基于Cosserat介质理论的层状岩体均匀化数值分析与应用研究
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摘要
层状结构岩体在实际工程中是很常见的。通常采用基于经典连续介质力学的显式节理单元或横观各向同性等效模型对其计算分析。对于这类岩体的岩层张裂、滑移、弯折、倾倒变形以及压溃屈曲失稳等现象采用传统连续介质理论的有限元分析尚不能提供充分的、合理的解释,尤其是在高应力梯度的情况。本文目的旨在尝试将Cosserat介质理论与渐近均匀化方法相结合,分析节理岩体在上述情况下的弯曲力学特性,以解决在岩土工程、采矿工程以及其他相关方面的工程应用实际问题。其研究成果无疑具有重要的理论意义,对提高工程应用分析的精度和可信度也具有指导意义。
本文主要的创新性研究成果如下:
1、本文采用Cosserat介质理论与渐近均匀化方法相结合建立了新的层状岩体Cosserat介质本构模型。即是,将层状岩体看作由代表性单元体(单胞)周期性重复排列组成的复合岩体。代表性单元体包括岩石层和节理层以及两种或两种以上不同物理力学特性的岩石材料,考虑它们自身的抗弯能力。在满足单胞的周期性边界条件下,进行细观均匀化分析得到各节点的细观位移值,再由均匀化公式推导的宏观弹性模量公式进一步求解得到一个新的Cosserat介质等效本构模型。
2、基于常规介质均匀化方法,构建适用于Cosserat介质的位移函数。采用正应力、剪应力、偶应力与对应的正应变、剪应变、曲率的广义应力、应变张量,首次得到Cosserat介质宏观弹性模量的计算公式。由于该公式包括了偶应力与曲率的关系,从而能反映节理岩体的弯曲特性。
3、根据本文所得的宏观弹性模量计算公式,在MATLAB平台上编制Cosserat介质均匀化方法应用于节理岩体的主函数程序。并利用计算实例与FLAC软件数值计算对比,验证编制程序的有效性。
4、在节理岩体中的洞室工程进行Cosserat介质有限元法数值模拟,分析了不同岩层间距、倾角、地应力及洞室高度等因素条件下,偶应力对围岩弯曲变形的影响;对节理岩体边坡工程,以某大型水电站坝址的进水口左岸顺向高边坡、右岸反倾向边坡的数值模拟,揭示了层状结构岩体缓倾角侧与陡倾角侧边坡表现出不同弯曲变形破坏特性。
通过本文数值分析,对于节理层间距很小的情况(高应力梯度)、两种或两种以上互层岩体的复杂情况,采用本文方法可以合理地反映层状岩体的弯曲特性。表明本文提出的均匀化Cosserat介质分析理论与传统连续介质理论的计算对比,其方法是有效、可行的。
Layered rock masses are very common in pratical engineering, which are often computated and analyzed by the explicit joint element or the anisotropy equivalent model based on the classical continua medium mechanics. The traditional continua medium theory FEM can’t provide satisfying interpretation on sliding, bending, buckling, flexural toppling failure phenomena, especially in case of the sharp stress gradients. The paper aims at analyze the bending mechanical properties of the layer rock masses, which combining the Cosserat medium theory into the asymptotic homogenization method, and solve the engineering practical problem in geotechnical engineering, mining engineering and correlative engineering aspects. The research results have no doubt the great theoretical significance, to improve the accuracy and credibility for the engineering application analysis also has the guiding sense.
The innovative research results in the paper are as follows:
1、A new Cosserat medium equivalent model was established in the paper, which connected the Cosserat medium theory with the homogenization method. At first, the layered rock mass was regarded as a composite with representative element volume (unit cell) periodic repetition rank. The representative element volume contained the rock layers and the joints,two or more different physical and mechanical characteristics the rock layers, which considering the rock material itself resist-bend ability. Satisfied with the periodic boundary conditions of unit cell,micro-displacement of all nodes can be obtained by micro homogenization analyzed at first, then a Cosserat medium equivalent model can be got by solving the macro elastic module formula educed from the homogenization process.
2、Based on the conventional medium homogenized, the new displacement function applying to the Cosserat medium is constructed. Then Young's modulus of the macro - formula can be solved from the corresponding generalized stress and strain elationships, such as the normal stress, the shear stress, couple stress and the corresponding normal strain, the shear strain and the curvature. For the formula including the relationship between the couple stress and the curvature, so it can be reflected the bending properties of the Cosserat medium materials.
3、The main functions program of Cosserat medium used in the homogenization methods were workouted in the MATLAB platform with help of the macro elastic modulus formula. Then the results were compared between the Cosserat medium equivalent model and the numerical method computated by the software FLAC showing the validity of the program.
4、To study the surrounding rock displacement and couple-stress, such as bending deformation impacted by the rock layers thickness, dip, ground stress and the cavern height and other factors in the different-shaped caverns in the layered rock masses for the finite element method numerical simulation. In addition, a large hydroelectric dam on the intake to high slope on the left bank and the slope on the right bank were a natural tendency to state the numerical simulation to study the layered rock slope with lower angle and the layered rock slope with steep dip performanced different characteristics of bending deformation and failure.
According to the numerical analysis, either in case of the layer thickness is very small (high strain gradient) produced or two or more interbedding layered rock masses, the new Cosserat models can reflect the bending characteristics of the layered rock masses. The results were compared between the Cosserat medium equivalent model and the conventional continuum model showing the feasibility and validity of the new method.
