Static Response of Reinforced Soil Retaining Walls with Nonuniform Reinforcement

Transcription

1 The International Journal of Geomechanics Volume 1, Number 4, (2001) Static Response of Reinforced Soil Retaining Walls with Nonuniform Reinforcement K. Hatami, R.J. Bathurst, and P. Di Pietro Received April 13, 2001 GeoEngineering Centre at Queen s-rmc, Department of Civil Engineering, Royal Military College of Canada, Kingston, Ontario, Canada GeoEngineering Centre at Queen s-rmc, Department of Civil Engineering, Royal Military College of Canada, Kingston, Ontario, Canada Maccaferri Gabions, Inc., Williamsport, Maryland, USA ABSTRACT. 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 wrappedface walls of given backfill types and reinforcement configurations similar to those investigated in this study. I. Introduction Reinforced soil retaining walls offer economic advantages over conventional retaining wall systems. The cost advantage of reinforced soil walls over conventional forms of retaining wall Key Words and Phrases. Numerical modeling, retaining walls, reinforced soil, geosynthetics, nonuniform reinforcement. Acknowledgements and Notes. The funding for this project was provided by research grants from the Natural Sciences and Engineering Research Council of Canada and Maccaferri Gabions, Inc. K. Hatami, corresponding author ASCE DOI: /(ASCE) (2001)1:4(477) ISSN

2 478 K. Hatami, R.J. Bathurst, and P. Di Pietro systems (e. g., gravity walls) increases with the height of the wall (Figure 1). The cost of reinforcement constitutes an important part of the total cost of a reinforced soil retaining wall and can be as great as about 25% of the cost of the wall, depending on the wall height, backfill type, and design loading conditions [2, 3]. This study addresses the possibility of further reducing the total cost of a reinforced soil wall by optimizing the use of more than one reinforcement type. FIGURE 1 Cost of different retaining wall types as a function of height (after Koerner et al. [1]). Notes: (1) MSE = Mechanically Stabilized Earth Walls; (2) Crib/bin walls are gravity wall structures formed by a soil mass confined by interlocking concrete, metal or timber elements. The reinforcement load in reinforced soil walls is commonly calculated from classic active earth pressure theory using the so-called contributory area approach [4, 5]. In this approach, the lateral earth pressure distribution from Rankine or Coulomb earth pressure theory is integrated over a distance equal to the spacing between reinforcement layers and the resultant load (demand) is assigned to the target reinforcement layer. In a tall retaining wall, the reinforcement load can vary with depth over a wide range of values. In such a case, more than one reinforcement type or spacing pattern along the wall height may be desirable. An example is a 12.6-m-high wrappedface wall in Seattle, Washington [6, 7] (Rainier Avenue wall), where four different reinforcement types with different tensile strength values were used in order to keep reinforcement spacing uniform. The ultimate wide-width tensile strength values [8] for the reinforcement types in the wall ranged from 31 kn/m to 186 kn/m. In general, stronger reinforcement products are typically stiffer materials. In the Rainier Avenue wall, the reinforcement secant modulus values at 5% strain from standard in-isolation laboratory index tensile tests ranged from 198 kn/m to 1068 kn/m. The ratio of minimum and maximum reinforcement index strength values was similar to the corresponding ratio for the reinforcement stiffness. The placement of a stiffer reinforcement layer will attract more load to the stiffer region of the reinforced zone. Therefore, the possibility of exceeding the tensile strength of the stiffer reinforcement layer must be checked. However, the

3 Static Response of Reinforced Soil Retaining Walls with Nonuniform Reinforcement 479 load increase of the type discussed here cannot be addressed rigorously using conventional limitequilibrium analysis approaches in combination with the contributory area method. This may be a more important issue for geosynthetic reinforcement products compared to much stiffer metallic reinforcement materials where variations of reinforcement stiffness and maximum reinforcement load are not as significant [9]. The influence of a single reinforcement type with a given stiffness and length on wall response has been the subject of previous investigations [10] [15]. Ho and Rowe [10] and Rowe and Ho [11, 12] found that the reinforcement stiffness, vertical spacing and length to wall height ratio, L/H, are important parameters that influence the wall displacement response. Ho and Rowe [10] found little variation in the magnitudes of reinforcement load and soil stress for L/H values larger than 0.7. It is worth noting that the ratio L/H = 0.7is the minimum reinforcement length ratio recommended by FHWA [4] and AASHTO [5] design guidelines for static stability of reinforced soil walls. A design chart to predict wall deformations as a function of L/H and reinforcement type (i. e., extensible geosynthetic or inextensible metallic) appears in the current FHWA [4] and AASHTO [5] guidelines. Ho and Rowe [10] concluded that placing equally spaced reinforcement layers with L/H = 0.7 is an efficient reinforcement distribution and recommended over other distribution patterns of reinforcement in reinforced soil walls. Rowe and Ho [13] showed that the magnitude of wall lateral displacement is influenced by the soil friction angle and a reinforcement stiffness factor,, defined as = J/(K a γhs v ). Here, J is the reinforcement stiffness, K a is the Rankine active earth pressure coefficient, γ is the soil unit weight, H is wall height, and S v is the vertical spacing between reinforcement layers. Helwany et al. [14] used a calibrated finite element model to investigate the effects of wall height, backfill type, and reinforcement stiffness on the response of reinforced soil walls with a hard facing. They found that the stiffness of geosynthetic reinforcement has an important influence on wall displacement response when the backfill shear strength and stiffness values are low. Bathurst and Hatami [15] showed that for a typical 6-m-high propped-panel wall, there was no significant difference in the distribution of maximum reinforcement load at the end of construction for uniform reinforcement schemes with different stiffness values in the range of typical geosynthetic materials. However, reinforcement layers with a stiffness value representative of steel strip materials showed higher reinforcement loads. All the above studies examined reinforced soil walls with one reinforcement type only. There are currently no guidelines that directly consider the influence of different stiffness reinforcement layers on the distribution of tensile load in reinforced soil wall systems. In this article, extended results of a numerical study [16] are reported where the potential for reducing the reinforcement cost by combining different reinforcement products is explored. Different nonuniform reinforcement configurations were examined while ensuring that wall models were structurally stable and no reinforcement yielding or pull-out would occur. The assumption of no slippage between the soil and reinforcement was adopted to simplify the numerical modeling and to focus the study on the effect of reinforcement layers with different stiffness values on wall response. The term nonuniform reinforcement in this article is used generically to identify reinforced soil walls in which two or more reinforcement types are used. The wall models in the current study are largely of wrapped-face type with a battered facing and different reinforcement arrangements: single reinforcement type (uniform reinforcement); two reinforcement types placed separately in top and bottom sections of the wall (grouped rein-

