Application of a two-dimensional model of continuous sliding friction to stick-slip

abstract Earthquakes, at least the shallow ones, take place along pre-existing fault planes. The controlling factor is, therefore, friction, and the fault growth process resembles that of stick-slip propagation. We have simulated this process in a two-dimensional model. It is found that propagation velocity can range from sub-shear to 1.1 Vs (the latter is not a limiting value).

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Derivation of Ice Sliding Properties from The Numerical Modelling of Surging Ice Masses

Journal of Glaciology ◽

10.1017/s0022143000030136 ◽

1979 ◽

Vol 23 (89) ◽

pp. 420-421 ◽

Cited By ~ 2

Author(s):

W. F. Budd ◽

B. J. McInnes ◽

I. Smith

Keyword(s):

Shear Stress ◽

Numerical Modelling ◽

Sliding Friction ◽

Two Dimensional ◽

Dimensional Model ◽

Flow Properties ◽

Two Dimensional Model ◽

Two Parameters ◽

Basal Shear ◽

Best Fit

Abstract It is difficult to deduce sliding properties from the numerical modelling of ordinary glaciers because the flow law of ice is still not known well enough to clearly differentiate sliding from internal deformation of the ice. For glaciers undergoing high-speed surges it appears that the majority of the total speed is due to sliding. Furthermore the average basal shear stress of the ice mass is lowered during the surge. This suggests that surging glaciers can be modelled by incorporating a sliding friction law which has the effective friction coefficient decreasing for high velocities. A relation of this type has been found for ice sliding on granite at −0.5°C by Barnes and others (1971) and has also been obtained for rough slabs with ice at the pressure-melting point by Budd and others (1979). A simple two-dimensional model was developed by Budd and McInnes (1974) and Budd (1975), which was found to exhibit the typical periodic surge-like characteristics of real ice masses. Since the sliding-stress relation for the low velocities and stresses was not known, and was not so important for the surges, it was decided to use the condition of gross equilibrium (i.e. that the ice mass as a whole does not accelerate) together with a single-parameter relation for the way in which the friction decreases with stress and velocity to prescribe the basal shear-stress distribution. The low-stress-velocity relation can thus be obtained as a result. This two-dimensional model has now been parameterized to take account of the three-dimensional aspects of real ice masses. A number of ice masses have since been closely matched by the model including three well-known surging ice masses: Lednik Medvezhiy, Variegated Glacier, and Bruarjökull. Since the flow properties of ice are so poorly known—especially for longitudinal stress and strain-rates—the model has been run with two unknown parameters: one a flow-law parameter (η) and the other a sliding parameter (ø). The model is run over a wide range of these two parameters to see if a good match can be made to the real ice masses and if so what the values of the parameters η and ø are for best fit. The matching of the three above ice masses gave very similar values for each of the two parameters η and ø, the value of η being within the range of values expected for the flow properties of temperate ice as determined by laboratory experiments. Using the same values of η and ø it is found that the ordinary glaciers modelled so far do not develop surging but that they could do if the value of ø were increased or if the mass-balance input were sufficiently increased. For Lednik Medvezhiy a detailed analysis of the friction coefficient with velocity was carried out and it was found that the values required for best fit showed a very close agreement to the sliding friction curve of Barnes and others (1971) at −0.5°C. It is concluded that this type of sliding relation can account for the major features of glacier surge phenomena. Finally it is apparent that the numerical modelling technique can be used very effectively to test any large-scale bulk sliding relation by the analysis of real surges of ice masses and in addition can provide further insight into the sliding relation in association with other stresses in the ice mass.

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Derivation of Ice Sliding Properties from The Numerical Modelling of Surging Ice Masses

Journal of Glaciology ◽

10.3189/s0022143000030136 ◽

1979 ◽

Vol 23 (89) ◽

pp. 420-421 ◽

Cited By ~ 1

Author(s):

W. F. Budd ◽

B. J. McInnes ◽

I. Smith

Keyword(s):

