Influence of uncertainty in geosynthetic stiffness on deterministic and probabilistic analyses using analytical solutions for three reinforced soil problems

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.     

Residual Deformation of Geosynthetic-Reinforced Sand in Plane Strain Compression Affected by Viscous Properties of Geosynthetic Reinforcement

A series of plane strain compression (PSC) tests were performed on large sand specimens unreinforced or reinforced with prototype geosynthetic reinforcements, either of two geogrid types and one geocomposite type. Local tensile strains in the reinforcement were measured by using two types of strain gauges. Sustained loading (SL) under fixed boundary stress conditions and cyclic loading (CL) tests were performed during otherwise monotonic loading at a constant strain rate to evaluate the development of creep deformation by SL and residual deformation by CL of geosynthetic-reinforced sand and also residual strains in the reinforcement by these loading histories. It is shown that the creep deformation of geosynthetic-reinforced sand develops due to the viscous properties of both sand and geosynthetic reinforcement, while the residual deformation of geosynthetic-reinforced sand during CL (defined at the peak stress state during CL) consists of two components: i) the one by the viscous properties of sand and reinforcement; and ii) the other by rate-independent cyclic loading effects with sand. The development of residual deformation of geosynthetic-reinforced sand by SL and CL histories had no negative effects on the subsequent stress-strain behaviour and the compressive strength was maintained as the original value or even became larger by such SL and CL histories. The local tensile strains in the geosynthetic reinforcement arranged in the sand specimen subjected to SL decreased noticeably with time, due mainly to lateral compressive creep strains in sand during SL of geosynthetic-reinforced sand. This result indicates that, with geosynthetic-reinforced soil structures designed to have a sufficiently high safety factor under static loading conditions because of seismic design, it is overly conservative to assume that the tensile load in the geosynthetic reinforcement is maintained constant for long life time. Moreover, during CL of geosynthetic-reinforced sand, the residual tensile strains in the geosynthetic reinforcement did not increase like global strains in the geosynthetic-reinforced sand that increased significantly during CL. These different trends of behaviour were also due to the creep compressive strains in the lateral direction of sand that developed during CL of geosynthetic-reinforced sand.     

A new apparatus for the study of pullout behaviour of soil-geosynthetic interfaces under sustained load over time

At present, the design of geosynthetic-reinforced soil structures is executed with reference to the tensile strength of the reinforcement obtained from in-air short-term tensile tests, decreasing this value by means of several factors. Among these, the creep effect resulting from in-air tensile creep tests reduces tensile strength the most. Consequently, this procedure does not take into account the effects of soil confinement and interaction on the tensile response of the reinforcements. This paper illustrates a new large-scale pullout prototype apparatus, with the capacity to investigate the behaviour of a geosynthetic reinforcement embedded in a compacted soil and subject to a tensile load kept constant over time. The apparatus allows the verification of how the soil can modify the prediction of the long-term behaviour of geosynthetics. Results in terms of confined tensile strains were analysed, and the comparison of those values with the strains obtained by in-air tensile creep tests has led to the conclusion that the creep reduction factor might be conservative. Moreover, the confined tensile strains were related to the apparent coefficients of friction to propose a new procedure capable of determining the design interaction parameter under long-term pullout load as a function of the allowable reinforcement strains.     

Reinforcement load and deformation mode of geosynthetic-reinforced soil walls subject to seismic loading during service life

A Finite Element procedure was used to investigate the reinforcement load and the deformation mode for geosynthetic-reinforced soil (GRS) walls subject to seismic loading during their service life, focusing on those with marginal backfill soils. Marginal backfill soils are hereby defined as filled materials containing cohesive fines with plasticity index (PI) >6, which may exhibit substantial creep under constant static loading before subjected to earthquake. It was found that under strong seismic loading reinforced soil walls with marginal backfills exhibited a distinctive “two-wedge” deformation mode. The surface of maximum reinforcement load was the combined effect of the internal potential failure surface and the outer surface that extended into the retained earth. In the range investigated, which is believed to cover general backfill soils and geosynthetic reinforcements, the creep rates of soils and reinforcements had small influence on the reinforcement load and the “two-wedge” deformation mode, but reinforcement stiffness played a critical role on these two responses of GRS walls. It was also found that the “two-wedge” deformation mode could be restricted if sufficiently long reinforcement was used. The study shows that it is rational to investigate the reinforcement load of reinforced soil walls subject to seismic loading without considering the previous long-term creep.     

