基于断裂力学和损伤理论的混凝土断裂模型试验和数值研究
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摘要
混凝土是一种复杂的多相复合材料。由于各组成部分不同的物理特性、结合面、外荷载作用以及环境的多方面影响,其破坏机理异常复杂,导致对混凝土的断裂机理的研究非常困难。近年来,基于损伤力学和断裂力学的混凝土开裂研究越来越受到人们的重视和认可,并取得了不少成果。但是其研究仍然处于起步阶段,无论是理论、还是试验都很不成熟。于是本文就此开展了以下研究:
(1)分析了损伤力学和断裂力学模型的优缺点,提出了一种基于宏观断裂力学并综合考虑细观损伤理论的混凝土断裂模型。该模型用细观损伤推导得到的混凝土本构模型来描述混凝土开裂前的应力应变关系,且能够考虑断裂扩展区对断裂的影响。它综合了目前各研究模型的优点,能得到解析解。
(2)进行普通混凝土的断裂试验来验证该模型。选用三组初始缝高比分别为0.1、0.2、0.3的混凝土试件,考查它们在八个不同龄期的断裂性能,计算裂缝尖端开口位移和应力强度因子这两个参数,从初始缝高比和龄期这两个方面进行了分析。
(3)对掺矿物外加剂的混凝土的断裂进行了试验研究。分别计算了单掺粉煤灰和掺矿粉的混凝土的断裂性能,分析了粉煤灰和矿粉的掺入对混凝土断裂性能的影响及其原因。
(4)运用大型有限元分析软件ABAQUS的弥散开裂模型,对混凝土的三点弯曲梁开裂过程进行数值模拟分析。分析比较了不同龄期和不同初始缝高比时普通混凝土的开裂性能,并与试验结果进行了对比。
Concrete is a kind of complex multi-phase composite material. Because of the different physical characteristics, cohesion surfaces of its various components, load conditions as well as the influence of environment, the failure mechanism of concrete is exceptionally complex, which makes the study of its fracture mechanism very difficult. In recent years, the researches on concrete cracking based on damage mechanics and fracture mechanics have draw more and more attentions and recognitions. However, the researches in this field are not mature enough although there are some achievements. Therefore, this paper carries out the relevant research as follows.
Firstly, the advantages and disadvantages of damage constitutive models and fracture models of concrete are analyzed respectively. Then a improved consolidated concrete fracture model combining the damage model and fracture model is proposed in this paper.In this model, the meso-damage model is used to get the stress distribution of the fracture extension area and the impact of the fracture extension area on the fracture is considered. It combines the advantages of the two models above and can achieve the analytical solution.
Secondly, the concrete fracture experiments are carried out to verify the new model above, using three concrete groups, whose initial seam height ratio of the concrete specimens are 0.1,0.2,0.3 respectively. The fracture behaviors of each group in eight different ages are reviewed. And the crack tip opening displacement and stress intensity factor are calculated using the theoretical model proposed in this paper.
Then, the experiments on the fracture of concrete with mineral admixture are carried out. The fracture properties of the concrete mixed with fly ash and slag respectively are obtained and compared to the corresponding plain cement concrete. Then the influence of the fly ash and slag to the fracture properties of concrete are analyzed as well as their reasons.
At last, the numerical simulation of the concrete cracking in the three-point bending beam is established with the finite element analysis software-ABAQUS. The finite element results and experimental results of the fracture properties of concrete with different ages and initial seam height ratios are compared.
