Introduction
It is estimated that about 200 – 300 million scrap tires are produced annually in the United States, and 3,469,000 tons of waste tires were discarded only in 2013 in the U.S [
1]. Since many states advocated abating stockpiled tires lately, the number of stockpiled scrap tires in the U.S. has remarkably decreased since the 1990’s, but there are still more than 75 million tires stocked in the field. Those stockpiled scrap tires caused significant health problems as well as environmental hazards. They occupied a huge space in landfills and have provided breeding grounds for mosquitoes and rodents [
2]. Furthermore, tire fires are serious disasters to the environment. Once it starts, a tire fire can be easily aggravated into an uncontrollable crisis that is expensive to clean up.
Nowadays, many countries prohibit legal and illegal stockpiling of scrap tires and promote recycling and recovering. In the U.S., more than 90% of scrap tires are recycled or recovered, and markets for recycling scrap tires continuously grow. Current big markets for scrap tires are tire derived fuel (TDF), civil engineering applications, and ground rubber applications/rubberized asphalt concrete [
1]. For the past several years, the usage of scrap tires in civil applications has dropped, whereas the TDF has been steadily strong in the U.S. scrap tire market. In European countries, the recovery rate of scrap tires or End-of-Life Tyres (ELTs) has been increased over the last 15 years. As a major drive, EC Directive 1999/31 on the landfill of waste (1999) banned whole tires and shredded tires from stockpiling. Accordingly, the recovery rate (both material and energy recovery rates) of ELTs increased with a decreasing rate of landfilling in recent years [
4].
The sustainable markets for scrap tires in some countries have been a positive sign for other countries to follow in the processing of their own scrap tires. Also, international organizations and agencies are very supportive of processing scrap tires to be used as secondary raw materials. For example, the Basel Convention developed and adopted the “Technical guidelines for the environmentally sound management of used and waste pneumatic tyres” where the current practice of material and energy recoveries of scrap tires were taken as a favorable way to eliminate and recycle wastes [
2]. The Basel Convention or the Basel Convention on the Control of Transboundary Movements of Hazardous Wastes and Their Disposal is an international treaty that was designed to reduce the movements of hazardous waste between nations, and specifically to prevent transfer of hazardous waste from developed to less developed countries. Also, the World Business Council for Sustainable Development is another international organization that facilitates recovery and recycling of used tires [
6].
Tire Derived Aggregate (TDA) is an engineered product made by cutting scrap tires into 25 mm (1 inch) to 305 mm (12 inch) pieces [
7]. Typically, TDA is used in civil engineering applications as lightweight aggregates. The term, TDA, emphasizes the value of this product as a construction material, which cannot be conceived in general terms such as tire chips or tire shreds. As a general guideline, ASTM D 6270 “Standard Practice for Use of Scrap Tires in Civil Engineering Applications” [
8] has been widely used in TDA applications.
In civil engineering applications, the primary benefit of TDA is lightweight. The dry density of compacted TDA is 1/3 – 1/2 of the dry density of compacted soil. Even after TDA is compressed under the self-weight and extra weight of overlying fill, the unit weight of TDA ranges 4.71 – 6.92 kN/m
3 [
9]. TDA is also highly permeable with thermal insulation capacity. Compressibility of TDA can be used to reduce excessive pressure applied to pipes in trenches, buried culvert walls, and abutment walls of an integral abutment [
10,
11]. In early applications, tire chips and tire shreds were used as lightweight fill in highway construction [
12–
16]. Lately, application areas were expanded including subgrade and embankment fill [
17–
20]; backfill for retaining walls and bridge abutments [
21–
24]; subgrade insulation for roads [
25,
26]; vibration damping layer below rail lines [
27]; daily cover and drainage for landfills [
28,
29]; and drain fields for septic systems [
30,
31].
In backfill applications for retaining walls, due to the lightweight of TDA, it was postulated that a less expensive retaining wall could be used with TDA backfill under gravity loading [
32]. Under seismic loading, TDA backfill was expected to reduce dynamic pressure exerted on a retaining wall as well as inertia force of the backfill. In a recent study [
33], a full-scale shake table test of a retaining wall with TDA backfill was conducted to acquire a better understanding of its seismic performance. The retaining wall was Caltrans (California Department of Transportation) Type 1SW and it was 2.21 m high including the height of the stem and footing. The backfill of the wall consisted of a bottom soil layer, a TDA layer, and a soil layer at the top, of which the thicknesses were 1.066 m, 1.236 m and 0.821 m, respectively.
