where Hrep is a representative horizontal action; HGk and HQk are defined above; Pa,Gk is the characteristic thrust due to active earth pressures on the side of the footing (a permanent action), A' is the footing's effective area (defined in Section 10.4.2), and ^ is the combination factor applicable to the ith variable action.

If we assume that only one variable horizontal action is applied to the footing, this equation simplifies to:

since ^ = 1.0 for the leading variable action (i = 1). The design shear stress is then:

where yg and yq are partial factors on permanent and variable actions, respectively.

10.5.2 Drained sliding resistance

Under drained conditions, the characteristic shear resistance TRk shown in Figure 10.7 (ignoring passive pressures for the time being) is given by:

VGk tan Sk

where VGk and V'Gk represent the characteristic total and effective permanent vertical actions on the footing, respectively; UGk is the characteristic uplift owing to pore water pressures acting on the underside of the base (also a permanent action); 5k is the characteristic angle of interface friction between the base and the ground; and the other symbols are as defined above. Variable actions have been excluded from this equation, since they are favourable.

This expression conservatively ignores any effective adhesion between the footing and the ground, as suggested by Eurocode 7. [en 1997-1 ยง6.5.3(10)]

The design shear resistance TRd (ignoring passive pressures) is then given by: = VGd tan Sd - Ua ) tan Sd

Rd~ YrA' ~ yRhA' where YRh is a partial factor on horizontal sliding resistance and the subscripts 'd' denote design values.

The vertical action VGd is favourable, since an increase in its value increases the shear resistance; whereas UGd is unfavourable action, since an increase in its value decreases the resistance. Introducing into this equation partial factors on favourable and unfavourable permanent actions (YG,fav and yg) results in:


Yru x YY

Un tan Sk

where y9 is the partial factor on shearing resistance.

If, however, partial factors are applied to the effects of actions rather than to the actions themselves, then the previous equation becomes:

Yru Y

YG, fav kYrh xYy

where y9 is the partial factor on shearing resistance.

The table below summarizes the values of these partial factors for each of Eurocode 7's three Design Approaches (see Chapter 6).

Individual partial factor or partial factor

Design Approach

Individual partial factor or partial factor


Combination 1

Combination 2

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