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Numerical modeling of the effects of joint orientation on rock fragmentation by TBM cutters


Tunnelling and Underground Space Technology
Tunnelling and Underground Space Technology 20 (2005) 183–191
incorporating Trenchless Technology Research

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Numerical modeling of the eects of joint orientation on rock fragmentation by TBM cutters
Qiu-Ming Gong *, Jian Zhao, Yu-Yong Jiao
Underground Technology and Rock Engineering Program, Protective Technology Research Centre and School of Civil and Environmental Engineering, Nanyang Technological University, Block N1, Nanyang Avenue, Singapore 639798, Singapore Received 28 April 2004; received in revised form 1 August 2004; accepted 18 August 2004 Available online 19 October 2004

Abstract The performance of tunnel boring machines (TBM) highly depends on the fragmentation eciency of the cutters. Many geological factors can inuence the rock fragmentation process. In this study, a series of two dimension numerical modeling were performed using the discrete element method (DEM) to explore the eect of joint orientation on rock fragmentation by a TBM cutter. Results show that the joint orientation can signicantly inuence the crack initiation and propagation as well as the fragmentation pattern, and hence aect the penetration rate of the TBM. Such observations are also noted by laboratory and site studies. It also indicates that discontinuum-based DEM has the potential in simulating rock indentation and fragmentation by TBM cutters when rock joints are taken into consideration. 2004 Elsevier Ltd. All rights reserved.
Keywords: TBM cutter; Indentation; Fragmentation; modeling; UDEC

1. Introduction The tunnel boring technology has been improved over the past years. This includes the signicant advances of tunnel boring machines (TBMs) on the capacities of thrust and torque as well as the development of large diameter rolling cutters with a constant section prole. Such cutters are capable of dealing with the high cutter loads required for hard rock and keeping a constant production and high abrasion resistance. Hence, TBM is extensively utilized in tunneling and its performance prediction in dierent rock masses has become an important topic for project planning and choice of economic tunneling methods. In the past years, many prediction models were proposed based on site observations and laboratory tests. However, the early
*

Corresponding author. Tel.: +65 67906895; fax: +65 67921650. E-mail address: pg02722582@ntu.edu.sg (Q.-M. Gong).

proposed prediction equations are only suitable for estimating the performance of TBMs on homogeneous and isotropic rocks (e.g., Graham, 1976; Nelson et al., 1985; Hughes, 1986). In the earliest proposed comprehensive prediction model by NTNU (Norwegian University of Science and Technology), the inuence of the joint orientation was observed, but not quantied in 1976 (Bruland, 1998). The 1979 edition of the model makes a rst attempt to quantify the inuence and the following updated editions considerate the inuence of the joint orientation based on the in situ measurements. In the recent models, the signicance of joint spacing and orientation on TBM performance are emphasized and regarded as important factors inuencing the TBM performance (Cheema, 1999; Barton, 2000). But, there seems to be a lack of complete understanding of the rock cutting process due to the very complex nature of the interaction of TBM cutters and rock masses (Rostami et al., 1996).

0886-7798/$ - see front matter 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.tust.2004.08.006