The shake table test and accompanying Finite Element Analysis (FEA) showed that TDA is a suitable alternative backfill material for retaining walls because the peak and residual wall displacements were small and the TDA backfill experienced no failure but substantial shear deformation. The dynamic behavior of a retaining wall with TDA backfill was found different from one with conventional soil backfill. In a previously conducted shake table test of a similar wall with conventional soil backfill, an active failure plane was formed in the backfill connecting the corner of the heel of a footing to the first surface crack [
34]. Overall, the top soil layer over the TDA layer vigorously vibrated because the dense, stiff soil sat on the flexible TDA layer. This raft effect increased as the intensity of the excitation increased. The residual displacements of the wall with TDA backfill were greater than those from the wall with soil backfill under small intensity excitations. As the intensity of an excitation increased (150% and 200% of the Northridge earthquake), the residual wall displacements from both TDA backfill and soil backfill became similar.
The objective of the present study is to numerically investigate the seismic behavior of TDA backfill used in field-scale retaining walls. In the previous research, the size of a retaining wall was small (2.21 m high) since it was limited to the size of an available soil box and the capacity of the shake table. In the present study, nonlinear time-history FEA is used to investigate the dynamic behavior of TDA backfill under earthquakes when the height of a wall is close to a field-scale, i.e., 6.10 m. As the height of a retaining wall increases, the weights of both wall and backfill increase accordingly. The frictional resistance increases due to greater normal force on the one hand; on the other hand, inertia force as well as dynamic pressure on the wall increases. From the nonlinear time history FEA, benefits and shortcomings of TDA backfill used with a moderately high retaining wall can be better understood.
FEA modeling and analysis
The retaining wall used in the present study is Caltrans Type 1 with a height of 6.10 m. Fig. 1 shows the typical cross-section of the wall. The footing is 4.04 m wide, and the stem is battered: the thickness changes from 0.29 m at the top to 0.55 m at the bottom. The optional key at the bottom of the footing is ignored and the minimum thickness (0.61 m) soil is placed over the toe of the wall in the modeling. In the 2004 California Bridge Design Specifications [
36], seismic forces applied shall be based on a horizontal seismic acceleration coefficient,
k h, equal to 1/3 of
A, the expected peak acceleration produced by the Maximum Credible Earthquake on bedrock at the site as defined in the Caltrans Seismic Hazard Map [
37]. For the subject retaining wall,
k h=0.2 was used in the seismic design.
For the nonlinear time-history analysis herein, the general FEA software, ABAQUS, is adopted. Two models are developed for comparison purpose: soil-backfill model and TDA-backfill model. The domain of analysis consists of two identical retaining walls at both ends, a bottom soil layer under the walls and backfill between the two walls as shown in Fig. 2. The thickness of the bottom soil layer is 6.10 m, and the width of the backfill is 18.3 m. The bottom soil layer is enclosed by a rigid foundation and rigid boundary walls that transfer seismic acceleration applied at the rigid bodies to the soil. Between the bottom soil layer and the rigid walls, viscous damping components are inserted. In the TDA-backfill case (Fig. 2(b)), the thickness of the TDA layer is 3.06 m and the soil layer is placed over the TDA layer. The TDA material is wrapped with geotextile fabric following the typical construction practice [
8]. The figure also shows different parts of the backfill and the soil in front of the toe that are separately modeled and loaded in order to represent the common construction sequence.
Materials
For the soil material model, the mass density is 2028 kg/m 3, and the Poisson’s ratio is 0.3 with an isotopic hardening model with the Mohr-Coulomb failure criterion. The isotropic hardening model is developed based on the tri-axial soil test results. Fig. 3 shows the tri-axial test results of the soil. The averaged maximum strain of three representative specimens under difference confining pressures is 12%. The elastic limit is assumed to be 1.2% strain that corresponds to 10% of the maximum value. The elastic modulus of the soil changes as the deviator stress increases. The secant stiffness from three different strain values is given in the figure. In the FEA, however, a fixed value of 30 MPa is used for the elastic stiffness of the soil. This stiffness matches well with the secant stiffness in the elastic range for a confining pressure of 45 kPa which is closer to the soil pressure at the average backfill height for the soil-backfill model.
