薄高拱坝坝体屈曲稳定初探
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摘要
高拱坝结构稳定是坝体结构与坝基及周边岩体之间的复杂耦合作用的结果,其当前主要研究内容包括坝肩稳定、坝体上滑稳定和坝体结构稳定等,高拱坝结构稳定是拱坝研究与设计的重要课题之一。由于我国西南和西北正在修建和即将修建的一些300m级的特高拱坝越来越多,且随着拱坝体形优化设计及高强度混凝土材料的应用使坝体的厚度越来越薄,拱坝部分区域已接近薄壳结构,可能导致坝体结构失稳的发生。以往坝工界对坝体应力、坝基坝肩稳定和坝体上滑失稳等问题研究较多,而对坝体结构稳定研究则较少,特别是对于坝高200m以上的高拱坝,无规范可依。目前高薄拱坝的坝体屈曲稳定影响研究的核心问题是:“高薄拱坝何时需考虑屈曲失稳影响?”、“在坝高一定下,‘临界柔度系数’是否存在?如果存在又是多少?”等。由于高薄拱坝的坝体屈曲稳定影响涉及因素较多,复杂性较大,当前国内外还未得出深刻的结论。因此,目前薄高拱坝实践设计中均逐一进行屈曲稳定校核,使得薄高拱坝的优化设计增加了相当大的计算量和不便。
基于以上问题,本文将通过理论分析和数值模拟等方法,结合其他学者的研究成果,并通过对国内外实际已建拱坝工程的运行情况,综合分析研究了高薄拱坝坝体屈曲稳定的影响,为高薄拱坝的坝体屈曲稳定影响的深入研究提供基础。本文主要研究内容如下:
(1)对拱坝的拱梁分载法理论进行归纳总结,对冯广宏(1980)提出的特殊拱梁分载法:“微分法(导数法)”进行分析,通过工程实例比较分析,认为微分法更简单实用。基于结构力学方法及数值分析原理,对拱梁分载法中梁的变位系数进行了深入研究,认为当前采用的变位系数误差在10%以内,基本满足工程计算要求,但部分变位系数误差相对较大,本文基于数值分析理论对其进行修正,修正后误差由原来最大8%降低到1%以内,并给出了张量表达式。
(2)基于拱梁分载法理论,对圆弧型双曲高拱坝的水平拱圈的非线性屈曲进行了初步研究,认为经典屈曲理论高估了水平拱圈的抗屈曲性能,拱坝水平拱圈的屈曲临界荷载应采用非线性屈曲理论计算。基于Pi等人的研究成果,应用能量法、数值内插和拟合的思想,得出了高拱坝水平拱圈在弹性地基(转动弹性约束、径向、环向弹性约束)和等温变荷载影响下的临界屈曲荷载近似计算公式,为高薄拱坝水平拱圈的抗屈曲稳定研究奠定了基础。
(3)基于拱梁分载法理论,对圆弧型双曲拱坝和抛物线型双曲拱坝的水平拱圈的力学特性进行比较研究,得出了不同矢跨比和厚跨比下两种拱圈的弯矩、轴力分布图,认为抛物拱拱端的弯矩比圆拱拱端的弯矩更集中,特别当水平拱圈的矢跨比较大时,抛物线型双曲拱坝水平拱圈的拱端上游易出现较大的拉应力,建议抛物线型双曲高拱坝水平拱圈拱端厚度大于拱冠厚度。对抛物线型双曲拱坝的水平拱圈的抗屈曲特性进行研究,并与圆弧拱进行比较分析,认为抛物拱的抗屈曲性能稍强于圆拱。基于结构扰动理论对两种拱结构进行了简单的敏感分析,认为当两种拱结构的厚跨比较小时(T/L<0.03),拱内应力随结构扰动较敏感;矢跨比对拱应力扰动影响不是很大,但矢跨比越小,其扰动敏感性增强。
(4)对抛物线型双曲拱坝在多拱多梁理论下的抗屈曲理论进行了近似分析,假设水荷载方向近似为垂直于水平拱跨距方向,通过虚功原理对水平拱圈在受非均布荷载下的抗屈曲特性进行了近似研究,得到水平拱圈临界屈曲荷载分布系数的控制方程,并给出了近似屈曲安全系数的求解方程。
(5)通过统计分析的方法得出了高拱坝的经验开裂界限柔度系数C与坝高H和坝顶河谷宽B之间的关系式;同时基于典型拱坝纵断面展开模型的几何计算,得出高拱坝的柔度系数C与厚高比之间T/H的关系式函数,该函数与坝高H无关,与拱坝纵断面展开图几何形状参数、拱冠梁厚度分布有关;结合以上两公式,通过参数代换得出典型高薄拱坝的厚高比T/H与坝高H和河谷宽B之间的关系式,从而得到拱坝底厚TB的建议公式。通过比较分析认为美国勘务局(1984)建议拱坝底厚公式对于坝高较高(300m)的拱坝计算的建议底厚太大,完全无参考价值;对于我国《水工设计手册》(1987)的建议底厚相对偏小,而本文建议公式更合理,更有设计参考价值。
(6)基于拱冠梁法,对圆弧型双曲高薄拱坝水平拱圈的抗屈曲和强度安全之间的力学关系进行了研究,分析了混凝土等级、设计工况等因素的影响,认为混凝土材料等级提高到C45时,且坝顶厚径比(T/R)大于0.03时(厚跨比T/B>0.0173),高拱坝的水平拱圈(等厚)的强度破坏一般先于屈曲破坏发生,此时可忽略屈曲稳定对坝体稳定的影响。但由于拱冠梁法未能充分体现拱坝的空间效应,并且拱坝结构稳定是坝体、坝基和库水之间复杂耦合的结果,其影响因素较大,因此该结论有待于通过拱坝空间理论的进一步证实。最后通过工程实际大量计算及本文基于拱冠梁法的研究成果,偏保守地建议对于坝顶拱圈的厚跨比T/B<0.015的高薄拱坝(300m级别的)应该进行抗屈曲稳定分析,特别是在进行优化设计过程中,需进行抗屈曲约束控制,并给出了临界柔度系数计算公式。
