|
Material Sciences 2022
含孔洞圆盘试样裂纹扩展规律的物模和数模分析
|
Abstract:
孔洞是岩石等地质材料中典型的天然缺陷,对岩体承载力和裂纹扩展具有重要影响。通过实验和数值模拟研究了包含单个圆孔或多个不同直径圆孔的特制混凝土圆盘试样中的裂纹扩展过程。圆盘试样是由硅酸盐水泥、细砂和水混合制备而成。首先对含单孔圆盘试样的承载力进行了实测分析;接着对含单孔和多孔圆盘试样的裂纹扩展模式进行了实验研究,分析了裂纹的起裂及贯通过程,再现了孔洞缺陷对裂缝扩展模式的影响;最后,通过改进的高阶位移不连续方法进行含孔洞圆盘试样的劈裂过程数值模拟,进一步揭示了孔洞缺陷对应力集中和裂纹扩展的主导作用,数值结果与物理实验结果吻合较好。
The hole is a typical natural defect in rock and other geological materials, which has an important influence on bearing capacity and crack propagation of rock mass. The crack propagation process in a special concrete disk specimen containing a single circular hole or several circular holes with different diameters is studied by experiments and numerical simula-tions. The disc sample is prepared by mixing portland cement, fine sand and water. Firstly, the bearing capacity of disk specimens with a single hole is measured and analyzed. Then, the crack propagation mode of single-hole and porous disk specimens is studied experimentally, the crack in-itiation and penetration process are analyzed, and the influence of hole defects on crack propaga-tion mode is reproduced. Finally, the improved high-order displacement discontinuity method is used to simulate the splitting process of disk specimens with holes, which further reveals the lead-ing role of hole defects in stress concentration and crack propagation. The numerical results are in good agreement with the physical experimental results.
[1] | Kato, T. and Nishioka, T. (2005) Analysis of Micro-Macro Material Properties and Mechanical Effects of Damaged Ma-terial Containing Periodically Distributed Elliptical Microcracks. International Journal of Fracture, 131, 247-266.
https://doi.org/10.1007/s10704-004-4558-z |
[2] | Hudson, J.A., Brown, E.T. and Rummel, F. (1972) The Con-trolled Failure of Rock Discs and Rings Loaded in Diametral Compression. International Journal of Rock Mechanics and Mining Sciences, 9, 241-248.
https://doi.org/10.1016/0148-9062(72)90025-3 |
[3] | Hudson, J.A. (1969) Tensil Strength and the Ring Test. Inter-national Journal of Rock Mechanics and Mining Sciences, 6, 91-97. https://doi.org/10.1016/0148-9062(69)90029-1 |
[4] | Sammis, C.G. and Ashby, M.F. (1986) The Failure of Brittle Porous Solids under Compressive Stress States. Acta Metallurgica, 34, 511-526. https://doi.org/10.1016/0001-6160(86)90087-8 |
[5] | Wong, R.H.C. and Chau, K.T. (1998) Crack Coalescence in a Rock-Like Material Containing Two Cracks. International Journal of Rock Mechanics and Mining Sciences, 35, 147-164. https://doi.org/10.1016/S0148-9062(97)00303-3 |
[6] | 段进超, 唐春安, 常旭. 脆性基多孔材料孔洞的尺寸效应及其破坏模式研究[J]. 岩土力学, 2007, 28(3): 631-634. https://doi.org/10.16285/j.rsm.2007.03.037 |
[7] | 朱万成, 黄志平, 唐春安, 逄铭璋. 含预制裂纹巴西盘试样破裂模式的数值模拟[J]. 岩土力学, 2004, 25(10): 1609-1612. https://doi.org/10.16285/j.rsm.2004.10.019 |
[8] | Park, C.H. (2008) Coalescence of Frictional Fractures in Rock Materials. PhD Thesis, Purdue University, West Lafayette. |
[9] | Yang, Q., Dai, Y.H., Han, L.J. and Jin, Z.Q. (2009) Experimental Study on Mechanical Behavior of Brittle Marble Samples Containing Different Flaws under Uniaxial Com-pression. Engineering Fracture Mechanic, 76, 1833-1845.
https://doi.org/10.1016/j.engfracmech.2009.04.005 |
[10] | Park, C.H. and Bobet, A. (2009) Crack Coalescence in Specimens with Open and Closed Flaws: A Comparison. International Journal of Rock Mechanics and Mining Sciences, 46, 819-829. https://doi.org/10.1016/j.ijrmms.2009.02.006 |
[11] | Park, C.H. and Bobet, A. (2010) Crack Initiation, Propagation and Coalescence from Frictional Flaws in Uniaxial Compression. Engineering Fracture Mechanic, 77, 2727-2748. https://doi.org/10.1016/j.engfracmech.2010.06.027 |
[12] | Tang, C.A. and Hudson, J.A. (2010) Rock Failure Mechanisms: Explained and Illustrated. Routledge, London. |
[13] | Yang, S.Q. (2011) Crack Coalescence Behav-ior of Brittle Sandstone Samples Containing Two Coplanar Fissures in the Process of Deformation Failure. Engineering Fracture Mechanic, 78, 3059-3081.