The soil hardening is modeled following a cohesion-based model that is built based on the tri-axial test results. When the elastic limit of the soil is determined as 1.2% strain (10% of the maximum strain) from the tri-axial test, the three points on the stress-strain curves (Fig. 3) determined a yield surface, which is the bottom solid line in Fig. 4(a). The friction angle is 39° and the cohesion intercept is 13.69 kPa. Then, three points on the stress-strain curves having 1.77% strain (15% of the maximum strain) in Fig. 3 are selected, and a line from the three points can be drawn in Fig. 4(a). If a fixed value of 39° is used for the friction angle, the cohesion intercept becomes 22.22 kPa for 1.77% strain. After repeating the same procedure for 20%, 25%, and 30% of the maximum strain, three more lines are identified in Fig. 4(a). The solid line in Fig. 4(b) shows the cohesion hardening model used in the analysis, which follows the assumed isotropic hardening rule. The adopted model does not consider softening effects observed in the tri-axial test shown by a dotted line in Fig. 4(b). The softening effects can be captured with a more sophisticated plasticity model, but that was not considered in the present study due to the lack of loading-unloading-reloading test results.
The material properties of TDA are mainly based on the data provided in a recent study [
9], where material properties of large-size TDA are summarized. In the implemented model, the mass density of TDA is 741 kg/m
3, and the Poisson’s ratio is 0.28. The TDA stiffness is assumed to be 500 kPa following the overbuild chart in [
38]. For the inelastic behavior, TDA is assumed to be a continuum that follows the Mohr-Coulomb failure criterion: the friction angle is 22.2° and the cohesion intercept is 13.3 kPa [
9]. From the conducted simple shear test of TDA, the measured dilation angle is 5.19° [
39]. For the TDA material, an elasto-perfectly-plastic model without hardening is used since there are not enough experimental results currently available to create a reasonable hardening model for large-size TDA material.
Finite element mesh and interface modeling
For the soil, TDA, and retaining walls, 4-node bilinear plane strain quadrilateral elements (CPE4R) with reduced integration and hourglass control are adopted. For the geotextile fabrics, 2-D truss elements (T2D2) are used with a cross-sectional area of 0.002 m 2. For the rigid foundation and rigid boundary walls, analytical rigid body elements are used. The FEA mesh size is 40 mm for the soil, TDA, and geotextile fabrics. The mesh size for the retaining walls is 80 mm.
The interface between different components in the retaining system is modeled by boundary interaction. A boundary interaction defines the mechanical properties of friction, damping, contact, or a combination of them. Where the backfill soil is divided into several parts to consider construction sequence, the “Rough” interface model provides continuous stress transfer through the interface. A 5% critical damping is employed for the retaining walls, backfill materials, and foundation soil. In particular, a contact model with over-closure is used between the retaining walls and the top soil layer in order to consider the impact effects between the two. For other interfaces, a static-kinetic friction model is mostly adopted. Between the bottom of the wall footing and the foundation soil, a static friction coefficient is assumed to be 0.78 (0.9 times tan 40.8°) and a kinetic friction coefficient is assumed to be 0.62 (80% of 0.78) with an exponential decay form of friction coefficient. From direct shear tests, the effective friction angle of the soil was 40.8°, which is slightly different from 39° measured from the tri-axial test.
Loadings
The self-weight of the walls, soil, and TDA are sequentially loaded before the application of earthquake load. In the dynamic analysis, acceleration time histories are applied to the rigid foundation and rigid boundary walls. In the present study, two strong motion records, the Northridge earthquake and the Takatori (Kobe) earthquake, were downloaded from the PEER Strong Motion Database. Table 1 shows the characteristics of each record, and Fig. 5 shows the acceleration time history of each.
In addition, the relative intensity of the two earthquakes is compared in the absolute acceleration response spectra in Figure 6. The Northridge earthquake shows a high peak in 0.2 – 0.3 seconds, and the Takatori earthquake has several peaks spread in 0.3 – 1.6 seconds.
