Tensile Strength Of Reinforcement Research Articles

Ultimate bearing capacity of geosynthetic reinforced soil abutment centrifuge model tests

Five centrifuge models of geosynthetic reinforced soil (GRS) abutments with segmental block facing were loaded in the acceleration field under plane strain condition. Influencing factors including reinforcement tensile strength, setback and bearing area width were considered and analysed. Results show that the abutment with stronger reinforcement remained stable under the maximum loading capacity. However, abutments with weaker reinforcement showed excessive vertical strain, local deformation or even collapse. The ultimate bearing capacity increased with the lengthening of setback but decreased due to a larger bearing area. The rupture of reinforcements was observed and considered as the cause of the failures. Compared with the measured ultimate bearing capacity, the values calculated by the semi-empirical formula of design guidelines were significantly conservative. The failure surface of failed abutment developed from the rear edge of the bearing area to the middle height of the abutment at an angle of nearly 45° + φ/2. The setback and the bearing area width affected the form and position of the failure surface. The difference between the potential failure surface predicted by available methods and the measured failure surfaces has been discussed, and suggestions for the design and ultimate bearing capacity prediction of GRS abutments with segmental block facing are provided.

Reliability analysis of geosynthetic-reinforced slopes under rainfall infiltration

The rainfall-induced instability of geosynthetic-reinforced is a time-dependent phenomenon owing to the infiltration process, and is influenced by rainfall patterns. Catering to the inherent uncertainty in soil properties, this study conducted a reliability analysis of three-dimensional (3D) vertical geosynthetic-reinforced slopes, in order to explore how the probabilistic stability of slope evolves over time under different rainfall patterns. A 3D horn-like mechanism incorporating the Conte-Troncone (CT) model is adopted as a framework for deterministic analysis. Through a Fourier transform-based theoretical reasoning, the CT model assesses the time-variable pore-water pressure of soils in response to any continuously varying rainfall intensity over time. Subsequently, the pore water pressure-driven changes in soil unsaturated strength and the corresponding extend power are integrated into the three-dimensional mechanism, enabling a rapid determination of the instantaneous safety factor at discrete time instants. To avoid the tedious computation generated by Monte Carlo simulation, a simplified Hasofer-Lind-Rackwitz-Fiessler (HLRF) algorithm is used to calculate the time-varying reliability indices. Using the implantation of the proposed method, the effects of rainfall pattern, slope width, and reinforcement tensile strength are investigated by parametric analysis.

Failure Mechanism and Deformation-Based Design of Narrow Geosynthetic Reinforced Soil Walls

In recent years, the working performance of mechanically stabilized earth (MSE) walls has shown their outstanding stability and capacity to accommodate large deformation. The behavior and failure mechanisms of conventional MSE walls have been carefully examined. In cases where space is limited, such as in mountainous regions, in coastal regions, and for road expansion, the conventional MSE wall can be modified by adjusting the length of reinforcement to conform the construction area. For narrow geosynthetic reinforced soil (GRS) wall, the modification and arrangement of reinforcement components, including reinforcement tensile strength, vertical spacing, and aspect ratio, play key roles in the behavior of reinforced earth walls and can also lead to differences in the distribution of lateral earth pressure compared with conventional MSE walls. In this study, a series of geotechnical centrifuge tests are conducted to clarify the failure behaviors, distribution of lateral earth pressure, and deformation progresses of narrow GRS walls. Among the investigated variants, it is verified that improved reinforcement strength leads to a significant decrease in horizontal wall displacement. The relationship among lateral earth pressure, zero-earth-pressure zone, and horizontal displacement can be applied to predict the deformation of a narrow GRS wall.

