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The problem of a reinforced fill over a void has been the subject of much research in the geosynthetics literature. Previous studies have mainly focused on finding closed-form solutions to predict the tensile loads and strains in the reinforcement layer once a void develops below the fill. In this paper, a 2D finite difference (FLAC) model that implements the hyperbolic isochronous load-strain model for the reinforcement by Bathurst and Naftchali (2021) is used to investigate the influence of the rate-dependent properties of polymeric geosynthetic reinforcement materials on reinforcement tensile strains and load, and overall system performance including vertical deformation at the reinforcement elevation and at the fill surface. The paper also investigates the influence of fill soil properties and constitutive model type, foundation condition, void geometry and fill height on system performance. The results of numerical modelling are compared to predictions made using the closed-form solution of Giroud et al. (1990) and in the BSI 8006-1 (2010) design code. The results of numerical modelling demonstrate that the choice of fill height to void width and the stiffness of the rate-dependent geosynthetic reinforcement layer are important to ensure that the maximum reinforcement strain, allowable strength and fill surface settlement criteria are not exceeded. • A numerical 2D FLAC model is used to perform a parametric analysis of the reinforced fill over a void problem. • The numerical approach is validated against a full-scale test reported in the literature. • A simple rate-dependent hyperbolic isochronous load-strain (creep) model is used for the geosynthetic reinforcement. • The ratio of fill height to void width and the reinforcement stiffness are shown to strongly influence numerical outcomes. • The results of numerical modelling are compared to predictions made using two well-known closed-form solutions. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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]

• 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]

Reliability-based design (RBD) can overcome some limitations and ambiguities in the partial factor design approach found in Eurocode 7 (EC7) and the load and resistance factor design (LRFD) method used in North America. The aim of this study is to show how RBD via the first-order reliability method (FORM) can complement LRFD and EC7 codes. Three geotechnical engineering examples are used to demonstrate that RBD-via-FORM can provide guidance to the partial factor design approach in situations with load-resistance duality, shear strength parameters with context-dependent sensitivities, parameters not covered in design codes, cross-correlated parameters, and designs aimed at a target reliability or failure probability. Insights from RBD-via-FORM are presented. The differences and similarities between the design points in RBD, partial factor, and LRFD methods are explained. Comparisons are made with Monte Carlo simulations, the mean-value first-order second-moment method, and the Bathurst–Javankhoshdel closed-form reliability index solution which is restricted to simple linear limit state performance functions with lognormally distributed load and resistance terms and bias factors. It is suggested that RBD-via-FORM can be conducted in tandem with EC7 and LRFD methods in order to overcome limitations and ambiguities which sometimes arise using these methods. [ABSTRACT FROM AUTHOR]

The mean (point) estimate of reliability index (β) for simple limit state performance functions is most often based on load and resistance model bias statistics taken from bias data of limited size. The paper shows how the confidence in the point estimate of β can be computed using the bootstrap method and a closed-form solution for the special case of lognormally distributed nominal and bias random variables. Bias data collected for the pullout limit state for steel strip mechanically stabilized earth walls are used to demonstrate the approach but the method is general. Mean and confidence intervals on β are computed using the entire available bias data sets and smaller sample sizes located in the tails of the original populations, or smaller sample sizes that result in upper and lower extreme point estimates of β. The closed-form solution for β varies linearly with the logarithm of the nominal factor of safety for the example pullout limit state. Depending on the load and resistance bias sample sizes and where they are taken from in the original larger population, results in a wide range of nominal factors of safety to satisfy a target β at time of design. [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]

