# Slope Stability – Causes of Instability, Analysis Methods, and Assumptions

A slope is an inclined boundary surface between air and the body of an earthwork such as highways, cut or fill, railway cut or fill, earth dams, levees and river training work. The slope stability analysis is crucial in engineering practice to ensure the stability of structures and prevent loss of human life and money.

The common methods for the analysis of a slope’s stability are Culmann Method, Ordinary Method of Slices and Bishop Method of Slices. These methods are developed on the assumption that the plane of failure is circular arc, apart from the Culmann method that assumes a plane surface of failure through the toe of the slope.

The quantitative determination of the stability of slopes is necessary for a number of engineering projects, for instance, the design of earth dams and embankments, analysis of the stability of natural slopes, analysis of the stability of excavated slopes, and analysis of the deep-seated failure of foundations and retaining walls.

**Causes of Slope Instability**

- Increased unit weight of soil by wetting.
- Added external loads (moving loads, buildings etc).
- Steepened slopes either by excavation or by erosion.
- Shock loads.
- Vibration and earthquakes.
- Increase in moisture content.
- Freezing and thawing action.
- Increase in pore pressure.
- Loss of cementing pressure.

## Purpose of Slope Stability Analysis

- Understand the development and form of natural slopes and the processes responsible for different natural features.
- Assess the stability of slopes under short-term (often during construction) and long-term conditions.
- Evaluate the possibility of landslides involving natural or existing engineered slopes.
- Analyze landslides and understand failure mechanisms and influence of environmental factors.
- To redesign failed slopes and plan for the design of preventive and remedial measures, where necessary.
- Study the effect of seismic loading on slopes and embankments.

**Types of Slope Failure**

**1. Circular slips**

They are related to homogenous, isotropic soil conditions.

### 2. Non-circular slips

Non-circular slips are associated with non-homogenous soil conditions.

### 3. Translational failure

This type of failure takes place where the form of failure surface is affected by the presence of an adjacent stratum of different strength, and the adjacent stratum is fairly shallow.

### 4. Compound Failure

It occurs where the form of failure surface is affected by the presence of an adjacent stratum of different strength, and the adjacent stratum is relatively deep.

**Slope Stability Analysis Assumptions**

- Problems are two dimensional.
- Coulomb’s theory can be used to compute shear strength.
- Shear strength is assumed as uniform along the slip surface.
- The flow net in case of seepage can be drawn and seepage forces evaluated.

**Factor of Safety**

There are different safety factors which are used in the analysis of slope stability. For instance, factor of safety with respect to strength, cohesion, friction, and height. the former is widely used.

**1. Safety Factor with Respect to Strength**

It is the ratio of the maximum load or stress that a soil can sustain to the actual load or stress that is applied, and expressed as follows:

**2. Safety Factor with Respect to Cohesion**

It is the ratio between the actual cohesion and the cohesion required for stability when the frictional component of strength is fully mobilized, expressed using the following formula:

**3. Safety Factor with Respect to Friction**

It is the ratio of the tangent of the angle of shearing resistance of the soil to the tangent of the mobilized angle of shearing resistance of the soil when the cohesive component of strength is fully mobilized.

**4. Safety Factor with Respect to Height**

It is the ratio between the maximum height of a slope to the actual height of a slope.

**Slope Stability Analysis Methods**

**1. Culmann Method**

It is not widely used because it is demonstrated that plane surfaces of sliding are noted only with very steep slopes, and for relatively flat slopes the surfaces of sliding are almost always curved.

**2. The Zero angle of Shearing Resistance Method**

This method of slope stability analysis is based on the assumption that the plane of failure is in the form of a circular arc. It is a practical method for the evaluation of the short-term stability of saturated clay slopes.

**3. Ordinary Method of Slices**

It is considered where the effective angle of shearing resistance is not constant over the failure surface, such as in zoned earth dams where the failure surface might pass through several different materials.

**4. Bishop Method of Slices**

In Bishop method of slices, the analysis is conducted in terms of stresses rather than forces which are used in the ordinary method of slices. The main difference this method and the Ordinary Method of Slices is that resolution of forces takes place in the vertical direction instead of a direction normal to the arc. The simplified Bishop method of slices provides a safety factor which is considerably close to those evaluated using more rigorous methods of analysis.

## 5. Morgenstern and Price (1965) and Janbu (1973)

These researchers developed methods of analysis for composite failure surfaces.