Bayesian Emulation of Computer Experiments of Infrastructure Slope Stability Models

We performed a fully-Bayesian Gaussian process emulation and sensitivity analysis of a numerical model that simulates transport cutting slope deterioration. In the southern UK, a significant proportion of transport infrastructure is built in overconsolidated high-plasticity clay that is prone to deterioration due to seasonal wetting-drying cycles and weather extremes (Stirling 2021; Postill et al. 2021). Geotechnical modelling software (FLAC) was used to simulate the dissipation of excess pore water pressure and seasonal pore water pressure cycles in cuttings (Rouainia et al. 2020). However, due to their high computational expense, it was impractical to perform the number of computer simulations that would be sufficient to understand deterioration behaviour over a range of cutting geometries and soil strength parameters. To address this, we used Gaussian processes and Bayesian inference to emulate the relation between deterioration factors and slope properties (Bastos and O'Hagan 2009). These factors include time to failure (Svalova et al. 2021), failure area, and factor of safety. For our training data, we used a Latin hypercube design to create a computer experiment of 76 numerical models whereby we varied slope height, angle, peak cohesion, peak friction, and permeability. Some of the runs did not reach ultimate limit state failure, resulting in censored times to failure and failure areas. We used Markov chain Monte Carlo sampling to obtain posterior distributions of the emulator parameters, as well as the censored times to failure (Brooks et al. 2010; Kyzyurova 2017). Our emulator could be used to inform slope design, management, and maintenance on different spatio-temporal scales of transport networks.

Keywords: emulation, Gaussian processes, infrastructure slopes, Bayesian inference.