Required Unfactored Strength of Geosynthetic in Reinforced Earth Structures

Current reinforced earth structure designs arbitrarily distinguish between reinforced walls and slopes, that is, the batter of walls is 20° or less while in slopes it is larger than 20°. This has led to disjointed design methodologies where walls employ a lateral earth pressure approach and slopes utilize limit equilibrium analyses. The earth pressure approach used is either simplified (e.g., ignoring facing effects), approximated (e.g., considering facing effects only partially), or purely empirical. It results in selection of a geosynthetic with a long-term strength that is potentially overly conservative or, by virtue of ignoring statics, potentially unconservative. The limit equilibrium approach used in slopes deals explicitly with global equilibrium only; it is ambiguous about the load in individual layers. Presented is a simple limit equilibrium methodology to determine the unfactored global geosynthetic strength required to ensure sufficient internal stability in reinforced earth structures. This approach allows for seamless integration of the design methodologies for reinforced earth walls and slopes. The methodology that is developed accounts for the sliding resistance of the facing. The results are displayed in the form of dimensionless stability charts. Given the slope angle, the design frictional strength of the soil, and the toe resistance, the required global unfactored strength of the reinforcement can be determined using these charts. The global strength is then distributed among individual layers using three different assumed distribution functions. It is observed that, generally, the assumed distribution functions have secondary effects on the trace of the critical slip surface. The impact of the distribution function on the required global strength of reinforcement is minor and exists only when there is no toe resistance, when the slope tends to be vertical, or when the soil has low strength. Conversely, the impact of the distribution function on the maximum unfactored load in individual layers, a value which is typically used to select the geosynthetics, can result in doubling its required long-term strength.     

Geosynthetic Reinforced Multitiered Walls

Current design of mechanically stabilized earth (MSE) walls shows that the tensile stress in the reinforcement increases rapidly with height. To take advantage of both the aesthetics and the economics of MSE walls while considering high heights, multitiered walls are often used. In such walls, an offset between adjacent tiers is used. If the offset is large enough, the tensile stress in the reinforcement in lower tiers is reduced. However, a rational design methodology for multitiered MSE walls that accurately predicts wall performance is lacking. AASHTO 98 design guidelines are limited to two-tiered walls with zero batter. In fact, this design is purely empirical using “calibrated” lateral earth pressures adopted from limited guidelines developed for metallic strip walls. Empirical data available for multitiered walls is limited and it seems to be nonexistent for geosynthetic walls. In fact, generation of an extensive database for tiered walls is a major challenge since there are practically limitless configurations for such systems. As an alternative, this study presents the results of parametric studies conducted in parallel using two independent types of analyses: One is based on limiting equilibrium (LE) and one on continuum mechanics. The premise of this work is that if the two uncoupled analyses produce similar results, an acceptable level of confidence in the results can be afforded. This confidence stems from the fact that LE is currently being used for design of reinforced and unreinforced slopes (i.e., having a slope angle less than 70°); the agreement with continuum mechanics facilitates its extrapolation to use in MSE walls. Parametric studies were carried out to assess the required tensile strength as a function of reinforcement length and stiffness, offset distance, the fill and foundation strength, water, surcharge, and number of tiers. It is concluded that LE analyses may be extended to the analysis of multitiered walls.     

Case History of Geosynthetic Reinforced Segmental Retaining Wall Failure

A geosynthetic reinforced segmental retaining wall was collapsed during a monsoon season in Korea, three months after the completion of wall construction. The circular type global slope failure was the dominant failure mode. The as-built design was examined for its appropriateness in meeting the current design requirements and the global slope stability. A comprehensive stress-pore pressure-coupled finite-element analysis was additionally conducted with due consideration of both positive and negative pore pressures in saturated and unsaturated zones. A number of relevant tests were also carried out on the backfill and the reinforcement collected from the site. The investigation revealed among other things that the inappropriate design and the low-quality backfill were mainly responsible for the wall failure, although the primary triggering factor was the rainfall infiltration. The results of the stress-pore pressure-coupled finite-element analysis provided sound evidences as to the wall performance over the rainfall period, supporting the field observation. Practical implications of the findings from this study are also discussed in view of reinforced wall design.     

