Abstract
When tunnel boring machines (TBMs) excavate through jointed rock masses, the cutting efficiency is strongly affected by the shear strength of joints, the mechanism of which, however, remains poorly understood. In this study, a series of disc-cutter indentation tests were conducted on granite rock mass specimens with different joint shear strengths. During the indentation, the cracking process was recorded by a digital image correlation (DIC) system. The deformation and strength of specimens, cracking behavior, rock breakage mode and cutting efficiency were quantitatively investigated. In addition, to investigate the combined effects of joint shear strength, orientation and spacing on the rock breakage mechanism, numerical rock mass models were established based on a particle flow code PFC2D. Experimental results reveal that the cracking of primary and secondary cracks changes from the mixed shear-tensile to tensile mode in the initial stage, while the joint shear strength does not affect the cracking mode in the subsequent propagation process. The rock breakage mode is classified to an internal block breakage mode, a cross-joint breakage mode and a cutters-dependent breakage mode. The cross-joint breakage mode is optimal for improving the cutting efficiency. Numerical simulation results reveal that the increase in the joint shear strength changes the internal block breakage mode to cross-joint breakage mode for rock masses of particular ranges of joint orientation and spacing. These findings provide basis for improving the TBM cutting efficiency through jointed rock masses.
Keywords: Indentation test; Joint shear strength; Disc cutter; Rock breakage mechanism; Cutting efficiency
(ProQuest: ... denotes formulae omitted.)
1 Introduction
Tunnel boring machine (TBM) is a kind of advanced excavation method in underground constructions. Compared with the drilling and blasting method, TBM has superior efficiency and safety, and lower labor costs and disturbance to the surrounding environments (Geng et al., 2016; Zhou et al., 2021; Chen et al., 2022; Li et al., 2022). Therefore, it has been widely and increasingly employed in the hydraulic engineering, mineral engineering and traffic engineering worldwide (Acaroglu et al., 2008; Liu et al., 2017). The cutting efficiency of TBM is significantly affected by the geo-mechanical and geological condition of a construction site, such as the uniaxial compressive strength (UCS) of rocks, the orientation, spacing and strength of rock joints, the rock mass quality for TBM (QTBM), etc. (Barton, 2000; Mohammadi et al., 2015; Macias et al., 2016; Li et al., 2020; Song et al., 2022). Particularly, the shear strength of rock joints plays an important role in the deformation and cracking process of rock masses, which determine the rock breakage mode and penetration rate of TBMs (Wang et al., 2022). Therefore, it is essential to investigate the influence of joint shear strength, Tj, on the rock breakage mechanism by disc cutters.
Previous studies have revealed that the primary factors influencing the rock breakage by disc cutters can be divided into two categories: geological and operational parameters. Specifically, geological parameters include the rock strength, joint orientation, joint spacing, rock mass quality for TBMs (QTBM), confining pressure, etc.; operational parameters include the penetration depth, cutter spacing, control mode, rotational speed of cutterheads, etc.
In the geological aspect, several classical prediction models were initially proposed to establish the relations between the UCS, tensile strength and forces acting on the disc cutter, such as the Norwegian University of Science and Technology (NTNU) model (Blindhcim, 1979) and the Colorado School of Mines (CSM) model (Rostami & Özdemir, 1993). Later, the prediction models were modified by taking a brittleness index (BI) and a rock fracture index (RFI) into account (Yagiz, 2002). When disc cutters penetrate a rock mass, the cracking behavior can differ greatly due to the existence of joints. Therefore, according to field observation data, Barton (2000) proposed a new model to estimate the advance rate of TBMs based on the Q rock mass classification system QTBM, which involves rock quality designation (RQD), joint condition, stress condition, intact rock strength, quartz content and TBM thrust. Compared with other rock mass classification indices, important factors influencing the cutting efficiency of TBMs were systematically considered in the Qtbm.? providing an efficient method for excavation design and analysis.
By means of numerical simulations and experiments, many scholars have attempted to investigate the influences of joint orientation and spacing on the cracking behavior of rock masses subject to disc cutting (Gong et al., 2005, 2006; Bejari & Khademi Hamidi, 2013; Yin et al., 2016; Zhai et al., 2016; Jiang et al., 2018; Afrasiabi et al., 2019; Liu et al., 2021). It is concluded that the joint orientation and spacing primarily influence the crack initiation and propagation direction, as well as the rock breakage mode. In general, two rock breakage modes were observed: (1) the cracks initiate beneath the crushed zone and propagate downwards to the joints; (2) the cracks initiate from the joints and propagate upwards to the free surface (Gong et al., 2005). The TBM cutting efficiency decreases with the increase of joint spacing under a given joint orientation (Gong et al., 2006). The optimal joint orientation for the TBM cutting efficiency is about 60°-75° against the cutting face (Bcjari & Khademi Hamidi, 2013). Regarding the influence of the confining pressure, it was found that the increase in the maximum confining pressure can promote the crack propagation to the deeper parts of the rock mass, and as a result, the cutting efficiency can be improved (Yin et al., 2014; Liu et al., 2016a). With the increase of the confining pressure, the rock breakage mode changes from over-breakage to under-breakage and finally to overbreakage (Pan et al., 2018).
