2.1 Experimental samples and equipment

Granite, which frequently appears in diaphragm wall construction due to its hardness, was chosen for experiments. Table 1 provides the fundamental physical and mechanical properties of the rock that were determined using uniaxial compression experiments and Brazilian splitting experiments. The dimensions of the sample were 300 mm × 200 mm × 210 mm, as depicted in Figure 3.

               

The test equipment used the multimode pick linear rock-breaking test system developed by the Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, as depicted in Figure 4a. The test system had a maximum loading capacity of 800 kN in the normal force and 200 kN in the horizontal force. It had a normal loading stroke of 300 mm and a tangential loading stroke of 2000 mm. The test system could achieve a maximum loading rate of 300 mm/s in the horizontal direction. The pick was equipped with a tungsten-cobalt alloy pick, as is commonly used in double-wheel trench cutters. According to previous research (Xiao, Lu, et al., 2022), the cutter's inclination angle was 75°, enabling it to break hard and extremely hard rock.

               

The high-pressure water jet rock-cutting test was performed using an HZ37G water jet system, as depicted in Figure 4b. The high-pressure pump in the system could generate a maximum pressure of 420 MPa, with a maximum flow rate of 3.7 L/min. The water jet nozzle could move at a maximum speed of 9000 mm/min.

2.2 Experimental process

               

2.3 Numerical model

A numerical model based on HPC fragmentation using the CDEM was established (Feng et al., 2015; Ju et al., 2016; Ren et al., 2022) to examine the auxiliary rock fragmentation process of a high-pressure water jet precutting groove. Table 3 and Figure 6 show the model's geometric dimensions and computation parameters derived based on the indoor experimental conditions. Drawing upon the physical and mechanical parameters of granite from the literature (Hu, 2008), the material parameters of the numerical model with the pick established as a rigid surface were set.

               

The CDEM introduces a virtual fracture to characterize the gradual process from the intact state to fracture initiation and development to fracture. When the material is intact, the spring of the contact surface between the elements transmits mechanical information. When the spring reaches the set fracture strength criterion, the contact surface breaks, the virtual interface is transformed into the real contact interface, and a new contact model and parameters are given for the real contact interface.

3.1 Rock fragmentation patterns

The HPC sample, pregrooved using high-pressure water jet equipment, was placed in the sample box of the multimode pick linear rock-breaking test system. The pick entered the rock mass from one side. The local strain energy of the rock mass accumulated to a certain extent, resulting in a low “bang” sound and splashing of small-sized cuttings (Figure 7a). The rock mass exhibited evident brittle fracture characteristics. At this moment, the pick vibrated and quickly moved forward, leading to a significant leap-forward intrusion phenomenon. This process occurred repeatedly during the crushing of the rock mass by the pick until the end of the cutting process. During the cutting process, a relatively large piece of rock debris was removed from the rock mass (Figure 7b).

               

When the sample was not pre-grooved, the cutting process became challenging due to PUC spacing, resulting in a loud “bang” sound and splashing of cuttings. When the pick was at a PRC distance, the rock-breaking difficulty was less than that of PUC. The sound of the rock-breaking process decreased, but it remained louder than that of pre-grooved samples.

Examination of the cutting samples revealed a dark indentation formed by the pick along its path. The directly contacted rock mass within the indentation showed significant fractures, indicative of a crushed state. The impacted rock mass was compressed and eroded by the pick to form a dense core (Figure 7e,f) that redistributed stress laterally, promoting further fracturing. Stress propagation halted upon reaching the free surface created by the water jet grooves on both sides, thus confining the rock breakage within the region between the pick's cut path and the water jet grooves. The testing outcomes for the PRC and PUC samples bore a resemblance to those of the HPC sample, with primary variations observed in two areas: the noise generated by the sample with no groove during fracturing exceeding that of the HPC sample, and a markedly smaller rock debris size of fragments produced by samples with no groove than their grooved counterparts during rock fragmentation (Figure 7c,d). This observation demonstrates that HPC simplifies rock pulverization, thereby channeling the energy used in mechanized fracturing toward the creation of fissures and the achievement of grand-scale fragmentation, in contrast to localized pulverization.

