高拱坝及反拱水垫塘结构泄洪安全分析与模拟
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摘要
我国虽然在高拱坝的建造、设计与研究上取得了丰硕的成果,但是高拱坝的设计还远未达到“自由王国”的境界,仍有一些重大问题需要解决:高拱坝的合理设计原则、标准和要求;高拱坝的精确动力分析和抗震措施;高拱坝的泄洪、消能、防冲问题;高拱坝的模型试验问题等。本文针对高拱坝的模型试验问题、拱坝流激振动响应及水垫塘防护结构稳定性这些问题,通过水弹性模型试验、理论分析及有限元分析对这些问题进行了研究,建立了相关的计算方法,得出一些有意义的结论。
水弹性模型可以同时满足水力学相似和结构力学相似,是对“结构-水体-地基-动荷载”四位一体的流固振动系统的模拟。本文详细论述了水弹性模型的相似原理及模拟范围、材料特性对拱坝动力特性的影响,给出水弹性模型的一般模拟范围。采用1:100大比尺水弹性模型对拉西瓦高拱坝及反拱型水垫塘流激振动响应进行了测试分析。
在实际工程的原型或模型动力试验中,实测动力响应测点总是有限的,特别是原型观测中的测点有时更少,难以全面反映水工结构的振动响应特征。本文在流激振动正反分析方法的基础上,将引起拱坝结构振动的三个激振源视为三个独立的、不相关的等效荷载,采用遗传算法得到等效荷载,进而利用正分析方法得到整个结构的动力响应以及进行振源分析。此外又针对具有多个测点同步测试结果的情况,给出一种基于模态叠加法的反分析方法,其实质是建立在模态的正交性及展开定理基础上的一种求解动力响应的近似方法。应用上述两种方法,对拉西瓦拱坝水弹性模型试验结果进行了反分析。
高坝水垫塘在泄洪期间起到消除下泄水流能量的作用,其自身的稳定是实现消能和防冲的关键。在水动力荷载的作用下,其受力和运动过程十分复杂。对它的数值模拟需要考虑以下三个方面:锚固钢筋与底板、地基之间的粘结滑移;底板之间、底板与基岩之间、底板与拱座之间的接触以及底板与水体之间的相互作用问题。本文基于粘结滑移理论、非线性接触理论及流固耦合理论,提出一种反拱水垫塘有限元模型,该模型采用三维非线性弹簧单元模拟锚固钢筋与基岩的位移协调、接触元模拟衬砌块接缝以及底板、拱座、基岩和边坡间的碰撞、滑移行为,采用附加质量考虑水体与底板之间的相互作用,较为全面反映水垫塘受力特点和底板-拱座-锚杆-基岩之间的相互作用机制。长潭岗水垫塘的工程实例说明了本模型的合理性及实用性。作为工程应用,本文以拉西瓦高拱坝的反拱型水垫塘为实例,对其在检修工况、正常工况以及泄洪工况下的结构稳定性进行了计算分析。然后,在建立有限元数学模型和反拱形水垫塘底板失稳模式基础上,分析了拉西瓦拱坝反拱水垫塘结构型式对稳定性的影响。
Although our country has made great achievement in the construction, design and research of the high arch dams, the design of high arch dams is still far from reaching the“realm of freedom”and some major problems still need to be solved. These problems include: rational design principle, standard and requirements of high arch dams; accurate dynamic analysis and seismic measures of high arch dams; hydraulic problems of flood discharging, energy dissipating and anti-scouring; model test of high arch dams, etc. This thesis aims to study the problems of model test of high arch dams, flow-induced vibration response and the stability of protective structure in plunge pool. Hydroelastic model test, theory analysis and finite element analysis are adopted in the study. Besides, in this paper the calculation method and some useful conclusion are presented.
The fluid-structure coupling system, which consists of dam, water, foundation and fluctuation pressure, is simulated by the hydroelastic model which can satisfy hydraulics similarity principle and structural dynamics similarity principle simultaneously. The similarity principle and the influence of both simulation context and material characteristics on dynamic characteristics of the arch dam are discussed in this paper, and then the proper simulation context is obtained. The hydroelastic model with a scale of 1:100 is adopted to measure and analysis the flow-induced vibration response of Laxiwa high arch dam and counter-arch plunge pool.
In the prototype or model test of project, there is always no enough survey points to reflect the vibration characteristic of hydro-structure overall, especially the survey points in the prototype test. Based on positive-back analysis algorithms of flow-induced vibration response, in this paper, three vibration sources are regard as three independent, incorrelate equivalent loads, genetic algorithm is adopted to get the equivalent loads, and then the positive analysis method is utilized to receive the whole structure’s vibratory response and carry on source analysis. Furthermore, aimed at having a lot of survey points’result by synchronous measure, a back analysis method is provided which is base on modal superposition. In essence, it is a similar method to solve the vibratory response which is base on the modal orthogonality and expansion theorem. The two above-mentioned methods are utilized to study an instance about hydroelastic model of Laxiwa arch dam.
The safety of protecting structure in high dam plunge pool is the key to the success of energy dissipation. Under the hydrodynamic load, the stress and movement course are complicated. In the numerical calculation three factors should be taken into account: the bond-slip between the anchor and slab or foundation, the contact action between slab and slab, slab and foundation, slab and abutment, and the fluid-structure coupling action. Based on bond-slip theory, nonlinear contact theory and fluid-structure coupling theory, a finite element model for counter-arch plunge pool is proposed in this paper. In the model, three-dimension nonlinear spring element is used to simulate the displacement cooperation between anchor and foundation, contact element is adopted to simulate the joint of slab and the collision or slip action among the slab, abutment, foundation and slope, the added mass is used to consider the fluid-structure coupling action, so this model reflects the stress characteristic and interaction of the slab, abutment, anchor and foundation overall. The case of the Changtangang plunge pool is demonstrated the rationality and practicability of the proposed model. As an engineering application, the structural stability under some important work condition of the plunge pool of Laxiwa arch dam is analyzed. Then based on the finite element model and destabilization mode of counter-arch plunge pool, the influence of the type of plunge pool is analyzed.