Many analytical and numerical analysis and design methods for geosynthetic-reinforced soil structures require a single-value (constant) estimate of reinforcement stiffness. However, geosynthetic reinforcement products are rate-dependent polymeric materials meaning that they exhibit time and strain-dependent behaviour under load. Hence, the appropriate selection of a constant (elastic) stiffness value requires careful consideration. A simple hyperbolic stiffness model is shown to be a useful approximation to the constant-load isochronous creep-strain behaviour of these materials at low load levels applicable to operational (serviceability) conditions of geosynthetic-reinforced soil structures. A large database of 606 creep tests on 89 different geosynthetic reinforcement products falling within seven different product categories was collected. From these data, isochronous stiffness values were determined for different combinations of duration of loading and strain level. Data from products falling within the same category were collected together to provide approximations linking the isochronous load-strain (creep) stiffness to the ultimate tensile strength of the material. These approximations are useful for analytical and numerical modelling particularly when parametric studies are undertaken to identify the sensitivity of model outcomes to reinforcement stiffness. Finally, three different geosynthetic-reinforced soil application examples are provided to demonstrate the important role of tensile stiffness on analysis and design outcomes. • A simple hyperbolic model is developed for the isochronous load-strain (creep) behaviour of geosynthetic reinforcement materials. • The model is used to estimate reinforcement stiffness at low load levels consistent with operational conditions of reinforced soil systems. • Model parameters are fitted from a large database of creep tests on geosynthetic reinforcement materials from different product categories. • Approximations linking the isochronous load-strain (creep) stiffness to the ultimate tensile strength of the material are provided. • Three different geosynthetic-reinforced soil examples demonstrate the important role of tensile stiffness on analysis and design outcomes. [ABSTRACT FROM AUTHOR]

6.Databaseofloaddata Miyata and Bathurst (2019) developed a database of 113 measured steel grid loads (T max) from 11 instrumented steel grid walls constructed with cohesive-frictional soils and purely frictional soils. Reliability-based design and analysis for internal limit states of steel grid-reinforced mechanically stabilized earth walls. Thegeneralapproachdescribedin thispaperisanimportantcontributiontonext-generationanalysis and design using modern concepts of RBD for internal stability design of both steel and polymeric soil-reinforced MSE walls and is thus in alignment with the international movement towards RBD for geotechnical structures (e.g., Low and Phoon 2015;Phoon2017;PhoonandChing2015;ISSMGE2017). Allen et al. (2001, 2004) quantified the level of accuracy of the Simplified Method for steel MSE walls using bias statistics deduced from a large number of instrumented walls. 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 soils and subjected to typical operational conditions. [Extracted from the article]

The paper demonstrates deterministic and reliability-based assessment of strength limit states (tensile resistance and pullout) and the service limit state for soil failure for mechanically stabilized earth (MSE) walls constructed with polyester (PET) strap reinforcement. The general approach considers the accuracy of the load and resistance models that appear in each limit state equation plus uncertainty in the estimate of nominal load and resistance values at time of design. Reliability index is computed using a closed-form solution that is easily implemented in a spreadsheet. Three PET strap MSE wall case studies are used to demonstrate the reliability-based assessment approach and to compare margins of safety using different load and resistance model combinations. In some walls using the Coherent Gravity Method to compute loads, the recommended nominal factors of safety for tensile strength and pullout limit states were not satisfied. However, reliability analyses showed that the walls satisfy recommended minimum target reliability index values for the limit states investigated, usually by large amounts. The most critical limit state is the soil failure limit state which is used in the Simplified Stiffness Method to keep the reinforced soil zone at working stress conditions assumed for geosynthetic MSE walls under operational conditions. • Describes deterministic and reliability-based analyses of internal limit states for PET strap walls. • Reliability index is computed using a closed-form solution that is easily implemented in a spreadsheet. • Three PET strap MSE wall case studies are used to demonstrate the reliability-based assessment approach. • Most critical limit state is the soil failure limit state which is used in the Simplified Stiffness Method. • General approach is applicable to MSE walls with extensible and inextensible reinforcement materials. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The focus of this paper is on quantitative evaluation of four different methods that use closed-form equations to calculate the nominal load in steel grid-reinforced soil walls under operational (end of construction) conditions. The four methods are the Coherent Gravity Method used in the UK, the AASHTO Simplified Method (USA), the PWRC Method used in Japan and the Simplified Stiffness Method. The accuracy of the methods is quantified based on analysis of bias statistics where bias is the ratio of measured to predicted (nominal) load. A large database of 113 measured reinforcement loads collected from 11 instrumented field walls is used in the study. For walls constructed with frictional soils, the Coherent Gravity Method and PWRC Method were the least accurate. The AASHTO Simplified Method demonstrated better accuracy and the Simplified Stiffness Method was the most accurate of all methods examined. The Coherent Gravity Method and the updated Simplified Stiffness Method for steel grid walls in the current study have the advantage that they can be used with soils that have a dependable soil cohesive strength component. However, the accuracy of the Simplified Stiffness Method was much better for all soil types based on bias analyses. [ABSTRACT FROM AUTHOR]

