A high efficient direct integration method is proposed for evaluating the variation effect of nonlinear numerical simulation results of geomechanics subject to multi-random parameters. In this method

taking the interested results as stochastic implicit response variables

firstly the integration points are determined by the multidimensional integration theory and direct integration reliability analysis method. Then the sample points are calculated by using the numerical simulation software; and then high order probability moments of response functions are evaluated by integration subroutine; at last the numerical probability density function of response variable then the confidence interval is obtained from several proposed method including curve fitting method

the weighted residual method and the maximum entropy distribution solver software developed by the authors. The numerical examples show that this method has higher accuracy and the computational efforts are reduced.