Centrifuge modeling test of a geotextile-reinforced wall with a very wet clayey backfill

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Geotextiles and Geomembranes 25 (2007) 346–359 www.elsevier.com/locate/geotexmem

Centrifuge modeling test of a geotextile-reinforced wall with a very wet clayey backfill Huei-Tsyr Chen, Wen-Yi Hung, Chin-Chang Chang, Yuan-Ji Chen, Chung-Jung Lee Department of Civil Engineering, National Central University, No. 300, Jhongda Rd., Jhongli City, Taoyuan County 32001, Taiwan, ROC Received 8 June 2006; received in revised form 4 December 2006; accepted 2 January 2007 Available online 20 February 2007

Abstract A clayey vertical geotextile-reinforced earth wall (VGREW) in a wet state due to poor drainage conditions after several consecutive days of heavy rainfall was simulated by a series of centrifuge VGREW models. The models were constructed using clayey soil very close to its liquid limit. Through centrifugal tests on these models, the effectiveness of various reinforcement arrangements, on the alleviation of deformation of the clayey VGREW subjected to the previously mentioned adverse conditions, was examined. For the reinforcement length, there exists a critical beyond which no further improvement can be attained, while smaller vertical reinforcement spacing leads to shorter critical reinforcement length. The improvement ratio, Ir, is defined as a relative measure for evaluating the efficiency of the improvement and is presented as contour plots to facilitate the consideration of the design. Four failure modes are observed in this study and their evolution for each reinforcement arrangement is also demonstrated. r 2007 Elsevier Ltd. All rights reserved. Keywords: Geotextile-reinforced wall; Clay backfill; Centrifuge modeling

1. Introduction The mechanically stabilized earth structure (MSES) is a type of geotechnical structure constructed by the introduction of various reinforcing materials such as metal strips and rods, wire grids, geotextile grids or sheets in the backfill. Because of its capability of absorbing differential deformations induced by poor foundation soil and its higher resistance to seismic loading than a rigid concrete wall, many MSESs have been constructed worldwide. Walls incorporating geotextile sheets are often referred to as geotextile-reinforced earth walls (GREW), and have become the topic of much research, both experimental and numerical (Al Hattamleh and Muhunthan, 2006; Nouri et al., 2006). Several new methods have also been developed for the design or stability analysis of reinforced structures (Skinner and Rowe, 2005; Bathurst et al., 2005). From the experimental point of view, performing a full-scale Corresponding author. Tel.: +886 3 4227151x34179; fax: +886 3 4252960. E-mail address: [email protected] (W.-Y. Hung).

0266-1144/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.geotexmem.2007.01.003

test is the most appropriate option (Wu et al., 1994; Kazimierowicz-Frankowska, 2005; Park and Tan, 2005); however, this is a costly and time-consuming exercise. In contrast, the centrifuge modeling technique, enabling the reconstruction of the stress conditions in the full-scale constructions using greatly reduced-scale models, provides a good alternative but requires less experimental time and budget. The centrifugal models tested in an acceleration field N times the earth gravity has dimensions N times smaller than the full-scale system, which is referred to as the prototype. It should be noted that both the model and the prototype should include all the important characteristics of the field situation of interest. As a result, the centrifuge modeling test is a convenient approach to performing parametric studies on the behavior of GREW. A significant amount of centrifuge research has been conducted for GREW using high-quality granular soil as the backfill (Zhang et al., 2000; Zornberg et al., 1996). Many guidelines and handbooks stipulate that high-quality granular soil should be adopted as the backfill material for GREW. In practice, however, a GREW is frequently constructed with low quality in situ clayey soil (referred to as clayey

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effectiveness of various reinforcement arrangements on the stability of a clayey GREW in a wet state caused by the worst climatic situations should be developed. To meet this need a series of centrifugal model tests for VGREWs with backfill in a wet state were conducted, and a quick assessment of the effectiveness of various combinations of reinforcement length and spacing in alleviating the deformations of the clayey VGREW in a wet state resulting from several consecutive days of heavy rainfall will be proposed. 2. Test programs 2.1. Test equipments In this study the experiments were undertaken using the geotechnical centrifuge at the Experimental Center of Civil Engineering of the National Central University (NCU) (Lee et al., 2004). The NCU geotechnical centrifuge has a nominal radius of 3 m and a capacity of 980g kN (100g ton). The product of the weight of the model and the centrifuge acceleration should be no more than 980g kN with g as the gravity acceleration. Upon starting, the centrifuge will automatically accelerate to a predetermined 10g level, after which the operator can boost the acceleration incrementally as desired. All the model walls were constructed in a rigid soil container. The soil container was a rectangular box made of aluminum alloy with internal dimensions of 223 mm in width, 820 mm in length and 580 mm in height. The front wall has a transparent window to allow one to observe the failure progress of the tested VGREW model. 2.2. Soil and reinforcement materials used in the model The soil used in the models was collected from the Linkou area in Taiwan. Fig. 1 shows the grain-size distribution curve of the soil. It seems that the soil was

100

Percent finer by weight, (%)

