Evaluation of rock mass permeability along a borehole by integrating the techniques of geological features and logistic regression: a case study in Taiwan

Abstract

When the budget for in situ hydraulic tests is constrained, cost-effective approaches for determining the variations in hydraulic conductivity along a borehole remain enticing for helping design and planning of groundwater-related engineering systems. This study proposes a practical method with probabilistic outputs for fulfilling engineering concerns. First, 474 sets of hydrogeological investigation and hydraulic test data of fractured rock masses in most of the watersheds of mountainous areas of Taiwan were collected. Then, seven geological indices [rock quality design (RQD), depth index (DI), gouge content design (GCD), lithology permeability index (LPI), fracture density (FD), fracture width (FW), and groundwater velocity (GV)] significantly correlated with rock mass permeability were identified. Third, using logistic regression analysis, the seven indices were used as explanatory variables, and the hydraulic conductivity was utilized as an outcome variable (its threshold value is 1 × 10−6 m/s) for developing prediction models of high groundwater potential zones along a borehole. All indices passed the collinearity test, indicating no collinearity between the indices. To make the prediction models proposed more flexible in practical applications, a total of 127 combinations based on the combination selection of seven explanatory variables were explored to develop various prediction models. Through the validation of the Hosmer–Lemeshow test, Omnibus test, and Wald test for all developed models, only 77 models were statistically significant. The 77 models were evaluated by three measures of Nagelkerke R2, SR (success rate), and AUC (area under the curve) to further understand the prediction performance of each model. The results show that the accuracy of the prediction model is positively correlated with the number of geological indices used. When all seven geological indices are used, Nagelkerke R2, SR, and AUC can reach the best values, which are 0.83, 91.6%, and 0.976, respectively. In conclusion, the prediction model developed by combining geological indices with logistic regression analysis can provide a more efficient way of understanding the hydrogeological conditions of a borehole site.