In this study, a new approach is developed to determine the starting pressure head gradient and flowrate of a Bingham plastic through a fractal fracture network. The trace length of fracture is assumed to follow a power-law fractal distribution. The aperture of the fracture is related to the trace length by a scaling relationship. Flow in each fracture is treated as rectangular channel-type flow. A dimensionless flowrate ratio is defined by the average fracture flowrate of Bingham plastic over the flowrate of Newtonian fluid in the smallest fracture. The impact of the input parameters that define the fractal characteristics of the network, the pressure head gradient condition and the Bingham plastic properties is quantified and discussed. It is found that the flowrate ratio significantly decreases with the fractal dimension of trace length as the contrast of fracture lengths in the fractal network decreases with the fractal dimension. The flowrate significantly increases with the maximum over minimum trace length ratio in the network. The scaling exponent dramatically enhances the flowrate in the scaled fractal network. The dimensionless flowrate ratio increases with the pressure head gradient in a non-linear fashion. When the Bingham number is small enough, the dimensionless flowrate ratio does not depend on the pressure head gradient. After flows in more fractures have been activated due to the increase in the pressure head gradient, the Bingham plastic flowrate dramatically increases with the pressure head gradient compared to the Newtonian fluid counterpart.

在这项研究中，开发了一种新方法来确定Bingham塑料通过分形断裂网络的起始压头梯度和流量。假定裂缝的迹线长度遵循幂律分形分布。裂缝的孔径通过比例关系与迹线长度相关。每个裂缝中的流动均视为矩形通道型流动。无量纲的流量比由宾厄姆塑料在最小裂缝中的平均裂缝流速与牛顿流体的流速之比定义。量化和讨论了定义网络分形特性，压头梯度条件和Bingham塑性特性的输入参数的影响。研究发现，随着分形网络中裂缝长度的反差随分形维数的减小，流量比随迹线长度的分形维数显着降低。随着网络中最大迹线长度与最小迹线长度之比的增加，流量显着增加。标度指数显着提高了标度分形网络中的流量。无量纲流量比以非线性方式随压头梯度的增加而增加。当宾厄姆数足够小时，无因次流量比不取决于压头梯度。由于压头梯度的增加而激活了更多裂缝中的流动后，与牛顿流体对应物相比，宾厄姆塑性流速随压头梯度的增加而急剧增加。