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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 [...]

The paper examines the quantitative influence of uncertainty in the estimate of geosynthetic reinforcement stiffness on numerical outcomes using analytical solutions for a) the maximum outward facing deformation in mechanically stabilized earth (MSE) walls, b) maximum reinforcement tensile loads and strain in MSE walls under operational conditions, and c) the mobilized reinforcement stiffness in a geosynthetic layer used to reinforce a fill over a void. The stiffness of the reinforcement is modelled using an isochronous two-parameter hyperbolic load-strain model. A linear relationship between isochronous stiffness and the ultimate tensile strength of the reinforcement is used to estimate reinforcement stiffness when product-specific creep data are not available at time of design. Solution outcomes are presented deterministically and probabilistically. The quantitative link between nominal factor of safety used in deterministic working stress design practice and reliability index is provided. The latter is preferred in modern performance-based design to quantify margins of safety within a probabilistic framework. Finally, the paper highlights the practical benefit of using product-specific isochronous secant stiffness data when available, rather than estimates of isochronous stiffness values based on reinforcement type or pooled data. • Uncertainty in the estimate of geosynthetic stiffness is investigated for three geosynthetic-reinforced soil applications. • The stiffness of the reinforcement is modelled using an isochronous two-parameter hyperbolic load-strain model. • Isochronous secant stiffness estimated using: a) product-specific creep data; b) type of reinforcement; and c) pooled data. • Closed-form solutions linking the nominal factor of safety to the reliability index for each application are provided. • Solution outcomes are presented deterministically and probabilistically. [ABSTRACT FROM AUTHOR]

Thin granular fill layers are routinely used to aid the construction of shallow footings seated over undrained soft clay foundations and to increase their load capacity. The influence of time- and strain-dependent reduction in reinforcement stiffness on the bearing capacity and load-settlement response of a footing seated on a thin reinforced granular fill layer over undrained soft clay foundations is examined in this paper using finite-difference method (FDM) numerical models. The time- and strain-dependent stiffness of the reinforcement described by a two-component hyperbolic isochronous tensile load-strain model is shown to influence the bearing capacity and load-settlement response of the reinforced granular base scenario. The additional benefit of a reinforced granular layer diminishes as the time-dependent stiffness of the geosynthetic reinforcement increases. An analytical solution for the ultimate bearing capacity of strip footings seated on thin unreinforced and reinforced granular layers over undrained clay is proposed in this study. The main practical outcome from this study are tables of bearing capacity factors to be used with the analytical solution. The bearing capacity factors were back-calculated from the numerical analyses and account for the influence of rate-dependent properties of geogrid reinforcement materials and clay foundations with soft to very soft undrained shear strength. • Load-settlement and ultimate bearing capacity of strip footing on reinforced granular layer over undrained clay is studied. • Stiffness of the reinforcement is described by a two-component hyperbolic isochronous tensile load-strain model. • Benefit of reinforced granular layer diminishes as time-dependent stiffness of the geosynthetic reinforcement increases. • Analytical solution for ultimate bearing capacity of strip footing on thin reinforced granular layer over clay is proposed. • Bearing capacity factors are back-calculated from numerical simulations using large-strain finite difference method model. [ABSTRACT FROM AUTHOR]

