Effect of Abrasive Concentration on Impact Performance of Abrasive Water Jet Crushing Concrete

It has been found that the impact performance of water jets can be changed by its properties, which include pressure, additive, and mode of jet. +us, an abrasive water jet (AWJ) has been developed as a new method. However, there is little research on the effect of abrasive concentration on the impact performance of abrasive jets. +us, the SPHmethod is used to establish an abrasive water jet crushing concrete model to study the effect of abrasive concentration on the impact force, concrete internal energy, abrasive particle distribution, crushing depth, and damage and crushing efficiencies under different concrete compressive strengths and abrasive densities. +e results indicate that there is little effect of the abrasive concentration on the peak impact force under different compressive strengths and abrasive densities, while the mean impact force tends to increase linearly with the abrasive concentration.+e internal energy of the concrete increases stepwise with the abrasive concentration under different compressive strengths and abrasive densities. +e concentration of 10%∼20% is the rapid increasing stage. +e crushing depth and damage efficiencies are all maximum at a concentration of 20% under different compressive strengths and abrasive densities. After the concrete was impacted by the water from the water jet, it is divided into rebounding particles and intrusive particles.+emore the intrusive particles, the easier the concrete to be crushed and damaged.


Introduction
Water jet technology has been widely applied in machinery, civil construction, gas drainage, and cleaning operations, especially in mining and petroleum drilling [1].Concrete breaking by using tools is assisted by water jets to not only decrease the contact between cutting tools and concrete but also increase the free surface around the concrete impact by using tools for superior breakage.
On the one hand, much research has focused on the impact performance of pure water jets.Material cutting by a pure water jet is shown in Figure 1(a).Ozcelik et al. [2,3] focused on the stone surface treatment with water jets and concluded that the application of water jets in surface treatment enabled obtaining a surface with required roughness while preserving aesthetic appearance of the stone.Dehkhoda and Hood [4,5] observed the capacity of pulsed water jets for creating an internal breakdown and the relative contributions of the pulse length and pulsation frequency on the surface and subsurface damage caused by a pulsed water jet on rock targets.
On the other hand, the assisting performance of water jets in rock breaking by using tools was also studied.Tools cutting the material assisted by the water jet are shown in Figures 1(b)-1(d), which include a disc cutter, drill bit, and conical tool.Ciccu and Grosso [7] dealt with the problems of assisting disc cutters with high-velocity water jets to increase the excavation rate and to improve the working conditions, with particular reference to wear.Yang et al. [6] studied the wear characteristics of cemented carbide blades in drilling limestone with a water jet, concluding that the wear rate decreases with the nozzle diameter in the drill bit.Ciccu and Grosso [8] carried out the experimental research aimed both at studying the processes by which mechanical excavation is improved and at quantifying the increment of the excavation performance parameters with water jets.In that paper, the water jet was directed in front of the tool.Liu et al. [9][10][11][12][13] performed numerical simulations and experiments to study the rock breaking performance of di erent con guration modes of conical tools assisted by water jets.
After a long period of research, researchers have found that the impact performance of water jets can be changed by changing their properties.e properties of water jets include pressure, additive (abrasive jet), and mode of jet (pulsed jet).us, with the development of water jet technique, an abrasive water jet (AWJ) assistance, as a new method, has been developed in hard rock mechanical cutting and drilling [14].Selvam et al. [15] observed abrasive water jet machining of composite laminates experimentally for various cutting parameters in terms of average surface roughness and kerf taper.By generating a response surface model, the experimental values obtained for quality characteristics were empirically related to those of cutting parameters.Wong et al. [16] pointed out that kerf taper and delamination were undesirable geometrical defects inherent to abrasive water jet machining (AWJM) of layered brereinforced polymer composites and described an experimental investigation in minimizing the defects for hybrid bre-reinforced polymer composites.All the above researchers conducted studies on abrasive water jets experimentally.Actually, it is di cult to research the fracture mechanism of target material crushing by using abrasive water jets in experiments because of high speed and high pressure of water jets and opaqueness of most target materials.And a water jet crushing a target material is a process of nonlinear impact dynamics, which contains many problems in short time, such as uid-solid coupling, high strain rate, and large deformation.As a very important method in current scienti c research, simulation technology has the advantages of high reliability and low economic cost.Domestic and foreign researchers have used this technology to conduct many numerical simulations on the process of abrasive water jet cutting and crushing materials.
For the simulation of abrasive water jet crushing materials, di erent scholars use di erent methods.Scholars usually use CFD methods for research when focusing on ow eld problems of abrasive jets.Liu et al. [17,18] studied the ow eld characteristics of the abrasive water jet by using the CFD method.e CFD model was established based on threephase (air, water, and particle) turbulent ow.Plausible characteristics of the ow as well as the particle velocity and trajectory under di erent input conditions were predicted and discussed.e powerful computational uid dynamics (CFD) analysis software Fluent was applied to numerical simulation of liquid-solid two-phase ow in the hard alloy nozzle of di erent cylindrical section lengths under a certain condition [19].Meng et al. [20] used Fluent software to get the isothermal, incompressible, steady ow eld out of a submerged abrasive water jet nozzle through numerical simulation, with di erent particle sizes and di erent con ning 2

