混凝土损伤分析及其工程应用
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摘要
损伤力学作为工程材料和结构的强度性能分析、破坏机理解释、失效预测以及寿命估计等方面定量分析的理论依据和手段，越来越广泛、合理的应用于混凝土材料和结构的强度、变形及破坏的分析上来。混凝土是由粗骨料、细骨料和水泥沙浆构成非均匀性多相复合材料，在成型期间就存在一些初始裂纹，在荷载等因素的作用下，初始裂纹会不断扩展、联结，并生成新的裂纹。将这些微缺陷对混凝土材料的劣化作用称之为损伤。研究证明：混凝土破坏是内部微裂纹逐渐发展的结果，亦可说破坏只是裂缝发展过程的最后阶段，而要真正描述混凝土的各种性能，就要研究其内部的微裂纹的演化规律，即进行混凝土损伤力学分析。
本文从混凝土材料到混凝土结构、从宏观到微观、从静态损伤到动态损伤、从各向同性损伤到各向异性损伤、从弹性损伤到弹塑性损伤等几个方面介绍并探讨研究了损伤理论在混凝土及其结构强度、变形、破坏特性分析中的应用。
首先介绍了损伤力学的基本内容以及混凝土损伤理论研究现状，比较了各种损伤演化模型。其后，发展了损伤力学中两个重要理论内容，即弹塑性损伤矩阵及其简单形式的推导和基于实验基础上的损伤演化方程的解析表达式的推导。通过形状函数的假定，提出了一种混凝土动力损伤本构模型。之后，考虑混凝土的循环荷载下力学特性，将一维损伤演化规律推广到多维问题，分析了重力坝在地震作用下的损伤破坏特性。并采用了正交各向异性弹性损伤矩阵编写了分析损伤场的有限元程序，应用于实际结构分析。最后，考虑混凝土材料的非均匀性，从细观层次对其损伤断裂进行了数值模拟，并探讨了本文中从一维损伤演化规律到多维问题推广的可行性。
文中的结论对评定混凝土结构的力学特性、估算其寿命等提供了参考。
Damage Mechanics, as the theoretic basis and measure of quantitative analysis which includes analysis of the intension capability of the engineering material and structure, the explanations of the destroying mechanism, forecast of invalidation and estimation of longevity and so on, is applied to analyze the intensity, distortion and destruction of the material and structure of concrete more and more broadly and reasonably. Concrete is a kind of inequality multiphase-compounding material which is constituted of rough aggregate and thin aggregate and cement and sand slurry. During the process of its formation, there exist many original cracks, and with the effect of the factors of load and so on, the original cracks will expand and combine continuously, and then create new cracks. We give the bad effect which is caused by these tiny limitations to the material of concrete a name-damage. It is proved by research that the destruction of concrete is the result of the gradual expansion of the interior tiny cracks,
or we can say that destruction is only the last phase of the expanding process of the cracks. However, if we want to describe every capability of concrete authentically, we should study the evolvement rule of its interior tiny cracks, that is to analyze Damage Mechanics of concrete.
This paper introduces and makes an inquiry into the application of Damage Mechanics to concrete and its structural intension, distortion and the analysis of destructing quality from macrocosmic to microcosmic, from static damage to dynamic damage , from isotropic damage to anisotropic damage, and from elastic damage to elastic-plastic damage and so on.
This paper introduces the basic theory of Damage Mechanics and compares all kinds of damage evolvement models firstly. Thereafter, it extends two important problems of damage Theory, which are the matrix of elastic-plastic damage and its symmetric inference and the inference of parsing expressing formula of damage evolvement equation based on experiments. Also, the paper adopts the matrix of perpendicular anisotropic elastic damage to workout the FEM program of analyzing damage, and applies it to practical analysis. The part of analyzing dynamics damage advances a model of dynamics damage constitutive on the basis of experiments and the presupposition of the shape function. Then, considering the Mechanics quality of cyclic loading of concrete, the paper extends single-dimensional damage evolvement rule to multi-dimensional damage and
analyzes the failure of gravity dam under the effect of earthquake. At last, taking the inequality of material of concrete into consideration, the paper simulates a numerical value to the damage and rupture from fine-sight levels and demonstrates the rationality from the single-dimensional damage evolvement rule to the extension of multi-dimensional damage.
