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Numerical analysis of geocell-reinforced retaining structures
Geotextiles and Geomembranes 39 (2013) 51e62
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Numerical analysis of geocell-reinforced retaining structures Rong-Her Chen*, Chang-Ping Wu, Feng-Chi Huang, Che-Wei Shen Department of Civil Engineering, National Taiwan University, Taipei 10617, Taiwan, ROC
a r t i c l e i n f o
a b s t r a c t
Article history: Received 6 December 2012 Received in revised form 27 April 2013 Accepted 2 July 2013 Available online
This paper presents numerical analysis on the behavior of geocell-reinforced retaining structures with various layouts. The constitutive model adopted for materials consisted of a nonlinear elastic stress estrain relationship with MohreCoulomb yield criterion. The strength parameters of the materials were obtained from relevant tests. For verification of the numerical model, three model-scale gravity-type walls with different facing angles were analyzed, and the finite difference program FLAC was utilized in the analysis. The results of the verification show good agreement in predicting the potential slip surface as well as estimating the critical load causing the wall to fail. The verified numerical model was then employed to study various layouts of retaining structures, which were constructed with the same amount of geocells, to compare the failure mode as well as the deformation of the structure. It has been found, irrespective of gravity type or facing type, the structure that extends the length of geocells in some layers to serve as reinforcement performs well in reducing the deformation of the structure and decreasing the potential slip zone. Moreover, with lengthening geocell layers as reinforcements, extended facing-type structures of various facing angles were analyzed. The results show that a wall with a facing angle less than 80 will significantly reduce the lateral displacement of the wall face. Further, the lateral earth pressures against the back of wall facing are somewhat higher than the horizontal stress in Rankine’s active state, while those along the back of the reinforced zone are in at-rest state. Ó 2013 Elsevier Ltd. All rights reserved.
Keywords: Geocells Retaining structure Numerical analysis Stability Deformation
1. Introduction The geocell retaining system can be made to conform to the topography of the place, and the system tolerates deformation or settlement due to flexibility. Vegetation can also be planted into the cells, thereby improving the aesthetics of the surrounding environment. Besides, geocells vastly improve the shear strength of granular soil by providing confinement to the soil; and, in turn, the increase in soil strength provides improved bearing capacity and/or prevents soil erosion. Previous research on geocells mainly utilized laboratory tests. Bathurst and Karpurapu (1993) reported the results of a series of large-scale triaxial compression tests carried out on 200 mm-high isolated geocellesoil composite samples and unreinforced soil samples. It was found that the peak friction angles of the soil infill and the composite were the same; while the effect of confinement from the geocells may be simulated by an apparent cohesion. Uniaxial compression tests have also been conducted on large
* Corresponding author. Tel./fax: þ886 2 23629851. E-mail addresses: [email protected] (R.-H. Chen), r98521126@ ntu.edu.tw (C.-P. Wu), [email protected] (F.-C. Huang), cwshen@ sinotech.org.tw (C.-W. Shen). 0266-1144/$ e see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.geotexmem.2013.07.003
samples. Bathurst and Crowe (1994) described two large-scale uniaxial compression tests to examine the stability of multiple layers of geocells under vertical surcharge. They also mentioned the stability analysis of a reinforced embankment with slopes of various inclinations, and the location and combination of geosynthetic reinforcement in the slopes were determined by conventional methods of analysis for the reinforced retaining wall and reinforced slope. Wesseloo et al. (2009) discussed the results of uniaxial compression tests performed on geocell packs of different sizes. Chen et al. (2013) performed tests on geocell-reinforced sand samples under triaxial compression. It has been found that the apparent cohesion of reinforced samples varies with the shape, size and number of cells, of which the cell size is the most significant factor. In addition, approximately linear relationships were found between the apparent cohesion and the inverse of the equivalent diameter of the cell. Regarding the interfacial strength between two layers of geocell-reinforced sand, Bathurst and Crowe (1994) performed a direct shear test and found the friction angle at the interface essentially equaled the friction angle of the sand and the cohesion was zero. This is because the geocells were thin, meaning their occupied area was very small compared to that of sand. Model test has been conducted by Racana et al. (2001) on a rigid wall reinforced with paper cells and a soft wall reinforced with
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polyan cells. The Young’s modulus of the polymer was thirty times less than the modulus of the paper. They concluded that the magnitude of the displacement was very sensitive to the Young’s modulus of the material; nevertheless, the same failure mechanism was observed: an active block with no passive anchorage movement. Chen and Chiu (2008) performed model tests to examine both the effect of geocells as a major material in retaining structures and the failure mechanism of the said structures under surcharge. The main variables in the tests included the height and facing angle of the structure, the type of surcharge, and the reinforcement embedded in two externally stabilized structures: the gravity type and the facing type. The gravity-type wall is narrow at the top and wide at the bottom, while the facing type is described as having equal width from top to bottom. According to the test results, they proposed several layouts of geocell-reinforced retaining structures. Even though considerable interest has been shown in reinforced walls or reinforced slopes (Bathurst et al., 2005; Skinner and Rowe, 2005; Al Hattamleh and Muhunthan, 2006; El-Emam and Bathurst, 2007; Won and Kim, 2007; Ling et al., 2009; Mehdipour et al., 2013), little research has been published concerning numerical analyses on geocell retaining structures. To enhance better understanding of the geocell retaining structures, this paper assesses the stability and deformation of geocell retaining structures with various layouts. The failure modes as well as the deformations of the structures, which were constructed with the same amount of geocells, were investigated and compared. 2. Material model The numerical analysis in this study utilized the finite difference program FLAC (Fast Lagrangian Analysis of Continua). Detailed descriptions and derivations of the method are referred to in Itasca (2005). In the numerical model shown in Fig. 1, there are several types of element: soils, including backfill and foundation soils; geocellreinforced soil in the reinforced zone; and an interface element between two materials. The constitutive model for the reinforced soil and backfill is a nonlinear elastic stressestrain relationship
Reinforced soil (sand infill geocell)
Backfill soil
1
with MohreCoulomb yield criterion. Details of these elements are described below. 2.1. Material elements Reinforced soil walls generally have steep facings (70 ), and the reinforcements in the walls are commonly shorter than their wall heights and are embedded in several layers. Geocell layers used as the reinforcements also are usually thick, comparing to other reinforcements such as geogrids. As a result, the zone constructed with geocells is as stiff as a monolithic composite. This has been shown by the model tests on geocell-reinforced walls (Racana et al., 2001), in which the failure mechanism observed was an active block with no passive anchorage movement. The result suggested that the failure mode was due to shear failure. Therefore, an elasticeplastic stressestrain relationship with MohreCoulomb yield criterion was adopted in this study. A similar model has been used by Xie and Yang (2009) who employed the finite element software, MARC, with the yield criterion of ideal elasticeplastic MohreCoulomb model, to evaluate the stress distribution in a geocell retaining wall constructed on an expressway in central north China. The constitutive model for geocell-reinforced soil is similar to that of soil, i.e., the strength parameters of the reinforced soil have an apparent cohesion in addition to friction angle. In this study, the apparent cohesion, resulting from the confinement effect provided by geocells, was obtained from the tests on samples of geocellreinforced sand under triaxial compression. Details about the test procedures and similar results can be found in Chen et al. (2013). On the other hand, the angle of dilatation was assumed to be zero because it was found to have insignificant effect on the analytical result. For an example studied (Type G in Fig. 8a), with the angles of dilation assumed to be j ¼ 0 and j ¼ 10 , respectively, the lateral displacements with the assumption of j ¼ 10 are slightly higher, but the differences between the two cases are less than 2%. Moreover, in plane-strain test or triaxial compression test, typical dense sand in drained condition tends to dilate when subjected to shear stress (Bolton, 1986). Nevertheless, Adams et al. (2002) conducted vertically loaded tests on representative soile geosynthetic composites to an average vertical stress of 1000 kPa, and reported that the presence of geosynthetic reinforcement reduced significantly the tendency for soil dilation, especially when the reinforcement was closely spaced. Consequently, they proposed a “postulate of zero volume change” based on observed behavior from the experiments. The postulate has been implemented in the FHWA GRS-IBS design manual for design of Geosynthetic Reinforced Soil (GRS) bridge abutments (Adams et al., 2011; Wu and Pham, 2013) and for predicting maximum lateral movement of bridge abutments. Note that for a typical reinforced soil mass with vertical spacing Sv 0.5 m, contraction is likely. In those cases, the assumption of j ¼ 0 is conservative. For geocell-reinforced walls, the dilation of soil could also be suppressed by the thick and closely spaced geocell layers. Due to above reasons, the angle of dilation was assumed to be zero in this analysis.
2
2.2. Interface element
Foundation soil
Cable elements - interface between soil and facing units Cable elements - interface between geocell layers Fig. 1. Numerical model for simulating the materials in a geocell-reinforced wall system.
Interface resistance between different materials may significantly affect the deformation of geocell reinforcements. In this study, two types of interface were modeled (Fig. 1): the interface between geocell-reinforced soil layers or between the reinforced zone and foundation soil; and the interface between the reinforced zone (geocells) and the backfill. These interfaces are simulated by cable elements. The parameters of the cable element are obtained
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53
unreinforced reinforced
1200
Deviatoric stress (kPa)
σ3r=196.2kPa σ3r=147.1kPa 800
σ3r=98.1kPa σ3r=49kPa σ3=196.2kPa σ3=147.1kPa σ3=98.1kPa
400
σ3=49kPa 0 0
5
10
15
20
25
Axial strain (%) Fig. 3. Typical results of compression tests on samples of sand and reinforced sand (at relative density Dr ¼ 70% and under various confining pressures).
3.1. Comparison with model tests Fig. 2 shows three gravity-type geocell-reinforced model walls that are 0.8 m high; each wall had facing angles of 70 , 80 , and 90 , respectively. These model-scale walls were employed to simulate 2.0 m high prototype-scale walls, and therefore the scaling factor of length, l, is 2.5 (¼ 2 m/0.8 m). In the numerical model, all walls were constructed in eight layers. The bottom boundary was fixed against movement in all directions, while the vertical boundaries were restricted in the horizontal direction and free to move in the vertical direction. Surcharge was applied at the top of the wall, and then the deformation and factor of safety of the wall were calculated. 3.1.1. Input parameters 3.1.1.1. Soil. The soil used for testing was uniform sub-angular silica sand with specific gravity Gs ¼ 2.64 and dry unit weight gd ¼ 15.3 kN/m3 (at relative density Dr ¼ 62%). According to the
Fig. 2. Model walls with different facing angles for validation of numerical model.
from direct shear test on the interface of two materials. Details about the values of these parameters at various interfaces are introduced later.
