Multi-objective Optimization Method for Anchor Cable Support in Deep Excavations in Soil-rock Composite Formations

This paper addresses the dual challenges of deformation control difficulties and insufficient economic viability in traditional support designs for deep excavations in confined soil-rock composite strata. It proposes an optimized anchor cable parameter method integrating geological sensitivity analysis with multi-objective decision-making. Using a deep excavation for a subway station as the engineering context, the study first employs a refined 3D finite element model (dimensions 130 m × 21 m × 65 m) to reveal: - A critical thickness effect for soil layers (critical value: 8.3 m) - A linear gain relationship between sandy tuff thickness and horizontal displacement (each 1 m increase in thickness increases bottom displacement by 3.5 mm) Subsequently, a multi-objective optimization function was established with variables including anchor prestress, horizontal spacing, vertical row count, and front-row position (objectives: horizontal displacement U, ground surface settlement S, and construction cost C). Finally, 16 design schemes were evaluated using orthogonal experimental design, combined with AHP-entropy weighting (cost 52.3% > displacement 32.1% > settlement 15.6%) and grey relational analysis to quantify overall performance. Results indicate the optimal parameter combination: prestressing force 300 kN, horizontal spacing 2.6 m, first-row anchor cable distance from second support 3.0 m, and three vertically arranged anchor cables (spacing 4 m and 7.5 m). Compared to the original scheme, this approach reduces costs by 56.36% while achieving significant deformation control (post-support removal horizontal displacement ≤21.36 mm, settlement ≤14.93 mm). The safety factor K=5.395 exceeds the standard value by 300%. This method overcomes technical bottlenecks in quantifying geological parameter thresholds and synergistically optimizing support parameters, providing a balanced solution for both safety and economy in deep excavations within soil-rock composite strata.