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The paper describes load and resistance factor design (LRFD) calibration for the resistance factor used in the Stiffness Method internal stability soil failure limit state for geogrid mechanically stabilized earth (MSE) walls. The Stiffness Method was recently adopted in the current American Association of State Highway and Transportation Officials LRFD Bridge Design Specifications in the US, and will appear in the next edition of the Canadian Highway Bridge Design Code. The paper describes the details of the calibration of the soil failure limit state which is unique to the Stiffness Method. Calibration outcomes include consideration of the concept of level of understanding in the selection of nominal load and resistance values which is unique to LRFD foundation engineering practice in Canada. A practical conclusion from these calculations is that if product line- specific creep test data are available to estimate the reinforcement secant creep stiffness used for design, then a resistance factor of 1.0 is reasonable for US practice. If only minimum average roll value tensile strength data are available, then a value of 0.95 is recommended for US practice. For Canadian practice, the corresponding values for typical level of understanding are 0.90 and 0.85, respectively. Key words: stiffness method, soil failure limit state, mechanically stabilized earth (MSE) walls, geosynthetic reinforcement, geogrid, load and resistance factor design (LRFD), Introduction The Stiffness Method is used to calculate the maximum tensile loads in geosynthetic and steel reinforced mechanically stabilized earth (MSE) walls under operational conditions (AASHTO 2020a; Allen and Bathurst [...]

The estimation of the resistance factor in load and resistance factor design (LRFD) calibration for simple soil–structure limit states is most often based on model bias data of limited size. Frequently, the bias data are only available or required for the resistance term. In this study, the confidence in the estimate of the mean of the resistance factor is computed for the case of one resistance factor and one load factor where limited model bias data are available for both load and resistance terms. The bootstrap method is used to compute synthetic load and resistance bias data sets from which confidence intervals on the point (mean) estimate of the resistance factor and load factor are computed. A closed-form solution is used to calculate the resistance factor for a single prescribed load factor and target reliability index, bias data, and nominal load and resistance variables that are lognormally distributed. However, the approach is general using Monte Carlo simulation. The method is demonstrated using the case of the internal stability pullout limit state for steel strip mechanically stabilized earth walls. The example demonstrates the quantitative influence on pullout design using upper and lower 95% confidence interval limits for load and resistance factors. [ABSTRACT FROM AUTHOR]

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 [...]

This document provides a summary of the different topics presented at the Special Session organized by the International Geosynthetics Society (IGS) Technical Committee on Soil Reinforcement (TC-R). This Special Session brings together very interesting studies regarding soil reinforcement in the field of geosynthetics. Studies presented include topics both from theoretical and practical points of view of reinforcement geosynthetics including general products and applications, cases studies on road embankments under challenging site boundary conditions, research on deterministic and probabilistic design of reinforced fills over voids, numerical analysis of reinforced soil wall structures, encased granular column technique, and geosynthetic-reinforced bridge abutment behavior.

Most often the focus on the mechanical contribution of reinforcement geosynthetics in soil reinforcement applications has been on the strength of the material. In fact, under operational conditions the performance of these systems is controlled by the stiffness of the geosynthetic, not its strength. An appreciation of the role of geosynthetic stiffness in soil reinforcement applications is complicated by the rate-dependency of many products which means that their load-strain properties are time-, strain- and temperature-dependent. This paper describes the quantification of these properties using a simple isochronous load-strain model with properties fitted from laboratory creep testing. The implementation of the model and its consequences on the quantitative performance of mechanically stabilized earth (MSE) wall loads and deformations, reinforced fills over voids, and a thin reinforced granular base over a soft clay foundation are demonstrated.