4 480 K. Hatami, R.J. Bathurst, and P. Di Pietro forcement); two reinforcement types in alternating layers (alternating reinforcement); and configurations with three reinforcement types (mixed reinforcement). In addition, a limited investigation of the influence of tiered and vertical gabion-faced wall construction on the wall structural performance was undertaken. The numerical analyses were carried out using the program FLAC [17]. The structural response of wall models at end of construction is presented in terms of facing lateral displacement, maximum reinforcement load, and equivalent lateral earth pressure coefficient, K h, backcalculated from the reinforcement load. The focus of the current study is on the influence of nonuniform reinforcement stiffness configurations on wall response. The reinforcement vertical spacing in each model wall was kept constant. Therefore, the effect of variable reinforcement spacing on wall response is not addressed here. A number of other studies have been cited where the influences of reinforcement geometrical arrangement and variable spacing are investigated [10, 13, 18]. It is worth noting that the numerical study reported in this article is restricted to a limited range of material properties and geometry. In addition, the numerical models have not been calibrated against monitored wrapped face full-scale walls. However, instrumented walls of the type reported here are very rare and, the only case reported in the literature that the writers are aware of does not contain sufficiently high-quality data to render a calibration exercise warranted. Therefore, the results of the study may be best interpreted in terms of relative performance of the wall case studies investigated. However, the numerical approach, soil, and reinforcement models used in this study have been successfully used to reproduce the measured response of a heavily instrumented, full-scale segmental retaining wall by the RMC Geotechnical Research Group [19]. The predicted response of the wall from the numerical simulation showed a very good match with the actual, measured results. In addition, the finite difference numerical model used in this study has been used to replicate the numerical results of a generic, reinforced soil propped-panel wall that was simulated using the finite element method [15]. Despite slightly different assumptions from what were made in the finite element simulation [20], the results compare satisfactorily. These comparison studies provide confidence about different detailing aspects of the numerical model (e. g., staged construction feature, interfaces, reinforcement/soil interaction properties, etc.) so that it can be used to investigate the influence of different parameters (e. g., reinforcement stiffness) on the wall response. In addition, the numerical modeling results do provide valuable insight regarding the influence of reinforcement stiffness and arrangement on wall performance under idealized conditions. II. Wall models A. General description and geometry A total of 21 numerical wall models are included in the parametric study. The geometry and reinforcement configuration of wall models are shown in Figure 2. The reinforcement stiffness values are listed in Table 1. The numerical model set consists of nineteen 8-m-high wrapped-face model walls (Walls 1-12 and 15-21, Figure 2). The wall models are considered to represent typical heights for wrapped-face retaining walls based on a survey of reinforced soil retaining walls constructed in the United States [21]. One model wall with a vertical gabion facing [Wall 13, Figure 2(d)] was investigated to examine the influence of facing type and batter on wall behavior. In addition, a model wall with a combined wrapped-face and gabion facing configuration [Wall 14, Figure 2(e)] was included in the study to examine the influence of a tiered wall configuration on structure response. Each of the wrapped-face model walls has an inclined facing with a batter angle β = 20 from vertical. Each structure includes a broken-back slope (sloped surcharge) with an initial

5 Static Response of Reinforced Soil Retaining Walls with Nonuniform Reinforcement 481 FIGURE 2 meters. Walls with uniform and nonuniform reinforcement configurations. Notes: see Table 1; all dimensions in