本文主要的创新性研究成果如下:
1、本文采用Cosserat介质理论与渐近均匀化方法相结合建立了新的层状岩体Cosserat介质本构模型。即是,将层状岩体看作由代表性单元体(单胞)周期性重复排列组成的复合岩体。代表性单元体包括岩石层和节理层以及两种或两种以上不同物理力学特性的岩石材料,考虑它们自身的抗弯能力。在满足单胞的周期性边界条件下,进行细观均匀化分析得到各节点的细观位移值,再由均匀化公式推导的宏观弹性模量公式进一步求解得到一个新的Cosserat介质等效本构模型。
2、基于常规介质均匀化方法,构建适用于Cosserat介质的位移函数。采用正应力、剪应力、偶应力与对应的正应变、剪应变、曲率的广义应力、应变张量,首次得到Cosserat介质宏观弹性模量的计算公式。由于该公式包括了偶应力与曲率的关系,从而能反映节理岩体的弯曲特性。
3、根据本文所得的宏观弹性模量计算公式,在MATLAB平台上编制Cosserat介质均匀化方法应用于节理岩体的主函数程序。并利用计算实例与FLAC软件数值计算对比,验证编制程序的有效性。
4、在节理岩体中的洞室工程进行Cosserat介质有限元法数值模拟,分析了不同岩层间距、倾角、地应力及洞室高度等因素条件下,偶应力对围岩弯曲变形的影响;对节理岩体边坡工程,以某大型水电站坝址的进水口左岸顺向高边坡、右岸反倾向边坡的数值模拟,揭示了层状结构岩体缓倾角侧与陡倾角侧边坡表现出不同弯曲变形破坏特性。
通过本文数值分析,对于节理层间距很小的情况(高应力梯度)、两种或两种以上互层岩体的复杂情况,采用本文方法可以合理地反映层状岩体的弯曲特性。表明本文提出的均匀化Cosserat介质分析理论与传统连续介质理论的计算对比,其方法是有效、可行的。
Layered rock masses are very common in pratical engineering, which are often computated and analyzed by the explicit joint element or the anisotropy equivalent model based on the classical continua medium mechanics. The traditional continua medium theory FEM can’t provide satisfying interpretation on sliding, bending, buckling, flexural toppling failure phenomena, especially in case of the sharp stress gradients. The paper aims at analyze the bending mechanical properties of the layer rock masses, which combining the Cosserat medium theory into the asymptotic homogenization method, and solve the engineering practical problem in geotechnical engineering, mining engineering and correlative engineering aspects. The research results have no doubt the great theoretical significance, to improve the accuracy and credibility for the engineering application analysis also has the guiding sense.
The innovative research results in the paper are as follows:
1、A new Cosserat medium equivalent model was established in the paper, which connected the Cosserat medium theory with the homogenization method. At first, the layered rock mass was regarded as a composite with representative element volume (unit cell) periodic repetition rank. The representative element volume contained the rock layers and the joints,two or more different physical and mechanical characteristics the rock layers, which considering the rock material itself resist-bend ability. Satisfied with the periodic boundary conditions of unit cell,micro-displacement of all nodes can be obtained by micro homogenization analyzed at first, then a Cosserat medium equivalent model can be got by solving the macro elastic module formula educed from the homogenization process.
2、Based on the conventional medium homogenized, the new displacement function applying to the Cosserat medium is constructed. Then Young's modulus of the macro - formula can be solved from the corresponding generalized stress and strain elationships, such as the normal stress, the shear stress, couple stress and the corresponding normal strain, the shear strain and the curvature. For the formula including the relationship between the couple stress and the curvature, so it can be reflected the bending properties of the Cosserat medium materials.
3、The main functions program of Cosserat medium used in the homogenization methods were workouted in the MATLAB platform with help of the macro elastic modulus formula. Then the results were compared between the Cosserat medium equivalent model and the numerical method computated by the software FLAC showing the validity of the program.
4、To study the surrounding rock displacement and couple-stress, such as bending deformation impacted by the rock layers thickness, dip, ground stress and the cavern height and other factors in the different-shaped caverns in the layered rock masses for the finite element method numerical simulation. In addition, a large hydroelectric dam on the intake to high slope on the left bank and the slope on the right bank were a natural tendency to state the numerical simulation to study the layered rock slope with lower angle and the layered rock slope with steep dip performanced different characteristics of bending deformation and failure.
According to the numerical analysis, either in case of the layer thickness is very small (high strain gradient) produced or two or more interbedding layered rock masses, the new Cosserat models can reflect the bending characteristics of the layered rock masses. The results were compared between the Cosserat medium equivalent model and the conventional continuum model showing the feasibility and validity of the new method.
引文
[1] Goodman R E, Introduction to rock mechanics[M], John wiley & sons.1980.
[2] Hoek E, Brown E T. Underground excavations in rock[M], London:The institution of mining and metallurgy,1980.
[3]孙广忠.岩体结构力学[M].北京:科学出版社,1988.10.
[4]范文,俞茂宏,李同录等.层状岩体边坡变形破坏模式及滑坡稳定性数值分析[J].岩石力学与工程学报,2000,19(S1):983-986.
[5]傅鹤林,周宁,罗强等.板裂介质理论在牟珠洞滑坡机理分析中的应用[J].中南大学学报(自然科学版),2006,37(01):188-192.
[6]傅鹤林,范臻辉,朱汉华等.板裂介质围岩中的隧道衬砌与围岩相互作用机理研究[J].公路交通科技,2003,20(05):64-67.
[7]蒋臻蔚,王启耀,石玉玲.陡倾角层状岩体中巨型地下洞室群的围岩稳定问题[J].公路交通科技,2005,22(6):127-130.
[8]刘小丽,周德培.用弹性板理论分析顺层岩质边坡的失稳[J].岩土力学,2002,(02):162-165.
[9]黄洪波,符文熹,尚岳全等.层状岩质边坡的屈曲破坏分析[J].山地学报,2003,21(01):96-100.
[10]蒋良潍,黄润秋.反倾层状岩体斜坡弯曲-拉裂两种失稳破坏之判据探讨[J].工程地质学报,2006,14(03):289-294.
[11]蒋良潍,黄润秋.层状结构岩体顺层斜坡滑移-弯曲失稳计算探讨[J].山地学报,2006,24(01):88-94.
[12]李宝春,王林华,王小明.浅谈岩石边坡的溃屈稳定分析[J].治淮,2006,(12):30-32.
[13]李亮,郭乃正,傅鹤林等.破碎围岩中连拱隧道荷载计算理论解[J].中国铁道科学, 2004(04):50-54.
[14]程强,周德培,寇小兵.红层软岩地区公路建设中的主要岩土工程问题[A].见:第八次全国岩石力学与工程学术大会论文集[C].成都:科学出版社,2004.9:128-131.
[15]胡厚田,赵晓彦.中国红层边坡岩体结构类型的研究[J].岩土工程学报,2006,28(06):689-694.
