An Efficient Geostress Inversion Method and Its Application under Complex Geological Conditions

Accurate initial geostress state is a prerequisite for the dynamic optimization design and construction of deep-buried tunnels, as well as for preventing disasters such as rockburst and large deformation. Inversion methods of the stress field for underground engineering, which utilize limited measurement data and numerical simulation techniques, have emerged as the primary approach. However, traditional inversion optimization models often treat stress components as independent scalars. This simplification overlooks issues of physical consistency and optimization complexity. Additionally, existing intelligent inversion methods, such as machine learning and heuristic optimization, require a large number of simulations, posing a challenge in balancing accuracy and efficiency. This issue becomes particularly problematic for large-scale tunnels in complex geological conditions where the computational time cost is exorbitantly high, thereby hindering the practical need for quick and precise stress field reconstruction.

 

To address these challenges, we propose a novel inversion method that integrates a tensor-based objective function with Bayesian optimization (TOF-BO). Concretely, this method regards the stress tensor as a whole, uses the Euclidean distance to measure the deviation between calculated and measured values during optimization, and formulates the objective function as the sum of deviations across all measurement points. Unlike traditional scalar objective functions, this tensor-based objective function preserves the physical correlations between stress components, reduces the dimensionality of the objective function, and effectively avoids the adverse effects of magnitude differences between components on optimization efficiency and accuracy. Given the objective function's dependency on costly simulation, we adopt Bayesian optimization, utilizing active learning to achieve global and efficient optimization.

 

This method was applied at the engineering site of a deep-buried tunnel under construction in southwestern China. The results showed that the TOF-BO method yielded satisfactory results (average accuracy=90.8%) with only 18 time-consuming numerical simulations, proving that the method can significantly reduce the demand for expensive simulations, effectively decrease computational costs, and possesses the ability to rapidly and reliably reconstruct the stress field within the study area. Compared to commonly neural network methods, the TOF-BO method improves accuracy by approximately 4.6% within the same time cost. In conclusion, the TOF-BO method provides an efficient and reliable solution for the inversion of geostress fields, demonstrating substantial potential for practical applications.