Back-Analysis of Rock Mass Parameters Using Displacement and Pressure Monitoring with Surrogate-Assisted NSGA-II and TOPSIS: A Zhaotong Tunnel Case Study

Abstract

A back-analysis of rock mass parameters in deep-buried tunnels with complex coal-bearing strata is often limited when only displacement monitoring is used, because support loading and local stress transfer may not be sufficiently constrained. In this study, a surrogate-assisted biobjective inversion framework is developed to integrate displacement and pressure monitoring data for a rock mass parameter back-analysis. A sensitivity analysis identifies the elastic modulus, Poisson’s ratio, and internal friction angle as the key inversion variables. Latin hypercube sampling and FLAC3D (version 7.0) simulations are used to generate training samples, and Gaussian process regression is adopted to establish the parameter–response mapping. Nondominated Sorting Genetic Algorithm II (NSGA-II) optimizes displacement and pressure errors in parallel, and the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) selects representative Pareto solutions under safety-oriented, balanced, and deformation-control preferences. The relative root-mean-square error serves as the scale-fair fitness metric, and the error contribution ratio (ECR) is introduced to quantify objective contributions and confirm scale invariance. The resulting Pareto front reveals the displacement–pressure trade-off, while the TOPSIS provides preference-dependent parameter sets and the ECR identifies the dominant source of error. Under three preference settings, the mean relative errors are 1.94%–3.28% for displacement and 4.61%–6.57% for pressure. The proposed framework provides decision-oriented parameter sets for design verification and construction control in deep-buried tunnels with multisource monitoring.