[16]李云鹏,安晓宁,王芝银.考虑不同拉压特性的边坡岩体结构稳定性位移判据[J].西安公路交通大学学报,1999,19(04):15-17.
[17]李云鹏,杨治林,王芝银.顺层边坡岩体结构稳定性位移理论[J].岩石力学与工程学报,2000,19(06):747-750.
[18]刘书田,程耿东,顾元宪等.基于均匀化理论的多孔板弯曲问题新解法[J].固体力学学报,1999,(03):195-200.
[19]张慧梅.板裂介质岩体边坡的后屈曲性态[J].湖南科技大学学报(自然科学版),2007,22(04):73-76.
[20]张慧梅,李云鹏,杨治林.顺层边坡岩体结构稳定性位移判据的研究[J].西安科技学院学报,2004,24(04):430-433.
[21]朱晗迓,马美玲,尚岳全.顺倾向层状岩质边坡溃屈破坏分析[J].浙江大学学报(工学版),2004,38(09):1144-1149.
[22]刘钧.顺层边坡溃层问题的计算方法[J],水文地质工程地质,1997,(6): 37-41.
[23]李云鹏,王芝银.单边自由的固支岩板黏弹性行为分析及其应用[J].力学与实践,2005,27(02):29-32.
[24]董其伍,王哲,刘敏珊.渐进均匀化理论研究复合材料有效力学性能[J].材料科学与工程学报,2008,26(01):72-75.
[25]杨治林.顺层边坡岩体结构的模态幅值研究[J],岩土力学,2003,24(05):764-767.
[26]金仁祥,任光明.陡倾角反倾层状岩质边坡变形特征数值模拟验证[J],中国地质灾害与防治学报,2003,14(02):35-38.
[27]冷先伦,盛谦,廖红建等.反倾层状岩质高边坡开挖变形破坏机理研究[J],岩石力学与工程学报,2004,23(S1):4468-4472.
[28]陈红旗,黄润秋.反倾层状边坡弯曲折断的应力及挠度判据[J].工程地质学报,2004,12(03):243-246.
[29]齐典涛.昌马水库倾倒变形边坡特征形成机制及发育深度[J],西部探矿工程,2001,(06):47-48.
[30]伍法权.云母石英片岩斜坡弯曲倾倒变形的理论分析[J].工程地质学报,1997,5(04):306-311.
[31]贾剑青,王宏图,李晓红等.深埋隧道软硬交替复合顶板岩体变形破坏分析[J].岩土力学,2005,26(06):937-940.
[32]王宏图,鲜学福,贺建民等.层状复合岩体力学的相似模拟[J].矿山压力与顶板管理,1999,(02):81-83.
[33]郭志华,盛谦,梅松华等.层状复合岩体宏观力学参数的计算机模拟试验[J].岩石力学与工程学报,2004,23(S2):4902-4906.
[34] Mühlhaus H B,Dufour F,Moresi L,et al. A director theory for visco-elastic folding instabilities in multilayered rock[J]. International Journal of Solids and Structures, 2002. 39(13-14): 3675-3691.
[35] Zhao, C., et al., Computer simulations of coupled problems in geological and geochemicalsystems[J]. Computer Methods in Applied Mechanics and Engineering, 2002. 191(29-30): 3137-3152.
[36] Mühlhaus H B,Hornby P, Energy and averages in the mechanics of granular materials[J]. Tectonophysics, 2001. 335(1-2): 63-80.
[37] Dai C,Mühlhaus H B,Meek J,et al. Modelling of blocky rock masses using the Cosserat method[J]. International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts, 1996. 33(4): p. 425-432.
[38] Dai, C., et al., Finite element analysis of Cosserat Theory for layered rock masses[J]. Computers and Geotechnics, 1993. 15(3): 145-162.
[39] Lemiale V, Mühlhaus H B, Moresi L, et al., Shear banding analysis of plastic models formulated for incompressible viscous flows[J]. Physics of the Earth and Planetary Interiors. In Press, Accepted Manuscript.2008,8:1-10
[40]杨春和,李银平.互层盐岩体的Cosserat介质扩展本构模型[J].岩石力学与工程学报, 2005,24(23):4226-4232.
[41]李银平,杨春和.层状盐岩体的三维Cosserat介质扩展本构模型[J].岩土力学,2006,27(04):509-513.
[42]刘俊,黄铭,葛修润.Cosserat介质理论针对节理岩体的应用[J].岩土力学,2004,25(S2):27-31.
[43] Adhikary D P,Dyskin A V. Modelling the deformation of underground excavations in layered rock masses[J]. International Journal of Rock Mechanics and Mining Sciences, 1997. 34(3-4): 714-725.
[44] Adhikary D P,Dyskin A V,Jewell R J . Numerical modelling of the flexural deformation of foliated rock slopes[J]. International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts, 1996.33(6):595-606
[45] Adhikary D P,Mühlhaus H B,Dyskin A V.A numerical study of flexural buckling of foliated rock slopes[J]. International Journal for numerical and analytical methods in geomechanics, 2001. 30(2): 871-884.
[46] Adhikary D P,Mühlhaus H B,Dyskin A V. Modelling the large deformations in stratified media - the Cosserat continuum approach[J]. Mechanics of Cohesive-Frictional Materials, 1999. 4(3): 195-213.
[47]佘成学,罗继铣,张玉珍.层状岩体的Cosserat介质理论中第二剪切模量G~c的研究[J].岩土力学,1996,17(04):62-69.
[48]佘成学,熊文林,陈胜宏.层状岩体的弹粘塑性Cosserat介质理论及其工程应用[J].水利学报,1996,(04):10-17.
[49]佘成学,熊文林,陈胜宏.具有弯曲效应的层状结构岩体变形的Cosserat介质分析方法[J].岩土力学,1994,15(04):12-19.
[50] Adhikary D P,Dyskin A V. A Cosserat continuum model for layered materials[J]. Computers and Geotechnics, 1997. 20(1): 15-45.
[51]陈胜宏,王鸿儒,熊文林.节理岩体的偶应力有限元分析.见:第一届全国计算岩土力学研讨会[C]. 1987:西南交通大学出版社.
[52] Adhikary D P,Dyskin A V. A continuum model of layered rock masses with non-associative joint plasticity[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 1998. 22(4):245-261.