Influence of geosynthetic stiffness on bearing capacity of strip footings seated on thin reinforced granular layers over undrained soft clay

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.     

One-step analytical method for required reinforcement stiffness of vertical reinforced soil wall with given factor of safety on backfill soil

The selection of geosynthetic reinforcements in the design of geosynthetic-reinforced soil (GRS) retaining walls has been based on the requirement on the long-term strength. However, the mobilized loads in the reinforcements are related to both the reinforcement stiffness and soil deformation, and the desired factor of safety may not exist in the earth structure if they are not properly considered. Therefore, it is also important to take into account the long-term reinforcement stiffness when designing GRS retaining walls. In this study, a simplistic analytical method is proposed to determine the required reinforcement stiffness with given factor of safety on the backfill soil. The method takes into account soil-reinforcement interaction, nonlinear stress-strain behavior of soil, and soil dilatancy. The reinforcement strains predicted by the proposed method were compared to those analyzed by validated nonlinear Finite Element analyses, and close agreement was obtained.     

Ultimate bearing capacity of strip footing resting on soil bed strengthened by wraparound geosynthetic reinforcement technique

In the recent past, the wraparound geosynthetic reinforcement technique has been recommended for constructing the geosynthetic-reinforced soil foundations. This paper presents the development of an analytical expression for estimating the ultimate bearing capacity of strip footing resting on soil bed reinforced with geosynthetic reinforcement having the wraparound ends. The wraparound ends of the geosynthetic reinforcement are considered to provide the shearing resistance at the soil-geosynthetic interface as well as the passive resistance due to confinement of soil by the geosynthetic reinforcement. The values of ultimate load-bearing capacity determined by using the developed analytical expression agree well with the model footing load test values as reported in the literature.     

Geosynthetic reinforced piled embankment modeling using discrete and continuum approaches

Understanding the load transfer mechanism can support engineers having more economical design of geosynthetic reinforced piled embankments. This study aims to investigate the load transfer mechanisms by two different numerical methods including the Discrete Element Method (DEM) and the Finite Difference Method (FDM). The DEM model adopts (a) discrete particles to simulate the micro-structure of the granular materials and (b) coupled discrete element – finite element method (DEM-FEM) to capture the interaction between granular materials and geotextiles. On the other hand, the FDM model uses an advanced constitutive soil model considering the hardening and softening behaviour of the granular materials. The numerical results show that the geotextiles can only contribute to the vertical loading resistance in cases where the soils between piles are soft enough. In terms of design, an optimum value of the geotextile tensile stiffness can be found considering the load, the soft soil stiffness and the thickness of the embankment. Both the DEM and the FDM show that a high geotextile tensile stiffness is not required since an extra stiffness will slightly contribute to the efficiency of the geosynthetic reinforced piled embankments. Nevertheless, both models are useful to optimize the design of geosynthetic reinforced piled embankments.     

An experimental evaluation of the behavior of footings on geosynthetic-reinforced sand

This research was performed to investigate the behavior of geosynthetic-reinforced sandy soil foundations and to study the effect of different parameters contributing to their performance using laboratory model tests. The parameters investigated in this study included top layer spacing, number of reinforcement layers, vertical spacing between layers, tensile modulus and type of geosynthetic reinforcement, embedment depth, and shape of footing. The effect of geosynthetic reinforcement on the vertical stress distribution in the sand and the strain distribution along the reinforcement were also investigated. The test results demonstrated the potential benefit of using geosynthetic-reinforced sand foundations. The test results also showed that the reinforcement configuration/layout has a very significant effect on the behavior of reinforced sand foundation. With two or more layers of reinforcement, the settlement can be reduced by 20% at all footing pressure levels. Sand reinforced by the composite of geogrid and geotextile performed better than those reinforced by geogrid or geotextile alone. The inclusion of reinforcement can redistribute the applied footing load to a more uniform pattern, hence reducing the stress concentration, which will result reduced settlement. Finally, the results of model tests were compared with the analytical solution developed by the authors in previous studies; and the analytical solution gave a good predication of the experimental results of footing on geosynthetic reinforced sand.     

