基于随机有限元法的圆形基础沉降最不利波动尺度分析

波动尺度(SOF)是表征土体空间变异性的重要参数，不同的波动尺度可以模拟土体参数的空间变异程度。基于随机有限元(RFEM)和蒙特卡罗模拟，假设弹性模量服从对数正态分布对土体实现非均质性建模，研究不同波动尺度下圆形基础的沉降变形规律。研究结果表明：中心沉降值符合对数正态分布，差异沉降值符合正态分布；随着波动尺度的增加，中心沉降和差异沉降均值基本不变，中心沉降标准偏差先增大最后趋于平缓，差异沉降标准偏差先增大后减少，在其峰值处平均绝对差异沉降达到最大，此时的波动尺度为最不利波动尺度，在勘察数据相对有限的情况下可以对基础沉降概率进行保守估计。

Worst-case settlement fluctuation scale analysis of circular foundations based on the random finite element method

The scale of fluctuation (SOF) is an important parameter for the characterization of soil spatial variability, and different fluctuation scales can be used to simulate different degrees of the spatial variability of soil parameters. Based on the random finite element method (RFEM) and Monte-Carlo simulation, the heterogeneous soil mass is modeled assuming that the elastic modulus follows a lognormal distribution, by which the settlement deformation of a circular foundation under different fluctuation scales is studied. The results show that the central settlement is well fitted by a log-normal distribution, and the differential settlement is closely approximated by a normal distribution. With the increase of SOF, the mean value of central settlement and differential settlement are basically constant. The standard deviation of central settlement first increases and then tends to level off. In contrast, the standard deviation of differential settlement first increases and then decreases; it reaches the maximum when the SOF is close to the diamenter of the circular foundation, at which the average absolute differential settlement also reaches the peak. This SOF is the most unfavorable scale and is termed as the worst-case SOF. The probability of foundation settlement can be conservatively estimated by assuming such a worst-case SOF when the site survey data are relatively insufficient to define a reliable SOF.