[53] Adhikary D P,Guo H, An orthotropic cosserat elasto-plastic model for layered rocks[J]. Rock Mechanics and Rock Engineering, 2002. 35(3): p. 161-170.
[54]佘成学,熊文林,张玉珍.层状岩体屈服准则的数值与试验分析[J].中国农村水利水电, 1996,(07):24-25.
[55]佘成学,范玉祥,陈胜宏.具有弯曲效应的三维层状岩体屈服准则[J].岩土力学,1998,19(03):38-42.
[56]李育超,凌道盛,陈云敏.Cosserat连续介质的Mohr-Coulomb屈服准则及其应用[J].浙江大学学报(工学版), 2005,39(02):253-258.
[57]王启耀,蒋臻蔚,杨林德.层状岩体巷道弯曲变形的有限元模拟[J].岩土力学,2006,27(07):1101-1104.
[58]王启耀,赵法锁.考虑偶应力的层状岩体地下洞室开挖模拟[J].西安科技大学学报, 2006,26(01):31-35.
[59]尹雪英,杨春和,李银平.层状盐岩体三维Cosserat介质扩展本构模型的程序实现[J].岩土力学,2007,28(07):1415-1420.
[60]杨乐,吴德伦,许年春.偶应力理论的层状岩体洞室数值模拟[J].重庆建筑大学学报,2008,30(3): 73-77.
[61]刘俊,陈胜宏.节理岩体三维偶应力弹性理论[J].岩土力学,1995,16(4): 20-29.
[62] Adler P M, et al., Real porous media: Local geometry and transports[J]. Journal of Engineering Mechanics, 2002. 128(8): p. 829-839.
[63] Auriault J L,Upscaling heterogeneous media by asymptotic expansions[J]. Journal of Engineering Mechanics, 2002. 128(8): p. 817-822.
[64] Didwania A K, Micromechanical basis of concept of effective stress[J]. Journal of Engineering Mechanics, 2002. 128(8): p. 864-868.
[65] Maghous S,Creus G J.Periodic homogenization in thermoviscoelasticity: Case of multilayered media with ageing[J]. International Journal of Solids and Structures, 2003. 40(4): 851-870.
[66]邱克鹏,张卫红,孙士平.蜂窝夹层结构等效弹性常数的多步三维均匀化数值计算分析[J].西北工业大学学报,2006,24(04):514-518.
[67]刘文辉,张新明,张淳源.均匀化方法在粘弹性多层复合材料中的应用[J].计算力学学报,2005,22(6): 722-727.
[68] Buhan P D,Felice G D. A homogenization approach to the ultimate strength of brick masonry[J]. Journal of the Mechanics and Physics of Solids, 1997. 45(7): 1085-1104.
[69]王达诠.应用RVE均质化方法的砌体非线性分析[D].重庆大学硕士学位论文. 2002.
[70]付海雄.水泥红土力学性能的试验研究及均匀化分析[D].湘潭大学硕士学位论文.2006.
[71]李春江.水化介质的细观力学模型与性能演化[D].北京工业大学硕士学位论文.2006.
[72]沈珠江,刘恩龙,陈铁林.岩土二元介质模型的一般应力应变关系[J].岩土工程学报, 2005,27(05):489-494.
[73] Abdelkrim M,Buhan P D. An elastoplastic homogenization procedure for predicting the settlement of a foundation on a soil reinforced by columns[J]. European Journal of Mechanics - A/Solids, 2007. 26(4): 736-757.
[74] Buhan D, Chateau P X, Dormieux L. The constitutive equations of finite strain poroelasticity in the light of a micro-macro approach[J]. European Journal of Mechanics - A/Solids, 1998. 17(6): 909-921.
[75] Buhan D, Chateau P X, Dormieux L.On the validity of the effective stress concept for assessing the strength of saturated porous materials: a homogenization approach[J]. Journal of the Mechanics and Physics of Solids, 1996. 44(10): 1649-1667.
[76]周维垣,杨强.岩石力学数值计算方法[M].北京:中国电力出版社. 2005: 110-136.
[77] Neves M M , Rodrigues H, Guedes J M.Optimal design of periodic linear elastic microstructures[J]. Computers and Structures, 2000. 76(1-3): 421-429.
[78] Kassbohm S, Muller W H, Fessler R.Improved approximations of Fourier coefficients for computing periodic structures with arbitrary stiffness distribution[J]. Computational Materials Science, 2006. 37(1-2): 90-93.
[79] Li K, Saigal S.Micromechanical modeling of stress transfer in carbon nanotube reinforced polymer composites[J]. Materials Science and Engineering A, 2007. 457(1-2): 44-57.
[80] Tyrus J M, Gosz M, DeSantiago E. A local finite element implementation for imposing periodic boundary conditions on composite micromechanical models[J]. International Journal of Solids and Structures, 2007. 44(9): 2972-2989.
[81] Whitaker S. Mechanics of composite solids[J]. Journal of Engineering Mechanics, 2002. 128(8): p. 823-828.
[82]朱其志,胡大伟,周辉等.基于均匀化理论的岩石细观力学损伤模型及其应用研究[J].岩石力学与工程学报,2008,27(02):266-272.
[83] Buhan P de,Freard J,Garnier D,et al. Failure properties of fractured rock masses as anisotropic homogenized media[J]. Journal of Engineering Mechanics-Asce, 2002. 128(8): 869-875.
[84]牛斌,杨海天.基于均匀化方法的斜交节理岩体复合本构关系研究[J].岩土工程学报,2007,29(05):773-778.
[85] Kanit T, et al., Determination of the size of the representative volume element for random composites: Statistical and numerical approach[J]. International Journal of Solids and Structures, 2003. 40(13-14): 3647-3679.
[86]秦玉静.均匀化节理单元及其应用[D].河海大学硕士学位论文.2005.
[87] Brocato M,Speciale M P.Layered materials[J]. Mathematical and Computer Modelling, 2003. 37(5-6): 477-484.
[88] Lydzba D,Pietruszczak S,Shao J F.On anisotropy of stratified rocks: Homogenization and fabric tensor approach[J]. Computers and Geotechnics, 2003. 30(4): 289-302.
