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 level11:34 pm

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

q_u = cN_c + γDN_q + 0.5γBN_γ

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

Given: c = 1 t/m^2 ɸ = 30 degrees γ = 2.00 t/m^3 (bulk unit weight) γ_sat = 2.50 t/m^3 (saturated unit weight) B = D = 2.00 m

For ɸ = 30 degrees, N_c = 57.3, N_q = 41.4, N_γ = 67.5 (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 = cN_c + γDN_q + 0.5γBN_γ = 157.3 + 2241.4 + 0.52267.5 = 57.3 + 165.6 + 135 = 358 t/m^2

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. The effective unit weight of soil (γ') is equal to the bulk unit weight above the water table and the submerged unit weight (γ_sub = γ_sat - γ_water) below the water table. Here, we assume γ_water = 1 t/m^3.

γ' = γ - (D - d)*γ_water = 2 - (2 - 1)*1 = 1.5 t/m^3

q_u = cN_c + γ'DN_q + 0.5γ'BN_γ = 157.3 + 1.5241.4 + 0.51.5267.5 = 57.3 + 124.2 + 101.25 = 282.75 t/m^2

c. G.W.T at ground level: Since the water table is at the ground level, the entire foundation is submerged. We use the submerged unit weight (γ_sub).

γ_sub = γ_sat - γ_water = 2.5 - 1 = 1.5 t/m^3

q_u = cN_c + γ_subDN_q + 0.5γ_subBN_γ = 157.3 + 1.5241.4 + 0.51.5267.5 = 57.3 + 124.2 + 101.25 = 282.75 t/m^2

d. G.W.T at foundation level: This case is similar to the previous one, as the entire foundation is submerged. The bearing capacity is the same as in case c.

q_u = 282.75 t/m^2

Please note that these are the ultimate bearing capacities. The allowable bearing capacity (q_a) can be obtained by dividing the ultimate bearing capacity by a factor of safety (typically 2.5 to 3).

q_a = q_u / FS

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

q_u = cN_c + γDN_q + 0.5γBN_γ

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

Given: c = 1 t/m^2 ɸ = 30 degrees B = D = 2 m γ = 2 t/m^3 (for case a and b) and γ = 2.5 t/m^3 (for case c and d)

For ɸ = 30 degrees, N_c = 57.3, N_q = 41.4, N_γ = 67.5

Case a. G.W.T at 5.0 m below ground level The water table is below the foundation, so the effective unit weight is the bulk unit weight. q_u = 157.3 + 2241.4 + 0.52267.5 = 57.3 + 165.6 + 135 = 358 t/m^2

Case b. G.W.T at 1.0 m below ground level The water table is below the foundation, so the effective unit weight is the bulk unit weight. q_u = 157.3 + 2241.4 + 0.52267.5 = 57.3 + 165.6 + 135 = 358 t/m^2

Case c. G.W.T at ground level The water table is at the foundation level, so the effective unit weight is the saturated unit weight. q_u = 157.3 + 2.5241.4 + 0.52.5267.5 = 57.3 + 207 + 168.75 = 433 t/m^2

Case d. G.W.T at foundation level The water table is at the foundation level, so the effective unit weight is the saturated unit weight. q_u = 157.3 + 2.5241.4 + 0.52.5267.5 = 57.3 + 207 + 168.75 = 433 t/m^2

So, the bearing capacity of the soil is 358 t/m^2 for cases a and b, and 433 t/m^2 for cases c and d.

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

q_u = cN_c + γDN_q + 0.5γBN_γ

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

Given: c = 1 t/m^2 ɸ = 30 degrees B = D = 2 m γ = 2 t/m^3 (for case a and b) and γ = 2.5 t/m^3 (for case c and d)

For ɸ = 30 degrees, N_c = 57.3, N_q = 33.3, N_γ = 47.7

Case a. G.W.T at 5.0 m below ground level The water table is below the foundation level, so the effective unit weight of soil (γ) is the bulk unit weight. q_u = 157.3 + 2233.3 + 0.52247.7 = 57.3 + 133.2 + 95.4 = 285.9 t/m^2

Case b. G.W.T at 1.0 m below ground level The water table is below the foundation level, so the effective unit weight of soil (γ) is the bulk unit weight. q_u = 157.3 + 2233.3 + 0.52247.7 = 57.3 + 133.2 + 95.4 = 285.9 t/m^2

Case c. G.W.T at ground level The water table is at the foundation level, so the effective unit weight of soil (γ) is the saturated unit weight. q_u = 157.3 + 2.5233.3 + 0.52.5247.7 = 57.3 + 166.5 + 119.25 = 343.05 t/m^2

Case d. G.W.T at foundation level The water table is at the foundation level, so the effective unit weight of soil (γ) is the saturated unit weight. q_u = 157.3 + 2.5233.3 + 0.52.5247.7 = 57.3 + 166.5 + 119.25 = 343.05 t/m^2

So, the bearing capacity of the soil is 285.9 t/m^2 when the water table is below the foundation level and 343.05 t/m^2 when the water table is at the foundation level.

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

q_u = cN_c + γDN_q + 0.5γBN_γ

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

Given: c = 1 t/m^2 ɸ = 30 degrees B = D = 2 m γ = 2 t/m^3 (for case a and b) and γ = 2.5 t/m^3 (for case c and d)

For ɸ = 30 degrees, N_c = 57.3, N_q = 41.4, N_γ = 44.7

Case a. G.W.T at 5.0 m below ground level The water table is below the foundation, so the effective unit weight is the bulk unit weight. q_u = 157.3 + 2241.4 + 0.52244.7 = 57.3 + 165.6 + 89.4 = 312.3 t/m^2

Case b. G.W.T at 1.0 m below ground level The water table is below the foundation, so the effective unit weight is the bulk unit weight. q_u = 157.3 + 2241.4 + 0.52244.7 = 57.3 + 165.6 + 89.4 = 312.3 t/m^2

Case c. G.W.T at ground level The water table is at the foundation level, so the effective unit weight is the saturated unit weight. q_u = 157.3 + 2.5241.4 + 0.52.5244.7 = 57.3 + 207 + 111.75 = 376.05 t/m^2

Case d. G.W.T at foundation level The water table is at the foundation level, so the effective unit weight is the saturated unit weight. q_u = 157.3 + 2.5241.4 + 0.52.5244.7 = 57.3 + 207 + 111.75 = 376.05 t/m^2

So, the bearing capacity of the soil is 312.3 t/m^2 for cases a and b, and 376.05 t/m^2 for cases c and d.