RELIABILITY ANALYSIS OF DAM BASED ON LAGRANGE MULTIPLIER RULE

In this paper, an improved method for reliability analysis of dam is established. Firstly, random parameters in accord with certain distribution are obtained using Monte-Carlo simulation method. Based on composite failure criterion, different performance functions are established, and then sample points of performance functions are obtained accordingly. Secondly, quadratic polynomial is used to model response surface. Using Lagrange multiplier rule, the nonlinear optimization constraint problem, which generates the design checking points under constraint of response surface, is converted into the problem of solving linear equations, which can be implemented by Jacobi iterative method. Finally, Lagrange multiplier and the design checking points are obtained by using bisection method. And the reliability of each element of the dam under composite failure criterion is calculated. The element reliability is defined as the minimum among all elements’ reliabilities. Compared with other conventional algorithm, this method has some advantages: 1) the gradient is not required in analysis; 2) wider application scope; 3) a nonlinear optimization constraint problem is converted into a problem of solving linear equations, so this method can analyze structure reliability with highly nonlinear limit states.