基于拉丁超立抽样桩基沉降概率有限元法研究

Study on Probabilistic Finite Element Method of Pile Settlement based on Latin Hypercube Sampling

概率设计方法与有限元相结合分析桩土相互作用问题,可利用已有的有限元程序而直接调用,使桩土相互作用问题计算结果更加可靠。基于拉丁超立抽样和直接抽样方法对桩基沉降的蒙特卡洛概率有限元法进行应用研究。计算结果表明:拉丁超立抽样仅需要较少的抽样点即可达到较高的结果精度要求,结果要优于直接抽样方法;桩顶及桩端沉降服从三参数对数Logistic分布,桩端阻力服从正态对数分布,而桩身变形服从三参数Gamma分布;内摩擦角、膨胀角、土层弹性模量是影响桩顶沉降的主要因素,占70%左右;内摩擦角和膨胀角是影响桩端阻力的主要因素;桩顶沉降、桩端沉降与土层参数取值负相关,与桩身材料参数表现出很弱的相关性。采用拉丁超立抽样进行蒙特卡洛概率有限元分析抽样点分布,试验次数少,离散性小,计算结果精度高,可以节省大量的计算时间。可靠度分析计算结果可为桩基设计提供设计依据。

Probabilistic design method combined with finite element method can be directly analyze the problem of pilesoil interaction,which can make the results of pile-soil interaction problems more reliable.Based on the Latin hypercube sampling（LHS） and direct sampling,Monte-Carlo probabilistic finite element method is used to study the settlement of pile foundation.The results show that： the higher precision requirements are easily reached by Latin hypercube sampling, which only require less sampling points and its results are better than those of direct sampling method.Settlement of pile from tip to top obey the logarithm distribution of three parameters,resistance of pile tip obeys normal log distribution,while deformation of pile shaft subjects to Gamma distribution of three parameters.Friction angle,swelling angle,elastic modulus of soil layer are the main factors that affecting the settlement of pile top,accounting for 70%.The friction angle and swelling angle are the main factors that affecting the resistance of pile tip.Settlement of pile from tip to top is negatively correlated with soil parameters values,and weakly correlated with pile material parameters. LHS method only needs few tests times,little dispersion,higher precision,and save large amount of computing time.The reliability analysis results can be as the design basis of pile foundation design.