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Confinement effect of geocells on sand samples under triaxial compression
Geotextiles and Geomembranes 37 (2013) 35e44
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Confinement effect of geocells on sand samples under triaxial compression Rong-Her Chen*, Yu-Wen Huang, Feng-Chi Huang Department of Civil Engineering, National Taiwan University, No. 1, Sec. 4, Roosevelt Rd., Taipei 10617, Taiwan
a r t i c l e i n f o
a b s t r a c t
Article history: Received 17 September 2012 Received in revised form 8 January 2013 Accepted 24 January 2013 Available online 1 March 2013
The confinement effect of geocells improves vastly the shear strength of granular soil. To understand the mechanism better, several tests have been performed on geocell-reinforced-sand samples of two different sizes. The geocells were made of high-density polyethylene sheets, and the influencing factors examined include the shape (circular, rectangular, and hexagonal cross-sections), size and number of cells. The effects of these variables on the compression strength of samples as well as the stressestrain behavior were investigated. It has been found that the apparent cohesion of reinforced samples vary with the shape, size and number of cells, of which the cell size is the most significant factor. Among the cells of all shapes, the circular cells induce the highest apparent cohesion. In addition, the effectiveness of the reinforcement is more significant at low confining pressure. This can be explained by theoretical analysis, which shows that the reinforced samples under low confining pressures tend to expand more and induce higher circumferential strain. When under high confining pressure, the samples undergo lesser dilation leading to lower hoop forces in geocells. Ó 2013 Elsevier Ltd. All rights reserved.
Keywords: Geocells Compression test Compression strength Confining effect Apparent cohesion
1. Introduction Geocells are widely applied in geotechnical engineering, such as controlling erosion of slopes and river banks, enhancing bearing capacities of pavements and footings, reinforcing soft grounds and slopes, and protecting shores and channel beds. The cells are often made from high-density polyethylene or polyethylene strips ultrasonically welded together to give an open-cell structure for containing soil. Such confinement provided by geocells improves vastly shear strength of granular soil; and, in turn, the increase in soil strength provides improved bearing capacity and/or prevents soil erosion. The confinement of geocells has been studied mainly in the laboratory using triaxial compression test and uniaxial compression test. With regard to triaxial compression tests, Bathurst and Karpurapu (1993) reported the results of a series of largescale triaxial compression tests carried out on 200-mm-high isolated geocell soil composite samples and unreinforced soil samples. The soils tested were silica sand and limestone, with free drainage of water in the soil samples allowed. The results illustrated stiffening effect and increase in strength imparted to the soil by the enhanced confinement effect. Moreover, comparison of reinforced
* Corresponding author. Tel.: þ886 2 3366 4242; fax: þ886 2 23629851. E-mail addresses: [email protected] (R.-H. Chen), [email protected] (Y.-W. Huang), [email protected] (F.-C. Huang). 0266-1144/$ e see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.geotexmem.2013.01.004
and unreinforced soil samples showed that the peak friction angle of the soil infill and that of the composite were the same. Rajagopal et al. (1999) performed triaxial compression tests on granular soils encased in single and multiple geocell samples with 100-mm diameter. The geocells were fabricated by hand using different woven and nonwoven geotextiles and soft mesh to investigate the effect of stiffness of geocell on overall performance of the composite. It was observed that the soil developed cohesive strength resulting from the confinement by the geocell, and the magnitude of the cohesive strength varied with the properties of the geocell. They also presented a simple methodology for estimating the magnitude of the apparent cohesive strength. Shen (2005) performed triaxial compression tests to investigate the effect of relative density of soils on compression strength of two different aggregates reinforced with geocells. It was found both the peak friction angle and apparent cohesion of the reinforced soils increased with relative density. Latha and Murthy (2007) studied and compared the relative efficiency of three forms of reinforcements, namely, horizontal geosynthetic layers, randomly oriented discrete fibers, and geocells. Uniaxial compression tests have also been conducted on large samples. Bathurst and Crowe (1994) described two large-scale uniaxial compression tests (1 m wide 1 m long 1.44 m high) to examine the stability of multiple layers of geocells under vertical surcharge. The geocells were 200 mm high and had a cell diameter of 200 mm. The soils tested were sand and limestone. They reported that the sand column and the limestone aggregate column were respectively stable up to
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10 m and 13.5 m of equivalent heights of the structure. Wesseloo et al. (2009) discussed the results of uniaxial compression tests performed on single cells and geocell packs of different sizes, and the geocells were mainly square in shape. They found that the strength of the geocell composite structure was indirectly proportional to the size of individual cells and that the strength reduced with increasing number of cells in the structure. To evaluate the interaction between hoop stresses and passive earth resistance, Emersleben and Meyer (2009) carried out radial load tests on single and multiple geocell structures. Considerable interest has also been shown in studying geocellreinforced structures, such as shallow foundations (Dash et al., 2003; Sireesh et al., 2009; Pokharel et al., 2010; Moghaddas Tafreshi and Dawson, 2010, 2012), slopes (Chen and Chiu, 2008; Leshchinsky et al., 2009), pavements (Thakur, et al., 2012; Leshchinsky and Ling, 2013), and embankments (Zhang et al., 2010). Nonetheless, there were few studies reporting the fundamental understanding of these systems. To make up for such deficiency, this study performed tests on geocell-reinforced-sand samples under triaxial compression to examine the effect of variables on compression strength and deformation characteristics of the samples. It is hoped that the results from this study will improve the understanding of the confinement effect of geocells when applied to geotechnical engineering. Furthermore, the test results will be good for calibrating numerical analysis, which allows for extrapolation to realistic setup of geocells in the field.
Table 1 Strength and elastic modulus of model and prototype materials.
Tensile strength T (kN/m) Junction shear strength Sj (kN/m) Junction peel strength Pj (kN/m) Junction split strength Uj (kN/m) Secant modulus Js (kN/m) a
Model material
Prototype materiala
15.0 8.2 6.4 8.6 101
17.0 13.5 9.5 12.8 494
Shen (2005).
strength as well as the stressestrain behavior of reinforced-sand samples under triaxial compression. In the literature, geocells adopted for testing were most commonly of circular cross-section, probably because it is easier to fit cylindrical geocells into the chamber of the triaxial apparatus (Bathurst and Karpurapu, 1993; Rajagopal et al., 1999; Shen, 2005). Geocells of square cross-section have also been adopted but not common (Wesseloo et al., 2009). In practice, geocells used in the field tend to be of rhombic crosssection. Thus, it is of interest to compare the confinement effects of cells of different cross-sections. In this study, the geocells for testing were of three types, namely, cylindrical, hexagonal and rectangular columns. Moreover, in order to study multiple-cell effect, the samples were prepared to contain one cell, three cells, and seven cells. 3. Testing program and procedure
2. Materials used for testing The variables considered in the testing program are as follows. 2.1. Soil The sample soil used in the present investigation was uniform, sub-angular sand containing 99.8% silica. It is classified as poorlygraded sand (SP) as per the Unified Soil Classification system, with a coefficient of uniformity Cu ¼ 2.07 and a coefficient of curvature Cc ¼ 1.04. The physical properties of the sand are as follows: specific gravity Gs ¼ 2.66, median grain size d50 ¼ 0.25 mm, effective grain size d10 ¼ 0.15 mm, maximum dry unit weight gd,max ¼ 16.1 kN/m3, and minimum dry unit weight gd,min ¼ 13.3 kN/m3. 2.2. Geocell material The material used for fabricating geocells was high-density polyethylene sheet, for it is easy to obtain and process. The physical properties of the material are as follows: specific gravity Gs ¼ 0.967 (ASTM D 792, 2008), thickness t ¼ 0.38 mm (ASTM D 5199, 2012), and mass per unit area mA ¼ 118 g/m2 (ASTM D 5261, 2010). The strength tests performed on this geocell material include tensile strength test on the material and the tests for three failure modes of the junction of a geocell: junction shear failure, junction peel failure, and junction split failure (Cancelli et al., 1993). The tensile strength is 15 kN/m obtained from a wide-width sample, according to ASTM D 4595 (2011). The sample for junction strength tests had a width equal to the seam spacing and a length equal to the height of cell. Forces were applied at both ends of the sample until the junction failed. The results presented in Table 1 are junction shear strength Sj ¼ 8.2 kN/m, junction peel strength Pj ¼ 6.4 kN/m, and junction split strength Uj ¼ 8.6 kN/m. In Table 1, the results of another geocell material (Shen, 2005), which is also made of HDPE and commonly used in the field, are presented for comparison. It is noteworthy that the secant modulus (Js at 2% strain) of the model material is only about 20% of the prototype material, though their tensile strengths are not much different. As mentioned previously, this study aimed to investigate the effects of shape, size, and number of geocells on the compression
Sand with and without reinforcement Sample size e small sample (2.8 inches in diameter and 6inches high) and large sample (6 inches in diameter and 12inches high) Cell shape e the cross-sections of cells were circular, rectangle, and hAexagonal Cell size e cells of the same shape but different sizes Number of cells e different numbers of cells in same area The content of the testing program is shown in Table 2. For the 10 tests listed, the first letter of the samples, S, represents sand; the second letter denotes the shape of the cells; and the third letter denotes the number of cells in the sample. Samples marked with an asterisk are small samples of 2.8-inch diameter, while those without an asterisk are large samples of 6-inch diameter. The configurations of all samples are depicted in Fig. 1. A photo of hexagonal geocell columns is shown in Fig. 2. The samples for triaxial compression were prepared according to the procedures of ASTM D 4767 (2011). Specifically, all samples
Table 2 The testing program. Soil
Sample Diameter of sample Shape of cell Number of cell
Sand Sand Reinforced Reinforced Reinforced Reinforced Reinforced Reinforced Reinforced Reinforced
S* S SC1* SH1* SH3* SC1 SC3 SB3 SH3 SH7
sand sand sand sand sand sand sand sand
2.8 in. (7.1 cm) 6 in. (15.2 cm) 2.8 in. (7.1 cm) 2.8 in. (7.1 cm) 2.8 in. (7.1 cm) 6 in. (15.2 cm) 6 in. (15.2 cm) 6 in. (15.2 cm) 6 in. (15.2 cm) 6 in. (15.2 cm)
e e Circle Hexagon Hexagon Circle Circle Rectangle Hexagon Hexagon
e e 1 1 3 1 3 3 3 7
Note: 1. S ¼ sand, C ¼ circle, H ¼ hexagon, B ¼ rectangle (or block). 2. The small sample (2.8 inches in diameter) is indicated with *; otherwise the sample is a large sample (6 inches in diameter).