In the aspect of operational parameters, the cutter spacing and control mode have attracted close attention. According to the linear cutting tests and numerical simulations on different types of intact rocks, the optimal ratio of cutter spacing to penetration depth s/p, was found to range from 7.5 to 10 (Cho et al., 2010, 2013). Mathematical relation among the optimal ratio s/p, rock brittleness and cutter tip width was established (Moon & Oh, 2012). Later, the optimal ratio s/p was modified taking into account the action of the confining pressure (Liu et al., 2016b). It was found that the increase of the differential stress is in favor of the propagation of cracks between cutters, causing the elongated optimal spacing. Recent studies also revealed that the horizontal displacement of jointed rock masses favors the development of shear cracks subject to the disc cutting, resulting in the increase in the optimal cutting spacing. The optimal cutting spacing reaches the maximum at a joint orientation of 60°, while the increase in joint spacing decreases the optimal cutting spacing (Song et al., 2022). During a TBM excavation, the cutting efficiency is directly related to the control mode, i.e., the fixed penetration mode and fixed normal force mode. Via rotary cutting tests, influences of the control mode on the normal force, rolling force, cutting coefficient, specific energy and rock boreability index were investigated. It was found that the fixed normal force mode is more effective in cutting rocks (Peng et al., 2018).
Previous studies have extensively investigated the rock breakage mechanism by disc cutters and the cutting efficiency of TBMs under different geological and operational conditions. The impact of τj, an important parameter determining the mechanical properties of rock masses, however, has received little attention. In addition, real-time monitoring of the cracking process and deformation of jointed rock masses subject to disc cutting remains a technical challenge. To fill the knowledge gap, a series of indentation tests were carried out on jointed rock specimens with different τj. The influence of Tj on the deformation and strength of specimens, real-time cracking behavior and rock breakage mode was investigated. Combined effects of τj, and orientation and spacing of joints on the rock breakage mechanism by disc cutters were numerically studied by particle based numerical simulations. The present study provides a method for obtaining the optimal joint shear strength, orientation and spacing for TBM, which is significant for the selection of tunnelling site and improving TBM tunnelling efficiency.
2 Experimental methodology
2.1 Preparation of specimens
In the experiment, 15 intact granite blocks with an identical size of 200 mm x 140 mm x 30 mm were prepared. To establish jointed rock models with different τj, the intact rock blocks were firstly cut into smaller blocks by a high pressure waterjet, and the orientation and spacing of resultant joints were 60° and 50 mm, respectively (see Fig. 1). Subsequently, the cut blocks were bounded by cement mortar with a thickness of 3 mm. The cement mortar was a mixture of the 32.5R cement, sand, water and water reducing agent. Since the strength of cement mortars is determined by the mixing ratio of components, specimens with different joint strengths were achieved by varying the mixing ratio. The physico-mechanical properties of granite and joints, as well as the corresponding mixing ratio are tabulated in Table 1. The elastic modulus E and the UCS gc of the granite and cement mortar were measured by the uniaxial compressive tests on standard cylinder samples with a diameter of 50 mm and a height of 100 mm. The tensile strength (7t was measured by the Brazilian tests on cylinder samples with a diameter of 50 mm and a thickness of 25 mm. The cohesive strength c and internal friction angle cp of granite were obtained by direct shear tests on cubic granite blocks with a side length of 100 mm. The cohesive strength q and friction angle of rock joints were measured via direct shear tests on cubic granite block samples bonded by a cement mortar layer with a side length of 100 mm. Implementation of these tests followed the specification of ISRM suggested methods (Ulusay, 2015).
The 15 specimens were divided into 5 groups evenly, in which specimens of groups 1-4 represent jointed rock models with different q (labelled as MJ1-MJ4) and the rest blocks were uncut representing intact rock models (labelled as MI). The established jointed specimens were cured for 28 d to stabilize the strength of cement mortars. After polishing, the front surface of each specimen was painted white and randomly distributed black speckles were sprayed. By doing so, the deformation of the rock surface can be measured by a digital image correlation (DIC) system.
