Uncertainties in geomechanical models – exhaustive vs. feasible approach
Authors: Ziegler Moritz , Heidbach Oliver 
Published: November 2021

Abstract. The stress state is a key component for the safety and stability of
deep geological repositories for the storage of nuclear waste. For the
stability assessment and prediction over the repository lifetime, the
stress state is put in relation to the rock strength. This assessment
requires knowledge of both the future stress changes and the current in situ stress
state. Due
to the limited number of in situ stress data records, 3D geomechanical
models are used to obtain continuous stress field
prediction. However, meaningful interpretation of the stress state
model requires quantification of the associated uncertainties that
result from the geological, stress and rock-property data. This would
require thousands of simulations which in a high-resolution model is called an
exhaustive approach. Here we present a feasible approach to reduce computation time significantly. The exhaustive approach quantifies uncertainties that are due to variabilities in stress data records. Therefore, all available data records within a model volume are used individually in separate simulations. Due to the inherent variability in the available data, each simulation represents one of many possible stress states supported by data. A combination of these simulations allows estimation of an individual probability density function for each component of the stress tensor represented by an average value and a standard deviation. If weighting of the data records can be performed, the standard deviation can usually be reduced and the significance of the model result is improved. Alternatively, a range of different stress states supported by the data can be provided with the benefit that no outliers are disregarded, but this comes at the cost of a loss in precision. Both approaches are only feasible since the number of stress data records is limited. However, it is indicated that large uncertainties are also introduced by variabilities in rock properties due to natural intra-lithological lateral variations that are not represented in the geomechanical model or due to measurement errors. Quantification of these uncertainties would result in an exhaustive approach with a high number of simulations, and we use an alternative, feasible approach. We use a generic model to quantify the stress state uncertainties from the model due to rock property variabilities. The main contributor is the Young's module, followed by the density and the Poisson ratio. They affect primarily the σxx and σyy components of the stress tensor, except for the density, which mainly affects the σzz component. Furthermore, a relative influence of the stress magnitudes, the tectonic stress regime and the absolute magnitude of rock properties is observed. We propose to use this information in a post-computation assignment of uncertainties to the individual components of the stress tensor. A range of lookup tables need to be generated that compile information on the effect of different variabilities in the rock properties on the components of the stress tensor in different tectonic settings. This allows feasible quantification of uncertainties in a geomechanical model and increases the significance of the model results significantly.