A general closed-form solution to compute the reliability index of a simple limit state function with two load terms and one resistance term is derived. The formulation considers contributions to margins of safety expressed in probabilistic terms due to the choice of load and resistance models, bias values, dependencies between nominal values and bias, uncertainty in estimates of nominal values for uncorrelated load and resistance terms at time of design, and average margin of safety expressed as the operational factor of safety. A sensitivity analysis and example application demonstrate the quantitative influence of the contributing random variables on reliability index. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Reliability analysis of bearing capacity of a strip footing at the crest of a simple slope with cohesive soil was carried out using the random finite element method (RFEM). Analyses showed that the coefficient of variation and the spatial correlation length of soil cohesion can have a large influence on footing bearing capacity, particularly for slopes with large height to footing width ratios. The paper demonstrates cases where a footing satisfies a deterministic design factor of safety of 3 but the probability of design failure is unacceptably high. Isotropic and anisotropic spatial variability of the soil strength was also considered. [ABSTRACT FROM AUTHOR]

The paper reports the details of numerical models used to predict the performance of two 3.6 m-high well-instrumented wrapped-face walls. The walls were nominally identical except that the reinforcement material in one wall was a steel welded wire mesh and in the other a biaxial polypropylene geogrid. The backfill soil was modelled using both linear and nonlinear elastic-plastic constitutive models. A general hyperbolic (nonlinear) axial load-strain-time model was used for the reinforcement. The numerical results show good agreement with measured performance features for the welded wire mesh wrapped-face wall. Agreement between numerical predictions of facing displacements and maximum reinforcement loads was less accurate for the very flexible geogrid wrapped-face wall. The discrepancies are believed to be related to the unusually flexible wrapped face used in the geogrid wall construction. Numerically predicted and measured maximum reinforcement loads are compared to loads using the AASHTO reinforcement strength-based design approach (Simplified Method) and the Simplified Stiffness Method which is an empirical reinforcement stiffness-based method. The paper provides physical test data that can be used to benchmark other numerical models, highlights lessons learned during the development of the models, and identifies reasonable expectations for numerical model accuracy for models of similar complexity used to simulate the performance of mechanically stabilized earth (MSE) wall structures under operational conditions. [ABSTRACT FROM AUTHOR]

Numerical modelers are often faced with the challenge to numerically reproduce the physical behavior of soil-geosynthetic interaction problems using assumed values for missing soil and interface model parameters. This paper examines two such examples using the finite-difference method, (1) horizontal pullout of a geosynthetic (geogrid) reinforcement layer in a pullout box and (2) a geosynthetic (geotextile)-reinforced soil layer over a void. It also presents the results of parametric sensitivity analyses for the missing soil and interface model parameter values and identifies the values that give the best agreement with measured data. The paper further demonstrates that correct modeling of geometrical nonlinearity is key to accurately predicting the performance of geosynthetic-reinforced soil systems controlled by the tensioned membrane effect. The lessons learned in this study will be of interest to numerical modelers during numerical model design of geosynthetic-reinforced soil systems. [ABSTRACT FROM AUTHOR]

