GGU-FOOTING: Analysis of bearing capacity safety

The bearing capacity analysis will be carried out according to DIN 4017:2006. The following relationship applies:

σ_0f,k = c · N_c + γ₁ · d · N_d + γ₂ · b' · N_b

where:

σ_0f,k = characteristic bearing stress
c = cohesion [kN/m²]
N_c = bearing capacity coefficient cohesion
γ₁ = unit weight of soil above footing base
d = embedment depth of footing
N_d = bearing capacity coefficient footing depth
γ₂ = unit weight of soil below footing base
b' = calculated depth of footing
N_b = bearing capacity coefficient footing width

Bearing capacity coefficients N_c N_d and N_b

N_c = N_c0 · ν_c · i_c · λ_c · ξ_c (· d_c)
N_d = N_d0 · ν_d · i_d · λ_d · ξ_d (· d_d)
N_b = N_b0 · ν_b · i_b · λ_b · ξ_b (· d_b)

The following values are adopted:

N_c0 N_d0 N_b0 according to DIN 4017
ν_c ν_d ν_b according to DIN 4017 (shape coefficients)

For settlement analysis, the length information is also needed for strip footings. The program consistently uses the values for a and b, including for calculation of the shape coefficients ν_d und ν_b for strip footings, as this delivers somewhat more favourable values.
ν_d = 1 + 0,2 · b/a (instead of 1.0 for strip footings)
ν_b = 1 + b/a · sin(φ) (instead of 1.0 for strip footings)

i_c i_d i_b according to DIN 4017 (load inclination coefficients)
λ_c λ_d λ_b according to DIN 4017 (ground inclination coefficient)
ξ_c ξ_d ξ_b according to DIN 4017 (base inclination coefficients)
d_c d_d d_b (depth coefficients), not envisaged in DIN 4017

Depth coefficients d_c d_d and d_b

The depth coefficients consider the favourable influence of shear strength in the failure plane above the footing base. In DIN 4017:2006 this effect is not taken into consideration, i.e. all depth coefficients are 1.0. In some European countries, on the other hand, the favourable effect may be considered by adopting depth coefficients > 1.0.

The following tables show several depth coefficient equations, compiled by Ziegler/Tafur (2015) in the context of a PRB project (PRB = Initiative Praxisgerechte Regelwerke im Bauwesen e.V., http://www.initiative-prb.de ).

The coefficient d_b in all cases is:

d_b = 1,0

For the influence of the embedment depth d_d :

For the influence of cohesion d_c :