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Compositional effects on the dynamic properties of municipal solid waste
Waste Management 31 (2011) 2380–2390
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Waste Management journal homepage: www.elsevier.com/locate/wasman
Compositional effects on the dynamic properties of municipal solid waste Pengbo Yuan a, Edward Kavazanjian Jr. b,⇑, Wenwu Chen a, Bongseong Seo c a
Key Laboratory of Mechanics on Disaster and Environment in Western in China, The Ministry of Education of China, Lanzhou 730000, China Arizona State University, Tempe, AZ 85287-5306, USA c Independent Consultant, Tempe, AZ 85282, USA b
a r t i c l e
i n f o
Article history: Received 27 February 2011 Accepted 5 July 2011 Available online 9 August 2011 Keywords: Solid waste Dynamic properties Modulus Damping Cyclic loading Seismic
a b s t r a c t Large-scale cyclic simple shear tests were conducted on reconstituted specimens of municipal solid waste (MSW) collected from the Tri-Cities landfill in Fremont, California, USA. The influence of waste composition and compacted unit weight on the shear wave velocity, small-strain shear modulus, and straindependent shear modulus reduction and damping ratio curves of MSW was investigated in these tests. Modulus reduction and damping ratio curves were evaluated over a strain range of 0.01–3%. Specimens were reconstituted using 100%, 65%, and 35%, by weight, of the material that passed through a 20 mm screen and four different levels of compaction effort. All specimens were consolidated under a normal stress of 75 kPa prior to testing. The test results show a very strong dependence of shear wave velocity and small strain shear modulus on unit weight. Unit weight also had an influence on modulus reduction and damping ratio. Waste composition had a very strong influence on damping and also influenced shear wave velocity, small strain shear modulus, and modulus reduction. The interrelationship between unit weight and waste composition made it difficult to separate out the effects of these parameters. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction The dynamic properties of municipal solid waste (MSW) for use in seismic analysis of landfills, including the small strain shear stiffness and equivalent linear modulus reduction and damping relationships, has been the subject of significant attention over the past 15 years. However, most studies of MSW dynamic properties treat waste as a singular material with one set of dynamic properties independent of waste composition or unit weight. This paper presents the results of 15 large-scale cyclic simple shear tests in which waste composition and compaction effort was systematically varied to investigate the influence of composition and compaction effort on the dynamic properties of MSW. The tests were conducted on reconstituted specimens of MSW retrieved from the Tri-Cities landfill in Fremont, California (USA).
2. Background The key material properties in state-of-the-practice equivalent linear seismic analyses of landfills are the small strain shear modulus, Gmax, the strain-dependent equivalent shear modulus G, and the strain dependent equivalent linear damping, c. The strain ⇑ Corresponding author. Address: School of Sustainable Engineering and the Built Environment, Arizona State University, Tempe, AZ 85287-4306, USA. Tel.: +1 480 727 8566; fax: +1 480 965 0557. E-mail address: [email protected] (E. Kavazanjian). 0956-053X/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.wasman.2011.07.009
dependent equivalent linear shear modulus is usually described in terms of Gmax and a modulus reduction curve that relates the ratio G/Gmax to a representative shear strain, cr (equal to the maximum shear strain in a uniform cyclic test). The equivalent linear damping is usually described in terms of the fraction of critical damping k, equal to c/ccrit, where ccrit, the critical damping, is the lowest damping at which the system returns to equilibrium without overshooting the equilibrium position after being perturbed. The fraction of critical damping is also related to the representative shear strain cr based upon the hysteretic damping from a uniform cyclic test with strain amplitude cr. The small strain shear modulus, Gmax, is usually evaluated based upon the shear wave velocity, VS, and the mass density of the soil, q, using the following relationship from classical elasticity theory:
Gmax ¼ qV 2s
ð1Þ
where q = mass density of the material (equal to the total unit weight of the material divided by the acceleration of gravity). Available data on the dynamic properties of MSW is limited. Kavazanjian et al. (1996) have presented VS versus depth profiles for six southern California MSW landfills from Spectral Analysis of Surface Wave (SASW) testing. Matasovic and Kavazanjian (1998) have presented the results of SASW-derived VS profiles from 24 locations at one landfill composed predominantly of MSW, the Operating Industries, Inc. (OII) landfill in southern California. Equivalent linear modulus reduction and damping relationships for MSW have been recommended by various researchers
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(Singh and Murphy, 1990; Idriss et al., 1995; Kavazanjian et al., 1995; Augello et al., 1998; Matasovic and Kavazanjian, 1998; Morochnik et al., 1998; Elgamal et al., 2004; Towhata et al., 2004; Thusyanthan et al., 2006; Zekkos et al., 2008; Choudhury and Savoikar, 2009). However, several of these proposed relationships are based solely on the authors’ intuition (e.g. Singh and Murphy, 1990) or upon mathematical fits to curves proposed by previous investigators (e.g. Choudhury and Savoikar, 2009). Most of the other recommendations (i.e. Idriss et al., 1995; Augello et al., 1998; Morochnik et al., 1998; Matasovic and Kavazanjian, 1998; Elgamal et al., 2004) are based upon the observed seismic response of the OII landfill, the only landfill at which strong ground motions have been recorded upon the waste mass. Only Towhata et al. (2004) and Zekkos et al. (2008) have developed data-based modulus reduction and damping curves independent of the OII-derived curves. Idriss et al. (1995), Augello et al. (1998), Morochnik et al. (1998), and Elgamal et al. (2004) have back-calculated modulus reduction and damping curves solely from the seismic response of the OII landfill based on the recorded ground motions in a series of small nearby and larger more distant earthquakes events. There is general agreement among these investigators that the curves derived from the observed response of the OII landfill are limited to cyclic shear strains on the order of 0.1%, as this is approximately equal to the maximum strain level induced in the waste at OII by the recorded events. Matasovic and Kavazanjian (1998) supplemented back analysis of the field data with the results of large-scale (457-mm diameter) cyclic simple shear tests on reconstituted specimens of waste recovered from the OII landfill. This laboratory test data provided supplemental information for cyclic shear strains between 0.1% and 7%. Most of the OII investigators presented either singular modulus reduction and damping curves for MSW based upon their analyses (e.g. Idriss et al., 1995) or a range of values within which the OII properties may lie (e.g. Elgamal et al., 2004). However, Matasovic and Kavazanjian (1998) presented a range of possible values for the modulus reduction and damping curves along with a set of singular recommended curves. Towhata et al. (2004) performed cyclic triaxial tests and shaking table tests on a biologically treated ‘‘equivalent organic waste’’ material imported from Germany. These investigators present modulus reduction curves for Young’s modulus from cyclic triaxial tests on the organic waste with and without plastic sheets added to the specimen for axial strains from approximately 0.02–0.4% and values for the damping ratio at an axial strain of approximately 0.15% for the organic waste without plastic and 0.25% for organic waste with plastic. They also present shear modulus and damping ratio values from shaking table tests for the organic waste with plastic at shear strains from 0.3% to 1%. However, no information is provided on the small strain shear modulus of the waste. Zekkos et al. (2008) performed a series of large-scale (300-mm diameter) uniform cyclic triaxial tests on reconstituted specimens of MSW from the Tri-Cities landfill (the same waste tested in the investigation reported herein). These investigators conducted a systematic study of the effect of compaction effort and waste composition on the shear wave velocity and the strain-dependent equivalent linear shear modulus reduction relationship (G/Gmax versus c) and damping ratio relationship (k versus c) for cyclic shear strains up to approximately 0.5%. Waste composition was varied by changing the relative proportions of material >20 mm and <20 mm in dimension screened from bulk samples of waste recovered from large diameter bucket auger borings. The material >20 mm in dimension was described as fibrous waste and the material <20 mm in dimension was referred to as soil-sized or soil-like waste. The maximum particle size in the screened waste was approximately 40 mm for bulky material and 80 mm for elongated particles. The waste was placed in the compaction mold such
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that the elongated particles has a preferential orientation in the horizontal plane and compaction effort was varied over a wide range between relatively light compaction and heavy compaction effort. All tests were conducted after isotropically consolidating the compacted specimens to 75 kPa. Three waste composition ratios were used in the Zekkos et al. (2008) study: 100% by weight <20 mm, 62% to 74% by weight <20 mm (the composition ratio of the material in the field was approximately 62% <20 mm), and 14% by weight <20 mm. Results of the Zekkos et al. (2008) study showed a strong correlation between composition ratio and compacted unit weight, with a higher percentage of <20 mm material resulting systematically in a higher compacted unit weight. Compaction effort also had a significant impact on compacted unit weight, with higher compaction effort resulting in higher compacted unit weight. Shear wave velocity (and small strain shear modulus) was also strongly correlated to compacted unit weight, with a higher compacted unit weight resulting in a systematically higher shear wave velocity (and small strain shear modulus). The influence of composition ratio on shear wave velocity (and small strain shear modulus) could not be discerned due the strong dependence of both composition ratio and shear wave velocity on compacted unit weight. However, composition ratio did have a systematic influence of modulus reduction and damping, with larger percentages of >20 mm (fibrous) material resulting in more elastic behavior, i.e. less modulus degradation and lower damping at the same shear strain compared to specimens with lower percentages of >20 mm material.
3. Testing program This paper presents the results of large-scale (304 406 mm rectangular specimen) uniform cyclic simple shear tests on reconstituted specimens of screened MSW recovered from the Tri-Cities landfill, the same waste tested by Zekkos et al. (2008). The effects of waste composition and compacted unit weight on shear wave velocity and the strain-dependent equivalent linear shear modulus reduction relationship (G/Gmax versus c) and damping ratio relationship (k versus c) were evaluated in these tests using essentially the same three waste composition ratios and similar levels of compaction effort (and therefore unit weight) as those employed by Zekkos et al. (2008). The tests reported herein were conducted using in the Arizona State University (ASU) Enamul and Mahmuda Hoque Geotechnical Laboratory. The testing program employed the same large scale cyclic simple shear device employed in the testing of the OII landfill waste described by Matasovic and Kavazanjian (1998), with some modifications to enhance its performance (as described subsequently). A vertical normal stress of 75 kPa was employed in all of the tests reported herein, equal to the isotropic confining pressure of 75 kPa used by Zekkos et al. (2008). The maximum size of the fibrous (>20 mm) material in the cyclic simple shear tests reported herein was approximately 100 mm, 25% larger than the maximum particle size employed by Zekkos et al. (2008) of 80 mm. As in the tests conducted by Zekkos et al. (2008), the waste in the simple shear tests reported here was placed such that the long axis of the large particles had a preferred horizontal orientation. The maximum cyclic shear strain in the ASU simple shear tests was on the order of 3%, compared to the 0.5% maximum value in the cyclic triaxial tests conducted by Zekkos et al. (2008). Another difference between the tests reported herein and the tests conducted by Zekkos et al. (2008) is the stress system induced by the testing equipment. Zekkos et al. (2008) employed cyclic triaxial testing. In a cyclic triaxial test the maximum cyclic shear stress is induced on a plane at 45 degrees to the horizontal, the normal stress on the 45 degree plane varies about the effective
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Table 1 Summary of waste sampled at the Tri-Cities landfill (after Zekkos, 2005).