Soil-cement deep mixing (DM) columns combined with geosynthetic basal reinforcement are an accepted technique in geotechnical engineering to construct road and railway embankments over soft foundations. Both full-width and unit cell models have been used to numerically simulate the performance of geosynthetic-reinforced and column-supported (GRCS) embankments. However, the typical unit cell model with horizontally fixed side boundaries cannot simulate the lateral spreading of the embankment fill and foundation soil. As a result, the calculated reinforcement tensile loads using typical unit cell models are much less than those from matching full-width models. The paper first examines GRCS embankments using a full-width model with small- and large-strain modes in FLAC and then compares the calculated results from the full-width model with those using a typical unit cell model, a recently proposed modified unit cell model, and a closed-form solution. The paper also examines the influence of the soft foundation soil modulus, reinforcement tensile stiffness, and DM column modulus on the reinforcement tensile loads. Numerical analyses show that the reinforcement tensile loads from the modified unit cell model are in good agreement with those from the full-width model for zones under the embankment crest for all cases and conditions examined in the paper. Both the full-width model and modified unit cell model perform better than the typical unit cell model for the prediction of the reinforcement tensile load when compared to the closed-form solution. However, while the modified unit cell developed by the writers is shown to be more accurate than the typical unit cell when predictions are compared to results using full-width numerical simulations, the benefit of using this approach to reduce computation times may be limited in practice. [ABSTRACT FROM AUTHOR]

A total of 123 measured maximum nail-load data were collected from instrumented soil nail walls reported in the literature. Filtered data sets corresponding to short-term and long-term measurements were used to evaluate the accuracy of the current Federal Highway Administration (FHWA) simplified method to calculate maximum nail loads under operational conditions. The accuracy of load predictions was quantified by the mean and coefficient of variation (COV) of the ratio (bias) of measured load to predicted load. Data in short-term and long-term categories were also investigated according to frictional-cohesive and frictional soil types. Based on the available data, the current FHWA simplified method was found to overestimate both long-term and short-term maximum nail loads on average. The spreads in prediction accuracy measured by the COVof bias were 38 and 52% for long-term and short-term data, respectively. Large spreads in prediction accuracy were also found using data for walls with cohesive-frictional soils alone. With the exception of the frictional soil data set, there was an undesirable correlation (dependency) between method accuracy and predicted maximum nail load using the current FHWA simplified method. A modified FHWA simplified method equation is proposed that has fewer empirical coefficients than the current formulation (i.e., three compared to five) and is shown to be more accurate on average and to have less spread in prediction accuracy for all data sets. Furthermore, hidden dependencies between method accuracy and magnitude of predicted load are not present. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Probabilistic slope stability analyses of simple geosynthetic reinforced soil slopes were carried out using the shear strength reduction method in combination with the finite element method (FEM). An existing open-source FEM code was modified to include bar elements to model horizontal layers of geosynthetic reinforcement. Analysis results using the modified code (mFEM) demonstrate that large reductions in probability of failure can be realized by adding geosynthetic reinforcement layers to constructed slopes. The modified code was also used to investigate the effect of variability of soil friction angle on probabilistic outcomes for constructed unreinforced and reinforced purely frictional soil slopes. [ABSTRACT FROM AUTHOR]

Geosynthetic-reinforced and column-supported (GRCS) embankments have proven to be an effective construction technique for fills on soft foundations. The paper introduces a modified unit cell approach to model GRCS embankments supported by deep mixed column walls. The modified unit cells include linear elastic springs at one or both vertical boundaries to simulate lateral displacements of the embankment fill and foundation soil. The finite difference program FLAC is used to compare numerical outcomes using the modified unit cells with those using the typical unit cell arrangement with lateral rigid side boundaries. Numerical results demonstrate good agreement between simulations using small-strain and large-strain modes in some cases and large differences in other cases. Lateral displacements of the embankment fill and foundation soil using the modified unit cells are shown to have large influence on reinforcement loads. Finally the paper demonstrates that calculated reinforcement loads are sensitive to choice of small-strain or large-strain mode when using program FLAC. [ABSTRACT FROM AUTHOR]

