The volume of backfill on top of the foundation is Vf = (Ab x d) - Vc = 379.8 m3

Thus, the characteristic self-weight of the foundation (concrete plus backfill) is then: ©

backfill WGkf = ykf x Vf = 6836 kN total WGk = WGk c + WGk f = 14217 kN

The characteristic uplift force from groundwater pressure acting on the underside of the base is:

UGk = yw x D x B x B = 6622 kN© Effects of actions

Partial factors on destabilizing permanent and variable actions are yG dst = 1.1 and yq dst = 1.5 and on stabilizing permanent actions yG,stb = 09 °

The design destabilizing moment about the toe is:©

MEd,dst = yQ,dstx (HQk x D + MQk) + yG,dstx UGk x y = 136MNm

The design stabilizing moment about the toe is:©

Verification of stability against overturning



The design is acceptable if AEqu is < 100%

Original design to International Electrotechnical Commission standard IEC 61400

Partial factors on unfavourable and favourable actions for abnormal loads are Yf = 1.1 and Yf fav = 0.9 respectively.©

The design destabilizing moment about the toe is: MEd,dst = Yf * (HQk D + MQk) = 60 MNm

The design stabilizing moment about the toe is:©


The degree of utilization is AEQU =-= 93 %


The design is acceptable if AEqu is < 100%

Traditional lumped factor of safety

If water thrust is regarded as a destabilizing force, then

If water thrust is regarded as a (negative) stabilizing force, then

7.7.2 Concrete dam

Example 7.2 considers the design of the mass concrete dam shown in Figure 7.11, which is sitting on a permeable rock and retaining a height h of water.

Figure 7.11. Concrete dam founded on permeable rock, retaining a body of water

The pore pressure beneath the dam can be obtained from an analysis10 of the flow beneath a structure with a single sheet pile which is resting on the surface of an infinite depth of porous material.

Figure 7.12 gives the solution for the dam of Figure 7.11 (with dimensions B = 2.6m, H = 5m, h = 4.5m, d = 2m, and D = 4) for three particular cases: with no cutoff; with sheet piles at the dam's heel; and with sheet piles at the dam's toe.

The pore pressure u shown in Figure 7.12 is based on the following equation:11

Ywh n

Ä2 d where yw is the weight density of water; h is the height of retained water; d is the depth of the sheet pile; x is the horizontal distance from the dam's heel; and the intermediate variables A1 and A2 are given by:

where 'a' is the distance of the sheet pile from the heel; and B is the width of the dam.

Distance x (m)

Figure 7.12. Pore water pressure beneath the dam of Figure 7.11 Notes on Example 7.2

O The weight density of concrete here is 24 kN/m3 because we assume it is unreinforced (for nominally reinforced concrete, Yck = 24 kN/m3). This example considers three different scenarios: with no cutoff, with sheet piles at the heel of the dam, and with sheet piles at its toe.

© Assuming the dam is broadly triangular in shape and of uniform weight density.

Example 7.2 Mass concrete dam Verification of static equilibrium (EQU)

Design situation

Consider a mass concrete dam of width B = 2.6m and height H = 5m which is founded on permeable rock. The height of water retained by the dam is maintained by a spillway at h = 4.5m above the foundation. A grout curtain or sheet pile cut-off wall of depth d = 2m is used to reduce uplift pressures on the base of the dam. The characteristic weight density of mass concrete is kN kN A Yk = 24-(as per EN 1991-1-1) and of water yw = 9.81-. V

Dam with no cutoff


The characteristic self-weight of dam is given approximately by: (Hx B^ kN,

0 0


  • Emaan
    Why do sheet piles reduce uplift thrust under a dam?
    8 years ago

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