水弹性模型可以同时满足水力学相似和结构力学相似,是对“结构-水体-地基-动荷载”四位一体的流固振动系统的模拟。本文详细论述了水弹性模型的相似原理及模拟范围、材料特性对拱坝动力特性的影响,给出水弹性模型的一般模拟范围。采用1:100大比尺水弹性模型对拉西瓦高拱坝及反拱型水垫塘流激振动响应进行了测试分析。
在实际工程的原型或模型动力试验中,实测动力响应测点总是有限的,特别是原型观测中的测点有时更少,难以全面反映水工结构的振动响应特征。本文在流激振动正反分析方法的基础上,将引起拱坝结构振动的三个激振源视为三个独立的、不相关的等效荷载,采用遗传算法得到等效荷载,进而利用正分析方法得到整个结构的动力响应以及进行振源分析。此外又针对具有多个测点同步测试结果的情况,给出一种基于模态叠加法的反分析方法,其实质是建立在模态的正交性及展开定理基础上的一种求解动力响应的近似方法。应用上述两种方法,对拉西瓦拱坝水弹性模型试验结果进行了反分析。
高坝水垫塘在泄洪期间起到消除下泄水流能量的作用,其自身的稳定是实现消能和防冲的关键。在水动力荷载的作用下,其受力和运动过程十分复杂。对它的数值模拟需要考虑以下三个方面:锚固钢筋与底板、地基之间的粘结滑移;底板之间、底板与基岩之间、底板与拱座之间的接触以及底板与水体之间的相互作用问题。本文基于粘结滑移理论、非线性接触理论及流固耦合理论,提出一种反拱水垫塘有限元模型,该模型采用三维非线性弹簧单元模拟锚固钢筋与基岩的位移协调、接触元模拟衬砌块接缝以及底板、拱座、基岩和边坡间的碰撞、滑移行为,采用附加质量考虑水体与底板之间的相互作用,较为全面反映水垫塘受力特点和底板-拱座-锚杆-基岩之间的相互作用机制。长潭岗水垫塘的工程实例说明了本模型的合理性及实用性。作为工程应用,本文以拉西瓦高拱坝的反拱型水垫塘为实例,对其在检修工况、正常工况以及泄洪工况下的结构稳定性进行了计算分析。然后,在建立有限元数学模型和反拱形水垫塘底板失稳模式基础上,分析了拉西瓦拱坝反拱水垫塘结构型式对稳定性的影响。
Although our country has made great achievement in the construction, design and research of the high arch dams, the design of high arch dams is still far from reaching the“realm of freedom”and some major problems still need to be solved. These problems include: rational design principle, standard and requirements of high arch dams; accurate dynamic analysis and seismic measures of high arch dams; hydraulic problems of flood discharging, energy dissipating and anti-scouring; model test of high arch dams, etc. This thesis aims to study the problems of model test of high arch dams, flow-induced vibration response and the stability of protective structure in plunge pool. Hydroelastic model test, theory analysis and finite element analysis are adopted in the study. Besides, in this paper the calculation method and some useful conclusion are presented.
The fluid-structure coupling system, which consists of dam, water, foundation and fluctuation pressure, is simulated by the hydroelastic model which can satisfy hydraulics similarity principle and structural dynamics similarity principle simultaneously. The similarity principle and the influence of both simulation context and material characteristics on dynamic characteristics of the arch dam are discussed in this paper, and then the proper simulation context is obtained. The hydroelastic model with a scale of 1:100 is adopted to measure and analysis the flow-induced vibration response of Laxiwa high arch dam and counter-arch plunge pool.
In the prototype or model test of project, there is always no enough survey points to reflect the vibration characteristic of hydro-structure overall, especially the survey points in the prototype test. Based on positive-back analysis algorithms of flow-induced vibration response, in this paper, three vibration sources are regard as three independent, incorrelate equivalent loads, genetic algorithm is adopted to get the equivalent loads, and then the positive analysis method is utilized to receive the whole structure’s vibratory response and carry on source analysis. Furthermore, aimed at having a lot of survey points’result by synchronous measure, a back analysis method is provided which is base on modal superposition. In essence, it is a similar method to solve the vibratory response which is base on the modal orthogonality and expansion theorem. The two above-mentioned methods are utilized to study an instance about hydroelastic model of Laxiwa arch dam.
The safety of protecting structure in high dam plunge pool is the key to the success of energy dissipation. Under the hydrodynamic load, the stress and movement course are complicated. In the numerical calculation three factors should be taken into account: the bond-slip between the anchor and slab or foundation, the contact action between slab and slab, slab and foundation, slab and abutment, and the fluid-structure coupling action. Based on bond-slip theory, nonlinear contact theory and fluid-structure coupling theory, a finite element model for counter-arch plunge pool is proposed in this paper. In the model, three-dimension nonlinear spring element is used to simulate the displacement cooperation between anchor and foundation, contact element is adopted to simulate the joint of slab and the collision or slip action among the slab, abutment, foundation and slope, the added mass is used to consider the fluid-structure coupling action, so this model reflects the stress characteristic and interaction of the slab, abutment, anchor and foundation overall. The case of the Changtangang plunge pool is demonstrated the rationality and practicability of the proposed model. As an engineering application, the structural stability under some important work condition of the plunge pool of Laxiwa arch dam is analyzed. Then based on the finite element model and destabilization mode of counter-arch plunge pool, the influence of the type of plunge pool is analyzed.