This paper demonstrates reliability-based design for tensile rupture and pullout limit states for mechanically stabilized earth (MSE) walls constructed with geosynthetic (geogrid) reinforcement. The general approach considers the accuracy of the load and resistance models that appear in each limit state equation plus uncertainty due to the confidence (level of understanding) of the designer at the time of design. The reliability index is computed using a closed-form solution that is easily implemented in a spreadsheet. The general approach provides a quantitative link between nominal factor of safety, which is familiar in allowable stress design practice, and reliability index used in modern civil engineering reliability-based design practice. A well-documented MSE wall case study is used to demonstrate the general approach and to compare margins of safety using different load and resistance model combinations. A practical outcome from the case study example is the observation that the pullout limit state is much less likely to control design than the ultimate tensile rupture state for walls with continuous reinforcement coverage. The more accurate 'simplified stiffness method' that is used to compute tensile loads in the reinforcement under operational conditions is shown to generate a more cost-effective reinforcement option than the less accurate American Association of State Highway and Transportation Officials (AASHTO) simplified method. Key words: mechanically stabilized earth (MSE) walls, geosynthetic reinforcement, internal stability limit states, reliability-based design. Cet article demontre une conception basee sur la fiabilite pour les etats limites de rupture en traction et darrachement pour les murs de terre stabilises mecaniquement (<>) avec un renforcement geosynthetique (geogrille). L'approche generale considere la precision des modeles de charge et de resistance qui apparaissent dans chaque equation d'etat limite plus l'incertitude due a la confiance (niveau de comprehension) du concepteur au moment de la conception. L'indice de fiabilite est calcule a l'aide d'une solution analytique facilement implementee dans une feuille de calcul. L'approche generale fournit un lien quantitatif entre le facteur de securite nominal connu dans la pratique de la conception des contraintes admissibles et l'indice de fiabilite utilise dans les pratiques de conception basee sur la fiabilite du genie civil moderne. Une etude de cas MSE bien documentee est utilisee pour demontrer l'approche generale et pour comparer les marges de securite en utilisant differentes combinaisons de modeles de charge et de resistance. Un resultat pratique de l'exemple de l'etude de cas est l'observation selon laquelle l'etat limite d'arrachement est beaucoup moins susceptible de controler la conception que l'etat de rupture en traction ultime pour les murs a couverture continue. La methode de rigidite simplifiee la plus precise utilisee pour calculer les charges de traction dans le renforcement dans des conditions operationnelles est montree comme generant une option de renforcement plus rentable que la methode simplifiee << American Association of State Highway and Transportation Officials >>(AASHTO) moins precise. [Traduit par la Redaction] Mots-cles : murs de terre stabilises mecaniquement (MSE), renforcement geosynthetique, etats limites de stabilite interne, conception basee sur la fiabilite., 1. Introduction The internal stability design of mechanically stabilized earth (MSE) walls in North America is most often based on load and resistance factor design (LRFD) which is a reliability [...]

Cross correlations between nominal load and resistance terms in limit state functions for geotechnical soil-structure interaction problems can be expected. A closed-form solution for the reliability index for a simple linear limit state function is used to examine the influence of nominal load and resistance correlations on computed margins of safety. The formulation also includes the contribution of the underlying accuracy of the load and resistance equations (method bias) and bias dependencies with the magnitude of nominal load and resistance values assumed in the limit state design function. Sensitivity analyses and example problems for the external sliding limit state for a cantilever wall and the pullout limit state for internal stability of reinforced soil walls with different soil reinforcement types are presented. Ignoring nominal correlations where they exist is shown to underestimate the reliability index in some cases and to overestimate the reliability index in other cases. In the example problems, these differences are shown to exceed one order of magnitude in terms of probability of failure, but in the sensitivity analyses using a wider range of input parameter values, the differences can be several orders of magnitude. Key words: geotechnical soil-structure interaction, reliability-based design, linear limit state, nominal correlation, bias dependency, sliding, pullout. Les correlations croisees entre la charge nominale et la resistance en termes de fonctions d'etat limite geotechnique pour les problemes d'interaction sol-structure peuvent etre prevues. Une solution a forme fermee pour l'indice de fiabilite pour une fonction d'etat limite lineaire simple est utilisee pour examiner l'influence de la charge nominale et de la resistance sur les correlations calculees des marges de securite. La formulation comprend egalement la contribution de l'exactitude des equations de charge et de resistance (methode de polarisation) et du biais les dependances avec l'ampleur de la charge nominale et les valeurs de resistance a l'etat suppose a limiter la fonction de conception. Des analyses de sensibilite et l'exemple des problemes pour l'etat limite de glissement externe pour un mur a porte a faux et l'etat limite d'arrachement pour la stabilite interne des murs de terre renforcee avec differents types de renforcement des sols sont presentes. Ignorant les correlations nominales lorsqu'ils existent est montre a sous-estimer l'indice de fiabilite dans certains cas et a surestimer l'indice de fiabilite dans les autres cas. Dans l'exemple des problemes, ces differences sont presentees pour depasser un ordre de grandeur en termes de probabilite d'echec, mais dans les analyses de sensibilite en utilisant un plus large eventail de valeurs de parametre d'entree, les differences peuvent etre de plusieurs ordres de grandeur. [Traduit par la Redaction] Mots-cles : interaction sol-structure geotechnique, conception basee sur la fiabilite, etat limite lineaire, correlation nominale, dependance biaisee, coulissant, retire., Introduction Geotechnical engineers are often faced with simple soil-structure interaction problems in which the same input parameter definitions appear in both load and resistance terms of a limit state function. [...]