(1)分析了损伤力学和断裂力学模型的优缺点,提出了一种基于宏观断裂力学并综合考虑细观损伤理论的混凝土断裂模型。该模型用细观损伤推导得到的混凝土本构模型来描述混凝土开裂前的应力应变关系,且能够考虑断裂扩展区对断裂的影响。它综合了目前各研究模型的优点,能得到解析解。
(2)进行普通混凝土的断裂试验来验证该模型。选用三组初始缝高比分别为0.1、0.2、0.3的混凝土试件,考查它们在八个不同龄期的断裂性能,计算裂缝尖端开口位移和应力强度因子这两个参数,从初始缝高比和龄期这两个方面进行了分析。
(3)对掺矿物外加剂的混凝土的断裂进行了试验研究。分别计算了单掺粉煤灰和掺矿粉的混凝土的断裂性能,分析了粉煤灰和矿粉的掺入对混凝土断裂性能的影响及其原因。
(4)运用大型有限元分析软件ABAQUS的弥散开裂模型,对混凝土的三点弯曲梁开裂过程进行数值模拟分析。分析比较了不同龄期和不同初始缝高比时普通混凝土的开裂性能,并与试验结果进行了对比。
Concrete is a kind of complex multi-phase composite material. Because of the different physical characteristics, cohesion surfaces of its various components, load conditions as well as the influence of environment, the failure mechanism of concrete is exceptionally complex, which makes the study of its fracture mechanism very difficult. In recent years, the researches on concrete cracking based on damage mechanics and fracture mechanics have draw more and more attentions and recognitions. However, the researches in this field are not mature enough although there are some achievements. Therefore, this paper carries out the relevant research as follows.
Firstly, the advantages and disadvantages of damage constitutive models and fracture models of concrete are analyzed respectively. Then a improved consolidated concrete fracture model combining the damage model and fracture model is proposed in this paper.In this model, the meso-damage model is used to get the stress distribution of the fracture extension area and the impact of the fracture extension area on the fracture is considered. It combines the advantages of the two models above and can achieve the analytical solution.
Secondly, the concrete fracture experiments are carried out to verify the new model above, using three concrete groups, whose initial seam height ratio of the concrete specimens are 0.1,0.2,0.3 respectively. The fracture behaviors of each group in eight different ages are reviewed. And the crack tip opening displacement and stress intensity factor are calculated using the theoretical model proposed in this paper.
Then, the experiments on the fracture of concrete with mineral admixture are carried out. The fracture properties of the concrete mixed with fly ash and slag respectively are obtained and compared to the corresponding plain cement concrete. Then the influence of the fly ash and slag to the fracture properties of concrete are analyzed as well as their reasons.
At last, the numerical simulation of the concrete cracking in the three-point bending beam is established with the finite element analysis software-ABAQUS. The finite element results and experimental results of the fracture properties of concrete with different ages and initial seam height ratios are compared.
引文
[1]李兆霞.损伤力学及其应用[M].北京:科学出版,2002.
[2]逯静洲.三轴受压混凝土损伤特性理论与试验研究[D].辽宁大连:大连理工大学博士论文,2001.
[3]Dougill,J.W.,et al.Journal of Engineering Mechanics[J].ASCE,1976,102:333.
[4]Loland,K E,Continuous damage model for load-responds estimation of concrete[J].Cement and concrete research,1980,Vol.10:395-402.
[5]Mazars J.Application de la mecanique de lendnnag emment an comportememt non lineaire de structure[J].These de doctorat detat Univ.Paris,ENEET,Mai 1984.
[6]Kajcinovic,D.Constitutive equation for damaging platerials[J].J.Appl.Mech,1983,50:355-360.
[7]Supartoko F,Sidoroff F.Anisotropic Damage Moddeling for Brittle Elastic Material[J].Symp.of Franco-Poland,1984.
[8]Bazant Z P.Microplane Model for Progressive Fracture of Concrete and Rock[J].Journal of Engineering Mechanics.1985Vol.111(4):559-582.
[9]李杰.混凝土随机损伤力学的初步研究[J].同济大学学报,2004,32(10):1270-1277.
[10]李杰.混凝土随机损伤本构关系研究新进展[J].东南大学学报,2002,32(5):750-755.
[11]王向东.混凝土损伤理论在水工结构仿真分析中的应用[D].江苏南京:河海大学博士学位论文,2004.
[12]李杰,卢朝辉,张其云.混凝土随机损伤本构关系-单轴受压分析.同济大学学报,2003,31(5):505-509.
[13]李杰,张其云.混凝土随机损伤本构关系.同济大学学报,2001,29(10):1135-1141.
[14]Sam-Young Noh,Wilfried B.Kr(a|¨)tzig,Konstantin Meskouris.Numerical simulation of serviceability,damage evolution and failure of reinforced concrete shells[J].Computer & Structure,2003,81(8-11):843-857.
[15]Griffith A.A.,The phenomena of rupture and flow in solids.Phil Trans.1921,221(A):179-180.