3D numerical study of the performance of geosynthetic-reinforced and pile-supported embankments

Geosynthetic-reinforced and pile-supported (GRPS) systems provide an economic and effective solution for embankments. The load transfer mechanisms are tridimensional ones and depend on the interaction between linked elements, such as piles, soil, and geosynthetics. This paper presents an extensive parametric study using three-dimensional numerical calculations for geosynthetic-reinforced and pile-supported embankments. The numerical analysis is conducted for both cohesive and non-cohesive embankment soils to emphasize the fill soil cohesion effect on the load and settlement efficacy of GRPS embankments. The influence of the embankment height, soft ground elastic modulus, improvement area ratio, geosynthetic tensile stiffness and fill soil properties are also investigated on the arching efficacy, GR membrane efficacy, differential settlement, geosynthetic tension, and settlement reduction performance. The numerical results indicated that the GRPS system shows a good performance for reducing the embankment settlements. The ratio of the embankment height to the pile spacing, subsoil stiffness, and fill soil properties are the most important design parameters to be considered in a GRPS design. The results also suggested that the fill soil cohesion strengthens the soil arching effect, and increases the loading efficacy. However, the soil arching mobilization is not necessarily at the peak state but could be reached at the critical state. Finally, the geosynthetic strains are not uniform along the geosynthetic, and the maximum geosynthetic strain occurs at the pile edge. The geosynthetic deformed shape is a curve that is closer to a circular shape than a parabolic one.     

Two-dimensional soil arching evolution in geosynthetic-reinforced pile-supported embankments over voids

Soil arching and tensioned membrane effects are two main load transfer mechanisms for geosynthetic-reinforced pile-supported (GRPS) embankments over soft soils or voids. Evidences show that the tensioned membrane effect interacts with the soil arching effect. To investigate the soil arching evolution under different geosynthetic reinforcement stiffness and embankment height, a series of discrete element method (DEM) simulations of GRPS embankments were carried out based on physical model tests. The results indicate that the deformation pattern in the GRPS embankments changed from a concentric ellipse arch pattern to an equal settlement pattern with the increase of the embankment height. High stiffness geosynthetic hindered the development of soil arching and required more subsoil settlement to enable the development of maximum soil arching. However, soil arching in the GRPS embankments with low stiffness reinforcement degraded after reaching maximum soil arching. Appropriate stiffness reinforcement ensured the development and stability of maximum soil arching. According to the stress states on the pile top, a concentric ellipse soil arch model is proposed in this paper to describe the soil arching behavior in the GRPS embankments over voids. The predicted heights of soil arches and load efficacies on the piles agreed well with the DEM simulations and the test results from the literature.     

A laboratory evaluation of reinforcement loads induced by rainfall infiltration in geosynthetic mechanically stabilized earth walls

A laboratory testing that simulates the mechanisms of a geosynthetic-reinforced layer was used to assess the impact of rainwater infiltration on reinforcement loads and strains in mechanically stabilized earth (MSE) walls. The testing device allows measuring loads transferred from a backfill soil subjected simultaneously to surcharge loading and controlled irrigation. Load-strain responses of geosynthetic-reinforced layers constructed with three different geosynthetics under a moderate rainfall are related to suction captured along the depth of reinforced layers. Results show infiltration leading to increases on strains and tensile loads mobilized by reinforcements. Rates of increases of both parameters were found to be dependent of global suction, geosynthetic stiffness and hydraulic properties. In addition, increases in water content at soil-geotextile interfaces due to capillary breaks also had a significant effect on mobilized loads. The loss of interaction due to the interface wetting was observed to affect the stress transference from soil to geosynthetic reinforcement. An approach suggested for calculation of lateral earth pressures in unsaturated GMSE walls under working stress conditions and subjected to rainfall infiltration demonstrated a reasonable agreement with experimental data.     

