ALBERT

Description: At the Last Glacial Maximum (LGM), the Rhine glacier in the Swiss Alps covered an area of about 16,000 km2. As part of an integrative study about the safety of repositories for radioactive waste under ice age conditions in Switzerland, we modeled the Rhine glacier using a fully-coupled, three-dimensional, transient, thermo-mechanical Stokes flow model down to a horizontal resolution of about 500 m. The accumulation and ablation gradients that roughly reproduced the geomorphic reconstructions of glacial extent and ice thickness suggested extremely cold (TJuly ~ 0 °C at the glacier terminus) and dry (~ 10 to 20 % of today's precipitation) climatic conditions. Forcing the numerical simulations with warmer and wetter conditions that better matched LGM climate proxy records yielded a glacier on average 500 to 700 m thicker than geomorphic reconstructions. Mass balance gradients also controlled ice velocities, fluxes, and sliding speeds. These gradients, however, had only a small effect on basal conditions. All simulations indicated that basal ice reached the pressure melting point over much of the Rhine and Linth piedmont lobes, and also in the glacial valleys that fed these lobes. Only the outer margin of the lobes, bedrock highs beneath the lobes, and Alpine valleys at high elevations in the accumulation zone remained cold based. The Rhine glacier was thus polythermal. Sliding speed estimated with a linear sliding rule ranged from 20 to 100 m a−1 in the lobes, and 50 to 250 m a−1 in Alpine valleys. Velocity ratios (sliding to surface speeds) were 〉 80 % (lobes) and ~ 60 % (valleys). Basal shear stress was very low in the lobes (0.03–0.1 MPa), much higher in Alpine valleys (〉 0.2 MPa). In these valleys, viscous strain heating was a dominant source of heat, particularly when shear rates in the ice increased due to flow constrictions, confluences, or flow past large bedrock obstacles, contributing locally up to several W m−2 but on average 0.03 to 0.2 W m−2. Basal friction acted as a heat source at the bed of about 0.02 W m−2, 4 to 6 times less than the geothermal heat flow which is locally high (up to 0.12 W m−2). In the lobes, despite low surface slopes and low basal shear stresses, sliding dictated main fluxes of ice which closely followed bedrock topography: ice was channeled in between bedrock highs along troughs, some of which coincided with glacially eroded overdeepenings. These sliding conditions may have favored glacial erosion by abrasion and quarrying. Our results confirmed general earlier findings but provided more insights into the detailed flow and basal conditions of the Rhine glacier at the LGM. Our model results suggested that the trimline could have been buried by a significant thickness of cold ice. These findings have significant implications for interpreting trimlines in the Alps and for our understanding of ice-climate interactions.

Description: Tree roots have long been recognized to increase slope stability by reinforcing the strength of soils. Slope stability models include the effects of roots by adding an apparent cohesion to the soil to simulate root strength. No model includes the combined effects of root distribution heterogeneity, stress-strain behavior of root reinforcement, or root strength in compression. Recent field observations, however, indicate that shallow landslide triggering mechanisms are characterized by differential deformation that indicates localized activation of zones in tension, compression, and shear in the soil. These observations contradict the common assumptions used in present models. Here we describe a new model for slope stability that specifically considers these effects. The model is a strain-step discrete element model that reproduces the self-organized redistribution of forces on a slope during rainfall-triggered shallow landslides. We use a conceptual sigmoidal-shaped hillslope with a clearing in its center to explore the effects of tree size, spacing, weak zones, maximum root-size diameter, and different root strength configurations. The model is driven by root data of Norway spruce obtained from laboratory and field measurements. Simulation results indicate that tree roots can stabilize slopes that would otherwise fail without them and, in general, higher root density with higher root reinforcement results in a more stable slope. Root tension provides more resistance to failure than root compression but roots with both tension and compression offer the best resistance to failure. Lateral (slope-parallel) tension can be important in cases when the magnitude of these forces is comparable to the slope-perpendicular tensile forces. In these cases, lateral forces can bring to failure tree-covered areas with high root reinforcement. Slope failure occurs when downslope soil compression reaches the soil maximum strength. When this occurs depends on the amount of root tension upslope in both the slope-perpendicular and slope-parallel directions. Roots in tension can prevent failure by reducing soil compressive forces downslope. When root reinforcement is limited, hillslopes form a crack parallel to the slope near its top. Simulations with roots that fail across this crack always resulted in a landslide. Slopes that did not form a crack could either fail or remain stable, depending on root reinforcement. Tree spacing is important for the location of weak zones but tree location on the slope (with respect to where a crack opens) is as important. Finally, for the specific cases tested here, large roots, greater than 20 mm, are too few too contribute significantly to root reinforcement. Omitting roots larger than 8 mm predicted a landslide when none should have occurred. Intermediate roots (5 to 20 mm) appear to contribute most to root reinforcement and should be included in calculations. To fully understand the mechanisms of shallow landslide triggering requires a complete re-evaluation of the traditional apparent-cohesion approach that does not reproduce the incremental loading of roots in tension or in compression. Our model shows that it is important to consider the forces held by roots in a way that is entirely different than done thus far. Our work quantifies the contribution of roots in tension and compression which now finally permits to analyze more realistically the role of root reinforcement during the triggering of shallow landslides.