The paper presents the numerical modelling details using the finite difference method (FDM) to simulate the performance of a well-instrumented geogrid-reinforced incremental concrete panel soil retaining wall. Two different constitutive models were investigated for the backfill soil (linear elastic-plastic model and nonlinear elastic-plastic model). Both constant stiffness and strain-dependent secant stiffness models were used for the reinforcement elements. The paper provides valuable lessons to modellers to simulate the performance of this type of earth retaining structure. For example, parametric investigation of the effect of a constant Young's modulus ranging from 40 to 120 MPa for the linear-elastic Mohr-Coulomb model had only minor influence on the wall facing displacements and reinforcement loads. However, the choice of magnitude of transient compaction pressure near the facing can result in large differences in facing displacements. The paper also demonstrates that the method of construction including the location, sequence, and stiffness of the temporary supports used to construct the wall plays an important role on measured and predicted wall performance. The physical measurements reported in this paper provide a benchmark for numerical modellers to verify other numerical models for walls of the type investigated here. Key words: geosynthetics, numerical modelling, instrumented wall, incremental panel facing, geogrid reinforcement, FLAC. Le document presente les details de modelisation numerique en utilisant la methode des differences finies (MDF) pour simuler les performances d'un mur de retenue de sol par panneaux de beton incrementaux avec une geogrille renforcee bien instrumentee. Deux modeles de comportement differents ont ete etudies pour le sol de remblayage (modele elastoplastique lineaire et modele elastoplastique non lineaire). Deux modeles a rigidite constante et a rigidite secante dependante a la deformation ont ete utilises pour les elements de renfort. L'article fournit des lemons precieuses pour les modelisateurs afin de simuler les performances de ce type de structure de soutenement de sol. Par exemple, la recherche parametrique de l'effet d'un module d'Young compris constant de 40 a 120 MPa pour le modele de Mohr-Coulomb elastique lineaire avait seulement une influence mineure sur la paroi faisant face a des deplacements et a des charges de renforcement. Cependant, le choix de la valeur de la pression de compactage transitoire a proximite du parement peut entramer des differences importantes dans les deplacements au parement. L'article demontre egalement que la methode de construction y compris l'emplacement, la sequence et la rigidite des supports temporaires utilises pour construire le mur joue un role important sur la performance de la paroi mesuree et predite. Les mesures physiques rapportees dans le present document constituent une reference pour les modelisateurs numeriques pour verifier les autres modeles numeriques pour les murs du type etudie ici. [Traduit par la Redaction] Mots-cles: geosynthetiques, modelisation numerique, paroi instrumentee, face incrementale du panneau, geogrille, FLAC., Introduction The internal stability design and analysis of geosynthetic-reinforced soil walls in North America is based on a limit-equilibrium tie-back wedge method (e.g., AASHTO 2014) that can be traced back [...]

