Statistics How To

Slope: Simple Definition, Example & Stability Analysis

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Contents:

  1. Definition
  2. Slope Stability Analysis.

1. Definition

The slope tells you how steep a line is. The larger the value, the steeper the line.

slope

The “b” in the formula is the y-intercept and the “m” is the slope.

In algebra, the slope is the “m” in the formula y = mx + b. In statistics, we’re interested in a particular type, found with the linear regression formula. In that case, “m” is replaced with the a in the equation y’ = b + ax. Here, the value tells you what the rate of change in y (the dependent variable) is, as x (the independent variable) changes.

2. Slope Stability Analysis

Slope stability analysis is the study of stability factors, and therefore safety, of both natural and man-made gradients.

Slope stability is generally defined as the resistance of a gradient to “failure”, where failure is collapse or sliding. Analysis typically involves working with two types of equations: equilibrium equations, which apply physics to the field conditions, and constitutive laws (i.e. laws specific to a particular substance) that describe the behavior of the soil.

Types of Analysis

Slope stability analysis is carried on in a number of different ways, but probably the most commonly used method is what is called limit equilibrium analysis. In this analysis one studies the equilibrium between the gradient and a slip surface (this may be a straight line, logarithmic spiral, or the arc of a circle). Shear stresses (τ) are calculated, the available resistance (τf) is calculated, and a ‘factor of safety’ is derived, F= τf / τ.

Some methods of analysis work with the slope as a rigid body, but most divide it into slices and calculate the equilibrium of each individual slice. This has the advantage of allowing an analyst to cater to non-homogeneous surfaces.

Applications

Slope stability analysis plays in an important role in the design and engineering of any architectural structure that contains sloped surfaces, including highway embankments and mountain roads. It also is crucial in earthquake damage prevention, and allows foresters and landscape designers to locate danger areas that are likely to be prone to mud slippages and avalanches.

References

Catanzarita, Filippo. Stability Analysis
Retrieved from https://www.geostru.eu/slope-stability-analysis/ on April 3, 2018
US Army Corps of Engineers. Engineering Manual.
Retrieved from http://www.civil.utah.edu/~bartlett/CVEEN5305/Handout%2010%20-%20EM_1110-2-1902.pdf on April 3, 2018

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Statistical concepts explained visually - Includes many concepts such as sample size, hypothesis tests, or logistic regression, explained by Stephanie Glen, founder of StatisticsHowTo.

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