基于随机多项式展开的流固耦合非饱和土坡概率反分析

降雨入渗条件下非饱和土坡流固耦合作用复杂,具有高度非线性的特点,一般采用数值方法模拟。数值模型计算量大已成为监测数据概率反分析的重要制约因素。提出一种基于随机多项式展开(PCE)的概率反分析方法。该方法采用随机多项式展开构建土性参数与数值模型响应的显式函数,作为概率反分析中原数值模型的代替模型,与基于贝叶斯理论和马尔可夫链蒙特卡罗(MCMC)模拟的概率反分析方法相结合,从而有效提高非饱和土坡流固耦合参数概率反分析的效率。通过降雨入渗非饱和土坡算例研究,结果表明,与基于数值模型的常规随机反分析相比,两种方法在后验分布统计值、95%置信区间等结果非常接近,基于PCE的概率反分析计算效率显著提高,结果可靠。

Probabilistic back analysis method for unsaturated soil slopes with fluid-solid coupling process based on polynomial chaos expansion

The seepage and stress-deformation in an unsaturated slope under rainfall infiltration are interacted with high nonlinearity. Numerical models are commonly adopted to solve the coupled governing equations. Tremendous computational cost of numerical modeling is the main obstacle for probabilistic back analysis with field monitoring data. A probabilistic back analysis method based on polynomial chaos expansion (PCE) is proposed in this study. PCE approximation is used to construct the explicit functions between unsaturated soil parameters and model responses to replace the original numerical model. The PCE surrogate model is adopted in parameter posterior inference with Markov chain Monte Carlo (MCMC) simulation based on the Bayesian theory. An example of unsaturated soil slope under rainfall infiltration is presented to illustrate the efficiency of the proposed method. The statistics of posterior distribution and 95% uncertainty bounds obtained using the PCE-based method are close to the results of the traditional back analysis based on the original numerical model. In addition, the proposed new method can significantly improve the efficiency of model calibration.