Shear stress, (kPa)
120
80
40
3. Validation of numerical model 0
The numerical model employed in this study was validated through the experimental results reported by Chen and Chiu (2008); the details concerning the arrangement of model tests can be found in the paper.
0
40
80
Normal stress,
120
(kPa)
Fig. 4. The results of direct shear test on different materials.
160
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0
E ¼ ð290 þ 177Dr Þpa
0:55 (3)
pa
20
Depth from the top (cm)
s3
s3
K ¼ ð290 þ 156Dr Þpa
0:54 (4)
pa
The average Poisson’s ratio of the soil was n ¼ 0.33.
40
60
3.1.1.2. Geocell-reinforced soil. The strength parameters of reinforced sand were also obtained from the results of compression tests on sand samples confined by geocells (e.g., solid curves in Fig. 3). The samples were 300 mm high and had a diameter of 150 mm. The geocell material was made of high density polyethylene and the physical properties are as follows: specific gravity Gs ¼ 0.95, thickness t ¼ 1.3 mm, and mass per unit area mA ¼ 894 g/ m2. The tensile strength of the material is 17.0 kN/m and the elastic modulus is 492 kN/m, obtained from a wide-width sample, according to ASTM 4595. The strength parameters of the reinforced sand, cr (kPa) and 4r , based on MohreCoulomb failure criterion, are as follows.
α =70°(Model 1) α = 80°(Model 2) α = 90°(Model 3) — — — model test — numerical analysis
80
100 0
0.4 0.8 1.2 1.6 Lateral displacement (cm)
2
(a) 0
cr ¼ 72:5Dr þ 48:0
1
4r ¼ 34:8 þ 3:40Dr þ 3:08Dr log
(5)
Settlement (cm)
α =70°(Model 1) α = 80°(Model 2) α = 90°(Model 3)
4
model test — numerical analysis
———
5 60
40 20 Distance from the wall face (cm)
0
Fig. 5. Comparison of the analytical and test results for various facing angles (q ¼ 45 kPa). (a) Wall face deformation. (b) Settlement at the top of wall.
Unified Soil Classification System, the soil was classified as SP. Moreover, from the results of compression test on sand samples at various relative densities and under different confining pressures (e.g., dash curves in Fig. 3), it was found that the peak friction angle of the sand increased with relative density and reduced as the confining pressure increased:
s3 pa
4ps > 34+
(6)
(1)
(2)
In addition, Young’s modulus, E (kPa), and bulk modulus, K (kPa), are in terms of relative density and confining pressure:
(7)
where m and p stand for model and prototype cells, respectively. Note that the ratio between the two diameters (dp/dm) is the scaling factor of length, l. Therefore, the apparent cohesions of the model sample and the prototype sample were chosen to be equal. The elastic moduli of the prototype-scale geocell-reinforced sand are expressed in the following equations.
Er ¼ ð321 þ 344Dr Þpa
where pa ¼ atmospheric pressure (101.4 kPa), Dr ¼ relative density (%), s3 ¼ confining pressure (kPa). An estimate of the plane-strain angle of internal friction, 4ps , is found from the triaxial test results, 4tx , using the following equation (Lade and Lee, 1976):
4ps ¼ 1:54tx 17+
pa
cr;m ¼ cr;p =l dp =dm ¼ cr;p =l ðlÞ ¼ cr;p
(b)
4 ¼ 30:8 þ 13:4Dr 4:2Dr log
As can be seen from Eq. (5), the reinforced sand shows a marked increase in apparent cohesion, which mainly resulted from the contribution of the geocell providing confinement to the sand. Correspondingly, the average Poisson’s ratio for the reinforced sand, n ¼ 0.17, was much less than that of the sand, n ¼ 0.33. Furthermore, the apparent cohesion in Eq. (5) was chosen for the model geocells, after considering both the relative cell size and the scaling factor of length between the propotype-scale wall and model-scale wall. The reason is explained as follows. Regarding the sizing effect, a linear relationship was found between apparent cohesion, cr, and the inverse of diameter of circular cell, 1/d (Chen et al., 2013). As to the scaling effect, the apparent cohesion of the model cell should be reduced by a scaling factor of length, l. Therefore,
2
3
s3
s3
(8)
pa
Kr ¼ ð135 þ 231Dr Þpa
0:65
s3 pa
0:58 (9)
Similarly, the values for the model material were modified from the above values of the prototype material by dividing the scaling factor of length. 3.1.1.3. Interface element. The geocells of the model walls were made from book-binding paper that was 1.3 mm thick (Chen and Chiu, 2008). In this study, the interfacial shear strength between the two materials was obtained from a direct shear test. From the
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55
Fig. 6. Comparison of failure modes between the experimental and analytical results (q ¼ 45 kPa). (a) Experimental results (Chen and Chiu, 2008). (b) Analytical results.
results of the direct shear test (Fig. 4), the friction angle between the geocell-reinforced layers was found to be 37.2 , while the fiction angle between the sand and paper was 31.3 . The other parameters related to the interface elements are shown in Table 1. 3.1.2. Results 3.1.2.1. Displacements. Fig. 5a shows the lateral displacements of model walls under a surcharge of 45 kPa, indicated as dash lines. The steep facing wall induced more displacement than the gentle facing wall, with the maximum value occurring at the top. This is because the center of gravity of the steep wall was closer to the wall face; thus the wall provided less resistance to overturning than the gentle facing wall. The analytical results are presented by solid lines. Although there are some differences between the analytical and experimental results, the two results are generally in good agreement.
Comparison of the settlement at the top of the wall between analytical and test results for various facing angles is shown in Fig. 5b. In general, the trends of the settlement curves are similar, but more settlement was recorded in the experiment, especially for the steeper wall. This is likely due to tilting of the wall (Fig. 6a), which formed a gap at the wall back. Subsequently, sand fell into the gap and thus resulted in more significant settlement than analytical result. 3.1.2.2. Failure mode. From the photograph and sketches of the sliding surfaces shown in Fig. 6a, it can be seen the failure modes of these gravity-type walls include a mode of horizontal sliding along the interface of the geocell layers and a mode of overturning of the wall. The gentle facing wall tended to fail in both sliding and tilting, while the steep facing wall tended to fail in sliding. Fig. 6b shows the stress states in the three walls based on the original shapes of
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also at the heel of the wall. This implies most of the wall was failed in tilting. As for the 80 wall (Model 2), the yellow zone appears also in the lower part of the wall, but it is more close to the back of the wall, which indicates tilting of the 80 wall occurred in the lower part.
Normalized horizontal displacement x/H
4
LVDT1 LVDT2 LVDT3 LVDT4 LVDT5
3
2
1
0 0
2
4
Normalized surcharge pressure
6
q/γH
Fig. 7. Facing displacement versus surcharge for a gravity-type wall model No. 5, H ¼ 4 m, a ¼ 70 (Chen and Chiu, 2008).
the numerical models. The yellow zone indicates the zone that yielded in tension, the red zone represents the zone that yielded in shear, and the zones in other colors are in elastic state. It can be seen the red zones in Fig. 6b are comparable to the failure surfaces shown in Fig. 6a. Moreover, the 90 wall (Model 3) failed like a tilting wall. This is evidenced by the distribution of the yellow zones that yielded in tension. In the 70 wall, the yellow zones are small and appear mainly in the upper part of the wall back. This suggests only a small upper part of the wall was failed in tilting. In contrast, the yellow zones in the 90 wall are large and appear mainly in the lower part of the wall; not only in the middle zone but
3.1.2.3. Critical load. Numerical analysis was also performed to examine the influence of surcharge on the stability of the wall and to find the critical load under which the wall is on the brink of failure. To obtain the factors of safety of the three model walls under various surcharges, the strength reduction method (SRM), proposed by Zienkiewicz et al. (1975), was used. In the method, soil strength parameters (such as c and tan 4) are reduced until the shear strength of the soil is unable to sustain the weight of the soil and the wall becomes unstable. The factor of safety is then defined as the ratio of the initial strength parameter and the reduced strength parameter. Table 2 presents the factors of safety of the three walls under various surcharges. The results show that, when there is no surcharge (q ¼ 0), all the factors of safety are greater than 1.5, indicating a stable condition. As expected, the gentler wall had a higher factor of safety. When the surcharge increases, the factor of safety correspondingly decreases. At q ¼ 20 kPa, all the factors of safety are close to 1.0, implying all the walls are either on the brink of failure or have failed. As the surcharge increased to q ¼ 45 kPa, all the factors of safety are well below 1.0. Nonetheless, the three walls did not fail dramatically, as shown in Fig. 6a. The critical loads can be estimated from the experimental results. Fig. 7 displays the relationship of normalized lateral displacement (x/H) versus normalized surcharge (q/gH), in which the symbols x and q denote lateral displacement and surcharge, respectively. The locations of the five LVDTs are indicated by the ordinates of the data points of the model tests (see Fig. 5), with LVDT1 is at the top and LVDT5 is at the bottom, and vice versa.
Fig. 8. Meshes and boundary conditions for geocell-reinforced walls with various layouts (a ¼ 70 ).
R.-H. Chen et al. / Geotextiles and Geomembranes 39 (2013) 51e62 Table 1 Input parameters of interface elements.
