Effect of the Quasi Rate of Loading in Particle Crushing and Engineering Properties of Black Tough Sand

In this study, the effect of the quasi rate of loading in the crushing of black tough sand will be studied experimentally. The experimental works will be conducted at different normal stresses, different relative densities, and different rates of loading using the direct shear tests. All test specimens were prepared with uniformly graded sand, passing sieve #4, and retained sieve #8. The results of direct shear tests were used to investigate the factors influencing the amount of particle breakage and consequently the friction angle. After shearing of each specimen, sieve analysis was performed in order to determine the percentage of particle breakage. Results showed that the rate of loading in direct shear plays a significant role in the amount of crushing and in internal friction angles. The amount of crushing as well as shear strength was increased with the increased rate of loading. Moreover, microstructural analysis used scanning electron microscopy (SEM) analysis shown that the crushing from granular have primarily resulted from disintegration, grinding and abrasion of particles.


Introduction
Granular crushing is one of the major themes attracted the attention of a wide spectrum of scientists and engineers (Xiao et al. 2020). The crushing of granular materials encounters in driven piles, rock fill dams, railways, and landslides (Altuhafi et  The granular materials composed a major part of the dams, foundations, base of highways pavements, highway embankments, retaining walls backfilled and rock fills, experience crushing as a result of variants loads either static or dynamic. Because of the persistence of the crushing, the initial engineering properties in which a structure designed was based upon it will alter during its engineering lifespan.
These changes in engineering properties due to crushing could affect the stability of the structure and jeopardize its safety. Thus, there is a need to understand the evolution of crushing in granular materials.
The evolution of crushing in granular materials will be very valuable to the geotechnical engineering community for the better design of civil engineering structures.
Past research has established that grain crushing is influenced by many factors. These factors are ranged from soil grain characteristics such as soil particle strength (Varadarajan et al. 2006 The aforementioned researches were conducted on different types of granular material, specifically of silica, carbonate, and gypsum sands (Yu, 2017, Xiao et al., 2017, Yamamuro et al., 1996. The other searched granular materials include but not limited to ballast, rock fill, coal, and snow, among others (Indraratna et al., 2020, Strahler et al., 2018, Zhang et al., 2017, Barraclough et al., 2016, and Xiao et al. 2020 Particle breakage quantification also was subject to extensive research and different methods were suggested according to the parameters assessed. Different particle crushing index used in literature based on either global variation of grading, particular variation in grading sizes, a fine content portion, or grain area evolution through the test (Xiao et al. 2020). The most commonly used approaches are based on the change of the grain size distribution before and after crushing occurs e.g.) Hardin, 1985;Einav 2007). Other methods that sparingly used focus on the change in percentage passing for particular particle size (Miura et al., 2003) or an increase in the specific surface area of the particles ( Einav (2007) postulates that the grain size distribution will start from an initial grading and ultimately reaches a final grading due to shearing and compression. The relative breakage index, BrE, is defined as an area ratio Where Bt and Bp are shown in Figure 1b.
In this figure, (Figure 1), Bp, the 'breakage potential', is defined by integrating the entire area confined between the initial and final grain size distribution whilst Bt is the area between the current (at given compression stress), and the initial one, when there is no applied shear or compression stresses.
Cerato and Lutenegger 2006 conducted direct shear tests in five different sands with different properties. They used three square shear boxes of differing sizes (60 mm, 101.6 mm, and 304.8 mm), each at three relative densities (dense, medium, and loose). It was found that the friction angle ϕ can be dependent on specimen size and that the impact of specimen size is also a function of the sand type and relative density. The tests show that for well-graded, angular sands, ϕ decreases as box size increases and that the impact of box size is dependent on relative density. Ovalle and Hicher (2019) studied the role of particle breakage in primary and secondary compression of wet and dry sand. The test results of one-dimensional compression tests on dry and saturated crushable sand show that flooding dry samples at constant stress promotes particle breakage and triggers collapse from the characteristic compression curve of the dry material to the compression curve of the initially saturated material. The link between the one-dimensional compressibility index and the amount of particle breakage does not depend on the stress level and the wetting condition. Saturated crushable sand is more compressible compared to dry sand, due to the increment of particle breakage with the material humidity. For a given stress path, when flooding dry crushable sand under constant stress, the creep index increases up to the same value obtained by a sample saturated from the beginning of loading.
The motivation of this work is the fact that the strength and stress characteristics of sands as determined from conventional testing such as direct shear tests are a function of their initial density and applied rate of loading. The initial density of the sand specimens is a function of the degree of compaction, with altering the densities the initial stiffness, peak strength, and volume dilation are The main objectives of the proposed research are to conduct laboratory investigations on the quasi rates affect sand shear strength and the consequent evolution of crushing in granular materials. The laboratory investigation will involve tests involve comprehensive direct shear tests. The tests will include specimens in the whole range of relative densities (very loose (Dr=20%), loose (Dr=40%), medium (Dr=60%) and dense (Dr=80%), four normal stresses (136 kPa, 245 kPa, 463kPa, and 899 kPa) and different quasi shearing rate (0.5 mm/minutes,1.0mm/ minutes, and 2.0 mm/ minutes). The evolution of crushing in these tests will be evaluated by comparing the grain size distribution curves before and after the shearing applied. The pertaining engineering properties will be evaluated thereafter.