(7)通过对典型高拱坝模型数值模拟成果的分析,分别得出典型单曲、双曲高拱坝的整体稳定超载安全系数与坝高及柔度系数之间的拟合关系式;同时得出坝高、坝体厚度、周边约束条件、坝址地质状况及河谷对称性等主要因素对坝体整体稳定的影响关系。并对锦屏一级拱坝和小湾拱坝的整体稳定性分别进行了深入研究,认为拱坝(锦屏拱坝)坝基的不对称性不仅影响把体内的应力分析不均,还降低了拱坝的结构稳定承载力;拱坝(小湾)设缝后拱坝拱的作用增强、梁的作用削弱,整体刚度略有降低,但对拱坝整体安全性影响很小,设缝位置处于拉应力区,可以起到释放拉应力的作用,对改善坝踵应力状态有利。
Structural stability of arch dams is comprehensive stability between dam body,foundation of dam and their interafee. It contains abutment stability,up-slide stability and structural stability of dam body etc,which is one of the vital subjects in arch dam design and research.There are many hight arch dam (hight of 300m level ) that buliding and would building in the south-west and north-west of china.As the increased levels of concrete and thinner dam body with the use of optimum designing, the local regions of hight arch dams approach thin shell structure,which will lead to the structural buckling. Anciently study almost on dam body stress,the abutment stability and up-slide stbaility is rather abundant by the dam engineers,but quite few on the structural stbaility of dam body. Because the hight arch whose hight is over 200m is not inclued in the Concrete arch dam design standard(2003) of china, the research structural stability of dam body is a difficult challenge for dam engineers.The dilemma of this subject is:“How thin the dam body is that arch dam should considering the structural stability?”,“Whether the critical flexibity confficient of arch dam which is difinited by DingXiao tang is exist ? And What’s it if exists?”,“What’s the relation between the structural stability of dam body and the stress safety of dam material?”Because this subject relates many other codition such as: the valley shape, distribution of faults around arch dam,earthquake and so on, the research of structural stability of arch dam is so difficult that the dam engineers always analysis the structural stability of hight arch dam in addtion in the arch dam designing.
