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BFC 4043
2.0 SHALLOW FOUNDATION :
2.1 General Concept A shallow foundation must :
be safe against overall shear failure in the soil
not undergo excessive settlement
Nature of bearing capacity failure are : (as shown in Figure 2.1)
general shear failure (for stiff clay or dense sand) local shear failure (for medium dense sand or clayey soil) punching shear failure(loose sand or soft clay)
Figure 2.1 Nature of bearing capacity failure : (a) general shear (b) local shear (c) punching shear
Vesic (1973) proposed a relationship for the bearing capacity failure on sands in terms of relative density, Dr depth of foundation, Df and B*, Figure 2.2 Where :
and B width, L length of foundation
NOTE : L IS ALWAYS GREATER THAN B For square; B=Land for circular; B=L=Diameter of foundation and B* = B
Figure 2.2 Modes of foundation failure in sand, (Vesic, 1973)
2.2 Terzaghis Bearing Capacity Terzaghi suggested for a continuous or strip foundation with failure surface as in Figure 2.3
Figure 2.3 Bearing capacity failure in soil under rough rigid continuous foundation
Soil above the bottom of foundation is surcharge, q = Df The failure zone under the foundation is separated into three parts namely;
triangular ACD under the foundation
radial shear zones ADF and CDE with curves DE and DF as arcs of logarithmic spiral
Rankine passive zones AFH and CEG
CAD and ACD are assume to equal friction angle, Thus ultimate bearing capacity, qu for general shear failure can be expressed as :
Where : c cohesion of soil
- unit weight of soil
q = Df
Nc, Nq, N- bearing capacity factors
And
where - passive pressure coefficient Table 2.1 summarizes values for Nc, Nq, and N
Table 2.1 Terzaghis Bearing Capacitys Factors
NcNqN
NcNqN
0
1
2
3
4
5
6
7
8
9
10
11
12
13
1415
16
17
18
19
20
21
22
23
24
255.706.00
6.30
6.62
6.97
7.34
7.73
8.15
8.60
9.09
9.6110.16
10.76
11.41
12.11
12.86
13.68
14.60
15.12
16.56
17.69
18.92
20.27
21.75
23.36
25.131.001.10
1.22
1.35
1.49
1.64
1.81
2.00
2.21
2.44
2.69
2.98
3.29
3.63
4.02
4.45
4.92
5.45
6.04
6.70
7.44
8.26
9.19
10.23
11.40
12.720.000.01
0.04
0.06
0.10
0.14
0.20
0.27
0.35
0.44
0.56
0.69
0.85
1.04
1.26
1.52
1.82
2.18
2.59
3.07
3.64
4.31
5.09
6.00
7.08
8.342627
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
5027.0929.24
31.61
34.24
37.16
40.41
44.04
48.09
52.6457.75
63.53
70.01
77.50
85.97
95.66
106.81
119.67
134.58
151.95
172.28
196.22
224.55
258.28
298.71
347.50
14.2115.90
17.81
19.98
22.46
25.28
28.52
32.23
36.50
41.44
47.16
53.80
61.55
70.61
81.27
93.85
108.75
126.50
147.74
173.28
204.19
241.80
287.85
344.63
415.149.8411.60
13.70
16.18
19.13
22.65
26.87
31.94
38.04
45.41
54.36
65.27
78.61
95.03
115.31
140.51
171.99
211.56
261.60
325.34
407.11
512.84
650.67
831.99
1072.80
From Kumbhojkar (1993)
And ultimate bearing capacity, qu for local shear failure can be expressed as :
Where : Nc, Nq, N(see Table 2.2) are reduced bearing capacity factors can be calculated by using Nc, Nq, N- bearing capacity factors with
Table 2.2 Terzaghis Modified Bearing Capacitys Factors
NcNqN
NcNqN
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
255.70
5.906.106.306.516.746.977.227.477.748.028.328.638.969.319.6710.0610.4710.9011.3611.8512.3712.9213.5114.1414.801.00
1.071.141.221.301.391.491.591.701.821.942.082.222.382.552.732.923.133.363.613.884.174.484.82
