The above equations for calculating the ultimate bearing capacity do not account for the case of rectangular footings  (where B/L< 1). Moreover, these equations do not consider eccentric (torques or non-vertical forces) loads, inclined foundation base, or footings on or near slopes. For example, the bearing capacity of footings placed into sloping ground is less than if the footings were on level ground. In fact, the bearing capacity of a footing is inversely proportional to ground slope. Modifications to the Terzaghi equations exist and enable one to calculate the ultimate bearing capacity under the above stated conditions.

The first modification considered is the addition of shape factors: F_cs, F_qs, F_gs which account for rectangularity of the footing, the second modification is the addition of depth factors: F_cd, F_qd, F_gd , the third modification is the addition of inclination Factors F_ci, F_qi, F_gi to account for the inclination of the load applied in case the load is not vertical. These factors enter into the bearing capacity equation as follows:

with those factors to be calculated as follows:

    Shape Factors:    (L>B)

    Depth Factors:

(a) D_f/B < 1

 

 

 

 

(b) D_f/B> 1

 

 

    Inclination Factors:

 

 

where b = inclination of the load on the foundation with respect to the vertical.

A correction in the failure surface is also accounted for in Meyerhof’s general equation, whereby in Figure 1, the angle f between the footing and the sides of the triangle becomes  f/2 + 45  instead of f, yielding a more correct assumption of smooth base instead of rough base.

This correction affects the original values of the bearing capacity factors N_c, N_q, and N_g since these factors are function of the angle f, these values become, after derivation: