岩体水力劈裂机理研究及其在地下洞室围岩稳定分析中应用
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摘要
岩体水力劈裂研究与应用虽从20世纪50年代就开始,但其机理并没有得到很好地解决,仍存在许多值得研究的课题,而且这些研究绝大数还是针对石油、天然气行业的人工致裂问题,对于水利水电、矿业等行业的自然营造力作用下产生的水力劈裂机理,尤其是单裂纹的水力劈裂机理研究却较少。
本研究首先根据目前水力劈裂机理研究的尺度,将岩体水力劈裂机理研究划分为两个层次,第一个层次是基于岩体在宏观、综合、统计意义上的水力劈裂,第二个层次是微观尺度的单裂纹水力劈裂;第二,分析总结了水利水电等行业自然营造力作用下水力劈裂与人工致裂的不同点;第三,针对自然营造力水力劈裂特点、不同研究尺度,从理论和数值分析两个方面对岩体水力劈裂机理问题进行研究;最后,通过具体工程地下高压隧洞的水力劈裂数值分析详细研究,揭示水力劈裂对地下洞室围岩稳定的影响规律。本文主要开展了以下工作:
(1) 从宏观、综合、统计意义研究深埋圆形隧洞在渗流场作用下弹性和弹塑性问题。提出了考虑渗流场作用下圆形隧洞的弹塑性解;并对不同内外水头比值时洞周应力场分布规律及塑性半径进行研究。研究表明,随内外水头差的增大其影响将显著增大,尤其是对环向应力的影响程度要比径向应力大,且径向应力和环向应力不再符合无渗流时的分布规律,出现大小值交换。同时,随着内水头的增大,洞周压应力和塑性半径逐渐减小,直到出现无塑性区,随内水压力的进一步不断增大,又会出现新的塑性区,此时,第一主应力已变为环向应力;另外,考虑渗流场影响计算得到的塑性半径要比不考虑时大。
(2) 应用工程近似裂纹复合失稳准则,分别推导出隧洞周围岩体内深埋裂纹两种破坏模式的临界水压计算公式,并对其随裂纹方向及地应力侧压系数变化规律进行分析。分析结果表明,当侧压力系数等于1.0时,临界水压并不随裂纹的方向而变化;在拉剪复合断裂模式下,裂纹与主应力方向平行时最易发生水力劈裂;在压剪复合断裂模式下,当λ-tanφ>0时,规律性与拉剪复合断裂模式基本一致,但λ-tanφ<0时,裂纹与最大主应力夹角呈45°及135°时最易发生水力劈裂。
(3) 假定岩体混凝土水力劈裂过程裂缝形态为椭圆形,根据自然营造力作用下产生水力劈裂的边界条件,从流体质量守恒和动量守恒定律出发,采用控制体积法推导出裂纹流体运动质量守恒定律的具体形式、缝内水压分布微分方程,并得到在裂纹扩展稳定状态某时刻缝内压力理论计算式。从定性和定量两个方面与已有实验的结果比较说明,提出的理论计算公式反映的规律性是正确的,在裂纹快速开裂前提下计算结果与实验吻合较好。得到的计算式对研究地震荷载作用下混
In spite of the study and application of rock hydraulic fracturing started at 20th century 50s early, its mechanism is not known well and there are many study topics. Most studies on rock hydraulic fracturing are focussed on artifical hydraulic farcturing applied in field of petroleum and nature gas. The hydraulic fracturing problems in field of water conservancy and hydropower and mining are producted by nature hydraulic power. The mechanism of nature hydraulic fracturing is more complex than that of artifical fracturing, so its studies are not enough ,espeically, the study on a single fracture.Fristly, In this paper the study level of hydraulic fracturing is divided into two based on study measure. The rock is considered as a homogeneous medium based on rock macroscopical, synthrtic and statistical characteristics in frist study level. But the secondary study level is focussed on a single fracture based on rock microcosic characteristics. Secondly, the differences between the artifical and nature hydraulic fracturing are analyzed and concluded. Thirdly, the mechanism of nature hydraulic fracturing is studied from two aspects of theortical analysis and numerical simulation according to its characteristics and study level. Finally, after deeply studyed on hydraulic fracturing simulation of higher pressure tunnel, the Influence laws of hydraulic fracturing on tunnel surrounding rock stability are proposed. The major studies and conclusions are followed.(l)The elastic and elasto-plastic problems of deep-buried circle tunnel considering influence of seepage field is studied based on rock macroscopical, synthrtic and statistical characteristics. The elasto-plastic analytical solution of deep-buried tunnel are obtained. Further, the influence laws of seepage field on stress field and plastic radius surrounding tunnel are studied according to different ratio of inner and outer water head. The study shows that the influence of seepage field on stress field is intensive along with the gradient increment of inner and outer water head of tunnel, and the influence degree on tangent stress is more than that on radial stress. The distribution law of stresses is not coincided with situation of without considering fluid flow. The compressive stresses and plastic radius are gradually decreased along with the increasing inner head, and plastic radius may be zero value if the inner head continually to some extent. But the new plastic radius will be reappeared along with the increment of inner head further, the first principle stress is alreadly turnned to tangent stress at that time. The plastic radius with considering influence of fluid flow
is larger than that without considering the influence.(2)Using fracture propagation engineering criterion, calculation formulae of critical inner water pressure of two kinds of failure model are obtained respectively and its effect laws as fracture direction and lateral geo-stress coefficient are studied. The study shows that critical inner pressure of two kinds of model is not varied as fracture direction changing when the lateral coefficient equals 1.0. Under tension-shear mixed model, fracture is most easily fracturing when fracture direction is parallel with direction of principle stress. Under compression-shear mixed model, distribution law of critical inner water pressure is same as tension-shear complex model when (λ-tanφ) large than 1.0 .But fracture is most easily fracturing when (λ-tanφ) less than 1.0 and fracture direction are 45° or 135° angle with principle stress.(3)It is assumed that fracture shape is a half ellipse-shaped in hydraulic fracturing of rock and concrete material. Based on boundary condition of natural hydraulic pressure, the mass conservation and momentum principle, the concrete formulae of liquid mass conservation and differential equation of water pressure distribution due to hydraulic fracturing are obtained using the finite control volume approach. The theoretical formula at any time of fracture stable propagating is obtained also. The theoretical formula is
本研究首先根据目前水力劈裂机理研究的尺度,将岩体水力劈裂机理研究划分为两个层次,第一个层次是基于岩体在宏观、综合、统计意义上的水力劈裂,第二个层次是微观尺度的单裂纹水力劈裂;第二,分析总结了水利水电等行业自然营造力作用下水力劈裂与人工致裂的不同点;第三,针对自然营造力水力劈裂特点、不同研究尺度,从理论和数值分析两个方面对岩体水力劈裂机理问题进行研究;最后,通过具体工程地下高压隧洞的水力劈裂数值分析详细研究,揭示水力劈裂对地下洞室围岩稳定的影响规律。本文主要开展了以下工作:
