Abstract The presence of cracks in soil slopes is of major concern to researchers and engineers, as this phenomenon is typically considered to be an early indication of instability and potential landslides. In this study, the kinematical approach of limit analysis was applied to evaluate the three-dimensional (3D) stability of soil slopes with pre-existing cracks and the reinforcement effects of piles. A vertical crack was accommodated in the classical 3D rotational failure mechanism by introducing a velocity discontinuity surface. Formulas for the external work rates and internal energy dissipation rates of the failure mechanism were derived within the framework of limit analysis. An optimization program was developed in combination with the strength reduction method to search for the most critical failure mechanism and the corresponding upper-bound factor of safety. A new parameter, the maximum crack depth coefficient, was introduced for evaluating the sensitivity of slopes to the presence of cracks. The numerical results indicated that slopes with large inclination angles are extremely sensitive to natural cracks, whereas gentle slopes are less likely to be affected. It was also found that stabilizing piles could effectively restrict the depth of the crack opening and thus, improve the stability of fissured slopes; the reinforcement effect was extremely dependent on the installation location and the density of the pile group.

中文翻译：

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桩加固3D开裂边坡稳定性分析

摘要 土壤边坡裂缝的存在是研究人员和工程师的主要关注点，因为这种现象通常被认为是不稳定和潜在滑坡的早期迹象。在这项研究中，极限分析的运动学方法被应用于评估具有预先存在裂缝的土坡的三维 (3D) 稳定性和桩的加固效果。通过引入速度不连续面，在经典的 3D 旋转破坏机制中容纳了垂直裂纹。在极限分析的框架内推导出失效机制的外功率和内能耗散率的公式。结合强度折减方法开发了优化程序，以寻找最关键的失效机制和相应的安全上限系数。引入了一个新参数，即最大裂缝深度系数，用于评估斜坡对裂缝存在的敏感性。数值结果表明，大倾角的边坡对天然裂缝极为敏感，而缓坡则不太可能受到影响。还发现稳定桩可以有效地限制裂缝张开的深度，从而提高裂隙边坡的稳定性；加固效果极大地取决于安装位置和桩组的密度。引入用于评估斜坡对裂缝存在的敏感性。数值结果表明，大倾角的边坡对天然裂缝极为敏感，而缓坡则不太可能受到影响。还发现稳定桩可以有效地限制裂缝张开的深度，从而提高裂隙边坡的稳定性；加固效果极大地取决于安装位置和桩组的密度。引入用于评估斜坡对裂缝存在的敏感性。数值结果表明，大倾角的边坡对天然裂缝极为敏感，而缓坡则不太可能受到影响。还发现稳定桩可以有效地限制裂缝张开的深度，从而提高裂隙边坡的稳定性；加固效果极大地取决于安装位置和桩组的密度。提高裂隙边坡的稳定性；加固效果极大地取决于安装位置和桩组的密度。提高裂隙边坡的稳定性；加固效果极大地取决于安装位置和桩组的密度。