极限荷载的突变模型研究
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摘要
结构的极限荷载是研究结构整体失效破坏和安全度的重要内容,该文以混凝土重力坝为对象,采用突变理论来研究混凝土重力坝的极限荷载,探讨重力坝沿建基面破坏时不同突变模型对极限荷载的影响。假定重力坝坝体和地基为刚性体,建基面存在一薄弱结合面,以建基面水平方向的位移为状态变量,施加的上游水压力为控制变量,分别建立反映此模型沿建基面失稳破坏的折迭突变模型和尖点突变模型,求出相应的极限荷载。研究表明,折迭突变模型得到的结果与力学系统稳定性理论解一致,而尖点突变模型给出的结果偏小。并指出,如果破坏面材料的本构关系为理想弹塑性或只考虑硬化阶段,确定重力坝整体稳定性的最大极限荷载宜采用折迭突变模型。如果需要研究破坏面材料进入软化阶段时的残余极限荷载,宜用尖点突变模型。
The determination of the ultimate load of structures is a key issue for the analysis of structural failure and safety index.In this paper,catastrophe theory is used to evaluate the ultimate load of a concrete gravity dam.Different catastrophe models of the ultimate load are discussed for the ultimate failure of the gravity dam along the base surface.In the analytical model,both the dam and the foundation are assumed as rigid bodies,and the base surface of the dam is considered sitting on a weak interface.With the horizontal displacement of the base surface regarded as a state variable and the applied upper water pressure as a control variable,the fold and cusp catastrophe models for the unstable failure of the above simple model are established,and the corresponding values of the ultimate load are obtained.It shows that the result by the fold catastrophe model is consistent with the available theoretical value,but the one by the cusp catastrophe model is smaller.It also demonstrates that the fold catastrophe model is capable of determining the maximal ultimate load against the ultimate failure of gravity dam when the material constitutive relationship of failure surface is elastic-perfectly plastic or only the hardening stage is considered.The cusp catastrophe model is suitable for obtaining the residual ultimate load when the material in failure surface goes in the softening stage.
The determination of the ultimate load of structures is a key issue for the analysis of structural failure and safety index.In this paper,catastrophe theory is used to evaluate the ultimate load of a concrete gravity dam.Different catastrophe models of the ultimate load are discussed for the ultimate failure of the gravity dam along the base surface.In the analytical model,both the dam and the foundation are assumed as rigid bodies,and the base surface of the dam is considered sitting on a weak interface.With the horizontal displacement of the base surface regarded as a state variable and the applied upper water pressure as a control variable,the fold and cusp catastrophe models for the unstable failure of the above simple model are established,and the corresponding values of the ultimate load are obtained.It shows that the result by the fold catastrophe model is consistent with the available theoretical value,but the one by the cusp catastrophe model is smaller.It also demonstrates that the fold catastrophe model is capable of determining the maximal ultimate load against the ultimate failure of gravity dam when the material constitutive relationship of failure surface is elastic-perfectly plastic or only the hardening stage is considered.The cusp catastrophe model is suitable for obtaining the residual ultimate load when the material in failure surface goes in the softening stage.
