8. Slope Stability

Chapter 1) What Is Slope Stability 

• Introduction to slope stability.  
• Discussion on various types of slopes.  
• Method to calculate the Factor of safety of soil against the slope failure.  

Chapter 2) Example 

• Modelling, boundary condition setting, applying load using Midas GTS NX software to simulate safety against circular failure of the slope.  
• Analysis and see the results for the same. 

Chapter 3) Comparison of results.  

• Compare the results with those obtained manually and using the program.  

Summary

1. The concept of Slope Stability

Slope failure is a shear failure along the fracture surface of the ground soil.
It occurs when the shear stress caused by self-weight or external forces exceeds the shear strength at a specific surface of the ground.

Figure 8.1 is an example of various slope failures that can occur.

The slope stability analysis is reviewed using a stability analysis method that satisfies the force equilibrium condition (limit equilibrium method).
The stability of a slope is defined as the ratio of the strength of the resistance generated at the failure plane.

The equation for the same is shown below:

2. Theory of Slope Stability

Quadrilateral activities are generally classified into finite quadrilaterals and infinite quadrilaterals.

- Infinite slope: A slope with a shallow depth of the activity face compared to its length.
- Finite slope: A slope with a deep depth of the activity face compared to its length.

The theoretical methods for slope stability analysis in soil mechanics are classified based on the assumed shape of the failure surface.

Infinite slope surface: Failure in the direction parallel to the slope
Circular failure surface: friction circle method
Arbitrary failure surface: Slice method

1. Infinite slope
   
   A) Infinite slope of dry sandy soil

It can be assumed that the failure surface of an infinite slope generally occurs in a direction parallel to the slope.
Assuming the free-body diagram for a slope slice with section width b in an infinite slope fracture body as shown in Figure 8.2.

The weight W per unit thickness is 𝛾𝑏ℎ(1).
At the failure surface, normal force N and resistance force T are N=Wcos⁡𝛽 and 𝑇=Wsin⁡𝛽, respectively.

The frictional resistance (𝑅𝑓) that can be mobilized on the failure side is shown in Equation 8.1 for the condition of 𝑐′ =0.

The safety factor, which is the ratio of the strength to maintain stability and the shear strength that can be mobilized, can be defined in Equation 8.2.

It can be seen that the safety factor of an infinite slope is not related to the height or depth of the slope, but only depends on the shear resistance angle (∅′) and the slope (𝛽) of the ground constituting the slope.

B) Infinite Slope of 𝑐′- ∅′ soil with Infiltration

By seeing Figure 8.3, the safety factor for the C- ∅ soil with infiltration parallel to the ground surface can be determined using the equilibrium condition of forces between the slices of the slope is expressed in equation 8.3.

In the case of granular soil with 𝑐′=0,
it can be simplified as in Equation 8.4. (𝛾′=𝛾𝑠𝑎𝑡 − 𝛾𝜔)

The safety factor of an infinite plane is independent of infiltration and is also independent of the height and depth of the slope.

However, the safety factor decreases by approximately 50% compared to a dry slope, considering the ratio of 𝛾′ (effective unit weight) to 𝛾𝑠𝑎𝑡 (unit weight of the soil).