Smaller than 20 mm Paper Soft plastics Wood Gravel Metals Stiff plastics Textiles Others
A-3
C-1
C-6
A-1
C-3
58.9 12.9 1.7 11.4 9.8 3.5 1.0 1.4 1.0
52.2 20.1 6.1 8.2 5.1 3.3 3.8 1.4 0.3
71.8 10.8 2.8 2.8 6.6 1.6 1.0 1.6 1.2
68.6 7.3 2.1 6.6 10.3 1.6 0.9 1.6 2.6
63.6 11.7 3.0 8.7 5.1 4.9 2.1 0.7 1.4
confining pressure (depending on the vertical normal stress), and there is no shear stress induced on vertical or horizontal planes in the specimen. In the simple shear tests reported herein, a shear stress is induced on the horizontal plane and the normal stress is constant on that plane. Direct shear tests conducted by Zekkos et al. (2010a) demonstrate that the shear strength of waste is greater when the failure plane cuts across the plane of preferred orientation of the large waste particles, as in the triaxial test, compared to tests where the maximum shear stress is aligned with the plane of preferred orientation of the large particles, as in the simple shear test. Thus, the difference in the stress state between the triaxial tests conducted by Zekkos et al. (2008) and the simple shear tests reported herein may be significant due to the reconstitution of the specimens using a preferred horizontal orientation for the large particles. Simple shear testing is generally regarded as providing a more accurate simulation of the stress state induced in the field by earthquake waves (i.e. by vertically propagating shear waves). Therefore, while some differences may be expected between the results of the triaxial tests reported by Zekkos et al. (2008) and the simple shear tests reported herein due to waste anisotropy, the behavior in simple shear may be expected to be more representative of behavior in an earthquake, all other factors being equal. 4. Material characterization and specimen preparation Detailed characterization of the MSW collected from the Tri-Cities landfill and details of the associated field investigation, including field borehole logs, SASW testing, and in situ unit weight tests, are provided by Zekkos (2005) and Zekkos et al. (2008). The composition of the waste recovered Tri-Cities landfill is summa-
rized in Table 1. The MSW tested at ASU came from the A-3 sample group and was composed, by weight, of approximately 62% soillike material smaller than 20 mm in dimension, 14% paper, 3% soft plastic, 11% wood, and 10% gravel larger than 20 mm in dimension. The field moisture content varied from slightly less than 8% to slightly greater than 25% (a value still well below the field capacity of the waste) by weight, measured using a temperature of 60 °C as recommended by Zekkos et al. (2010b) to minimize volatilization of organic compounds. In preparing the reconstituted specimens of Tri-Cities MSW for the ASU simple shear tests, a procedure as close as possible to the specimen preparation procedure employed by Zekkos et al. (2008) was used. The waste was first screened to separate the >20 mm material from the <20 mm material. The maximum size of the >20 mm particles was then reduced to a maximum dimension of approximately 100 mm by either removing oversized particles or reducing them in size. Specimens at ASU were then compacted using 100%, 65% and 35% <20 mm material, by weight. Prior to compacting the MSW, it was mixed thoroughly in a small mechanical mixer. The waste was then compacted in lifts into the stack of rectangular Teflon coated steel frames used to maintain the zero lateral strain condition during the simple shear test. Specimens were compacted in three layers placed such that the long axis of the large particles had a preferred horizontal orientation. Compaction was accomplished using a 13.6 kg hammer that was dropped repeatedly on a rectangular steel plate 114.3 mm 114.3 mm in dimension from a constant height to achieve a specific compaction effort. Compaction was applied at 12 spots in each layer, and a multiple of 12 blows was applied to each layer. The final height after compaction of the ASU specimens was approximately 152 mm, resulting in a cubical specimen with a length of 406 mm (in the direction in which the shear stress was applied), a width of 304 mm, and about a height of about 152 mm. Four different levels of compaction effort were employed for each composition ratio. Five specimens were prepared for each composition ratio, including two using the same compaction effort in order to investigate the reproducibility of the results. A summary of information on the reconstituted MSW specimens used in the cyclic simple shear testing program at ASU, including total unit weight after compression under a normal stress of 75 kPa, compaction moisture content, composition, and number of blows per layer, is presented in Table 2. The maximum dimension of the waste particles employed in the simple shear testing program of 100 mm was less than twice
Table 2 Summary of ASU cyclic simple shear test specimens.
a b
Specimen
Moisture content (%)
Total unit weight (kN/m3)a
Composition (% by weight) <20 mm
Paper
Soft plastic
Wood
Gravel
100% <20 mm-1 100% <20 mm-2 100% <20 mm-2a 100% <20 mm-3 100% <20 mm-4 65% <20 mm-1 65% <20 mm-2 65% <20 mm-2a 65% <20 mm-3 65% <20 mm-4 35% <20 mm-1 35% <20 mm-2 35% <20 mm-2a 35% <20 mm-3 35% <20 mm-4
14.8 16.6 16.3 15.9 16.4 19.1 22.4 23.1 23.4 21.6 22.1 22.9 23.0 22.8 23.9
14.1 13.2 12.9 12.5 11.9 10.8 10.2 10.1 9.1 8.9 7.5 7.1 7.0 6.5 6.1
100 100 100 100 100 65 65 65 65 65 35 35 35 35 35
0 0 0 0 0 15 15 15 15 15 45 45 45 45 45
0 1 3 3 6 0 1 3 3 6 0 1 3 3 6
0 0 0 0 0 7 7 7 7 7 5 5 5 5 5
0 0 0 0 0 10 10 10 10 10 10 10 10 10 10
Unit weight after compression under 75 kPa normal stress. Every specimen has three layers and compaction effort was applied at 12 spots in each layer.
Compaction style (blow/spot)b
Compaction energy (J/cm3)
6 3 3 1 0 6 3 3 1 0 6 3 3 1 0
0.54 0.27 0.27 0.09 0 0.54 0.27 0.27 0.09 0 0.54 0.27 0.27 0.09 0
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Fig. 1. ASU large-scale cyclic simple shear testing device.
the height of the specimen. However, since the long axis of the particles was oriented sub-parallel to the long axis of the specimen, and the large particles typically had an aspect ratio of greater than 3, the specimen height was always greater than 5 times the maximum vertical thickness of the particles. Furthermore, because the simple shear test simulates a vertically propagating shear wave under one-dimensional conditions, the ratio of 4 between the 406 mm length of the specimen and the maximum dimension of the large particles was considered acceptable.
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frames within which the specimen is compacted is mounted on the carriage. The tests were conducted as strain-controlled tests. The MSW specimens were subject to a normal stress of 75 kPa for approximately 24 h prior to testing. Six series of 3–5 symmetrical cycles of loading with a constant maximum displacement were applied to each specimen at progressively increasing maximum displacements in each series. The displacements employed in the testing program corresponded to cyclic shear strains from 0.01% (the lower limit at which good resolution could be achieved) to 3%. To monitor vertical and shear deformations, 5 large linear variable differential transformers (LVDTs) and one small LVDT were installed on the simple shear testing device. Three of the large LVDTs were employed to monitor horizontal displacement: one on the carriage, one at mid-height of the frame stack, and one at the top of the frame stack, as shown in Fig. 1. The bottom LVDT was used for servo-control of the carriage translation, the top LVDT was used to evaluate the fixity of the top of the specimen, and the middle LVDT was used to evaluate the uniformity of the shear strain induced in the specimen. For measurement and servo control at shear strains from 0.01% to 0.03%, a smaller, more sensitive LVDT was attached to the carriage. The other two LVDTs were mounted vertically at the center and edge of the top cap to measure vertical compression and any rocking or tilting of the top cap. Data acquisition and cyclic strain control were accomplished using a Universal Digital Signal Conditioning and Control Unit. A horizontal striker plate was placed at the base of the specimen and a 1 Hz geophone was placed at the top of the specimen to enable measurement of shear wave velocity. The striker plate was instrumented with a strain gage to record the initiation of the shear wave induced by gently tapping the plate horizontally. The plate was tapped twice, in opposing directions, and first arrival of the shear wave at the geophone was determined by superimposing the two wave forms and picking off the first reversal of polarity. More details about the ASU large-scale cyclic simple shear device may be found in Seo (2008). 6. Test results
5. Testing equipment and test program 6.1. Shear wave velocity and small-strain (maximum) shear modulus The large-scale cyclic simple shear device employed in the tests conducted at ASU is shown in Fig. 1. The specimens were sheared by fixing the top of the specimen against translation and applying a sinusoidal horizontal movement with a frequency of 0.1 Hz to a carriage on roller bearings. A stack of Teflon-coated rectangular
Fig. 2 presents a plot of the laboratory-measured VS versus the unit weight of the specimen after compression under 75 kPa vertical normal stress. Fig. 3 presents a plot of the corresponding values of Gmax (calculated from the shear wave velocity and unit weight in
Fig. 2. Shear wave velocity, VS, versus total unit weight for reconstituted Tri-Cities MSW.
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accordance with Eq. (1)) versus total unit weight. Figs. 2 and 3 show that both the shear wave velocity and the small-strain shear modulus of the MSW specimens are strongly correlated to unit weight. Approximately linear relationships can be developed for each composition ratio over the range of unit weights employed in the testing program. Significantly, the extrapolated linear trends for the three composition ratios employed in the testing program do not line up but instead show an en echelon behavior, as can be seen from Figs. 2 and 3. This en echelon behavior suggests a dependence of VS and Gmax on composition ratio, with a greater amount of >20 mm material resulting in a greater stiffness and higher shear wave velocity for the same total unit weight. However, given the strong dependence of unit weight upon compaction effort and composition ratio, it is unlikely that two specimens with significantly different composition would have the same in situ unit weight when subject to similar compaction effort. Figs. 2 and 3 also compare the shear wave velocity and small strain shear modulus derived from field measurements at the Tri-Cities landfill as reported by Zekkos et al. (2008) at a depth corresponding to an overburden stress of 75 kPa to the values from the laboratory testing program described herein. As the average waste composition in the field is approximately 62% by weight <20 mm, Fig. 2 indicates that the field values of VS (evaluated using spectral analysis of surface wave testing) are of the same order of
magnitude, but slightly greater than, the laboratory values. The discrepancy between the field and laboratory values is even more apparent in Fig. 3, where the Gmax values calculated using the field VS and unit weight values reported by Zekkos et al. (2008) are compared to the laboratory Gmax values. These discrepancies may be due to time under confinement effects, as Zekkos et al. (2008) reported that Gmax of reconstituted Tri-Cities landfill waste specimens subject to an applied confining stress for 1000 h increased by approximately 100% to 200% compared to the value measured after 1 h of confinement. 6.2. Shear modulus reduction Fig. 4 presents the normalized shear modulus reduction curves for the 15 cyclic simple shear tests performed on reconstituted waste from the Tri-Cities landfill for this study. The results shown in Fig. 4 indicate that the normalized shear modulus reduction curve shifts to right (i.e. become more elastic) with increasing percentage of material >20 mm. The effect of unit weight on the normalized shear modulus reduction is shown in Figs. 5–7 for composition ratios of 100% <20 mm, 65% <20 mm, and 35% <20 mm, respectively. These figures indicate that that the normalized shear modulus reduction curves become more elastic (shift to right) with decreasing unit
Fig. 3. Small-strain shear modulus, Gmax, versus total unit weight for reconstituted Tri-Cities MSW.
