WEAC
_{^{Weak Layer Anticrack Nucleation Model}}

Implementation of closed-form analytical models for the analysis of dry-snow slab avalanche release.

View the demo · Report a bug · Request a feature · Read the docs · Cite the software

Contents

1. About the project
2. Installation
3. Usage
4. Roadmap
5. Release history
6. How to contribute
7. License
8. Contact

About the project

WEAC implements closed-form analytical models for the mechanical analysis of dry-snow slabs on compliant weak layers, the prediction of anticrack onset, and, in particular, allows for the analysis of stratified snow covers. The model covers propagation saw tests (a), and uncracked (b) or cracked (c) skier-loaded buried weak layers.

Cite the repository as: Rosendahl, P. L., Schneider, J., & Weissgraeber, P. (2022). Weak Layer Anticrack Nucleation Model (WEAC). Zenodo. https://doi.org/10.5281/zenodo.5773113

Read the 📄 white paper for model derivations, illustrations, dimensions, material properties, and kinematics:

• Weißgraeber, P. & Rosendahl, P. L. (2023). A closed-form model for layered snow slabs. The Cryosphere, 17(4), 1475–1496. https://doi.org/10.5194/tc-17-1475-2023

For more background info, please refer to the companion papers:

• Rosendahl, P. L. & Weißgraeber, P. (2020). Modeling snow slab avalanches caused by weak-layer failure – Part 1: Slabs on compliant and collapsible weak layers. The Cryosphere, 14(1), 115–130. https://doi.org/10.5194/tc-14-115-2020
• Rosendahl, P. L. & Weißgraeber, P. (2020). Modeling snow slab avalanches caused by weak-layer failure – Part 2: Coupled mixed-mode criterion for skier-triggered anticracks. The Cryosphere, 14(1), 131–145. https://doi.org/10.5194/tc-14-131-2020

Written in 🐍 Python and built with 💻 Visual Studio Code, 🐙 GitKraken, and 🪐 Jupyter. Note that release v1.0 was written and built in 🌋 MATLAB.

Installation

Install globally using the pip Package Installer for Python sh pip install -U weac or clone the repo sh git clone https://github.com/2phi/weac for local use.

Needs (runtime dependencies are declared in pyproject.toml):

• Python ≥ 3.12
• Numpy ≥ 2.0.1
• Scipy ≥ 1.14.0
• Matplotlib ≥ 3.9.1
• Pydantic ≥ 2.11.7
• Snowpylot ≥ 1.1.3

Usage

The following describes the basic usage of WEAC. Please refer to the demo for more examples and read the documentation for details.

Load the module.

python import weac

Choose a snow profile from the preconfigured profiles (see dummy_profiles in demo) or create your own using the Layer Pydantic class. One row corresponds to one layer counted from top (below surface) to bottom (above weak layer).

```python from weac.components import Layer

layers = [ Layer(rho=170, h=100), # (1) surface layer Layer(rho=190, h=40), # (2) Layer(rho=230, h=130), # : Layer(rho=250, h=20), Layer(rho=210, h=70), Layer(rho=380, h=20), # : Layer(rho=280, h=100) # (N) last slab layer above weak layer ] ```

Create a WeakLayer instance that lies underneath the slab.

```python from weac.components import WeakLayer

weak_layer = WeakLayer(rho=125, h=20) ```

Create a Scenario that defines the environment and setup that the slab and weak layer will be evaluated in.

```python from weac.components import ScenarioConfig, Segment

Example 1: SKIER

skierconfig = ScenarioConfig( systemtype='skier', phi=30, ) skiersegments = [ Segment(length=5000, hasfoundation=True, m=0), Segment(length=0, hasfoundation=False, m=80), Segment(length=0, hasfoundation=False, m=0), Segment(length=5000, has_foundation=True, m=0), ] # Scenario is a skier of 80 kg standing on a 10 meter long slab at a 30 degree angle

Exampel 2: PST

pstconfig = ScenarioConfig( systemtype='pst-', # Downslope cut phi=30, # (counterclockwise positive) cutlength=300, ) pstsegments = [ Segment(length=5000, hasfoundation=True, m=0), Segment(length=300, hasfoundation=False, m=0), # Crack Segment ] # Scenario is Downslope PST with a 300mm cut ```

Create a SystemModel instance that combines the inputs and handles system solving and field-quantity extraction.

```python from weac.components import Config, ModelInput from weac.core.system_model import SystemModel

Example: build a model for the skier scenario defined above

modelinput = ModelInput( weaklayer=weaklayer, scenarioconfig=skierconfig, layers=customlayers, segments=skiersegments, ) systemconfig = Config( touchdown=True ) skiersystem = SystemModel( modelinput=modelinput, config=systemconfig, ) ```

Unknown constants are cachedproperties; calling `skiersystem.unknown_constants` solves the system of linear equations and extracts the constants.

python C = skier_system.unknown_constants

Analyzer handles rasterization + computation of involved slab and weak-layer properties Sxx, Sxz, etc. Prepare the output by rasterizing the solution vector at all horizontal positions xsl (slab). The result is returned in the form of the ndarray z. We also get xwl (weak layer) that only contains x-coordinates that are supported by a foundation.

```python from weac.analysis.analyzer import Analyzer

skieranalyzer = Analyzer(skiersystem) xslskier, zskier, xwlskier = skieranalyzer.rasterizesolution(mode="cracked") Gdif, GdifI, GdifII = skieranalyzer.differentialERR() Ginc, GincI, GincII = skieranalyzer.incremental_ERR()

and Sxx, Sxz, Tzz, principal stress, incremental_potential, ...

