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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]

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]

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 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]

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]

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]

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]

• Buried steel grids used in mechanically stabilized earth (MSE) walls can corrode. • Probability of failure is computed for limit states of galvanized steel grids. • Three-stage corrosion model is coupled with reinforcement load and resistance models. • Probability of steel grid tensile and pullout failure with time is computed. • Pullout failure of coated steel members due to corrosion is shown to be unlikely. Design for internal limit states of steel grid reinforcement in mechanically stabilized earth (MSE) walls must provide for loss of steel thickness due to corrosion. The paper combines key features of zinc and steel corrosion models used in North American practice with corrosion rate statistics reported in the literature for the zinc coating on buried galvanized steel strips and for steel rebar. Examples of loss of strength and pullout capacity of steel grid elements constructed with different member diameters and up to 120 years after construction are presented in probabilistic terms. Results of reliability-based analysis for the tensile strength and pullout limit state at design lives of 75 and 120 years are demonstrated for a typical wall under operational conditions using tensile load and resistance models in combination with non-aggressive soils recommended in North American design codes. The results of calculations show that for the wall example the influence of different zinc cover thickness on probability of tensile failure of longitudinal members is detectable at the end of design life. However, the typical minimum specified zinc thickness of 0.086 mm recommended in North American practice is likely sufficient to keep probabilities of failure to 1% or less (i.e., reliability index of 2.33 or greater). The influence of a range of initial zinc thickness reported in the literature on probability of pullout failure of the same steel grid elements was found to be negligible. [ABSTRACT FROM AUTHOR]

Model checking, evaluation and comparison are critical steps in Bayesian data analysis but not routinely considered in statistical analysis of geotechnical data. This paper presents an overview of model checking and comparison concepts and techniques employed in modern Bayesian data analysis that are useful for analysis of geotechnical engineering data. These methods are applied to statistical analysis of load and pullout model bias data for steel strip mechanically stabilized earth walls. It is shown how model checking can result in statistical models with better fits. The practical implications of using improved statistical models are discussed in the context of reliability-based design and load and resistance factor design calibration of the internal stability pullout limit state. Finally, statistical model uncertainty and Bayesian model averaging are discussed and explored using an example of reliability-based design for the same limit state. [ABSTRACT FROM AUTHOR]

This paper describes a strategy to compute deterministic and probabilistic estimates of maximum outward deformation of mechanically stabilized earth (MSE) modular block wall structures of particular type, materials and boundary conditions. The reference walls in this study were a group of MSE modular block walls constructed under carefully controlled laboratory conditions. A numerical FLAC model was first demonstrated to give reasonable estimates of measured maximum wall deformations. The model was then used to carry out a sensitivity analysis using a modest number of simulations with different values of key input parameters. Six key control parameters were selected based on the results of the sensitivity analysis and a review of the literature on wall performance. A response surface of full quadratic form was used to predict maximum normalized wall deformations as a function of the six key parameters. The results of a second set of 729 numerical simulations corresponding to the maximum number of possible permutations of three different values for each of the six control parameters were used to find the coefficient terms for the response surface equation using a conventional least squares method. The response surface method (RSM) equation was then used to carry out a large number of Monte Carlo simulations using random sampling of distributions for soil friction angle, surcharge pressure, block–block interface shear stiffness and reinforcement stiffness input parameters. The resulting statistics were used to construct a cumulative distribution function (CDF) for maximum normalized wall deformations. The CDF is then used to link reliability performance-based design to a reasonable range of serviceability criteria for wall deformations generated under operational conditions. [ABSTRACT FROM AUTHOR]

Abstract: The paper describes the novel use of recycled construction and demolition waste (RCDW) material as the backfill material in an otherwise conventional 3.6-m high wrapped-face geosynthetic reinforced soil wall. The wall was constructed over a collapsible foundation soil which is common in the area around the capital city of Brasilia. The wall was instrumented and then monitored though dry and wet rainy seasons. The influence of cumulative rainfall on foundation compressibility was detectable and seasonal wetting and drying was shown to quantitatively influence wall deformations, settlement, horizontal earth pressures and reinforcement strains. Nevertheless, wall performance was judged to be satisfactory when compared to the performance of other walls of similar size constructed with traditional select granular soils over non-collapsible foundation soils. The results of this investigation demonstrate that significant project cost savings may be possible by avoiding more expensive traditional backfill materials and larger societal economic savings accrued by diverting RCDW waste streams from landfills. [Copyright &y& Elsevier]