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~~NOTOC~~
===== User Function Weertman Friction Law =====

==== General Informations ====
  * **USF Fortran File:** ''USF_Sliding.f90''
  * **USF Name:** ''Sliding_Weertman''
  * **Required Input Variable(s):** A ''Flow Solution'' in ''Flow Solution Name'', ''Normal Vector''


==== General Description ====
The file ''USF_Sliding.f90'' contains 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 in this page. 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 [[:userfunctions:coulomb|here]]. The third user function (''Sliding_Budd'') is described [[:userfunctions:budd|here]] and is from Budd et al 1984 (Annals of Glaciology 5, page 29-36).
  
 
The friction law in ''Weertman_Sliding'' is of the form:\\
<m>  tau_b = C.{u_b}^{m - 1} . u_b  </m>\\

The //Slip Coefficient// in Elmer is then given as\\
<m>  C.{u_b}^{m - 1}  </m>\\
When  <m>u_b < u_{t0}</m>, <m>u_b</m> in the previous equation is replaced by <m>u_{t0}</m> (linearisation for small velocity).


The parameters to be given are:\\
  * ''Weertman Friction Coefficient''      -> <m>C</m> 
  * ''Weertman Exponent''         -> <m>m</m>
  * ''Weertman Linear Velocity'' -> <m>u_{t0}</m>  

==== SIF contents ====
The required keywords in the SIF file for this user function are:
<code>
!!! Bedrock Boundary Condition 
Boundary Condition 1
  Target Boundaries = 1

  Normal-Tangential Velocity = Logical True
  Flow Force BC = Logical True

  Velocity 1 = Real 0.0
  
  Slip Coefficient 2 =  Variable Coordinate 1
    Real Procedure "ElmerIceUSF" "Sliding_Weertman"
  Slip Coefficient 3 =  Variable Coordinate 1
    Real Procedure "ElmerIceUSF" "Sliding_Weertman"
    
  Weertman Friction Coefficient = Real 2.412579e-2        
  Weertman Exponent = Real $1.0/3.0
  Weertman Linear Velocity = Real 0.00001

End

</code>


==== Examples ====
The Weertman friction law is used in the tests ''[ELMER_TRUNK]/elmerice/Tests/GL_MISMIP'' and ''[ELMER_TRUNK]/elmerice/Tests/Contact'' and especially tested in ''[ELMER_TRUNK]/elmerice/Tests/Friction_Weertman''.