```

Visualize the results.

```python from weac.analysis.plotter import Plotter

plotter = Plotter()

Visualize slab profile

fig = plotter.plotslabprofile( weaklayers=weaklayer, slabs=skier_system.slab, )

Visualize deformations as a contour plot

fig = plotter.plotdeformed( xslskier, xwlskier, zskier, skier_analyzer, scale=200, window=200, aspect=2, field="Sxx" )

Plot slab displacements (using x-coordinates of all segments, xsl)

plotter.plotdisplacements(skieranalyzer, x=xslskier, z=zskier)

Plot weak-layer stresses (using only x-coordinates of bedded segments, xwl)

plotter.plotstresses(skieranalyzer, x=xwlskier, z=zskier) ```

Compute output/field quantities for exporting or plotting.

```python

Compute stresses in kPa in the weaklayer

tau = skiersystem.fq.tau(Z=zskier, unit='kPa') sig = skiersystem.fq.sig(Z=zskier, unit='kPa')

w = skiersystem.fq.w(Z=zskier, unit='um')

Example evaluation vertical displacement at top/mid/bottom of the slab

utop = skiersystem.fq.u(Z=zskier, h0=top, unit='um') umid = skiersystem.fq.u(Z=zskier, h0=mid, unit='um') ubot = skiersystem.fq.u(Z=zskier, h0=bot, unit='um') psi = skiersystem.fq.psi(Z=z_skier, unit='deg') ```

Roadmap

See the open issues for a list of proposed features and known issues.

v4.0

• [ ] Change to scenario & scenario_config: InfEnd/Cut/Segment/Weight

v3.2

• [ ] Complex terrain through the addition of out-of-plane tilt
• [ ] Up, down, and cross-slope cracks

v3.1

• [ ] Improved CriteriaEvaluator Optimization (x2 time reduction)

Release history

v3.0

• Refactored the codebase for improved structure and maintainability
• Added property caching for improved efficiency
• Added input validation
• Adopted a new, modular, and object-oriented design

v2.6

• Introduced test suite
• Mitraged from setup.cfg to pyproject.toml
• Added parametrization for collaps heights

v2.5

• Analyze slab touchdown in PST experiments by setting touchdown=True
• Completely redesigned and significantly improved API documentation

v2.4

• Choose between slope-normal ('-pst', 'pst-') or vertical ('-vpst', 'vpst-') PST boundary conditions

v2.3

• Stress plots on deformed contours
• PSTs now account for slab touchdown

v2.2

• Sign of inclination phi consistent with the coordinate system (positive counterclockwise)
• Dimension arguments to field-quantity methods added
• Improved aspect ratio of profile views and contour plots
• Improved plot labels
• Convenience methods for the export of weak-layer stresses and slab deformations provided
• Wrapper for (re)calculation of the fundamental system added
• Now allows for distributed surface loads

v2.1

• Consistent use of coordinate system with downward pointing z-axis
• Consitent top-to-bottom numbering of slab layers
• Implementation of PSTs cut from either left or right side

v2.0

• Completely rewritten in 🐍 Python
• Coupled bending-extension ODE solver implemented
• Stress analysis of arbitrarily layered snow slabs
• FEM validation of
  • displacements
  • weak-layer stresses
  • energy release rates in weak layers
• Documentation
• Demo and examples

v1.0

• Written in 🌋 MATLAB
• Deformation analysis of homogeneous snow labs
• Weak-layer stress prediction
• Energy release rates of cracks in weak layers
• Finite fracture mechanics implementation
• Prediction of anticrack nucleation

How to contribute

1. Fork the project

2. Initialize submodules

   bash git submodule update --init --recursive

3. Create your feature branch (git checkout -b feature/amazingfeature)

4. Commit your changes (git commit -m 'Add some amazing feature')

5. Push to the branch (git push origin feature/amazingfeature)

6. Open a pull request

Workflows

License

WEAC is licensed under CC BY-NC-SA 4.0

You are free to:

• Share — copy and redistribute the material in any medium or format
• Adapt — remix, transform, and build upon the material for any purpose, even commercially.

Under the following terms:

• Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.

• NonCommercial — You may not use the material for commercial purposes.

• ShareAlike — If you remix, transform, or build upon the material, you must distribute your contributions under the same license as the original.

Contact

E-mail: mail@2phi.de · Web: https://2phi.de · Project Link: https://github.com/2phi/weac · Project DOI: http://dx.doi.org/10.5281/zenodo.5773113