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were prepared under dry condition. Five layers of pre-weighted quantity of sand were placed in the sample mold with light tamping. Each layer of sand was 30 mm and 60 mm thick for small and large samples, respectively. This procedure produced uniform samples with a relative density of 55%. All samples were then saturated and consolidated to reach equilibrium in a drained state at the effective consolidation stress for which a strength determination is required. All tests were carried out at a compressive strain rate of 0.1% per minute. During the test, water was allowed to drain freely from the sample. This is because the soil infill with geocells in the field is often permeable and the test soil is also a pervious material. In addition, the effect of rubber membrane increases as the sample is compressed; therefore, the effect of the membrane should be corrected so that the compression strength of the sample can be obtained accurately. The correction of the effect of membrane, which is 1.58 mm thick, was made according to ASTM D 4767 (2011). Generally speaking, the correction will be of significance only when the effective stresses are small (Henkel and Gilbert, 1952). It also needs to note that a reinforced-sand sample is a composite material, in which the stress and strain may not be as uniform as in an unreinforced-sand sample. Before the effect is fully understood, the test results in the following were obtained on the assumption that the stress and strain in reinforced-sand samples are uniformly distributed. 4. Test results 4.1. Unreinforced sand
Fig. 1. Different configurations of the samples used in compression tests.
To examine the effect of sample size on compression strength of sand without reinforcement, a small sample (S*) and a large sample (S), shown in Fig. 1, were tested for comparison. The peak stresses of the two samples occurred at axial strains of about 6% (Fig. 3a). After that, the large sample displayed more obvious strain-softening behavior, especially under high confining pressure (200 kPa). As for volume change, the samples were compressed in the beginning and subsequently dilated as axial strain increased (Fig. 3b). The small sample tended to dilate more than the large sample; however, the dilation of both samples decreased when the samples were subjected to higher confining pressures. From MohreCoulomb failure envelopes, the friction angles of the small and large samples were 37 and 38 , respectively. The cohesion intercepts were both small and thus neglected. From this result, it can be concluded that sample size has insignificant effect on compression strength of unreinforced sand. 4.2. Reinforced sand (2.8-inch sample) For the small sample of reinforced sand, three tests were conducted: SC1*, SH1*, and SH3* (Fig. 1). The results of the first two samples, SC1* and SH1*, are employed to study the effect of cell shape; these two samples had equal area confined by each geocell. On the other hand, the effect of multiple cells are compared by examining the results of SH1* and SH3*.
Fig. 2. Photo of hexagonal geocell columns.
4.2.1. Effect of cell shape In Fig. 4, the results of reinforced samples, SC1* and SH1*, and unreinforced sample, S*, are compared. It can be seen from Fig. 4a that the curves of reinforced samples do not show the strainsoftening phenomenon as occurred in the unreinforced sample. The geocells changed the sand from brittle to ductile, and therefore the reinforced samples displayed better strength. Furthermore, the sample with circular cell, SC1*, had higher compression strength than that with hexagonal cell, SH1*. Correspondingly, the volumetric
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Deviatoric stress , Δσ (kPa)
1000
Confining pressure … S*
— S 50 kPa 50 kpa 100 kPa 100 kPa 200 kPa 200 kPa
800
600
400
200
0 0
4
8 12 Axial strain , εa (%)
16
20
(a)
(a)
Volumetric stress , εv (%)
5
3
Confining pressure … S*
— S 50 kPa 50 kpa 100 kPa 100 kPa 200 kPa 200 kPa
1
-1 0
4
8 12 Axial strain , εa (%)
16
(b)
20
(b) Fig. 3. Results of compression tests on 2.8-inch and 6-inch samples of sand. (a) Stress versus strain. (b) Volumetric strain versus axial strain.
strain of SC1* is greater than that of SH1* (Fig. 4b), because the circular shape expands more easily than the irregular hexagonal shape. The strength parameters of the three tests are tabulated in Table 3. As can be seen, S* has c ¼ 0 and f ¼ 37 ; SC1* has cr ¼ 79 kPa and f ¼ 38 ; SH1* has cr ¼ 35 kPa and f ¼ 38 . Obviously, reinforcement improved the cohesion but had little contribution to the friction angle of the reinforced samples. This finding is in line with previously reported results (e.g., Bathurst and Karpurapu, 1993). It can also be concluded that the improvement in cohesion is attributed to the induced tensile strain in the geocell, which is a function of cell shape as well. 4.2.2. Effect of cell size With regard to the effect of the size of cells, Fig. 5 shows photos of two samples after failure. The single-cell sample, SH1*, were significantly deformed, while its corners were less affected. On the other hand, the sample with three cells had shorter sides, and consequently the deformation was not as significant as that of SH1*. Comparing the stressestrain curves under different confining pressures shows that the curves of SH3* are higher than those of SH1* (Fig. 6a). Correspondingly, the curves of volumetric strain for SH3* should also be higher, irrespective of the confining pressure (Fig. 6b). Likewise, the strength parameters of SH3*, cr ¼ 44.2 kPa and f ¼ 39 , are also higher than those of SH1* (Table 3). It is concluded that apparent cohesion decreases with the size of cells; however, the friction angles were about the same.
Fig. 4. Results of compression tests on 2.8-inch samples comprising cells of different shapes. (a) Stress versus strain. (b) Volumetric strain versus axial strain.
Findings on small samples are summarized as follows. First, reinforced samples presented higher stiffness, or steeper stresse strain curve, than unreinforced samples; nevertheless, this difference became less significant with increasing confining pressure. Second, samples consisted of more small cells showed stiffer behavior than those consisted of large but fewer cells. Third, among the three samples (SC1*, SH1*, and SH3*), the cylindrical sample was the stiffest. 4.3. Reinforced sand (6-inch sample) For large samples of reinforced sand, five tests were conducted (see Fig. 1). The three samples used for comparing the effect of Table 3 Results of compression test. Sample
Diameter of sample D0 (cm)
Equivalent diameter de (cm)
Apparent cohesion cr (kPa)
Friction angle 4 ( )
Ratio crde (kN/m)
S* SC1* SH1* SH3* S SC1 SC3 SB3 SH3 SH7
7.1 7.1 7.1 7.1 15.2 15.2 15.2 15.2 15.2 15.2
7.1 6.0 6.0 3.15 15.2 15 7.0 7.0 7.0 4.62
0 79.0 35.0 44.2 0 33.7 59.4 31.0 23.7 34.5
37 38 38 39 38 37 36 36 38 38
e 4.74 2.10 1.39 e 5.06 4.16 2.17 1.66 1.59
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39
(a)
Fig. 5. Photos of 2.8-inch samples after test. (a) SH1*. (b) SH3*.
(b) shape are SC3, SH3, and SB3. In order to have equal basis for comparison, the cell of each shape had the same area, as marked by the shaded area in Fig. 7a. With regard to the effect of number of cells, SC1 versus SC3 and SH3 versus SH7 are compared, respectively. 4.3.1. Effect of cell shape Figs. 8a and b presents the stressestrain curves of three reinforced samples and one unreinforced sample under low and high confining pressures, respectively. The curves of the three reinforced samples under low confining pressure (Fig. 8a) were significantly higher than that of unreinforced sand. Among the reinforced samples, SC3 showed the highest strength, while the strength of SB3 was the lowest. Notably, a rapid increase in deviatoric stress was observed for SC3 when axial strain exceeded 10%. In contrast, the stressestrain curves of all samples under high confining pressure (Fig. 8b) were much closer, compared with those in Fig. 8a, suggesting that the effect of reinforcement was more significant under low confining pressure. The variations in volumetric strain for large samples were similar to those for small samples (e.g., Figs. 4b and 6b). Of the three reinforced samples, SC3 showed the highest trend of increase in volume, which is comparable to its highest compression strength. However, the variations in volumetric strain for rectangular-shaped cell, SB3, were found to be not as regular as those of SC3 and SH3, probably due to unsymmetrical geometry of blocks. The photos of the three samples after tests are displayed in Fig. 7b for clarifying this explanation. The strength parameters of SC3, SB3, and SH3 are tabulated in Table 3. Among them, SC3 has the highest apparent cohesion cr ¼ 59.4 kPa, while SH3 has the slightly highest friction angle, f ¼ 38 . These results are attributed to the cell shape as well as the junction between cells. As shown in Fig. 7a, the three circles were
Fig. 6. Results of compression tests on 2.8-inch samples comprising different number of hexagonal cells. (a) Stress versus strain. (b) Volumetric strain versus axial strain.
connected only at three points, while the hexagons and blocks were connected along the junctions between cells. As a result, the circles expanded more freely than the hexagons and blocks and mostly along their outer boundaries. As seen in the photos shown in Fig. 7b, the circles became somewhat irregular, but the hexagons still maintained their original shapes. Notably, the rectangles shows quite irregular deformation with their edges deformed much more than their inner junctions. This demonstrates that adjacent cells restrained one another from expansion, consequently resulting in reduced development of tensile strain as well as tensile strength in the cells. 4.3.2. Effect of cell size The effect of cell size is examined by comparing SH3 and SH7 (see Fig. 1). As shown in Fig. 9, the stressestrain curves of SH7 are higher than those of SH3 under all confining pressures, though the difference is not significant at confining pressure of 50 kPa. Correspondingly, the curves of volumetric strain for SH7 are also higher than those of SH3 (Fig. 9b). In summary, using greater number of smaller cells to confine soil will induce higher compression strength as well as greater volumetric strain in the reinforced soil samples. The other comparison is obtained from circular cells, i.e., SC1 versus SC3. Similar observation as that for hexagonal geocells (SH3 versus SH7) was observed, and hence no further discussion will be made. The strength parameters of SC1, SC3, SH3, and SH7 are summarized in Table 3. As can be seen, the friction angles for cells of the same shape show little variations, but the apparent cohesion is
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Fig. 7. Comparison of three 6-inch samples reinforced with cells of different shapes. (a) Different configurations. (b) Photos of samples after tests (s3 ¼ 200 kPa).
much higher for samples with small cells, e.g., 59.4 kPa of SC3 greater than 33.7 kPa of SC1.
