Bearing Capacity Problems: . Conc

Bearing capacity problems P3.1

Proportion the dimensions (B x L) for the footing shown in the figure below. Given that the undrained shear strength q u = 75 kPa,  clay =18 kN/m3, and  conc. = 24 kN/m3 (Use Hansen’s equation, S.F. = 3.0).

600 kN 300 kN-m G.S.

0.6m 0.3m

Rectangular footing

B

L P3.2

For the wall footing shown in the figure below, calculate the factor of safety against the bearing capacity failure for the following cases (using Meyerhof's equation): a- The load is vertical, and if Center line b- The load is inclined at 15  to the vertical.

e = 0.25m 1.0m

0.5m 0.5m

1.5m

  25 , c = 40 kN/m2

 = 18 KN/m3  sat = 20 KN/m3

2m 1.5m W.T.

P3.3

For the circular oil tank shown in the figure beside, find the minimum diameter of footing if F.S. = 2.5 and  oil  8 kN/m3,  soil  14.4 kN/m3,  concrete  24 kN/m3 , and Vfooting  0.1...Vtan k ?

0.5m 0.5m 12m

10m

G.S.

B =? Silty sand c = 40 kN/m2,   15

Assist.Prof. / Dr.Raf’Mahmoud Sulaiman

Bearing Capacity of Shallow Foundations P3.4

An offshore concrete oil tank of B = 6m, L = 10m and H = 9m is as shown in the figure below. Find:1. F.S. against bearing capacity, 2. F.S. against sliding (   2 / 3 ), 3. F.S. against floating, and 4. F.S. against overturning. Notes:  Neglecte the active and passive sides forces, 300 kN/m  Use Meyerhof's equation.  Take  oil  8 kN/m3, and  concrete  24 kN/m3. 6m 500 kN 2.0m 6m

0.4m

Water

2.5m 6m

Water G.S.

Oil

1.0m 6m Sand

P3.5

  30 ,  soil  18 kN/m3

For the tank shown in the figure below, if F.S. = 2.0, weight of tank (empty) = 500 kN, and weight of tank (full) = 10000 kN, check the adequacy of footing (against bearing capacity and sliding failures).

500 kN 2.5m

0.5m 3m G.S.

G.S. 0.75m

0.75m

2m 2m

2m 6m

3m Sand   30 ,  = 18 kN/m3

2

Assist.Prof. / Dr.Raf’Mahmoud Sulaiman

Bearing Capacity of Shallow Foundations P3.6

For the cabling tower shown in the figure below, if the weight of tower = 2000 kN, moment due to wind load = 8000 kN-m, minimum factor of safety = 2.0, check the adequacy of the proposed four spread footings each of (4m x 4m x 1m) dimensions (against bearing capacity failure and uplift). y

Wind load

x

6m

45

4mx4mx1m 6m Sand

G.S. W.T.

  30 ,  = 18 kN/m3

3m

G s  2 .7

P3.7

1m 4mx4mx1m

A raft foundation of 15m diameter is placed at 2.5m below the ground surface in clay soil with sat.  20 kN/m3, Gs  2.65 as shown in the figure below. The raft supports a tower of 40 MN weight and wind load moment of 20 MN-m. Find the thickness of footing if S.F.=2.5.

G.S. 2.5m

C = 120 kN/m2

Raft: 15m diameter 30m

Clay  sat.  20 kN/m3, G s  2.65

Sand

3

C = 300 kN/m2

W.T.

Assist.Prof. / Dr.Raf’Mahmoud Sulaiman

Bearing Capacity of Shallow Foundations Footings on layered soils problems P3.8

A (3m x 6m) rectangular footing is to be placed on a two-layered clay deposits as shown in the figure below. Compute the F.S. against the bearing capacity failure and check whether the soil may squeeze beneath the footing or not. Total load = 900 kN

G.S.

P3.9

0.6m

3m x 6m

1.2m

Clay

q u = 192 kPa,  = 0

2.4m

Clay

q u = 576 kPa,  = 0

Rock

RQD = 50%, q u = 3000 kPa

A (1.5m x 2.0m) rectangular footing is to be placed on c   soils shown in the figure below. Check its adequacy against shear failure (assume F.S.= 3.0, and 𝛾𝜔 =10 kN/m3 ) using Vesic’s equation. P Parameter

Gs e c (kPa) 

Soil

Soil

Soil

(I)

(II)

(III)

2.70 0.8 10 35

2.65 0.9 60 30

2.75 0.85 80 0

G.S. Soil (1)

1.2m W.T.

1.5m x 2.0m

Soil (2)

1.5m

Soil (3)

Footings on slope Problems P3.10 A (1.2m x 1.2m) square footing is to be placed near a slope of c   soil. If   15 ,

Df  0.9m, c = 50 kN/m2,   33 ,   17.3 kN/m3, and the ground water table is located at a great depth, find the maximum allowable load that the footing can carry using: (a) Meyerhof's method, and Qall.  ? (b) Hansen's method. G.S.

0.9m 3.6m

1.2m x 1.2m

15

Df  0.9m

c = 50 kN/m2,   33 ,   17.3 kN/m3

4

Assist.Prof. / Dr.Raf’Mahmoud Sulaiman

Bearing Capacity of Shallow Foundations

P3.11 A (3m x 6m) rectangular combined footing that supports two columns each of (0.4m x 0.4m) is to be constructed near a slope as shown in the figure below. Find F.S. against bearing capacity failure. Note:

6m

Since (L) direction of foundation is in the same direction of slope, check the F.S. in (B) direction also.

0.4m x 0.4m

3m 4.8m 1000 kN

1m 2000 kN G.S.

4.5m 3m 20

W.T.

6m

Sand

  30 ,  sat.  18 kN/m3, G s  2.65

P3.12 For the cabling tower near a slope shown in the figure below. if the weight of tower = 6000 kN, moment due to wind load = 10000 kN-m, and minimum factor of safety = 2.0, check the S.F. of (4m x 4m x 1m) spread footings against bearing capacity failure. y

Wind load 45

x

5m

4mx4mx1m 3m

5m

G.S.

3m

1m 4mx4mx1m

  20

W.T.

4mx4mx1m

Sand   30 ,  = 18 kN/m3, G s  2.7

5

Assist.Prof. / Dr.Raf’Mahmoud Sulaiman

Bearing Capacity of Shallow Foundations Footings on rocks Problems

P3.13 The unweathered quartzite below excavation level for a multistory building has an RQD of 30% for the upper 1.5m and 70% for the next 6m. A load of 1500 tons is delivered to the rock through a square reinforced concrete pedestal. What would be the size of the pedestal to restrict the settlement to about 12.7mm? 1500 Tons

B=? 1.5m

RQD =30%

6.0m

RQD =70%

6