Out-of-Plane Flexural Performance of GFRP-Reinforced Masonry Walls

The objective of this paper is to assess the out-of-plane flexural performance of masonry walls that are reinforced with glass fiber-reinforced polymers (GFRPs) rods, as an alternative for steel rebars. Eight 1?m×3?m full-scale walls were constructed using hollow concrete masonry units and tested in four-point bending with an effective span of 2.4 m between the supports. The walls were tested when subjected to increasing monotonic loads up to failure. The applied loads would represent out-of-plane loads arising from wind, soil pressure, or inertia force during earthquakes. One wall is unreinforced; another wall is reinforced with customary steel rebars; and the other six walls are reinforced with different amounts of GFRP reinforcement. Two of the GFRP-reinforced walls were grouted only in the cells where the rods were placed to investigate the effect of grouting the empty cells. The force-deformation relationship of the walls and the associated strains in the reinforcement were monitored throughout the tests. The relative performance of different walls is assessed to quantify the effect of different design variables. The range of GFRP reinforcement ratios covered in the experiments was used to propose a capacity diagram for the design of FRP-reinforced masonry walls similar to that of reinforced concrete elements.     

Predicted Loads in Steel Reinforced Soil Walls Using the AASHTO Simplified Method

The paper investigates the accuracy of the AASHTO simplified method by using load measurements reported in a large database of full-scale instrumented walls for bar mat, welded wire, and steel strip soil reinforced walls. The accuracy of the AASHTO simplified method is quantified by computing the mean and coefficient of variation of the ratio (bias) of measured loads under operational conditions to predicted loads. The paper shows that for steel strip walls, the AASHTO simplified method is reasonably accurate for granular backfill soils with friction angles less than 45°. For bar mat walls, the method is demonstrated to be slightly conservative. The simplified method underpredicts reinforcement loads at shallow overburden depths for steel strip walls with backfill friction angles greater than 45° due to compaction-related effects. It is concluded that these compaction-induced loads near the wall top do not contribute to internal instability due to pullout.     

Long-Term Reinforcement Load of Geosynthetic-Reinforced Soil Retaining Walls

As increasing number of geosynthetic-reinforced soil (GRS) retaining walls are built for permanent purpose, and their long-term behaviors have become one of the most critical issues in design. However, there has been very limited study on long-term reinforcement load and its relation to various parameters of GRS walls. A finite-element procedure for the long-term response of geosynthetic-reinforced soil structures with granular backfills was first validated against the long-term model test. Extensive finite-element analyses considering the viscous properties of geosynthetic reinforcements were then carried out to investigate the load distributions in geosynthetic reinforcements of GRS walls under operational condition. Construction sequence was simulated and a creep analysis of 10?years was subsequently conducted on each model wall. The effects of wall parameters, including backfill soil, reinforcement length, reinforcement spacing, reinforcement stiffness, and creep rate of reinforcement were investigated. It is found from the analyses that: (1) the maximum reinforcement load of GRS walls under working stress condition was generally smaller than that estimated using the FHwA design but it is dependent on the global reinforcement stiffness Sglobal; (2) the surface of maximum reinforcement load did not coincide with the Rankine’s surface suggested by FHwA design guidelines for vertical GRS walls and it was affected by the strength of backfill soil, reinforcement length, reinforcement spacing, and reinforcement stiffness; (3) for GRS walls under operational condition, reinforcement loads were closely related to the mobilized stiffness of backfill soil; (4) isochrone curves can be used to interpret the effects of reinforcement stiffness and creep rate on both short-term and long-term performances of GRS walls under operational condition, and with an increase in the reinforcement stiffness, the maximum reinforcement load increased; and (5) the global reinforcement stiffness Sglobal, which is related to the isochrones stiffness of reinforcement as well as reinforcement spacing was related to the total reinforcement load Ttotalmax and with an increase in the global stiffness, the total reinforcement load increased.     

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.     