GREW hereafter) to cut the construction cost in remote areas, an obvious violation of the current design requirements. Such a practice leads to the need for a series of investigations of the behavior of the clayey GREW using centrifugal testing. Suah and Goodings (1989) studied the effects of the backfill properties, reinforcement length and overlap length on the stability of vertical geotextilereinforced earth walls (VGREW). The backfill used was a mixture of sand and clay in varying ratios. Porbaha and Goodings (1996) built 24 reduced-scale centrifuge models using kaolin as the backfill. All were loaded to failure by gradually increasing the self-weight, to investigate the failure mechanism of vertical and steeply sloped GREWs. Porbaha and Goodings (1997) also studied the influence of uniform and non-uniform reinforcement lengths on the performance of vertical and sloped model walls with clayey-soil backfill. They tested the models to failure using a geotechnical centrifuge. Porbaha et al. (2000) used a kinematical approach based on the framework of limit analysis to analyze the stability of reinforced vertical and sloping model walls with cohesive backfill, brought to failure under self-weight in a geotechnical centrifuge. However, a clayey soil may clog the drainage system of a clayey GREW, leading to an increase in the water content of the GREW. In Taiwan, there have been reports of the failure of clayey GREWs after several consecutive days of heavy rainfall. According to these reports (Huang, 1994; Chou et al., 2002; Wu and Tang, 2005), the reduction in the shear strength of the clayey backfill due to an increase in the water content as a result of the infiltration of rainwater due to poor drainage is one of the major reasons for the collapses. In fact, in some cases the failing clayey backfill was nearly fully saturated. Thus, how to design a clayey GREW which will remain stable in the worst climatic situation is an important issue for engineers. Despite many studies conducted on a clayey GREW using a geotechnical centrifuge in the past, none of them investigated the adverse effects of clayey backfill in a wet state resulting from several consecutive days of heavy rainfall and poor drainage on the stability of the GREW. To approximate such an effect, Chen et al. (2004a, b) used clayey soil from the Linkou area as backfill. By changing the water content of the backfill they found that the increase in the water content of the clayey-soil backfill would lead to a decrease in the stability of the VGREW. The results also indicated that if a low quality in situ clayey soil is used as backfill, the reinforcement spacing, as determined from the current design guidelines, should be reduced, in order to maintain the stability of the VGREW in a wet state while the use of 0.31 m for the reinforcement spacing can ensure the stability of the VGREW, even when the water content of the clayey-soil backfill reaches 41%, which is near the liquid limit. From the previous studies, it is well known that both the reinforcement spacing and the reinforcement length have a great influence on the stability of the GREW. Therefore, for engineering practices, a quick assessment of the

347

80

60

40

20

0 1

0.1

0.01

0.001

Grain size, (mm)

Fig. 1. Distribution curve of grain-size in the soil used in the study.

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well graded. It had a specific gravity, a plastic limit and a liquid limit of 2.67, 23% and 42%, respectively, and was classified as CL in the Unified Soil Classification System. The maximum dry unit weight and the optimum moisture content of the soil, as determined by the standard proctor compaction test, were 16.8 kN/m3 and 18%, respectively. Clayey soil was used as the reinforced fill for all the models, as well as the retained fill and the foundation soil. The clayey soil taken from the field was purged first to remove the impurities, such as the plant material or mildew, and then ventilated in the open air before each test to achieve the desired water content. The reinforcement used in this study is a kind of composite material that combines geotextile with polymeric grids. It has an ultimate tensile strength of 1.62 kN/m and fails at 9.1% strain, according to a wide-width test. The thickness of the reinforcement is 0.35 mm, which is chosen after considering the scaling relation of the centrifuge model. Therefore, it is much thinner than that what is used in actual construction. 2.3. Design of the model In order to evaluate the effectiveness of various reinforcement arrangements in alleviating deformations of clayey VGREW in a wet state, a standard model, built for normal climatic condition, was designed first. The other models were just variations of this standard model, made by changing the water content of the backfill to 41% and adopting different combinations of reinforcement lengths and spacings according to the experimental design. Therefore, in the following, only the design process for the standard model will be described. It should also be noted that due to the difficulties involved in the simulation of the infiltration processes of rain water into a VGREW using a centrifuge at present, in this study, the use of backfill soil with a 41% water content, which is very near to the liquid limit, is used to simulate the worst VGREW situations after a long period of heavy rainfall and poor drainage. Sawicki (1998) considered a model tested in a centrifuge. The small model was placed in a high g condition. That is, if a model of the selected dimension is put in an N g field, it is equivalent to a model built of the same material but with a unit weight N times that in the 1g condition. In this study, we adopt this concept to design the standard model of VGREW. According to the design guidelines, the water content of the standard model should be as close to the optimum moisture content as possible. However, it is difficult to compact the soil at optimum moisture content (18%), so in this study, to reach the desired relative compaction evenly and without damaging the reinforcement, it is found after several trials, that the lowest water content, which can facilitate the construction of a standard model, is 28%. The degree of saturation, Sr, of the backfill for all the models in this study range from 99% to 100%, close to that obtained in some of the failure cases in Taiwan.