57
0 Interface geocell layers
Modulus of elasticity E (MPa) Ultimate tensile strength Fy (kN/m) Shear stiffness Kbond (N/m/m) Interfacial adhesion Sbond (N/m) Interfacial friction angle Sfric ( ) Area a (m2) Perimeter peri (m)
21.0 0 0.64 0 31.3 0.0013 2.0
21.0 0 0.77 0 37.2 0.0013 2.0
Fig. 7 was obtained from the model wall that simulated a 4-m high wall; nevertheless, the normalized relation can still be used as a reference. As seen in this figure, the normalized displacement increases almost linearly with increasing normalized surcharge up to q/gH ¼ 2, which indicates the critical load. Thus, the critical load is estimated as q ¼ 24.5 kPa (for the model wall, g ¼ 15.3 kPa and H ¼ 0.8 m) by the experiment, which is close to the critical load, 22.0 kPa, obtained from the FLAC program (see Table 2). In summary, comparing the results of model walls, this analytical model is capable of, and suitable for, simulating the behavior of geocell-reinforced retaining structures. Therefore, the numerical model was employed to assess the performance of the retaining structures with various layouts. 4. Effect of structure layout To assess the effect of the structure layout, four geocell walls were studied, as presented in Fig. 8. In the four layouts, layouts G (gravity type) and FE (extended facing type) are commonly adopted in practice. The installation guidelines for walls of these types can be found easily in the market. The other two types, GU and GE, are possible modification of the gravity type. These walls were 4 m high and had a 70 facing angle. All walls were composed of 16 layers of geocells, and the amount of geocells in the walls was made to be the same. Each layout is briefly introduced as follows. Layout 1 (G) e The wall consisted of several zones, each zone having an equal length of geocells. Layout 2 (GU) e Geocell layers were extended in the upper part of the wall to prevent this gravity-type wall from tilting. Layout 3 (GE) e Alternatively, geocell layers were lengthened at certain depths, to act as reinforcements and to enhance stability. The increase in the length of geocells can be regarded as providing reinforcements similar to geogrids; the difference is geocells have larger and thicker cells than the grids of geogrids. Layout 4 (FE) e Generally, a facing-type wall is not as stable as a gravity-type wall in resisting lateral earth pressure. This is because the facing-type wall has equal width from top to bottom. Consequently, providing reinforcement over the full height of the structure by extending geocell layers at certain depths was the preferred method. In practice, reducing differential settlements of a wall is usually achieved by installing a leveling pad or concrete base pad beneath
Table 2 Factors of safety of model walls under various surcharges. Surcharge q(kPa)
Model 1 a ¼ 70
Model 2 a ¼ 80
Model 3 a ¼ 90
0 20 45
1.89 1.03 0.81
1.69 1.0 0.75
1.57 0.98 0.75
0.2
Depth form the top (h/H)
Interface sand/paper
0.4
0.6 G GU
0.8
GE FE
1 0
0.1 0.2 0.3 Lateral displacement (x/H) (%)
0.4
(a) 0 0.1 Settlement (s/H) (%)
Parameter
0.2 0.3 0.4 G GU
0.5
GE FE
0.6 0.8
0.6 0.4 0.2 Distance form the wall face (L/H)
0
(b) Fig. 9. Comparison of displacements for various wall layouts (q ¼ 50 kPa). (a) Lateral displacement of wall facing. (b) Settlement of the backfill.
the wall (Xie and Yang, 2009). In this section, the depth of bottom boundary was assumed to be the same as that used in the previous section of validation of numerical model. Nevertheless, the effect of bottom boundary on the whole wall behavior may be significant for other situations. 4.1. Displacement A comparison of the deformation of the wall face and the settlement of the backfill is presented in Fig. 9. Fig. 9a shows the normalized lateral displacement of the wall face when the surcharge was 50 kPa. Among the four layouts, Type G (Layout 1) has the largest deformation, with a maximum normalized displacement of more than 0.33% occurring at the top, while Type FE (Layout 4) shows much less normalized displacement, 0.055% (about 1/6 of 0.33%), occurring at the middle height of the wall. In general, gravity-type walls such as Types G and GU display more lateral displacements at the top. In contrast, Types GE or FE with a lengthening of geocell layers from top to bottom induces a completely different pattern of much less displacement, with the
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maximum value occurring at the mid-height of the wall. Note that the maximum normalized displacement of 0.33% approximately corresponds to a typical value of 0.4% H for walls with inextensible reinforcements and is less than 1.0% H for walls with extensible reinforcements (Mitchell and Christopher, 1990).
The curves of settlement of the backfill display correspondingly to the curves of lateral displacement (Fig. 9b). For instance, the maximum normalized settlements of Types G and GU are about 0.5% and occur close to the wall face. This indicates a tilting type of failure mode. On the contrary, the maximum normalized
Fig. 10. Yield zones in the walls with different layouts (q ¼ 50 kPa). (a) Layout. (b) Yield zone.
R.-H. Chen et al. / Geotextiles and Geomembranes 39 (2013) 51e62
settlements of Types GE and FE are less than 0.2% and occur far from the wall face. This implies a different failure mode, i.e., sliding failure. As seen from Fig. 9a,b, Type GE induces the smallest settlement among the four curves, though its lateral displacement is somewhat more than that of Type FE (Fig. 9a). It can thus be concluded that lengthening the geocell layer at certain depths from top to bottom is a potentially effective method of construction in terms of wall movement as well as settlement of the backfill. 4.2. Yield zone Fig. 10 shows the stress states in the four walls subjected to a surcharge of 50 kPa. In Layout 1 (G), a clear potential failure surface
59
is seen starting from the crest and passing through the heel of the wall. Moreover, an active wedge and several radial slip lines form behind the wall. This phenomenon is similar to the bearing capacity failure due to the surcharge acting at the crest. In Layout 2 (GU) the potential failure surface is still clear, but the radial slip lines were shorter, owing to the upper, lengthened, geocell layers preventing the slip lines from extending into the layers. Instead, some yellow tension spots develop along the back of wall from the top to the bottom of lengthening layers, from where several radial slip lines are formed. In Layout 3 (GE) the potential failure surface is also clear, yet it becomes smaller than those of Layouts 1 and 2. Further, the radial slip lines become unclear, and several isolated yellow spots
Fig. 11. Comparison of stress states among walls with different facing angles (q ¼ 50 kPa). (a) Numerical model. (b) Stress state.
R.-H. Chen et al. / Geotextiles and Geomembranes 39 (2013) 51e62
distributed along the back of the wall. As mentioned previously, Layouts 3 and 4 result in less lateral displacements than the other layouts. Correspondingly, the potential failure surface in Layout 3 becomes small and passes above the heel of wall, as a result of the lengthening layer at the lower zone. However, it can be seen an active wedge extending to a significant depth, and a shear plane, though somewhat obscure, forms along the back of the reinforced zone, implying the zone behaves as a monolithic composite wall. In Layout 4 (FE), most of the stress states are elastic, and the zones that yielded in shear are difficult to find. Therefore, Layout 4 that is an extended facing-type reinforced wall performs best among all the four layouts.
0
Depth from the top (h/H)
60
5. Analysis of extended facing-type reinforced walls
0.2 0.4 0.6
Since the extended facing-type reinforced wall performs quite well, it is of interest to compare the performance of these walls with different facing angles. The numerical models of the three analyzed walls, which were constructed with the same amount of geocells, are shown in Fig. 11a.
1
5.1. Yield zone
0
5.2. Displacements
0
0.2 0.4 Lateral displacement (x/H) (%)
0.6
(a)
Settlement (s/H) (%)
Fig. 11b shows the stress states in the three walls when subjected to a surcharge of 50 kPa. The 70 wall (FE-7) only shows two inclined shear planes, starting from the bottom of the second extended geocell layer (counting from the top) and dipping to a significant depth. In the wall with an 80 facing angle (FE-8), a few zones are yielded in shear together with many isolated yellow spots, which are yielded in tension and distributed along the geocell layers. In the vertical wall (FE-9), there is a large wedge failure behind the reinforced zone. Many locations along the geocell layers are yielded in tension, suggesting the wall has titled. Evidently, these tensile zones are caused by the settlement of the large wedge that pushes the wall aside, causes the wall to tilt, resulting in geocells under tension.
FE-7 (α = 70 ) FE-8 (α = 80 ) FE-9 (α = 90 )
0.8
0.2
0.4
FE-7 (α = 70 ) FE-8 (α = 80 ) FE-9 (α = 90 )
0.6
0.8 0.8
0.6 0.4 0.2 Distance from the wall face (L/H)
0
As for the deformation of the wall, Fig. 12a shows the normalized lateral displacement of the wall when q ¼ 50 kPa. As expected, the vertical wall displays much more displacement than the other two walls, and the maximum normalized displacement is 0.53% occurring at the top; however, those in the walls of 70 and 80 are only 0.09% and 0.13 % (about 1/6e1/4 of 0.53%), respectively, occurring at mid-height of the walls. The settlement of the backfill is shown in Fig. 12b. Correspondingly, the vertical facing wall induces more displacement than the gentle facing walls. The maximum normalized settlement of the vertical wall is about 0.5%, occurring at the wall face; this type of settlement suggests that the mode of failure is tilting. In contrast, for walls with facing angles of 70 and 80 , most settlements are uniformly distributed, except near the wall face; this distribution of settlement indicates the gentle facing wall fails more like a sliding mode. From the above observation, reducing the facing angle of an extended facing-type reinforced wall from 90 to less than 80 will significantly reduce the lateral displacement of the wall face, change the deformation pattern, and alter the failure mode from tilting to sliding.
the friction angles of the soil and the plane-strain angle of friction at relative density Dr ¼ 62% are 4tx ¼ 41 and 4ps ¼ 44 , respectively. Herein 4ps ¼ 44 was used to calculate the coefficients of respective earth pressures shown in Eqs. (10)e(12). The symbols in the equations are defined in Fig. 13: b ¼ inclination of ground surface above wall, z ¼ inclination of wall from vertical, z ¼ vertical distance from ground surface, and sh ¼ horizontal component of active earth pressure. The sign convention is considered positive for the angle measured counterclockwise from the reference line. The interfacial friction angle (d ¼ 31 ) between the wall and the backfill was taken into consideration for the Coulomb earth pressure. Note that the cohesion was ignored.
5.3. Lateral earth pressure
Ko ðatrestÞ ¼ 1 sin 4
As mentioned, the internal friction angle of the soil and the plane-strain angle of friction can be estimated from Eqs. (1) and (2). By taking the stress at the mid-height of the 4-m wall as the mean stress to represent the whole wall and substituting it into Eq. (1),
(b) Fig. 12. Comparison of deformation among facing-type geocell walls with different facing angles (q ¼ 50 kPa). (a) Lateral displacement. (b) Settlement of the backfill.
Ka ðCoulombÞ ¼
cos2 ð4 zÞ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2 ð4þdÞsin ð4bÞ cos2 zcos ðd þ zÞ 1 þ sin cos ðzþdÞcos ðzbÞ
(10) (11)
R.-H. Chen et al. / Geotextiles and Geomembranes 39 (2013) 51e62
61
0
α = 70°
A-A' B-B'
Depth from the top (h/H)
0.2
Ka z
Backfill soil
At rest Rankine 0.4
Coulomb
0.6
0.8
, 1
0
0.1
0.2
0.3
0.4
(a)
h
0 A-A'
α = 80°
B-B'
Depth from the top (h/H)
0.2
Fig. 13. Definition of symbols.
