强度折减有限元法中边坡失稳的塑性区判据及其应用

A Criterion for Evaluating Slope Stability Based on Development of Plastic Zone by Shear Strength Reduction FEM

将抗剪强度折减法基本概念、弹塑性有限元分析原理与计算结果图形实时显示技术相结合,提出了以广义塑性应变及塑性开展区作为边坡失稳的评判依据,并与以非线性迭代收敛条件作为失稳评判指标的强度折减有限元方法进行了对比。对于天然垂直边坡的算例数值分析表明,采用广义塑性应变与塑性开展区作为失稳判据可以比较准确地预测边坡潜在破坏面的形状与位置及相应的稳定安全系数,验证了这种失稳判据的合理性。对开挖边坡和开挖支护边坡的实例计算结果表明本文方法对于复杂的边坡稳定性分析是实用的。

The shear strength reduction technique has been commonly incorporated into the elastroplastic FEM.Based on the computed displacements and generalized shear strain of slope for a given state, nonconvergence state of finite element analyses for displaying an unstable condition of slope will be certainly defined. At the moment of overall failure, the variations and distributions for some physical variables such as plastic strain, stress level, will take a certain characteristics. Therefore, the evaluation criteria by preassuming an allowable iteration number employed in current practice is fairly inappropriate. Furthermore, the evaluation criteria for limiting allowable minimum ratio of unbalanced force to external load less than 10-3 will, in some cases, lead to numerically computational nonconvergence and also display a certain uncertainties. The distribution zone of generalized shear strain can be manifested based on the results of elastoplastic FEM by use of strength reduction technique. If the generalized shear strain zone with a given value is developed from the toe to the top, the slope will approach a critical instable state. However, the critical value of generalized shear strain at which a critical state will be initiated cannot be determined beforehand and therefore the safety factor determined by this type of methods is not sufficiently meaningful. In fact, the generalized shear strain or displacement is composed of both plastic and elastic components. Therefore, it is not rational and accurate to evaluate the initiation and development of plastic zone or shear failure zone based on the feature of variations and distributions of these variables. However, shear failure of soil is directly associated with the initiation, development and redistribution of plastic zones, and plastic strain can give a clear representation of development of plastic zone. Therefore, in this paper, the elastoplastic FEM by using shear strength reduction procedure (SSRFEM) is incorporated with the dynamic display technique of computed numerical results. Elastoplastic FEM is the essential part of this method. In the procedure, the following main issues have been effectively solved, e.g., (1) Considering the elastoplastic behavior of soil, an efficient nonlinear iterative algorithm in FEM is developed; (2) The appropriate formulation together with numerical scheme for stress modification is established to assure that the updated stress state computed is compatible with the current yield surface in a fair accuracy. (3) The basic rules for evaluating critical overall instable state of slope is proposed based on the development pattern of generalized plastic strain or plastic zone and is compared with the conventional procedures by controlling maximum allowable iterative number. The reasonable safety factor can be defined by the proposed method. Through numerical analyses for a natural vertical slope, it is indicated that the proposed method can rather rationally predict both safety factor of slope and the corresponding shape and position of the potential slip surface. The computed safety factor can agree well with those obtained by other SSRFEM analyses based on the conventional procedures. For an actual excavated slope and an excavated slope with reinforcement of soil nailing, numerical analyses are performed. Accordingly, practical applicability of the proposed technique to complicated cases is verified.