[89] Ichikawa Y,Kawamura K,Uesugi K,et al. Micro- and macrobehavior of granitic rock: observations and viscoelastic homogenization analysis[J]. Computer Methods in Applied Mechanics and Engineering, 2001. 191(1-2): 47-72.
[90]杨海天,邬瑞锋,王刚等.节理岩体的复合本构有限元仿真计算[J].岩土工程学报,1996,18(06):69-76.
[91]杨海天,邬瑞锋.双向正交节理岩体的一个复合蠕变模型[J].大连理工大学学报,1991,31(03):267-273.
[92]刘书田,常崇义,杨海天等.单向节理岩石粘弹性性能预测[J].岩石力学与工程学报, 2003,22(04):582-588.
[93] Maghous S,Buhan P D,Dormieux L. Non-linear global elastic behaviour of a periodically jointed material[J]. Mechanics Research Communications, 2002. 29: 45-51.
[94] Wang M, Kulatilake P H, Um J,et al .Estimation of REV size and three-dimensional hydraulic conductivity tensor for a fractured rock mass through a single well packer test and discrete fracture fluid flow modeling[J]. International Journal mechanics and mining sciences.2002,39(7):887-904.
[95]张倬元,王士天,王兰生编著.工程地质分析原理[M].北京:地质出版社,1994.
[96]周维垣编著.高等岩石力学[M].北京:水利电力出版社,1993.
[97]刘立,邱贤德,黄木坤等.三维复合岩层损伤本构关系与演化方程[J].西安矿业学院学报,1999,19(3):221-224.
[98]晏石林,黄玉盈,陈传尧.贯通节理岩体模型与弹性参数确定[J].华中科技大学学报,2001,29(6):60-63.
[99]张武,张宏宪.节理岩体的弹性模型[J].岩土工程学报,1987,9(4):33-44.
[100]张玉军.节理岩体等效模型及其数值计算和室内试验[J].岩土工程学报,2006,28(1):29-32.
[101]陈胜宏.节理岩体偶应力影响的研究[J].水利学报,1990,(1):44-48.
[102]佘成学,罗继铣,张玉珍.Cosserat介质理论与连续介质理论的耦合计算方法[J].武汉水利电力大学学报,1996,29(6):40-44
[103]王启耀,杨林德,赵法锁.陡倾角层状岩体中地下洞室围岩的变形[J].长安大学学报(自然科学版),2006,26(5):69-73.
[104]郑颖人,沈珠江,龚晓南著.岩土塑性力学原理[M].中国建筑工业出版社,2002.11
[105]唐辉明,晏鄂川,胡新丽编著.工程地质数值模拟的理论与方法[M].武汉:中国地质大学出版社,2001.10
[106]王元汉,李丽娟,李银平编著.有限元法基础与程序设计[M].广州:华南理工大学出版社,2001.2
[107]赵平劳,姚增.层状结构岩体的复合材料本构模型[J].兰州大学学报(自然科学版),1990,26(2):114-118.
[108]鲜学福.层状岩体破坏机理[M].重庆大学出版社,1989.10.
[109]马格雷伯等著,高会生等译,MATLAB原理与工程应用[M],北京:电子工业出版社,2006.1
[110]孙祥,徐流美,吴清编著.MATLAB7.0基础教程[M],北京:清华大学出版社,2005.5.
[111]张洪武,王辉.平面Cosserat模型有限元分析的4和8节点单元与分片试验研究[J].计算力学学报.2005,22(5):512-517.
[112] Hassani B, Hinton E.A review of homogenization and topology optimization I–homogenization theory for media with periodic structure[J],Computers and Structures, 1998,69(6):707-717
[113] Hassani B, Hinton E.A review of homogenization and topology optimization II– analytical and numerical solution of homogenization equations[J],Computers and Structures, 1998,69 (6): 719-738
[114]宋广兴.基于均匀化理论非编织碳-碳复合材料力学性能数值研究[D].西北工业大学硕士学位论文.2007.
[115]冯森林.三维编织复合材料均匀化方法宏细观数值研究[D].国防科学技术大学博士学位论文. 2001.
[116]朱伯芳.有限单元法原理与应用[M].北京:中国水利水电出版社,1998.
[117] Samuel F,Francis P,Karam S. Asymptotic analysis of heterogeneous Cosserat media[J],International Journal of Solids and Structures,2001,38:4585-4608.
[118] Xi Yuan,Yoshihiro Tomita,Tomoaki Andou. A micromechanical approach of nonlocalmodeling for media with periodic microstructures[J],Mechanics Research Communications,2007:1-10
[119] O.van der Sluis,Vosbeek P H J,Schreurs P J G, et al. Homogenization of heterogeneous polymers[J].International Journal of Solids and Structures,1996,36:3193-3214.
[120] Rekik A, Bornert M, Auslender F,et al. A methodology for an accurate evaluation of the linearization procedures in nonlinear mean field homogenization[J].C.R.Mecanique,2005,333:789-795.
[121]黄润秋.中国西部岩石高边坡应力场特征及其卸荷破裂机理[J].工程地质学报,2004,12(s1):7-13.
[2] Hoek E, Brown E T. Underground excavations in rock[M], London:The institution of mining and metallurgy,1980.
[3]孙广忠.岩体结构力学[M].北京:科学出版社,1988.10.
[4]范文,俞茂宏,李同录等.层状岩体边坡变形破坏模式及滑坡稳定性数值分析[J].岩石力学与工程学报,2000,19(S1):983-986.
[5]傅鹤林,周宁,罗强等.板裂介质理论在牟珠洞滑坡机理分析中的应用[J].中南大学学报(自然科学版),2006,37(01):188-192.
[6]傅鹤林,范臻辉,朱汉华等.板裂介质围岩中的隧道衬砌与围岩相互作用机理研究[J].公路交通科技,2003,20(05):64-67.
[7]蒋臻蔚,王启耀,石玉玲.陡倾角层状岩体中巨型地下洞室群的围岩稳定问题[J].公路交通科技,2005,22(6):127-130.
[8]刘小丽,周德培.用弹性板理论分析顺层岩质边坡的失稳[J].岩土力学,2002,(02):162-165.
