Multiple Linear Regression Inversion of the Ground Stress Field in Rock Masses for Tunnel Engineering: A Novel Approach to Stress Field Reconstruction

The inversion of the ground stress field in rock masses is critical for accurate tunnel and underground engineering design. This study addresses the challenge of accurately capturing both the primary and secondary stress field components in rock masses. The ground stress field consists of the primary stress field, generated by applied tectonic loads, and a secondary stress field, which cannot be fully explained by these loads and is attributed to long-term tectonic processes. This unexplained secondary stress field is often non-random in nature. To improve the accuracy of the ground stress field inversion, we propose prioritizing the use of a regression model with a constant term. This model better accounts for the secondary stress field by capturing long-term tectonic influences. The constant term in the regression model is shown to represent the non-random secondary stress field, which cannot be explained by applied tectonic loads. Furthermore, we define two key conditions for applying this regression model: (1) the constant term should not exceed the maximum measured stress and preferably should not surpass the minimum measured stress, and (2) the residual sum of squares of the regression model with a constant term should be smaller than that of the model without a constant term. By incorporating the constant term, the model improves the representation of both primary and secondary stress fields, offering a more accurate inversion of the ground stress field, especially when the stress field contribution from independent variables is incomplete.

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