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pressures under submerged conditions.Deepak et al. [21] carried out the jet flow through the AWJ nozzle with different nozzle geometries using computational analysis.ese studies provide a viable method for fluid-solid coupling simulation of water and abrasives in abrasive jets.However, this method cannot simulate the cutting process of abrasive jets.at is to say, the target material cannot be included in the established simulation model, and the impact performance of the abrasive jet cannot be studied.
In the simulation of abrasive jet cutting materials, the target material is usually established using the Lagrangian finite element method (FEM).To make the established abrasive jet model both couple with the material model and simulate the large deformation characteristics of water, the ALE method is used to establish the water, abrasive, and air models.Gong et al. [22] used LS-DYNA to simulate the abrasive water jet crushing materials and analyzed the effect of moving speed and pressure on cutting depth and erosion.Shahverdi et al. [23] used LS-DYNA to numerically simulate the abrasive water jet crushing low carbon steel alloy by using the ALE method.
Although the ALE method can effectively simulate abrasive jets, it still cannot fully simulate the actual crushing process.For example, the splash process after water impacted the material and the discrete properties of the abrasive particles cannot be simulated.To this end, researchers have begun to use the smooth particle hydrodynamics (SPH) method to simulate abrasive jets.Liu et al. [1] and Jiang et al. [24] used the SPH method to establish a pure continuous water jet and a discontinuous jet to study the performance of water jet cutting rock, respectively.Feng et al. [25] adopted the SPH-coupled FEM, in which SPH particles were used to model the highspeed water jet to adapt their extremely large deformation and FEM was applied to model the discrete abrasive particle, cutting head, and workpiece.However, only the acceleration process of a single abrasive particle was studied using this method.Compared with this method, Wang et al. [26] and Guo et al. [27] used SPH to model the abrasive and water at the same time, realized the random distribution of abrasive particles in water by a random algorithm, and studied the cutting performance of the abrasive jet cutting steel.
e above SPH method can effectively simulate water jets or even abrasive jets cutting and impacting materials, but there are still some shortcomings.First, there is little research on the effect of abrasive concentration on the impact performance of abrasive jets.And the range of abrasive concentrations studied is not comprehensive enough.For instance, Xue et al. [28] compared only the depth of concentrations of 6% and 12% of the abrasive jet impacting coal.Li et al. [29] performed simulation analysis and experimental study on the effect of different abrasive concentrations (2%, 4%, 6%, and 8%) on the quality of abrasive flow.Mu and Rong [30] studied the effect of the abrasive concentration, and the concentration was expressed by the amount of abrasive (1 particle, 2 particles, and 3 particles).Second, for the study of the SPH method, most scholars have neglected the study of the interaction and distribution between water and abrasive particles after crushing.erefore, in this paper, the SPH method was used to establish the abrasive water jet crushing concrete model to study the effect of abrasive concentration on the impact force, concrete internal energy, abrasive particle distribution, crushing depth, and damage and crushing efficiencies under different concrete compressive strengths and abrasive densities.

