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.     

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.     

Applied bearing pressure beneath a reinforced soil foundation used in a geosynthetic reinforced soil integrated bridge system

Geosynthetic reinforced soil integrated bridge system (GRS-IBS) design guidelines recommend the use of a reinforced soil foundation (RSF) to support the dead loads that are applied by the reinforced soil abutment and bridge superstructure, as well as any live loads that are applied by traffic on the bridge or abutment. The RSF is composed of high-quality granular fill material that is compacted and encapsulated within a geotextile fabric. Current GRS-IBS interim implementation design guidelines recommend the use of design methodologies for bearing capacity that are based around rigid foundation behavior, which yield a trapezoidal applied pressure distribution that is converted to a uniform applied pressure that acts over a reduced footing width for purposes of analysis. Recommended methods for determining the applied pressure distribution beneath the RSF for settlement analyses follow conventional methodologies for assessing the settlement of spread footings, which typically assume uniformly applied pressures beneath the base of the foundation that are distributed to the underlying soil layers in a fashion that can reasonably be modeled with an elastic-theory approach. Field data collected from an instrumented GRS-IBS that was constructed over a fine-grained soil foundation indicates that the RSF actually behaves in a fairly flexible way under load, yielding an applied pressure distribution that is not uniform or trapezoidal, and which is significantly different than what conventional GRS-IBS design methodologies assume. This paper consequently presents an empirical approach to determining the applied pressure distribution beneath the RSF in GRS-IBS construction. This empirical approach is a useful first step for researchers, as it draws important attention to this issue, and provides a framework for collecting meaningful field data on future projects which accurately capture real GRS-IBS foundation behavior.     

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.     

An integrated limiting equilibrium approach for design of reinforced soil retaining structures:: Part III—optimal design

Classical retaining structures and conventional reinforced soil designs are limiting points of a continuous spectrum of potential solutions. These limiting cases represent legitimate designs, but they are not necessarily optimal. The present work considers the issue of optimal design of reinforced soil retaining structures in this spectrum. For the particular example considered in the present study the cost of the optimal solution is 47% of the cost of classical cantilever wall without soil reinforcement and 65% of the cost of the conventional reinforced soil design which neglects the wall contribution during reinforcement design. These values depend, naturally, on the support problem under consideration, and component's unit prices, but they clearly illustrate the large potential benefit of the proposed design process.

Conventional design procedures do not have the tools needed in order to evaluate interaction between the wall and the supporting system. As a result, conventional design procedures are restricted to the two end points of the spectrum of potential designs, in which one or the other of the two main components of the support system (wall, or reinforced soil) is practically neglected. The design procedure presented by Baker and Klein (Geotext. Geomembranes 22 (3) (2003a) 119–150; Geotext. Geomembranes 22 (3) (2003b) 151–177) overcomes the limitation of the classical design approach by the introduction of participation factors which quantify the interaction between the wall and the reinforced soil. As a result, the proposed design procedure allows one to quantify the economic trade-off between different walls and supporting systems, making it possible to consider optimal design issues.     

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.     

New procedure for active earth pressure calculation in retaining walls with reinforced cohesive-frictional backfill

A new approach is suggested to determine the active earth pressure on retaining walls with reinforced and unreinforced cohesive-frictional backfill based on the horizontal slices method. A 4n formulation for unreinforced backfill and a 5n formulation for reinforced backfill are introduced and the tensile forces of the reinforcements and angle of failure wedge are calculated. The proposed method shows that the variation of active earth pressure by the depth of the wall in cohesive-frictional soils has a non-linear distribution. Also, the point of application of the pressure always shifts to the lower two-thirds of the wall height. The angle of failure wedge for cohesive-frictional soils increases linearly with an increase in the cohesive strength of the soil. A comparison of the analytical results obtained from the proposed method with those of previous research and AASHTO method results shows a negligible difference. The analytical method presented can be used to calculate the active earth pressure, tensile force of reinforcements and angle of failure wedge for unreinforced and reinforced walls in cohesive-frictional soil.     

Numerical study on maximum reinforcement tensile forces in geosynthetic reinforced soil bridge abutments

This paper presents a numerical study of maximum reinforcement tensile forces for geosynthetic reinforced soil (GRS) bridge abutments. The backfill soil was characterized using a nonlinear elasto-plastic constitutive model that incorporates a hyperbolic stress-strain relationship with strain softening behavior and the Mohr-Coulomb failure criterion. The geogrid reinforcement was characterized using a hyperbolic load-strain-time constitutive model. The GRS bridge abutments were numerically constructed in stages, including soil compaction effects, and then loaded in stages to the service load condition (i.e., applied vertical stress?=?200?kPa) and finally to the failure condition (i.e., vertical strain?=?5%). A parametric study was conducted to investigate the effects of geogrid reinforcement, backfill soil, and abutment geometry on reinforcement tensile forces at the service load condition and failure condition. Results indicate that reinforcement vertical spacing and backfill soil friction angle have the most significant effects on magnitudes of maximum tensile forces at the service load condition. The locus of maximum tensile forces at the failure condition was found to be Y-shaped. Geogrid reinforcement parameters have little effect on the Y-shaped locus of the maximum tensile forces when no secondary reinforcement layers are included, backfill soil shear strength parameters have moderate effects, and abutment geometry parameters have significant effects.     

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 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.     