引文
[1] 朱伯芳,高季章,陈祖煜等,拱坝设计与研究,北京:中国水利水电出版社,2002
[2] 潘家铮,水工结构分析文集,北京:电力工业出版社,1981
[3] 潘家铮,何璄,中国大坝五十年,北京:中国水利水电出版社,2002
[4] 水工设计手册第五卷,混凝土坝,北京:水力电力出版社,1984
[5] 李瓒,陈飞,郑建波等,特高拱坝枢纽分析与重点问题研究,北京:中国电力出版社,2004
[6] 王日宣,崔广涛,拱坝溢流水舌冲击下游河床诱发坝体振动的研究,水利学报,1991(2),26-34
[7] 刑景棠,周盛等,流固耦合力学概述,力学进展,1997,27(1):19-38
[8] 傅作新,水-坝相互作用的若干有效解法,华东科技情报,1985,2:1-10
[9] 傅作新,吴斌元等,水坝库水与地基动力相互作用分析,华东水利学院学报,1985,1:1-10
[10] 傅作新,结构与水体的动力相互作用问题,水利水运科学研究,1982,2:105-119
[11] Javier Aviles,Xiangyue Li,Analytical-numerical solution for hydrodynamic pressures on dams with sloping face considering compressibility and viscosity of water,Computer & Structure,1998,56(4):481-488
[12] Tsai,C. S,Lee,Hydrodynamic pressure on gravity dams subjected to ground motion,Journal of Engineering Mechanics,ASCE,1989,115:598-617
[13] Aviles J.,Sanchez Sesma F.J.,Hydrodynamic pressures on dams with nonvertical upstream face,Journal of Engineering Mechanics,ASCE,1986,112:1054-1061
[14] Chong-Shien Tsal,George C.Lee and Robert L.Ketter,A semi-analytical method for time-domain analysis of dam-reservoir interactions,Inter.Jou.Numer.Meth.Eng.,1990,29:913-933
[15] O.C.Zienkiewicz,The finite element method,MCGRAW-WILL,1977
[16] 杜庆华,吴有生等,流固耦合振动问题的某些工程处理方法,固体力学学报,1988,9:49-61
[17] K.J.Bathe,W.F.Hahn,On transient analysis of fluid-structure systems,Computers & Structures,1979,10:383-391
[18] N.Akkas,H.U.Akay,C Yilmaz,Applicability of general-purpose finite element programs in solid-fluid interaction problems,Computers & Structures,1979,10:773-783
[19] E. L. Wilson,M. Khalvati,Finite element for dynamic analysis of fluid-solid systems,International Journal for Numerical Methods in Engineering,1983,19:1657-1668
[20] W.K.Liu,H.G.Chang,A method for computation for fluid-structure interaction,Computers & Structures,1985,20:31-320
[21] Harn C. Chen,Robert L. Taylor,Vibration analysis of fluid-solid systems using finite element displacement formulation , International Journal for Numerical Methods in Engineering,1990,29,683-698
[22] M.R.Maheri,M.R.Khodaer,Dynamic solution of 3-D structure-fluid system using a new lagrangian-based curvilinear fluid element,Dam Engineering,1997,8:83-122
[23] O.C.Zienkiewicz,P.Bettess,Fluid-structure dynamic interaction and wave forces,An introduction to numerical treatment,International Journal for Numerical Methods in Engineering,1978,13:1-16
[24] L Olson,K Bathe,Analysis of fluid-structure interactions,A direct symmetric coupled formulation based on the fluid velocity potential,Computers & Structures,1985,21:21-32
[25] 吴一红,谢省宗,水工结构流固耦合动力特性分析,水利学报,1995,1:27-32
[26] 吴一红,李世琴等,拱坝-库水-地基耦合系统坝身泄洪动力分析,1996,11:6-12
[27] 戴大农,王瑁成等,流固耦合系统动力响应的模态分析理论,固体力学学报,1990,11:306-312
[28] W.J.T.Daniel,Modal method in finite element fluid-structure Eigenvalue problems,International Journal for Numerical Methods in Engineering,1980,15(8):1161-1176
[29] 牟建耀,流固耦合分析的模态综合法,常州工业技术学院学报(自然科学版),1996,9:82-90
[30] 刑景棠,郑兆昌,基于弹性力学变分原理的模态综合法研究,固体力学学报,1983,2:248-257
[31] 刑景棠,考虑自由线性波的流固耦合动力分析的两个变分公式,航空学报,1988,9:A568-A571
[32] Hanna Y.G ., Humar J.L ., Boundary element analysis of fluid-domain ,J.Eng.Mech.Div.ASCE 108,1982
[33] Saini S.S.,Bettess P.,Zienkiweicz O.C.,Coupled Hydrodynamic Response of concrete gravity dams using finite and infinite elements.Earthquake Engineering and Structural Dynamics,1978,6,363-374
[34] R.K.Singh,T.Kant,A.Kakodkar,Coupled shell-fluid interaction problems with degenerate shell and three-dimensional fluid elements,Computers & Structures,1991,38:515-528
[35] Antes H.,Estorff O.V.,Analysis of absorption effects on the dynamic response of dam reservoir systems by BEM,Earthquake Engineering and Structural Dynamics,1987,15,1023-1036
[36] 宋崇民,张楚汉,水坝抗震分析的动力边界元方法,地震工程与工程振动,1988,4
[37] Zhang C.H.,Jin F,Time domain procedure of FE-BE-IBE coupling for seismic interaction of arch dam and canyons,Earthquake Engineering and Structural Dynamics,1181995,1,651-666
[38] 徐艳杰,张楚汉等,非线性拱坝-地基动力相互作用的 FE-BE-IBE 模型,清华大学学报,1998,11:99-103
[39] 傅作新,王立新等,拱坝的动水压力和拱坝库水的相互作用分析,第三届全国地震工程会议论文集(Ⅲ),1990,1271-1276