New Method for Prediction of Loads in Steel Reinforced Soil Walls

The paper describes a new working stress design methodology introduced by the writers for geosynthetic reinforced soil walls (K-Stiffness Method) that is now extended to steel reinforced soil walls. A large database of full-scale steel reinforced soil walls (a total of 20 fully instrumented wall sections) was used to develop the new design methodology. The effects of global wall stiffness, soil strength, reinforcement layer spacing, and wall height were investigated. Results of simple statistical analyses using the ratio of measured to predicted peak reinforcement loads (i.e., method bias) demonstrate the improved prediction accuracy. The AASHTO Simplified Method results in an average method bias of 1.1 with a coefficient of variation (COV) of 45%, whereas the proposed K-Stiffness Method results in an average bias of 0.95 and a COV of 32%. Soil strength was found to have limited influence on reinforcement loads for steel reinforced soil walls, especially for high shear strength soils, while global wall stiffness and wall height had a major influence on reinforcement loads.     

Finite-Element Simulations of Full-Scale Modular-Block Reinforced Soil Retaining Walls under Earthquake Loading

A finite-element procedure was used to simulate the dynamic behavior of four full-scale reinforced soil retaining walls subjected to earthquake loading. The experiments were conducted at a maximum horizontal acceleration of over 0.8 g, with two walls subjected to only horizontal accelerations and two other walls under simultaneous horizontal and vertical accelerations. The analyzes were conducted using advanced soil and geosynthetic models that were capable of simulating behavior under both monotonic and cyclic loadings. The soil behavior was modeled using a unified general plasticity model, which was developed based on the critical state concept and that considered the stress level effects over a wide range of densities using a single set of parameters. The geosynthetic model was based on the bounding surface concept and it considered the S-shape load-strain behavior of polymeric geogrids. In this paper, the calibrations of the models and details of finite-element analysis are presented. The time response of horizontal and vertical accelerations obtained from the analyses, as well as wall deformations and tensile force in geogrids, were compared with the experimental results. The comparisons showed that the finite-element results rendered satisfactory agreement with the shake table test results.     

Optimum Design for External Seismic Stability of Geosynthetic Reinforced Soil Walls: Reliability Based Approach

In this paper, an analytical study considering the effect of uncertainties in the seismic analysis of geosynthetic-reinforced soil (GRS) walls is presented. Using limit equilibrium method and assuming sliding wedge failure mechanism, analysis is conducted to evaluate the external stability of GRS walls when subjected to earthquake loads. Target reliability based approach is used to estimate the probability of failure in three modes of failure, viz., sliding, bearing, and eccentricity failure. The properties of reinforced backfill, retained backfill, foundation soil, and geosynthetic reinforcement are treated as random variables. In addition, the uncertainties associated with horizontal seismic acceleration and surcharge load acting on the wall are considered. The optimum length of reinforcement needed to maintain the stability against three modes of failure by targeting various component and system reliability indices is obtained. Studies have also been made to study the influence of various parameters on the seismic stability in three failure modes. The results are compared with those given by first-order second moment method and Monte Carlo simulation methods. In the illustrative example, external stability of the two walls, Gould and Valencia walls, subjected to Northridge earthquake is reexamined.     

Resultant Force of Lateral Earth Pressure in Unstable Slopes

Traditionally, resultant force of lateral earth pressure serves as the basis for design of nearly vertical walls. Conversely, slopes are designed to be internally stable using a factor of safety approach. However, with the availability of heavy facing elements such as gabions, steep slopes are increasingly being constructed. Steep slopes are considered to be unstable unless supported; that is, such slopes require facings to resist lateral earth pressure. Extending Coulomb’s formulation to such slopes may not be conservative as a planar slip surface may not be critical. Presented are the results of a formulation to find the resultant lateral force which utilizes a log spiral failure mechanism. Unlike Caquot and Kerisel or Coulomb, the soil-facing interface friction is assumed to act on segments of vertical surface only, thus replicating the geometry of stacked rectangular facing units. Given the batter, the backslope, the height, the interface friction, and the unit weight and design friction angle of the backfill, one can quickly determine the corresponding lateral earth pressure coefficient. Formulation assuming the interface friction is acting on an imaginary surface inclined at the batter angle, essentially equivalent to Coulomb and Caquot and Kerisel, is also presented. Its results show that for batters up to 20°, the common approach of using the Coulomb method, including the assumed interface friction direction to coincide with the batter, yields results that are quite close to those stemming from the log spiral analysis. Hence, use of Coulomb’s analysis for such small batters is reasonable as its formulation is simple. However, the lateral resultant is grossly underestimated for larger batters, especially when Coulomb analysis is used.     

