The Analysis Of Reliability Of The Settlement Of Single-Pile With The Spectral Stochastic Finite Element Based On Collocation Points

As we all know, the settlement of pile is an important consideration for the design of pile foundation engineering. There exists uncertainty in all the aspects that affect pile settlement, such as material properties of soil, geometry and upper load of pile. There are many uncertainty analysis methods, but the traditional method for such complicated random field as pile foundation model is far from feasible. Stochastic finite element method (SFEM) is currently an extensive analysis method of handling complex random fields. But under many circumstances, as stochastic analysis and finite element calculation is coupled, its practicability is severely limited. Even the Monte Carlo FEM without considering coupling is lacking in applicability, since repetitive independent finite element calculations for a large number of samples are required. However, collocation-point stochastic response surface method (CSFEM) is an very effective analysis method in dealing with uncertain problem.In this thesis, settlement reliability of a concrete pile is analyzed by CSFEM for the first. The shear modulus of soil is a random field, and the stress-strain relationship of soil is linear. Different from the other SFEMs, CSFEM presents the response using polynomial chaos expansion. Sampling points are selected according to stochastic collocation point method. Then outputs are computed by deterministic FEM at each collocation point, and the expression for the response is obtained sequentially. Finally, a Monte Carlo simulation is employed to rapidly output the probability distribution of the structure. The advantage of this method lies in that the computation of FEM is decoupled with stochastic analysis, allowing the general finite element program to be used as"black boxes". Besides, high computational accuracy can be achieved by calculating a small amount of samples.Through the reliability analysis for the settlement of pile with CSFEM, we can draw the following conclusions: Only a few points are needed in CSFEM to obtain the same high precision as Monte Carlo simulation which based on a large number of samples, thus greatly improving the efficiency of reliability analysis. During the analysis process, stochastic analysis is independent of finite element calculation. And only in the positions of collocation points, the deterministic finite element calculations are used. By the introduction and numerical simulations of the CSFEM theory, the advantages of CSFEM can be further shown, and provide a better method for analysis of complex model at the same time.