PSI - Issue 5

H Hammoum et al. / Procedia Structural Integrity 5 (2017) 69–76 H Hammoum et al./ Structural Integrity Procedia 00 (2017) 000 – 000

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velocity under the Reno mattress, at the interface with the base soil or with the filter, can be determined from the Manning formula as a function of the canal slope and the average size of the stone. The stability with regard to the erosion of the base material is verified if the velocity V e that the soil can withstand without being eroded is less than the velocity V b . We can define the ultimate limit state function G 5 of exceeding the residual velocity at the underside of the revetment as follow: 5 b e G : V -V (11) 4. The case study The canal which is the subject of this study and which aims to rehabilitate and to arrange the bed of Allaghane River in Bejaia province, Algeria, is a trapezoidal canal (Fig. 2), the slope of the River bed is 0.038. The canal rests on a sandy soil with d 50 = 0.50 mm. The thickness of the Reno mattress is 25 cm, with mesh size 5x7, the wire diameter is 2 mm, the dimensions of the mattress filling stones vary from 100 to 180 mm with d 50 = 140 mm and d 90 = 170 mm.

Fig. 2. Cross section of Allaghane River, Bejaia, Algeria.

Fig. 3. General view of Allaghane River canal covered by the Reno mattress.

4.1. Identification of the random variable

The deterministic approach used by engineers is affected by many uncertainties. To take the uncertainties into account, the water flow rate is considered as random variable, generated by Poisson law. The simplest and most general probabilistic theory is that of the Poisson process which applies to any accidental phenomenon (not predictable by deterministic laws) with extreme values such as water flow rate in this study. The parameter characterizing the Poisson law is the flood flow rate noted λ . We present in table 1 the flood flow for different frequencies (return period) according to the hydrology study conducted by African Geosystem Company (AGC, 2004).

Table 1. Results of frequential flood flow.

Return period (years)

Flood flow (m 3 /s)