Shear Stress ◽

Numerical Modelling ◽

Sliding Friction ◽

Two Dimensional ◽

Dimensional Model ◽

Flow Properties ◽

Two Dimensional Model ◽

Two Parameters ◽

Basal Shear ◽

Best Fit

AbstractIt is difficult to deduce sliding properties from the numerical modelling of ordinary glaciers because the flow law of ice is still not known well enough to clearly differentiate sliding from internal deformation of the ice. For glaciers undergoing high-speed surges it appears that the majority of the total speed is due to sliding. Furthermore the average basal shear stress of the ice mass is lowered during the surge. This suggests that surging glaciers can be modelled by incorporating a sliding friction law which has the effective friction coefficient decreasing for high velocities. A relation of this type has been found for ice sliding on granite at −0.5°C by Barnes and others (1971) and has also been obtained for rough slabs with ice at the pressure-melting point by Budd and others (1979).A simple two-dimensional model was developed by Budd and McInnes (1974) and Budd (1975), which was found to exhibit the typical periodic surge-like characteristics of real ice masses. Since the sliding-stress relation for the low velocities and stresses was not known, and was not so important for the surges, it was decided to use the condition of gross equilibrium (i.e. that the ice mass as a whole does not accelerate) together with a single-parameter relation for the way in which the friction decreases with stress and velocity to prescribe the basal shear-stress distribution. The low-stress-velocity relation can thus be obtained as a result.This two-dimensional model has now been parameterized to take account of the three-dimensional aspects of real ice masses. A number of ice masses have since been closely matched by the model including three well-known surging ice masses: Lednik Medvezhiy, Variegated Glacier, and Bruarjökull. Since the flow properties of ice are so poorly known—especially for longitudinal stress and strain-rates—the model has been run with two unknown parameters: one a flow-law parameter (η) and the other a sliding parameter (ø). The model is run over a wide range of these two parameters to see if a good match can be made to the real ice masses and if so what the values of the parameters η and ø are for best fit.The matching of the three above ice masses gave very similar values for each of the two parameters η and ø, the value of η being within the range of values expected for the flow properties of temperate ice as determined by laboratory experiments. Using the same values of η and ø it is found that the ordinary glaciers modelled so far do not develop surging but that they could do if the value of ø were increased or if the mass-balance input were sufficiently increased.For Lednik Medvezhiy a detailed analysis of the friction coefficient with velocity was carried out and it was found that the values required for best fit showed a very close agreement to the sliding friction curve of Barnes and others (1971) at −0.5°C. It is concluded that this type of sliding relation can account for the major features of glacier surge phenomena.Finally it is apparent that the numerical modelling technique can be used very effectively to test any large-scale bulk sliding relation by the analysis of real surges of ice masses and in addition can provide further insight into the sliding relation in association with other stresses in the ice mass.

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Commitment to pro- versus counter-attitudinal behavior and the dynamics of social representations

Swiss Journal of Psychology ◽

10.1024//1421-0185.61.1.34 ◽

2002 ◽

Vol 61 (1) ◽

pp. 34-44 ◽

Cited By ~ 8

Author(s):

Eric Tafani ◽

Lionel Souchet

Keyword(s):

Higher Education ◽

Social Representations ◽

Cognitive Restructuring ◽

Social Representation ◽

Two Dimensional ◽

Dimensional Model ◽

Social Actions ◽

The Social ◽

Two Dimensional Model ◽

Students Attitudes

This research uses the counter-attitudinal essay paradigm ( Janis & King, 1954 ) to test the effects of social actions on social representations. Thus, students wrote either a pro- or a counter-attitudinal essay on Higher Education. Three forms of counter-attitudinal essays were manipulated countering respectively a) students’ attitudes towards higher education; b) peripheral beliefs or c) central beliefs associated with this representation object. After writing the essay, students expressed their attitudes towards higher education and evaluated different beliefs associated with it. The structural status of these beliefs was also assessed by a “calling into question” test ( Flament, 1994a ). Results show that behavior challenging either an attitude or peripheral beliefs induces a rationalization process, giving rise to minor modifications of the representational field. These modifications are only on the social evaluative dimension of the social representation. On the other hand, when the behavior challenges central beliefs, the same rationalization process induces a cognitive restructuring of the representational field, i.e., a structural change in the representation. These results and their implications for the experimental study of representational dynamics are discussed with regard to the two-dimensional model of social representations ( Moliner, 1994 ) and rationalization theory ( Beauvois & Joule, 1996 ).

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