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In situ measurements by Aeberli and Wanner (1978) in a homogeneous zone of schistose phyllite showed that the advance rate of TBM increases with the increase of the angle between TBM axis and the planes of schistosity. Similar phenomena were also observed by Thuro and Plinninger (2003) in phyllite and phyllite-carbonate-schist inter-stratication. Bruland (1998) summarized the in situ measurement results over 250 km of TBM tunnels. The eects of joint orientation were respectively obtained for dierent classes of joints. The same rule was observed. However, he noted that with the increase of joint spacing, the eect of joint orientation on TBM penetration decreases. A theoretical analysis of the interaction between cutter and rock mass by Sanio (1985) showed a similar trend. Although the above mentioned phenomenon was noticed, little research has been undertaken to explain the mechanism of rock fragmentation by TBM cutters in rock mass with dierent joint orientation. This may probably owe to the theoretical diculty in simulating crack growth in discontinuous medium. During the past years, nite element method (FEM) has been used to simulate the rock material fragmentation using an indenter. Cook et al. (1984) employed a linear axisymmetric elastic nite element model to numerically investigate the fracture process in a strong, brittle rock by a circular, at-bottomed punch. The results showed a good agreement with the laboratory experiment. Chiaia (2001) used a lattice model implemented in the FEM program to simulate the penetration process in heterogeneous material by a hard cutting indenter. He found that the indentation process characterizes various interaction mechanisms, amongst them the dominant modes would be plastic crushing and brittle chipping. To reproduce the progressive process of rock fragmentation in indentation, Liu et al. (2002) presented a numerical code R-T2D based on rock failure process analysis model in the simulation, where realistic crack pattern can be observed. Other simulation of brittle material penetration by high speed hard projectile using FEM and nite dierence method (FDM) procedures were also reported (Hanchak et al., 1992; Resnyansky, 2002). Unfortunately, the numerical efforts mainly concentrate on the modeling of indentation in continua. When discontinuities, such as rock joints are taken into account, continuum-based methods are not able to meet the need. This study presents an attempt to simulate the cutting process of rock mass by a TBM cutter using a 2-D discrete element method (DEM) code (Cundall, 1971), the Universal distinct element code (UDEC) (Itasca, 1996). The numerical modeling results are compared with the eld observation results. The eect of joint orientation is highlighted in this study.

2. Discrete element modeling UDEC is a discontinuous code to simulate fractured rock masses. In UDEC, a rock mass is treated as an assemblage of discrete blocks separated by discontinuities, namely rock joints. Individual block can be dened either as rigid or deformable by specifying the material models. The calculation conducted in the DEM alternates between a force-displacement law and an equation of motion. At the contact faces, interacting forces are governed by the force–displacement relationship; while at the centroid of each block, Newtons second law in central dierence format is used to govern the motion of blocks. The solution scheme is identical to that used by the explicit FDM for continuum analysis. The dynamic behavior is represented numerically by a temporal stepwise algorithm. For simulating rock failure, the Mohr–Coulomb model which uses a shear yield function and a non-associated shear ow rule is employed in this study. When a jointed rock mass is excavated by a TBM, the eect of joint orientation on the cutter penetration is shown in Fig. 1. Cutter penetration may be aected by two angles: the angle a between the tunnel axis and the joint plane, and the attack angle b between the cutter rolling direction and the joint outcrop in the tunnel face. Experiments by Howarth (1981) and Sanio (1985) indicated that the inuence of the angle b on the TBM performance was not obvious. The inuence of the angle b can also be evaluated geometrically. As one joint outcrop moves across the tunnel face when the TBM advances, and the cutter moves in concentric circles, the b is evened out and the eect disappears. This study

Tunnel Axis

Tunnel Axis

Tunnel Axis

Fig. 1. Inuence of discontinuity orientation on TBM penetration.

Q.-M. Gong et al. / Tunnelling and Underground Space Technology 20 (2005) 183–191 Table 2 Properties of joints Property

185

Value 10 5 1.5 25 0.04

s σxx α

Normal stiness (GPa/m) Shear stiness (GPa/m) Cohesion (MPa) Friction angle (°) Tensile strength (MPa)

3. Rock fragmentation at dierent joint orientation Fig. 3 shows the pattern of the rock indentation and fracture formation by the cutter when the angle a is 45°. The plastic zones are plotted. In order to highlight the cutter indentation process, the zone of the cracks initiation and propagation immediately beneath the cutter is zoomed in at dierent iteration step while the angle a varies, as shown in Figs. 4–10. As shown in the gures, the indentation process can be divided into three stages, namely the formation of a crushed zone, cracks initiation and propagation, and chip formation. When the cutter rst acts on the rock, a fan-shaped rock failure zone is formed as shown in Figs. 4(a), 5(a), 6(a), 7(a) and 10(a). Immediately beneath the cutter is a zone of compressive failure. Further is a zone of tensile failure. At the cutter edge, a conical, Hertzian crack is initiated as shown in Figs. 5(a), 6(a), 7(a) and 10(a). An interesting phenomenon can be observed that immediately beneath the cutter the rock remains relatively intact because of the high conning pressure in this zone. It is the so-called hydrostatic compression state (Cook et al., 1984; Chiaia, 2001; Liu et al., 2002). As the penetration increases, the crushed zone is formed including compression failure zone and tensile failure zone. This zone is directly located under the cutter and composed of numerous microcracks that comminute the rock to produce powder or extremely small particles (Pang and Goldsmith, 1990). The multiple cracks zone is also formed beneath the crushed zone. The median and radial cracks are initiated form the tensile zone as shown in Figs. 4(b), 5(b), 6(b), 7(b) and (c) and 10(b). The

