Limit state design framework for geosynthetic-reinforced soil structures

Conventional design of geosynthetic-reinforced soil structures is divided into two categories, walls and slopes, based on the batter of its facing system. Internal stability, characterized as sufficient reinforcement anchoring and strength, is performed using earth pressure-based design criteria for reinforced walls while reinforced slopes are founded on limit equilibrium (LE) slope stability analyses. LE analyses are also used to assess the global or compound stability of both types of structures, accounting for the geometry of the reinforced, retained and foundation soils. The application of LE-based methods typically results in determination of a slip surface corresponding to the lowest attained Safety Factor (SF), known as the Factor of Safety (Fs); however, it yields little information about reinforcement loading or connection load. In this study, use of the analyzed spatial distribution of SF known as a Safety Map, is modified to attain a prescribed constant Fs at any location in the reinforced soil mass. This modified framework, implemented through an iterative, top-down procedure of LE slope stability analyses originating from the crest of a reinforced structure and exiting at progressively lower elevations on the facing, enables the determination of a Tension Map that illustrates the required distribution of reinforcement tension to attain a prescribed limit state of equilibrium. This tension map is directly constrained by a pullout capacity envelope at both the rear and front of each reinforcement layer, providing a unified, LE-based approach towards assessing an optimal selection of mutually dependent strength and layout of the reinforcement. To illustrate the utility of the Limit State framework, a series of instructive examples are presented. The results demonstrate the effects of facing elements, closely-spaced reinforcements, secondary reinforcement layers, and is compared to conventional design approaches.     

Required unfactored strength of geosynthetics in reinforced 3D slopes

The design of reinforced earth structures uses idealized two-dimensional (2D) geometry – classifying as a plane-strain analysis. This 2D idealization greatly simplifies design by ignoring stabilizing effects posed by three-dimensional (3D) characteristics. While the outcome of this 2D idealization is conservative in terms of required reinforcement strength, ignoring 3D end effects in back-calculations of experimental and field data may overestimate the contribution of the reinforcement to stability thus possibly leading to unconservative learned lessons related to design. The objective of this study is to explore 3D effects on the required strength of reinforcement in geosynthetic-reinforced earth structures (GRESs) using a modified 3D limit equilibrium (LE) slope stability analysis. To determine the stability of GRESs, a rotational, 3D failure mechanism, derived from variational LE analysis, is applied using a log-spiral surface generalized to 3D conditions. In order to determine the long-term strength of geosynthetics required to ensure sufficient internal stability, the moment equilibrium approach is applied and its respective equations solved. In order to conveniently assess the end effects on the required total strength of reinforcement and the volume of failing mass considering the feasible length of potential failure, a series of design charts are presented. These charts can also be useful in forensic studies when back-calculating the in-situ mobilized strength of the geosynthetic for 3D failures. The impact of seismicity and the assumed function of forces distributed amongst the reinforcement layers were investigated to highlight their importance. To keep this study focused on 3D end effects, this study is limited to a simple 3D GRES problem; however, extending the present framework to deal with complex homogenous problems is straightforward.     

Corner reinforced slopes: Required strength and length of reinforcement based on internal stability

This paper develops an analysis procedure for turning corner in Geosynthetic-Reinforced Soil Structures (GRSS's). The procedure includes the calculations of the required strength and length of the reinforcement for internal stability. The calculations are based on the variational limit equilibrium analysis of three-dimensional (3D) stability of slopes. Seismic effects are also considered using the pseudo-static method. Results are presented in a condensed form of design charts, providing a simple tool to determine the required tensile strength and embedment length of the reinforcement. Two examples are given to demonstrate the use of the design charts. Compared with the conventional design based on plane-strain analysis, the presented design procedure yields longer reinforcement for the 3D internal stability of the corners. Generally, 3D design requires longer reinforcement than 2D as the seismic acceleration increases. The trend of obtained result is in good agreement with performance observations related to corners reported in commentary of AASHTO.     