Methodology
In this paper, the computer program LS-DYNA, finite element software for simulation of geomaterials, was used.e numerical model for concrete crushing by using the abrasive water jet is shown in Figure 2.
e water jet and abrasive were first established by a set of SPH particles.
en, by extracting the series of SPH particle numbers, the established SPH particles were divided into a water particle group and an abrasive particle group according to the ratio of the abrasive to the water, and the abrasive particle group was randomly distributed in the water particle group, as shown in Figure 2. e set of SPH particles is shown in box, and the length is 12 mm.e width of the water jet is 1.2 mm. e velocity of the water jet is 280 m/s.Different abrasive concentrations of 5%, 10%, 20%, and 30% and different abrasive densities of 2000 kg/m 3 , 3000 kg/m 3 , 4000 kg/m 3 , and 5000 kg/m 3 were set.
If the coordinate of a particle was x i at initial time, it would be x j at t time.us, the position of this particle was a function of the initial coordinate x i , namely, x j � x j (x i , t).In hydromechanics, the following equations were often used to describe the motion and status of the fluid when the hydrodynamics problems were solved by using the SPH method [1,[25][26][27].
Position equation of the particle is Mass conservation equation of the particle is Momentum conservation equation of the particle is Energy conservation equation of the particle is where ρ i is the density of particle i, m j is the mass of the particle j (kg), σ αβ is the stress tensor (Pa), v i is the velocity of particle i (m/s), E i is the energy per unit mass of particle i (J), Π is the artificial viscosity force (N), H is the artificial heat flux (J/s), and W is the kernel function of the particle.e water jet was described by using the MAT_NULL and the GRUNEISEN equation of state (EOS) for pressure response.Its density was 1000 kg/m 3 , the dynamic viscosity was 0.001 Pa•s, and Poisson's ratio was 0.5 [1,27].e abrasive was also described by using the MAT-NULL model.

Shock and Vibration
e EOS_GRUNEISEN is given by the following equation to describe its pressure and volumetric strain relation: where c is the intercept of the curve μ s − μ p , E is the internal energy of unit volume (J), S i is the slope of the curve μ s − μ p , c 0 is the EOS_GRUNEISEN coe cient, and α 0 is the correction coe cient about the relationship between c 0 and volume.e model of concrete was also established by using the SPH method.e concrete was 12 × 24 mm in dimension.X and Y direction displacement constraints were applied to the bottom of concrete.To simulate the strain and stress of concrete impacted by the abrasive water jet e ectively, the material Johnson-Holmquist concrete was adopted to describe concrete material.e constitutive model has been used widely for simulating concrete subjected to large strains, high strain rates, and high pressures.Di erent concrete strengths of 20 MPa, 40 MPa, 60 MPa, and 80 MPa were set.e parameters are given in Table 1.
To determine the accuracy of the material model, the compressive strength and tensile strength of the concrete material were tested.e test model and results are shown in Figure 3.
e concrete is 50 × 100 mm in dimension.A displacement constraint in the Y direction is applied to the bottom of the concrete, and a Y displacement load is applied to the top.According to repeated tests, the load rate has little e ect on the concrete strength results.e test results show that the compressive strengths of the four materials are 20 MPa, 40 MPa, 60 MPa, and 80 MPa, and the tensile strengths are about 4 MPa, 4 MPa, 5 MPa, and 6 MPa, which basically satisfy that the tensile strength is about 1/20∼1/10 of compressive strength for concrete.erefore, the model parameters can be used to simulate concrete from 20 MPa to 80 MPa.

