中文摘要：

将土性参数中的压缩模量建模为随机场而非传统意义上的随机变量,利用随机场的局部平均理论,确立了计算参数由点特性过渡到空间平均特性的方差计算方法。结合目前基础设计中主流的沉降计算方法（分层总和法）,推导了能够反映土性参数空间变化特性的基础沉降表达式,地基土分单层和多层两种情况;在假定自相关函数的条件下,利用5点Gauss积分,实现了基础沉降概率反映特性的一次二阶矩分析,进而提出了基础沉降的概率预报方法及给定沉降控制标准下的可靠性分析步骤;避免了随机场模拟的复杂性和Monte-Carlo抽样的庞大计算量,实现了与通常计算方法相互兼容的目的,便于一般工程设计人员所采用。最后,通过一个工程算例再现了此方法的分析过程和适用性。这对岩土工程的风险评价和可靠度分析具有重要的应用价值。

英文摘要：

By modelling the compressive modulus of soil properties as a spatially random field instead of the traditional random variable and by using the local average theory of random field,a method to calculate the spatial average variance from just the ＂point＂ variance is proposed.Then the derivation of an expression for random foundation settlement,which can reflect the effect of the spatial variability characteristics of soil parameters,is accomplished in combination with the common settlement calculation method at present in foundation design,namely the layer-wise summation method.The derivation includes dealing with both single and layered soil.At the same time,the first order second moment（FOSM） analysis of probabilistic foundation settlement is achieved by using the 5-point Gaussian integral based on an assumed autocorrelation function.On this basis,approaches for probabilistic forecast of foundation settlement and reliability analysis of foundation under a given limitation of settlement are recommended.All of those can avoid the complicacy of random field simulation and the expensive computation of Monte-Carlo sampling,and achieve the purpose of compatibility with the common calculation methods,which can be accepted by ordinary designers conveniently.Finally,an example of application is presented in order to demonstrate the analysis procedure and capabilities of the proposed algorithm.It is believed that it has significantly applicable values to risk assessment or reliability analysis in geotechnical engineering.