Design charts to estimate the factor of safety for simple slopes with cohesive-frictional (c-φ) soils are now available in the literature; however, the factor of safety is an imperfect measure for quantifying the margin of safety of a slope because nominal identical slopes with the same factor of safety can have different probabilities of failure due to variability in soil properties. In this study, simple circular slip slope stability charts for φ = 0 soils by Taylor in 1937 and c- φ soils published by Steward et al. in 2011 are extended to match estimates of factors of safety to corresponding probabilities of failure. A series of new charts are provided that consider a practical range of coefficient of variation for cohesive and frictional strength parameters of the soil. The data to generate the new charts were produced using conventional probabilistic concepts together with closed-form solutions for cohesive soil cases, and Monte Carlo simulation in combination with conventional limit equilibrium-based circular slip analyses using the SVSlope program for c-φ soil cases. The charts are a useful tool for geotechnical engineers when making a preliminary estimate of the probability of failure of a simple slope without running Monte Carlo simulations. Key words: slope stability, probabilistic analysis, Monte Carlo simulation, design chart, spatial variability. Des chartes de conception servant a estimer le facteur de securite de pentes simples faites en sols c-φ (c est la cohesion; φ est l'angle de frottement) sont maintenant disponibles dans la litterature. Cependant, le facteur de securite est une mesure imparfaite pour quantifier la marge de securite d'une pente puisque des pentes nominales identiques avec le meme facteur de securite peuvent avoir des probabilites de rupture differentes en raison de la variabilite des proprietes des sols. Dans cette etude, les chartes de stabilite pour des glissements circulaires simples dans des pentes de sols avec φ = 0 publiees par Taylor en 1937 et pour des sols c-φ publiees par Steward et al. en 2011 sont etendues pour concorder avec les estimations de facteur de securite correspondant aux probabilites de rupture. Une serie de nouvelles chartes sont presentees qui considerent une gamme pratique de coefficients de variation pour les parametres de cohesion et de resistance a la friction du sol. Les donnees ayant servi a generer les nouvelles chartes ont ete produites a l'aide de concepts probabilistes conventionnels combines a des solutions fermees pour les cas des sols cohesifs, et des simulations Monte Carlo combinees avec les analyses de glissement circulaire basees sur l'equilibre limite conventionnel a l'aide du logiciel SVSlope pour le cas des sols c-φ. Les chartes sont un outil utile pour les ingenieurs en geotechnique qui font des estimations preliminaries de la probabilite de rupture d'une pente simple sans realiser de simulations Monte Carlo. [Traduit par la Redaction] Mots-cles: stabilite de pente, analyse probabiliste, simulation Monte Carlo, charte de conception, variabilite spatiale., Introduction Slope stability charts are used routinely to estimate the factor of safety of slopes with isotropic, homogeneous soil properties and simple geometry. Taylor (1937) published design charts to calculate [...]