Internal stability analysis of reinforced convex highway embankments considering seismic loading

The seismic internal stability of reinforced, convex embankments that are three-dimensional in nature is analyzed. A limit equilibrium based three-dimensional rotational failure mechanism is adopted to calculate the required reinforcement strength to maintain the stability of convex embankments. The results are presented in the form of stability charts and the effects of various parameters on the three-dimensional solution are investigated. The calculation of the required strength and length of reinforcement is demonstrated by two examples using an approach consistent with AASHTO (2012). Comparing the strengths obtained under two and three-dimensional conditions, the results show that the two-dimensional results are more conservative with respect to the strength of reinforcement, but could be unconservative considering the required length of reinforcement, especially for reinforced convex embankments with gentle turning angles. The influence of seismicity causes greater three-dimensional effects when the reinforced convex embankment is vertical, but less so when the slope inclination is gentle.     

Overall stability of geosynthetic-reinforced embankments on soft soils

Overall stability of geosynthetic-reinforced embankments on soft soils is analysed using two different methodologies: application of a numerical model based on the finite element method; use of a limit equilibrium method. These two methodologies are described and also applied on three geosynthetic-reinforced embankments on soft soils. One of the cases is a case history constructed up to failure. Considering the analysis of the results, some conclusions are formulated on the limit equilibrium method accuracy, namely regarding the critical slip surface, overall safety factor and overturning and resisting moments.     

Seismic analysis of 3D geosynthetic-reinforced soil structures in cohesive backfills with cracks

This study proposes a procedure for predicting the required tensile strength of geosynthetics for three-dimensional (3D) geosynthetic-reinforced soil structures (GRSSs) comprised of cohesive backfills subjected to earthquake loadings. This procedure is undertaken using the kinematic approach of limit analysis together with a pseudo-dynamic approach. The influence of cracks is incorporated into the analysis by using a 3D horn-like failure mechanism that includes a vertical crack to characterize the collapse of GRSSs. Two different forms of cracks are considered: cracks forming prior to the collapse of GRSSs (open cracks) and cracks forming simultaneously with the collapse (formation cracks). Based on the work-energy balance equation, the amount of reinforcements needed to maintain the stability of GRSSs is determined. The results of this paper show that the required reinforcements significantly decrease when soil cohesion and 3D effects are considered, whereas accounting for the existence of cracks and seismic forces has an opposite effect.     

Effects of seismic amplification on the stability design of geosynthetic-reinforced soil walls

Many researches of geosynthetic-reinforced soil (GRS) walls under earthquakes demonstrate seismic acceleration amplification along the wall height. Current design methods of GRS walls often neglect the amplification effect on seismic stability and could yield an unconservative result. A pseudo-static method based on limit equilibrium (LE) analyses is carried out to calculate the distribution of required tension of seismic GRS walls following a top-down procedure. The connection load between the reinforcement and facing is correspondingly determined by the front-end pullout capacity. The approach assumes that the horizontal seismic acceleration coefficient varies linearly from the bottom to the top of GRS walls. The obtained results of the required tension involving the seismic amplification are in good agreement with other LE results in previous studies. Parametric studies are conducted to investigate the effects of horizontal seismic coefficient, primary and secondary reinforcement lengths and wall batter on the seismic stability of GRS walls. The seismic amplification yields more required reinforcement tension, significantly for the lower layers of the GRS wall subjected to strong earthquakes. In this situation, lengthening the bottom 1/2 of reinforcement layers could reduce the required tension to avoid tensile breakage of the reinforcements.     

Earth pressure coefficients for design of geosynthetic reinforced soil structures

There are several methods proposed in the last two decades that can be used to design geosynthetic reinforced soil retaining walls and slopes. The majority of them are based on limit equilibrium considerations, assuming bi-linear or logarithmic spiral failure surfaces. Based on these failure mechanisms, design charts have been presented by several authors. However, the use of design charts is less and less frequent. The paper presents results from a computer program, based on limit equilibrium analyses, able to quantify earth pressure coefficients for the internal design of geosynthetic reinforced soil structures under static and seismic loading conditions. Failure mechanisms are briefly presented. Earth pressure coefficients calculated by the developed program are compared with values published in the bibliography. The effect of seismic loading on the reinforcement required force is also presented. To avoid the use of design charts and based on the obtained results, approximate equations for earth pressure coefficients estimation are proposed. The performed analyses show that the failure mechanism and the assumptions made have influence on the reinforcement required strength. The increase of reinforcement required strength induced by the seismic loading, when compared to the required strength in static conditions, grows with the backfill internal friction angle. The effects of the vertical component of seismic loading are not very significant.     

