Experimental Investigation on the Granite Erosion Characteristics of a Variable Cross-Section Squeezed Pulsed Water Jet

Abstract

The exploitation of deep resources and energy needs to break hard rock. Aiming at the problem of deep hard rock fragmentation, this paper proposes a variable cross-section squeezing pulsed water jet technology (SPWJ). SPWJ was generated under pump pressures of 5.2, 6.8, 8.5, 10, 11.9, and 13.8 MPa to carry out erosion experiments. Features such as rock spalling area, erosion depth, volume loss, and decomposition per unit inlet pressure are used to characterize the erosion performance of SPWJ. The results show that SPWJ can effectively crush granite under low input pressure. Granite crushing modes caused by SPWJ are mainly divided into three types: I: drilling type, II: erosion type, and III: cracking type. Compared with continuous water jet (CWJ), SPWJ has better overall erosion ability than CWJ when the erosion pressure is higher than 60 MPa, the dimensionless target distance is greater than 200, and the erosion time is less than 90 s. In addition, the erosion ability of SPWJ is better than that of CWJ under the condition of unit input pressure. The research results provide a reference for further optimizing the performance of SPWJ crushed granite in the future.

1. Introduction

Hot dry rock and coalbed methane are very important clean energy sources with abundant resource reserves and huge mining potential, which can effectively support China’s “carbon peak” and “carbon neutral” programs [1]. In the process of underground resource extraction, rock fragmentation, especially hard rock fragmentation, is required. Compared to traditional mechanical and explosive rock fragmentation, water jet rock fragmentation technology has advantages such as non-contact, precision, and low cost [2,3,4,5,6,7,8,9,10]. The crushing of hard rock often requires extremely high jet pressure, which also means that larger pump sets are not suitable for practical on-site applications. Pulse water jet technology has received widespread attention for its ability to enhance the water hammer effect generated by the jet’s impact on rocks. Because of their unique water hammer effect, pulsed water jets (PWJs) can periodically apply surge pressure waves when they erode the rock mass [11,12,13]. Currently, this is considered a good way to break rock in underground space excavation engineering and is particularly suitable for breaking brittle rock masses. When a PWJ impacts a rock mass, the tensile stress formed on the rock mass surface is utilized to break it through tensile failure, and the tensile strength of a rock mass is significantly less than its compressive strength. The PWJ can effectively utilize the physical and mechanical properties of the rock and improve crushing efficiency [14,15]. Furthermore, water jet technology helps reduce the dust produced in the process of rock breaking, and the rock-breaking device does not need to contact the rock mass directly, thus avoiding wear on the device and making it suitable for breaking and tunneling different strata [16,17,18]. The PWJ is superior to the CWJ in many aspects because of its unique erosion ability. Many researchers have changed the focus of their research from simply increasing the pressure of the water jet to improving its striking ability, thus creating the PWJ.

The existing PWJ technology can be divided into two types: associated pulsed water jet (APWJ) and modulated pulsed water jet (MPWJ). In the APWJ, the free water mass is interfered with by an external force before the hydrostatic pressure in the pipe is converted into jet pressure by the transducer element (orifice or nozzle). The water jet ejected by the transducer has the characteristics of pulse, pulsation, intermittence, and oscillation. Water cannons and other devices [19,20] belong to the APWJ type. In the MPWJ, the free water mass is converted into jet flow pressure through transducer elements (such as orifices or nozzles) by hydrostatic pressure. After the formation of a CWJ, the original fluid characteristics are changed by external disturbances or mechanical interference, resulting in characteristics such as jet pulse and intermission. The disc-truncated pulsed water jet [21], internal excitation pulsed water jet [22], self-excited oscillating water jet [23], and acoustic wave-modulated pulsed jet [24] belong to the MPWJ type. Current research has been mainly focused on the erosion mechanism and performance enhancement of the MPWJ on the rock.

