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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
a = {(q - 1)^{q-1}}/{q^q}
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 CoefficientA_s
  • Friction Law Post-Peak Exponentq >= 1
  • Friction Law Maximum ValueC ~ max bed slope
  • Friction Law Exponent → m = (n Glen's law)
  • Friction Law Linear Velocityu_{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 (Positive - Compressive convention).

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 this parameter (Positive = 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         


An example of the usage of the user function Friction_Weertman 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.

userfunctions/coulomb.1355423253.txt.gz · Last modified: 2012/12/13 18:27 by gag
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