Preliminary analysis of spatial development of karst using a geostatistical simulation approach

Earth science phenomena are primarily spatially dependent with variations occurring on varying scales. Geostatistics is a well-known approach for the assessment of spatial models of regionalized variables, such as porosity. In this study, we used the results of 953 Lugeon tests (402 tests in exploratory wells and 550 tests in grouting wells) to assess effective porosity and karst development at the Tangab Dam site, Iran. Lugeon values were first normalized, following which the variogram method (i.e., range, sill, and nugget effect) was used to identify the spatial variability of Lugeon values. A high correlation range of 200 m was obtained along the grout curtain galleries, while the range was about 40 m in the vertical direction. The simple kriging method with Gaussian variograms was determined to be the best method for estimating the Lugeon values in the study area using cross validation-criteria (e.g., RMSE = 0.835 and ρ = 0.914). Spatial variation of Lugeon values was mapped using a simulated annealing approach. The analysis revealed: (1) a higher potential for karst development on the left abutment of the Tangab Dam site, (2) the average of simulated Lugeon values decreased from values of about 180 close to the ground surface at 1,440 m a.s.l. to lower values of about 50 at 1,260 m a.s.l., and (3) high Lugeon values in the abutments of the dam site approximately followed the 15° bedrock dip, which confirms the potential development of karst features in the Asmari limestone. A schematic model for development of karst at the Tangab Dam site is proposed based on hydrogeological data and results of simulated Lugeon values around the dam site.