5. Discussion The effects of shape, size, and number of cells are discussed in this section. In addition, improvement in the elastic modulus and compression strength of reinforced sand due to confinement of cell is presented.
5.1. Effect of cell shape As summarized in Table 3, the friction angles of unreinforced samples, S and S*, are 37e38 , while those of reinforced samples are 36e39 , revealing insignificant effect of geocell on friction angle of test sand. It is worthy to note that hexagonal cells induced slightly higher friction angle than cells of the other two shapes. On the other hand, the increase in apparent cohesion due to reinforcement of cells of all shapes is obvious. This can be explained by examining the photos of samples after failure. For the unreinforced sample (Fig. 10a), a clear failure plane can be determined as several inclined stretches were seen on the rubber membrane. For the reinforced sample (Fig. 10b), it did not fail when the test terminated at an axial strain of 15%. As a result, the rubber membrane of this sample showed only horizontal wrinkles. Evidently, the confining effect provided by the cells mobilized the confining strength to prevent the soil from failure. As for the contribution to the compression strength of the reinforced sand, cells of circular shapes demonstrated the best effect among those of all shapes.
5.2. Effect of cell size The relationship between apparent cohesion and the equivalent diameter of a single cell, de, is shown in Fig. 11. The equivalent diameter originates from the concept of the circumference per unit area under confinement. For example, if a circular cell has a diameter d, then its circumference is pd and the confined area is pd2/4. Hence, the circumference per unit area is 4/d. For cells other than the circular ones, their areas are assumed equivalent to the areas of circles, so their equivalent diameters can be obtained in this way. Note that this relationship is considered only for a single cell. To compare the difference in mobilization of apparent cohesion among various shapes, the relationships between apparent cohesion and the inverse of equivalent diameter are plotted in Fig. 11: a. Circular cells (for SC1 and SC1*)
cr ¼ 4:97=de R2 ¼ 0:997
(1)
b. Hexagonal cells (for SH3 and SH3*)
cr ¼ 2:92=ðde Þ0:78 R2 ¼ 0:999
(2)
where cr ¼ apparent cohesion (kPa), de ¼ equivalent diameter of a single cell (m). The relationships show linear relation for circular cells and somewhat nonlinear relation for hexagonal cells; thus, the
R.-H. Chen et al. / Geotextiles and Geomembranes 37 (2013) 35e44
(a)
(a)
(b)
(b) Fig. 8. Results of compression tests on 6-inch samples reinforced with three cells of different shapes. (a) s3 ¼ 50 kPa. (b) s3 ¼ 200 kPa.
apparent cohesion is approximately proportional to the inverse of the cell diameter, and small cells induce higher apparent cohesion. Note that the curves are assumed to pass through the origin because a very large cell will induce very small apparent cohesion. In addition to that, the slope of Eq. (1) is more than that of Eq. (2), also demonstrating greater effectiveness in using smooth cells of circular shape.
41
Fig. 9. Results of compression tests on 6-inch samples with different number of hexagonal cells. (a) Stress versus strain. (b) Volumetric strain versus axial strain.
versa. Therefore, for cells of circular shape, the multiple-cell effect between one cell and three cells is estimated to be 0.82 (¼4.16/ 5.06). As for samples having more than three cells, comparison is made between SH3 and SH7, and the result is 0.96 (¼1.59/1.66). From this observation, according to the results of the compression tests conducted in drained condition, multiple-cell effect seems to be significant only for samples comprising less than three cells. Although this result is consistent with the observations made by Rajagopal et al. (1999), further research is still needed.
5.3. Multiple-cell effect It is of interest also to know the difference in apparent cohesion mobilized by a single cell and multiple cells. As seen in Fig. 11, the deviation of SC3 from the line through SC1 and SC1* is the effect of multiple cells; the same effect is seen between SH1* and the curve through SH3* and SH3. This topic is important because multiple cells are more constrained than a single cell, and the effect may be so significant as to affect the strength parameters of reinforced soil. Nevertheless, due to limitation of the apparatus, it is almost impossible to conduct tests on samples with many cells. Despite the difficulty, the following prediction is made according to the test results in this study. In order to eliminate the effect of cell size for direct comparison of the data, each data in Fig. 11 is expressed as a ratio of the ordinate to the x-coordinate, i.e., cr/(1/de) or crde, as displayed in the last column in Table 3. By doing so, theoretically, the ratio of 5.06 obtained from the single-cell sample (SC1) can be compared with the ratio of 4.16 obtained from the three-cell sample (SC3), and vice
5.4. Improvement in compression strength The effectiveness of reinforcement can be represented by a deviatoric stress ratio, SR, which is defined as
SR ¼ ðDsr Þmax =ðDsÞmax
(3)
where (Dsr)max and (Ds)max are the maximum deviatoric stresses of reinforced and unreinforced samples, respectively. As shown in Fig. 12, the values of SR at confining pressure of 50 kPa are in the range of 1.5e2.5. However, the ratio decreases as confining pressure increases, e.g., the ratios at confining pressure of 200 kPa are in the range of 1.0e1.5. This result indicates good improvement in the compression strength of unreinforced soil under low confining pressure. The other findings from Fig. 12 concern the size of sample and the number of cells. With regard to the size of sample, smaller samples have higher deviatoric stress ratios, e.g., SC1* versus SC1
42
R.-H. Chen et al. / Geotextiles and Geomembranes 37 (2013) 35e44 3 SC1* SH1* SH3* SC1 SC3 SH3 SH7 SB3
2.5
SR
2
1.5
1
0.5 0
150
200
250
Fig. 12. Relationship between deviatoric stress ratio and confining pressure.
Ds3 ¼
2Js εc D ð1 εa Þ
(5)
where Ds3 ¼ the rubber correction in this case (kPa), Js ¼ secant modulus of the membrane at εa (kN/m), D ¼ diameter of the sample at εa (m), εa ¼ axial strain (%), and εc ¼ circumferential strain (%). Again, Ds3 is in functions of the reciprocal of the diameter of sample, the modulus of membrane, and the deformed shape of the sample, εc/(1 εa).
6. Theoretical analysis In studying the effect of rubber membranes on the measured compression strength of saturated clay sample in undrained condition, Henkel and Gilbert (1952) introduced two theories, compression shell theory and hoop tension theory, to correct the compression strength of the sample. In the compression shell theory, only the axial strain of the sample is taken into consideration; while in the hoop tension theory, it considers both the axial strain and radial strain of the sample. The equations of the two theories are as follows:
100
Confining pressure , σ (kPa)
Fig. 10. Photos of reinforced and unreinforced samples after tests (s3 ¼ 200 kPa). (a) Unreinforced sample, S. (b) Reinforced sample, SH7.
(also for SH3* versus SH3). Regarding the number of cells, greater amount of smaller cells develops higher stress ratio, such as SH3* versus SH1* (also for SC3 versus SC1 and SH7 versus SH3).
50
In studying the behavior of reinforced granular soils, Bathurst and Karpurapu (1993) and Rajagopal et al. (1999) used the hoop tension theory to predict the apparent cohesion for samples under drained and undrained conditions, respectively.
a. Compression shell theory 6.1. Derivation of circumferential strain
sr ¼
pD0 Jc εa
(4)
Ac
where sr ¼ the rubber correction (kPa), Jc ¼ compression modulus of the rubber membrane (kN/m), D0 ¼ initial diameter of the sample (m), εa ¼ axial strain (%), and Ac ¼ corrected area of the sample at strain εa (m2). Note that the ratio, pD0/Ac, in Eq. (4) is similar to the circumference per unit confined area mentioned previously. b. Hoop tension theory
Apparent cohesion , cr (kPa)
100
In order to employ Eq. (5) for the drained tests conducted in this study, the circumferential strain of the sample need to be derived. Assuming a sample has an initial volume of V0, and it subsequently decreases to V, as a result of the consolidation of soil and water drainage. Therefore,
V ¼ 1 εv V0
(6)
Herein, the volumetric strain, εv, is assumed positive for compression and negative for extension. By substituting the diameter and the length of the sample into above equation, it can be written as
p
80
4
p
60
4 SC1* SC1 SC3 SH1* SH3* SH3 SH7
40
20
20
40
60
1/Equivalent cell diameter , 1/de
80
D20 L0
¼ 1 εv
(7)
Rearranging this equation leads to the following:
D ¼ D0
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð1 εv ÞL0 L
(8)
Now, using axial strain εa, the equation is changed as below
0 0
D2 L
100
(m-1 )
Fig. 11. Relationship between apparent cohesion and equivalent diameter of cell.
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u ð1 ε Þ ð1 εv Þ u v D ¼ D0 u ¼ D0 tðL0 DLÞ ð1 εa Þ L0
(9)
R.-H. Chen et al. / Geotextiles and Geomembranes 37 (2013) 35e44
The circumferential strain, εc, which is the change in length per unit circumferential length, can be expressed as
pD pD0 D D0 ¼ pD0 D0
(10)
By substituting the diameter, D, from Eq. (9) into the above equation, it then becomes
εc ¼
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð1 εv Þ D0 D0 ð1 εa Þ D0
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð1 εv Þ ¼ 1 ð1 εa Þ
800
400
200
(11) 0
Accordingly, the circumferential strain can be substituted into Eq. (5) to calculate the induced confining stress in the reinforcement, with the secant modulus of membrane, Js, in Eq. (12) replaced by that of the geocell material.