Model Verification
To verify the FEA model developed in the present study, previous shake table test results [
33] are extracted for comparison. A retaining structure was built in a large soil box containing a full-scale retaining wall and TDA backfill as shown in Fig. 7. The retaining wall was 2.21 m high including the footing, and the footing was 2.36 m wide. The soil box was excited on a shake table, and displacement, acceleration, and pressure of the retaining wall and backfill were measured under various seismic events. The FEA models of this specimen were developed based on the same approach described in the previous sections. The models regenerated measured wall displacement with a reasonable accuracy.
In Fig. 8, the measured displacements at the top of the retaining wall stem are compared with the FEA results under the Northridge earthquake and the Takatori earthquake. The measured displacement shows that the sliding of the wall occurred at peak displacements, and the FEA model successfully captures the wall sliding. At peak displacements, the wall slid when the frictional resistance became less than the sum of lateral force and inertia effects of the wall and the backfill. Since the wall was short and stocky, the wall underwent rigid rotation rather than stem bending, which caused an uplift at the heel of the footing. The uplift reduced a contact area for frictional resistance and induced stress concentration to the soil under the toe part of the footing. For the FEA model, the uplift makes analysis results sensitive to soil plasticity model and friction model because the wall motion depends on a smaller interface area. More accurate modeling technique for the interaction between the soil plasticity and friction is demanding, and the lack of capability to model this interaction in the FEA model can be the major reason for slightly different wall displacements in Fig. 8.
For the retaining walls used in the present paper, it is anticipated that accurate interaction modeling is not critical. The translational movement of retaining walls is prevented by the soil in front of the toe instead of the friction resistance of the footing. The influence from the interaction to the wall motion will be minor.
Analysis results
The dynamic response of retaining systems having 6.10 m high retaining walls and different types of backfill is analyzed by an explicit time integration procedure in ABAQUS. The analysis results of the TDA-backfill model are compared with those of the conventional soil-backfill model in order to understand the differences in plastic strain, wall movement, and backfill responses.
Principal plastic strain in the backfill
Fig. 9 shows the principal plastic strain developed in the two models under the Northridge earthquake. For both models, black regions indicate where the plastic strain is equal to or greater than 3%. Therefore, if failure surfaces are formed in soil, they will match with the black regions. In the soil-backfill model, regions of large plastic strain (regions “S-a” and “S-b”) are formed over the toe of both footings. The shear failure over the toe is caused by the upward movement of the toe, and the failure of the foundation soil under the toe is generated by the downward movement of the toe. These types of failure due to the rotation of the footing are commonly observed at both walls of the two models. For the TDA-backfill model, region “T-a” shows passive failure in the soil over the toe of the left wall. There is no noticeable region of large plastic strain in the backfill of the soil-backfill model and in the top soil layer over the TDA layer of the TDA-backfill model. Regions of large plastic strain (region “T-c”) are formed in the TDA layer, but failure surface may not be formed since TDA allows large shear deformation. From the direct shear test, it was reported that TDA could sustain more than 3% of plastic strain without compromising its load carrying capacity [
39].
Fig. 10 shows the principal plastic strain developed in the two models under the Takatori earthquake. Overall, the regions of large plastic strain are extensive and substantial for both models. In the soil over the toe and next to the toe, regions “S-a” and “S-b” in Fig. 10(a) and regions “T-a” and “T-b” in Fig. 10(b) imply excessive damage due to shear failure and compression failure caused by upward and downward movement of the toe for both models. Also, soil heaving adjacent to the wall, friction failure at the interface between the footing and the foundation soil, and passive soil failure can be found for both models. In the soil under the heel of the footings in the soil-backfill model, regions “S-c” and “S-d” show compressive failure due to downward movement of the heel; whereas, such failure cannot be seen in the TDA-backfill model.
The major difference in the regions of large plastic strain between the two models can be observed in the backfill. In region “S-e” of the soil-backfill model, there can be significant active and passive soil failures combined with shear failure due to upward movement of the heel. In regions “T-c” and “T-d” of the TDA-backfill model, the regions of large plastic strain are developed mainly in the TDA layer; specifically, along the line connecting the tip of the heel and the corner of the TDA layer at the interface with the wall. This damage occurs as the heel moves upward due to wall rotation since the stiffness of the TDA is much smaller than the soil. More significant wall rotation can be developed in the TDA layer. Additionally, large plastic strain regions (region “T-e”) can be found at the interface area between the TDA layer and the soil layer below. Due to the significant damage made in the backfill, the soil heaves on the surface in the soil-backfill model. In the TDA-backfill model, damage is minor in the top soil layer over the TDA layer.
