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内源瞬态荷载作用下圆柱形孔洞的动力响应解答是土动力学的经典问题之一。已有研究大都假设孔洞周围土体为理想弹性介质或完全饱和多孔介质。然而,实际工程中不存在完全弹性和完全饱和土体。分别视衬砌结构和周围土体为弹性材料和准饱和多孔介质(饱和度Sr≥95%),根据牛顿第二定律、达西定律和Biot波动理论推导出准饱和土体的控制方程。根据边界条件导出衬砌和土体的位移、应力和孔隙压力的Laplace变换空间的解答。利用反Laplace变换数值计算方法,将解答转换为时域解。分析了饱和度对衬砌位移、应力和孔压的影响,结果表明,当95%≤Sr≤99%时,饱和度对径向位移和切向应力的影响较小;99%≤Sr≤100%时,饱和度对径向位移和切向应力的影响较大;但饱和度对孔隙压力的影响远大于对径向位移和切向应力的影响。得出位移、应力和孔压沿径向的衰减规律,当95%≤Sr≤99%时,饱和度对径向位移和切向应力沿径向衰减影响较小,99%≤Sr≤100%时,饱和度对径向位移和切向应力沿径向衰减影响较大,但饱和度对孔压沿径向的衰减影响远大于对径向位移和切向应力沿径向的衰减。
Dynamic Response of Cylindrical Cavity under Transient Internal Loads is one of the classic problems of soil dynamics. Most of the researches have assumed that the soil around the hole is an ideal elastic medium or a completely saturated porous medium. However, there is no fully elastic and fully saturated soil in the actual project. Considering the lining structure and the surrounding soil as the elastic material and quasi-saturated porous medium (the saturation is Sr≥95%), the governing equations of the quasi-saturated soil are deduced according to Newton’s second law, Darcy’s law and Biot’s wave theory. Derivation of Laplace Transform Spaces for Displacement, Stress and Pore Pressure of Lining and Soil Based on Boundary Conditions. The inverse Laplace transform is used to convert the solution to time domain solution. The effects of saturation on displacement, stress and pore pressure of lining are analyzed. The results show that the saturation has less effect on radial displacement and tangential stress when 95% ≤Sr≤99%; 99% ≤Sr≤100% , The effect of saturation on radial displacement and tangential stress is larger; however, the effect of saturation on pore pressure is far greater than that on radial displacement and tangential stress. When 95% ≤Sr≤99%, the effect of saturation on radial and tangential stress attenuation is small, and 99% ≤Sr≤100% , The effect of saturation on the radial displacement and the tangential stress is greatly influenced by the radial attenuation. However, the effect of saturation on the attenuation of pore pressure along the radial direction is far greater than that on the radial displacement and tangential stress.