E ect of Abrasive Concentration under Di erent Compressive Strengths.
To study the e ect of abrasive concentrations on impact performance of the abrasive water jet under di erent compressive strengths, the abrasive concentrations were 5%, 10%, 20%, and 30% according to the existing literature that abrasive concentration ranged from 3% to 30%; the concrete compressive strengths were set as 20 MPa, 40 MPa, 60 MPa and 80 MPa; the jet velocity was set at 280 m/s; and the abrasive density was set at 3000 kg/m 3 .As the concentration of abrasive increases, the initial kinetic energy of the abrasive jet increases.e initial kinetic energy of the abrasive water jet with di erent abrasive concentrations is shown in Table 2.
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E ect on Impact Force.
e increase in the initial kinetic energy of the jet will lead to the increase in jet impact force.To study the e ect of the abrasive concentrations on the jet impact force under di erent compressive strengths, the Y direction force of the constrained particles in Figure 2 is extracted as the jet impact force, shown in Figure 4(a).e e ects of abrasive concentrations on the peak and mean of jet impact force under di erent compressive strengths are shown in Figures 4(b) and 4(c), respectively.e peak of jet impact force is the "water hammer" force generated when the jet is just in contact with concrete, and the mean impact force is the average value of the impact force from 5.2e − 6 s to 4.0e − 5 s.

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It can be seen from Figure 4(b) that, although the peak impact force of the abrasive jet is signi cantly improved compared with the pure water jet, the change in the abrasive concentrations under di erent compressive strengths has little e ect on the peak of impact force.Especially for 20∼60 MPa, the tested peak of impact force uctuates between 40 and 45 N. is is mainly related to the number of abrasives rst contacting the concrete.From Figure 2, the number of abrasives in the 5%, 10%, 20%, and 30% abrasive jet rst contacting the concrete is 4, 2, 8, and 5, respectively.At 20 MPa and 60 MPa, the peak of impact force shows a decreasing trend rst and then increasing and decreasing as the abrasive concentration changes from 5% to 30%.Especially at 10% concentration, the peak force is the lowest under di erent compressive strengths.In addition, the impact force increases with the compressive strength under di erent abrasive concentrations, which indicates that the impact force is also related to the fracture of concrete.e concrete with high strength is more likely to transmit the impact force continuously, and the crushing of concrete will lead to the discontinuous transmission of the impact force.
From Figure 4(c), it can be observed that the mean impact force under di erent compressive strengths tends to increase linearly with the abrasive concentrations and the increasing rate is basically the same.e curves of 60 MPa and 80 MPa have basically coincided, indicating that the mean impact force gradually converges with the increase of compressive strength.

E ect on Internal Energy of Concrete.
From the perspective of energy, the process of water jet crushing the concrete material is mainly the process of transforming the kinetic energy of the water jet into the kinetic energy and internal energy of the concrete material.e so-called kinetic energy of the concrete material includes the kinetic energy of the spattered particles, the pressed particles, and the block concrete because of cracks, as shown in Figure 5.Because the kinetic energy of concrete particles was relatively low, corresponding statistical studies was not made.
e internal energy of concrete mainly refers to the deformation energy because of its extrusion, which can characterize the damage to a certain extent.erefore, it is of great signi cance to study the internal energy of concrete.Figure 6(a) shows the time history curve of the internal energy of concrete when the compressive strength is 20 MPa e internal energy of concrete increases stepwise with the abrasive concentrations under di erent compressive strengths.e so-called stepwise growth trend means that the internal energy of concrete increases by 5% compared with that of the pure water jet, while the growth of 10% is slower than that of 5%, and it increases greatly by 20%, while growth slows again from 20% to 30%.Due to the increase of compressive strength, the damage resistance ability of concrete becomes stronger.e internal energy decreases with the compressive strength under the same abrasive concentrations, and the decrease amplitudes under di erent compressive strengths are not much di erent.