Numerical Study of Reinforced Soil Segmental Walls Using Three Different Constitutive Soil Models

A numerical finite-difference method (FLAC) model was used to investigate the influence of constitutive soil model on predicted response of two full-scale reinforced soil walls during construction and surcharge loading. One wall was reinforced with a relatively extensible polymeric geogrid and the other with a relatively stiff welded wire mesh. The backfill sand was modeled using three different constitutive soil models varying as follows with respect to increasing complexity: linear elastic-plastic Mohr-Coulomb, modified Duncan-Chang hyperbolic model, and Lade’s single hardening model. Calculated results were compared against toe footing loads, foundation pressures, facing displacements, connection loads, and reinforcement strains. In general, predictions were within measurement accuracy for the end-of-construction and surcharge load levels corresponding to working stress conditions. However, the modified Duncan-Chang model which explicitly considers plane strain boundary conditions is a good compromise between prediction accuracy and availability of parameters from conventional triaxial compression testing. The results of this investigation give confidence that numerical FLAC models using this simple soil constitutive model are adequate to predict the performance of reinforced soil walls under typical operational conditions provided that the soil reinforcement, interfaces, boundaries, construction sequence, and soil compaction are modeled correctly. Further improvement of predictions using more sophisticated soil models is not guaranteed.     

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.     

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.     

Allowable Bearing Pressures of Bridge Sills on GRS Abutments with Flexible Facing

Compared to geosynthetic-reinforced soil (GRS) retaining walls, GRS abutment walls are generally subjected to much greater intensity surface loads that are fairly close to the wall face. A major issue with the design of GRS abutments is the allowable bearing pressure of the bridge sill on the abutments. The allowable bearing pressure of a bridge sill over reinforced soil retaining walls has been limited to 200?kPa in the current NHI and Demo 82 design guidelines. A study was undertaken to investigate the allowable bearing pressures of bridge sills over GRS abutments with flexible facing. The study was conducted by the finite element method of analysis. The capability of the finite element computer code for analyzing the performance of GRS bridge abutments with modular block facing has been evaluated extensively prior to this study. A series of finite element analyses were carried out to examine the effect of sill type, sill width, soil stiffness/strength, reinforcement spacing, and foundation stiffness on the load-carrying capacity of GRS abutment sills. Based on the results of the analytical study, allowable bearing pressures of GRS abutments were determined based on two performance criteria: A limiting displacement criterion and a limiting shear strain criterion, as well as the writers’ experiences with GRS walls and abutments. In addition, a recommended design procedure for determining the allowable bearing pressure is provided.     

Cyclic Flexure Tests of Masonry Walls Reinforced with Glass Fiber Reinforced Polymer Sheets

The research work reported here investigates the out-of-plane flexural behavior of masonry walls reinforced externally with glass fiber reinforced polymer (GFRP) sheets and subjected to cyclic loading. A full-scale test program consisting of eight wall specimens was conducted. Nine tests were performed, in which three parameters were studied. These included the level of compressive axial load, amount of internal steel reinforcement, and amount of externally bonded GFRP sheet reinforcement. Of the three parameters studied, varying the amount of GFRP sheets was the only parameter that significantly affected the behavior of the walls. The GFRP sheet reinforcement governed the linear response of the bending moment versus centerline deflection hysteresis. Increasing or decreasing the amount of GFRP sheet reinforcement either increased or decreased both the wall stiffness and the ultimate strength, respectively. Except for visible cracks, the walls maintained their structural integrity throughout the out-of-plane cyclic loading. The unloading/reloading paths for successive loading cycles were similar, indicating little degradation. Thus, the general behavior of the walls was very predictable. The system, therefore, could be used to advantageously rehabilitate older masonry structures that are inadequately reinforced to withstand seismic events. A simple model of the behavior is also presented to allow for the evaluation of the strength and deformation characteristics of these elements.     

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.     

Out-of-Plane Strengthening of Masonry Walls with Reinforced Composites

This paper presents an investigation into the effectiveness of using fiber-reinforced composite overlays to strengthen existing unreinforced masonry walls to resist out-of-plane static loads. A total of fifteen wall panels [1,200 × 1,800 × 200 mm (4 ft × 6 ft × 8 in.)] were tested. Twelve panels were assembled with fiber-reinforcing systems attached to the tension side, and the remaining three control walls were left without any external reinforcement. Two configurations of external reinforcement were evaluated. The first reinforcement configuration consisted of two layers of fiber-reinforced plastic webbing and the second consisted of vertical and horizontal bands of undirectional fiber composites. The three wall specimens without external reinforcement were tested to evaluate the change in the system strength and behavior with application of the external reinforcing systems. In addition to the two fiber configurations, the testing program also evaluated two methods of surface preparation of the walls, sand blasting, and wire brush. All specimens were thoroughly washed by water jet, 48 hours prior to application of the fiber-reinforcing systems. Three specimens were tested for each variable. A uniformly distributed lateral load was applied to each panel using the procedures described in the ASTM Standard E-72 Test Method (airbag). Failure loads, strains in the external reinforcement (FRP), out-of-plane deformations, and failure modes were recorded. Recommendations on the usefulness of the proposed technique as a means of strengthening masonry walls for out-of-plane loads are presented. In general, flexural strength of masonry walls can be increased if the shear failure is controlled.     

