RELIABILITY ANALYSIS OF FRP LAMINATED PLATES WITH CONSIDERATION OF BOTH INITIAL IMPERFECTION AND FAILURE SEQUENCE

A probabilistic progressive failure analyzing method is applied to estimating the reliability of a simply supported laminated composite plate with an initial imperfection under bi-axial compression load. The initial imperfection and the strength parameters are considered as random variables. Ply-level failure probability is evaluated by the first order reliability method (FORM) together with the Tsai-Wu strength criterion and Tan criterion. Current stresses in the laminated structure are calculated by the classical lamination theory with the stiffness modified based on the last step ply failure. Probabilistically dominant ply-level failure sequences leading to overall system failure are identified, based on which the system failure probability is estimated. A numerical example is presented to demonstrate the methodology proposed. Through parameter studies it is shown that the deviation of the initial imperfection and some of the strength parameters largely influence the system reliability.

Empirical approach for reliability evaluation of tunnel excavation stability using the Q rock mass classification system

The critical strain concept has been widely used in analytical or numerical approaches to evaluate the stability of underground excavations.Analytical,empirical,and numerical procedures are usually used to determine the critical strain values.This paper presents a reliability assessment procedure for evaluating excavation stability using the empirical approach based on the rock mass classification Q and the first order reliability method(FORM).In contrast to deterministic critical strain values,a probabilistic critical strain,which considers uncertainties in rock mass parameters,was incorporated in a limit state function for reliability analysis.Using the rock mass classification Q,the empirically estimated tunnel stain was included in the limit state function.The critical strain and estimated tunnel strain were probabilistically characterized based on the rock mass classification Q-derived rock mass properties.Monte Carlo simulations were also conducted for comparing the reliability analysis results with those derived from the FORM algorithm.A highway tunnel case study was used to demonstrate the reliability assessment procedure.The effects of the input ground parameter correlations,probability distributions,and coefficients of variation on tunnel reliability were investigated.Results show that uncorrelated and normally distributed input parameters(intact rock strength and elastic modulus)have generated more conservative reliability.The reliability analysis results also show that the tunnel had relatively high reliability(reliability index of 2.78 and probability of failure of 0.27%),indicating the tunnel is not expected to experience instability after excavation.The tunnel excavation stability was assessed using analytical and numerical approaches for comparison.The results were consistent with the reliability analysis using the FORM algorithm’s Q-based empirical method.

Method of a New Iteration Scheme Combined with Kriging Model for Structural Reliability Evaluation

The first order reliability method (FORM) is widely adopted for structural reliability evaluation due to its numerical efficiency. Concerning the issue of FORM often failing to converge when the limit state function (LSF) behaves high nonlinearity, a new iteration scheme called "rotated gradient algorithm (RGA)" is proposed and combined with Kriging model to evaluate the reliability of implicit performance function. In this paper, the Kriging model is applied to approximate the real LSF first. Then the scheme of RGA, constructed in terms of gradient information of two adjacent design points obtained during the process of calculation, is used to calculate the reliability index. Numerical examples show the validity in convergence and accuracy of the proposed methodfor arbitrary nonlinear performance function.