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Forecasting the Number of Soil Samples Required to Reduce Remediation Cost Uncertainty

^a Eidgenössische Technische Hochschule Zürich, Institut für Raumplanung und Landschaftsentwicklung, Hönggerberg, CH-8093 Zürich, Switzerland (current address: University of Neuchâtel, Centre for Hydrogeology, 11 rue Emile Argand, CH-2007 Neuchâtel, Switzerland)
^b Ecole Nationale Supérieure des Mines de Paris, Centre de Géostatistique, 35 rue Saint Honoré, 77305 Fontainebleau, France
^c Université de Neuchâtel, Centre d'Hydrogéologie de Neuchâtel, 11 rue Emile Argand, CH-2007 Neuchâtel, Switzerland

View larger version (36K): [in a new window]   Fig. 1. The different steps of a common remediation works (soil selection, excavation, transport, storage, and treatment), and the corresponding soil volumes (Ve, excavated volume; Vs, stored volume; Vc, cleanup volume).

View larger version (16K): [in a new window]   Fig. 2. Information effect: the true block concentration, always unknown, is estimated by the concentration of a composite of samples collected in the block.

View larger version (23K): [in a new window]   Fig. 3. Theoretical graph of block concentration as a function of block probabilities of exceeding the remediation cutoff S. It illustrates the meaning of the low-risk volume Vlr (blocks of soils with probabilities less than ), the uncertain volume Vu (blocks of soils with probabilities greater than and less than ß), and the excavated volume Ve (blocks of soils with probabilities greater than ß). The excavated volume is composed of the cleanup volume Vc (blocks of soils with pollutant concentrations greater than S) and the stored volume Vs (blocks of soils with pollutant concentrations less than S).

View larger version (25K): [in a new window]   Fig. 4. Location of the 75 samples, collected in six investigation stages, on the map of the former smelting work.

View larger version (41K): [in a new window]   Fig. 5. Maps showing the location (white dots) of the simulated additional samples for the successive values of N7. The points are superimposed on the simplified map of the probabilities where block concentration exceeds 300 mg kg–1 in the superficial layer (estimated at Stage 6 with the 75 real site investigation data points).

View larger version (47K): [in a new window]   Fig. 6. Simplified maps of probabilities where block concentrations exceed 300 mg kg–1 in the superficial layer. These maps illustrate how the forecasted uncertain volume reduces when additional data are "simulated." Note that these maps are only an illustration of the uncertainty reduction but are not real forecasts as the additional data are simulated and not actual data.

View larger version (24K): [in a new window]   Fig. 7. Volume forecasts graph: excavated volumes Ve and uncertain volumes Vu as a function of the number N7 of additional data whose sampling is "simulated" at Stage 7.

View larger version (23K): [in a new window]   Fig. 8. Cost forecasts graph: investigation costs Ci, cleanup costs Cc, and uncertain costs Cu as a function of the number N7 of additional data whose sampling is "simulated" at Stage 7.