抗拉强度空间变异性对重力坝地震开裂的影响分析
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摘要
由于施工质量不均匀和混凝土自身的非均质性,重力坝坝体混凝土强度具有空间变异性,这一特性会对大坝的抗震性能造成影响,而当前的重力坝地震动力分析中很少考虑混凝土强度参数的空间变异性。应用随机场理论构建大坝抗拉强度的空间变异随机场,采用中心点法离散随机场并构建自相关函数得到相关系数矩阵,对相关系数矩阵进行Cholesky分解和线性变换,结合独立标准正态分布样本矩阵生成相关对数正态分布样本矩阵,实现抗拉强度空间变异性的抽样模拟。考虑混凝土抗拉强度的空间变异性,采用混凝土塑性损伤模型对Koyna重力坝进行地震非线性动力分析,基于统计意义研究了坝体裂缝条数、裂缝深度、上游面裂缝分布范围和坝顶位移等动力响应特征。成果分析表明:考虑抗拉强度的空间变异性后,Koyna重力坝动力响应具有明显的离散性,且上游面裂缝条数增加后导致坝顶水平位移整体偏向下游,垂直位移整体上抬,残余位移增大;同时裂缝深度均值较均质材料情况增大,坝体震损程度总体加剧;Koyna重力坝实际观察到的裂缝位于计算得到的裂缝分布范围之内。对抗拉强度变异系数和水平向自相关距离的参数敏感性分析表明,坝体动力响应的均值和变异性随变异系数的增大而增大,但对抗拉强度的水平自相关距离变化不敏感。
Since the uneven construction quality and the inherent heterogeneity of concrete, the material properties of the gravity dam have spatial variability. The spatial variability of the concrete strength parameters will affect the seismic performance of dams, while it is rarely considered in the current seismic dynamic analysis of gravity dams. The random field theory was employed to generate the spatial variation random field of concrete tensile strength. The Midpoint method was used to discretize the random field and then Cholesky decomposition and linear transformation were performed on the generated correlation coefficient matrix. A series of independent standard normal distribution sample matrices were utilized to generate corresponding correlation lognormal distribution sample matrices to simulate the spatial variability of tensile strength. Considering the spatial variability of concrete tensile strength, the seismic nonlinear dynamic analysis of Koyna gravity dam was carried out by using Concrete Damaged Plasticity model. Based on the statistical significance, the dynamic response characteristics of the dam, such as the number of cracks, the depth of cracks, the distribution range of cracks on the upstream surface and the displacement of the dam crest were studied. The results showed that, after considering the spatial variability of tensile strength, the dynamic response of the Koyna gravity dam has obvious dispersion, and the additional cracks on the upstream causes the horizontal displacement of the dam crest to be downstream, the vertical displacement to be uplifted, and the residual displacement to be increased. Meanwhile, the mean depth of crack is larger than that of homogeneous assumption,and the extent of dam damage is generally aggravated. The actual observed cracks in the Koyna gravity dam are within the calculated crack distribution. The parameter sensitivity analysis showed that the mean value and variability of the dynamic response of the dam increases with the increase of the coefficient of variation of tensile strength, while they are not sensitive to the horizontal autocorrelation distance of tensile strength.
Since the uneven construction quality and the inherent heterogeneity of concrete, the material properties of the gravity dam have spatial variability. The spatial variability of the concrete strength parameters will affect the seismic performance of dams, while it is rarely considered in the current seismic dynamic analysis of gravity dams. The random field theory was employed to generate the spatial variation random field of concrete tensile strength. The Midpoint method was used to discretize the random field and then Cholesky decomposition and linear transformation were performed on the generated correlation coefficient matrix. A series of independent standard normal distribution sample matrices were utilized to generate corresponding correlation lognormal distribution sample matrices to simulate the spatial variability of tensile strength. Considering the spatial variability of concrete tensile strength, the seismic nonlinear dynamic analysis of Koyna gravity dam was carried out by using Concrete Damaged Plasticity model. Based on the statistical significance, the dynamic response characteristics of the dam, such as the number of cracks, the depth of cracks, the distribution range of cracks on the upstream surface and the displacement of the dam crest were studied. The results showed that, after considering the spatial variability of tensile strength, the dynamic response of the Koyna gravity dam has obvious dispersion, and the additional cracks on the upstream causes the horizontal displacement of the dam crest to be downstream, the vertical displacement to be uplifted, and the residual displacement to be increased. Meanwhile, the mean depth of crack is larger than that of homogeneous assumption,and the extent of dam damage is generally aggravated. The actual observed cracks in the Koyna gravity dam are within the calculated crack distribution. The parameter sensitivity analysis showed that the mean value and variability of the dynamic response of the dam increases with the increase of the coefficient of variation of tensile strength, while they are not sensitive to the horizontal autocorrelation distance of tensile strength.
