## Utilization Factor Structural Design

The design is unacceptable if the degree of utilization is > 100%

Traditional factor of safety against piping

The soil's critical hydraulic gradient is i crit =-= 1

Factor of safety on hydraulic gradient is F =-= 3.38 w ik

©0 The degree of utilization using expression 2.9(a) is close to 100%, whereas using 2.9(b) it is less than 50%. Eurocode 7 does not explicitly state where the partial factors should be applied, which leads to the discrepancy between these expressions, which was not anticipated by the authors of the standard.

© The traditional global factor of safety for this situation is 3.38. Recommended values for the global factor are between 1.5 and over 4.0. Generally, where the consequences of piping failure may have serious effects, then higher global factors are adopted. It is appears that when Eq. 2.9(a) is used, equivalent traditional factors of safety are between 3.0 and 4.5 but, when Eq. 2.9(b) is used, it is closer to 1.5. We conclude that Eq. 2.9(b) does not provide a sufficient level of reliability.

7.7.6 Piping due to heave (HYD)

Example 7.6 considers the design of an embedded retaining wall against piping due to heave, as shown in Figure 7.16.

The wall forms part of a temporary cofferdam to allow the construction of a bridge pier in the dry. The river water level remains reasonably constant at H = 1.9m above bed level and the water level inside the cofferdam is being kept at or just below bed level by pumping. In order to reduce seepage into the cofferdam and to overcome the potential for piping as water seeps upwards into the excavation, it is proposed to embed the sheet pile wall into the ground by d = 6m. The example investigates the application of the two procedures recommended in EN 1997-1 for hydraulic failure to assess the suitability of this depth of penetration.

Notes on Example 7.6

O Text books suggest it is acceptable to consider the upward seepage forces over a width equivalent to half the embedment of the wall.

© To assess the excess pressure head at the toe of the wall, an acceptable approximation is to assume that half the total head loss is achieved on each side of the wall. This is only an approximation. In reality, it will vary across the base of the soil column being considered and a detailed flow analysis would be required if the result was critical to the design.

© Partial factors for limit state HYD given in Annex A to EN 1997-1.

© Stabilizing and destabilizing forces on the soil column are calculated here using Expression 2.9(b) of EN 1997-1, with appropriate partial factors.

© Expression 2.9(b) suggests the design has ample reliability against heave.

© Stabilizing and destabilizing pressures on the soil column are calculated here using Expression 2.9(a). This expression suggests the design is only just adequate against heave.

& Expression 2.9(a) suggests the design just has enough reliability to avoid heave.

© Eurocode 7 is not specific about where the partial factors YG,dst and YG,stb should be applied. In this alternative calculation, the excess pore water pressure is multiplied by YG,dst and the effective stress at the base of the soil column multiplied by YG,stb.

© The alternative calculation gives an identical result to Expression 2.9(b), see ©.

® This calculation of heave results in a traditional global factor of safety of 4.63, which is more than adequate for this problem according to some authors (who suggest F should be 1.5-2.0) but only just adequate according to others (who suggest F > 4). See the discussion in Section 7.5.1 for details of these recommended values for F.

Example 7.6 Piping due to heave Verification of stability against hydraulic failure (HYD)

### Design situation

Consider a sheet pile wall cofferdam that retains water at a height H = 1.9m above its formation level. The walls of the cofferdam are embedded d = 6m below formation. The characteristic weight density of the foundation soil is kN kN Yk = 17-and of water is Yw = 9.81-. The stability of the zone of soil of m m d width — = 3 m next to the embedded part of the wall must be checked for hydraulic failure by piping. © Actions

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