The standard model, with the weight of the clayey soil multiplied by 20, is designed according to the Mechanically Stabilized Earth Walls and Reinforced Soil Slopes Design and Construction Guidelines (FHWA-NHI-00-043, Elias et al., 2001). The model to be tested was at an acceleration field of 20g. The height of the wall and the thickness of the foundation in the model are 300 and 150 mm, respectively, simulating a moderate 6 m-high wall, frequently used in Taiwan for retaining soil in remote mountain areas. The prototype is built on a 3 m-thick firm foundation. In the standard model the reinforcement length is 213 mm, equivalent to 71% the wall height (0.71H). Assuming the reinforcement spacing of 40 mm (0.8 m in the prototype), the strength of the reinforcement required is 3.2 kN/m for the model, thus double sheets of reinforcement are utilized in each layer, meaning two sheets of reinforcements placed together. Compaction of soil in sample construction can further increase the bonding between them, making very difficult to cause relative displacement between the two sheets when shear is applied. After each test, the reinforcements were examined and in fact there was no relative motion between the reinforcements. 2.4. Test models Twenty-two models, divided into four groups, were tested in this study. The properties of all the models are given in Table 1. Model MA1 indicates the wall without reinforcement. It is tested to see if an unreinforced wall can fail before 20g, and the test results are used for verification of the test. Model MA2 indicates the standard model, and serves as the basis for evaluating the effectiveness of different measures in reducing the deformations of the clayey VGREW. The stability of the wall was evaluated by examining the wall deformation at the crest of the wall face. All the models in this study were designed to be tested at an acceleration level of 20g. This is different from the model tests of past studies which were tested to failure, by increasing acceleration or external loading (Benrabah et al., 1996). Models MA3 and MB4, together with models MA4 and MC4, are used to ascertain the reproducibility of the model preparation process. The models, labeled as Group B, Group C and Group D in Table 1, were first tested at 20g to investigate the effectiveness of various reinforcement arrangements in reducing the deformations of the VGREW in a wet state. Group B consists of 6 models, denoted as MB1–MB6 and the reinforcement lengths of this group are 0.71, 0.85, 1, 1.15, 1.35 and 1.5H, while the vertical reinforcement spacing is kept at 40 mm. Each Group C and Group D contains 5 test models, denoted as MC1–MC5 and MD1–MD5, respectively; the reinforcement lengths of these two groups are 0.71, 0.85, 1, 1.15 and 1.35H, while the vertical reinforcement spacing is kept at 30 mm for Group C and 20 mm for Group D. The reason for not considering the model with reinforcement length of 1.5H in Group C and Group D is that no further reduction of

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compression tests (UC test), which prevents the foundation of the wall from bearing load failure.

Table 1 Main features of the tested models Test Model group no.

L/Hb wc(%) Sva (mm) ratio

sud (kPa)

Remarks

A

MA1 MA2 MA3 MA4 MA5

— 40 40 30 30

0 0.71 1.15 1.15 1.15

42 28 41 41 41

16.4 61.8 13.4 14.7 13.7

MA6

30

0.30

42

12.9

No reinforcement Standard model Repeatability test Repeatability test Effect of half reinforcement strength Effect of short reinforcement

B

MB1 MB2 MB3 MB4 MB5 MB6

40 40 40 40 40 40

0.71 0.85 1.00 1.15 1.35 1.50

42 42 41 39 42 42

C

MC1 MC2 MC3 MC4 MC5

30 30 30 30 30

0.71 0.85 1.00 1.15 1.35

41 40 41 40 40

D

MD1 MD2 MD3 MD4 MD5

20 20 20 20 20

0.71 0.85 1.00 1.15 1.35

41 42 40 41 41

9 > > > > > > > > > > > > > > > > > > > > > > > > > > > > 17.0 > > = 16.7 14.6 > > > > 16.2 > > > > 16.3 > > > > > > > 14.0 > > > > 12.5 > > > > > 18.1 > > > > 13.7 > > ; 13.7 17.2 18.3 18.4 21.1 18.4 19.2

Effect of reinforcement length

a

Vertical spacing in model dimensions. L/H ¼ ratio of the reinforcement length to wall height. c Water content of clayey backfill. d Undrained shear strength. b

deformation was observed for the reinforcement length of 1.35H, as compared with the deformation of the model with the reinforcement length 1.15H. Some of the tests of Group B, C and D are described later. Models MA5 and MA6 will be further driven to failure to investigate the failure mechanism.

2.6. Construction of a VGREW and configuration of the equipments To build an homogeneous backfill VGREW model Chen et al. (2004a, b) developed a rolling compaction method. A concrete cylinder, with a diameter of 150 mm, a length of 210 mm and a weight of 82.6 N, was rolled backward and forward 5 times to produce a 20 mm-thick backfill layer. By this method, the backfill possessed a relative compaction of 81% and 88%, determined by the standard compaction testing, and a water content of 41% and 28%, respectively. This was done due to the fact that in Taiwan the relative compaction in failure cases is initially low in practice, ranging from 80% to 90% after being saturated by rain. The compaction will increase as the water content decreases. The backfilled soil had an average shear strength of about 62 and 18 kPa at the water content of 28% and 41%, respectively, simulating the strength of backfill before and after heavy rainfall. This compaction method was utilized in this study to construct all the VGREW models. After completing the foundation, several wood boards were piled vertically on the top of the foundation to provide lateral supports for the model wall. The first reinforcement layer was placed on the exposed portion of the foundation after which the rolling compaction method was applied until the thickness of soil reached the required reinforcement spacing. This was followed by wrapping a length of reinforcement 100 mm long, the overlap length, back into the soil to provide a flexible facing for the wall. This process was repeated for successive layers until the wall reached a height of 300 mm. However, in order to avoid pull-out failure or local instability in the top portion of wall, the overlapping length of the top layer is the same as the length of the reinforcement, on top of which a 20 mm-thick soil layer was placed. A typical model profile is shown in Fig. 2.

2.5. Construction of foundation Top of wall

Reinforcement spacing, Sv

Wall face

Crest of wall face

Wall height, H

The inside vertical faces of the container were sprayed with lubricant and overlaid with a thin rubber membrane before constructing the VGREW model to reduce the boundary friction as much as possible. The foundation of all the models was made of clayey soil with 28% water content. The foundation of the model was constructed on 4 lifts. In the first lift, the foundation soil was gently pressed to smooth its surface and then compacted evenly with a 24.5 N hammer freely dropped from 300 mm above the surface; with the process we can achieve a compacted dry unit weight of 90% the maximum dry unit weight as determined by the standard compaction test. The process was then repeated until the thickness of the foundation reached 150 mm. The foundation had an average shear strength of about 65 kPa determined by unconfined

Reinforced zone

Reinforcement length, L Wall foundation

Fig. 2. Definitions of each part of a VGREW.

