沥青混凝土心墙简化解析受力分析模型
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摘要
沥青混凝土心墙作为堆石坝的防渗结构,其受力安全备受工程领域的关注,对其进行快速简便地受力变形分析具有重要意义。利用薄板小挠度弯曲理论以及里兹法求解了置于Winkler弹性地基上三边固支一边自由矩形薄板在水压力作用下的挠曲变形函数,推导了矩形薄板的变形、内力和应力计算公式;建立了矩形薄板与实际沥青混凝土心墙之间的一一映射关系,将矩形薄板的变形、内力和应力映射到实际河谷断面心墙上,从而建立了沥青混凝土心墙简化解析受力分析模型。借助有限元方法对模型的可靠性进行了验证,最后将该模型应用于工程实例。研究结果表明,此模型有助于快速预估沥青混凝土心墙受力变形,同时研究思路也拓展了沥青混凝土心墙受力变形的计算方法。
As the anti-seepage structure of the rock-fill dam, the force safety of asphalt concrete core is well concerned by the engineering field. So it is important to quickly and easily study the force and deformation of the asphalt concrete core. Firstly, the deflection deformation function of the rectangular thin plate with three sides clamped and one side free(CCCF) on the Winkler elastic foundation under the hydrostatic pressure is solved via the small deflection bending theory of the thin plate and Ritz method.Moreover, the deformation, internal force and stress calculation formulae of the CCCF rectangular thin plate are derivated. Secondly,the one-to-one mapping relation between the CCCF rectangular thin plate and the asphalt concrete core is established. The deformation, internal force and stress of the CCCF rectangular thin plate are transformed to the actual valley section core. Thus, a simplified analytical force analysis model of the asphalt concrete core is established. Then the reliability of the model is verified via the FEM. Finally, the simplified analytical force analysis model is applied to an engineering example. This model helps to quickly estimate the force and deformation of the asphalt concrete core. At the same time, the research idea expands the calculation method for the force and deformation of the asphalt concrete core.
As the anti-seepage structure of the rock-fill dam, the force safety of asphalt concrete core is well concerned by the engineering field. So it is important to quickly and easily study the force and deformation of the asphalt concrete core. Firstly, the deflection deformation function of the rectangular thin plate with three sides clamped and one side free(CCCF) on the Winkler elastic foundation under the hydrostatic pressure is solved via the small deflection bending theory of the thin plate and Ritz method.Moreover, the deformation, internal force and stress calculation formulae of the CCCF rectangular thin plate are derivated. Secondly,the one-to-one mapping relation between the CCCF rectangular thin plate and the asphalt concrete core is established. The deformation, internal force and stress of the CCCF rectangular thin plate are transformed to the actual valley section core. Thus, a simplified analytical force analysis model of the asphalt concrete core is established. Then the reliability of the model is verified via the FEM. Finally, the simplified analytical force analysis model is applied to an engineering example. This model helps to quickly estimate the force and deformation of the asphalt concrete core. At the same time, the research idea expands the calculation method for the force and deformation of the asphalt concrete core.
引文
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[9]杨柯,顾淦臣.土石坝心墙成拱作用的一个综合评价[J].岩土工程学报,1999,21(2):240-241.YANG Ke,GU Gan-chen.A synthetic index for the arch action of earth-rock dams[J].Chinese Journal of Geotechnical Engineering,1999,21(2):240-241.
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[11]殷宗泽,朱俊高,袁俊平,等.心墙堆石坝的水力劈裂分析[J].水利学报,2006,37(11):1348-1353.YIN Zong-ze,ZHU Jun-gao,YUAN Jun-ping,et al.Hydraulic fracture analysis of rockfill dam with core[J].Journal of Hydraulic Engineering,2006,37(11):1348-1353.
[12]朱俊高,王俊杰,张辉.土石心墙水力劈裂机制研究[J].岩土力学,2007,28(3):487-492.ZHU Jun-gao,WANG Jun-jie,ZHANG Hui.Study on mechanism of hydraulic fracturing in core of earth-rockfill dam[J].Rock and Soil Mechanics,2007,28(3):487-492.
