基于强度折减的拉格朗日差分方法分析土坡稳定性

Slope stability analysis by Lagrangian difference method based on shear strength reduction

运用连续介质显式拉格朗日有限差分方法,通过逐步折减土体的抗剪强度,来分析土坡稳定的安全系数。实例计算表明,强度折减系数达到某一数值时,土坡顶点的水平位移会快速增加。根据这一现象,提出了界定土坡破坏的坡顶位移增量标准。即坡顶位移增量与折减系数增量之比大于系数sc为土坡破坏,并建议了sc的取值。这样可避免强度采用折减方法分析土坡稳定时,以不收敛等"模糊"概念作为土坡破坏状态的判别标准,具有物理意义明确、客观具体、便于数值计算等特点。与瑞典圆弧法、简化Bishop法及Spencer法比较可见,这些方法的潜在滑动面形状相似、位置十分接近,说明本文方法及"破坏"状态的判别标准是合适的。文中对剪胀角的影响进行了讨论,得到"不考虑"剪胀性的关联流动法则会高估土坡稳定安全系数的结论。

In this paper, the stability analysis of the slope has been studied by the explicit Lagrangian difference method for the continuum body using shear strength discount. In some case study, it is shown that the horizontal displacement of the slope top will be increasing rapidly when the reduction factor reaches a certain value.According to this phenomenon, a criterion has been proposed, which is used to distinguish the collapse of slope .If this criterion, which is the ratio of the horizontal displacement increment of the slope top and the increment of reduction factor, is larger than some suggested value sc then the slope is in failure state.Therefore the non-convergence or other indistinctness will not be used as criterion to identify slope failure state when slope stability analysis is done using the shear strength discount method.This criterion has the clear physical meaning and is objective and explicit, and easily to be implemented in analysis. Compared with the limit equilibrium methods, such as Swedish slip-circle method, simplified Bishop method and Spencer method, it is shown that the sliding surface of this method is coincident with those of other method basically. It is explained that the method and the criterion of the 'failure' state proposed in this paper is appropriate.The influence of dilative angle on stability factor is also discussed, and the conclusion has been got that the stability factor of the slope would be overestimated if the associate plastic flow rule is adopted.