Required unfactored geosynthetic strength of three-dimensional reinforced soil structures comprised of cohesive backfills

Conservative design of Geosynthetic-reinforced soil structures (GRSSs) is commonly limited to two-dimensional (2D) conditions, ignoring the influence of possible cohesion in backfill material. However, the actual stability of GRSSs is directly influenced by the presence of cohesion – true or apparent – in backfill as well as three-dimensional (3D) effects. In this study, a 3D rational failure mechanism based on the kinematic approach of limit analysis is adopted to assess the stability of GRSSs comprised of cohesive backfills. Within this study, the influence of 3D effects, varying pore water pressures, varying backfill cohesion, and a range of slopes on long-term stability are illustrated in a series of convenient design charts. The results of 3D stability analyses for geosynthetic reinforced walls constructed with cohesive backfills are compared with the results obtained from design guidelines. As expected, when GRSSs are well-drained and relatively narrow in width - or when increasing levels of cohesion are present in the backfill - more stable conditions are realized. For practical scenarios, however, it is critical that cohesive soils should be utilized as backfill with great caution and reliable drainage conditions. Nonetheless, the presented solutions are directly useful towards the assessment of failures of real GRSSs, as they may be constructed with marginal fills that exhibit cohesion, accumulate pore water pressure and often exhibit failure conditions that are three-dimensional in nature.     

Effect of dynamic soil properties and frequency content of harmonic excitation on the internal stability of reinforced soil retaining structure

The effect of dynamic soil properties and frequency content of harmonic excitation on the internal stability of reinforced soil retaining structure is investigated. Arc of a log-spiral is considered as the failure surface in the present limit equilibrium analysis. Backfill and reinforced soil is modeled as a visco-elastic material. The whole structure is considered to be resting on a rigid stratum. Backfill soil and the reinforced soil retaining structure are subjected to harmonic shaking at the base. Present methodology satisfies the stress boundary condition at the ground surface. In the present study, amplitude and phase of the horizontal and vertical seismic accelerations change with depth and the variation of accelerations along the depth is found to be time dependent and nonlinear. All the four possible combinations of horizontal and vertical seismic inertia force directions are considered to determine the total reinforcement force and critical length of the reinforcement. In the present study, amplification of accelerations towards the ground surface depends on the dynamic soil properties and frequency content of input excitation. Detailed parametric study is done to understand their implications on the solution. An algorithm is proposed at the end of this paper which uses strain dependent equivalent linear values of shear wave velocity (V_s) and damping ratio (ξ) to compute the total reinforcement force and critical length of the reinforcement. The limitation of equivalent linear based approach is that it only considers vertically propagating shear wave. Comparison of present method with other theories is also presented showing the merit of the present study.     

Evaluation of permeability characteristics of a geosynthetic-reinforced soil through laboratory tests

The objective of this paper is to examine the permeability characteristics of geosynthetic layers under confinement with soils having relatively low permeability. For this purpose, a large permeameter was custom designed and a series of permeability tests were carried-out by varying soil type and number of geosynthetic layers. Further, effect of provision of sand cushion and the thickness of sand cushion on permeability characteristics was also examined. Normal stress was increased in intervals of 50 kPa up to 200 kPa. With an increase in normal stress, a decrease in the permeability characteristics of a geosynthetic-reinforced soil was observed. The permeability characteristics were found to improve significantly with the provision of sand cushion and an increase in its thickness. Based on the definition of equivalent coefficient of permeability of stratified soils for parallel flow, an equation for estimating coefficient of permeability of soil–geosynthetic system with and without sand cushion is proposed. Considering the application of geosynthetics in reinforced slopes and walls with low-permeable backfill soils, a suitable geosynthetic with a thin layer of sand cushion is recommended. This in turn can also help in enhancing the pore-water pressure dissipation.     

