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Design Approach 2 (summary)

Verification of rotational stability Nominal depth of embedment dnom = 9.8 m kNm m

Rotational equilibrium MEd = 3204-

Degree of utilization

Design is unacceptable if the degree of utilization is > 100%

Degree of utilization

Design is unacceptable if the degree of utilization is > 100%

Design Approach 3 (summary)

Verification of rotational stability Nominal depth of embedment dnom = 9.8 m kNm m

Rotational equilibrium MEd = 3353-

Degree of utilization

Design is unacceptable if the degree of utilization is > 100%

Degree of utilization

Design is unacceptable if the degree of utilization is > 100%

© In traditional practice, the bottom 20% of the wall's embedment is assumed to be below the point of fixity 'O'.39 This is not specified in Eurocode 7 and would be regarded as part of the calculation model.

© The partial factor applied to undrained strength in Design Approach Combination 2 (ycu = 1.4) is higher than that applied to the angle of shearing resistance (y9 = 1.25), reflecting the greater uncertainty in reliably determining this parameter.

© There is debate as to whether the characteristic value of ^cv should be factored to obtain its design value. Proponents of critical state soil mechanics argue that ^cv is effectively a 'worst credible' value already and should therefore not be factored. Others argue that ^cv should be treated no differently to other measures of shearing resistance. In this calculation we illustrate the application of the partial factor y9 to tan (^cv).

© The angle of wall friction is estimated from the soil's constant volume angle of shearing resistance, ^cv. For steel sheet piling 5 must be no more than 2/3

times <pCv.

© The earth pressure coefficients are obtained from Annex C of EN 1997-1.

© The partial factor on unfavourable permanent actions (yg) is applied to effective earth pressures on both the retained and restraining sides of the wall. The passive earth pressures are considered to come from the same 'source' as the active earth pressures and hence they are factored in the same way (involving the Single-Source Principle, discussed in Chapter 3). This is somewhat counter-intuitive to engineers who are used to treating passive earth pressures as a resistance.

© Combination 2 governs the wall's required embedded length. Separate calculations to determine the maximum bending moment Mdmax and shear force Vdmax are given on the book's website (see ® below). Combination 2 governs, giving M^ = 222 kNm/m and Vd,max = 59 kN/m.

© It is usual to assume that this horizontal force will be provided by passive resistance below the wall's effective toe, particularly with the assumed extra 20% embedment from © above.

® The results for Design Approaches 2 and 3 are presented in summary only. The full calculations are available from the book's website at www.decodingeurocode7.com.

Design Approach 2 applies factors greater than 1.0 to action effects (i.e. active earth pressures) and resistance (i.e. passive earth pressures). The degree of utilization (111%) is higher than for DA1.

Design Approach 3 applies factors greater than 1.0 to structural actions and material properties. Earth pressures arising from the self-weight of the ground are treated as a geotechnical action and factored by yg = 1.0; earth pressures arising from the surcharge are treated as structural and factored by Yq = 1.5 (versus 1.3 in DA1-2). Hence the degree of utilization (100%) is the same as in DA1.

12.10.2 Anchored sheet pile wall

Example 12.2 considers the design of the anchored sheet pile retaining wall shown in Figure 12.16. The wall supports a sandy soil with a nominal retained height of 6m and is propped 1m below its top by a single row of anchorages. Water level is at ground level on the retained side and maintained at formation level on the restraining side.

Figure 12.16. Anchored sheet pile wall in sandy soil with groundwater at ground and formation levels

Notes on Example 12.2

O Eurocode 7 requires an unplanned 'overdig' to be considered in ultimate limit states. In this example, the upper limit of AH } 0.5m governs.

© The hydraulic head is assumed to fall linearly around the wall, resulting in simple triangular distributions of pore water pressure on each side of the wall and the same pore pressure on both sides at the wall toe.

Example 12.2 Anchored sheet pile wall Verification of strength (limit state GEO)

Design situation

Consider an embedded sheet pile retaining wall which retains Hnom = 6m of kN

medium dense sand with characteristic weight density Yk = 19-, angle of m shearing resistance ^k = 36°, and effective cohesion c'k = 0kPa. The soil's angle of shearing resistance under constant volume conditions is estimated to be Pcv k = 32°. Groundwater is located at ground level on both sides of the wall. A variable imposed surcharge of qQk = 10kPa acts at the head of the wall. The wall is supported by a single row of anchors placed at da = 1m below ground level. The wall toe is at a nominal depth dnom = 5.85m below kN

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