Directing Exploration with 3D FEM Sensitivity and Data Uncertainty
Publication: Journal of Geotechnical and Geoenvironmental Engineering
Volume 125, Issue 11
Abstract
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.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Baecher, G. B., and Ingra, T. S. (1981). “Stochastic FEM in settlement predictions.”J. Geotech. Engrg. Div., ASCE, 107(4), 449–463.
2.
Bischof, C., Carle, A., Khademi, P., Maure, A., and Hovland, P. (1995). “ADIFOR 2.0 user's guide (revision C).” Tech. Memo. No. 192 and Ctr. for Res. on Parallel Computation Tech. Rep. CRPC-95516-S, Mathematics and Comp. Sci. Div., Argonne National Laboratory, Argonne, Ill.
3.
Casagrande, A. (1965). “Role of the `calculated risk' in earthwork and foundation engineering.” J. Soil Mechanics and Foundations Div., ASCE, 91(SM4), 1–40.
4.
Davis, C. D. (1986). Statistics and data analysis in geology. Wiley, New York.
5.
Ditmars, J. D., Baecher, G. B., Edgar, D. E., and Dowding, C. H. ( 1988). “Radioactive waste isolation in salt: A method for evaluating the effectiveness of site characterization measurements.” U.S. Department of Energy, Civilian Radioactive Waste Management Salt Repository Project Office, available from National Technical Information Service, U.S. Department of Commerce, Springfield, Va.
6.
Dowding, C. H., ed. (1978). Site characterization and exploration. Proc., Geotech. Div., ASCE, New York.
7.
Finno, R. J. ( 1983). “Response of cohesive soil to advanced shield tunneling,” PhD thesis, Stanford Univ., Stanford, Calif.
8.
Finno, R. J. ( 1996). “LIGO report.” Internal Northwestern University document. Civ. Engrg. Dept., Northwestern University, Evanston, Ill.
9.
Freeze, R. A., Massmann, J., Smith, L., Sperling, T., and James, B. (1990). “Hydrogeological decision analysis: 1. A framework.” Ground Water, 28(5), 738–766.
10.
Gelman, A., Carlin, J. B., Stern, H. S., and Rubin, D. B. ( 1995). Bayesian data analysis. Chapman & Hall, London, 478–479.
11.
Graettinger, A. J. ( 1998). “Reliability-based exploration: A quantitative method for evaluating and directing subsurface characterization,” PhD thesis, Northwestern University, Evanston, Ill.
12.
Graettinger, A. J., and Dowding, C. H. (1997). “Quantitative site exploration directed by interface location uncertainty.” Proc., 5th Great Lakes Geotech./Geoenvir. Conf., Site Characterization for Geotech. and Geoenvir. Problems, University of Michigan, College of Engrg., Ann Arbor, Mich., 117–131.
13.
Grivas, D. A. (1977). “Probability theory and reliability analysis in geotechnical engineering.” Rep. of an NSF-Sponsored Workshop at Rensselaer Polytechnic Institute, Rensselaer Polytechnic Inst., New York.
14.
Harr, M. E. (1996). Reliability-based design in civil engineering. Dover, New York.
15.
Horwedel, J. E., Raridon, R. J., and Wright, R. Q. (1992). “Automated sensitivity analysis of an atmospheric dispersion model.” Atmospheric Envir., 26A(9), 1643-1649.
16.
Isaaks, E. H., and Srivastava, R. M. ( 1989). An introduction to applied geostatistics. Oxford University Press, New York, 278–322.
17.
Johnson, R. L. (1996). “A Bayesian geostatistical approach to the design of adaptive sampling programs.” Geostatistics for environmental and geotechnical applications, ASTM STP 1283, ASTM, West Conshohocken, Pa.
18.
Johnston, P. R. ( 1981). “Finite element consolidation analysis of tunnel behavior in clay,” PhD thesis, Stanford Univ., Stanford, Calif.
19.
Kulhawy, F. H., and Trautmann, C. H. ( 1996). “Estimation of in-situ uncertainty.” Uncertainty in the geologic environment: From theory to practice, Geotech. Spec. Publ. No. 58, ASCE, New York, 269–286.
20.
Lacasse, S., and Nadim, F. ( 1996). “Uncertainties in characterizing soil properties.” Uncertainty in the geologic environment: From theory to practice, Geotech. Spec. Publ. No. 58, ASCE, New York, 49–75.
21.
National Research Council. (1995). Probabilistic methods in geotechnical engineering. Board on Energy and Environmental Systems, National Research Council, Washington, D.C.
22.
Poeter, E. P., and McKenna, S. A. (1995). “Reducing uncertainty associated with ground-water flow and transport prediction.” Ground Water, 33(6), 899–904.
23.
Reeves, H. W., Dowding, C., and Igusa, T. ( 1998). “An efficient reliability based approach to aquifer remediation design” EPA Res. Proj., 98 NCERQA, EPA, Washington, D.C.
24.
Ripley, B. D. (1987). Stochastic simulation. Wiley, New York, 237.
25.
Shackelford, C. D., Nelson, P. P., and Roth, M. J. S., eds. (1996). Uncertainty in the geologic environment: From theory to practice, Geotech. Spec. Publ. No. 58, ASCE, New York.
26.
Smith, A. D. ( 1989). “Computerized modeling of geotechnical stratigraphic data,” PhD thesis, Massachusetts Institute of Technology, Mass.
27.
Tomasko, D., Reeves, M., Kelley, V. A., and Pickens, J. F. (1987). “Parameter Sensitivity and Importance for Radionuclide Transport in Double-Porosity Systems.” Proc., Conf. on Geostatistical, Sensitivity, and Uncertainty Methods for Ground-Water Flow and Radionuclide Transport Modeling, Battelle Press, Columbus, Ohio, 297–321.
28.
Wilson, J. L., and Metcalfe, D. E. (1985). “Illustration and verification of adjoint sensitivity theory for steady state groundwater flow.” Water Resour. Res., 21(11), 1602–1610.
Information & Authors
Information
Published In
History
Received: Apr 9, 1998
Published online: Nov 1, 1999
Published in print: Nov 1999
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.