2Js D
ð1 εa Þ
0
400
800
(a) 800
(12)
6.2. Interpretation In the following, the compression strengths of reinforced samples are obtained according to Eqs. (4) and (5), respectively. Note that it was not possible to measure the compression modulus of rubber membrane; and hence, the compression modulus was assumed to be the same as the secant modulus of the membrane (Henkel and Gilbert, 1952).
test 50 kPa test 200 kPa shell 50 kPa shell 200 kPa
600
400
200
0 0
400
800
(b)
(14)
where s1 is the compression strength of unreinforced soil sample, and Kp is Rankine’s coefficient of passive earth pressure. The comparison between Mohr circles from test results and theoretical prediction are plotted in Fig. 13. The correction for membrane effect, according to ASTM D 4767 (2011), has already been subtracted from the compression strength before the appropriate Mohr circle is drawn. In the figure, the test results are denoted by hollow symbols, while solid symbols represent the prediction. As can be seen from Fig. 13a, the prediction by the hoop tension theory matches well the test results under low confining pressure of 50 kPa. On the other hand, Fig. 13b shows the prediction by the compression shell theory is in good agreement with the test results under high confining pressure of 200 kPa. In an alternative way, the maximum mean normal stresses at various confining pressures are compared in Fig. 14. This figure shows the transition of the failure states with increasing confining pressure. It is clearly seen the test result agrees well with the prediction by the hoop tension theory when confining pressure is lower than 50 kPa. This behavior is attributed to the high tendency for the reinforcement under low confining pressure to expand laterally under axial compression. When the confining pressure exceeds 100 kPa, the
Fig. 13. Comparison between Mohr’s circles from test results and two theories (sample SH3*). (a) Hoop tension theory. (b) Compression shell theory.
prediction by the shell compression theory shows better agreement, meaning that the sample under high confining pressure behaves like a compressed column with small volume expansions. This is because at high confining pressure the dilation of soils is lesser. As shown in Fig. 10b, several horizontal wrinkles appear on the surface of the rubber membrane, which were mainly resulted from axial compression of the sample.
600
Mean normal stress, p' (kPa)
(13)
b. Hoop tension theory
s1;hoop ¼ Kp ðs3 þ Ds3 Þ
12 0 0
Normal stress , σ (kPa)
a. Compression shell theory
s1;shell ¼ s1 þ sr
1200
Normal stress, σ (kPa)
Shear stress , τ (kPa)
Ds3 ¼
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ! ð1 εv Þ 1 ð1 εa Þ
test 50 kPa test 200 kPa hoop 50 kPa hoop 200 kPa
600
Shear stress, τ (kPa)
εc ¼
43
400
200 SH3* (Test) SH3* (Shell) SH3* (Hoop)
0 0
50
100
150
200
250
Confining pressure, σ3 (kPa)
Fig. 14. Comparison between mean normal stresses obtained from test results and two theories.
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R.-H. Chen et al. / Geotextiles and Geomembranes 37 (2013) 35e44
7. Conclusions This study has employed tests on geocell-reinforced sand subjected to triaxial compression to examine the confinement effect of geocells. It was found that the confinement effect provided by geocells related mainly to the mobilization of the tensile strength in the geocells, which varies with the volumetric strain induced. The induced volumetric strain is affected by the size and shape of the cell, confining pressure, as well as multiple-cell effect. The findings are summarized as follows. The apparent cohesion of reinforced samples varies mainly with the size, shape, and number of cells, of which cell size is the most significant factor. Approximately linear relationships were found between the apparent cohesion and the inverse of the equivalent diameter of the cell. Moreover, circular cells induced the highest apparent cohesion among cells of all shapes, while the apparent cohesion induced by hexagonal cell was the lowest. The difference in friction angle between the reinforced and unreinforced-sand samples was insignificant. For cells of various shapes, hexagonal ones showed slightly higher friction angle, owing to many corners of hexagons. The constraint by adjacent cells prevents the cells from expanding laterally, and consequently the mobilization of the tensile strength of geocells is restrained in multi-cell configurations. This effect may be significant and should be considered when using the data from tests on a single cell. With increase in confining pressure on the reinforced soil, the reinforcing effect becomes less significant, meaning that the reinforcement is more effective under low confining pressure. Comparison between theoretical and test results show that the behavior of reinforced soil under low confining pressure can be predicted by the hoop tension theory. The behavior of reinforced soil samples under high confining pressure is more similar to a stiff column under axial compression. Acknowledgments This work was supported by the National Science Council of Taiwan (99-2221-E-002-121). We would also like to thank the three anonymous reviewers for their valuable and constructive suggestions. References ASTM D 792, 2008. Standard test methods for density and specific gravity (relative density) of plastics by displacement. American Society for Testing and Materials, West Conshohocken, Pennsylvania, USA. 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. ASTM D 4767, 2011. Standard test method for consolidated undrained triaxial compression test for cohesive soils. American Society for Testing and Materials, West Conshohocken, Pennsylvania, USA. ASTM D 5199, 2012. Standard test method for measuring the nominal thickness of geosynthetics. American Society for Testing and Materials, West Conshohocken, Pennsylvania, USA. ASTM D 5261, 2010. Standard test method for measuring mass per unit area of geotextiles. American Society for Testing and Materials, West Conshohocken, Pennsylvania, USA. 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. Cancelli, A., Rimoldi, P., Montanelli, F., 1993. Index and performance tests for geocells in different applications. In: Cheng, S.C.J. (Ed.), Geosynthetic Soil Testing Procedures, ASTM STP 1190, pp. 64e75. Chen, R.H., Chiu, Y.M., 2008. Model tests of geocell retaining structures. Geotextiles and Geomembranes 26, 56e70.
Dash, S.K., Sireesh, S., Sitharam, T.G., 2003. Model studies on circular footing supported on geocell reinforced sand underlain by soft clay. Geotextiles and Geomembranes 21, 197e219. Emersleben, A., Meyer, N., 2009. Interaction between hoop stresses and passive earth resistance in single and multiple geocell structures. In: GIGSA GeoAfrica 2009 Conference, Cape Town, September 2e5. Henkel, D.J., Gilbert, G.C., 1952. The effect of rubber membranes on the measured triaxial compression strength of clay samples. Géotechnique 3, 20e29. Leshchinsky, B., Ling, H.I., 2013. Numerical modeling of behavior of railway ballasted structure with geocell confinement. Geotextiles and Geomembranes 36, 33e43. Leshchinsky, D., Ling, H.I., Wang, J.-P., Rosen, A., Mohri, Y., 2009. Equivalent seismic coefficient in geocell retention systems. Geotextiles and Geomembranes 27, 9e18. Latha, G., Murthy, V.S., 2007. Effects of reinforcement form on the behavior of geosynthetic reinforced sand. Geotextiles and Geomembranes 25, 23e32. Moghaddas Tafreshi, S.N., Dawson, A.R., 2010. Comparison of bearing capacity of a strip footing on sand with geocell and with planar forms of geotextile reinforcement. Geotextiles and Geomembranes 28, 72e84. Moghaddas Tafreshi, S.N., Dawson, A.R., 2012. A comparison of static and cyclic loading responses of foundations on geocell-reinforced sand. Geotextiles and Geomembranes 32, 55e68. Pokharel, S.K., Han, J., Leshchinsky, D., Parsons, R.L., Halahmi, I., 2010. Investigation of factors influencing behavior of single geocell-reinforced bases under static loading. Geotextiles and Geomembranes 28, 570e578. Rajagopal, K., Krishnaswamy, N.R., Latha, G., 1999. Behavior of sand confined with single and multiple geocells. Geotextiles and Geomembranes 17, 171e184. Shen, C.W., 2005. The mechanical characteristics of geocell-reinforced earth. Master Thesis. Department of Civil Engineering, National Taiwan University (in Chinese). Sireesh, S., Sitharam, T.G., Dash, S.K., 2009. Bearing capacity of circular footing on geocell-sand mattress overlying clay bed with void. Geotextiles and Geomembranes 27, 89e98. Thakur, J.K., Han, J., Pokharel, S.K., Parsons, R.L., 2012. Performance of geocellreinforced recycled asphalt pavement (RAP) bases over weak subgrade under cyclic plate loading. Geotextiles and Geomembranes 35, 14e24. Wesseloo, J., Visser, A.T., Rust, E., 2009. The stressestrain behavior of multiple cell geocell packs. Geotextiles and Geomembranes 27, 31e38. Zhang, L., Zhao, M., Shi, C., Zhao, H., 2010. Bearing capacity of geocell reinforcement in embankment engineering. Geotextiles and Geomembranes 28, 475e482.
Notations Basic SI units are given in parentheses Ac: corrected cross-sectional area (m2) Cc: coefficient of curvature (dimensionless) Cu: coefficient of uniformity (dimensionless) c: cohesion intercept (N/m2) cr: apparent cohesion (N/m2) D: diameter of sample at εa (m) Dr: relative density (%) D0: initial diameter of sample (m) d: diameter of circular cell (m) de: equivalent diameter of cell (m) d10: effective grain size (m) d50: median grain size (m) Gs: specific gravity (dimensionless) Jc: compression modulus (N/m) Js: secant modulus (N/m) Kp: Rankine’s coefficient of passive earth pressure (dimensionless) L: length of sample at εa (m) L0: initial length of sample (m) Pj: junction peel strength (kN/m) p0 : mean normal stress (kN/m) Sj: junction shear strength (kN/m) T: tensile strength of geocell material (kPa) t: thickness of geotextile (m) Uj: junction split strength (kN/m) εa: axial strain (%) εc: circumferential strain (%) εv: volumetric strain (%) f: friction angle of soil ( ) gd,max: maximum dry unit weight (N/m3) gd,min: minimum dry unit weight (N/m3) mA: areal density of geotextile (kg/m2) r: density of soil (kg/m3) s: normal stress (N/m2) Ds: deviatoric stress (N/m2) sr: rubber correction or increment in axial stress (N/m2) s1: axial stress (N/m2) s3: confining pressure (kPa) Ds3: rubber correction or increment in confining pressure (kPa) s: shear stress (N/m2)
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Geotextiles and Geomembranes journal homepage: www.elsevier.com/locate/geotexmem
Confinement effect of geocells on sand samples under triaxial compression Rong-Her Chen*, Yu-Wen Huang, Feng-Chi Huang Department of Civil Engineering, National Taiwan University, No. 1, Sec. 4, Roosevelt Rd., Taipei 10617, Taiwan
a r t i c l e i n f o
a b s t r a c t
Article history: Received 17 September 2012 Received in revised form 8 January 2013 Accepted 24 January 2013 Available online 1 March 2013
The confinement effect of geocells improves vastly the shear strength of granular soil. To understand the mechanism better, several tests have been performed on geocell-reinforced-sand samples of two different sizes. The geocells were made of high-density polyethylene sheets, and the influencing factors examined include the shape (circular, rectangular, and hexagonal cross-sections), size and number of cells. The effects of these variables on the compression strength of samples as well as the stressestrain behavior were investigated. It has been found that the apparent cohesion of reinforced samples vary with the shape, size and number of cells, of which the cell size is the most significant factor. Among the cells of all shapes, the circular cells induce the highest apparent cohesion. In addition, the effectiveness of the reinforcement is more significant at low confining pressure. This can be explained by theoretical analysis, which shows that the reinforced samples under low confining pressures tend to expand more and induce higher circumferential strain. When under high confining pressure, the samples undergo lesser dilation leading to lower hoop forces in geocells. Ó 2013 Elsevier Ltd. All rights reserved.