The paper reports numerical model details and predictions of the end-of-construction performance for two instrumented and well-documented mechanically stabilized earth (MSE) walls. The walls were constructed as part of the highway SR-18 approach fills for a bridge near Seattle, Washington. The geogrid reinforced block face walls were modeled using a commercially available two-dimensional (2D) finite-difference program. The paper provides details on how material properties were selected from laboratory testing of wall components and how the computer modeling was carried out. The paper shows that predicted wall deformations and reinforcement strains were in reasonable agreement with measured data using both linear elastic-plastic and nonlinear elastic-plastic constitutive models for the soil. The geogrid reinforcement was simulated using a nonlinear load-strain-time secant stiffness model and cable elements. The paper compares numerical predictions of reinforcement loads at end of construction with measured values and predictions using a AASHTO Simplified Method, K-stiffness Method, and Simplified Stiffness Method. The paper is a useful benchmark for modelers because it demonstrates what the authors believe are reasonable expectations of model accuracy for Class C predictions of deformations and reinforcement strains for these types of walls when high-quality project information is available. [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-) 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. [ABSTRACT FROM AUTHOR]

Two nominal identical 4 m high steel strip reinforced soil walls varying only with respect to reinforcement layer length arrangement were constructed and instrumented in an indoor laboratory environment. A novel feature of the tests was a foundation arrangement that allowed for simulated loss of toe support. Both walls performed well at the end of construction (EOC). Predicted unfactored maximum reinforcement tensile loads at the EOC using four different load models were judged to be conservative (safe for design) based on comparison with measured loads for both walls. Reinforcement loads were observed to increase with decreasing toe support, particularly at the base of the walls. A fully developed composite soil failure mechanism propagating from the heel of the foundation bulkhead and behind the reinforcement layers was observed during excavation of the stepped base wall model. There were no visual indications of soil failure within or behind the wall with longer uniform reinforcement lengths. However, predicted EOC loads for this wall were exceeded for most layers after loss of toe support. Implications for the design, analysis and performance of steel strip reinforced soil walls with similar reinforcement arrangements constructed over initially competent soil foundations and then subject to loss of toe support are identified. [ABSTRACT FROM AUTHOR]

The Simplified Method as reported in AASHTO and Federal Highway Administration (FHWA) manuals has been demonstrated to give poor predictions of unfactored reinforcement loads and strains, especially for geosynthetic reinforced soil walls. The writers have proposed the K-stiffness Method to improve the load prediction accuracy for walls under working stress (operational) conditions. However, it has also been recognized in recent publications by the writers and others that further improvements to the K-stiffness Method are needed. Furthermore, acceptance of the K-stiffness Method has been hindered due to its perceived complexity and the use of the plane strain friction angle to quantify the strength of the reinforced soil. This paper takes a fresh look at both methods and uses lessons learned from the K-stiffness Method development to improve the accuracy of the AASHTO/FHWA Simplified Method. Key parameters introduced during the development of the K-stiffness Method are applied to the Simplified Method and updated to further improve load prediction accuracy. Additional wall case histories have been added to the database used for the original K-stiffness Method to calibrate the new model and to broaden its utility. An important improvement is a single model that allows for seamless load prediction across a range of walls constructed with relatively extensible geosynthetic reinforcement and inextensible steel reinforcement materials. The quantitative improvement of the new model (Simplified Stiffness Method) compared to the current AASHTO/FHWA Simplified Method is demonstrated through statistical analysis of load bias values (i.e., the ratio of measured to predicted reinforcement load). [ABSTRACT FROM AUTHOR]

Steel bar mat is a common reinforcing material in mechanically stabilized earth (MSE) walls. The current method to calculate the pullout capacity of these materials is an empirical-based formulation found in AASHTO and Federal Highway Administration (FHWA) design guidance documents. The accuracy of the current formulation is evaluated using a large database of laboratory pullout tests including data that were not available at the time the current model was developed. A new model is proposed, and it is shown to have advantages over the current formulation particularly when pullout capacity design and analysis will be carried out in a load and resistance factor design (LRFD) framework. Calibration of the new model and quantitative comparisons of the accuracy of the two models are evaluated using statistical characteristics of bias values where bias is the ratio of measured pullout capacity to predicted pullout capacity. The accuracy of both models is evaluated for two cases: (1) when project-specific pullout data are not available (the typical case) and presumptive default coefficients must be used; and (2) when project-specific laboratory pullout box data are available. The influence on calibration outcomes of data sets corresponding to markedly different soils and test methodology is demonstrated in the paper. The data reported in the paper are a necessary precursor to future LRFD calibration of the pullout limit state in the internal stability design of bar mat reinforced soil walls. [ABSTRACT FROM AUTHOR]

