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The mean (point) estimate of reliability index (β) for simple limit state performance functions is most often based on load and resistance model bias statistics taken from bias data of limited size. The paper shows how the confidence in the point estimate of β can be computed using the bootstrap method and a closed-form solution for the special case of lognormally distributed nominal and bias random variables. Bias data collected for the pullout limit state for steel strip mechanically stabilized earth walls are used to demonstrate the approach but the method is general. Mean and confidence intervals on β are computed using the entire available bias data sets and smaller sample sizes located in the tails of the original populations, or smaller sample sizes that result in upper and lower extreme point estimates of β. The closed-form solution for β varies linearly with the logarithm of the nominal factor of safety for the example pullout limit state. Depending on the load and resistance bias sample sizes and where they are taken from in the original larger population, results in a wide range of nominal factors of safety to satisfy a target β at time of design. [ABSTRACT FROM AUTHOR]

A general closed-form solution to compute the reliability index of a simple limit state function with two load terms and one resistance term is derived. The formulation considers contributions to margins of safety expressed in probabilistic terms due to the choice of load and resistance models, bias values, dependencies between nominal values and bias, uncertainty in estimates of nominal values for uncorrelated load and resistance terms at time of design, and average margin of safety expressed as the operational factor of safety. A sensitivity analysis and example application demonstrate the quantitative influence of the contributing random variables on reliability index. [ABSTRACT FROM AUTHOR]

Reliability analysis of bearing capacity of a strip footing at the crest of a simple slope with cohesive soil was carried out using the random finite element method (RFEM). Analyses showed that the coefficient of variation and the spatial correlation length of soil cohesion can have a large influence on footing bearing capacity, particularly for slopes with large height to footing width ratios. The paper demonstrates cases where a footing satisfies a deterministic design factor of safety of 3 but the probability of design failure is unacceptably high. Isotropic and anisotropic spatial variability of the soil strength was also considered. [ABSTRACT FROM AUTHOR]

Probabilistic slope stability analyses of simple geosynthetic reinforced soil slopes were carried out using the shear strength reduction method in combination with the finite element method (FEM). An existing open-source FEM code was modified to include bar elements to model horizontal layers of geosynthetic reinforcement. Analysis results using the modified code (mFEM) demonstrate that large reductions in probability of failure can be realized by adding geosynthetic reinforcement layers to constructed slopes. The modified code was also used to investigate the effect of variability of soil friction angle on probabilistic outcomes for constructed unreinforced and reinforced purely frictional soil slopes. [ABSTRACT FROM AUTHOR]

Model checking, evaluation and comparison are critical steps in Bayesian data analysis but not routinely considered in statistical analysis of geotechnical data. This paper presents an overview of model checking and comparison concepts and techniques employed in modern Bayesian data analysis that are useful for analysis of geotechnical engineering data. These methods are applied to statistical analysis of load and pullout model bias data for steel strip mechanically stabilized earth walls. It is shown how model checking can result in statistical models with better fits. The practical implications of using improved statistical models are discussed in the context of reliability-based design and load and resistance factor design calibration of the internal stability pullout limit state. Finally, statistical model uncertainty and Bayesian model averaging are discussed and explored using an example of reliability-based design for the same limit state. [ABSTRACT FROM AUTHOR]

The choice of structure element to simulate soil reinforcement and soil–structure interaction details for numerical modelling of mechanically stabilized earth (MSE) walls can have a significant influence on numerical outcomes. Program FLAC (finite difference method) offers three different options (beam, cable and strip element) to model the reinforcement and program PLAXIS (finite element method) has two (beam and geogrid element). Both programs use different models and properties to simulate the mechanical behaviour of the interface between dissimilar materials. The paper describes the details of the linear elastic Mohr–Coulomb interface model available in the two software packages to model material interaction and how to select model parameters to give the same numerical outcomes. The numerical results quantitatively demonstrate the conditions that give good agreement between the two programs for the same steel strip reinforced soil–structure problem and the situations where they do not. For example, the paper demonstrates that results can be very different depending on the type of structure element used to model horizontal reinforcement layers that are discontinuous in the plane-strain direction. [ABSTRACT FROM AUTHOR]