General Bearing Capacity Equation

General Bearing Capacity Equation

Determination of the bearing capacity of a foundation The bearing capacity of a foundation can be determined in terms of a general shear mode, which is based on the theory of plasticity. This was the basis of Terzaghi's theory, which was based on Prandt and Reissner's solution assuming a rough foundation surface. Lower and upper bound plasticity theorems can be applied to get exact solutions, however this is based on the assumption that the soil is a perfectly plastic material.This assumption is only realistic for homogenous clays of low compressibility and subjected to the general shear mode of failure. However in most cases, it is settlement and servicability that are the limiting criteria. Various equations have been established for calculating the ultimate bearing capacity of shallow foundations based on Terzaghi's equation. These take into account the shape, depth and the loading conditions as well as the variability of the soil strata. An exact stability analysis would involve solving simultaneously the conditions of equilibrium and compatibility throughout the failure surface. This is impractical since all the following conditions must be satisfied: Each point within the soil mass must be in equilibrium The stresses within the soil must be in equilibrium wit the applied stresses to the foundations The strains occurring at a point must be compatible with the strains at all the surrounding points The strains must be related to the stresses at every point by an appropriate stress-strain relationship for the soil The failure criteria for the soil must not be exceeded at any point within the soil A complete stress-strain assessment of the soil mass would be very complicated because of the difficulty in modelling the actual stress-strain behaviour of the soil. The most successful method are limit equilibrium methods - a collapse mechanism is assumed with blocks of soil sliding along their slip surfaces and the stability of the soil mass is examined with each component block in static equilibrium. The critical condition is found and the external loading on this is taken to be approximately equal to the collapse load. This method combines some of the features of the upper and lower bound methods. Like the upper bound method, a collapse method is assumed but it is assumed that the soil can deform sufficiently for the mechanism to become compatible. The equilibrium is also examined as in the case of the lower bound method but no check is made on the stresses in the soil mass surrounding the slip surface. Therefore in general the method does not provide an upper or lower bound solution, nor is the critical failure mechanism necessarily the actual collapse mechanism, but it is one that has been observed to develop in laboratory models and full size foundations.

General Bearing Capacity Formula Various equations have been established for calculating the ultimate bearing capacity based on the original Terzaghi equation. These are comprehensive and take into account the shape and depth of the foundation, the inclination and eccentricity of the loading, as well as the position of the water table and the ground surface. General forms of the bearing capacity equation have been suggested by Meyerhof and Hansen. The basic form for both equations is:qf = (c x Nc x Fcs x Fcd x Fci) + (p' x Nq x Fqs x Fqd x Fqi) + (0.5 x y x B xNy x Fys x Fyd x Fyi)Where: c = cohesion of the soil p' = effective stress at the level of the base of the footing y = unit weight of soil B = width/diameter of footing Fcs, Fqs and Fys = shape factors Fcd, Fqd and Fyd = depth factors Fci, Fqi and Fyi = incilnation factors Nc, Nq and Ny = bearing capacity factors related to values of phi All factors will be given in tables within the formula sheet for the exam.

Skempton - saturated clays under undrained conditions It is important to note that the most critical condition for the foundation is immediately after loading and it is for this reason that the assessment of bearing capacity is usually based upon total stress shear strength parameters. This is particularly true in the case of clay soils. In a review of bearing capacity theory, Skempton concluded that in the case of saturated clays under undrained conditions, the ultimate bearing capacity of a foundation can be expressed by the equation:qf = (Cu x Nc) + (y x D)The factor Nc is a function of the shape of the footing and the depth/width ratio. It ranges from 5.14 fpr a surface strip to 9 for a circular or square footing at a depth/width ratio in excess of 4. This conforms with the general recommendations in the questions of Meyerhof and Hansen and is simpler to use in practice for conventional foundations.It is also important to note that the shearing zone extends to a depth of approximately two thirds the width of the foundation and hence the relevant shear parameters to use will be the average values of those in this zone.