“…Rheologists have suggested such models to describe the ductile fracture of samples of rock, soil, high-performance metal alloys, concrete, polymers and ice (see Varnes, 1983 for a review and Voitkovskii, 1960;Szyszkowski and Glockner 1986;Mahrenholtz and Wu 1992 for laboratory ice). At large scales, finite time singularity models have been proposed to describe the mechanisms of landslides (e.g.…”
Abstract. The velocity of unstable large ice masses from hanging glaciers increases as a power-law function of time prior to failure. This characteristic acceleration presents a finite-time singularity at the theoretical time of failure and can be used to forecast the time of glacier collapse. However, the non-linearity of the power-law function makes the prediction difficult. The effects of the non-linearity on the predictability of a failure are analyzed using a non-linear regression method. Predictability strongly depends on the time window when the measurements are performed.Log-periodic oscillations have been observed to be superimposed on the motion of large unstable ice masses. The value of their amplitude, frequency and phase are observed to be spatially homogeneous over the whole unstable ice mass. Inclusion of a respective term in the function describing the acceleration of unstable ice masses greatly increases the accuracy of the prediction.
“…Rheologists have suggested such models to describe the ductile fracture of samples of rock, soil, high-performance metal alloys, concrete, polymers and ice (see Varnes, 1983 for a review and Voitkovskii, 1960;Szyszkowski and Glockner 1986;Mahrenholtz and Wu 1992 for laboratory ice). At large scales, finite time singularity models have been proposed to describe the mechanisms of landslides (e.g.…”
Abstract. The velocity of unstable large ice masses from hanging glaciers increases as a power-law function of time prior to failure. This characteristic acceleration presents a finite-time singularity at the theoretical time of failure and can be used to forecast the time of glacier collapse. However, the non-linearity of the power-law function makes the prediction difficult. The effects of the non-linearity on the predictability of a failure are analyzed using a non-linear regression method. Predictability strongly depends on the time window when the measurements are performed.Log-periodic oscillations have been observed to be superimposed on the motion of large unstable ice masses. The value of their amplitude, frequency and phase are observed to be spatially homogeneous over the whole unstable ice mass. Inclusion of a respective term in the function describing the acceleration of unstable ice masses greatly increases the accuracy of the prediction.
A constitutive law for snow derived from a complementary power potential is proposed. The total deformation of snow is divided into elastic and creep parts. A hereditary integral using Norton’s power law is employed to describe primary creep. The concept of effective stress, which takes compressibility of snow into account, is used to calculate creep deformation. The hereditary integral is approximated by a non-linear spring–dashpot model. Results from uniaxial compression experiments (stress range 15– 45 kPa) on sieved snow of density range 180–470 kgm-3 were used to determine the constants appearing in the constitutive equation. The response of snow to constant strain rate (7.4×10-6 s-1 to 2.2×10-5 s-1) under bilaterally confined conditions was found with an iterative scheme employing the proposed constitutive law. The simulated results agree well with the measured axial stresses and volumetric changes.
“…A number of models exist to describe this behavior. The model used in this paper is based on work of Szyszkowski and Glockner (1986, 1987). In this model ice is treated as an isotropic, non-linear viscoelastic material.…”
Section: Constitutive Formulationmentioning
confidence: 99%
“…With this second term added to Equation (16) the strain e ij c associated with the integral term was accurately represented. For a more detailed discussion the reader is referred to Szyszkowski and Glockner (1986, 1987). Fig.…”
A constitutive theory of snow is developed to describe the mechanical properties of snow in terms of the properties of the ice grains and the necks that interconnect them. The principle of virtual work is used to calculate the stresses in the particles and necks. A number of different deformation mechanisms are investigated and, depending upon the deformation mechanism which is dominant for given load conditions, different equations are used to calculate the strains in the grains and necks. These strains around a representative ice grain are then averaged and scaled to obtain the global strains in the snow. The theory is then compared with experimental data to determine if the mechanical properties of snow can be adequately represented. Results show that the constitutive theory does work, but that it is cumbersome to implement, and that for practical use substantial computational capability is needed.
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