Risk assessment method of gas explosion based on quantification of margins and uncertainties (QMU):a case study on beam structures in buildings

Combustible gas explosions are common accidents in residential areas. Key building structural components, such as beams, slabs and columns, can be quickly damaged and destroyed by explosive overpressure loads, which may also result in continual collapse. Risk of interior gas explosions in buildings should be assessed to analyze the ability of structures to withstand disasters, which can also offer a theoretical basis for improving the structural design and construction of buildings. In this study, reinforced concrete beams in buildings were selected as the research object, and the risks to beam structures under mixed methane and air explosions were assessed using the quantification of margins and uncertainties (QMU) method. First, the uncertainty of the existing methods to calculate gas explosion and beam bending loads was analyzed. Through an influence regularity analysis, the expansion factor of combustible gas combustion products in enclosed explosion chamber, the initial density of the gas mixture in the explosion chamber before deflagration, the compressive strength of concrete, and the tensile strength of reinforcement were selected as the key uncertainty parameters. Furthermore, the Monte Carlo method was used to create 5000 samples of the selected uncertainty parameters, and statistical analysis was conducted to obtain the probability distribution of the gas explosion overpressure load and reinforced concrete beam bending load. Based on the sampling results, the beam structure’s safety margin and uncertainty analysis were analyzed to determine the probability of structural failure at the 90% confidence level. Finally, this paper provides guidelines for determining structural failure under different boundary value conditions of combustion explosion overpressure loads and reveals the sensitivity of different uncertainty parameters to structural safety margins using stepwise regression analysis. Compared to previous methods, this work includes the uncertainty features of disasters and disaster-bearing items when analyzing combustible gas explosion accidents; we anticipate it offers a fresh perspective on the quantitative assessment of gas explosion risks in buildings.

Seismic probabilistic risk estimation of Japanese railway embankments and risk-based design strength of soil and reinforcement

For the rational seismic design of railway embankments considering seismic risk, high-strength geomaterials and reinforcements should be used in areas with high seismic probability, and low-strength geomaterials and reinforcements should be used in areas with low seismic probability. In this study, a seismic probabilistic risk estimation of Japanese railway embankments was conducted using publicly available information on seismic hazards in Japan and previously estimated seismic-fragility curves for Japanese railway embankments. To determine the required average friction angle of backfill soil and average reinforcement tensile strength for satisfying the prescribed allowable seismic risk, a sensitivity analysis of the railway embankment was conducted by changing the average friction angle of the backfill soil and the average reinforcement tensile strength. Using the sensitivity-analysis results, the required average friction angle of the backfill soil and average reinforcement tensile strength of the railway embankment satisfying the prescribed allowable seismic risk considering the occurrence probability of earthquakes were analytically obtained.

Shear Strength Model for Reinforced Concrete Corner Joints Based on Soft Computing Techniques

The shear strength of cyclically loaded RC corner joints, resulting in opening and closing moments, has not been extensively studied. In addition, experimental studies of the joint shear strength are time-consuming and expensive. Therefore, to overcome this challenge, two separate gene expression programming (GEP) based empirical models are developed for the shear strength of the corner joints, one under the opening moment and the other under the closing moments. One of the key parameters overlooked in previous studies is the joint shear reinforcement, which has been incorporated in the GEP models. These models are developed by compiling an experimental database of 59 specimens in terms of the concrete compressive strength, the joint aspect ratio, the reinforcement tensile strength, and the reinforcement compressive strength. A detailed statistical study is undertaken that indicates superior accuracy of the proposed models and a high potential for their application in the design practice.

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.

Numerical investigation of the interaction of back-to-back MSE walls

This paper presents a numerical investigation of the interaction of back-to-back mechanically stabilized earth (MSE) walls under static loading. The numerical model was validated using measurements from instrumented field back-to-back MSE walls. A parametric study was then conducted to investigate the effects of horizontal distance between the MSE walls, soil friction angle, and wall height on the interaction of back-to-back MSE walls. Maximum facing displacement, lateral soil thrust behind reinforced soil zone, and required reinforcement tensile force generally increase nonlinearly with increasing horizontal distance up to a certain critical value, and the effects of interaction between back-to-back MSE walls are stronger for lower friction angle and higher wall. The critical horizontal distances for different soil friction angles and wall heights are generally close to the theoretical Federal Highway Administration (FHWA) values for the full active failure wedge to be developed and could be approximated as 0.5. The FHWA method significantly underestimates the lateral soil thrusts for the range of horizontal distances involving interaction between back-to-back MSE walls but significantly overestimates the required reinforcement tensile strengths. Design recommendations on lateral soil thrust and required reinforcement tensile strength calculations that account for the interaction between back-to-back MSE walls are provided.