The longitudinal pulsation generated by ultrasonic interference in the cavity can effectively improve the rock-breaking ability of the water jet. Under the same hydraulic parameters, the rock-breaking effect is substantially better than that of the CWJ. Raj et al. [25] found that the depths of trace formed by 20 Hz and 40 Hz PWJs are 11 times and 15 times greater than those of a CWJ, respectively. Moreover, they compared the erosion of granite by a sonic-modulated pulsating water jet and a CWJ, and the groove formed by erosion was analyzed by profile scanning and electron microscopy. The results show that the CWJ erosion is mainly composed of microcracks, fractures, and lamellar grain removal, whereas that of the pulsating water jet is mainly composed of a deep depression, a meteorite crater, and wavy deformation. The erosion depth of the pulsating water jet is much greater than that of the CWJ [26]. During their research, Tripathi et al. [27] analyzed the corresponding relationship between acoustic emission signals and the degree of jet erosion to further conduct non-destructive testing of the erosion process. The enhanced technology of disc-truncated pulsed water jets has been studied for efficient rock crushing. Lu et al. [20] captured the flow field structure of a truncated pulsed water jet using high-speed photography and verified it by conducting numerical simulations. Rock-breaking experiments show that there are two main modes of breaking hard rock with a truncated pulsed water jet: deep hole erosion and macroscopic fracture. Wang et al. [28] studied the flow field characteristics of a truncated pulsed water jet and found that the jet deflected after being intercepted by a rotating disk. Therefore, the positional relationship between the disc and the nozzle was analyzed in detail. After the research, it was found that the depth of the erosion pit first increased and then decreased with an increase in the ratio between the distance from the cutting disc to the nozzle and the distance between the cutting disc and the target. Additionally, Dehkhod et al. [29] analyzed the damage to a hard rock surface and subsurface eroded by an interrupted PWJ. It was found that the length and frequency of the pulse are the main factors leading to internal damage. Moreover, it was shown that the propagation of subcritical cracks in the interior has a stronger correlation with the length of the pulse. The micro-cracks in the impacted rock mass were measured, and the effective damage of the truncated pulsed water jet to the interior of the rock mass was verified. Polyakov et al. [30] fitted the generalized equation of rock-cutting efficiency by using the experimental data of a rock mass cut with a truncated pulsed water jet. To further enhance the original ability of the jet by mechanical cutting, a miniature hydraulic cutting disk was set in the exploratory well bit to generate a PWJ, thereby effectively improving the drilling ability of the bit [31]. In addition, Li et al. [32] studied the pressure fluctuation characteristics of a self-excited oscillating pulsed jet and concluded that a stable fluid flowing through the constriction generates self-excited pulsation when it collides with the opposite inner wall, which then feeds back to the resonant cavity and creates pressure oscillation. Lu et al. [33] studied the influence of air content on pulse frequency; Du et al. [34] added abrasive particles to the oscillation cavity; and Li et al. [35,36] studied the influence of feed pipe diameter and nozzle inlet discontinuity on the characteristics of a self-excited oscillating jet. Furthermore, Qu et al. [37] studied the influence of the main structural parameters on jet dynamics through orthogonal experiments. The aforementioned research results have played a key role in the development of PWJs.

Although several studies have been conducted on the MPWJ, there are few studies on the APWJ and its rock erosion characteristics. Rehbinder [38] conducted a theoretical and experimental study on a supersonic PWJ produced by an impact pipe. The study showed that a strong radial burst occurred when the jet was sprayed under the influence of the pressure wave formed by impact piston extrusion. Politzer et al. [39] calculated a high-speed pulsed jet generated by the piston impact caused by combustion chamber expansion. Semko [40] evaluated the influence of fluid compressibility on the performance of a pulse water cannon. Additionally, Sripanagul et al. [41] used electromagnetic braking to generate a high-speed pulsed jet. However, these studies were mainly focused on the flow field characteristics of the impact PWJ and less on the rock-breaking performance of the variable cross-section squeezed pulsed water jet (SPWJ). The rock erosion performance of the SPWJ is significantly different and, under certain conditions, may be better than that of the CWJ. Therefore, this study is based on the SPWJ [42,43], and experimental research is conducted to study the rock erosion characteristics of the SPWJ in terms of the erosion area, depth, and erosion stripping volume of hard rock. The significance of this study lies in the experimental study of the mechanism of SPWJ erosion damage to granite and the analysis of the influence of different erosion parameters on the rock-breaking effect. The research results provide a reference for the fragmentation of rocks during the extraction of underground space resources, as shown in Figure 1.

2. Theoretical Background

2.1. Working Principles of SPWJ

As shown in Figure 2, the SPWJ is generated by a single-stage, single-acting supercharger with hydraulic oil as the driving medium. The hydraulic oil drives a piston to reciprocate back and forth so that the small-diameter end of the piston squeezes water in a pressurization cavity and intermittently sprays a PWJ through the nozzle. As shown in Figure 3a, when the piston presses the water body forward, the water in the pressurization chamber is squeezed and sprayed as a PWJ, and the one-way valve is closed at this time. When the piston moves backward, water is replenished in the chamber. The state of the nozzle is controlled by the flow rate of water replenishment, so the nozzle sprays a low-pressure continuous jet or intermittent water drops, and the one-way valve is in an open state, as shown in Figure 3b. The reciprocating motion of the piston depends on the reversing slide valve at the upper end of the piston, and automatic commutation can be performed.