(1) 从宏观、综合、统计意义研究深埋圆形隧洞在渗流场作用下弹性和弹塑性问题。提出了考虑渗流场作用下圆形隧洞的弹塑性解;并对不同内外水头比值时洞周应力场分布规律及塑性半径进行研究。研究表明,随内外水头差的增大其影响将显著增大,尤其是对环向应力的影响程度要比径向应力大,且径向应力和环向应力不再符合无渗流时的分布规律,出现大小值交换。同时,随着内水头的增大,洞周压应力和塑性半径逐渐减小,直到出现无塑性区,随内水压力的进一步不断增大,又会出现新的塑性区,此时,第一主应力已变为环向应力;另外,考虑渗流场影响计算得到的塑性半径要比不考虑时大。
(2) 应用工程近似裂纹复合失稳准则,分别推导出隧洞周围岩体内深埋裂纹两种破坏模式的临界水压计算公式,并对其随裂纹方向及地应力侧压系数变化规律进行分析。分析结果表明,当侧压力系数等于1.0时,临界水压并不随裂纹的方向而变化;在拉剪复合断裂模式下,裂纹与主应力方向平行时最易发生水力劈裂;在压剪复合断裂模式下,当λ-tanφ>0时,规律性与拉剪复合断裂模式基本一致,但λ-tanφ<0时,裂纹与最大主应力夹角呈45°及135°时最易发生水力劈裂。
(3) 假定岩体混凝土水力劈裂过程裂缝形态为椭圆形,根据自然营造力作用下产生水力劈裂的边界条件,从流体质量守恒和动量守恒定律出发,采用控制体积法推导出裂纹流体运动质量守恒定律的具体形式、缝内水压分布微分方程,并得到在裂纹扩展稳定状态某时刻缝内压力理论计算式。从定性和定量两个方面与已有实验的结果比较说明,提出的理论计算公式反映的规律性是正确的,在裂纹快速开裂前提下计算结果与实验吻合较好。得到的计算式对研究地震荷载作用下混
In spite of the study and application of rock hydraulic fracturing started at 20th century 50s early, its mechanism is not known well and there are many study topics. Most studies on rock hydraulic fracturing are focussed on artifical hydraulic farcturing applied in field of petroleum and nature gas. The hydraulic fracturing problems in field of water conservancy and hydropower and mining are producted by nature hydraulic power. The mechanism of nature hydraulic fracturing is more complex than that of artifical fracturing, so its studies are not enough ,espeically, the study on a single fracture.Fristly, In this paper the study level of hydraulic fracturing is divided into two based on study measure. The rock is considered as a homogeneous medium based on rock macroscopical, synthrtic and statistical characteristics in frist study level. But the secondary study level is focussed on a single fracture based on rock microcosic characteristics. Secondly, the differences between the artifical and nature hydraulic fracturing are analyzed and concluded. Thirdly, the mechanism of nature hydraulic fracturing is studied from two aspects of theortical analysis and numerical simulation according to its characteristics and study level. Finally, after deeply studyed on hydraulic fracturing simulation of higher pressure tunnel, the Influence laws of hydraulic fracturing on tunnel surrounding rock stability are proposed. The major studies and conclusions are followed.(l)The elastic and elasto-plastic problems of deep-buried circle tunnel considering influence of seepage field is studied based on rock macroscopical, synthrtic and statistical characteristics. The elasto-plastic analytical solution of deep-buried tunnel are obtained. Further, the influence laws of seepage field on stress field and plastic radius surrounding tunnel are studied according to different ratio of inner and outer water head. The study shows that the influence of seepage field on stress field is intensive along with the gradient increment of inner and outer water head of tunnel, and the influence degree on tangent stress is more than that on radial stress. The distribution law of stresses is not coincided with situation of without considering fluid flow. The compressive stresses and plastic radius are gradually decreased along with the increasing inner head, and plastic radius may be zero value if the inner head continually to some extent. But the new plastic radius will be reappeared along with the increment of inner head further, the first principle stress is alreadly turnned to tangent stress at that time. The plastic radius with considering influence of fluid flow
is larger than that without considering the influence.(2)Using fracture propagation engineering criterion, calculation formulae of critical inner water pressure of two kinds of failure model are obtained respectively and its effect laws as fracture direction and lateral geo-stress coefficient are studied. The study shows that critical inner pressure of two kinds of model is not varied as fracture direction changing when the lateral coefficient equals 1.0. Under tension-shear mixed model, fracture is most easily fracturing when fracture direction is parallel with direction of principle stress. Under compression-shear mixed model, distribution law of critical inner water pressure is same as tension-shear complex model when (λ-tanφ) large than 1.0 .But fracture is most easily fracturing when (λ-tanφ) less than 1.0 and fracture direction are 45° or 135° angle with principle stress.(3)It is assumed that fracture shape is a half ellipse-shaped in hydraulic fracturing of rock and concrete material. Based on boundary condition of natural hydraulic pressure, the mass conservation and momentum principle, the concrete formulae of liquid mass conservation and differential equation of water pressure distribution due to hydraulic fracturing are obtained using the finite control volume approach. The theoretical formula at any time of fracture stable propagating is obtained also. The theoretical formula is
引文
[1] 赵阳升.矿山岩石流体力学[M].北京:煤炭工业出版社,1994.125～143
[2] 曹洪.混凝土衬砌隧洞在内水压力作用下的渗流、应力应变分析[A].见:刘汉东,路新景,霍润科(编)岩石力学理论与工程实践论文集[C].郑州:黄河水利出版社,1997.98～104
[3] 倪才胜.不衬砌隧洞水力劈裂三维数值模拟[J].广东水利水电,2000,(3):27～30
[4] 黄润秋,王贤能,陈龙生.深埋隧道涌水过程的水力劈裂作用分析[J].岩石力学与工程学报,2000,19(5):573～576
[5] 谢兴华,速宝玉.裂隙岩体水力劈裂研究综述[J].岩土力学,2004,25(2):330～336
[6] 王媛,徐志英,速宝玉.裂隙岩体渗流计算模型综述[J].水科学进展,1995,(4):276～282
[7] 盛金昌.三维裂隙岩体渗流应力耦合数值分析及工程应用[博士学位论文D].南京:河海大学,2000
[8] 郑少河,朱维申,王书法.承压水上采煤的固流耦合问题研究[J].岩石力学与工程学报,2000,19(4):421～424
[9] 柴军瑞,仵彦卿.岩体渗流场与应力场耦合分析的多重裂隙网络模型[J].岩石力学与工程学报,2000,19(6):712～717
[10] 郑少河,朱维申.裂隙岩体渗流损伤耦合模型的理论分析[J].岩石力学与工程学报,2003,20(5):156～159
[11] 杨延毅,周维垣.裂隙岩体的渗流—损伤耦合分析模型及其工程应用[J].水利学报,1991,(5):19～27
