瞬态扭矩作用下横观各向同性饱和地基的响应

Dynamic response of transversely isotropic saturated soil under transient torsional loading

通过Laplace-Hankel联合变换技术求解了横观各向同性饱和地基在瞬态扭转荷载作用下的动力方程,结合冲击荷载的具体分布形式,给出了地基内位移和剪应力在积分变换域内的解;通过Laplace-Hankel逆变换给出了位移和剪应力的积分形式解.数值算例考虑了作用于地基表面圆形区域的荷载分别为线性分布和静刚性分布两种情况,分析了地基内的最大切向位移和最大剪应力沿径向和竖向的变化规律.数值研究表明,冲击剪应力的分布形式对地基内最大位移和剪应力的变化规律影响不大,土体的渗透系数对瞬态扭转荷载作用下地基的动力响应影响不明显,而地基的各项异性程度指标对最大切向位移和最大剪应力都有很大的影响.

Laplace-Hankel transform, was used to solve the dynamic governing differential equations for transversely isotropic saturated poroelastic medium under the action of transient torsional loading. Based on the distributing form of impulsive shear stress, the tangential displacement and shear stresses in the soil were given in integral transform domains. After using inverse Laplace-Hankel transform, the tangential displacement and shear stresses in the soil were presented in integral form. Two different types of impulsive shear stress, linear distribution and static rigidity distribution, were considered in the numerical examples. And the regularities of the maximal displacement and shear stresses in radial and vertical directions were also investigated in the examples. Numerical results indicated that the distributing form of the impulsive shear stress has slight effect on the regularities of the maximal displacement and shear stresses in the saturated soil; that the permeability coefficient of the saturated soil has unobvious effect on the transient dynamic response. Furthermore, the maximal tangential displacement and shear stresses are significantly affected by the anisotropy of transversely isotropic saturated soil.