E ect on Crushing Depth and Damage of Concrete.
Impact force and concrete internal energy can re ect the impact performance of the abrasive jet to a certain extent, but the purpose of impacting is to make crushing and damage concrete.us, crushing and damage of concrete is a more important criterion to measure the impact performance of the abrasive jet.
e crushing and damage of concrete under di erent compressive strengths and abrasive concentrations obtained using numerical simulation are shown in Figure 7.
It can be seen from Figure 7 that the concrete particles splash and extrude to form a crushing pit under the impact

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of the water jet, and the unbroken part is damaged by the extrusion.e crushing pit and the damage area become larger gradually as the abrasive concentration increases under different compressive strengths.In addition to the crushing pit and damage, there are cracks in the concrete with small compressive strength at the same time, and the cracks become more and more obvious as the abrasive concentration increases.For this reason, crushing and damage of concrete is a more important criterion to measure the impact performance of the jet, and the quantitative statistics was taken on the crushing depth and damage.e method is shown in Figure 8. e crushing depth is the maximum coordinate of the jet particles in the −Y direction, and the damage area is characterized by the number of particles whose extracted stress values are close to 0. e effects of the abrasive concentration on the crushing depth and damage under different compressive strengths are shown in Figures 9(a From Figure 9(a), the crushing depth under different compressive strengths shows an increasing trend with the abrasive concentration, but the change trend is different.For 20 MPa and 40 MPa, the crushing depth changes linearly with the abrasive concentration from 0% to 20%, while the growth rate from 20% to 30% becomes slower.For 60 MPa and 80 MPa, the abrasive water jet has little effect on increasing the crushing depth with abrasive concentration changing from 5% to 10%.e depth increases greatly until the concentration is 20%, and when exceeding 20%, the crushing depth increases slowly or even hardly increases.
From Figure 9(b), the trends of the damage with the abrasive concentration are basically the same under different compressive strengths, and all show a stepwise increasing trend.e so-called stepwise trend is similar to the change in concrete internal energy (Figure 6(b)).It can be seen that the concrete internal energy can indeed reflect the damage to a certain extent.e difference is that the damage decreases with the compressive strength, and the decreasing amplitude increases gradually with the abrasive concentration, which indicates that it is easier to increase the damage by increasing abrasive concentration for the concrete with small compressive strength.In order to further analyze the impact performance of the abrasive jet, two indexes of crushing depth e ciency and damage e ciency are introduced, which are the ratio of the crushing depth h and the damage N to the initial kinetic energy of the abrasive jet E s .
e e ects of the abrasive concentration on the crushing depth e ciency and damage e ciency under di erent compressive strengths are shown in Figures 10(a From Figure 10(a), the crushing depth e ciency increases rst and then decreases with the abrasive concentration under di erent compressive strengths and peaks at a concentration of 20%.It means that the crushing depth e ciency will not increase but decrease when the abrasive concentration exceeds 20%.Compared with the pure water jet, the crushing e ciency increasing rate of the 20% concentration jet increases with the compressive strength, indicating that the abrasive jet is more meaningful to improve crushing depth e ciency of high compressive strength concrete.In addition, although the crushing depth e ciency is the largest when the abrasive concentration is 20% for di erent compressive strengths, the change trend is di erent.For example, the di erence is not large in crushing depth e ciency between the abrasive concentrations of 10% and 20% for 20 MPa concrete, and the jet with the abrasive concentration of 10% has met the Fringe levels 1.000e + 01 9.000e + 00 8.000e + 00 7.000e + 00 6.000e + 00 5.000e + 00 4.000e + 00 3.000e + 00 2.000e + 00 1.000e + 00 0.000e + 00

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requirements for the crushing depth efficiency.However, for 80 MPa concrete, there is a large difference in crushing depth efficiency between the abrasive concentrations of 10% and 20%.And the concentrations must reach 20% to achieve higher crushing depth efficiency.
From Figure 10(b), the trend of damage efficiency is the same with that of crushing depth efficiency.And it also peaks at the concentration of 20%.Compared with the pure water jet, the damage efficiency increasing rate of the jet with the 20% concentration of abrasive decreases with the compressive strength, indicating that the abrasive jet is more meaningful to improve damage efficiency of low compressive strength concrete.Moreover, the damage efficiency increases slowly with the abrasive concentrations from 0 to 10% under different compressive strengths and shows a rapid increase from 10% to 20%.It can be concluded that it is necessary to use an abrasive jet of concentration of about 20% to greatly improve the damage efficiency.

