Probabilistic foundation settlement based on random field theory

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.