Ka ðRankineÞ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi cos b 1 þ sin2 4 2sin 4cos q qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ cos b þ sin2 4 sin2 b
At rest Rankine 0.4
Coulomb
0.6
0.8
(12)
1 0
1
where q ¼ 2z þ ub b and ub ¼ sin ðsin b=sin 4Þ. The inclination of Rankine’s active earth pressure to the normal of the plane is
α = 90° 0.2
(13)
The curves of normalized lateral earth pressure acting along the backs of wall facing and the reinforced zone are shown in Fig. 14 for q ¼ 0. The data are obtained from the five extended geocell-reinforced layers (see Fig. 11a). It is observed that the distributions of lateral earth pressure for these walls with steep facings are not much different. For all three walls, the lateral earth pressures along the back of facing (AeA0 ) are less than those along the back of reinforced zone (BeB0 ). Specifically, the distributions of the lateral earth pressure along AeA0 are somewhat higher than the horizontal stress in Rankine’s active state, while those along BeB0 are close to the earth pressures at-rest. Note that the coefficients of earth pressure acting on a vertical plane (a ¼ 90 or z ¼ 0 ) are Ka ¼ 0.18 and K0 ¼ 0.305 for active and at-rest states, respectively. The active earth pressures according to Coulomb’s method that considers interfacial friction angle are lower than those using Rankine’s theory, especially for the gentler facing walls (Fig. 13a and b). Thus Coulomb’s method appears to be unsuitable for these walls. When limit equilibrium method is adopted in the design, it is suggested that the lateral earth pressure against the back of wall facing be considered higher than the horizontal stress in Rankine’s active state, and that along the back of the reinforced zone be the earth pressure at-rest.
0.3
0.4
(b)
sin 4sin q 1 sin 4cos q
0.2
0
Depth from the top (h/H)
dðRankineÞ ¼ tan1
0.1
A-A' B-B' At rest Rankine
0.4
Coulomb
0.6
0.8
1 0
0.1 0.2 0.3 Lateral earth pressure (σh /γH)
0.4
(c) Fig. 14. Normalized lateral earth pressure distribution at the backs of wall facing and reinforced zone (q ¼ 0). (a) a ¼ 70 , (b) a ¼ 80 , (c) a ¼ 90 .
6. Conclusion This paper presents a numerical model for analyzing the performance and stability of geocell-reinforced retaining structures. The constitutive model adopted for analysis consisted of a nonlinear elastic stressestrain relationship with MohreCoulomb yield criterion. For verification of the numerical model, three
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model-scale gravity-type walls were examined in terms of the lateral displacement of the wall face, the failure mode of the structure, and the critical load to cause failure. To assess the effect of the structure layout, four walls of various layouts were compared from the aspects of the deformation and yield zone of the structure. In the end, the extended facing-type reinforced walls with different facing angles were studied. Comparison of yield zone, deformation of the structure, and the distribution of lateral earth pressure against the backs of the wall facing and the reinforced zone were made. According to the results of analysis, the following conclusions are drawn. In verification of the numerical model, comparable results show good agreement in predicting potential slip surface as well as estimating critical load under which the wall is at the brink of failure. The lateral displacements of the walls between the model test and analytical results are also comparable. For the model walls studied, the factor of safety close to 1.0 corresponds to a surcharge of q/gH ¼ 2. As the surcharge continued to increase, the factor of safety decreases to less than 1.0; nevertheless, the model walls did not fail dramatically. The failure mode of the gentler slope consists of a few slides passing along the interface between geocell layers, while that of the steep vertical wall displays both modes of interlayer sliding and overturning failure. Among the four walls constructed with the same amount of geocells, the wall with lengthening geocell layers at certain depths, irrespective of gravity type (GE) or facing type (FE), performs better than the other layouts (G and GU). Lengthening the geocell layer at certain depths from top to bottom is a potentially effective method of construction in terms of wall movement as well as settlement of the backfill. According to the analysis of three extended facing-type walls with different facing angles, the wall with a facing angle less than 80 (e.g., FE-7 and FE-8), will significantly reduce the lateral displacement of the wall face, change the deformation pattern, and have the sliding mode of failure. The lateral earth pressures against the back of wall facing were found to be somewhat higher than the horizontal stress in Rankine’s active state, while those along the back of the reinforced zone were close to the earth pressures at-rest. References Adams, M.T., Lillis, C.P., Wu, J.T.H., Ketchart, K., 2002. Vegas mini pier experiment and postulate of zero volume change. In: Proceedings of the 7th International Conference on Geosynthetics. Balkema, Rotterdam, pp. 389e394. Adams, M.T., Nicks, J., Stabile, T., Wu, J.T.H., Schlatter, W., Hartmann, J., 2011. Geosynthetic Reinforced Soil Integrated Bridge System - Interim Implementation Guide. Report FHWA-HRT-11-026. Federal Highway Administration, McLean, Virginia, USA. Al Hattamleh, O., Muhunthan, B., 2006. Numerical procedures for deformation calculations in the reinforced soil walls. Geotextiles and Geomembranes 24 (1), 52e57. ASTM D 4595, 2011. Standard Test Method for Tensile Properties of Geotextiles by the Wide-width Strip Method. American Society for Testing and Materials, West Conshohocken, Pennsylvania, USA. Bathurst, R.J., Allen, T.M., Walters, D.L., 2005. Reinforcement loads in geosynthetic walls and the case for a new working stress design method. Geotextiles and Geomembranes 23 (4), 287e322. Bathurst, R.J., Crowe, R.E., 1994. Recent case histories of flexible geocell retaining walls in North America. In: Tatsuoka, F., Leshchinsky, D. (Eds.), Recent Case Histories of Permanent Geosynthetic-reinforced Soil Retaining Walls. Balkema, Rotterdam, pp. 3e19. Bathurst, R.J., Karpurapu, R., 1993. Large scale triaxial compression testing of geocellsreinforced granular soils. Geotechnical Testing Journal 16 (3), 296e303. Bolton, M.D., 1986. The strength and dilatancy of sands. Géotechnique 36 (1), 65e78.
Chen, R.H., Chiu, Y.M., 2008. Model tests of geocell retaining structures. Geotextiles and Geomembranes 26, 56e70. Chen, R.H., Huang, Y.W., Huang, F.C., 2013. Confinement effect of geocells on sand samples under triaxial compression. Geotextiles and Geomembranes 37, 35e44. El-Emam, M.M., Bathurst, R.J., 2007. Influence of reinforcement parameters on the seismic response of reduced-scale reinforced soil retaining walls. Geotextiles and Geomembranes 25 (1), 33e49. Itasca Consulting Group, 2005. FLAC: Fast Lagrangian Analysis of Continua, Version 5.0. Itasca Consulting Group, Inc., Minneapolis, Minnesota, USA. Lade, P.V., Lee, K.L., 1976. Engineering Properties of Soils. Report UCLA-ENG-7652. University of California at Los Angeles, USA, p. 145. Ling, H.I., Leshchinsky, D., Wang, J.-P., Mohri, Y., Rosen, A., 2009. Seismic response of geocell retaining walls: experimental studies. Journal of Geotechnical and Geoenvironmental Engineering, ASCE 135 (4), 515e524. Mitchell, J.K., Christopher, B.R., 1990. North American practice in reinforced soil systems. In: Proceedings of the ASCE Conference on Design and Performance of Earth Retaining Structures. Cornell University, pp. 322e346. Mehdipour, I., Ghazavi, M., Moayed, R.Z., 2013. Numerical study on stability analysis of geocell reinforced slopes by considering the bending effect. Geotextiles and Geomembranes 37, 23e34. Racana, N., Gourvès, R., Grédiac, M., 2001. Mechanical behavior of soil reinforced by geocells. In: Proceedings of the International Symposium on Earth Reinforcement. Taylor and Francis, Japan, pp. 437e442. Skinner, G..D., Rowe, R.K., 2005. Design and behavior of a geosynthetic reinforced retaining wall and bridge abutment on a yielding foundation. Geotextiles and Geomembranes 23 (3), 235e260. Wesseloo, J., Visser, A.T., Rust, E., 2009. The stressestrain behavior of multiple cell geocell packs. Geotextiles and Geomembranes 27, 31e38. Won, M.S., Kim, Y.S., 2007. Internal deformation behavior of geosyntheticreinforced soil walls. Geotextiles and Geomembranes 25 (1), 10e22. Wu, J.T.H., Pham, T.Q., 2013. Load-carrying capacity and required reinforcement strength of closely-spaced soilegeosynthetic composites. Journal of Geotechnical and Geoenvironmental Engineering. http://dx.doi.org/10.1061/(ASCE) GT.1943-5606.0000885. Xie, Y., Yang, X., 2009. Characteristics of a new-type geocell flexible retaining wall. Journal of Materials in Civil Engineering, ASCE 21 (4), 171e175. Zienkiewicz, O.C., Humpheson, C., Lewis, R.W., 1975. Associated and non-associated visco-plasticity and plasticity in soil mechanics. Géotechnique 25 (4), 671e689.
Glossary
Basic SI units are given in parentheses c: cohesion intercept of soil strength (N/m2) cr: apparent cohesion of geocell-reinforced soil (N/m2) Dr: relative density (%) E: modulus of elasticity (N/m2) Fy: ultimate tensile strength (N/m) G: shear modulus (N/m2) Gs: specific gravity (dimensionless) H: wall height (m) h: vertical distance from the top of wall (m) K: bulk modulus (N/m2) Ka: coefficient of active earth pressure (dimensionless) Kbound: shear stiffness (N/m2) K0: coefficient of earth pressure at-rest (dimensionless) L: length (m) pa: atmospheric pressure (N/m2) q: surcharge (N/m2) Sbond: interfacial adhesion (N/m) Sfric: interfacial friction angle ( ) s: settlement (m) x: lateral displacement (m) z: vertical distance from ground surface (m) a: facing angle of wall ( ) b: inclination of ground surface above wall ( ) d: interfacial friction angle or inclination of active earth pressure to the normal of a plane ( ) f: friction angle of soil ( ) fps : plane-strain angle of friction ( ) fr : friction angle of geocell-reinforced sand ( ) ftx : triaxial compression angle of friction ( ) g: unit weight (N/m3) gd: dry unit weight (N/m3) z: inclination of wall from vertical ( ) l: scaling factor of length (dimensionless) n: Poisson’s ratio (dimensionless) j: angle of dilation ( ) sh: lateral earth pressure or horizontal component of active earth pressure (N/m2) s3: confining pressure (N/m2)
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Geotextiles and Geomembranes journal homepage: www.elsevier.com/locate/geotexmem
Numerical analysis of geocell-reinforced retaining structures Rong-Her Chen*, Chang-Ping Wu, Feng-Chi Huang, Che-Wei Shen Department of Civil Engineering, National Taiwan University, Taipei 10617, Taiwan, ROC
a r t i c l e i n f o
a b s t r a c t
Article history: Received 6 December 2012 Received in revised form 27 April 2013 Accepted 2 July 2013 Available online
This paper presents numerical analysis on the behavior of geocell-reinforced retaining structures with various layouts. The constitutive model adopted for materials consisted of a nonlinear elastic stress estrain relationship with MohreCoulomb yield criterion. The strength parameters of the materials were obtained from relevant tests. For verification of the numerical model, three model-scale gravity-type walls with different facing angles were analyzed, and the finite difference program FLAC was utilized in the analysis. The results of the verification show good agreement in predicting the potential slip surface as well as estimating the critical load causing the wall to fail. The verified numerical model was then employed to study various layouts of retaining structures, which were constructed with the same amount of geocells, to compare the failure mode as well as the deformation of the structure. It has been found, irrespective of gravity type or facing type, the structure that extends the length of geocells in some layers to serve as reinforcement performs well in reducing the deformation of the structure and decreasing the potential slip zone. Moreover, with lengthening geocell layers as reinforcements, extended facing-type structures of various facing angles were analyzed. The results show that a wall with a facing angle less than 80 will significantly reduce the lateral displacement of the wall face. Further, the lateral earth pressures against the back of wall facing are somewhat higher than the horizontal stress in Rankine’s active state, while those along the back of the reinforced zone are in at-rest state. Ó 2013 Elsevier Ltd. All rights reserved.
