Upper Bound Solution for Stability Analysis of Deep Underground Cavities Under the Influence of Varying Saturation

In order to study the influence of rock mechanical behavior under different saturation conditions on the stability of deep caverns, this paper establishes a mechanical model for bottom drum failure in deep chambers based on Pratt’s pressure arch theory and the upper bound theorem of limit analysis, comprehensively considering the effect of rock saturation. An analytical solution for the surrounding rock pressure under the nonlinear Hoek–Brown criterion is derived, and the optimal upper bound solution is obtained. The study systematically investigates the influence of rock saturation, geostress, and Hoek–Brown parameters (GSI, σc0, σc100, mi, D) on the surrounding rock pressure and the characteristics of potential failure surfaces. The results indicate that the surrounding rock pressure exhibits two-stage variation with saturation degree (Sr): when Sr = 0~0.6, the surrounding rock pressure increases significantly, and the growth rate slows and tends to stabilize when Sr exceeds 0.6. Increases in ground stress field parameters (σv, λ) significantly raise the surrounding rock pressure and expand the potential failure zone. Among the Hoek–Brown parameters, increases in GSI, σc0, σc100, and mi enhance the stability of the surrounding rock, while an increase in the disturbance factor D reduces its bearing capacity. The results of this paper can provide theoretical guidance for the stability evaluation of deep underground chambers.