竖向非均质饱和地基中埋置扭转荷载的动力响应  

Dynamic Response of Buried Torsional Load in VerticallyNon-Homogeneous Saturated Soil

作　　者：邹新军[1] 贺琼 覃玉兰 ZOU Xinjun;HE Qiong;QIN Yulan(College of Civil Engineering,Hunan University,Changsha 410082,China)

机构地区：[1]湖南大学土木工程学院,湖南长沙410082

出　　处：《湖南大学学报（自然科学版）》2020年第3期11-18,共8页Journal of Hunan University:Natural Sciences

基　　金：国家自然科学基金资助项目(51578231,51378197)。

摘　　要：为探讨竖向非均质饱和地基中埋置简谐扭转荷载的动力响应,考虑地基为饱和半空间,并假定土体剪切模量随深度呈指数函数非线性分布,基于Biot固结理论与弹性动力学原理,建立饱和地基扭转振动的动力微分方程,引入边界条件并利用Hankel变换方法求解获得变换域内的剪应力、切向位移表达式,进而通过Hankel逆变换求得饱和地基内部的剪应力、切向位移解答,据此基于Mathematica编制出相应计算程序,并通过参数分析发现:地基土剪应力、切向位移沿径向呈现出明显的波动规律,曲线波动频率随荷载频率增大而增大;荷载作用面土体切向位移最大,剪应力发生突变,主要影响范围是荷载作用面上、下各两倍荷载作用半径(2a)区域;土体最大切向位移随荷载埋深h增大而减小,h=2a时最大切向位移下降90%,h>4a时,最大切向位移近似为零.To discuss the dynamic response of buried harmonic torsional load in vertically non-homogeneous sat-urated soil,the soil shear modulus was assumed as a nonlinear distribution with the depth defined as an exponential function,and the dynamic differential equations of half space were established by using the Biot's consolidation theory and elastic-dynamic theory.The expressions of stress and tangential displacement in the Hankel transform domain were then acquired by solving the dynamic differential equations using the method of Hankel transform,and the true stress and tangential displacement can be obtained by Hankel inverse transformation as well.The corresponding cal-culation program by Mathematica was compiled based on the obtained solutions.A detailed parameter analysis com-pleted by the program indicates that,the stress and tangential displacement of the soil show obvious fluctuations with the change of radius,and the frequency of fluctuant curves increases with the loading frequency.In addition,the maxi-mum tangential displacement of soil occurs and there is a sharp change of stress on the loading surface.The influence range of the buried harmonic torsional load is about two times the action radius to the loading surface.Furthermore,the largest tangential displacement of the soil is negatively correlated with the depth of buried load,and it is reduced by 90%when the depth of buried load is 2 times the action radius.When the depth of buried load is greater than 4 times the action radius,the largest tangential displacement is approximately equal to zero.

关 键 词：饱和地基 埋置扭转荷载 动力响应 剪切模量 HANKEL变换 

分 类 号：TU471.4[建筑科学—结构工程]