In this paper,we studied the tructural stability of hight arch dam by crown-cantilever method and theory of shell and FEM numerical analysis. Mainly includes the several aspects as following:
(1) The trial load method of arch dam is comprehensive dicribed in this paper,and a new method called differential method which is given by FengGuang hong in 1980.Compared by actual project, we conclude that the differential method is more practical and convenient than the common crown contilever method. Beside, the displacement cofficient of crown contilever are also discussed. By actual project,we conclue that the errors of the existing cofficients of crown contilever in arch dam are less than 10%. And some of cofficients whose errors are more larger are corrected.
(2) The critical buckling load of arches are researched. We conclude that the classic theory overestimated the critical buckling load of arches, and the non-linear theory is more suitable for horizontal arch buckling in arch dam. Beside, we discuss the influence of the elasic foundation and temperature load to the horizontal arch buckling in arch dam.And the empirical formula of the critical buckling load of arches which are effected by the elasic foundation and temperature load is given.
(3) Base on crown-cantilever method, the mechanical properties and structural stability of the parabolic arch and circular arch are compared.And the internal forces of parabolic arch in different f/L are given. We conclude that circular arch is better than parabolic arch in mechanical properties aspact. However, parabolic arch is little better than circular arch in structural stability aspact. The effect of the internal force in arches with structural perturbation are discussed.And we conclude that the effect of the internal force in arches with structural perturbation is more sensitivity when T/B of arch is smaller than 0.03.
(4) The buckling of parapoblic arches with non-uniform loads of arch dam are approximate researched by the pinciple of virtual work method. And structual safety factors of parapoblic arches in arch dam are given in this paper.
(5) Base on the calculation of statistical method, the experience function of the critical cracking flexibility cofficient of arch dam which is related with the height of arch dam and ratio of the valley width to height is given. Beside, we also get the experience function of the thickness to height ratio with the height of arch dam and the ratio B/H of arch dam. Those experience function of key cofficient for arch dam is very helpful for dam engineers.
(6) By the crown-cantilever method, the relations between the tructural stability of arch dam and the stress safety of dam material in the circular arch dam under different condition and level of concrete are researched. And we conclued that the safety of arch dam is dominated by the sress safety of of dam material when the thickness to radius ratio of horizontal arch in hight arch dam is larger than 0.03, and the structual stability of dam body could be ignored at that condition. However, as the stability of arch dam is related with many other complex factors and the crown-cantilever method is approximation, we should continue confirming those conclusion by 3D-method.
(7) Base on the FEM numerical calculation, the experience function of tructural stability cofficient of arch dams which are related with the flexibility cofficient and dam heigh are given. Beside, we also analysis the relation between tructural stability of arch dam and other main factors such as dam heigh, thickness of dam, end-restraits and so on. And the JinPing hight arch dam and XiaoWan hight arch dam is analysised by FEM numerical method. At last, we consist that the tructural stability of arch dam should must be considered when the thickness to valley width ratio of top arch in arch dam is smaller than 0.015, expecially in the shape optinoization of hight arch dam.
