A Comparative Method of Slope Stability Analysis

Image by Residential Slope Stabilization | South Hadley, MA (wellnesscapes.com)

In geotechnical engineering, the method of slices is a foundational technique for analysing the stability of slopes. The factor of safety is determined by slicing the soil mass along a potential failure surface into a series of vertical slices and calculating the forces operating on each slice. The factor of safety (FS) quantifies the margin of safety against slope failure. It is the ratio between the shear strength and the shear stress necessary to maintain equilibrium.

The process of slicing involves three essential steps:

1. The failure surface is a hypothetical surface along which the soil material may slide as a result of external forces like gravity or seepage. The failure surface is selected based on engineering judgement and field observations.
2. Division of the soil mass into segments: The soil mass is divided into equal or variable-width vertical slices. The size and number of slices are determined by geometry and accuracy.
3. Calculation of the safety factor: The factor of safety is computed by taking into account the equilibrium of forces operating on each slice, such as the weight of the soil, the pore water pressure, and the soil's shear resistance.

OMS: Ordinary Method of Slices

The Ordinary Method of Slices, also known as the Fellenius Method, is the most straightforward and fundamental method of slice techniques. It involves slicing the soil mass vertically and determining the safety factor by calculating the forces acting on each slice. The equilibrium equations for each segment are determined by force equilibrium in the vertical direction and moment equilibrium at the centre of the base.

The OMS assumes that the inter-slice forces, or forces acting between adjacent slices, are parallel to the slice's base. This assumption frequently leads to an underestimation of the factor of safety, rendering the OMS less precise than alternative methods. Despite this, the OMS is still used for preliminary slope stability assessments due to its simplicity.

The simplified method of Bishop

The simplified method of Bishop is superior to the ordinary method of slices. Intertreatment-slice forces are the principal difference between the two methods. Bishop's method assumes that the resultant of the inter-slice forces is horizontal, whereas the OMS assumes that these forces are parallel to the base of the slice.

Utilising an iterative procedure, the Bishop's Simplified Method determines the factor of safety. The method is more precise than the OMS because it realistically accounts for the inter-slice forces. However, the method's iterative nature makes it more time-consuming and laborious.

Follow these procedures to determine the factor of safety using Bishop's Simplified Method:

• Assume an initial factor of safety before slicing the soil mass into pieces.
• Calculate the normal and shear forces acting on the base of each slice while assuming horizontal inter-slice forces.
• Calculate the moment balance with respect to the centre of the base of each segment.
• Revise the factor of safety based on the determined moments and repeat steps 2 through 4 until the difference in the factor of safety between iterations is minimal.
• When the difference between consecutive factors of safety falls below a predetermined tolerance value, the final factor of safety is determined.

The Simplified Method of Janbu

Janbu's Simplified Method is a popular variation of the segment method that provides a more precise estimate of the safety factor than the OMS. Based on the stress pattern within the soil mass, Janbu's method implies that the forces between slices are set at a constant angle relative to the base of the slice.

Similarly to Bishop's method, the Simplified Method of Janbu employs an iterative process. This method provides a reasonable estimate of the safety factor while requiring fewer assumptions than other approaches. Due to the iterative process and the need to determine the inter-slice force angle, however, the method can be complicated and laborious.

To implement Janbu's simplified method, the steps below must be taken:

• Assume an initial factor of safety before slicing the soil mass into pieces.
• Calculate the normal and shear forces acting on the base of each slice, assuming that the inter-slice forces are perpendicular to the base of each slice.
• Calculate the equations of force equilibrium for each slice.
• Update the factor of safety based on the calculated force equilibrium and repeat steps 2 through 4 until the change in the factor of safety between successive iterations is negligible.
• When the difference between consecutive factors of safety falls below a predetermined tolerance value, the final factor of safety is determined.

The Morgenstern-Price Approach

The Morgenstern-Price Method is one of the most precise and complex slice techniques. It is a general method that can accommodate different assumptions regarding inter-slice forces, making it applicable to a wide variety of slope stability issues.

The Morgenstern-Price Method entails a trial-and-error approach to determining the safety factor, which can be time-consuming. The method takes into account the actual distribution of forces between slices, resulting in a more precise estimate of the factor of safety. However, the method's complexity makes it less suitable for preliminary analyses or situations requiring a rapid evaluation.

The following stages are required to implement the Morgenstern-Price Method:

• Assume an initial factor of safety before slicing the soil mass into pieces.
• Calculate the normal and shear forces acting on the base of each segment, taking into account their actual distribution.
• Determine the equilibrium equations for force and moment for each segment through a systematic computation process.
• Repeat steps 2-4 until the change in the factor of safety between successive iterations is negligible.
• When the difference between consecutive factors of safety falls below a predetermined tolerance value, the final factor of safety is determined.

In conclusion, the method of segmentation is an indispensable technique for analysing the stability of slopes. It provides options that differ in terms of their complexity and precision. Method selection depends on the project's specific requirements, available resources, and intended level of precision. Although the Ordinary Method of Slices is suitable for preliminary analyses, more precise methods, such as Bishop's Simplified Method, Janbu's Simplified Method, and the Morgenstern-Price Method, are recommended for comprehensive slope stability analyses. By grasping the distinctions between these methods and their underlying assumptions, geotechnical engineers can select the most appropriate method for slope stability analysis, thereby ensuring safety.

M. Azmir Abd Mutalib

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