7/21/2019 CEN 512 Meyerhof_s General Bearing Capacity Equation

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GENERAL BEARING CAPACITY EQUATION

Vesic (1973) confirmed that basic nature of failure surface in soil suggested

by Terzaghi was correct based on laboratory and field studies. However, the

value of α was closer to 45 + φ/2 than to φ, originally assumed by Terzaghi.

Hence, new relations for bearing capacity factors were establishedconsidering the new value of α = 45 + φ/2. 

= ( − 1)ϕ  Prandtl (1921)

= 45+   Reissner (1924)

= 2( + 1)ϕ  Caquot and Kerisel (1953) and Vesic (1973)

The soil bearing capacity equation for strip footing can be modified for

general use by incorporating the empirical correction factors:

1)  Depth factor

-  to account for the shearing resistance developed along the

failure surface in soil above the base of the footing

2)  Shape factor

- 

to determine the bearing capacity of rectangular and circular

footings 

3)  Inclination factor

-  To determine the bearing capacity of a footing on which the

direction of load application is inclined at a certain angle to the

vertical

Thus, the ultimate general bearing capacity equation can be written as

(Meyerhof, 1963):

=     +     + 12        

Where:

λcs, λqs, λγs = shape factors

λcd, λqd, λγd  = depth factors

λci, λqi, λγi = inclination factors

Note: 

The effect of the ground water table must be considered in

determining the values of q and γ in general bearing capacity equation. 

Sample Problem

A square footing is shown. Determine the safe gross bearing capacity that the

footing can carry. Use the general bearing capacity equation.

7/21/2019 CEN 512 Meyerhof_s General Bearing Capacity Equation

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Table 6. Bearing Capacity Factors - NC, Nq, Nγ – (General Bearing Capacity

Equation)

Φ (deg)  NC  Nq  Nγ  Φ (deg)  NC  Nq  Nγ 

0 5.14 1.00 0.000 26 22.25 11.85 8.002

1 5.38 1.09 0.002 27 23.94 13.20 9.463

2 5.63 1.20 0.010 28 25.80 14.72 11.190

3 5.90 1.31 0.023 29 27.86 16.44 13.236

4 6.19 1.43 0.042 30 30.14 18.40 15.668

5 6.49 1.57 0.070 31 32.67 20.63 18.668

6 6.81 1.72 0.106 32 35.49 23.18 22.022

7 7.16 1.88 0.152 33 38.64 26.09 26.166

8 7.53 2.06 0.209 34 42.16 29.44 31.145

9 7.92 2.25 0.280 35 46.12 33.30 37.152

10 8.35 2.47 0.367 36 50.59 37.75 44.426

11 8.80 2.71 0.471 37 55.63 42.92 53.270

12 9.28 2.97 0.596 38 61.35 48.93 64.073

13 9.81 3.26 0.744 39 67.87 55.96 77.332

14 10.37 3.59 0.921 40 75.31 64.20 93.690

15 10.98 3.94 1.129 41 83.86 73.90 113.985

16 11.63 4.34 1.375 42 93.71 85.38 139.985

17 12.34 4.77 1.664 43 105.11 99.02 171.141

18 13.10 5.26 2.003 44 118.37 115.31 211.406

19 13.93 5.80 2.403 45 133.88 134.88 262.73920 14.83 6.40 2.871 46 152.10 158.51 328.728

21 15.82 7.07 3.421 47 173.64 187.21 414.322

22 16.88 7.82 4.066 48 199.26 222.31 526.444

23 18.05 8.66 4.824 49 229.93 265.51 674.908

24 19.32 9.60 5.716 50 266.89 319.07 873.843

25 20.72 10.66 6.765

Table 7. Approximate shape, depth, and inclination factors recommended

by Meyerhof

Shape Factors

For φ = 0o  For φ > 0

o 

= 1 + 0 . 2

  = 1 + 0 . 2

45+

2 

= 1  = 1 + 0 . 1 45+

2 

= 1  =  

Depth Factors 

For φ = 0o  For φ > 0

o 

= 1 + 0 . 2   = 1 + 0 . 2

45+ 2 

= 1  = 1 + 0 . 1 45+

2 

= 1 

=  

Inclination Factors 

= 1 −

90 

= 1 −

90 

= 1 −