Search for Critical Slip Surface in Slope Stability Analysis by Spline-Based GA Method

The stability of a soil slope is usually analyzed by limit equilibrium methods, in which the identification of the critical slip surface is of principal importance. In this study the spline curve in conjunction with a genetic algorithm is used to search the critical slip surface, and Spencer’s method is employed to calculate the factor of safety. Three examples are presented to illustrate the reliability and efficiency of the method. Slip surfaces defined by a series of straight lines are compared with those defined by spline curves, and the results indicate that use of spline curves renders better results for a given number of slip surface nodal points comparing with the approximation using straight line segments.     

Numerical Model for Reinforced Soil Segmental Walls under Surcharge Loading

The construction and surcharge loading response of four full-scale reinforced-soil segmental retaining walls is simulated using the program FLAC. The numerical model implementation is described and constitutive models for the component materials (i.e., modular block facing units, backfill, and four different reinforcement materials) are presented. The influence of backfill compaction and reinforcement type on end-of-construction and surcharge loading response is investigated. Predicted response features of each test wall are compared against measured boundary loads, wall displacements, and reinforcement strain values. Physical test measurements are unique in the literature because they include a careful estimate of the reliability of measured data. Predictions capture important qualitative features of each of the four walls and in many instances the quantitative predictions are within measurement accuracy. Where predictions are poor, explanations are provided. The comprehensive and high quality physical data reported in this paper and the lessons learned by the writers are of value to researchers engaged in the development of numerical models to extend the limited available database of physical data for reinforced soil wall response.     

Quasi-Three-Dimensional Slope Stability Analysis Method for General Sliding Bodies

A quasi-three-dimensional procedure has been developed for computing the stability of earth slopes and waste containment facilities along general slip surfaces. The procedure, termed the Resistance-Weighted procedure, is an extension of existing quasi-three-dimensional procedures, which utilize results from two-dimensional slope stability analyses to estimate three-dimensional stability. As a part of this procedure, a scheme has been developed for modeling realistic three-dimensional sites and efficiently generating input data for two-dimensional analyses. This scheme enables Resistance-Weighted calculations to be performed using existing commercial spreadsheet and two-dimensional slope stability software. The method can also be incorporated into existing two-dimensional slope stability software with relatively little development effort. The Resistance-Weighted procedure and geometric modeling scheme are presented in this paper. Application of the procedure to a case history and results of a series of analyses to validate the procedure are described. The results of the analyses show that the Resistance-Weighted procedure produces results that compare favorably with more rigorous three-dimensional procedures. Although the Resistance-Weighted procedure is approximate, it serves as a simple means for estimating the magnitude of three-dimensional effects when a more rigorous three-dimensional procedure is not available.     

Evaluation of Interslice Force Function and Discussion on Convergence in Slope Stability Analysis by the Lower Bound Method

The interslice force function f(x) is a major assumption of the limit equilibrium method, which is important but has not been adequately considered in the past. In this paper, f(x) is taken as the control variable, and the upper and lower limits of the factor of safety for a general slope will be determined by a global optimization analysis. Based on this approach, f(x) will be determined and investigated. We demonstrate that f(x) cannot be arbitrarily assigned if a set of acceptable internal forces is required. The present approach can be presented practically as a lower bound approach with the advantage that failure to converge is virtually eliminated, which is not possible with all other existing “rigorous” methods. The “present proposal” attempts to answer several important questions in the basic theory of slope stability analysis, and provides a f(x) based on the lower bound approach statically admissible forces throughout the whole failure zone. Currently, different assumptions will give different factors of safety to the same problem, and this situation will be overcome by the use of the present proposal. The present proposal is also proven to give a result equal to the slip line solution for a simple footing on clay which is not possible for other classical slope stability methods, which has demonstrated that the applicability of the “present proposal” for general difficult problems.     