Keywords: Geocells Retaining structure Numerical analysis Stability Deformation
1. Introduction The geocell retaining system can be made to conform to the topography of the place, and the system tolerates deformation or settlement due to flexibility. Vegetation can also be planted into the cells, thereby improving the aesthetics of the surrounding environment. Besides, geocells vastly improve the shear strength of granular soil by providing confinement to the soil; and, in turn, the increase in soil strength provides improved bearing capacity and/or prevents soil erosion. Previous research on geocells mainly utilized laboratory tests. Bathurst and Karpurapu (1993) reported the results of a series of large-scale triaxial compression tests carried out on 200 mm-high isolated geocellesoil composite samples and unreinforced soil samples. It was found that the peak friction angles of the soil infill and the composite were the same; while the effect of confinement from the geocells may be simulated by an apparent cohesion. Uniaxial compression tests have also been conducted on large
* Corresponding author. Tel./fax: þ886 2 23629851. E-mail addresses: [email protected] (R.-H. Chen), r98521126@ ntu.edu.tw (C.-P. Wu), [email protected] (F.-C. Huang), cwshen@ sinotech.org.tw (C.-W. Shen). 0266-1144/$ e see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.geotexmem.2013.07.003
samples. Bathurst and Crowe (1994) described two large-scale uniaxial compression tests to examine the stability of multiple layers of geocells under vertical surcharge. They also mentioned the stability analysis of a reinforced embankment with slopes of various inclinations, and the location and combination of geosynthetic reinforcement in the slopes were determined by conventional methods of analysis for the reinforced retaining wall and reinforced slope. Wesseloo et al. (2009) discussed the results of uniaxial compression tests performed on geocell packs of different sizes. Chen et al. (2013) performed tests on geocell-reinforced sand samples under triaxial compression. It has been found that the apparent cohesion of reinforced samples varies with the shape, size and number of cells, of which the cell size is the most significant factor. In addition, approximately linear relationships were found between the apparent cohesion and the inverse of the equivalent diameter of the cell. Regarding the interfacial strength between two layers of geocell-reinforced sand, Bathurst and Crowe (1994) performed a direct shear test and found the friction angle at the interface essentially equaled the friction angle of the sand and the cohesion was zero. This is because the geocells were thin, meaning their occupied area was very small compared to that of sand. Model test has been conducted by Racana et al. (2001) on a rigid wall reinforced with paper cells and a soft wall reinforced with
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polyan cells. The Young’s modulus of the polymer was thirty times less than the modulus of the paper. They concluded that the magnitude of the displacement was very sensitive to the Young’s modulus of the material; nevertheless, the same failure mechanism was observed: an active block with no passive anchorage movement. Chen and Chiu (2008) performed model tests to examine both the effect of geocells as a major material in retaining structures and the failure mechanism of the said structures under surcharge. The main variables in the tests included the height and facing angle of the structure, the type of surcharge, and the reinforcement embedded in two externally stabilized structures: the gravity type and the facing type. The gravity-type wall is narrow at the top and wide at the bottom, while the facing type is described as having equal width from top to bottom. According to the test results, they proposed several layouts of geocell-reinforced retaining structures. Even though considerable interest has been shown in reinforced walls or reinforced slopes (Bathurst et al., 2005; Skinner and Rowe, 2005; Al Hattamleh and Muhunthan, 2006; El-Emam and Bathurst, 2007; Won and Kim, 2007; Ling et al., 2009; Mehdipour et al., 2013), little research has been published concerning numerical analyses on geocell retaining structures. To enhance better understanding of the geocell retaining structures, this paper assesses the stability and deformation of geocell retaining structures with various layouts. The failure modes as well as the deformations of the structures, which were constructed with the same amount of geocells, were investigated and compared. 2. Material model The numerical analysis in this study utilized the finite difference program FLAC (Fast Lagrangian Analysis of Continua). Detailed descriptions and derivations of the method are referred to in Itasca (2005). In the numerical model shown in Fig. 1, there are several types of element: soils, including backfill and foundation soils; geocellreinforced soil in the reinforced zone; and an interface element between two materials. The constitutive model for the reinforced soil and backfill is a nonlinear elastic stressestrain relationship
Reinforced soil (sand infill geocell)
Backfill soil
1
with MohreCoulomb yield criterion. Details of these elements are described below. 2.1. Material elements Reinforced soil walls generally have steep facings (70 ), and the reinforcements in the walls are commonly shorter than their wall heights and are embedded in several layers. Geocell layers used as the reinforcements also are usually thick, comparing to other reinforcements such as geogrids. As a result, the zone constructed with geocells is as stiff as a monolithic composite. This has been shown by the model tests on geocell-reinforced walls (Racana et al., 2001), in which the failure mechanism observed was an active block with no passive anchorage movement. The result suggested that the failure mode was due to shear failure. Therefore, an elasticeplastic stressestrain relationship with MohreCoulomb yield criterion was adopted in this study. A similar model has been used by Xie and Yang (2009) who employed the finite element software, MARC, with the yield criterion of ideal elasticeplastic MohreCoulomb model, to evaluate the stress distribution in a geocell retaining wall constructed on an expressway in central north China. The constitutive model for geocell-reinforced soil is similar to that of soil, i.e., the strength parameters of the reinforced soil have an apparent cohesion in addition to friction angle. In this study, the apparent cohesion, resulting from the confinement effect provided by geocells, was obtained from the tests on samples of geocellreinforced sand under triaxial compression. Details about the test procedures and similar results can be found in Chen et al. (2013). On the other hand, the angle of dilatation was assumed to be zero because it was found to have insignificant effect on the analytical result. For an example studied (Type G in Fig. 8a), with the angles of dilation assumed to be j ¼ 0 and j ¼ 10 , respectively, the lateral displacements with the assumption of j ¼ 10 are slightly higher, but the differences between the two cases are less than 2%. Moreover, in plane-strain test or triaxial compression test, typical dense sand in drained condition tends to dilate when subjected to shear stress (Bolton, 1986). Nevertheless, Adams et al. (2002) conducted vertically loaded tests on representative soile geosynthetic composites to an average vertical stress of 1000 kPa, and reported that the presence of geosynthetic reinforcement reduced significantly the tendency for soil dilation, especially when the reinforcement was closely spaced. Consequently, they proposed a “postulate of zero volume change” based on observed behavior from the experiments. The postulate has been implemented in the FHWA GRS-IBS design manual for design of Geosynthetic Reinforced Soil (GRS) bridge abutments (Adams et al., 2011; Wu and Pham, 2013) and for predicting maximum lateral movement of bridge abutments. Note that for a typical reinforced soil mass with vertical spacing Sv 0.5 m, contraction is likely. In those cases, the assumption of j ¼ 0 is conservative. For geocell-reinforced walls, the dilation of soil could also be suppressed by the thick and closely spaced geocell layers. Due to above reasons, the angle of dilation was assumed to be zero in this analysis.
2
2.2. Interface element
Foundation soil
Cable elements - interface between soil and facing units Cable elements - interface between geocell layers Fig. 1. Numerical model for simulating the materials in a geocell-reinforced wall system.
Interface resistance between different materials may significantly affect the deformation of geocell reinforcements. In this study, two types of interface were modeled (Fig. 1): the interface between geocell-reinforced soil layers or between the reinforced zone and foundation soil; and the interface between the reinforced zone (geocells) and the backfill. These interfaces are simulated by cable elements. The parameters of the cable element are obtained
R.-H. Chen et al. / Geotextiles and Geomembranes 39 (2013) 51e62
53
unreinforced reinforced
1200
Deviatoric stress (kPa)
σ3r=196.2kPa σ3r=147.1kPa 800
σ3r=98.1kPa σ3r=49kPa σ3=196.2kPa σ3=147.1kPa σ3=98.1kPa
400
σ3=49kPa 0 0
5
10
15
20
25
Axial strain (%) Fig. 3. Typical results of compression tests on samples of sand and reinforced sand (at relative density Dr ¼ 70% and under various confining pressures).
3.1. Comparison with model tests Fig. 2 shows three gravity-type geocell-reinforced model walls that are 0.8 m high; each wall had facing angles of 70 , 80 , and 90 , respectively. These model-scale walls were employed to simulate 2.0 m high prototype-scale walls, and therefore the scaling factor of length, l, is 2.5 (¼ 2 m/0.8 m). In the numerical model, all walls were constructed in eight layers. The bottom boundary was fixed against movement in all directions, while the vertical boundaries were restricted in the horizontal direction and free to move in the vertical direction. Surcharge was applied at the top of the wall, and then the deformation and factor of safety of the wall were calculated. 3.1.1. Input parameters 3.1.1.1. Soil. The soil used for testing was uniform sub-angular silica sand with specific gravity Gs ¼ 2.64 and dry unit weight gd ¼ 15.3 kN/m3 (at relative density Dr ¼ 62%). According to the
Fig. 2. Model walls with different facing angles for validation of numerical model.
from direct shear test on the interface of two materials. Details about the values of these parameters at various interfaces are introduced later.
