Fracture pattern of anisotropic rock by drilling or cutting using the PFC N. Schormair & K. Thuro Engineering Geology, Technische Universität München, Germany ABSTRACT: Anisotropy plays a key role in fracture propagation models and rock fragmentation processes by rock drilling and cutting. Drilling tests with a percussive rock drill have been performed to examine the influence of anisotropy and inhomogeneity on fracture propagation in different rock types. Subsequently, thin sections of the bottom of the borehole were analyzed to get the associated crack patterns. Based on that, the attempt was made to simulate the drilling process in a specific rock material with the Particle Flow Code (PFC). Since the code is based on the discontinous mechanical approch, a rock sample is converted into an assembly of spheres, where the particles are able to interact with each other and fractures are able to propagate. Different rock cutting tools were applied such as button bits or disc cutters to penetrate different rock samples. The aim of the numerical simulation of the drilling and cutting processes was to examine the crack patterns in correlation with foliation. In this paper the first results of the PFC modeling are presented. 1 INTRODUCTION Geological parameters such as foliation, acting as weakness planes in the rock, may have a high impact on the fragmentation process underneath rock cutting tools. Extensive field and laboratory studies have been performed to examine drilling or cutting progress in correlation with the orientation of foliation and other rock properties (Thuro 1997, 2002, 2003, Thuro & Spaun 1996, Thuro et al. 2002). It has been found, that the drilling velocity as well as the disc cutter penetration is best orthogonal to foliation or schistosity and poor parallel to it. Between those angles, the drilling or cutting rates decrease significantly. After these field studies it seemed promising to investigate the obtained microscopic fracture patterns underneath rock cutting tools in different rock types and to perform a numerical simulation of it. Using the Particle Flow Code PFC, which is based on discontinuous mechanical properties, virtual rock samples were modeled and virtual drilling and cutting tests were performed. given to the crack formation at the bottom of the borehole. The aim of the study was to detect and analyze the cracks, which were produced by the drilling process. In the first step, foliated (anisotropic) and isotropic rock samples (size approx. 0,4 m x 0,4 m x 0,3 m) were selected. Using an Atlas Copco COP 1838 25kW rock drill under on-site-conditions, about 10 cm deep boreholes were drilled into the samples. To examine the influence of the anisotropy according to the drilling process, the boreholes were drilled under different angles to foliation. 2 ROCK FRAGMENTATION BY DRILLING To investigate the rock fragmentation process in detail, on-site drilling tests have been performed with a common percussive rock drill using different rock types (Schormair 2003). Special attention was Figure 1. Formatted and drilled granite rock sample.
After the drilling process, the samples were filled with a two-component epoxy resin containing a yellow fluorescent colour (0,2 % of the quantity of resin) under vacuum conditions. A very low viscosity guaranteed good filling also of small fissures. The colour in the resin was used to visualize the cracks under the microscope. A series of subsequent thin sections were produced, especially to get the interesting parts of the bottom of the borehole. The main task was to detect the crack patterns. Details about the findings are given in Schormair et al. (2006). To get an impression of the crack patterns, a mylonitic granite slanting to foliation is shown in Figure 2. Figure 2. Thin section of the mylonitic granite sample. Drilling direction slanting to foliation, cracks propagate parallel to foliation marked black. With subsequent thin sections, the microscopic crack patterns of different rock types were investigated. A correlation of the crack patterns between the spacing of the foliation and the grain size could be detected in all of the thin sections. In the very tight foliated, fine-grained mylonitic granite, the cracks run along the mica layers as zones of weakness (Fig. 2). Rarely found are cracks across mineral components (since they are no zones of weakness). At the bottom of the borehole a roof-shaped or stair-like structure of the crack patterns could be detected. The opening of the mica layers seems to be caused by the percussive process and the shearing process of the bit created the breakout of the fragments. An angle of about 15 degrees seems to be useful to break out the fragments. After the crack patterns of different rock samples were investigated normal, parallel and slanting to foliation according to macroscopic and microscopic crack patterns, schematic drawings were made to illustrate the results of the investigations (Fig. 3). Knowing that drilling