“Which Slope Stability Method Should I Use?” Here’s What You Need to Know
Slopes can fail in a variety of ways, from rotational failures to complex mechanisms like compound or planar instability, so it’s important to choose the right methods for your stability analysis. An inappropriate method can lead to unsafe designs, unseen failures, or overly conservative results that waste resources.
In 2021, Dr. Reginald Hammah hosted a webinar in which he shared foundational slope stability design principles and best practices to help you apply them. Specifically, he outlined the widely used limit equilibrium methods and their applications, and the insights remain highly relevant to engineering challenges today.
This article revisits those technical discussions: the strengths and limitations of popular methods of slices, the critical role of factor of safety (FoS), and the integration of numerical techniques. Below, we’ll guide you on how to validate results, analyze failure mechanisms, and optimize designs for complex slope conditions.
Selecting the Right Method for Your Slope
Choosing the most appropriate method of slices is critical to obtaining reliable results in slope stability analysis — and there’s no universal approach. In the webinar, Dr. Hammah detailed six popular methods — Ordinary, Bishop Simplified, Janbu, Spencer, Morgenstern-Price, and Sarma — each with specific strengths and limitations.
Ordinary Method of Slices
The Ordinary Method offers a quick and conservative solution for simple, homogenous slopes with circular failure surfaces. But its tendency to underestimate the FoS, particularly in complex or non-homogeneous conditions, limits its practical use. It also does not account for inter-slice forces, which are needed in these conditions.
Bishop Simplified Method
The Bishop Simplified Method is a better choice when vertical force and moment equilibrium are sufficient for the analysis. While it performs well for circular slip surfaces, it can struggle with non-circular geometries or seismic forces, making it less suitable for these conditions. Its assumptions make it less applicable to irregular or highly layered material profiles.
Janbu Method
This method is a versatile slope stability analysis approach, especially when the assumptions of circular failure surfaces are not applicable. The Janbu method is suitable for more complex geometries and layered soil profiles because it accounts for non-circular failure surfaces. However, because it does not satisfy moment equilibrium, it can generate less reliable FoS values under some conditions. Dr. Hammah highlighted that the Janbu Simplified Method is often used as a preliminary tool to assess slope stability due to its efficiency and relative simplicity.
Spencer and Morgenstern-Price Methods
For complex scenarios — including slopes influenced by seismic forces, layered materials, or irregular geometries — rigorous methods like Spencer and Morgenstern-Price are ideal. Because they satisfy all static equilibrium conditions, they’re highly reliable for capturing realistic failure mechanisms in both circular and non-circular slip surfaces. But even these rigorous methods occasionally produce results that do not align with physical expectations, especially under certain boundary conditions.
Sarma Method
The Sarma Method is uniquely suited for non-vertical slice analysis of slopes, like those with discontinuities. This makes it a strong choice for slopes with highly variable material strengths or complex geological layouts. It is particularly sensitive to the assumptions made about sliding surfaces, however, so careful calibration is needed to avoid errors.
Overall, your analysis will provide more accurate and practical results if you align your slope’s characteristics to the proper method, but keep in mind that there’s no one-size-fits-all solution and you’ll likely need to use multiple methods.
“Limit equilibrium methods, also known as methods of slices… are the most common slope stability methods as they are relatively simple, fast, and engineers have experience with these methods for over 100 years. They are very useful for evaluating the sensitivity of slopes to different conditions and input parameters.” (6:10-6:33)
Validating Results with a Line of Thrust
The validity of your FoS depends on more than just the numerical output of the method. Dr. Hammah emphasized the importance of validating results through the line of thrust, which represents the location of inter-slice forces. For a solution to be physically reasonable, the line of thrust must remain entirely within the failure mass.
When the line of thrust deviates — commonly due to high pore pressures, tension, or complex failure surfaces — it signals that adjustments are needed. Introducing tension cracks or modifying inter-slice force assumptions can correct these issues. But you should be cautious — misapplying tension cracks can lead to unrealistic solutions and compromise both safety and practicality. Rigorous methods like Spencer and Morgenstern-Price often highlight these issues, which require careful attention to their output.
“Our line of thrust should exist within the failure mass; it should not go outside the boundary of the sliding mass.” (21:52-22:00)
Enhancing Analysis With Numerical Methods
Numerical methods are powerful tools for geotechnical analysis. They do not require assumptions about the failure surface shape and satisfy both equilibrium and compatibility equations. Unlike limit equilibrium methods, they also provide detailed displacement and deformation data, offering insights into soil-structure interaction and failure mechanisms.
The webinar illustrated how numerical methods can validate or challenge the results of limit equilibrium analyses. For example, when Spencer or Morgenstern-Price results appear unreliable, numerical methods can confirm whether the failure mechanism and FoS align with real-world behavior. This integration of methods ensures thorough analyses, particularly in cases involving non-circular surfaces, seismic forces, or layered materials.
“Numerical methods... satisfy all the equations of equilibrium. They also satisfy additional equations, which are called compatibility equations, so they are more robust.” (28:33-29:11)
Follow This Workflow:
To achieve reliable and practical slope stability designs, the webinar recommended a workflow that integrates limit equilibrium and numerical methods:
1. Start with Rigorous Methods
Begin by applying the Spencer and Morgenstern-Price methods, which satisfy all static equilibrium conditions. They are ideal for capturing complex failure mechanisms and non-circular slip surfaces. Ensure that input parameters, such as material properties, and model quantities, such as inter-slice forces, are well-calibrated for reliable results.
2. Cross-Check With Simplified Methods
Use Bishop Simplified or Janbu to cross check your work. These methods can quickly reveal whether rigorous solutions have converged correctly. For instance, if Bishop results show a significantly lower FoS than Spencer or Morgenstern-Price, it may indicate convergence issues in the rigorous methods. Remember, Bishop works best for circular surfaces, while Janbu does not account for moment equilibrium.
3. Validate Results Physically
Inspect the line of thrust and check for the presence of tension. Ensure that the line of thrust remains within the failure mass and that tension is either minimal or appropriately addressed with tension cracks. Avoid over-reliance on tension cracks, as they can distort results if applied indiscriminately.
4. Incorporate Numerical Methods
For complex geometries, seismic forces, or irregular material properties, supplement the analysis with numerical methods like FEM. These methods naturally identify failure surfaces and offer additional insights, such as displacements and stress distributions, that enhance the reliability of FoS values.
5. Iterate and Compare
Compare results across methods to ensure consistency. If numerical methods and limit equilibrium results diverge significantly, revisit model assumptions, inter-slice forces, and boundary conditions. Use these insights to refine your analysis for a reliable slope stability assessment.
Key Takeaways for Slope Design
By combining rigorous limit equilibrium methods, simplified checks, and numerical techniques, you can streamline your slope stability analysis. Validating results through the line of thrust and incorporating displacement data from numerical methods helps address complex conditions. Overall, this practical approach can lead to safer, more efficient slope designs while minimizing errors and uncertainty.