General Analytical Framework for Design of Flexible Reinforced Earth Structures

Current design methods divide reinforced earth structures into walls and slopes by using an arbitrary face inclination of 70° as the boundary. The required maximum strength of reinforcement computed for reinforced walls are significantly higher than that computed for reinforced slopes even if the inclination is practically the same. Presented is a general analytical framework for design of flexible reinforced earth structures regardless of the slope face inclination. In fact, the framework is consistent for any structural geometry and any applicable slope stability analysis although, for demonstration purposes, the simple Culmann formulation is utilized for simple geometry with zero batter. Using an adequate slope stability formulation, the required tensile resistance of reinforcement for a given layout is calculated so as to produce the same prescribed factor of safety anywhere within the reinforced zone. That is, using the design shear strength of the soil, the required reinforcement resistance along each layer is computed to fully mobilize this shear strength for all possible slip surfaces. That is, a baseline solution is produced for an ideal long-term strength of reinforcement at any location. Consequently, the required strength of the connection between each reinforcement layer and the facing unit can also be determined. This connection strength, however, assumes small facing units with negligibly small shear and moment resistance. Parametric study is conducted to demonstrate the reasonableness of the presented framework. It is shown that the required tensile resistance and connection strength depend on factors such as: reinforcement length; intermediate reinforcement; percent coverage; and quality of fill. When compared with the current AASHTO design for walls, the required maximum long-term strength of the reinforcement as well as the required connection strength in the proposed approach are substantially smaller.     

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.     

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.     

Static Response of Reinforced Soil Retaining Walls with Nonuniform Reinforcement

The structural response of reinforced‐soil wall systems with more than one reinforcement type (nonuniform reinforcement) is investigated using a numerical approach. The selected reinforcement types and mechanical properties represent actual polyester geogrid and woven wire mesh products. The model walls are mainly of wrapped‐face type and have different reinforcement lengths, arrangements, and stiffness values. Additional wall models with tiered and vertical gabion facings are included for comparison purposes. The numerical simulation of wall models has been carried out using a finite difference‐based program and includes sequential construction of the wall and placement of reinforcement at uniform vertical spacing followed by a sloped surcharge. The wall lateral displacements and backcalculated lateral earth pressure coefficient behind the facing in all nonuniform reinforcement wall models show a clear dependence on relative stiffness values of reinforcement layers at different elevations. An equation is proposed that can be used to predict the maximum reinforcement load in nonuniform reinforced wrapped‐face walls of given backfill types and reinforcement configurations similar to those investigated in this study.     

Tests on Seismically Damaged Reinforced Concrete Walls Repaired and Strengthened Using Fiber-Reinforced Polymers

The behavior of six 1:2.5-scale reinforced concrete cantilever wall specimens having an aspect ratio of 1.5, tested to failure and subsequently repaired and strengthened using fiber-reinforced polymer (FRP) sheets is investigated. Specimens were first repaired by removing heavily cracked concrete, lap splicing the fractured steel bars by welding new short bars, placing new hoops and horizontal web reinforcement, and finally casting nonshrink high-strength repair mortar. The specimens were then strengthened using FRP sheets and strips, with a view to increasing flexural as well as shear strength and ductility. In addition to different arrangements of steel and FRP reinforcement in the walls, a key parameter was the way carbon-FRP strips added for flexural strengthening were anchored; steel plates and steel angles were used to this effect. Steel plates were anchored using U-shaped glass-FRP (GFRP) strips or bonded metal anchors. Test results have shown that by using FRP reinforcement, the flexural and shear strength of the specimens can be increased. From the anchorage systems tested, metal plates combined with FRP strips appear to be quite efficient. The effectiveness of the bonded metal anchors used was generally less than that of the combination of plates and GFRP strips. In all cases, final failure of the FRP anchorage is brittle, but only occurs after the peak strength is attained and typically follows the fracture of steel reinforcement in critical areas, hence the overall behavior of the strengthened walls is moderately ductile.     