performance is best normal to foliation and worst parallel, the observed macroscopic crack patterns support the following statements: When the direction of drilling is normal to the orientation of foliation, rock material is compressed normal but sheared parallel to it. Although cracks will develop radial to compression, the cracks parallel to the bottom of the borehole will be used for chipping. Usually in this case the highest drilling velocities are obtained because of the favourable schist orientation. Drilling is controlled by the shear strength of the foliated rock material. This causes large sized chips and a maximum drilling performance. If the drilling axis is oriented parallel to foliation, compression also is parallel but shear stress is normal to foliation. Less and smaller cracks (1 mm observed) develop for reasons of higher strength normal to the weakness planes. Drilling is controlled by the tensile strength parallel to the foliation producing small sized fragments and minimum drilling performance. Generally, drilling is controlled by the dip angle of foliation, submitting medium sized fragments during the crushing process. Drilling performance is, by geometrical reasons, mainly a cosine function of the dip angle. Anyway, it is for sure, that in the parallel case, rock properties are the highest and drilling rates are low. In addition blasting conditions are often related with drilling. So if the tunnel axis is parallel to the main foliation, drilling and blasting conditions suppose to be very poor. Figure 3. Schematic drawing of crack patterns slanting to foliation. Macroscopic and microscopic cracks marked. In the thin sections, there seems to be a relationship between the crack pattern and the direction and condition of the foliation. Fractures in widely foliated rock types sometimes propagate along the
mica layers, but it is not compelling. The cracks develop parallel to the surface and use foliation only if the foliation runs along a surface-parallel crack. Mainly they propagate across mineral components and the crack pattern looks like the one in isotropic rock. In the mylonitic granite samples it can be clearly seen, that the spacing and the condition of the foliation is important. It can be imagined, that the better the condition of the foliation (clear mica layers) and the closer the foliation is, the more the cracks are running along the mica layers. This means, that mica layers as zones of weakness were used to develop fractures almost exclusively. This reflects, as already suggested by Thuro & Spaun (1996) and Thuro & Plinninger (2003), that the dip angle of anisotropy plays a key role in rock fragmentation. But up to now, no precise statement can be made about the role of the foliation. To obtain a deeper understanding of the crack propagation in anisotropic rock, a simulation of the drilling process has been conducted using the numerical code PFC ( Itasca). By varying the micromechanical parameters, reasonable rock properties can be gained. Using the PFC, it is possible to simulate micro- and macromechanical processes simultaneously. For example, on a loaded block simultaneously the micromechanical process of destruction and the macromechanical process of movements and cracks can be simulated. Therefore in the first step, virtual rock samples had to be designed and tested in a biaxial load test to examine rock properties like the unconfined compressive strength. 3 ROCK FRAGMENTATION IN VIRTUALITY Since the drilling investigations and subsequent thin section analyses only provided crack patterns, the attempt was made to simulate the drilling process and the rock material with a numerical code. The Particle Flow Code (PFC Itasca) seemed to have all necessary features to perform this simulation, allowing to design tools with different shapes as well as the rock material with its anisotropy and inhomogeneity. The code is based on a discontinuous mechanical approach, this means a sample can be composed of particles and the particles interact with each other. In PFC, movements and interactions of loaded element assembleys are shown with two- or threedimensional balls (although still in 2d). Through the randomized connection, arrangement and interaction of these elements, different physical systems can be simulated. Figure 4. Stress-strain-curve of a virtual anisotropic material (see Figure 5) under biaxial loading (UCS = 63 MPa). 3.1 Procedure A common problem with PFC is, that the material parameters in PFC don t correlate with the rock properties in continuous mechanical models. When designing the rock material, micromechanical parameters have to be defined such as bond strength. For calibration purposes, a virtual laboratory test, such as the unconfined compressive test, has to be performed to get the unconfined compressive strength and other properties as macroscopic values. Figure 5. Virtual anisotropic rock sample tested under uniaxial loading at failure with typical sandglass failure structures.
