Effect of Soil Layer Permeability on Seepage Beneath Hydraulic Structures: An Explainable Machine Learning Approach

Abstract

Alluvial foundations of weirs and barrages are stratified, yet classical design methods and existing machine-learning (ML) surrogates treat the foundation as a single homogeneous layer. This study quantifies how the permeability of soil layers controls the seepage discharge (q), uplift force (U) and exit gradient (ie) beneath a floor with upstream and downstream cutoffs, and proposes a physics-guided deep-ensemble (PG-DE) surrogate. A finite-volume solver, verified against exact conformal-mapping solutions (deviation ≤ 0.31%), generated 16,384 two-layer cases with permeability ratios k1/k2 = 0.01– 100. PG-DE learns similarity-normalised responses from dimensionless (Buckingham-Π) groups. On unseen test cases it achieved R 2 = 0.99992, 0.99996 and 0.99991 for q, U and ie, with mean absolute percentage errors ≤ 0.43%, whereas seven conventional learners trained on raw variables reached at most R 2 = 0.876, 0.969 and 0.976. On a public MODFLOW exit-gradient database, the same physicsguided strategy raised R 2 from 0.710 to 0.902 under the original cross-validation protocol. Relative to homogeneous soil, the layer contrast changed q by factors of 0.06–82 and ie by up to 5.3; a less permeable surface layer sharply raises ie, while uplift is most sensitive when the downstream cutoff tip reaches the layer interface. The framework offers an accurate and explainable tool for preliminary design on stratified foundations.