6 482 K. Hatami, R.J. Bathurst, and P. Di Pietro TABLE 1 Reinforcement Stiffness and Arrangement of Wall Models Reinforcement Reinforcement Reinforcement Wall stiffness stiffness at bottom, stiffness at top, No. Figure 2 configuration J b (kn/m) J t (kn/m) R a Grouped b Alternating 5500, , a Grouped a Uniform a Grouped b Alternating 8000, , a Grouped a Uniform a Grouped a Uniform a Uniform c Mixed 8000, 4000, d Mixed 8000, 4000, (1) e Uniform f Uniform 5500 with S v = 1.0m f Uniform 8000 with S v = 1.0m g Uniform g Uniform g (2) Uniform g Alternating 2000 (L = 4.0m), 8000 (L = 8.0m) g Alternating 8000 (L = 4.0m), 2000 (L = 8.0m) 2407 Notes: (1) L = 3m, also includes longer, less stiff reinforcement layers [see Figure 2(e)]; (2) Alternating length schemes. 2H:1V slope. A fixed boundary condition representing a rigid foundation is assumed at a depth of 0.5 m below the lowermost reinforcement layer in all wall models. In addition, the foundation soil zone in numerical models is extended to a distance of 2.25 m in front of the wall toe and to a height of 1.25 m above the rigid foundation. The wall models have a total width of 25 m, in order to contain any shear failure wedge that can develop in the retained backfill under the end-of-construction loading condition. B. Reinforcement stiffness and arrangement The reference reinforcement length, L, in all wall models (except for Wall 14 and shorter reinforcement layers in Walls 17-21) is 8 m, which corresponds to a length-to-height ratio L/H = 1 for the reinforced soil zone. This reinforcement length is larger than the minimum length ratio L/H = 0.7 in accordance with FHWA [4] recommendations for static stability of walls with sloping surcharge fills. In addition, L/H = 1 (compared with the minimum value of 0.7) provides sufficient average reinforcement length (i. e., L/H = 0.75) in model walls with alternating half- and full-length reinforcement schemes [Figure 2(g)]. The vertical spacing between the reinforcement layers, S v, is constant and equal to 0.5 m in all model configurations except Walls 15 and 16.

7 Static Response of Reinforced Soil Retaining Walls with Nonuniform Reinforcement 483 The stiffness, J, of planar reinforcement materials (including geosynthetic products) is normally expressed in terms of the tensile force per unit width of reinforcement, T, for unit strain (i. e., units of kn/m) as (Figure 3): J = T ε (1) where ε is the tensile strain in the reinforcement. The reinforcement is modeled as plane-strain FIGURE 3 Mechanical response parameter definition for reinforcement. sheets with the same cross-sectional area, perimeter and stiffness values as those of an equivalent number of cable elements per unit length of the wall (i. e., perpendicular to the model wall plane). The reference reinforcement stiffness values are chosen from properties reported for woven wire mesh and polyester geogrid reinforcement products [22] [25]. However, additional stiffness values are included in this investigation to extend the range of the parametric study and to capture a wider range of geosynthetic reinforcement products manufactured from high-density polyethylene (HDPE) and polypropylene (PP) polymers. In the following, the wall configurations are described with reference to Figure 2 and Table Figure 2(a) Walls 1, 3-5, and 7-11 include both uniform and nonuniform reinforcement layouts. The nonuniform layouts in these walls are referred to as grouped reinforcement configurations that include two different reinforcement types in the bottom and top halves of the reinforced soil zone.

8 484 K. Hatami, R.J. Bathurst, and P. Di Pietro Walls 4 and 8 contain uniform reinforcement with stiffness values equal to the average of stiffness values in Walls 1-3 and 5-7, respectively. Wall 9 is a variation of Wall 8 with two slightly different reinforcement stiffness values in a grouped reinforcement configuration. Walls 10 and 11 are uniformly reinforced with each of the component reinforcement types used in Walls Figure 2(b) Walls 2 and 6 are constructed with alternating reinforcement arrangements composed of reinforcement layers with significantly different stiffness values. 3. Figure 2(c) Wall 12 is a wrapped-face wall constructed with a mixed reinforcement arrangement using three different stiffness values that decrease in magnitude toward the top of the wall. 4. Figure 2(d) Wall 13 is identical to Wall 12 with respect to reinforcement configuration but with a vertical gabion facing. 5. Figure 2(e) Wall 14 is a combined (tiered-wrapped face) cross section, which is included in this study as an example tiered wall configuration. The wall consists of an inclined wrapped-face section seated on a vertical gabion facing system with a combination of short secondary reinforcement lengths (L = 3 m) and longer primary reinforcement layers placed at vertical spacings of 2 m. The shorter reinforcement layers (L = 3 m) in the gabion and wrapped-face sections of the wall are different products (i. e., woven wire mesh and polyester geogrid) but have the same stiffness values (J = 5500 kn/m). 6. Figure 2(f) Walls 15 and 16 are uniform reinforcement walls with a reinforcement spacing, S v, twice as large as the reference spacing used in the other model walls (i. e., S v = 1 m). This value for reinforcement vertical spacing is within the typical range (i. e., 0.3 m <S v < 1.5 m) used in reinforced soil wall structures [20]. However, reinforcement spacing values as low as 0.15 m and as large as 1.8 m have been reported in the literature for actual walls [21]. 7. Figure 2(g) Walls include uniform and alternating reinforcement stiffness configurations with alternating reinforcement length over the height of the wall. C. Reinforcement quantity In this study, the amount of reinforcement in each model wall is quantified using the reinforcement stiffness, length, and vertical spacing. The amount of reinforcement supply for a wall