Design charts to estimate the factor of safety for simple slopes with cohesive-frictional ( c-) 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 = 0 soils by Taylor in 1937 and c- 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- 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. [ABSTRACT FROM AUTHOR]

Abstract: Geosynthetic reinforced soil walls and slopes are now a mature technology in geotechnical engineering. Nevertheless, the mechanisms of soil-geosynthetic interaction are not fully understood for pullout of a geogrid material in the anchorage zone of a reinforced structure. It is also difficult to quantify the interactions between the geogrid and the soil. A new strategy to overcome these difficulties is to use a pullout box with a transparent glass bottom, a transparent soil, and non-contact measurement technology. This paper describes such a pullout box apparatus which is used in combination with a recently developed transparent granular soil. Embedded geogrid specimens are visible through the transparent bottom of the box and the surrounding soil. The displacements of the geogrid and seed (target) particles placed in the transparent soil are tracked using digital images captured by a row of synchronized cameras located below the apparatus. Digital processing is carried out using the Digital Image Correlation (DIC) technique to quantify the in-situ displacement of the geogrid specimen and surrounding soil. The displacements are used to compute continuous longitudinal strain profiles in the geogrid specimen over the duration of each pullout test and relative shear displacements between the geogrid and the soil. Also reported are lessons learned to improve the method of clamping geogrid specimens at the front of the pullout box which are also applicable to conventional pullout box equipment. [Copyright &y& Elsevier]

A high-density polyethylene (HDPE) geogrid soil-reinforced dry-cast concrete block retaining wall 6.3-m high was designed using the K-stiffness method as part of a highway-widening project southeast of Seattle, Washington. The amount of reinforcement needed for the original wall design using the K-stiffness method was approximately 50% of that required using the AASHTO simplified method. This paper describes the construction, instrumentation program, and interpretation of the measurements. Geogrid strains were measured using strain gauges and extensometers attached to reinforcement layers. An extensive materials testing program was conducted to characterize the backfill soil properties and geogrid stiffness properties and to calibrate strain gauge readings. The reinforcement loads deduced from the measured strains are compared with Class A, B, and C1 predictions using the AASHTO 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 consistent with the measured results. This paper describes lessons learned, the influence of construction activities on wall performance, and the limitations of both methods in estimating connections loads. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper presents the derivation of an analytical expression for the dynamic active thrust from c-ø (c = cohesion, ø = angle of shearing resistance) soil backfill on rigid retaining walls with wall friction and adhesion. The derivation uses the pseudo-static approach considering tension cracks in the backfill, a uniform surcharge on the backfill, and horizontal and vertical seismic loadings. The development of an explicit analytical expression for the critical inclination of the failure plane within the soil backfill is described. It is shown that the analytical expression gives the same results for simpler special cases previously reported in the literature. [ABSTRACT FROM AUTHOR]

The paper reports the results of load and resistance factor design (LRFD) calibration for pullout and yield limit states for steel strip reinforced soil walls under self-weight loading. An important feature of the calibration method is the use of bias statistics to account for prediction accuracy of the underlying deterministic models for reinforcement load, pullout capacity and yield strength of the steel strips, and random variability in input parameters. To improve the accuracy of reinforcement load predictions, small adjustments to current semiempirical American Association of State Highway and Transportation Officials (AASHTO) load design charts are proposed. Similarly, current empirical-based design charts found in AASHTO and Federal Highway Administration (FHWA) guidance documents for the estimation of the pullout resistance factor for smooth and ribbed steel strips are adjusted to improve the accuracy of pullout capacity predictions. The results of calibration lead to a load factor of 1.35 that is consistent with current practice and resistance factors that together give a consistent probability of failure of 1% for all three limit states considered. Furthermore, comparison with allowable stress design (ASD) past practice (AASHTO simplified method) shows that the operational factors of safety using a rigorous LRFD approach give the same or higher factors of safety and lower probabilities of failure. In this study, data for steel strip reinforced soil walls are used as an example to illustrate rigorous reliability theory-based LRFD calibration concepts. However, the general approach is applicable to other reinforced soil wall technologies and calibration outcomes can be updated as more data become available. [ABSTRACT FROM AUTHOR]