Given the characteristics of the SPWJ, the authors focused on the piston extrusion stroke. As shown in Figure 3, a typical SPWJ-generating device includes a squeezing plunger, an impact chamber, and a nozzle installed in the chamber. Compared to conventional high-pressure continuous water jets, the variable cross-section extrusion type pulse water jet generator converts low-pressure fluid into high-pressure pulse water jets, as shown in Figure 4a. The occurrence of SPWJ is composed of two interrelated basic mechanisms, namely, the strong disturbance of the compression wave and the periodic change in volume. When the squeezing piston pushed into the impact chamber comes into contact with water, the generated pressure disturbance propagates to the bottom at the speed of sound and is reflected after propagating to the end. The pressure behind the compression wave is always higher than the pressure before, which also means that when the piston squeezes the water in the impact cavity, the pressure in the cavity will rise in a discontinuous manner. In other words, when the first compression wave continuously reaches its peak, the subsequent wave is the coupling wave of the compression wave and reflection wave, showing discontinuous rising and falling oscillation. When the piston retreats, the pressure in the cavity quickly drops to the initial input pressure, which is in good agreement with the actual test results (as shown in Figure 4b). To further clarify the mechanism of the SPWJ, the control body is shown in Figure 5. The mass conservation equation is applied to obtain the initial value equation involving the plunger and water mass, expressed in Equation (1) [38]:

Table 1. Relationship between input and output pressures of SPWJ generator and CWJ.

Nozzle Diameter	SPWJ Input Pressure psi (MPa)	SPWJ Output Peak Pressure pso (MPa)	CWJ Input Pressure pci (MPa)
0.5	5.2	30	30
	6.8	40	40
	8.5	50	50
	10.0	60	60
	11.9	70	70
	13.8	80	80

presents the output pressure of the SPWJ and CWJ, and the erosion and crushing behavior of granite by the SPWJ was studied by using the obtained nozzle output peak pressure.

$$\left\{\begin{array}{c}\begin{array}{c}\rho av+\stackrel{•}{\rho }A(h-x)-A\rho \stackrel{•}{x}=0\\ p=E_{wf}(\rho /{\rho }_w-1)\\ l_e\stackrel{•}{v}+v^2/2={\displaystyle {\int }_0^{p}dp/\rho }\\ \stackrel{••}{x}=-(A/M)p\\ x(0)=v(0)=p(0)=0\\ \stackrel{•}{x}(0)=U_0\\ \rho (0)={\rho }_w\end{array}\end{array}\right.$$

(1)

Among them: ρ represents the fluid density, kg/cm³; a represents the nozzle outlet area, m²; v represents the plunger speed, m/s; A represents the cross-sectional area of the booster chamber, m²; h represents the plunger stroke, m; x represents the actual stroke of the plunger, m; p represents the pressure of the booster chamber, MPa; E_wf represents the elastic modulus of the fluid, ρ_w represents the initial density of the fluid, kg/cm³; l_e represents the equivalent length of the nozzle; M represents the mass of the plunger, kg; and U₀ represents the initial velocity of the plunger, m/s.

However, in reality, the propagation mode of this wave is very complicated. The wave propagation in the cavity is three-dimensional, which makes the mechanism of the change in fluid physical properties and the interaction of waves in the cavity complex. Therefore, further research is needed to clarify this aspect.

2.2. Impingement Characteristics of Pulsed Jets on a Rock Surface

The process of rock erosion by the SPWJ is mainly composed of two stages. In the initial stage, the front end of the SPWJ contacts the surface of the rock mass, producing a powerful water hammer shock wave in the center of the rock mass and propagating inside it, as shown in Figure 6. Moreover, when the liquid at the jet boundary moves outward, the liquid pressure is released. A dilution wave is transmitted into the jet. When it is transmitted to the jet center, the surge pressure in the jet center is reduced to stagnation pressure, and the jet flows radially along the rock mass surface. In the second stage, the plunger retreats, the pressurized cavity is filled with water, water drops with weak pressure are generated and rushed to the rock surface, and the elastic tensile wave caused by the pulse water hammer in the initial stage of the jet collides, reflecting and interfering with the rock mass. Moreover, the jet has pressure pulsation, which easily causes fatigue damage on the rock mass surface. In addition, the SPWJ enters the cracks in the rock mass, expands and cracks it, and promotes crack propagation and breaking of the rock mass.

The duration of the pulse water hammer wave in the initial stage is very short, at only microseconds, but the dynamic pressure generated by it is undoubtedly massive compared with the stagnation pressure, as shown in Equations (2) and (3):

$$p_h=\rho cv$$

(2)

$$p_s=\frac{1}{2}\rho v^2$$

(3)

Among them, p_h represents the water hammer pressure at the jet tip, MPa; p_s represents the stagnation pressure of the jet, MPa; c represents the transmission speed of sound waves in water, m/s; and v represents the jet velocity, m/s. From this, we can observe that the SPWJ exerts a cyclic load and periodic water hammer wave on the rock mass surface, which will help to enhance the rock mass fracture. As a result, the SPWJ has stronger erosion ability than the CWJ.