Study on stability of reinforced soil slope based on upper limit method

Based on the nonlinear Mohr-Coulomb failure criterion, the upper bound method of limit analysis is used to investigate slope stability by introducing new strength parameters ct and φt. It is assumed that the potential weak zone in the soil layer is a straight line, so the straight line fracture surface is used to study the non-reinforced soil and reinforced soil in this study, and the expression of the stability coefficient Ns of the non-reinforced soil slope is derived. In addition, the calculation equations of the safety factor F, the ultimate slope height H, and the ultimate slope height H of the reinforced soil slope are also derived. The CVX toolbox developed by Stanford University and a MATLAB program developed by the authors are used for illustrations, and good results are obtained. The relationship between the nonlinear parameter m and the limit slope height H, the included angle θ, the new strength parameter φt, the slope stability coefficient Ns, the relationship between the slope angle β and the safety factor F, and the relationship between different reinforcement tensile strength Kt and the limit slope height H are summarized.

Experimental and Numerical Investigation of Load Bearing Capacity of Thinned End Precast Purlin Beams and Solution Proposals

Türkiye’de inşaat sektörü 1960’lı yılların sonu itibari ile beton prefabrikasyon ile tanışmıştır. Prefabrike olarak üretilen yapılar seri üretimlerinin ve montajlarının hızlı olmasından dolayı özellikle sanayi yapılarında daha fazla tercih edilmişlerdir. Bu yapı türünün en büyük dezavantajı özellikle mafsallı birleşim bölgelerinde oluşan hasarlardır. Çatı kirişleri ile aşık kirişlerinin birleştiği bölgelerde de bağlantı genellikle mafsallı olarak gerçekleştirilir. Bundan dolayı mesnet bölgelerinde teorik olarak moment oluşmamakta ve bu tip kirişlerin kesit tesirleri basit mesnetli kirişlerde olduğu gibi hesaplanmaktadır. Ancak aşık inceltilmiş uç bölgelerinde yoğunlaşan kesme kuvveti, kesme gerilmelerinin artmasına neden olduğundan bu bölgenin detaylandırılması için bir takım özel tasarım kuralları ilgili standartlarda yer almıştır. Bu birleşim bölgelerinde özellikle etkili ve uzun süreli kar yağışlarından sonra çatıda biriken yoğun kar neticesinde hasarlar gözlemlenmektedir. Bu hasarlar nispeten daha eski prefabrike yapı stokunda bulunanlar başta olmak üzere inceltilmiş uçlu aşık kirişleri için önemli bir risk oluşturmaktadır. Bu çalışmada, şimdiye kadar kapsamlı olarak araştırılmamış olan inceltilmiş uçlu aşıkların düşey yük etkisi altında davranışları, aşıkların değişen mekanik parametrelerine göre deneysel ve numerik olarak incelenmiştir. İlk olarak yürürlükteki standartlara uygun olan ve olmayan iki adet aşık kirişinin deneyleri gerçekleştirilmiştir. Ardından yine standarda uygun bir adet aşık kiriş inceltilmiş uç hasarının önlenlenmesi amacıyla CFRP ile güçlendirilerek test edilmiştir. Daha sonra ABAQUS programıyla modellenen aşıklardan elde edilen sonuçlar ile deneysel çalışma sonuçları ile doğrulanmıştır. Tüm deneysel sonuçlarla numerik modelleme sonuçlarının oldukça yakın olduğu görülmüştür. Numerik model numunelerinde gözlenen hasarlar ile deneylerde oluşan hasarların benzer olması yeni parametrik çalışmalarda numerik modellerin kullanılabileceğini göstermiştir. Doğrulamanın ardından aşıkların mekanik özellikleri ile güçlendirme alternatiflerine bağlı bir dizi parametrik çalışma numerik olarak gerçekleştirilmiştir. Parametrik çalışmada; özellikle mevcut aşıklarda beton basınç dayanımı, donatı çekme dayanımı ve aşık kirişlerin üretiminde kullanılan öngerme seviyesinin tasarlanandan farklı olabileceği düşüncesiyle bir parametre olarak değerlendirilmiştir. Ayrıca karbon elyaf takviyeli polimer (CFRP) kumaş ile güçlendirilen ve yönetmeliğe göre tasarlanmayan aşıkların davranışı da yine parametrik çalışma kısmında incelenmiştir. Parametrik çalışmanın sonuçlarına göre beton basınç dayanımı daha etkin olmakla beraber beton ve çelik dayanımının artışı ile kesme kapasitesinde önemli ölçüde artış sağlandığı görülmüştür. Elde edilen sonuçlarda öngerme değeri artışının kapasiteye hatırı sayılır bir etki sağlamadığı görülmüştür. CFRP ile güçlendirilen numunelerde aşığın yük taşıma kapasitesinin %50’ye arttığı ve hasarın inceltilmiş uç bölgesi dışına kaydığı (inceltilmemiş bölgeye) görülmüştür. Parametrik çalışma ile farklı ve uygulanabilir CFRP alternatifleri de modellenerek en iyi güçlendirme alternatifi önerildi. Bununla beraber inceltilmiş uçlu aşıkların donatı tasarımına esas bazı öneriler getirilmiştir.

