非饱和地基上多层矩形板稳态响应解析研究  

Analytical study on dynamic response of multi-layered plate in unsaturated half-space

作　　者：王春玲[1] 赵鲁珂 李东波[1] WANG Chun-ling;ZHAO Lu-ke;LI Dong-bo(School of Science,Xi'an University of Architecture and Technology,Xi'an 710055,China)

机构地区：[1]西安建筑科技大学理学院

出　　处：《岩土工程学报》2019年第12期2182-2190,共9页Chinese Journal of Geotechnical Engineering

基　　金：国家自然科学基金项目（51878547）

摘　　要：采用积分变换法和消元法求得了非饱和地基受任意竖向简谐荷载作用下的稳态响应积分变换解。同时对四边自由多层矩形薄板提出了带有补充项的双重余弦级数通解,并与地表竖向位移的级数展开式相结合,建立了地基和矩形板的协调方程,再联合矩形板的控制方程和边界条件,构成了非饱和地基上四边自由多层矩形薄板稳态振动的解析方程组。选取非饱和土体参数和矩形板参数,利用该方程组,求解了竖向稳态荷载作用下该地基板的接触压力幅值、板挠度幅值以及板弯矩幅值,分析了非饱和地基参数对矩形板稳态响应的影响规律。The study on the dynamic interaction between plate and foundation is widely concerned. Especially, the dynamic response of plate on unsaturated foundation contains theoretical and practical values. The steady-state response of multi-layered rectangular plate on unsaturated half-space is investigated. Based on the governing equation proposed by the previous literatures, the integral solution for unsaturated half-space is derived by using the integral transformation and elimination method. Meanwhile, a double-cosine form function is proposed for the multi-layered rectangular plate so as to establish the compatibility equation between plate and foundation. Considering the governing equation, boundary conditions and compatibility equation of layered rectangular plate, the amplitudes of vertical displacement and bending moment are calculated. The parameters of foundation and multi-layered plate are selected, and some computed results for steady-state vibration of multi-layered plate are given. To further investigate how the factors of unsaturated soils influence the steady-state response of multi-layered plate, the specific numerical results of displacement of multi-layered plate are calculated, and the rules how the factors influence the deformation of plate are analyzed.

关 键 词：非饱和地基 积分变换 多层矩形板 稳态响应 解析研究 

分 类 号：TU470[建筑科学—结构工程]