我毕业设计要的，那个帮我翻译一下啊！文章是美国土木工程学会的，跪求翻译！ Behavior of Rigid-Soft Particle MixturesJong-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.
我毕业设计要的，那个帮我翻译一下啊！
文章是美国土木工程学会的，跪求翻译！
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
2楼
Experimental study
The rigid-soft granular mixtures are prepared using shredded rubber tires and Ottawa 50/70sand. Rubber and sand properties are summarized in Table 1. The selected grain size of the sand (D50=0.35mm) is about 4 times larger than the mean grain size of the rubber particles (D50=0.09mm). Photographic images are shown in Fid.1.
The sand-rubber mixtures are carefully placed in the oedometer and triaxial cells to prevent segregation. Densification is attained by tamping. Specimens are prepared at the following sand volume fractions sf=Vsand/Vtotal:0,0.2,0.4,0.6,0.7,0.8,0.9,and 1.0. The mass density of the mixtures increases with sand fraction as shown in Fis.2. A linear mixing model mix= (sf) ρsand+ (1-sf) ρrubber is superimposed on the date. At high sand fraction (sf>0.6, the mass density of the mixture is higher than the linear model because small rubber particles fill the porosity between the large sand grains.
Specimens are incrementally loaded in the oedometer cell until the effective vertical stress reaches 556 kPa (cell diameter: 100 mm, specimen height: 30-40 mm; load increment ratio is 2). The shear wave propagation velocity is measured at each stress level using bender elements installed on the top and bottom plates of the oedometer cell. Consolidated drained triaxial tests are conducted on 35 mm diameter and 70 mm height specimens subjected to a confining pressure of σ´c=80 kPa.
Experimental results
The measured load-deformation response of the different mixtures is summarized next, starting of with the small-strain shear modulus Gmax, followed by mid-strain k0 compressibility and large strain triaxial response.
Small Strain Shear Modulus Gmax
Fig.3 show tow sequences of measured S-wave time series gathered during oedometic loading and unloading (sf=0.2 and sf=0.8). The low sand fraction mixtures point to the low stiffness of these mixtures. The evolution of S-wave velocity versus vertical effective stress σ´ during oedometer loading and unloading is plotted in Fig.4 for the same tow mixtures (sf=0.2 and sf=0.8). Clearly, the higher the sand fraction, the higher the S-wave velocity Vs at the same stress level. The hysteretic Vs-σ´ behavior in the both mixtures is characteristically observed in k0 loading and reflects the evolution of k0 during unloading, that is, the contribution of the locked-in horizontal stress on shear stiffness in the vertical plane.
Fig.5 is a summary plot of Gmax versus vertical effective stress during loading for all tested rigid-soft mixtures . The measured responses fall into either of tow well-defined groups: Specimens with sf≥ 0.7 are “sand-like” and exhibit high shear modulus, however, specimens with sf≤0.4 are “rubber-like” and exhibit low shear moduli. The transition mixture sf=0.6 display very high stress sensitivity: it behaves rubber-like at low confinement, but it turns sand-like at high stress.
回复
3楼
Zero Lateral Strain Loading (k0 Condition)
The oedometric stress-strain response is shown in Fig.6 for selected specimens (sf=0,0.6,0.8,and 1.0). The vertical strain decreases with increasing sand fraction for any given load. All mixtures retain residual deformation after unloading (in agreement with the hysteresis in Vs-σ´ observed in Fig.4).
The slop of the stress-strain curve is calculated at each load increment to determine the evolution of the constrained modulus M with vertical stress. The summary plot in Fig.7 shows the increase in stiffness M with increasing and fraction; there is a marked increase observed for mixtures with sf≥0.9 (notice loglog scale).
Strength at Constant Confining Stress
The stress difference σ1-σ3 versus axial strain response is shown in Fig.8 (a) for all rigid-soft mixtures. The stress-strain response of the rubber specimen (sf=0.0) is quasilinear. Peak strengths are observed in high sand fraction specimen for the tested densities and applied low confinement (refer to Fis.2). the strain at peak strength increases with decreasing sand fraction, the peak strength decreases, and no peak strength is apparent in specimens with low sand fraction (sf≤0.6). similar stress-strain response for rubber-sand mixtures was observed by other researchers (Lee et al. 1999; Youwai and Bergado 2003). Peak and large-strain (ξz=15 axial strain ) friction angles are plotted in Fig. 8(b). both the peak and large-strain friction angles increase with increasing sand fraction.
回复
4楼
Analyses and Discussion
The packing of binary mixtures of two-size spherical rigid particles of relative size Dlarge/Dsmall≈4 is schematically drawn in Fig. 9(a). As the volume fraction of small particles increases[right-to-left in Fig. 9(a)],large particles become increasingly disconnected. Eventually, small particles form the percolating granular skeleton and large particles “float” within. The packing is densest when there are enough small particles to fill the voids left between large particles; this occurs when the ratio between the volume of large particles relative to the total volume is approximately 0.6[Fig.9(b)-Guyou et al. 1987]. Consequently, the measured porosity of rubber-sand mixtures is minimum near the sand fraction sf≈0.6[Fig.9(c)].
The excess of soft rubber particles when sf<0.6 separates sand particles and forms a soft “rubber fabric.” Stiffness-stress data show that a mixture with some excess rubber fraction may behave rubber-like at low confinement, but become sand-like at high confining stress when rubber particles deform alloy sand particles to come in contact to form a sand skeleton(Fig.5 and 7).
Fig.10 shows (1) the large-strain elastic Modulus E from triaxial tests; (2) the middle-strain constrained Modulus M from oedometer tests; and (3) the small-strain shear Modulus G max from shear wave velocity measurements. Middle-and large-strain moduli gathered in oedometer and triaxial cells reflect contact deformation and skeletal changes. The transition sand fraction from rubber-like behavior to sand-like behavior is similar in E and M and it is observed at sf≈0.8. an earlier rise is apparent in Gmax; further, the sand fraction that distinguishes rubber-like from sand –like behaviors varies with stress lever: the rigid particle percolation threshold decreases at high stress.
回复
5楼
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.
回复
6楼
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.
回复
