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工程中,地下衬砌隧道会遇到水压破裂压力、爆炸及突然开挖等瞬态荷载作用,将这些荷载理想化为作用在衬砌内边界上的均布瞬态荷载,研究圆柱形衬砌隧道在突加荷载、阶跃荷载和三角形脉冲荷载作用下的动力响应规律。根据Biot波动理论推导出半空间饱和介质的控制方程;视衬砌结构为弹性材料导出衬砌结构的控制方程。用极大半径凸圆弧近似半空间直边界,采用Graff加法公式进行坐标变换,将直角坐标表示的通解转化为极坐标表示的通解。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变换域的解答。利用反Laplace变换数值计算方法,将解答转换为时域解,得出3种瞬态荷载作用下衬砌隧道地面位移峰值、衬砌应力和孔隙压力的分布规律。
In the project, the underground lining tunnel will encounter the transient load such as hydraulic fracturing pressure, explosion and sudden excavation. These loads are idealized as the uniform transient load acting on the inner boundary of lining. Dynamic response of sudden load, step load and triangular pulse load. According to the Biot wave theory, the governing equations of the saturated medium in the half space are derived. The governing equations of the lining structure are derived from the lining structure as the elastic material. The approximate boundary of the semi-space is approximated by a convex arc of a very large radius, and the coordinate transformation is performed by using the formula of Graff addition. The general solution of the rectangular coordinate representation is transformed into the general solution of the polar coordinate representation. Derivation of Solutions to Laplace Transform Domain of Lining and Soil Mass Displacement, Stress and Pore Pressure Based on Boundary Conditions. The inverse Laplace transform method is used to convert the solution into the time-domain solution, and the distribution law of the peak ground displacement, liner stress and pore pressure of the lining tunnel under three kinds of transient loads is obtained.