3D effects of turning corner on stability of geosynthetic-reinforced soil structures

Current design procedures of Geosynthetic-Reinforced Soil Structures (GRSS's) are for walls/slopes with long straight alignments. When two GRSS segments intersect, an abrupt change in the alignment forms a turning corner. Experience indicate potential instability problems occurring at corners. The purpose of this study is to explore the effects of turning corner on the stability of reinforced slopes. Three-dimensional (3D) slope stability analysis, based on limit equilibrium, resulted in the maximum tensile force of reinforcement. Parametric studies required numerous computations considering various geometrical parameters and material properties. The computed results produced efficient practical format of stability charts. For long-term stability of reinforced slopes with turning corner, the influences of pore water pressure and seismic loading are also considered. Turning corner can improve the stability of reinforced slopes by virtue of inclusion of end effects. However, localized increase of pore water pressure or directional seismic amplification may decrease locally thus stability requiring strength of reinforcement larger than in two-dimensional (2D) plane-strain. While using 2D analysis for non-localized conditions may require stronger reinforcement, it also requires shorter reinforcement than in 3D analysis; i.e., 2D analysis may be unconservative in terms of reinforcement length.     

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 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.     

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.     

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.     

Finite element limit analysis of load-bearing performance of reinforced slopes using a non-associated flow rule

This paper presents a numerical study on the load-bearing performance of reinforced slopes under footing load using a finite element limit analysis (FELA) method where a non-associated flow rule is assumed in the analysis. The method was validated against results from full-scale model tests and a limit equilibrium (LE) analytical method. A series of parametric analyses was subsequently carried out to examine the influences that the soil dilation angle, footing location, and reinforcement design (i.e. length, tensile strength, and vertical spacing) could have on the load-bearing performance of reinforced slopes. Results indicate that dilation angle has a significant influence on the predicted magnitudes of bearing capacity, slope deformation, and mobilized reinforcement load. The predicted values of bearing capacity using the FELA are smaller than those from the Meyerhof's analytical method for unreinforced semi-infinite foundation, especially for larger friction angle values. Additionally, the ultimate bearing capacity of the slope and its corresponding horizontal deformation increase with the reinforcement tensile strength. Finally, the slip planes under the applied footing load are found to be y-shaped and primarily occur in the upper half of the slope.     

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.     

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.     

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.     

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.     

Limited reinforced space in segmental retaining walls

Current design of geosynthetic reinforced segmental retaining walls considers an a priori limitless length for reinforcement installation. Such length is typically 0.5–0.7 times the height of the wall. However, often there are constraints on such space; e.g., bedrock formation located at a small distance behind the facing. The objective of this note is to introduce a procedure for assessing the required long-term strength of the reinforcement while considering its limited length. Predictions by a conventional slope stability analysis were first checked against a continuum-mechanics based numerical analysis. Upon obtaining good agreement, a design chart was developed. The chart enables the determination of the reduction in the lateral earth pressure coefficient due to the constrained space. The revised earth pressure coefficient can be used with current analytical methods to account for the limited space. The results appear to be valid for conventional walls retaining a limited volume of soil. Comparison with limited experimental results for unreinforced backfill shows reasonably good agreement.     

Earth pressure coefficients for reinforcement loads of vertical geosynthetic-reinforced soil retaining walls under working stress conditions

Based on the nonlinear elastic theory and stress-dilatancy theory, two earth pressure coefficients were proposed to analyze the reinforcement loads at the potential failure surface of vertical geosynthetic-reinforced soil retaining walls under working stress conditions. The earth pressure coefficients take into account the force equilibrium and compatible deformations between soil and reinforcement, and can be obtained by solving two implicit functions by an iterative or graphic method. The effects of backfill compaction and facing restriction are taken into account in the earth pressure coefficients by two additional stress factors, which have been derived analytically using straightforward approaches. To validate the effectiveness of the proposed methods, comparisons were made with the results from large scale tests and numerical simulations. It was demonstrated that the reinforcement loads predicted by the proposed methods were in good agreement with the experimental or numerical results.     

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.     

Evaluating the effects of the magnitude and amplification of pseudo-static acceleration on reinforced soil slopes and walls using the limit equilibrium Horizontal Slices Method

The effects of horizontal and vertical pseudo-static forces on reinforced soil structures are investigated in the paper. In particular, the effects of the magnitude and amplification of the ground acceleration on the seismic stability of reinforced soil slopes and walls have been investigated using the Horizontal Slices Method (HSM). The HSM is a limit equilibrium method for the analysis of reinforced soil structures, which offers a number of benefits over conventional vertical slice methods. First, a parametric study using acceptable geotechnical, geometrical and design parameters was undertaken. The results of the parametric analysis are presented in dimensionless form relating to the force required to maintain stability of the slope (K) and the required length of the reinforcements (L_c/H). Different rotational and planar slip surfaces are shown for various slopes and walls with different geotechnical strength parameters. Second, the capability of the HSM to consider the effect of earthquake amplification on the stability analysis of reinforced soil structures was considered. It has been shown that the effect of horizontal seismic acceleration on the response of reinforced slopes and walls depends mainly on the geotechnical strength parameters. The effect of vertical seismic acceleration on the performance of reinforced slopes is not significant for low values of horizontal seismic acceleration. It has been concluded that ignoring the effect of the amplification phenomenon could result in an underestimated design.     

关于土工合成材料加筋设计的若干问题

目前土工合成材料加筋技术被广泛应用,但人们对于加筋土中筋材与土间的相互作用的机理的认识还不够深入,因而在设计中总体上趋于保守。结合岩土工程的设计理论,指出土工合成材料在设计方法方面的不合理性;对于加筋挡土墙、加筋土坡、加筋软土地基上的土堤和桩网结构的设计分别进行了讨论;结合一些案例中的实测和预计的筋材应变和应力,进一步指出目前设计的保守性。最后指出,目前基于极限平衡法的设计不尽合理,而通过变形协调的筋土共同作用的研究,采用更能反映其相互作用机理的设计方法是非常必要的。     

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.     

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.     

A performance-based approach to design reinforced-earth retaining walls

This paper describes a pseudo-static approach developed for geosynthetic-reinforced earth (GRE) retaining walls, calibrated against given levels of wall performance defined by specified values of earthquake-induced displacements. The GRE walls generally show a good performance under severe seismic loading due to the capability of reinforcements to redistribute the deformations induced by the seismic actions within the reinforced zone. This can be achieved by promoting the activation of internal plastic mechanisms involving the reinforcements strength, providing that they are characterised by adequate extensional ductility. In the proposed procedure, the seismic coefficient k to be used in a pseudo-static calculation is assumed equal to the internal seismic resistance of the wall k_c^int, related, through the kinematic theorem of limit analysis, to the maximum strength demand of geosynthetic reinforcements. The seismic coefficient is then calibrated against given levels of seismic wall performance, defined by threshold values of earthquake-induced displacements that result by the temporary activation of plastic mechanisms during severe seismic loading. Permanent displacements induced by earthquake loadings are evaluated through empirical relationships based on a parametric integration of a large number of Italian seismic records and are expressed as a function of the critical and the maximum horizontal accelerations. A procedure is finally proposed to conceive a reinforced-earth retaining wall with an internal seismic resistance lower than the external one, so that a prescribed level of seismic performance and the activation of internal mechanisms are ensured during severe seismic shaking.     

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.