Dynamic Properties of Clean Sand Modified with Granulated Rubber

Waste automobile tires are used as additives or replacements instead of traditional materials in civil engineering works. In geotechnical engineering, tires are shredded to certain sizes and mixed with soil, especially used as backfill material behind retaining walls or fill material for roadway embankments. Compared to soil, rubber has high damping capacity and low shear modulus. ,erefore, it requires the determination of the dynamic characteristics of rubber/soil mixtures. In this paper, the cyclic behavior of recycled tire rubber and clean sand was studied, considering the effects of the amount and particle size of the rubber and confining stresses. A total of 40 stress-controlled tests were performed on an integrated resonant column and dynamic torsional shear system. ,e effects of the relative size and proportion of the rubber on the dynamic characteristics of the mixtures are discussed.,e dynamic properties, such as the maximum shearmodulus, strain-dependent shear modulus, and damping ratio, are examined. For practical purposes, simple empirical relationships were formulated to estimate the maximum shear modulus and the damping ratio. ,e change in the shear modulus and damping ratio with respect to shear strain with 5% of rubber within the mixture was found to be close to the behavior of clean sand.


Introduction
In civil engineering practice, the use of automobile tire waste has gained wide popularity in various applications in the last three decades.It is used as additives or replacements for conventional materials in construction work.Regulations such as ASTM D6720-98 have standardized the use of waste tire for the classification [1].Standardization of waste tire is done according to the disintegration method and the size of the disintegrated product during the recycling process.Waste automobile tires are generally cut up into small pieces of different sizes and mixed with structural materials in some predetermined proportions in order to achieve the desired engineering properties.In transportation engineering, waste tires have been used as asphalt binder modifiers and asphalt mixture additives in gap-graded or open-graded asphalt mixtures and surface treatments.Also, it has been reported that adding recycled tire to asphalt provides increased rutting resistance, friction resistance, ride quality, extended pavement life, and reduced noise and vibration levels [2,3].
Due to the low cost of application, waste tires are preferred in geotechnical engineering projects as well.After some shredding processes, they can be used alone, embedded, or mixed with soils.e geotechnical use of waste tire-soil mixtures is mainly preferred within transportation infrastructures or in vibration damping systems to reduce vibrations, such as on railroad subgrades or machine foundations.Other geotechnical applications have been reported as embankment fills, retaining walls and bridge abutment backfills, insulation layers to limit frost penetration, and drainage layers.Sometimes whole tires are used as retaining walls or reinforcement layers in an earth-fill or floating breakwater [4][5][6].
Extensive studies on the behavior of recycled tire/soil mixtures have been conducted over the last few decades.
ese studies are usually based on the evaluation of conventional engineering properties such as compaction characteristics, permeability, and shear strength parameters where the tire/soil mixtures are mostly considered under static loading conditions.Investigations of the dynamic characteristics of recycled tire/soil mixtures are rather limited and new.
In terms of physical properties, tire rubber structure is quite different from the soil fabric.e damping capacity of tire rubber is much higher because of its high elasticity as compared to soil.erefore, tire rubber exhibits much more elastic deformation than the soil.Its stress-strain curve is almost reversible when the stress is released, and its Young's modulus and shear strength are extremely low as compared to soil.e presence of such differences in their physical properties makes the behavior of the new composite material quite complicated.erefore, understanding the behavior of recycled tire-soil mixtures under cyclic loads is essential in determining the factors and parameters to be used in the design.e purpose of this work was to understand the controlling factors responsible for the dynamic behavior of recycled tire/soil mixtures of varying proportions by conducting cyclic tests under different cyclic shear amplitudes.
e variations of the dynamic soil parameters, such as maximum shear modulus (the value of the shear modulus at a very small strain, c ≈ 5 × 10 −4 %), strain-dependent shear modulus, and damping ratio, were investigated.e effects of the particle size and the amount of recycled tire in the mixtures were also examined.e test results were compared with similar studies in the literature.For reference purposes, some relationships are also proposed regarding the shear modulus and the damping ratio.

