In situ stress inversion using nonlinear stress boundaries achieved by the bubbling method

Due to the heterogeneity of rock masses and the variability of in situ stress, the traditional linear inversion method is insufficiently accurate to achieve high accuracy of the in situ stress field. To address this challenge, nonlinear stress boundaries for a numerical model are determined through regression analysis of a series of nonlinear coefficient matrices, which are derived from the bubbling method. Considering the randomness and flexibility of the bubbling method, a parametric study is conducted to determine recommended ranges for these parameters, including the standard deviation () of bubble radii, the non-uniform coefficient matrix number () for nonlinear stress boundaries, and the number (m) and positions of in situ stress measurement points. A model case study provides a reference for the selection of these parameters. Additionally, when the nonlinear in situ stress inversion method is employed, stress distortion inevitably occurs near model boundaries, aligning with the Saint Venant's principle. Two strategies are proposed accordingly: employing a systematic reduction of nonlinear coefficients to achieve high inversion accuracy while minimizing significant stress distortion, and excluding regions with severe stress distortion near the model edges while utilizing the central part of the model for subsequent simulations. These two strategies have been successfully implemented in the nonlinear in situ stress inversion of the Xincheng Gold Mine and have achieved higher inversion accuracy than the linear method. Specifically, the linear and nonlinear inversion methods yield root mean square errors (RMSE) of 4.15 and 3.2, and inversion relative errors () of 22.08% and 17.55%, respectively. Therefore, the nonlinear inversion method outperforms the traditional multiple linear regression method, even in the presence of a systematic reduction in the nonlinear stress boundaries.