In the literature, the influence of spatial variability of the undrained shear strength of foundation soils on the bearing capacity of footings is limited to footings seated directly on the foundation. This is an unlikely arrangement in practice. This paper revisits the footing problem by considering a thin granular layer between a strip footing and soft foundation soil using analytical and stochastic numerical modeling. The analyses are extended to the case of a geosynthetic-reinforced granular layer and to the idealized case of no granular layer. The study shows that the probability that the ultimate bearing capacity for the footing is smaller than the deterministic design value is greater for all three scenarios with randomly uniform clay soil than for the same soil with isotropic or anisotropic spatial variability of strength at practical levels of reliability index β (e.g., β≥3.09 for a permanent footing). The reason for this outcome, which may appear counterintuitive, is explained. Design charts are provided to estimate the deterministic design bearing capacity of a rigid strip footing required to meet a range of target reliability index for the three footing scenarios examined in this study. [ABSTRACT FROM AUTHOR]

This paper focuses on the calculation of probability of failure of simple unreinforced slopes and the influence of the magnitude of cross correlation between soil parameters on numerical outcomes. A general closed-form solution for cohesive slopes with cross correlation between cohesion and unit weight was investigated and results compared with cases without cross correlation. Negative cross correlations between cohesion and friction angle and positive cross correlations between cohesion and unit weight, and friction angle and unit weight were considered in the current study. The factors of safety and probabilities of failure for the slopes with uncorrelated soil properties were obtained using probabilistic slope stability design charts previously reported by the writers. Results for cohesive soil slopes and positive cross correlation between cohesion and unit weight are shown to decrease probability of failure. Probability of failure also decreased for increasing negative cross correlation between cohesion and friction angle, and increasing positive correlation between cohesion and unit weight, and friction angle and unit weight. Probabilistic slope stability design charts presented by the writers in an earlier publication are extended to include cohesive-frictional (c-φ) soil slopes with and without cross correlation between soil input parameters. An important outcome of the work presented here is that cross correlation between random values of soil properties can reduce the probability of failure for simple slope cases. Hence, previous probabilistic design charts by the writers for simple soil slopes with uncorrelated soil properties are conservative (safe) for design. This study also provides one explanation why slope stability analyses using uncorrelated soil properties can predict unreasonably high probabilities of failure when conventional estimates of factor of safety suggest a stable slope. Key words: slope stability, probabilistic analysis, cross correlation, Monte Carlo simulation. Le present article decrit le calcul de probabilite de rupture de pentes simples non consolidees et l'influence de l'amplitude des correlations croisees entre les parametres du sol sur les resultats numeriques obtenus. On a etudie une solution generale de type ferme s'appliquant aux pentes cohesives pour laquelle il existe une correlation croisee entre la cohesion et le poids unitaire et les resultats obtenus ont ete compares a des cas pour lesquels il n'existe pas une telle correlation. Dans la presente etude, on a tenu compte des correlations croisees negatives entre la cohesion et l'angle de frottement ainsi que des correlations croisees positives entre la cohesion et le poids unitaire. Les facteurs de securite et les probabilites de rupture des pentes dont les proprietes du sol ne sont pas correlees ont ete obtenus a l'aide d'abaques probabilistes de stabilite des pentes precedemment fournis par les auteurs. Les resultats obtenus dans le cas des pentes de sols cohesifs et la correlation croisee positive entre la cohesion et le poids unitaire semblent avoir pour effet de diminuer la probabilite de rupture. En outre, la probabilite de rupture diminue lorsque la correlation croisee negative entre la cohesion et l'angle de frottement augmente, lorsque la correlation positive entre la cohesion et le poids unitaire et la correlation entre l'angle de frottement et le poids unitaire augmentent. Le champ d'application des abaques probabilistes de stabilite des pentes presentes par les auteurs dans une publication precedente est etendu pour inclure les pentes des sols de type cohesive-frictionnelle (c-φ) pour lesquels il existe ou non une correlation croisee entre les parametres de depart caracterisant le sol considere. Une des conclusions importantes de la presente etude est que la correlation croisee entre les valeurs aleatoires des parametres du sol peut avoir pour effet de reduire la probabilite de rupture dans le cas de pentes simples. Ainsi, les abaques probabilistes fournis precedemment par les auteurs dans le cas de pentes simples de sols dont les proprietes ne sont pas correlees restent assez prudents (fiables) pour pouvoir etre utilises en conception. La presente etude explique egalement comment les analyses de stabilite des pentes effectuees a l'aide de parametres de sol non correles peuvent produire des predictions de probabilites de rupture anormalement elevees alors que les estimations habituelles du facteur de securite montrent que la pente consideree est stable. [Traduit par la Redaction] Mots-cles: stabilite des pentes, analyse probabiliste, correlation croisee, simulation de Monte-Carlo., Introduction Slope stability charts are used routinely to estimate the conventional factor of safety of unreinforced slopes with isotropic, homogeneous soil properties, and simple geometry. Design charts by Taylor (1937), [...]