2.2 Experimental setup and procedure
Schematic diagram of the indentation experiment is shown in Fig. 2. The indentation experiment by disc cutters was conducted on the WDAJ-600 rock shear rheological testing apparatus with a maximum loading capacity of 600 kN and a full cylinder stroke of 100 mm. The loading rate is 0.1-100 kN/min under the load controlled mode and 0.001-10 mm/min under the displacement controlled mode. To realistically simulate the rock breaking process by disc cutters, two half disc cutters were installed on the normal loading platen to apply normal loads on the specimen. The manufactured full-scale disc cutters made of H13 alloy steel represent the widely employed 17-in disc cutters (diameter: 432 mm) with a central angle of 19°. The cutter tip width is 12 mm and the tip angle is 20° (Fig. 2(b) and (c)). The spacing between the two cutters is 80 mm. During the loading, the deformation and cracking process of specimens were measured by a DIC system, composed of a Basler acA2440-75um charge coupled device (CCD) camera, a fixed focal length lens, a Light-Emitting Diode (LED) light with a luminous flux of 18000 lm, and a computer. Specifically, the CCD camera has a resolution of 2448 x 2048 pixels and a frame rate of 75 fps, digitally controlled by the computer.
The experimental procedure is as follows. First, the specimen was installed on the apparatus. To simulate the in situ condition of relatively shallow tunnels (less than 100 m) that are common in engineering practice, the confining pressure of 2 MPa was selected in the experiment. A horizontal load of 2 MPa x 140 mm x 30 mm = 8.4 к N was uniformly applied to the laterally sides of the specimen. Silicon grease lubrication was provided on the loading platens to reduce the end friction. Then, the specimen was preloaded to 1 kN in the normal direction by disc cutters for 10 min to consolidate the specimen and stabilize the deformation before the indentation. The CCD camera and LED lights were installed at a distance of 0.8 m from the specimen. Finally, the disc cutters were loaded at a rate of 0.5 mm/min until reaching a penetration depth of 8 mm. During the loading, the normal force and the penetration depth were recorded, and the cracking process was captured by the CCD camera simultaneously with a frequency of 1 fps.
3 Experimental results and discussions
The shear strength of rock joints is an important parameter influencing the failure mechanism of jointed rock masses (Karachaliosa et al., 2013; Ghabezi & Farahani, 2017). Through laboratory experiments, the deformation and failure characteristics of jointed rock masses subject to indentation forces were investigated and three kinds of rock-breaking modes were identified. The effect of τj on the rock cutting efficiency was estimated.
3.1 Deformation and strength of specimens subject to indentation forces
The relation between the normal force (Fn) and the penetration displacement (p) is plotted in Fig. 3(a). All curves exhibit a similar evolutional pattern through five sequential stages: a nonlinear compaction stage, a linear elastic stage, a yield stage, a post-peak descending stage, and a residual stage. The initial compaction is universally observed in geo-materials during which the grains of rock matrix and the joints are compacted with an increasing load (Avanthi Isaka et al., 2019; Liu et al., 2019). The rocks then deform elastically until reaching a yield stage when microcracks start to occur and accumulate (Wang et al., 2018). A brittle failure happens in rocks at the peak loading force, followed by a fast descending stage. Finally, the normal force reaches some constant values in the residual stage. To investigate the effect of τj on the penetration behavior, the peak normal force (Fnp), penetration depth at the peak normal force (p0), residual normal force (Fnr), and residual coefficient (cr) were calculated as shown in Fig. 3(b) and (c). The average value of the three cases of each group was used in analysis. The residual coefficient is defined as the ratio of Fnr to Fnp. Fnp increases monotonically as tj increases and reaches the maximum for the intact case, p0 exhibits a decreasing trend with undulations of the curve due to the brittle failure nature of granites. Fnr shows a similar trend with Fnp, and cv of the intact rock mass is much smaller than those of the jointed rock masses.
The above results indicate that the increase in τj can enhance the resistance of a rock mass to cutter-induced penetration, unfavorable to TBM excavation. Since the strength of the rock matrix is much greater than that of the joint, the rock blocks are prone to slip along the joints. A force balance analysis of a representative block in the jointed rock mass is shown in Fig. 4. At the boundaries, a normal force (Fn0) acts vertically on the top surface and a confining force (Fc) acts horizontally on the lateral surfaces. Hence, a block undergoes normal and shear forces along the joints from the surrounding blocks. At the equilibrium state, the force balance equations can be established as follows.
... (1)
... (2)
where Fn0 is the normal force acting on a disc cutter, Fn1 and Fn2 represent the normal forces acting on the upper and lower surfaces of the rock block, and Fs1 and Fs2 denote the shear forces of the upper and lower joints. Fs1 =-τ1A1 and Fs2 = τ1A2, where τ1 and τ2 are the shear stresses, and A1 and A2 are the areas of the upper and lower joints, respectively. Fc is the lateral force originating from the confining pressure.
The Coulomb failure criterion for the joints is written as
... (3)
where σn is the normal stress acting on the joint, and cj and ... are the cohesion and friction angle of the joint respectively. When the shear stress exceeds τj under the normal stress of σn, a shear failure occurs along the joint.
