This study presents a novel coupled hydraulic–mechanical algorithm for analysing nonlinear seepage in circular tunnels with elastic strain softening characteristics. The model integrates porosity changes with permeability coefficients to formulate a set of nonlinear seepage equations. The Mohr–Coulomb criterion is used to determine the of rock stress yielding state, and the plastic strain εθp is used as a softening parameter to assess the degradation of rock strength. The proposed model is validated through a comparison with established numerical and analytical solutions. The pore water pressure distribution exhibits a distinctive three-stage curve under coupling conditions, with the seepage behaviour transitioning to a classical Laplace-type equation as the coupling coefficient weights diminish. Parametric analysis reveals that the brittleness index β is a pivotal factor governing the extent of the softening region. A decrease in residual strength σc∗ intensifies strain softening, leading to a more extensive softening zone. Conversely, a reduction in the angle of internal friction φ affects only the rock's strength without altering the softening intensity. The study also demonstrated that the pore water pressure diminishes the effective stress within the rock mass, resulting in a larger plastic zone than that under dry conditions. Finally, internal reinforcement and external support can effectively mitigate the effects of strain softening and seepage on the stability of the surrounding rock.

中文翻译：

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一种基于水力耦合的弹性-应变软化圆形隧道的新型半解析方法


本研究提出了一种新的水力学耦合算法，用于分析具有弹性应变软化特性的圆形隧道中的非线性渗流。该模型将孔隙度变化与渗透率系数相结合，以形成一组非线性渗流方程。采用 Mohr-Coulomb 准则确定岩石应力屈服状态，塑性应变 εθp 作为软化参数评价岩石强度的退化。通过与已建立的数值和解析解进行比较，验证了所提出的模型。在耦合条件下，孔隙水压力分布表现出独特的三阶段曲线，随着耦合系数权重的减小，渗流行为转变为经典的拉普拉斯型方程。参数分析表明，脆性指数β是控制软化区域程度的关键因素。残余强度 σc∗ 的降低加剧了应变软化，导致更广泛的软化区。相反，内摩擦角的减小φ仅影响岩石的强度，而不会改变软化强度。该研究还表明，孔隙水压力降低了岩体内的有效应力，导致塑性区比干燥条件下更大。最后，内筋外支护可以有效缓解应变软化和渗流对围岩稳定性的影响。