A closed-form solution for column-supported embankments with geosynthetic reinforcement

Soil arching effect results from the non-uniform stiffness in a geosynthetic-reinforced and column-supported embankment system. However, most theoretical models ignore the impact of modulus difference on the calculation of load transfer. In this study, a generalized mathematical model is presented to investigate the soil arching effect, with consideration given to the modulus ratio between columns and the surrounding soil. For simplification, a cylindrical unit cell is drawn to study the deformation compatibility among embankment fills, geosynthetics, columns, and subsoils. A deformed shape function is introduced to describe the relationship between the column and the adjacent soil. The measured data gained from a full-scale test are applied to demonstrate the application of this model. In the parametric study, certain influencing factors, such as column spacing, column length, embankment height, modulus ratio, and tensile strength of geosynthetic reinforcement, are analyzed to investigate the performance of the embankment system. This demonstrates that the inclusion of a geosynthetic reinforcement or enlargement of the modulus ratio can increase the load transfer efficiency. When enhancing the embankment height or applying an additional loading, the height of the load transfer platform tends to be reduced. However, a relatively long column has little impact on the load transfer platform.     

Modelling of geosynthetic-reinforced column-supported embankments using 2D full-width model and modified unit cell approach

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.     

Combined effect of PVDs and reinforcement on embankments over rate-sensitive soils

A numerical study of the behavior of geosynthetic-reinforced embankments constructed on soft rate-sensitive soil with and without prefabricated vertical drains (PVDs) is described. The time-dependent stress–strain-strength characteristic of rate-sensitive soil is taken into account using an elasto-viscoplastic constitutive model. The effects of reinforcement stiffness, construction rate, soil viscosity as well as PVD spacing are examined both during and following construction. A sensitivity analysis shows the effect of construction rate and PVD spacing on the short-term and long-term stability of reinforced embankments and the mobilized reinforcement strain. For rate-sensitive soils, the critical period with respect to the stability of the embankment occurs after the end of the construction due to a delayed, creep-induced, build-up of excess pore pressure in the viscous foundation soil. PVDs substantially reduce the effect of creep-induced excess pore pressure, and hence not only allow a faster rate of consolidation but also improve the long-term stability of the reinforced embankment. Furthermore, PVDs work together with geosynthetic reinforcement to minimize the differential settlement and lateral deformation of the foundation. The combined use of the geosynthetic reinforcement and PVDs enhances embankment performance substantially more than the use of either method of soil improvement alone.     

Soil-reinforcement interaction: Stress regime evolution in geosynthetic-reinforced soils

Understanding the stress regime that develops in the vicinity of reinforcements in reinforced soil masses may prove crucial to understanding, quantifying, and modeling the behavior of a reinforced soil structures. This paper presents analyses conducted to describe the evolution of stress and strain fields in a reinforced soil unit cell, which occur as shear stresses are induced at the soil-reinforcement interface. The analyses were carried out based on thorough measurements obtained when conducting soil-reinforcement interaction tests using a new large-scale device developed to specifically assess geosynthetic-reinforced soil behavior considering varying reinforcement vertical spacings. These experiments involved testing a geosynthetic-reinforced mass with three reinforcement layers: an actively tensioned layer and two passively tensioned neighboring layers. Shear stresses from the actively tensioned reinforcement were conveyed to the passively tensioned reinforcement layers through the intermediate soil medium. The experimental measurements considered in the analyses presented herein include tensile strains developed in the reinforcement layers and the displacement field of soil particles adjacent to the reinforcement layers. The analyses provided insights into the lateral confining effect of geosynthetic reinforcements on reinforced soils. It was concluded that the change in the lateral earth pressure increases with increasing reinforcement tensile strain and reinforcement vertical spacing, and it decreases with increasing vertical stress.     

A novel 2D-3D conversion method for calculating maximum strain of geosynthetic reinforcement in pile-supported embankments

For design of a geosynthetic-reinforced pile-supported (GRPS) embankment over soft soil, the methods used to calculate strains in geosynthetic reinforcement at a vertical stress were mostly developed based on a plane-strain or two-dimensional (2-D) condition or a strip between two pile caps. These 2-D-based methods cannot accurately predict the strain of geosynthetic reinforcement under a three-dimensional (3-D) condition. In this paper, a series of numerical models were established to compare the maximum strains and vertical deflections (also called sags) of geosynthetic reinforcement under the 2-D and 3-D conditions, considering the following influence factors: soil support, cap shape and pattern, and a cushion layer between cap and reinforcement. The numerical results show that the maximum strain in the geosynthetic reinforcement decreased with an increase of the modulus of subgrade reaction. The 2-D model underestimated the maximum strain and sag in the geosynthetic reinforcement as compared with the 3-D model. The cap shape and pattern had significant influences on the maximum strains in the geosynthetic reinforcements. An empirical method involving the geometric factors of cap shape and pattern, and the soil support was developed to convert the calculated strains of geosynthetic reinforcement in piled embankments under the 2-D condition to those under the 3-D condition and verified through a comparison with the results in the literature.     