The Determination of Pullout Parameters for Sand with a Geogrid

The concept of designing mechanically stabilized earth (MSE) walls is divided into internal and external stability review methods, and one of the design factors required in internal stability analysis is the frictional characteristics between soil and geogrids for civil engineering applications. Typical methods for evaluating the frictional characteristics between soil and geogrids include the direct shear test and pullout test. It is desirable to apply the pullout test to geogrid reinforcements for pulling out geogrids embedded in soil, to measure both the surface-frictional force and passive resistance at the same time. Pullout parameters can be significantly affected by confining the stress and tensile strength of reinforcements. In general, the pullout parameters tend to be overestimated for low confining stresses in the pullout test, and underestimated for high confining stresses. Therefore, to address these issues, this study aims to evaluate the influence of the confining stress and the tensile strength of a geogrid reinforcement in the pullout test, and to propose a reasonable method for obtaining practical pullout parameters. Based on the pullout tests, the maximum pullout force depending on the tensile strength of the geogrid reinforcement was measured for one-third of the reinforcement tensile strength, and it was ruptured when pullout force greater than the maximum pullout force was exerted. Furthermore, it was observed that, in the reinforcement pullout test, pullout force was measured in the whole area of the reinforcement at a confining stress smaller than one-half of the tensile strength of the grid. As a result, the effective confining stress method considering only the confining stress at which the reinforcement is fully pulled out to develop the pullout characteristics can be a practical method for obtaining pullout parameters without regard to the reinforcement tensile strength.

Design Theory and Method of Geo-Synthetic Reinforced Soil Retaining Wall Combined with a Gravity Retaining Wall or Full Height Rigid Facing

Geo-synthetic reinforced soil retaining wall (GRS-RW) combined with a Gravity Retaining wall (GRW) facing or Full High Rigid (FHR) facing is a new type of retaining wall. This type of retaining wall is used to get full advantages of GRW and reinforced soil retaining wall (RS-RW) and to avoid their drawbacks. The design method based on the principle of working strain considers the backfill in the limit state but the reinforcement not in the limit state; while in traditional design method based on the tensile strength of reinforcement, consider both backfill and reinforcements in the limit state and it cannot reflect the influence of reinforcement stiffness. In this paper, numerical analyses were performed to evaluate the stress and strain of both reinforcement and backfill. From the analyses, deformation of the retaining wall, the working performance of GRS-RW with GRW facing, and contribution of geo-grids to GRS-RW with a GRW facing, were evaluated. Analyses are performed for determining the force between GRS-RW with a GRW facing and reinforced soil. Analytical methods, for the calculation of soil pressure acting on the back of GRW, based on the principle of working stress are obtained by comparative analysis between the working performance characteristics of common GRS-RW and GRS-RW with GRW facing. A new analytical method for determining the force between GRS-RW with a GRW facing and reinforced soil “E” is proposed. By comparative study between theoretical and numerical analysis results, method 1 and method 2 are recommended for determining the “E”. A method for determining the tension in the reinforcement of GRS-RW with a GRW facing based on the principle of working strain is also presented in this paper.

