Spatial modeling of discontinuity intensity from borehole observations at El Teniente mine, Chile

Abstract This work addresses the problem of predicting the discontinuity intensity P 32 (discontinuity area per unit volume of rock mass) in space and of quantifying the uncertainty in the true P 32 values, using information from observed discontinuities intersecting boreholes. This problem is relevant in various fields of engineering, including mining applications, hydrocarbon extraction, groundwater modeling and civil works. The main idea is to calculate experimental P 32 values for borehole segments (composites), based on a Terzaghi weighting of the discontinuities that intersect the boreholes. A validation exercise performed on simulated discrete fracture networks demonstrates that the calculated P 32 values provide unbiased predictions of the true P 32 , at both global and local scales, and can therefore be used as experimental data for spatial interpolation purposes. By using geostatistical simulation techniques, the spatial prediction of the P 32 and the corresponding measures of uncertainty can be obtained on a block-by-block basis. This methodology is applied to a data set from the El Teniente copper mine, Codelco-Chile. The objective is to map the expected values of the intensity of stockwork veins with a weak infill mineral assemblage and a typical thickness greater than 1 mm, which are referred to as weak veins. Confidence limits on this intensity and its probability of exceeding given critical values are also estimated. The quality of the prediction and of the uncertainty quantification is checked by leave-one-out cross-validation. The resulting confidence limits and probability maps can be used as indicators to define geotechnical domains in the rock mass.