Reinforcement load in geosynthetic-reinforced pile-supported model embankments

The stress conditions of geosynthetic reinforcements (GRs) are crucial in achieving the accurate serviceability design of geosynthetic-reinforced pile-supported (GRPS) embankments. However, the sensitivity of load distribution to the settlement process has been reported in geosynthetic-reinforced embankment overlying cavities. In this study, a three-dimensional model embankment was used to perform experiments and evaluate the load acting on the GR. A flexible pressure-mapping sensor was introduced to investigate the pressure distribution for two types of supporting conditions: partitioned displacement by multiple movable trapdoors and even trapdoor settlement underneath different subsoil materials. The results showed that the load on the GR was concentrated on the strip areas between adjacent pile heads along with the settlement. The measured load on the GR strip area was related to the settlement process and finally exhibited a U-shaped distribution after detachment from the support underneath. The soil arch height in the subgrade continuously increased with the settlement; meanwhile, the pile head load increased rapidly at first and then decreased slightly or remained stable depending on the foundation support stiffness. For both types of settlement behaviours, soil arching exhibited stress history-related characteristics that influence the load transfer in GRPS embankments.     

Long-term behavior of GRS retaining walls with marginal backfill soils

The creep of geosynthetics leads to the increase of Geosynthetic-Reinforced Soil (GRS) wall's deformation. More importantly, the influences of creep of geosynthetics are also affected by the creep properties of soils. In this paper, a Finite Element procedure was validated against a model test on the creep response of a clay–geotextile composite. An extensive parametric study was then carried out to investigate the long-term response of 8-meter-high model GRS walls with marginal backfill soils. The influences of backfill creep, reinforcement creep, reinforcement stiffness, reinforcement length and reinforcement spacing were analyzed. A long-term analysis was conducted for 5 years and the results at the end of construction (EOC) and 5 years afterwards were compared. It is found from the analysis that the relative creep rate between geosynthetic reinforcement and backfill soil influenced not only wall deformation but also reinforcement loads and stress states in the soils. The load distribution in backfill soil and reinforcement is the result of battling between their time-dependent properties. Large reinforcement creep can lead to large post-construction deformation and increase in soil stress; on the other hand, large soil creep can induce a significant increase in reinforcement load. It is hence necessary to take into account the relative creep rate of reinforcement and backfill soil in the design of GRS walls. It may not be adequate to consider only the long-term strength of reinforcement, which is the state-of-the-practice at present.     

An analytical method for predicting load acting on geosynthetic overlying voids

Soil arching often occurs in geosynthetic-reinforced structures, where the underlying soil has voids, resulting in load transmission from the subsided area to surrounding less deformed area. A new method is proposed to predict load acting on gensynthetic overlying voids. The shape of soil arch and stress states of all the points at the soil arch can be obtained by combining nonlinear M-C yielding criterion, non-associated flow rule with static equilibrium of segmental arch through a dilatancy coefficient. The load applied to the geosynthetic can be determined by load transmission from the overlying soil, to the soil arch, and onto the collapsed soil. The model is verified using a model test conducted by Zhu et al. (2012), the soil pressure acting on the deflected geosynthetic is reasonably predicted. Due to the inherent nonlinear behaviour of soil, nonlinear failure criterion can better describe the stresses and deformations of the soil and geosynthetic. Soil nonlinearity has significant influence on the evaluation of arching effect. Ignoring the nonlinear behaviour of soil tends to underestimate the soil pressure acting on the geosynthetic. There exists an optimal subsidence width for which the soil pressure acting on the geosynthetic is minimal. The method used in this study is more appropriate where a large deflection occurs in the geosynthetic and provides a novel approach to evaluating soil arching under these conditions.