[12] Bai M, Meng F, Elsworth D, Roegiers J. -C. Analysis of stress-dependent permeability in nonorthogonal flow and deformation fields[J]. Rock Mechanics and Rock Engineering, 1999, 32(3): 195～219
[13] 张有天,张武功.隧洞水荷载的静力计算[J].水利学报,1980,(3):52～62
[14] 王建秀,杨立中,何静.深埋隧洞外水压力计算的解析--- 数值法[J].水文地质工程地质,2002,(3):17～19,28
[15] 朱珍德,胡定.裂隙水压对岩体强度的影响[J].岩土力学,2000,21(1):64～67
[16] Tsang Y W; Tsang C F. Channel model of flow through fractured media[J]. Water Resources Research, 1987, 23(3): 467～479
[17] Haimson B C, Fairhust C. In-situ stress determination at great depth by means of hydraulic fracturing[A]. In: Somerton W H(ed). Rock mechanics-theory and practice: Proceedings of the 11th symposium on rock mechanics [C], New York: The American Institute of Mining, Metallurgical, and Petroleum Engineers, 1970. 559～584
[18] 蔡美峰,何满潮,刘东燕等.岩石力学与工程[M].北京:科学出版社,2002.141～150
[19] 刘允芳.水压致裂法三维地应力测量[J].岩石力学与工程学报,1991,10(3):246～256
[20] 刘允芳,罗超文,景峰.水压致裂法三维地应力测量及其修正和工程应用[J].岩土工程 学报,1999,21(4):465～470
[21] 陈群策,安美建,李方全.水压致裂法三维地应力测量的理论探讨[J].地质力学学报,1998,4(1):37～44
[22] Ito T, Evans K, Kawai K, Hayashi. Hydraulic fracture reopening pressure and the estimation of maximum horizontal stress[J]. Int. J. of Rock Mechanics and Mining sciences, 1999, 36: 811～826
[23] 王建军.应用水压致裂法测量三维地应力的几个问题[J].岩石力学与工程学报,2000,19(2):229～233
[24] 郭启良,安其美,赵仕广.水压致裂法应力测量在广州抽水蓄能电站设计中的应用研究[J].岩石力学与工程学报,2002,21(6):828～832
[25] 屠厚泽,高森.岩石破碎学[M].地质出版社,1990.192～194
[26] 周群力.岩石压剪判据及其应用[J].岩土工程学报,1987,9(6):67～73
[27] 朱维申,何满潮.复杂条件下围岩稳定性与岩体动态施工力学[M].北京;科学出版社,1995.72～127
[28] Shao J F. Poroelastic behavior of brittle rock materials with anisotropic damage[J]. Mechanics of mterials, 1998, 30: 41～53
[29] 杨友卿.岩石强度的损伤力学分析[J].岩石力学与工程学报,1999,18(1):23～27
[30] 潘一山,徐秉业.考虑损伤的圆形洞室岩爆分析[J].岩石力学与工程学报,1999,18(2):152～156
[31] Shlyapobersky J. Energy analysis of hydraulic fracturing[A]. In: Ashworth E(ed). Research & engineering applications in rock masses: The 26th U. S. Symposium on Rock Mechanics[C]. Boston: A. A. Balkema Publishers, 1985. 539～546
[32] Advansi S H, Lee T S, Avasthi J M. Parameteric sensitivity investigations for hydraulic fracture configuration optimization[A]. In: Khair A W(ed). Rock Mechanics as a Guide for Efficient Utilization of Natural Resources: Proceedings of the 30th U. S. Symposium[C]. Rotterdam: A. A. Balkema, 1989. 451～458
[33] Dersoches J, Thiercelin M. Modelling the propagation and closure of micro-hydraulic fractures[A]. In: Haimson B(ed). Rock mechanics in 1990s: pre-print proceedings of the 34th U. S. Symposium on Rock Mechanics[C]. Madison: University of Wisconsin-madison, 1993. 331～334
[34] Papanastasiou P, Thiercelin M. Influence of inelastic rock behavior in hydraulic fracturing[A]. In: Haimson B(ed). Rock mechanics in 1990s: pre-print proceedings of the 34th U. S. Symposium on Rock Mechanics[C]. Madison: University of Wisconsin-madison, 1993. 339～342
[35] Thiercelin M. On the modelling of near tip processes in hydraulic fractures[A]. In: Haimson B(ed). Rock mechanics in 1990s: pre-print proceedings of the 34th U. S. Symposium on Rock Mechanics[C]. Madison: University of Wisconsin-madison, 1993. 537～540
[36] Papanastasiou P. An efficient algorithm for propagating fluid-driven fractures[J]. Computational Mechanics, 1999, 24(4): 258～267
[37] Slowik V, Saouma V E. Water pressure in propagating concrete cracks[J]. Journal of Structural Engineering, 2000, 126(2): 235～242
[38] 丁遂栋,孙利民.断裂力学[M].北京:机械工业出版社,1997.148～152
[39] Hillerborg A, Modeer M, Petersson P E. Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements[J]. Cement and Concrete Research, 1976, 6: 773～782
[40] 章梓雄,董曾南.粘性流体力学[M].北京:清华大学出版社,1998.62～63
[41] 仵彦卿.岩体水力学基础(二):岩体水力学基础理论[J].水文地质工程地质,1997,(1):24～28
[42] Barton N, Bandis S, Bakhtur K. Strength, deformation and conductivity coupling of rock joints[J]. Int. J. Rock Mechanics Mining Science and Geomechanics Abstract, 1985, 22: 121～140
[43] 耿克勤,陈凤翔,刘光廷,陈兴华.岩体裂隙渗流水力特性的实验研究[J].清华大学学报(自然科学版),1996,36(1):102～106
[44] Esaki T, Du S, Mitani Y, Ikusada K, Jing L. Development of a shear-flow test apparatus and determination of coupled properties for a single rock joint[J]. Int. J. Rock Mechanics and Mining Sciences, 1999, 36: 641～650
[45] Lee H S, Cho T F. Characteristics of rough fractures in linear flow under normal and shear load[J]. Int. J. Rock Mechanics and Rock Engineering, 2002, 35(4): 299～318
[46] 速宝玉,詹美礼,王媛.裂隙渗流与应力耦合特性的实验研究[J].岩土工程学报,1997,19(4):1～3
[47] 郑少河,赵阳升.三维应力作用下天然裂隙渗流规律的实验研究[J].岩石力学与工程学报,1999,18(2):133～136
[48] 刘才华,陈从新,付少兰.剪应力作用下岩体裂隙渗流特性研究[J].岩石力学与工程学报,2003,22(10):1651～1655
[49] 朱珍德,徐卫亚,张爱军.脆性岩石损伤断裂机理分析与实验研究[J].岩石力学与工程学报,2003,22(9):1411～1416
[50] Blair S C, Thorpe R K, Shaffer F E. Laboratory observations of the effect of geologic discontinuities on hydrofracture propagation[A]. In: Khair A W(ed). Rock Mechanics as a Guide for Efficient Utilization of Natural Resources: Proceedings of the 30th U. S. Symposium[C]. Rotterdam: A. A. Balkema, 1989. 443～450
[51] Van den Hoke P J, Van den Berg J T M, Shlyapobersky J. Theoretical and experimental investigation of rock dilatancy near the tip of a propagating hydraulic fracture[A]. In: Haimson B(ed). Rock mechanics in 1990s: pre-print proceedings of the 34th U. S. Symposium on Rock Mechanics[C]. Madison: University of Wisconsin-madison, 1993. 351～354
[52] Ito T, Hayashi K. Analysis of crack reopening behavior for hydrofrac stress measurement[A]. In: Haimson B(ed). Rock mechanics in 1990s: pre-print proceedings of the 34th U. S. Symposium on Rock Mechanics[C]. Madison: University of Wisconsin-madison, 1993. 335～338.