Since the lateral confining force is constant, the shear failure along joints may happen as the normal force increases, determined by the Coulomb failure criterion. The weaker the τj, the smaller Fnp. The residual normal forces are almost identical for all jointed models under an identical confining force. In contrast, Fnp is controlled solely by the strength of the intact rock for group MI. When the local stress at the cutter tip reaches the strength of the granite, a crushed zone is generated, leading to a splitting failure.
The horizontal and vertical displacement fields at Fnp obtained from the DIC measurement are shown in Fig. 5. The average displacement for each specimen was calculated, as plotted in Fig. 6. Large displacement occurs along the joints for models MJ1-MJ4, resulting from the slip failure along the joints. Large displacement was observed at the central top of Mil where an indentation-induced crushed zone exists. Meanwhile, the differential displacement across joints suggests that joint slip happens. Therefore, the deformation of Mil exhibits a mixed local and shear deformation mode. With the increase of tj (MJ2, MJ3 and MJ4), the bond between the rock blocks is strengthened, leading to the increase in the overall strength of the rock mass. As a result, local deformation around the cutter tips gradually transitions to the global deformation under action of the disc cutters (Fig. 5(b)-(d)). The global deformation causes the average horizontal and vertical displacements to increase (Fig. 6), accompanied by the increase in p^. For the intact rock, the normal load mainly results in the vertical deformation of the rock. Since there are no joints to allow slip deformation, the average horizontal displacement is much less than the vertical displacement (Fig. 6).
According to the experimental results, during the TBM tunneling, the joint strength should be controlled in a proper range. Specially, a low joint shear strength only causes the local damage of the tunnel face under the disc cutter. On the contrary, a high joint shear strength will increase the thrust cutterhead, causing the drastic vibration of cutterhead and the increase in cutter wear. In engineering practice, it is recommended that the joints with a high shear strength should be weakened in advance by blasting or hydraulic splitting. On the contrary, the joints with a low shear strength can be strengthened by grouting to avoid large deformation.
3.2 Cracking during the penetration by disc cutters
In addition to the strength and deformation, the cracking process in the rock mass reflects the rock breakage performance of the disc cutter. The cracking behavior determines the rock breakage mode and in turn influences the cutting efficiency. The cracking processes in the specimens were recorded and analyzed by the DIG system, and the crack type and damage degree were quantitatively estimated.
3.2.1 Cracking processes in specimens
During the penetration, the cracking processes in jointed specimens of all groups show analogous characteristics. Thus, a specimen of MJ2 was taken as an example to illustrate the cracking process as shown in Fig. 7. Correspondingly, the tensile strain ε1 and shear train γ fields on the front surface of the specimen are plotted. According to previous studies, the radial cracks beneath the disc cutters can be classified as primary and secondary cracks (Gong et al., 2005). The primary crack represents the central crack in a group of radial cracks with the maximum length and the secondary cracks are those surrounding the primary crack. Except the radial cracks, there are also single cracks in the rock mass that are typically generated by tensile failure (white lines in Fig. 7). In the present experiment, the ing is divided into a crack initiation stage, a crack propagation stage and a rock spalling stage.
(1) Crack initiation stage (penetration depth p = 0-2.2 8 mm). When the penetration depth reached 1.08 mm, a primary crack was firstly generated beneath the left cutter (Fig. 7(b)). The crack initiated from the joint and propagated upwards. At this moment, tensile and shear strain concentration was found along the joint. Subsequently, a secondary crack beneath the left cutter and a primary crack beneath the right cutter initiated from the top surface and the joint respectively when p = 1.36 mm and 1.50 mm (Fig. 7(c) and (d)). A single crack was also formed away from the radial cracks. Correspondingly, the tensile strain concentration was found along the generated cracks (Fig. 7(c) and (d)), indicating that the initiation of primary, secondary and single cracks was all caused by the tensile failure of the rock.
(2) Crack propagation stage (p = 2.28-2.43 mm). When the normal force reached the peak value corresponding to p = 2.28 mm, two crushed zones were formed beneath the two cutters (Fig. 7(e)). The secondary cracks propagated downwards and the primary crack propagated upwards simultaneously (Fig. 7(e)). Particularly, secondary cracks beneath the right disc cutter initiated from the top surface and propagated downwards to reach the joint (Fig. 7(f) and (g)). The tensile strain concentration zone expanded continuously, resulting in the growth of single cracks, while the shear strain concentrated along the secondary crack beneath the right disc cutter (Fig. 7(c) and (f)). The evolution of the strain field illustrates that the propagation of cracks can promote the shear failure of the rock.
(3) Rock spalling stage (Fig. 7(h)). When the radial cracks coalesce with the joints, rock spalling took place, generating pieces of rock chips (Fig. 7(h)). The singe cracks have little effect on the spalling zone.
