pySlope

pySlope is a 2D slope stability module based on bishops method of slices. This module allows for the following parameters:

• unlimited horizontal geological units
• water table
• uniform loads
• line loads
• slope search limits

This module can return plots for the critical failure slope or plots for all failure slopes below a certain factor of safety.

Project Purpose

The purpose of this project is two fold:

1. Create a free online slope stability software
2. Provide a pythonic solution to implementing Bishop's method based on object oriented coding principles

Performing a slope stability calculation by hand is extremely uneconimical and time consuming. The problem involves a lot of geometrical mathematics which can make the calculation hard to achieve with only excel. Python packages exist for geometrical mathematics which makes Python well suited for implementing a slope stability analysis package. There is however, no well-documented open-source slope stability software that can currently be found online. This package aims to fill that gap.

Functionality and usage

A typical use case of the pySlope package involves the following steps:

1. Create a Slope object
2. Create Material objects and assign to Slope
3. Create Udl or LineLoad objects and assign to Slope
4. Set water table
5. Set analysis limits
6. Analyse slope for critical factor of safety
7. Create plots

You can follow along with this example below in this web-based binder jupyter notebook.

Creating a Slope

The creation of a Slope instance involves the input of the:

• slope height (m) and
• angle (deg) or
• length (m)

Only one of the values is used out of the length and angle, the other value should be set to None.

s = Slope(height=3, angle=30, length=None)

Defining Materials

The creation of a Material object involves the input of:

• unit weight (kN/m3)
• friction angle
• cohesion (kPa)
• depth from top of slope to bottom of material layer (m)

Once a material is defined it can then be assigned to the Slope instance.

m1 = Material(
    unit_weight=20,
    friction_angle=45,
    cohesion=2,
    depth_to_bottom=2
)
m2 = Material(20, 30, 2, 5)    # Material defined with positional arguments
s.set_materials(m1, m2)        # An unlimited number of materials can be assigned at one time

The slope will know to order the materials based on the depth to the bottom of the strata so the order that the materials are provided isn't important. It is important that the same depth isnt provided twice for two different materials, and attempting this will raise an error.

Defining Uniform Loads

The creation of a Udl (uniform distributed load) object involves the input of:

• magnitude of load (kPa)
• offset of load from crest of slope (m) (default 0 m)
• length of load (m) (default infinite)

u1 = Udl(magnitude = 100, offset = 2, length = 1)

# by default offset = 0 (m) and length = None.
u2 = Udl(magnitude = 20)    

# assign uniform loads to model 
s.set_udls(u1, u2)

Defining Line Loads

The creation of a LineLoad object involves the input of:

• magnitude of load (kN / m)
• offset of load from crest of slope (m) (default 0 m)

# define line load, similiar to Udl except there is no length parameter and magnitude is in units (kN/m)
p1 = LineLoad(magnitude = 10, offset = 3)

# assign line loads to slope
s.set_lls(p1)

Defining Water Table

By default there is no water table. The water table is defined by its depth from the top of the slope (m).

s.set_water_table(4)

Defining Analysis Limits

Analysis limits can be specified as a general left and right limit, OR as a set of limits which control the range from which the top of failures can occur and the bottom of failures can occur.

Currently the model coordinates are dynamic in that the overall model dimensions are based on the size of the slope.

The get_top_coordinates and get_bottom_coordinates methods can be useful to help define limits in reference to the top and bottom of the slope.

s.set_analysis_limits(s.get_top_coordinates()[0] - 5, s.get_bottom_coordinates()[0] + 5)

Analysing Slope

To analyse the Slope the analyse_slope() method is called. By default 2000 iterations are run with 50 slices per failure plane.

# The user can change the number of slices and iterations with the method below.
# The line below is implicitly called and only required by the user if they want to change iterations
s.update_analysis_options(slices=50, iterations=2500)

# run analysis
s.analyse_slope()

Interpretting results

After analysing the slope the critical factor of safety can be taken as below.

print(s.get_min_FOS())

A more useful output might be a plot. Currently there are 3 main plots that can be called.

s.plot_boundary()  # plots only the boundary
s.plot_critical()  # plots the boundary with the critical failure of the slope
s.plot_all_planes(max_fos=i) # plots boundary with all slope failures below fos i (where i is number)

You can show the plot or save the plot to a local html file or image.

fig = s.plot_boundary()  # store a plot in local variable

fig.show()                          # shows the plot
fig.write_html("./example.html")    # save the plot as a html

# writing image requires - pip install -U kaleido
fig.write_image("./example.png")
fig.write_image("./example.jpg")
fig.write_image("./example.svg")

Examples of the plots are shown below.

Dynamic Analysis

Instead of standard static analysis the user also has the option to make load objects dynamic. The user can then perform a dynamic analysis rather than static, which moves the load in order to determine the required offset for a minimum factor of safety.

Considering the example above, we can continue and make u1 dynamic.

# remove udl object load from slope
s.remove_udls(u1)

# now lets add the udl again but this time set the load as 'dynamic'
# for all loads and materials we also have the option to set the color ourselves
# lets try set the color as 'purple'
s.set_udls(
    Udl(magnitude=100, length=1, offset=2, dynamic_offset=True, color='purple')
)

# run dynamic analysis aiming for a FOS of 1.4
s.analyse_dynamic(critical_fos=1.4)

# get dictionary of all determined minimum FOS with key value pairing of offset : value
s.get_dynamic_results()

# or can print the values out
s.print_dynamic_results()

From this we get the following output results:

• Offset: 0.000 m, FOS: 1.288
• Offset: 0.735 m, FOS: 1.402
• Offset: 1.463 m, FOS: 1.510
• Offset: 5.186 m, FOS: 1.684

We can also get a plot as after running dynamic analysis all plots are based on the final iteration of the dynamic analysis.

Installing the package

If you want to install the pyslope package, you run this one-liner:

pip install pyslope

NOTE: You need Python 3 to install this package (you may need to write pip3 instead of pip).

The library dependencies are listed in the file requirements.txt, but you only need to look at them if you clone the repository. If you install the package via pip, the listed dependencies should be installed automatically.

Testing

This project uses pytest to run tests and also to test docstring examples.

Install the test dependencies.

pip install -r requirements.txt

Run the tests from the top level directory.

$ pytest
=== 3 passed in 0.13 seconds ===

Validation

The results of this project have been validated against Slidev6.0 and Hyrcanv1.75. See the documentation for more detail

Future Work

There is a lot of room for expansion of the project, and the direction of the project will strongly be affected by open-source contribution from the community. Some things in the short to medium term scope of work are:

• better documentation
• unit testing
• horizontal loads

Contributing

The guidelines for contributing are specified here.

Support

The guidelines for support are specified here.

Developing

This project uses black to format code and flake8 for linting. We also support pre-commit to ensure these have been run. To configure your local environment please install these development dependencies and set up the commit hooks.

$ pip install black flake8 pre-commit
$ pre-commit install

Run UI deployment With Poetry

1. Install deps poetry install

2. Set secret key The Django app will look for a secret key to run. export SECRET_KEY=<your_key>

3. Run UI deployment poetry run pyslope

Releasing

Releases are published automatically when a tag is pushed to GitHub.

# Set next version number
export RELEASE=vX.X.X

# Create tags
git commit --allow-empty -m "Release $RELEASE"
git tag -a $RELEASE -m "Version $RELEASE"

# Push (for working from a fork)
git push upstream --tags

# if not working from fork would instead be
# git push origin --tags

Or set a tag with Github Desktop.

License