Bayesian Inference for Geotechnical Modelling and Parameter Calibration

The accurate calibration of constitutive model parameters is fundamental for representative modelling in geotechnical engineering. Recent developments in full-field displacement measurement techniques have created significant improvements from standard element tests as means of calibration. However, implicit assumptions of determinism lead to a failure of uncertainty consideration and the incorporation of unknown error in calibration. Bayesian Inference is increasingly applied to geotechnical engineering problems (e.g. Contreras and Brown, 2019 or Jin et al., 2018). This proposal suggests assessing the application of Bayesian Inference to geotechnical engineering problems holistically, beginning with parameter calibration and extending into constitutive model definition, as means of addressing current issues, improving modelling approach and building on existing research.

Fundamental issues exist with the current approach to calibration. It is assumed in conventional calibration that minimizing the difference between model response and measured data minimises calibration error, implying that uncertainty is only associated with the model and not the measured data. However, both measurement uncertainty (error, systematic or random, created within experimental practice and observation) and parametric uncertainty (that which cannot be controlled experimentally including the inherent variability of material properties) exist as well. Identifying uncertainty only with the model can introduce bias and, combined with leaving modelling error un-assessed, may amplify model uncertainty (Muehleisen and Bergerson, 2016). As a consequence, models are 'over-fitted' to the noise of measured data (Dietterich, 1995).

Further issues exist with conventional calibration methods (predominantly standard element tests). Allowances in modelling assumptions for ease of practice can lead to poor calibration. For example, some tests (such as triaxial compression) justify recording average values at boundaries by assuming a homogeneous element response. This can be non-representative (and an invalid assumption) if it ignores localised deformation in shear band formation and associated stress and strain paths (Gylland et al., 2014). As a consequence of difficulty in calibration, subjectivity in model fit is introduced, exemplied in Ragni et al. (2015) hypoplastic model simulated response. Recent developments in full-field displacement measurement techniques, including direct image correlation (DIC) and particle image velocimetry (PIV) (Stanier & White, 2016), facilitate measurement of inhomogeneity, therefore greatly assisting in addressing the aforementioned method issues. For example, an alternative framework for calibrating strain-softening parameters, proposed and theoretically validated by Singh and Stanier (unpublished), is currently under experimental trialling by Smith and Stanier (unpublished). The technique employs the Virtual Fields Method (Grediac and Pierron, 1998) which applies the principle of energy conservation and virtual work to derive constitutive model parameters. Within the framework, parameter optimisation is achieved by minimising an objective function, an expression of energy conservation. Assuming a constitutive model response (with consideration of initial conditions), stress fields are developed from the strain fields. Despite great improvement, accuracy remains limited by uncharacterised uncertainty associated with measurement and model error due to the underlying approach of fitting to noisy data.