Final answer:
The maximum pressure on the shoring at the subgrade dredge line is approximately 1650 psf. The angle of the failure plane from the face of the trench is approximately 18.43°. The soil pressure at the original ground is 1650 psf.
Step-by-step explanation:
When supporting an excavation with a shoring system, it is important to determine the maximum pressure on the shoring at the subgrade dredge line. This can be calculated using the soil properties provided.
The maximum pressure on the shoring can be determined using the Rankine's earth pressure theory. According to this theory, the maximum pressure on the shoring is given by the equation:
P = Y * H + c * B + (1/2) * Y * H^2 * tan^2(o)
Where:
- P is the maximum pressure on the shoring
- Y is the unit weight of the soil (110 pcf)
- H is the depth of the cut (15' deep)
- c is the cohesion of the soil (200 psf)
- o is the friction angle of the soil (24°)
Substituting the given values into the equation:
P = 110 * 15 + 200 * B + (1/2) * 110 * 15^2 * tan^2(24°)
Since the surcharge loads are assumed to be standard, the term involving B can be neglected. Therefore, the maximum pressure on the shoring at the subgrade dredge line is:
P = 1650 + (1/2) * 110 * 15^2 * tan^2(24°)
To find the angle of the failure plane from the face of the trench, we can use the Coulomb's earth pressure theory. According to this theory, the angle of the failure plane is given by the equation:
tan(φ) = (1 - sin(φ)) / (1 + sin(φ))
Where φ is the angle of the failure plane.
Substituting the given values into the equation:
tan(φ) = (1 - sin (24°)) / (1 + sin(24°))
Solving for φ:
φ ≈ 18.43°
The soil pressure at the original ground can be calculated using the equation:
P' = Y * H'
Where:
- P' is the soil pressure at the original ground.
- Y is the unit weight of the soil (110 pcf)
- H' is the depth of the cut (15' deep)
Substituting the given values into the equation:
P' = 110 * 15
Therefore, the soil pressure at the original ground is:
P' = 1650 psf