有自由面三维稳定渗流的等效管网模型

An Equivalent Pipe Network Model for Three-Dimensional Steady Seepage with Free Surface

岩土工程普遍涉及有自由面三维稳定渗流问题,传统求解自由面的数值方法以连续介质假定为基础,将孔隙流动平均到包含固体颗粒的整个区域。事实上,水体仅能沿多孔介质空隙发生流动。通过将多孔介质的孔隙结构概化为三维正交管网,基于水头和流量等效原则,推导了管网模型的等效渗流速度、连续性方程及边界条件。基于局部坐标系、连续型罚Heaviside函数及变分原理,建立了等效管网模型的有自由面三维稳定渗流分析方法,从而将三维渗流问题简化为一维形式求解,大大减小了有自由面三维稳定渗流问题的求解难度。通过均质直角梯形坝的三维自由面渗流分析,验证了等效管网模型的有效性。开展卡基娃水电站左岸坝肩边坡三维稳定渗流分析,通过与变分不等式方法的对比分析,等效管网模型很好地反映了卡基娃水电站左岸坝肩边坡渗流场特征,对三维复杂工程渗流问题具有较强的适用性和较高的计算效率。

Geotechnical engineering generally involves three-dimensional steady seepage problem with free surface.Traditional numerical methods for solving free surface are based on the assumption of continuum,and the pore flow is averaged over the whole area containing solid particles.In fact,water flow can only occur along the pores of porous media.Based on the equivalent principle of head and flow,the equivalent seepage velocity,continuity equation and boundary conditions of the pipe network model were derived by simplifying the pore structure of porous media into a three-dimensional orthogonal pipe network.Based on the local coordinate system,continuous penalty Heaviside function and variational principle,a three-dimensional steady seepage analysis method with free surface was established for equivalent pipe network model.Thus,the three-dimensional seepage problem was simplified to a one-dimensional form,which greatly reduces the difficulty of solving the three-dimensional steady seepage problem with free surface.The effectiveness of the equivalent pipe network model was verified by the three-dimensional free surface seepage analysis of homogeneous right-angle trapezoidal dam.The three-dimensional steady seepage analysis of the left abutment slope of Kajiwa Hydropower Station was carried out.By comparing with the variational inequality method,the equivalent pipe network model can well reflect the seepage field characteristics of the left abutment slope of Kajiwa Hydropower Station,and has strong applicability and high computational efficiency for the seepage problem of 3D complex engineering.