為分析異向性多裂縫岩體之破壞力學性質，本研究以異向性線彈性理論配合材料基本解(Green’s Function)、邊界積分方程式及裂縫尖端模式為理論基礎，藉以Fortran語言撰寫成BEM 分析程式，其可成功的分析等向性及異向性材料之多裂縫尖端應力強度因子等相關問題。為檢驗數值分析結果之可靠度，並與歷代相關文獻進行驗證，其分析之比較結果非常吻合，且可成功地求得混合模態載重下多裂縫尖端之應力強度因子。進一步分析不同異向性程度之無限域多裂縫問題，發現應力強度因子亦受材料異向性程度不同及多裂縫的幾何形式而有顯著的影響。

　　This study presents a single-domain boundary element method (BEM) for linear elastic fracture mechanics analysis in the 2-D anisotropic material in order to analyze fracture mechanics of multiple cracks. In this formulation, the displacement integral equation is only collocated on the un-cracked boundary, and the traction integral equation is collocated on one side of the crack surface. A special crack-tip element was introduced to capture exactly the crack-tip behavior. A computer program with the FORTRAN language has been developed to effectively calculate the stress intensity factors of multiple cracks for isotropic and anisotropic material under mixed-mode loading, and has a good accuracy with the previous researches. Finally, analyzing multiple-crack materials present that it has apparent effect because of different to anisotropic degree and geometric form.

1.Abbas A., Makoto O. and Sia N. N., Alternative solution methods for crack problems in plane anisotropic elasticity, with examples. Int. J. of Solids and Structures, Vol. 37, pp. 6433–6478, (2000).

2.Aliabadi, M. H., Fracture of Rock., WIT press, Boston, (1999).

3.Amadei, B., Rock anisotropy and the theory of stress measurements,Springer-Verlag, New York, (1983).

4.Atkinson, B. K., Fracture Mechanics of Rocks : Experimental fracture chanics data of rock and minerals., Academic press, London, (1987).

5.Bhattacharya, J. P. and Walker, R. G., Facies Models Response to sea level change. Geol. Assoc. Canada., pp. 157-178, (1992).

6.Binienda, W., Wang, A. S. D. and Delale, F., Analysis of bent crack in unidirectional fibre reinforced composites. Int. J. Fracture, Vol. 47, pp. 1-24, (1991).

7.Cerrolaza, M. and Alarcon, E., A bi-cubic transformation for the numerical evaluation of the Cauchy principal value integrals in boundary methods. Int. J. Numer. Methods Engng., Vol. 28, pp. 987-999, (1989).

8.Chen, C. S., Characterization of deformability, strength, and fracturing of anisotropic rocks using Brazilian tests. Ph.D. thesis, Department of Civil Eng., University of Colorado, (1996).

9.Chen, C. S., Pan, E., and Amadei, B., Fracture mechanics analysis of cracked discs of anisotropic rock using the boundary element method. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., Vol. 35, No. 2, pp. 195-218, (1998).

10.Chen, K. L. and Atluri, S. N., A finite-difference alternating method for a cost-effective determination of weight-functions for orthotropic materials in mixed-mode fracture. Engineering Fracture Mechanics, Vol. 36 , pp. 327-340, (1990).

11.Chen, Y. Z., Multiple crack problems of anti-plane elasticity in an infinite body. Engineering Fracture Mechanics, Vol. 20, No.5 6, pp. 767-775, (1984).
12.Denda, M. and Dong, Y. F. Complex variable approach to the BEM for multiple crack problems. Comput. Mechods Appl. Mech. Engrg., Vol. 141, pp. 247-264, (1997).

13.Du, Y. and Aydin, A. Interaction of multiple cracks and formation of echelon crack arrays. Int. J. Numerical and Analytical Methods in geomechanics, Vol. 15, pp. 205-218, (1991).

14.Dwyer, J. F., and Amadei, B., The edge function method and singular problems in rock mechanics. Int. J. Rock Mech. Sci. Geomech. Abstr, Vol. 32, No.2, pp. 121-133, (1995).

15.Dwyer, J.F., Edge function analysis of crack interaction in anisotropic materials. Engineering Fracture Mechanics, Vol. 56, No.2, pp. 233-248, (1997).

16.Elliott, T., Sedimentary environments and facies. Blackwell, pp. 113-154, (1986).

17.Fujimoto, T. and Sumi, S., Local buckling of thin tensioned plates with a crack. Memoirs of the Fraculty of Engineering, Kyushu University, Vol.42, (1982).

18.Gramberg, J., A Non-conventional View on Rock Mechanics and Fracture Mechanics., Published of the Commission of the European Communities by A. A. Balkema, Rotterdam, (1989).

19.Griffith, A. A., The phenomena of rupture and flow in solids. Phil. Trans. Roy. Soc. London, Series A, Vol. 221, pp. 163-198, (1920).

20.Hai-Tao, C., A periodic array of cracks in an infinite anisotropic medium. Engineering Fracture Mechanics, Vol. 46, No.2, pp. 133-142, (1993).