Effect on Distribution of Abrasive Particles.
After the water from the water jet impacted the concrete, it was divided into two parts.One part was the rebounding particles with higher speed, and the other part was the intrusive particles with lower speed.e rebounding particles moved away from the concrete mass at a constant speed after a direct or indirect interaction with the concrete, generally formed by the outer edge of the jet.e intrusive particles were mainly formed by the center of the jet and contributed mainly to the crushing and damage of the concrete.e more the intrusive particles, the more the energy of the concrete directly impacted by the jet, especially the abrasive intrusive particles.
Figure 11 shows the distribution of abrasive particles after a water jet of 20% abrasive concentration impacted 20 MPa concrete.e jet is divided into 6 columns, with columns 1, 2 in the center and columns 5, 6 at the outer edge.Figure 11(a) shows the distribution of all abrasive particles after the impact was completed.It can be seen from Figures 11(b)-11(d) that the abrasive intrusive particles are mainly formed by columns 1, 2; both intrusive particles and rebounding particles are formed by columns 3, 4; and columns 5, 6 form substantially only rebounding particles.
Figure 12 shows the abrasive particle distribution of water jets with different abrasive concentrations impacting 20 MPa concrete.It can be seen that, as the abrasive concentration increases, the intrusive particles almost increase proportionally, which effectively explains the increasing trend of the crushing depth and damage.
However, from Figure 10, the proportional increase of intrusive particles does not make the crushing depth and damage increase proportionally.It means that the crushing depth and damage has shown a slow growth trend, especially for that of the 10% concentration relative to the 5% concentration and that of the 30% concentration relative to the 20% concentration.e main reason is that the particles accumulation occurs so that the impact energy is buffered and consumed, and the due crushing and damage effects are not achieved.From Figure 12, the accumulation of intrusive particles is serious in Figures 12(c) and 12(e) compared with that in Figures 12(b) and 12(d).It indicates that the intrusive particles that are in contact with the concrete first form a water cushion before the impact of the later particles.When impacting, the later particles is actually in direct contact with the previous intrusive particles, rather than the concrete, so that the early particles have a buffering effect on the impact of the later particles, and the crushing and damage effects are not achieved that of the direct impact.
Figure 13 shows the abrasive particle distribution of different compressive strength concrete impacted by using the water jet with 20% abrasive concentration.As the compressive strength of the concrete increases, the depth of the jet particles intruding into the concrete decreases gradually.When the depth becomes smaller, the abrasive particles surrounded by the concrete crushing pit become less, which results in larger rebounding angle and more rebounding abrasive particles.
e more the rebounding And the depth will be further smaller.

Effect of Abrasive Concentration under Different Abrasive
Densities.To study the effect of abrasive concentration on impact performance of the abrasive water jet under different abrasive densities, the abrasive densities were set as 2000 kg/ m 3 , 3000 kg/m 3 , 4000 kg/m 3 , and 5000 kg/m 3 ; the concrete compressive strength was set at 40 MPa; the jet velocity was still set at 280 m/s.e initial kinetic energy of the water jet with different abrasive concentrations is shown in Table 3.

Effect on Impact
Force. e increase in abrasive density and the abrasive concentration increase the initial kinetic energy of the jet, which leads to the increase of jet impact force at the same time.
e effects of abrasive concentration on the peak and mean of jet impact force under different abrasive densities are shown in Figures 14(a) and 14(b), respectively.e statistical method of peak and mean of impact force is the same as in Figure 4.
It can be seen from Figure 14(a) that the change of the abrasive concentration under different abrasive densities has little effect on the peak of impact force.Especially for the jet of abrasive density 2000 kg/m 3 , the tested peak of impact force fluctuates around 40 N.And there is a small increasing trend under the other densities.e drop in 10% concentration is also related to the number of abrasives first contacting with the concrete.Under the same abrasive concentration, the peak force basically increases uniformly with the abrasive density, but the larger the concentration, the greater the increase.
Intrusive and rebounding particles

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From Figure 14(b), the mean impact force increases linearly with the abrasive concentration under di erent abrasive densities.e larger the abrasive density, the greater the increase.Under the same abrasive concentration, same with the peak force in trend, the mean force basically increases uniformly with the abrasive density, and the larger the concentration, the greater the increase.