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Fig. 3. Layout of the model wall and configuration of instrumentations in the model scale.

Fig. 3 describes the layout of the model and the configuration of the instrumentation. On top of the wall, six linear variable differential transformers (LVDTs) were installed at distances of 0, 50, 100, 375, 425 and 475 mm from the crest of the wall face, to measure surface settlement. Two CCD cameras were installed to continuously monitor the crack development on the upper surface of the wall and the evolution of failure from the side acrylic window of the container. Two laser displacement sensors (LDSs), located at the elevations z1 ¼ 260 mm (0.87H) and z2 ¼ 100 mm (0.33H) above the foundation, were set up to measure the horizontal displacement of the wall face. 2.7. Testing procedures After completion of the test setup, the test package was placed on the centrifuge platform prior to conducting the test, which proceeded in the stages as described in the following. In the first stage the model wall with wood boards was placed in an acceleration field of 20g until the measured settlement at the top of the wall became stable. Then the centrifuge was decelerated to a complete stop. It should be mentioned that the degrees of compaction for the models described previously were sampled before the centrifuge modeling test. This stage was done to compress any voids between the backfill soil and the reinforcement layers through increasing the self-weight to minimize the lateral wall movement during acceleration to 20g in the second stage.

Before conducting the second stage test, the wood boards were removed. Next two LDSs were installed in front of the wall face to measure its horizontal displacement. For each test in this stage, upon reaching the predetermined 10g level, the acceleration was boosted with an increment of 2g and it was maintained for 30 s at each level of acceleration. The centrifuge was operated at the final acceleration of 20g until the LVDT and LDS readings became stable, after which it was decelerated to a complete stop. The reason for adopting such a scheme was to ensure that the stresses in the soil and the reinforcements developed completely in each step. The development of cracks in the ground surface and movement of the wall could then be recorded by the LVDT, LDS and CCD at the actual acceleration. In the following discussion, the settlement, horizontal displacement and the positions of crack on the outer surface of the wall of the scale prototype are reported. The third stage of the study is dedicated to the failure mechanisms at selected models by increasing the selfweight. In this stage, all the LDSs and LVDTs were removed to avoid them being damaged by sudden failure of wall. After reaching the predetermined 10g level, the acceleration of the centrifuge was boosted at increments of 5g until the wall failed or until an acceleration of 100g was reached. Throughout the test, a CCD camera continuously monitored the development of tension cracks in the ground surface and wall movements through the side window. After the test, the water content of the soil in the

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3. Test results and analysis 3.1. Verification tests Model MA1 is an unreinforced vertical wall model with high water content for which the theoretical critical height can be calculated from the following: cu H cr ¼ , (1) gm where Hcr is the critical height of the wall, cu is the undrained shear strength of the soil, g is the unit weight of the soil and m is the stability number obtained from the Taylor Stability Chart (Das, 2002). Based on the properties of this model, cu ¼ 16.4 kPa, g ¼ 16.2 kN/m3 and m ¼ 0.26, the theoretical critical height of this prototype wall is 3.5 m. The test results indicate that the main crack on the wall is 4.2 m from the crest of the wall face and occurred at an acceleration of 5g. The wall collapsed in a nearly plane failure mode at an acceleration of 12g, corresponding to a critical height of 3.6 m in prototype scale which is very close to the theoretical value. Also, the failure of this wall at 12g verifies the need of the use of reinforcement for 20g tests to study the effect on reducing the deformation of VGREW in a wet state. Four tests, MA3, MB4, MA4 and MC4 as shown in Table 2, were designed to examine the repeatability of the test results. Test models MA3 and MB4 are denoted as Set 1 and the test models MA4 and MC4 are denoted as Set 2. The properties of the models in each set are almost

identical. The reinforcement in Set 1 is 1.15H long and the vertical reinforcement spacing is 0.8 m (in the prototype scale), while the length of the reinforcement and vertical reinforcement spacing of the Set 2 models are 1.15H and 0.6 m (in the prototype scale), respectively. As can be seen from Table 2, the maximum settlements of the crest of the wall face of Set 1 are 0.400 and 0.428 m, and 0.296 and 0.316 m for Set 2, respectively. The maximum horizontal displacements of the crest of the wall face are 0.300 and 0.306 m for Set 1, and 0.204 and 0.184 m for Set 2, respectively. Thus, the test results demonstrate that the model tests conducted in this study are reproducible. 3.2. Wall deformations for various reinforcement arrangement Figs. 4 and 5 show the settlement of the wall crest and the horizontal displacement of the wall face at a height of Reinforcement Spacing, Sv (m) 0.2

0.5

0.6

0.7

0.8

0.9

1.0

0.1 MA2

0.2 0.3 0.4 L/H = 0.71 L/H = 0.85 L/H = 1.0 L/H = 1.15 L/H = 1.35 L/H = 1.5 Result of Standard Model

0.5 0.6 0.7

MB1

Fig. 4. Settlement of the wall crest for the various reinforcement length ratios and reinforcement spacing in the prototype. Reinforcement Spacing, Sv (m) 0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0

