Variations of hydraulic conductivity of fracture sets and fractured rock mass with test scale: Case study at Heshe well site in Central Taiwan

• We develop a method for determining hydraulic conductivity of ith fracture sets (kJi).
• kJi obtained from lab. Results differ from those by in situ tests by eight orders.
• kJis increase with the test scale, exhibiting a negative exponential distribution.
• The method minimizes deviation of kJi and gives value with statistical significance.
• Both effects of test scale and in situ stress on kJi can be considered.

Variations of the equivalent hydraulic conductivity of a fractured rock mass with investigating scale typically cause difficulties in the hydraulic characterization of a site. A mechanistic model regarding water flow through fractured rock masses and associated methods of multiple regression analysis have been established to determine the transmissivities of dominant fracture sets with statistical significance using in situ hydrogeological test results. Accordingly, this manuscript decomposes the transmissivity of a fracture set into the product of its hydraulic conductivity and its aperture. The ultimate purpose is to investigate the effects of scale on the hydraulic characteristics of fractured rock masses. The results of in situ hydrogeological tests at various scales, performed at the Heshe well site, are utilized to determine the equivalent hydraulic conductivity thereof. A series of laboratory tests are planned and carried out to obtain the apertures of fracture sets, which are applied in determining the respective hydraulic conductivities of those sets. Analyzed results reveal that the hydraulic conductivities of fracture sets can be determined with statistical significance. The comparison of equivalent hydraulic conductivities that are obtained in in situ multiple borehole pumping (MBP) tests with those determined using the combination of the hydraulic conductivities and geometric parameters of fracture sets verifies the proposed method. The hydraulic conductivities of fracture sets that are determined from their apertures, which are obtained from laboratory tests, differ from those obtained by in situ MBP tests by eight orders of magnitude. The magnitudes of hydraulic conductivities of fracture sets initially increase with the test scale, subsequently approaching an asymptote, exhibiting a negative exponential distribution. The proposed method yields the hydraulic conductivities of fracture sets and the equivalent hydraulic conductivity of a fractured rock site from the spatial distribution, hydraulic conductivities, and aperture of each dominant fracture set. Such an approach can minimize the deviation of the hydraulic conductivity of a fracture set with the measured aperture, and can be used to determine hydraulic conductivity, which is affected by both test scale and in situ stress.