Numerical modeling of the effects of joint orientation on rock fragmentation by TBM cutters
Introduction
The tunnel boring technology has been improved over the past years. This includes the significant 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 profile. 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 different 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 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 influence of the joint orientation was observed, but not quantified in 1976 (Bruland, 1998). The 1979 edition of the model makes a first attempt to quantify the influence and the following updated editions considerate the influence of the joint orientation based on the in situ measurements. In the recent models, the significance of joint spacing and orientation on TBM performance are emphasized and regarded as important factors influencing 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).
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-stratification. Bruland (1998) summarized the in situ measurement results over 250 km of TBM tunnels. The effects of joint orientation were respectively obtained for different classes of joints. The same rule was observed. However, he noted that with the increase of joint spacing, the effect 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 different joint orientation. This may probably owe to the theoretical difficulty in simulating crack growth in discontinuous medium.
During the past years, finite element method (FEM) has been used to simulate the rock material fragmentation using an indenter. Cook et al. (1984) employed a linear axisymmetric elastic finite element model to numerically investigate the fracture process in a strong, brittle rock by a circular, flat-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 finite difference 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 field observation results. The effect of joint orientation is highlighted in this study.
Section snippets
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 defined 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
Rock fragmentation at different joint orientation
Fig. 3 shows the pattern of the rock indentation and fracture formation by the cutter when the angle α 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 different iteration step while the angle α varies, as shown in Fig. 4, Fig. 5, Fig. 6, Fig. 7, Fig. 8, Fig. 9, Fig. 10. As shown in the figures, the indentation process can be divided into three stages,
Effect of joint orientation on rock chipping angle
Due to the influence 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 α changes as illustrated in Fig. 12. With the increase of the angle α from 15° to 75°, the rock chipping angle also increases. When the angle α is 90°, the side crack propagation is not affected by the joint orientation and the chipping angle is about
Effect of joint plane on stress field
When a normal point load acts on an isotropic, linear elastic half-space, the stress field was first given by Boussinesq in 1885, commonly known as the Boussinesq elastic field. When a smooth spherical indenter acts on an isotropic, linear elastic half-space, the field stress is known as the ideal Hertzian elastic field. Liu et al. (2002) gave the simulated quasi-photoelastic stress fringe pattern induced by a single indenter when the rock is considered as a homogeneous material. The stress
Comparisons with field observation results
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 first column shows the variation of the angle α. 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
Conclusions
The rock chipping process induced by the TBM cutter is simulated by DEM modeling to examine the effect of joint orientation. The modeling results indicate that there are two modes of crack initiation and propagation in a jointed rock mass affected 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
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