9 Static Response of Reinforced Soil Retaining Walls with Nonuniform Reinforcement 485 of given height, H, is proportional to the ratio J L/S v. The demand from lateral earth pressure behind the wall is proportional to K ah γh 2 where γ is the backfill unit weight and K ah is the horizontal component, active Coulomb earth pressure coefficient given by: where K ah = K a cos [ δ + ( α π 2 sin 2 (α + ϕ) K a = [ sin 2 α sin(α δ) 1 + )] sin(ϕ+δ) sin(ϕ θ) sin(α δ) sin(α+θ) (2) ] 2. (3) In equations (2) and (3), φ is the backfill soil friction angle, δ is the friction angle between the backfill and a hard facing, α is the wall batter angle from horizontal (i. e., α = π/2 + β) and θ is the backfill surcharge slope. The active earth pressure coefficient is considered in the lateral earth pressure demand formulation because a plastic, active zone typically develops in reinforced zones with geosynthetic reinforcement materials due to their relatively low stiffness values (i. e., compared with metallic reinforcement stiffness). The reinforcement ratio, R λ,is introduced here as a non-dimensionalized, single-valued parameter to quantify the reinforcement supply-to-demand ratio for a wall model of given height and backfill material as: ni=1 J i l fi (λ)l i S R λ = vi K ah γh 2 (4) where J i, L i, and S vi are the stiffness, length and vertical spacing (contributory height) of reinforcement layer i, respectively, and, n denotes the total number of reinforcement layers. The length factor, l fi, of the reinforcement layer i is defined as: l fi (λ) = 1 + L i/h λ L i /H + λ (5) where λ is a reference reinforcement length-to-wall height ratio that corresponds to an optimum L/H ratio value for the stability of reinforced soil walls. The value for λ is taken as 0.7 in accordance with the results of previous numerical and experimental studies reported in Section I. However, a lower value for λ (i. e., optimum L/H ratio for wall stability) may be considered for higher backfill friction angles [26]. The mathematical expression of equation (5) represents the direct influence of reinforcement length on wall stability for the range L i /H λ and its reduced effect for L i /H > λ as was found in a number of earlier studies [10, 13, 15, 27]. The parameter R λ defined in equation (4) includes both reinforcement supply and backfill friction angle which are the two most important parameters influencing the horizontal displacement of reinforced soil walls [13]. Specifically, a higher magnitude for the parameter R λ indicates a stronger backfill and/or greater reinforcement supply in the wall, both of which would result in lower wall lateral displacement. Equation (4) can be understood to be an indicator of the reinforcement cost. The reinforcement ratio values for the wall models with λ = 0.7 (i. e., R 0.7 ) are listed in Table 1. D. Soil The backfill soil and sloped surcharge are modeled as purely frictional, elastic-plastic materials with the Mohr Coulomb failure criterion. The friction angle, dilation angle and unit weight of backfill (including the sloped surcharge) are assumed as φ = 32, ψ = 12, and γ = 18 kn/m 3,

10 486 K. Hatami, R.J. Bathurst, and P. Di Pietro respectively. The bulk modulus and shear modulus values of the backfill material are assumed as K = 16 MPa and G = 9.6 MPa, respectively. Greater strength and elastic property values were assigned to the foundation region in wall models with a gabion facing (Walls 13 and 14 in Figure 2) in order to provide sufficient foundation bearing resistance and stiffness directly below the facing (i. e., φ = 35, (cohesion) c = 5kPa, ψ = 12, K = 800 MPa, and G = 480 MPa). These values were used to ensure stability and are believed to have had little influence on the toe lateral restraint of gabion facing wall models compared to the lateral restraint due to the embedded toe of wrapped-face models. This expectation is confirmed by examining the calculated lateral displacement response of the corresponding model walls close to the foundation region [i. e., Walls 12 and 13 in Figure 4(c)]. The rockfill in the gabion baskets is modeled as a frictional material with a Mohr Coulomb failure criterion similar to the backfill but, with a higher friction angle (i. e., φ = 40 ). It is worth noting that a hyperbolic model [28] would better represent the state of soil stiffness as a function of confining stress in the soil. However, using the more complicated hyperbolic model (i. e., compared with linear elastic model) requires consistently accurate values for the soil stiffness parameters (e. g., k m,k e,m,n,r f in the hyperbolic model) from experimental data for any meaningful gain over the use of the simpler constant stiffness model. To the best of the authors knowledge, such measured data for the backfill of actual wrapped-face walls are not available. In addition, the introduction of these additional parameters in the model would necessitate a significant set of parametric studies on the effect of hyperbolic parameters on the overall wall response, which is avoided at this stage of study. The focus of the current study is the influence of reinforcement stiffness and configuration on model wall response for a given linear elastic soil model. III. Numerical approach The numerical simulations were carried out with the assumption of plane-strain conditions. The simulations modeled the sequential bottom-up construction of the wall facing, soil, reinforcement, and sloped surcharge. A fixed boundary condition in the horizontal direction was assumed at the numerical grid points at the backfill far-end boundary. The backfill and facing units (where applicable) of each wall model were elevated in lifts of 0.5 m, and the reinforcement layers were placed in the model as each reinforcement elevation was reached. The numerical results presented here correspond to the end of construction for each wall after the placement of the entire sloped surcharge. The numerical models at each stage were solved to equilibrium with a prescribed tolerance before placing the next lift of soil and reinforcement layer. The wrapped-face portion of each reinforcement layer at the facing (i. e., between two subsequent reinforcement layers) was assigned the same mechanical properties as those of the lower layer. The reinforcement layers, including the wrapped-face portions and gabion facing, were modeled using linear elastic, perfectly plastic cable elements with tensile yield strength, T y and negligible compressive strength (Figure 3). The cable elements (reinforcement) interact with the backfill material through grout interfaces. The stiffness and strength of the grout interface which was modeled as a spring-slider system were set to k b = 100 MPa and s b = 1 MPa, respectively. Details of the soil-reinforcement grout interface are reported by Itasca [17]. The maximum reinforcement load at the end of construction in all model walls examined was less than the yield strength of reinforcement materials used in each model.

