156
Shallow Foundations: Bearing Capacity and Settlement
where Nc, Nq, Ng = bearing capacity factors (see Table 2.3 for Nc and Nq and Table 2.4 for Ng) l cb , l qb , lgb = slope factors q = gDf According to Hansen,28
lqβ = lγβ = (1 - tan β )2 lcβ =
N q l qβ - 1 Nq - 1
lcβ = 1 -
2β π +2
(4.78)
(for φ > 0)
(4.79)
(for φ = 0)
(4.80)
For the f = 0 condition Vesic12 pointed out that, with the absence of weight due to the slope, the bearing capacity factor Ng has a negative value and can be given as
Nγ = -2sin β
(4.81)
Thus, for the f = 0 condition with Nc = 5.14 and Nq = 1, equation (4.77) takes the form
2β + γ D f (1 - tan β )2 - γ B sin β (1 - tan β )2 qu = c(5.14) 1 5.14
or
qu = (5.14 - 2β )c + γ D f (1 - tan β )2 - γ B sin β (1 - tan β )2
(4.82)
4.9.3 Solution by Limit Equilibrium and Limit Analysis Saran, Sud, and Handa29 provided a solution to determine the ultimate bearing capacity of shallow continuous foundations on the top of a slope (Figure 4.35) using the limit equilibrium and limit analysis approach. According to this theory, for a strip foundation,
qu = cN c + qN q + 12 γ BNγ
(4.83)
where Nc, Nq, Ng = bearing capacity factors q = gDf Referring to the notations used in Figure 4.35, the numerical values of Nc, Nq, and Ng are given in Table 4.4.