基于Copula函数的基桩荷载-位移双曲线概率分析

Probabilistic analysis of load-displacement hyperbolic curves of single pile using Copula

提出了基于Copula函数的基桩荷载-位移双曲线概率分析方法。首先将基桩标准化荷载-位移双曲线模型不确定性转化为双曲线参数不确定性,然后在Copula理论框架下建立了双曲线参数的联合分布函数。最后以钻孔现浇灌注桩试验数据为例证明了所提方法的有效性,并进行了基桩正常使用极限状态可靠度分析。结果表明:Copula函数是构造基桩标准化荷载-位移双曲线参数联合分布函数一种有效的方法,它能够更加准确地实现基桩荷载-位移双曲线的随机模拟,从而得到更为合理的可靠度结果。钻孔现浇灌注桩双曲线模型中两个参数间具有较强的负相关关系,忽略了这种负相关性将会高估基桩的失效概率。此外,常用的Gaussian Copula函数并不是拟合双曲线模型中两个参数间相关结构最优的Copula函数,采用Gaussian Copula函数将会明显低估基桩的失效概率。

This paper aims to propose a method for probabilistic analysis of load-displacement hyperbolic curves of single pile using Copula. Firstly, the uncertainties of probabilistic load-displacement hyperbolic model are transformed to the uncertainties of two curve-fitting parameters. Then the Copula theory is adopted to model the joint probability distribution function of the two curve-fitting parameters. The direct integration method is used to carry out the reliability computations for serviceability limit state of single pile. Finally, an example of load-test dataset for Augered Cast-in-Place （ACIP） pile is illustrated to demonstrate the validity and capability of the proposed method. The results indicate that the proposed Copula-based method can provide a more general and flexible way of modeling and simulating the bivariate probability distribution of the two curve-fitting parameters in isolation from their marginal probability distributions, which facilitates the generation of normalized load-displacement hyperbolic curves and thus results in more accurate reliability results for serviceability limit state of single pile. A strong negative correlation between the two parameters underlying the normalized load-displacement hyperbolic model can be observed. Neglecting such negative correlation will overestimate the probability of failure. In addition, the Gaussian Copula, often adopted out of expedience without proper validation, is not the best Copula for modeling the dependence structure underlying the two curve-fitting parameters. If the Gaussian Copula is adopted, the probability of failure of ACIP pile will be underestimated significantly. Key words：