Fig. 4. Normalized shear modulus reduction curves for reconstituted Tri-Cities MSW.
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Fig. 5. Normalized shear modulus reduction curves for Tri-Cities MSW reconstituted using 100% <20 mm material.
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Fig. 7. Normalized shear modulus reduction curves for Tri-Cities MSW reconstituted using 35% <20 mm material.
The strain-dependent damping ratio of reconstituted Tri-Cities landfill MSW was also affected by both waste composition and unit weight (or compaction effort), as shown in Figs. 8–11. Fig. 8 presents the damping ratio data for all three composition ratios. Figs. 9–11 present the data for composition ratios of 100% <20 mm, 65% <20 mm, and 35% <20 mm, respectively. Fig. 8 shows a significant increase in damping ratio with an increase in the relative amount of <20 mm material. However, Figs. 9–11 show a decrease in damping with an increase in unit weight, indicating that the effect of composition on damping is even more significant than shown in Fig. 8 if the influence of composition on unit weight is separated out from the data. 7. Comparison with other test results
Fig. 6. Normalized shear modulus reduction curves for Tri-Cities MSW reconstituted using 65% <20 mm material.
weight (or decreasing of compaction energy). However, as increasing the amount of <20 mm material will increase unit weight for the same compaction effort (shifting the modulus reduction curves to the left), small variations in composition ratio in the field may to some extent be self compensating with respect to modulus reduction. The data in Figs. 4–7 suggest that both unit weight and composition can have a significant influence on the normalized shear modulus reduction curve for MSW. 6.3. Damping ratio In calculating the damping ratio from the hysteresis loops generated in the uniform cyclic tests, a strain-dependent correction factor was applied to the calculated damping ratio to compensate for the internal damping in the testing device. Uniform cyclic tests were conducted on ASTM 20-30 Ottawa sand the large scale testing device. The strain-dependent damping ratio for this sand was also calculated using the equations developed by Darendeli (2001). The difference in the strain-dependent damping ratio calculated using the two approaches was as applied as a correction factor to the large scale test results on MSW.
Figs. 12 and 13 compare the shear wave velocity and small strain shear modulus data for the tests reported herein to the results from Zekkos et al. (2008), denoted as UCB data, for reconstituted Tri-Cities MSW with composition ratios of 100% <20 mm, 62–76% <20 mm, and 8–25% <20 mm. These figures show that the ASU data is in good agreement with the UCB data. It should be pointed out that ASU used Eq. (1) to calculate the small strain shear modulus while UCB measured the small strain shear modulus directly using displacement transducers mounted on the triaxial test specimens and then back-calculated the shear wave velocity values. The data in Figs. 12 and 13 show a strong dependence of shear wave velocity and small strain shear modulus on unit weight, with increasing shear wave velocity and shear stiffness with increasing unit weight. A 25% increase in unit weight results in an approximately 50% increase in shear wave velocity. The trend lines for the ASU cyclic simple shear data in Figs. 2 and 3 also suggests a systematic impact of waste composition on shear wave velocity and small strain shear modulus, with increased amounts of >20 mm material (i.e. fibrous waste) resulting in increased stiffness and shear wave velocity. These results suggest that increases in the percent of daily cover soil and additional compaction effort may increase the stiffness of MSW. However, the dependence of small strain stiffness on composition ratio inferred from Fig. 3 suggests that an increase in the degree of degradation of MSW resulting in a decrease in the amount of large fibrous material could decrease the stiffness of MSW even if there was not a concurrent decrease in unit weight.
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Fig. 8. Damping ratio for reconstituted Tri-Cities MSW.
Fig. 9. Damping ratio for Tri-Cities MSW reconstituted using 100% <20 mm material.
Fig. 11. Damping ratio for Tri-Cities MSW reconstituted using 35% <20 mm material.
Fig. 10. Damping for Tri-Cities MSW reconstituted using 65% <20 mm material.
Fig. 12. Comparison of ASU and UCB shear wave velocity values for reconstituted Tri-Cities MSW.
Fig. 14 compares the modulus reduction data for the tests reported herein to the fitted curves from Zekkos et al. (2008) for reconstituted Tri-Cities MSW with composition ratios of 100%
<20 mm, 62–76% <20 mm, and 8–25% <20 mm. The ASU and Zekkos et al. (2008) results show excellent agreement. The normalized modulus reduction data indicates that increased amounts of the fi-
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brous >20 mm material results in less modulus degradation, i.e. more elastic behavior. Zekkos et al. (2008) attributed the reduction in modulus degradation with increasing >20 mm material to the fibrous nature of the larger than 20 mm fraction and the size of the fibers. The modulus degradation trend is counter to the initial stiffness trend with respect to waste composition, suggesting that at larger strains, e.g. during strong earthquake shaking, differences in initial stiffness due to waste composition may be countered by differences in modulus degradation. Fig. 15 compares the damping ratio data for the for large-diameter cyclic simple shear tests on reconstituted specimens of Tri-Cities MSW reported herein to fitted curves from Zekkos et al. (2008) for reconstituted Tri-Cities MSW with composition ratios of 100% <20 mm, 62–76% <20 mm, and 8–25% <20 mm. The damping ratio from the ASU cyclic simple shear tests is as much as 50% higher than the damping ratio recommended by UCB for the same (or similar) composition ratio. However, the damping ratio trends with respect to unit weight and composition data from the simple shear and triaxial tests are consistent. The impact of composition on damping appears to be particularly significant, with a decrease in strain-dependent damping ratio of
approximately 50% for the specimens with 35% <20 mm compared to the specimens with 100% <20 mm. amounts of >20 mm material. The effect of composition on damping is to some extent masked by the influence of density on damping, as the data shows decreasing damping ratio with increasing unit weight for a given composition ratio, but unit weight decreases (and thus damping increases) with increasing amounts of >20 mm material for the same compaction effort. Reasons for the difference between the damping ratios measured in the ASU and Zekkos et al. (2008) tests are not clear, but may in part be attributable to the difference between the triaxial and simple shear stress states. Simple shear loading in which the shear stress is applied parallel to the orientation of the fibrous particles may result in more slippage and relative displacement among the waste constituents than in a triaxial stress. However, some of the difference may also be due to issues associated with the strain dependent correction factor for machine damping applied to the simple shear testing results. Furthermore, Zekkos et al. (2008) appears to have employed the lower bound of the damping data from their cyclic triaxial tests as the recommended damping values. For instance, for a composition ratio of 100% <20 mm, a damping ratio as high as 7% at 0.01% strain and as high as 12% was reported by Zekkos et al. (2008). These damping values correspond approximately to the lower end of the range of damping values for the ASU tests on waste with 100% <20 mm material, suggesting that the discrepancy in damping values is not as great as indicted in Fig. 15. Fig. 16 compares the modulus reduction and damping curves from this testing program for the 65% <20 mm material (representative of field composition) to the curves for 62–76% <20 mm from Zekkos et al. (2008) for the same Tri-Cities waste and to the upper and lower bound curves from Matasovic and Kavazanjian (1998) for waste from the OII landfill (established, in part, using the same large scale simple shear testing equipment used herein). Matasovic and Kavazanjian (1998) identified the upper bound modulus and lower bound damping curves as their best-estimates of OII waste properties based upon internal consistency and comparison with values back calculated for cyclic shear strains up to 0.1% from strong motion records captured at the site. These curves again show good agreement for modulus reduction and damping but suggest that the damping ratios from the ASU simple shear tests reported herein may be systematically high at strains less than 0.1%.
Fig. 14. Comparison of ASU and UCB normalized shear modulus reduction values for reconstituted Tri-Cities MSW.
Fig. 15. Comparison of ASU and UCB strain-dependent damping ratio values for reconstituted Tri-Cities MSW.
Fig. 13. Comparison of ASU and UCB small strain shear modulus values for reconstituted Tri-Cities MSW.
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Fig. 16. Comparison of Tri-Cities data with OII upper and lower bound relationships from Matasovic and Kavazanjian (1998): (a) Modulus reduction; (b) Damping.
8. Waste shear strength The objective of this study was to evaluate compositional effects upon the modulus and damping of waste subject to cyclic loading. Neither compositional effects on the shear strength of waste subject to dynamic loading nor the dynamic shear strength of waste itself was a subject of this study. None of the tests reported herein were taken to a state that would constitute failure under cyclic, or dynamic, loading. The largest cyclic shear strain imposed upon the specimens tested herein was on the order of 3%. However, all test specimens were monotonically loaded to failure following cyclic loading. Fig. 17a shows the monotonic loading stress–strain curves for specimens with a waste composition ratio of 64% at three different initial unit weights subject to a vertical normal stress of 75 kPa. Fig. 17b shows the monotonic stress strain curves from six specimens reconstituted using the same compaction energy but at three different composition ratios. All tests were sheared at a strain rate of approximately 0.17% per minute. Evaluation of shear strength from cyclic simple shear tests is neither a simple nor a straightforward process due to uncertainty about the value of the horizontal normal stress, i.e. the normal stress on the vertical plane (Kavazanjian, 2001). The data in Fig. 17 do show qualitatively the influence of unit weight on waste shear strength. Waste shear strength as measured in simple shear loading clearly increases with increasing unit weight. However, the
Fig. 17. Results of monotonic shear tests after cyclic loading: (a) Tests with 65% by weight <20 mm; (b) Tests with compaction energy equal to 0.27 J/cm3.
