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The volume of backfill on top of the foundation is Vf = (Ab x d)  Vc = 379.8 m3
Thus, the characteristic selfweight 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
MEd,dst
MEd,stb
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:©
MEd,dst
The degree of utilization is AEQU == 93 %
MEd,stb
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.
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 cutoff 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 199111) and of water yw = 9.81. V
Dam with no cutoff
Actions
The characteristic selfweight of dam is given approximately by: (Hx B^ kN,
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