Abstract
The failure probability and the reliability index have been determined for a pipe submitted to internal pressure, exhibiting a corrosion defect, embedded in a soil with a ground reaction, and submitted to displacement due to seismic activity. Results are obtained by computing the condition of failure: strain demand higher than strain resistance which is typically the Strain Based Design (SBD) basis. From the probabilistic point of view, this condition results as the product of the two probability distributions, demand and resistance. An analytical method is proposed to compute the common area between the strain demand and resistance distribution and then get the probability of failure. The strain demand is assumed to follow a power-law distribution and the strain resistance, a Normal one. The strain demand is computed assuming that the probability density of seism follows a Gutenberg –Richter distribution law as it is found in the south of France. This simple method is also used to predict the failure probability of different reference periods or seismic zone. It is also used to examine the influence of the coefficient of variation of the strain resistance distribution when using vintage pipe steels.
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Abbreviations
- a :
-
Parameter of the Gutenberg –Richter distribution law
- b :
-
Parameter of the Gutenberg –Richter distribution law
- d :
-
Defect depth
- c :
-
Defect semi-axis width
- e :
-
Defect semi-axis length
- f s :
-
Safety factor
- f s,det :
-
Deterministic safety factor
- f s,prob :
-
Probabilistic safety factor
- B :
-
Material constant for the triaxiality correction
- C :
-
Material constant for the triaxiality correction
- M :
-
Seism amplitude
- X ef :
-
Effective distance
- \(\beta \) :
-
Stress triaxiality
- δ :
-
Material constant for the Lode correction
- \({\varepsilon }_{d}\) :
-
Strain demand
- \({\varepsilon }_{D}\) :
-
Design strain
- \({\varepsilon }_{R}\) :
-
Strain resistance
- \({\varepsilon }_{ d ,l}\) :
-
Local strain demand
- \({\varepsilon }_{ R ,l}\) :
-
Local strain resistance
- \({\epsilon }_{f}\) :
-
Elongation at failure in tension
- \({\epsilon }_{f,s}\) :
-
Elongation at failure in shear
- \({\epsilon }_{R }^{0}\) :
-
Reference strain resistance
- \(\gamma \) :
-
Reliability index
- \({\theta }_{l}\) :
-
Lode angle
- λ and η :
-
Parameter of the strain demand distribution
- \( \mu _{f} \;{\text{and}}\;\mu _{d} \) :
-
Means for resistance and demand strain distribution
- \( \sigma _{R} \;{\text{and}}\;\sigma _{d} \) :
-
Standard deviation for resistance and demand strain distribution
- Δ :
-
Local seismic displacement
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Jean-Pierre, A.K., Guy, P. & Julien, C. A Simple Strain-Based Method to Compute the Probability of Failure of a Pipe Submitted to Seismic Displacement. J Fail. Anal. and Preven. 22, 1637–1645 (2022). https://doi.org/10.1007/s11668-022-01454-1
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DOI: https://doi.org/10.1007/s11668-022-01454-1