Abstract
In geotechnical reliability analysis, random volatility in marginal distributions of shear strength parameters has been rarely considered. Unfortunately, conventional marginal distribution models cannot characterize real probability distribution accurately, leading to considerable dispersion with incomplete probabilistic information. In this paper, an estimation methodology is proposed based on copula theory coupling information diffusion technique. Firstly, information diffusion distribution is extended to represent one-dimensional marginal distributions of shear strength parameters. Secondly, copula theory is employed to characterize the dependence structures among the parameters. Eventually, equivalent sample is yielded by information diffusion distribution that has been already established. A case study in Singapore is implemented to enunciate and validate the competence of the proposed method. The performances of the candidate copulas coupling different marginal distributions are further discussed. Results indicate that information diffusion distribution can efficiently capture the random volatility of real distributions of shear strength parameters and hold remarkable superiority in modeling marginal distributions. The equivalent sample, estimated by information diffusion technique in conjunction with Gaussian copula, has considerable consistency with original data. The proposed method can provide a reference to reliability analysis in geotechnical engineering.
Highlights
It is well recognized that shear strength parameters are significantly crucial to geotechnical reliability analysis [1,2,3,4]
C and φ are often viewed as random variables, and their joint cumulative distribution function (CDF) or probability density function (PDF) seriously affects the accuracy of risk assessment [5, 6]
Marginal distributions and correlation coefficients are approximately estimated with inevitable uncertainty [7, 8]. e joint CDF or PDF is challenged by data scarcity and uncertainty, leading to a large dispersion in the probability of failure
Summary
It is well recognized that shear strength parameters (cohesive force c and internal friction angle φ) are significantly crucial to geotechnical reliability analysis [1,2,3,4]. Based on the information diffusion theory, Gong et al [37] and Huang et al [38] specified information diffusion distribution and successfully captured the random volatility of geotechnical parameters, providing a new enlightenment to marginal distribution deduction These studies did not perform model construction for multivariate distribution. E information diffusion technique is further explored to deduce the optimal marginal distributions of shear strength parameters, in conjunction with copula theory employed to model the dependence structure among them. For this objective, the rest of the study is organized as follows.
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