The presence of complex geometric morphology of single rough-walled rock fractures and the occurrence of nonlinear flow complicate the fracture flow process. Even though the nonlinear flow behaviour in single rock fractures has been studied for decades, existing models are still limited in adequately evaluating nonlinear flow behaviour during shearing. In this study, a series of coupled shear-flow tests are conducted on single rock fractures with different surface characteristics under constant normal loads. Regression analyses of the experimental data demonstrate that the Forchheimer equation provides a robust description of nonlinear flow through rough fractures, and its nonlinear coefficients can be determined by quantifying the fracture geometries. The surface and interior geometric characteristics of the fracture are quantitatively represented. The evolutions of these geometric parameters, specifically the peak asperity height and hydraulic aperture, induced by shearing and their effects on nonlinear flow behaviours in rock fractures are also considered and incorporated. An empirical equation is then proposed for the parametric expression of the Forchheimer nonlinear coefficient, which is further used for the prediction of the flow rate during the shear-flow process and the representation of the critical Reynolds number with the fracture geometric characteristics. The proposed equations are validated against experimental results and proven to be effective in predicting and characterising the nonlinear flow behaviour in rock fractures during shearing. The experimental results and the proposed models are expected to advance the understanding and numerical modelling of the nonlinear flow behaviours in fractured rock masses for more practical applications.

中文翻译：

---

剪切过程中通过粗糙壁裂缝的非线性流动的 Forchheimer 方程系数的评估


单个粗糙壁岩石裂缝的复杂几何形态的存在和非线性流动的出现使裂缝流过程复杂化。尽管单岩裂缝中的非线性流动行为已经研究了几十年，但现有模型在充分评估剪切过程中的非线性流动行为方面仍然存在局限性。在本研究中，在恒定法向载荷下，对具有不同表面特征的单个岩石裂缝进行了一系列耦合剪切流试验。实验数据的回归分析表明，Forchheimer 方程为通过粗糙裂缝的非线性流动提供了稳健的描述，并且其非线性系数可以通过量化裂缝几何形状来确定。裂缝的表面和内部几何特征被定量表示。还考虑并纳入了剪切引起的这些几何参数的演变，特别是峰值凹凸高度和水力孔径，以及它们对岩石裂缝中非线性流动行为的影响。然后，提出了一个 Forchheimer 非线性系数参数表达式的经验方程，该方程进一步用于预测剪切流过程中的流速以及具有断裂几何特性的临界雷诺数的表示。所提出的方程式根据实验结果进行了验证，并被证明可以有效地预测和表征剪切过程中岩石裂缝中的非线性流动行为。实验结果和所提出的模型有望促进对裂隙岩体中非线性流动行为的理解和数值建模，以获得更多实际应用。