[53] 吴景浓,李健康,颜玉定,廖远群.室内水压致裂法的初步实验研究[J].水利学报,1982,(7):52～57
[54] 陈卫忠,朱维申,罗超文.万家寨引黄工程总干一、二级泵站水力劈裂实验研究[J],岩土力学,2001,22(1):26～28
[55] 丁卫华,仵彦卿,蒲毅彬,廖全荣.CT技术应用于岩石实验动态观测的新进展[J].冰川冻土,2000,22(3):218～222
[56] Bruhwiler E, Saouma V E. Water fracture interaction in concrete—part Ⅰ: Fracture properties[J]. ACI Materials Journal, 1995, 92(3): 296～303
[57] Bruhwiler E, Saouma V E. Water fracture interaction in concrete—part Ⅱ: Hydrostatic pressure in cracks[J]. ACI Materials Journal, 1995, 92(4): 383～390
[58] Jing L. A review of techniques, advances and outstanding issues in numerical modeling for rock mechanics and rock engineering[J]. Int. Journal of Rock Mechanics and Mining Sciences, 2003, 40: 283～353
[59] Linsbaurer H N, Ingraffea A R. Simulation of cracking in large arch dam. Part 1. [J]. J. of Structural Engineering, 1989, 115(7): 1599～1615
[60] Linsbaurer H N, Ingraffea A R. Simulation of cracking in large arch dam. Part 2. [J]. J. of Structural Engineering, 1989, 115(7): 1616～1630.
[61] Feng L M, Pekau O A, Zhang C H. Cracking analysis of arch dam by 3D boundary element method[J]. J. of Structural Engineering, 1996, 122(6): 691～699
[62] Saleh A L, Aliabadi M H. Crack growth analysis in concrete using boundary element method[J]. Engineering Fracture Mechanics, 1995, 51(4): 533～545
[63] Simoni L, Secchi S. Cohesive fracture mechanics for a multi-phase porous medium[J]. Enginering Computatoins, 2003, 20(5/6): 675～698
[64] 佘成学.一种新的断裂计算方法[J].岩土力学,2000,21(20):130～133
[65] 陈胜宏,汪卫明,徐明毅,邹丽春.小湾高拱坝坝踵开裂的有限单元法分析[J].水利学报,2003(1):66～71
[66] Daux C, Moes N, Dolbow J, Sukumar N, Belytschko T. Arbitrary branched and intersecting cracks with the extended finite element method[J]. Int. J. Numerical Methods in Engineering, 2000, 48: 1741～1760
[67] Belytschko T, Moes N, Usui S, Parimi C. Arbitrary discontinuities in finite elements[J]. Int. J. Numerical Methods in Engineering, 2001, 50: 993～1013
[68] Stazi F L, Budyn E, Chessa J, Belytschko T. An extended finite element method with higher-order elements[J]. Computational Mechanics, 2003, 31: 38～48
[69] 彭自强,李小凯,葛修润.广义有限元法对动态裂纹扩展的数值模拟[J].岩石力学与工程学报,2004,23(18):3132～3137
[70] Bazant Z P, Cedolin L. Blunt crack band propagation in finite element analysis[J]. J. of Structural Engineering, 1979, 105, EM2: 297～315
[71] 蔡四维,蔡敏.混凝土的损伤断裂[M].北京:人民交通出版社,2000.55～65
[72] Petrangeli M, Ozbolt J. Smeared crack approaches-material modeling[J]. J. of Structural Engineering, 1996, 122(6): 545～554
[73] 刘涛,杨凤鹏.精通ANSYS[M].清华大学出版社,2002,9
[74] 陈火红.Marc有限元实例分析教程[M].机械工业出版社,2002,4
[75] Alfaiate J, Pires E B, Marins J A C. A finite element analysis of non-prescribed crack propagation in concrete[J]. Computers & Structure, 1997, 63(1): 17～26
[76] Alfaiate J, Pires E B. A discrete crack numerical model[A]. In: Alberto Carpinteri, Mohammad Aliabadi. Computational Fracture Mechanic in Concrete Technology[C]. Boston: Computational Mechanics Publications. 1999. 133～162
[77] 石根华.数值流形方法与非连续变形分析[M].北京:清华大学出版社,1997
[78] Belytschko T, Lu Y Y, Gu L. Element-free Galerkin method[J]. Int. J. for Numerical Methods in Engineering, 1994, 37: 229～256
[79] 寇晓东,周维垣.应用无单元法近似计算拱坝开裂[J].水利学报,2000(10):28～35
[80] 卓家寿,章青.不连续介质力学问题的界面元法[M].北京:科学出版社,2000
[81] Horii H, Nemat-Nasser S. Compression-Induced micro-crack growth in brittle solids: Axial splitting and shear failure[J]. J. of Geophysical Research, 1985, 90(B4): 3105～3125
[82] 周群力,刘格非.脆性材料的压剪断裂[J].水利学报,1982(7):63～69
[83] 王桂尧,孙宗颀,徐纪成.岩石压剪断裂机理及强度准则的探讨[J].岩土工程学报,1996,18(4):68～74
[84] Sousa J L, Carter B J, Ingraffea A R. Numerical simulation of three-dimensional hydraulic fracturing using Newtonian and power-law fluids[A]. In: Haimson B(ed). Rock mechanics in 1990s: pre-print proceedings of the 34th U. S. Symposium on Rock Mechanics[C]. Madison: University of Wisconsin-madison, 1993: 355～358
[85] 李连崇,杨天鸿,唐春安,杨春和.岩石水压致裂过程的耦合分析[J].岩石力学与工程学报,2003,22(7):1060～1066
[86] Rene Tinwai, Lotfi Guizani. Formulation of hydrodynamic pressure in cracks due to earthquakes in concrete dams[J]. Earthquake Engineering and Structural Dynamics, 1994, 23(7): 699～715
[87] 阳友奎,肖长富,邱贤德,吴刚.水力压裂裂缝形态与缝内压力分布[J].重庆大学学报(自然科学版),1995,18(3):20～26
[88] 杨秀夫,陈勉,刘希圣.水压裂缝缝内流场理论研究[J].西南石油学院,2002,24(1):87～90
[89] 任青文.岩体破坏分析方法的研究进展[J].岩石力学与工程学报,2001,20(增2):1303～1309
[90] 任青文,钱向东,赵引,傅树红.高拱坝沿建基面抗滑稳定性的分析方法研究[J].水利学报,2002,(2):1～7
[91] 周伟,常晓林,唐忠敏,黎满林.溪洛渡高拱坝渐进破坏过程仿真分析与稳定安全度研究[J].四川大学学报(工程科学版),2002,34(4):46～50
[92] 黄润秋,许强.开挖过程的非线性理论分析[J].工程地质学报,1999,17(1):9～14
[93] 朱维申,程峰.能量耗散本构模型及其在三峡船闸高边坡稳定性分析中的应用[J].岩石力学与工程学报,2000,19(3):261～264
[94] 秦四清.初论岩体失稳过程中耗散结构的形成机制[J].岩石力学与工程学报,2000,19(3):265～269