Shear stress, (kPa)
120
80
40
3. Validation of numerical model 0
The numerical model employed in this study was validated through the experimental results reported by Chen and Chiu (2008); the details concerning the arrangement of model tests can be found in the paper.
0
40
80
Normal stress,
120
(kPa)
Fig. 4. The results of direct shear test on different materials.
160
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R.-H. Chen et al. / Geotextiles and Geomembranes 39 (2013) 51e62
0
E ¼ ð290 þ 177Dr Þpa
0:55 (3)
pa
20
Depth from the top (cm)
s3
s3
K ¼ ð290 þ 156Dr Þpa
0:54 (4)
pa
The average Poisson’s ratio of the soil was n ¼ 0.33.
40
60
3.1.1.2. Geocell-reinforced soil. The strength parameters of reinforced sand were also obtained from the results of compression tests on sand samples confined by geocells (e.g., solid curves in Fig. 3). The samples were 300 mm high and had a diameter of 150 mm. The geocell material was made of high density polyethylene and the physical properties are as follows: specific gravity Gs ¼ 0.95, thickness t ¼ 1.3 mm, and mass per unit area mA ¼ 894 g/ m2. The tensile strength of the material is 17.0 kN/m and the elastic modulus is 492 kN/m, obtained from a wide-width sample, according to ASTM 4595. The strength parameters of the reinforced sand, cr (kPa) and 4r , based on MohreCoulomb failure criterion, are as follows.
α =70°(Model 1) α = 80°(Model 2) α = 90°(Model 3) — — — model test — numerical analysis
80
100 0
0.4 0.8 1.2 1.6 Lateral displacement (cm)
2
(a) 0
cr ¼ 72:5Dr þ 48:0
1
4r ¼ 34:8 þ 3:40Dr þ 3:08Dr log
(5)
Settlement (cm)
α =70°(Model 1) α = 80°(Model 2) α = 90°(Model 3)
4
model test — numerical analysis
———
5 60
40 20 Distance from the wall face (cm)
0
Fig. 5. Comparison of the analytical and test results for various facing angles (q ¼ 45 kPa). (a) Wall face deformation. (b) Settlement at the top of wall.
Unified Soil Classification System, the soil was classified as SP. Moreover, from the results of compression test on sand samples at various relative densities and under different confining pressures (e.g., dash curves in Fig. 3), it was found that the peak friction angle of the sand increased with relative density and reduced as the confining pressure increased:
s3 pa
4ps > 34+
(6)
(1)
(2)
In addition, Young’s modulus, E (kPa), and bulk modulus, K (kPa), are in terms of relative density and confining pressure:
(7)
where m and p stand for model and prototype cells, respectively. Note that the ratio between the two diameters (dp/dm) is the scaling factor of length, l. Therefore, the apparent cohesions of the model sample and the prototype sample were chosen to be equal. The elastic moduli of the prototype-scale geocell-reinforced sand are expressed in the following equations.
Er ¼ ð321 þ 344Dr Þpa
where pa ¼ atmospheric pressure (101.4 kPa), Dr ¼ relative density (%), s3 ¼ confining pressure (kPa). An estimate of the plane-strain angle of internal friction, 4ps , is found from the triaxial test results, 4tx , using the following equation (Lade and Lee, 1976):
4ps ¼ 1:54tx 17+
pa
cr;m ¼ cr;p =l dp =dm ¼ cr;p =l ðlÞ ¼ cr;p
(b)
4 ¼ 30:8 þ 13:4Dr 4:2Dr log
As can be seen from Eq. (5), the reinforced sand shows a marked increase in apparent cohesion, which mainly resulted from the contribution of the geocell providing confinement to the sand. Correspondingly, the average Poisson’s ratio for the reinforced sand, n ¼ 0.17, was much less than that of the sand, n ¼ 0.33. Furthermore, the apparent cohesion in Eq. (5) was chosen for the model geocells, after considering both the relative cell size and the scaling factor of length between the propotype-scale wall and model-scale wall. The reason is explained as follows. Regarding the sizing effect, a linear relationship was found between apparent cohesion, cr, and the inverse of diameter of circular cell, 1/d (Chen et al., 2013). As to the scaling effect, the apparent cohesion of the model cell should be reduced by a scaling factor of length, l. Therefore,
2
3
s3
s3
(8)
pa
Kr ¼ ð135 þ 231Dr Þpa
0:65
s3 pa
0:58 (9)
Similarly, the values for the model material were modified from the above values of the prototype material by dividing the scaling factor of length. 3.1.1.3. Interface element. The geocells of the model walls were made from book-binding paper that was 1.3 mm thick (Chen and Chiu, 2008). In this study, the interfacial shear strength between the two materials was obtained from a direct shear test. From the
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55
Fig. 6. Comparison of failure modes between the experimental and analytical results (q ¼ 45 kPa). (a) Experimental results (Chen and Chiu, 2008). (b) Analytical results.
results of the direct shear test (Fig. 4), the friction angle between the geocell-reinforced layers was found to be 37.2 , while the fiction angle between the sand and paper was 31.3 . The other parameters related to the interface elements are shown in Table 1. 3.1.2. Results 3.1.2.1. Displacements. Fig. 5a shows the lateral displacements of model walls under a surcharge of 45 kPa, indicated as dash lines. The steep facing wall induced more displacement than the gentle facing wall, with the maximum value occurring at the top. This is because the center of gravity of the steep wall was closer to the wall face; thus the wall provided less resistance to overturning than the gentle facing wall. The analytical results are presented by solid lines. Although there are some differences between the analytical and experimental results, the two results are generally in good agreement.
Comparison of the settlement at the top of the wall between analytical and test results for various facing angles is shown in Fig. 5b. In general, the trends of the settlement curves are similar, but more settlement was recorded in the experiment, especially for the steeper wall. This is likely due to tilting of the wall (Fig. 6a), which formed a gap at the wall back. Subsequently, sand fell into the gap and thus resulted in more significant settlement than analytical result. 3.1.2.2. Failure mode. From the photograph and sketches of the sliding surfaces shown in Fig. 6a, it can be seen the failure modes of these gravity-type walls include a mode of horizontal sliding along the interface of the geocell layers and a mode of overturning of the wall. The gentle facing wall tended to fail in both sliding and tilting, while the steep facing wall tended to fail in sliding. Fig. 6b shows the stress states in the three walls based on the original shapes of
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R.-H. Chen et al. / Geotextiles and Geomembranes 39 (2013) 51e62
also at the heel of the wall. This implies most of the wall was failed in tilting. As for the 80 wall (Model 2), the yellow zone appears also in the lower part of the wall, but it is more close to the back of the wall, which indicates tilting of the 80 wall occurred in the lower part.
Normalized horizontal displacement x/H
4
LVDT1 LVDT2 LVDT3 LVDT4 LVDT5
3
2
1
0 0
2
4
Normalized surcharge pressure
6
q/γH
Fig. 7. Facing displacement versus surcharge for a gravity-type wall model No. 5, H ¼ 4 m, a ¼ 70 (Chen and Chiu, 2008).
the numerical models. The yellow zone indicates the zone that yielded in tension, the red zone represents the zone that yielded in shear, and the zones in other colors are in elastic state. It can be seen the red zones in Fig. 6b are comparable to the failure surfaces shown in Fig. 6a. Moreover, the 90 wall (Model 3) failed like a tilting wall. This is evidenced by the distribution of the yellow zones that yielded in tension. In the 70 wall, the yellow zones are small and appear mainly in the upper part of the wall back. This suggests only a small upper part of the wall was failed in tilting. In contrast, the yellow zones in the 90 wall are large and appear mainly in the lower part of the wall; not only in the middle zone but
3.1.2.3. Critical load. Numerical analysis was also performed to examine the influence of surcharge on the stability of the wall and to find the critical load under which the wall is on the brink of failure. To obtain the factors of safety of the three model walls under various surcharges, the strength reduction method (SRM), proposed by Zienkiewicz et al. (1975), was used. In the method, soil strength parameters (such as c and tan 4) are reduced until the shear strength of the soil is unable to sustain the weight of the soil and the wall becomes unstable. The factor of safety is then defined as the ratio of the initial strength parameter and the reduced strength parameter. Table 2 presents the factors of safety of the three walls under various surcharges. The results show that, when there is no surcharge (q ¼ 0), all the factors of safety are greater than 1.5, indicating a stable condition. As expected, the gentler wall had a higher factor of safety. When the surcharge increases, the factor of safety correspondingly decreases. At q ¼ 20 kPa, all the factors of safety are close to 1.0, implying all the walls are either on the brink of failure or have failed. As the surcharge increased to q ¼ 45 kPa, all the factors of safety are well below 1.0. Nonetheless, the three walls did not fail dramatically, as shown in Fig. 6a. The critical loads can be estimated from the experimental results. Fig. 7 displays the relationship of normalized lateral displacement (x/H) versus normalized surcharge (q/gH), in which the symbols x and q denote lateral displacement and surcharge, respectively. The locations of the five LVDTs are indicated by the ordinates of the data points of the model tests (see Fig. 5), with LVDT1 is at the top and LVDT5 is at the bottom, and vice versa.
Fig. 8. Meshes and boundary conditions for geocell-reinforced walls with various layouts (a ¼ 70 ).
R.-H. Chen et al. / Geotextiles and Geomembranes 39 (2013) 51e62 Table 1 Input parameters of interface elements.
