Inversion of in-situ stress in soft rock tunnels with large deformation using a whale optimization–BP neural network: A case study of the monitoring section in the Liren Tunnel

Accurate determination of initial in-situ stress is essential for tunnel support design and safety evaluation. However, direct measurement methods are often restricted by geological conditions and economic factors. To address the absence of hydraulic fracturing data for the Liren Tunnel, this study develops an intelligent inversion method integrating the Whale Optimization Algorithm (WOA) with a Backpropagation (BP) neural network. A three-dimensional numerical model was established using FLAC3D, and displacement monitoring data (including crown settlement and horizontal convergence) were used to constrain the boundary stress parameters. Eighteen forward simulations based on the U18*(3) uniform design generated training samples, establishing a nonlinear mapping relationship between deformation responses and stress boundary conditions. The WOA was employed to globally optimize the initial weights and biases of the BP neural network, significantly enhancing convergence speed and inversion accuracy. The developed WOA–BP model achieves an average inversion error of 5.73% for vertical deformation, which is 5.48% and 1.61% lower than that of the traditional iterative method and the standalone BP model, respectively. For horizontal deformation, the average inversion error is 6.85%, corresponding to reduction of 6.27% and 4.18%. In addition, the proposed method requires only about one-third of the iterations needed by the BP model. These results indicate that the WOA–BP method offers a highly accurate and computationally efficient solution for estimating in-situ stress fields in soft rock tunnels, providing practical guidance for deformation control and support optimization in similar engineering contexts.