#75 A soil profile consisting of three layers is shown in Figure

A soil profile consisting of three layers is shown in Figure - Civil Engineering

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Questions

Through 9.3 A soil profile consisting of three layers is shown in Figure 9.25. Calculate the values of σ, μ, and σ’ at points A, B, C, and D for the following cases. In each case, plot the variations of σ, μ, and σ with depth. Characteristics of layers 1, 2, and 3 for each case are given below:

Answer

Srep 1
Calculate the effective stress using the formula,
 â€¦â€¦ (1)
Here,  is the total stress, and u is the pore water pressure.
Calculate the pore water pressure using the formula,
 â€¦â€¦ (2)
Here,  is the unit weight of water, and H is the depth of the groundwater table.
Calculate the total stress using the formula,
 â€¦â€¦ (3)
Here, H is the height of the soil layer and  is the unit weight of the soil.
Step 2
Consider point A.
As depth of soil layer and depth of ground water table at point A is zero, total stress, pore water pressure and effective stress at point A is zero.

Therefore, the pore water pressure at A is , total stress at A is , and effective stress at A is .
Step 3
Consider point B.
Here, the depth of the soil layer is , and dry unit weight of sand layer is .
Substitute 0 for ,  for , and  for  in equation (3), to calculate the total stress at B.

As the depth of ground water table at point B is zero, pore Water pressure at B is zero.

Substitute  for , and  for  in equation (1), to calculate the effective stress at B.

Therefore, the pore water pressure at B is , total stress at B is , and effective stress at B is .
Step 4
Consider point C.
Here, the depth of the soil layer is , and saturated unit weight of sand layer is .
Substitute  for ,  for , and  for  in equation (3), to calculate the total stress at C.

Substitute  for , and  for  in equation (2), to calculate pore water at C.

Step 5
Substitute  for , and  for  in equation (1), to calculate the effective stress at C.

Therefore, the pore water pressure at C is , total stress at C is , and effective stress at C is .
Step 6
Consider point D.
Here, the depth of the soil layer is , and saturated unit weight of sand layer is .
Substitute  for ,  for , and  for  in equation (3), to calculate the total stress at D.

Step 7
Substitute  for ,  for , and  for  in equation (2), to calculate pore water at D.

Substitute  for , and  for  in equation (1), to calculate the effective stress at C.

Therefore, the pore water pressure at D is , total stress at D is , and effective stress at D is .
Step 8
Tabulate the obtained values of , , and  for different layers.

Points
A	0	0	0	0
B	3	48	0	48
C	9	156	58.86	97.14
D	11.5	198.5	83.38	115.12

Step 9
Plot the variation of total stress with depth for points A, B, C, and D using the tabulated values.