Geotechnical tutorial
5
Tutorial: Shallow Foundation Dr Eric Loh 1) a) A surface strip footing of width B carrying a uniformly distributed stress of q per unit area is resting on the surface of saturated clay. Assume that the unit weight and undrained shear strength of the clay is γ kN/m 3 and C u kN/m 2 respectively. Evaluate the ultimate bearing stress per square metre that can be carried by the footing for the probable failure mechanisms as shown in the FIGURE Q1A and FIGURE Q1B respectively. Critically compare your answer with that one obtained from Terzaghi’s bearing capacity equation. b) A 3m square footing is to be founded at a depth of 3m below ground surface. It is loaded with an axial load of 6MN and M xx = 600 kNm; M yy = 1200 kNm. A borehole shows that the water table is at the ground level. The saturated unit weight of the sand is 20kN/m 3 and effective angle of friction, Φ’ is 30°. Calculate the factor of safety against bearing capacity failure. FIGURE Q1A (NOT TO SCALE) FIGURE Q1B (NOT TO SCALE) q B 60° 60° 30° 30° q 0 B 2θ
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Shallow Foundation Tutorial
Transcript of Geotechnical tutorial
Tutorial: Shallow Foundation
Dr Eric Loh
1) a) A surface strip footing of width B carrying a uniformly distributed stress of q per unit
area is resting on the surface of saturated clay. Assume that the unit weight and undrained shear strength of the clay is γ kN/m3 and Cu kN/m2 respectively. Evaluate the ultimate bearing stress per square metre that can be carried by the footing for the probable failure mechanisms as shown in the FIGURE Q1A and FIGURE Q1B respectively. Critically compare your answer with that one obtained from Terzaghi’s bearing capacity equation.
b) A 3m square footing is to be founded at a depth of 3m below ground surface. It is loaded with an axial load of 6MN and Mxx = 600 kNm; Myy = 1200 kNm. A borehole shows that the water table is at the ground level. The saturated unit weight of the sand is 20kN/m3 and effective angle of friction, Φ’ is 30°. Calculate the factor of safety against bearing capacity failure.
FIGURE Q1A (NOT TO SCALE)
FIGURE Q1B (NOT TO SCALE)
q
B
60° 60°
30° 30°
q 0
B
2θ
Tutorial: Shallow Foundation
Dr Eric Loh
2) a) A surface strip footing of width B carrying a uniformly distributed stress of q per unit
area rests on the surface of a saturated clay. Assume that the unit weight and undrained shear strength of the clay is γ kN/m3 and Cu kN/m2 respectively. Evaluate the ultimate bearing stress per square metre that can be carried by the footing for the probable failure mechanism shown in the FIGURE Q2A. Critically compare your answer with the one obtained from Terzaghi’s bearing capacity equation.
b) A cylindrical reservoir (gross self-weight = 15MN) has a diameter of 17m is to be
constructed at a depth of 2m below ground surface. The soil profile at the site consists of a thick layer of CLAY which is underlying by 2.5m GRAVEL fill. A borehole shows that the water table is 1.5m below the ground surface. The geotechnical properties of the soil are as given in the table below.
Geotechnical Properties GRAVEL CLAY
Dry Unit Weight (kN/m3) 20 18
Saturated Unit Weight (kN/m3) 21 19
Undrained Shear Strength (kN/m2) - 50
Effective Cohesion (kN/m2) - 7
Angle of Effective Friction (º) 32 9
Investigate the safe depth of water that can be stored in the reservoir if the factor of safety on bearing capacity is to be 2.5.
FIGURE Q2A (NOT TO SCALE)
q
B
45° 45°
45° 45°
Tutorial: Shallow Foundation
Dr Eric Loh
3) a) A 2m wide strip footing is founded on the top of a 60 stiff clay slope as shown in
FIGURE Q3A. The saturated unit weight of the clay is 20 kN/m3 and the undrained cohesion is 120 kN/m2. What is the value of Qult–1, the ultimate load per meter of the footing as evaluated from the equation derived in the lecture.
b) Use the design table in FIGURE Q3B to obtain the value of Qult–1 and Qult–2, the ultimate load per meter of the other footing, which is founded on the face of the same 60 stiff clay slope. Compare and discuss the difference in the values of Qult–1 and Qult–2.