influence of particle size on shear strength is not easily discerned from these figures due to the inter-dependence of particle size and initial unit weight. It is possible to obtain a lower bound value on the equivalent friction angle, /eq (the friction angle assuming zero cohesion, sometimes referred to as the secant friction angle) from simple shear tests by interpreting them as a direct shear test (Kavazanjian, 2001). If the simple shear test is interpreted as a direct shear test, /eq is given by Eq. (2) as:
/eq ¼ tan1 ðsf =rV Þ
ð2Þ
where sf is the shear strength at failure and rv is the vertical normal stress (75 kPa in this testing program). Shear strengths interpreted in this manner for the tests shown in Fig. 17 are presented in Tables 3 and 4. Tables 3 and 4 also presents the friction angle calculated
Table 3 Lower bound shear strength at 75 kPa normal stress from simple shear tests for waste with 65% by weight <20 mm. Composition ratio
Total Unit weight (kN/m3)
Equivalent friction angle /eq (degrees)
Friction angle for 15 kPa cohesion /15 (degrees)
65% <20 mm-3 65% <20 mm-2 65% <20 mm-1
9.1 10.2 10.8
34 41 44
25 34 38
P. Yuan et al. / Waste Management 31 (2011) 2380–2390 Table 4 Lower bound shear strength at 75 kPa normal stress from simple shear tests for waste compacted using 0.27 J/cm3 (average of two tests). Composition ratio
Total unit weight (kN/m3)
Equivalent friction angle /eq (degrees)
Friction angle for 15 kPa cohesion /15 (degrees)
35% <20 mm-2 65% <20 mm-2 100% <20 mm-2
7.1 10.2 13.2
38 41 47
30 34 41
using the direct shear test interpretation but assuming a cohesion of 15 kPa, denoted as /15. A cohesion of 15 kPa is the value recommended by Bray et al. (2009) for a normal stress dependent shear strength of municipal solid waste. Except for the tests with a unit weight of less than 10 kN/m3, the values for /15 reported in Table 3 are consistent with the value of 36° suggested by Bray et al. (2009) for an overburden stress of 1 atmosphere (98 kPa). 9. Limitations The large diameter cyclic simple shear laboratory tests reported in this study were conducted on reconstituted specimens of municipal solid waste from one landfill. Prior to reconstitution, the waste was separated into fractions >20 mm and <20 mm and the fraction >20 mm was processed to remove all particles with a maximum dimension larger than 100 mm The >20 mm and <20 mm fractions were then combined at a moisture content representative of the field moisture at three different pre-designated proportions, or composition ratios, including a composition ratio consider representative of the in situ condition, using a range of compaction efforts to evaluate the influence of composition ratio and compaction effort (or compacted unit weight) on small strain stiffness and equivalent linear shear modulus and damping ratio. All tests were conducted using uniform cyclic (sinusoidal) loading. The behavior of the reconstituted specimens tested herein may not truly represent the behavior of waste in situ due to differences in unit weight, differences in waste composition (e.g. removal of particles greater than 100 mm in dimension from the reconstituted waste) and waste structure (even if the waste is reconstituted to the in situ unit weight), and changes in the field moisture content over time (e.g. seasonally). Furthermore, the behavior of waste from one solid waste landfill may not be representative of the behavior of waste at other solid waste landfills. Therefore, the test results reported herein are strictly applicable only to reconstituted specimens of the specific waste that was employed in this testing program. Additional factors that may influence the behavior of a waste mass subject to seismic loading include the non-uniform nature of seismic loads, stress states within the waste mass during seismic loading, and the heterogeneity of the waste mass in the field. Waste behavior under non-uniform cyclic loading, as occurs during an earthquake, may differ from the behavior of waste subject to uniform cyclic loading, as reported herein. Stress states within the waste mass may differ from the simple shear stress state employed in the tests reported herein (though the simple shear stress state is considered more representative of seismic loading field conditions than the triaxial stress state), influencing waste behavior. The composition of waste in the field varies from point to point and thus the behavior of specimens reconstituted at a representative composition ratio may be different than the behavior of a waste mass with the same average composition ratio but with local variability about that average. Testing device limitations may also influence the properties of the waste reported herein, particularly with respect to damping.
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The simple shear device used to conduct the tests reported herein is more susceptible to internal resistance than the triaxial device used by Zekkos et al. (2008) to test the same waste. Thus the discrepancy between damping at large strains in the tests reported herein and the tests reported by Zekkos et al. (2008), while possibly due to the difference is stress states between the two tests and waste anisotropy, may be due, at least in part, to internal resistance (damping) associated with the simple shear testing device. Despite these limitations, the Tri-Cities landfill is one of only two landfills upon which there is data on the dynamic properties of waste at cyclic strains greater than 0.01% from either large scale laboratory testing or back analysis of strong motion data. Comparison of the shear wave velocity measurements on the reconstituted specimens tested herein with the in situ shear wave velocity measurements at the Tri-Cities landfill gives some confidence that the reconstitution procedure created specimens with a structure similar to that measured in the field at the same landfill. Comparison of the behavior of the waste from the Tri-Cities landfill tested herein with the behavior of the waste at the OII landfill as determined from both field measurements of landfill response and large scale testing (Matasovic and Kavazanjian, 1998) also suggests that the behavior reported herein is reasonably representative of field behavior and shows that waste from at least two different municipal solid waste landfills in the western United States follows a similar pattern of behavior. Therefore, until additional information on the dynamic properties of waste is available from large scale laboratory tests on waste recovered from other landfills or from back analysis of strong motion data recorded at landfills, the modulus and damping properties reported herein and by Zekkos et al. (2008) for the Tri-Cities waste combined with the OII landfill data reported by Matasovic and Kavazanjian (1998) remain the only reliable measurements of municipal solid waste properties at cyclic strains in excess of 0.01%. While the modulus reduction curves from among these data sets is reasonably consistent, sensitivity studies over the range of behavior reported herein are recommended for use in landfill design. Furthermore, it is probably prudent to use the lower damping values reported by Zekkos et al. (2008) until the discrepancy between the damping reported herein and in the Zekkos et al. (2008) study is resolved.
10. Summary The results of 15 large-scale cyclic simple shear tests performed on reconstituted specimens of MSW from the Tri-Cities landfill are presented in terms of the shear wave velocity and small-strain shear modulus versus unit weight and strain-dependent normalized shear modulus reduction and damping ratio curves. The specimens were reconstituted using either 100%, 65%, or 35% of material (by weight) that passed through a 20 mm screen (i.e. 100%, 65%, and 35% <20 mm material). The maximum size of the >20 mm material was limited to 100 mm and the specimens were reconstituted such that the large particles had a preferred horizontal orientation. All tests were conducted at a normal stress of 75 kPa. The data presented herein supplements available data on the properties of MSW subject to cyclic loading. While the data is based upon reconstituted specimens, it provides substantial insight into the effects of unit weight and waste composition of the cyclic behavior of MSW. Results of the tests presented herein are consistent with results of large scale cyclic triaxial tests on reconstituted specimens of the same waste reported by Zekkos et al. (2008) except that the damping ratio from the ASU cyclic simple shear tests appeared to be systematically larger than the damping ratio from the cyclic triaxial tests. The difference in damping ratio is particularly notable at shear strains greater than 0.1%. The inter-dependence of composi-
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tion ratio and unit weight complicate separation of the effects of these two parameters on the MSW properties presented herein. However, the test results clearly show a very strong dependence of shear wave velocity and small strain shear modulus on unit weight as well as a dependence on composition ratio. Waste composition had a very strong influence on damping and a somewhat lesser influence on shear wave velocity, small strain shear modulus, and modulus reduction. Modulus reduction and damping ratio also depended to some extent upon unit weight. To some extent, the influence of waste composition on modulus reduction counteracted its influence on small strain shear stiffness at large strains. The shear wave velocity and small strain modulus data reported herein are shown to be consistent with the data presented by Zekkos et al. (2008) when plotted on an unit weight basis. The shear wave velocity and small strain shear modulus as measured in the laboratory tests on composition ratios representative of field conditions appears to be somewhat lower than the values measured in the field at an overburden stress of approximately 75 kPa. The discrepancy between the lab and field data may be attributable to time under confinement effects. Modulus reduction curves developed herein are consistent with the modulus reduction curves developed by Zekkos et al. (2008) for waste from the same landfill at similar waste composition ratios and by Matasovic and Kavazanjian (1998) for waste from the OII landfill. The damping data presented herein suggests somewhat higher damping than reported by Zekkos et al. (2008) and Matasovic and Kavazanjian (1998). The reason for the discrepancy in damping ratio is unclear but may be related to particle orientation effects and/or the internal damping of the simple shear device. Acknowledgments The work described in this paper was funded by the National Science Foundation Division of Civil, Mechanical, and Manufacturing Innovation under Grant CMMI-0635435. This work was conducted as part of a collaborative study by Arizona State University, the University of California at Berkeley, the University of Texas at Austin, and Geosyntec Consultants on the mechanical properties of municipal solid waste. Any opinions, findings, conclusions, and recommendations expressed herein are those of the authors and do not reflect the views of the National Science Foundation. The authors also wish to acknowledge the contribution of John Kondziolka and Zachery Shafer, undergraduate laboratory assistants at Arizona State University, to this work, who helped conduct the tests and reduce the data reported herein.