An Incan-Pro 3D laser scanner was used to examine the topographic features of the rock mass surface post-combined rock breaking. Figure 8 depicts the scan results. A pronounced discrepancy existed between the surfaces of the HPC samples and those of the PRC and PUC samples. Figure 8a,b illustrates that when a water jet groove was present on the sample surface, the pick cut into the rock mass, generating a crack extending from the pick to the groove base. The rock mass above the fracture plane broke off and separated from the sample to form a Λ-shaped rock ridge on the sample surface (Figure 8c). The rock ridge summit corresponded to the pick-cutting line, similar to Xu's rock-breaking test law (Xu et al., 2021; Xu, Lu, et al., 2022). The rock mass at the rock ridge exhibited incomplete features with numerous non-penetrating cracks, thus compromising its integrity compared with a complete rock mass.

               

As depicted in Figure 8f, the interaction between the pick and the PRC/PUC samples resulted in a V-shaped indentation, mirroring the pick's tip. This suggests the pick's limited efficiency in fracturing hard and extremely hard rock masses such as granite, as it primarily disrupts the rock mass at the penetration point, failing to induce substantial fissures in the surrounding rock. As displayed in Figure 8d,e, impenetrable cracks formed when a nonrelated cutting mode spacing was used, resulting in a largely unfractured boss on the sample's surface. However, when PRC spacing was implemented, the ensuing fissures intersected, eliminating the interjacent boss. It is further explained that the free surface plays an auxiliary role in crushing extremely hard rock for the adjacent pick.

3.2 Pick load-cutting displacement curve

The load-cutting displacement curve of the pick in the rock-breaking process directly reflects the pick-sample relationship, demonstrating the energy accumulation and dispersion in rocks and the rock mass fracturing triggered by the pick-cutting action. Figure 9 illustrates the process of the rock-breaking load under HPC, PRC, and PUC conditions, revealing that the horizontal and normal loads were similar, while the lateral load was minimal; this indicates that the pick's horizontal and normal loads exerted on the rock mass surface were primarily responsible for rock mass fragmentation.

               

The pick's rock-breaking load displayed a continuous trend of peak value followed by a decline, signifying a distinct leap-forward intrusion phenomenon. The rock-breaking load initially increased from a minimal value to an apex value and then decreased. The rock mass comprises three stages: linear elastic deformation, elastic-plastic deformation, fracture development, and expansion. Externally, it embodies a gradual sequence involving the elastic deformation of rock mass and the formation cum fragmentation of the compact core. The transition from plasticity to brittleness ensues swiftly in light of the granite's high tensile strength and brittle features. During the experimental process, it was observed that the plastic deformation phase was quite brief throughout the deformation and fracturing process of the rock mass, and it occurred almost simultaneously with the fracturing of the rock. When the pick cut through the intact rock, a significant amount of strain energy accumulated within the rock due to its high strength. However, because of the rock's high brittleness, the strain energy release rate during plastic deformation and fracturing was very rapid (Wang et al., 2023). Concurrently, a dense core formed as a medium for force transmission. As a result, when the rock reached its strength limit, the cutting load of the pick peaked, then suddenly dropped, and transitioned into a leap-forward intrusion phase. Thus, the plastic deformation phase of the rock mass is virtually absent in the curve representation (Figure 9), and the presence of the compact core observable on the rock mass surface in Figure 7 validates that this stage exists, serving as the medium for transmitting the rock-breaking force, thus leading to rock mass fracture.

The pick average rock-breaking load was evaluated. As illustrated in Figure 10, under PUC spacing conditions (with no precut groove), the average normal and horizontal loads were recorded as 19.547 and 18.529 kN, respectively. Under PRC spacing conditions (with no precut groove), the normal and horizontal loads decreased to 15.7 and 15.588 kN, respectively, that is, reductions of 19.95% and 15.87%, respectively. With the adoption of the HPC mode, normal and horizontal loads decreased to 10.011 and 10.5 kN, respectively, reflecting decreases of 36.02% and 32.07%, respectively, compared with PRC, and decreases of 48.78% and 42.85%, respectively, compared with PUC.

