拱坝伏格特地基变位系数公式推导修订与验证  

Deduction,Analysis and Verification of Arch Dam Vogt Foundation Displacement Coefficient Formula

作　　者：刘国华[1] 黄芯怡 王昱 苗智超 LIU Guohua;HUANG Xinyi;WANG Yu;MIAO Zhichao(College of Civil Engineering and Architecture,Zhejiang University,Hangzhou 310058,Zhejiang,China)

机构地区：[1]浙江大学建筑工程学院,浙江杭州310058

出　　处：《水力发电》2023年第9期47-52,共6页Water Power

基　　金：国家自然科学基金资助项目(51979244)。

摘　　要：拱梁分载法是现行规范规定的计算拱坝应力的主要方法,其中,通常采用伏格特变位系数来计算基础变位。然而,不同出处的伏格特变位系数计算公式不完全一致。由于伏格特变形系数为三重积分式,被积函数比较复杂,推求解析表达式的求积过程十分繁复,为此,借助于Matlab工具,结合一些推导技巧,从伏格特基本假定和波辛涅斯克Boussinesq理论解出发,重新对伏格特变位系数的显式解析表达式进行推导,并采用高精度的数值积分手段,对显式解析表达式的正确性进行验证。最后,以两座特高拱坝作为算例进行应力分析,比较不同来源伏格特系数差异对拱坝应力分析结果的影响,得出修订前后的应力、位移计算结果差异不大。修订后伏格特公式的正确性得到了可靠的验证,使伏格特方法更加完善。The trial load method is the main method of calculating stresses in arch dams as specified in current code,in which,the Vogt foundation displacement coefficient is generally used to calculate the foundation deformation.However,the Vogt foundation displacement coefficient formula of different sources is not completely consistent.Because the Vogt displacement coefficient is a triple integral,the integrand function is complex and the quadrature process of deducting analytical expressions is very complicated,the analytical expression of Vogt foundation displacement coefficient is re-derived based on the Vogt hypothesis and the Boussinesq theoretical solution and with the help of Matlab and some deduction skills,and at the same time,the high-precision numerical integration is used to verify the correctness of the analytical expression.Finally,two extra-high arch dams are used as examples to compare the influence of the difference in Vogt coefficient from different sources on the stress analysis results.There is little difference between the stress and displacement calculation results before and after the revision,and the correctness of the revised Vogt formula has been reliably verified,which makes the Vogt method more perfect.

关 键 词：拱坝 伏格特地基 伏格特公式 修订 实例验证 数值积分 

分 类 号：TV223[水利工程—水工结构工程] TV624.4