References Augello, A.J., Bray, J.D., Abrahamson, N.A., Seed, R.B., 1998. Dynamic properties of solid waste based on back-analysis of OII landfill. Journal of Geotechnical and Geoenvironmental Engineering 124, 211–222. Bray, J.D., Zekkos, D., Kavazanjian Jr., E., Athanasopoulos, G.A., Reimer, M., 2009. Shear strength of municipal solid waste. Journal of Geotechnical and Geoenvironmental Engineering 135, 709–722. Choudhury, D., Savoikar, P., 2009. Simplified method to characterize municipal solid waste properties under seismic conditions. Waste Management 29, 924–933. Darendeli, M.B., 2001. Development of a new family of normalized modulus reduction and material damping curves. Ph.D. Dissertation, University of Texas, Austin, Texas, USA. Elgamal, A., Lai, T., Gunnturi, R., Zeghal, M., 2004. System identification of landfill seismic response. Journal of Earthquake Engineering 8, 545–566. Idriss, I.M., Fiegel, G.L., Hudson, M.B., Mundy, P.K., Herzig, R., 1995. Seismic response of the operating industries landfill. In: Yegian, M.K., Finn, W.D.L. (Eds.), Earthquake Design and Performance of Solid Waste Landfills. ASCE Geotechnical Special Publication No. 54, pp. 83–118. Kavazanjian Jr., E., Matasovic, N., Bonaparte, R., Schmertmann, G.R., 1995. Evaluation of MSW properties for seismic analysis. In: Acar, Y.B., Daniel, D.E. (Eds.), Geoenvironment 2000. ASCE Geotechnical Special Publication No. 46, pp. 1126–1141. Kavazanjian Jr., E., Matasovic, N., Stokoe II, K.H., Bray, J.D., 1996. In situ shear wave velocity of solid waste from surface wave measurements. In: Second International Congress Environmental Geotechnics Proceedings, Osaka, Japan, 1, pp. 97–104. Kavazanjian Jr., E., 2001. Mechanical properties of municipal solid waste. In: Sardinia 1–8th International Waste Management and Landfill Symposium Proceedings, Cagliari, Sardinia, III, pp. 415–424. Matasovic, N., Kavazanjian Jr., E., 1998. Cyclic characterization of OII landfill solid waste. Journal of Geotechnical and Geoenvironmental Engineering 124, 197– 210. Morochnik, V., Bardet, J.P., Hushmand, B., 1998. Identification of dynamic properties of OII landfill. Journal of Geotechnical and Geoenvironmental Engineering 124, 186–196. Seo, B., 2008. Compositional effects on the mechanical properties of municipal solid waste. Ph.D. Dissertation, Arizona State University, USA. Singh, S., Murphy, B., 1990. Evaluation of the stability of solid waste landfills. In: Landva, A., Knowles, G.D. (Eds.), Geotechnics of Waste Landfills – Theory and Practice. ASTM Special Technical Publication 1070, pp. 240–258. Thusyanthan, N.I., Madabhushi, S.P.G., Singh, S., 2006. Centrifuge modelling of solid waste landfill systems – Part 2: centrifuge testing of model waste. Geotechnical Testing Journal 29, 223–229. Towhata, I., Kawano, Y., Yonai, Y., Koelsch, F., 2004. Laboratory tests on dynamic properties of municipal wastes. In: 11th Conference on Soil Dynamics and Earthquake Engineering and Third International Conference on Earthquake Geotechnical Engineering Proceedings, pp. 688–693. Zekkos, D.P., 2005. Evaluation of static and dynamic properties of municipal solidwaste. Ph.D. Dissertation, University of California, Berkeley, CA, USA. Zekkos, D., Bray, J.D., Riemer, M.F., 2008. Shear modulus and material damping of municipal solid waste based on large-scale triaxial testing. Canadian Geotechnical Journal 45, 45–58. Zekkos, D., Athanasopoulos, G.A., Bray, J.D., Grizi, A., Theodoratos, A., 2010a. Largescale direct shear testing of municipal solid waste. Waste Management 30, 1544–1555. Zekkos, D., Kavazanjian Jr., E., Bray, J.D., Matasovic, N., Reimer, M.R., 2010b. Physical characterization of municipal solid waste for geotechnical purposes. ASCE Journal of Geotechnical and Geoenvironmental Engineering 136, 1231–1241.
Contents lists available at ScienceDirect
Waste Management journal homepage: www.elsevier.com/locate/wasman
Compositional effects on the dynamic properties of municipal solid waste Pengbo Yuan a, Edward Kavazanjian Jr. b,⇑, Wenwu Chen a, Bongseong Seo c a
Key Laboratory of Mechanics on Disaster and Environment in Western in China, The Ministry of Education of China, Lanzhou 730000, China Arizona State University, Tempe, AZ 85287-5306, USA c Independent Consultant, Tempe, AZ 85282, USA b
a r t i c l e
i n f o
Article history: Received 27 February 2011 Accepted 5 July 2011 Available online 9 August 2011 Keywords: Solid waste Dynamic properties Modulus Damping Cyclic loading Seismic
a b s t r a c t Large-scale cyclic simple shear tests were conducted on reconstituted specimens of municipal solid waste (MSW) collected from the Tri-Cities landfill in Fremont, California, USA. The influence of waste composition and compacted unit weight on the shear wave velocity, small-strain shear modulus, and straindependent shear modulus reduction and damping ratio curves of MSW was investigated in these tests. Modulus reduction and damping ratio curves were evaluated over a strain range of 0.01–3%. Specimens were reconstituted using 100%, 65%, and 35%, by weight, of the material that passed through a 20 mm screen and four different levels of compaction effort. All specimens were consolidated under a normal stress of 75 kPa prior to testing. The test results show a very strong dependence of shear wave velocity and small strain shear modulus on unit weight. Unit weight also had an influence on modulus reduction and damping ratio. Waste composition had a very strong influence on damping and also influenced shear wave velocity, small strain shear modulus, and modulus reduction. The interrelationship between unit weight and waste composition made it difficult to separate out the effects of these parameters. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction The dynamic properties of municipal solid waste (MSW) for use in seismic analysis of landfills, including the small strain shear stiffness and equivalent linear modulus reduction and damping relationships, has been the subject of significant attention over the past 15 years. However, most studies of MSW dynamic properties treat waste as a singular material with one set of dynamic properties independent of waste composition or unit weight. This paper presents the results of 15 large-scale cyclic simple shear tests in which waste composition and compaction effort was systematically varied to investigate the influence of composition and compaction effort on the dynamic properties of MSW. The tests were conducted on reconstituted specimens of MSW retrieved from the Tri-Cities landfill in Fremont, California (USA).
2. Background The key material properties in state-of-the-practice equivalent linear seismic analyses of landfills are the small strain shear modulus, Gmax, the strain-dependent equivalent shear modulus G, and the strain dependent equivalent linear damping, c. The strain ⇑ Corresponding author. Address: School of Sustainable Engineering and the Built Environment, Arizona State University, Tempe, AZ 85287-4306, USA. Tel.: +1 480 727 8566; fax: +1 480 965 0557. E-mail address: [email protected] (E. Kavazanjian). 0956-053X/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.wasman.2011.07.009
dependent equivalent linear shear modulus is usually described in terms of Gmax and a modulus reduction curve that relates the ratio G/Gmax to a representative shear strain, cr (equal to the maximum shear strain in a uniform cyclic test). The equivalent linear damping is usually described in terms of the fraction of critical damping k, equal to c/ccrit, where ccrit, the critical damping, is the lowest damping at which the system returns to equilibrium without overshooting the equilibrium position after being perturbed. The fraction of critical damping is also related to the representative shear strain cr based upon the hysteretic damping from a uniform cyclic test with strain amplitude cr. The small strain shear modulus, Gmax, is usually evaluated based upon the shear wave velocity, VS, and the mass density of the soil, q, using the following relationship from classical elasticity theory:
Gmax ¼ qV 2s
ð1Þ
where q = mass density of the material (equal to the total unit weight of the material divided by the acceleration of gravity). Available data on the dynamic properties of MSW is limited. Kavazanjian et al. (1996) have presented VS versus depth profiles for six southern California MSW landfills from Spectral Analysis of Surface Wave (SASW) testing. Matasovic and Kavazanjian (1998) have presented the results of SASW-derived VS profiles from 24 locations at one landfill composed predominantly of MSW, the Operating Industries, Inc. (OII) landfill in southern California. Equivalent linear modulus reduction and damping relationships for MSW have been recommended by various researchers
P. Yuan et al. / Waste Management 31 (2011) 2380–2390
(Singh and Murphy, 1990; Idriss et al., 1995; Kavazanjian et al., 1995; Augello et al., 1998; Matasovic and Kavazanjian, 1998; Morochnik et al., 1998; Elgamal et al., 2004; Towhata et al., 2004; Thusyanthan et al., 2006; Zekkos et al., 2008; Choudhury and Savoikar, 2009). However, several of these proposed relationships are based solely on the authors’ intuition (e.g. Singh and Murphy, 1990) or upon mathematical fits to curves proposed by previous investigators (e.g. Choudhury and Savoikar, 2009). Most of the other recommendations (i.e. Idriss et al., 1995; Augello et al., 1998; Morochnik et al., 1998; Matasovic and Kavazanjian, 1998; Elgamal et al., 2004) are based upon the observed seismic response of the OII landfill, the only landfill at which strong ground motions have been recorded upon the waste mass. Only Towhata et al. (2004) and Zekkos et al. (2008) have developed data-based modulus reduction and damping curves independent of the OII-derived curves. Idriss et al. (1995), Augello et al. (1998), Morochnik et al. (1998), and Elgamal et al. (2004) have back-calculated modulus reduction and damping curves solely from the seismic response of the OII landfill based on the recorded ground motions in a series of small nearby and larger more distant earthquakes events. There is general agreement among these investigators that the curves derived from the observed response of the OII landfill are limited to cyclic shear strains on the order of 0.1%, as this is approximately equal to the maximum strain level induced in the waste at OII by the recorded events. Matasovic and Kavazanjian (1998) supplemented back analysis of the field data with the results of large-scale (457-mm diameter) cyclic simple shear tests on reconstituted specimens of waste recovered from the OII landfill. This laboratory test data provided supplemental information for cyclic shear strains between 0.1% and 7%. Most of the OII investigators presented either singular modulus reduction and damping curves for MSW based upon their analyses (e.g. Idriss et al., 1995) or a range of values within which the OII properties may lie (e.g. Elgamal et al., 2004). However, Matasovic and Kavazanjian (1998) presented a range of possible values for the modulus reduction and damping curves along with a set of singular recommended curves. Towhata et al. (2004) performed cyclic triaxial tests and shaking table tests on a biologically treated ‘‘equivalent organic waste’’ material imported from Germany. These investigators present modulus reduction curves for Young’s modulus from cyclic triaxial tests on the organic waste with and without plastic sheets added to the specimen for axial strains from approximately 0.02–0.4% and values for the damping ratio at an axial strain of approximately 0.15% for the organic waste without plastic and 0.25% for organic waste with plastic. They also present shear modulus and damping ratio values from shaking table tests for the organic waste with plastic at shear strains from 0.3% to 1%. However, no information is provided on the small strain shear modulus of the waste. Zekkos et al. (2008) performed a series of large-scale (300-mm diameter) uniform cyclic triaxial tests on reconstituted specimens of MSW from the Tri-Cities landfill (the same waste tested in the investigation reported herein). These investigators conducted a systematic study of the effect of compaction effort and waste composition on the shear wave velocity and the strain-dependent equivalent linear shear modulus reduction relationship (G/Gmax versus c) and damping ratio relationship (k versus c) for cyclic shear strains up to approximately 0.5%. Waste composition was varied by changing the relative proportions of material >20 mm and <20 mm in dimension screened from bulk samples of waste recovered from large diameter bucket auger borings. The material >20 mm in dimension was described as fibrous waste and the material <20 mm in dimension was referred to as soil-sized or soil-like waste. The maximum particle size in the screened waste was approximately 40 mm for bulky material and 80 mm for elongated particles. The waste was placed in the compaction mold such
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that the elongated particles has a preferential orientation in the horizontal plane and compaction effort was varied over a wide range between relatively light compaction and heavy compaction effort. All tests were conducted after isotropically consolidating the compacted specimens to 75 kPa. Three waste composition ratios were used in the Zekkos et al. (2008) study: 100% by weight <20 mm, 62% to 74% by weight <20 mm (the composition ratio of the material in the field was approximately 62% <20 mm), and 14% by weight <20 mm. Results of the Zekkos et al. (2008) study showed a strong correlation between composition ratio and compacted unit weight, with a higher percentage of <20 mm material resulting systematically in a higher compacted unit weight. Compaction effort also had a significant impact on compacted unit weight, with higher compaction effort resulting in higher compacted unit weight. Shear wave velocity (and small strain shear modulus) was also strongly correlated to compacted unit weight, with a higher compacted unit weight resulting in a systematically higher shear wave velocity (and small strain shear modulus). The influence of composition ratio on shear wave velocity (and small strain shear modulus) could not be discerned due the strong dependence of both composition ratio and shear wave velocity on compacted unit weight. However, composition ratio did have a systematic influence of modulus reduction and damping, with larger percentages of >20 mm (fibrous) material resulting in more elastic behavior, i.e. less modulus degradation and lower damping at the same shear strain compared to specimens with lower percentages of >20 mm material.