[95] 潘一山,章梦涛,李国臻.洞室岩爆的尖角突变模型[J].应用数学与力学,1994,15(10):893～900
[96] 秦四清.斜坡失稳的突变模型与混沌机制[J].岩石力学与工程学报,2000,19(4):486～492
[97] 孙树林,侯玉宾.边坡水平卸荷裂隙的突变理论模型[J].河海大学学报,1997,25(6):4～7
[98] 徐芝纶.弹性力学(第二版)[M].北京:高等教育出版社,1982.85～91
[99] 孙钧,侯学渊.地下结构(上册)[M].北京:科学出版社,1991.132～168
[100] 1972, (5): 35～38
[101] 张有天,张武功,王镭.再论隧洞水荷载的静力计算[J].水利学报,1985,(3):22～32
[102] 任青文,张宏朝.关于芬纳公式的修正[J].河海大学学报,2001,29(6):109～111
[103] 李俊亭,王愈吉.地下水动力学[M].北京:地质出版社,1987.27～33
[104] 沈明荣.岩体力学[M].上海:同济大学出版社,1999.132～137
[105] 王成,邓安福.岩体节理内压致裂解析研究[J].岩石力学与工程学报,2002,21(5):640～643
[106] 杨天鸿,唐春安,万成等.岩石破裂过程渗流与应力耦合分析[J].岩土工程学报,2001,23(4):489～493
[107] 倪才胜.不衬砌隧洞水力劈裂三维数值模拟[J].广东水利水电,2000,(3):27～30
[108] 黄云,金峰,王光纶,张楚汉.高拱坝上游坝踵裂缝稳定性及其扩展[J].清华大学学报(自然科学版),2002,42(4):555～559
[109] 吴持恭.水力学(上册)[M].北京:高等教育出版社,1979.160～162,117
[110] 吴持恭.水力学(下册)[M].北京:高等教育出版社,1979.189～198
[111] 张也影.流体力学[M].北京:高等教育出版社,1999.385～389
[112] 著.脆性断裂力学[M].黄克智译.北京:科学出版社,1990.286
[113] Cook N G W. Natural joints in rock. Mechanical, Hydraulic and seismic behavior and properties[J]. Int. J. of Rock Mechanics and Mining Science & Geomechanics Abstract, 1992, 29(3): 198～223
[114] 夏才初,孙宗颀.工程岩体节理力学[M].上海:同济大学出版社,2002.145～154
[115] 王媛.单裂隙面渗流与应力的耦合特性[J].岩石力学与工程学报,2002,21(1):83～87
[116] 速宝玉,詹美礼,赵坚.光滑裂隙水流模型实验及其机理初探[J].水利学报,1994,(5):19～24
[117] 周创兵,熊文林.岩石节理的渗流广义立方定律[J].岩土力学,1996,17(4):1～7
[118] 周创兵,叶自桐,何炬林,张辉.岩石节理张开度的概率模型与随机模拟[J].岩石力学与工程学报,1998,17(3):267～272
[119] 许光祥,哈秋舲,张永兴.岩体裂隙渗流的频率水力隙宽[J].重庆建筑大学学报,2001,23(5):50～55
[120] Boone T J, Ingraffea A R. A numerical procedure for simulation of hydraulically-driven fracture propagation in poroelastic media[J]. J. for Numerical and Analytical Methods in Geomechanics, 1990, 14: 27～47.
[121] 杨桂通.弹塑性力学[M].北京:人民教育出版社,1980
[122] 华东水利学院.弹性力学问题的有限元法[M].北京:水利水电出版社,1978
[123] 王勖成,邵敏.有限单元法基本原理和数值方法(第2版)[M].北京:清华大学出版社,2002
[124] 朱伯芳.有限单元法原理与应用(第二版)[M].北京:中国水利水电出版社,1998
[125] 孙钧,汪炳鑑.地下结构有限元法解析[M].上海:同济大学出版社,1988.243～248
[126] 郑雨天.岩石力学的弹塑粘性理论基础[M].北京:煤炭工业出版社,1988
[127] (美) 陈惠发,萨里普 A F 著,余天庆等译.土木工程材料的本构方程 (第一卷 塑性与建模)[M].武汉:华中科技大学出版社,2001
[128] 王仁,熊祝华,黄文彬.塑性力学基础[M].北京:科学出版社,1982
[129] 于学馥,郑颖人,刘怀恒,方正昌.地下工程围岩稳定分析[M].煤炭工业出版社,1983
[130] Owen D R J, Hinton E. Finite Elements in Plasticity: Theory and Practice [M]. Swansea(U. K.): Pineridge Press Ltd., 1980
[131] 任青文.非线性有限单元法(校内教材)[M].南京:河海大学,2001
[132] 周维垣.高等岩石力学[M].北京:水利水电出版社,1989
[133] 谢和平,陈忠辉.岩石力学[M].北京:科学出版社,2004
[134] 李守得,俞洪良.Goodman接触面单元的修正与探讨[J].岩石力学与工程学报,2004,23(15):2628～2631
[135] 黄克智,余寿文.弹塑性断裂力学[M].北京:清华大学出版社,1985
[136] 寇晓东,周维垣.应用无单元法追踪裂纹扩展[J].岩石力学与工程学报,2000,19(1):18～23
[137] 田荣.连续与非连续变形分析的有限覆盖无单元方法及其应用[D博士学位论文].大连:大连连理工大学,2000
[138] 徐世烺,赵国藩.混凝土断裂力学研究[M].辽宁:大连理工大学出版社,1991.38～81
[139] 江见鲸,冯乃田谦.混凝土力学[M].北京:中国铁道出版社,1991.253～278
[140] 谢和平.岩石混凝土损伤力学[M].徐州:中国矿业大学出版社,1990.130～146
[141] 凌建明,刘尧军.岩体损伤的断裂效应及其对洞室围岩稳定的影响[J].石家庄铁道学院学报,1994,7(3):23～30
[142] 李兆霞.损伤力学及其应用[M].北京:科学出版社,2002
[143] 候靖,胡敏云.水工高压隧洞结构设计中若干问题的讨论[J].水利学报,2001,(7):36～40
[144] 张有天.论有压隧洞最小覆盖厚度[J].水利学报,2002,(9):1～5
[145] 王立忠,冯永冰.倾斜坡体中水工高压隧洞围岩应力场特性分析[J].岩石力学与工程学报,2004,23(23):4038～4046
[146] 中华人民共和国水利行业标准编写组 水工隧洞设计规范(SL279-2002)[S].北京:中国水利水电出版社,2003
[2] 曹洪.混凝土衬砌隧洞在内水压力作用下的渗流、应力应变分析[A].见:刘汉东,路新景,霍润科(编)岩石力学理论与工程实践论文集[C].郑州:黄河水利出版社,1997.98～104
[3] 倪才胜.不衬砌隧洞水力劈裂三维数值模拟[J].广东水利水电,2000,(3):27～30
[4] 黄润秋,王贤能,陈龙生.深埋隧道涌水过程的水力劈裂作用分析[J].岩石力学与工程学报,2000,19(5):573～576
[5] 谢兴华,速宝玉.裂隙岩体水力劈裂研究综述[J].岩土力学,2004,25(2):330～336
[6] 王媛,徐志英,速宝玉.裂隙岩体渗流计算模型综述[J].水科学进展,1995,(4):276～282
[7] 盛金昌.三维裂隙岩体渗流应力耦合数值分析及工程应用[博士学位论文D].南京:河海大学,2000
[8] 郑少河,朱维申,王书法.承压水上采煤的固流耦合问题研究[J].岩石力学与工程学报,2000,19(4):421～424
[9] 柴军瑞,仵彦卿.岩体渗流场与应力场耦合分析的多重裂隙网络模型[J].岩石力学与工程学报,2000,19(6):712～717
[10] 郑少河,朱维申.裂隙岩体渗流损伤耦合模型的理论分析[J].岩石力学与工程学报,2003,20(5):156～159
[11] 杨延毅,周维垣.裂隙岩体的渗流—损伤耦合分析模型及其工程应用[J].水利学报,1991,(5):19～27
[12] Bai M, Meng F, Elsworth D, Roegiers J. -C. Analysis of stress-dependent permeability in nonorthogonal flow and deformation fields[J]. Rock Mechanics and Rock Engineering, 1999, 32(3): 195～219
[13] 张有天,张武功.隧洞水荷载的静力计算[J].水利学报,1980,(3):52～62
[14] 王建秀,杨立中,何静.深埋隧洞外水压力计算的解析--- 数值法[J].水文地质工程地质,2002,(3):17～19,28
[15] 朱珍德,胡定.裂隙水压对岩体强度的影响[J].岩土力学,2000,21(1):64～67
[16] Tsang Y W; Tsang C F. Channel model of flow through fractured media[J]. Water Resources Research, 1987, 23(3): 467～479
[17] Haimson B C, Fairhust C. In-situ stress determination at great depth by means of hydraulic fracturing[A]. In: Somerton W H(ed). Rock mechanics-theory and practice: Proceedings of the 11th symposium on rock mechanics [C], New York: The American Institute of Mining, Metallurgical, and Petroleum Engineers, 1970. 559～584
[18] 蔡美峰,何满潮,刘东燕等.岩石力学与工程[M].北京:科学出版社,2002.141～150
[19] 刘允芳.水压致裂法三维地应力测量[J].岩石力学与工程学报,1991,10(3):246～256