基于以上问题,本文将通过理论分析和数值模拟等方法,结合其他学者的研究成果,并通过对国内外实际已建拱坝工程的运行情况,综合分析研究了高薄拱坝坝体屈曲稳定的影响,为高薄拱坝的坝体屈曲稳定影响的深入研究提供基础。本文主要研究内容如下:
(1)对拱坝的拱梁分载法理论进行归纳总结,对冯广宏(1980)提出的特殊拱梁分载法:“微分法(导数法)”进行分析,通过工程实例比较分析,认为微分法更简单实用。基于结构力学方法及数值分析原理,对拱梁分载法中梁的变位系数进行了深入研究,认为当前采用的变位系数误差在10%以内,基本满足工程计算要求,但部分变位系数误差相对较大,本文基于数值分析理论对其进行修正,修正后误差由原来最大8%降低到1%以内,并给出了张量表达式。
(2)基于拱梁分载法理论,对圆弧型双曲高拱坝的水平拱圈的非线性屈曲进行了初步研究,认为经典屈曲理论高估了水平拱圈的抗屈曲性能,拱坝水平拱圈的屈曲临界荷载应采用非线性屈曲理论计算。基于Pi等人的研究成果,应用能量法、数值内插和拟合的思想,得出了高拱坝水平拱圈在弹性地基(转动弹性约束、径向、环向弹性约束)和等温变荷载影响下的临界屈曲荷载近似计算公式,为高薄拱坝水平拱圈的抗屈曲稳定研究奠定了基础。
(3)基于拱梁分载法理论,对圆弧型双曲拱坝和抛物线型双曲拱坝的水平拱圈的力学特性进行比较研究,得出了不同矢跨比和厚跨比下两种拱圈的弯矩、轴力分布图,认为抛物拱拱端的弯矩比圆拱拱端的弯矩更集中,特别当水平拱圈的矢跨比较大时,抛物线型双曲拱坝水平拱圈的拱端上游易出现较大的拉应力,建议抛物线型双曲高拱坝水平拱圈拱端厚度大于拱冠厚度。对抛物线型双曲拱坝的水平拱圈的抗屈曲特性进行研究,并与圆弧拱进行比较分析,认为抛物拱的抗屈曲性能稍强于圆拱。基于结构扰动理论对两种拱结构进行了简单的敏感分析,认为当两种拱结构的厚跨比较小时(T/L<0.03),拱内应力随结构扰动较敏感;矢跨比对拱应力扰动影响不是很大,但矢跨比越小,其扰动敏感性增强。
(4)对抛物线型双曲拱坝在多拱多梁理论下的抗屈曲理论进行了近似分析,假设水荷载方向近似为垂直于水平拱跨距方向,通过虚功原理对水平拱圈在受非均布荷载下的抗屈曲特性进行了近似研究,得到水平拱圈临界屈曲荷载分布系数的控制方程,并给出了近似屈曲安全系数的求解方程。
(5)通过统计分析的方法得出了高拱坝的经验开裂界限柔度系数C与坝高H和坝顶河谷宽B之间的关系式;同时基于典型拱坝纵断面展开模型的几何计算,得出高拱坝的柔度系数C与厚高比之间T/H的关系式函数,该函数与坝高H无关,与拱坝纵断面展开图几何形状参数、拱冠梁厚度分布有关;结合以上两公式,通过参数代换得出典型高薄拱坝的厚高比T/H与坝高H和河谷宽B之间的关系式,从而得到拱坝底厚TB的建议公式。通过比较分析认为美国勘务局(1984)建议拱坝底厚公式对于坝高较高(300m)的拱坝计算的建议底厚太大,完全无参考价值;对于我国《水工设计手册》(1987)的建议底厚相对偏小,而本文建议公式更合理,更有设计参考价值。
(6)基于拱冠梁法,对圆弧型双曲高薄拱坝水平拱圈的抗屈曲和强度安全之间的力学关系进行了研究,分析了混凝土等级、设计工况等因素的影响,认为混凝土材料等级提高到C45时,且坝顶厚径比(T/R)大于0.03时(厚跨比T/B>0.0173),高拱坝的水平拱圈(等厚)的强度破坏一般先于屈曲破坏发生,此时可忽略屈曲稳定对坝体稳定的影响。但由于拱冠梁法未能充分体现拱坝的空间效应,并且拱坝结构稳定是坝体、坝基和库水之间复杂耦合的结果,其影响因素较大,因此该结论有待于通过拱坝空间理论的进一步证实。最后通过工程实际大量计算及本文基于拱冠梁法的研究成果,偏保守地建议对于坝顶拱圈的厚跨比T/B<0.015的高薄拱坝(300m级别的)应该进行抗屈曲稳定分析,特别是在进行优化设计过程中,需进行抗屈曲约束控制,并给出了临界柔度系数计算公式。
(7)通过对典型高拱坝模型数值模拟成果的分析,分别得出典型单曲、双曲高拱坝的整体稳定超载安全系数与坝高及柔度系数之间的拟合关系式;同时得出坝高、坝体厚度、周边约束条件、坝址地质状况及河谷对称性等主要因素对坝体整体稳定的影响关系。并对锦屏一级拱坝和小湾拱坝的整体稳定性分别进行了深入研究,认为拱坝(锦屏拱坝)坝基的不对称性不仅影响把体内的应力分析不均,还降低了拱坝的结构稳定承载力;拱坝(小湾)设缝后拱坝拱的作用增强、梁的作用削弱,整体刚度略有降低,但对拱坝整体安全性影响很小,设缝位置处于拉应力区,可以起到释放拉应力的作用,对改善坝踵应力状态有利。
Structural stability of arch dams is comprehensive stability between dam body,foundation of dam and their interafee. It contains abutment stability,up-slide stability and structural stability of dam body etc,which is one of the vital subjects in arch dam design and research.There are many hight arch dam (hight of 300m level ) that buliding and would building in the south-west and north-west of china.As the increased levels of concrete and thinner dam body with the use of optimum designing, the local regions of hight arch dams approach thin shell structure,which will lead to the structural buckling. Anciently study almost on dam body stress,the abutment stability and up-slide stbaility is rather abundant by the dam engineers,but quite few on the structural stbaility of dam body. Because the hight arch whose hight is over 200m is not inclued in the Concrete arch dam design standard(2003) of china, the research structural stability of dam body is a difficult challenge for dam engineers.The dilemma of this subject is:“How thin the dam body is that arch dam should considering the structural stability?”,“Whether the critical flexibity confficient of arch dam which is difinited by DingXiao tang is exist ? And What’s it if exists?”,“What’s the relation between the structural stability of dam body and the stress safety of dam material?”Because this subject relates many other codition such as: the valley shape, distribution of faults around arch dam,earthquake and so on, the research of structural stability of arch dam is so difficult that the dam engineers always analysis the structural stability of hight arch dam in addtion in the arch dam designing.