21.Huang, C. Y. and Cheng, Y. M., Oligocene and Miocene planktic foraminiferal biostratigraphy of northern Taiwan. Proc. Geol. Soc. China.,Vol. 26, pp. 21-56, (1983).

22.Irwin, G. R., Analysis of stresses and strains near the end of a crack. Trans. ASME, J. Appl. Mech., Vol. 24, pp. 361-364, (1957).

23.Isida, M., Arbitrary loading problems of doubly symmetric regions containing a central crack. Engineering Fracture Mechanics, Vol. 7, pp. 505-514, (1975).

24.Isida, M., Elastic analysis of cracks and stress intensity factors (in Japanese).Fracture Mechanics and Strength of Materials 2, Baifuukan, pp. 181-184, (1976).

25.Lekhnitskii, S.G., Anisotropic plates, translated by S. W. Tsai., Gordon and Breath, (1957).

26.Lekhnitskii, S.G., Theory of elasticity of an anisotropic elastic body. translated by P. Fern, Holden-Day Inc, San Francisco, (1963).

27.Liu, D. S. and Chiou, D. Y., A coupled IEM/FEM approach for solving elastic problems with multiple cracks. Int. J. of Solids and Structures, Vol. 40, pp. 1973–1993, (2003).

28.Mauge, C. and Kachanov, M., Anisotropic material with interacting arbitrarily oriented cracks. Stress intensity factors and crack-microcrack interactions. Int. J. Fracture, Vol. 65, pp. 115-139, (1994).

29.Murakami, Y., A simple procedure for the accurate determination of stress intensity factors by finite element method. Engineering Fracture Mechanics, Vol. 8, pp. 643-655, (1976).

30.Murakami, Y., Stress intensity factors handbook, (1986).

31.Muskhelishvili, N.I, Singular Integral Equations, Noordhoff, Gronigen, (1953).

32.Pan, E. and Amadei, B., Fracture mechanics analysis of cracked 2-D anisotropic media with a new formulation of the boundary element method. Int. J. Fracture, Vol. 77, pp.161-174, (1996).

33.Pan, E., A general boundary element analysis of 2-D linear elastic fracture mechanics. Int. J. Fracture, Vol. 88, pp.41-59, (1997).

34.Rice, J. R., A path independent integral and the approximate analysis of strain concentration by notches and cracks. Trans. ASME, J. Appl. Mech. Vol. 35, pp. 379-386, (1968).

35.Rooke, D. P. and Tweed, J., The stress intensity factors of a radial crack in a point loaded disc. Int. J. Engng. Sci., Vol. 11, pp. 285-290, (1973).

36.Schijve, J., Some calculations on the stress distribution in an infinite sheet with a single crack and with periodic collinear cracks. Engineering Fracture Mechanics, Vol. 55, No. 2, pp. 313-320, (1996).

37.Shu, H.M., Petit, J. and Bezine, G., Stress intensity factors for radial cracks in thick walled cylinders. I. Symmetrical cracks II. Combination of autofrettage and internal pressure. Engineering Fracture Mechanics, Vol. 49, No. 4, pp. 611-629, (1994).

38.Sih, G. C., Handbook of stress intensity factors. Inst. Of Fracture and Solid Mechanics, Lehigh University, Bethlehem, Pennsylvania, (1973).

39.Sih, G. C., Paris, P. C. and Irwin, G. R., On cracks in rectilinearly anisotropic bodies. Int. J. Fracture, Vol. 3, pp. 189-203, (1965).

40.Sollero, P. and Aliabadi, M. H., Fracture mechanics analysis of anisotropic plates by the boundary element method. Int. J. Fracture, Vol. 64, pp. 269-284, (1993).

41.Tada, H., Paris, P. C. and Irwin, G. R., The Stress Analysis of Cracks, Handbook, Del Research Corporation., (1987).

42.Tsang, D. K. L., Oyadiji, S. O. and Leung, A. Y. T., Multiple penny-shaped cracks interaction in a finite body and their effect on stress intensity factor. Engineering Fracture Mechanics, Vol. 70, pp. 2199-2214, (2003).

43.Whittaker, B. N., Singh, R. N. and Sun, G., Rock Fracture Mechanics ：Principles, Design and Applications, Elsevier, New York, (1992).

44.Whittaker, B. N., Singh, R. N. and Sun, G., Rock Fracture Mechanics ： Principles, Design and Applications., Elsevier, New York, (1992).

45.Yokobori, T., Ohashi, M. and Ichikawa, M., The Interaction of Two Collinear Asymmetrical Elastic Cracks, Reports of the Research Institute for Strength and Fracture of Materials, Tohoku University, Vol. 1., No.2, pp.33-39, (1965).

46.Zarzour, J., On interacting cracks in unidirectional fibrous composites. Int. J. of Solids and Structures, Vol. 29, pp.3239-3250, (1992).

47.王建力，岩石破壞力學講義，國立成功大學資源工程學系，(2000)。

48.柯建仲，異向性大理岩之破壞力學性質分析，國立成功大學資源工程學系碩士論文，(2000)。

49.彭文彬，二維異向性裂紋交互作用之探討，國立成功大學土木工程學系碩士論文，(2000)。