Bearing capacity and failure mechanisms of two-tiered reinforced soil retaining walls under footing load

The paper presents a numerical modeling study on the bearing capacity of two-tiered reinforced soil retaining walls. Numerical simulations are carried out using the finite element limit analysis (FELA) method, which is validated against results from model tests and other numerical simulation studies. Parametric analyses are carried out to examine the influences that footing location and width, upper wall setback, and reinforcement properties could have on the bearing capacity of two-tiered reinforced soil retaining walls. Results indicate that the variation of bearing capacity with footing distance from the facing is humped-shaped when the footing is located directly above the reinforced zone; the influences of upper wall setback and reinforcement length on bearing capacity diminish with the height of upper wall; and, the bearing capacity of the footing when placed near the wall facing can depend on the ratio of the reinforcement tensile strength values used in the two tiers of the wall. These findings are explained in conjunction with the geometries of slip planes observed in the numerical models.

The pull-out test on knit bamboo reinforcement embedded into concrete beam

The pull-out test is generally conducted to obtain accurately the carrying capacity of the flexural strength of the knit bamboo reinforced concrete beam, which is more determined by the bonding strength than the tensile strength of reinforcement in concrete. Bamboo bar with braid knit which was coated with sikadur as bonding agent based on selected epoxy resin was expected to improve a good friction with concrete. In the pull-out test method, a hydraulic jack was applied to encourage bamboo embedded into a pair of concrete blocks, whose size was 15cm x 30cm x 40cm. The experimental variable of specimens were types of knitted bamboo, and type of coating. Based on the test results, either the bond strength or the tensile strength, which was calculated based on the failure mechanism, increased with respect to the concrete quality. The compressive strength of concrete was averaged as much as 25,97 MPa. The usage of outer skin surface on the cutting braid knit bamboo (type 1), which was coated with sikadur experimentally could increase the pull-out load. In the pull-out test, bond failure occurred with using of the plain bamboo bar with the bond stress of 1.18 MPa, while tensile failure occurred with using of knit bar type 1 with peak tensile strength of 85.84 Mpa.

Enhancement of soil–geogrid interactions in direct shear mode using attached elements as anchors

Soil reinforcement employing geosynthetics is significantly influenced by interactions which are governed by friction and adhesion at interface. To enhance interactions at soil–geogrid interface under direct shear conditions, effects of attaching elements as anchors to reinforcement has been evaluated. A well and poorly graded sand, one geogrid type, anchors with three different size and clamping lengths of 2, 4 and 6 cm from shear surface were used. Samples were prepared with a relative density of 80% and tested dry under normal pressures of 12.5, 25 and 50 kPa using large direct shear test. Factors investigated included soil grading and particle size, anchor size and anchorage length together with normal pressures. Results shows by attachment of anchors to upper geogrid surface, shear resistance to failure is significantly enhanced with increase in normal pressure and anchor size. This is attributed to soil-anchor friction at interfaces, mobilisation of soil passive resistance in front of anchors and tensile strength of reinforcement. Non-uniform sand having larger and angular particles resulted in more effective interactions with geogrid and anchors at interfaces and resulted in greater resistance to shear failure under direct shear loading. Soil particle size and anchorage length were found to be less influential factors on soil–geogrid interactions.

Assessment of reinforced embankment stability over soft soils based on monitoring results

The stability of a reinforced embankment relies on the contribution of the soil shear strength as well as the reinforcement tensile strength. Typical geotechnical monitoring programmes implemented during construction focus on the deformation of foundation soils without quantifying the contribution of the reinforcement. Therefore, the collected information does not provide a direct indication of the stability of the reinforced embankment. This paper presents a semi-empirical method to assess the stability during construction of a reinforced embankment constructed over soft ground. A finite-element model was used to analyse the stability of a 20 m high, 2.4 km long reinforced embankment being constructed over soft dredge/alluvium. The finite-element model was used to evaluate the process of how the reinforcement tensile strength and foundation shear strength are mobilised during the course of construction and to study the potential correlations between the degree of mobilisation for soil shear strength and monitoring results. The analyses show that the ratio of maximum lateral displacement (δ) to embankment settlement (S) can be used to assess the degree of shear strength mobilised in the foundation soils.