An 11 m high dry-stacked masonry concrete block wall reinforced with a high-density polyethylene (HDPE) geogrid was designed, instrumented, and monitored for a period of 2 years as part of a highway-widening project southeast of Seattle, Washington, in the USA. An extensive materials-testing program was conducted to characterize the geogrid and backfill soil properties. The empirical-based K-stiffness method was used to design the wall, and this approach resulted in a 35% reduction in total required reinforcement strength compared with the American Association of State Highway and Transportation Officials / Federal Highway Administration (AASHTO/FHWA) simplified method. The cost savings more than compensated for the cost of the instrumentation program. Geogrid strains were measured using strain gauges and extensometers, and the walls were surveyed to monitor facing deformations. The stiffness of the geogrid materials was computed from the results of laboratory in-isolation constant-load (creep) tests. The time- and strain-dependent stiffness values, in combination with measured strains, were used to compute measured reinforcement loads at the reinforcement connections and at locations within the reinforced soil backfill. The measured loads were compared with class A, B, and C1 predictions using the AASHTO/FHWA simplified and K-stiffness methods. These comparisons demonstrate that the simplified method significantly overestimated reinforcement loads, whereas the K-stiffness method provided estimates that were judged to be in better agreement with the measured results. The paper also quantifies the influence of construction procedures on reinforcement strains and load, shows that long- term creep of the reinforcement after 2 years after construction is negligible, and identifies lessons learned. Key words: geosynthetics, walls, stresses, strains, design, soil reinforcement, simplified method, K-stiffness method, hyperbolic isochronous model. Un mur en maconnerie de 11 metres de haut, fait de blocs de beton places sec et renforce d'une geogrille en polyethylene de haute densite (HDPE), a ete concu, instrumente et suivi sur une periode de 2 ans. Ce mur faisait partie d'un projet d'elargissement d'une autoroute au sud-est de Seattle, Washington, aux Etats-Unis. Un vaste programme d'essais sur les materiaux a ete realise afin de caracteriser les proprietes de la geogrille et du sol de remblayage. La methode de rigidite K, basee sur des lois empiriques, a ete utilisee pour concevoir le mur et cette approche a permis de reduire de 35 % la resistance en renforcement totale requise comparativement a celle requise selon la methode simplifiee de l'American Association of State Highway and Transportation Officials / Federal Highway Administration (AASHTO/FHWA). Les economies en argent ont plus que compense pour le cout du programme d'instrumentation. Les deformations de la geogrille ont ete mesurees a l'aide de jauges de deformation et d'extensometres, tandis que le mur a ete instrumente pour mesurer les deformations de la face. La rigidite des materiaux de la geogrille a ete obtenue a partir des resultats d'essais de laboratoire a charge constante en isolation (fluage). Les valeurs de rigidite dependantes du temps et des deformations, combinees aux deformations mesurees, ont ete utilisees pour calculer les charges de renforcement mesurees aux connections de renforcement et aux endroits a l'interieur du sol de remblayage renforce. Les charges mesurees ont ete comparees aux predictions de class A, B et C1 obtenues avec les methodes de l'AASHTO/FHWA simplifiee et de rigidite K. Ces comparaisons demontrent que la methode simplifiee surestime significativement les charges de renforcement, tandis que la methode de rigidite K offre des estimations qui sont jugees plus en accord avec les resultats mesures. Cet article quantifie aussi l'influence des procedures de construction sur les deformations et charges de renforcement, demontre que le fluage a long terme du renforcement 2 ans apres la construction est negligeable, et identifie les lemons apprises. [Traduit par la Redaction] Mots-cles: geosynthetiques, murs, contraintes, deformations, conception, renforcement du sol, methode simplifiee, methode de rigidite K, modele hyperbole isochrones., Introduction An 11 m high masonry-block geosynthetic-reinforced soil wall (wall C) was constructed at a highway project located southeast of Seattle, Washington, in 2005-2006. A 6.3 m high companion wall [...]

This paper presents the results of load and resistance factor design (LRFD) calibration of the facing limit states for soil nail walls. The current AASHTO facing load model and a modified model together with the AASHTO facing resistance models for both permanent and temporary facing load cases are considered. The facing design includes flexure, punching shear, and headed-stud tensile limit states. The calibration of resistance factors captures uncertainty in the accuracy of the load and resistance models, uncertainties in the nominal load and resistance values at time of design, and bias dependencies between model bias and nominal values. Resistance factors are calibrated for a range of load factors and target reliability indexes. Example designs for facing limit states demonstrate the implementation of the calibrated resistance factors in a LRFD framework using the current AASHTO and modified load models for the permanent facing load case. The practical values of this study are calibrated load and resistance factors for facing limit states of soil nail walls that are of interest to code writers for future editions of LRFD codes in the United States and Canada. [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 model was made purposely simple to focus attention on the qualitative influence of stiffness on reinforcement loads. • Using numerical models to infer quantitative performance of actual MSE walls must be undertaken with caution and skill. • Small changes in numerical model details can give widely different estimates of reinforcement loads. • The veracity of any numerical model should be based on comparisons with more than one physical wall of realistic height. • The accuracy of design methods must be assessed using measured loads from full-scale walls, not numerical models. [ABSTRACT FROM AUTHOR]