Keywords: Geocells Compression test Compression strength Confining effect Apparent cohesion
1. Introduction Geocells are widely applied in geotechnical engineering, such as controlling erosion of slopes and river banks, enhancing bearing capacities of pavements and footings, reinforcing soft grounds and slopes, and protecting shores and channel beds. The cells are often made from high-density polyethylene or polyethylene strips ultrasonically welded together to give an open-cell structure for containing soil. Such confinement provided by geocells improves vastly shear strength of granular soil; and, in turn, the increase in soil strength provides improved bearing capacity and/or prevents soil erosion. The confinement of geocells has been studied mainly in the laboratory using triaxial compression test and uniaxial compression test. With regard to triaxial compression tests, Bathurst and Karpurapu (1993) reported the results of a series of largescale triaxial compression tests carried out on 200-mm-high isolated geocell soil composite samples and unreinforced soil samples. The soils tested were silica sand and limestone, with free drainage of water in the soil samples allowed. The results illustrated stiffening effect and increase in strength imparted to the soil by the enhanced confinement effect. Moreover, comparison of reinforced
* Corresponding author. Tel.: þ886 2 3366 4242; fax: þ886 2 23629851. E-mail addresses: [email protected] (R.-H. Chen), [email protected] (Y.-W. Huang), [email protected] (F.-C. Huang). 0266-1144/$ e see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.geotexmem.2013.01.004
and unreinforced soil samples showed that the peak friction angle of the soil infill and that of the composite were the same. Rajagopal et al. (1999) performed triaxial compression tests on granular soils encased in single and multiple geocell samples with 100-mm diameter. The geocells were fabricated by hand using different woven and nonwoven geotextiles and soft mesh to investigate the effect of stiffness of geocell on overall performance of the composite. It was observed that the soil developed cohesive strength resulting from the confinement by the geocell, and the magnitude of the cohesive strength varied with the properties of the geocell. They also presented a simple methodology for estimating the magnitude of the apparent cohesive strength. Shen (2005) performed triaxial compression tests to investigate the effect of relative density of soils on compression strength of two different aggregates reinforced with geocells. It was found both the peak friction angle and apparent cohesion of the reinforced soils increased with relative density. Latha and Murthy (2007) studied and compared the relative efficiency of three forms of reinforcements, namely, horizontal geosynthetic layers, randomly oriented discrete fibers, and geocells. Uniaxial compression tests have also been conducted on large samples. Bathurst and Crowe (1994) described two large-scale uniaxial compression tests (1 m wide 1 m long 1.44 m high) to examine the stability of multiple layers of geocells under vertical surcharge. The geocells were 200 mm high and had a cell diameter of 200 mm. The soils tested were sand and limestone. They reported that the sand column and the limestone aggregate column were respectively stable up to
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10 m and 13.5 m of equivalent heights of the structure. Wesseloo et al. (2009) discussed the results of uniaxial compression tests performed on single cells and geocell packs of different sizes, and the geocells were mainly square in shape. They found that the strength of the geocell composite structure was indirectly proportional to the size of individual cells and that the strength reduced with increasing number of cells in the structure. To evaluate the interaction between hoop stresses and passive earth resistance, Emersleben and Meyer (2009) carried out radial load tests on single and multiple geocell structures. Considerable interest has also been shown in studying geocellreinforced structures, such as shallow foundations (Dash et al., 2003; Sireesh et al., 2009; Pokharel et al., 2010; Moghaddas Tafreshi and Dawson, 2010, 2012), slopes (Chen and Chiu, 2008; Leshchinsky et al., 2009), pavements (Thakur, et al., 2012; Leshchinsky and Ling, 2013), and embankments (Zhang et al., 2010). Nonetheless, there were few studies reporting the fundamental understanding of these systems. To make up for such deficiency, this study performed tests on geocell-reinforced-sand samples under triaxial compression to examine the effect of variables on compression strength and deformation characteristics of the samples. It is hoped that the results from this study will improve the understanding of the confinement effect of geocells when applied to geotechnical engineering. Furthermore, the test results will be good for calibrating numerical analysis, which allows for extrapolation to realistic setup of geocells in the field.
Table 1 Strength and elastic modulus of model and prototype materials.
Tensile strength T (kN/m) Junction shear strength Sj (kN/m) Junction peel strength Pj (kN/m) Junction split strength Uj (kN/m) Secant modulus Js (kN/m) a
Model material
Prototype materiala
15.0 8.2 6.4 8.6 101
17.0 13.5 9.5 12.8 494
Shen (2005).
strength as well as the stressestrain behavior of reinforced-sand samples under triaxial compression. In the literature, geocells adopted for testing were most commonly of circular cross-section, probably because it is easier to fit cylindrical geocells into the chamber of the triaxial apparatus (Bathurst and Karpurapu, 1993; Rajagopal et al., 1999; Shen, 2005). Geocells of square cross-section have also been adopted but not common (Wesseloo et al., 2009). In practice, geocells used in the field tend to be of rhombic crosssection. Thus, it is of interest to compare the confinement effects of cells of different cross-sections. In this study, the geocells for testing were of three types, namely, cylindrical, hexagonal and rectangular columns. Moreover, in order to study multiple-cell effect, the samples were prepared to contain one cell, three cells, and seven cells. 3. Testing program and procedure
2. Materials used for testing The variables considered in the testing program are as follows. 2.1. Soil The sample soil used in the present investigation was uniform, sub-angular sand containing 99.8% silica. It is classified as poorlygraded sand (SP) as per the Unified Soil Classification system, with a coefficient of uniformity Cu ¼ 2.07 and a coefficient of curvature Cc ¼ 1.04. The physical properties of the sand are as follows: specific gravity Gs ¼ 2.66, median grain size d50 ¼ 0.25 mm, effective grain size d10 ¼ 0.15 mm, maximum dry unit weight gd,max ¼ 16.1 kN/m3, and minimum dry unit weight gd,min ¼ 13.3 kN/m3. 2.2. Geocell material The material used for fabricating geocells was high-density polyethylene sheet, for it is easy to obtain and process. The physical properties of the material are as follows: specific gravity Gs ¼ 0.967 (ASTM D 792, 2008), thickness t ¼ 0.38 mm (ASTM D 5199, 2012), and mass per unit area mA ¼ 118 g/m2 (ASTM D 5261, 2010). The strength tests performed on this geocell material include tensile strength test on the material and the tests for three failure modes of the junction of a geocell: junction shear failure, junction peel failure, and junction split failure (Cancelli et al., 1993). The tensile strength is 15 kN/m obtained from a wide-width sample, according to ASTM D 4595 (2011). The sample for junction strength tests had a width equal to the seam spacing and a length equal to the height of cell. Forces were applied at both ends of the sample until the junction failed. The results presented in Table 1 are junction shear strength Sj ¼ 8.2 kN/m, junction peel strength Pj ¼ 6.4 kN/m, and junction split strength Uj ¼ 8.6 kN/m. In Table 1, the results of another geocell material (Shen, 2005), which is also made of HDPE and commonly used in the field, are presented for comparison. It is noteworthy that the secant modulus (Js at 2% strain) of the model material is only about 20% of the prototype material, though their tensile strengths are not much different. As mentioned previously, this study aimed to investigate the effects of shape, size, and number of geocells on the compression
Sand with and without reinforcement Sample size e small sample (2.8 inches in diameter and 6inches high) and large sample (6 inches in diameter and 12inches high) Cell shape e the cross-sections of cells were circular, rectangle, and hAexagonal Cell size e cells of the same shape but different sizes Number of cells e different numbers of cells in same area The content of the testing program is shown in Table 2. For the 10 tests listed, the first letter of the samples, S, represents sand; the second letter denotes the shape of the cells; and the third letter denotes the number of cells in the sample. Samples marked with an asterisk are small samples of 2.8-inch diameter, while those without an asterisk are large samples of 6-inch diameter. The configurations of all samples are depicted in Fig. 1. A photo of hexagonal geocell columns is shown in Fig. 2. The samples for triaxial compression were prepared according to the procedures of ASTM D 4767 (2011). Specifically, all samples
Table 2 The testing program. Soil
Sample Diameter of sample Shape of cell Number of cell
Sand Sand Reinforced Reinforced Reinforced Reinforced Reinforced Reinforced Reinforced Reinforced
S* S SC1* SH1* SH3* SC1 SC3 SB3 SH3 SH7
sand sand sand sand sand sand sand sand
2.8 in. (7.1 cm) 6 in. (15.2 cm) 2.8 in. (7.1 cm) 2.8 in. (7.1 cm) 2.8 in. (7.1 cm) 6 in. (15.2 cm) 6 in. (15.2 cm) 6 in. (15.2 cm) 6 in. (15.2 cm) 6 in. (15.2 cm)
e e Circle Hexagon Hexagon Circle Circle Rectangle Hexagon Hexagon
e e 1 1 3 1 3 3 3 7
Note: 1. S ¼ sand, C ¼ circle, H ¼ hexagon, B ¼ rectangle (or block). 2. The small sample (2.8 inches in diameter) is indicated with *; otherwise the sample is a large sample (6 inches in diameter).