The above results show that the cracking transforms from the tensile mode to the mixed shear-tensile mode under the penetration of the disc cutter. Specifically, the crack initiation is induced by the tensile failure, and the propagation of the cracks lead to the shear deformation of the rock mass, causing the mixed shear-tensile failure.
3.2.2 Effect of τj on the cracking mode
The above results reveal that the slip along rock joints is one of the main factors influencing the crack propagation process and the cracking mode. To quantitatively mine the mode, the maximum principal strain ε1 and shear strain y at the tip of typical primary and secondary cracks beneath the left cutter were measured and analyzed. The evolution of ε1 and y for specimens with different τj is plotted in Fig. 8(a)-(e). γ/ε1 of the primary and secondary cracks when they initiate were calculated, as shown in Fig. 8(f).
Sharafisafaa et al. (2018) reported that ε1 of tensile cracks is much greater than y, while y of shear cracks is much greater than ε1 when the crack initiates. If ε1 and γ both increase dramatically, the crack mode can be defined as the mixed shear-tensile mode. According to this classification, the cracking mode of the primary and secondary cracks was determined. As shown in Fig. 8(a), ε1 and γ of the primary and secondary cracks of Mil both increase dramatically as the crack initiates and then evolve in a sim- ilar manner, indicating that these cracks are generated under the mixed shear-tensile mode. In contrast, the change of ε1 and γ of the primary and secondary cracks exhibit different modes for specimens of MJ2, MJ3 and MJ4 (Fig. 8(b)-(d)). In the crack initiation stage, ε1 is several times greater than y, and as the penetration proceeds, y increases rapidly and the difference between γ and ε1 is mostly reduced. Therefore, the cracks initiate under the tensile mode, which transform to the mixed shear-tensile mode afterwards. For the intact specimen MI (Fig. 8(e)), the initiation and propagation of the primary crack are caused by tensile failure, and the initiation of the secondary cracks is under the tensile mode while the propagation is under the mixed shear-tensile mode. From Fig. 8(f), the γ/ε1 of primary and secondary cracks both decrease with the increase of τ1. The value of γ/ε1 of MJ1 is much greater than those of the rest specimens, indicating that the cracking in MJ1 is under the mixed shear-tensile mode while the cracking mode of MJ2, MJ3 and MJ4 is tensile failure.
Experimental results mentioned above show that with the increase of τj, the cracking modes of primary and secondary cracks change from the mixed shear-tensile to tensile in the initiation stage. However, τj docs not affect the cracking mode in the propagation process. As illustrated in Fig. 4, during the loading, the bending deformation of rock blocks occurs due to the combined effects of normal and shear forces, increasing the tensile strain. For MJ1, before the crack initiation, slip failure occurs along the joints, leading to the uneven deformation of the entire specimen. Under the combined effects of tensile and shear strain, the cracks initiate from the joint. With the increase of the joint strength, the shear strain decreases before the crack initiation. Therefore, the crack initiation is mainly caused by the tensile strain. In the crack propagation process, the cracks weaken the integrality of the rocks, which in turn promotes the shear strain along the cracks. Under this condition, the influence of tj on the shear deformation is less significant than that of the cracks. As a result, the cracking mode in the propagation process is dominated by the mixed shear-tensile failure.
3.3 Rock breakage mode
The breakage mode of tested specimens was recorded after the test, as shown in Fig. 11. According to the ing the breakage modes can be classified to an internal block breakage mode (MJI and MJ2), a crossjoint breakage mode (MJ3 and MJ4) and a cutters-dependent breakage mode (M1).
(1) Internal block breakage mode (mode I). As shown in Fig. 9(a) and (b), spalling zones arc formed in the rock blocks, without penetrating the rock joints. The secondary cracks initiate from the top surface and propagate downwards in the specimens of MII and MJ2. The trajectory is approximately parallel to the joint. When the cracks reach the joints, spalling of rock chips occurs. Under this condition, the rock blocks are prone to slip along the joint due to the relatively small shear strength. As a result, the propagation of cracks crossing the joints is prohibited. This breakage mode is similar with the DEM based numerical simulation results reported by Jiang et al. (2018). They found that the cracks tend to propagate along the joints, and the joints facilitate the coalescence of small cracks underneath the cutters, in case of a joint orientation of 60° (i.e., a = 30° in this study).
(2) Cross-joint breakage mode (mode II). As shown in Fig. 9(c) and (d), greater damage zones crossing the joints are formed compared with the cases of Mil and MJ2. With the increase of tj, the integrity of the entire rock mass is improved, and the shear failure along joints is restricted. As a result, cracks can propagate through the joints, and when the cracks coalesce with each other, spalling occurs. The specimen MJ4 also exhibits the internal block mode due to the local joint slip beneath the right cutter (Fig. 5 (d)). These results are consistent with the "across the jointed plane" phenomena observed in the experiment conducted by Lin et al. (2018).
