geoENV 2024

Geostatistical modeling of stratigraphical layers and geotechnical parameters: Cone Penetration Test, Modulus and Limit Pressure from Menard pressure-meter test

Authors: Pedram MASOUDI (1), Cyril SIMON (2), Claire FAUCHEUX (1), Margaux BLANCKAERT (2) et Hélène BINET (1)

(1) Geovariances, (2) EDF-DI-TEGG

Abstract:

Stratigraphical information is usually more abundant on a site under investigation than geotechnical information. Geotechnical parameters depend on stratigraphical layers. So, the constructed stratigraphical model could be used to create a robust geotechnical model. The objective of this study is to build 3D block models of the Cone Penetration Test (CPT), Modulus (Em), and Limit Pressure (Pl) from Menard Pressure-meter tests on a nuclear power plant site under development. From a geological viewpoint, the site is on recent sediments (less than 2000 years) with three sandy strata, N1, N2, and N3, with a total thickness of about 30 m. N2 is sandwiched between N1 from the top and N3 from the bottom, and N3 is laid on a shale deposit. A thin silt stratum (thickness between 0.5 m and 2.5 m) is deposited between N2 and N3. The geotechnical behavior of the silty-thin stratum is very different from the adjacent sandy layers, e.g., the CPT is much lower in the silt. Therefore, this thin stratum is the primary concern of the geotechnical investigations.

The geostatistics theory provides various modeling tools to create 2D maps and 3D block models of categorical variables, like stratigraphical units, and continuous variables, like geotechnical parameters. Following an exploratory data analysis, completed by the analysis of the spatial stationarity, three approaches were designed for stratigraphical modeling:
(I) interpolating top strata by cokriging,
(II) interpolating strata thickness by kriging and
(III) generating 100 possible realizations by Truncated Gaussian Simulation (TGS).
The approaches (I) and (II) provide the most probable stratigraphical model, whereas the approach (III) provides a probabilistic evaluation of stratigraphical units.

To create geotechnical models for the CPT, Em, and Pl, three approaches were designed:
(A) interpolating the parameters independent from the stratigraphical model,
(B) interpolating the parameters in each stratigraphic unit individually and
(C) estimating the parameters by considering the probability of each stratigraphical unit, previously calculated during the approach (III).

In all the approaches, the interpolation method was ordinary kriging for CPT and ordinary cokriging for Em and Pl. The variographical and interpolation steps were performed in a flattened space following the application of an unfolding method. After comparing the results, it is concluded that the approach (C) provides the best result because geotechnical parameters depend on the stratigraphical model. In this approach, both the stratigraphical model and its uncertainty are considered in geotechnical modeling. In addition, stratigraphical information is more abundant and smoother than geotechnical parameters. Hence, the stratigraphical model splits the geotechnical information into a more homogenous space.

Geostatistical modeling of total precipitation for hydrological forecast over south shore river basins of Quebec to improve hydroelectric power management

Authors: Dominique TAPSOBA (1) et Pedram MASOUDI (2)

(1) Hydro-Québec, (2) Geovariances

Abstract:

The ERA5 is a global reanalysis dataset that has monitored the earth’s climate and weather hourly since 1940. It has good geographical coverage and high spatial resolution; however, no uncertainty is associated with the available data. The ERA5 dataset is widely used in different studies. This project aims to use multivariate geostatistical methods in modeling the ERA5 data and site observations, i.e., hourly measurements of total precipitation at meteorological stations. The study area is south of Quebec, covering several drainage basins. Estimating total precipitation in each drainage basin is important in hydrological forecasts and improving hydroelectric power management. The results will be used to calibrate the hydrological model of flow simulation and meteorological post-processing.

From a metrological viewpoint, the advantage of site observations is direct measurements, while the ERA5 dataset is indirect information. From the perspective of data configuration, the site measurements are irregularly distributed, and the distance between the adjacent stations could vary from a few kilometers to more than one hundred kilometers; meanwhile, the ERA5 data are regularly spaced with a distance of about 10 km. In the language of statistics, the coefficient of variation of site observations is in the order of magnitude of 0.1. In contrast, the coefficient of variation of ERA5 is in the order of magnitude of 0.001. It means that ERA5 data are smoother than site observations, and the smoothness is a general disadvantage of indirect information, here ERA5.

The site observations and ERA5 dataset are heterotopic, i.e., there is a distance between these two datasets. Hence, the application of statistical multivariate analysis is limited, and a prerequisite could be interpolating one dataset to the other, so cross-variogram and co-simulation could be used. The implemented workflow contains two main steps: (i) Sequential Indicator Simulation (SIS) for calculating the probability of precipitation and (ii) Turning Bands Co-Simulation (TBS) for predicting total precipitation in areas with a probability of precipitation above zero. So, quantile maps of total precipitation are provided in an hourly frequency. Close to the principal data, i.e., site observations, the geostatistical interpolation tends to the direct measurement of total precipitation, and far from the principal data, spatial behavior of total precipitation would be inferred from the auxiliary data, i.e., ERA5, which has better spatial coverage. The geostatistical analysis is applied for 24 hours over a period of several weeks to confirm the robustness of results over the weeks.