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

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

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. Figure D.1 — Notations

Eurocode 7 Geotechnical design Part 1 : General rules