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The bearing capacity of soil is defined as the capacity of the soil to bear the loads coming from the foundation. The pressure which the soil can easily withstand against load is called allowable bearing pressure.Types of Bearing Capacity of Soil
Following are some types of bearing capacity of soil:1. Ultimate bearing capacity (q_{u})
The gross pressure at the base of the foundation at which soil fails is called ultimate bearing capacity.2. Net ultimate bearing capacity (q_{nu})
By neglecting the overburden pressure from ultimate bearing capacity we will get net ultimate bearing capacity. Where = unit weight of soil, D_{f} = depth of foundation3. Net safe bearing capacity (q_{ns})
By considering only shear failure, net ultimate bearing capacity is divided by certain factor of safety will give the net safe bearing capacity.q_{ns }= q_{nu}/ F
Where F = factor of safety = 3 (usual value)4. Gross safe bearing capacity (q_{s})
When ultimate bearing capacity is divided by factor of safety it will give gross safe bearing capacity.q_{s} = q_{u}/F
5. Net safe settlement pressure (q_{np})
The pressure with which the soil can carry without exceeding the allowable settlement is called net safe settlement pressure.6. Net allowable bearing pressure (q_{na})
This is the pressure we can used for the design of foundations. This is equal to net safe bearing pressure if q_{np} > q_{ns. }In the reverse case it is equal to net safe settlement pressure.Calculation of Bearing Capacity
For the calculation of bearing capacity of soil, there are so many theories. But all the theories are superseded by Terzaghi’s bearing capacity theory.1. Terzaghi’s bearing capacity theory
Terzaghi’s bearing capacity theory is useful to determine the bearing capacity of soils under a strip footing. This theory is only applicable to shallow foundations. He considered some assumptions which are as follows.- The base of the strip footing is rough.
- The depth of footing is less than or equal to its breadth i.e., shallow footing.
- He neglected the shear strength of soil above the base of footing and replaced it with uniform surcharge. ( D_{f})
- The load acting on the footing is uniformly distributed and is acting in vertical direction.
- He assumed that the length of the footing is infinite.
- He considered Mohr-coulomb equation as a governing factor for the shear strength of soil.
Load from footing x weight of wedge = passive pressure + cohesion x CB sin
Where P_{p }= resultant passive pressure = (P_{p})_{y} + (P_{p})_{c} + (P_{p})_{q} (P_{p})_{y is} derived by considering weight of wedge BCDE and by making cohesion and surcharge zero. (P_{p})_{c is} derived by considering cohesion and by neglecting weight and surcharge. (P_{p})_{q }is derived by considering surcharge and by neglecting weight and cohesion. Therefore, By substituting, So, finally we get q_{u }= c’N_{c }+ y D_{f} N_{q} + 0.5 y B N_{y} The above equation is called as Terzaghi’s bearing capacity equation. Where q_{u }is the ultimate bearing capacity and N_{c}, N_{q}, N_{y} are the Terzaghi’s bearing capacity factors. These dimensionless factors are dependents of angle of shearing resistance (). Equations to find the bearing capacity factors are: Where Kp = coefficient of passive earth pressure. For different values of , bearing capacity factors under general shear failure are arranged in the below table.Nc | Nq | Ny | |
0 | 5.7 | 1 | 0 |
5 | 7.3 | 1.6 | 0.5 |
10 | 9.6 | 2.7 | 1.2 |
15 | 12.9 | 4.4 | 2.5 |
20 | 17.7 | 7.4 | 5 |
25 | 25.1 | 12.7 | 9.7 |
30 | 37.2 | 22.5 | 19.7 |
35 | 57.8 | 41.4 | 42.4 |
40 | 95.7 | 81.3 | 100.4 |
45 | 172.3 | 173.3 | 297.5 |
50 | 347.5 | 415.1 | 1153.2 |
q_{u }= c’N_{c }+ D_{f} N_{q} + 0.5 B N_{y}
By the modification of above equation, equations for square and circular footings are also given and they are. For square footingq_{u }= 1.2 c’N_{c }+ D_{f} N_{q} + 0.4 B N_{y}
For circular footingq_{u }= 1.2 c’N_{c }+D_{f} N_{q} + 0.3 B N_{y}
2. Hansen’s bearing capacity theory
For cohesive soils, Values obtained by Terzaghi’s bearing capacity theory are more than the experimental values. But however it is showing same values for cohesionless soils. So Hansen modified the equation by considering shape, depth and inclination factors. According to Hansen’sq_{u }= c’N_{c }Sc dc ic + D_{f} N_{q} Sq dq iq + 0.5 B N_{y }Sy dy iy
Where Nc, Nq, Ny = Hansen’s bearing capacity factors Sc, Sq, Sy = shape factors dc, dq, dy = depth factors ic, iq, iy = inclination factors Bearing capacity factors are calculated by following equations. For different values of Hansen bearing capacity factors are calculated in the below table.Nc | Nq | Ny | |
0 | 5.14 | 1 | 0 |
5 | 6.48 | 1.57 | 0.09 |
10 | 8.34 | 2.47 | 0.09 |
15 | 10.97 | 3.94 | 1.42 |
20 | 14.83 | 6.4 | 3.54 |
25 | 20.72 | 10.66 | 8.11 |
30 | 30.14 | 18.40 | 18.08 |
35 | 46.13 | 33.29 | 40.69 |
40 | 75.32 | 64.18 | 95.41 |
45 | 133.89 | 134.85 | 240.85 |
50 | 266.89 | 318.96 | 681.84 |
Shape of footing | Sc | Sq | Sy |
Continuous | 1 | 1 | 1 |
Rectangular | 1+0.2B/L | 1+0.2B/L | 1-0.4B/L |
Square | 1.3 | 1.2 | 0.8 |
Circular | 1.3 | 1.2 | 0.6 |
Depth factors | Values |
dc | 1+0.35(D/B) |
dq | 1+0.35(D/B) |
dy | 1.0 |
Inclination factors | Values |
ic | 1 – [H/(2 c B L)] |
iq | 1 – 1.5 (H/V) |
iy | (iq)^{2} |