E ect on Internal Energy of Concrete.
Figure 15 shows the e ect of the abrasive concentration on the internal energy of the concrete under di erent abrasive densities.Under di erent abrasive densities, the internal energy of concrete increases stepwise with the abrasive concentration.10%∼20% is the rapid increasing stage, and the larger the abrasive density, the greater the increase; while 5%∼10% and 20%∼30% are the slow increasing stages, and the increase of di erent abrasive densities is not much di erent.Under the same abrasive concentration, the internal energy of the concrete increases uniformly with the abrasive density, and the larger the concentration, the greater the increase.

E ect on Crushing Depth and Damage of Concrete.
Figure 16 shows the crushing and damage of concrete under di erent abrasive concentrations and densities.e quantitative statistics was also taken on the crushing depth and damage.And the e ects of the abrasive concentration on the crushing depth and damage under di erent abrasive densities are shown in Figures 16(b) and 16(c), respectively.
From Figure 16, the crushing pit and the damage area become larger gradually as the abrasive concentration and density increase.And the trends of concrete crushing depth and damage with concentration are basically consistent with the trend of internal energy, and both are in a stepwise increasing trend.10%∼20% is still the rapid increasing stage, and the larger the abrasive density, the greater the increase.It can be proved again that the concrete internal energy can re ect the damage to some extent.
Similarly, to further analyze the impact performance of the jet, crushing depth e ciency and damage e ciency are introduced.e e ects of the abrasive concentration on the crushing depth e ciency and damage e ciency under di erent abrasive densities are shown in Figures 17(a From Figure 17, rstly, the crushing depth e ciency and the damage e ciency are both maximum when the abrasive concentration is 20% under di erent abrasive densities, and the e ciency increase is not obvious or even decreases greatly when the concentration is higher than 20%; secondly,  the e ciency of concentration of 10% is not much di erent from that of concentration of 5%, which even has a downward trend; thirdly, the crushing depth e ciency and damage e ciency of concentration of 20% and density of 2000 kg/m 3 are higher than those of concentrations of 5% and 10% under all abrasive densities.

E ect on Distribution of Abrasive
Particles.e abrasive particle distribution of abrasive jets with di erent abrasive concentrations impacting concrete has been given above and will not be studied again.Figure 18 shows the abrasive particle distribution of the abrasive jets with different abrasive densities impacting concrete.
As the abrasive density increases, the depth of the jet particles intruding into the concrete increases gradually.
When the depth becomes larger, the abrasive particles surrounded by the concrete crushing pit become more, which results in smaller rebounding angle and less rebounding abrasive particles.
e less the rebounding abrasive particles, the more the intrusive abrasive particles.And the depth will be further larger.Moreover, the depth is continuously deepened so that the intrusive particles can continuously intrude downward, which reduces the accumulation of abrasive particles and then the impact energy loss, and improves the impact e ciency.

