An Efficient Semi-Analytical Operator-Splitting Framework for Coupled Finite Element Liquefaction Analysis

This paper presents an efficient semi-analytical operator-splitting framework for coupled finite element liquefaction analysis in saturated granular soils under dynamic loading. The methodology decomposes the coupled hydro-mechanical problem into a mechanical equilibrium sub-problem and a pore pressure diffusion sub-problem, each addressed with closed-form analytical integration within a staggered time-stepping scheme. A modified cyclic nonlinear hysteretic constitutive model with analytical pore pressure generation and post-liquefaction stiffness degradation is embedded at the Gauss-point level, bypassing the need for iterative constitutive integration through closed-form backbone relations. The Ladyzhenskaya-Babuška-Brezzi stability condition is verified for the Q2/Q1 Taylor-Hood element pair, and convergence rates of 𝑂 ⁡ ( ℎ 2 ) for displacement and 𝑂 ⁡ ( ℎ ) for pore pressure are established theoretically and confirmed numerically. Validation against independent monolithic FEM benchmark simulations demonstrates relative errors below 3.5% for both displacement and excess pore pressure. Computational cost analysis reveals a speedup exceeding three orders of magnitude compared with monolithic integration for large-scale problems. Parametric studies quantify the sensitivity of liquefaction onset to hydraulic conductivity and cyclic resistance to relative density.