Materials
Black tough sand was selected for this study. The Black tuff obtained from Al-Hala area (Al Tafila) in southern Jordan. The main properties of the investigated sandy materials such as specific gravity, Gs, maximum density, ρmax, and minimum density, ρmin, and the corresponding standards, were these tests conducted according to, are given in  Figure 2. The surface roughness as well as the present of phillipsite occurs as prismatic crystals, rosettes of radiating and spherulitic crystal are clearly shown in the image.

Test Setup
The device used for performing the experiments was a direct shear box produced by CONTROLS GROUP/ Italy. The maximum horizontal and vertical force is 5 kN with three analogue channels, one for load cell and two for displacement transducers. The data form direct shear tests were analyzed to examine the stress-strain response to the Mohr-Coulomb envelope and hence the shear strength parameters. Sieve analysis was performed on the sample taken to determine the extent of the percentage of particle breakage.

Experimental Results
Direct shear tests conducted on the prepared specimens as outlined in Table 3. Figure 3 illustrates the relationship between horizontal displacement vs. shear stress at the different relative density and normally applied stresses for black tuff sand at a shearing rate of 2.00mm/minutes. From the figure above, As the shear displacement increased, the shear stress increased arrived at the peak value, then when the shear displacement increased, the shear stress decreased arrived to a critical state. It can be noted the normal stress was small, the movement of sand particles was relatively easy and the relative displacement could quickly reach a stable state while the normal stress was large, the interaction between particles of sand was large and the displacement was relatively difficult, so a larger shear displacement was needed to realize a more stable state. On the other hand, the vertical displacement vs. horizontal displacement for the same applied pressure and shearing rate at given relative densities were shown in Figure 4. As expected as applied pressure increased the amount of contraction is increased in all densities. However, the extent of contraction was a substantial decrease with increasing the relative densities, and in the medium range of applied stresses (245 kPa and 463 kPa) the contraction switch to dilation with progressing of shearing.
Mohr-Coulomb failure envelopes were obtained by plotting the attained shear stresses with vertical applied stresses under a different combination of test variables are presented in Figure 5. The presented envelopes are the those of the black tuff (BT) sand at low, medium and dense state (Dr=20%, 40%, 60%, and 80%) at a different rate of loading (0.50mm/minute, 1.0mm/minute, and 2.00mm/minute). It can be observed that the failure envelopes are generally nonlinear for the range of applied vertical stresses used. This is attributable to the dilation of the sand especially at the low-stress levels. However, the increasing of vertical stress leads to more crushing of particles as well shown later, and therefore, the voids between sand particles were filled by smaller granules that will let the sand to become more densified.
The grain size distribution obtained from sieve analysis for Black Tough sand before and after subjected to shearing stresses at different normal stresses at different relative densities at a shearing rate of 1.0mm/minutes is shown in Figure 6.