Canada has two national civil codes of practice that include geotechnical design provisions: the National Building Code of Canada and the Canadian Highway Bridge Design Code. For structural designs, both of these codes have been employing a load and resistance factor format embedded within a limit states design framework since the mid-1970s. Unfortunately, limit states design in geotechnical engineering has been lagging well behind that in structural engineering for the simple fact that the ground is by far the most variable (and hence uncertain) of engineering materials. Although the first implementation of a geotechnical limit states design code appeared in Denmark in 1956, it was not until 1979 that the concept began to appear in Canadian design codes, i.e., in the Ontario Highway Bridge Design Code, which later became the Canadian Highway Bridge Design Code (CHBDC). The geotechnical design provisions in the CHBDC have evolved significantly since their inception in 1979. This paper describes the latest advances appearing in the CHBDC along with the steps taken to calibrate its recent geotechnical resistance and consequence factors. Key words: geotechnical code development, reliability-based geotechnical design, load and resistance factor design, Canadian codes, code comparison. Au Canada, il existe deux codes comportant des specifications en matiere de conception geotechnique : Code national du batiment du Canada et le Code canadien sur le calcul des ponts routiers (Canadian Highway Bridge Design Code). Dans le cas de la conception de structures, ces deux codes font appel, depuis le milieu des annees 1970, au concept de facteur de charge et de resistance integre a un cadre de travail base sur le calcul aux etats limites. Malheureusement, le calcul aux etats limites est desormais beaucoup plus utilise en ingenierie structurale qu'en geotechnique appliquee pour la simple raison que le sol constitue de loin le plus changeant (et donc le moins controlable) de tous materiaux utilises par les ingenieurs. Bien que le premier code regissant la conception geotechnique basee sur le calcul aux etats limites ait ete mis en place au Danemark en 1956, il a fallu attendre jusqu'a 1979 pour que cette methode de calcul apparaisse dans les codes canadiens regissant la conception, plus precisement dans l'Ontario Highway Bridge Design Code, devenu plus tard le Code canadien sur le calcul des ponts routiers (CCCPR). Les specifications en matiere de conception geotechnique figurant dans le CCCPR ont beaucoup evolue depuis leur mise en place en 1979. Le present article decrit les dernieres modifications apportees aux CCCPR et les mesures prises pour calibrer les tout derniers facteurs geotechniques de consequence et de resistance qui y figurent. [Traduit par la Redaction] Mots-cles: creation d'un code regissant la conception technique, conception geotechnique basee sur la fiabilite, mise au point du facteur de charge et de resistance, codes canadiens, comparaison des codes., Introduction Worldwide, geotechnical design codes have been migrating towards reliability-based design concepts for several decades now. For example, the ISO 2394 (International Organization for Standardization 2015), which provides general principles [...]

This article describes a rate-dependent hyperbolic model that was developed to predict the tensile load-strain behavior of a polypropylene geogrid reinforcement material under monotonic and stepped constant rate-of-strain testing. A more general three-component model previously reported in the literature was also used in the current study but with some modifications to compute model parameters. Details of the trial and error procedure to select three-component model parameters, not previously reported in the literature, are explained. Both models gave similar good agreement between measured and predicted constant rate-of-strain tests. The accuracy of the three-component model to simulate stepped constant rate-of-strain tests was judged to be better, but for practical purposes, the simpler hyperbolic model was judged to be satisfactory. An advantage of the hyperbolic model is that the model parameters are easy to determine, only monotonic constant rate-of-strain tests are required, and numerical implementation is simple. However, the hyperbolic model is restricted to monotonic or stepped constant rate-of-strain load paths. An advantage of the more complicated three-component model is that it has been demonstrated in previous studies to be more general and thus can be used for other load paths and other polymeric reinforcement material types that do not have characteristic hyperbolic load-strain behavior., INTRODUCTION Polymeric geogrid materials, including punched and drawn polypropylene (PP) geogrids, are used routinely for soil reinforcement. In reinforced soil wall, slope and embankment applications, they provide additional strength and [...]