Stability of Steep Slopes in Cemented Sands

The analysis of steep slope and cliff stability in variably cemented sands poses a significant practical challenge as routine analyses tend to underestimate the actually observed stability of existing slopes. The presented research evaluates how the degree of cementation controls the evolution of steep sand slopes and shows that the detailed slope geometry is important in determining the characteristics of the failure mode, which in turn, guide the selection of an appropriate stability analysis method. Detailed slope-profile cross sections derived from terrestrial lidar surveying of otherwise inaccessible cemented sand cliffs are used to investigate failure modes in weakly cemented [unconfined compressive strength (UCS)<30?kPa] and moderately cemented (30相似文献   

Parametric Studies on the Behavior of Reinforced Soil Retaining Walls under Earthquake Loading

The finite element procedures are extremely useful in gaining insights into the behavior of reinforced soil retaining walls. In this study, a validated finite element procedure was used for conducting a series of parametric studies on the behavior of reinforced soil walls under construction and subject to earthquake loading. The procedure utilized a nonlinear numerical algorithms that incorporated a generalized plasticity soil model and a bounding surface geosynthetic model. The reinforcement layouts, soil properties under monotonic and cyclic loadings, block interaction properties, and earthquake motions were among major variables of investigation. The performance of the wall was presented for the facing deformation and crest surface settlement, lateral earth pressure, tensile force in the reinforcement layers, and acceleration amplification. The effects of soil properties, earthquake motions, and reinforcement layouts are issues of major design concern under earthquake loading. The deformation, reinforcement force, and earth pressure increased drastically under earthquake loading compared to end of construction.     

On Global Equilibrium in Design of Geosynthetic Reinforced Walls

Common design of MSE walls is based on a lateral earth pressure approach. A key aspect in design is the determination of the reactive force in each reinforcement layer so as to maintain the system in equilibrium. This force leads to the selection of reinforcement with adequate long term strength. It is also used to calculate the pullout resistive length needed to ensure the capacity of each layer to develop strength. Lateral earth pressures used in design may or may not satisfy basic global equilibrium of the reinforced soil mass. Hence, the present work establishes a benchmark test using a simple statically determinate approach, in order to check if different design procedures satisfy equilibrium. Basic statics indicate that such a test is necessary, but not sufficient, to ascertain the validity of the calculated reactive force. Three existing design methods are examined: AASHTO, National Concrete Masonry Association, and Ko-stiffness. AASHTO, which is the simplest to apply and generally considered conservative, satisfies the benchmark test. However, it may yield very conservative results if one considers the facing to play a major role. NCMA is likely satisfactory if one explicitly accounts for the facing shear resistance in assessing the reaction in the reinforcement. The emerging Ko-stiffness approach, which is empirical, may violate statics potentially leading to underestimation of the reinforcement force.     

Centrifuge Model Studies of the Seismic Response of Reinforced Soil Slopes

Centrifuge tests were used to study the dynamic behavior of soil slopes reinforced with geosynthetics and metal grids. The main objectives were to determine the failure mechanism and amount of deformations under seismic loading and to identify the main parameters controlling seismically induced deformations. Geosynthetically reinforced soil slopes (2V:1H) and vertical walls reinforced with metallic mesh strips were subjected to earthquake motions with maximum foundation accelerations of up to 1.08g. The experimental results show that slope movement can occur under relatively small base accelerations, and significant lateral and vertical deformations can occur within the reinforced soil mass under strong shaking. However, no distinct failure surfaces were observed, and the magnitude of deformations is related to the backfill density, reinforcement stiffness and spacing, and slope inclination.     

New Approach to Limit Equilibrium and Reliability Analysis of Soil Nailed Walls

A new approach to the limit equilibrium method is developed and used for the analysis of soil nailed walls. The basic procedure of the new approach is to compute the interslice forces by recursion and to fulfill the equilibrium requirement for interslice forces of the last boundary slice by iteration. Reliability analysis for soil nailed walls is carried out by considering the cohesion and internal friction angle of soil as random variables. The degree of mobilization of friction resistance between the nails and surrounding soil is taken as a third random variable. A parametric study is carried out to study the effect of soil behavior and the arrangement pattern of nails on the factor of safety and reliability index. Finally, an optimization technique is employed to obtain the minimum cost design of soil nailed walls with an object function expressed by the total nail length, which is considered an appropriate measure of the total cost of a soil nailed wall.     