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37
were prepared under dry condition. Five layers of pre-weighted quantity of sand were placed in the sample mold with light tamping. Each layer of sand was 30 mm and 60 mm thick for small and large samples, respectively. This procedure produced uniform samples with a relative density of 55%. All samples were then saturated and consolidated to reach equilibrium in a drained state at the effective consolidation stress for which a strength determination is required. All tests were carried out at a compressive strain rate of 0.1% per minute. During the test, water was allowed to drain freely from the sample. This is because the soil infill with geocells in the field is often permeable and the test soil is also a pervious material. In addition, the effect of rubber membrane increases as the sample is compressed; therefore, the effect of the membrane should be corrected so that the compression strength of the sample can be obtained accurately. The correction of the effect of membrane, which is 1.58 mm thick, was made according to ASTM D 4767 (2011). Generally speaking, the correction will be of significance only when the effective stresses are small (Henkel and Gilbert, 1952). It also needs to note that a reinforced-sand sample is a composite material, in which the stress and strain may not be as uniform as in an unreinforced-sand sample. Before the effect is fully understood, the test results in the following were obtained on the assumption that the stress and strain in reinforced-sand samples are uniformly distributed. 4. Test results 4.1. Unreinforced sand
Fig. 1. Different configurations of the samples used in compression tests.
To examine the effect of sample size on compression strength of sand without reinforcement, a small sample (S*) and a large sample (S), shown in Fig. 1, were tested for comparison. The peak stresses of the two samples occurred at axial strains of about 6% (Fig. 3a). After that, the large sample displayed more obvious strain-softening behavior, especially under high confining pressure (200 kPa). As for volume change, the samples were compressed in the beginning and subsequently dilated as axial strain increased (Fig. 3b). The small sample tended to dilate more than the large sample; however, the dilation of both samples decreased when the samples were subjected to higher confining pressures. From MohreCoulomb failure envelopes, the friction angles of the small and large samples were 37 and 38 , respectively. The cohesion intercepts were both small and thus neglected. From this result, it can be concluded that sample size has insignificant effect on compression strength of unreinforced sand. 4.2. Reinforced sand (2.8-inch sample) For the small sample of reinforced sand, three tests were conducted: SC1*, SH1*, and SH3* (Fig. 1). The results of the first two samples, SC1* and SH1*, are employed to study the effect of cell shape; these two samples had equal area confined by each geocell. On the other hand, the effect of multiple cells are compared by examining the results of SH1* and SH3*.
Fig. 2. Photo of hexagonal geocell columns.
4.2.1. Effect of cell shape In Fig. 4, the results of reinforced samples, SC1* and SH1*, and unreinforced sample, S*, are compared. It can be seen from Fig. 4a that the curves of reinforced samples do not show the strainsoftening phenomenon as occurred in the unreinforced sample. The geocells changed the sand from brittle to ductile, and therefore the reinforced samples displayed better strength. Furthermore, the sample with circular cell, SC1*, had higher compression strength than that with hexagonal cell, SH1*. Correspondingly, the volumetric
38
R.-H. Chen et al. / Geotextiles and Geomembranes 37 (2013) 35e44
Deviatoric stress , Δσ (kPa)
1000
Confining pressure … S*
— S 50 kPa 50 kpa 100 kPa 100 kPa 200 kPa 200 kPa
800
600
400
200
0 0
4
8 12 Axial strain , εa (%)
16
20
(a)
(a)
Volumetric stress , εv (%)
5
3
Confining pressure … S*
— S 50 kPa 50 kpa 100 kPa 100 kPa 200 kPa 200 kPa
1
-1 0
4
8 12 Axial strain , εa (%)
16
(b)
20
(b) Fig. 3. Results of compression tests on 2.8-inch and 6-inch samples of sand. (a) Stress versus strain. (b) Volumetric strain versus axial strain.
strain of SC1* is greater than that of SH1* (Fig. 4b), because the circular shape expands more easily than the irregular hexagonal shape. The strength parameters of the three tests are tabulated in Table 3. As can be seen, S* has c ¼ 0 and f ¼ 37 ; SC1* has cr ¼ 79 kPa and f ¼ 38 ; SH1* has cr ¼ 35 kPa and f ¼ 38 . Obviously, reinforcement improved the cohesion but had little contribution to the friction angle of the reinforced samples. This finding is in line with previously reported results (e.g., Bathurst and Karpurapu, 1993). It can also be concluded that the improvement in cohesion is attributed to the induced tensile strain in the geocell, which is a function of cell shape as well. 4.2.2. Effect of cell size With regard to the effect of the size of cells, Fig. 5 shows photos of two samples after failure. The single-cell sample, SH1*, were significantly deformed, while its corners were less affected. On the other hand, the sample with three cells had shorter sides, and consequently the deformation was not as significant as that of SH1*. Comparing the stressestrain curves under different confining pressures shows that the curves of SH3* are higher than those of SH1* (Fig. 6a). Correspondingly, the curves of volumetric strain for SH3* should also be higher, irrespective of the confining pressure (Fig. 6b). Likewise, the strength parameters of SH3*, cr ¼ 44.2 kPa and f ¼ 39 , are also higher than those of SH1* (Table 3). It is concluded that apparent cohesion decreases with the size of cells; however, the friction angles were about the same.
Fig. 4. Results of compression tests on 2.8-inch samples comprising cells of different shapes. (a) Stress versus strain. (b) Volumetric strain versus axial strain.
Findings on small samples are summarized as follows. First, reinforced samples presented higher stiffness, or steeper stresse strain curve, than unreinforced samples; nevertheless, this difference became less significant with increasing confining pressure. Second, samples consisted of more small cells showed stiffer behavior than those consisted of large but fewer cells. Third, among the three samples (SC1*, SH1*, and SH3*), the cylindrical sample was the stiffest. 4.3. Reinforced sand (6-inch sample) For large samples of reinforced sand, five tests were conducted (see Fig. 1). The three samples used for comparing the effect of Table 3 Results of compression test. Sample
Diameter of sample D0 (cm)
Equivalent diameter de (cm)
Apparent cohesion cr (kPa)
Friction angle 4 ( )
Ratio crde (kN/m)
S* SC1* SH1* SH3* S SC1 SC3 SB3 SH3 SH7
7.1 7.1 7.1 7.1 15.2 15.2 15.2 15.2 15.2 15.2
7.1 6.0 6.0 3.15 15.2 15 7.0 7.0 7.0 4.62
0 79.0 35.0 44.2 0 33.7 59.4 31.0 23.7 34.5
37 38 38 39 38 37 36 36 38 38
e 4.74 2.10 1.39 e 5.06 4.16 2.17 1.66 1.59
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39
(a)
Fig. 5. Photos of 2.8-inch samples after test. (a) SH1*. (b) SH3*.
(b) shape are SC3, SH3, and SB3. In order to have equal basis for comparison, the cell of each shape had the same area, as marked by the shaded area in Fig. 7a. With regard to the effect of number of cells, SC1 versus SC3 and SH3 versus SH7 are compared, respectively. 4.3.1. Effect of cell shape Figs. 8a and b presents the stressestrain curves of three reinforced samples and one unreinforced sample under low and high confining pressures, respectively. The curves of the three reinforced samples under low confining pressure (Fig. 8a) were significantly higher than that of unreinforced sand. Among the reinforced samples, SC3 showed the highest strength, while the strength of SB3 was the lowest. Notably, a rapid increase in deviatoric stress was observed for SC3 when axial strain exceeded 10%. In contrast, the stressestrain curves of all samples under high confining pressure (Fig. 8b) were much closer, compared with those in Fig. 8a, suggesting that the effect of reinforcement was more significant under low confining pressure. The variations in volumetric strain for large samples were similar to those for small samples (e.g., Figs. 4b and 6b). Of the three reinforced samples, SC3 showed the highest trend of increase in volume, which is comparable to its highest compression strength. However, the variations in volumetric strain for rectangular-shaped cell, SB3, were found to be not as regular as those of SC3 and SH3, probably due to unsymmetrical geometry of blocks. The photos of the three samples after tests are displayed in Fig. 7b for clarifying this explanation. The strength parameters of SC3, SB3, and SH3 are tabulated in Table 3. Among them, SC3 has the highest apparent cohesion cr ¼ 59.4 kPa, while SH3 has the slightly highest friction angle, f ¼ 38 . These results are attributed to the cell shape as well as the junction between cells. As shown in Fig. 7a, the three circles were
Fig. 6. Results of compression tests on 2.8-inch samples comprising different number of hexagonal cells. (a) Stress versus strain. (b) Volumetric strain versus axial strain.
connected only at three points, while the hexagons and blocks were connected along the junctions between cells. As a result, the circles expanded more freely than the hexagons and blocks and mostly along their outer boundaries. As seen in the photos shown in Fig. 7b, the circles became somewhat irregular, but the hexagons still maintained their original shapes. Notably, the rectangles shows quite irregular deformation with their edges deformed much more than their inner junctions. This demonstrates that adjacent cells restrained one another from expansion, consequently resulting in reduced development of tensile strain as well as tensile strength in the cells. 4.3.2. Effect of cell size The effect of cell size is examined by comparing SH3 and SH7 (see Fig. 1). As shown in Fig. 9, the stressestrain curves of SH7 are higher than those of SH3 under all confining pressures, though the difference is not significant at confining pressure of 50 kPa. Correspondingly, the curves of volumetric strain for SH7 are also higher than those of SH3 (Fig. 9b). In summary, using greater number of smaller cells to confine soil will induce higher compression strength as well as greater volumetric strain in the reinforced soil samples. The other comparison is obtained from circular cells, i.e., SC1 versus SC3. Similar observation as that for hexagonal geocells (SH3 versus SH7) was observed, and hence no further discussion will be made. The strength parameters of SC1, SC3, SH3, and SH7 are summarized in Table 3. As can be seen, the friction angles for cells of the same shape show little variations, but the apparent cohesion is
40
R.-H. Chen et al. / Geotextiles and Geomembranes 37 (2013) 35e44
Fig. 7. Comparison of three 6-inch samples reinforced with cells of different shapes. (a) Different configurations. (b) Photos of samples after tests (s3 ¼ 200 kPa).
much higher for samples with small cells, e.g., 59.4 kPa of SC3 greater than 33.7 kPa of SC1.