3.2 Virtual drilling tests The graph in Figure 4 shows that the stress-straincurve of the virtual biaxial load test corresponds with the diagram of the real unconfined compressive test. Also the samples in Figure 5 show typical sandglass failure structures like in a laboratory test. In the virtual sample, the number of micro cracks can be counted and it is possible to determine, if the cracks are developing from shear forces or normal forces. In Figure 5 for example 13761 micro cracks have been generated. The black coloured cracks develop from shear stress, the white coloured cracks from normal stress. Most of the black coloured cracks propagate through the simulated mica layers. After the rock materials were designed and the unconfined compressive strength gained, it was possible to simulate drilling tests. For the rotary percussive drilling tests different bits and buttons had to be designed as well, e.g. conical, ballistic and spherical buttons (Figure 6). The hard metal buttons of the drilling bits used in underground construction are made of tungsten carbide and are crucial for the drilling performance. cracks are caused by normal failure. In the area of high bond strength, only cracks caused by normal failure occur. Looking at the distribution of the cracks around the bits, a roof-shaped or stair-like structure of the crack patterns can be detected, which is traced by the line in Figure 8. The biaxial compressive strength of this rock sample is 48,1 MPa. In the entire sample 423 cracks were created by the indentation of the bits. Figure 7. Anisotropic rock sample after the drilling test. The forces from the bits are traced in black. Dark balls are zones of weakness (foliation). Figure 6. Hard metal bits for drilling tests. From the left: conical, ballistic and spherical bit shapes. Figure 8. Fracture pattern after the drilling test according to Figure 7. Cracks caused by shear failure are marked in black; cracks caused by normal failure are marked white. To simulate the percussive component, a vertical movement had to be implemented, to simulate the rotational component, a horizontal movement had to be implemented accordingly. In this way, it was possible to examine developing crack patterns in different virtual rock samples. Four types of virtual anisotropic rock samples were created varying the spacing of foliation, the width of the zones of weakness and the bond strength. The orientation of foliation and its influence was tested from 0 to 90 in steps of 10. The rock sample in Figure 7 (sample 1) shows typical orientation of the forces induced by the bit penetration. The forces enter the sample at the right side of the bit shape, because the movement of the bits is to the right. In the area of the bit in the middle, the shearing of of the dark coloured zone of weakness can be seen. The crack pattern shown in Figure 8 corresponds to the rock sample shown in Figure 7 at the same moment of the test. Most of the cracks in the zones of weakness are caused by shear failure, only a few All different rock samples were tested accordingly. Different crack patterns could be seen, depending on the parameters of foliation like spacing, width and orientation angle. To get a comparison between different crack patterns, a very tight foliated rock sample under the same testing parameters and direction of foliation is shown in Figure 9. In this rock sample, a very tightly foliated assembly is displayed. The shape of the forces indented by the bits (moving to the right) look similar to those of the rock sample in Figure 7. The crack pattern in Figure 9 (and 10) differs significantly from the one shown in Figure 7 (and 8). Most of the cracks are caused by shear failure; fewer cracks are caused by normal failure. Looking at the distribution of the cracks around the bits, a roofshaped or stair-like structure of the crack patterns can be stated, which is marked by the line in Figure 10. The biaxial compressive strength of this rock sample is 37,4 MPa. In the entire sample 807 cracks were created by the indentation of the bits.
Furthermore the three different bit shapes of Figure 6 were tested in the same rock sample to analyze the influence of the bit geometry. In rock sample 1, the ballistic bit shape created the highest number of cracks (Figure 12). Figure 9. Anisotropic rock sample after the drilling test. The forces from the bits are marked in black. Dark balls are zones of weakness (foliation). Figure 10. Fracture pattern after the drilling test according to Figure 8. Cracks caused by shear failure marked in black, cracks caused by normal failure marked white. Figure 12. Number of cracks after the drilling test plotted against the dip angle of foliation using three types of bit shapes. In this very tightly foliated rock sample, the number of cracks produced by the bit indentation is nearly twice as high as in the rock sample shown in the Figures 7 and 8. This implies, that in a tightly foliated rock, bonded with the same forces as a rock sample with a wider spacing of the foliation, the crack formation and therefore the fragmentation in the mineral bonds are much better. To show the impact of anisotropy on the drilling tests, different degrees of foliation were tested and the total number of cracks was counted for each orientation angle. In the tightly foliated rock sample 2 the number of produced cracks is twice as high as in rock sample 1. 3.3 Virtual cutting tests Another type of rock fragmentation in tunnelling is cutting performed by a tunnel boring machine (TBM). Therefore disc cutters were simulated as wedge indenters with a defined vertical load (penetration) into the rock samples. The cutting test endures 1000 steps in the code and every 250 steps, the penetrating forces by the disc cutters and the resulting crack patterns were analyzed. Furthermore, symmetrical and asymmetrical wear of a disc cutter were simulated to analyze the influence of tool wear during to crack formation. In the tests, two discs with a distinct distance from each other according to reality were modeled to investigate the interference of the forces. When these forces are high enough, chipping will occur. Figure 13. Disc cutters used for the indentation tests. From left: new disc, symmetric wear and asymmetric wear. Figure 11. Number of cracks after the drilling test plotted against the dip angle of foliation. Sample 1 related to Figure 7 and 8, sample 2 related to Figure 9 and 10. During the penetration process, the development of the forces by increasing indentation of the cutter can be observed. In Figure 14 the development of the forces is shown every 250 steps until the end of the test (1000 steps).
