Understanding Triaxial Test Stress Application

The triaxial compression test is a fundamental procedure in soil mechanics used to determine the strength and deformation characteristics of soil samples under controlled conditions. In this test, a cylindrical soil specimen is subjected to a confining pressure (cell pressure, denoted as $\sigma_3$) and then an additional axial stress (axial load, represented by $\Delta\sigma$) is applied.

Axial Stress and Shear Stress Generation

When additional axial stress ($\Delta\sigma$) is applied to the soil specimen, it increases the major principal stress ($\sigma_1$). The confining pressure ($\sigma_3$) acts as the minor principal stress, acting perpendicular to the axis of the sample. The difference between these principal stresses ($\sigma_1 > \sigma_3$) is what causes the soil to deform and potentially fail.

Key points regarding stress distribution:

• The axial stress acts vertically, and the cell pressure acts horizontally (radially).
• These represent the principal stresses acting on the soil specimen.
• Shear stress is not present on the planes where the principal stresses act (i.e., the horizontal plane experiencing $\sigma_3$ and the vertical plane experiencing $\sigma_1$).
• However, shear stress develops on planes oriented at an angle to these principal planes.

Mohr's Circle and Stress Planes

Mohr's circle is a graphical representation used to illustrate the state of stress on a material element. In the context of the triaxial test:

• The horizontal axis of the Mohr's circle represents normal stress.
• The vertical axis represents shear stress.
• The circle is drawn with a center at $\frac{\sigma_1 + \sigma_3}{2}$ and a radius of $\frac{\sigma_1 - \sigma_3}{2}$.
• The points on the circle represent the stresses on different planes passing through a point in the soil mass.
• Planes experiencing only normal stress (principal planes) are represented by the points on the horizontal axis of the circle where shear stress is zero. These correspond to the horizontal and vertical planes in the triaxial test setup.
• Shear stress ($\tau$) is present on all other planes, as indicated by the vertical coordinate of points on the circle away from the horizontal axis.

Therefore, the application of additional axial stress creates shear stresses on planes that are inclined to both the horizontal and vertical directions.

Identifying Planes with Shear Stress

Based on the principles of stress transformation and Mohr's circle:

• Horizontal Plane: Experiences the minor principal stress ($\sigma_3$) and zero shear stress.
• Vertical Plane: Experiences the major principal stress ($\sigma_1$) and zero shear stress.
• Other Planes: Planes oriented at angles other than 0° or 90° relative to the principal stress directions experience both normal stress and shear stress. The maximum shear stress occurs on planes at 45° to the principal stress directions.

The application of additional axial stress directly leads to the generation of these shear stresses on inclined planes.