Behavior of Rigid-Soft Particle Mixtures
Jong-Sub Lee, Jake Dodds, and J. Carlos Santamarina,
Abstract: Mixtures of rigid sand particles and soft fine-grained rubber particles are tested to investigate their small and large-strain responses. Mixtures are prepared with different volumetric sand fraction sf to identify the transition from a rigid to a soft granular skeleton using wave propagation, k0 loading, and triaxial testing. Deformation moduli at small, middle, and large strains do not change linearly with the volume fraction of rigid particles; instead, deformation moduli increase dramatically when the sand fraction exceeds a threshold value between sf=0.6 — 0.8 that marks the formation of a percolating network of stiff particles. The friction angle increases with the volume fraction of rigid particles. Conversely, the axial strain at peak strength increases with the content of soft particles, and no apparent peak strength is observed in specimens with low sand fraction (sf0.6). The presence of soft particles alters the formation of force chains. Although soft particles are not part of high-load carrying chains, they play the important role of preventing the buckling of stiff particle chains.
Introduction
The number of disposed tires in the United States exceeds 500 million per year. Therefore, there is a very large stock of rubber particles from recycled tires. Previous studies gave explored their use in soil mixtures for highway construction, lightweight backfills, and highway embankments (Ahmed and Lovell 1993; Bosscher et al.1997; Lee et al. 1999; Garga and O’Shaughnessy 2000; Feng and Sutter 2000; Zornberg et al. 2004). Typically, these studies involve rubber particles larger than sand particles (Drubber/Dsand≈5-10). It has been reported that the addition of rubber particles to sand causes a decrease in permeability, a reduction in the minimum void ratio but an increase in the maximum void ratio, a decrease in stiffness, and a reduction in friction angle (Masad et al. 1966; Feng and Stutter 2000). When used as backfill material in retaining walls, the tire shred settles more and produces less horizontal pressure than gravel backfill (Lee et al. 1999).
Two mechanisms are involved in the deformation of granular materials: Distortion of individual particles and relative motion between particles as the result of sliding or rolling (Lambe and Whitman 1979). These are seldom independent of one another: A small particle distortion allows particles to move past one another and may cause a previously stable chain of particles to collapse.
Chains made of “primary” particles carry most of the load transferred through granular materials; the role of “secondary” particles is to prevent the buckling of these chains (Radjai et al. 1998). Because rubber particles have much lower stiffness than mineral sand particles may show surprising performance due to the different roles particles may assume, as either load carriers or buckling preventers.
The purpose of this study is to explore particle-level mechanisms that are responsible for the macro scale small-to-large strain behavior of rigid-soft granular mixtures, for the special case where Drubber<Dsand [a complementary study for Drubber>Dsand is presented by Kim (2005)]. The choice of Drubber<Dsand reflects our interest to explore particle-level pore filling and chain distortion effects rather than relative stiffness and arching effects that develop when Drubber≥Dsand.
Mixtures are tested in oedometer and triaxial devices; shear wave velocity is measured during k0 loading in the oedometer cell. From these measurements, the evolution of elastic modulus (strain ～10-2, constrained modulus (strain～10-2-10-4) and small-strain shear modulus (strain≤10-6) are investigated at different stress levels and for different sand volume fractions. Test procedures and results follow.
Experimental study
Conclusions and Recommendations
The load-deformation behavior of rigid-soft granular mixtures is studied using specimens prepared with uniform sand and small rubber particles (Dsand/Drubber≈4) at different volume fractions. The main observations from this study follow:
Small-,middle-, and large-strain deformation moduli are not linear functions of the volume fraction of rigid particles, a threshold volume fraction separates soft from rigid skeleton conditions. The threshold volume fraction is confining stress dependent.
In transition mixtures, the coordination among stiff particles increases with confinement so that the mixture behaves rubber-like at low confinement and sand-like at high confinement. The highest value of the b exponent in Gmax=A(σ´0/kPa)b is observed for sf≈0.6and it reflects the high increase in coordination number among stiff particles during this transition.
The friction angle increases with sand fraction and no peak strength is apparent in specimens with low sand fraction(sf≤0.6).
In most cases, load carrying particle chains do not involve soft particles. However, soft particles do participate in preventing the buckling of load carrying chains.
Acknowledgments
This study is part of a research initiative on engineered soils and was supported by Vulcan Materials and other Georgia mining companies, the Goizueta Foundation, and the National Science Foundation.
Trends in Gmax can be further analyzed by recognizing that the small strain shear stiffness Gmax is a “measure of state” (constant fabric measurement), which is controlled by the nature of interparticle contacts and interparticle coordination. The effective stress governs the shear stiffness Gmax of uncemented particulate materials when capillary effects are negligible, as predicted by the semiempirical power relation
Gmax=ρV2S=A(σ0/kPa)b (1)
Whereσ´0 =average effective stress on the polarization plane; A and b=experimentally determined parameters; and ρ is the mass density. The A factor is the value of Gmax when σ´0=1 kPa and it is related to packing (porosity and coordination number which is the average number of contacts per particle0, the properties of the particles, contact behavior, and fabric changes; the A factor is low for rubber-like mixtures, and high for sand-like mixtures[Fig.10(b)].