A verified fast Lagrangian analysis of continua (FLAC) numerical model is used to investigate the influence of horizontal toe stiffness on the performance of reinforced soil segmental retaining walls under working stress (operational) conditions. Results of full-scale shear testing of the interface between the bottom of a typical modular block and concrete or crushed stone levelling pads are used to back-calculate toe stiffness values. The results of numerical simulations demonstrate that toe resistance at the base of a reinforced soil segmental retaining wall can generate a significant portion of the resistance to horizontal earth loads in these systems. This partially explains why reinforcement loads under working stress conditions are typically overestimated using current limit equilibrium- based design methods. Other parameters investigated are wall height, interface shear stiffness between blocks, wall facing batter, reinforcement stiffness, and reinforcement spacing. Computed reinforcement loads are compared with predicted loads using the empirical-based K-stiffness method. The K-stiffness method predictions are shown to better capture the qualitative trends in numerical results and be quantitatively more accurate compared with the AASHTO simplified method. Key words: reinforced soil, segmental walls, numerical modelling, toe restraint, K-stiffness method, simplified method. Un modele numerique veerifie FLAC est utilise; pour investiguer l'influence de la rigidite; du pied horizontal sur la performance de murs de soutenement segmentes faits de sol renforcee en conditions de contraintes de travail (operationnelles). Des essais en cisaillement a grande echelle a l'interface entre le bas d'un bloc modulaire typique et les plaques de nivellement de beton ou de pierre concassee ont etee effectues. Les resultats de ces essais ont ete utilises pour deduire les valeurs de rigidite; du pied. Les resultats des simulations numeeriques demontrent que la resistance du pied a la base d'un mur de soutenement segmente en sol renforce peut geenerer une portion importante de la resistance au chargement horizontal dans ces systemes. Ceci explique en partie pourquoi les chargements de renforcement en conditions de contraintes de travail sont geeneralement surestimesa partir des meethodes courantes de conception baseees sur les limites a l'equilibre. Les autres parameetres qui ont eete evaluees sont la hauteur du mur, la rigidite; en cisaillement a l'interface entre les blocs, ainsi que l'espacement entre les renforcements. Les chargements de renforcement calcules sont comparees aux chargements predits a l'aide de la methode empirique baseee sur la rigidite K. Les predictions obtenues a partir de la methode de la rigidite; K permettent de mieux representer les tendances qualitatives des resultats numeeriques et d'etre plus precis quantitativement que la me;thode AASHTO simplifiee. Mots-cles: sol renforce, murs segmentes, modelisation numeerique, restriction au pied, methode de la rigiditee K, meethode simplifieee. [Traduit par la Re;daction], Introduction Current design for the internal stability of geosynthetic reinforced soil walls is based on the 'tie back wedge method' or variants thereof (BSI 1995; AASHTO 2002; CFEM 2006; NCMA [...]

A numerical finite-difference method (FLAC) model was used to investigate the influence of constitutive soil model on predicted response of two full-scale reinforced soil walls during construction and surcharge loading. One wall was reinforced with a relatively extensible polymeric geogrid and the other with a relatively stiff welded wire mesh. The backfill sand was modeled using three different constitutive soil models varying as follows with respect to increasing complexity: linear elastic-plastic Mohr-Coulomb, modified Duncan-Chang hyperbolic model, and Lade's single hardening model. Calculated results were compared against toe footing loads, foundation pressures, facing displacements, connection loads, and reinforcement strains. In general, predictions were within measurement accuracy for the end-of-construction and surcharge load levels corresponding to working stress conditions. However, the modified Duncan-Chang model which explicitly considers plane strain boundary conditions is a good compromise between prediction accuracy and availability of parameters from conventional triaxial compression testing. The results of this investigation give confidence that numerical FLAC models using this simple soil constitutive model are adequate to predict the performance of reinforced soil walls under typical operational conditions provided that the soil reinforcement, interfaces, boundaries, construction sequence, and soil compaction are modeled correctly. Further improvement of predictions using more sophisticated soil models is not guaranteed. DOI: 10.1061/(ASCE)GT.1943-5606.0000092 CE Database subject headings: Soil stabilization; Walls; Constitutive models; Numerical models; Reinforcement.