Materials and Methods
e synthetic material used in the study was "waste tire," but for convenience, it will be referred to as "rubber" henceforth.Chipped rubber obtained from recycled tires was processed through a series of mechanical shredding operations.After the grinding process, the material was sieved and separated into three different uniform sizes.e specific gravity of the pure crumb rubber (free from fabric and wire) was calculated using the ASTM D854 [14], specification as G S � 1.11.It is important to note that the thermal expansion capacity of the crumb rubber was much higher than that of the soil grains; therefore, specific gravity can vary depending on the ambient temperature.Typical results from studies reported the specific gravity of crumb rubber between 1.00 and 1.30 depending on the amount of contamination or fabric content [15][16][17].e chipped rubber particles were coded according to their sizes as R#1 fraction between #3/8 and 4 sieve, R#2 fraction between #4 and 10 sieve, and R#3 fraction under #100 sieve (Figure 1).
For the soil material, standard clean sand was used.e mean diameter of the quartz-rich sand is D 50 � 0.53 mm, uniformity coefficient of C U � 6.3, G S � 2.68, e max � 0.88, and e min � 0.55.Poisson's ratio of rubber is almost 0.5, meaning volumetric compressibility is almost zero and rubber solids can be assumed to be incompressible.e grain size distribution curves of the rubber samples and the sand are shown in Figure 2. e samples were prepared by mixing the chipped tire and sand at different weight ratios.It was reported that the structural matrix created by different techniques of sample preparation could change the cyclic response of sandy soils [18].Hence, if dynamic tests are to be conducted on reconstituted samples, a general routine is to outline the sample preparation technique.Since in situ applications of rubber/soil mixtures are generally constructed above groundwater level, it is apparent that a dry deposition method is considered to best reproduce field conditions.erefore, the dry deposition technique was chosen for sample preparation.e quartz sand was dried out in an oven for 24 hours at 105 °C, and the granular rubber was left at room temperature for 36 hours.e sand and granular rubber were then mixed with a mechanical mixer for 15 minutes in order to generate as homogeneous a mixture as possible.e samples were prepared by pouring the rubber/sand into an aluminum mold 50 mm in diameter and 105 mm in height.To obtain the target densities, the samples were compacted by a wooden hammer.e initial void ratios of the samples with respect to rubber volume are given in Table 1.Advances in Civil Engineering e cyclic loading tests were carried out by using an integrated resonant column/cyclic torsional shear test.e resonant column (RC) test is based on the theory of the wave propagation of prismatic bars.e test data analysis followed that was described in detail by Drnevich [19] and used Standard ASTM D4015 [20].
Harmonic torsional excitation was applied to the top of the specimen by an electric motor.A torsional harmonic load with constant amplitude was applied over a range of frequencies, and the response curve (strain amplitude) was measured (Figure 3).e shear wave velocity was obtained by measuring the rst-mode resonant frequency.e maximum shear modulus was calculated from this shear wave velocity and the soil density.Material damping obtained from the free-vibration decay after the forced vibration was stopped.After the determination of the maximum shear modulus and the minimum damping ratio, the cyclic torsional harmonic load amplitude was increased to obtain the strain-dependent shear modulus and damping values for a wide strain range (10 −4 %-10 0.7 %).

