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.     

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 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.     

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.     

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.     

Sustainable design of reinforced concrete structures through embodied energy optimization

As the world struggles to reduce energy consumption and greenhouse gas emissions, much attention is focused on making buildings operate more efficiently. However, there is another, less recognized aspect of the built environment: the embodied energy of buildings, which represents the energy consumed in construction, including the entire life cycle of materials used. Architects and structural engineers extensively perform designs of buildings with steel and reinforced concrete-materials that, to different degrees, are energy intensive. This presents an opportunity to use structural optimization techniques, which have traditionally been employed to minimize the total cost or total weight of a structure, to minimize the embodied energy. With this in mind, an analysis is carried out to determine the implications, from the point of view of cost, of optimizing a simple reinforced concrete structural member, in this case a rectangular beam of fixed moment and shear strengths, such that embodied energy is minimized. For the embodied energy and cost values assumed, results indicate a reduction on the order of 10% in embodied energy for an increase on the order of 5% in costs.     

Shaking table performance of reinforced soil retaining walls with different facing configurations

In this paper, a new type of MSE wall facing, termed as hybrid facing, is introduced and studied, which is built using a combination of concrete modular blocks and cast-in-place concrete. Two shaking table tests were carried out to compare seismic performances of model reinforced soil retaining walls with full-height vs. hybrid facing configurations. Results of this study show that the stability and performance of the hybrid facing model were similar to those of the full-height panel wall for peak input acceleration magnitudes less than 0.40 g. The amplification factors along the height of the facing were more uniform and smaller in the hybrid facing model as compared to the full-height panel wall, especially at higher peak acceleration amplitudes. Dynamic increment of lateral earth loads acting on the facing in both cases were found to be only 20% of the values calculated using pseudo-static methods. Connection loads in the hybrid facing model were smaller than those in the full-height panel wall, which was attributed to its smaller facing displacements.     

Reliability evaluation in nonlinear analysis of reinforced concrete structures

Modern building codes provide a basis for development of advanced nonlinear models for analysis and design of reinforced concrete (RC) structures. Application of nonlinear models permits direct evaluation of reliability of the whole structure at the stage of a structural analysis. In this paper a probabilistic method for reliability evaluation of plane frame structures with respect to ultimate limit states is proposed. The method is based on a combination of the nonlinear finite element structural model and the first-order reliability method (FORM). Implementation of the FORM for nonlinear analysis of RC structures is considered. Uncertainties associated with the structural model are taken into account and their influence on structural reliability is examined via sensitivity analysis.     

Rational approach for the analysis of segmental reinforced soil walls based on kinematic constraints

The paper presents an analytical method for the solution of reinforced soil walls in which the wall facing has a structural role. The three-component (soil–reinforcement–wall) system is statically indeterminate, and hence cannot be solved by equilibrium equations alone. The paper follows up on the work of Baker and Klein [2004. An integrated limiting equilibrium approach for design of reinforced soil retaining structures part I – formulation. Geotextiles and Geomembranes 22, 119–150] where an interaction model, incorporating factors that divide forces between the reinforcement layers and the wall, was introduced to solve the statically indeterminate system. In the current work, the division factors are resolved such that the kinematic constraints of compatibility between the reinforcement layers and the wall are satisfied. This is achieved by solving an optimization problem in which the objective function includes the relative displacement between the reinforcement layers and the wall. The resultant system is fully coupled whereby upper reinforcement layers are affected by the behavior of lower layers. As such, the method overcomes the limitation of the original framework in which the top-down procedure omits such coupling. A non-dimensional parametric study was conducted on walls with 10 face blocks (9 reinforcement layers). Results are given in a normalized manner for cases in which the reinforcement pullout stiffness is uniform and linearly increasing with depth. Analysis results show that in cases where the wall is relatively stiff compared to the reinforcement, the upper reinforcement layers are clearly affected by the lower layers (this is a direct outcome of the fully coupled system). On the other hand, when the relative stiffness of the wall is low, the system behavior tends towards that of a hinged system, which is statically determinate. In this case the solution becomes independent of the reinforcement pullout stiffness. Analysis results indicate that current design codes, which do not explicitly consider the structural role of the facing in the calculation procedure, may be overconservative in certain cases. This result supports the argument for introducing the structural role of the facing into design procedures.     

Dynamic response of Mechanically Stabilised Earth (MSE) structures: A numerical study

With increasing construction feasibility, lower costs and proven performance throughout past major seismic events, MSE retention systems have become one of the more preferred retention systems. To study the dynamic performance of MSE walls, the 2D FE simulation using the OpenSees programme with the Manzari and Dafalias constitutive relationship has been utilised. A series of one-dimensional (1D) and 2D site response analyses subjected to sinusoidal inputs at various frequencies have been conducted to find the natural period of the soil medium. Then, using three earthquake time-histories recorded on engineering bedrock (Vs > 700 m/s), the behaviour of MSE walls with geogrid length to wall height ratios of 0.50 and 0.75 has been investigated. Multi-pulse Ricker wavelets have been deployed for a closer inspection of possible failure mechanisms of these MSE walls. Finally, the possibility of simulating an elastic orthotropic block instead of the reinforced soil with geogrids has been examined.