5. Discussion The effects of shape, size, and number of cells are discussed in this section. In addition, improvement in the elastic modulus and compression strength of reinforced sand due to confinement of cell is presented.
5.1. Effect of cell shape As summarized in Table 3, the friction angles of unreinforced samples, S and S*, are 37e38 , while those of reinforced samples are 36e39 , revealing insignificant effect of geocell on friction angle of test sand. It is worthy to note that hexagonal cells induced slightly higher friction angle than cells of the other two shapes. On the other hand, the increase in apparent cohesion due to reinforcement of cells of all shapes is obvious. This can be explained by examining the photos of samples after failure. For the unreinforced sample (Fig. 10a), a clear failure plane can be determined as several inclined stretches were seen on the rubber membrane. For the reinforced sample (Fig. 10b), it did not fail when the test terminated at an axial strain of 15%. As a result, the rubber membrane of this sample showed only horizontal wrinkles. Evidently, the confining effect provided by the cells mobilized the confining strength to prevent the soil from failure. As for the contribution to the compression strength of the reinforced sand, cells of circular shapes demonstrated the best effect among those of all shapes.
5.2. Effect of cell size The relationship between apparent cohesion and the equivalent diameter of a single cell, de, is shown in Fig. 11. The equivalent diameter originates from the concept of the circumference per unit area under confinement. For example, if a circular cell has a diameter d, then its circumference is pd and the confined area is pd2/4. Hence, the circumference per unit area is 4/d. For cells other than the circular ones, their areas are assumed equivalent to the areas of circles, so their equivalent diameters can be obtained in this way. Note that this relationship is considered only for a single cell. To compare the difference in mobilization of apparent cohesion among various shapes, the relationships between apparent cohesion and the inverse of equivalent diameter are plotted in Fig. 11: a. Circular cells (for SC1 and SC1*)
cr ¼ 4:97=de R2 ¼ 0:997
(1)
b. Hexagonal cells (for SH3 and SH3*)
cr ¼ 2:92=ðde Þ0:78 R2 ¼ 0:999
(2)
where cr ¼ apparent cohesion (kPa), de ¼ equivalent diameter of a single cell (m). The relationships show linear relation for circular cells and somewhat nonlinear relation for hexagonal cells; thus, the
R.-H. Chen et al. / Geotextiles and Geomembranes 37 (2013) 35e44
(a)
(a)
(b)
(b) Fig. 8. Results of compression tests on 6-inch samples reinforced with three cells of different shapes. (a) s3 ¼ 50 kPa. (b) s3 ¼ 200 kPa.
apparent cohesion is approximately proportional to the inverse of the cell diameter, and small cells induce higher apparent cohesion. Note that the curves are assumed to pass through the origin because a very large cell will induce very small apparent cohesion. In addition to that, the slope of Eq. (1) is more than that of Eq. (2), also demonstrating greater effectiveness in using smooth cells of circular shape.
41
Fig. 9. Results of compression tests on 6-inch samples with different number of hexagonal cells. (a) Stress versus strain. (b) Volumetric strain versus axial strain.
versa. Therefore, for cells of circular shape, the multiple-cell effect between one cell and three cells is estimated to be 0.82 (¼4.16/ 5.06). As for samples having more than three cells, comparison is made between SH3 and SH7, and the result is 0.96 (¼1.59/1.66). From this observation, according to the results of the compression tests conducted in drained condition, multiple-cell effect seems to be significant only for samples comprising less than three cells. Although this result is consistent with the observations made by Rajagopal et al. (1999), further research is still needed.
5.3. Multiple-cell effect It is of interest also to know the difference in apparent cohesion mobilized by a single cell and multiple cells. As seen in Fig. 11, the deviation of SC3 from the line through SC1 and SC1* is the effect of multiple cells; the same effect is seen between SH1* and the curve through SH3* and SH3. This topic is important because multiple cells are more constrained than a single cell, and the effect may be so significant as to affect the strength parameters of reinforced soil. Nevertheless, due to limitation of the apparatus, it is almost impossible to conduct tests on samples with many cells. Despite the difficulty, the following prediction is made according to the test results in this study. In order to eliminate the effect of cell size for direct comparison of the data, each data in Fig. 11 is expressed as a ratio of the ordinate to the x-coordinate, i.e., cr/(1/de) or crde, as displayed in the last column in Table 3. By doing so, theoretically, the ratio of 5.06 obtained from the single-cell sample (SC1) can be compared with the ratio of 4.16 obtained from the three-cell sample (SC3), and vice
5.4. Improvement in compression strength The effectiveness of reinforcement can be represented by a deviatoric stress ratio, SR, which is defined as
SR ¼ ðDsr Þmax =ðDsÞmax
(3)
where (Dsr)max and (Ds)max are the maximum deviatoric stresses of reinforced and unreinforced samples, respectively. As shown in Fig. 12, the values of SR at confining pressure of 50 kPa are in the range of 1.5e2.5. However, the ratio decreases as confining pressure increases, e.g., the ratios at confining pressure of 200 kPa are in the range of 1.0e1.5. This result indicates good improvement in the compression strength of unreinforced soil under low confining pressure. The other findings from Fig. 12 concern the size of sample and the number of cells. With regard to the size of sample, smaller samples have higher deviatoric stress ratios, e.g., SC1* versus SC1
42
R.-H. Chen et al. / Geotextiles and Geomembranes 37 (2013) 35e44 3 SC1* SH1* SH3* SC1 SC3 SH3 SH7 SB3
2.5
SR
2
1.5
1
0.5 0
150
200
250
Fig. 12. Relationship between deviatoric stress ratio and confining pressure.
Ds3 ¼
2Js εc D ð1 εa Þ
(5)
where Ds3 ¼ the rubber correction in this case (kPa), Js ¼ secant modulus of the membrane at εa (kN/m), D ¼ diameter of the sample at εa (m), εa ¼ axial strain (%), and εc ¼ circumferential strain (%). Again, Ds3 is in functions of the reciprocal of the diameter of sample, the modulus of membrane, and the deformed shape of the sample, εc/(1 εa).
6. Theoretical analysis In studying the effect of rubber membranes on the measured compression strength of saturated clay sample in undrained condition, Henkel and Gilbert (1952) introduced two theories, compression shell theory and hoop tension theory, to correct the compression strength of the sample. In the compression shell theory, only the axial strain of the sample is taken into consideration; while in the hoop tension theory, it considers both the axial strain and radial strain of the sample. The equations of the two theories are as follows:
100
Confining pressure , σ (kPa)
Fig. 10. Photos of reinforced and unreinforced samples after tests (s3 ¼ 200 kPa). (a) Unreinforced sample, S. (b) Reinforced sample, SH7.
(also for SH3* versus SH3). Regarding the number of cells, greater amount of smaller cells develops higher stress ratio, such as SH3* versus SH1* (also for SC3 versus SC1 and SH7 versus SH3).
50
In studying the behavior of reinforced granular soils, Bathurst and Karpurapu (1993) and Rajagopal et al. (1999) used the hoop tension theory to predict the apparent cohesion for samples under drained and undrained conditions, respectively.
a. Compression shell theory 6.1. Derivation of circumferential strain
sr ¼
pD0 Jc εa
(4)
Ac
where sr ¼ the rubber correction (kPa), Jc ¼ compression modulus of the rubber membrane (kN/m), D0 ¼ initial diameter of the sample (m), εa ¼ axial strain (%), and Ac ¼ corrected area of the sample at strain εa (m2). Note that the ratio, pD0/Ac, in Eq. (4) is similar to the circumference per unit confined area mentioned previously. b. Hoop tension theory
Apparent cohesion , cr (kPa)
100
In order to employ Eq. (5) for the drained tests conducted in this study, the circumferential strain of the sample need to be derived. Assuming a sample has an initial volume of V0, and it subsequently decreases to V, as a result of the consolidation of soil and water drainage. Therefore,
V ¼ 1 εv V0
(6)
Herein, the volumetric strain, εv, is assumed positive for compression and negative for extension. By substituting the diameter and the length of the sample into above equation, it can be written as
p
80
4
p
60
4 SC1* SC1 SC3 SH1* SH3* SH3 SH7
40
20
20
40
60
1/Equivalent cell diameter , 1/de
80
D20 L0
¼ 1 εv
(7)
Rearranging this equation leads to the following:
D ¼ D0
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð1 εv ÞL0 L
(8)
Now, using axial strain εa, the equation is changed as below
0 0
D2 L
100
(m-1 )
Fig. 11. Relationship between apparent cohesion and equivalent diameter of cell.
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u ð1 ε Þ ð1 εv Þ u v D ¼ D0 u ¼ D0 tðL0 DLÞ ð1 εa Þ L0
(9)
R.-H. Chen et al. / Geotextiles and Geomembranes 37 (2013) 35e44
The circumferential strain, εc, which is the change in length per unit circumferential length, can be expressed as
pD pD0 D D0 ¼ pD0 D0
(10)
By substituting the diameter, D, from Eq. (9) into the above equation, it then becomes
εc ¼
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð1 εv Þ D0 D0 ð1 εa Þ D0
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð1 εv Þ ¼ 1 ð1 εa Þ
800
400
200
(11) 0
Accordingly, the circumferential strain can be substituted into Eq. (5) to calculate the induced confining stress in the reinforcement, with the secant modulus of membrane, Js, in Eq. (12) replaced by that of the geocell material.