3. Testing program This paper presents the results of large-scale (304 406 mm rectangular specimen) uniform cyclic simple shear tests on reconstituted specimens of screened MSW recovered from the Tri-Cities landfill, the same waste tested by Zekkos et al. (2008). The effects of waste composition and compacted unit weight on shear wave velocity and the strain-dependent equivalent linear shear modulus reduction relationship (G/Gmax versus c) and damping ratio relationship (k versus c) were evaluated in these tests using essentially the same three waste composition ratios and similar levels of compaction effort (and therefore unit weight) as those employed by Zekkos et al. (2008). The tests reported herein were conducted using in the Arizona State University (ASU) Enamul and Mahmuda Hoque Geotechnical Laboratory. The testing program employed the same large scale cyclic simple shear device employed in the testing of the OII landfill waste described by Matasovic and Kavazanjian (1998), with some modifications to enhance its performance (as described subsequently). A vertical normal stress of 75 kPa was employed in all of the tests reported herein, equal to the isotropic confining pressure of 75 kPa used by Zekkos et al. (2008). The maximum size of the fibrous (>20 mm) material in the cyclic simple shear tests reported herein was approximately 100 mm, 25% larger than the maximum particle size employed by Zekkos et al. (2008) of 80 mm. As in the tests conducted by Zekkos et al. (2008), the waste in the simple shear tests reported here was placed such that the long axis of the large particles had a preferred horizontal orientation. The maximum cyclic shear strain in the ASU simple shear tests was on the order of 3%, compared to the 0.5% maximum value in the cyclic triaxial tests conducted by Zekkos et al. (2008). Another difference between the tests reported herein and the tests conducted by Zekkos et al. (2008) is the stress system induced by the testing equipment. Zekkos et al. (2008) employed cyclic triaxial testing. In a cyclic triaxial test the maximum cyclic shear stress is induced on a plane at 45 degrees to the horizontal, the normal stress on the 45 degree plane varies about the effective
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Table 1 Summary of waste sampled at the Tri-Cities landfill (after Zekkos, 2005).
Smaller than 20 mm Paper Soft plastics Wood Gravel Metals Stiff plastics Textiles Others
A-3
C-1
C-6
A-1
C-3
58.9 12.9 1.7 11.4 9.8 3.5 1.0 1.4 1.0
52.2 20.1 6.1 8.2 5.1 3.3 3.8 1.4 0.3
71.8 10.8 2.8 2.8 6.6 1.6 1.0 1.6 1.2
68.6 7.3 2.1 6.6 10.3 1.6 0.9 1.6 2.6
63.6 11.7 3.0 8.7 5.1 4.9 2.1 0.7 1.4
confining pressure (depending on the vertical normal stress), and there is no shear stress induced on vertical or horizontal planes in the specimen. In the simple shear tests reported herein, a shear stress is induced on the horizontal plane and the normal stress is constant on that plane. Direct shear tests conducted by Zekkos et al. (2010a) demonstrate that the shear strength of waste is greater when the failure plane cuts across the plane of preferred orientation of the large waste particles, as in the triaxial test, compared to tests where the maximum shear stress is aligned with the plane of preferred orientation of the large particles, as in the simple shear test. Thus, the difference in the stress state between the triaxial tests conducted by Zekkos et al. (2008) and the simple shear tests reported herein may be significant due to the reconstitution of the specimens using a preferred horizontal orientation for the large particles. Simple shear testing is generally regarded as providing a more accurate simulation of the stress state induced in the field by earthquake waves (i.e. by vertically propagating shear waves). Therefore, while some differences may be expected between the results of the triaxial tests reported by Zekkos et al. (2008) and the simple shear tests reported herein due to waste anisotropy, the behavior in simple shear may be expected to be more representative of behavior in an earthquake, all other factors being equal. 4. Material characterization and specimen preparation Detailed characterization of the MSW collected from the Tri-Cities landfill and details of the associated field investigation, including field borehole logs, SASW testing, and in situ unit weight tests, are provided by Zekkos (2005) and Zekkos et al. (2008). The composition of the waste recovered Tri-Cities landfill is summa-
rized in Table 1. The MSW tested at ASU came from the A-3 sample group and was composed, by weight, of approximately 62% soillike material smaller than 20 mm in dimension, 14% paper, 3% soft plastic, 11% wood, and 10% gravel larger than 20 mm in dimension. The field moisture content varied from slightly less than 8% to slightly greater than 25% (a value still well below the field capacity of the waste) by weight, measured using a temperature of 60 °C as recommended by Zekkos et al. (2010b) to minimize volatilization of organic compounds. In preparing the reconstituted specimens of Tri-Cities MSW for the ASU simple shear tests, a procedure as close as possible to the specimen preparation procedure employed by Zekkos et al. (2008) was used. The waste was first screened to separate the >20 mm material from the <20 mm material. The maximum size of the >20 mm particles was then reduced to a maximum dimension of approximately 100 mm by either removing oversized particles or reducing them in size. Specimens at ASU were then compacted using 100%, 65% and 35% <20 mm material, by weight. Prior to compacting the MSW, it was mixed thoroughly in a small mechanical mixer. The waste was then compacted in lifts into the stack of rectangular Teflon coated steel frames used to maintain the zero lateral strain condition during the simple shear test. Specimens were compacted in three layers placed such that the long axis of the large particles had a preferred horizontal orientation. Compaction was accomplished using a 13.6 kg hammer that was dropped repeatedly on a rectangular steel plate 114.3 mm 114.3 mm in dimension from a constant height to achieve a specific compaction effort. Compaction was applied at 12 spots in each layer, and a multiple of 12 blows was applied to each layer. The final height after compaction of the ASU specimens was approximately 152 mm, resulting in a cubical specimen with a length of 406 mm (in the direction in which the shear stress was applied), a width of 304 mm, and about a height of about 152 mm. Four different levels of compaction effort were employed for each composition ratio. Five specimens were prepared for each composition ratio, including two using the same compaction effort in order to investigate the reproducibility of the results. A summary of information on the reconstituted MSW specimens used in the cyclic simple shear testing program at ASU, including total unit weight after compression under a normal stress of 75 kPa, compaction moisture content, composition, and number of blows per layer, is presented in Table 2. The maximum dimension of the waste particles employed in the simple shear testing program of 100 mm was less than twice
Table 2 Summary of ASU cyclic simple shear test specimens.
a b
Specimen
Moisture content (%)
Total unit weight (kN/m3)a
Composition (% by weight) <20 mm
Paper
Soft plastic
Wood
Gravel
100% <20 mm-1 100% <20 mm-2 100% <20 mm-2a 100% <20 mm-3 100% <20 mm-4 65% <20 mm-1 65% <20 mm-2 65% <20 mm-2a 65% <20 mm-3 65% <20 mm-4 35% <20 mm-1 35% <20 mm-2 35% <20 mm-2a 35% <20 mm-3 35% <20 mm-4
14.8 16.6 16.3 15.9 16.4 19.1 22.4 23.1 23.4 21.6 22.1 22.9 23.0 22.8 23.9
14.1 13.2 12.9 12.5 11.9 10.8 10.2 10.1 9.1 8.9 7.5 7.1 7.0 6.5 6.1
100 100 100 100 100 65 65 65 65 65 35 35 35 35 35
0 0 0 0 0 15 15 15 15 15 45 45 45 45 45
0 1 3 3 6 0 1 3 3 6 0 1 3 3 6
0 0 0 0 0 7 7 7 7 7 5 5 5 5 5
0 0 0 0 0 10 10 10 10 10 10 10 10 10 10
Unit weight after compression under 75 kPa normal stress. Every specimen has three layers and compaction effort was applied at 12 spots in each layer.
Compaction style (blow/spot)b
Compaction energy (J/cm3)
6 3 3 1 0 6 3 3 1 0 6 3 3 1 0
0.54 0.27 0.27 0.09 0 0.54 0.27 0.27 0.09 0 0.54 0.27 0.27 0.09 0
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Fig. 1. ASU large-scale cyclic simple shear testing device.
the height of the specimen. However, since the long axis of the particles was oriented sub-parallel to the long axis of the specimen, and the large particles typically had an aspect ratio of greater than 3, the specimen height was always greater than 5 times the maximum vertical thickness of the particles. Furthermore, because the simple shear test simulates a vertically propagating shear wave under one-dimensional conditions, the ratio of 4 between the 406 mm length of the specimen and the maximum dimension of the large particles was considered acceptable.
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frames within which the specimen is compacted is mounted on the carriage. The tests were conducted as strain-controlled tests. The MSW specimens were subject to a normal stress of 75 kPa for approximately 24 h prior to testing. Six series of 3–5 symmetrical cycles of loading with a constant maximum displacement were applied to each specimen at progressively increasing maximum displacements in each series. The displacements employed in the testing program corresponded to cyclic shear strains from 0.01% (the lower limit at which good resolution could be achieved) to 3%. To monitor vertical and shear deformations, 5 large linear variable differential transformers (LVDTs) and one small LVDT were installed on the simple shear testing device. Three of the large LVDTs were employed to monitor horizontal displacement: one on the carriage, one at mid-height of the frame stack, and one at the top of the frame stack, as shown in Fig. 1. The bottom LVDT was used for servo-control of the carriage translation, the top LVDT was used to evaluate the fixity of the top of the specimen, and the middle LVDT was used to evaluate the uniformity of the shear strain induced in the specimen. For measurement and servo control at shear strains from 0.01% to 0.03%, a smaller, more sensitive LVDT was attached to the carriage. The other two LVDTs were mounted vertically at the center and edge of the top cap to measure vertical compression and any rocking or tilting of the top cap. Data acquisition and cyclic strain control were accomplished using a Universal Digital Signal Conditioning and Control Unit. A horizontal striker plate was placed at the base of the specimen and a 1 Hz geophone was placed at the top of the specimen to enable measurement of shear wave velocity. The striker plate was instrumented with a strain gage to record the initiation of the shear wave induced by gently tapping the plate horizontally. The plate was tapped twice, in opposing directions, and first arrival of the shear wave at the geophone was determined by superimposing the two wave forms and picking off the first reversal of polarity. More details about the ASU large-scale cyclic simple shear device may be found in Seo (2008). 6. Test results
5. Testing equipment and test program 6.1. Shear wave velocity and small-strain (maximum) shear modulus The large-scale cyclic simple shear device employed in the tests conducted at ASU is shown in Fig. 1. The specimens were sheared by fixing the top of the specimen against translation and applying a sinusoidal horizontal movement with a frequency of 0.1 Hz to a carriage on roller bearings. A stack of Teflon-coated rectangular
Fig. 2 presents a plot of the laboratory-measured VS versus the unit weight of the specimen after compression under 75 kPa vertical normal stress. Fig. 3 presents a plot of the corresponding values of Gmax (calculated from the shear wave velocity and unit weight in
Fig. 2. Shear wave velocity, VS, versus total unit weight for reconstituted Tri-Cities MSW.
