考虑不排水抗剪强度空间变异性的条形基础极限承载力随机分析

目前有关抗剪强度参数随深度变化对地基稳定性影响的研究还不深入。为此,提出了考虑土体不排水抗剪强度均值和标准差随深度变化的地基稳定性随机分析方法。建立了表征不排水抗剪强度空间变异性的不平稳随机场模型,采用Karhunen-Loeve（KL）展开离散随机场。探讨了土体不排水抗剪强度参数空间变异性对地基极限承载力的影响规律,并比较了不排水抗剪强度参数平稳和不平稳随机场模型对地基稳定的影响。以不排水黏性地基稳定随机分析问题为例验证了所提方法的有效性。结果表明：考虑不排水抗剪强度参数空间变异性时,地基极限承载力均值和标准差随相关距离的增大而增大,地基极限承载力对竖直向相关距离更为敏感。地基极限承载力均值随不排水抗剪强度变异系数的增加而减小,标准差随变异系数的增加而增加。不排水抗剪强度变异性对地基失效概率有明显的影响,安全系数较大时,不排水抗剪强度相关距离越小,地基失效概率越小。与不排水抗剪强度参数的不平稳随机场相比,不排水抗剪强度的平稳随机场模型会高估地基极限承载力的变异性,在相同的安全度水平下,当地基的安全系数较低时,平稳随机场模型会导致对地基失效概率的低估；当地基安全系数较高时,平稳随机场模型会导致对地基失效概率的高估。

Stochastic analysis of ultimate bearing capacity of strip footing considering spatial variability of undrained shear strength

The effect of the variation of shear strength parameters of soils with depth on the stability of footing has not been thoroughly studied. A stochastic method is proposed for bearing capacity analysis of strip footing considering the variation of the mean and standard deviation of undrained shear strength parameters with depth. A non-stationary random field model is established, and the random field is discretized by the Karhunen-Loeve (KL) expansion. The effect of spatial variability of the undrained shear strength parameters on the ultimate bearing capacity is investigated. The results of bearing capacity associated with stationary and non-stationary random field models are compared. An undrained clay foundation is presented to demonstrate the effectiveness of the proposed method. The results indicate that both the mean and standard deviation of bearing capacity increase with the increasing correlation length, and that the ultimate bearing capacity is more sensitive to the vertical correlation length than to the horizontal one. The mean of the ultimate bearing capacity decreases but the standard deviation increases as the coefficient of variance increases. The spatial variability of shear strength parameters of soils has a significant influence on the failure probability of foundation. When the factor of safety is large, the failure probability of foundation decreases with the decreasing correlation lengths. Compared with the non-stationary random field, stationary random field will highly overestimate the variation of the ultimate bearing capacity. When the factor of safety against shear failure is low, the stationary random field model will induce a lower probability of failure than the non-stationary random field model. On the contrary, when the factor of safety against shear failure is high, the stationary random field model will induce a higher probability of failure.