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userfunctions:coulomb [Elmer/Ice Wiki]

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userfunctions:coulomb [2012/11/15 01:40]
gag created
userfunctions:coulomb [2015/12/02 12:24]
gag [General Description]
Line 1: Line 1:
 ~~NOTOC~~ ~~NOTOC~~
-===== User Function Weertman Friction Law =====+===== User Function Coulomb Friction Law =====
  
 ==== General Informations ==== ==== General Informations ====
-  * **USF Fortran File:** //USF_Sliding.f90// +  * **USF Fortran File:** ''USF_Sliding.f90'' 
-  * **USF Name:** //Sliding_Weertman// +  * **USF Name:** ''Friction_Coulomb'' 
-  * **Required Input Variable(s):** A //Flow Solution// in //Flow Solution Name////Normal Vector//+  * **Required Input Variable(s):** A ''Flow Solution'' in ''Flow Solution Name''''Normal Vector'', ''Stress'' or the ''Effective Pressure'' variable.
  
  
 ==== General Description ==== ==== General Description ====
-The file //USF_Sliding.f90// contains two user functions to apply non-linear friction at the base of glacier.  +The file ''USF_Sliding.f90'' contains three 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 first user function (''Sliding_Weertman'') is a non-linear Weertman-type friction law and is described [[:userfunctions:weertman|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 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 //Friction_Coulomb// is of the form:\\
 +<m>  tau_b = C.N {[{ {chi . {u_b}^{-n} }/ {(1 + a . chi^q)} }]}^{1/n} . u_b  </m>\\
 +where \\
 +<m>  a = {(q - 1)^{q-1}}/{q^q}  </m>\\
 +and\\
 +<m>  chi = {u_b}/{C^n N^n A_s}  </m>\\
 +
 +The //Slip Coefficient// in Elmer is then given as\\
 +<m>  C.N {[{ {chi . {u_b}^{-n} }/ {(1 + a . chi^q)} }]}^{1/n}  </m>\\
 +When  <m>u_b < u_{t0}</m>, <m>u_b</m> in the previous equation is replaced by <m>u_{t0}</m>.
 +
 +
 +The parameters to be given are:\\
 +  * ''Friction Law Sliding Coefficient''      -> <m>A_s</m>
 +  * ''Friction Law Post-Peak Exponent''       -> <m>q >= 1</m>
 +  * ''Friction Law Maximum Value''            -> <m>C</m> ~ max bed slope
 +  * ''Friction Law Exponent''       -> m = (n Glen's law)
 +  * ''Friction Law Linear Velocity'' -> <m>u_{t0}</m>  
 +
 +The effective pressure is defined as <m>N = -sigma_{nn} -p_w</m>,  where <m>sigma_{nn}</m> is the normal Cauchy stress and <m>p_w</m> the water pressure. If a variable ''Effective Pressure'' exists, it is used to evaluate directly <m>N</m>. Else, the normal Cauchy stress is estimated from the stress computed at previous timestep. The water pressure is prescribed as an ''External Pressure'' (Negative - Compressive convention, and therefore 'External Pressure' should be equal to the opposite of the water pressure in the sif). 
 +      
 + 
  
 ==== SIF contents ==== ==== SIF contents ====
Line 25: Line 46:
   Normal-Tangential Velocity = Logical True   Normal-Tangential Velocity = Logical True
   Flow Force BC = 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   Velocity 1 = Real 0.0
      
   Slip Coefficient 2 =  Variable Coordinate 1   Slip Coefficient 2 =  Variable Coordinate 1
-    Real Procedure "./USF_Sliding" "Sliding_Weertman"+    Real Procedure "ElmerIceUSF" "Friction_Coulomb"
   Slip Coefficient 3 =  Variable Coordinate 1   Slip Coefficient 3 =  Variable Coordinate 1
-    Real Procedure "./USF_Sliding" "Sliding_Weertman"+    Real Procedure "ElmerIceUSF" "Friction_Coulomb"
          
-  Weertman Friction Coefficient = Real 2.412579e-2         +  !! Parameters needed for the Coulomb Friction Law 
-  Weertman Exponent = Real $1.0/3.0 +  Friction Law Sliding Coefficient = Real 4.1613e5   
-  Weertman Linear Velocity = Real 0.00001 +  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 End
- 
 </code> </code>
  
  
 ==== Examples ==== ==== Examples ====
-An example of the usage of the user function //Sliding_Weertman// TODO +The Coulomb friction law is tested in ''[ELMER_TRUNK]/elmerice/Tests/Friction_Coulomb'' with a direct input of the effective pressure and ''[ELMER_TRUNK]/elmerice/Tests/Friction_Coulomb_Pw'' with the effective pressure computed from the stress and a prescribed water pressure.   
 + 
 + 
 +==== 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.txt · Last modified: 2015/12/02 12:24 by gag
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