4.7 OTHER SOLUTIONS FOR BEARING CAPACITY FACTORS

At this time, the general trend among geotechnical engineers is to accept the method of supposition as a proper means to estimate the ultimate bearing capacity of shallow rough foundations. For rough continuous foundations, the nature of failure surface in soil as shown in Fig. 4.13 has also found acceptance, and so have Prandtl's (1921) and Reissner's (1924) solutions for N _c and N _q, which are the same as Meyerhof's solution (1951) for surface foundations, or

and

There has, however, been considerable controversy over the theoretical values of N _?. Hansen (1970) has proposed an approximate relationship for N _? in the form

In the preceding equation, the relationship for N _c is that given by Prandtl's solution [Eq. (4.65)]. Caquot and Kerisel (1953) assumed that the elastic triangular soil wedge under a rough continuous foundation to be of the shape shown in Fig. 4.13. Using integration of Boussinesq's differential equation, they presented numerical values of N _? for various soil friction angles ?. Vesic (1973) has approximated their solution in the form

where N _q is given by Eq. (4.64) (Table 4.3).

Equation (4.73) has an error not exceeding 5% for 20 < ? < 40 as compared to the exact solution. Lundgren and Mortensen (1953) have developed numerical methods, by means of the theory of plasticity, for exact determination of rupture lines as well as the bearing capacity factor (