https://doi.org/10.1016/j.engfracmech.2011.09.002 |
[14] | Mellor, M. and Hawkes, I. (1971) Measurement of Tensile Strength by Diametral Compression of Discs and Annuli. Engineering Geology, 5, 173-225. https://doi.org/10.1016/0013-7952(71)90001-9 |
[15] | Ayatollahi, M.R. and Aliha, M.R.M. (2008) On the Use of Brazilian Disc Specimen for Calculating Mixed Mode I-II Fracture Toughness of Rock Materials. Engineering Fracture Mechanics, 75, 4631-4641.
https://doi.org/10.1016/j.engfracmech.2008.06.018 |
[16] | Wang, Q.Z. (2010) Formula for Calculating the Critical Stress Intensity Factor in Rock Fracture Toughness Tests Using Cracked Chevron Notched Brazilian Disc (CCNBD) Specimens. International Journal of Rock Mechanics and Mining Sciences, 47, 1006-1011. https://doi.org/10.1016/j.ijrmms.2010.05.005 |
[17] | Dai, F., Chen, R., Iqbal, M.J. and Xia, K. (2010) Dynamic Cracked Chevron Notched Brazilian Disc Method for Measuring Rock Fracture Parameters. International Journal of Rock Mechanics and Mining Sciences, 47, 606-613.
https://doi.org/10.1016/j.ijrmms.2010.04.002 |
[18] | Dai, F., Xia, K., Zheng, H. and Wang, Y.X. (2011) Determina-tion of Dynamic Rock Model Fracture Parameters Using Cracked Chevron Notched Semi-Circular Bend Specimen. En-gineering Fracture Mechanics, 78, 2633-2644.
https://doi.org/10.1016/j.engfracmech.2011.06.022 |
[19] | Ayatollahi, M.R. and Sistaninia, M. (2011) Mode II Frac-ture Study of Rocks Using Brazilian Disk Specimens. International Journal of Rock Mechanics and Mining Sciences, 48, 819-826. https://doi.org/10.1016/j.ijrmms.2011.04.017 |
[20] | Wang, Q.Z., Feng, F., Ni, M. and Gou, X.P. (2011) Measurement of Mode I and Mode II Rock Dynamic Fracture Toughness with Cracked Straight through Flattened Bra-zilian Disc Impacted by Split Hopkinson Pressure Bar. Engineering Fracture Mechanics, 78, 2455-2469. https://doi.org/10.1016/j.engfracmech.2011.06.004 |
[21] | Wang, Q.Z., Gou, X.P. and Fan, H. (2012) The Minimum Dimensionless Stress Intensity Factor and Its Upper Bound for CCNBD Fracture Toughness Specimen Analyzed with Straight through Crack Assumption. Engineering Fracture Mechanics, 82, 1-8. https://doi.org/10.1016/j.engfracmech.2011.11.001 |
[22] | Awaji, H. and Sato, S. (1978) Combined Mode Fracture Toughness Measurement by the Disk Test. Journal of Engineering Materials and Technology, 100, 175-182. https://doi.org/10.1115/1.3443468 |
[23] | Sanchez, J. (1979) Application of the Disk Test to Mode-I-II Fracture Toughness Analysis. M.S. Thesis, Department of Mechanical Engineering, University of Pittsburgh, Pitts-burgh. |
[24] | Atkinson, C., Smelser, R.E. and Sanchez, J. (1982) Combined Mode Fracture via the Cracked Brazilian Disk. International Journal of Fracture, 18, 279-291. https://doi.org/10.1007/BF00015688 |
[25] | Shetty, D.K., Rosenfield, A.R. and Duckworth, W.H. (1986) Mixed Mode Fracture of Ceramic in Diametrical Compression. Journal of the American Ceramic Society, 69, 437-443. https://doi.org/10.1111/j.1151-2916.1986.tb07441.x |
[26] | Fowell, R.J. and Xu, C. (1994) The Use of the Cracked Brazilian Disk Geometry for Rock Fracture Investigations. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 31, 571-579.
https://doi.org/10.1016/0148-9062(94)90001-9 |
[27] | Krishnan, G.R., Zhao, X.L., Zaman, M. and Rogiers, J.C. (1998) Fracture Toughness of a Soft Sandstone. International Journal of Rock Mechanics and Mining Sciences, 35, 195-218. https://doi.org/10.1016/S0148-9062(97)00324-0 |
[28] | Khan, K. and Al-Shayea, N.A. (2000) Effects of Specimen Geometry and Testing Method on Mixed-Mode I-II Fracture Toughness of a Limestone Rock from Saudi Ara-bia. Rock Mechanics and Rock Engineering, 33, 179-206.