Set 1

Set 2

MA3

MB4

MA4

MC4

40 16.6 28

41 13.4 28

41 14.6 30

40 16.2 28

68.6

55.7

63.05

64.2

6 0.8 1.15H 0.400

6 0.8 1.15H 0.428

6 0.6 1.15H 0.296

6 0.6 1.15H 0.316

0.300

0.306

0.204

0.184

Horizontal Displacement , (m)

Backfill water content (%) Shear strength of backfill (kPa) Water content of foundation soil (%) Shear strength of foundation soil (kPa) Wall height H (m) Reinforcement spacing (m) Reinforcement length Max. settlement of the crest of the wall (m) Max. displacement of the crest of the wall (m)

0.4

0.8

Table 2 Reproducibility of test results in the prototype Item

0.3

0.0 Settlement of the Wall Crest, (m)

non-failing rear zone of the model was measured to see if there was any significant change from before to after the test. The shear strength of the soil in the non-failing zone was also measured using mini-torvane and the UC test. Finally, the model was disassembled and the deformation of the reinforcements at different elevations examined. The intersection of the failed surfaces and the reinforcement was recorded to allow us to investigate the failure modes of the VGREW.

351

0.1

MA2

0.2 0.3 0.4 0.5 0.6

L/H = 0.71 L/H = 0.85 L/H = 1.0 L/H = 1.15 L/H = 1.35 Result of Standard Model

MB1

0.7

Fig. 5. Horizontal displacements of the wall face at the elevation of 0.87H for various reinforcement length ratios and reinforcement spacing in the prototype.

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0.87H of all tests. The deformation of the standard model (model MA2) is also presented. The data points corresponding to Sv ¼ 0.8 m and the reinforcement length ratio, L/H, of 0.71 in both figures indicate model MB1 results. Model MB1 is constructed by changing the water content of the backfill of a standard model to 41%. A significant increase in settlement and horizontal displacement can be observed when the water content of the backfill changes from 28% to 41%. By comparing the deformation of model MB1 with those of the standard model, it can be seen that although the standard model satisfies the design requirements and performs well under normal conditions, if the water content of the backfill reaches 41%, due to several consecutive days of heavy rainfall, a significant increase in the deformation can occur, which may lead to failure. From Figs. 4 and 5, it can be seen that, for a given vertical reinforcement spacing, increasing the reinforcement length can lead to a reduction in the deformation of VGREW in a wet state; however, there is a threshold L/H ratio beyond which no further reduction in deformation can be achieved. For Sv ¼ 0.8 m, this threshold value is 1.35, while for Sv ¼ 0.6 and 0.4 m, it is 1.0. In this study, this ratio is referred to as the critical reinforcement length ratio. Note should also be made that there also exists a threshold value for the vertical reinforcement spacing with respect to the critical reinforcement length ratio beyond which the critical reinforcement length ratio will remain constant. In this study it seems to be 0.6 m. On the other hand, it can also be found that reducing the deformation of VGREW in a wet state will be more effective if a scheme for decreasing the vertical reinforcement spacing is adopted. Figs. 6 and 7 depict the horizontal displacement at 0.33H (hollow circles) and 0.87H (solid circles) above the bottom of the model walls for different reinforcement length ratios

Reinforcement Length Ratio, L/H 0.6

0.8

1.0

1.2

1.4

1.6

Horizontal Displacement, (m)

0.0

0.1

0.2 Sv=0.4 m 0.3

z1=0.87H z2=0.33H

0.4

Fig. 6. Horizontal displacement of the wall face for various L/H and a spacing of 0.4 m in the prototype.

Reinforcement Length Ratio, L/H 0.6 0.0

Horizontal Displacement, (m)

352

0.8

1.0

1.2

1.4

1.6

0.1

0.2

Sv=0.6 m 0.3 z1=0.87H z2=0.33H 0.4

Fig. 7. Horizontal displacement of the wall face for various L/H and a spacing of 0.6 m in the prototype.

and with vertical reinforcement spacing of 0.4 and 0.6 m, respectively. Fig. 6 shows that the upper part of the model wall has moved further out than the lower part of the wall, for all reinforcement length ratios considered. Such a deformation pattern corresponds to a tilting mode. The results in Fig. 7, however, show an opposite trend, where the lower part of the model wall has moved further out than the upper part of the wall, for all reinforcement length ratios considered. This type of deformation pattern corresponds to a bulging mode. The pictures shown in Fig. 8 indicate the wall deformation modes. These pictures indicate that the VGREW model with smaller spacing (Sv ¼ 20 mm) is apparently more rigid than that with the larger spacing (Sv ¼ 30, 40 mm). Fig. 9 illustrates the wall deformation processes during the passage obtained from the CCD camera installed at the side acrylic window of the container. At low g levels, all prototype models in Group B, C and D, with 0.8, 0.6 and 0.4 m of reinforcement spacing, respectively, deformed in a tilting mode. However, as the g level became higher, the deformation pattern varied among these models. The test results for Groups C and D confirm that the deformation at a stiff wall should be due to the tilting mode, and a soft wall should deform with a bulging wall shape. This indicates that a reduction of the reinforcement spacing can enhance the stiffness of the wall and significantly curtail the deformations. In Group B, however, models MB1, MB2 and MB3 with reinforcement lengths of 0.71–1.00H tilted continuously as the acceleration level increased finally leading to large settlement and horizontal displacement of the wall crest (Fig. 9(a) B-1, B-2 and B-3). The MB4, MB5 and MB6 models with reinforcement lengths of 1.15–1.50H first tilted, and then showed bulging at the middle part of the wall face (Fig. 9(a) B-1, B-2 and B-4) as the values of the

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Fig. 8. Wall deformation modes: (a) tilting mode and (b) bulging mode.

