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USF_Sliding.f90
Friction_Coulomb
Flow Solution
in Flow Solution Name
, Normal Vector
, Stress
The file USF_Sliding.f90
contains two user functions to apply non-linear friction at the base of glacier.
The first user function (Sliding_Weertman
) is a non-linear Weertman-type friction law and is described here. The second user function (Friction_Coulomb
) is a non-linear water pressure dependant friction law, as proposed by Schoof (2005) and Gagliardini et al. (2007), and is presented in this page.
The friction law in Friction_Coulomb is of the form:
where
and
The Slip Coefficient in Elmer is then given as
When , in the previous equation is replaced by .
The parameters to be given are:
Friction Law Sliding Coefficient
→ Friction Law Post-Peak Exponent
→ Friction Law Maximum Value
→ ~ max bed slopeFriction Law Exponent
→ m = (n Glen's law)Friction Law Linear Velocity
→
The effective pressure is defined as , where is the normal Cauchy stress and the water pressure. Here, at time t+dt, the normal Cauchy stress is estimated from the stress computed at time t. The water pressure is prescribed as an External Pressure
(Negative - Compressive convention, and therefore the water pressure is the opposite of the 'External Pressure').
The required keywords in the SIF file for this user function are:
!!! Bedrock Boundary Condition Boundary Condition 1 Target Boundaries = 1 Normal-Tangential Velocity = Logical True Flow Force BC = Logical True !! Water pressure given through the Stokes 'External Pressure' parameter !! (Negative = Compressive) External Pressure = Equals Water Pressure Velocity 1 = Real 0.0 Slip Coefficient 2 = Variable Coordinate 1 Real Procedure "ElmerIceUSF" "Friction_Coulomb" Slip Coefficient 3 = Variable Coordinate 1 Real Procedure "ElmerIceUSF" "Friction_Coulomb" !! Parameters needed for the Coulomb Friction Law Friction Law Sliding Coefficient = Real 4.1613e5 Friction Law Post-Peak Exponent = Real 1.0 !(q=1) Friction Law Maximum Value = Real 1.0 !(C=1) Friction Law PowerLaw Exponent = Real 3.0 !(m = n = 3 Glen's law) Friction Law Linear Velocity = Real 0.01 End
An example of the usage of the user function Friction_Coulomb TODO
When this friction law is used, it can be cited using the following reference:
Gagliardini O., D. Cohen, P. Råback and T. Zwinger, 2007. Finite-Element Modeling of Subglacial Cavities and Related Friction Law. J. of Geophys. Res., Earth Surface, 112, F02027.