[9]黄洪波,符文熹,尚岳全等.层状岩质边坡的屈曲破坏分析[J].山地学报,2003,21(01):96-100.
[10]蒋良潍,黄润秋.反倾层状岩体斜坡弯曲-拉裂两种失稳破坏之判据探讨[J].工程地质学报,2006,14(03):289-294.
[11]蒋良潍,黄润秋.层状结构岩体顺层斜坡滑移-弯曲失稳计算探讨[J].山地学报,2006,24(01):88-94.
[12]李宝春,王林华,王小明.浅谈岩石边坡的溃屈稳定分析[J].治淮,2006,(12):30-32.
[13]李亮,郭乃正,傅鹤林等.破碎围岩中连拱隧道荷载计算理论解[J].中国铁道科学, 2004(04):50-54.
[14]程强,周德培,寇小兵.红层软岩地区公路建设中的主要岩土工程问题[A].见:第八次全国岩石力学与工程学术大会论文集[C].成都:科学出版社,2004.9:128-131.
[15]胡厚田,赵晓彦.中国红层边坡岩体结构类型的研究[J].岩土工程学报,2006,28(06):689-694.
[16]李云鹏,安晓宁,王芝银.考虑不同拉压特性的边坡岩体结构稳定性位移判据[J].西安公路交通大学学报,1999,19(04):15-17.
[17]李云鹏,杨治林,王芝银.顺层边坡岩体结构稳定性位移理论[J].岩石力学与工程学报,2000,19(06):747-750.
[18]刘书田,程耿东,顾元宪等.基于均匀化理论的多孔板弯曲问题新解法[J].固体力学学报,1999,(03):195-200.
[19]张慧梅.板裂介质岩体边坡的后屈曲性态[J].湖南科技大学学报(自然科学版),2007,22(04):73-76.
[20]张慧梅,李云鹏,杨治林.顺层边坡岩体结构稳定性位移判据的研究[J].西安科技学院学报,2004,24(04):430-433.
[21]朱晗迓,马美玲,尚岳全.顺倾向层状岩质边坡溃屈破坏分析[J].浙江大学学报(工学版),2004,38(09):1144-1149.
[22]刘钧.顺层边坡溃层问题的计算方法[J],水文地质工程地质,1997,(6): 37-41.
[23]李云鹏,王芝银.单边自由的固支岩板黏弹性行为分析及其应用[J].力学与实践,2005,27(02):29-32.
[24]董其伍,王哲,刘敏珊.渐进均匀化理论研究复合材料有效力学性能[J].材料科学与工程学报,2008,26(01):72-75.
[25]杨治林.顺层边坡岩体结构的模态幅值研究[J],岩土力学,2003,24(05):764-767.
[26]金仁祥,任光明.陡倾角反倾层状岩质边坡变形特征数值模拟验证[J],中国地质灾害与防治学报,2003,14(02):35-38.
[27]冷先伦,盛谦,廖红建等.反倾层状岩质高边坡开挖变形破坏机理研究[J],岩石力学与工程学报,2004,23(S1):4468-4472.
[28]陈红旗,黄润秋.反倾层状边坡弯曲折断的应力及挠度判据[J].工程地质学报,2004,12(03):243-246.
[29]齐典涛.昌马水库倾倒变形边坡特征形成机制及发育深度[J],西部探矿工程,2001,(06):47-48.
[30]伍法权.云母石英片岩斜坡弯曲倾倒变形的理论分析[J].工程地质学报,1997,5(04):306-311.
[31]贾剑青,王宏图,李晓红等.深埋隧道软硬交替复合顶板岩体变形破坏分析[J].岩土力学,2005,26(06):937-940.
[32]王宏图,鲜学福,贺建民等.层状复合岩体力学的相似模拟[J].矿山压力与顶板管理,1999,(02):81-83.
[33]郭志华,盛谦,梅松华等.层状复合岩体宏观力学参数的计算机模拟试验[J].岩石力学与工程学报,2004,23(S2):4902-4906.
[34] Mühlhaus H B,Dufour F,Moresi L,et al. A director theory for visco-elastic folding instabilities in multilayered rock[J]. International Journal of Solids and Structures, 2002. 39(13-14): 3675-3691.
[35] Zhao, C., et al., Computer simulations of coupled problems in geological and geochemicalsystems[J]. Computer Methods in Applied Mechanics and Engineering, 2002. 191(29-30): 3137-3152.
[36] Mühlhaus H B,Hornby P, Energy and averages in the mechanics of granular materials[J]. Tectonophysics, 2001. 335(1-2): 63-80.
[37] Dai C,Mühlhaus H B,Meek J,et al. Modelling of blocky rock masses using the Cosserat method[J]. International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts, 1996. 33(4): p. 425-432.
[38] Dai, C., et al., Finite element analysis of Cosserat Theory for layered rock masses[J]. Computers and Geotechnics, 1993. 15(3): 145-162.
[39] Lemiale V, Mühlhaus H B, Moresi L, et al., Shear banding analysis of plastic models formulated for incompressible viscous flows[J]. Physics of the Earth and Planetary Interiors. In Press, Accepted Manuscript.2008,8:1-10
[40]杨春和,李银平.互层盐岩体的Cosserat介质扩展本构模型[J].岩石力学与工程学报, 2005,24(23):4226-4232.
[41]李银平,杨春和.层状盐岩体的三维Cosserat介质扩展本构模型[J].岩土力学,2006,27(04):509-513.
[42]刘俊,黄铭,葛修润.Cosserat介质理论针对节理岩体的应用[J].岩土力学,2004,25(S2):27-31.
[43] Adhikary D P,Dyskin A V. Modelling the deformation of underground excavations in layered rock masses[J]. International Journal of Rock Mechanics and Mining Sciences, 1997. 34(3-4): 714-725.
[44] Adhikary D P,Dyskin A V,Jewell R J . Numerical modelling of the flexural deformation of foliated rock slopes[J]. International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts, 1996.33(6):595-606
[45] Adhikary D P,Mühlhaus H B,Dyskin A V.A numerical study of flexural buckling of foliated rock slopes[J]. International Journal for numerical and analytical methods in geomechanics, 2001. 30(2): 871-884.