FIGURE Q3A (NOT TO SCALE)
Qult - 1
2m wide strip
60˚
Qult - 2 2m wide strip
SATURATED STIFF CLAY Cu = 120 kN/m2 Unit weight = 20 kN/m3
3m
Tutorial: Shallow Foundation
Dr Eric Loh
FIGURE Q3B Bearing capacity Ncs, Nqs & Nγs for footing on or adjacent to a slope
(modified from Bowles, 1997)
β↓ Φ = 0 10 20 30 40 0 10 20 30 40 0 10 20 30 40
N cs = 5.14 8.35 14.83 30.14 75.31 5.14 8.35 18.43 30.14 75.31 5.14 8.35 14.83 30.14 75.31
N qs = 1.00 2.47 6.40 18.40 64.20 1.00 2.47 6.40 18.40 64.20 1.00 2.47 6.40 18.40 64.20
4.89 7.80 13.37 26.80 64.42 5.14 8.35 14.83 30.14 75.31 5.14 8.35 14.83 30.14 75.311.00 2.47 6.40 18.40 64.20 0.92 1.95 4.43 11.16 33.94 1.00 2.47 5.85 14.13 40.81
4.63 7.28 12.39 23.78 55.01 5.14 8.35 14.83 30.14 66.81 5.14 8.35 14.83 30.14 75.311.00 2.47 6.40 18.40 64.20 0.94 1.90 4.11 9.84 28.21 1.00 2.47 5.65 12.93 35.14
4.51 7.02 11.82 22.38 50.80 5.14 8.35 14.83 28.76 62.18 5.14 8.35 4.83 30.14 73.571.00 2.47 6.40 18.40 64.20 0.92 1.82 3.85 9.00 25.09 1.00 2.47 5.39 12.04 31.80
4.38 6.77 11.28 21.05 46.88 5.14 8.35 14.83 27.14 57.76 5.14 8.35 14.83 30.14 68.641.00 2.47 6.40 18.40 64.20 0.88 1.71 3.54 8.08 21.91 1.00 2.47 5.04 10.99 28.33
3.62 5.33 8.33 14.34 28.56 4.70 6.83 10.55 17.85 34.84 5.14 8.34 2.76 21.37 41.121.00 2.47 6.40 18.40 64.20 0.37 0.63 1.17 2.36 5.52 0.62 1.04 1.83 3.52 7.80
5.14 8.33 14.34 28.02 66.60 5.14 8.35 14.83 30.14 75.31 5.14 8.35 14.83 30.14 75.311.00 2.47 6.40 18.40 64.20 1.00 2.34 5.34 13.47 40.83 1.00 2.47 6.40 15.79 45.45
5.14 8.31 13.90 26.19 59.31 5.14 8.35 14.83 30.14 71.11 5.14 8.35 14.83 30.14 75.311.00 2.47 6.40 18.40 64.20 1.00 2.47 6.04 14.39 40.88 1.00 2.47 6.40 16.31 43.93
5.14 8.29 13.69 25.36 56.11 5.14 8.35 14.83 30.14 67.49 5.14 8.35 14.83 30.14 75.311.00 2.47 6.40 18.40 64.20 1.00 2.47 6.27 14.56 40.06 1.00 2.47 6.40 16.20 42.35
5.14 8.27 13.49 24.57 53.16 5.14 8.35 14.83 30.14 64.04 5.14 8.35 14.83 30.14 74.921.00 2.47 6.40 18.40 64.20 1.00 2.47 6.40 14.52 38.72 1.00 2.47 6.40 15.85 40.23
5.14 7.94 12.17 20.43 39.44 5.14 8.35 14.38 23.94 45.72 5.14 8.35 14.83 27.46 52.001.00 2.47 6.40 18.40 64.20 1.00 2.47 5.14 10.05 22.56 1.00 2.47 4.97 9.41 20.30
5.14 8.35 14.83 29.24 68.78 5.14 8.35 14.83 30.14 75.31 5.14 8.35 14.83 30.14 75.311.00 2.47 6.40 18.40 64.20 1.00 2.47 6.01 15.39 47.09 1.00 2.47 6.40 17.26 49.77
5.14 8.35 14.83 28.59 63.60 5.14 8.35 14.83 30.14 75.31 5.14 8.35 14.83 30.14 75.311.00 2.47 6.40 18.40 64.20 1.00 2.47 6.40 18.40 53.21 1.00 2.47 6.40 18.40 52.58
5.14 8.35 14.83 28.33 61.41 5.14 8.35 14.83 30.14 72.80 5.14 8.35 14.83 30.14 75.311.00 2.47 6.40 18.40 64.20 1.00 2.47 6.40 18.40 55.20 1.00 2.47 6.40 18.40 52.97
5.14 8.35 14.83 28.09 59.44 5.14 8.35 14.83 30.14 70.32 5.14 8.35 14.83 30.14 75.311.00 2.47 6.40 18.40 64.20 1.00 2.47 6.40 18.40 56.41 1.00 2.47 6.40 18.40 52.63
5.14 8.35 14.83 26.52 50.32 5.14 8.35 14.83 30.14 56.60 5.14 8.35 14.83 30.14 62.881.00 2.47 6.40 18.40 64.20 1.00 2.47 6.40 18.40 46.18 1.00 2.47 6.40 16.72 36.17
25º
30º
60º
D/B = 0 b/B =1.50 D/B = 0.75 b/B = 1.50 D/B = 1.50 b/B = 1.50
10º
20º
10º
20º
25º
30º
60º
D/B = 1.50 b/B = 0.75
D/B = 0 b/B = 0 D/B = 0.75 b/B = 0 D/B = 1.50 b/B = 0
0º
10º
20º
25º
30º
60º
D/B = 0 b/B = 0.75 D/B = 0.75 b/B = 0.75
D
D
b
β
B
B
Tutorial: Shallow Foundation
Dr Eric Loh
4) FIGURE Q4A shows a 3m square footing to be founded at a depth of 3m below ground surface. The water table is at a depth of 1m from the ground surface. A piezometer installed at a depth of 5m gave a standing water level of 2.0m above the ground level. The geotechnical properties of the clay are as follows: Bulk Unit Weight = 18kN/m3 Saturated Unit Weight = 19kN/m3 Undrained Shear Strength = 50 kN/m2 Effective Cohesion = 7 kN/m2 Angle of Effective Friction = 9º Calculate and critically comment on the factor of safety against bearing capacity failure, if the footing is loaded with an axial load of 5MN and Mxx = 500 kNm; Myy = 1000 kNm.
[17 marks]
FIGURE Q4A
CLAY
CHALK
Ground Level
5m
2m
3m x 3m
3m
1m WT