Fig. 9. Sketch of the wall deformation process during the passage from 1 to 20g for the models of (a) Group B, (b) Group C and (c) Group D (not to scale).

settlement and horizontal displacement were smaller than those of the models MB1, MB2 and MB3. These results confirm that the use of longer length of reinforcement can decrease wall deformation. In Group B, the reinforcement spacing is 0.8 m. It seems that with such spacing, a reinforcement length of 0.71–1.00H is insufficient to hold the top of the wall effectively, leading to a tilting mode; however, as the reinforcement length increases from 1.15 to 1.50H, the capability of holding the top of wall increases, leading to a bulging mode (Table 3). From the above discussion, it seems that the reinforcement spacing plays an important role in enhancing the rigidity of the wall, while lengthening the reinforcement does not contribute significantly to the rigidity of the wall, especially for the Group B models with larger reinforcement spacing. Thus, if a scheme is adopted to reduce the reinforcement spacing, increased reinforcement will lead to

more rigid walls; however, if the increase in reinforcement is done by lengthening the reinforcement, but there is a large fixed reinforcement spacing, it seems to mean that the use of more reinforcement does not necessarily mean greater rigidity. 3.3. Improvement ratio In order to evaluate the effectiveness of various reinforcement arrangements for reducing the deformation of VGREW in a wet state, an improvement ratio, Ir, is defined as follows: Ir ¼

DH  D  100%, DH  DS

(2)

where Ds is the deformation (either of the settlement or the horizontal displacement at the wall crest) of the standard

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Reinforcement Length Ratio, L/H

Table 3 Summary of the model test results

0.6

Sv (mm)

L/H

Deformation mode

Acceleration at failure (g)

MA1 MA6 MA2 MB1 MB2 MB3 MA3 MB4 MB5 MB6 MC1 MC2 MC3 MA4 MC4 MC5 MD1 MD2 MD3 MD4 MD5 MA5

— 30 40 40 40 40 40 40 40 40 30 30 30 30 30 30 20 20 20 20 20 30

0.00 0.30 0.71 0.71 0.85 1.00 1.15 1.15 1.35 1.50 0.71 0.85 1.00 1.15 1.15 1.35 0.71 0.85 1.00 1.15 1.35 1.15

Plane failure Circular arc failure Tilting Tilting Tilting Tilting Bulging Bulging Bulging Bulging Bulging Bulging Bulging Bulging Bulging Bulging Tilting Tilting Tilting Tilting Tilting Breaking failure

12 30 Not tested 40 Not tested Not tested Not tested 60 Not tested Not tested 40 Not tested Not tested 80 Not tested Not tested 50 65 70 100 4100 65

to failure to failure to failure to failure to failure to failure to failure to failure

model (MA2), DH is the deformation of a model wall where the backfill of the standard model is replaced with clayey soil in a wet state (model MB1) and D is the deformation of a model wall backfilled with clayey soil in a wet state and reinforced with an adopted reinforcement arrangement. From this definition, the higher the value of Ir is, the more effective the adopted reinforcement arrangement is. An Ir of 100% implies that the adopted reinforcement scheme can make the VGREW in a wet state have the same deformation as that of the standard model. That is, no additional deformation of the VGREW will occur when the water content of the backfill becomes high, compared to that of the standard model. In this study, all the deformation values (DH, Ds, and D) were measured for an acceleration of 20g. The improvement ratios for the settlement and the horizontal displacement were computed from the test results and are shown in Figs. 10 and 11, respectively. It can be seen that for a given reinforcement spacing, the improvement ratio increases as the reinforcement length ratio increases; however, this will remain constant after the critical reinforcement length ratio is reached. The figures also show that there is a significant increase in the improvement ratio. This can be obtained when the vertical reinforcement spacing changes from 0.8 to 0.4 m (for the reinforcement ratio smaller than the critical reinforcement length ratio). A further decrease in the reinforcement spacing to 0.4 m does not lead to a significant increase in the improvement ratio. For Sv ¼ 0.8 m, the improvement ratio of settlement at the wall crest can reach only 69% at

1.2

1.4

1.6

80

60

40 Sv = 0.8 m Sv = 0.6 m

20

Sv = 0.4 m

0

Fig. 10. Improvement ratio of settlement at the wall crest for various reinforcement length ratios and reinforcement spacings in the prototype.

Reinforcement Length Ratio, L/H Improvement Ratio of Horizontal Displacement, (%)

to failure to failure

1.0

100 Improvement Ratio of Settlement, (%)

Test no.

0.8

0.6

0.8

1.0

1.2

1.4

1.6

100

80

60

40

20

Sv = 0.8 m Sv = 0.6 m Sv = 0.4 m

0

Fig. 11. Improvement ratios for horizontal displacement of the wall face at the elevation of 0.87H for various reinforcement length ratios and reinforcement spacings in the prototype.

the critical reinforcement length ratio; however, for Sv ¼ 0.6 m, the improvement ratio is 72% even when the reinforcement length ratio is merely 0.71. If a reinforcement spacing of 0.4 m is introduced, then the improvement ratios achieved for both the settlement and the horizontal displacement are nearly 90%. A note should be made that the water content of the standard model MA2, 28%, is still higher than the optimum water content, 18%. Backfill with 28% water content was used because of the technical difficulty of building models using backfill with a water content of 18%. Chen et al. (2004a) studied the effect of water content of clayey backfill on the stability of MSEW. Although, their results showed that the settlement and the horizontal displacement decreased with decreasing water content, the

