Deformation Prediction of Tunnel-Surrounding Rock Considering the Time Effect of the Viscosity Coefficient: A Case of an NATM-Excavated Tunnel

Considering engineering problems such as complicated stress and the difficulty in controlling large deformation while a tunnel passes through a soft rock stratum, a theoretical prediction model of convergence deformation of tunnel-surrounding rock is proposed. Based on the longitudinal displacement profile curve reflecting the “space effect” of the excavation surface, the Hoek formula with better applicability was introduced to analyze and theoretically deduct the “time–space effect comprehensively.” By taking the influence of the “time effect” coefficient into account, an improved Nishihara model was established to derive the analytical equation of the viscoelastic–viscoplastic convergence of surrounding rock. Taking the Dingxi Tunnel of Wujing Expressway in Hunan Province, the physical and mechanical parameters of surrounding rock in the tunnel were firstly determined then they were used to calculate and predict the vault down of three typical sections with the scoping equation of surrounding rock deformation. Based on the calculation results, the causes of the differences between the measured and theoretical values were analyzed; moreover, it is indicated that the minimum root-mean-square error is 1.68, the minimum average error is 1.3%, and the correlation coefficient is 0.99. The comparison shows that the theoretical prediction results agree well with the corresponding field test results. The improved Nishihara model can accurately predict the final deformation of the surrounding rock. Simultaneously, it is also proved that the relevant parameters and the hypothesis and correlation of the nonlinear viscosity coefficient equation are reasonable, with particular effectiveness and applicability in practical engineering. This study is significant for further studying the tunnel-surrounding rock’s stability and accumulating theoretical and practical experience to develop rheological theory.