坝基界面在非线性水压力驱动下的非线性断裂过程模拟
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摘要
基于多边形比例边界有限元法和粘聚裂缝模型提出了混凝土坝坝基界面在随缝宽非线性变化的水压力驱动下的非线性断裂数值模型。混凝土和基岩采用多边形比例边界单元模拟,界面裂缝的断裂过程区采用粘性界面单元模拟。因为界面裂缝总是处于复合断裂模态,故同时引入了法向和切向的界面单元,且考虑了裂纹面作用有法向和切向任意荷载时的应力强度因子求解。以裂尖为原点,裂尖附近的位移场和应力场在径向上解析求解,在环向具有有限元精度。因此无需在裂尖附近加密网格或采用富集技术即可求得高精度的解。对于界面断裂,可模拟出与两种材料差异性相关的非1/2奇异性。断裂过程区的水压力随缝面宽度变化,采用指数函数的形式进行表征,通过参数调整可实现不同分布的水压力的模拟。水压力与粘聚力考虑为与裂缝宽度相关的组合函数,便于非线性迭代的实现。结合多边形网格生成和重剖分技术,可方便地模拟界面裂缝在水力驱动下的扩展过程。算例研究表明了该文模型的有效性,从中也可看出考虑缝内水压及其具体分布形式对研究坝的稳定性具有重要影响。
A model for the water fracture modeling at dam-foundation interface is proposed based on Scaled Boundary Polygons and Cohesive Crack Model. Both the dam and foundation rock are modelled by Scaled Boundary polygons, while the fracture process zone of the interfacial crack is modeled by interface elements embodying a cohesive softening law. Since interfacial crack is always in mixed mode loading, interface elements are introduced in both the normal and tangential directions. The stress intensity factors are solved for cracks subscribed with arbitrary side-face tractions. The displacement field and stress field are solved semi-analytically, contributing to the high precision of the solution without asymptotic enrichment or local mesh refinement. The polygon generation and remeshing technique facilitates convenient modeling of the crack propagation process. The proposed model is verified by a numerical example, which also shows that the water pressure and its distribution pattern inside the crack influence remarkably the stability of the crack.
A model for the water fracture modeling at dam-foundation interface is proposed based on Scaled Boundary Polygons and Cohesive Crack Model. Both the dam and foundation rock are modelled by Scaled Boundary polygons, while the fracture process zone of the interfacial crack is modeled by interface elements embodying a cohesive softening law. Since interfacial crack is always in mixed mode loading, interface elements are introduced in both the normal and tangential directions. The stress intensity factors are solved for cracks subscribed with arbitrary side-face tractions. The displacement field and stress field are solved semi-analytically, contributing to the high precision of the solution without asymptotic enrichment or local mesh refinement. The polygon generation and remeshing technique facilitates convenient modeling of the crack propagation process. The proposed model is verified by a numerical example, which also shows that the water pressure and its distribution pattern inside the crack influence remarkably the stability of the crack.
引文
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[13]Hillerborg A,Modéer 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.
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[15]马存旺,金延伟.基于界面断裂的粘聚区长度计算方法研究[J].工程力学,2013,30(1):448―453.Ma Cunwang,Jin Yanwei.Study on computational method for cohesive zone length based on interface fracture[J].Engineering Mechanics,2013,30(1):448―453.(in Chinese)
[16]Zhong H,Ooi E T,Song C,et al.Experimental and numerical study of the dependency of interface fracture in concrete-rock specimens on mode mixity[J].Engineering Fracture Mechanics,2014(124/125):287―309.
[17]刘钧玉,林皋,胡志强.重力坝-地基-库水系统动态断裂分析[J].工程力学,2009,26(11):114―120.Liu Junyu,Lin Gao,Hu Zhiqiang.Dynamic fracture analysis of the gravity dam-foundation-reservoir system[J].Engineering Mechanics,2009,26(11):114―120.(in Chinese)
[18]Song C,Tin-Loi F,Gao W.A definition and evaluation procedure of generalized stress intensity factors at cracks and multi-material wedges[J].Engineering Fracture Mechanics,2010(77):2316―2336.
[19]Ooi E T,Song C,Tin-Loi F,Yang Z.Polygon scaled boundary finite elements for crack propagation modeling[J].International Journal for Numerical Methods in Engineering,2012,91(3):319―342.