[16]Kaplan M F.Crack propagation and the fracture of concrete[J].Journal of the American Concrete Institute,1961,58(5):591-610.
[17]宣方龙.混凝土双参数和双K参数模型的比较研究.辽宁大连:大连理工硕士论文,2002.
[18]Wells,A.A.Application of Fracture Mechanics at and beyond General Yielding[J].British Welding J.,1963,Vol.10,563-570.
[19]Rice,J.R.A Path Indepandent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks[J].J.App.Mech,1968,Vol35,379-386.
[20]Y S JENQ,S P SHAH.A fracture toughness criterion for concrete[J].Engineering Fracture Mechanics,1985,21(5):1055-1069.
[21]Yeoushang J,Surendra P S.Two parameter fracture model for concrete[J].Journal of Engineering Mechanics,1985,111(10):1227-1241.
[22]A Hillerborg,M Modeer,P E Petersson.Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements[J].Cement and concrete research,1976,Vol.6,pp773-782.
[23]Bazant Z.P.and Oh B.h.Crack band theory for fracture of concrete[J].Material and Structure RILEM,1983,16:155-177.
[24]B.L.Karihaloo P.Nallathambi.An improved effective crack model for the determination of fracture toughness of concrete[J].Cement and Concrete Research,1989,19(4):603-610.
[25]徐世烺,赵国藩.混凝土结构裂缝扩展的双K断裂准则[J].土木工程学报,1992,25(2):32-38.
[26]Bazant,Z.P.,and Kim,S.S.,Plastic-fracture theory for concrete[J].Journal of Engineering Mechanics Division Proceedings,ASCE,Vol.105,1979,429-446.
[27]Mohamed A R,Hansen W.Micro-mechanical modeling of concrete response under static loading-Part 1:Model development and validation[J].ACI Materials Journal,196(2):196-203.
[28]Dougill,J.W.,et al.Journal of Engineering Mechanics[J].ASCE,1976,102:333.
[29]Krajcinovic D,Silva M A G..Statical aspects of the continuous damage theory [J].Int J Solids Stryctures,1982,18(7):551-562.
[30]Sivasambu Mahesh,S.leigh phoenix.[J].International journal of fracture,2002,115:41-85.
[31]Rabotnov Yu N.On the equations of state for creep[M].Progress in Applied Mechanics,1963,307-315.
[32]Lemaitre J.A continuous damage mechanics model for ductile materials [M].1985.
[33]Jenq,Y.S.and Shah,S.P.Determination of fracture parameters of plain concrete using three-point bend tests[J].Materials and Structures,1990,23(138):457-460.
[34]江见鲸,陆新征,叶列平.混凝土结构的有限元分析[M].北京:清华大学出版社,2005.
[35]Reinhardt H.W,Cornelissan A.W,Hordijk D.A.Tensile tests and failure analysis of concrete[J].J Struct Eng ASCE,1986,112(112):2426-2477.
[36]PETERSON P E.Crack growth and development of fracture zones in plain concrete and similar materials[J].Division of Building Materials,1981.
[37]HIROSHI TADA,P C PARIS,G R IRWINTHE.Stress Analysis Of Cracks Handbook[M].1973.
[38]中国航空研究院主编.应力强度因子手册.北京:科学出版社,1981.
[39]吴政.基于损伤的混凝土拉压全过程本构模型研究.水利水电技术,1995,11:58-63.
[40]解德,钱勤,李长安.断裂力学中的数值计算方法及其工程应用.北京:科学出版社,2009.
[41]金南国,金贤玉,郑砚国.早龄期混凝土断裂性能和微观结构的试验研究[J].浙江大学学报.2005,39(9):1374-1377.
[42]彭伟.粉煤灰和矿渣粉对海工混凝土性能的影响[J].四川建材,2009,35(4):5-7.
[43]王永春.粉煤灰及矿粉在大体积混凝土中的应用[J].山西建筑,2009,35(22):178-179.
[44]S.Demirdag,L.Gunduz.Strength properties of volcanic slag aggregate lightweight concrete for high performance masonry units[J].Construction and Building Materials,2008,22:135-142.
[45]Ngo D,Scordelis A C.Finite element analysis of reinforced concrete beams[J].ACI Journal,1967,64(2):152-163.
