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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 [...]

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 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 [...]

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 [...]

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 [...]

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 [...]

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.

Reliability-based design concepts and their application to load and resistance factor design (LRFD or limit states design (LSD) in Canada) are well known, and their adoption in geotechnical engineering design is now recommended for many soil-structure interaction problems. Two important challenges for acceptance of LRFD for the design of reinforced soil walls are (i) a proper understanding of the calibration methods used to arrive at load and resistance factors, and (ii) the proper interpretation of the data required to carry out this process. This paper presents LRFD calibration principles and traces the steps required to arrive at load and resistance factors using closed-form solutions for one typical limit state, namely pullout of steel reinforcement elements in the anchorage zone of a reinforced soil wall. A unique feature of this paper is that measured load and resistance values from a database of case histories are used to develop the statistical parameters in the examples. The paper also addresses issues related to the influence of outliers in the datasets and possible dependencies between variables that can have an important influence on the results of calibration. Key words: load and resistance factor design (LRFD), limit states design (LSD), reliability-based design, closed-form solutions, reinforced soil walls, steel reinforcement, pullout. On connait bien les concepts de conception bases sur la fiabilite et leur application au facteur de conception de charge et de resistance (LRFD ou la conception aux etats limites au Canada), et on recommande maintenant leur adoption en conception d'ingenierie geotechnique pour plusieurs problemes d'interaction sol-structure. Deux importants defis pour l'acceptation du LRFD pour le calcul de murs en sol arme sont : (i) une bonne comprehension des methodes de calibrage utilisees pour arriver aux facteurs de charge et de resistance, et (ii) la bonne interpretation des donnees requises pour realiser ce processus. Cet article presente les principes de calibrage du LRFD et trace les etapes requises pour arriver aux facteurs de charge et de resistance en utilisant des solutions exactes pour un etat limite typique d'arrachement d'elements d'armature en acier dans la zone d'ancrage d'un mur en sol arme. Une caracteristique unique de cet article est que des valeurs de charges et de resistances mesurees provenant d'une base de donnees d'histoires de cas sont utilisees pour developper les parametres statistiques dans les exemples. Cet article traite aussi des problemes relies a l'influence des donnees etrangeres dans les ensembles de donnee et des dependances possibles rentre les variables qui peuvent avoir une influence importante sur les resultats du calibrage. Mots-cles: facteurs de conception de charge et de resistance << LRFD >> conception d'etat limite << LSD >>, conception base e sur la fiabiliite, solutions exactes, murs en sol arme, armature d'acier, arrachement. [Traduit par la Redaction], Introduction Use of reliability theory to determine load and resistance factors for limit states design of civil engineering structures (called load and resistance factor design, or LRFD in the USA, [...]