本文从混凝土材料到混凝土结构、从宏观到微观、从静态损伤到动态损伤、从各向同性损伤到各向异性损伤、从弹性损伤到弹塑性损伤等几个方面介绍并探讨研究了损伤理论在混凝土及其结构强度、变形、破坏特性分析中的应用。
首先介绍了损伤力学的基本内容以及混凝土损伤理论研究现状，比较了各种损伤演化模型。其后，发展了损伤力学中两个重要理论内容，即弹塑性损伤矩阵及其简单形式的推导和基于实验基础上的损伤演化方程的解析表达式的推导。通过形状函数的假定，提出了一种混凝土动力损伤本构模型。之后，考虑混凝土的循环荷载下力学特性，将一维损伤演化规律推广到多维问题，分析了重力坝在地震作用下的损伤破坏特性。并采用了正交各向异性弹性损伤矩阵编写了分析损伤场的有限元程序，应用于实际结构分析。最后，考虑混凝土材料的非均匀性，从细观层次对其损伤断裂进行了数值模拟，并探讨了本文中从一维损伤演化规律到多维问题推广的可行性。
文中的结论对评定混凝土结构的力学特性、估算其寿命等提供了参考。
Damage Mechanics, as the theoretic basis and measure of quantitative analysis which includes analysis of the intension capability of the engineering material and structure, the explanations of the destroying mechanism, forecast of invalidation and estimation of longevity and so on, is applied to analyze the intensity, distortion and destruction of the material and structure of concrete more and more broadly and reasonably. Concrete is a kind of inequality multiphase-compounding material which is constituted of rough aggregate and thin aggregate and cement and sand slurry. During the process of its formation, there exist many original cracks, and with the effect of the factors of load and so on, the original cracks will expand and combine continuously, and then create new cracks. We give the bad effect which is caused by these tiny limitations to the material of concrete a name-damage. It is proved by research that the destruction of concrete is the result of the gradual expansion of the interior tiny cracks,
or we can say that destruction is only the last phase of the expanding process of the cracks. However, if we want to describe every capability of concrete authentically, we should study the evolvement rule of its interior tiny cracks, that is to analyze Damage Mechanics of concrete.
This paper introduces and makes an inquiry into the application of Damage Mechanics to concrete and its structural intension, distortion and the analysis of destructing quality from macrocosmic to microcosmic, from static damage to dynamic damage , from isotropic damage to anisotropic damage, and from elastic damage to elastic-plastic damage and so on.
This paper introduces the basic theory of Damage Mechanics and compares all kinds of damage evolvement models firstly. Thereafter, it extends two important problems of damage Theory, which are the matrix of elastic-plastic damage and its symmetric inference and the inference of parsing expressing formula of damage evolvement equation based on experiments. Also, the paper adopts the matrix of perpendicular anisotropic elastic damage to workout the FEM program of analyzing damage, and applies it to practical analysis. The part of analyzing dynamics damage advances a model of dynamics damage constitutive on the basis of experiments and the presupposition of the shape function. Then, considering the Mechanics quality of cyclic loading of concrete, the paper extends single-dimensional damage evolvement rule to multi-dimensional damage and
analyzes the failure of gravity dam under the effect of earthquake. At last, taking the inequality of material of concrete into consideration, the paper simulates a numerical value to the damage and rupture from fine-sight levels and demonstrates the rationality from the single-dimensional damage evolvement rule to the extension of multi-dimensional damage.
引文
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[3] 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．
[4] Kachanov L.M.Time of the rapture process under creep conditions[J].TVZ Akad.Nank.S.S.R.Otd.Tech.Nuak. 1958,8
[5] Rabonov Y N.Creep rapture[C],Proc 12,Ienter.Congress,Appl.Mech.Stanford, Springer berlin,1969.