(3) Cutters-dependent breakage mode (mode III). The radial cracks initiate from the top surface of the specimen and propagate downwards in the intact specimen MI (Fig. 9(e)). In this case, the propagation of cracks is controlled by the specification and arrangement of the two cut-ters (e.g., cutter geometry and their distance) given that the rock is homogenous (Cho et al., 2013). When the secondary cracks coalesce with each other, rock failure occurs in the area between the two cutters, eventually forming a spalling zone much greater than other cases.
3.4 Cutting efficiency of jointed rock masses with different joint shear strengths
The specific energy is an important and extensively adopted index to evaluate the TBM cutting efficiency. The specific energy SE is defined as the ratio of energy consumed to the volume of spalled rocks (Teale, 1965):
... (4)
where SE is the specific energy, V is the volume of rock chips, Fn is the normal force acting on the disc cutter, and p is the penetration depth. Obviously, less specific energy represents greater cutting efficiency.
Calculated specific energy of tested specimens is shown in Fig. 10. SE reaches the minimum value for the specimen MJ3. Recalling the breakage mode of different specimens, it is inferred that the cutting efficiency is intimately correlated with the rock breakage mode. Specifically, the cross-joint breakage mode is optimal for improving the cutting efficiency. Propagation of cracks terminates at the rock joints under the internal block breakage mode, restricting the volume of the damage zone. The resultant volumes of spalled rocks are 175 and 173 cm3 for MJ1 and MJ2, respectively. Under the cross-joint breakage mode, cracks can propagate through the joints, expanding the spalled rock volume up to 243 cm3 for MJ3. As τj further increases, the integrity of the rock mass is enhanced, increasing the required energy for rock failure. As a result, the volume of spalled rocks decreases to 109 cm3 for MJ4.
These results suggest that the cutting efficiency is not early with the shear strength of rock joints. An optimal value of τj exists, under which the maximum rock damage volume can be achieved. In this experiment, MJ3 is the optimal condition for TBM cutting efficiency. Therefore, auxiliary techniques such as grouting or presplitting blasting may be employed to adjust the joint strength in order to achieve an optimum cutting efficiency. 4
Numerical analysis on the combined effects of shear strength, orientation and spacing of joints on the rock breakage mechanism by disc cutters
In addition to τj, the joint orientation α and spacing S are important geological parameters determining the mechanical behavior of rock masses (Li et al., 2015; Mohammadi et al., 2015). To reveal the combined effects of τj, α and S on the rock breakage mechanism by disc cut- ters, a series of numerical simulations were conducted by a two-dimensional particle flow code, PFC2D. The mesoscopic parameters of the rock matrix and joints in the numerical model were firstly calibrated by the indentation tests. Subsequently, the cracking behavior and rock breakage mode of rock masses with different joint geometric characteristics were analyzed.
4.1 Calibration of the mesoscopic parameters of the numerical model
In the numerical model, the minimum and maximum radius of balls arc 1 and 1.66 mm, respectively. The linear parallel bond (PB) model and the smooth joint (SJ) model were employed to simulate the contacts in the rock matrix and the joints, respectively. The PB model restricts both sliding and rotation between particles, representing the bond of minerals in the rock matrix (De Silva et al., 2018; Chen et al., 2020). The SJ model can effectively simulate the slipping and dilation of rock joints (Afrasiabi et al., 2019). The physical and mechanical properties of rock matrix and joints arc determined by built-in micro parameters. The micro parameters of the rock matrix and joints arc typically calibrated by uniaxial compressive tests and direct shear tests, respectively (Jiang et al., 2018; Zhang et al., 2020). According to the physical and mechanical properties tabulated in Table 1, the micro parameters of rock matrix and joints with different shear strengths were determined as shown in Tables 2 and 3. The resultant physical and mechanical properties arc tabulated in Table 4. Comparison between Tables 1 and 4 shows that the numerically simulated parameters well match the experimental results.
4.2 Modeling the indentation test
Numerical jointed rocks with a width of 200 mm and a height of 140 mm, and two cutters with a distance of 80 mm modelled by wall elements were established as shown in Fig. 11. A confining pressure of 2 MPa was applied to the left and right boundaries, and the bottom boundary was fixed. The loading procedure was identical to that of the experiment. Because the disc cutters arc made of H13 steel, the rigidity is much bigger than that of rock. Thus the cutters in the numerical model is modeled as rigid walls, the deformation of cutters is neglected. Two groups of numerical models were prepared. In the first group, joints possess five different a (0°, 30°, 45°, 60° and 90°) with a fixed S of 50 mm. In the second group, a is fixed to 60° and five different S (30, 40, 50, 60 and 70 mm) were arranged. The joint shear strengths (labelled as τj1, τj2, τj3 and τj4) identical to those of MJ1, MJ2, MJ3 and MJ4 were further applied to these models, leading to 40 numerical cases. During the loading, the normal force acting on the rock mass, crack number and rock breakage mode was monitored.
