准饱和土中圆柱形衬砌的瞬态动力响应分析  

Analysis of transient dynamic response of cylindrical lined cavity in nearly saturated soil

作　　者：王滢[1,2] 高广运[1,2] 

机构地区：[1]同济大学地下建筑与工程系,上海200092 [2]同济大学岩土及地下工程教育部重点实验室,上海200092

出　　处：《岩土力学》2015年第12期3400-3409,共10页Rock and Soil Mechanics

基　　金：国家自然科学基金项目(No.41372271)~~

摘　　要：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。A solution to dynamic response of cylindrical lined cavity under internal transient load is one of the classical soil dynamics problems. Most previous literatures about the problem assumed that soil surrounding with cavity is an elastic medium or full-saturated poroelastic medium. In fact, perfectly elastic and completely saturated soil does not exist in practical engineering. The lining structure and its surrounding soil are treated as an ideal elastic medium and a nearly saturated poroelastic medium, respectively. On the basis of Newton＇s second law, Darcy＇s law and Biot＇s theory, the governing equation of nearly saturated soil is derived. According to boundary conditions, solutions for the radial displacement, hoop stress and pore stress of the lining and saturated soil are obtained in Laplace transform space; and then they are transformed to solutions in time domain using inverse Laplace transforms numerical method. Also, the influence of the saturation degree（Sr） on the dynamic response of the lining and soil is investigated. It is indicated that the saturation degree has a less effect on the radial displacement and hoop stress when 95%≤Sr≤ 99% and has a significant influence on them when 99%≤Sr≤ 100%. But the saturation degree has much more effect on the pore stress than on the former two. The same conclusion can be drawn that the influence of saturation degree on the attenuation of dynamics response along radial direction. The saturation degree has a less effect on the radial displacement and hoop stress when 95%≤Sr≤ 99% and has a significant influence on them when 99%≤Sr≤100%. It also indicates that the saturation degree on the attenuation has more effect on pore stress than that of raidial displacement and hoop stress.

关 键 词：准饱和土 圆柱形衬砌 瞬态荷载 拉普拉斯变换 反变换 时域解 

分 类 号：TU431[建筑科学—岩土工程]