57
0 Interface geocell layers
Modulus of elasticity E (MPa) Ultimate tensile strength Fy (kN/m) Shear stiffness Kbond (N/m/m) Interfacial adhesion Sbond (N/m) Interfacial friction angle Sfric ( ) Area a (m2) Perimeter peri (m)
21.0 0 0.64 0 31.3 0.0013 2.0
21.0 0 0.77 0 37.2 0.0013 2.0
Fig. 7 was obtained from the model wall that simulated a 4-m high wall; nevertheless, the normalized relation can still be used as a reference. As seen in this figure, the normalized displacement increases almost linearly with increasing normalized surcharge up to q/gH ¼ 2, which indicates the critical load. Thus, the critical load is estimated as q ¼ 24.5 kPa (for the model wall, g ¼ 15.3 kPa and H ¼ 0.8 m) by the experiment, which is close to the critical load, 22.0 kPa, obtained from the FLAC program (see Table 2). In summary, comparing the results of model walls, this analytical model is capable of, and suitable for, simulating the behavior of geocell-reinforced retaining structures. Therefore, the numerical model was employed to assess the performance of the retaining structures with various layouts. 4. Effect of structure layout To assess the effect of the structure layout, four geocell walls were studied, as presented in Fig. 8. In the four layouts, layouts G (gravity type) and FE (extended facing type) are commonly adopted in practice. The installation guidelines for walls of these types can be found easily in the market. The other two types, GU and GE, are possible modification of the gravity type. These walls were 4 m high and had a 70 facing angle. All walls were composed of 16 layers of geocells, and the amount of geocells in the walls was made to be the same. Each layout is briefly introduced as follows. Layout 1 (G) e The wall consisted of several zones, each zone having an equal length of geocells. Layout 2 (GU) e Geocell layers were extended in the upper part of the wall to prevent this gravity-type wall from tilting. Layout 3 (GE) e Alternatively, geocell layers were lengthened at certain depths, to act as reinforcements and to enhance stability. The increase in the length of geocells can be regarded as providing reinforcements similar to geogrids; the difference is geocells have larger and thicker cells than the grids of geogrids. Layout 4 (FE) e Generally, a facing-type wall is not as stable as a gravity-type wall in resisting lateral earth pressure. This is because the facing-type wall has equal width from top to bottom. Consequently, providing reinforcement over the full height of the structure by extending geocell layers at certain depths was the preferred method. In practice, reducing differential settlements of a wall is usually achieved by installing a leveling pad or concrete base pad beneath
Table 2 Factors of safety of model walls under various surcharges. Surcharge q(kPa)
Model 1 a ¼ 70
Model 2 a ¼ 80
Model 3 a ¼ 90
0 20 45
1.89 1.03 0.81
1.69 1.0 0.75
1.57 0.98 0.75
0.2
Depth form the top (h/H)
Interface sand/paper
0.4
0.6 G GU
0.8
GE FE
1 0
0.1 0.2 0.3 Lateral displacement (x/H) (%)
0.4
(a) 0 0.1 Settlement (s/H) (%)
Parameter
0.2 0.3 0.4 G GU
0.5
GE FE
0.6 0.8
0.6 0.4 0.2 Distance form the wall face (L/H)
0
(b) Fig. 9. Comparison of displacements for various wall layouts (q ¼ 50 kPa). (a) Lateral displacement of wall facing. (b) Settlement of the backfill.
the wall (Xie and Yang, 2009). In this section, the depth of bottom boundary was assumed to be the same as that used in the previous section of validation of numerical model. Nevertheless, the effect of bottom boundary on the whole wall behavior may be significant for other situations. 4.1. Displacement A comparison of the deformation of the wall face and the settlement of the backfill is presented in Fig. 9. Fig. 9a shows the normalized lateral displacement of the wall face when the surcharge was 50 kPa. Among the four layouts, Type G (Layout 1) has the largest deformation, with a maximum normalized displacement of more than 0.33% occurring at the top, while Type FE (Layout 4) shows much less normalized displacement, 0.055% (about 1/6 of 0.33%), occurring at the middle height of the wall. In general, gravity-type walls such as Types G and GU display more lateral displacements at the top. In contrast, Types GE or FE with a lengthening of geocell layers from top to bottom induces a completely different pattern of much less displacement, with the
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maximum value occurring at the mid-height of the wall. Note that the maximum normalized displacement of 0.33% approximately corresponds to a typical value of 0.4% H for walls with inextensible reinforcements and is less than 1.0% H for walls with extensible reinforcements (Mitchell and Christopher, 1990).
The curves of settlement of the backfill display correspondingly to the curves of lateral displacement (Fig. 9b). For instance, the maximum normalized settlements of Types G and GU are about 0.5% and occur close to the wall face. This indicates a tilting type of failure mode. On the contrary, the maximum normalized
Fig. 10. Yield zones in the walls with different layouts (q ¼ 50 kPa). (a) Layout. (b) Yield zone.
R.-H. Chen et al. / Geotextiles and Geomembranes 39 (2013) 51e62
settlements of Types GE and FE are less than 0.2% and occur far from the wall face. This implies a different failure mode, i.e., sliding failure. As seen from Fig. 9a,b, Type GE induces the smallest settlement among the four curves, though its lateral displacement is somewhat more than that of Type FE (Fig. 9a). It can thus be concluded that lengthening the geocell layer at certain depths from top to bottom is a potentially effective method of construction in terms of wall movement as well as settlement of the backfill. 4.2. Yield zone Fig. 10 shows the stress states in the four walls subjected to a surcharge of 50 kPa. In Layout 1 (G), a clear potential failure surface
59
is seen starting from the crest and passing through the heel of the wall. Moreover, an active wedge and several radial slip lines form behind the wall. This phenomenon is similar to the bearing capacity failure due to the surcharge acting at the crest. In Layout 2 (GU) the potential failure surface is still clear, but the radial slip lines were shorter, owing to the upper, lengthened, geocell layers preventing the slip lines from extending into the layers. Instead, some yellow tension spots develop along the back of wall from the top to the bottom of lengthening layers, from where several radial slip lines are formed. In Layout 3 (GE) the potential failure surface is also clear, yet it becomes smaller than those of Layouts 1 and 2. Further, the radial slip lines become unclear, and several isolated yellow spots
Fig. 11. Comparison of stress states among walls with different facing angles (q ¼ 50 kPa). (a) Numerical model. (b) Stress state.
R.-H. Chen et al. / Geotextiles and Geomembranes 39 (2013) 51e62
distributed along the back of the wall. As mentioned previously, Layouts 3 and 4 result in less lateral displacements than the other layouts. Correspondingly, the potential failure surface in Layout 3 becomes small and passes above the heel of wall, as a result of the lengthening layer at the lower zone. However, it can be seen an active wedge extending to a significant depth, and a shear plane, though somewhat obscure, forms along the back of the reinforced zone, implying the zone behaves as a monolithic composite wall. In Layout 4 (FE), most of the stress states are elastic, and the zones that yielded in shear are difficult to find. Therefore, Layout 4 that is an extended facing-type reinforced wall performs best among all the four layouts.
0
Depth from the top (h/H)
60
5. Analysis of extended facing-type reinforced walls
0.2 0.4 0.6
Since the extended facing-type reinforced wall performs quite well, it is of interest to compare the performance of these walls with different facing angles. The numerical models of the three analyzed walls, which were constructed with the same amount of geocells, are shown in Fig. 11a.
1
5.1. Yield zone
0
5.2. Displacements
0
0.2 0.4 Lateral displacement (x/H) (%)
0.6
(a)
Settlement (s/H) (%)
Fig. 11b shows the stress states in the three walls when subjected to a surcharge of 50 kPa. The 70 wall (FE-7) only shows two inclined shear planes, starting from the bottom of the second extended geocell layer (counting from the top) and dipping to a significant depth. In the wall with an 80 facing angle (FE-8), a few zones are yielded in shear together with many isolated yellow spots, which are yielded in tension and distributed along the geocell layers. In the vertical wall (FE-9), there is a large wedge failure behind the reinforced zone. Many locations along the geocell layers are yielded in tension, suggesting the wall has titled. Evidently, these tensile zones are caused by the settlement of the large wedge that pushes the wall aside, causes the wall to tilt, resulting in geocells under tension.
FE-7 (α = 70 ) FE-8 (α = 80 ) FE-9 (α = 90 )
0.8
0.2
0.4
FE-7 (α = 70 ) FE-8 (α = 80 ) FE-9 (α = 90 )
0.6
0.8 0.8
0.6 0.4 0.2 Distance from the wall face (L/H)
0
As for the deformation of the wall, Fig. 12a shows the normalized lateral displacement of the wall when q ¼ 50 kPa. As expected, the vertical wall displays much more displacement than the other two walls, and the maximum normalized displacement is 0.53% occurring at the top; however, those in the walls of 70 and 80 are only 0.09% and 0.13 % (about 1/6e1/4 of 0.53%), respectively, occurring at mid-height of the walls. The settlement of the backfill is shown in Fig. 12b. Correspondingly, the vertical facing wall induces more displacement than the gentle facing walls. The maximum normalized settlement of the vertical wall is about 0.5%, occurring at the wall face; this type of settlement suggests that the mode of failure is tilting. In contrast, for walls with facing angles of 70 and 80 , most settlements are uniformly distributed, except near the wall face; this distribution of settlement indicates the gentle facing wall fails more like a sliding mode. From the above observation, reducing the facing angle of an extended facing-type reinforced wall from 90 to less than 80 will significantly reduce the lateral displacement of the wall face, change the deformation pattern, and alter the failure mode from tilting to sliding.
the friction angles of the soil and the plane-strain angle of friction at relative density Dr ¼ 62% are 4tx ¼ 41 and 4ps ¼ 44 , respectively. Herein 4ps ¼ 44 was used to calculate the coefficients of respective earth pressures shown in Eqs. (10)e(12). The symbols in the equations are defined in Fig. 13: b ¼ inclination of ground surface above wall, z ¼ inclination of wall from vertical, z ¼ vertical distance from ground surface, and sh ¼ horizontal component of active earth pressure. The sign convention is considered positive for the angle measured counterclockwise from the reference line. The interfacial friction angle (d ¼ 31 ) between the wall and the backfill was taken into consideration for the Coulomb earth pressure. Note that the cohesion was ignored.
5.3. Lateral earth pressure
Ko ðatrestÞ ¼ 1 sin 4
As mentioned, the internal friction angle of the soil and the plane-strain angle of friction can be estimated from Eqs. (1) and (2). By taking the stress at the mid-height of the 4-m wall as the mean stress to represent the whole wall and substituting it into Eq. (1),
(b) Fig. 12. Comparison of deformation among facing-type geocell walls with different facing angles (q ¼ 50 kPa). (a) Lateral displacement. (b) Settlement of the backfill.
Ka ðCoulombÞ ¼
cos2 ð4 zÞ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2 ð4þdÞsin ð4bÞ cos2 zcos ðd þ zÞ 1 þ sin cos ðzþdÞcos ðzbÞ
(10) (11)
R.-H. Chen et al. / Geotextiles and Geomembranes 39 (2013) 51e62
61
0
α = 70°
A-A' B-B'
Depth from the top (h/H)
0.2
Ka z
Backfill soil
At rest Rankine 0.4
Coulomb
0.6
0.8
, 1
0
0.1
0.2
0.3
0.4
(a)
h
0 A-A'
α = 80°
B-B'
Depth from the top (h/H)
0.2
Fig. 13. Definition of symbols.