Upper bound seismic limit analysis of geosynthetic-reinforced unsaturated soil walls

The assessment of the internal stability of geosynthetic-reinforced earth retaining walls has historically been investigated in previous studies assuming dry backfills. However, the majority of the failures of these structures are caused by the water presence. The studies including the water presence in the backfill are scarce and often consider saturated backfills. In reality, most soils are unsaturated in nature and the matric suction plays an important role in the wall's stability. This paper investigates the internal seismic stability of geosynthetic-reinforced unsaturated earth retaining walls. The groundwater level can be located at any reinforced backfill depth. Several nonlinear equations relating the unsaturated soil shear strength to the matric suction and different backfill type of soils are considered in this study. The log-spiral failure mechanism generated by the point-to-point method is considered. The upper-bound theorem of the limit analysis is used to evaluate the strength required to maintain the reinforced soil walls stability and the seismic loading are represented by the pseudo-dynamic approach. A parametric study showed that the required reinforcement strength is influenced by several parameters such as the soil friction angle, the horizontal seismic coefficient, the water table level, the matric suction distribution as well as the soil types and the unsaturated soils shear strength.     

Seismic behavior of geosynthetic-reinforced retaining walls backfilled with cohesive soil

This study investigates the seismic performance of geosynthetic-reinforced modular block retaining walls backfilled with cohesive, fine grained clay-sand soil mixture. Shaking table tests were performed for three ½ scaled (wall height 190 cm) and ¼ scaled model walls to investigate the effects of backfill type, the influence of reinforcement length and reinforcement stiffness effects. The El Centro and Kobe earthquake records of varying amplitudes were used as base acceleration. Displacement of the front wall, accelerations at different locations, strains on the reinforcements, and the visual observations of the facing and the backfill surface were used to evaluate the seismic performance of model walls. The model walls were subjected to rigorous shaking and the walls did not exhibit any stability problems or signs of impending failure. The maximum deformations observed on the models with cohesive backfill was less than half of the deformation of the sand model. The load transfers between the geogrid and cohesive soil was comparable to that of sand and hence the needed reinforcement length was similar as well. As a result; the model walls with cohesive backfills performed within acceptable limits under seismic loading conditions when compared with granular backfilled counterparts.     

Three-dimensional finite element analysis of geosynthetic-reinforced soil walls with turning corners

The paper presents in-depth three-dimensional finite element analyses investigating geosynthetic-reinforced soil walls with turning corners. Validation of the 3D numerical procedure was first performed via comparisons between the simulated and reported results of a benchmark physical modeling built at the Royal Military College of Canada. GRS walls with corners of 90°, 105°, 120°, 135°, 150°, and 180° were simulated adopting the National Concrete Masonry Association guidelines. The behaviors of the GRS walls with corners, including the lateral facing displacement, maximum reinforcement load, factor of safety, potential failure surface, vertical separation of facing blocks, and types of corners were carefully evaluated. Our comprehensive results show (i) minimum lateral displacement occurs at the corner; (ii) lower strength of reinforcements are required at the corner; (iii) higher corner angles lead to lower stability; (iv) potential failure surface forms earlier at the end walls; (v) deeper potential failure surfaces are found at the corners; (vi) larger numbers of vertical separations are found at walls with smaller corner angles. The paper highlighted the salient influence of the corners on the behaviors of GRS walls and indicated that a 3D analysis could reflect the required reinforcement length and the irregular formation of the potential failure surfaces.     

Predicting the settlement of geosynthetic-reinforced soil foundations using evolutionary artificial intelligence technique

In order to ensure safe and sustainable design of geosynthetic-reinforced soil foundation (GRSF), settlement prediction is a challenging task for practising civil/geotechnical engineers. In this paper, a new hybrid technique for predicting the settlement of GRSF has been proposed based on the combination of evolutionary algorithm, that is, grey-wolf optimisation (GWO) and artificial neural network (ANN), abbreviated as ANN-GWO model. For this purpose, the reliable pertinent data were generated through numerical simulations conducted on validated large-scale 3-D finite element model. The predictive power of the model was assessed using various well-established statistical indices, and also validated against several independent scientific studies as reported in literature. Furthermore, the sensitivity analysis was conducted to examine the robustness and reliability of the model. The results as obtained have indicated that the developed hybrid ANN-GWO model can estimate the maximum settlement of GRSF under service loads in a reliable and intelligent way, and thus, can be deployed as a predictive tool for the preliminary design of GRSF. Finally, the model was translated into functional relationship which can be executed without the need of any expensive computer-based program.     

