Abstract The geometric properties accompanying a priori stress conditions determine the physical behaviors of a sand heap. In this study, the incipient failure solution, obeying the Mohr-Coulomb criterion, was successfully applied to an asymmetric planar sand heap under active condition. The shooting technique, based on the 5th order Runge-Kutta method in association with Brent's method, was put in place. Moreover, Sokolovskii's theory of active planar heaps was extended to facilitate the numerical stress solution by refining the boundary conditions. The new integration scheme was handled with appropriate numerical perturbations to cope with the singularity problem. Regarding the experimental validation, the active condition in an asymmetric prismatic sand heap was experimentally triggered by seismic loading. The results revealed that the distribution of vertical stress was uneven before shaking; however, the vertical stress conformed to the theory after the first period of shaking. Furthermore, the deformation threshold of the limit equilibrium state was also revealed. On the other hand, the trajectory of the major principal stress characterizing the load transfer mechanism in an asymmetric planar heap were seen to be different from those in a symmetric planar heap.

中文翻译：

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非对称棱柱砂堆在失效边缘的塑性行为

摘要 伴随先验应力条件的几何特性决定了沙堆的物理行为。在这项研究中，初始破坏解遵循 Mohr-Coulomb 准则，成功应用于活动条件下的非对称平面沙堆。基于五阶龙格-库塔方法和布伦特方法的射击技术已经到位。此外，Sokolovskii 的活动平面堆理论得到扩展，以通过细化边界条件来促进数值应力求解。使用适当的数值扰动处理新的积分方案以应对奇异性问题。关于实验验证，不对称棱柱形沙堆中的活动条件是由地震加载实验触发的。结果表明，振动前竖向应力分布不均匀；然而，在第一次振动后，垂直应力符合理论。此外，还揭示了极限平衡状态的变形阈值。另一方面，在非对称平面堆中表征载荷传递机制的主要主应力的轨迹与对称平面堆中的轨迹不同。