total normal stresses of 110 and 40 kpa are applied to two planes at right angles in an element of soil. the shear stress acting on those palnes is 20 kpa. what must be the value of the pore pressure in the element if the minor principle stress in the elemnt is to be zero?
To find the value of the pore pressure in the element, we need to consider the concept of effective stress. Effective stress is the difference between the total stress and the pore pressure acting on a soil element.
Given:
Total normal stress on the first plane (major principle stress) = 110 kPa
Total normal stress on the second plane (minor principle stress) = 40 kPa
Shear stress on both planes = 20 kPa
We can use the concept of principle stresses and Mohr's circle to solve this problem. Mohr's circle is a graphical representation of normal and shear stresses acting on different planes.
Step 1: Construct Mohr's circle
Draw a horizontal line representing the normal stress axis (sigma axis), and a vertical line representing the shear stress axis (tau axis). Plot the points for the major and minor normal stresses on the sigma axis. In this case, the major normal stress (110 kPa) will be to the right, and the minor normal stress (40 kPa) will be to the left. Plot the shear stress of 20 kPa on the tau axis.
Step 2: Draw the Mohr's circle
Now, draw a circle with the shear stress as the diameter, intersecting the major and minor normal stress points on the sigma axis. The center of the circle represents the average normal stress (sigma_avg) and is located halfway between the major and minor normal stresses. Draw a line connecting the center of the circle to the origin (intersection of sigma and tau axes), and extend it further to determine the pore pressure (p).
Note: The difference between the sigma_avg and p will give us the effective stress (sigma').
Step 3: Solve for the pore pressure
Measure the distance between the center of the circle (sigma_avg) and the origin on the sigma axis. This represents the average effective stress (sigma_avg - p). Since the minor principle stress is required to be zero, the sigma_avg (center of the circle) should lie on the tau axis.
By measuring this distance and noting the position of sigma_avg, we can calculate the pore pressure (p) required for the minor principle stress to be zero. The pore pressure is given by the following equation:
p = sigma_avg - distance between center of circle and origin on sigma axis
By following these steps and the graphical representation of Mohr's circle, you can determine the value of the pore pressure in the given soil element.