Fig. 2. Numerical simulation model with xed joint spacing of 200 mm.

therefore focuses on the inuence of the angle a by numerical modeling. The conguration of the computational model is schematically shown in Fig. 2. The dimension of the model is 1.2 1.2 m. The cutter is modeled by a normal force applied at mid height of the left boundary through contact thickness of 15 mm. The rolling force acting on the cutter is not taken into consideration in the two dimensional model. The upper, lower and right boundaries were regarded as xed displacement boundaries. One joint set with a xed spacing of 200 mm was included in the computation model. The dip direction of the joint set is assumed to be in the same direction as the cutting load, and the joint dip angle varies from 0°, 15°, 30°, 45°, 60° and 75° to 90°. In all the models, the joint outcrop is at 80 mm above the contact point between the cutter and the rock. The rock blocks between the joint set are discretized with ne nite dierence meshes, namely zones in UDEC. The zone size in the blocks is set to 10 mm and the damping value 0.1. The rock material modeled is typical granite found in Singapore (Wallace et al., 1995; Zhao, 1996). The intact granite is assumed to be the Mohr–Coulomb material and its properties are listed in Table 1, while all joints satisfy the Coulomb slip model with the properties summarized in Table 2.

Table 1 Properties of intact granite Property Bulk density (kg/m3) Bulk modulus (GPa) Shear modulus (GPa) Cohesion (MPa) Friction angle (°) Tensile strength (MPa) Dilation angel (°) Value 2600 55 32 66 31 11.3 10

Fig. 3. Rock failure pattern at a = 45°.

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(a)

step:30

(b)

step:100

(c)

step:500

Fig. 4. Failure status of rock at selected steps at a = 0° (circle denotes tensile failure, cross denotes compressive failure).

(a) step:30

(b) step:100

(c)

step:500

(d) step:1000

Fig. 5. Failure status of rock at selected steps at a = 15° (circle denotes tensile failure, cross denotes compressive failure).

(a) step:30

(b) step:100

(c) step:300

(d) step:500

Fig. 6. Failure status of rock at selected steps at a = 30° (circle denotes tensile failure, cross denotes compressive failure).

cracks mainly propagate along the tensile failure elements. In this stage, it is interesting to note that the crushed zone is asymmetric as shown in Figs. 5(b), 6(b) and 7(c) because of the inuence of the joint. Sub-

sequently, it causes the cracks initiating from the crushed zone to propagate asymmetrically as shown in Figs. 5(b), 6(b) and 7(c). As the penetration continuously increases, the crushed zone keeps the same. The

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(a) step:30

(b) step:100

(c) step:300

(d) step:500

(e) step:700

(f) step:100

Fig. 7. Failure status of rock at selected steps at a = 45° (circle denotes tensile failure, cross denotes compressive failure).

(a) step:100

(b) step:300

(c) step:500

(d) step:1000

Fig. 8. Failure status of rock at selected steps at a = 60° (circle denotes tensile failure, cross denotes compressive failure).

cracks extend along certain directions, for example the median direction and side direction, as shown in Figs. 4(c), 5(c), 6(c), 7(d) and (e) and 10(c). The crack propagation is induced by the element tensile failure at the tip of the crack. As the cutter penetration increases to some

extent, the side crack reaches to the joint plane, the chip is formed, as shown in Figs. 4(c), 5(d), 6(d), 7(f), 8(e) and 9(d). When the angle a is at 60° or 75°, the crack initiation and propagation show a completely dierent mode, as

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(a) step:60

(b) step:100

(c) step:300

(d) step:500

(e) step:1000

Fig. 9. Failure status of rock at selected steps at a = 75° (circle denotes tensile failure, cross denotes compressive failure).