11 Static Response of Reinforced Soil Retaining Walls with Nonuniform Reinforcement 487 A. Wall lateral displacements IV. Results 1. Effect of reinforcement stiffness arrangement Figure 4 shows the calculated lateral displacement, X d, of walls at end of construction. Parameter h in the figure is elevation measured from the wall base (Figure 2). The data in Figure 4 include the numerical results for most of the model walls to illustrate important differences in wall response. The displacement responses of Walls 1 and 3 are close to the responses of Walls 5 and 7, respectively, and are not shown for clarity of the plots. In Figure 4(a), Wall 11 with uniformly stiff reinforcement over the entire height shows the smallest amount of lateral displacement. Replacing half of the reinforcement layers with a less stiff reinforcement material (Walls 5 7 with identical R 0.7 values in Table 1) increases the wall lateral displacement. However, the maximum displacement value and the displacement distribution pattern depend on the reinforcement arrangement. Placing the less stiff reinforcement in the upper half of the wall (Wall 5) results in local bulging of the facing in the upper half of the wall height. The wall lateral displacement within the lower half does not increase noticeably compared to Wall 11. Placing the less stiff reinforcement in the lower half of the wall height (Wall 7) results in a considerable increase in wall lateral displacement in the lower half of the wall height (by about 70% on average in comparison with Wall 11). Distributing the less stiff reinforcement material evenly between stiff reinforcement layers (Wall 6) results in a wall displacement profile similar to the displacement response of uniformly reinforced Wall 11 but with larger lateral displacement magnitude at all reinforcement elevations. The amount of displacement increase in Wall 6 compared to Wall 11 is uniform over the wall height and about half the maximum value observed in either of the grouped reinforcement arrangements (i. e., Walls 5 and 7). Therefore, an alternating reinforcement scheme appears to be a more effective reinforcement arrangement than grouped schemes with the same reinforcement ratio value to limit wall lateral displacement. A comparison of displacement results for Walls 2 and 4 as well as those of Walls 6 and 8 in Figure 4(b) shows the influence of using an alternating reinforcement arrangement with the same average reinforcement stiffness as an otherwise, identical configuration with uniform reinforcement. The alternating reinforcement configurations show only a slightly larger amount of deformation at end of construction compared with uniformly reinforced walls. Accordingly, the deformation response of walls with alternating reinforcement stiffness arrangement can be considered to be practically the same as (and therefore can be estimated from) the response of uniformly reinforced walls with identical reinforcement ratio values. The influence of mixed reinforcement arrangement on wall displacement for a wrapped-face wall is illustrated in Figure 4(c). The reinforcement ratio of mixed-reinforced Wall 12 (with a gradually decreasing reinforcement stiffness toward the top) is 70% of the reinforcement ratio of Wall 6 (Table 1). However, displacement response of Wall 12 (maximum value m) is only slightly greater than displacement response of Wall 6 (maximum value m) that contains several layers of stiffer reinforcement. Therefore, the intuitive scheme of reducing reinforcement stiffness with height appears to be a cost-effective configuration that would not result in a significantly larger wall displacement compared to the alternating scheme. However, the reduction of reinforcement stiffness with elevation using an alternating reinforcement arrangement is more desirable (i. e., compared with grouped schemes) to avoid local, excessive deformation of the facing along the wall height.

12 488 K. Hatami, R.J. Bathurst, and P. Di Pietro FIGURE 4 Lateral displacement profiles of reinforced model walls (numbers on plots refer to wall models in Table 1).