2Js D
ð1 εa Þ
0
400
800
(a) 800
(12)
6.2. Interpretation In the following, the compression strengths of reinforced samples are obtained according to Eqs. (4) and (5), respectively. Note that it was not possible to measure the compression modulus of rubber membrane; and hence, the compression modulus was assumed to be the same as the secant modulus of the membrane (Henkel and Gilbert, 1952).
test 50 kPa test 200 kPa shell 50 kPa shell 200 kPa
600
400
200
0 0
400
800
(b)
(14)
where s1 is the compression strength of unreinforced soil sample, and Kp is Rankine’s coefficient of passive earth pressure. The comparison between Mohr circles from test results and theoretical prediction are plotted in Fig. 13. The correction for membrane effect, according to ASTM D 4767 (2011), has already been subtracted from the compression strength before the appropriate Mohr circle is drawn. In the figure, the test results are denoted by hollow symbols, while solid symbols represent the prediction. As can be seen from Fig. 13a, the prediction by the hoop tension theory matches well the test results under low confining pressure of 50 kPa. On the other hand, Fig. 13b shows the prediction by the compression shell theory is in good agreement with the test results under high confining pressure of 200 kPa. In an alternative way, the maximum mean normal stresses at various confining pressures are compared in Fig. 14. This figure shows the transition of the failure states with increasing confining pressure. It is clearly seen the test result agrees well with the prediction by the hoop tension theory when confining pressure is lower than 50 kPa. This behavior is attributed to the high tendency for the reinforcement under low confining pressure to expand laterally under axial compression. When the confining pressure exceeds 100 kPa, the
Fig. 13. Comparison between Mohr’s circles from test results and two theories (sample SH3*). (a) Hoop tension theory. (b) Compression shell theory.
prediction by the shell compression theory shows better agreement, meaning that the sample under high confining pressure behaves like a compressed column with small volume expansions. This is because at high confining pressure the dilation of soils is lesser. As shown in Fig. 10b, several horizontal wrinkles appear on the surface of the rubber membrane, which were mainly resulted from axial compression of the sample.
600
Mean normal stress, p' (kPa)
(13)
b. Hoop tension theory
s1;hoop ¼ Kp ðs3 þ Ds3 Þ
12 0 0
Normal stress , σ (kPa)
a. Compression shell theory
s1;shell ¼ s1 þ sr
1200
Normal stress, σ (kPa)
Shear stress , τ (kPa)
Ds3 ¼
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ! ð1 εv Þ 1 ð1 εa Þ
test 50 kPa test 200 kPa hoop 50 kPa hoop 200 kPa
600
Shear stress, τ (kPa)
εc ¼
43
400
200 SH3* (Test) SH3* (Shell) SH3* (Hoop)
0 0
50
100
150
200
250
Confining pressure, σ3 (kPa)
Fig. 14. Comparison between mean normal stresses obtained from test results and two theories.
44
R.-H. Chen et al. / Geotextiles and Geomembranes 37 (2013) 35e44
7. Conclusions This study has employed tests on geocell-reinforced sand subjected to triaxial compression to examine the confinement effect of geocells. It was found that the confinement effect provided by geocells related mainly to the mobilization of the tensile strength in the geocells, which varies with the volumetric strain induced. The induced volumetric strain is affected by the size and shape of the cell, confining pressure, as well as multiple-cell effect. The findings are summarized as follows. The apparent cohesion of reinforced samples varies mainly with the size, shape, and number of cells, of which cell size is the most significant factor. Approximately linear relationships were found between the apparent cohesion and the inverse of the equivalent diameter of the cell. Moreover, circular cells induced the highest apparent cohesion among cells of all shapes, while the apparent cohesion induced by hexagonal cell was the lowest. The difference in friction angle between the reinforced and unreinforced-sand samples was insignificant. For cells of various shapes, hexagonal ones showed slightly higher friction angle, owing to many corners of hexagons. The constraint by adjacent cells prevents the cells from expanding laterally, and consequently the mobilization of the tensile strength of geocells is restrained in multi-cell configurations. This effect may be significant and should be considered when using the data from tests on a single cell. With increase in confining pressure on the reinforced soil, the reinforcing effect becomes less significant, meaning that the reinforcement is more effective under low confining pressure. Comparison between theoretical and test results show that the behavior of reinforced soil under low confining pressure can be predicted by the hoop tension theory. The behavior of reinforced soil samples under high confining pressure is more similar to a stiff column under axial compression. Acknowledgments This work was supported by the National Science Council of Taiwan (99-2221-E-002-121). We would also like to thank the three anonymous reviewers for their valuable and constructive suggestions. References ASTM D 792, 2008. Standard test methods for density and specific gravity (relative density) of plastics by displacement. American Society for Testing and Materials, West Conshohocken, Pennsylvania, USA. 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. ASTM D 4767, 2011. Standard test method for consolidated undrained triaxial compression test for cohesive soils. American Society for Testing and Materials, West Conshohocken, Pennsylvania, USA. ASTM D 5199, 2012. Standard test method for measuring the nominal thickness of geosynthetics. American Society for Testing and Materials, West Conshohocken, Pennsylvania, USA. ASTM D 5261, 2010. Standard test method for measuring mass per unit area of geotextiles. American Society for Testing and Materials, West Conshohocken, Pennsylvania, USA. 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. Cancelli, A., Rimoldi, P., Montanelli, F., 1993. Index and performance tests for geocells in different applications. In: Cheng, S.C.J. (Ed.), Geosynthetic Soil Testing Procedures, ASTM STP 1190, pp. 64e75. Chen, R.H., Chiu, Y.M., 2008. Model tests of geocell retaining structures. Geotextiles and Geomembranes 26, 56e70.
Dash, S.K., Sireesh, S., Sitharam, T.G., 2003. Model studies on circular footing supported on geocell reinforced sand underlain by soft clay. Geotextiles and Geomembranes 21, 197e219. Emersleben, A., Meyer, N., 2009. Interaction between hoop stresses and passive earth resistance in single and multiple geocell structures. In: GIGSA GeoAfrica 2009 Conference, Cape Town, September 2e5. Henkel, D.J., Gilbert, G.C., 1952. The effect of rubber membranes on the measured triaxial compression strength of clay samples. Géotechnique 3, 20e29. Leshchinsky, B., Ling, H.I., 2013. Numerical modeling of behavior of railway ballasted structure with geocell confinement. Geotextiles and Geomembranes 36, 33e43. Leshchinsky, D., Ling, H.I., Wang, J.-P., Rosen, A., Mohri, Y., 2009. Equivalent seismic coefficient in geocell retention systems. Geotextiles and Geomembranes 27, 9e18. Latha, G., Murthy, V.S., 2007. Effects of reinforcement form on the behavior of geosynthetic reinforced sand. Geotextiles and Geomembranes 25, 23e32. Moghaddas Tafreshi, S.N., Dawson, A.R., 2010. Comparison of bearing capacity of a strip footing on sand with geocell and with planar forms of geotextile reinforcement. Geotextiles and Geomembranes 28, 72e84. Moghaddas Tafreshi, S.N., Dawson, A.R., 2012. A comparison of static and cyclic loading responses of foundations on geocell-reinforced sand. Geotextiles and Geomembranes 32, 55e68. Pokharel, S.K., Han, J., Leshchinsky, D., Parsons, R.L., Halahmi, I., 2010. Investigation of factors influencing behavior of single geocell-reinforced bases under static loading. Geotextiles and Geomembranes 28, 570e578. Rajagopal, K., Krishnaswamy, N.R., Latha, G., 1999. Behavior of sand confined with single and multiple geocells. Geotextiles and Geomembranes 17, 171e184. Shen, C.W., 2005. The mechanical characteristics of geocell-reinforced earth. Master Thesis. Department of Civil Engineering, National Taiwan University (in Chinese). Sireesh, S., Sitharam, T.G., Dash, S.K., 2009. Bearing capacity of circular footing on geocell-sand mattress overlying clay bed with void. Geotextiles and Geomembranes 27, 89e98. Thakur, J.K., Han, J., Pokharel, S.K., Parsons, R.L., 2012. Performance of geocellreinforced recycled asphalt pavement (RAP) bases over weak subgrade under cyclic plate loading. Geotextiles and Geomembranes 35, 14e24. Wesseloo, J., Visser, A.T., Rust, E., 2009. The stressestrain behavior of multiple cell geocell packs. Geotextiles and Geomembranes 27, 31e38. Zhang, L., Zhao, M., Shi, C., Zhao, H., 2010. Bearing capacity of geocell reinforcement in embankment engineering. Geotextiles and Geomembranes 28, 475e482.
Notations Basic SI units are given in parentheses Ac: corrected cross-sectional area (m2) Cc: coefficient of curvature (dimensionless) Cu: coefficient of uniformity (dimensionless) c: cohesion intercept (N/m2) cr: apparent cohesion (N/m2) D: diameter of sample at εa (m) Dr: relative density (%) D0: initial diameter of sample (m) d: diameter of circular cell (m) de: equivalent diameter of cell (m) d10: effective grain size (m) d50: median grain size (m) Gs: specific gravity (dimensionless) Jc: compression modulus (N/m) Js: secant modulus (N/m) Kp: Rankine’s coefficient of passive earth pressure (dimensionless) L: length of sample at εa (m) L0: initial length of sample (m) Pj: junction peel strength (kN/m) p0 : mean normal stress (kN/m) Sj: junction shear strength (kN/m) T: tensile strength of geocell material (kPa) t: thickness of geotextile (m) Uj: junction split strength (kN/m) εa: axial strain (%) εc: circumferential strain (%) εv: volumetric strain (%) f: friction angle of soil ( ) gd,max: maximum dry unit weight (N/m3) gd,min: minimum dry unit weight (N/m3) mA: areal density of geotextile (kg/m2) r: density of soil (kg/m3) s: normal stress (N/m2) Ds: deviatoric stress (N/m2) sr: rubber correction or increment in axial stress (N/m2) s1: axial stress (N/m2) s3: confining pressure (kPa) Ds3: rubber correction or increment in confining pressure (kPa) s: shear stress (N/m2)