Search

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 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]

• 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]

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 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]

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]

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]

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]

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]

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 focus of the paper is on the influence of reinforcement design parameters (i.e. stiffness, length and vertical spacing) on the simulated earthquake response of reinforced soil retaining walls using reduced-scale model shaking table tests. A series of instrumented 1/6-scale model walls was constructed and dynamically loaded using a stepped-amplitude harmonic base acceleration record. The reinforcement design parameters investigated were found to have a significant effect on model response. Experimental results showed that the magnitude of accumulated facing lateral displacement under base excitation decreased with increasing reinforcement length, greater number of reinforcement layers and larger reinforcement stiffness. Significant down-drag forces at the back of the rigid facing were measured for all model configurations. However, the measured vertical load at the footing was not significantly influenced by changes in reinforcement parameters. The horizontal restrained (hinged) toe at the bottom of the rigid facing was shown to attract 30–60% of the total horizontal earth force depending on the reinforcement configuration. The magnitude and distribution of reinforcement connection loads was significantly affected by the reinforcement length, vertical spacing and stiffness. Measured footing loads, reinforcement connection loads and amplification factors are compared to values calculated using current practice in North America for geosynthetic reinforced soil walls and discrepancies between experimental results and design methods are identified. Implications of the physical test results to level of conservatism in current design practice are noted. [Copyright &y& Elsevier]

Abstract: The paper provides a synthesis of work by the writers that has the objective of developing a new working stress method for the calculation of reinforcement loads in geosynthetic reinforced soil walls. As a precursor to this objective, careful back-analyses of a database of instrumented and monitored full-scale field and laboratory walls are used to demonstrate that the current American Association of State Highway and Transportation Officials (AASHTO) Simplified Method used in North America results in excessively conservative estimates of the volume of reinforcement required to generate satisfactory long-term wall performance. The new design method captures the essential contributions of the different wall components and properties to reinforcement loads. The method is calibrated against measured in situ wall reinforcement loads using a careful interpretation of reinforcement strains and the conversion of strain to load using a suitably selected reinforcement stiffness value. A novel feature of the method is to design the wall reinforcement so that the soil within the wall backfill is prevented from reaching a failure limit state, consistent with the notion of working stress conditions. [Copyright &y& Elsevier]

The paper describes a series of short-term in-isolation tensile tests that were carried out to investigate the load–strain–time performance of typical knitted polyester (PET), biaxial polypropylene (PP) and uniaxial high-density polyethylene (HDPE) geogrid products. The specimens were subjected to constant rate of strain (CRS) loading and variable rate of strain (VRS) loading. Variables between test specimens included specimen length and specimen aspect ratio (e.g. number of ribs). A novel feature of these tests was that internal strains in the specimens were recorded using non-contact measurements taken with a video-extensometer apparatus. The data shows that at large strains the PP and HDPE geogrid specimens exhibited large lateral strains while lateral strains were negligible for the PET product. Results of CRS tests carried out with different specimen aspect ratios showed that there was no change in tensile strength, axial strain and lateral strain at rupture for HDPE and PET materials. The PP material in this investigation did show an increase in axial and lateral strain at rupture for a specimen tested at an aspect ratio approaching one. The polyolefin geogrids (PP and HDPE) were shown to exhibit tensile stiffness and ultimate tensile load capacities that increased with rate of strain. Implications of the contractive behaviour of the polyolefin geogrid products to the selection of in-soil reinforcement stiffness values and rheological modelling are identified. [Copyright &y& Elsevier]

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]