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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` or the `Effective Pressure` variable``` ==== 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: <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. 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.1448552474.txt.gz · Last modified: 2015/11/26 15:41 by gag 