               

The above data illustrate that under PRC/PUC conditions, the free surface created by picks can facilitate the fracture process of adjacent picks to some degree, but the auxiliary effect is not optimal. Significantly, current experimental findings indicated that the minimal pick spacing necessary for the picks to create PRC conditions is small in hard and extremely hard rock conditions. This implies that more picks are essential within the same milling wheel width during the design phase of the pick arrangement system to fracture hard and extremely hard rock. While this design approach reduces the fracture load and wear per pick, it substantially augments the overall torque and power required for the complete milling wheel's rock fracture, increasing energy consumption, which presents an unfavorable trade-off. In summary, when using the PUC pattern for pick arrangement, the picks do not benefit from the assistance of adjacent picks in forming free surfaces during the cutting process, resulting in higher rock-breaking loads. Consequently, the more picks there are on the milling wheel, the greater the torque required for the milling wheel to rotate. When using the PRC pattern for pick arrangement, the picks can benefit from the free surfaces formed by the cutting action of adjacent picks. However, when using the PRC pattern, the spacing between picks is relatively close, necessitating more picks on the milling wheel. Thus, while the wheel may be capable of breaking hard rock, the increased number of picks may lead to higher overall torque on the milling wheel. When using the HPC pattern, the free surfaces generated by the high-pressure water jets cutting into the rock assist in the breaking action of adjacent picks. Therefore, HPC effectively increases the relieved cutting spacing, thereby reducing the number of picks arranged on the milling wheel, decreasing the torque required during milling wheel rotation, and enabling the fragmentation of larger volumes of rock mass. Consequently, the HPC mode is an efficient approach for rock fracture under hard and extremely hard rock conditions.

3.3 Rock-breaking performance evaluation

The statistical analysis based on the rock debris size classification was performed, with results as depicted in Figure 11. Under the PUC condition, the primary distribution of rock debris was within the 0–2.5 mm range, indicating small particle sizes. A decrease in the mass fraction of rock debris was observed as the particle size increased. Under the PRC condition, there was a slight increase in the mass fraction of rock debris within the 2.5–5.0 mm range; however, smaller debris within the 0–2.5 mm range remained predominant. When HPC was used for rock breaking, the rock debris was predominantly within the 5–10 mm range. A notable increase in the mass fraction of larger-sized rock debris and a significant decrease in smaller-sized rock debris were observed. This is due to the auxiliary effect of the water jet cutting groove; a through-going crack was formed within the rock mass from the tip of the pick to the bottom of the water jet cutting slot (Figure 8d), causing the rock mass on both sides of the pick to the water jet slot to fall off directly. This part of the rock mass did not directly undergo the impact and cutting action of the pick. Thus, it did not undergo a significant degree of fragmentation, thereby increasing the mass fraction of large-diameter rock debris.

               

Table 4 provides the SE consumption and CI for three distinct rock-breaking scenarios that were determined based on the statistical analysis of rock debris data. Under PUC conditions, a higher SE consumption was observed during rock breaking via pick. Compared with PUC, PRC exhibited a reduction of 46.03% in SE consumption. Utilization of HPC led to an 88.58% reduction in SE consumption compared with PRC and a 93.84% decrease compared with PUC. From these values, it can be seen that the HPC method has achieved good rock-breaking effects. However, HPC can achieve good auxiliary rock-breaking effects in the indoor experimental environment because it is relatively simple compared with the construction environment, and fewer factors can disturb the rock-breaking process. In actual construction scenarios, due to the complexity of the environment, the auxiliary rock-breaking effect of HPC will be reduced to some extent. Current practical results (such as the Longyan TBM) have shown that water jet grooving-assisted rock breaking can still achieve good auxiliary effects. Therefore, in practical engineering practice, further adaptive design of water jet parameters should be performed according to the type of rock to enhance the performance of HPC.