3. Experimental Facilities and Procedures

3.1. Facilities

Figure 7 is a schematic of a SPWJ erosion test device. A SPWJ generation system was used in this experiment, which was independently developed and processed by our research team. A SPWJ is generated by the system and acts on the rock mass specimen. Specifically, the hydraulic pump provides the hydraulic power source, which passes through the reversing valve. Power hydraulic oil is supplied to the SPWJ generating device, which drives the extrusion plunger in the generating device to move forward after entering the generating device. The hydraulic oil drives the reversing slide valve in the cavity to move and controls the reciprocating movement of the extrusion plunger back and forth through the slide valve. Water is supplied to the front of the generating device through a water pump and a one-way valve, and this action occurs in the backward movement gap of the squeezing plunger, supplying water to the front part of the generating device. The reciprocating plunger periodically squeezes the water in the front part and forms a water jet through the nozzle, eroding and destroying the rock sample fixed on the clamping device. Rock fragments falling from the test pieces are splashed onto the platform for recycling. In addition, the adjustable range of the hydraulic pump is 0–15 MPa, the adjustable range of the water pump is 0–56 MPa, the pressure increase ratio can reach 5.8, and the highest output pressure of the PWJ generator can reach 80 MPa. As shown in Figure 7, three pressure sensors (model: SDA1000), calibrated by the manufacturer with an accuracy of ±0.1% FS, are installed on the hydraulic oil inlet, hydraulic oil outlet, and pressurization chamber, and the changes in hydraulic oil inlet pressure, hydraulic oil outlet pressure, and pressure in the pressurization chamber are obtained, respectively. During each test, the pressure changes at three positions in the entire experimental process can be obtained directly from the data acquisition system. In addition, the nozzle is installed at the center of the outlet on the right side of the pressurization chamber, and the rock sample is fixed on the clamping device. The clamping device can move axially in the range of 0–3000 mm, and thus the target distance from the nozzle outlet to the specimen surface can be continuously adjusted by moving the clamping device. After the nozzle diameter is normalized, this distance is defined as the dimensionless standoff distance S.

3.2. Nozzle and Materials

Figure 8 shows the nozzle profile, physical picture, and granite specimen of the SPWJ generator, specifically the inlet diameter D, outlet diameter D, and convergence angle θ. The length of the convergent section (L₁) and the total length of the nozzle (L) were d = 7 mm and d = 0.5 mm, respectively, with θ = 23°, L₁ = 12.5 mm, and L = 16.7 mm. The outlet diameter (d) of the nozzle could be selectively changed from 0.3 mm to 0.5 mm, as shown in Figure 8a,b. Additionally, erosion tests were conducted with CWJ nozzles having the same structural parameters, and a comparative analysis was performed.

Granite has good brittleness and strong abrasiveness. The granite specimens, as shown in Figure 8c, were used in the test and are commonly employed to evaluate and test the rock-breaking effect and performance of PWJs [13,20]. To ensure that the structure and mechanical parameters of granite were minimally disturbed, when making the granite specimens with a length of 100 mm, the granite was cut into cubic specimens by wire cutting. To eliminate the stress produced in the cutting process, the cut specimens were left standing for seven days. Subsequently, the physical and mechanical parameters of the granite specimens were measured, as listed in

Table 2. Physical and mechanical properties of granite samples.

Type	Density /kg·m−3	Elastic Modulus /GPa	Poisson’s Ratio	Compressive Strength /MPa	Tensile Strength /MPa
Granite	2683	49	0.27	218.2	14.10

.

3.3. Experimental Procedures

In every test of granite erosion by SPWJ, the SPWJ generated from the squeezed PWJ generator periodically impacted and damaged the rock samples on the clamping device, as shown in Figure 9. The SPWJ-generating device was fixed, a nozzle was arranged at the front end of the pressurization chamber, and then a granite specimen was clamped. The target distance parameter was set by adjusting the position of the clamping frame, and then the clamping device was locked.

Then, the water pump was started, and water was injected into the pressurization chamber. The aluminium alloy baffle in front of the granite specimen was then positioned, followed by starting the hydraulic pump and injecting hydraulic oil into the generator. The device was activated to squeeze the water body and generate a PWJ. The pressurization chamber pressure was monitored, and the inlet oil pressure was adjusted synchronously until it reached the predetermined pressure level, after which the aluminium alloy baffle was removed. Erosion interference of the jet on granite during pressure adjustment was avoided, as shown in Figure 10.