[46] Adhikary D P,Mühlhaus H B,Dyskin A V. Modelling the large deformations in stratified media - the Cosserat continuum approach[J]. Mechanics of Cohesive-Frictional Materials, 1999. 4(3): 195-213.
[47]佘成学,罗继铣,张玉珍.层状岩体的Cosserat介质理论中第二剪切模量G~c的研究[J].岩土力学,1996,17(04):62-69.
[48]佘成学,熊文林,陈胜宏.层状岩体的弹粘塑性Cosserat介质理论及其工程应用[J].水利学报,1996,(04):10-17.
[49]佘成学,熊文林,陈胜宏.具有弯曲效应的层状结构岩体变形的Cosserat介质分析方法[J].岩土力学,1994,15(04):12-19.
[50] Adhikary D P,Dyskin A V. A Cosserat continuum model for layered materials[J]. Computers and Geotechnics, 1997. 20(1): 15-45.
[51]陈胜宏,王鸿儒,熊文林.节理岩体的偶应力有限元分析.见:第一届全国计算岩土力学研讨会[C]. 1987:西南交通大学出版社.
[52] Adhikary D P,Dyskin A V. A continuum model of layered rock masses with non-associative joint plasticity[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 1998. 22(4):245-261.
[53] Adhikary D P,Guo H, An orthotropic cosserat elasto-plastic model for layered rocks[J]. Rock Mechanics and Rock Engineering, 2002. 35(3): p. 161-170.
[54]佘成学,熊文林,张玉珍.层状岩体屈服准则的数值与试验分析[J].中国农村水利水电, 1996,(07):24-25.
[55]佘成学,范玉祥,陈胜宏.具有弯曲效应的三维层状岩体屈服准则[J].岩土力学,1998,19(03):38-42.
[56]李育超,凌道盛,陈云敏.Cosserat连续介质的Mohr-Coulomb屈服准则及其应用[J].浙江大学学报(工学版), 2005,39(02):253-258.
[57]王启耀,蒋臻蔚,杨林德.层状岩体巷道弯曲变形的有限元模拟[J].岩土力学,2006,27(07):1101-1104.
[58]王启耀,赵法锁.考虑偶应力的层状岩体地下洞室开挖模拟[J].西安科技大学学报, 2006,26(01):31-35.
[59]尹雪英,杨春和,李银平.层状盐岩体三维Cosserat介质扩展本构模型的程序实现[J].岩土力学,2007,28(07):1415-1420.
[60]杨乐,吴德伦,许年春.偶应力理论的层状岩体洞室数值模拟[J].重庆建筑大学学报,2008,30(3): 73-77.
[61]刘俊,陈胜宏.节理岩体三维偶应力弹性理论[J].岩土力学,1995,16(4): 20-29.
[62] Adler P M, et al., Real porous media: Local geometry and transports[J]. Journal of Engineering Mechanics, 2002. 128(8): p. 829-839.
[63] Auriault J L,Upscaling heterogeneous media by asymptotic expansions[J]. Journal of Engineering Mechanics, 2002. 128(8): p. 817-822.
[64] Didwania A K, Micromechanical basis of concept of effective stress[J]. Journal of Engineering Mechanics, 2002. 128(8): p. 864-868.
[65] Maghous S,Creus G J.Periodic homogenization in thermoviscoelasticity: Case of multilayered media with ageing[J]. International Journal of Solids and Structures, 2003. 40(4): 851-870.
[66]邱克鹏,张卫红,孙士平.蜂窝夹层结构等效弹性常数的多步三维均匀化数值计算分析[J].西北工业大学学报,2006,24(04):514-518.
[67]刘文辉,张新明,张淳源.均匀化方法在粘弹性多层复合材料中的应用[J].计算力学学报,2005,22(6): 722-727.
[68] Buhan P D,Felice G D. A homogenization approach to the ultimate strength of brick masonry[J]. Journal of the Mechanics and Physics of Solids, 1997. 45(7): 1085-1104.
[69]王达诠.应用RVE均质化方法的砌体非线性分析[D].重庆大学硕士学位论文. 2002.
[70]付海雄.水泥红土力学性能的试验研究及均匀化分析[D].湘潭大学硕士学位论文.2006.
[71]李春江.水化介质的细观力学模型与性能演化[D].北京工业大学硕士学位论文.2006.
[72]沈珠江,刘恩龙,陈铁林.岩土二元介质模型的一般应力应变关系[J].岩土工程学报, 2005,27(05):489-494.
[73] Abdelkrim M,Buhan P D. An elastoplastic homogenization procedure for predicting the settlement of a foundation on a soil reinforced by columns[J]. European Journal of Mechanics - A/Solids, 2007. 26(4): 736-757.
[74] Buhan D, Chateau P X, Dormieux L. The constitutive equations of finite strain poroelasticity in the light of a micro-macro approach[J]. European Journal of Mechanics - A/Solids, 1998. 17(6): 909-921.
[75] Buhan D, Chateau P X, Dormieux L.On the validity of the effective stress concept for assessing the strength of saturated porous materials: a homogenization approach[J]. Journal of the Mechanics and Physics of Solids, 1996. 44(10): 1649-1667.
[76]周维垣,杨强.岩石力学数值计算方法[M].北京:中国电力出版社. 2005: 110-136.
[77] Neves M M , Rodrigues H, Guedes J M.Optimal design of periodic linear elastic microstructures[J]. Computers and Structures, 2000. 76(1-3): 421-429.
[78] Kassbohm S, Muller W H, Fessler R.Improved approximations of Fourier coefficients for computing periodic structures with arbitrary stiffness distribution[J]. Computational Materials Science, 2006. 37(1-2): 90-93.
[79] Li K, Saigal S.Micromechanical modeling of stress transfer in carbon nanotube reinforced polymer composites[J]. Materials Science and Engineering A, 2007. 457(1-2): 44-57.
[80] Tyrus J M, Gosz M, DeSantiago E. A local finite element implementation for imposing periodic boundary conditions on composite micromechanical models[J]. International Journal of Solids and Structures, 2007. 44(9): 2972-2989.
[81] Whitaker S. Mechanics of composite solids[J]. Journal of Engineering Mechanics, 2002. 128(8): p. 823-828.
