs over inclined bedrock cannot be predicted with the current theoretical methods, although they have been widely adopted in engineering. An analytical method is proposed in this investigation to analyze the vertical bearing characteristics of dissimilar PCFs over inclined bedrock. A pile–soil system is decomposed into fictitious piles and extended soil, and then a control equation to determine the axial force along the fictitious piles is established, stemming from the compatibility conditions between them. The vertical behaviors of dissimilar PCFs can be obtained by solving the control equation with iterative procedures, and the equation is verified by two field load tests of single piles from the Honghe bridge and a numerical case. Then, the settlement and load transfer behaviors of 3 × 1 dissimilar PCFs and their influence factors are analyzed, and the results are as follows. (1) Obvious differences can be observed concerning the axial force distribution, settlement w, and load-sharing ratio (LSR) of each pile element for different pile–soil stiffness ratios (Ep/Es). (2) The LSR of pile 1 increases from 0.074 to 0.253 for the rigid pile and from 0.062 to 0.161 for the flexible pile condition when the cushion stiffness Kc changes from 1 × 104 kN/m to 3 × 108 kN/m. The non-dimensional vertical stiffness of the foundation, N0/wdEs, increases from 10.21 to 28.95 for the rigid pile condition and increases from 8.69 to 14.44 for the flexible pile condition, when Kc increases from 1 × 104 kN/m to 4 × 105 kN/m. (3) The neutral layer depth of the pile zn, the average settlement w, and the differential settlement wd of each element head decrease with Kc, and no negative friction zone exists (zn = 0 m) for all the pile elements when Kc> 2 × 105 kN/m. (4) The N0/wdEs decreases with the distance between the pile bottom and the inclined bedrock Δ. For the rigid and flexible pile conditions, the N0/wdEs is 22.16 and 13.48 for Δ = 1 m, and 13.13 and 10.10 for Δ = 8 m. The wd reaches 16.7 mm and 4.0 mm for Δ = 1 m and Δ = 8 m, respectively. (5) The N0/wdEs increases almost linearly with an increase in l/d for the rigid pile condition, and it gradually decreases for the flexible pile condition. The developed model can improve the design and analysis of PCFs located over inclined bedrock under vertical loading.