Results
e hysteretic nature of the rubber materials of three different sizes is shown in Figure 4.
e cyclic stress-strain behavior of the three di erent sizes of rubber is almost identical irrespective of the dimensions, as expected.Under cyclic loading, the deformation behavior of rubber material is purely elastic and recoverable.is trend is similar to the observed behavior of soils, which does not change with the increase of cycles if the amplitude of cyclic shear strains is on the order of 10 −6 .During the period of cyclic stress application in this stage, the modulus and damping characteristics stay the same.For soils, however, after a certain cyclic shear strain threshold, nonlinear hysteretic behavior is observed.is type of response is seen when the induced shear strain is within the range of 10 −5 and 10 −3 .
In the seismic response analysis, three main essential dynamic characteristics of soil need to be evaluated.e rst one is the maximum shear modulus, G 0 , which can be measured in the order of ∼10 −5 -10 −3 % cyclic strain range.In this strain range, the soil behavior is assumed to be elastic.
e other major parameters are the shear modulus ratio, G/G 0 , and the damping ratio, which are generally used in the nonlinear analysis.In the following, these characteristics will be discussed with respect to the size and amount of rubber in the mixture.
e consolidation process was performed isotropically to a preidenti ed e ective con ning stress of 50, 100, 150, and 200 kPa.In similar studies [21], the time of consolidation was suggested from 30 min to 1 hour (depending on the percentage of rubber) due to the possible axial compression creep of rubber.In this study, 1 hour was allowed to elapse for consolidation in each con ning stress increment regardless of the rubber content.At each stage of con ning stress, the maximum shear modulus and minimum damping ratio values were determined by using the resonant column test.e half power bandwidth method was used to  Advances in Civil Engineering compute damping.Immediately after that, the torsional shear test was conducted to determine strain-dependent dynamic characteristics.e nonlinear cyclic response of soils is generally dened by a simple relationship using the hyperbolic model [22].Cyclic response of soils is strain dependent.In the hyperbolic model, it is assumed that the stress-strain curve of the soil is constrained between two tangent lines for small and large strains, respectively.Figure 5 illustrates these margins.From the gure, the maximum shear modulus, G max , is de ned as the tangent line at a strain value of c < 10 −5 % and the strength of soil τ f which represents the upper boundary is de ned as the tangent line at a strain value of c > 10 −3 %. e stress-strain diagram between these two tangential lines can be expressed by the following equation: where n is chosen arbitrarily.Equation ( 1) can be solved by integrating for the case n 1; to satisfy an initial condition, c 0 when τ f 0: where c r is de ned as the reference strain.It is the value of strain for an elastic material at failure stress and is de ned as e stress-strain curve can be calculated from (2) by placing n 2 as follows: e secant modulus can be determined as follows: where c a is the cyclic shear strain amplitude and G τ a /c a .e maximum shear modulus values were in the range of 60 to 200 MPa.e hyperbolic model was used to predict the strain-dependent characteristics of sand samples.e dots represent the experimental data, and the solid lines represent the numerical results (Figure 6).
As mentioned above, the deformation properties of soil under cyclic loading are greatly nonlinear after a certain threshold strain.Also, due to the elastic nature of the rubber, the exhibited cyclic deformations of rubber/soil mixtures are purely elastic and recoverable as the amount of rubber increases.is is shown by the variation of the shear modulus 4 Advances in Civil Engineering and damping ratio with respect to cyclic shear strain amplitude.In these gures, the shear modulus values normalized to the maximum shear modulus at a strain amplitude of 10 −6 and plotted against the cyclic shear strain.e results of the tests under the con ning stresses of 50, 100, 150, and 200 kPa with the rubber proportions of 5%, 10%, and 15% are presented in Figures 7-9 and summarized in Table 1.To see the e ects of the rubber, the results are superimposed with the results of the clean sand.e clean sand and rubber/sand mixtures are represented by the solid lines and markers, respectively.e degradation of the mixture sti ness is shown in the modulus reduction curves with the progression of cyclic strain.From the gures, it is apparent that the shape of the rubber and the e ective con ning pressure are the major factors a ecting cyclic behavior.
As can be seen in Figure 7(a), the R#1 mixture has a very low sti ness value compared to clean sand.For each mixture type, the degradation response of the shear modulus with increasing rubber content (for 10% and 15%) becomes smaller.
e maximum shear modulus and secant shear modulus decrease with increasing rubber content, and con ning stress decreases almost about half of the values of clean sand.
e degradation in sti ness is more signi cant with an increasing amount of rubber.e rubber sizes of R#1 and R#2 are relatively bigger; therefore, they have larger void ratios as compared to R#3. e shear modulus at a given cell pressure decreases with an increase in the void ratio.For mixtures R#2 and R#3, the shear modulus is almost coincident with the shear modulus of clean sand over the whole strain range for the rubber content of 5%.e shear modulus  Advances in Civil Engineering values were also somewhat higher for both R#2 and R#3 compared to clean sand.
However, for higher rubber content, R#2 and R#3 show practically the same behavior as R#1.For the con ning pressures higher than 50 kPa, this fact can be attributed to the small amount of rubber particles lling the gaps between the sand particles and making the mixture denser, therefore exhibiting greater sti ness.However, a signi cant reduction in sti ness occurs with 10% and 15% of rubber content regardless of the size and shape of the rubber.erefore, adding more than 5% rubber into the mixture does a ect the sti ness, and the mixture then acts as if it were pure rubber.is fact can be observed in the gures that show 15% rubber content because the shear modulus ratio barely changes with the shear strain amplitude at all levels of con ning stresses.
e degradation of the shear modulus with strain falls into a narrow area.Also, the decrease rate in the straindependent shear modulus is smaller in R#1 and R#2 compared to that in R#3. is di erence can be attributed to insu cient coupling between the rubber and the sand particles because of the relatively bigger size of R#1 and R#2, which acts like voids.On the contrary, with a considerably ner particle dimension, R#3 seems to show more resistance to cyclic loading. is fact can be considered as the same reasoning in the reduction of the maximum shear modulus values of the rubber/sand mixtures.e damping characteristics of sand and the rubber/sand mixtures evaluated from the same test groups above are shown in Figures 7(a e R#1 and R#2 mixtures have lower damping ratios than clean sand for the same cyclic strain amplitude.is can be agreed as a result of the void ratio fact as explained in the previous paragraphs.Also, the variation of damping with respect to cyclic shear strain is more correlated with clean sand curves.is correlation is clear for the R#2 and R#3 mixtures at 100 kPa con ning stresses.
e damping ratio of clean sand converges to a value of about 22% when the shear strain approaches 0.2%.e same behavior can be seen with 5% R#2 and R#3. e decreasing trend of the damping ratio with increasing rubber content is also seen in the gures.e damping ratio at failure strain decreases as the rubber content increases.As the con ning stress increases, the reduction rate increases and converges to a value between 15 and 20%.e gures also indicate that there is practically no in uence of sand particles on the strain-dependent damping of mixtures with rubber content higher than 10%.
e damping ratio at failure strain is approximately 50% less than the corresponding damping of sand for R#1 and R#2. e e ect of con ning stress on the strain-dependent damping is negligible.However, the damping at low strains has decreased slightly as the cell pressure increases.Clean sand samples have smaller voids compared to rubber/sand mixtures.Also, the modulus of rubber is lower compared to that of sand in mixtures.For the test data, a relationship was adjusted from [12] to model the decrease rate in shear modulus cyclic strain amplitude using the hyperbolic model [23,24] as where c is the cyclic shear strain amplitude and c ref,mix is the reference strain of the mixture for G/G 0 0.5.Presenting this condition into the equation proposed by Senetakis et al. [12], the reference strain is shown to be related as where c ref,mix is the reference strain for all data sets under all con nement pressures.e constants A c and n c were determined by the regression analysis and are presented in Table 2. c ref,mix,100 is the reference strain of mixtures under 100 kPa con nement given as 6 Advances in Civil Engineering where c ref,sand,100 is the reference strain de ned as a function of 100 kPa con ning pressure of clean sand.e damping ratio shown as f(x c ) is a function of rubber content in the mixtures such as 5, 10, and 15% given in the following equation: where C 1 , C 2 , and C 3 are the constants and the values are presented in Table 3 considering the rubber types in the mixtures.
Based on the results of the tests shown in Figures 7-9, it was possible to adopt a relationship.Another aim of this work is to develop a practical method to evaluate the strain-dependent damping ratio as a function of the dynamic shear modulus ratio  Advances in Civil Engineering in a similar manner of [12].As it is easier, less time-consuming, and less subjected to probable miscalculations, it may be needed to determine the damping ratio based on the dynamic shear modulus.On the basis of the model achieved by the equations, the results are presented with the test data in Figure 7 for R#1. e recommended practical models for the shear modulus and damping ratio increase regarding the strain amplitude show reasonably good t to the experimentally  12).For practical purposes, these relationships can be very useful, but for design purposes, tests are needed on case-speci c materials.