[40] Westergard H M,Water pressures on dams during earthquakes,ASCE,1933,98:418-472
[41] Zienkiewicz O C,Nath B,Earthquake hydrodynamic pressures on arch-dams and electric analogue solution,Proc.Inst.Civ.Eng.,1963,25:165-176
[42] A.K.Chopra,Hydrodynamic effects in earthquake response of arch dams,Proceedings of China-US Workshop on Earthquake Behavior of Arch Dams,Beijing,China,1987:110-129
[43] Ka-Lun Fok,A.K.Chopra,Earthquake analysis of arch dams including dam -water interaction,reservoir boundary absorption and foundation flexibility,Earthquake Engineering and Structural Dynamics,1986,14:155- 184
[44] Craig S.Porter,A.K.Chopra,Dynamic analysis of simple arch dams including hydrodynamic interaction,Earthquake Engineering and Structural Dynamics,1981,9:573-597
[45] J.F.Ha ll,A.K.Chopra,Hydrodynamic effects in the dynamic response of concrete gravity dams,Earthquake Engineering and Structural Dynamics,1982,10:333-345
[46] B.Nath,et al.,Coupled dynamic behavior of realistic arch dams including hydrodynamic and foundation interaction,Proc. Inst. of Civ.Eng.,Part2,Vol.73,Sept.,1982
[47] K a-Lun Fok,A.K.Chopra,Earthquake analysis and response of concrete arch dams,UCB/EERC-85/07
[48] 阎承大,张楚汉,拱坝地震动水压力分析的配点法,地震工程与工程振动,1990(4):73-82
[49] 陈厚群,候顺载,杨大伟,地震条件下拱坝库水相互作用的试验研究,水利学报,1989(7),29-39
[50] 崔广涛等,高水头大流量泄洪结构脉动荷载及其振动和地基反应,“七.五”国家重点科技攻关,国家自然科学基金资助项目研究成果之一——二滩水电站拱坝泄洪振动实验研究,天津大学水资源与港湾工程系,1991.3
[51] 崔广涛,林继镛,彭新民等,二滩拱坝泄洪振动水弹性模型研究,天津大学学报,1991,1
[52] 崔广涛等,高水头大流量泄洪振动及新型水垫塘研究,“八.五”国家重点科技攻关,国家自然科学基金资助项目研究成果之一——高拱坝大流量泄洪诱发振动研究,1996.3
[53] 崔广涛等,高水头大流量泄洪振动及新型水垫塘研究,“八.五”国家重点科技攻关,国家自然科学基金资助项目研究成果之二——高拱坝大流量泄洪动态仿真及振119动影响评估,1996.3
[54] 练继建等,金沙江溪洛渡水电站拱坝泄洪水弹性模型研究,天津大学水利水电工程系,2001
[55] 练继建等,黄河拉西瓦水电站坝身泄洪流激振动水弹性模型试验研究报告,天津大学水利水电工程系,2006.5
[56] 郭怀志,马启超,薛玺成等,岩体初始应力场的分析方法,岩土工程学报,1983,5(3):64-75
[57] 林世胜,中尾健儿,反算法的进一步探讨,岩土工程学报,1987,9(3)
[58] 陈国荣,姜弘道等,三维粘弹性参数反分析,河海大学学报,1996,24(6):25-28
[59] 沈珠江,堆石坝渗流变形的反馈分析,水利学报,1998(6):1-6
[60] 刘文宝,李术才,大坝位移反分析中测量误差对反演结果的影响,大坝观测与土工测试,1995,19(4):24-28
[61] 吴中如等著,水工建筑物安全监控理论及其应用,河海大学出版社,1990
[62] 吴中如,陈继愚,范树平等,用反演分析法推求连拱坝混凝土的力学参数和断裂韧度,大坝观测与土工测试,1986(1)
[63] 练继建,崔广涛,董淑芳,水工结构流激振动响应的反分析,水利水电技术,1998(8):51-54
[64] 练继建,崔广涛,林继镛,高拱坝泄洪振动的计算分析与验证,水利学报,1999,12:23-32
[65] 崔广涛,彭新民,苑希民等,高拱坝泄洪振动水弹性模型,1996,4:1-9
[66] 水利电力部成都勘测设计院,卡里巴(KARIBA)双曲拱坝—挑流消能,国外高坝泄洪消能工程实例,1984.8
[67] 刘沛清,高拱坝泄洪布置形式与消能防冲设计中的若干问题探讨,长江科学院院报,1999(5),17-21
[68] 刘沛清,高拱坝下游水垫塘底板块稳定性设计,水利学报,1999(2),5-12
[69] 安芸周一,关于自由跌落水舌的水垫效果的研究,国外科技增刊 (2),天津大学图书馆,1981.10
[70] 罗铭,郭亚昆,有界二元掺气射流水下扩散规律研究,水利学报,1992(7),29-34
[71] 安芸周一,关于拱坝中央溢流泄洪护坦上水垫效果的研究,国外科技增刊 (1),天津大学图书馆,1981(10),1-38
[72] Spyridon Beltaos and Nallamuthu Rajaratnam, Impinging Circular Turbulent Jets, Journal of the Hydraulics Division, ASCE, HY10, 1974.10
[73] 孙建,高拱坝坝身泄洪消能防冲研究[博士学位论文],北京:清华大学,2001。
[74] 石川中晴,自由跌落式消能工的水力机理(1),水工高速水流译文集,天津大学水工高速水流研究室,1980.7
[75] 练继建,二元射流作用下边壁动水荷载及其应用[硕士学位论文],天津:天津大学,1987
[76] 许多鸣,余常昭,平面射流对槽底的冲击压强极其脉动特性,水利学报,1983(5),52-58
[77] 崔广涛,陈荣光,林继镛,挑跌流对河床的动水压力及基岩的防护问题,天津大学学报,1982(2)
[78] 黄种为,陈瑾,高拱坝泄洪与水垫塘底板动水压力问题的试验研究,水利学报,1992(11),50-56
[79] S.M.Borghei, Effect of Plunge Pool Width on Hydrodynamic Pressures due to Vertical Jet. 29thIAHR Proceedings, 2001, Them D,Vol.Ⅰ , 622-627.
[80] 尤季茨基,依沃依洛夫,西沃洛式斯卡亚等,水流动水压力对溢流坝挑流鼻坎下游河床影响的模型试验和原型观测,高速水流译文集,长科院译,水利电力出版社,1979,242-252。
[81] 林继镛,练继建,二元射流作用下点面脉动壁压的幅值计算,水利学报,1988(12),34-40
[82] G.Rehbinder, Slot Cutting in Rock with A High Speed A Water Jet, Int. J.Rock Mech. Min. Sic., Vol.14, 1977, 229-234
[83] 赵耀南,梁兴蓉,水流脉动压力沿缝隙的传播规律,天津大学学报,1988(3),55-65
[84] Fiorotto, V. and Rinaldo , A . , Turbulent pressure fluctuations under hydraulic jumps, J. Hydr. Res., IAHR, VOL. 30, NO. 4, 1992.
[85] 刘沛清,冬俊瑞,余常昭,在岩缝中脉动压力传播机理探讨,水利学报,1994(12),31-36。
[86] 刘沛清,李忠义,冬俊瑞,用二维瞬变流方程分析缝面层中脉动压力传播规律,水利学报,1996(4),27-32。
[87] 艾克明,拱坝泄洪与消能的水力设计和计算,水利电力出版社,1987.8。
[88] Г.И.卓高瓦泽著,郑顺炜译,英古里水电站,中国电力企业联合会,1992
[89] 崔广涛,彭新民,杨敏,反拱形水垫塘——窄河谷大流量高坝泄洪消能工的合理选择,水利水电技术,2001,12:1-3
[90] 杨敏,彭新民,崔广涛,水垫塘底板的试验仿真模拟研究,水力水电技术,2002,33(3):40-42
[91] 彭新民,王继敏等,拱坝水垫塘拱形底板受力与稳定性实验研究,水力发电学报,1999,(2):52-59.