The rock-breaking process exhibited a low CI under the PUC condition. Compared with PUC, the CI under the PRC condition increased by 112.77%, a modest enhancement. With the application of HPC, the CI was 159.28% relative to PRC and 189.77% relative to PUC, an approximate doubling compared with PUC.

Through statistical analysis of SE consumption data and the CI, it is concluded that a free surface substantially reduces energy consumption and enhances the CI of broken rock masses. Under the PRC condition, the cutting surface of the pick creates a shallow, free surface that facilitates rock mass breaking. This surface has a V shape with a certain cracking level near the free surface. The pick can induce extensive cracking near the free surface in soft and medium-hard rocks. The fracture zone alongside the free surface can thus play a significant auxiliary role. The pick generates a limited range and number of cracks around the free surface in hard and extremely hard rocks, resulting in a reduced auxiliary effect from the fissure zone alongside the free surface. A high-pressure water jet can generate a specific depth of free surface on the exterior of both hard and extremely hard rock structures, thus offering substantial auxiliary benefits.

When considering the CI, it was observed that the presence of a free surface significantly enhanced the roughness of rock debris, lowering the SE consumption. This suggests that the free surface alters the crack's development pattern. The rock-breaking mechanism transforms from a fine-crack crushing mode to a large-chunk stripping mode, which implies a transformation in the energy conversion mechanism of the pick during the rock-breaking process. Without a free surface, the pick's kinetic energy primarily translates to energy concentrated on crushing the proximal rock mass near the pick's apex. Due to granite's high uniaxial compressive strength, a substantial amount of energy is required in its crushing process. Consequently, the leftover energy post-crushing cannot produce extensive cracking in the surrounding rock mass. The introduction of a free surface alters this process.

4.1 Rock mass fragmentation process

The process of rock mass fracturing reveals that the precut grooves on the rock mass surface provide a free surface for rock breaking. CDEM numerical calculations were used to obtain the simulation results for both preset-free surfaces and non-preset-free surface rock mass models. Figure 12 depicts the fracturing process of a rock mass model without a preset-free surface. Rock mass deformation occurred as the pick initiated penetration (Figure 12a). Concurrently, radial fractures from the penetration point developed and generated a compact core (Figure 12b). As the pick continuously penetrated, the rock mass presented an ongoing development of fractures. The fractures beneath the pick tips expanded extensively (Figure 12c,d). This phenomenon can be attributed to the horizontal extrusion force generated by the pick's penetration, which induces tensile stress and subsequent fracturing in the underlying rock mass.

               

Figure 13 shows the breaking process of a rock mass model with preset-free surfaces (HPC). Deformation occurred as the picks initiated penetration into the rock mass (Figure 13a). Concurrently, a compact core formed within the rock mass; a Λ-shaped fracture then emerged, stretching from the point of penetration to the base of the preset-free surfaces (Figure 13b). As the pick penetration increased, the development of Λ-shaped fractures persisted (Figure 13c,d). Ultimately, the Λ-shaped crack traversed both the penetration point and the base of the preset-free surfaces, expanding the crack opening. Simultaneously, the rock blocks on either side of the fracture dissociated from the original rock mass.

               

4.2 Auxiliary rock-breaking mechanism

A rock mass fracture classification and statistical program was developed based on JavaScript, as shown in Figure 14, to further reveal the mechanism of HPC reducing rock-breaking force. The program monitors the fracture of the spring elements of each contact surface by traversing the contact surfaces in the numerical model and classifies the fracture modes of each contact surface, including tensile, shear, and tensile-shear composite fractures. Rupture patterns are distinguished by different colors, and the numbers of ruptures in different patterns are counted. In postprocessing, the displacement vector of the element section is drawn.

