受预应力双重孔隙介质层动力问题的研究

发布时间：2018-02-12 19:55

本文关键词： 拓展的Biot理论双重孔隙介质不均匀弹性介质初应力　出处：《上海交通大学》2014年硕士论文　论文类型：学位论文

【摘要】：双重孔隙介质理论一直是研究土动力学,地球物理学的主要手段之一。通过对地表平面波的研究有助于预测地表的内部结构,从而发现埋藏在地下的自然资源;也可以用来对地震进行分析,为降低地震造成的危害提供理论依据。通过对土层在激励下响应情况的研究,有助于解决地表沉降和对周边建筑物的振动破坏等问题。由于外部载荷的存在,温度的变化,重力场的影响,会导致土层和地壳中有预应力的存在,故研究双重孔隙介质动力问题时需考虑初应力的影响。迄今为止,尽管已有大量学者对单相介质和单一孔隙介质中的动力学问题做了许多卓有成效的研究工作,但双重孔隙介质中的相应问题还少见有研究,有必要进一步的探讨,尤其是受初应力双重孔隙介质中表面波的传播和动力响应问题。本文根据Berryman等基于拓展的Biot理论建立的双重孔隙介质模型,研究了覆盖于不均匀弹性半空间上的流体饱和双重孔隙介质层中Love波的传播,与平面应变条件下下卧垂向不均匀基岩的有限厚度双重孔隙地基在简谐线载荷作用下的动力响应问题。考虑有限厚度的流体饱和双重孔隙地基和半无限不均匀基岩都含有初应力。对于Love波问题,本文推导出Love波的频散方程以及Love波速的上下界限,讨论了孔隙率、不均匀性、各向异性和预应力等参数对Love波传播速度的影响。对于动力响应问题,本文通过引入势函数和运用Helmholtz原理,并利用Fourier变换求解本问题的控制微分方程,得到变换域内应力、位移和孔隙水压力的一般解。再结合边界条件,利用Fourier逆变换可以得到相应的数值计算结果。本文的计算结果表明,孔隙介质层基质孔隙的孔隙率、裂隙孔隙率及基质孔隙的孔隙率占总孔隙率的比重越大,Love波的波速越大;随着不均匀程度的提高及各向异性系数的增大,Love波的波速增大。无论是在双重孔隙介质层中还是弹性半空间中,预拉应力会使Love波的波速提高,而预压应力会降低Love波的波速。在简谐激励下,竖向位移会随载荷频率,有限层基质孔隙,半平面阻尼因子和不均匀系数的增大而单调递减。双重孔隙介质层和半空间所受初应力对动力响应下竖向位移幅值的影响效果相同。初始拉应力会减小竖向位移的幅值,而初始压应力会增大竖向位移的幅值。基质孔隙水压力和裂缝孔隙水压力随着渗透率的减小,频率的增大而增大。频率对裂缝孔隙水压力的影响更大。
[Abstract]:The theory of double pore media has been one of the main methods of studying soil dynamics and geophysics. The study of surface plane waves is helpful to predict the internal structure of the surface and to find the natural resources buried underground. It can also be used to analyze earthquakes and provide a theoretical basis for reducing the damage caused by earthquakes. It is helpful to solve the problems of ground subsidence and vibration damage to surrounding buildings. Due to the existence of external load, temperature change and the influence of gravity field, the existence of prestress in soil layer and crust will be caused. So it is necessary to consider the influence of initial stress when studying the dynamic problem of dual porous medium. Although a large number of scholars have done many fruitful research work on the dynamic problem in single phase medium and single pore medium so far, However, the corresponding problems in dual porous media are rarely studied, so it is necessary to further study them. In particular, the propagation and dynamic response of surface waves in dual porous media subjected to initial stress are discussed. Based on the extended Biot theory of Berryman and others, a model of dual pore media is established in this paper. In this paper, the propagation of Love waves in a fluid saturated dual porous media layer covering an inhomogeneous elastic half-space is studied. The dynamic response of double pore foundation with finite thickness to plane strain under harmonic loading. Fluid-saturated double pore foundation and semi-infinite heterogeneous foundation with finite thickness are considered. All rocks contain initial stress. For Love wave problems, In this paper, the dispersion equation of Love wave and the upper and lower bounds of Love wave velocity are derived. The effects of porosity, inhomogeneity, anisotropy and prestress on the propagation velocity of Love wave are discussed. In this paper, by introducing the potential function and applying the Helmholtz principle and using the Fourier transform to solve the governing differential equation of this problem, the general solutions of stress, displacement and pore water pressure in the transform domain are obtained. The corresponding numerical results can be obtained by using the inverse Fourier transform. The results show that the larger the proportion of porosity, fracture porosity and matrix porosity to the total porosity is, the larger the wave velocity of the wave is. With the increase of the inhomogeneity and the anisotropy coefficient, the wave velocity of Love wave increases, both in the double porous media layer and in the elastic half-space, the pretensile stress will increase the wave velocity of the Love wave. Under harmonic excitation, the vertical displacement will change with the loading frequency and the pore size of the finite layer matrix. The effect of initial stress on the amplitude of vertical displacement under dynamic response is the same, and the initial tensile stress decreases the amplitude of vertical displacement. The initial compressive stress increases the amplitude of vertical displacement. The matrix pore water pressure and fracture pore water pressure increase with the decrease of permeability and the frequency increases.
【学位授予单位】：上海交通大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TU435

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