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accordance with Eq. (1)) versus total unit weight. Figs. 2 and 3 show that both the shear wave velocity and the small-strain shear modulus of the MSW specimens are strongly correlated to unit weight. Approximately linear relationships can be developed for each composition ratio over the range of unit weights employed in the testing program. Significantly, the extrapolated linear trends for the three composition ratios employed in the testing program do not line up but instead show an en echelon behavior, as can be seen from Figs. 2 and 3. This en echelon behavior suggests a dependence of VS and Gmax on composition ratio, with a greater amount of >20 mm material resulting in a greater stiffness and higher shear wave velocity for the same total unit weight. However, given the strong dependence of unit weight upon compaction effort and composition ratio, it is unlikely that two specimens with significantly different composition would have the same in situ unit weight when subject to similar compaction effort. Figs. 2 and 3 also compare the shear wave velocity and small strain shear modulus derived from field measurements at the Tri-Cities landfill as reported by Zekkos et al. (2008) at a depth corresponding to an overburden stress of 75 kPa to the values from the laboratory testing program described herein. As the average waste composition in the field is approximately 62% by weight <20 mm, Fig. 2 indicates that the field values of VS (evaluated using spectral analysis of surface wave testing) are of the same order of
magnitude, but slightly greater than, the laboratory values. The discrepancy between the field and laboratory values is even more apparent in Fig. 3, where the Gmax values calculated using the field VS and unit weight values reported by Zekkos et al. (2008) are compared to the laboratory Gmax values. These discrepancies may be due to time under confinement effects, as Zekkos et al. (2008) reported that Gmax of reconstituted Tri-Cities landfill waste specimens subject to an applied confining stress for 1000 h increased by approximately 100% to 200% compared to the value measured after 1 h of confinement. 6.2. Shear modulus reduction Fig. 4 presents the normalized shear modulus reduction curves for the 15 cyclic simple shear tests performed on reconstituted waste from the Tri-Cities landfill for this study. The results shown in Fig. 4 indicate that the normalized shear modulus reduction curve shifts to right (i.e. become more elastic) with increasing percentage of material >20 mm. The effect of unit weight on the normalized shear modulus reduction is shown in Figs. 5–7 for composition ratios of 100% <20 mm, 65% <20 mm, and 35% <20 mm, respectively. These figures indicate that that the normalized shear modulus reduction curves become more elastic (shift to right) with decreasing unit
Fig. 3. Small-strain shear modulus, Gmax, versus total unit weight for reconstituted Tri-Cities MSW.
Fig. 4. Normalized shear modulus reduction curves for reconstituted Tri-Cities MSW.
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Fig. 5. Normalized shear modulus reduction curves for Tri-Cities MSW reconstituted using 100% <20 mm material.
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Fig. 7. Normalized shear modulus reduction curves for Tri-Cities MSW reconstituted using 35% <20 mm material.
The strain-dependent damping ratio of reconstituted Tri-Cities landfill MSW was also affected by both waste composition and unit weight (or compaction effort), as shown in Figs. 8–11. Fig. 8 presents the damping ratio data for all three composition ratios. Figs. 9–11 present the data for composition ratios of 100% <20 mm, 65% <20 mm, and 35% <20 mm, respectively. Fig. 8 shows a significant increase in damping ratio with an increase in the relative amount of <20 mm material. However, Figs. 9–11 show a decrease in damping with an increase in unit weight, indicating that the effect of composition on damping is even more significant than shown in Fig. 8 if the influence of composition on unit weight is separated out from the data. 7. Comparison with other test results
Fig. 6. Normalized shear modulus reduction curves for Tri-Cities MSW reconstituted using 65% <20 mm material.
weight (or decreasing of compaction energy). However, as increasing the amount of <20 mm material will increase unit weight for the same compaction effort (shifting the modulus reduction curves to the left), small variations in composition ratio in the field may to some extent be self compensating with respect to modulus reduction. The data in Figs. 4–7 suggest that both unit weight and composition can have a significant influence on the normalized shear modulus reduction curve for MSW. 6.3. Damping ratio In calculating the damping ratio from the hysteresis loops generated in the uniform cyclic tests, a strain-dependent correction factor was applied to the calculated damping ratio to compensate for the internal damping in the testing device. Uniform cyclic tests were conducted on ASTM 20-30 Ottawa sand the large scale testing device. The strain-dependent damping ratio for this sand was also calculated using the equations developed by Darendeli (2001). The difference in the strain-dependent damping ratio calculated using the two approaches was as applied as a correction factor to the large scale test results on MSW.
Figs. 12 and 13 compare the shear wave velocity and small strain shear modulus data for the tests reported herein to the results from Zekkos et al. (2008), denoted as UCB data, for reconstituted Tri-Cities MSW with composition ratios of 100% <20 mm, 62–76% <20 mm, and 8–25% <20 mm. These figures show that the ASU data is in good agreement with the UCB data. It should be pointed out that ASU used Eq. (1) to calculate the small strain shear modulus while UCB measured the small strain shear modulus directly using displacement transducers mounted on the triaxial test specimens and then back-calculated the shear wave velocity values. The data in Figs. 12 and 13 show a strong dependence of shear wave velocity and small strain shear modulus on unit weight, with increasing shear wave velocity and shear stiffness with increasing unit weight. A 25% increase in unit weight results in an approximately 50% increase in shear wave velocity. The trend lines for the ASU cyclic simple shear data in Figs. 2 and 3 also suggests a systematic impact of waste composition on shear wave velocity and small strain shear modulus, with increased amounts of >20 mm material (i.e. fibrous waste) resulting in increased stiffness and shear wave velocity. These results suggest that increases in the percent of daily cover soil and additional compaction effort may increase the stiffness of MSW. However, the dependence of small strain stiffness on composition ratio inferred from Fig. 3 suggests that an increase in the degree of degradation of MSW resulting in a decrease in the amount of large fibrous material could decrease the stiffness of MSW even if there was not a concurrent decrease in unit weight.
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Fig. 8. Damping ratio for reconstituted Tri-Cities MSW.
Fig. 9. Damping ratio for Tri-Cities MSW reconstituted using 100% <20 mm material.
Fig. 11. Damping ratio for Tri-Cities MSW reconstituted using 35% <20 mm material.
Fig. 10. Damping for Tri-Cities MSW reconstituted using 65% <20 mm material.
Fig. 12. Comparison of ASU and UCB shear wave velocity values for reconstituted Tri-Cities MSW.
Fig. 14 compares the modulus reduction data for the tests reported herein to the fitted curves from Zekkos et al. (2008) for reconstituted Tri-Cities MSW with composition ratios of 100%
<20 mm, 62–76% <20 mm, and 8–25% <20 mm. The ASU and Zekkos et al. (2008) results show excellent agreement. The normalized modulus reduction data indicates that increased amounts of the fi-
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brous >20 mm material results in less modulus degradation, i.e. more elastic behavior. Zekkos et al. (2008) attributed the reduction in modulus degradation with increasing >20 mm material to the fibrous nature of the larger than 20 mm fraction and the size of the fibers. The modulus degradation trend is counter to the initial stiffness trend with respect to waste composition, suggesting that at larger strains, e.g. during strong earthquake shaking, differences in initial stiffness due to waste composition may be countered by differences in modulus degradation. Fig. 15 compares the damping ratio data for the for large-diameter cyclic simple shear tests on reconstituted specimens of Tri-Cities MSW reported herein to fitted curves from Zekkos et al. (2008) for reconstituted Tri-Cities MSW with composition ratios of 100% <20 mm, 62–76% <20 mm, and 8–25% <20 mm. The damping ratio from the ASU cyclic simple shear tests is as much as 50% higher than the damping ratio recommended by UCB for the same (or similar) composition ratio. However, the damping ratio trends with respect to unit weight and composition data from the simple shear and triaxial tests are consistent. The impact of composition on damping appears to be particularly significant, with a decrease in strain-dependent damping ratio of
approximately 50% for the specimens with 35% <20 mm compared to the specimens with 100% <20 mm. amounts of >20 mm material. The effect of composition on damping is to some extent masked by the influence of density on damping, as the data shows decreasing damping ratio with increasing unit weight for a given composition ratio, but unit weight decreases (and thus damping increases) with increasing amounts of >20 mm material for the same compaction effort. Reasons for the difference between the damping ratios measured in the ASU and Zekkos et al. (2008) tests are not clear, but may in part be attributable to the difference between the triaxial and simple shear stress states. Simple shear loading in which the shear stress is applied parallel to the orientation of the fibrous particles may result in more slippage and relative displacement among the waste constituents than in a triaxial stress. However, some of the difference may also be due to issues associated with the strain dependent correction factor for machine damping applied to the simple shear testing results. Furthermore, Zekkos et al. (2008) appears to have employed the lower bound of the damping data from their cyclic triaxial tests as the recommended damping values. For instance, for a composition ratio of 100% <20 mm, a damping ratio as high as 7% at 0.01% strain and as high as 12% was reported by Zekkos et al. (2008). These damping values correspond approximately to the lower end of the range of damping values for the ASU tests on waste with 100% <20 mm material, suggesting that the discrepancy in damping values is not as great as indicted in Fig. 15. Fig. 16 compares the modulus reduction and damping curves from this testing program for the 65% <20 mm material (representative of field composition) to the curves for 62–76% <20 mm from Zekkos et al. (2008) for the same Tri-Cities waste and to the upper and lower bound curves from Matasovic and Kavazanjian (1998) for waste from the OII landfill (established, in part, using the same large scale simple shear testing equipment used herein). Matasovic and Kavazanjian (1998) identified the upper bound modulus and lower bound damping curves as their best-estimates of OII waste properties based upon internal consistency and comparison with values back calculated for cyclic shear strains up to 0.1% from strong motion records captured at the site. These curves again show good agreement for modulus reduction and damping but suggest that the damping ratios from the ASU simple shear tests reported herein may be systematically high at strains less than 0.1%.
Fig. 14. Comparison of ASU and UCB normalized shear modulus reduction values for reconstituted Tri-Cities MSW.
Fig. 15. Comparison of ASU and UCB strain-dependent damping ratio values for reconstituted Tri-Cities MSW.
Fig. 13. Comparison of ASU and UCB small strain shear modulus values for reconstituted Tri-Cities MSW.