The b exponent captures the sensitivity of Gmax to stress changes. General guidelines for b values are: b≈0 for ideal solid or a cemented soil; b=1/3 for Hertzian contact; b=0.33-0.40 for rounded and dense sands;b≈0.5 for loose or angular sands; and b≥0.6 for soft clays. As the shear wave velocity is measured at different stress states, the b exponent reflects not only contact behavior but fabric changes as well (Santa marina et al. 2001). These guidelines help analyze the evolution of the b exponent with sand fraction: rubber-like mixtures (sf <0.5) resemble soft systems such as clays, sand-like mixtures (sf>0.7)are like sand (b→0.5), and the transition mixture experiences a large increase in sand-to-sand coordination that causes a very high b value (b～1.0).the observed behavior is summarized in Fig.11. photo elasticity is used to gain further insight into the interaction between small-soft and large-stiff particles, and the role of this interaction in force propagation and stiffness. Rigid particles are modeled with 12.6 mm diameter stiff photo elastic disks, whereas soft particles are represented b 9.3 mm rubber cylinders. Both particle types are 12.6 mm thick. A typical force percolation chain observed in photo elastic studies is shown in Fig12(volumetric rigid particle fraction is ～0.8). the rubber particles are generally not members of primary force chains; in fact, the prevalence of force chains and the amount of load each chain carries depends on the number of viable rigid particle paths. When there are few viable rigid particle paths, the resulting force chains carry high load. Soft particles often play the secondary yet important role of preventing the buckling of stiff particle chains.
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Conclusions and Recommendations
2007-06-05 19:19:05
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Trends in Gmax can be further analyzed by recognizing that the small strain shear stiffness Gmax is a “measure of state” (constant fabric measurement), which is controlled by the nature of interparticle contacts and interparticle coordination. The effective stress governs the shear stiffness Gmax of uncemented particulate materials when capillary effects are negligible, as predicted by the semiempirical power relation
2007-06-05 19:19:05
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加载更多The load-deformation behavior of rigid-soft granular mixtures is studied using specimens prepared with uniform sand and small rubber particles (Dsand/Drubber≈4) at different volume fractions. The main observations from this study follow:
Small-,middle-, and large-strain deformation moduli are not linear functions of the volume fraction of rigid particles, a threshold volume fraction separates soft from rigid skeleton conditions. The threshold volume fraction is confining stress dependent.
In transition mixtures, the coordination among stiff particles increases with confinement so that the mixture behaves rubber-like at low confinement and sand-like at high confinement. The highest value of the b exponent in Gmax=A(σ´0/kPa)b is observed for sf≈0.6and it reflects the high increase in coordination number among stiff particles during this transition.
The friction angle increases with sand fraction and no peak strength is apparent in specimens with low sand fraction(sf≤0.6).
In most cases, load carrying particle chains do not involve soft particles. However, soft particles do participate in preventing the buckling of load carrying chains.
Acknowledgments
This study is part of a research initiative on engineered soils and was supported by Vulcan Materials and other Georgia mining companies, the Goizueta Foundation, and the National Science Foundation.
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Gmax=ρV2S=A(σ0/kPa)b (1)
Whereσ´0 =average effective stress on the polarization plane; A and b=experimentally determined parameters; and ρ is the mass density. The A factor is the value of Gmax when σ´0=1 kPa and it is related to packing (porosity and coordination number which is the average number of contacts per particle0, the properties of the particles, contact behavior, and fabric changes; the A factor is low for rubber-like mixtures, and high for sand-like mixtures[Fig.10(b)].
The b exponent captures the sensitivity of Gmax to stress changes. General guidelines for b values are: b≈0 for ideal solid or a cemented soil; b=1/3 for Hertzian contact; b=0.33-0.40 for rounded and dense sands;b≈0.5 for loose or angular sands; and b≥0.6 for soft clays. As the shear wave velocity is measured at different stress states, the b exponent reflects not only contact behavior but fabric changes as well (Santa marina et al. 2001). These guidelines help analyze the evolution of the b exponent with sand fraction: rubber-like mixtures (sf <0.5) resemble soft systems such as clays, sand-like mixtures (sf>0.7)are like sand (b→0.5), and the transition mixture experiences a large increase in sand-to-sand coordination that causes a very high b value (b～1.0).the observed behavior is summarized in Fig.11. photo elasticity is used to gain further insight into the interaction between small-soft and large-stiff particles, and the role of this interaction in force propagation and stiffness. Rigid particles are modeled with 12.6 mm diameter stiff photo elastic disks, whereas soft particles are represented b 9.3 mm rubber cylinders. Both particle types are 12.6 mm thick. A typical force percolation chain observed in photo elastic studies is shown in Fig12(volumetric rigid particle fraction is ～0.8). the rubber particles are generally not members of primary force chains; in fact, the prevalence of force chains and the amount of load each chain carries depends on the number of viable rigid particle paths. When there are few viable rigid particle paths, the resulting force chains carry high load. Soft particles often play the secondary yet important role of preventing the buckling of stiff particle chains.
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