4.3 Effects of joint shear strength and orientation
4.3.1 Strength and cracking behavior
According to the experimental results, Fnp is a representative index reflecting the strength of rock masses subject to disc cutting. The monitored Fnp of numerical models is plotted in Fig. 12(a). Furthermore, for the models with the same α, the difference between the maximum and minimum Fnp of models with different τj were calculated, as shown in Fig. 12(b). The experimental results are located on the surface diagram formed by numerical results in Fig. 12(a) and fit well with the curve of the differential Fnp, providing reasonable validation of the numerical models. Fnp for the cases with a of 30°-60° is smaller than the cases of 0° and 90°. This is reasonable because α of 30°-60°, especially 60°, has long been considered as an unfavorable configuration for the strength of jointed rock masses (Gong et al., 2005). This is also the basis for selecting 60° to establish the experimental models. Meanwhile, τj can improve the integrity of the rock mass and increase Fnp for models of all orientations. Such improvement is greater for the cases with a of 30°-60° comparing to the cases of 0° and 90° (Fig. 12(b)).
Different cracking modes are responsible for the strength difference of rock masses. The shear-tensile failure mode transforms to the tensile failure mode as τj increases, leading to an obvious increase in Fnp. This is supported by the crack counts shown in Fig. 13, which reveal that the number of tensile cracks is greater than shear cracks for most cases, suggesting that the tensile cracking mode prevails in rock masses subject to disc cutting (Gong et al., 2005; Liu et al., 2021). For the models with α of 30°-60°, however, shear cracks prevail when τj is small. This phenomenon is consistent with the experimental results shown in Fig. 10. In these cases, the rock strength is mainly con- trolled by the shear failure along the joints (Fig. 4(a)), and the increase in τj can efficiently increase Fnp.
43.2 Rock breakage mode
The failure modes of rock mass models with different α and τj are shown in Fig. 14. When α is 0° or 30°, the cracks initiate beneath the cutters and propagate downwards (Gong et al., 2005). The secondary cracks propagate through the joints and coalesce with each other, expanding the failure zone. In these cases, breakage mode II prevails. For the models with α of 45° and 60°, most cracks are restricted in single rock blocks without penetrating the joints when τj is relatively small, i.e., breakage mode I, which was observed in the specimens of MJ1 and MJ2 (Fig. 11(a) and (b)). As τj increases, a part of cracks penetrates the joints, as shown in the white circle, indicating the transformation of the breakage mode from I to II. This result is consistent with the observation made on specimens MJ3 and MJ4. The models with α of 90° exhibit the breakage mode I, almost identical to the specimen ML In this case, the existence of rock joints has little influence on the penetration behavior of disc cutters.
4.4 Effects of joint shear strength and spacing
4.4.1 Strength and cracking behavior
Fnp of numerical models with different Tj and S are shown in Fig. 15(a). Under an identical S, the difference between the maximum and minimum Fnp of models with different Tj is calculated, as shown in Fig. 15(b). Again, the experimental results agree well with the simulation results. Obviously, Fnp increases simultaneously with the increase of Tj and S, and Fnp seems to be more sensitive to S. The difference of Fnp increases monotonically with the increase of S, suggesting that the effect of Tj is enhanced as 5 increases in the studied range.
As shown in Fig. 16, with the increase of τj and S, the number of tensile cracks increases while the number of shear cracks decreases. According to the analysis presented in Sections 3.1 and 4.3, the decrease in the number of shear cracks indicates the increase of shear stress along the joints, which tends to increase Fnp. When S is 30 mm, the joints arc close to the disc cutters, therefore the joints fail immediately underneath the cutters due to the high stress concentration (Bejari & Khademi Hamidi, 2013). As a result, the influence of Tj is less significant in the densely jointed rock masses. These results arc in agreement with the studies conducted by Yang et al. (2018) and Afrasiabi et al. (2019).
Previous numerical simulations and rolling indentation abrasion tests have also revealed that the trust of cutterhead increases as S increases, and the greater the value of S, the less the penetration rate of TBM (Gong et al., 2006; Bejari & Khademi Hamidi, 2013). For sparsely jointed rock masses, it is potentially useful to weaken the strength of joints to improve the excavation efficiency.
4.4.2 Rock breakage mode
The rock breakage modes of rock masses with different Tj and S are shown in Fig. 17. For the densely jointed model (5 = 30 mm), the cracks can easily penetrate the joints since the joints are close to the cutters, triggering the breakage mode II. For models with 5 of 40, 50, 60 and 70 mm, cracks in most cases propagate along the joints, following the breakage mode I. The breakage mode II only appears for the cases with a large value of τj, forcing the cracks to propagate through the joints, as seen in the white circle. Therefore, τj could potentially change the breakage mode from I to II for rock masses with a moderate joint spacing.
