## Pqy

Figure 11.9. Earth pressures acting on a mass gravity wall

The horizontal component oah of the total earth pressure oa acting on the back of the wall at depth z below ground surface is then given by:

Annex C of EN 1997-1 provides a numerical procedure5 for determining the active earth pressure coefficients KaY, Kaq, Kac based on the following expressions:

where the auxiliary coefficient Kn is a function of the soil's angle of shearing resistance (9), the angle of interface friction between the soil and the wall (5), the slope of the ground surface (P), and the angle of inclination of the back face of the wall (0). Chapter 12 provides a full discussion of the numerical procedure given in Annex C, which includes expressions for passive earth pressure coefficients as well.

Integration of these equations allows the horizontal components (P'ah and Uah on Figure 11.9) of the active effective earth and water thrusts (P'a and Ua) to be calculated:

where H is the wall's height above formation level. Both of these actions are unfavourable for bearing and sliding of the wall and destabilizing for toppling.

The vertical components (P'av and Uav on Figure 11.9) of the active effective earth and water thrusts (P'a and Ua) can then be determined from the horizontal components (P'ah and Uah), as follows: P'v = P'h x tan (0 + S) and Uav = Uah x tan (0 + S)

These actions are unfavourable for bearing, favourable for sliding, and stabilizing for toppling of the wall. However, the Single-Source Principle (discussed in Chapter 3) requires these forces to be treated as unfavourable in all these verifications.

Verification of bearing, sliding, and toppling resistance for a mass gravity wall is similar to that for a reinforced concrete wall (discussed in Sections 11.4.1-11.4.3), except that the self-weight of the mass gravity wall does not include the weight of backfill. Instead, any vertical force that backfill imposes on the wall is incorporated in the vertical component P'av of the active effective earth thrust P'a.

11.5.1 Bearing

Verification of bearing resistance for a mass gravity wall is similar to that for a reinforced concrete wall (discussed in Section 11.4.1).

The total design bearing pressure qEd beneath the base of the wall is given by:

-Tyq ,i qEd = To ^ a where WGk is the wall's characteristic permanent self-weight; P'av,Gk is the vertical component of the characteristic permanent active effective earth thrust; UavGk is the vertical component of the characteristic permanent water thrust; qQk is a characteristic variable vertical surcharge on the ground surface behind the wall; A' is the effective area of the base; yg and yq are partial factors on permanent and variable actions, respectively; and ^ is the combination factor applicable to the ith variable action (see Chapter 2).

Since the self-weight of the wall and backfill are unfavourable actions for bearing, their characteristic weight densities should be selected as upper (or 'superior') values.

The effective design bearing pressure q'Ed beneath the base is given by:

where UGk is the characteristic permanent uplift from water pressure beneath the wall's base. Note that the uplift here is treated as an unfavourable action (and multiplied by yg not YG,fav) owing to the 'Single-Source Principle' discussed in Chapter 3 (see the section Distinction between favourable and unfavourable actions). Since it arises from the same water table as Uah and Uav (which are unfavourable actions), so the uplift U is also treated as unfavourable.

Chapter 3 discusses whether water pressures should be factored or not. 11.5.2 Sliding

Verification of the sliding resistance for a mass gravity wall is similar to that for a reinforced concrete wall (as discussed in Section 11.4.2).

The effective earth thrust (P'a) is an unfavourable action for sliding. Thus both its horizontal and vertical components (P'a,h and P'av) should be treated as unfavourable and design values obtained by multiplying by the partial factor yg.

The water thrust (Ua) is also an unfavourable action for sliding. Both its horizontal and vertical components (U'ah and U'av) should be treated as unfavourable and design values obtained by multiplying by the partial factor Yg. Since the 'Single-Source Principle' applies, the uplift beneath the wall (Uv) should also be treated as unfavourable.

11.5.3 Toppling

Verification of toppling resistance for a mass gravity wall is similar to that for a reinforced concrete wall (as discussed in Section 11.4.3).

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