考虑拉剪强度特性的反倾岩坡悬臂梁极限平衡模型

    Cantilever beam limit equilibrium model of anti-dip rock slopes considering tensile-shear strength characteristics

    • 摘要: 反倾岩质边坡稳定性分析是岩石力学与工程领域重点关注的问题之一。传统的悬臂梁极限平衡模型将岩层间相互作用力简化为集中力处理,易忽视剪应力存在导致岩石抗拉强度降低对稳定性的影响。本项研究采用简化的分布荷载作用模型对岩层应力状态进行分析,证实了弯曲倾倒时岩层最危险点处剪应力的存在。然后,基于双直线型和拉伸截断型两种Mohr-Coulomb准则,建立了考虑岩石拉剪强度特性的悬臂梁极限平衡改进模型,使用工程算例验证了改进模型的有效性,并分析了改进模型与传统模型安全系数差异的影响因素。结果表明:与传统模型相比,改进模型的安全系数降低,双直线型改进模型降低12%~16%,拉伸截断型改进模型降低5%~8%。安全系数的降幅受岩石抗拉强度σt和黏聚力C的比值η、层间相互作用力分布形式等因素影响。随着比值η增加,拉伸截断型改进模型与传统模型安全系数差异增大,与双直线型改进模型差异减小。与均布荷载形式相比,层间相互作用力采用三角形形式分布时,改进模型相比传统模型的安全系数降幅更加显著。

       

      Abstract: Stability analysis of anti-dip rock slopes is a critical concern in rock mechanics and engineering. The classical cantilever beam limit equilibrium model often simplifies the interlayer interaction forces as concentrated forces, potentially overlooking the impact of reduced rock tensile strength due to shear stress on stability. This study employs a simplified distributed load model to analyze the stress state of rock layers, confirming the existence of shear stress at the most critical point during flexural toppling. Subsequently, based on the bi-linear and tensile cut-off types of the Mohr-Coulomb criterion, two improved cantilever beam limit equilibrium models are established, which consider the tensile-shear strength characteristics of rocks. The effectiveness of the improved models is validated through a case study, and the factors influencing the differences in safety factors between the improved models and the classical model are analyzed. The results indicate that, compared to the traditional model, the safety factors of the improved models decrease, with the bilinear improved model showing a reduction of 12% to 16% and the tensile cut-off improved model showing a reduction of 5% to 8%. The reduction in the safety factor is influenced by factors such as the ratio η of the tensile strength σt to the cohesion C, as well as the distribution form of the interlayer interaction forces. As the ratio η increases, the difference in safety factors between the tensile cut-off improved model and the classical model increases, while the difference with the bilinear improved model decreases. Compared to the uniformly distributed load form, when the interlayer interaction forces adopt a triangular distribution form, the reduction in the safety factor of the improved models compared to the traditional model is more pronounced.

       

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