Figure 14. Development of forces by indenting disc cutters. Dark balls are zones of weakness (foliation). From the top: 250, 500, 750, 1000 calculated time steps. Figure 15. Development of cracks by indenting disc cutters (250, 500, 750, 1000 steps). Cracks caused by normal failure marked white, cracks caused by shear failure marked in black. The overlap of the forces increases with increasing penetration. In Figure 14, picture 3 (750 steps) and 4 (1000 steps) the overlapping forces form a large chip that can be released between the two disc cutters. In direct contact to the cutter, the bonds between the particles are completely broken. This corresponds with the zone of crushed and powdered rock underneath a real disc cutter. With increasing forces, the number of cracks in the assembly rises too. The number of cracks and the crack patterns is dependent on the generated rock type. In Figure 15 the development of the crack patterns of the rock sample corresponding to Figure 14 and for the same time steps in the cutting test can be seen. In the zones of weakness most of the cracks are caused by shear failure; only a few cracks are created by normal failure. In the zones of high strength cracks produced by normal failure are abundant. Directly under the disc cutters, where the highest forces are applied, cracks are induced mainly in the zones of weakness. The cracks form a radial corona around the discs as it can be observed at the tunnel face. The orientation of the cracks seems to be independent from the foliation. Most of the cracks are oriented slanting or normal to foliation. The density of the crack pattern decreases with depth, respectively distance from the disc cutter wedges. The biaxial compressive strength of this rock sample was determined with 48,1 MPa. In the entire sample 1605 cracks were created by the indentation of the disc cutters. To get the influence of anisotropy on the indenting forces and the resulting crack patterns, rock types with different spacing of foliation (zones of weakness) were tested in the same way. The distribution of the forces induced by the disc cutters in Figure 16 after the cutting test look similar to the distribution in Figure 14. But in this tightly foliated rock sample, the forces propagate much deeper into the rock. The overlap of the forces is not as clear as in the rock sample shown in Figure 14. It seems, that this phenomena is mainly caused by the tight foliation of the rock.
Figure 16. Development of forces by indenting cutters after the cutting test. Dark balls are zones of weakness (foliation). Figure 18. Number of cracks after the cutting test plotted against the dip angle of foliation. Sample 1 related to Figure 14 and 15, sample 2 related to Figure 16 and 17. Figure 17. Development of cracks by indenting cutters after the cutting test. Cracks caused by normal failure marked in white, cracks caused by shear failure marked in black. The crack pattern in Figure 17 differs significantly from the crack pattern shown in Figure 15. The propagation of the cracks is connected with the forces shown in figure 16. Zones of weakness and zones of high strength can t be distinguished like it is possible in Figure 15. Furthermore most of the cracks occur directly under the cutting edge and crack density decreases with increasing distance from the disc cutters. The biaxial compressive strength of this rock sample is 37,4 MPa. In the entire sample 3801 cracks were created by the indentation of the disc cutters. Here, the number of cracks in the rock sample is much higher than in the rock sample shown in Figure 15. This phenomenon was already observed in the drilling tests within the same rock samples. Also, there is an analogy in the decreasing density of the crack pattern with increasing depth respectively distance from the cutting edge. To show the impact of anisotropy on the cutting tests, different degrees of foliation were tested and the total number of cracks was counted for each orientation. In the tightly foliated rock sample 2 the number of produced cracks is about twice as high as in rock sample 1 (Fig. 18). In TBM tunneling the wear of the disc cutters play a key role in the economics of a project. The two main wear types are the symmetric wear under general conditions and the asymmetric wear of the outer disc cutters. In Figure 19 symmetric worn disc cutters are cutting the rock sample 2. The forces propagating into the rock sample are distributed in a very remote area around the discs only. The overlap of the forces between the disc traces is minor and the breaking of bonds around the disc cutters is limited. The crack pattern traces the obtained force distribution (Fig. 20). In contrast to a new disc, cracks are concentrated in a limited area around the cutters. The range of the cracks produced is only about half compared to the one of a new disc. Also there are only few cracks developed between the cutter traces. Similar to the crack pattern of a new disc cutter, the orientation of foliation doesn t play a significant role and is not represented in the distribution of the cracks. In the entire sample 2316 cracks were created by the indentation of the disc cutters. Figure 19. Development of forces by indenting disc cutters with symmetric wear after the cutting test. Dark balls are zones of weakness (foliation). Figure 20. Development of cracks by indenting disc cutters with symmetric wear at the end of the cutting test. Cracks caused by normal failure marked in white, cracks caused by shear failure marked in black.
