Annex D

(informative)

A sample analytical method for bearing resistance calculation

D.1 Symbols used in Annex D

(1) The following symbols are used in Annex D.

A' = B' × L'   the design effective foundation area

b   the design values of the factors for the inclination of the base, with subscripts c, q and γ

B   the foundation width

B'   the effective foundation width

D   the embedment depth

e   the eccentricity of the resultant action, with subscripts B and L

i   the inclination factors of the load, with subscripts cohesion c, surcharge q and weight density γ

i   hydraulic gradient

L   the foundation length

L'   the effective foundation length

m   exponent in formulas for the inclination factor I

N   the bearing capacity factors, with subscripts for c, q and γ

q   overburden or surcharge pressure at the level of the foundation base

q'   the design effective overburden pressure at the level of the foundation base

s   the shape factors of the foundation base, with subscripts for c, q and γ

V   the vertical load

α   the inclination of the foundation base to the horizontal

γ'   the design effective weight density of the soil below the foundation level

θ   direction angle of H

(2) The notations used in this method are given in Figure D.1.

D.2 General

(1) Approximate equations for the design vertical bearing resistance, derived from plasticity theory and experimental results, may be used. Allowance should be made for the effects of the following:

  • the strength of the ground, generally represented by the design values of cu, c' and φ';
  • eccentricity and inclination of design loads;
  • the shape, depth and inclination of the foundation;
  • the inclination of the ground surface;
  • ground-water pressures and hydraulic gradients;
  • the variability of the ground, especially layering.

D.3 Undrained conditions

(1) The design bearing resistance may be calculated from:

R/A' = (π + 2)cubcscic + q
(D.1)

with the dimensionless factors for:

  • the inclination of the foundation base: bc = 1 – 2α/(π + 2);
  • the shape of the foundation:

sc = 1 + 0,2(B'/L'), for a rectangular shape;

sc = 1,2, for a square or circular shape.

  • the inclination of the load, caused by a horizontal load H:

with H ≤ A'cu.

D.4 Drained conditions

(1) The design bearing resistance may be calculated from:

R/A' = c'Ncbcscic + q'Nqbqsqiq + 0,5γ'B'Nγbγsγiγ
(D.2)

with the design values of dimensionless factors for:

  • the bearing resistance:

Nq = eπtanφ'tan2(45° + φ'/2)

Nc = (Nq – 1)cot φ'

Nγ = 2(Nq – 1)tan φ', where δ ≥ φ'/2 (rough base)

  • the inclination of the foundation base:

bc = bq – (1 – bq)/Nc × tan φ'

bq = bγ = (1 – α · tan φ’)2

  • the shape of foundation:

sq = 1 + (B'/L')sin φ', for a rectangular shape;

sq = 1 + sin φ', for a square or circular shape;

  • sγ = 1 – 0,3(B'/L'), for a rectangular shape;

sγ = 0,7, for a square or circular shape

  • sc = (sq · Nq – 1)/(Nq – 1) for rectangular, square or circular shape;
  • the inclination of the load, caused by a horizontal load H:

ic = iq – (1 – iq)/Nc · tan φ';

iq = [1 – H/(V + A'c'cot φ')]m;

iγ = [1 – H/(V + A'c'cot φ')]m+1.

where:

m = mB = [2 + (B'/L')]/[1 + (B'/L')] when H acts in the direction of B';

m = mL = [2 + (L'/B')]/[1 + (L'/B')] when H acts in the direction of L'.

In cases where the horizontal load component acts in a direction forming an angle θ with the direction of L', m may be calculated by:

m = mθ = mLcos2θ + mBsin2θ.

Notations
Figure D.1 — Notations

Eurocode 7 Geotechnical design Part 1 : General rules