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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:
Parameters: Friction Law Sliding Coefficient → As ! Friction Law Post-Peak Exponent → q >= 1 ! Friction Law Maximum Value → C ~ max bed slope ! Friction Law Linear Velocity → ut0 ! Friction Law PowerLaw Exponent → m = (n Glen's law) ! ! Water Pressure (BC) (Compressive - positive) ! ! tau_b = C.N.[ X . ub^-n / (1 + a.X^q) ]^1/n . ub ! with a = (q-1)^(q-1) / q^q and X = ub / (C^n N^n As) ! ! ⇒ Bdrag = C.N.[ X . ub^-n / (1 + a.X^q) ]^1/n
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 Velocity 1 = Real 0.0 Slip Coefficient 2 = Variable Coordinate 1 Real Procedure "./USF_Sliding" "Friction_Coulomb" Slip Coefficient 3 = Variable Coordinate 1 Real Procedure "./USF_Sliding" "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 !(=1m/a dans un premier temps) End
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.