Bearing Capacity of Shallow Foundations and Piles

The problems solved in this chapter are related to the ultimate bearing capacity of shallow footings, piles and pile groups. The ultimate bearing capacity of a shallow footing is evaluated using traditional methods ( Terzaghi, 1943 ; Meyerhof, 1951 , 1953, 1963, 1965 and 1976) including methods by Hansen (1961 and 1970) and Vesić (1973) with modifications by Bowles (1996) ; (Problems 10.1 to 10.4). All the above solutions introduce bearing capacity factors of Nc, Nq, N γ, that are functions of the internal friction angle ϕ’. These factors represent the effects of cohesion, surcharge load adjacent to the footing and the weight of the soil within the failure zone. The improvements suggested by Hansen and Vesić take account of the geometry of the footing and inclinations of the load and ground surface. The base capacity of a pile in c ’, ϕ’ soil or cu , ϕ u = 0 soil is calculated using modified methods of Hansen and Vesić (Problems 10.5 and 10.6). For piles in sands ( c ’ = 0, ϕ’) a solution proposed by Fleming et al. (1992) is used (Problem 10.7). This solution is based on the known values of density index ID , the critical friction angle ϕ’ cr and the effective overburden pressure p ’ o . The ϕ’- Nq relationship used is taken from the theory of ultimate bearing capacity developed by Berezantzev et al. (1961) . The shaft capacity of a pile may be calculated by α method ( Skempton, 1959 ; Tomilinson, 1977 ) where the average limiting shear stress τ s mobilized on the shaft is estimated as a fraction of the undrained cohesion cu . The improvements proposed by Fleming et al. (1992) and Randolph and Murphy (1985) are used in the solution of Problem 10.8. An alternative effective stress analysis suggested by Burland (1973) , ( β method) is considered in Problem 10.9. A pile group is treated using Equation 5.50 assuming a rigid cap resting on piles. Thus the individual axial force can be evaluated (Problem 10.10). The settlement of each pile is estimated by establishing the vertical stress distribution under the pile using Mindlin solution (Problem 10.11). With the settlement calculated, The Winkler spring model can be applied to analyse the cap as an elastic beam supported by springs.