Effect of Shearing Rate in Internal Friction Angle
The mobilized friction angles of the tested Black Tough sand were assessed to evaluate the effect of applying shearing rates. The mobilized peak friction angle and the mobilized residual friction angle which define respectively as: where peak: the peak shearing stresses, residual , and =the applying normal stresses.
The peak and mobilized residual friction angles of the tested sands for various applied normal stresses, various relative densities, and rate of loading are determined and presented in Figure 7  is shown in Figure 8. It is obvious from this figure that increasing the shearing rate increased both friction angles regardless of the relative density. However, the amount of increasing seemed to be asymptote with a further increase in the shearing rate.

Analysis of Particle Breakage during shearing for black tuff sand
The amounts of particle crushing (breakage) reported here are based on what so-called global grading indices (Xiao et al. 2020). The particle breakage, BrE (Einav (2007), calculated from grain size distribution parameters before and after shearing. The gradation curve shifts from the large to the smaller sieve sizes. The grain size distribution for the black tuff sand specimen after direct shear tests under different normal stresses and different relative densities at a different rate of loading were already shown in Figure 6. After that, the percent of breakage, BrE was calculated and presented for each rate of loading as a function of applying vertical stress in Figure 9A, 8B, and 8C for the rate of loading 0.50 mm/minutes, 1.00 mm/minutes, and 2.00 mm/minutes respectively.
It can be noted that the amount of crushing increased with the magnitude of the applied vertical stress and high relative density. Additionally, the particle breakage increases with an increased rate of loading. The results of sieve analysis tests showed the amount of crushing, BrE, at low-stress level (136kPa) is slightly at ranges of (0.00-3.00) % while at moderate stress level (245kPa and 463kPa), the amount of crushing is increasing to (0.53-7.00) %. While at the high stress level (899kPa), the amount of crushing is significantly increasing to the range of (10.00-12.00) %. The amount of crushing was increased with relative density increased.
Lastly, a microstructural analysis, that used scanning electron microscopy (SEM) supplied with energy-dispersive X-ray spectroscopy (SEM/EDX), of samples taken from the shearing zone of tested specimens were conducted at different scales and magnifications to inspect what happened to the BT granules after shearing. Figure 10 shows

Conclusions
The effect of the quasi rate of loading in the crushability sands and mechanical engineering properties of black tough sand was studied experimentally. This study utilized the direct shear test to conduct this task. Based on the results of the tests the following conclusion may be drawn: 1. The Mohr-Coulomb failure envelopes of this sand, in the range of normal stresses applied in this study, were nonlinear, specifically for peak shear strength.
2. For loose and medium state specimens, the shear stress increases uniformly with no peak. Whilst for dense specimens, the shear stress-shear displacement is shown to increase to peak then decreased to residual shear strength.
3. The rate of loading in the direct shear test plays a crucial role at shear strength, where the shear strength increases with increasing the rate of loading.
4. The peak friction angle is found to decrease with increasing of void ratio and normal stresses applied, while the opposites in the case of relative density as it well known.
5. The crushing of sand depends on normal stress and relative density which it was found that the amount of crushing increases with increasing normal stress and relative density, while the rate of loading increase the amount of crushing.
6. The crushed granules were derived from disintegration, abrasion and grinding processes.

Disclosure statement
Tables list Table 1: Main properties of black tuff (BT) sand.          Grain size distribution for Black Tough sand before and after subjected to shearing stresses at different normal stresses at different relative densities at shearing rate of 1.0mm/minutes. Effect of shearing rate on mobilized peak friction angle taken from Failure Criterion Envelope for the black tuff (BT) Figure 9 Evolution of Percentage particle crushing of Black Tough in direct shear at different normal stresses and different relative density at different shearing Rate.

Figure 10
SEM images at different scales.