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从统计资料不足的角度出发,研究一种岩土工程隐式功能函数非概率可靠性方法,作为概率可靠性方法的有益补充。首先利用系列区间扩展函数降低区间相关性,建立基于子区间法的隐式函数区间解的迭代程序;然后采用试验设计的方法,从全面设计的角度建立统计优化模型搜索最优解,达到一个目标区间内获得一个简单计算方案的目的;最后通过对功能函数中应力函数的区间解设置置信区间,形成有限计算代价下的偏向于绝对安全的隐式功能函数非概率可靠性模型。通过岩土工程中最小支护阻力函数演示该方法的具体操作程序。工程算例结果表明,由此得到的最小支护阻力上限值与蒙特卡洛模拟法最大值的相对误差为0.83%,偏向于绝对安全。
From the perspective of insufficient statistical data, a non-probabilistic reliability method of implicit functional of geotechnical engineering is studied as a useful supplement to the probabilistic and reliable method. First, a series of interval expansion functions are used to reduce the correlation between intervals, and an iterative program of implicit function interval solution based on subinterval method is established. Then, a trial design method is used to establish a statistical optimization model to search for the optimal solution from a comprehensive design perspective, A simple calculation scheme is obtained. Finally, the confidence interval of the stress solution in the function function is set to establish a non-probabilistic reliability model of the implicit function that is biased towards absolute safety under the finite computational cost. The specific operation procedure of this method is demonstrated through the minimum support resistance function in geotechnical engineering. The engineering example shows that the relative error between the upper limit value of the minimum support resistance and the maximum value of the Monte Carlo simulation method is 0.83%, which is biased towards absolute safety.