Disturbed State constitutive modeling of two Pleistocene tills

The Disturbed State Concept (DSC) provides a general approach for constitutive modeling of deforming materials. Here, we briefly explain the DSC and present the results of laboratory tests on two regionally significant North American tills, along with the results of a numerical simulation to predict the behavior of one of the tills in an idealized physical system. Laboratory shear tests showed that plastic strain starts almost from the beginning of loading, and that failure and resulting motion begin at a critical disturbance, when about 85% of the mass has reached the fully adjusted or critical state. Specimens of both tills exhibited distributed strain, deforming into barrel shapes without visible shear planes. DSC parameters obtained from shear and creep tests were validated by comparing model predictions against test data used to find the parameters, as well as against data from independent tests. The DSC parameters from one of the tills were applied in a finite-element simulation to predict gravity-induced motion for a 5000-m long, 100-m thick slab of ice coupled to an underlying 1.5-m thick layer of till set on a 4° incline, with pore-water pressure in the till at 90% of the load. The simulation predicted that in the middle segment of the till layer (i.e., from x=2000 to 3000 m) the induced (computed) shear stress, strain, and disturbance increase gradually with the applied shear stress. Induced shear stress peaks at ∼60 kPa. The critical disturbance, at which failure occurs, is observed after the peak shear stress, at an induced shear stress of ∼23 kPa and shear strain of ∼0.75 in the till. Calculated horizontal displacement over the height of the entire till section at the applied shear stress of 65 kPa is ∼4.5 m. We note that the numerical prediction of critical disturbance, when the displacement shows a sharp change in rate, compares very well with the occurrence of critical disturbance observed in the laboratory triaxial tests, when a sharp change in the rate of strain occurs. This implies that the failure and concomitant initiation of motion occur near the residual state, at large strains. In contrast to the Mohr–Coulomb model, which predicts failure and motion at very small (elastic) strain, the DSC thus predicts failure and initiation of motion after the till has undergone considerable (plastic) strain. These results suggest that subglacial till may be able to sustain stress in the vicinity of 20 kPa even after the motion begins. They also demonstrate the potential of the DSC to model not only local behavior, including potential “sticky spot” mechanisms, but also global behavior for soft-bedded ice.