Directing exploration with 3D FEM sensitivity and data uncertainty

Quantitatively directed exploration (QDE) employs a first-order Taylor series expansion to combine sensitivity of a 3D finite-element model (FEM) and uncertainty in geologic data to calculate the variance in project performance, which is employed to direct exploration. This approach is made practical by calculating model sensitivity with direct differentiation of the engineering analysis code, thus producing sensitivity with a single model run rather than multiple runs required by parameter perturbation. Uncertainty in subsurface data is computed through two different extrapolation methods for comparison: kriging and conditional probability (Bayesian updating). Although either of these methods can be employed in QDE, conditional probability is required to quantifiably terminate exploration. The QDE framework is applicable to any subsurface analysis that employs a 3D FEM. A case study illustrates the QDE approach, where settlement is the performance criterion, and layer interface elevations are the uncertain geologic data. Additional boring locations identified by QDE were placed where a combination of model sensitivity and subsurface uncertainty was the greatest, thus directing exploration toward the building footprint and away from existing sampled points.