5 Conclusions
Shear strength of rock joints determine the mechanics of the rock mass. When TBMs excavate in the rock mass, the cutting efficiency varies. In order to reveal the influence of joint strength on the breakage mechanics of rock mass by disc cutters, a scries of disc-cutter indentation tests were carried out in this study. The deformation and strength of specimens, progressive cracking behavior and rock breakage mode were quantitatively investigated. Combined effects of the joint shear strength, orientation and spacing on the rock breakage mechanism by disc cutters were numerically studied. This study will enrich the understanding of breakage mechanics of rock mass by disc cutters. Besides, it might provide basis for improving the TBM cutting efficiency through jointed rock masses. The main concluding remarks are as follows:
(1) During a loading process by disc cutters, a jointed rock mass evolves from local deformation surrounding the cutter tips to global deformation of the entire rock mass. The increase in the joint shear strength restricts the slip failure along the joints and enhances the resistance of the rock mass to cutter-induced penetration, unfavorable to TBM excavation.
(2) As the joint shear strength increases, the primary and secondary cracks change from the mixed shear-tensile to tensile mode at the initial stage. In contrast, the cracking mode is not relevant to the joint shear strength in the subsequent propagation process.
(3) Three rock breakage modes, i.e., the internal block breakage mode, cross-joint breakage mode and cutters-dependent breakage mode, were identified from experimental and numerical results. The increase in the joint shear strength promotes the transformation from the internal block breakage mode to the cross-joint breakage mode. According to the specific energy, an optimal joint shear strength exists, under which the combined tensile cracking mode and cross-joint breakage mode can effectively enhance rock damages.
(4) The increase in the joint shear strength can significantly increase Fnp by changing the shear-tensile failure mode to the tensile failure mode for rock masses with joint orientations of 30°-60°. It also promotes the transformation from the internal block breakage mode to the cross-joint breakage mode for rock masses with joint orientations of 45° and 60° and with a moderate joint spacing.
The dynamic loads induced by the rotation of cutterheads, the confinement of the front and back boundaries of tested specimens, and rock masses of multiple joint sets could complicate the failure mode and penetration process. These arc important issues for future studies.
Data availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.
CRediT authorship contribution statement
Bolong Liu: Methodology, Software, Writing - original draft. Bo Li: Data curation, Investigation, Supervision, Writing - review & editing. Liang Zhang: Data curation, Formal analysis, Resources. Rui Huang: Methodology, Validation. Huicai Gao: Resources, Visualization. Shilin Luo: Data curation, Visualization. Tao Wang: Investigation, Validation.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgement
The financial support from the National Natural Science Foundation of China (Grant Nos. 41831290, 41907167 and 51708354), Natural Science Foundation of Zhejiang Province (Grant No. LTGS23E040001) and Natural Science Foundation of Hunan Province (Grant No. 2022JJ40521) is greatly appreciated.
Received 15 January 2023; received in revised form 17 November 2023; accepted 24 December 2023
Available online 24 April 2024
Peer review under the responsibility of Tongji University
* Corresponding authors at: Key Laboratory of Rock Mechanics and Geohazards of Zhejiang Province, Shaoxing University, Shaoxing 312000, China.
E-mail addresses: [email protected] (B. Li), [email protected] (H. Gao).
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Abstract
When tunnel boring machines (TBMs) excavate through jointed rock masses, the cutting efficiency is strongly affected by the shear strength of joints, the mechanism of which, however, remains poorly understood. In this study, a series of disc-cutter indentation tests were conducted on granite rock mass specimens with different joint shear strengths. During the indentation, the cracking process was recorded by a digital image correlation (DIC) system. The deformation and strength of specimens, cracking behavior, rock breakage mode and cutting efficiency were quantitatively investigated. In addition, to investigate the combined effects of joint shear strength, orientation and spacing on the rock breakage mechanism, numerical rock mass models were established based on a particle flow code PFC2D. Experimental results reveal that the cracking of primary and secondary cracks changes from the mixed shear-tensile to tensile mode in the initial stage, while the joint shear strength does not affect the cracking mode in the subsequent propagation process. The rock breakage mode is classified to an internal block breakage mode, a cross-joint breakage mode and a cutters-dependent breakage mode. The cross-joint breakage mode is optimal for improving the cutting efficiency. Numerical simulation results reveal that the increase in the joint shear strength changes the internal block breakage mode to cross-joint breakage mode for rock masses of particular ranges of joint orientation and spacing. These findings provide basis for improving the TBM cutting efficiency through jointed rock masses.
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Details
1 Key Laboratory of Rock Mechanics and Geohazards of Zhejiang Province, Shaoxing University, Shaoxing 312000, China
2 College of Civil and Architectural Engineering, Xi'an University of Science and Technology, Xi'an 710054, China