[92] 练继建,杨敏等,反拱型水垫塘底板结构的稳定性研究,水利水电技术,2001, 32 (12):24-27
[93] 孙建,陈长植,反拱水垫塘与平底水垫塘底板稳定性诸方面之比较,长江科学院院报,2003,20(4):3-6
[94] 中川博次,洪崎一博,多田敏一,拱坝泄水建筑物的水力学性能研究,国外科技增刊(1),天津大学图书馆,1981,10。
[95] 岩佐义郎,中川博次,藤本成,日本多目标工程消能工的历史性发展,高速水流译文集,水利电力出版社,1979,12,433-440。
[96] 杨敏,高坝消力塘水动力特性与防护结构的安全研究:[博士学位论文],天津:天津大学,2003
[97] 郭航忠,水垫塘底板稳定性判别标准研究:[硕士学位论文],天津:天津大学,2003,12
[98] 符晓,水垫塘衬砌结构非线性静动力特性研究:[硕士学位论文],天津:天津大学,2004,12
[99] 王继敏,王珮璜,长潭岗水电站反拱形水垫塘研究及应用,水利水电技术,2002,33 (7):10-12
[100] 杨令强,练继建,张社荣等,高拱坝水垫塘反拱底板衬砌结构的非线性静力分析,水利学报,2002,9:77-81
[101] 史军,杨敏等,水垫塘反拱形底板稳定性的块体弹簧元分析,水力发电学报,2004,23(2):73-78
[102] 郭怀志,溢流拱坝下反拱式消力池试验研究与工程设计,海河水利,1980, 7
[103] 杨敏,练继建,水垫塘反拱形底板体型研究,水力发电学报,2002,(4):45-50
[104] 孙建,陈长植,反拱水垫塘拱端力变化规律的试验研究,水力发电学报,2002,(4):51-60
[105] 崔广涛,练继建,彭新民等,水流动力荷载与流固相互作用,北京:中国水利水电出版社,1999,11
[106] 赵耀南,重力相似水力模型中紊流微结构的相似律,水利学报,1988,8:97-101
[107] 谢省宗,李世琴,吴一红等,高拱坝坝身泄洪流激振动水弹性模型模拟研究,水利学报,1997,12:1-9
[108] Holland J.H.,Adaptation in natural and artificial system,The University of Michigan Press,1975,MIT press,1992
[109] 周明,孙树栋,遗传算法原理及应用,北京:国防工业出版社,1999
[110] 王小平,曹立明,遗传算法——理论、应用与软件实现,西安:西安交通大学出版社,2001
[111] 李东序,高等结构力学,长沙:国防科技大学出版社,1997
[112] 王传志、腾志明,钢筋混凝土结构原理,中国建筑工业出版社,1985
[113] 周志祥主编,高等钢筋混凝土结构,北京:人民交通出版社,2002
[114] Bresler B and Bertero V V,Behavior of Reinforced Concrete under Repeated Loads,J.Struct.DIV.,ASEC,1968.9,94,ST6:1567～1590
[115] Nilson A H,Nonlinear Analysis of Reinforced Concrete by the Finite Element Method,ACI Journal,1968.9:757～766
[116] Houde J,Study of Force-Displacement Relationships for the Finite Element Analysis of Reinforced Concrete,In:Dept. of Civil England Applied Mechanics. Report No.73-2 Montreal:Mc Gill University,1973.12
[117] 腾志明主编,钢筋混凝土基本构件(第二版),北京:清华大学出版社,1987
[118] Comite Euro-International du Betu.D’information No.213/214 CEB-FIP Model Code 1990(Concrete Structures).Lausanne,May 1993
[119] 徐有邻,钢筋混凝土粘结滑移本构关系的简化模型,工程力学,1997 增刊:34-38,
[120] 徐有邻,沈文都,汪洪,钢筋混凝土粘结锚固性能的试验研究,建筑结构学报,1994(3):26-37
[121] ANSYS 高级技术分析指南,ANSYS 中国,2000.1
[122] ANSYS 非线性分析指南,ANSYS 中国,2000.1
[123] ANSYS Element Reference,Electronic Release,SAS IP,Inc.,1998
[124] ANSYS Theory Reference,Electronic Release,SAS IP,Inc.,1998
[125] Bangash M Y H.Numercical modeling of bond and bond-slip.Concrete and Concrete Structures:Numerical Modeling and Applications.London,New York:Eisevier Applied Science,1985
[126] Bazant Z P,et.al..Task Committee on Finite Element Analysis of Reinforced Concrete Structures.State-of-theArt Report on Finite Element Analysis of Reinforced Concrete, New York:Published by ASCE,1982
[127] 朱伯芳,有限单元法原理与应用,北京:中国水利水电出版社,1998
[128] 沈聚敏,王传志,江见鲸.钢筋混凝土有限元与板壳极限分析.北京:清华大学出版社,1993
[129] 宋启根,单炳梓,金芷生,朱万福编著.钢筋混凝土力学.南京:南京工学院出版社,1986
[130] 朱伯龙,董振祥,钢筋混凝土非线性分析,上海:同济大学出版社,1985
[131] 杨勇,型钢混凝土粘结滑移基本理论及应用研究:[博士学位论文],西安:西安建筑科技大学,2003
[132] 王彦宏,型钢混凝土偏压柱粘结滑移性能及应用研究:[博士学位论文],西安西安建筑科技大学,2004
[133] 张健民,杨永全,王玉容等,水垫塘底板上举力的数值研究,水动力学研究与进展,2003,(18)1:63-67
[134] 崔广涛,彭新民,练继建等,高拱坝大流量泄洪振动及新型水垫塘研究,“八.五”国家重点科技攻关,国家自然科学基金资助项目研究成果之三——拱坝水垫塘反拱形底板研究,天津大学水资源与港湾工程系,1996.3
[135] 刘鹏,反拱形水垫塘衬砌结构的稳定性研究:[硕士学位论文],天津:天津大学,2005
[136] 王继敏,崔广涛,李延农等,拱坝反拱形水垫塘原型研究,新世纪水利工程科技前沿,天津大学出版社,2006,299-312
[137] 崔广涛,练继建,彭新民等,水流诱发水工结构振动与水弹性模型,新世纪水利工程科技前沿,天津大学出版社,2006,568-578
[2] 潘家铮,水工结构分析文集,北京:电力工业出版社,1981
[3] 潘家铮,何璄,中国大坝五十年,北京:中国水利水电出版社,2002
[4] 水工设计手册第五卷,混凝土坝,北京:水力电力出版社,1984
[5] 李瓒,陈飞,郑建波等,特高拱坝枢纽分析与重点问题研究,北京:中国电力出版社,2004
[6] 王日宣,崔广涛,拱坝溢流水舌冲击下游河床诱发坝体振动的研究,水利学报,1991(2),26-34
[7] 刑景棠,周盛等,流固耦合力学概述,力学进展,1997,27(1):19-38
[8] 傅作新,水-坝相互作用的若干有效解法,华东科技情报,1985,2:1-10
[9] 傅作新,吴斌元等,水坝库水与地基动力相互作用分析,华东水利学院学报,1985,1:1-10
[10] 傅作新,结构与水体的动力相互作用问题,水利水运科学研究,1982,2:105-119
[11] Javier Aviles,Xiangyue Li,Analytical-numerical solution for hydrodynamic pressures on dams with sloping face considering compressibility and viscosity of water,Computer & Structure,1998,56(4):481-488
