A surrogate model for estimating rock stress by a hollow inclusion strain cell in a three-layer medium

Abstract

Accurate acquisition of the rock stress is crucial for various rock engineering applications. The hollow inclusion (HI) technique is widely used for measuring in-situ rock stress. This technique calculates the stress tensor by measuring strain using an HI strain cell. However, existing analytical solutions for stress calculation based on an HI strain cell in a double-layer medium are not applicable when an HI strain cell is used in a three-layer medium, leading to erroneous stress calculations. To address this issue, this paper presents a method for calculating stress tensors in a three-layer medium using numerical simulations, specifically by obtaining a constitutive matrix that relates strain measurements to stress tensors in a three-layer medium. Furthermore, using Latin hypercube sampling (LHS) and orthogonal experimental design strategies, 764 groups of numerical models encompassing various stress measurement scenarios have been established and calculated using FLAC^3D software. Finally, a surrogate model based on artificial neural network (ANN) was developed to predict constitutive matrices, achieving a goodness of fit (R²) of 0.999 and a mean squared error (MSE) of 1.254. A software program has been developed from this surrogate model for ease of use in practical engineering applications. The method’s accuracy was verified through numerical simulations, analytical solution and laboratory experiment, demonstrating its effectiveness in calculating stress in a three-layer medium. The surrogate model was applied to calculate mining-induced stress in the roadway roof rock of a coal mine, a typical case for stress measurement in a three-layer medium. Errors in stress calculations arising from the use of existing analytical solutions were corrected. The study also highlights the significant errors associated with using double-layer analytical solutions in a three-layer medium, which could lead to inappropriate engineering design.

Keywords

Stress measurement / Over-coring stress relief method / Three-layer medium / Surrogate model / Numerical simulation

Acknowledgements

We acknowledge the funding support from the National Natural Science Foundation of China (Nos. 42477208 and 52079134), the Natural Science Foundation of Hubei Province, China (No. 2024AFA072), the Youth Innovation Promotion Association CAS (No. 2022332), the National Key R&D Program of China (No. 2024YFF0508203), and the Open Research Fund of State Key Laboratory of Geomechanics and Geotechnical Engineering Safety (Nos. SKLGME-JBGS2402 and SKLGME022022).

Supplementary material

Supplementary material to this article can be found online at https://doi.org/10.1016/j.ijmst.2025.02.003.

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