Solution:

Given data:

Water Content = 20%
Specific gravity of solids = 2.7
Unit weight of water = 10KN/M3

(a) Saturated unit weight of sand (KN/M3):

The saturated unit weight of sand can be calculated using the following formula:

γsat = γdry + w × γw

where, γsat = Saturated unit weight of sand
γdry = Dry unit weight of sand
w = Water content
γw = Unit weight of water

Dry unit weight of sand can be calculated using the specific gravity of solids as follows:

γdry = Gs × γw

where, Gs = Specific gravity of solids

Substituting the given values,

γdry = 2.7 × 10 = 27 KN/M3

Now, substituting the values of γdry, w, and γw in the formula for γsat, we get:

γsat = 27 + 0.2 × 10 = 29 KN/M3

Therefore, the saturated unit weight of sand is 29 KN/M3.

(b) Total stress, pore water pressure, and effective stress at point P:

Total stress:

The total stress at point P can be calculated as the sum of the effective stress and the pore water pressure.

σt = σ' + u

where, σt = Total stress
σ' = Effective stress
u = Pore water pressure

Effective stress:

The effective stress at point P can be calculated using the following formula:

σ' = γsat × z

where, z = Depth of point P below the ground surface

Substituting the given values of γsat and z, we get:

σ' = 29 × 4 = 116 KN/M2

Pore water pressure:

The pore water pressure at point P can be calculated using the following formula:

u = uw × z

where, uw = Unit weight of water

Substituting the given value of uw and z, we get:

u = 10 × 4 = 40 KN/M2

Total stress:

Substituting the values of σ' and u in the formula for total stress, we get:

σt = 116 + 40 = 156 KN/M2

Therefore, the total stress, pore water pressure, and effective stress at point P are 156 KN/M2, 40 KN/M2, and 116 KN/M2, respectively.

Explanation:

The given problem involves the calculation of the saturated unit weight of sand and the total stress, pore water pressure, and effective stress at point P.

The saturated unit weight of sand is calculated using the dry unit weight of sand and the unit weight of water. The dry unit weight of sand is calculated using the specific gravity of solids.

The total stress at point P is calculated as the sum of the effective stress and the pore water pressure. The effective stress is calculated using the saturated unit weight of sand and the depth of point P below the ground surface. The pore water pressure is calculated using the unit weight of water and the depth of point P below the ground surface.

The effective stress is the stress carried by the soil skeleton, and the pore water pressure is the pressure exerted by the water in the voids of the soil. The total stress is the sum of