13 Static Response of Reinforced Soil Retaining Walls with Nonuniform Reinforcement Gabion facing vs. battered wrapped-face wall The effect of facing type and batter on wall displacement can be examined in Figure 4(c). Wall 12 with an inclined wrapped face at 20 to the vertical generated less lateral displacement at the end of construction than Wall 13 constructed with a vertical gabion facing. It may be concluded that the effect of an inclined face may be more effective than a vertical wall constructed with a relatively stiffer gabion column in reducing wall displacement. The displacement plots in Figure 4(c) also show that the pattern of displacement profiles between wrapped-face and gabion facing walls is quite different. The maximum end-of-construction displacement occurs much higher up the face of the gabion wall ( 0.75H ) compared to the wrapped-face wall ( 0.35H ). The displacement of the wrapped-face wall is considered to be due to lateral spreading of the backfill under soil self-weight, while the pattern of displacement for the vertical gabion wall is due to rotation of the facing column about the toe. 3. Effect of reinforcement arrangement and vertical spacing Figure 4(d) shows that the displacement response of a uniformly reinforced wall (Wall 8) is practically indistinguishable from the response of a corresponding wall with grouped reinforcement configuration where the stiffness values of the two reinforcement groups are not substantially different (Wall 9 with variation of J within 10% and difference in R 0.7 equal to 5% with respect to Wall 8). Comparison of the plots in the same figure shows that the combined influence of reduced reinforcement length and tiered wall construction (Wall 14) results in greater facing displacements than Wall 9. However, comparison of displacements for Walls 14 (R 0.7 = 1692) and 15 (R 0.7 = 1369) shows that the combined influence of tiered wall construction and reduced reinforcement length is more effective in controlling wall deformation than a battered wrapped-face structure constructed with a wider reinforcement spacing. Figure 4(e) further illustrates the influence of reinforcement stiffness and spacing on wall deformation. Wall 11 (R 0.7 = 7967) is uniformly reinforced with reinforcement stiffness J = 8000 kn/m. Replacing the reinforcement with a considerably less stiff material (J = 2000 kn/m) increases average wall deformation by a factor of 2 (Wall 10, R 0.7 = 1992). On the other hand, doubling the vertical spacing between the reinforcement layers (i. e., S v = 1m Wall16, R 0.7 = 1992) while maintaining reinforcement stiffness of J = 8000 kn/m results in substantial increases in wall lateral displacement (increase in maximum value by about a factor of 5) with significant local bulging between reinforcement layers. The displacement magnitude of Wall 16 is excessive from a serviceability standpoint and may be considered to have failed. It can be concluded that using a larger number of lower stiffness reinforcement layers at relatively lower spacing is more effective to reduce wall deformations than stiffer reinforcement layers with a wider spacing. This finding appears to be more important for wrapped-face walls compared to previous results on propped-panel retaining wall systems [13]. It is worth noting that a smaller S v value does not necessarily result in a longer construction time. Experience with wrapped-face reinforced soil walls in the past has shown that a larger reinforcement spacing requires more complicated forming systems [21]. Accordingly, the time saved using less number of lifts is typically cancelled by the increased forming time. The above results (including those discussed in Section 1) suggest that reducing reinforcement stiffness with height while maintaining constant vertical spacing is recommended over increasing the spacing with height (as reported for a number of reinforced soil walls constructed in the past [3, 21], [29] [33]) to limit the facing lateral displacement and ensure the stability of the structure.

14 490 K. Hatami, R.J. Bathurst, and P. Di Pietro 4. Effect of reinforcement length Figure 4(f) shows plots of wall displacement at end of construction for the uniform reinforcement case with J = 8000 kn/m (Wall 11, R 0.7 = 7967) and three alternating reinforcement schemes. In one scheme (Wall 19, R 0.7 = 5394), the length of every other reinforcement layer (L = 4 m) is one half of the reinforcement length of the reference case, Wall 11. In another scheme (Wall 6, R 0.7 = 4979), a less stiff reinforcement (J = 2000 kn/m) is placed in an alternating scheme with the reference reinforcement (i. e., J = 8000 kn/m). In the third alternating scheme (Wall 20, R 0.7 = 4336), the less stiff reinforcement is truncated to half length (L = 4m) and is placed alternating with the full-length, stiff reinforcement. The uniform reinforcement case of Wall 8 (R 0.7 = 4979) with average reinforcement stiffness value comparable to the case of Wall 6 is also shown for comparison. Results of Figure 4(f) show that the magnitude and profile shape of lateral displacements of walls with the above reinforcement configurations are only marginally different. The displacement response of Wall 19 is slightly smaller than the response magnitude of Wall 6. The displacement response of Wall 20 is almost the same as the response of Wall 6. It can be concluded that reducing the length of reinforcement for every other layer is a viable strategy to reduce the required amount of reinforcement with little impact on the displacement response of the wall. The effect of alternating reinforcement length scheme on wall displacement response is further examined in Figure 4(g). In the figure, three pairs of displacement profile curves are shown. Each pair includes wall models with uniform and alternating reinforcement length schemes. The reinforcement stiffness for each pair is uniform. The reinforcement stiffness values for the three pairs are 2000 kn/m (Walls 10 and 17), 5000 kn/m (Walls 8 and 18) and 8000 kn/m (Walls 11 and 19). Figure 4(g) shows that the displacement response of uniformly reinforced retaining walls increases only slightly by reducing the reinforcement length of every other layer by half. The amount of increase is less for stiffer reinforcements and is almost undetectable for the stiff reinforcement case of Walls 11 (R 0.7 = 7967) and 19 (R 0.7 = 5394). Figure 4(h) shows plots of displacement response for Walls 10, 20, and 21. It can be seen that replacing every other reinforcement layer (of Wall 10 with J = 2000 kn/m) with a half-length layer but with a considerably stiffer reinforcement (i. e., J = 8000 kn/m) can result in noticeable reduction of wall lateral displacement (cf. Walls 10, R 0.7 = 1992 and 21, R 0.7 = 2407). The reduction in wall lateral displacement will be greater by adopting a long-stiff, short-secondary reinforcement scheme (Wall 20, R 0.7 = 4336) for the same total length of reinforcement material (i. e., compared to Wall 21). 5. Effect of reinforcement ratio on wall displacement Figure 5 summarizes the variation of maximum wall lateral displacement with reinforcement ratio, R 0.7, for all wall models listed in Table 1. The wall lateral displacements are normalized with respect to reinforcement spacing, S v. The following main observations can be made by inspecting Figure 5: 1. The wall lateral displacement, normalized to reinforcement vertical spacing, shows a consistent trend of reduction in magnitude with reinforcement ratio value for all model walls examined. The presence of S v in the normalized parameter (X d ) max /S v emphasizes the significance of reinforcement spacing in the magnitude of wall lateral displacement compared with the influence of reinforcement length and stiffness. This is in contrast to displacement response of propped-panel walls where the influence of reinforcement vertical spacing on wall lateral displacement (normalized to wall height) due to soil