[20] 刘允芳,罗超文,景峰.水压致裂法三维地应力测量及其修正和工程应用[J].岩土工程 学报,1999,21(4):465～470
[21] 陈群策,安美建,李方全.水压致裂法三维地应力测量的理论探讨[J].地质力学学报,1998,4(1):37～44
[22] Ito T, Evans K, Kawai K, Hayashi. Hydraulic fracture reopening pressure and the estimation of maximum horizontal stress[J]. Int. J. of Rock Mechanics and Mining sciences, 1999, 36: 811～826
[23] 王建军.应用水压致裂法测量三维地应力的几个问题[J].岩石力学与工程学报,2000,19(2):229～233
[24] 郭启良,安其美,赵仕广.水压致裂法应力测量在广州抽水蓄能电站设计中的应用研究[J].岩石力学与工程学报,2002,21(6):828～832
[25] 屠厚泽,高森.岩石破碎学[M].地质出版社,1990.192～194
[26] 周群力.岩石压剪判据及其应用[J].岩土工程学报,1987,9(6):67～73
[27] 朱维申,何满潮.复杂条件下围岩稳定性与岩体动态施工力学[M].北京;科学出版社,1995.72～127
[28] Shao J F. Poroelastic behavior of brittle rock materials with anisotropic damage[J]. Mechanics of mterials, 1998, 30: 41～53
[29] 杨友卿.岩石强度的损伤力学分析[J].岩石力学与工程学报,1999,18(1):23～27
[30] 潘一山,徐秉业.考虑损伤的圆形洞室岩爆分析[J].岩石力学与工程学报,1999,18(2):152～156
[31] Shlyapobersky J. Energy analysis of hydraulic fracturing[A]. In: Ashworth E(ed). Research & engineering applications in rock masses: The 26th U. S. Symposium on Rock Mechanics[C]. Boston: A. A. Balkema Publishers, 1985. 539～546
[32] Advansi S H, Lee T S, Avasthi J M. Parameteric sensitivity investigations for hydraulic fracture configuration optimization[A]. In: Khair A W(ed). Rock Mechanics as a Guide for Efficient Utilization of Natural Resources: Proceedings of the 30th U. S. Symposium[C]. Rotterdam: A. A. Balkema, 1989. 451～458
[33] Dersoches J, Thiercelin M. Modelling the propagation and closure of micro-hydraulic fractures[A]. In: Haimson B(ed). Rock mechanics in 1990s: pre-print proceedings of the 34th U. S. Symposium on Rock Mechanics[C]. Madison: University of Wisconsin-madison, 1993. 331～334
[34] Papanastasiou P, Thiercelin M. Influence of inelastic rock behavior in hydraulic fracturing[A]. In: Haimson B(ed). Rock mechanics in 1990s: pre-print proceedings of the 34th U. S. Symposium on Rock Mechanics[C]. Madison: University of Wisconsin-madison, 1993. 339～342
[35] Thiercelin M. On the modelling of near tip processes in hydraulic fractures[A]. In: Haimson B(ed). Rock mechanics in 1990s: pre-print proceedings of the 34th U. S. Symposium on Rock Mechanics[C]. Madison: University of Wisconsin-madison, 1993. 537～540
[36] Papanastasiou P. An efficient algorithm for propagating fluid-driven fractures[J]. Computational Mechanics, 1999, 24(4): 258～267
[37] Slowik V, Saouma V E. Water pressure in propagating concrete cracks[J]. Journal of Structural Engineering, 2000, 126(2): 235～242
[38] 丁遂栋,孙利民.断裂力学[M].北京:机械工业出版社,1997.148～152
[39] Hillerborg A, Modeer M, Petersson P E. Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements[J]. Cement and Concrete Research, 1976, 6: 773～782
[40] 章梓雄,董曾南.粘性流体力学[M].北京:清华大学出版社,1998.62～63
[41] 仵彦卿.岩体水力学基础(二):岩体水力学基础理论[J].水文地质工程地质,1997,(1):24～28
[42] Barton N, Bandis S, Bakhtur K. Strength, deformation and conductivity coupling of rock joints[J]. Int. J. Rock Mechanics Mining Science and Geomechanics Abstract, 1985, 22: 121～140
[43] 耿克勤,陈凤翔,刘光廷,陈兴华.岩体裂隙渗流水力特性的实验研究[J].清华大学学报(自然科学版),1996,36(1):102～106
[44] Esaki T, Du S, Mitani Y, Ikusada K, Jing L. Development of a shear-flow test apparatus and determination of coupled properties for a single rock joint[J]. Int. J. Rock Mechanics and Mining Sciences, 1999, 36: 641～650
[45] Lee H S, Cho T F. Characteristics of rough fractures in linear flow under normal and shear load[J]. Int. J. Rock Mechanics and Rock Engineering, 2002, 35(4): 299～318
[46] 速宝玉,詹美礼,王媛.裂隙渗流与应力耦合特性的实验研究[J].岩土工程学报,1997,19(4):1～3
[47] 郑少河,赵阳升.三维应力作用下天然裂隙渗流规律的实验研究[J].岩石力学与工程学报,1999,18(2):133～136
[48] 刘才华,陈从新,付少兰.剪应力作用下岩体裂隙渗流特性研究[J].岩石力学与工程学报,2003,22(10):1651～1655
[49] 朱珍德,徐卫亚,张爱军.脆性岩石损伤断裂机理分析与实验研究[J].岩石力学与工程学报,2003,22(9):1411～1416
[50] Blair S C, Thorpe R K, Shaffer F E. Laboratory observations of the effect of geologic discontinuities on hydrofracture propagation[A]. In: Khair A W(ed). Rock Mechanics as a Guide for Efficient Utilization of Natural Resources: Proceedings of the 30th U. S. Symposium[C]. Rotterdam: A. A. Balkema, 1989. 443～450
[51] Van den Hoke P J, Van den Berg J T M, Shlyapobersky J. Theoretical and experimental investigation of rock dilatancy near the tip of a propagating hydraulic fracture[A]. In: Haimson B(ed). Rock mechanics in 1990s: pre-print proceedings of the 34th U. S. Symposium on Rock Mechanics[C]. Madison: University of Wisconsin-madison, 1993. 351～354
[52] Ito T, Hayashi K. Analysis of crack reopening behavior for hydrofrac stress measurement[A]. In: Haimson B(ed). Rock mechanics in 1990s: pre-print proceedings of the 34th U. S. Symposium on Rock Mechanics[C]. Madison: University of Wisconsin-madison, 1993. 335～338.
