对3种著名边坡稳定性计算方法的改进

MODIFICATIONS TO THREE WELL-KNOWN METHODS OF SLOPE STABILITYANALYSIS

对 3 种著名边坡稳定性计算方法即 Morgenstern–Price 法、严格 Janbu 法与 Sarma 法进行了实质性的改进,基于这些方法的基本假设,重新推导出更为简洁实用的安全系数计算公式。对于 Morgenstern–Price 法,根据条块力与力矩平衡条件,分别推导出安全系数 Fs与比例系数 λ 的代数表达式(取代了传统的积分或微分表达式),只需简单迭代即可快速得到解答。对于严格 Janbu 法,发现了原始计算格式不收敛的根本原因;通过设定若干个点的推力线位置,采用光滑条间力矩分布,便可使该法稳定收敛。对于 Sarma 法,采用更简明的过程推导出安全系数Fs 的隐式表达式、临界震动影响系数 Kc 及临界加固力系数 Kp 的显式表达式。这 3 种方法改进后,计算过程大为简化,收敛性得到保证,极大地方便了边坡工程技术人员的掌握与应用。

Substantial modifications to three well-known methods of slope stabilility analysis, i.e., the Morgenstern-Price method, the rigorous Janbu method, and the Sarma method, are presented. Based on the basic assumptions used by these methods, formulas for computation of factor of safety are re-derived which are more concise and applicable than their original versions. For the Morgenstern-Price method, according to the force and moment equilibrium conditions of the slice, the expressions in algebric form (instead of differential or integral form) for the factor of safety Fs and for the scaling factor λ, are derived respectively, and only a simple iterative scheme is involved for rapidly obtaining converged solutions. For the rigorous Janbu method, the cause of non-convergence inherently in the original solution process is discovered, which can be eliminated by using smooth interslice moment distribution prescribed at certain locations within the sliding body, leading to stable convergence. For the Sarma method, a more concise process is involved in deriving the implicit expression for the factor of safety and the explicit expressions for critical seismic coefficient and critical reinforcing load factor. On modification, the computation processes associated with the three methods are largely simplified and converged solutions are always obtained. The modified versions of the three methods of slope stability analysis can be used by geotechnical engineers in the design of slopes and treatment of landslides.