Ka ðRankineÞ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi cos b 1 þ sin2 4 2sin 4cos q qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ cos b þ sin2 4 sin2 b
At rest Rankine 0.4
Coulomb
0.6
0.8
(12)
1 0
1
where q ¼ 2z þ ub b and ub ¼ sin ðsin b=sin 4Þ. The inclination of Rankine’s active earth pressure to the normal of the plane is
α = 90° 0.2
(13)
The curves of normalized lateral earth pressure acting along the backs of wall facing and the reinforced zone are shown in Fig. 14 for q ¼ 0. The data are obtained from the five extended geocell-reinforced layers (see Fig. 11a). It is observed that the distributions of lateral earth pressure for these walls with steep facings are not much different. For all three walls, the lateral earth pressures along the back of facing (AeA0 ) are less than those along the back of reinforced zone (BeB0 ). Specifically, the distributions of the lateral earth pressure along AeA0 are somewhat higher than the horizontal stress in Rankine’s active state, while those along BeB0 are close to the earth pressures at-rest. Note that the coefficients of earth pressure acting on a vertical plane (a ¼ 90 or z ¼ 0 ) are Ka ¼ 0.18 and K0 ¼ 0.305 for active and at-rest states, respectively. The active earth pressures according to Coulomb’s method that considers interfacial friction angle are lower than those using Rankine’s theory, especially for the gentler facing walls (Fig. 13a and b). Thus Coulomb’s method appears to be unsuitable for these walls. When limit equilibrium method is adopted in the design, it is suggested that the lateral earth pressure against the back of wall facing be considered higher than the horizontal stress in Rankine’s active state, and that along the back of the reinforced zone be the earth pressure at-rest.
0.3
0.4
(b)
sin 4sin q 1 sin 4cos q
0.2
0
Depth from the top (h/H)
dðRankineÞ ¼ tan1
0.1
A-A' B-B' At rest Rankine
0.4
Coulomb
0.6
0.8
1 0
0.1 0.2 0.3 Lateral earth pressure (σh /γH)
0.4
(c) Fig. 14. Normalized lateral earth pressure distribution at the backs of wall facing and reinforced zone (q ¼ 0). (a) a ¼ 70 , (b) a ¼ 80 , (c) a ¼ 90 .
6. Conclusion This paper presents a numerical model for analyzing the performance and stability of geocell-reinforced retaining structures. The constitutive model adopted for analysis consisted of a nonlinear elastic stressestrain relationship with MohreCoulomb yield criterion. For verification of the numerical model, three
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model-scale gravity-type walls were examined in terms of the lateral displacement of the wall face, the failure mode of the structure, and the critical load to cause failure. To assess the effect of the structure layout, four walls of various layouts were compared from the aspects of the deformation and yield zone of the structure. In the end, the extended facing-type reinforced walls with different facing angles were studied. Comparison of yield zone, deformation of the structure, and the distribution of lateral earth pressure against the backs of the wall facing and the reinforced zone were made. According to the results of analysis, the following conclusions are drawn. In verification of the numerical model, comparable results show good agreement in predicting potential slip surface as well as estimating critical load under which the wall is at the brink of failure. The lateral displacements of the walls between the model test and analytical results are also comparable. For the model walls studied, the factor of safety close to 1.0 corresponds to a surcharge of q/gH ¼ 2. As the surcharge continued to increase, the factor of safety decreases to less than 1.0; nevertheless, the model walls did not fail dramatically. The failure mode of the gentler slope consists of a few slides passing along the interface between geocell layers, while that of the steep vertical wall displays both modes of interlayer sliding and overturning failure. Among the four walls constructed with the same amount of geocells, the wall with lengthening geocell layers at certain depths, irrespective of gravity type (GE) or facing type (FE), performs better than the other layouts (G and GU). Lengthening the geocell layer at certain depths from top to bottom is a potentially effective method of construction in terms of wall movement as well as settlement of the backfill. According to the analysis of three extended facing-type walls with different facing angles, the wall with a facing angle less than 80 (e.g., FE-7 and FE-8), will significantly reduce the lateral displacement of the wall face, change the deformation pattern, and have the sliding mode of failure. The lateral earth pressures against the back of wall facing were found to be somewhat higher than the horizontal stress in Rankine’s active state, while those along the back of the reinforced zone were close to the earth pressures at-rest. References Adams, M.T., Lillis, C.P., Wu, J.T.H., Ketchart, K., 2002. Vegas mini pier experiment and postulate of zero volume change. In: Proceedings of the 7th International Conference on Geosynthetics. Balkema, Rotterdam, pp. 389e394. Adams, M.T., Nicks, J., Stabile, T., Wu, J.T.H., Schlatter, W., Hartmann, J., 2011. Geosynthetic Reinforced Soil Integrated Bridge System - Interim Implementation Guide. Report FHWA-HRT-11-026. Federal Highway Administration, McLean, Virginia, USA. Al Hattamleh, O., Muhunthan, B., 2006. Numerical procedures for deformation calculations in the reinforced soil walls. Geotextiles and Geomembranes 24 (1), 52e57. ASTM D 4595, 2011. Standard Test Method for Tensile Properties of Geotextiles by the Wide-width Strip Method. American Society for Testing and Materials, West Conshohocken, Pennsylvania, USA. Bathurst, R.J., Allen, T.M., Walters, D.L., 2005. Reinforcement loads in geosynthetic walls and the case for a new working stress design method. Geotextiles and Geomembranes 23 (4), 287e322. Bathurst, R.J., Crowe, R.E., 1994. Recent case histories of flexible geocell retaining walls in North America. In: Tatsuoka, F., Leshchinsky, D. (Eds.), Recent Case Histories of Permanent Geosynthetic-reinforced Soil Retaining Walls. Balkema, Rotterdam, pp. 3e19. Bathurst, R.J., Karpurapu, R., 1993. Large scale triaxial compression testing of geocellsreinforced granular soils. Geotechnical Testing Journal 16 (3), 296e303. Bolton, M.D., 1986. The strength and dilatancy of sands. Géotechnique 36 (1), 65e78.
Chen, R.H., Chiu, Y.M., 2008. Model tests of geocell retaining structures. Geotextiles and Geomembranes 26, 56e70. Chen, R.H., Huang, Y.W., Huang, F.C., 2013. Confinement effect of geocells on sand samples under triaxial compression. Geotextiles and Geomembranes 37, 35e44. El-Emam, M.M., Bathurst, R.J., 2007. Influence of reinforcement parameters on the seismic response of reduced-scale reinforced soil retaining walls. Geotextiles and Geomembranes 25 (1), 33e49. Itasca Consulting Group, 2005. FLAC: Fast Lagrangian Analysis of Continua, Version 5.0. Itasca Consulting Group, Inc., Minneapolis, Minnesota, USA. Lade, P.V., Lee, K.L., 1976. Engineering Properties of Soils. Report UCLA-ENG-7652. University of California at Los Angeles, USA, p. 145. Ling, H.I., Leshchinsky, D., Wang, J.-P., Mohri, Y., Rosen, A., 2009. Seismic response of geocell retaining walls: experimental studies. Journal of Geotechnical and Geoenvironmental Engineering, ASCE 135 (4), 515e524. Mitchell, J.K., Christopher, B.R., 1990. North American practice in reinforced soil systems. In: Proceedings of the ASCE Conference on Design and Performance of Earth Retaining Structures. Cornell University, pp. 322e346. Mehdipour, I., Ghazavi, M., Moayed, R.Z., 2013. Numerical study on stability analysis of geocell reinforced slopes by considering the bending effect. Geotextiles and Geomembranes 37, 23e34. Racana, N., Gourvès, R., Grédiac, M., 2001. Mechanical behavior of soil reinforced by geocells. In: Proceedings of the International Symposium on Earth Reinforcement. Taylor and Francis, Japan, pp. 437e442. Skinner, G..D., Rowe, R.K., 2005. Design and behavior of a geosynthetic reinforced retaining wall and bridge abutment on a yielding foundation. Geotextiles and Geomembranes 23 (3), 235e260. Wesseloo, J., Visser, A.T., Rust, E., 2009. The stressestrain behavior of multiple cell geocell packs. Geotextiles and Geomembranes 27, 31e38. Won, M.S., Kim, Y.S., 2007. Internal deformation behavior of geosyntheticreinforced soil walls. Geotextiles and Geomembranes 25 (1), 10e22. Wu, J.T.H., Pham, T.Q., 2013. Load-carrying capacity and required reinforcement strength of closely-spaced soilegeosynthetic composites. Journal of Geotechnical and Geoenvironmental Engineering. http://dx.doi.org/10.1061/(ASCE) GT.1943-5606.0000885. Xie, Y., Yang, X., 2009. Characteristics of a new-type geocell flexible retaining wall. Journal of Materials in Civil Engineering, ASCE 21 (4), 171e175. Zienkiewicz, O.C., Humpheson, C., Lewis, R.W., 1975. Associated and non-associated visco-plasticity and plasticity in soil mechanics. Géotechnique 25 (4), 671e689.
Glossary
Basic SI units are given in parentheses c: cohesion intercept of soil strength (N/m2) cr: apparent cohesion of geocell-reinforced soil (N/m2) Dr: relative density (%) E: modulus of elasticity (N/m2) Fy: ultimate tensile strength (N/m) G: shear modulus (N/m2) Gs: specific gravity (dimensionless) H: wall height (m) h: vertical distance from the top of wall (m) K: bulk modulus (N/m2) Ka: coefficient of active earth pressure (dimensionless) Kbound: shear stiffness (N/m2) K0: coefficient of earth pressure at-rest (dimensionless) L: length (m) pa: atmospheric pressure (N/m2) q: surcharge (N/m2) Sbond: interfacial adhesion (N/m) Sfric: interfacial friction angle ( ) s: settlement (m) x: lateral displacement (m) z: vertical distance from ground surface (m) a: facing angle of wall ( ) b: inclination of ground surface above wall ( ) d: interfacial friction angle or inclination of active earth pressure to the normal of a plane ( ) f: friction angle of soil ( ) fps : plane-strain angle of friction ( ) fr : friction angle of geocell-reinforced sand ( ) ftx : triaxial compression angle of friction ( ) g: unit weight (N/m3) gd: dry unit weight (N/m3) z: inclination of wall from vertical ( ) l: scaling factor of length (dimensionless) n: Poisson’s ratio (dimensionless) j: angle of dilation ( ) sh: lateral earth pressure or horizontal component of active earth pressure (N/m2) s3: confining pressure (N/m2)