引文
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[2]Zhong Hong,Li Xiaoyan,Lin Gao.Analyses of failure modes-based seismic fragility of gravity dams[J].Journal ofDalian University of Technology,2012,52(1):60-65.[钟红,李晓燕,林皋.基于破坏形态的重力坝地震易损性研究[J].大连理工大学学报,2012,52(1):60-65.]
[3]Vanmarcke E.Random Fields:Analysis and synthesis[M].Singapore:World Scientific,2010.
[4]Van der Have R.Random fields for non-linear finite element analysis of reinforced concrete[D].Delft:Delft University of Technology,2015.
[5]Qi X H,Li D Q.Effect of spatial variability of shear strength parameters on critical slip surfaces of slopes[J].Engineering Geology,2018,239:41-49.
[6]Cho S E.Probabilistic assessment of slope stability that considers the spatial variability of soil properties[J].Journal of Geotechnical and Geoenvironmental Engineering,2010,136(7):975-984.
[7]Chen Zhaohui,Lei Jian,Huang Jinghua,et al.Finite element limit analysis of slope stability considering spatial variability of soil strengths[J].Chinese Journal of Geotechnical Engineering,2018,40(6):985-993.[陈朝晖,雷坚,黄景华,等.考虑参数空间变异性的边坡稳定可靠性有限元极限分析[J].岩土工程学报,2018,40(6):985-993.]
[8]Liu Y,Shields M D.A direct simulation method and lowerbound estimation for a class of gamma random fields with applications in modelling material properties[J].Probabilistic Engineering Mechanics,2017,47:16-25.
[9]Altunisik A C,Sesli H.Dynamic response of concrete gravity dams using different water modelling approaches:Westergaard,lagrange and euler[J].Computers and Concrete,2015,16(3):429-448.
[10]Lubliner J,Oliver J,Oller S,et al.A plastic-damage model for concrete[J].International Journal of Solids and Structures,1989,25(3):299-329.
[11]Lee J,Fenves G L.Plastic-damage model for cyclic loading of concrete structures[J].Journal of Engineering Mechanics,1998,124(8):892-900.
[12]Zhang S,Wang G,Yu X.Seismic cracking analysis of con-crete gravity dams with initial cracks using the extended finite element method[J].Engineering Structures,2013,56(6):528-543.
[13]Long Yuchuan,Zhang Chuhan,Xu Yanjie.Nonlinear seismic analyses of a high gravity dam with and without the presence of reinforcement[J].Engineering Structures,2009,31(10):2486-2494.
[14]Hariri-Ardebili M A,Seyed-Kolbadi S M,Saouma V E,et al.Random finite element method for the seismic analysis of gravity dams[J].Engineering Structures,2018,171:405-420.
[15]Tang Xinwei,Zhou Yuande,Zhang Chuhan,et al.Study on the heterogeneity of concrete and its failure behavior using the equivalent probabilistic model[J].Journal of Materials in Civil Engineering,2011,23(4):402-413.
[16]Hicks M A,Spencer W A.Influence of heterogeneity on the reliability and failure of a long 3D slope[J].Computers&Geotechnics,2010,37(7):948-955.
[17]Wu Zhenjun,Wang Shuilin,Ge Xiurun.Slope reliability analysis by random FEM under constraint random field[J].Rock and Soil Mechanics,2009,30(4):3086-3092.[吴振君,王水林,葛修润.约束随机场下的边坡可靠度随机有限元分析方法[J].岩土力学,2009,30(4):3086-3092.]
[18]Wen Dezhi,Zhuo Renhong,Ding Dajie,et al.Generation of correlated pseudorandom variables in Monte Carlo simulation[J].Acta Physica Sinica,2012,61(22):514-518.[文德智,卓仁鸿,丁大杰,等.蒙特卡罗模拟中相关变量随机数序列的产生方法[J].物理学报,2012,61(22):514-518.]
[19]中华人民共和国住房和城乡建设部.混凝土结构设计规范:GB 50010-2010[S].北京:中国建筑工业出版社,2015.
[20]Guo Shenshan,Chen Houqun,Li Deyu,et al.Seismic damage and failure analysis of gravity dam and foundation system[J].Journal of Hydraulic Engineering,2013,44(11):1352-1358.[郭胜山,陈厚群,李德玉,等.重力坝与坝基体系地震损伤破坏分析[J].水利学报,2013,44(11):1352-1358.]