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s

Roughness characterization of concave fracture surface
and coefficient fitting of modified cubic law

GAN Lei， MA Hongying， SHEN Zhenzhong
（College of Water Conservancy and Hydropower Engineering， Hohai University， Nanjing 210098， China）

Abstract：Roughness of fracture surface directly affects the seepage characteristics of fracture. A high-pow⁃
er digital camera is adopted to collect the rough information of the fracture surface on the porous medium.
Combined with digital imaging and MATALB technology， the typical roughness fracture surface is deter⁃
mined. The concavity describing the roughness of fracture surface is proposed to study the influence of con⁃
cave degree on the fracture flow capacity through the fracture. The modified coefficient formula of the cubic
law for rough fracture with concave shape is proposed. The results show that the percentage of concave ar⁃
ea decreases with the increase of the concave degree. The relationship between the correction coefficient of
cubic law and the relative concavity is quadratic polynomial. The numerical simulation results by using the
equivalent hydraulic fracture width are closer to the experimental results of hydraulic characteristics of du⁃
al-media seepage model than the smooth fracture with the fracture aperture of 1.0 mm. The mean absolute
2
error （MAE），root mean square error （RMSE） and square root （R ） of the modified calculated values and
test values are 1.35% ， 1.06 × 10 -4 and 0.995， respectively. The values of the correction coefficient of the
cubic law of concave rough fracture are consistent with the measured values，and the formula of the modi⁃
fied coefficient model is reasonable. The proposed roughness characterization method and modified cubic law
can thus effectively describe the seepage characteristics of rough fractures with concave morphology.
Keywords：fracture surface；roughness；degree of concavity；cubic law；correction coefficient

（责任编辑：耿庆斋）

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