Bayesian emulation of deterioration curves using quadratic and B-spline hierarchical models

The stability of geotechnical infrastructure assets, such as cuttings and embankments, is crucial to the safe and efficient delivery of transport services. The successful emulation of geotechnical models of deterioration of infrastructure slopes has the potential to inform slope design, maintenance and remediation by introducing the time dependency of deterioration into geotechnical asset management. We have performed computer experiments of deterioration, measured by the factor of safety (FoS), for a set of cutting slope geometries and soil properties that are common in the southern UK. Whilst computer experiments are an extremely useful and cost-effective method of better understanding deterioration mechanisms, it would not be practical to run enough experiments to understand relations between high-dimensional inputs and outputs. Therefore, we trained a fully-Bayesian Gaussian process emulator using an ensemble of 75 computer experiments to predict the FoS. We construct two different emulator models, one approximating the FoS temporal evolution with a quadratic model and one approximating the temporal evolution with a B-spline model; and we emulated their parameters. We also compare the ability of our models to predict failure time. The developed models could be used to inform infrastructure cutting slope design and management, and extend serviceable life.