[12] Tsai,C. S,Lee,Hydrodynamic pressure on gravity dams subjected to ground motion,Journal of Engineering Mechanics,ASCE,1989,115:598-617
[13] Aviles J.,Sanchez Sesma F.J.,Hydrodynamic pressures on dams with nonvertical upstream face,Journal of Engineering Mechanics,ASCE,1986,112:1054-1061
[14] Chong-Shien Tsal,George C.Lee and Robert L.Ketter,A semi-analytical method for time-domain analysis of dam-reservoir interactions,Inter.Jou.Numer.Meth.Eng.,1990,29:913-933
[15] O.C.Zienkiewicz,The finite element method,MCGRAW-WILL,1977
[16] 杜庆华,吴有生等,流固耦合振动问题的某些工程处理方法,固体力学学报,1988,9:49-61
[17] K.J.Bathe,W.F.Hahn,On transient analysis of fluid-structure systems,Computers & Structures,1979,10:383-391
[18] N.Akkas,H.U.Akay,C Yilmaz,Applicability of general-purpose finite element programs in solid-fluid interaction problems,Computers & Structures,1979,10:773-783
[19] E. L. Wilson,M. Khalvati,Finite element for dynamic analysis of fluid-solid systems,International Journal for Numerical Methods in Engineering,1983,19:1657-1668
[20] W.K.Liu,H.G.Chang,A method for computation for fluid-structure interaction,Computers & Structures,1985,20:31-320
[21] Harn C. Chen,Robert L. Taylor,Vibration analysis of fluid-solid systems using finite element displacement formulation , International Journal for Numerical Methods in Engineering,1990,29,683-698
[22] M.R.Maheri,M.R.Khodaer,Dynamic solution of 3-D structure-fluid system using a new lagrangian-based curvilinear fluid element,Dam Engineering,1997,8:83-122
[23] O.C.Zienkiewicz,P.Bettess,Fluid-structure dynamic interaction and wave forces,An introduction to numerical treatment,International Journal for Numerical Methods in Engineering,1978,13:1-16
[24] L Olson,K Bathe,Analysis of fluid-structure interactions,A direct symmetric coupled formulation based on the fluid velocity potential,Computers & Structures,1985,21:21-32
[25] 吴一红,谢省宗,水工结构流固耦合动力特性分析,水利学报,1995,1:27-32
[26] 吴一红,李世琴等,拱坝-库水-地基耦合系统坝身泄洪动力分析,1996,11:6-12
[27] 戴大农,王瑁成等,流固耦合系统动力响应的模态分析理论,固体力学学报,1990,11:306-312
[28] W.J.T.Daniel,Modal method in finite element fluid-structure Eigenvalue problems,International Journal for Numerical Methods in Engineering,1980,15(8):1161-1176
[29] 牟建耀,流固耦合分析的模态综合法,常州工业技术学院学报(自然科学版),1996,9:82-90
[30] 刑景棠,郑兆昌,基于弹性力学变分原理的模态综合法研究,固体力学学报,1983,2:248-257
[31] 刑景棠,考虑自由线性波的流固耦合动力分析的两个变分公式,航空学报,1988,9:A568-A571
[32] Hanna Y.G ., Humar J.L ., Boundary element analysis of fluid-domain ,J.Eng.Mech.Div.ASCE 108,1982
[33] Saini S.S.,Bettess P.,Zienkiweicz O.C.,Coupled Hydrodynamic Response of concrete gravity dams using finite and infinite elements.Earthquake Engineering and Structural Dynamics,1978,6,363-374
[34] R.K.Singh,T.Kant,A.Kakodkar,Coupled shell-fluid interaction problems with degenerate shell and three-dimensional fluid elements,Computers & Structures,1991,38:515-528
[35] Antes H.,Estorff O.V.,Analysis of absorption effects on the dynamic response of dam reservoir systems by BEM,Earthquake Engineering and Structural Dynamics,1987,15,1023-1036
[36] 宋崇民,张楚汉,水坝抗震分析的动力边界元方法,地震工程与工程振动,1988,4
[37] Zhang C.H.,Jin F,Time domain procedure of FE-BE-IBE coupling for seismic interaction of arch dam and canyons,Earthquake Engineering and Structural Dynamics,1181995,1,651-666
[38] 徐艳杰,张楚汉等,非线性拱坝-地基动力相互作用的 FE-BE-IBE 模型,清华大学学报,1998,11:99-103
[39] 傅作新,王立新等,拱坝的动水压力和拱坝库水的相互作用分析,第三届全国地震工程会议论文集(Ⅲ),1990,1271-1276
[40] Westergard H M,Water pressures on dams during earthquakes,ASCE,1933,98:418-472
[41] Zienkiewicz O C,Nath B,Earthquake hydrodynamic pressures on arch-dams and electric analogue solution,Proc.Inst.Civ.Eng.,1963,25:165-176