Conclusions
(1) ere is little e ect of the abrasive concentration on the peak impact force under di erent compressive strengths and abrasive densities, while the mean impact force tends to increase linearly with the abrasive concentration.e mean impact force gradually converges with the increase of compressive strength and basically increases uniformly with the abrasive density.
(2) e internal energy of concrete increases stepwise with the abrasive concentrations under di erent compressive strengths and abrasive densities.Concentration of 10%∼20% is the rapid increasing stage.Under the same abrasive concentration, the internal energy of the concrete decreases with the compressive strength, and the decrease in amplitude under di erent compressive strengths is not much di erent; while the internal energy increases uniformly with the abrasive density, and the larger the concentration, the greater the increase.Moreover, it has been proved that the internal energy can re ect the damage to some extent.Shock and Vibration di erent compressive strengths.e crushing depth ciency of concentration of 10% has almost achieved that of concentration of 20% for small compressive strength concrete (20 MPa), while the concentration must reach 20% to achieve higher crushing e ciency for great compressive strength concrete (80 MPa).In contrast, it is necessary to use an abrasive jet of concentration of about 20% to greatly improve the damage e ciency.Compared with the pure water jet, the crushing depth e ciency and damage e ciency increasing rate of the 20% concentration jet increases and decreases with the compressive strength, respectively, indicating that the abrasive jet is more meaningful to    Shock and Vibration improve crushing depth efficiency of high compressive strength concrete and damage efficiency of low compressive strength concrete.e crushing depth efficiency and the damage efficiency are both maximum when the abrasive concentration is 20% under different abrasive densities, and the efficiency increase is not obvious or even decreases greatly when the concentration is higher than 20%.e efficiencies of concentration of 10% is not much different from that of concentration of 5% and even has a downward trend.e efficiencies of concentration of 20% and density of 2000 kg/m 3 are higher than those of concentrations of 5% and 10% under all abrasive densities.e conclusion that most efficient concentration is 20% can be verified by the experiment in reference [31], in which the effect of abrasive concentration on damaged volume rate was studied, and the maximum value is at a concentration of about 20%.(4) After the water from the water jet impacted the concrete, it was divided into two parts.One part was the rebounding particles with higher speed formed by the outer edge of the jet, and the other part was the intrusive particles with lower speed formed by the center of the jet.e more the intrusive particles, the easier the concrete to be crushed and damaged.
e intrusive particles almost increase proportionally with the abrasive concentration, which effectively explains the increasing trend of the crushing depth and damage.However, the proportional increase of intrusive particles does not make the crushing depth and damage increase proportionally, which is because of the particle's accumulation so that the impact energy is buffered and consumed, and the due crushing and damage effects are not achieved.
e intrusive abrasive particle increases with the abrasive density and decreases with the compressive strength.e more the intrusive abrasive particle, the greater the crushing depth.
e intrusive particles can continuously intrude downward with the depth continuously deepened, which reduces the accumulation of abrasive particles and then the impact energy loss and improves the impact efficiency.

Figure 2 :
Figure 2: Numerical model for concrete crushing by the abrasive water jet.

Figure 3 :
Figure 3: Test of compressive and tensile strengths.

Figure 4 :
Figure 4: E ects of abrasive concentrations on the peak and mean values of jet impact force under di erent compressive strengths.(a) Impact force (20 MPa, abrasive concentration 5%).(b) Peak of impact force.(c) Mean impact force.

Figure 7 :
Figure 7: Crushing and damage of concrete under different compressive strengths and abrasive concentrations.

Figure 10 :
Figure 10: Effects of the abrasive concentration on the (a) crushing depth efficiency and (b) damage efficiency under different compressive strengths.

Figure 12 :
Figure 12: Abrasive particle distribution of water jets with di erent abrasive concentrations impacting 20 MPa concrete.

Figure 13 :
Figure 13: Abrasive particle distribution of di erent compressive strength concrete impacted by using the water jet with 20% abrasive concentration.

Figure 14 :Figure 15 :
Figure 14: E ects of abrasive concentration on the peak (a) and mean (b) of jet impact force under di erent abrasive densities.

FIGURE 16 :
FIGURE 16: (a) Crushing and damage of concrete and quantitative statistics: (b) crushing depth (h) and (c) damage (N), under di erent abrasive concentrations and densities.

Figure 17 :Figure 18 :
Figure 17: E ects of the abrasive concentration on the crushing depth e ciency (a) and damage e ciency (b) under di erent abrasive densities.

Table 1 :
Mechanical parameters of concrete.

Table 2 :
Initial kinetic energy of the abrasive water jet with di erent abrasive concentrations.

Table 3 :
Initial kinetic energies of the water jet with di erent abrasive concentrations and densities.