Probability, Reliability and Statistical Methods in Engineering Design

In this paper, firstly basic concepts of the structural reliability will be summarized in terms of two basic variables, i.e. structural response (R) and load effect (S). The uncertainty in structural response could be statistically characterized by mean and coefficient of variation (OmegaR). Based on these formulations, there must be an upper limit of OmegaR for the pre-specified acceptable level of reliability (pf). The increment of coefficient of variation of load effect (OmegaS) shows minor influence on the central factor of safety (FS) and its effect diminishes rapidly where OmegaR approaches the upper limit. Below this limit, the structural system could be used safely for a pre-specified target reliability. For lower value of OmegaR, the target FS could be determined from the quadratic relationship between OmegaR and OmegaS. The structural response for foundations is typically a function of soil properties, sections and dimensions. It is not uncommon that uncertainties in soil properties could be normal or non-normal probability distribution and the relationship among basic variables in forming the structural response could be either non-linear or so complicated that results could be obtained from finite element analyses only. Fortunately, the randomness of structural response could be obtained by Monte Carlo simulation technique. Then the fitted distribution of outcome experiments could be specified by Goodness-of-Fit tests. The applicability of proposed concepts could be demonstrated in numerical examples, e.g. driven pile, spread footing and bored pile. For the conventional design approach, soil parameters are considered to be constant. The solution is simplified thorough the use of deterministic safety factor. In reality, soil is neither isotropic nor homogeneous such that their uncertainties could not be ignored. References to the calculated failure probability evidence that deterministic safety factor could not guarantee enough safety. In some cases, an FS of 3 or more is not considered too conservative to apply for the structural response.

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Phadet Ngamcharoen

Papers

The concept of asymptotic coefficients of variation of structural response applied for foundation design