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User Function Coulomb Friction Law

General Informations

USF Fortran File: USF_Sliding.f90
USF Name: Friction_Coulomb
Required Input Variable(s): A Flow Solution in Flow Solution Name, Normal Vector, Stress

General Description

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:
$tau_b = C.N {[{ {chi . {u_b}^{-n} }/ {(1 + a . chi^q)} }]}^{1/n} . u_b$
where
$a = {(q - 1)^{q-1}}/{q^q}$
and
$chi = {u_b}/{C^n N^n A_s}$

The Slip Coefficient in Elmer is then given as
$C.N {[{ {chi . {u_b}^{-n} }/ {(1 + a . chi^q)} }]}^{1/n}$
When $u_b < u_{t0}$ , u_b in the previous equation is replaced by $u_{t0}$ .

The parameters to be given are:

Friction Law Sliding Coefficient →
Friction Law Post-Peak Exponent →
Friction Law Maximum Value → ~ max bed slope
Friction Law Exponent → m = (n Glen's law)
Friction Law Linear Velocity → $u_{t0}$

The effective pressure is defined as $N = -sigma_{nn} -p_w$ , where $sigma_{nn}$ is the normal Cauchy stress and p_w 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').

SIF contents

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

Examples

An example of the usage of the user function Friction_Coulomb TODO

Reference

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.

userfunctions/coulomb.1389084247.txt.gz · Last modified: 2014/01/07 08:44 by gag

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