[13]李全明,张丙印,于玉贞,等.土石坝水力劈裂发生过程的有限元数值模拟[J].岩土工程学报,2007,29(2):212-217.LI Quan-ming,ZHANG Bing-yin,YU Yu-zhen,et al.Numerical simulation of the process of hydraulic fracturing in earth and rockfill dams[J].Chinese Journal of Geotechnical Engineering,2007,29(2):212-217.
[14]朱晟,魏匡民,饶锡保.土石坝沥青混凝土心墙水力劈裂研究[J].水力发电学报,2013,32(1):218-222.ZHU Sheng,WEI Kuang-min,RAO Xi-bao.Study on hydraulic fracturing of asphalt concrete core in earth-rock dam[J].Journal of Hydroelectric Engineering,2013,32(1):218-222.
[15]王仁超,刘金飞,李仕奇.高心墙堆石坝填筑分期分区优化模型[J].土木工程学报,2008,41(2):105-110.WANG Ren-chao,LIU Jin-fei,LI Shi-qi.Optimization model for substage-zoning filling design of high core rockfill dams[J].China Civil Engineering Journal,2008,41(2):105-110.
[16]李守义,马成成,李炎隆,等.沥青混凝土心墙堆石坝的地震反应特性分析[J].水力发电学报,2013,32(6):198-202.LI Shou-yi,MA Cheng-cheng,LI Yan-long,et al.Seismic response analysis of rockfill dam with asphaltic concrete core[J].Journal of Hydroelectric Engineering,2013,32(6):198-202.
[17]徐芝纶.弹性力学[M].第五版.北京:高等教育出版社,2016.XU Zhi-lun.Elasticity mechanics[M].5th ed.Beijing:Higher Education Press,2006.
[18]TERZAGHI K.Evaluation of the coefficient of subgrade reaction[J].Geotechnique,1955,5(4):197-326.
[2]杨超,党发宁,薛海斌,等.河谷形状对沥青混凝土心墙坝变形特性的影响[J].水利水运工程学报,2016(4):54-62.YANG Chao,DANG Fa-ning,XUE Hai-bin,et al.Influences of valley topography on deformation properties of asphalt concrete core dam[J].HydroScience and Engineering,2016(4):54-62.
[3]丁艳辉,袁会娜,张丙印,等.超高心墙堆石坝应力变形特点分析[J].水力发电学报,2013,32(4):153-158.DING Yan-hui,YUAN Hui-na,ZHANG Bing-yin,et al.Stress-deformation characteristics of super-high central core rock-fill dams[J].Journal of Hydroelectric Engineering,2013,32(4):153-158.
[4]吴海林,彭云枫,杜晓帆,等.沥青混凝土心墙坝应力变形及水力劈裂研究[J].水力发电学报,2015,34(4):119-127.WU Hai-lin,PENG Yun-feng,DU Xiao-fan,et al.Study on stress-deformation and hydraulic fracturing of rockfill dam with asphalt concrete core[J].Journal of Hydroelectric Engineering,2015,34(4):119-127.
[5]荣冠,朱焕春.茅坪溪土石坝沥青混凝土心墙施工期变形分析[J].水利学报,2003(7):115-119+123.RONG Guan,ZHU Huan-chun.Deformation of asphalt concrete core of Maopingxi earth-rockfill dam in the stage of construction[J].Journal of Hydraulic Engineering,2003(7):115-120+123.
[6]张继宝,陈五一,李永红,等.双江口土石坝心墙拱效应分析[J].岩土力学,2008,29(增刊):185-188.ZHANG Ji-bao,CHEN Wu-yi,LI Yong-hong,et al.Analysis of core arching effect of Shuangjiangkou earth-rockfill dam[J].Rock and Soil Mechanics,2008,29(Suppl.):185-188.