Does the Use of FRP Reinforcement Change the One-Way Shear Behavior of Reinforced Concrete Slabs?

For members with no transverse reinforcement, numerous models have been proposed for determining shear capacity, most often based on a statistical curve fit to experimental beam test results. The shear provisions of the Canadian code (CSA) for steel-reinforced concrete, by contrast, are based on a theoretical model, the modified compression field theory. This paper demonstrates that the CSA shear provisions for steel-reinforced members can be safely applied to members with internal fiber-reinforced polymer (FRP) bars by adjusting the term EsAs in the method to ErAr. A database of 146 shear failures of specimens reinforced with carbon, glass, or aramid FRP or steel is presented and gives an average test to predicted ratio of 1.38 with a coefficient of variation (COV) of 17.2%. The CSA code equations were optimized for the typical strain range of steel-reinforced concrete and when an equation appropriate for the wider range of strains associated with FRP is used, then a better statistical result can be achieved. Application of this expression to the database resulted in an average test to predicted strength ratio of 1.15 with a COV of 14.9%. As both methods are based on a theoretical shear model that was derived for steel-reinforced concrete and since both methods work safely, it can be concluded that the use of internal FRP bars does not change the one-way shear behavior of reinforced concrete beams and slabs without stirrups.     

Reliability-Based Design for Internal Stability of Mechanically Stabilized Earth Walls

A parametric study was conducted using Monte Carlo simulation to assess how uncertainty in design parameters affects the probability of internal failure of mechanically stabilized earth (MSE) walls. Bishop’s simplified method was used to conduct the internal stability analyses. The results of the analyses indicate that the mean and coefficient of variation of the backfill friction angle, mean and coefficient of variation of the tensile strength of reinforcement, mean unit weight of the backfill, mean surcharge, mean reinforcement vertical spacing, and mean reinforcement length have a significant effect on the probability of internal failure of MSE walls. Based on the results of the parametric study, a series of additional simulations were conducted where the significant parameters were varied over a broad range. The results of these simulations were used to develop a set of reliability-based design (RBD) charts for internal stability of MSE walls. A method to adapt these charts to address model bias and model uncertainty is also presented. A MSE wall was designed using the RBD method and two other deterministic design methods. The required tensile strength of the reinforcement obtained from the RBD method fell between the strengths determined from the deterministic methods.     

Analyzing the Reinforcement Loads of Geosynthetic-Reinforced Soil Walls Subject to Seismic Loading during the Service Life

It is more rational to analyze permanent geosynthetic reinforced soil (GRS) walls against seismic loading based on their behavior during service life, but it has seldom been attempted. Calibrated finite-element procedure was used to investigate the reinforcement loads of GRS walls subject to seismic loading during service life, the results of which were compared to those predicted by Federal Highway Administration (FHwA) guideline. Parametric studies were carried out to investigate the effects of various wall parameters and characteristics of earthquake excitations. It is found that due to the isotach behavior of geosynthetics, the reinforcement loads during earthquake that occurs 10 years after construction were similar to those if the earthquake occurs at the end of construction. The FHwA method predicted roughly the maximum reinforcement load but it could not consider strain softening of soil and characteristics of earthquakes. The horizontal locations of maximum reinforcement load in lower reinforcement layers were farther away from the facing units than Rankine’s surface, which is believed to come from the potential compound failure.     

Evaluation of Masonry Deep Beams Externally Strengthened with CFRP Sheets

In this study, carbon fiber-reinforced polymer (CFRP) sheets were examined as a means to strengthening existing masonry walls allowing for efficient creation of doors, windows, and passage openings. The research reported here deals with eight masonry walls made with concrete blocks, subjected to three-point quasistatic loading. The parameters examined include the reinforcement configuration and their amount. While CFRP sheets were used as external reinforcement, companion studies were carried out with conventional steel rebars. Test results indicate an increase of 180% in shear strength of the reinforced walls as compared to reference unreinforced walls. Load-deflection relationships indicate that the combined plain masonry and CFRP laminate system possessed some nonlinear deformability. The use of CFRP laminates on the walls was found to have an influence on the mode of failure. Anchoring the CFRP laminates at both support regions helped in using a larger portion of the strength of the laminates. The reinforced walls exhibited diagonal shear cracks that developed at a much slower rate and were ultimately accompanied by the peeling off of the CFRP laminates.