[53] 吴景浓,李健康,颜玉定,廖远群.室内水压致裂法的初步实验研究[J].水利学报,1982,(7):52～57
[54] 陈卫忠,朱维申,罗超文.万家寨引黄工程总干一、二级泵站水力劈裂实验研究[J],岩土力学,2001,22(1):26～28
[55] 丁卫华,仵彦卿,蒲毅彬,廖全荣.CT技术应用于岩石实验动态观测的新进展[J].冰川冻土,2000,22(3):218～222
[56] Bruhwiler E, Saouma V E. Water fracture interaction in concrete—part Ⅰ: Fracture properties[J]. ACI Materials Journal, 1995, 92(3): 296～303
[57] Bruhwiler E, Saouma V E. Water fracture interaction in concrete—part Ⅱ: Hydrostatic pressure in cracks[J]. ACI Materials Journal, 1995, 92(4): 383～390
[58] Jing L. A review of techniques, advances and outstanding issues in numerical modeling for rock mechanics and rock engineering[J]. Int. Journal of Rock Mechanics and Mining Sciences, 2003, 40: 283～353
[59] Linsbaurer H N, Ingraffea A R. Simulation of cracking in large arch dam. Part 1. [J]. J. of Structural Engineering, 1989, 115(7): 1599～1615
[60] Linsbaurer H N, Ingraffea A R. Simulation of cracking in large arch dam. Part 2. [J]. J. of Structural Engineering, 1989, 115(7): 1616～1630.
[61] Feng L M, Pekau O A, Zhang C H. Cracking analysis of arch dam by 3D boundary element method[J]. J. of Structural Engineering, 1996, 122(6): 691～699
[62] Saleh A L, Aliabadi M H. Crack growth analysis in concrete using boundary element method[J]. Engineering Fracture Mechanics, 1995, 51(4): 533～545
[63] Simoni L, Secchi S. Cohesive fracture mechanics for a multi-phase porous medium[J]. Enginering Computatoins, 2003, 20(5/6): 675～698
[64] 佘成学.一种新的断裂计算方法[J].岩土力学,2000,21(20):130～133
[65] 陈胜宏,汪卫明,徐明毅,邹丽春.小湾高拱坝坝踵开裂的有限单元法分析[J].水利学报,2003(1):66～71
[66] Daux C, Moes N, Dolbow J, Sukumar N, Belytschko T. Arbitrary branched and intersecting cracks with the extended finite element method[J]. Int. J. Numerical Methods in Engineering, 2000, 48: 1741～1760
[67] Belytschko T, Moes N, Usui S, Parimi C. Arbitrary discontinuities in finite elements[J]. Int. J. Numerical Methods in Engineering, 2001, 50: 993～1013
[68] Stazi F L, Budyn E, Chessa J, Belytschko T. An extended finite element method with higher-order elements[J]. Computational Mechanics, 2003, 31: 38～48
[69] 彭自强,李小凯,葛修润.广义有限元法对动态裂纹扩展的数值模拟[J].岩石力学与工程学报,2004,23(18):3132～3137
[70] Bazant Z P, Cedolin L. Blunt crack band propagation in finite element analysis[J]. J. of Structural Engineering, 1979, 105, EM2: 297～315
[71] 蔡四维,蔡敏.混凝土的损伤断裂[M].北京:人民交通出版社,2000.55～65
[72] Petrangeli M, Ozbolt J. Smeared crack approaches-material modeling[J]. J. of Structural Engineering, 1996, 122(6): 545～554
[73] 刘涛,杨凤鹏.精通ANSYS[M].清华大学出版社,2002,9
[74] 陈火红.Marc有限元实例分析教程[M].机械工业出版社,2002,4
[75] Alfaiate J, Pires E B, Marins J A C. A finite element analysis of non-prescribed crack propagation in concrete[J]. Computers & Structure, 1997, 63(1): 17～26
[76] Alfaiate J, Pires E B. A discrete crack numerical model[A]. In: Alberto Carpinteri, Mohammad Aliabadi. Computational Fracture Mechanic in Concrete Technology[C]. Boston: Computational Mechanics Publications. 1999. 133～162
[77] 石根华.数值流形方法与非连续变形分析[M].北京:清华大学出版社,1997
[78] Belytschko T, Lu Y Y, Gu L. Element-free Galerkin method[J]. Int. J. for Numerical Methods in Engineering, 1994, 37: 229～256
[79] 寇晓东,周维垣.应用无单元法近似计算拱坝开裂[J].水利学报,2000(10):28～35
[80] 卓家寿,章青.不连续介质力学问题的界面元法[M].北京:科学出版社,2000
[81] Horii H, Nemat-Nasser S. Compression-Induced micro-crack growth in brittle solids: Axial splitting and shear failure[J]. J. of Geophysical Research, 1985, 90(B4): 3105～3125
[82] 周群力,刘格非.脆性材料的压剪断裂[J].水利学报,1982(7):63～69
[83] 王桂尧,孙宗颀,徐纪成.岩石压剪断裂机理及强度准则的探讨[J].岩土工程学报,1996,18(4):68～74
[84] Sousa J L, Carter B J, Ingraffea A R. Numerical simulation of three-dimensional hydraulic fracturing using Newtonian and power-law fluids[A]. In: Haimson B(ed). Rock mechanics in 1990s: pre-print proceedings of the 34th U. S. Symposium on Rock Mechanics[C]. Madison: University of Wisconsin-madison, 1993: 355～358
[85] 李连崇,杨天鸿,唐春安,杨春和.岩石水压致裂过程的耦合分析[J].岩石力学与工程学报,2003,22(7):1060～1066