https://doi.org/10.1007/s006030070006 |
[29] | Al-Shayea, N.A., Khan, K. and Abduljauwad, S.N. (2000) Effects of Confining Pressure and Temperature on Mixed-Mode (I-II) Fracture Toughness of a Limestone Rock Formation. Inter-national Journal of Rock Mechanics and Mining Sciences, 37, 629-643. https://doi.org/10.1016/S1365-1609(00)00003-4 |
[30] | Al-Shayea, N.A., Khan, K. and Abdulraheem, A. (2001) Fracture Toughness vs. Tensile Strength Reservoir Rocks from Saudi Arabia. Proceeding of the 2001 ISRM Sponsored International, 2nd Asian Rock Mechanics Symposium, Beijing, 11-14 September 2001, 169-172. https://doi.org/10.1201/9781003077510-37 |
[31] | Al-Shayea, N.A. (2005) Crack Propagation Trajectories for Rocks under Mixed Mode I-II Fracture. Engineering Geology, 81, 84-97. https://doi.org/10.1016/j.enggeo.2005.07.013 |
[32] | Tang, C.A., Lin, P., Wong, R.H.C. and Chau, K.T. (2001) Analysis of Crack Coalescence in Rock-Like Materials Containing Three Flaws—Part II: Numerical Approach. Interna-tional Journal of Rock Mechanics and Mining Sciences, 38, 925-939. https://doi.org/10.1016/S1365-1609(01)00065-X |
[33] | Erdogan, F. and Sih, G.C. (1963) On the Crack Extension in Plates under Loading and Transverse Shear. Journal of Fluids Engineering, 85, 519-527. https://doi.org/10.1115/1.3656897 |
[34] | Hussian, M.A., Pu, E.L. and Underwood, J.H. (1974) Strain Energy Re-lease Rate for a Crack under Combined Mode I and Mode II. In: Fracture Analysis, ASTM STP 560, American Society for Testing and Materials, Philadelphia, 2-28.
https://doi.org/10.1520/STP33130S |
[35] | Sih, G.C. (1974) Strain-Energy-Density Factor Applied to Mixed Mode Crack Problems. International Journal of Fracture, 10, 305-321. https://doi.org/10.1007/BF00035493 |
[36] | Shen, B. and Stephansson, O. (1994) Modification of the G-Criterion for Crack Propagation Subjected to Compression. Engi-neering Fracture Mechanic, 47, 177-189. https://doi.org/10.1016/0013-7944(94)90219-4 |
[37] | Chen, J.T. and Wong, F.C. (1997) Analytical Derivations for One-Dimensional Eigenproblems Using Dual BEM and MRM. Engineer-ing Analysis with Boundary Elements, 20, 25-33. https://doi.org/10.1016/S0955-7997(97)00032-5 |
[38] | Chen, J.T. and Hong, H.K. (1999) Review of Dual Boundary Element Methods with Emphasis on Hyper Singular Integrals and Divergent Series. Applied Mechanics Reviews, ASME, 52, 17-33. https://doi.org/10.1115/1.3098922 |
[39] | Hong, H.K. and Chen, J.T. (1988) Generality and Special Cases of Dual Integral Equations of Elasticity. Journal of the Chinese Society of Mechanical Engineers, 9, 1-9. |
[40] | Hong, H.K. and Chen, J.T. (1988) Derivation of Integral Equations of Elasticity. Journal of Engineering Mechanics, ASCE, 114, 1028-1044. https://doi.org/10.1061/(ASCE)0733-9399(1988)114:6(1028) |
[41] | Marji, M.F., Hosseini-nasab, H. and Hosse-inmorsgedy, A. (2009) Numerical Modeling of the Mechanism of Crack Propagation in Rocks under TBM Disc Cutters. Journal of Mechanics of Materials and Structures, 2, 439-457. |
[42] | Haeri, H., Shahriar, K., Marji, M.F. and Moaref Vand, P. (2013) A Coupled Numerical Experimental Study of the Breakage Process of Brittle Substances. Arabian Journal of Geosciences, 8, 809-825.
https://doi.org/10.1007/s12517-013-1165-1 |
[43] | Haeri, H., Shahriar, K., Marji, M.F. and Moaref Vand, P. (2014) On the Strength and Crack Propagation Process of the Pre-Cracked Rock-Like Specimens under Uniaxial Compression. Strength of Materials, 46, 171-185.
https://doi.org/10.1007/s11223-014-9525-y |
[44] | Irwin, G.R. (1957) Analysis of Stress and Strains near the End of a Crack. Journal of Applied Mechanics, 24, 361-364.
https://doi.org/10.1115/1.4011547 |
[45] | Marji, M.F., Hosseinin Nasab, H. and Kohsary, A.H. (2006) On the Uses of Special Crack-Tip Elements in Numerical Rock Fracture Mechanics. International Journal of Solids and Structures, 43, 1669-1692.
https://doi.org/10.1016/j.ijsolstr.2005.04.042 |
[46] | Shou, K.J. (1997) A Higher Order Displacement Discontinuity Method for Three Dimensional Elastostatic Problems. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 34, 317-322.
https://doi.org/10.1016/S0148-9062(96)00052-6 |
[47] | Shou, K.J. (1997) A Two-Dimensional Displacement Dis-continuity Method for Multi-Layered Elastic Media. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 34, 509.
https://doi.org/10.1016/S1365-1609(97)00178-0 |