Expanded polystyrene (EPS) geofoam seismic buffers can be used to reduce earthquake-induced loads acting on rigid retaining wall structures. A numerical study was carried out to investigate the influence of wall height; EPS geofoam type, thickness, and stiffness; and excitation record on seismic buffer performance. The numerical simulations were carried out using a verified FLAC code. The influence of parameter values was examined by computing the maximum forces on the walls, the buffer compressive strains, and the relative efficiency of the buffer system. In general, the closer the predominant frequency of excitation to the fundamental frequency of the wall model, the greater the seismic loads and buffer compression. The choice of earthquake record is shown to affect the magnitude of maximum earth force and isolation efficiency. However, when the wall response for walls 3 to 9 m in height are presented in this study in terms of isolation efficiency, the data from scaled accelerograms and matching harmonic records with the same predominant frequency fall within a relatively narrow band when plotted against relative buffer thickness. For the range of parameters investigated, a buffer stiffness value less than 50 MN/[m.sup.3] was judged to be the practical range for the design of these systems. Key words: geofoam, seismic buffer, rigid retaining wall, numerical analysis, parametric analysis, earthquake. Des tampons sismiques faits de geo mousse de polystyrene expanse << EPS >> peuvent etre utilises pour reduire les charges appliquees aux murs de soutenement rigides causees par les tremblements de terre. Une etude numerique a ete effectuee pour investiguer l'influence de la hauteur du mur, du type de geo mousse << EPS >>, de l'epaisseur, de la rigidite, des donnees d'excitation sur le tampon sismique. Les simulations numeriques ont ete faites a l'aide d'un code FLAC verifie. L'influence de la valeur des parametres a ete examinee en calculant les forces maximales sur les murs, la deformation en compression du tampon et l'efficacite relative du systeme de tampon. De facon generale, plus la frequence predominante d'excitation est pres de la frequence fondamentale du modele de mur, plus eleves seront les charges sismiques et la compression du tampon. Le choix des donnees sismiques affecte la magnitude de la force maximale de la terre et l'efficacite d'isolation. Cependant, dans cette etude, lorsque les resultats pour des murs de 3 a 9 metres de hauteur sont presentes en termes d'efficacite d'isolation, les donnees provenant des accelerogrammes et des donnees harmoniques correspondantes avec la meme frequence predominante se retrouvent a l'interieur d'une plage mince quand ils sont places sur un graphique en fonction de l'epaisseur relative du tampon. Pour la gamme de parametres evalues, une rigidite du tampon de moins de 50 MN/[m.sup.3] est jugee comme un intervalle de valeurs approprie pour la conception de ces systemes. Mots-cles : geo mousse, tampon sismique, mur de soutenement rigide, analyse numerique, analyse parametrique, tremblement de terre. [Traduit par la Redaction], Introduction Previous research has shown that placing a suitable compressible vertical inclusion against a rigid structure can reduce static earth pressures to values that are close to the minimum theoretical [...]

The paper investigates the accuracy of the AASHTO simplified method by using load measurements reported in a large database of full-scale instrumented walls for bar mat, welded wire, and steel strip soil reinforced walls. The accuracy of the AASHTO simplified method is quantified by computing the mean and coefficient of variation of the ratio (bias) of measured loads under operational conditions to predicted loads. The paper shows that for steel strip walls, the AASHTO simplified method is reasonably accurate for granular backfill soils with friction angles less than 45[degrees]. For bar mat walls, the method is demonstrated to be slightly conservative. The simplified method underpredicts reinforcement loads at shallow overburden depths for steel strip walls with backfill friction angles greater than 45[degrees] due to compaction-related effects. It is concluded that these compaction-induced loads near the wall top do not contribute to internal instability due to pullout. DOI: 10.1061/(ASCE) 1090-0241 (2009) 135:2(177) CE Database subject headings: Soil stabilization; Walls; Steel; Static loads; Statistics; Data analysis.