徐明江, 魏德敏. 非饱和土地基的三维非轴对称动力响应[J]. 工程力学, 2011, 28(3): 78-085.
引用本文: 徐明江, 魏德敏. 非饱和土地基的三维非轴对称动力响应[J]. 工程力学, 2011, 28(3): 78-085.
XU Ming-jiang, WEI De-min. 3D NON-AXISYMMETRICAL DYNAMIC RESPONSE OF UNSATURATED SOILS[J]. Engineering Mechanics, 2011, 28(3): 78-085.
Citation: XU Ming-jiang, WEI De-min. 3D NON-AXISYMMETRICAL DYNAMIC RESPONSE OF UNSATURATED SOILS[J]. Engineering Mechanics, 2011, 28(3): 78-085.

非饱和土地基的三维非轴对称动力响应

3D NON-AXISYMMETRICAL DYNAMIC RESPONSE OF UNSATURATED SOILS

  • 摘要: 考虑土颗粒、孔隙流体的压缩性以及各相物质间的黏性、惯性耦合,采用Bishop有效应力公式和毛管压力函数的V-G模型,建立了非饱和土的动力控制方程。通过引入位移函数,并利用Cauchy-Reimann条件,在直角坐标系下将非饱和土的波动方程进行解耦,进而采用双重Fourier变换,求得了位移和应力在变换域上的一般解。结合一定的边界条件,研究了非饱和半空间体在任意分布的表面谐振荷载作用下的动力响应问题。数值分析中,考虑了饱和度对土的动剪切模量的影响,并提出了一个计算任意饱和度下粘性土的动剪切模量的经验公式。算例结果表明:饱和度对地基动力响应的影响非常显著,通常情况下,饱和度增大时,地表位移幅值随之增大,但当土体接近完全饱和时,地表位移幅值随饱和度进一步增大而减小。孔隙渗透性和地表排水条件则只有在饱和度很高时才会对地表位移产生明显的影响。

     

    Abstract: The paper derives dynamic governing equations for unsaturated soils by adopting Bishop’s effective stress formula and van Genuchten’s capillary pressure function. These equations consider the compression of solid grain and pore fluids, the viscous-coupling interactions and the inertial forces of fluids. By introducing the displacement function and making use of Cauchy-Reimann conditions, the 3D wave equations in rectangular coordinates are transformed into two uncoupled governing differential equations. Then, with the help of double Fourier transform, general solutions of displacement and stress as well as pore pressure are obtained. With boundary conditions imposed, dynamic responses of unsaturated half-space under arbitrary distributed harmonic loads are solved. The influence of saturation on dynamic shear modulus is considered in numerical calculations, and an empirical formula is raised here to describe the relations between saturation and shear modulus. Numerical results show that (1) with the increase of saturation, the displacement of ground surface increases firstly, then decreases when soils are nearly saturated; (2) permeability of pore and drainage conditions of ground surface have insignificant effects on the displacement when soils are nearly saturated.

     

/

返回文章
返回