考虑土体参数空间变异性的边坡稳定性研究

为考察土体强度参数空间变异性对评价边坡稳定的影响, 以及使用概率方法评价对边坡稳定的适宜性, 以简易Morgenstern-Price法对土体参数空间变异性条件下的边坡稳定性进行了计算分析.通过Karhunen-Loève法对参数的空间协方差矩阵进行正交分解,并使用拉丁超立方抽样法和Cholesky法对空间场进行优化处理,确定了边坡土体的强度参数空间样本取值,完成了空间随机场的生成；以简易Morgenstern-Price法对参数空间变异边坡进行安全系数求解和破坏概率计算.对生成土体参数的抽样检验发现,拉丁超立方抽样和Cholesky分解共同使用后生成的抽样样本能很好地吻合目标分布.边坡稳定性计算分析显示,在抽样计算所得的边坡失稳收敛概率与Monte Carlo方法非常接近的情况下,抽样随机场能极大地降低模型达到收敛所需的计算次数,表明抽样方法用来计算边坡的失稳概率是可行的.对给定边坡的概率性失稳的研究表明：单独使用安全系数或者失效概率都无法完整地对边坡稳定性作出评价,只有同时使用两者,边坡的安全评价才会更加安全有效.

Slope stability analysis considering spatial variability of soil properties

In order to investigate the influence of spatial variability of soil strength on the slope stability, as well as the adaptability of probabilistic method for evaluating the slope stability, a new concise Morgenstern-price method was adopted to analyze the slope stability, which considering the spatial variability of soil properties. Orthogonal decomposition was performed to spatial covariance matrix of soil strength by Karhunen-Loève (K-L) expansion, and the Latin hypercube sampling (LHS) method and Cholesky decomposition method were used to optimize the generated spatial stochastic field. Thus, the spatial sample of the soil strength could be determined, which is also named random field. The concise Morgenstern-price method was then employed to conduct the calculation of the factor of safety and the failure probability of the slope. The generated samples were examined to be rational for they were good enough to match the objective function. Results show that the samples can reduce the simulation number greatly compared to the Monte Carlo (MC) method, under the condition that the calculated failure probabilities from LHS method and MC method are close to each other. It demonstrates the adaptability of using LHS method to calculate the failure probability of embankment slope. For a given slope, the results show that neither the factor of safety nor the failure probability can assess the slope safety completely. Only the combined using of these two indexes could be effective enough for the slope safety evaluation.