##### When it comes to understanding soil behavior and stability, one crucial aspect is its shear strength.

The shear strength of a soil is defined as the soil’s ability to resist sliding along a plane when subjected to shear forces or loading. In geotechnical engineering, we are generally concerned with the shear strength of soil because, in most of our problems in foundations, slopes and excavations, failure results from excessive applied or induced shear stresses.

The shear strength of soils can be established through correlations with in-situ site testing or by testing samples of the soil in the laboratory. Geotechnical engineers often rely on the laboratory direct shear test to determine the shear strength parameters of a soil sample. Below is an outline of the process of calculating shear strength parameters from direct shear test results.

**Laboratory direct shear test**

The direct shear test is a laboratory experiment designed to measure the shear strength of soil. It involves taking a soil sample and subjecting it to an applied vertical loading and controlled horizontal displacement to simulate shearing of the soil sample. The data is then used to determine the soil’s shear strength parameters which can then be used in engineering calculations (i.e., Stability of a retaining wall). The apparatus is shown below.

**Shear strength parameters**

Two main factors are used to quantify shear strength of a soil: cohesion (*c*) and angle of internal friction (f). In simple terms, the cohesion represents the shear strength contributed by the bonding forces between soil particles, while the angle of internal friction relates to the resistance offered by the soil particles’ frictional interactions.

Shear parameters from direct shear test results are calculated in the following way:

- 1: Determining shear stress and shear displacement data

During the direct shear test, the shear stress (t) and shear displacement measurements are recorded for several values of applied vertical load or stress (s). These results are typically plotted in graphical form, with the calculated shear stress on the vertical axis and shear displacement or strain (e) on the horizontal axis (refer figure below).

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- 2: Identify key points

The relationship between the shear stress and shear displacement can be described by an equation known as the Mohr-Coulomb failure criteria for soils. Two key points to identify are the peak shear stress and the residual shear stress. The peak shear stress represents the maximum shear strength the soil can withstand, while the residual shear stress indicates the shear strength after the soil has experienced significant displacement.

- 3: Calculating cohesion

To determine the cohesion, a line of best fit is drawn through the peak shear stress points and the cohesion is taken where this line intercepts the vertical shear stress axis. The cohesion is often zero for sands and greater than zero for clay soils.

- 4: Calculate angle of internal friction

The angle of internal friction (f) is calculated from the slope of the line of best fit through the peak shear stress points.

Calculating shear parameters from direct shear test results allows geotechnical engineers to better understand soil behavior and make informed decisions when designing structures in contact with the ground or assessing the stability of excavations and slopes. By analysing the shear stress and shear displacement data, and identifying key points on the graph, engineers can determine cohesion and angle of internal friction, which are essential for geotechnical analyses.