Geometrical Reliability Algorithm Of Geotechnical Structures Under Multivariate Random Variables

The effective interpretation of complex reliability theory will encourage engineers and technicians to apply it in engineering practice.In order to interpret reliability index more intuitively,many methods for calculating reliability index have been developed.Among them,the geometric reliability method provides a new solution method for the calculation of reliability index.The method solves the reliability index in the original physical space so that the physical meaning of each variable is retained.In addition,the intuitiveness of geometry makes the solution of reliability index more intuitive.However,at present,the algorithm is limited to the reliability analysis of low-dimension(within three dimension)random variables.Therefore,the geometric reliability algorithm is required to further extend to multivariate random variables.This thesis gives the calculation method of the standard deviation super ellipsoid under a specific confidence or a specific multiple,and uses the Copula function combined with the idea of meshing and discrete to develop and construct in the original physical space.It is suitable for the calculation method of geometric reliability index of geotechnical structures under multivariate random variables.At the same time,each component of the algorithm theory is deeply analyzed.The methods suggested in this paper mainly include: The setting of the limit state surface;the establishment of the single standard deviation super ellipsoid;the determination of the probability density equivalent contour point;the discrimination of the limit state;the establishment of the single equivalent core configuration and the geometric reliability index.Using the proposed algorithm,the reliability analysis of CFG pile composite foundation with bivariate random variables,seawall with trivariate random variables,tunnel stability examples with four random variables,and extended foundation with five random variables are carried out respectively.Furthermore,the calculation results of the conventional reliability method and random sampling method were compared respectively to verify the accuracy and efficiency of the algorithm.Based on the powerful and open source R language platform,a graphical solution can be implemented in low-dimensional(bivariate,trivariate)spaces and can be solved numerically in multiple dimensional spaces.This makes the interpretation of reliability theory more intuitive.