[20]钟红,宋平平.任意裂纹面荷载作用下界面断裂分析[J].哈尔滨工业大学学报,2016(2):152―157.Zhong Hong,Song Pingping.The analysis of interface crack with arbitrary crack tractions[J].Journal of Harbin Institute of Technology,2016(2):152―157.(in Chinese)
[2]金剑,雷冬,余快.混凝土水力劈裂的数值模拟[J].计算机辅助工程,2014,23(1):44―51.Jin Jian,Lei Dong,Yu Kuai.Numerical simulation on hydraulic fracture in concrete[J].Computer Aided Engineering,2014,23(1):44―51.(in Chinese)
[3]贾金生,汪洋,冯炜,常凊睿.重力坝高压水劈裂模拟方法与特高重力坝设计准则初步探讨[J].水利学报,2013,44(2):127―133.Jia Jinsheng,Wang Yang,Feng Wei,Chang Qingrui.Simulation method of hydraulic fracturing and discussions on design criteria for super high gravity dams[J].Journal of Hydraulic Engineering,2013,44(2):127―133.(in Chinese)
[4]Brühwiler E,Saouma V E.Water fracture interaction in concrete-Part II:Hydrostatic pressure in cracks[J].ACI Materials Journal,1995(92):383―390.
[5]Slowik V,Saouma V E.Water pressure in propagating concrete cracks[J].Journal of Structural Engineering,2000(126):235―242.
[6]Segura J M,Carol I.Numerical modelling of pressurized fracture evolution in concrete using zero-thickness interface elements[J].Engineering Fracture Mechanics,2010(77):1386―1399.
[7]Desroches J,Detournay E,Lenoach B,Papanastasiou P,Pearson J R A,Thiercelin M,Cheng A.The crack tip region in hydraulic fracturing[J].Proceedings of the Royal Society,1994(447):39―48.
[8]贾金生,李新宇,郑璀莹.特高重力坝考虑高压水劈裂影响的初步研究[J].水利学报,2006,37(12):1509―Jia Jinsheng,Li Xinyu,Zheng Cuiying.Studies on safety problem of high gravity dams higher than 200 m with consideration of hydraulic fracturing under water pressure[J].Journal of Hydraulic Engineering,2006,37(12):1509―1515.(in Chinese)
[9]Bolzon G,Cocchetti G.Direct assessment of structural resistance against pressurized fracture[J].International Journal for Numerical and Analytical Methods in Geomechanics,2003(27):353―378.
[10]Barpi F,Valente S.Modeling water penetration at dam-foundation joint[J].Engineering Fracture Mechanics,2008(75):629―642.
[11]Barpi F,Valente S.The cohesive frictional crack model applied to the analysis of the dam-foundation joint[J].Engineering Fracture Mechanics,2010(77):2182―2191.
[12]董玉文,任青文.重力坝水力劈裂分析的扩展有限元法[J].水利学报,2011,42(11):1361―1367.Dong Yuwen,Ren Qingwen.An extended finite element method for modeling hydraulic fracturing in gravity dam[J].Journal of Hydraulic Engineering,2011,42(11):1361―1367.(in Chinese)
[13]Hillerborg A,Modéer 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.
[14]卿龙邦,李庆斌,管俊峰,王娟.基于虚拟裂缝模型的混凝土断裂过程区研究[J].工程力学,2012,29(9):112―116.Qing Longbang,Li Qingbin,Guan Junfeng,Wang Juan.Study of concrete fracture process zone based on fictitious crack model[J].Engineering Mechanics,2012,29(9):112―116.(in Chinese)
[15]马存旺,金延伟.基于界面断裂的粘聚区长度计算方法研究[J].工程力学,2013,30(1):448―453.Ma Cunwang,Jin Yanwei.Study on computational method for cohesive zone length based on interface fracture[J].Engineering Mechanics,2013,30(1):448―453.(in Chinese)
[16]Zhong H,Ooi E T,Song C,et al.Experimental and numerical study of the dependency of interface fracture in concrete-rock specimens on mode mixity[J].Engineering Fracture Mechanics,2014(124/125):287―309.
[17]刘钧玉,林皋,胡志强.重力坝-地基-库水系统动态断裂分析[J].工程力学,2009,26(11):114―120.Liu Junyu,Lin Gao,Hu Zhiqiang.Dynamic fracture analysis of the gravity dam-foundation-reservoir system[J].Engineering Mechanics,2009,26(11):114―120.(in Chinese)
[18]Song C,Tin-Loi F,Gao W.A definition and evaluation procedure of generalized stress intensity factors at cracks and multi-material wedges[J].Engineering Fracture Mechanics,2010(77):2316―2336.
[19]Ooi E T,Song C,Tin-Loi F,Yang Z.Polygon scaled boundary finite elements for crack propagation modeling[J].International Journal for Numerical Methods in Engineering,2012,91(3):319―342.
[20]钟红,宋平平.任意裂纹面荷载作用下界面断裂分析[J].哈尔滨工业大学学报,2016(2):152―157.Zhong Hong,Song Pingping.The analysis of interface crack with arbitrary crack tractions[J].Journal of Harbin Institute of Technology,2016(2):152―157.(in Chinese)