基于强度理论的岩石损伤弹塑性模型
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摘要
根据单轴受力特性曲线唯象地考察岩石材料损伤演化,定义弹性应变表示的一维损伤变量及其本构模型,利用双剪强度理论将其推广至三维模型.塑性是潜在破坏面的摩擦滑移,在传统塑性理论的框架中,建立了基于摩尔-库仑强度理论与潜在滑移面摩擦软-硬化特性的各向异性损伤弹塑性本构关系.结果表明,计算的损伤演化与CT观测结果符合很好,用本文的弹塑性模型反映损伤材料的力学特性是可行的.
The one-dimensional damage variable was defined based on the elasto-brittle behavior of rock under uniaxial loading.To define the damage and its evolution in three-dimensional loading,the twin-shear theory was introduced to generalize the one-dimensional damage model into the three-dimensional model.The elastic behavior of the damaged material under loading can be expressed by reducing the elastic module,and the plastic flow can be represented by the slide on the plane between the two parts of the fractured rock.To establish the elastoplastic model of the damaged material,the concept of effective stress was used to contain the effects of damage in the yielding equation as well as in the function of plastic potential.The model was established in the frame of the classical plasticity theory in which the Mohr-Coulomb criterion was employed as the yielding criterion,and the friction law on the pre-sliding plane was taken as the hardening-softening rule to describe the change of the yielding surface with the progressive yielding.The comparison of the calculated results with tested results by a CT machine shows that the damage model presented in the paper can accurately describe the damage evolution of rock in Nanqiao Sandstone,and that the damage-elasto-plastic model is indeed feasible in describing the mechanical properties of the damaged material.
The one-dimensional damage variable was defined based on the elasto-brittle behavior of rock under uniaxial loading.To define the damage and its evolution in three-dimensional loading,the twin-shear theory was introduced to generalize the one-dimensional damage model into the three-dimensional model.The elastic behavior of the damaged material under loading can be expressed by reducing the elastic module,and the plastic flow can be represented by the slide on the plane between the two parts of the fractured rock.To establish the elastoplastic model of the damaged material,the concept of effective stress was used to contain the effects of damage in the yielding equation as well as in the function of plastic potential.The model was established in the frame of the classical plasticity theory in which the Mohr-Coulomb criterion was employed as the yielding criterion,and the friction law on the pre-sliding plane was taken as the hardening-softening rule to describe the change of the yielding surface with the progressive yielding.The comparison of the calculated results with tested results by a CT machine shows that the damage model presented in the paper can accurately describe the damage evolution of rock in Nanqiao Sandstone,and that the damage-elasto-plastic model is indeed feasible in describing the mechanical properties of the damaged material.
引文
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[14]Yu M H.Twin Shear Theory and Its Applications.Beijing:Science Press,1988(俞宏茂.双剪理论及其应用.北京:科学出版社,1998)
[15]Liu B,Han Y H.Guide to Principle,Examples and Applica-tions of FLAC.Beijing:China Communications Press,2005:18(刘波,韩彦辉.FLAC原理、实例与应用指南.北京:人民交通出版社,2005:18)
[16]You MQ.Strength and Deformation Course of Rock Samples.Beijing:Geology Press,2000:128(尤明庆.岩石试样的强度及其变形破坏过程.北京:地质出版社,2000:128)
[17]Wang L.Elasto-Plastic Damage Model and Its Applications[Dissertation].Beijing:University of Science and Technology Beijing,2007(王利.岩石弹塑性损伤模型及其应用研究[学位论文].北京:北京科技大学2007.)
[2]Zhao Y H,Huang J F,Wang R.Study of instantaneous observa-tion of microcracks developingin SEM.Chin J Rock Mech Eng,1992,11(3):284(赵永红,黄杰藩,王仁.岩石微破裂发育的扫描电镜即时观测研究.岩石力学与工程学报,1992,11(3):284)
[3]Li L,Xu Y,Li Q G,et al.Microcosmic research on gradual fracturing of granite.Chin J Rock Mech Eng,2002,21(7):940(李炼,徐钺,李启光,等.花岗岩渐进破坏的微观研究.岩石力学与工程学报,2002,21(7):940)
[4]Ge X R,Ren J X,Fu Y B,et al.Macro-mesoscopic Experimen-tal Research on Rock Damage Mechanics.Beijing:Science Press,2004:153(葛修润,任建喜,蒲毅彬,等.岩土损伤力学宏细观实验研究.北京:科学出版社,2004:153)
[5]Yu Sh W,Feng X Q.Damage Mechanics.Beijing:Tsinghua U-niversity Press,1997:78(余寿文,冯西桥.损伤力学.北京:清华大学出版社,1997.78)
[6]Yu T Q,Qian J Ch.Damage Theory and Its Application.Bei-jing:Science Press,1993:1(于天庆,钱济成.损伤理论及其应用.北京:科学出版社,1993:1)
[7]Zhou WY,Shan G R,Yang R Q.Elasto-brittle damage consti-tutive model of rock and its application in engineering.Chin J Geotech Eng,1998,20(5):54(周维垣,剡公瑞,杨若琼.岩体弹脆性损伤本构模型及工程应用.岩土工程学报,1998,20(5):54)
[8]Lemaitre J.Introduction to Continuum Damage Mechanics.El-sevier Science Ltd,2002:235
[9]Li Q B.Static,dynamic damage constitutive theory of concrete.J Hydraul Eng,1995(2):27(李庆彬.混凝土静、动力双剪损伤本构理论.水利学报,1995(2):27)
[10]Chen Y.Rock Properties ofthe Earth’s Crust.Beijing:Seism Press,1988(陈隅.地壳岩石的力学性能.北京:地震出版社,1988.)
[11]Basista M,Gross D.The sliding crack model of brittle deforma-tion:an internal variable approach.Int J Solids Struct,1998,35(5/6):487
[12]Dragon A,Hal m D,Desoyer T.Anisotropic damage in quasi-brittle solids:modeling,computational issues and applications.Comput Methods Appl Mech Eng,2000,183(3/4):331
[13]Yu M H,Yoshimine M,Qiang H F,et al.Advances and prospects for strength theory.Eng Mech,2004:21(6):2(俞宏茂,Yoshimine M,强洪夫,等.强度理论的发展和展望.工程力学,2004,21(6):2)
[14]Yu M H.Twin Shear Theory and Its Applications.Beijing:Science Press,1988(俞宏茂.双剪理论及其应用.北京:科学出版社,1998)
[15]Liu B,Han Y H.Guide to Principle,Examples and Applica-tions of FLAC.Beijing:China Communications Press,2005:18(刘波,韩彦辉.FLAC原理、实例与应用指南.北京:人民交通出版社,2005:18)
[16]You MQ.Strength and Deformation Course of Rock Samples.Beijing:Geology Press,2000:128(尤明庆.岩石试样的强度及其变形破坏过程.北京:地质出版社,2000:128)
[17]Wang L.Elasto-Plastic Damage Model and Its Applications[Dissertation].Beijing:University of Science and Technology Beijing,2007(王利.岩石弹塑性损伤模型及其应用研究[学位论文].北京:北京科技大学2007.)
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