[42] A.K.Chopra,Hydrodynamic effects in earthquake response of arch dams,Proceedings of China-US Workshop on Earthquake Behavior of Arch Dams,Beijing,China,1987:110-129
[43] Ka-Lun Fok,A.K.Chopra,Earthquake analysis of arch dams including dam -water interaction,reservoir boundary absorption and foundation flexibility,Earthquake Engineering and Structural Dynamics,1986,14:155- 184
[44] Craig S.Porter,A.K.Chopra,Dynamic analysis of simple arch dams including hydrodynamic interaction,Earthquake Engineering and Structural Dynamics,1981,9:573-597
[45] J.F.Ha ll,A.K.Chopra,Hydrodynamic effects in the dynamic response of concrete gravity dams,Earthquake Engineering and Structural Dynamics,1982,10:333-345
[46] B.Nath,et al.,Coupled dynamic behavior of realistic arch dams including hydrodynamic and foundation interaction,Proc. Inst. of Civ.Eng.,Part2,Vol.73,Sept.,1982
[47] K a-Lun Fok,A.K.Chopra,Earthquake analysis and response of concrete arch dams,UCB/EERC-85/07
[48] 阎承大,张楚汉,拱坝地震动水压力分析的配点法,地震工程与工程振动,1990(4):73-82
[49] 陈厚群,候顺载,杨大伟,地震条件下拱坝库水相互作用的试验研究,水利学报,1989(7),29-39
[50] 崔广涛等,高水头大流量泄洪结构脉动荷载及其振动和地基反应,“七.五”国家重点科技攻关,国家自然科学基金资助项目研究成果之一——二滩水电站拱坝泄洪振动实验研究,天津大学水资源与港湾工程系,1991.3
[51] 崔广涛,林继镛,彭新民等,二滩拱坝泄洪振动水弹性模型研究,天津大学学报,1991,1
[52] 崔广涛等,高水头大流量泄洪振动及新型水垫塘研究,“八.五”国家重点科技攻关,国家自然科学基金资助项目研究成果之一——高拱坝大流量泄洪诱发振动研究,1996.3
[53] 崔广涛等,高水头大流量泄洪振动及新型水垫塘研究,“八.五”国家重点科技攻关,国家自然科学基金资助项目研究成果之二——高拱坝大流量泄洪动态仿真及振119动影响评估,1996.3
[54] 练继建等,金沙江溪洛渡水电站拱坝泄洪水弹性模型研究,天津大学水利水电工程系,2001
[55] 练继建等,黄河拉西瓦水电站坝身泄洪流激振动水弹性模型试验研究报告,天津大学水利水电工程系,2006.5
[56] 郭怀志,马启超,薛玺成等,岩体初始应力场的分析方法,岩土工程学报,1983,5(3):64-75
[57] 林世胜,中尾健儿,反算法的进一步探讨,岩土工程学报,1987,9(3)
[58] 陈国荣,姜弘道等,三维粘弹性参数反分析,河海大学学报,1996,24(6):25-28
[59] 沈珠江,堆石坝渗流变形的反馈分析,水利学报,1998(6):1-6
[60] 刘文宝,李术才,大坝位移反分析中测量误差对反演结果的影响,大坝观测与土工测试,1995,19(4):24-28
[61] 吴中如等著,水工建筑物安全监控理论及其应用,河海大学出版社,1990
[62] 吴中如,陈继愚,范树平等,用反演分析法推求连拱坝混凝土的力学参数和断裂韧度,大坝观测与土工测试,1986(1)
[63] 练继建,崔广涛,董淑芳,水工结构流激振动响应的反分析,水利水电技术,1998(8):51-54
[64] 练继建,崔广涛,林继镛,高拱坝泄洪振动的计算分析与验证,水利学报,1999,12:23-32
[65] 崔广涛,彭新民,苑希民等,高拱坝泄洪振动水弹性模型,1996,4:1-9
[66] 水利电力部成都勘测设计院,卡里巴(KARIBA)双曲拱坝—挑流消能,国外高坝泄洪消能工程实例,1984.8
[67] 刘沛清,高拱坝泄洪布置形式与消能防冲设计中的若干问题探讨,长江科学院院报,1999(5),17-21
[68] 刘沛清,高拱坝下游水垫塘底板块稳定性设计,水利学报,1999(2),5-12
[69] 安芸周一,关于自由跌落水舌的水垫效果的研究,国外科技增刊 (2),天津大学图书馆,1981.10
[70] 罗铭,郭亚昆,有界二元掺气射流水下扩散规律研究,水利学报,1992(7),29-34
[71] 安芸周一,关于拱坝中央溢流泄洪护坦上水垫效果的研究,国外科技增刊 (1),天津大学图书馆,1981(10),1-38
[72] Spyridon Beltaos and Nallamuthu Rajaratnam, Impinging Circular Turbulent Jets, Journal of the Hydraulics Division, ASCE, HY10, 1974.10
[73] 孙建,高拱坝坝身泄洪消能防冲研究[博士学位论文],北京:清华大学,2001。
[74] 石川中晴,自由跌落式消能工的水力机理(1),水工高速水流译文集,天津大学水工高速水流研究室,1980.7
[75] 练继建,二元射流作用下边壁动水荷载及其应用[硕士学位论文],天津:天津大学,1987
[76] 许多鸣,余常昭,平面射流对槽底的冲击压强极其脉动特性,水利学报,1983(5),52-58
[77] 崔广涛,陈荣光,林继镛,挑跌流对河床的动水压力及基岩的防护问题,天津大学学报,1982(2)
[78] 黄种为,陈瑾,高拱坝泄洪与水垫塘底板动水压力问题的试验研究,水利学报,1992(11),50-56
[79] S.M.Borghei, Effect of Plunge Pool Width on Hydrodynamic Pressures due to Vertical Jet. 29thIAHR Proceedings, 2001, Them D,Vol.Ⅰ , 622-627.
[80] 尤季茨基,依沃依洛夫,西沃洛式斯卡亚等,水流动水压力对溢流坝挑流鼻坎下游河床影响的模型试验和原型观测,高速水流译文集,长科院译,水利电力出版社,1979,242-252。
[81] 林继镛,练继建,二元射流作用下点面脉动壁压的幅值计算,水利学报,1988(12),34-40
[82] G.Rehbinder, Slot Cutting in Rock with A High Speed A Water Jet, Int. J.Rock Mech. Min. Sic., Vol.14, 1977, 229-234
[83] 赵耀南,梁兴蓉,水流脉动压力沿缝隙的传播规律,天津大学学报,1988(3),55-65
[84] Fiorotto, V. and Rinaldo , A . , Turbulent pressure fluctuations under hydraulic jumps, J. Hydr. Res., IAHR, VOL. 30, NO. 4, 1992.
[85] 刘沛清,冬俊瑞,余常昭,在岩缝中脉动压力传播机理探讨,水利学报,1994(12),31-36。
[86] 刘沛清,李忠义,冬俊瑞,用二维瞬变流方程分析缝面层中脉动压力传播规律,水利学报,1996(4),27-32。
[87] 艾克明,拱坝泄洪与消能的水力设计和计算,水利电力出版社,1987.8。
[88] Г.И.卓高瓦泽著,郑顺炜译,英古里水电站,中国电力企业联合会,1992
[89] 崔广涛,彭新民,杨敏,反拱形水垫塘——窄河谷大流量高坝泄洪消能工的合理选择,水利水电技术,2001,12:1-3
[90] 杨敏,彭新民,崔广涛,水垫塘底板的试验仿真模拟研究,水力水电技术,2002,33(3):40-42
[91] 彭新民,王继敏等,拱坝水垫塘拱形底板受力与稳定性实验研究,水力发电学报,1999,(2):52-59.
