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This paper demonstrates reliability-based design (RBD) and analysis for tensile strength (rupture) and pullout limit states for mechanically stabilized earth (MSE) walls constructed with steel grid reinforcement in combination with frictional soils. Five different reinforcement tensile load models for walls under operational conditions are considered in combination with six different pullout models and one tensile strength model. The general approach considers the accuracy of the load and resistance models that appear in each limit state equation plus uncertainty in the choice of nominal values at the time of design that is linked to the concept of 'level of understanding' used in Canadian load and resistance factor design (LRFD) foundation engineering practice. The effect of potential steel corrosion on reliability index for the tensile strength limit state is considered in calculations. A well-documented MSE wall case study is used to demonstrate the general approach. The relationship between nominal factor of safety and reliability index is used to demonstrate how to optimize steel grid member diameters and arrangement to achieve a target reliability index of [beta] = 2.33. The approach described in this paper is an important contribution to next-generation analysis and design using modern concepts of RBD for MSE walls. Key words: reliability-based design (RBD), mechanically stabilized earth (MSE) walls, steel grid reinforcement, internal stability limit states. Cet document demontre la conception basee sur la fiabilite (CBF) et l'analyse de la resistance a la traction (rupture) et des etats limites d'arrachement pour les murs en terre stabilisee mecaniquement (TSM) construits avec un renforcement de grille en acier en combinaison avec des sols de friction. Cinq modeles differents de charge de traction des armatures pour les murs dans des conditions operationnelles sont consideres en combinaison avec six modeles d'arrachage differents et un modele de resistance a la traction. L'approche generale tient compte de la precision des modeles de charge et de resistance qui apparaissent dans chaque equation d'etat limite plus l'incertitude dans le choix des valeurs nominales au moment de la conception qui est liee au concept de << niveau de comprehension >> qui est utilise dans la pratique canadienne d'ingenierie des fondations en matiere de conception des facteurs de charge et de resistance (CFCR). L'effet de la corrosion potentielle de l'acier sur l'indice de fiabilite pour l'etat limite de resistance a la traction est pris en compte dans les calculs. Une etude de cas bien documentee sur le mur des TSM est utilisee pour demontrer l'approche generale. La relation entre le facteur nominal de securite et l'indice de fiabilite est utilisee pour demontrer comment optimiser le diametre et la disposition des elements de la grille en acier afin d'atteindre un indice de fiabilite cible de [beta] = 2,33. L'approche decrite dans ce document est une contribution importante a l'analyse et a la conception de la prochaine generation utilisant les concepts modernes de CBF pour les murs des TSM. [Traduit par la Redaction] Mots-cles : conception basee sur la fiabilite (CBF), murs en terre stabilisee mecaniquement (TSM), renforcement de la grille en acier, etats limites de stabilite interne., 1. Introduction This paper is focused on reliability-based design (RBD) and analysis for tensile strength and pullout limit states of steel grid-reinforced mechanically stabilized earth (MSE) walls constructed with frictional [...]

Ground conditions comprised of slightly or completely weathered rock are frequently encountered in design of bridge foundations in Korea. It is rather challenging to assess the accuracy of the common design methodologies for shallow foundations in these ground conditions as the foundation bearing capacity depends on the degree of weathering. This paper presents reliability-based derivation of resistance factors for the bearing capacity of shallow foundations on slightly and completely weathered rock using field plate load test data. More than 140 plate load tests were performed at 52 sites, 33 of which were considered to be of high quality and reliable. These high-quality tests were used to evaluate the uncertainties associated with the bearing capacity equations, and the resistance factors corresponding to current prescribed load factors. A reliability-based approach, with target annual failure probabilities of 1.0 × 10−3, 2.0 × 10−4, 1.0 × 10−4, was adopted to estimate the required resistance factors for different design equations. A Bayesian approach was adopted to facilitate quantification and propagation of statistical parameter uncertainty due to limited available data. The best estimates of the calibrated resistance factors range from 0.40 to about 0.47 for the considered target reliability levels, which is in good agreement with currently used values in Korea. [ABSTRACT FROM AUTHOR]

Geotechnical data used for reliability-based design (RBD) and load and resistance factor design (LRFD) calibration can be parsed into subgroups based on material type, location, test method, and so on. Most often statistical analyses assume all data fall within a representative envelope, and pool (combine) all data into a single large data set without rigorously evaluating the veracity of this assumption. Adopting a Bayesian view, we introduce hierarchical/multilevel models as the more suitable alternative that takes into account multiple variation sources. Rather than assuming an identical parameter for data in all groups, hierarchical models assume exchangeable group-specific parameters, or informally, "similar but not identical" parameters. The utility of Bayesian hierarchical modelling is demonstrated by examining the accuracy of three reinforcement load models for polyester strap mechanically stabilised earth (MSE) walls and a simple hierarchical model as an example. We show that hierarchical models (i) have the customary complete pooling approach as their limiting case, (ii) quantify uncertainty from different sources of variation, (iii) prevent under-fitting, and (iv) can be used as tools for understanding the variations in the data. A simple RBD/LRFD example shows practical implications of hierarchical modelling of bias data. Finally, more complex/flexible hierarchical models are briefly discussed. Abbreviations: AASHTO: American Association of State Highway and Transportation Officials; ANOVA: analysis of variance; CDF: cumulative distribution function; CI: credible interval; COV coefficient of variation; DIC: deviance information criterion; LOGOIC: leave-one-group-out information criteria; LOOIC: leave-one-out information criteria; LM: load model; lppd: log pointwise predictive density; LRFD: load and resistance factor design; MCMC: Markov chain Monte Carlo; MSE: mechanically stabilised earth (wall); NHT: null hypothesis testing; PET: polyester; PGM: probabilistic graphical model; RBD: reliability-based design; WAIC: Watanabe-Akaike information criterion. [ABSTRACT FROM AUTHOR]

The discusser quotes the mean value of HT ht when assessing method performance. • If a normalized stress term is defined as HT ht , then the ratio of the post-equalization term and the installation term is HT ht . 3 and 5 to HT ht values up to 142. [Extracted from the article]

A shortcoming of the typical use of the frequentist probabilistic approach in reliability analysis of limit state equations that appear in the geotechnical literature is that estimates of the uncertainty in reliability index (probability of failure) are not made. A Bayesian approach is demonstrated in the paper to overcome this shortcoming using the example of the pullout limit state for internal stability of mechanically stabilised earth (MSE) walls. The paper shows that in the Bayesian context, reliability index or probability of failure are modelled as probability distributions, and therefore readily incorporate the uncertainty in their estimates. The general approach provides a tool to communicate the level of risk to stakeholders that follows from the choice of design method and guidance to reduce uncertainty on the estimate of reliability. For practical purposes, the predictive reliability index may be used as an alternative measure of margin of safety that takes this uncertainty into account. [ABSTRACT FROM AUTHOR]