15 Static Response of Reinforced Soil Retaining Walls with Nonuniform Reinforcement 491 FIGURE 5 Variation of normalized wall lateral displacement with reinforcement ratio. Notes: (1) all simulation cases except for the solid circles (S v = 1 m) correspond to reinforcement vertical spacing S v = 0.5 m; (2) data groups denoted by numbered lines indicate similar configurations with different reinforcement ratio values (i. e., from one data group to another). self weight has been found to be negligible [13, 34] provided that the value of (see Section I) remains the same and no reinforcement slippage occurs. 2. The alternating reinforcement length schemes provide the lowest wall displacement response magnitude for a given reinforcement ratio value. The magnitude of wall lateral displacement for a given reinforcement ratio value increases with reinforcement configuration in the following order (data points along each of the lines 1 and 2 in the figure): (1) uniform stiffness and alternating length; (2) uniform stiffness and length; (3) uniform length and alternating stiffness; (4) grouped stiffness (uniform length) with stiffer reinforcement at the bottom; and (5) grouped stiffness (uniform length) with less stiff reinforcement at the bottom. The magnitude of wall lateral displacement is less sensitive to reinforcement configuration for greater reinforcement ratio values (cf. lines 1 and 2). 3. An estimate of the optimal reinforcement configuration that will minimize the reinforcement cost can be made from Figure 5. B. Reinforcement loads 1. Load distribution with height Figure 6 shows the distributions of maximum reinforcement load, T max, for the wrapped-face walls at the end of construction. The plots in Figure 6(a) summarize the reinforcement loads for walls with a single reinforcement type and two different reinforcement spacing values.

16 492 K. Hatami, R.J. Bathurst, and P. Di Pietro FIGURE 6 Distributions of maximum reinforcement load (wrapped-face walls only). (Cont.).

17 Static Response of Reinforced Soil Retaining Walls with Nonuniform Reinforcement 493 FIGURE 6 (Cont.). Distributions of maximum reinforcement load (wrapped-face walls only). (Cont.).

18 494 K. Hatami, R.J. Bathurst, and P. Di Pietro FIGURE 6 (Cont.). Distributions of maximum reinforcement load (wrapped-face walls only).

19 Static Response of Reinforced Soil Retaining Walls with Nonuniform Reinforcement 495 In general, reinforcement loads increase linearly with depth until the rigid frictional foundation boundary is approached. Earth pressure developed at the bottom of each wall is carried by the model boundary and therefore the reinforcement load at the bottom of the wall is attenuated. At the end of construction, the magnitude and distribution of maximum reinforcement load in uniform reinforcement schemes are essentially independent of reinforcement stiffness for the range J = 1000 to 8000 kn/m examined in this study. This observation is consistent with the results of previous numerical studies by the authors and others on propped-panel walls at end of construction [11, 12, 15, 34, 35]. However, these earlier studies revealed that the distribution of reinforcement loads with wall height was essentially uniform. Therefore, it can be concluded that the type of facing (i. e., propped panel viz. flexible wrapped-face) has a large influence on both the distribution and magnitude of reinforcement load. This conclusion is also consistent with the results of full-scale experimental geosynthetic reinforced-soil wall tests reported by Bathurst et al. [36] who examined the influence of hard-face and wrapped-face construction on the development of reinforcement loads on a series of 3.6-m-high retaining wall structures. The reinforcement load response in model walls with grouped or alternating reinforcement arrangements is different from load response of uniformly reinforced walls [Figure 6(b)]. In grouped reinforcement schemes with considerably different stiffness values in the top and bottom sections of the wall, the stiffer reinforcement attracts more load than the less stiff reinforcement. For example, in Walls 1, 3, 5, and 7 the variation of reinforcement load with depth is significantly influenced by the grouped arrangement of reinforcement stiffness. In Walls 1 and 5, the maximum reinforcement load is greater and practically constant over the lower half of the wall height. The reason is that these walls undergo relatively large displacement in the upper half due to the less stiff reinforcement in that region [see Wall 5, Figure 2(a)]. This sheds additional load on the upper reinforcement layers in the lower half of the wall and changes the generally linear load variation with depth to a more uniform distribution. For walls with reinforcement spacing S v = 0.5 m, the largest reinforcement load and the largest local deviation from a smooth load distribution with elevation occurs in alternating reinforcement schemes [Walls 2 and 6 in Figure 6(b)]. It appears that reinforcement layers with significantly different stiffness values in a wall with an alternating reinforcement scheme act as primary and secondary reinforcement layers, respectively, with the stiffer reinforcement layers attracting larger lateral earth loads. It can be argued that the effective spacing, S v, between primary layers results in a stiff reinforcement load magnitude that is equivalent to the magnitude expected for a uniformly reinforced wall with 0.5 <S v < 1 m [Figure 6(c)]. Figure 6(d) shows the plots of reinforcement load distribution for uniformly reinforced walls and walls with constant reinforcement stiffness and alternating length scheme. It can be concluded that with the exception of a slightly staggered pattern at the top, reducing the length of every other reinforcement layer by one half has essentially no effect on maximum reinforcement load in the wall. Figure 6(e) summarizes the comparison of reinforcement load distribution plots for model walls with uniform reinforcement stiffness J = 8000 kn/m (Wall 11) and selected other reinforcement schemes that include reinforcement layers with J = 8000 kn/m. The results shown in Figure 6(e) indicate that reducing the length of every other reinforcement layer while maintaining the same reinforcement stiffness value (Wall 19) is the only cost-saving strategy among the alternatives examined that would not result in a significant increase in maximum reinforcement load with respect to uniform reinforcement schemes. Figure 6(f) shows reinforcement load distributions corresponding to two contrasting reinforcement configurations with different lengths and stiffness values (Walls 20 and 21 in Table 1). Plots of reinforcement load response for uniform stiffness cases of Walls 10 and 17 are also