               

As depicted in Figure 15, a free surface markedly altered the rock mass's displacement vector during the pick rock-breaking process. Figure 15a demonstrates that without a free surface, the rock mass was compressed by the pick's edge surface, moving toward its normal direction and producing numerous nonpenetrating cracks proximal to the pick tip. As illustrated in Figure 15c, the rock mass near the pick tips exhibited abundant cracking. Owing to granite's attributes, such as high strength, substantial cohesion, and significant internal friction angle, the predominant fracture type of the rock mass was shear fractures, featuring minor segments of tensile and tensile-shear composed fractures. Given that the rock mass's compressive strength significantly surpassed its tensile strength, more significant energy input was necessitated during its crushing process, thereby increasing the difficulty of breaking the rock mass.

               

Counting the number of fractures in different modes (Table 5), we see that the proportion of shear fractures in the rock mass was largest when the rock mass was broken by pick or HPC. When HPC rock breaking was used, the proportion of tension-shear composite rock-breaking in the rock mass increased to 565.14% compared with pick rock-breaking, and the proportion of tension fracture increased slightly to 109.20%. Due to the mechanical properties of rock masses that are compressive but not tensile (Nishimatsu, 1972), the increase in the proportion of tension and tension-shear composite fractures will reduce the force and energy required for rock breaking, thereby reducing its difficulty. The scanning results of the sample by scanning electron microscopy (SEM) verified this point. As shown in Figure 16, when the rock was broken by a pick (Figure 16a), the cuttings section was relatively flat and had scratch marks. When HPC was used to break the rock (Figure 16b), other than the shear fracture, a large undulating fracture surface appeared in the cuttings section, which shows the occurrence of tensile fracture.

               

As depicted in Figure 15b, when the free surfaces were preset within the rock mass model, significant horizontal movements within the rock mass were observed on both sides of the pick, moving toward the direction of the precut free surface. Simultaneously, the rock mass developed a Λ shape through fracture extending from the pick penetration point to the base of the free surface, causing the rock mass above the fracture to strip away and form a rock ridge. The numerical simulation results produced the same phenomenon as the experimental sample slice, as shown in Figure 17c,d; this phenomenon did not occur in pick cutting (Figure 17a,b). This observation aligns with our experimental findings in Figure 8a. In addition, Figure 15d demonstrates that, while assisted by the free surface, the penetration force of the pick displaced the rock mass to both sides. The rock mass can generate tensile stress, forming tensile and tensile-shear composite fractures within the rock mass near the pick tips and Λ-shaped fractures. Simultaneously, a reduction in the number of cracks beneath the pick was observed. These findings suggest that the free surface altered the rock mass breakage mode and decreased its difficulty. Furthermore, the free surface changed the trajectory of fracture development, fostered the formation of larger fragments, and enhanced the roughness of the fractured rocks.

               

Figure 18 depicts the intermediate principal stress within the rock mass. The intermediate principal stress of the rock mass model with the free surface (Figure 18b) proved to be significantly lower than that of the model without the free surface (Figure 18a). The intermediate principal stress in the rock mass was released during the penetration of the picks due to the free surface. Based on the intermediate principal stress effect, the free surface may reduce the required strength and difficulty encountered during rock mass breaking by decreasing the intermediate principal stress.

               

Energy curves further demonstrate the aforementioned mechanism. As depicted in Figure 19a, the penetration force increased as the pick penetrated deeper into the rock mass. The compression and fragmentation of the rock mass transitioned the pick's kinetic energy into strain energy, thereby continuously extending the range of a compact core. Generally, the accumulation of strain energy within the rock mass exhibited an increasing trend. When the internal fracture of the rock mass occurred, the pick had a leap-forward intrusion phenomenon. The strain energy in the rock mass decreased to a certain extent. Still, the strain energy in the rock mass could not be released entirely. At this time, the kinetic energy curve appeared to peak. As illustrated in Figure 19b, when a free surface existed within the rock mass, a compact core formed during the initial stages of pick penetration. Here, the accumulated strain energy continually increased but was significantly lower than in situations where pick penetration occurred without a free surface (Figure 19a). When the Λ-shaped fracture propagated, it released the strain energy stored in the compact core, causing a decrease in amplitude. As a result, the existence of a free surface assisted in releasing accumulated strain energy during pick penetration, which mitigated the fracturing difficulty of the rock mass.