PSI - Issue 5

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

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An overall safety factor for the dam stability based on the mean values of the calculation parameters is determined. In 1928, in an international forum framework, the notion of safety coefficient was criticized, because it was considered devoid of real meaning. Uncertainties and hazards inherent in each parameter involved in the safety coefficient calculation were not taken into account rigorously. This awoke only a low echo in the research and engineering world. But this did not prevent some researchers to undertake studies in order to develop basic notions of random events, thus marking a break with the classic rules of structural design, such as (Mayer, 1926), (Weibull, 1939) et (Prot et al., 1951). Therefore, this stage favored emergence of probabilistic approach of structural safety (Cornell, 1967), (Madsen, 1990). Also, many researchers and engineers from Northern Europe were associated in the development of reliability theory of structures (Thoft et al., 1984). Currently, the advances in the uncertainties quantification linked to dam behavior allowed to use reliability approaches for a better assessment of the safety of these structures. (Peyras et al, 2012) proposed a methodology of coupling the dependability method (FMEA) with the reliability approach in order to assess the structural safety of dams. The work of Lupoi et al (2011) focused on the development of a probabilistic method of seismic assessment which is able to manage the physical complexity of the dam-foundation damage and uncertainties regarding the structural data and external actions. The reliability theory proposes an analysis of new or existing structures by a probabilistic approach by the evaluation of their failure probability, taking into account uncertainties in the structural design, then this probability is compared to admissible value set by the design codes, to assess their stability (Lemaire et al., 2005), (Breysse, 2009), (Cremona, 2003,2011), (JCSS, 2001). In this work, mechano-reliability analysis of stability to sliding of the embankment upstream slope is performed. For this, a modified Fellenius method considering seismic effect and dam saturation line is coupled with Monte Carlo simulation to assess the failure probability. The seismic acceleration is considered as a random variable. The study of overall stability of an earthen dam consists of the stability analysis of its upstream and downstream slope and its foundation. A slope is stable if the forces that tend to produce a movement are less than the shear strengths. Deterministic methods consist to verify the embankment slope stability by introducing safety coefficient notion. Fellenius method assumes that the break of a slope occurs along a circular slip surface of radius R (Fig.1). The method decomposes the slope into vertical slices of small juxtaposed thicknesses of weight noted W i , to study equilibrium of set. It also considers that the existing forces between the slices are neglected and therefore the interaction is eliminated. For a slice of order (i), its weight W i is decomposed into a normal force stabilizing (N i ) and a tangential force (T i ) acting at the base (Fig. 2). The safety coefficient F s is given by the United Nations Development Plan (PNUD, 1987) as the ratio of stabilizing forces moment M s on driving forces moment M m : M s /M m (1) Seismic effect is taken into account for each slice of order (i) by introducing an horizontal component F h and a vertical component Fv of a seismic force, as recommended by the Algerian seismic code (RPA, 2003). The collapse of the structure is related to the exceeding of the limit state G({X}) =0, and reliability analysis consists to calculate the probability of failure defined by: F h = 0,5AW i (2) and: F v = 0,3F h (3) The coefficient of the seismic zone noted (A) is defined depending on use group (structure importance) and the seismic zone (Table 1) by the RPA which classes hydraulic structures in the 1B usage group (Public structures of national interest or of certain socio-cultural and economic importance). 2. Deterministic model

Table 1. Coefficient of the seismic zone (A) as a function of the use group and zone type.