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a

0.80

Reinforcement Spacing, (m)

0.75 0.70 0.65 0.60 0.55 0.50 0.45 0.40 0.71

b

0.8

0.9 1.0 1.1 1.2 Reinforcement Length Ratio, L/H

1.3

0.8

0.9 1.0 1.1 1.2 Reinforcement Length Ratio, L/H

1.3

0.80 0.75

Reinforcement Spacing, (m)

relationship was not linear, trending toward a threshold value. By extrapolation, the horizontal displacement for a wall model with 18% water content backfill was about 70% or higher then that for the wall model with a backfill of 28% water content. To evaluate the difference in the improvement ratio, we use the deformations for the cases with water content 28% and 18%. The model MC1 results are taken as an example. For this model, the DS values for 28% water content, DH and D are 0.1, 0.6 and 0.34 m, respectively. The calculated improvement ratio is 52.0%. If the DS value for 18% water content is taken as 70% of that for DS at 28% water content, a new improvement ratio is 49.1%. The difference is at most 2.9%, with the current value being slightly higher. Thus, it seems that the proposed improvement ratio contour is still reasonable. The improvement ratio discussed previously is based on the deformation of wall models subjected to an acceleration of 20g, for a 6-m height prototype. A model subjected to different g levels corresponds to prototype walls of different heights, reinforcement lengths and reinforcement spacing, and the deformations will certainly be different. However, the threshold values for the critical reinforcement length and the improvement ratios are defined in a relative sense. Therefore, despite that the values of the deformation and length dimension for various g values will be different, when they are used for calculating the improvement ratio and threshold values, the difference from the current proposed values will not be significant. However, further research on this issue is still needed. The previous discussions can be summarized. Increasing the reinforcement length or decreasing the vertical reinforcement spacing can reduce the deformation of VGREW in a wet state and it is more effective to decrease the vertical reinforcement spacing. Also, many combinations of L/H and Sv can render the same improvement ratio. However, in engineering practice, there are two key issues that still need to be considered for the final reinforcement arrangements: the availability of land and adequate budget. From the viewpoint of land availability, the use of a longer reinforcement length requires a larger excavation zone; this may not be suitable for a restricted construction site. As for the budget considerations, despite the fact that decreasing the reinforcement spacing is more effective than increasing the reinforcement length, an increase in the number of reinforced layers will result in an increase in the amount of reinforcement material and a longer construction time. To facilitate engineering decisions, the relationship of L/H and Sv for various Ir are plotted as contour plots in Figs. 12(a) and (b), indicating the settlement and the horizontal displacement at wall crest, respectively. For a given improvement ratio of settlement or horizontal displacement, the contour plots can be used to determine the possible combinations of L/H and Sv and then compare with the required amount of reinforcement for each possible reinforcement arrangement.

355

0.70 0.65 0.60 0.55 0.50 0.45 0.40 0.71

Fig. 12. Contour plots for improvement ratio of (a) settlement and (b) horizontal displacement of VGREW in the prototype.

3.4. Failure modes of VGREW in a wet state The discussion on wall deformation in the previous section is based on the results obtained for an acceleration of 20g. From the design point of view, it is helpful to have knowledge of the evolution of the failure modes with the reinforcement arrangement of VGREW in a wet state. Since the centrifuge model can be tested to failure simply by gradually increasing the model’s self-weight, models MA1, MA5, MA6, MB1, MB4, MC1, MC4, MD1, MD4 and MD5 were then driven to failure to investigate the

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failure mechanism. Among these models, only the model MD5 did not fail even at the acceleration of 100g. The prototype equivalent height Hp at failure is defined as H  Nf, where H is the model height and Nf indicates the multiples of g at which the wall failed. Fig. 13 shows the Hp for various reinforcement arrangements of the wall. The

Prototype Equivalent Height, (m)

40 Unreinforced earth wall Sv = 0.8 m 30

Sv = 0.6 m Sv = 0.4 m Sv = 1 m (actual failure case 1)

20

Sv = 0.6 m (actual failure case 2)

10

0 0.0

equivalent height of the prototype at failure increases as the L/H ratio increases. Although, the equivalent height of the prototype at failure increases with the decrease in vertical reinforcement spacing; this effect is more pronounced for higher reinforcement length ratios. In the test results, four failure modes: i.e., circular arc failure mode, overturning failure mode, bearing capacity failure mode and internal instability failure mode, depending on various combinations of reinforcements, were observed.

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Reinforcement Length Ratio, (L/H)

Fig. 13. Effect of the reinforcement ratio on the prototype equivalent height at failure for walls with different vertical spacings.

3.4.1. Circular arc failure mode This type of failure mode is observed for model MA5 with Sv ¼ 30 mm and L/H ¼ 0.3. The reinforcement length is apparently shorter than the minimum value of 0.71H specified by the design guidelines; the reinforced zone thus lies entirely within the active zone. Fig. 14 describes the failure process as sketched from CCD images, where the dashed line indicates the positions of the reinforcement. In this case, the anchoring function of the reinforcement is not developed at all, leading to an active zone, which slides along the circular arc with increasing acceleration. Even so, the equivalent height of the prototype at failure, 9 m, is still larger than that of 3.6 m in the unreinforced model MA1.

Fig. 14. Evolution of circular arc failure with increasing acceleration.

