Probabilistic Analysis of Laterally Loaded Piles using Commercial Finite Difference Software-Paper

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The paper presents <strong>AllPile Randomizer</strong>, a free Python application that enables Monte Carlo probabilistic analysis of laterally loaded piles using the commercial finite-difference program AllPile. It modifies AllPile input files to vary soil properties, addressing the fact that commercial pile-analysis software generally assumes deterministic inputs and does not directly support probabilistic simulations.

The application samples corrected standard penetration test (SPT) values and water-table depths, runs repeated AllPile analyses, and estimates failure probability and reliability index for a specified performance limit. Because AllPile restricts the number of soil layers, the study uses random variables rather than spatial random fields. The current application is limited to a single sand layer, though future expansion is planned.

A parametric study considered a 50-foot-long, 1-foot-diameter pile in dense sand. For a one-inch deflection limit, 10,000 simulations were performed at varying coefficients of variation (COV). Uncertainty in corrected SPT values had a substantially greater effect on failure probability than uncertainty in water-table depth. SPT variability caused failure probability to rise sharply at low COVs before leveling off; water-table variability produced a smaller, gradual increase.

The authors also demonstrated reliability-based calibration of deflection limits using 100,000 simulations. Under the assumed soil variability, a target reliability index of 3.7 (failure probability of 1 in 10,000) corresponded to a deflection limit of approximately 0.42 inches. This value applies only to the example pile and soil conditions.

The study shows how probabilistic analysis can make pile-design risk more explicit and support more informed, potentially economical decisions. Broader application will require extending the tool to multiple soil layers and soil types.

Keywords

AllPile Randomizer

Monte Carlo analysis

laterally loaded piles

probabilistic analysis

finite-difference software

SPT variability

water table depth

failure probability

reliability index

pile design