Probabilistic slope-stability analysis
A completed geotechnical engineering study of slope stability under uncertain soil strength and groundwater conditions using Bishop and Spencer limit-equilibrium methods.
Project definition
Problem statement
A single slope factor of safety can hide how uncertain soil strength and groundwater conditions change the likelihood of instability.
The engineering problem is to combine a transparent limit-equilibrium model with reproducible uncertainty analysis while keeping all assumptions, correlations and evidence limits visible.
Project objectives
- Model a homogeneous residual-soil slope using Bishop and Spencer methods.
- Compare deterministic stability across four declared groundwater conditions.
- Propagate unit weight, cohesion and friction-angle uncertainty through Latin hypercube sampling.
- Estimate conditional probability of failure for each groundwater scenario.
- Identify the input parameters that most strongly affect factor of safety.
- Provide an XSLOPE-compatible workbook for independent inspection and extension.
Project structure
Project components
Slope model
Defines the 12 m high, 1V:2.5H residual-soil slope, material properties and candidate slip surfaces.
Limit-equilibrium analysis
Calculates factor of safety with Bishop and Spencer methods using forty slices.
Groundwater scenarios
Compares low, moderate, high and ground-surface water conditions under the same geometry and strength model.
Reliability analysis
Runs 5,000 seeded Latin hypercube samples for each groundwater scenario and retains every valid result.
Sensitivity analysis
Measures the effect of unit weight, cohesion and friction angle on the calculated factor of safety.
Evidence package
Exports tables, figures, JSON summaries and the XSLOPE workbook for review.
Methodology
Project workflow
- 01Inspect assumptions
Review geometry, soil properties, uncertainty ranges, water levels and analysis settings.
- 02Run deterministic cases
Calculate Bishop and Spencer factors of safety for the four groundwater scenarios.
- 03Run reliability cases
Generate seeded samples, reject invalid combinations and calculate the retained stability results.
- 04Measure sensitivity
Compare parameter changes and rank their influence on factor of safety.
- 05Review evidence
Inspect CSV, JSON and figure outputs and compare the Python model with the prepared XSLOPE workbook.
- 06Explain limitations
Separate academic screening results from site-specific geotechnical design conclusions.
Demonstration scenario
The Spencer factor of safety decreases from 1.761 under the low-water case to 1.093 when groundwater reaches the slope surface. No sampled failures occur in the low and moderate cases, while the high-water case records 0.22 percent and the surface-water case records 23.68 percent. Cohesion and friction angle dominate the retained sensitivity evidence.
Engineering
Tools and method
- Tools
- The project uses Python 3.12, XSLOPE 0.3.0, NumPy, SciPy, Pandas, Matplotlib for subject analysis, simulation, and results.
- Engineering model
- A documented sliced limit-equilibrium implementation evaluates circular slip surfaces with Bishop and Spencer methods.
- Statistical experiment
- Seeded Latin hypercube sampling provides repeatable coverage of the declared input uncertainty.
- Groundwater comparison
- Four pore-pressure conditions isolate the stability effect of rising groundwater.
- Open compatibility
- The model workbook can be opened and independently explored with XSLOPE 0.3.0.
- Verification
- Thirty-five tests, dependency checks, repository validation and a clean Linux container verify the released package.
Testing
Evaluation
Evaluation measures
- Bishop and Spencer factor of safety for every groundwater scenario
- Difference between the two limit-equilibrium methods
- Probability of failure from 5,000 samples per scenario
- Valid and rejected sample counts
- Parameter sensitivity for unit weight, cohesion and friction angle
- Reproducibility under the fixed random seed
- Complete software, document and repository verification evidence
Project boundaries
- The geometry, material properties, probability distributions and groundwater levels are declared teaching assumptions.
- The model uses a homogeneous soil profile and circular slip surfaces.
- The probability estimates are conditional on the selected distributions and do not represent a surveyed site.
- The zero observed failures in finite samples are not proof of zero failure probability.
- Seismic loading, rainfall infiltration, unsaturated behaviour, progressive failure and reinforcement are outside the prepared scope.
- Field use requires investigation, monitoring, current standards and qualified geotechnical engineering review.
Included
- 01Complete Python slope-stability and reliability workflow
- 02XSLOPE-compatible workbook for the prepared slope model
- 03Bishop and Spencer factor-of-safety calculations
- 04Four groundwater scenarios from low to ground-surface conditions
- 05Twenty thousand retained Latin hypercube simulations
- 06Probability-of-failure and parameter-sensitivity results
- 07Five labelled engineering figures and fifteen labelled tables
- 08Thirty-five automated tests with 98.61 percent branch-aware coverage
- 09Complete project files, calculations and evidence in a private GitHub repository
- 1090-page project documentation in PDF and editable Word formats
- 1117-page setup and usage guide in PDF and editable Word formats
- 12Forty-eight annotated references
Project record
No information is collected on this page.
- Permanent project ID
- GP-CV-0MBO97Y
- Catalogued
- 21 Aug 2026
- Completed
- 28 Aug 2026
- Verified
- 28 Aug 2026
- Demonstration
- Included in repository
Handover
After purchase
- 01Payment is confirmed
The project is marked unavailable and cannot be purchased again.
- 02Repository access is granted
The buyer's submitted GitHub account receives access to the private repository.
- 03The purchase record is delivered
The certification sheet is prepared from the reviewed buyer details and sent privately by email.