Reliability Analysis of Partial Safety Factor Design Method for Cantilever Retaining Walls in Granular Soils

Uncertainties in the geotechnical design variables and design equations have a significant impact on the safety of cantilever retaining walls. Traditionally, uncertainties in the geotechnical design are addressed by incorporating a conservative factor of safety in the analytical model. In this paper, a risk-based approach is adopted to assess the influence of the geotechnical variable and design equation uncertainties on the design of cantilever retaining walls in sand using the “partial factor of safety on shear strength” approach. A random model factor based on large-scale laboratory test data from the literature has been incorporated into the reliability analyses to quantify the uncertainty in the geotechnical calculation model. Analyses conducted using Monte Carlo simulation show that the same partial factor can have very different levels of risk depending on the degree of uncertainty of the mean value of the soil friction angle. Calibration studies show the partial factor necessary to achieve target probability values of 1 and 0.1%.     

Simplified Trial Wedge Method for Soil Nailed Wall Analysis

This paper presents a new approach that allows soil nailed walls to be analyzed using a trial wedge method. Most soil nailed wall analysis methods are rooted in traditional slope stability solutions with curvilinear or bilinear slip surfaces. This has led to limited access to these methods due to the cost of commercial software. In addition, there are at least two well-documented test walls brought to failure that indicated evidence of relatively steep, approximately linear slip surfaces instead of the more complex surfaces assumed by most software packages. The simplified trial wedge method is intended as a relatively simple and inexpensive method for preliminary or supplemental design calculations for soil nailed walls. The method stems from the existing Federal Highway Administration analysis guidelines. Procedures are outlined for implementing the trial wedge method using a spreadsheet-based approach. The method is applied to two test walls that were intentionally brought to failure, the Amherst Test Wall in clay, and the Clouterre Test Wall No. 1 in sand. In each case, the trial wedge analysis produces results consistent with the failure mode of the wall.     

Development and Validation of a Two-Phase Model for Reinforced Soil by Considering Nonlinear Behavior of Matrix

The paper presents the formulation of a two-phase system applied for reinforced soil media, which accounts for nonlinear behavior of matrix phase. In a two-phase material, the soil and inclusion are treated as two individual continuous media called matrix and reinforcement phases, respectively. The proposed algorithm is aimed to analyze the behavior of reinforced soil structures under operational condition focusing on geosynthetics-reinforced-soil (GRS) walls. The global behavior of such deformable structures is highly dependent to the soil behavior. By accounting for mechanical characteristics of the soil in GRS walls, a relatively simple soil model is introduced. The soil model is formulated in bounding surface plasticity framework. The inclusion is regarded as a tensile two-dimensional element, which owns a linear elastic-perfectly plastic behavior. Perfect bonding between phases is assumed in the algorithm. For validation of the proposed model, the behavior of several single element reinforced soil samples, containing horizontal and inclined inclusions, is simulated and the results are compared with experiment. It is shown that the model is accurately capable of predicting the behavior especially before peak shear strength. The proposed algorithm is then implemented in a numerical code and the behavior of a full-scale reinforced soil wall is simulated. The results of analysis are also reasonably well compared with those of experiment.     

Investigation of Load-Transfer Mechanisms in Geotechnical Earth Structures with Thin Fill Platforms Reinforced by Rigid Inclusions

The reinforcement of soft soils by rigid inclusions is a practical and economical technique for wide-span buildings and the foundations of embankments. This method consists of placing a granular layer at the top of the network of piles to reduce vertical load on the supporting soil and vertical settlement of the upper structure. The study focuses on the modeling of load-transfer mechanisms occurring in the reinforced structure located over the network of piles with a coupling between the finite-element method (geosynthetic sheets) and discrete element method (granular layer; concrete slab in some cases). The importance of granular layer thickness to increase load-transfer intensity and to reduce vertical settlement was observed. However, without a basal geosynthetic sheet, the compressibility of soft soil has a great influence on the mechanisms. A method predicting the intensity of load transfers was proposed, based on Carlsson’s solution. The main parameters concerned are the geometry of the work and the peak and residual friction angles of the granular layer.