[92] 练继建,杨敏等,反拱型水垫塘底板结构的稳定性研究,水利水电技术,2001, 32 (12):24-27
[93] 孙建,陈长植,反拱水垫塘与平底水垫塘底板稳定性诸方面之比较,长江科学院院报,2003,20(4):3-6
[94] 中川博次,洪崎一博,多田敏一,拱坝泄水建筑物的水力学性能研究,国外科技增刊(1),天津大学图书馆,1981,10。
[95] 岩佐义郎,中川博次,藤本成,日本多目标工程消能工的历史性发展,高速水流译文集,水利电力出版社,1979,12,433-440。
[96] 杨敏,高坝消力塘水动力特性与防护结构的安全研究:[博士学位论文],天津:天津大学,2003
[97] 郭航忠,水垫塘底板稳定性判别标准研究:[硕士学位论文],天津:天津大学,2003,12
[98] 符晓,水垫塘衬砌结构非线性静动力特性研究:[硕士学位论文],天津:天津大学,2004,12
[99] 王继敏,王珮璜,长潭岗水电站反拱形水垫塘研究及应用,水利水电技术,2002,33 (7):10-12
[100] 杨令强,练继建,张社荣等,高拱坝水垫塘反拱底板衬砌结构的非线性静力分析,水利学报,2002,9:77-81
[101] 史军,杨敏等,水垫塘反拱形底板稳定性的块体弹簧元分析,水力发电学报,2004,23(2):73-78
[102] 郭怀志,溢流拱坝下反拱式消力池试验研究与工程设计,海河水利,1980, 7
[103] 杨敏,练继建,水垫塘反拱形底板体型研究,水力发电学报,2002,(4):45-50
[104] 孙建,陈长植,反拱水垫塘拱端力变化规律的试验研究,水力发电学报,2002,(4):51-60
[105] 崔广涛,练继建,彭新民等,水流动力荷载与流固相互作用,北京:中国水利水电出版社,1999,11
[106] 赵耀南,重力相似水力模型中紊流微结构的相似律,水利学报,1988,8:97-101
[107] 谢省宗,李世琴,吴一红等,高拱坝坝身泄洪流激振动水弹性模型模拟研究,水利学报,1997,12:1-9
[108] Holland J.H.,Adaptation in natural and artificial system,The University of Michigan Press,1975,MIT press,1992
[109] 周明,孙树栋,遗传算法原理及应用,北京:国防工业出版社,1999
[110] 王小平,曹立明,遗传算法——理论、应用与软件实现,西安:西安交通大学出版社,2001
[111] 李东序,高等结构力学,长沙:国防科技大学出版社,1997
[112] 王传志、腾志明,钢筋混凝土结构原理,中国建筑工业出版社,1985
[113] 周志祥主编,高等钢筋混凝土结构,北京:人民交通出版社,2002
[114] Bresler B and Bertero V V,Behavior of Reinforced Concrete under Repeated Loads,J.Struct.DIV.,ASEC,1968.9,94,ST6:1567～1590
[115] Nilson A H,Nonlinear Analysis of Reinforced Concrete by the Finite Element Method,ACI Journal,1968.9:757～766
[116] Houde J,Study of Force-Displacement Relationships for the Finite Element Analysis of Reinforced Concrete,In:Dept. of Civil England Applied Mechanics. Report No.73-2 Montreal:Mc Gill University,1973.12
[117] 腾志明主编,钢筋混凝土基本构件(第二版),北京:清华大学出版社,1987
[118] Comite Euro-International du Betu.D’information No.213/214 CEB-FIP Model Code 1990(Concrete Structures).Lausanne,May 1993
[119] 徐有邻,钢筋混凝土粘结滑移本构关系的简化模型,工程力学,1997 增刊:34-38,
[120] 徐有邻,沈文都,汪洪,钢筋混凝土粘结锚固性能的试验研究,建筑结构学报,1994(3):26-37
[121] ANSYS 高级技术分析指南,ANSYS 中国,2000.1
[122] ANSYS 非线性分析指南,ANSYS 中国,2000.1
[123] ANSYS Element Reference,Electronic Release,SAS IP,Inc.,1998
[124] ANSYS Theory Reference,Electronic Release,SAS IP,Inc.,1998
[125] Bangash M Y H.Numercical modeling of bond and bond-slip.Concrete and Concrete Structures:Numerical Modeling and Applications.London,New York:Eisevier Applied Science,1985
[126] Bazant Z P,et.al..Task Committee on Finite Element Analysis of Reinforced Concrete Structures.State-of-theArt Report on Finite Element Analysis of Reinforced Concrete, New York:Published by ASCE,1982
[127] 朱伯芳,有限单元法原理与应用,北京:中国水利水电出版社,1998
[128] 沈聚敏,王传志,江见鲸.钢筋混凝土有限元与板壳极限分析.北京:清华大学出版社,1993
[129] 宋启根,单炳梓,金芷生,朱万福编著.钢筋混凝土力学.南京:南京工学院出版社,1986
[130] 朱伯龙,董振祥,钢筋混凝土非线性分析,上海:同济大学出版社,1985
[131] 杨勇,型钢混凝土粘结滑移基本理论及应用研究:[博士学位论文],西安:西安建筑科技大学,2003
[132] 王彦宏,型钢混凝土偏压柱粘结滑移性能及应用研究:[博士学位论文],西安西安建筑科技大学,2004
[133] 张健民,杨永全,王玉容等,水垫塘底板上举力的数值研究,水动力学研究与进展,2003,(18)1:63-67
[134] 崔广涛,彭新民,练继建等,高拱坝大流量泄洪振动及新型水垫塘研究,“八.五”国家重点科技攻关,国家自然科学基金资助项目研究成果之三——拱坝水垫塘反拱形底板研究,天津大学水资源与港湾工程系,1996.3
[135] 刘鹏,反拱形水垫塘衬砌结构的稳定性研究:[硕士学位论文],天津:天津大学,2005
[136] 王继敏,崔广涛,李延农等,拱坝反拱形水垫塘原型研究,新世纪水利工程科技前沿,天津大学出版社,2006,299-312
[137] 崔广涛,练继建,彭新民等,水流诱发水工结构振动与水弹性模型,新世纪水利工程科技前沿,天津大学出版社,2006,568-578
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