Deterministic and probabilistic failure analysis of simple geosynthetic reinforced soil slopes

Reinforced slopes with horizontal layers of geosynthetic reinforcement can have different mechanisms of failure. In this paper two major mechanisms of failure of reinforced slopes are investigated. External mechanisms occur when the critical slip surface passes beyond the reinforced zone. Internal mechanisms are characterised by failure surfaces that intersect all of the reinforcement layers. For a target value of the factor of safety and a specific value of the reinforcement length, there is a minimum value of the reinforcement tensile strength that will generate only external mechanism types. For greater reinforcement strength values, there is no change in the mechanism of failure and the value of the factor of safety. On the other hand, increasing the minimum reinforcement length, while keeping the reinforcement tensile strength equal to or less than the minimum value obtained for an external failure mechanism, will generate an internal mechanism type with the same mean value of factor of safety. In this study, probabilistic slope stability analysis of these two mechanisms is carried out using Monte Carlo simulation of slopes with different purely frictional and cohesive-frictional (c − ϕ) soils and different slope angles. Margins of safety are expressed in terms of a conventional factor of safety and in terms of maximum probability of failure. Cross correlation between soil strength parameters is also considered in this paper. It is shown that considering practical values of cross correlation coefficient reduces the maximum probability of failure for both internal and external failure mechanisms.

A Multiple Regression Equation for Prediction of Bearing Capacity of Geosynthetic Reinforced Sand Beds

Several researchers have studied the effects of various important parameters like number of layers of reinforcement (N), depth of the upper most layer of reinforcement from the base of the footing (u), spacing of the reinforcement layers (h), width of reinforcement layer (b), tensile strength of reinforcement (T) and density of soil (γ) on the ultimate bearing capacity of footings on reinforced soils. However, very few of them have attempted to develop equations to estimate the bearing capacity of the footings on reinforced soils by considering all the above parameters. Review of the existing state of the art in this area is presented in this paper and the ability of the existing analytical models to predict the ultimate bearing capacity of reinforced sand beds is verified using results from laboratory model tests. A multiple regression equation to estimate the ultimate bearing capacity of square footing resting on geosynthetic reinforced sand beds based on the laboratory model studies is presented. This equation is verified against the experimental results of model studies and also with the experimental measurements of other researchers. Statistical analysis of the model test data revealed that the aperture size of the reinforcement is very influential in altering the bearing capacity of reinforced sand beds. The regression equation developed in this study is reasonably good in predicting the bearing capacity of square footing on dense sand reinforced with planar geosynthetics.

Pseudo Static Seismic Stability Analysis of Reinforced Soil Structures

The paper pertains to the pseudo-static seismic stability analysis of reinforced soil structures. Using limit equilibrium method and assuming the failure surface to be logarithmic spiral, analysis has been conducted to maintain internal stability against both tensile and pullout failure of the reinforcements. The external stability of the reinforced earth wall is also assessed in terms of its sliding, overturning, eccentricity and bearing modes of failure. The influence of the intensity of the surcharge load placed on the backfill is also considered in the analysis. The obtained results are validated by comparing the same with those reported in literature. Studies have also been made regarding the influence of backfill soil friction angle, horizontal and vertical seismic accelerations, surcharge load, the tensile strength of reinforcement, pullout length of the reinforcement and number of reinforcement layers on the seismic stability against various failure modes as mentioned earlier.

Reinforcement design for construction of cover soil over soft sludge

This paper presents a design procedure for selecting the reinforcement tensile strength and strain that are required for the construction of cover soils over soft low-permeability sludge using the ‘finger fill soil placement technique’, which consists in placing a high-strength reinforcement over the soft, low-permeability sludge and building parallel narrow berms over the reinforcement. The design procedure described in this paper: (1) considers the proposed construction sequence; (2) takes advantage of the ability of the high-strength reinforcement to withstand tensile stresses; and (3) considers the large vertical displacement due to the applied load. The proposed design procedure allows the design engineer to select the reinforcement characteristics as well as the initial berm thickness and spacing.