二元函数逼近在斜坡可靠度分析中的应用研究

极限平衡分析方法是斜坡稳定性评价中的常用方法，在长期的工程实践中积累了丰富的经验，但其不能考虑斜坡岩土体中实际存在的不确定性，在应用中具有一定的局限性。可靠度分析方法可有效地考虑斜坡系统内的不确定性和相关性，但因状态函数偏导数的求解比较困难，使可靠度分析方法在实际中应用不便。为解决上述问题，根据二元函数插值逼近原理，在矩形区域上构造拉格朗日不完全双二次多项式逼近状态函数，从而近似地计算状态函数的偏导数，求得状态函数的均值和方差，并利用精度较高的一次二阶矩方法来计算斜坡的可靠指标和破坏概率。据鄂西恩施地区马堡营滑坡实例分析表明，引入二元函数插值逼近的一次二阶矩方法计算结果与剩余推力法及Monte-carlo模拟方法结果一致，其精度可满足工程需求。

Study on application of dual function approximation to slope realibility analysis

Limit equilibrium analysis method is used to estimate slope stability in common. And abundant experience has been accumulated in long time practice. However, a weakness of limit equilibrium method is that uncertainties of parameters and models can not be considered. And its application would be influenced in practice. Uncertain and correlative problems in slope system can be solved effectively by reliability theory. But the partial derivative of performance function is hard to be calculated. The reliability analysis method is inconvenient to be applied in practice. So as to solve the deficiency, a numerical computational method based on dual function approximation is developed. In a rectangle area, an incomplete dual quadratic polynomial which is constructed by Lagrange method is used to approximate the performance function. Then its partial derivative can be calculated approximately; and the mean and deviation can also be obtained. So the reliability index and failure probability can be calculated by the first-order second-moment method. Mabaoying landslide in Enshi region of Hubei province is used to be a case study. It shows that the results with first-order second-moment method based on dual function approximation is consistent with the results by the push method and Monte-Carlo method; and it can be satisfied the engineering requirements in practice.