[7]林江,胡万雨,孟凡理,等.瀑布沟大坝心墙拱效应分析[J].岩土力学,2013,34(7):2031-2035.LIN Jiang,HU Wan-yu,MENG Fan-li,et al.Arching effect analysis of core in Pubugou dam[J].Rock and Soil Mechanics,2013,34(7):2031-2035.
[8]高昂,苏怀智,刘春高.超高心墙堆石坝拱效应分析[J].水力发电学报,2015,34(9):138-145.GAO Ang,SU Huai-zhi,LIU Chun-gao.Analysis of soil arching in high core-wall rockfill dam[J].Journal of Hydroelectric Engineering,2015,34(9):138-145.
[9]杨柯,顾淦臣.土石坝心墙成拱作用的一个综合评价[J].岩土工程学报,1999,21(2):240-241.YANG Ke,GU Gan-chen.A synthetic index for the arch action of earth-rock dams[J].Chinese Journal of Geotechnical Engineering,1999,21(2):240-241.
[10]陈五一,赵颜辉.土石心墙水力劈裂计算方法研究[J].岩石力学与工程学报,2008,27(7):1380-1385.CHEN Wu-yi,ZHAO Yan-hui.Study of calculation method of hydraulic fracturing for core of earth-rockfill dam[J].Chinese Journal of Rock Mechanics and Engineering,2008,27(7):1380-1385.
[11]殷宗泽,朱俊高,袁俊平,等.心墙堆石坝的水力劈裂分析[J].水利学报,2006,37(11):1348-1353.YIN Zong-ze,ZHU Jun-gao,YUAN Jun-ping,et al.Hydraulic fracture analysis of rockfill dam with core[J].Journal of Hydraulic Engineering,2006,37(11):1348-1353.
[12]朱俊高,王俊杰,张辉.土石心墙水力劈裂机制研究[J].岩土力学,2007,28(3):487-492.ZHU Jun-gao,WANG Jun-jie,ZHANG Hui.Study on mechanism of hydraulic fracturing in core of earth-rockfill dam[J].Rock and Soil Mechanics,2007,28(3):487-492.
[13]李全明,张丙印,于玉贞,等.土石坝水力劈裂发生过程的有限元数值模拟[J].岩土工程学报,2007,29(2):212-217.LI Quan-ming,ZHANG Bing-yin,YU Yu-zhen,et al.Numerical simulation of the process of hydraulic fracturing in earth and rockfill dams[J].Chinese Journal of Geotechnical Engineering,2007,29(2):212-217.
[14]朱晟,魏匡民,饶锡保.土石坝沥青混凝土心墙水力劈裂研究[J].水力发电学报,2013,32(1):218-222.ZHU Sheng,WEI Kuang-min,RAO Xi-bao.Study on hydraulic fracturing of asphalt concrete core in earth-rock dam[J].Journal of Hydroelectric Engineering,2013,32(1):218-222.
[15]王仁超,刘金飞,李仕奇.高心墙堆石坝填筑分期分区优化模型[J].土木工程学报,2008,41(2):105-110.WANG Ren-chao,LIU Jin-fei,LI Shi-qi.Optimization model for substage-zoning filling design of high core rockfill dams[J].China Civil Engineering Journal,2008,41(2):105-110.
[16]李守义,马成成,李炎隆,等.沥青混凝土心墙堆石坝的地震反应特性分析[J].水力发电学报,2013,32(6):198-202.LI Shou-yi,MA Cheng-cheng,LI Yan-long,et al.Seismic response analysis of rockfill dam with asphaltic concrete core[J].Journal of Hydroelectric Engineering,2013,32(6):198-202.
[17]徐芝纶.弹性力学[M].第五版.北京:高等教育出版社,2016.XU Zhi-lun.Elasticity mechanics[M].5th ed.Beijing:Higher Education Press,2006.
[18]TERZAGHI K.Evaluation of the coefficient of subgrade reaction[J].Geotechnique,1955,5(4):197-326.
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