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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。
A probabilistic method based on Copula for load-displacement hyperbolic curves is proposed. Firstly, the uncertainty of the normalized load-displacement hyperbola model of piles is transformed into the uncertainty of hyperbolic parameters. Then, the joint distribution function of hyperbolic parameters is established under the framework of Copula theory. Finally, the experimental data of cast-in-situ cast-in-place bored pile is taken as an example to prove the effectiveness of the proposed method and the reliability analysis of the limit state of normal use of pile is carried out. The results show that Copula function is an effective method to construct the combined load-displacement hyperbola parameter joint distribution function of pile foundation, which can more stably realize the stochastic simulation of load-displacement hyperbolic curve of pile foundation so as to obtain more reasonable and reliable Degree result. There is a strong negative correlation between the two parameters in the cast-in-place bored pile hyperbola model. Neglecting this negative correlation will overestimate the failure probability of the pile. In addition, the commonly used Gaussian Copula function is not the best Copula function for fitting the correlation between two parameters in the hyperbolic model. Gaussian Copula function will obviously underestimate the failure probability of the pile.