(Solved): Calculate and plot the active pressure distribution on the frictionless wall shown below. Also calcu ...

Expert Answer

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To calculate the active pressure distribution on the frictionless wall, we can use Rankine's theory. The active pressure coefficient (Ka) for Rankine's theory is given by:

Ka = (1 - sin?) / (1 + sin?)

Where ? is the internal friction angle of the soil. In this case, we have two different types of soil: sand and silt. Therefore, we need to calculate the active pressure separately for each soil layer.

For the sand layer:
?sand = 18 kN/m^3
?sand = 34°
csand = 0 kPa
H1 = 3 m

Using the formula for active pressure coefficient, we have:
Kasand = (1 - sin?sand) / (1 + sin?sand)
= (1 - sin(34°)) / (1 + sin(34°))

For the silt layer:
?silt = 22 kN/m^3
?silt = 28°
csilt = 8 kPa
H2 = 11 m

Similarly,
Kasilt = (1 - sin?silt) / (1 + sin?silt)
= (1 - sin(28°)) / (1 + sin(28°))

Now, let's calculate the active pressure distribution. We'll assume a small width ?x and calculate the active pressure at each height H along the wall. The total thrust will be the sum of all the active pressures and the hydrostatic force acting on the wall.

Let's assume ?x = 1 m for simplicity. We'll calculate the active pressure at each height H and accumulate the total thrust.

import numpy as np