The SPWJ began to erode granite, and the erosion duration was 60 s in the rock erosion strength test. In the rock erosion failure rate test, the erosion time increased from 30 to 180 s and increased once every 30 s. In the optimum target distance test of rock erosion, the dimensionless standoff distance of the rock was changed from 100 to 300, and Δs = 50, as shown in Figure 10. After each erosion test, the large pieces of rock scattered on the platform were collected, and the eroded granite samples were taken out for measurement. Moreover, six outlet pressures were used in the test: 30, 40, 50, 60, 70, and 80 MPa. In addition, under the same conditions, each rock erosion test was repeated three times. The parameters describing the rock erosion characteristics of the SPWJ were measured and averaged to reduce systematic and accidental errors in the test process and make the results more reliable. The experimental conditions of the rock erosion test with the CWJ were exactly the same as those with the squeezed PWJ, including the jet outlet pressure, target distance, and erosion time. The specific experimental process parameters are shown in

Table 3. Experimental design of SPWJ and CWJ erosion granite.

SPWJ/CWJ	Outlet Pressure of Nozzle /MPa	Dimensionless Standoff Distance	Erosion Time/s
1	30, 40, 50, 60, 70, 80	150	60
2	60	50, 100, 150, 200, 250, 300	60
3	60	150	30, 60, 90, 120, 150, 180

.

3.4. Evaluation Methods

To characterize the erosion crushing performance of the SPWJ on granite, the erosion crushing area, erosion depth, erosion spalling quality, and erosion crushing rate of the rock mass were quantitatively analyzed. As shown in Figure 11a, the erosion area was measured using computer-aided design (CAD) software [44]. Specifically, a ruler or vernier caliper was used to measure rock mass samples, calibrated along the whole bit size of the vernier caliper, as shown in Figure 11. It can be observed from the images that the curve contains dual attributes, namely, the true length L_c of the calibration line and the CAD length L_d of the calibration curve. In addition, the envelope of the erosion and crushing area is drawn, the CAD area of the erosion and crushing area can be read as A_d by the software, and the actual area of the crushing area is expressed as A_c. The following relationship exists:

$$\frac{L_c{}^2}{L_d{}^2}=\frac{A_c}{A_d}$$

(4)

The actual surface area of the envelope of the broken area is as follows:

$$A_c=A_d\frac{L_c{}^2}{L_d{}^2}$$

(5)

The depth measurements of the erosion and fracture areas of the rock samples are shown in Figure 11b,c. Due to the irregular distribution and tortuosity of erosion pits at the bottom of the granite after being destroyed by water jet erosion, the conventional vernier caliper measurement method was unable to accurately measure their depth. Therefore, the granite specimen damaged by water jet erosion was scanned using computed tomography (CT) technology. The point source data of the fracture pit was obtained, and the fracture pit depth, Δh was determined by 3D reconstruction using Solidworks. The rock erosion intensity was determined based on the volume loss of the sample evaluation, ΔV, and the volume measurement method was consistent with the depth measurement method. In addition, the erosion was evaluated by the curve slope of the cumulative volume loss changing with time. The granite erosion per unit input pressure level is used to evaluate the erosion performance of water jets.

$$\Delta V_{ps}=\frac{\Delta V}{p_{si}}$$

(6)

$$\Delta V_{pc}=\frac{\Delta V}{p_{ci}}$$

(7)

3.5. Experimental Uncertainty

The uncertainty of this experiment is mainly reflected in the accuracy of the measurements and the chaos of the granite samples. The errors of the oil inlet pressure, oil outlet pressure, and pressurization chamber pressure obtained by the pressure sensor were less than 0.1% FS. The acquisition of erosion area parameters depends on the verticality of the picture shooting and the accuracy of the envelope drawing. Therefore, to improve the reliability and accuracy of the calculation results, the erosion damage area of each sample was measured three times, and the average value was taken as the result. Further, owing to the brittleness and chaos of the granite itself, when the granite is destroyed by water jet erosion, the result of the crushing pit is random. Therefore, to improve the accuracy of granite crushing, each rock sample surface was eroded at least three times; the average value of the erosion results was used as the test result, and the other results were treated as the variance.

4. Results and Discussions

To study the pressure output characteristics of the SPWJ, a preliminary experiment was conducted on the nozzle output pressure of a SPWJ generator with a nozzle diameter of 0.5 mm under different oil inlet pressure conditions.

4.1. SPWJ Erosion Granite Failure Mode

To understand how crushed granite specimens are eroded by the SPWJ, the macroscopic crushing morphology of granite after erosion by the CWJ and SPWJ was analyzed. Under a jet outlet pressure of 60 MPa, the damaged volume and area of the granite specimens reached a maximum, as shown in Figure 12. Owing to the erosion effect of the high-pressure water jet, there was an erosion hole in the center of each granite specimen. With the formation of the central hole, some granite specimens began to crack under the action of the water wedge, forming a large-scale erosion pit, indicating that the granite specimens are damaged by water jet erosion in the form of “drilling and cracking”. This type of damage is characterized by a shallow depth and a large erosion fracture area. Large-scale granite fragments were stripped. It can also be observed from Figure 13 that when the erosion pit produced by the CWJ is damaged by “drilling”, the damaged area is smaller than that of the SPWJ, whereas when it is damaged by “drilling–expanding”, the erosion pit produced by the CWJ is larger than that of the SPWJ. This is likely due to the water hammer effect of the SPWJ in the initial drilling stage, which generates strong tensile stress and shock waves on the surface of the granite specimen, effectively drilling it. However, after the drilling stage, the opening of the granite crack requires lateral stagnation pressure. At this time, the CWJ has more advantages than the SPWJ, which leads to larger expansion and crack areas and erosion pits after entering the expansion and crack modes.