(a) step:60

(b) step:100

(c) step:300

(d) step:1000

Fig. 10. Failure status of rock at selected steps at a = 90° (circle denotes tensile failure, cross denotes compressive failure).

shown in Figs. 8 and 9. Due to the joint inuence, the element closest to the joint plane is rstly failed, as shown in Figs. 8(a) and 9(a). As the penetration increases, the crack propagates along the intensity zone of tensile stress as shown in Figs. 8(b) and (c) and 9(b) and (c). The tensile cracks are also initiated below the cutter edge because of the deformation of the rock immediately beneath the cutter. When the penetration continuously increases, the crack reaches to the free face. At the same time, the chip is formed, as shown in Figs. 8(d) and 9(e). The above analysis on crack initiation and propagation shows that there are two possible chipping modes of rock fragmentation. One is that the crack initiates beneath the crushed zone and propagates downwards to the joint plane. The other is that the crack initiates from the joint plane and propagates upwards to the free surface. It is worth noting that in all cases of dierent angle a, the growth of a crack terminates at the joint interface. In

other words, fragmentation mainly occurs within the block immediate under the cutter. These phenomena are commonly observed at eld excavation, as shown in Fig. 11. It was taken from the TBM cutterhead chamber in a tunnelling project in the Bukit Timah granite in Singapore. When the cutter rolled over a joint set, the cracks directly propagate to the joint interface, and then form the rock chips.

4. Eect of joint orientation on rock chipping angle Due to the inuence of the joint and its orientation, the cracks induced by TBM cutters do not initiate and propagate symmetrically. Subsequently, the rock chipping angle between the tunnel face and the rock damage plane varies while the angle a changes as illustrated in Fig. 12. With the increase of the angle a from 15° to 75°, the rock chipping angle also increases. When the angle a is 90°, the side crack propagation is not aected

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rock is considered as a homogeneous material. The stress eld is symmetrical and the stresses are extremely high close to the loading point and decrease rapidly with the increasing distance form the loading point. Figs. 13– 15 show the major principal stress elds when the angle a is equal to 0°, 15° and 90°, respectively. As can be seen, the major principal stress contours are deected to the joint plane, owing to the introduction of the joint set. The stress elds induced by the cutter in jointed rock mass are not symmetrical. Furthermore, the deection of the stress eld is dierent with the variation of the angle a. From this stress nature one can understand why the cracks initiate and propagate in an asymmetrical
Fig. 11. Eect of joint orientation on rock chipping formation.

90 80 70

Chipping angle ()

60 50 40 30 20 10 0 0 10 20 30 40 50 60 70 80 90

Angle

()

Fig. 12. Chipping angle vs. the angle a.

by the joint orientation and the chipping angle is about 30–35° that is agreement with the Hertzian cone crack with the chipping angle 30–40° (Chiaia, 2001). As the angle a is 0°, the chipping angle is about 56° which is greater than that at a = 90°. The main reason of such phenomenon is that the inuence of the near side joint deformation and the corresponding connement stress decreases. It is worth noting that with the increase of angle a, the rock breakage seems to be easier under the same cutting conditions.

Fig. 13. Major principal stress contour at a = 0°.

5. Eect of joint plane on stress eld When a normal point load acts on an isotropic, linear elastic half-space, the stress eld was rst given by Boussinesq in 1885, commonly known as the Boussinesq elastic eld. When a smooth spherical indenter acts on an isotropic, linear elastic half-space, the eld stress is known as the ideal Hertzian elastic eld. Liu et al. (2002) gave the simulated quasi-photoelastic stress fringe pattern induced by a single indenter when the

Fig. 14. Major principal stress contour at a = 15°.

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Q.-M. Gong et al. / Tunnelling and Underground Space Technology 20 (2005) 183–191 Table 3 The eect of the angle a on the TBM penetration a (°) 0 15 30 45 60 75 90 Chipping stress (MPa) 140 110 70 55 35 20 136 Chipping area (cm2) 27.5 23.4 20.31 19.42 15.8 8.57 42.16 The ratio of chipping area to chipping stress 0.196 0.213 0.290 0.353 0.451 0.429 0.310 Pa/P0 1.00 1.08 1.48 1.80 2.30 2.18 1.58

Fig. 15. Major principal stress contour at a = 90°.

