Numerical Simulation of In Situ Stress Fields in Deep Geotechnical Engineering Using Nonlinear Iterative Inversion

The mechanical behavior of deep rock masses under high-stress conditions exhibits significant nonlinear characteristics. However, current in situ stress field inversion methods typically rely on linear elastic constitutive models and multiple linear regression analysis. By analyzing the results of triaxial stress–strain tests and confining pressure calibration experiments on rocks, and drawing on the nonlinear concepts from the Duncan-Zhang model, a nonlinear characterization function was developed, represented by mean stress p, bulk modulus K, and shear modulus G. The nonlinear elastic constitutive model was integrated into a numerical simulation framework, and a new in situ stress field inversion fitting method based on nonlinear elastic constitutive modeling was proposed. This method uses initial linear iterations followed by multiple nonlinear iterations until convergence is achieved. Applied to the inversion of the deep in situ stress field at the Xishan Iron Mine, the results demonstrate that compared to traditional linear regression-based methods, the errors in mean stress, deviatoric stress, and the Lode parameter were reduced by 58%, 50%, and 22%, respectively, confirming the effectiveness of this method in in situ stress field inversion in rock mechanics.