A CT scan of the granite sample after SPWJ erosion was performed and the results are shown in Figure 14. SPWJ formed a large number of cracks in the granite and spalled in different ranges, as shown in Figure 14a. As shown in Figure 14b, the jet eroded the granite to create a main hole channel and produced a large number of main holes around the main hole. In the fissure, the granite is cracked by the pressure of the water wedge. The surface of the granite after erosion has formed several completely closed and incompletely closed fissures, as shown in Figure 14c, including the first gradient of erosion pits, the second gradient of complete cracking pits, and the first three-gradient incomplete cracking. The formation of erosion pits is related to the mechanism by which SPWJ decomposes granite, as shown in Figure 15. There are three models of SPWJ erosion granite. SPWJ uses its erosion effect on granite to form drilling holes. This is model I, the drilling model. After the SPWJ drilled the hole, the reverse jet scoured the hole and formed the scouring pit, which is model II. After SPWJ erodes the granite to form holes, cracks are formed around the holes and further enter the rock mass through the cracks, expanding the propagation of the cracks in the rock body and cracking and destroying the granite. The area of the cracking pit is much larger than the diameter of the jet. This is model III, the initiation model.

4.2. Influence of Nozzle Outlet Pressure on Rock Breaking Effect

Figure 16 shows the trend of area, depth, volume loss, and cumulative volume loss of crushed granite by SPWJ and CWJ under the outlet pressure of six nozzles. It can be clearly observed from Figure 16 that the size of the erosion pits produced by SPWJ and CWJ is similar. More specifically, the erosion depth of the two jets first increases and then decreases with an increase in nozzle outlet pressure, whereas the erosion area generally increases with an increase in pressure. However, there are certain singularities in the erosion area, which are due to the chaos of granite itself, and granite will occasionally crack and break on a large scale in the erosion process, forming a large area of erosion pit. Similarly, with an increase in pressure, the volume of granite spalling tends to increase first and then decrease. This is because the dimensionless standoff distance, S, in this experiment was fixed at 100. With the increase in pressure, the velocity nuclei of the two jets will obviously increase, and the optimal dimensionless standoff distance of the jet will move backward. Therefore, with the increase in nozzle outlet pressure, the loss of depth, area, and volume of granite crushed by the two types of jet erosion first increases and then decreases. In addition, with the increase in pressure, the cumulative spalling volume of granite increases continuously.

Furthermore, Figure 16 shows that at an initial low pressure, the erosion pit, erosion area, and spalling rock sample volume caused by the SPWJ were smaller than those of the CWJ. However, as the pressure increased, the erosion depth, area, and spalling volume of the SPWJ became greater than those of the CWJ. These characteristics have a strong relationship with the water cushion utility of the CWJ and the optimal target distance. For the CWJ, as the output pressure increases, the optimal dimensionless standoff distance also increases. This leads to an increase in the negative water cushion effect and a weakening of the stress wave effect produced by the jet during the erosion process. However, the water wedge ability of the CWJ is enhanced. At a certain drilling depth, the water wedge effect of the continuous water jet is dominant, which gives priority to releasing energy and cracking granite. Therefore, with an increase in the pressure of the CWJ, the volume and area of the broken granite increase, whereas the depth decreases. In contrast, the water cushion effect is further weakened for the SPWJ. At 70 MPa, the depth, area, and spalling volume of the crushing pit are better than those of the CWJ, which occurs because the SPWJ is intermittent.

Intermittent spraying leads to attenuation of water cushion effect. The jet head can generate a water hammer shock wave at high frequency at the granite contact surface, stretch the granite repeatedly, and further crack it by using its water wedge effect. It can be seen from Figure 16e that the erosion volume of SPWJ is higher than that of continuous water jets under unit input pressure.