[46]Rashid Y R.Analysis of prestressed concrete pressure vessels[J].Nuclear engneering and Design,1968,7:334-344.
[47]朱万成,赵启林,唐春安等.混凝土断裂过程的力学模型与数值模拟[J].力学进展,2002,32(4):579-598.
[48]Rots J.G,Nauta P,Kusters GMA,Blaauwendraad J.Smeared Crack Approach and Fracture Localization in concrete[M].Heron,1985.
[49][美]陈惠发,A.F.萨里普,余天庆等.混凝土和土的本构方程[M].北京:中国建筑工业出版社,2004.
[50]曲蒙.早龄期混凝土损伤断裂的数值分析[D].浙江杭州:浙江大学硕士论文,2006.
[51]龙渝川,张楚汗,周元德.基于弥散与分离裂缝模型的混凝土开裂比较研究[J].工程力学,2008,25(3):80-84.
[52]S MBU M,S L PHOENIX,I J BEYERLEIN.Strength distribution and size effects for 2D and 3D composites with Weibull fibers in an elastic matrix[J].International Journal of Fracture.2002,115:41-85.
[2]逯静洲.三轴受压混凝土损伤特性理论与试验研究[D].辽宁大连:大连理工大学博士论文,2001.
[3]Dougill,J.W.,et al.Journal of Engineering Mechanics[J].ASCE,1976,102:333.
[4]Loland,K E,Continuous damage model for load-responds estimation of concrete[J].Cement and concrete research,1980,Vol.10:395-402.
[5]Mazars J.Application de la mecanique de lendnnag emment an comportememt non lineaire de structure[J].These de doctorat detat Univ.Paris,ENEET,Mai 1984.
[6]Kajcinovic,D.Constitutive equation for damaging platerials[J].J.Appl.Mech,1983,50:355-360.
[7]Supartoko F,Sidoroff F.Anisotropic Damage Moddeling for Brittle Elastic Material[J].Symp.of Franco-Poland,1984.
[8]Bazant Z P.Microplane Model for Progressive Fracture of Concrete and Rock[J].Journal of Engineering Mechanics.1985Vol.111(4):559-582.
[9]李杰.混凝土随机损伤力学的初步研究[J].同济大学学报,2004,32(10):1270-1277.
[10]李杰.混凝土随机损伤本构关系研究新进展[J].东南大学学报,2002,32(5):750-755.
[11]王向东.混凝土损伤理论在水工结构仿真分析中的应用[D].江苏南京:河海大学博士学位论文,2004.
[12]李杰,卢朝辉,张其云.混凝土随机损伤本构关系-单轴受压分析.同济大学学报,2003,31(5):505-509.
[13]李杰,张其云.混凝土随机损伤本构关系.同济大学学报,2001,29(10):1135-1141.
[14]Sam-Young Noh,Wilfried B.Kr(a|¨)tzig,Konstantin Meskouris.Numerical simulation of serviceability,damage evolution and failure of reinforced concrete shells[J].Computer & Structure,2003,81(8-11):843-857.
[15]Griffith A.A.,The phenomena of rupture and flow in solids.Phil Trans.1921,221(A):179-180.
[16]Kaplan M F.Crack propagation and the fracture of concrete[J].Journal of the American Concrete Institute,1961,58(5):591-610.
[17]宣方龙.混凝土双参数和双K参数模型的比较研究.辽宁大连:大连理工硕士论文,2002.
[18]Wells,A.A.Application of Fracture Mechanics at and beyond General Yielding[J].British Welding J.,1963,Vol.10,563-570.
[19]Rice,J.R.A Path Indepandent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks[J].J.App.Mech,1968,Vol35,379-386.
[20]Y S JENQ,S P SHAH.A fracture toughness criterion for concrete[J].Engineering Fracture Mechanics,1985,21(5):1055-1069.
[21]Yeoushang J,Surendra P S.Two parameter fracture model for concrete[J].Journal of Engineering Mechanics,1985,111(10):1227-1241.
[22]A Hillerborg,M Modeer,P E Petersson.Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements[J].Cement and concrete research,1976,Vol.6,pp773-782.
[23]Bazant Z.P.and Oh B.h.Crack band theory for fracture of concrete[J].Material and Structure RILEM,1983,16:155-177.
