A Predictive Model for the Equivalent Hydraulic Aperture of Single Fracture Using Gene Expression Programming.

The accurate prediction of the equivalent hydraulic aperture (EHA) in a single fracture is of paramount importance for the investigation of fracture flow capacity. Previous studies primarily relied on fitting experimental data to obtain the EHA, failing to accurately characterize the impact of the strong nonlinearity among fracture geometric parameters on EHA. This research integrates 170 datasets of measured EHA, incorporating key geometric parameters: average mechanical aperture (<italic>b</italic>m), peak roughness height (<italic>ξ</italic>), and the joint roughness coefficient (<italic>JRC</italic>). These three main geometric characteristic parameters, used as input parameters, are the primary factors influencing the EHA. The Gene Expression Programming (GEP) method was utilized to construct a model for predicting EHA (<italic>b</italic>h). The developed GEP model was then compared with 6 existing empirical models, as well as 2 AI models (Random Forest (RF) and Support Vector Machine (SVM)). The results indicate that the GEP model (R2 = 0.997) and the SVM model (R2 = 0.9944) both demonstrate high accuracy, evidenced by the GEP model's low RMSE (0.014) and MAE (0.01) values. The sensitivity analysis indicates that in the GEP model, the hydraulic aperture increases linearly with the increase of <italic>b</italic>m, decreases linearly with the increase of <italic>ξ</italic>, and initially increases but then decreases as JRC increases. These findings provide insightful contributions to the assessment of hydraulic conductivity in the rough single fracture. [ABSTRACT FROM AUTHOR]