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3.4.2. Overturning failure mode Models MA5, MA6, MB1, MB4, MC1, MC4 and MD1 with reinforcement lengths larger than or equal to 0.71H, exhibit this type of failure mode. It can be seen that as the L/H ratio grew larger, the prototype equivalent height increased and the failure mode gradually evolved from the circular arc failure mode to the overturning failure mode. Fig. 15 depicts the process of failure outlined by the CCD images. The dashed line indicates the profile of wall before the test. The hyphenated line and the solid line represent the positions of reinforcement and wall surface from 1 to 45g, respectively. As the acceleration increases, the lateral earth pressures on the wall and the tension in the reinforcements also become larger, due to an increase in the self-weight. The elongation of the reinforcement and the main crack gradually extended downward from the upper surface of the wall, causing the soil between the reinforcement layers to move forward and downward, and

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the spacing of the reinforcement layers to become thinner. The wall face bulged significantly before failure. Finally, a big crack developed at the end of the reinforcement, and the reinforced zone collapsed in the overturning failure mode. 3.4.3. Bearing capacity failure mode Except for foundation heaving near the foot of the wall, model MD5 with Sv ¼ 20 mm and a reinforcement length ratio larger than 1.15, no failure of the wall was observed even at 100g, and the failure mode changed from the overturning failure mode to the bearing capacity failure mode. This may be due to the smaller reinforcement spacing and the longer reinforcement used in this model, so that the reinforcements are subjected to less tension and less elongation, resulting in less forward and downward movements in the lower part of the wall. However, the pressure borne at the bottom of the wall increases as the

Fig. 15. Evolution of overturning failure with increasing acceleration.

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self-weight increases. In this test the contact pressure exerted by the wall on the foundation soil is about 480 kN/ m2 at the 100-g acceleration field. Using the Meyholf ultimate bearing capacity formula, the ultimate bearing capacity of the foundation soil of the model (su ¼ 63 kN/ m2) is about 371 kN/m2. Hence the foundation soil cannot bear the weight of the VGREW, leading to bearing capacity failure mode, with foundation heaving near the foot of wall. 3.4.4. Internal instability failure mode Model MA5 was designed to see how the strength of the reinforcement affects the failure mechanism. The reinforcement strength was reduced to half of that adopted in the model MC4. From Fig. 16, it can be observed that each layer, except for the bottom two layers, ruptured. The profile of the failure surface starts from the end of overlap of bottom layer reinforcement, 0.1H above the base, extending upward along the inclination angle of 451 until the height of 0.5H, and then propagates vertically to the top surface of the wall. 3.5. Comparisons with actual failure cases and tested models Two actual failure cases were selected for comparison, as shown in Fig. 13 (Huang, 1994; Chou et al., 2002). In case 1, a reinforced wall with inclination of 801 was constructed as a soil retaining structure for highway expansion. Geogrid is the reinforcement. The reinforcement spacing, reinforcement length and wall height are 1, 2 and 8 m, respectively and L/H ¼ 0.25. The initial instability was triggered by the pull-out of the reinforcement near the base of the wall due to a decrease in strength and increase in self-weight of the soil during a period of heavy rainfall. The reinforcement spacing and reinforcement length of model MA6 were 0.6 m and 0.3H, respectively, and the failure height is 9 m, which is larger than 8 m. However, the result is reasonable, since for model MA6 the reinforcement length is longer and the reinforcement spacing is smaller.

Fig. 16. Failure surface caused by internal instability.

The wall in Case 2 is a three-step reinforced wall with 1 m offset and 801 of inclination, constructed (using geogrid as reinforcement material) to store the discarded soil. The reinforcement spacing, reinforcement length and wall height are 0.6, 16 and 16 m, respectively, and a 10 mhigh pile of soil with an inclination of 451 is placed on top of the wall. Global instability is triggered by debris flow due to a drainage system failure, saturation with underground water and the infiltration of rainwater and surface flow during a typhoon. The failure height of the prototype model (estimated by interpolating results obtained in this study) is 20 m, which is higher than that of case 2. Such a difference may be due to the surcharge load in the second failure case. Thus, although the type of reinforcement material and geometry of walls of the cases that failed are different from those of the tested models, the prototype failure heights for the failure cases and the tested models are in good agreement. 4. Summary and conclusions To simulate the worst field conditions after several consecutive days of heavy rainfall and poor drainage, a series of centrifugal VGREW model tests, with clayey backfill near the liquid limit, were constructed. Tests were performed for models with various reinforcement arrangements. The test results show that such walls can be stable even in the worst climatic conditions if an appropriate reinforcement arrangement is introduced. From this study, the following conclusions can be drawn. (1) Decreasing the reinforcement spacing is more effective than increasing the reinforcement length in terms of alleviation of wall deformations for clayey VGREW in a wet state. (2) There exists a critical reinforcement length. If the reinforcement length is longer than the critical reinforcement length, it provides no further benefit to alleviate the wall deformations. A smaller reinforcement spacing leads to a shorter critical reinforcement length ratio. (3) Different reinforcement arrangements can render the same improvement ratio for VGREW in a wet state. In this study contour plots showing the relationships between the reinforcement length ratio and the vertical reinforcement spacing for various Ir are provided, to be used to select the appropriate reinforcement arrangement for a desired improvement ratio. (4) Depending on the reinforcement arrangement and reinforcement strength, there are four failure modes for clayey VGREW in a wet state: the circular arc failure mode, overturning failure mode, bearing capacity failure mode and internal instability failure mode. The circular arc failure mode occurs for cases with reinforcement lengths shorter than the minimum value specified by the design guidelines, while the bearing capacity failure mode occurs for small vertical

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