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Fig. 16. Comparison of Tri-Cities data with OII upper and lower bound relationships from Matasovic and Kavazanjian (1998): (a) Modulus reduction; (b) Damping.
8. Waste shear strength The objective of this study was to evaluate compositional effects upon the modulus and damping of waste subject to cyclic loading. Neither compositional effects on the shear strength of waste subject to dynamic loading nor the dynamic shear strength of waste itself was a subject of this study. None of the tests reported herein were taken to a state that would constitute failure under cyclic, or dynamic, loading. The largest cyclic shear strain imposed upon the specimens tested herein was on the order of 3%. However, all test specimens were monotonically loaded to failure following cyclic loading. Fig. 17a shows the monotonic loading stress–strain curves for specimens with a waste composition ratio of 64% at three different initial unit weights subject to a vertical normal stress of 75 kPa. Fig. 17b shows the monotonic stress strain curves from six specimens reconstituted using the same compaction energy but at three different composition ratios. All tests were sheared at a strain rate of approximately 0.17% per minute. Evaluation of shear strength from cyclic simple shear tests is neither a simple nor a straightforward process due to uncertainty about the value of the horizontal normal stress, i.e. the normal stress on the vertical plane (Kavazanjian, 2001). The data in Fig. 17 do show qualitatively the influence of unit weight on waste shear strength. Waste shear strength as measured in simple shear loading clearly increases with increasing unit weight. However, the
Fig. 17. Results of monotonic shear tests after cyclic loading: (a) Tests with 65% by weight <20 mm; (b) Tests with compaction energy equal to 0.27 J/cm3.
influence of particle size on shear strength is not easily discerned from these figures due to the inter-dependence of particle size and initial unit weight. It is possible to obtain a lower bound value on the equivalent friction angle, /eq (the friction angle assuming zero cohesion, sometimes referred to as the secant friction angle) from simple shear tests by interpreting them as a direct shear test (Kavazanjian, 2001). If the simple shear test is interpreted as a direct shear test, /eq is given by Eq. (2) as:
/eq ¼ tan1 ðsf =rV Þ
ð2Þ
where sf is the shear strength at failure and rv is the vertical normal stress (75 kPa in this testing program). Shear strengths interpreted in this manner for the tests shown in Fig. 17 are presented in Tables 3 and 4. Tables 3 and 4 also presents the friction angle calculated
Table 3 Lower bound shear strength at 75 kPa normal stress from simple shear tests for waste with 65% by weight <20 mm. Composition ratio
Total Unit weight (kN/m3)
Equivalent friction angle /eq (degrees)
Friction angle for 15 kPa cohesion /15 (degrees)
65% <20 mm-3 65% <20 mm-2 65% <20 mm-1
9.1 10.2 10.8
34 41 44
25 34 38
P. Yuan et al. / Waste Management 31 (2011) 2380–2390 Table 4 Lower bound shear strength at 75 kPa normal stress from simple shear tests for waste compacted using 0.27 J/cm3 (average of two tests). Composition ratio
Total unit weight (kN/m3)
Equivalent friction angle /eq (degrees)
Friction angle for 15 kPa cohesion /15 (degrees)
35% <20 mm-2 65% <20 mm-2 100% <20 mm-2
7.1 10.2 13.2
38 41 47
30 34 41
using the direct shear test interpretation but assuming a cohesion of 15 kPa, denoted as /15. A cohesion of 15 kPa is the value recommended by Bray et al. (2009) for a normal stress dependent shear strength of municipal solid waste. Except for the tests with a unit weight of less than 10 kN/m3, the values for /15 reported in Table 3 are consistent with the value of 36° suggested by Bray et al. (2009) for an overburden stress of 1 atmosphere (98 kPa). 9. Limitations The large diameter cyclic simple shear laboratory tests reported in this study were conducted on reconstituted specimens of municipal solid waste from one landfill. Prior to reconstitution, the waste was separated into fractions >20 mm and <20 mm and the fraction >20 mm was processed to remove all particles with a maximum dimension larger than 100 mm The >20 mm and <20 mm fractions were then combined at a moisture content representative of the field moisture at three different pre-designated proportions, or composition ratios, including a composition ratio consider representative of the in situ condition, using a range of compaction efforts to evaluate the influence of composition ratio and compaction effort (or compacted unit weight) on small strain stiffness and equivalent linear shear modulus and damping ratio. All tests were conducted using uniform cyclic (sinusoidal) loading. The behavior of the reconstituted specimens tested herein may not truly represent the behavior of waste in situ due to differences in unit weight, differences in waste composition (e.g. removal of particles greater than 100 mm in dimension from the reconstituted waste) and waste structure (even if the waste is reconstituted to the in situ unit weight), and changes in the field moisture content over time (e.g. seasonally). Furthermore, the behavior of waste from one solid waste landfill may not be representative of the behavior of waste at other solid waste landfills. Therefore, the test results reported herein are strictly applicable only to reconstituted specimens of the specific waste that was employed in this testing program. Additional factors that may influence the behavior of a waste mass subject to seismic loading include the non-uniform nature of seismic loads, stress states within the waste mass during seismic loading, and the heterogeneity of the waste mass in the field. Waste behavior under non-uniform cyclic loading, as occurs during an earthquake, may differ from the behavior of waste subject to uniform cyclic loading, as reported herein. Stress states within the waste mass may differ from the simple shear stress state employed in the tests reported herein (though the simple shear stress state is considered more representative of seismic loading field conditions than the triaxial stress state), influencing waste behavior. The composition of waste in the field varies from point to point and thus the behavior of specimens reconstituted at a representative composition ratio may be different than the behavior of a waste mass with the same average composition ratio but with local variability about that average. Testing device limitations may also influence the properties of the waste reported herein, particularly with respect to damping.
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The simple shear device used to conduct the tests reported herein is more susceptible to internal resistance than the triaxial device used by Zekkos et al. (2008) to test the same waste. Thus the discrepancy between damping at large strains in the tests reported herein and the tests reported by Zekkos et al. (2008), while possibly due to the difference is stress states between the two tests and waste anisotropy, may be due, at least in part, to internal resistance (damping) associated with the simple shear testing device. Despite these limitations, the Tri-Cities landfill is one of only two landfills upon which there is data on the dynamic properties of waste at cyclic strains greater than 0.01% from either large scale laboratory testing or back analysis of strong motion data. Comparison of the shear wave velocity measurements on the reconstituted specimens tested herein with the in situ shear wave velocity measurements at the Tri-Cities landfill gives some confidence that the reconstitution procedure created specimens with a structure similar to that measured in the field at the same landfill. Comparison of the behavior of the waste from the Tri-Cities landfill tested herein with the behavior of the waste at the OII landfill as determined from both field measurements of landfill response and large scale testing (Matasovic and Kavazanjian, 1998) also suggests that the behavior reported herein is reasonably representative of field behavior and shows that waste from at least two different municipal solid waste landfills in the western United States follows a similar pattern of behavior. Therefore, until additional information on the dynamic properties of waste is available from large scale laboratory tests on waste recovered from other landfills or from back analysis of strong motion data recorded at landfills, the modulus and damping properties reported herein and by Zekkos et al. (2008) for the Tri-Cities waste combined with the OII landfill data reported by Matasovic and Kavazanjian (1998) remain the only reliable measurements of municipal solid waste properties at cyclic strains in excess of 0.01%. While the modulus reduction curves from among these data sets is reasonably consistent, sensitivity studies over the range of behavior reported herein are recommended for use in landfill design. Furthermore, it is probably prudent to use the lower damping values reported by Zekkos et al. (2008) until the discrepancy between the damping reported herein and in the Zekkos et al. (2008) study is resolved.
10. Summary The results of 15 large-scale cyclic simple shear tests performed on reconstituted specimens of MSW from the Tri-Cities landfill are presented in terms of the shear wave velocity and small-strain shear modulus versus unit weight and strain-dependent normalized shear modulus reduction and damping ratio curves. The specimens were reconstituted using either 100%, 65%, or 35% of material (by weight) that passed through a 20 mm screen (i.e. 100%, 65%, and 35% <20 mm material). The maximum size of the >20 mm material was limited to 100 mm and the specimens were reconstituted such that the large particles had a preferred horizontal orientation. All tests were conducted at a normal stress of 75 kPa. The data presented herein supplements available data on the properties of MSW subject to cyclic loading. While the data is based upon reconstituted specimens, it provides substantial insight into the effects of unit weight and waste composition of the cyclic behavior of MSW. Results of the tests presented herein are consistent with results of large scale cyclic triaxial tests on reconstituted specimens of the same waste reported by Zekkos et al. (2008) except that the damping ratio from the ASU cyclic simple shear tests appeared to be systematically larger than the damping ratio from the cyclic triaxial tests. The difference in damping ratio is particularly notable at shear strains greater than 0.1%. The inter-dependence of composi-
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tion ratio and unit weight complicate separation of the effects of these two parameters on the MSW properties presented herein. However, the test results clearly show a very strong dependence of shear wave velocity and small strain shear modulus on unit weight as well as a dependence on composition ratio. Waste composition had a very strong influence on damping and a somewhat lesser influence on shear wave velocity, small strain shear modulus, and modulus reduction. Modulus reduction and damping ratio also depended to some extent upon unit weight. To some extent, the influence of waste composition on modulus reduction counteracted its influence on small strain shear stiffness at large strains. The shear wave velocity and small strain modulus data reported herein are shown to be consistent with the data presented by Zekkos et al. (2008) when plotted on an unit weight basis. The shear wave velocity and small strain shear modulus as measured in the laboratory tests on composition ratios representative of field conditions appears to be somewhat lower than the values measured in the field at an overburden stress of approximately 75 kPa. The discrepancy between the lab and field data may be attributable to time under confinement effects. Modulus reduction curves developed herein are consistent with the modulus reduction curves developed by Zekkos et al. (2008) for waste from the same landfill at similar waste composition ratios and by Matasovic and Kavazanjian (1998) for waste from the OII landfill. The damping data presented herein suggests somewhat higher damping than reported by Zekkos et al. (2008) and Matasovic and Kavazanjian (1998). The reason for the discrepancy in damping ratio is unclear but may be related to particle orientation effects and/or the internal damping of the simple shear device. Acknowledgments The work described in this paper was funded by the National Science Foundation Division of Civil, Mechanical, and Manufacturing Innovation under Grant CMMI-0635435. This work was conducted as part of a collaborative study by Arizona State University, the University of California at Berkeley, the University of Texas at Austin, and Geosyntec Consultants on the mechanical properties of municipal solid waste. Any opinions, findings, conclusions, and recommendations expressed herein are those of the authors and do not reflect the views of the National Science Foundation. The authors also wish to acknowledge the contribution of John Kondziolka and Zachery Shafer, undergraduate laboratory assistants at Arizona State University, to this work, who helped conduct the tests and reduce the data reported herein.
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