manner beneath the cutter, which lead to explanation on the variation of chipping angle at dierent a values. It is interesting to note that the stress eld induced by the cutter shows a discontinuous nature at joint interfaces. Due to the non-uniformity in stress transmission at the nearest joint interface, there is rare possibility for stress in the next block to reach failure. Therefore, the joint plane protects the neighboring rock block from damage. These phenomena are observed in all of the simulation results at dierent a, as shown in Figs. 13– 15. It is also observed in TBM tunneling site extensively, as an example shown in Fig. 11. The convincing results suggest that discrete element methods have the potential in reproducing the fragmentation process of jointed rock mass.

to a and P0 denotes the penetration rate at a = 0°. The simulated results are plotted in Fig. 16 showing the inuence of the angle a on the penetration rate. As the angle a increases, the penetration rate increases until a reaches 60°, then the penetration rate decreases with the increase a. When a is equal to 60°, the penetration rate achieves the maximum value that is more than the double of the penetration rate at a = 0°. Based on eld studies and statistics from TBM tunneling in hard rock conditions over 250 km tunnel in more than twenty years, Bruland (1998) summarized the eects of joints including joint spacing and orientation on TBM penetration rate. The joints are divided into ve classes according to the joint spacing. Then, the eects of joint orientation are given respectively for dierent classes of joints. When the joint spacing is equal to 200 mm that was used in the simulation, the effect of the joint orientation on the penetration rate is also plotted in Fig. 16. As can be seen, the simulated Pa/P0 ratio is more than 2.0 and also more than the observed results as a maximum, since there is not a linear relation between the Pa/P0 ratio and penetration rate. But the shape of two curves is in good agreement. Here, it should be noted that the observed results are the average values during TBM boring in a rock mass

3.0

6. Comparisons with eld observation results
2.5

The comparisons present the correlation between the numerical simulation results and the observation results carried out in TBM tunneling projects. The simulated results are summarized in Table 3. The rst column shows the variation of the angle a. The second column shows the stress on the cutter tip needed to fragment the rock. The third column shows the chipping zone area induced by the cutter. The fourth column shows the ratio of the chipping area to the chipping stress which denotes the yield of rock chips per the unit cutter force at the dierent a values and it indirectly stands for the TBM penetration. The fth column shows the ratio of Pa/P0, where Pa denotes the penetration rate as the angle between the tunnel axis and the joint plane is equal

2.0

Pα/P0

1.5 1.0 0.5 0.0 0 10 20 30 40 50 60 70 80 90 simulated results observed results

Angle

α

(°)

Fig. 16. Eect of the angle a on the penetration.

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with the same average joint spacing at dierent angle a. The simulated results are only the instantaneous values when the cutter loads on a rock mass, because this paper mainly focuses on the mechanism of rock fragmentation induced by a TBM cutter. It does not considerate the continuous boring process of the TBM and the interaction of the neighboring cutters. Moreover, the simulation is only conducted in granite rock mass. The eects of the joint orientation on the TBM penetration should be further studied in terms of the numerical modeling of the interaction of neighboring cutters and physical modeling tests. 7. Conclusions The rock chipping process induced by the TBM cutter is simulated by DEM modeling to examine the eect of joint orientation. The modeling results indicate that there are two modes of crack initiation and propagation in a jointed rock mass aected by the joint orientation. One mode is the rock fragmentation process induced by cutter indenter. As the cutter indentation increases continuously, stress is concentrated below the indenter, leading to the forming of crushed zone, initiating and propagating of cracks, chipping of rock. Because of the existence of the joint and its orientation, the crushed zones and the initiation and propagation of cracks are not symmetrical. The other mode is the occurrence of rock chipping induced by the tensile crack initiated from the joint plane. Furthermore, the joint and its orientation make the stress eld deecting to the joint plane, which leads to the variations of the rock chipping angle. The rock chipping angle increases as the angle between the tunnel axis and the joint plane increases, except when a = 0° and 90°. The results also show that rock joint can act as a discontinuous interface for crack propagation and rock fragmentation. The modeling results conclude that the smaller the angle a, the easier the fragmentation of the rock mass. The simulated eect of the joint orientation on the TBM penetration is compared with the eld observed results. They are in a good agreement. As the angle a increases, the penetration rate increases until a reaches 60°, then the penetration rate decreases with the increase a. References
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