[82]朱其志,胡大伟,周辉等.基于均匀化理论的岩石细观力学损伤模型及其应用研究[J].岩石力学与工程学报,2008,27(02):266-272.
[83] Buhan P de,Freard J,Garnier D,et al. Failure properties of fractured rock masses as anisotropic homogenized media[J]. Journal of Engineering Mechanics-Asce, 2002. 128(8): 869-875.
[84]牛斌,杨海天.基于均匀化方法的斜交节理岩体复合本构关系研究[J].岩土工程学报,2007,29(05):773-778.
[85] Kanit T, et al., Determination of the size of the representative volume element for random composites: Statistical and numerical approach[J]. International Journal of Solids and Structures, 2003. 40(13-14): 3647-3679.
[86]秦玉静.均匀化节理单元及其应用[D].河海大学硕士学位论文.2005.
[87] Brocato M,Speciale M P.Layered materials[J]. Mathematical and Computer Modelling, 2003. 37(5-6): 477-484.
[88] Lydzba D,Pietruszczak S,Shao J F.On anisotropy of stratified rocks: Homogenization and fabric tensor approach[J]. Computers and Geotechnics, 2003. 30(4): 289-302.
[89] Ichikawa Y,Kawamura K,Uesugi K,et al. Micro- and macrobehavior of granitic rock: observations and viscoelastic homogenization analysis[J]. Computer Methods in Applied Mechanics and Engineering, 2001. 191(1-2): 47-72.
[90]杨海天,邬瑞锋,王刚等.节理岩体的复合本构有限元仿真计算[J].岩土工程学报,1996,18(06):69-76.
[91]杨海天,邬瑞锋.双向正交节理岩体的一个复合蠕变模型[J].大连理工大学学报,1991,31(03):267-273.
[92]刘书田,常崇义,杨海天等.单向节理岩石粘弹性性能预测[J].岩石力学与工程学报, 2003,22(04):582-588.
[93] Maghous S,Buhan P D,Dormieux L. Non-linear global elastic behaviour of a periodically jointed material[J]. Mechanics Research Communications, 2002. 29: 45-51.
[94] Wang M, Kulatilake P H, Um J,et al .Estimation of REV size and three-dimensional hydraulic conductivity tensor for a fractured rock mass through a single well packer test and discrete fracture fluid flow modeling[J]. International Journal mechanics and mining sciences.2002,39(7):887-904.
[95]张倬元,王士天,王兰生编著.工程地质分析原理[M].北京:地质出版社,1994.
[96]周维垣编著.高等岩石力学[M].北京:水利电力出版社,1993.
[97]刘立,邱贤德,黄木坤等.三维复合岩层损伤本构关系与演化方程[J].西安矿业学院学报,1999,19(3):221-224.
[98]晏石林,黄玉盈,陈传尧.贯通节理岩体模型与弹性参数确定[J].华中科技大学学报,2001,29(6):60-63.
[99]张武,张宏宪.节理岩体的弹性模型[J].岩土工程学报,1987,9(4):33-44.
[100]张玉军.节理岩体等效模型及其数值计算和室内试验[J].岩土工程学报,2006,28(1):29-32.
[101]陈胜宏.节理岩体偶应力影响的研究[J].水利学报,1990,(1):44-48.
[102]佘成学,罗继铣,张玉珍.Cosserat介质理论与连续介质理论的耦合计算方法[J].武汉水利电力大学学报,1996,29(6):40-44
[103]王启耀,杨林德,赵法锁.陡倾角层状岩体中地下洞室围岩的变形[J].长安大学学报(自然科学版),2006,26(5):69-73.
[104]郑颖人,沈珠江,龚晓南著.岩土塑性力学原理[M].中国建筑工业出版社,2002.11
[105]唐辉明,晏鄂川,胡新丽编著.工程地质数值模拟的理论与方法[M].武汉:中国地质大学出版社,2001.10
[106]王元汉,李丽娟,李银平编著.有限元法基础与程序设计[M].广州:华南理工大学出版社,2001.2
[107]赵平劳,姚增.层状结构岩体的复合材料本构模型[J].兰州大学学报(自然科学版),1990,26(2):114-118.
[108]鲜学福.层状岩体破坏机理[M].重庆大学出版社,1989.10.
[109]马格雷伯等著,高会生等译,MATLAB原理与工程应用[M],北京:电子工业出版社,2006.1
[110]孙祥,徐流美,吴清编著.MATLAB7.0基础教程[M],北京:清华大学出版社,2005.5.
[111]张洪武,王辉.平面Cosserat模型有限元分析的4和8节点单元与分片试验研究[J].计算力学学报.2005,22(5):512-517.
[112] Hassani B, Hinton E.A review of homogenization and topology optimization I–homogenization theory for media with periodic structure[J],Computers and Structures, 1998,69(6):707-717
[113] Hassani B, Hinton E.A review of homogenization and topology optimization II– analytical and numerical solution of homogenization equations[J],Computers and Structures, 1998,69 (6): 719-738
[114]宋广兴.基于均匀化理论非编织碳-碳复合材料力学性能数值研究[D].西北工业大学硕士学位论文.2007.
[115]冯森林.三维编织复合材料均匀化方法宏细观数值研究[D].国防科学技术大学博士学位论文. 2001.
[116]朱伯芳.有限单元法原理与应用[M].北京:中国水利水电出版社,1998.
[117] Samuel F,Francis P,Karam S. Asymptotic analysis of heterogeneous Cosserat media[J],International Journal of Solids and Structures,2001,38:4585-4608.
[118] Xi Yuan,Yoshihiro Tomita,Tomoaki Andou. A micromechanical approach of nonlocalmodeling for media with periodic microstructures[J],Mechanics Research Communications,2007:1-10
[119] O.van der Sluis,Vosbeek P H J,Schreurs P J G, et al. Homogenization of heterogeneous polymers[J].International Journal of Solids and Structures,1996,36:3193-3214.
[120] Rekik A, Bornert M, Auslender F,et al. A methodology for an accurate evaluation of the linearization procedures in nonlinear mean field homogenization[J].C.R.Mecanique,2005,333:789-795.
[121]黄润秋.中国西部岩石高边坡应力场特征及其卸荷破裂机理[J].工程地质学报,2004,12(s1):7-13.
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