桩承式加筋路堤的改进设计方法研究

具有深厚软土层的路堤若采用桩承加筋式复合地基,可提高地基承载力,减少路堤不均匀沉降,也可布置成疏桩,降低工程成本,在国内外得到越来越广泛的应用,但还没有可靠实用的设计计算方法,且现有的设计均忽略了桩间土的承载作用,这与工程实际有很大差别。基于三维土拱效应,改进Hewlett土拱效应算法,得到桩承式路堤的桩土荷载分担比,进而考虑加筋体影响以及桩间土承载作用,推导桩土应力比计算式,并将此式应用于路堤的设计。     

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.     

Experimental study on the load bearing behavior of geosynthetic reinforced soil bridge abutments on yielding foundation

This paper presents an experimental study of the load bearing behavior of geosynthetic reinforced soil (GRS) bridge abutments constructed on yielding clay foundation. The effects of two different ground improvement methods for the yielding clay foundation, including reinforced soil foundation and stone column foundation, were evaluated. The clay foundation was prepared using kaolin and consolidated to reach desired shear strength. The 1/5-scale GRS abutment models with a height of 0.8 m were constructed using sand backfill, geogrid reinforcement, and modular block facing. For the GRS abutments on three different yielding foundations, the reinforced soil zone had relatively uniform settlement and behaved like a composite due to the higher stiffness than the foundation layers. The wall facing moved outward with significant movements near the bottom of facing, and the foundation soil in front of facing showed obvious uplifting movements. The vertical stresses transferred from the footing load within the GRS abutment and on the foundation soil are higher for stiffer foundation. The improvement of foundation soil using geosynthetic reinforced soil and stone columns could reduce the deformations of GRS abutments on yielding foundation. Results from this study provide insights on the practical applications of GRS abutments on yielding foundation.     

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.     

Limit analysis in stability calculations of reinforced soil structures

Stability analyses of reinforced soil structures are traditionally based on limit equilibrium calculations. Results from such analyses are sometimes ambiguous because of different assumptions made in addition to the limit state. It is shown in this paper that these ambiguities can be removed if the kinematic approach of limit analysis is used, in which a rigorous bound to the required strength of reinforcement is sought. The required strength of reinforcement is the strength needed to maintain stability of the structure. Since limit analysis leads to a rigorous bound on the reinforcement strength, limit loads, or a safety factor, the geometry of the failure mechanisms considered can be optimized, so that the best bound is obtained (a solution closest to the exact solution). A dual formulation of kinematic limit analysis is possible in terms of limit force equilibrium, but the former is preferable since the kinematics of collapse mechanisms appeals to engineering intuition more than the distribution of forces does.     

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.     

Deformation of model reinforced soil structures: Comparison of theoretical and experimental results

The problem of accurate prediction of deformations of reinforced soil structures under serviceable loading is discussed in this paper. First, a short overview of existing guidelines and methods is presented. Second, an analytical approach developed in IBW PAN to calculate horizontal and vertical deformations of such structures is described. Third, results of the verification of the proposed methodology are discussed. The modeling approach is validated against measured results from a literature review and an original laboratory program. Experimental studies under laboratory conditions were carried out to evaluate the accuracy of the proposed methodology. A model of a reinforced soil (RS) wall with a height of 0.5 m was constructed at a geotechnical laboratory and subjected to external loading. Horizontal deformations of the model RS wall were investigated at the end of construction and during the surcharge application (post-construction displacements). A theoretical analysis of the experimental results is elaborated on. A comparison of theoretical and experimental values of deformations is presented. The main conclusions are pointed out.     

Development of a numerical model for performance-based design of geosynthetic liner systems

A numerical model for performance-based design of the geosynthetic elements of waste containment systems has been developed. The model offers a rational alternative to the current state of practice for design of geosynthetic containment system elements in which neither the strains nor the forces in liner system elements are explicitly calculated. To explicitly assess the ability of the geosynthetic elements of a containment system to maintain their integrity under both static and seismic loads, a large strain finite difference model of waste-liner system interaction was developed. Modular features within the model allow the user to select the appropriate features required for any particular problem. A beam element with zero moment of inertia and with interface elements on both sides is employed in the model to represent a geosynthetic element in the liner system. This enables explicit calculation of the axial forces and strains within the liner system element. Non-linear constitutive models were developed to represent the stress-strain behavior of geomembrane and geosynthetic clay liner beam elements and the load-displacement behavior of the beam interfaces. The use of the various features on the model is illustrated using available experimental data, including shaking table test data on rigid and compliant blocks sliding on geomembranes. Analysis of geomembranes subject to waste settlement and subject to seismic loading demonstrate applications of the model and provide insight into the behavior of geosynthetic liner system elements subject to tensile loads.     

Electrically conductive geosynthetics for consolidation and reinforced soil

The concept of electrically conductive geosynthetics (EKG) materials has recently been introduced. These materials extend the traditional functions of geosynthetic materials by incorporating electro-kinetic phenomena. Electro-kinetic geosynthetics offer technical benefits over conventional electrodes in that they can be formed as strips, sheets, blankets or three-dimensional structures. They are light and easy to install and can be structured so as not to be susceptible to electro-chemical corrosion, whilst continuing to provide conventional functions of filtration, drainage, separation, reinforcement or to act as impervious membranes. This paper describes initial laboratory tests on different types of EKG materials which can be used as combined electrodes/drains in electro-osmotic consolidation and as conductive geosynthetic reinforcement used to improve and reinforced weak cohesive soil. Results of the consolidation tests showed that the EKG electrodes were as efficient as a copper electrode and that the filtration and drainage characteristics did not deteriorate under electro-osmotic conditions. Results of the reinforced soil tests showed that EKG reinforcement can be used to increase the undrained shear strength of cohesive fill and that reinforcement/soil bond increases in proportion to the increase in shear strength.     

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.