Novel concepts for the mechanical modelling of warming permafrost rock slopes

This paper discusses mechanical modelling strategies for instable permafrost bedrock. Modelling instable permafrost bedrock is a key requirement to anticipate magnitudes and frequency of rock slope failures in a changing climate but also to forecast the stability of high-alpine infrastructure throughout its lifetime.  The last 5-10 years have brought upon significant advances in the (i) knowledge of relevant hydrostatic pressures in permafrost rock, (ii) the brittle-ductile transitions of ice relevant for larger permafrost rock slope failures, (iii) techniques that can help to decipher the preparation phase of large rockslides and also (iv) many new examples have delivered additional insight into multi-phase failure.High-alpine rock faces witness the past and present mechanical limit equilibrium. Rock segments where driving forces exceed resisting forces fall of the cliff often leaving a rock face behind which is just above the limit equilibrium. All significant changes in rock mechanical properties or significant changes in state of stress will evoke rock instability which often occurs with response times of years to 1000 years. Degrading permafrost will act to alter (i) rock mechanical properties such as compressive and tensile strength, fracture toughness and most likely rock friction, (ii) warming subcero conditions will weaken ice and rock-ice interfaces and (iii) increased cryo- and (iv) hydrostatic pressures are expected. Laboratory experiments provide estimations of the serious impact of thawing and warming rock and ice-mechanical properties (ad i and ii), which often lose 25-75% of their strength between -5°C and -0.5°C.  Approaches to calculate cryostatic pressure (ad iii) have been published and are experimentally confirmed. However, the importance and dimension of extreme hydrostatic forces (ad iv) due to perched water above permafrost-affected rocks has been assumed but has not yet been quantitatively recorded.This paper presents data and strategies how to obtain relevant (i) rock mechanical parameters (compressive and tensile strength and fracture toughness, lab), (ii) ice- and rock-ice interface mechanical parameters (lab), (iii) cryostatic forces in low-porosity alpine bedrock (lab and field) and (iv) hydrostatic forces in perched water-filled fractures above permafrost (field).We demonstrate mechanical models that base on the conceptual assumption of the rock ice mechanical (Krautblatter et al. 2013) and rely on frozen/unfrozen parameter testing in the lab and field. Continuum mechanical models (no discontinuities) can be used to demonstrate permafrost rock wall destabilization on a valley scale over longer time scales, as exemplified by progressive fjord rock slope failure in the Lateglacial and Holocene. Discontinuum mechanical models including rock fracture patterns can display rock instability induced by permafrost degradation on a singular slope scale. Discontinuum mechanical models also have capabilities to link permafrost slope stability to structural loading induced by high-alpine infrastructure such as cable cars and mountains huts. Over longer time scales the polycyclicity of hydro- and cryostatic forcing as well as material fatigue play an important role. We also introduce a mechanical approach to quantify cryo-forcing related rock-fatigue. This paper shows benchmark approaches to develop mechanical models based on a rock-ice mechanical model for degrading permafrost rock slopes.