PSI - Issue 5

K Bouzelha et al. / Procedia Structural Integrity 5 (2017) 77–84 K Bouzelha et al./ Structural Integrity Procedia 00 (2017) 000 – 000

79 3

Usage group

Zone

Low seismicity (I)

Medium seismicity (IIa)

Medium seismicity (IIb)

High seismicity (III)

1A 1B

0.15 0.12

0.25

0.3

0.4 0.3

0.2

0.25

2 3

0.1

0.15

0.2

0.25 0.18

0.07

0.1

0.14

The safety coefficient is then given by the Fellenius modified relation as follow: F s = ∑ [C.dL i +[( W i + Fv) cos θ i − (Fh sin θ i )] tanφ i n i=1 ] .R ∑ [( W i + Fv) n i=1 sin θ i − (Fh cos θ i )]R. ሺͶሻ Saturation line is also introduced in safety coefficient calculation in order to take account wet and saturated mass of each slice (i). In case of drained homogeneous dam, which rests on an impermeable base, Kozeney (PNUD, 1987) shown that saturation line is parabola with an horizontal axis whose focal point is the upstream extremity of the drain to which connects water line (Fig.1).

Fig. 1. Typical cross section of an earthen embankment with slip circle and saturation line.

3. Reliability analysis of risk to sliding of earthen dam

To quantify the failure risk of earthen dam with respect to ultimate limit state which characterizes the sliding of its upstream slope, it is appropriate to define the limit state function G ({X}), which defines the failure and the safety domain. This state function G({X}) is given by Lemaire et al. (2005) by the relation (5): G({X}) = R({X}) − S({X}) (5) Where, G({X}) is the limit state function of the structure (G>0 : safety domain, G=0 : limit state function, G<0 : failure domain), {X}is a random vector constituted by random variables xi, R({X}) is the strength of the structure related to a considered failure mode, and S({X}) is the active loading. In case of stability of earthen dam, the limit state function G ({X}) is given by relation (6): G(X) = Ms − Mm (6)