[86] Rene Tinwai, Lotfi Guizani. Formulation of hydrodynamic pressure in cracks due to earthquakes in concrete dams[J]. Earthquake Engineering and Structural Dynamics, 1994, 23(7): 699～715
[87] 阳友奎,肖长富,邱贤德,吴刚.水力压裂裂缝形态与缝内压力分布[J].重庆大学学报(自然科学版),1995,18(3):20～26
[88] 杨秀夫,陈勉,刘希圣.水压裂缝缝内流场理论研究[J].西南石油学院,2002,24(1):87～90
[89] 任青文.岩体破坏分析方法的研究进展[J].岩石力学与工程学报,2001,20(增2):1303～1309
[90] 任青文,钱向东,赵引,傅树红.高拱坝沿建基面抗滑稳定性的分析方法研究[J].水利学报,2002,(2):1～7
[91] 周伟,常晓林,唐忠敏,黎满林.溪洛渡高拱坝渐进破坏过程仿真分析与稳定安全度研究[J].四川大学学报(工程科学版),2002,34(4):46～50
[92] 黄润秋,许强.开挖过程的非线性理论分析[J].工程地质学报,1999,17(1):9～14
[93] 朱维申,程峰.能量耗散本构模型及其在三峡船闸高边坡稳定性分析中的应用[J].岩石力学与工程学报,2000,19(3):261～264
[94] 秦四清.初论岩体失稳过程中耗散结构的形成机制[J].岩石力学与工程学报,2000,19(3):265～269
[95] 潘一山,章梦涛,李国臻.洞室岩爆的尖角突变模型[J].应用数学与力学,1994,15(10):893～900
[96] 秦四清.斜坡失稳的突变模型与混沌机制[J].岩石力学与工程学报,2000,19(4):486～492
[97] 孙树林,侯玉宾.边坡水平卸荷裂隙的突变理论模型[J].河海大学学报,1997,25(6):4～7
[98] 徐芝纶.弹性力学(第二版)[M].北京:高等教育出版社,1982.85～91
[99] 孙钧,侯学渊.地下结构(上册)[M].北京:科学出版社,1991.132～168
[100] 1972, (5): 35～38
[101] 张有天,张武功,王镭.再论隧洞水荷载的静力计算[J].水利学报,1985,(3):22～32
[102] 任青文,张宏朝.关于芬纳公式的修正[J].河海大学学报,2001,29(6):109～111
[103] 李俊亭,王愈吉.地下水动力学[M].北京:地质出版社,1987.27～33
[104] 沈明荣.岩体力学[M].上海:同济大学出版社,1999.132～137
[105] 王成,邓安福.岩体节理内压致裂解析研究[J].岩石力学与工程学报,2002,21(5):640～643
[106] 杨天鸿,唐春安,万成等.岩石破裂过程渗流与应力耦合分析[J].岩土工程学报,2001,23(4):489～493
[107] 倪才胜.不衬砌隧洞水力劈裂三维数值模拟[J].广东水利水电,2000,(3):27～30
[108] 黄云,金峰,王光纶,张楚汉.高拱坝上游坝踵裂缝稳定性及其扩展[J].清华大学学报(自然科学版),2002,42(4):555～559
[109] 吴持恭.水力学(上册)[M].北京:高等教育出版社,1979.160～162,117
[110] 吴持恭.水力学(下册)[M].北京:高等教育出版社,1979.189～198
[111] 张也影.流体力学[M].北京:高等教育出版社,1999.385～389
[112] 著.脆性断裂力学[M].黄克智译.北京:科学出版社,1990.286
[113] Cook N G W. Natural joints in rock. Mechanical, Hydraulic and seismic behavior and properties[J]. Int. J. of Rock Mechanics and Mining Science & Geomechanics Abstract, 1992, 29(3): 198～223
[114] 夏才初,孙宗颀.工程岩体节理力学[M].上海:同济大学出版社,2002.145～154
[115] 王媛.单裂隙面渗流与应力的耦合特性[J].岩石力学与工程学报,2002,21(1):83～87
[116] 速宝玉,詹美礼,赵坚.光滑裂隙水流模型实验及其机理初探[J].水利学报,1994,(5):19～24
[117] 周创兵,熊文林.岩石节理的渗流广义立方定律[J].岩土力学,1996,17(4):1～7
[118] 周创兵,叶自桐,何炬林,张辉.岩石节理张开度的概率模型与随机模拟[J].岩石力学与工程学报,1998,17(3):267～272
[119] 许光祥,哈秋舲,张永兴.岩体裂隙渗流的频率水力隙宽[J].重庆建筑大学学报,2001,23(5):50～55
[120] Boone T J, Ingraffea A R. A numerical procedure for simulation of hydraulically-driven fracture propagation in poroelastic media[J]. J. for Numerical and Analytical Methods in Geomechanics, 1990, 14: 27～47.
[121] 杨桂通.弹塑性力学[M].北京:人民教育出版社,1980
[122] 华东水利学院.弹性力学问题的有限元法[M].北京:水利水电出版社,1978
[123] 王勖成,邵敏.有限单元法基本原理和数值方法(第2版)[M].北京:清华大学出版社,2002
[124] 朱伯芳.有限单元法原理与应用(第二版)[M].北京:中国水利水电出版社,1998
[125] 孙钧,汪炳鑑.地下结构有限元法解析[M].上海:同济大学出版社,1988.243～248
[126] 郑雨天.岩石力学的弹塑粘性理论基础[M].北京:煤炭工业出版社,1988
[127] (美) 陈惠发,萨里普 A F 著,余天庆等译.土木工程材料的本构方程 (第一卷 塑性与建模)[M].武汉:华中科技大学出版社,2001
[128] 王仁,熊祝华,黄文彬.塑性力学基础[M].北京:科学出版社,1982
[129] 于学馥,郑颖人,刘怀恒,方正昌.地下工程围岩稳定分析[M].煤炭工业出版社,1983
[130] Owen D R J, Hinton E. Finite Elements in Plasticity: Theory and Practice [M]. Swansea(U. K.): Pineridge Press Ltd., 1980
[131] 任青文.非线性有限单元法(校内教材)[M].南京:河海大学,2001
[132] 周维垣.高等岩石力学[M].北京:水利水电出版社,1989
[133] 谢和平,陈忠辉.岩石力学[M].北京:科学出版社,2004
[134] 李守得,俞洪良.Goodman接触面单元的修正与探讨[J].岩石力学与工程学报,2004,23(15):2628～2631
[135] 黄克智,余寿文.弹塑性断裂力学[M].北京:清华大学出版社,1985
[136] 寇晓东,周维垣.应用无单元法追踪裂纹扩展[J].岩石力学与工程学报,2000,19(1):18～23
[137] 田荣.连续与非连续变形分析的有限覆盖无单元方法及其应用[D博士学位论文].大连:大连连理工大学,2000
[138] 徐世烺,赵国藩.混凝土断裂力学研究[M].辽宁:大连理工大学出版社,1991.38～81
[139] 江见鲸,冯乃田谦.混凝土力学[M].北京:中国铁道出版社,1991.253～278
[140] 谢和平.岩石混凝土损伤力学[M].徐州:中国矿业大学出版社,1990.130～146
[141] 凌建明,刘尧军.岩体损伤的断裂效应及其对洞室围岩稳定的影响[J].石家庄铁道学院学报,1994,7(3):23～30
[142] 李兆霞.损伤力学及其应用[M].北京:科学出版社,2002
[143] 候靖,胡敏云.水工高压隧洞结构设计中若干问题的讨论[J].水利学报,2001,(7):36～40
[144] 张有天.论有压隧洞最小覆盖厚度[J].水利学报,2002,(9):1～5
[145] 王立忠,冯永冰.倾斜坡体中水工高压隧洞围岩应力场特性分析[J].岩石力学与工程学报,2004,23(23):4038～4046
[146] 中华人民共和国水利行业标准编写组 水工隧洞设计规范(SL279-2002)[S].北京:中国水利水电出版社,2003
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