13th International Conference on Fracture June 16–21, 2013, Beijing, China -6- Figure 5. The normalized stress intensity factors ) /( K p R I and ) /( K p R II , for different C/R ratios, for a center inclined micro crack , in a semi-infinite plane 4. Modeling of eroded disc cutter Since, after a while, TBM disc cutters erosion caused by contact with the rock, therefore, the effect of erosion is modeled numerically. For this purpose, four special elements are used to simulate the disc cutter tips. This model estimates the required curvature near the disc cutter tips, reducing the computing efficiency and increases the required specific energy for chips formation under disc cutters during a rock indentation process. In the Figure 6, the micro crack propagation path for artifact cracks of AC1, AC2, AC3 and AC4 which represents the coalescing of propagated micro cracks from artifact cracks, and also this path for S/Pd=10, disc edge angle ψ=60, Pd=6mm and extended length of δ=4mm (8 iteration) are estimated. Micro cracks propagate with respect to direction of the artifact cracks, then after several (8) iteration propagated micro cracks from artifact cracks coalesce to each other at the region between cutters. Considering a typical TBM with a thrust of 250 kN per cutter, with disc cutters of 15 mm width and 432 mm diameter. The typical rock is the Aspo diorite with the Mode I and Mode II fracture toughnesses KIC=3.83 MPa m 1/2, and KIIC=5.09 MPa m1/2 respectively. The other parameters of this rock as quoted by Backers (2004) are: 15 t MPa, 220 C MPa, and E= 68 GPa and 0.24 [20].
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