[24]B.L.Karihaloo P.Nallathambi.An improved effective crack model for the determination of fracture toughness of concrete[J].Cement and Concrete Research,1989,19(4):603-610.
[25]徐世烺,赵国藩.混凝土结构裂缝扩展的双K断裂准则[J].土木工程学报,1992,25(2):32-38.
[26]Bazant,Z.P.,and Kim,S.S.,Plastic-fracture theory for concrete[J].Journal of Engineering Mechanics Division Proceedings,ASCE,Vol.105,1979,429-446.
[27]Mohamed A R,Hansen W.Micro-mechanical modeling of concrete response under static loading-Part 1:Model development and validation[J].ACI Materials Journal,196(2):196-203.
[28]Dougill,J.W.,et al.Journal of Engineering Mechanics[J].ASCE,1976,102:333.
[29]Krajcinovic D,Silva M A G..Statical aspects of the continuous damage theory [J].Int J Solids Stryctures,1982,18(7):551-562.
[30]Sivasambu Mahesh,S.leigh phoenix.[J].International journal of fracture,2002,115:41-85.
[31]Rabotnov Yu N.On the equations of state for creep[M].Progress in Applied Mechanics,1963,307-315.
[32]Lemaitre J.A continuous damage mechanics model for ductile materials [M].1985.
[33]Jenq,Y.S.and Shah,S.P.Determination of fracture parameters of plain concrete using three-point bend tests[J].Materials and Structures,1990,23(138):457-460.
[34]江见鲸,陆新征,叶列平.混凝土结构的有限元分析[M].北京:清华大学出版社,2005.
[35]Reinhardt H.W,Cornelissan A.W,Hordijk D.A.Tensile tests and failure analysis of concrete[J].J Struct Eng ASCE,1986,112(112):2426-2477.
[36]PETERSON P E.Crack growth and development of fracture zones in plain concrete and similar materials[J].Division of Building Materials,1981.
[37]HIROSHI TADA,P C PARIS,G R IRWINTHE.Stress Analysis Of Cracks Handbook[M].1973.
[38]中国航空研究院主编.应力强度因子手册.北京:科学出版社,1981.
[39]吴政.基于损伤的混凝土拉压全过程本构模型研究.水利水电技术,1995,11:58-63.
[40]解德,钱勤,李长安.断裂力学中的数值计算方法及其工程应用.北京:科学出版社,2009.
[41]金南国,金贤玉,郑砚国.早龄期混凝土断裂性能和微观结构的试验研究[J].浙江大学学报.2005,39(9):1374-1377.
[42]彭伟.粉煤灰和矿渣粉对海工混凝土性能的影响[J].四川建材,2009,35(4):5-7.
[43]王永春.粉煤灰及矿粉在大体积混凝土中的应用[J].山西建筑,2009,35(22):178-179.
[44]S.Demirdag,L.Gunduz.Strength properties of volcanic slag aggregate lightweight concrete for high performance masonry units[J].Construction and Building Materials,2008,22:135-142.
[45]Ngo D,Scordelis A C.Finite element analysis of reinforced concrete beams[J].ACI Journal,1967,64(2):152-163.
[46]Rashid Y R.Analysis of prestressed concrete pressure vessels[J].Nuclear engneering and Design,1968,7:334-344.
[47]朱万成,赵启林,唐春安等.混凝土断裂过程的力学模型与数值模拟[J].力学进展,2002,32(4):579-598.
[48]Rots J.G,Nauta P,Kusters GMA,Blaauwendraad J.Smeared Crack Approach and Fracture Localization in concrete[M].Heron,1985.
[49][美]陈惠发,A.F.萨里普,余天庆等.混凝土和土的本构方程[M].北京:中国建筑工业出版社,2004.
[50]曲蒙.早龄期混凝土损伤断裂的数值分析[D].浙江杭州:浙江大学硕士论文,2006.
[51]龙渝川,张楚汗,周元德.基于弥散与分离裂缝模型的混凝土开裂比较研究[J].工程力学,2008,25(3):80-84.
[52]S MBU M,S L PHOENIX,I J BEYERLEIN.Strength distribution and size effects for 2D and 3D composites with Weibull fibers in an elastic matrix[J].International Journal of Fracture.2002,115:41-85.