引文
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[10]刘健,刘康,王广月.混凝土重力坝沿建基面滑动的尖点突变模型研究[J].山东大学学报,2006,36(1):65―68.Liu Jian,Liu Kang,Wang Guangyue.Cusp catastrophe model of concrete gravity dam sliding along the contact surface between dam and foundation[J].Journal of Shandong University,2006,36(1):65―68.(in Chinese)
[11]邓跃进,董兆伟,张正禄.大坝变形失稳的尖点突变模型[J].武汉测绘科技大学学报,1999,24(2):170―173.Deng Yuejin,Dong Zhaowei,Zhang Zhenglu.A cusp catastrophe model of large dam deformation destabili-zation[J].Journal of Wuhan Technical University of Surveying and Mapping,1999,24(2):170―173.(in Chinese)
[12]刘仲秋,章青,徐兰玉.重力坝沿建基面滑动的能量突变理论分析研究[J].水电能源科学,2008,26(5):86―89.Liu Zhongqiu,Zhang Qing,Xu Lanyu.Study on energy catastrophe theory analysis of gravity dam sliding along foundation plane[J].Water Resources and Power,2008,26(5):86―89.(in Chinese)
[13]秦四清,王思敬,孙强.非线性岩土力学基础[M].北京:地质出版社,2008:28―34.Qin Siqing,Wang Sijing,Sun Qiang.Non-linear basis of rock and soil mechanics[M].Beijing:Geological Publishing House,2008:28―34.(in Chinese)
[2]DLT5353-2006,水电水利工程边坡设计规范[S].中华人民共和国国家发展和改革委员会,2007.DLT5353-2006,Design specification for hydro hydraulic slope[S].The National Development and Reform Commission of the People’s Republic of China,2007.(in Chinese)
[3]王均星,李永明,李泽.重力坝的塑性极限分析法[J].水利学报,2004(8):81―84.Wang Junxing,Li Yongming,Li Ze.Plastic limit analysis method for gravity dam[J].Journal of Hydraulic Engineering,2004(8):81―84.(in Chinese)
[4]杨永忠,王经,赖秋映.重力坝极限承载能力分析[J].湖北水力发电,2000(1):49―52.Yang Yongzhong,Wang Jing,Lai Qiuying.The ultimate bearing capacity analysis of gravity dam[J].Hubei Water Power,2000(1):49―52.(in Chinese)
[5]Ren Qingwen,Xu Lanyu,Wan Yunhui.Research advance of safety analysis methods for high concrete dam[J].Science in China(E),2007,50(S):62―78.
[6]李士勇,田新华.非线性科学与复杂性科学[M].哈尔滨:哈尔滨工业大学出版社,2006:51―61.Li Shiyong,Tian Xinhua.Nonlinear science and complexity science[M].Harbin:Harbin institute of technology Press,2006:51―61.(in Chinese)
[7]殷有泉,郑顾团.断层地震的尖角型突变模型[J].地球物理学报,1988,31(6):657―663。Yin Youquan,Zheng Gutuan.A cusp type catastrophic model of fault earthquake[J].Acta Geophysica Sinica,1988,31(6):657―663.(in Chinese)
[8]唐春安,徐小荷.岩石破裂过程失稳的尖点灾变模型[J].岩石力学与工程学报,1990,9(2):100―107.Tang Chun’an,Xu Xiaohe.A cusp catastrophic model of rock unstable failure[J].Chinese Journal of Rock Mechanics and Engineering,1990,9(2):100―107.(in Chinese)
[9]秦四清,张倬元,王士天.顺层斜坡失稳的突变理论分析[J].中国地质灾害与防治学报,1993,4(1):38―45.Qin Siqing,Zhang Zhuoyuan,Wang Shitian.Research on losing stability of the consequent slope by the catas-trophe theory[J].Chinese Journal of Geologi-cal Hazard and Control,1993,4(1):38―45.(in Chinese)
[10]刘健,刘康,王广月.混凝土重力坝沿建基面滑动的尖点突变模型研究[J].山东大学学报,2006,36(1):65―68.Liu Jian,Liu Kang,Wang Guangyue.Cusp catastrophe model of concrete gravity dam sliding along the contact surface between dam and foundation[J].Journal of Shandong University,2006,36(1):65―68.(in Chinese)
[11]邓跃进,董兆伟,张正禄.大坝变形失稳的尖点突变模型[J].武汉测绘科技大学学报,1999,24(2):170―173.Deng Yuejin,Dong Zhaowei,Zhang Zhenglu.A cusp catastrophe model of large dam deformation destabili-zation[J].Journal of Wuhan Technical University of Surveying and Mapping,1999,24(2):170―173.(in Chinese)
[12]刘仲秋,章青,徐兰玉.重力坝沿建基面滑动的能量突变理论分析研究[J].水电能源科学,2008,26(5):86―89.Liu Zhongqiu,Zhang Qing,Xu Lanyu.Study on energy catastrophe theory analysis of gravity dam sliding along foundation plane[J].Water Resources and Power,2008,26(5):86―89.(in Chinese)
[13]秦四清,王思敬,孙强.非线性岩土力学基础[M].北京:地质出版社,2008:28―34.Qin Siqing,Wang Sijing,Sun Qiang.Non-linear basis of rock and soil mechanics[M].Beijing:Geological Publishing House,2008:28―34.(in Chinese)
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