A square footing 2.00 x 2.00 m2 at a depth of 1.50 m in a sand deposit. The bulk and saturated unit weights are 2.00 t/m3 and 2.50 t/m3. The shear strength parameters are c = 1 and ɸ = 30o. Determine the bearing capacity of the soilfollowing cases: a. G.W.T at 5.0 m below ground level.b. G.W.T at 1.0 m below ground level. c. (G.W.T at ground leveld. G.W.T at foundation level

The bearing capacity of soil can be determined using Terzaghi's bearing capacity equation:

q_u = cNc + γDNq + 0.5γBNγ

Where: q_u = ultimate bearing capacity c = cohesion of soil γ = effective unit weight of soil D = depth of foundation B = width of foundation Nc, Nq, Nγ = bearing capacity factors which depend on the angle of internal friction (ɸ)

Given: c = 1 t/m2 ɸ = 30 degrees B = D = 2 m γ = 2 t/m3 (bulk unit weight) γ_sat = 2.5 t/m3 (saturated unit weight)

For ɸ = 30 degrees, Nc = 57.3, Nq = 41.4, Nγ = 44.9 (from standard tables)

a. G.W.T at 5.0 m below ground level Since the water table is below the foundation, we use the bulk unit weight (γ). The effective unit weight of soil (γ') is equal to the bulk unit weight.

q_u = cNc + γDNq + 0.5γBNγ = 157.3 + 2241.4 + 0.52244.9 = 57.3 + 165.6 + 89.8 = 312.7 t/m2

b. G.W.T at 1.0 m below ground level Since the water table is below the foundation but within its zone of influence, we need to adjust the unit weight.

γ' = γ - (γ_sat - γ) = 2 - (2.5 - 2) = 1.5 t/m3

q_u = cNc + γ'DNq + 0.5γ'BNγ = 157.3 + 1.5241.4 + 0.51.5244.9 = 57.3 + 124.2 + 67.35 = 248.85 t/m2

c. G.W.T at ground level Since the water table is at the ground level, the effective unit weight of soil is equal to the submerged unit weight.

γ' = γ - γ_sat = 2 - 2.5 = -0.5 t/m3

Since the effective unit weight cannot be negative, we consider it as zero.

q_u = cNc = 1*57.3 = 57.3 t/m2

d. G.W.T at foundation level Since the water table is at the foundation level, the effective unit weight of soil is equal to the submerged unit weight.

γ' = γ - γ_sat = 2 - 2.5 = -0.5 t/m3

Since the effective unit weight cannot be negative, we consider it as zero.

q_u = cNc = 1*57.3 = 57.3 t/m2

So, the bearing capacity of the soil decreases as the water table rises.

The bearing capacity of soil can be determined using Terzaghi's bearing capacity equation:

q_u = cNc + γDNq + 0.5γBNγ

Where: q_u = ultimate bearing capacity c = cohesion of soil γ = effective unit weight of soil D = depth of foundation B = width of foundation Nc, Nq, Nγ = bearing capacity factors which depend on the angle of internal friction (ɸ)

Given: c = 1 t/m2 ɸ = 30° B = D = 2 m γ = 2 t/m3 (bulk unit weight) γ_sat = 2.5 t/m3 (saturated unit weight)

For ɸ = 30°, Nc = 57.3, Nq = 41.4, Nγ = 44.9 (from standard tables)

a. G.W.T at 5.0 m below ground level Since the water table is below the foundation, we use the bulk unit weight (γ). The effective unit weight of the soil (γ') is equal to the bulk unit weight.

q_u = cNc + γDNq + 0.5γBNγ = 157.3 + 2241.4 + 0.52244.9 = 57.3 + 165.6 + 89.8 = 312.7 t/m2

b. G.W.T at 1.0 m below ground level Since the water table is below the foundation but within its zone of influence, we need to adjust the unit weight.

γ' = γ - (γ_sat - γ) = 2 - (2.5 - 2) = 1.5 t/m3

q_u = cNc + γ'DNq + 0.5γBNγ = 157.3 + 1.5241.4 + 0.52244.9 = 57.3 + 124.2 + 89.8 = 271.3 t/m2

c. G.W.T at ground level Since the water table is at the ground level, the effective unit weight of the soil is equal to the submerged unit weight.

γ' = γ - γ_sat = 2 - 2.5 = -0.5 t/m3

q_u = cNc + γ'DNq + 0.5γBNγ = 157.3 - 0.5241.4 + 0.52244.9 = 57.3 - 41.4 + 89.8 = 105.7 t/m2

d. G.W.T at foundation level Since the water table is at the foundation level, the effective unit weight of the soil is equal to the submerged unit weight.

γ' = γ - γ_sat = 2 - 2.5 = -0.5 t/m3

q_u = cNc + γ'DNq + 0.5γBNγ = 157.3 - 0.5241.4 + 0.52244.9 = 57.3 - 41.4 + 89.8 = 105.7 t/m2

Please note that the negative value of γ' in cases c and d is physically unrealistic and indicates that the water table is too close to the foundation level, which reduces the bearing capacity of the soil. In such cases, it is necessary to take measures to lower the water table or to use a different type of foundation.