## Summary of key points

The design of embedded walls to Eurocode 7 involves checking that the wall has sufficient embedment to prevent the wall rotating about a fixed point (for example, a point of fixity below formation or a single row of anchors), sufficient strength to mobilize resistance over the full length of the wall, and sufficient stiffness to keep wall displacements and settlement behind the wall within acceptable limits. The design must also demonstrate that the wall has sufficient bearing resistance to withstand any significant vertical load.

Verification of ultimate limit states is demonstrated by satisfying:

Vd < Rd, and Hd < Rd + Rpd, and MEdM < MEd,sft

(where the symbols are defined in Section 10.3). These equations are merely specific forms of:

Ed z Rd which is discussed at length in Chapter 6. 12.10 Worked examples

The worked examples in this chapter consider the design of an embedded cantilever wall (Example 12.1); and the same wall but singly propped (Example 12.2).

Specific parts of the calculations are marked O, ©, ©, etc., where the numbers refer to the notes that accompany each example.

### 12.10.1 Cantilever embedded wall

Example 12.1 considers the design of a cantilever embedded wall retaining 4m of medium dense sand overlying low to medium strength clay as shown in Figure 12.15. The sand is assumed to be drained for the purposes of this example, with the groundwater table at least below excavation level. The analysis considers a short-term situation and therefore treats the clay as undrained. This allows the principles of Eurocode 7 to be demonstrated for undrained conditions.

Figure 12.15. Cantilever embedded wall in sand and clay y i_

Figure 12.15. Cantilever embedded wall in sand and clay

Notes on Example 12.1

O Retaining walls are the one geotechnical structure where a dimensional tolerance is specified in Eurocode 7.

Example 12.1 Embedded cantilever wall Verification of strength (limit state GEO)

### Design situation

Consider an embedded sheet pile retaining wall which is retaining Hnom = 4m of medium dense sand overlying low/medium strength clay. A characteristic variable surcharge qQk = 10kPa acts at the head of the wall. The sand has kN

characteristic weight density Yk = 18-, angle of shearing resistance

^k = 36°, and effective cohesion c'k = 0kPa. Its angle of shearing resistance under constant volume conditions is estimated to be ^>cv k = 32°.

The clay has characteristic weight density Yk = 20-and undrained

2 m strength cuk = 40kPa. The wall toe is at a nominal depth dnom = 9.8m below formation level. The ground is dry throughout.

Design Approach 1 Geometry

Unplanned 'overdig' AH = min(10%x Hnom, 0.5m) = 0.4m

Unplanned height of excavation Hd = Hnom + AH = 4.4 m © Reduced depth of embedment dd = dnom - AH = 9.4 m

For cantilever walls, earth pressures below the effective wall toe (point O) can be replaced by an equivalent reaction R. The design embedment depth is dd conservatively calculated as: dOd = y^T = 7.83 m and the nominal embedment depth as dO nom = dOd + AH = 8.23m© Actions

Vertical total stresses on retained side of wall (from soil self-weight only): at top of sand avk = 0kPa at bottom of sand avk = Yk x Hnom = 72 kPa at top of clay o^ = ovk = 72 kPa

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