为了解决采用标准Monte Carlo法计算复杂基坑工程上常见小概率失效,导致计算效率低的问题,以南京市湖南路地下商业街工程为工程背景,首先,将随机响应面法与基坑工程三维模型相结合,求解极限功能函数的响应面方程,并用标准 Monte Carlo 法计算失效概率和可靠指标,探讨采用倒边盖挖逆作法作为基坑支护结构施工方法的可行性;其次,基于该响应面方程,以土体的弹性模量为随机变量参数,采用马尔可夫链蒙特卡罗子集模拟法(MCMC子集模拟法)计算基坑支护结构的失效概率,并与标准Monte Carlo法结果进行对比分析.结果表明:当支护结构最大侧移控制指标为 25 mm时,计算得到的可靠指标均大于 4.6,即采用倒边盖挖逆作法施工过程中基坑是安全的;10 万次和 50 万次标准 Monte Carlo 法计算得到的失效概率均为零,说明对于标准Monte Carlo法,在计算小概率失效问题时 10 万与 50 万的样本量是不足的;而MCMC子集模拟法用2.98 万个样本计算出的结果与标准 Monte Carlo 法采用 100 万个样本计算的结果相对误差仅为1.7%,表明MCMC子集模拟法对于小概率失效问题求解的优势.所提算法在一定程度上提高了计算结构系统小概率失效问题的效率,对结构系统可靠性的相关研究具有一定参考价值.
Reliability analysis of supporting structure of foundation pit with inverted cover excavation and top-down construction method
To solve the low computational efficiency of the standard Monte Carlo method to calculate the common small probability of failure problems in complex foundation pit projects,took the underground commercial street project on Hunan Road in Nanjing as the engineering background.Firstly,the stochastic response surface method was combined with the three-dimensional model of the foundation pit project,the response surface equation of the limit function was solved,and the probability of failure and the reliability index were calculated with the standard Monte Carlo method.Then,based on the response surface equation,the Markov chain Monte Carlo subset simulation method(MCMC subset simulation method)was used to calculate the failure probability of the foundation pit support structure with the elastic modulus of the soil as the random variable parameter,and the results were compared with those of the standard Monte Carlo method.The results show that when the maximum lateral displacement control index of the supporting structure is 25 mm,the calculated reliability index is greater than 4.6,indicating that the pit is safe during the construction of inverted cover excavation;The failure probability of 100000 and 500000 times of the standard Monte Carlo method is zero,which indicates that for the standard Monte Carlo method,the sample sizes of 100000 and 500000 times are not enough to calculate the problem of small probability of failure.The relative error between the results calculated by MCMC subset simulation method with 29800 samples and the result calculated by the standard Monte Carlo method with 1000000 samples is only 1.7%,which shows the advantage of MCMC subset simulation method for the solution of small probability of failure problems.The proposed algorithm improves the efficiency of calculating the small probability failure problem of structural systems to a certain extent,which is of some reference value for the research related to the reliability of structural systems.
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维普