The results of load and resistance factor design (LRFD) calibration are reported for the pullout limit state in geogrid reinforced soil walls under self-weight loading and permanent uniform surcharge. Bias statistics are used to account for the prediction accuracy of the underlying deterministic models for load and pullout capacity and the random variability in the input parameters. The paper shows that the current AASHTO simplified method to calculate reinforcement loads under operational conditions is overly conservative leading to poor prediction accuracy of the underlying deterministic model used in LRFD calibration. Refinements to the load and default pullout capacity models in the AASHTO and Federal Highway Administration guidance documents are proposed. These models generate reasonable resistance factors using a load factor of 1.35 and give a consistent probability of pullout failure of 1%. A comparison with the allowable stress design (ASD) past practice shows that the operational factors of safety using a reliability-based LRFD approach give factors of safety greater than 1.5. Regardless of the design approach (ASD or LRFD), the analysis results demonstrate that the current empirical minimum reinforcement length criteria will likely control the design for pullout. [ABSTRACT FROM AUTHOR]

A response is from the authors to the reviewers of their article “Predicted Loads in Steel Reinforced Soil Walls Using the AASHTO Simplified Method” which is in Volume 135 of the February 2009 issue is presented.

Abstract: North American design codes are now committed to the development of load and resistance factor design (LRFD) for reinforced soil structures including internal stability limit states. Reliability-based analysis is required to carry out these calibrations. A framework for LRFD calibration has been proposed by the writers that requires bias statistics for load and resistance terms for each limit state function. In this paper the formulation of the limit state for reinforcement tensile rupture is developed and the component strength-reduction bias statistics identified. The paper describes how to compute bias statistics from project-specific installation damage trials for use in reliability-based design for the reinforcement rupture limit state or using data from multiple sources for LRFD calibration. A database of results from field installation damage trials on 103 different geosynthetic products was collected from 20 different sources. A total of 799 and 2248 in-air tensile test results were reviewed for undamaged and damaged geosynthetic specimens, respectively. This database is used to compute installation damage bias statistics for six different categories of geosynthetic and four categories of backfill soils classified according to the D 50 particle size. A practical outcome is that for analysis purposes, bias statistics can be grouped into two ranges for each geosynthetic type based on D 50 of the soil greater than or less than 19 mm. The paper shows how bias statistics together with load and resistance factors for the geosynthetic rupture limit state function recommended by can be used to calculate probability of failure using Monte Carlo simulation and demonstrates the sensitivity of probability of failure to magnitude of installation damage bias statistics. The installation damage data is valuable for future LRFD calibration to select resistance factors for use in design codes for the geosynthetic rupture limit state in reinforced soil structures. [Copyright &y& Elsevier]