Wall displacement
Fig. 11 shows the displacement time history of the walls at the top of the stem for both models under the Northridge earthquake. For both models, the overall motions of the left wall and the right wall are similar. When the excitation is severe, the displacements of the two walls get different: the wall against the motion of the backfill usually experiences more displacement than the other wall. For the soil-backfill model, the absolute maximum wall displacement is 56 mm and 47 mm for the left and right wall, respectively. At the end of the excitation, the two walls are separated about 39 mm more due to the residual deformation made in supporting soil. For the TDA-backfill model, the absolute maximum wall displacement is 96 mm and 46 mm for the left and right wall, respectively. The separation made by residual deformation in supporting soil and TDA is 38 mm. The retaining walls in the TDA-backfill model bend and rotate more than those in the soil-backfill model, which results in larger maximum wall displacements. However, the amount of wall sliding is comparable between the two models, which is observed by the similar residual displacements. Moreover, the walls in the soil-backfill model vibrates with higher frequencies than the walls in the TDA-backfill model, specifically at t= 5 – 15 seconds. This indicates that the TDA backfill essentially changes the dynamic characteristics of the entire retaining structure.
Fig. 12 shows the displacement time history of the walls at the top of the stem under the Takatori earthquake. Compared to the responses under the Northridge earthquake, both walls in the two models experience substantially large maximum displacement. For the soil-backfill model, the maximum displacement is 112 mm and 93 mm for the left and the right wall, respectively. The maximum displacement from the TDA-backfill model is 426 mm and 499 mm for the left and the right wall, respectively. The extra separation between the two walls is 72 mm and 269 mm for the soil-backfill and the TDA-backfill models, respectively, at the end of the excitation due to residual deformation in supporting soil and TDA.
The Takatori earthquake contains significantly large vibration components when the period of a system is 0.5 – 1.5 seconds as seen in Fig. 6. Unlike the Northridge earthquake, the Takatori earthquake excites the retaining system more as the natural periods of the system are closer to the periods having large excitation energy. Among the residual displacement of 30 mm occurred to the right wall in the soil-backfill model, 8 mm (27%) are induced by a permanent translation and 22 mm (73%) are induced by a permanent rotation of the wall. For the right wall of the TDA-backfill model, 69 mm (48%) are from a permanent translation and 75 mm (52%) are from a permanent rotation out of a total residual displacement of 144 mm.
Backfill displacement and acceleration
Figs. 13 and 14 show the displacements and accelerations calculated at several locations along the depth of the retaining system at the plane in the middle of the two walls under the Takatori earthquake. The y-value is the height measure from the bottom of the bottom soil layer (or from the top of the rigid foundation). These locations are indicated in Fig. 2. A point at y= 2.805 m is located in the mid-height of the bottom soil layer for both models. In Figs. 13(b) and 14(b), the point at y= 7.561 m is located in the mid-height of the TDA layer, and the point at y= 10.511 m is located in the mid-height of the top soil layer in the TDA-backfill model. The points at y= 7.580 m and y= 10.460 m in Figs. 13(a) and 14(a) are closest FEA nodes to those points in the soil-backfill model. A point at y= 11.900 m in the soil-backfill model and a point at y= 11.899 m in the TDA-backfill model are on the surface of the backfill.
For the soil-backfill model in Fig. 13(a), the displacement histories at three locations with different heights, y= 7.580 m, 10.460 m, and 11.900 m, show similar patterns and the maximum displacements of the three histories are not much different. For example, the displacements are −66 mm, −77 mm, and −79 mm at those three locations at t= 8.325 seconds, and they are −82 mm, −71 mm, and −73 mm at t= 9.450 seconds. There are not much significant differences in the displacement along the height of the backfill in the soil-backfill model.
However, for the TDA-backfill model in Fig. 13(b), the displacement histories at three locations, y= 7.651 m, 10.511 m, and 11.899 m, indicate changes in their magnitudes as the earthquake excitation propagates from the TDA layer to the top soil layer. For example, the maximum displacement are 201 mm, 305 mm, and 296 mm at those three locations at t= 9.225 seconds. Substantially large displacements at the mid-height of the top soil layer and on the surface can be noticed.