4.3. Influence of the Dimensionless Standoff Distance on the Rock-Breaking Effect

Figure 17 shows the crushing ability of jet erosion for granite under different dimensionless standoff distances, and the influence of jet target distance on the erosion ability was analyzed. It can be clearly observed from the figure that for the CWJ, with an increase in the dimensionless standoff distance, the crushing ability gradually decreases, and the depth, area, and volume loss of the crushing pit are negatively correlated. Moreover, the crushing ability of the SPWJ first increases and then decreases with an increase in the dimensionless standoff distance. For both the CWJ and SPWJ, the area, depth, and erosion ability of the jet-crushing rock are closely related to the dimensionless standoff distance of the jet, and all of them depend on the characteristics of the jet’s external flow field. As can be clearly observed from Figure 17, when S = 100, the crushing capacity of the CWJ reaches its peak, whereas that of the SPWJ reaches its peak when S = 200. Under the same nozzle outlet conditions, there are significant differences between SPWJ and CWJ, and the optimal dimensionless standoff distance of the SPWJ is increased by 100%.

Furthermore, it can be clearly observed from Figure 17a–c that, compared with the CWJ, the erosion crushing area of the SPWJ is weaker than that of the CWJ at the initial stages of S = 100 and 150. However, with an increase in the dimensionless standoff distance, the crushing volume of the SPWJ is better than that of the CWJ at S = 200. This is because the optimal dimensionless standoff distance of the CWJ is approximately 100. Additionally, the experimental results are close to the previously reported results, which proves the validity of the experimental results. Nevertheless, with the increase in the dimensionless standoff distance, the crushing capacity of the CWJ gradually decreases, whereas that of the SPWJ gradually increases. At the initial stage, the CWJ is at the optimal target distance, and granite is cracked in a large range by drilling, expansion, and cracking failure modes. In contrast, the energy in the core section of the SPWJ is not completely released, and thus the granite is broken by drilling and eroded in a small range. However, with an increase in the dimensionless standoff distance, the SPWJ gradually reaches the optimal target distance. Owing to the increase in the target distance and the intensification of mixing with air, the shearing effect of air on the jet is enhanced, the crushing ability of the jet is obviously weakened, and the effective length of crushing is further reduced. When the dimensionless standoff distance increases from 100 to 200, the erosion area caused by the SPWJ decreases from less than 17.6 times to 53.6% of the area caused by the CWJ. Similarly, the erosion depth caused by the SPWJ changes from less than 3.57 times to better than 1.34 times the depth caused by the CWJ. Additionally, the spalling volume of granite caused by the SPWJ decreases from less than 48.3 times to better than 1.22 times the volume caused by the CWJ. With a further increase in the dimensionless standoff distance, the crushing capacity of the SPWJ and CWJ begins to decline because, with the increase in the target distance, the energy interaction between the jet and environment becomes more intense, the core segment of the jet begins to dissipate, and the axial jet tends to atomize. Moreover, the downward trend of the SPWJ is weaker than that of the CWJ. As shown in Figure 17c, when the continuous water jet is at the optimal dimensionless standoff distance S = 100 in the experiment, the dimensionless standoff distance is offset by 50 and the jet erosion volume is reduced by 25.8%. However, for SPWJ, when it is offset from the experimental optimal standoff distance S = 200 by 50 to 150 or 250, the jet erosion volume is reduced by 87.5% and 78.7%, respectively.

Furthermore, in the cumulative comparison of the spalling volume of granite with different dimensionless standoff distances, the CWJ was significantly better than the SPWJ. As shown in Figure 17d, the sensitivity of the SPWJ to the target distance is stronger than that of the CWJ in the process of engineering practice. In other words, the SPWJ has higher requirements for the target distance in the process of erosion and crushing because it is intermittently sprayed from the nozzle and is not only in a high-pressure state but also has strong pressure disturbance and pressure pulsation. As shown in Figure 4, the erosion drilling ability of this jet on granite is better than that of the CWJ because of its periodic water hammer effect. However, because of its intermittent emission, when the jet enters the fracture channel to crack granite, it cannot maintain a continuous crack, and the water wedge effect on granite is weaker than that of the CWJ. When both jets are at the optimal target distance, the distance of the SPWJ is considerably longer than that of the CWJ, and its application range is wider. It can be seen from Figure 17e that when the dimensionless target distance is between 100 and 150, the rock-breaking volume of the unit input pressure of SPWJ is lower than that of CWJ. When the dimensionless target distance is 200, 250, or 300, the rock-breaking volume of the unit input pressure is higher than that of CWJ.

4.4. Influence of Erosion Time on Rock Breaking Effect

The rate trend of granite erosion by the SPWJ and CWJ is shown in Figure 18, and it is an important index for characterizing the erosion and crushing performance of the water jet. As presented in Table 3, the destruction ability of the SPWJ and CWJ under different erosion times was studied. As shown in Figure 18c, the breaking rates of the two types of jets have similar laws. With the extension of erosion time, the volume of erosion spalling increases first and then decreases. This change is related to the process of granite erosion. At the initial stage of jet erosion of the granite specimens, the jet forms shallow pits on the surface of the rock samples, a small hole is formed by drilling, and the jet further expands the small hole. The target distance of the jet increases owing to the drilling of the small hole, and the space in the hole also prevents deep erosion by the jet. At this time, the jet starts to enter the granite’s internal pores, and cracks are generated by the jet, which overcomes the tensile strength in the rock body, expanding and cracking the rock mass, peeling off large granite rock blocks, and further prolonging the target distance of the jet contacting the rock mass surface. At this time, with an increase in the target distance, the ability of the jet is weakened, and the erosion efficiency of the jet decreases gradually.