Effect of soil-reinforcement interaction coefficient on reinforcement tension distribution of reinforced slopes

This paper examines the effect of the mobilized reinforcement tension within reinforced soil slope at a different level of soil-geosynthetic interaction. The mobilized reinforcement tension is assumed, in most design methods for the internal stability of reinforced slopes, to be equal to mobilized soil forces computed using a limit equilibrium method. However, comparison with the reinforcement tension force measured in the field has shown that this approach is conservative. This paper examines the effects of the soil-reinforcement interaction coefficient on the tensile redistribution of geosynthetics. The modified process of Bishop Method of slope stability analysis is used to locate the critical slip surface and to calculate the mobilized reinforcement tensile force. The reinforcement forces obtained from field data and on centrifuge model test results for a reinforced slope problem are used to examine the relationship between mobilized reinforcement tensile force and mobilized soil shear strength.     

Numerical investigation of reinforcement pullout resistance effects on behavior of geosynthetic-reinforced soil (GRS) piers

In this study, three-dimensional numerical analyses were carried out to investigate the effects of reinforcement pullout resistance including facing connection strength on the behavior of geosynthetic-reinforced soil (GRS) piers under a service load condition. Three different piers were investigated in this study, which simulated different levels of reinforcement pullout resistance. Each pier had two cases with different reinforcement stiffness J and reinforcement spacing S_v but the same ratio of J/S_v. Numerical results showed that reinforcement pullout resistance had a significant effect on the behavior of GRS piers. When the pullout mode prevailed, the case with small S_v and low J had smaller lateral facing displacements and vertical strain of the pier under the same applied pressure as compared to the case with large S_v and high J when the ratio of J/S_v was kept constant. When the pullout mode did not prevail, two cases with the same ratio of J/S_v showed similar performance despite different combinations of S_v and J were used. To more effectively mobilize reinforcement strength and improve GRS pier performance, small reinforcement spacing or high-strength facing connection should be considered when sufficient reinforcement pullout resistance cannot be guaranteed otherwise.     

Bottom ash as a backfill material in reinforced soil structures

The paper describes the interface behaviour of bottom ash, obtained from two thermal power plants, and geogrid for possible utilization as a reinforced fill material in reinforced soil structures. Pullout tests were conducted on polyester geogrid embedded in compacted bottom ash samples as per ASTM D6706-01. Locally available natural sand was used as a reference material. The pullout resistance offered by geogrid embedded in bottom ash was almost identical to that in sand. In order to study the influence of placement condition of the material on pullout resistance, test were conducted on uncompacted fill materials. Pullout resistance offered by geogrids embedded in uncompacted specimen reduced by 30–60% than that at the compacted condition.     

Stability assessment of 3D reinforced soil structures under steady unsaturated infiltration

Internal stability assessment of geosynthetic-reinforced soil structures (GRSSs) has been commonly carried out assuming plane-strain conditions and dry backfills. However, failures of GRSSs usually show three-dimensional (3D) features and occur under unsaturated conditions. A procedure based on the kinematic limit-analysis method is proposed herein to assess 3D effects and the role of steady unsaturated infiltration on the required geosynthetic strength for GRSSs. A suction stress-based framework is used to describe the soil stress behavior under steady unsaturated infiltration. Based on the principle of energy-work balance, the required geosynthetic strength is determined. A comparison analysis with the prior research is conducted to verify the developed method. Two kinds of backfills, i.e., high-quality backfill and marginal backfill, are considered for comparison in this work. It is shown that accounting for 3D effects and the role of unsaturated infiltration considerably reduces the required geosynthetic strength. The 3D effects are primarily affected by the width-to-height ratio of GRSSs, and the contribution of unsaturated infiltration is mainly influenced by the soil type, flow rate, GRSS's height, and location of the water table.