Figure 21. Development of forces by indenting disc cutters with asymmetric wear at the end of the cutting test. Dark balls are zones of weakness (foliation). entire sample 2316 cracks were created by the indentation of the disc cutters. It is amazing, that the wear status of the disk cutter is crucial to crack formation and fragmentation of the rock material (Fig. 23). Nearly twice as much cracks are formed with a new and sharp disc cutter in contrast to a cutter with symmetrical or asymmetrical wear. Unlike this, the difference between symmetrical or asymmetrical wear is negligible. 4 CONCLUSIONS Figure 22. Development of cracks by indenting disc cutters with asymmetric wear at the end of the cutting test. Cracks caused by normal failure marked in white, cracks caused by shear failure marked in black. The crack patterns in correlation with foliation could be examined successfully. It could be demonstrated, that fracture propagation is mainly influenced by the spacing of foliation an therefore the presence of zones of weakness. No clear correlation with the orientation could be determined in the microcracks. This may be due to the forming of large cracks that can t be created by the numerical model. anyhow, large (macroscopic) fragments could be estimated by surrounding forces and the breakage of bonds e.g. between disc cutter traces. Notably the different bit shapes and disc wear types had a significant impact on the crack pattern and the depth of the induced forces. 5 REFERENCES Figure 23. Number of cracks according to the dip angle of foliation and disc shape after a full cutting test. During penetration with asymmetric worn disc cutters, two areas of the induced forces can be distinguished (Fig. 21). The main area is located near the long side of the cutter; here the forces penetrate much deeper into the rock. The smaller area underneath the short edge leads to a low range of the induced forces. All in all, the forces propagate a little bit deeper into the rock sample than in the case with asymmetric worn disc cutters. Again, the crack pattern traces the obtained force distribution (Fig. 22). At the long side of the cutter more cracks are visible than along the short side. Also there are only few cracks developed between the cutter traces. Similar to the crack pattern of a new disc cutter, the dip angle of foliation is not represented in the crack distribution under the asymmetrically worn cutter since cracks are more or less oriented slanting or normal to foliation. In the Schormair, N. 2003. Rock fragmentation during rotary percussive drilling. Diploma Thesis, Technische Universität München (in German). Schormair, N., Thuro, K. & Plinninger, R.J. 2006. The influence of anisotropy on hard rock drilling and cutting. In Culshaw, M., Reeves, H., Spink, T. & Jefferson, I. (eds): IAEG Engineering geology for tomorrow s cities. Proceedings of the 10 th IAEG International Congress, Nottingham, United Kingdom, 6-10 Sept. 2006, Paper No. 491, Rotterdam: Balkema. Thuro, K. 1997. Drillability prediction - geological influences in hard rock drill and blast tunnelling. Geol. Rundsch. 86, 426-437. Thuro, K. 2002. Geologisch-felsmechanische Grundlagen der Gebirgslösung im Tunnelbau. Geological and rock mechanical fundamentals of excavatability in tunnelling. Münchner Geologische Hefte, B18, Technische Universität München. Thuro, K. & Plinninger, R.J. 2003. Hard rock tunnel boring, cutting, drilling and blasting: rock parameters for excavatability. Proceedings of the 10th ISRM Int. Congr. on Rock Mech., Johannesburg, South Africa, 8-12. September 2003, 1227-1234. Thuro, K., Plinninger, R.J. & Spaun, G. 2002. Drilling, blasting and cutting is it possible to quantify geological parameters of excavation? In: van Roy & Jermy (eds): Engineering geology for developing countries. Proceedings of the 9 th Congress of the Intern. Ass. for Eng. Geol. and the Environment, Durban, South Africa, 16-20 Sept. 2002, Rotterdam: Balkema, 2853-2861. Thuro, K. & Spaun, G. 1996. Drillability in hard rock drill and blast tunnelling. Felsbau, 14, 103-109.