When the erosion time of the jet is 30, 60, or 90 s, the erosion crushing volume and depth of the SPWJ are larger than those of the CWJ, and the area of the crushing pit is not significantly different from that of the CWJ. Then, when the erosion time of the jet is prolonged to 120, 150, and 180 s, the crushing performance of granite by the SPWJ and CWJ is quite different, as shown in Figure 18a–c. With an increase in time, the erosion depth, crushing area, and spalling volume of the SPWJ change smoothly, thus indicating that the SPWJ is less sensitive to erosion time. In a short time, the optimum crushing volume will be reached, and its crushing efficiency will be at its maximum. However, for the CWJ, with the extension of erosion time, when the erosion time exceeds 90 s, the crushing ability is significantly improved, the depth and area of the eroded granite and the volume of the exfoliated granite are significantly greater, and the sensitivity to erosion time is strong. The extension of erosion time can effectively increase the ability of the CWJ to erode and break the granite. This occurs because, for the SPWJ, jet erosion peels off the granite, which can form multi-layered swelling and cracking rings. As shown in Figure 13, shallow pits are formed at the initial stage of erosion damage, and the rock samples are further cracked. However, owing to the intermittent jet emission, it is difficult to store water in rock fissures, and with an increase in time, the crushing effect is limited. For the CWJ, the continuous injection can cause more water bodies to enter the cracks, which are expanded, and the spalling volume of granite increases with the extension of erosion time. As shown in Figure 18d, to further simulate the practical application of the jet in engineering, the crushing rate of the accumulated erosion time of the jet is analyzed, and it is found that the SPWJ has an advantage in the initial stage, but with the accumulation of time, the CWJ will peel off more granite. As shown in Figure 18e, the crushing volume of SPWJ is lower than CWJ at the unit input pressure when the erosion time is 120 s, and it is higher than CWJ at other erosion times.

In summary, under the same pressure level, compared to continuous water jets, SPWJ can effectively erode and destroy granite, resulting in larger fracture pits. However, there are still some shortcomings in this technology, such as the very limited diameter of the nozzle, which temporarily prevents the use of larger-diameter nozzles. The effectiveness of the jet in destroying other rocks needs further experimental verification.

5. Conclusions

This study aimed to investigate the rock erosion and crushing characteristics of an SPWJ, and the experimental results were evaluated based on factors such as erosion depth, erosion area, spalling volume, and unit input pressure erosion volume. The goal was to improve the performance of water jet erosion and crushing of granite and apply it to the erosion and crushing of hard rock. The main results of this study are as follows:

(1)

During the process of SPWJ erosion of hard rock, the water hammer stress waveforms tensile cracks inside the rock, and the jet enters the cracks to further water wedge and crack the granite, forming preliminary erosion pits. As the jet erosion target distance increases, the jet energy decays to the point where cracks cannot be formed, and the rock fragmentation reaches the limit position.

(2)

With an increase in pressure, the rock-breaking capacity of SPWJ initially increases and then decreases, reaching its maximum at 60 MPa. Under the experimental conditions, the erosion ability of CWJ is better than that of SPWJ when the pressure is lower than 60 MPa, and the erosion ability of SPWJ is better than that of CWJ when the pressure is above 60 MPa.

(3)

The optimal dimensionless standoff distance for the SPWJ is approximately twice that of the CWJ. Under the experimental conditions, the optimal dimensionless target distance for the CWJ is 100, while for the SPWJ, it is 200. Moreover, the SPWJ is more sensitive to the target distance than the CWJ. When the SPWJ is offset from the experimental optimal standoff distance of S = 200 by either 50 to 150 or 250, the jet erosion volume is reduced by 87.5% and 78.7%, respectively. In comparison, for CWJ, this reduction in jet erosion volume is only 25.8%.

(4)

SPWJ’s feedback on the erosion time is relatively rapid, and the peak value of crushing can be reached at the beginning of the erosion. With the extension of the erosion time, the effective crushing amount of the squeeze pulse water jet hardly increases. When the erosion time is less than the 90 s, the crushing ability of SPWJ is better than CWJ.

(5)

Under the condition of unit input pressure, the overall erosion ability of SPWJ on granite is better than that of CWJ. The mechanism of SPWJ erosion and decomposition of granite needs to be analyzed theoretically and experimentally.