Spatial variability of kinematic pile response in liquefiable slopes: effects of static shear bias and partial drainage

Liquefaction-induced lateral spreading in sloping, layered ground can impose highly non-uniform kinematic demands on adjacent piles, yet most design checks assume uniform soil pressures. We present dynamic centrifuge tests on a three-layer deposit (dense crust over loose sand, underlain by a dense crust) at slopes of 5° and 10° with piles at upslope, midslope, and downslope positions, and propose an effective Deborah number (De eff ) to time drainage feasibility, based on the classical one-dimensional consolidation theory and the duration of upward seepage. During shaking, response is largely undrained (De eff > 1), with a greater tendency for stress non-reversal at the steeper slope; partial drainage becomes effective mainly post-shaking, first near the surface, with vertical extent governed by drainage-path length and loose-layer permeability. Spatial heterogeneity in excess pore pressure and stiffness yields inter-pile differences: downslope piles mobilize the largest co-seismic moments; and after shaking pile-head segments re-stiffen quickly, while deeper segments retain 0.6–0.9 M peak over the 0–250 s post-shaking window. Japan Road Association-based envelopes reproduce overall shape at 5° but, under stronger static bias (10°), systematically underpredict mid-column curvature near the loose-crust interface and overpredict base demand; free-field Rankine bounds confirm the plausibility of measured magnitudes. The results establish a mechanism-driven framework to identify where and when curvature concentrates, to interpret the role of post-shaking drainage, and inform the use of code-based envelopes.