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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 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.

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]

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]

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]

In this paper, upper bound limit analysis that includes a horizontal pseudostatic seismic force is used for the first time to obtain the limit load on strip footings seated on cohesive-frictional soils reinforced with a single geosynthetic layer. Reinforcement tensile rupture and sliding failure modes for the geosynthetic layer are included in the analyses. Results of analyses are presented as optimum reinforcement depths and a bearing capacity equation with a single term and different bearing capacity factors for tensile rupture and sliding failure modes. The bearing capacity factors are presented in tables and capture the combined influence of the reinforcement strength, soil frictional strength and cohesion, soil unit weight, footing geometry, uniform surcharge, and magnitude of horizontal ground acceleration. [ABSTRACT FROM AUTHOR]

The paper demonstrates load and resistance factor design (LRFD) calibration for tensile strength and pullout strength limit states for steel strip mechanically stabilized earth (MSE) walls using a reliability theory-based approach. The analyses adopt load models found in current North American LRFD specifications in combination with a coupled mechanical-corrosion model for the reinforcement tensile strength and pullout models found in design guidelines and in the research literature. Resistance factors for prescribed load factors and different load and resistance model combinations are compiled in tables. The limitations of the LRFD approach to generate resistance factors that are judged to be acceptable based on current practice are demonstrated. The challenges to generate consistent design outcomes with the same margin of safety expressed probabilistically are identified, and the link to reliability-based design is described. Example designs are provided to show the impact on steel reinforcement quantities and length when using different models in combination with proposed and current specified load and resistance factors. The calibration outcomes will be of value to code writers in Canada and the US for MSE wall design sections in the next editions of national geotechnical foundation LRFD codes. [ABSTRACT FROM AUTHOR]