20 496 K. Hatami, R.J. Bathurst, and P. Di Pietro shown in the figure. Comparison of load distribution plots for Walls 17, 20, and 21 with the plot for Wall 10 indicates that maximum loads in different reinforcement layers are essentially proportional to their relative stiffness values regardless of reinforcement length in alternating reinforcement arrangements. 2. Effect of reinforcement ratio on reinforcement load Figure 7 summarizes the magnitude of maximum reinforcement load in wall models listed in Table 1. An inspection of the figure shows that greater reinforcement load magnitudes develop in walls with a vertical facing, large reinforcement spacing, or alternating scheme with significant stiffness differences between reinforcement types. The magnitude of maximum reinforcement load is otherwise almost the same for all other reinforcement configurations and does not show any dependence on the reinforcement ratio value. The reinforcement loads and backfill shear strain at end of construction are shown in Figure 8, which further illustrate the above observations for wall models listed in Table 1. Plots of Figure 8 for Walls 15 and 16 indicate large soil strain and reinforcement load at the facing. Large soil strain and reinforcement load have been reported as the possible reasons for the failure of an actual wrapped-face wall [21]. FIGURE 7 Variation of maximum reinforcement load in each wall with reinforcement ratio. Notes: (1) all simulation cases except for the solid circles (S v = 1 m) correspond to reinforcement vertical spacing S v = 0.5m. C. Lateral earth pressure coefficient Figure 9 shows the distribution of normalized lateral earth pressure coefficient K h /K ah acting behind each wall (wrapped-face configurations only) where:

21 Static Response of Reinforced Soil Retaining Walls with Nonuniform Reinforcement 497 FIGURE 8 Shear strain in backfill and reinforcement load at end of construction. Notes: contour intervals = 0.2 %; T max in kn/m. (Cont.).

22 498 K. Hatami, R.J. Bathurst, and P. Di Pietro FIGURE 8 (Cont.). Shear strain in backfill and reinforcement load at end of construction. Notes: contour intervals = 0.2 %;T max in kn/m. (Cont.).

23 Static Response of Reinforced Soil Retaining Walls with Nonuniform Reinforcement 499 FIGURE 8 (Cont.). Shear strain in backfill and reinforcement load at end of construction. Notes: contour intervals = 0.2 %;T max in kn/m.

24 500 K. Hatami, R.J. Bathurst, and P. Di Pietro FIGURE 9 Normalized equivalent lateral earth pressure coefficient of wrapped-face walls. (Cont.).

25 Static Response of Reinforced Soil Retaining Walls with Nonuniform Reinforcement 501 FIGURE 9 (Cont.). Normalized equivalent lateral earth pressure coefficient of wrapped-face walls. K hi = T maxi γ (H h i ) S v. (6) In equation (6), K hi is the earth pressure coefficient corresponding to reinforcement layer i, T maxi is the maximum reinforcement load in layer i and h i is the elevation of reinforcement layer i measured from the rigid foundation. It is worth noting that earth pressure coefficient, K hi, calculated from equation (6) is an equivalent design parameter which corresponds to the mobilized load in reinforcement layers. The K hi values calculated from equation (6) for the bottom reinforcement layers do not represent the true value of the lateral earth pressure coefficient near the toe which is close to the at rest value, K o. Equation (6) overestimates the value of K hi for the top reinforcement layer due to its small depth in the backfill. Accordingly, the interpretation of the results for lateral earth pressure coefficient in the following sections is limited to the middle section of the wall height where boundary effects are minimal. For uniform reinforcement configurations with S v = 0.5 m and for all reinforcement stiffness values examined [Figure 9(a)], the lateral earth pressure coefficient along the wall height (except for the regions near the top and bottom boundaries) was found to be constant and close to the theoretical value, K ah. This observation can be expected from the data in Figure 6(a) and equation (6). According to equation (6), a linearly increasing reinforcement load with depth is equivalent to constant K h values over the backfill depth. A similar conclusion can be reached for the cases with S v = 1.0 m. However, the elevation range with constant K h value in the latter case is not as great as the range for S v = 0.5 m case. This is because the greater reinforcement vertical spacing of S v = 1.0 m results in a larger wall deformation and excessive load in the reinforcement layers. Nonetheless, results of Figure 9(a) indicate that for the range of reinforcement stiffness values examined, a uniform reinforcement distribution in wrapped-face walls results in K h values over the middle portion of the wall height that are close to K ah and independent of