Conclusions
e cyclic behavior of waste tire/sand mixtures was studied in detail based on a set of resonant column and cyclic torsional tests conducted on di erent mixture ratios.e purpose was to con rm the e ecting parameters and to develop semiempirical relationships to determine the cyclic characteristics of rubber/sand mixtures.e maximum shear modulus, minimum damping ratio, strain dependency of shear modulus, and damping of rubber/sand material were evaluated under di erent cell pressures for di erent conditions of packing which were characterized by di erent  Advances in Civil Engineering shapes and sizes of rubber.Unlike clean sand, rubber/sand mixtures have smaller values of shear modulus. is fact can be attributed to the decreasing of strength by the increasing amount of the rubber.From the results of these tests, it can be concluded that the mixtures with 5% rubber show almost the same cyclic stress-strain and damping behavior as clean sand.Additionally, the lower the con ning stress, the higher the degree of similarity to the response of clean sand.e best t was obtained from the con ning stress of 50 kPa and the R#3 material, which was the nest in size.e degradation of the sti ness and increase in damping with decreasing con ning stress are in agreement with the strain-dependent deformation characteristics of soils.
Despite the con ning stresses varying between 50 and 200 kPa, there was almost no e ect of the con ning stress on the strain-dependent damping behavior of the mixtures with 10% and 15% rubber.is tendency is the opposite behavior of soil.In comparing the minimum damping ratio at a shear strain of 5 × 10 −4 %, the damping ratio increases with rubber content irrespective of rubber size.

Figure 1 :
Figure 1: Granular rubber material used in the study. 2

Figure 2
Figure 2: e grain size distribution curves of the rubber and sand.

Figure 3 :
Figure 3: Schematic diagram of the resonant column/torsional shear system.

Figure 4 :Figure 5 :
Figure 4: Typical cyclic stress-stain behavior of rubber materials used in the study.

Figure 6 :
Figure 6: (a) Shear modulus versus shear strain amplitude for clean sand.(b) Damping ratio versus shear strain amplitude for clean sand.

Figure 12 :
Figure 12: Relationship between shear modulus and damping ratio for 15% rubber content.

Table 1 :
Summary of parameters of dynamic tests.

Table 3 :
A c and n c constants determined by the regression analysis.

Table 2 :
C 1 , C 2 , and C 3 constants determined by the regression analysis.