The vertical total stress in an element of soil at a depth of 5m within a clay embankment has been estimated to be 139 kPa. The porewater table has been found to be 1.1 m above the element. Estimate the horizontal shear strength in kPa in the element (take the effective cohesion to be 15.2 kPa, the effective friction angle to be 30.3o and the unit weight of water to be 10 kN/m3).(give your answer to 1 d.p.)
Question
The vertical total stress in an element of soil at a depth of 5m within a clay embankment has been estimated to be 139 kPa. The porewater table has been found to be 1.1 m above the element. Estimate the horizontal shear strength in kPa in the element (take the effective cohesion to be 15.2 kPa, the effective friction angle to be 30.3o and the unit weight of water to be 10 kN/m3).(give your answer to 1 d.p.)
Solution
To solve this problem, we need to use the Mohr-Coulomb failure criterion, which describes the linear envelope that represents the failure conditions of a material in a shear stress versus normal stress plot. The equation is:
τ = c' + σ' tan(φ')
where: τ is the shear strength, c' is the effective cohesion, σ' is the effective normal stress, and φ' is the effective friction angle.
First, we need to calculate the effective normal stress (σ'). The total vertical stress (σ) is given as 139 kPa. The pore water pressure (u) can be calculated using the equation u = γw * h, where γw is the unit weight of water (10 kN/m^3 = 10 kPa/m) and h is the height of water above the point of interest (1.1 m). So, u = 10 * 1.1 = 11 kPa.
The effective normal stress (σ') is then calculated as σ - u = 139 - 11 = 128 kPa.
Next, we substitute the values into the Mohr-Coulomb failure criterion equation. The effective cohesion (c') is given as 15.2 kPa and the effective friction angle (φ') is given as 30.3 degrees. However, we need to convert this to radians before using it in the equation, as the tan function in most calculators uses radians. So, φ' = 30.3 * π/180 = 0.529 radians.
Substituting these values into the equation gives:
τ = 15.2 + 128 * tan(0.529) = 15.2 + 128 * 0.619 = 94.2 kPa
So, the horizontal shear strength in the element is approximately 94.2 kPa to 1 decimal place.
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