Question

a circular footing 10m in diameter is proposed to carry a total load of 9000 KN. The footing is to be placed at a depth of 2m below ground surface. The soil is normally consolidated silty clay with a unit weight of 20KN/m^3 and undrained shear strength of 50 KPa.

1) determine the short-term factor of safety using the General bearing capacity equation.

2) Calculate the expected consolidation settlement of the footing if the compression index is 0.2 and the initial void ratio is 1.0.

3) if the calculated settlement is not acceptable, indicate the necessary steps to be taken before construction to reduce the consolidation settlement.

Answer 1

Load = P = 9000 kN

A = πx10²/4 = 78.54 m²

Net Bearing pressure = q_p = P/A = 9000/78.54

= 114.6 kN/m²

Ultimate Bearing Capacity of soil given by General Bearing Capacity equation is given by

q_u =cN_cs_cd_ci_c + qN_qs_qd_qi_q + 0.5YBN_ys_yd_yi_y

where

c = c_u = 50 kN/m²

For, φ_u = 0

N_c = 5.14 , N_q = 1 and N_y = 0

Shape factors

s_c = 1.2

s_q = 1

Depth factors

d_c = 1.2

d_q = 1

Inclination factors

For zero inclination with ground

i_c = i_q = 1

q = overburden pressure = YD_f

where Y = unit wt of soil = 20 kN/m³

D_f = depth of foundation = 2 m

=> q = 20x2 = 40 kN/m²

Putting values we get

q_u = 50x5.14 x1.2x1.2 x1 + 40x1x1x1x1 + 0

q_u = 370.08 + 40

= 410.08 kN/m²

Net ultimate Bearing Capacity is given by

q_nu = q_u - YD_f

= 410.08 - 40

= 370.08 kN/m²

Factor of Safety against short - term Bearing Capacity is given by

F = q_nu/q_na

= 370.08/114.6

= 3.23

b) Taking clay depth H = 10 m

Initial effective overburden at mid-depth of clay(at 5 m from suface)= q' = 20x5 = 100 kN/m²

Footing is placed at a depth of 2 m from surface

Depth of soil below footing = 8 m

Increase in stress at mid-depth of clay layer from bottom of footing i.e at depth at 3 m from footing bottom by assuming 2: 1 load distribution is given by

dq' = 9000/(10 + 3)²

= 53.25 kN/m²

Final effective stress = q'_f = 100 + 53.25 = 153.25 kN/m²

Settlement for normally Consolidated soils is given by

S = (C_cH/1+e₀)xlog(q'_f/q')

= (0.2x10/1+1)xlog(153.25/100)

= 0.1854 m

= 185.4 mm

c) If the settlement is not acceptable we can do following methods to reduce settlement

1. By Consolidating the soil with a placement of fill to allow pore pressure to diisipate

2. By placing sand drains in the soil to shorten the drainage path and allow pore pressure tro dissipate

3. By compacting the soil with rollers

4. By reinforcing the soil with geotextiles to improve soil properties

5. By using Compaction piles to reinforce the soil