In this paper,we studied the tructural stability of hight arch dam by crown-cantilever method and theory of shell and FEM numerical analysis. Mainly includes the several aspects as following:
(1) The trial load method of arch dam is comprehensive dicribed in this paper,and a new method called differential method which is given by FengGuang hong in 1980.Compared by actual project, we conclude that the differential method is more practical and convenient than the common crown contilever method. Beside, the displacement cofficient of crown contilever are also discussed. By actual project,we conclue that the errors of the existing cofficients of crown contilever in arch dam are less than 10%. And some of cofficients whose errors are more larger are corrected.
(2) The critical buckling load of arches are researched. We conclude that the classic theory overestimated the critical buckling load of arches, and the non-linear theory is more suitable for horizontal arch buckling in arch dam. Beside, we discuss the influence of the elasic foundation and temperature load to the horizontal arch buckling in arch dam.And the empirical formula of the critical buckling load of arches which are effected by the elasic foundation and temperature load is given.
(3) Base on crown-cantilever method, the mechanical properties and structural stability of the parabolic arch and circular arch are compared.And the internal forces of parabolic arch in different f/L are given. We conclude that circular arch is better than parabolic arch in mechanical properties aspact. However, parabolic arch is little better than circular arch in structural stability aspact. The effect of the internal force in arches with structural perturbation are discussed.And we conclude that the effect of the internal force in arches with structural perturbation is more sensitivity when T/B of arch is smaller than 0.03.
(4) The buckling of parapoblic arches with non-uniform loads of arch dam are approximate researched by the pinciple of virtual work method. And structual safety factors of parapoblic arches in arch dam are given in this paper.
(5) Base on the calculation of statistical method, the experience function of the critical cracking flexibility cofficient of arch dam which is related with the height of arch dam and ratio of the valley width to height is given. Beside, we also get the experience function of the thickness to height ratio with the height of arch dam and the ratio B/H of arch dam. Those experience function of key cofficient for arch dam is very helpful for dam engineers.
(6) By the crown-cantilever method, the relations between the tructural stability of arch dam and the stress safety of dam material in the circular arch dam under different condition and level of concrete are researched. And we conclued that the safety of arch dam is dominated by the sress safety of of dam material when the thickness to radius ratio of horizontal arch in hight arch dam is larger than 0.03, and the structual stability of dam body could be ignored at that condition. However, as the stability of arch dam is related with many other complex factors and the crown-cantilever method is approximation, we should continue confirming those conclusion by 3D-method.
(7) Base on the FEM numerical calculation, the experience function of tructural stability cofficient of arch dams which are related with the flexibility cofficient and dam heigh are given. Beside, we also analysis the relation between tructural stability of arch dam and other main factors such as dam heigh, thickness of dam, end-restraits and so on. And the JinPing hight arch dam and XiaoWan hight arch dam is analysised by FEM numerical method. At last, we consist that the tructural stability of arch dam should must be considered when the thickness to valley width ratio of top arch in arch dam is smaller than 0.015, expecially in the shape optinoization of hight arch dam.
引文
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