Abstract: Geotextiles are routinely used in separation and filtration applications. Design of these systems is currently based on saturated properties of the geotextiles and the surrounding soils. However, in the field, soil and geotextile can be in an unsaturated state for much of their design life during which they are essentially hydraulically non-conductive. Periodic wetting and drying cycles can result in rapid and large changes in hydraulic performance of soil–geotextile systems. The writers have reported the results from physical water infiltration tests on sand columns with and without a geotextile inclusion. The geotextile inclusions were installed in new and modified states to simulate the influence of clogging due to fines and to broaden the range of hydraulic properties of the geotextiles in the physical tests. This paper reports the results of numerical simulations that were undertaken to reproduce the physical tests and strategies adopted to adjust soil and geotextile properties from independent laboratory tests to improve the agreement between numerical and physical test results. For example the paper shows that the hydraulic conductivity function of the geotextile must be reduced by up to two orders of magnitude to give acceptable agreement. The lower hydraulic conductivity is believed to be due to soil intrusion that is not captured in conventional laboratory permeability tests. The calibrated numerical model is used to investigate the influence of geotextile and soil hydraulic conductivity and thickness as well as height of ponded water at the surface on wetting front advance below the geotextile and potential ponding of water above the geotextile due to a capillary break mechanism. A simple analytical model is also developed that predicts the maximum ponding height of water above the geotextile based on two-layer saturated media and 1-D steady state flow assumptions. The analytical model is used to generate a design chart to select geotextiles to minimize potential ponding of water above the geotextile. Ponding can lead to lateral flow of water along the geotextile in reinforced wall, slope, embankment and road base applications. [Copyright &y& Elsevier]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Abstract: The paper describes two constitutive models for the simulation of expanded polystyrene (EPS) seismic buffer shaking table tests previously reported by the writers. The first model is linear elastic–plastic with Mohr–Coulomb criterion and Rayleigh damping. The second is called the equivalent-linear method (ELM) which incorporates hysteretic load–unload cycles using Masing-type functions and strain-dependent shear modulus and damping ratio functions. The constitutive models were applied to both the geofoam buffer and sand backfill in both approaches. Both models are shown to capture qualitative features of measured peak load-time response of the physical tests. The advanced ELM model gave predictions that were closer to the measured results for the seismic buffer test with the most compressible EPS when model accelerations and total wall forces were greatest. However, the simpler model is judged to be sufficiently accurate for practical purposes when the dynamic force increment is considered only. [Copyright &y& Elsevier]

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/m3 was judged to be the practical range for the design of these systems. [ABSTRACT FROM AUTHOR]

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°. 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° 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Abstract: The paper describes the details and verification of a FLAC numerical code that was used to simulate the results of an experimental program of reduced-scale wall models constructed with a seismic geofoam buffer inclusion and loaded using a large shaking table. Five physical tests constructed with expanded polystyrene (EPS) geofoam materials having different modulus values and a control case with no geofoam inclusion were carried out. The paper shows that the numerical model was able to capture the trend in earth forces with increasing base acceleration for all six models and in most cases quantitative dynamic load–time response of the numerical simulations was in good agreement with measured values. [Copyright &y& Elsevier]

The paper investigates the accuracy of the coherent gravity method by using measurements reported in a large database of full-scale instrumented walls that was not available at the time the original method was developed. The new database includes data for bar mat, welded wire and steel strip soil reinforced walls. Measured reinforcement loads under operational conditions are compared with predicted values for bar mat and steel strip reinforced walls. The accuracy of the coherent gravity method as presented in the BS 8006 design standard is quantified by computing the mean and coefficient of variation of the ratio (bias) of measured to predicted loads. The paper shows that for steel strip walls the coherent gravity method is reasonably accurate for soils with friction angles less than 458. For granular soils with higher friction angles and bar mat walls, the current coherent gravity method is shown to be less accurate and, on average, non-conservative for design. Modifications to the method as currently described in BS 8006 are proposed to improve the accuracy of the method for bar mat reinforced soil walls and steel strip reinforced soil walls with high friction angle backfill soils. [ABSTRACT FROM AUTHOR]

In this paper the K-stiffness method is extended to the case of c-φ soils using data obtained from a total of nine new case studies – six from Japan and three from the USA. A common feature in this new data set is that the walls were all constructed with a vertical face using backfill soils with a range of fines content. The walls varied widely with respect to facing type. This new data set together with previously published data for vertical walls is now used to isolate the effect of soil cohesion on reinforcement loads within the framework of the original K-stiffness method. The new data set is used to calibrate a modified K-stiffness method equation that includes a cohesion influence factor. The modified K-stiffness method is demonstrated to quantitatively improve the estimate of the magnitude and distribution of reinforcement loads for internal stability design of vertical-faced geosynthetic reinforced soil walls with c-φ soil backfills when compared to the current American Association of State Highway and Transportation Officials simplified method. [ABSTRACT FROM AUTHOR]

The article presents a response to the discussions made by Robert K. Barrett and Dov Leshchinsky on the authors' paper "The influence of facing stiffness on the performance of two geosynthetic reinforced soil retaining walls." They appreciate the comments raised by Barrett and Leshchinsky. In doing so, they clarify and elucidate a number of points related to the details and contingents of the test program described in the referring paper. Moreover, they provide various implications to current practice.