The acceleration time histories at different heights of the backfill from the soil-backfill model are shown in Fig. 14(a). As excitation acceleration at y= 2.805 m (mid-height of the bottom soil) propagates to the surface of the backfill, the maximum acceleration increases from 1.5 g ( y= 7.580 m) to 1.9 g ( y= 10.460 m) and to 2.1 g ( y= 11.900 m) with phase shifting. However, for the TDA-backfill model as shown in Fig. 14(b), the maximum acceleration decreases from 2.3 g ( y= 2.805 m) to 1.2 g ( y= 7.651 m) and to 1.0 g ( y=10.511 m). At the top surface, the maximum acceleration is 0.9g. Under the Takatori earthquake, the top surface of the backfill in the TDA-backfill model experiences much less acceleration, but the displacements are substantially greater than the soil-backfill model. The overall backfill behavior is similar to the base-isolation concept that changes the natural period of a system in order to take less amount of energy but allow more displacement. This also implies a possibility of controlling the dynamic behavior of a backfill by changing the thickness of the TDA layer and the soil layer in the TDA-backfill model.
Discussion on dynamic responses
In general, under the Northridge earthquake, the TDA-backfill model performs well as does the soil-backfill model although the dynamic characteristics has been changed in the TDA-backfill model due to the flexibility of the TDA layer. The regions of large plastic strain formed in the TDA layer are moderate, and there is no region of large plastic strain in the top soil layer close to the surface that will be directly related to the serviceability of a retaining structure after a seismic event.
Under the Takatori earthquake, regions of large plastic strain in the TDA-backfill model are mainly formed in the TDA layer, and there is no such region developed in the top soil layer unlike the soil-backfill model. In the top soil layer, the damage presumed by the large plastic strain is moderate, which indicates the top soil layer can safely support a riding surface or a structure built on it. The Takatori earthquake developed substantially large displacement in both retaining walls. Also, the displacement in the backfill is large likewise. Therefore, large movement should be allowed in the backfill and for the walls if TDA backfill is adopted. Residual deformation can develop a gap between the wall and the top soil layer. In practice, the gap can be filled with soil after the seismic event since there is no significant damage in the top soil layer, and the TDA layer sufficiently supports the top soil layer although it experiences large deformation.
Conclusions
TDA is a recycled construction material produced by cutting scrap tires into small pieces. TDA has been successfully used in various civil engineering applications including backfill of retaining walls and bridge abutments. In the present study, the seismic behavior of TDA backfill used with 6.10 m high retaining walls is investigated based on nonlinear time-history FEA. The material models and interface models used in the FEA models have been verified based on the shake table tests that the authors previously performed. Dynamic responses are calculated from two FEA models: the soil-backfill model and the TDA-backfill model. Plastic strain, wall displacement, and backfill displacement and acceleration under the Northridge earthquake and the Takatori earthquake are compared.
The TDA-backfill model performed well with only moderate plastic deformation in TDA material under the Northridge earthquake. Under the Takatori earthquake, the TDA-backfill model experienced substantially larger displacement in the retaining walls and in the backfill compared with the soil-backfill model. Regions of large plastic strain were mainly formed in the TDA layer, and the top soil layer did not experience such large plastic strain. In the top soil layer, the damage presumed by the large plastic strain was much less significant than that from the soil-backfill model, which suggested that a riding surface or a structure built on the backfill surface be safer. As a main benefit of TDA-backfill, the acceleration on the surface of the backfill decreased substantially. When acceleration sensitive objects and structures are placed on the surface of the backfill, TDA-backfill may induce less damage to them.
The observed benefits and shortcomings of TDA-backfill need to be verified by additional numerical analyses. Those analyses should include different retaining wall heights, various backfill widths, and other earthquake strong motion records. In addition, more material tests are required to understand the dynamic characteristics of TDA material. Since strength and stiffness of TDA depend on the unit weight of TDA and applied vertical stress, large-scale direct shear and simple shear tests involving a wide range of vertical stress need to be conducted. Failure criteria and strain-hardening (softening) models for TDA can be improved based on these test results.
PDF
(2899KB)
