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GGU-FOOTING: Analysis of bearing capacity safety

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

σ0f,k = c · Nc  + γ1 · d · Nd + γ2 · b' · Nb

where:

  • σ0f,k = characteristic bearing stress
  • c = cohesion [kN/m²]
  • Nc = bearing capacity coefficient cohesion
  • γ1 = unit weight of soil above footing base
  • d = embedment depth of footing
  • Nd = bearing capacity coefficient footing depth
  • γ2 = unit weight of soil below footing base
  • b' = calculated depth of footing
  • Nb = bearing capacity coefficient footing width

Bearing capacity coefficients Nc Nd and Nb

  • Nc = Nc0 · νc · ic · λc · ξc  (· dc)
  • Nd = Nd0 · νd · id · λd · ξd  (· dd)
  • Nb = Nb0 · νb · ib · λb · ξb  (· db)

The following values are adopted:

  • Nc0  Nd0  Nb0 according to DIN 4017
  • νc  νd   νb  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  νd und νb for strip footings, as this delivers somewhat more favourable values.
νd = 1 + 0,2 · b/a       (instead of 1.0 for strip footings)
νb = 1 + b/a · sin(φ)   (instead of 1.0 for strip footings)

  • ic  id  ib according to DIN 4017 (load inclination coefficients)
  • λc  λd  λb according to DIN 4017 (ground inclination coefficient)
  • ξc  ξd  ξb according to DIN 4017 (base inclination coefficients)
  • dc  dd  db (depth coefficients), not envisaged in DIN 4017

Depth coefficients dc dd and db

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 db in all cases is:

db = 1,0

For the influence of the embedment depth dd :

grafik-20240924-145930.png

For the influence of cohesion dc :

grafik-20240924-145954.pnggrafik-20240924-150017.png

Message "delta => phi" and undrained layers

The message appears for inclined loads if the angle δ given in the message reaches or exceeds the averaged friction angle; a bearing capacity analysis to DIN 4017 is then not possible. Enter undrained layers with φu = 0 and c = cu; they may be mixed with drained layers (φ', c'). If the failure figure also intersects drained layers, the averaged friction angle is greater than zero, and the message may occur even though individual layers have φ = 0 (see "Theoretical principles: Determining the mean governing soil properties").

Verification across the short and the long footing side

For a single footing the program verifies bearing capacity in both plan directions and displays the less favourable direction. Across the long side the failure figure extends deeper and can reach soft layers that it does not reach across the short side; this is why the long side can be governing. In the analysis mode for multiple footings and with the "Verify bearing capacity for short side only" check box, only the short side is analysed (see "Enter system parameters (Example 1)").