[6] Lemaitre J.Application of damage concepts to predict creep-fatigue failure[C]. J.Eng. Mat.Tech,ASME, 1979,101(1):202-209
[7] Hult J.Damage induced tensile instability[C]. Trans.3rd AMIRT, London,1974.
[8] Leckie F A,Hayhurst D R.Creep rupture of structure[C].Proc.R.Soc.A340,1974.
[9] 村上澄男．大野信忠．微观的空有效面积减小阳表多轴损伤变数[J]．日本机械学会论文集(A编)，昭和54年，46卷，409号．
[10] Kajcionovic D.Continuum damage theory of brittle materials[J].J.Appl. Mech. 1981 (48):809-824
[11] Sidoroff F.Discription of anistropic damage application to elasticity[C]. IUTAM Colloquium, physical Nonlinearities in structural analysis, 1981:237-244
[12] 宋玉普．多种混凝土材料的本构关系和破坏准则[M]．中国水利水电出版社．2002．
[13] 李灏．损伤力学基础[M]．山东：山东科学技术出版社，1992．
[14] 余天庆，钱济成．损伤理论及其应用[M]．北京：国防工业出版社，1993．
[15] 王军．损伤力学的理论与应用[M]．北京：科学出版社，1997．
[16] Dougill J W,et al. J. Eng[J]. Mech. Div,ASCE, 1976(102): 333.
[17] Mazars J. Application de la mecanigue de I'endommagement au comportement non lineaire et a la rupture du beton de structure.These de Doctorat d'Etat.Univ, paris Ⅵ,1984.
[18] Supartono F, Sidoroff F.Anisotropic damage modeling for brittle elastic materials[C]. Symposium of Franc-poland, 1984.
[19] Loland K E. Concrete damage model for load-response estimation of Concrete[J]. Cement and Concrete Research,1980(10):392-492
[20] Kajcinovic D.Constitutive equation for damaging platerials[J].J.Appl. Mech, 1983 (50):355-360
[21] 宋玉普．多种混凝土材料的本构关系和破坏准则[M]．中国水利水电出版社．2002．
[22] 逯静洲．三轴受压混凝土损伤特性理论与实验研究[D]．大连：大连理工大学博士学位论文，2001．
[23] Sauris W.Shah S P.J.Eng[J].Mech.Div, ASCE,1984(10):985
[24] Bui H O,Ehrlacher A.ICF-5[C],Cannes,1983(1):86
[25] Brooks J J.,AL-Samaraie N.V.Fracture of concrete and Rock.S.P.Shah Ed[M], Elsevier Applied Science, 1989:397-408
[26] 李庆斌，张楚汉，王光纶．单轴状态下混凝土的动力损伤本构模型[J]．水利学报，1994(12)：55-60
[27] 李庆斌．混凝土静、动双剪损伤本构理论[J]．水利学报，1995(2)：27-34
[28] 李兆霞，钱济成．混凝土徐变损伤演变方程及其在非线性徐变理论中的应用[J]．河海大学学报，1989，17(2)：26-24
[29] Miner M A.Cumulative damage in fatigue[J].J.Appl.Mech.1945,12(3):A159-A164
[30] Manson S.S,et al.Re-examination of cumulative analysis-An engineering prospectinve[J]. Engng.Frac.Mech, 1986.25-26
[31] Marco S M,Starkey W J.A concept of fatigue damage[C].Trans ACSE,1954, 76:627-632
[32] Henry D L.A theory of fatigue damage accumulation in steel[C].Trans ASME, 1955 (77):913-918
[33] Chaboche J L,Lemaitre J.A nolinear model of creep-fatigue damage cumulation and interaction[C].Proceeding of IUTAM Symposium of Visco-elastic Media and Bodies, Springerverlag, 1974.
[34] J．勒迈特著，倪金刚，陶春虎译．损伤力学教程[M]．北京：科学出版社，1996．
[35] 蔡四维，蔡敏．混凝土的损伤断裂[M]．北京：人民交通出版社，1999．
[36] 余天庆．混凝土的分段线性损伤模型．岩石、混凝土断裂与强度，1985(2)：14-16
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