Description: Tree roots have long been recognized to increase slope stability by reinforcing the strength of soils. Slope stability models usually include the effects of roots by adding an apparent cohesion to the soil to simulate root strength. No model includes the combined effects of root distribution heterogeneity, stress-strain behavior of root reinforcement, or root strength in compression. Recent field observations, however, indicate that shallow landslide triggering mechanisms are characterized by differential deformation that indicates localized activation of zones in tension, compression, and shear in the soil. Here we describe a new model for slope stability that specifically considers these effects. The model is a strain-step discrete element model that reproduces the self-organized redistribution of forces on a slope during rainfall-triggered shallow landslides. We use a conceptual sigmoidal-shaped hillslope with a clearing in its center to explore the effects of tree size, spacing, weak zones, maximum root-size diameter, and different root strength configurations. Simulation results indicate that tree roots can stabilize slopes that would otherwise fail without them and, in general, higher root density with higher root reinforcement results in a more stable slope. The variation in root stiffness with diameter can, in some cases, invert this relationship. Root tension provides more resistance to failure than root compression but roots with both tension and compression offer the best resistance to failure. Lateral (slope-parallel) tension can be important in cases when the magnitude of this force is comparable to the slope-perpendicular tensile force. In this case, lateral forces can bring to failure tree-covered areas with high root reinforcement. Slope failure occurs when downslope soil compression reaches the soil maximum strength. When this occurs depends on the amount of root tension upslope in both the slope-perpendicular and slope-parallel directions. Roots in tension can prevent failure by reducing soil compressive forces downslope. When root reinforcement is limited, a crack parallel to the slope forms near the top of the hillslope. Simulations with roots that fail across this crack always resulted in a landslide. Slopes that did not form a crack could either fail or remain stable, depending on root reinforcement. Tree spacing is important for the location of weak zones but tree location on the slope (with respect to where a crack opens) is as important. Finally, for the specific cases tested here, intermediate-sized roots (5 to 20 mm in diameter) appear to contribute most to root reinforcement. Our results show more complex behaviors than can be obtained with the traditional slope-uniform, apparent-cohesion approach. A full understanding of the mechanisms of shallow landslide triggering requires a complete re-evaluation of this traditional approach that cannot predict where and how forces are mobilized and distributed in roots and soils, and how these control shallow landslides shape, size, location, and timing.

Description: At the Last Glacial Maximum (LGM), the Rhine glacier in the Swiss Alps covered an area of about 16 000 km2. As part of an integrative study about the safety of repositories for radioactive waste under ice age conditions in Switzerland, we modeled the Rhine glacier using a thermodynamically coupled three-dimensional, transient Stokes flow and heat transport model down to a horizontal resolution of about 500 m. The accumulation and ablation gradients that roughly reproduced the geomorphic reconstructions of glacial extent and ice thickness suggested extremely cold (TJuly∼0∘C at the glacier terminus) and dry (∼10 % to 20 % of today's precipitation) climatic conditions. Forcing the numerical simulations with warmer and wetter conditions that better matched LGM climate proxy records yielded a glacier on average 500 to 700 m thicker than geomorphic reconstructions. Mass balance gradients also controlled ice velocities, fluxes, and sliding speeds. These gradients, however, had only a small effect on basal conditions. All simulations indicated that basal ice reached the pressure melting point over much of the Rhine and Linth piedmont lobes, and also in the glacial valleys that fed these lobes. Only the outer margin of the lobes, bedrock highs beneath the lobes, and Alpine valleys at high elevations in the accumulation zone remained cold based. The Rhine glacier was thus polythermal. Sliding speed estimated with a linear sliding rule ranged from 20 to 100 m a−1 in the lobes and 50 to 250 m a−1 in Alpine valleys. Velocity ratios (sliding to surface speeds) were 〉80 % in lobes and ∼60 % in valleys. Basal shear stress was very low in the lobes (0.03–0.1 MPa) and much higher in Alpine valleys (〉0.2 MPa). In these valleys, viscous strain heating was a dominant source of heat, particularly when shear rates in the ice increased due to flow constrictions, confluences, or flow past large bedrock obstacles, contributing locally up to several watts per square meter but on average 0.03 to 0.2 W m−2. Basal friction acted as a heat source at the bed of about 0.02 W m−2, 4 to 6 times less than the geothermal heat flow which is locally high (up to 0.12 W m−2). In the lobes, despite low surface slopes and low basal shear stresses, sliding dictated main fluxes of ice, which closely followed bedrock topography: ice was channeled in between bedrock highs along troughs, some of which coincided with glacially eroded overdeepenings. These sliding conditions may have favored glacial erosion by abrasion and quarrying. Our results confirmed general earlier findings but provided more insights into the detailed flow and basal conditions of the Rhine glacier at the LGM. Our model results suggested that the trimline could have been buried by a significant thickness of cold ice. These findings have significant implications for interpreting trimlines in the Alps and for our understanding of ice–climate interactions.