https://github.com/ajacquey/ddmfrictionalslip.jl

A Displacement Discontinuity Method (DDM) implementation for fault slip
https://github.com/ajacquey/ddmfrictionalslip.jl

ddm fault friction injection-induced slip

Last synced: 9 days ago
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A Displacement Discontinuity Method (DDM) implementation for fault slip

• Host: GitHub
• URL: https://github.com/ajacquey/ddmfrictionalslip.jl
• Owner: ajacquey
• License: mit
• Created: 2022-01-10T16:23:04.000Z (almost 3 years ago)
• Default Branch: main
• Last Pushed: 2022-08-12T19:38:43.000Z (over 2 years ago)
• Last Synced: 2024-11-13T13:10:20.946Z (about 2 months ago)
• Topics: ddm, fault, friction, injection-induced, slip
• Language: Julia
• Homepage:
• Size: 67.4 KB
• Stars: 5
• Watchers: 2
• Forks: 1
• Open Issues: 2
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
# DDMFrictionalSlip

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[![Coverage](https://codecov.io/gh/ajacquey/DDMFrictionalSlip.jl/branch/main/graph/badge.svg)](https://codecov.io/gh/ajacquey/DDMFrictionalSlip.jl)

[![DOI](https://zenodo.org/badge/446497093.svg)](https://zenodo.org/badge/latestdoi/446497093)

DDMFrictionalSlip is a julia implementation of the Displacement Discontinuity Method (DDM) for two-dimensional domains (one-dimensional fracture).

Main features:

* Choice of Piecewise Constant (PWC), Piecewise Linear Collocation (PWLC), and Piecewise Quadratic Collocation (PWQ) shape functions

* Multithreaded assembly and solve

* Flexible problem formulation

* Non-equally sized elements

This package discretize the quasi-static changes in stress (normal or shear)  $\tau$ expressed as a integral of the displacement discontinuity $\delta$:

$$

    \tau\left(x\right) = \tau_{0}  + \frac{\mu^{\prime}}{\pi} \int_{\Omega} \frac{1}{s - x} \frac{\partial \delta}{\partial s} ds.

$$

$\tau_{0}$ is here the initial stress and $\mu^{\prime}$ the effective shear modulus. The previous expression is discretized into:

$$

    \tau_{i} = \tau_{0} + E_{ij} : \delta_{j},

$$

where $E_{ij}$ is the elastic collocation matrix (dense matrix).

This package can be used to solve for systems of coupled equations which can be expressed in the following way:

$$

    R_{\tau} = \Delta \tau\left(\Delta \delta\right) - f_{\tau}\left(\Delta \epsilon, \Delta \delta\right) = 0

$$

$$

    R_{\epsilon} = \Delta \sigma\left(\Delta \epsilon\right) - f_{\epsilon}\left(\Delta \epsilon, \Delta \delta\right) = 0

$$

where $\Delta \tau = E: \Delta \delta$ and $\Delta \sigma = E : \Delta \epsilon$ are the changes in shear and normal stress respectively, $\Delta \delta$ and $\Delta \epsilon$ the changes in slip and opening repectively, and the two functions $f_{\tau}$ and $f_{\epsilon}$ can be defined to account for applied stress, frictional constraints, and/or fluid pressure coupling.

The user needs to specify the two functions $f_{\tau}$ and $f_{\epsilon}$ together with their derivatives with respect to the displacement discontinuity variables to properly calculate the jacobian matrix of the problem.

Please see the test suite in `test/` for examples of formulations.

Author: Dr. Antoine B. Jacquey