5.205.600.00
0.0050.020.040.055
0.0740.100.1280.160.200.240.300.350.420.480.570.670.760.881.031.121.351.551.741.972.25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
5015.5316.3017.1318.0318.9920.0321.1622.3923.7225.1826.7728.5130.4332.5334.8737.4540.3343.5447.1351.1755.7360.9166.8073.5581.31
6.056.547.077.668.319.039.8210.6911.6712.75
13.9715.3216.8518.5620.5022.7025.2128.0631.3435.1139.4844.4550.4657.4165.602.592.883.293.764.394.835.516.327.22
8.359.4110.9012.7514.7117.2219.7522.5026.2530.4036.00
41.70
49.30
59.2571.4585.75
Example 2.1
Given : A square foundation, 1.5m x 1.5m in plan view
Soil parameters :
= 20, c = 15.2 kN/m2, =17.8 kN/m3Assume : FS = 4, general shear failure condition and Df= 1 m
Find : Allowable gross load on the foundation
Solution :
For = 20, (Table 2.1); Nc = 17.69, Nq = 7.44, N= 3.64
Thus
Allowable bearing capacity :
Thus total allowable gross load, Q
Example 2.2
Given : Repeat example 2.1Assume : Local shear failure condition
Solution:
For = 20, (Table 2.2); Nc = 11.85, Nq = 3.88, N= 1.12
Allowable load :
;
2.3 Effect of Water Table on Bearing Capacity All equations mentioned before are based on the location of water table well below the foundation; if otherwise, some modification should be made according to the location of the water table, see Figure 2.4
Figure 2.4 Modification of bearing capacity for water table
Case I : 0 D1 Df q(effective surcharge) =
where :
- effective unit weight =
- saturated unit weight of soil
- unit weight of water = 9.81kN/m3 or 62.4 lb/ft3 in the last term of the equation Case II : 0 d B the value
Case III : d B water has no effect on the quNote : the values of bearing capacity factors used strictly depending on whether the condition is general or local shear failure.2.4 Factor of Safety, FS
, where :
qall - gross allowable load-bearing capacity, qu gross ultimate bearing capacity,
FS factor of safety Values of FS against bearing capacity failure is 2.5 to 3.0.
Net stress increase on soil = net ultimate bearing capacity/FS
, and :
;
Where : qall(net) net allowable bearing capacity
qu(net) net ultimate bearing capacity
Procedure for FSsheara. Find developed cohesion,cd and angle of friction,d;
b. Terzaghis equations become (with cd and d):
With : Nc, Nq, N- bearing capacity factors for dc. Thus, the net allowable bearing capacity :
Example 2.3
Using ; and FS = 5; find net allowable load for the foundation in example 2.1 with qu = 521 kN/m2
With qu = 521 kN/m2; q = 1(17.8) = 17.8 kN/m2
HenceQall(net) = 100.64(1.5x1.5) = 226.4 kN
Example 2.4
Using Example 3.1, and Terzaghis equation
with FSshear = 1.5;
Find net allowable load for the foundation
For c=15.2 kN/m2, = 20 and
cd =
d = tan-1[] = tan-1[] = 13.64
With:
From Table 2.1 : =13.6 ; ; ; (estimation)Hence :
2.5 The General Bearing Capacity Equation The need to address for rectangular shape foundation where :(0 1
NOTE : tan-1(Df/B) is in radian inclination
Where : inclination of load from vertical For undrained condition ( = 0)
Skemptons :
Table 2.3 Vesics Bearing Capacity Factors for General Equation (1973)NcNqN
Nq/ NcTan NcNqN
Nq/ NcTan
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
255.145.38
5.63
5.90
6.19
6.49
6.81
7.16
7.53
7.92
8.35
8.80
9.28
9.81
10.37
10.98
11.63
12.34
13.10
13.93
14.83
15.82
16.88
18.05
19.32
20.721.001.09
1.20
1.311.43
1.57
1.72
1.88
2.06
2.25
2.47
2.71
2.97
