REIABIITY OF BURIE PIPEIES WITH CORROSIO EFECTS UER VARYIG BOUARY COITIOS Ouk-Sub ee 1 and ong-hyeok Kim 1. School o Mechanical Engineering, InHa University #53, Yonghyun-ong, am-ku, Incheon, 40-751, Korea leeos@inha.ac.kr. epartment o Mechanical Engineering, InHa University #53, Yonghyun-ong, am-ku, Incheon, 40-751, Korea kdonghyeok@cricmail.net Abstract This paper presents the eects o boundary conditions o ailure pressure models or buried pipelines on ailure prediction by using a ailure probability model and a inite element analysis. The irst order Taylor series expansion o the limit state unction (SF) is used in order to estimate the probability o ailure associated with corroded deects under varying boundary conditions or long exposure periods in years. Two ailure pressure models based on a ailure unction composed o ailure and operation pressures are adopted or the assessment o pipeline ailure. The eects o random variables such as varying boundary conditions on the ailure probability o the buried pipelines are systematically analyzed by using a ailure probability model or the corroded pipeline. Furthermore, the engineering results estimated by a ailure probability model are compared with those obtained by a inite element analysis. The inluences o statistical distributions, such as normal and lognormal, o random variables on the ailure probabilities are also investigated in detail. Introduction The buried pipelines transporting gas and oil are usually laid underground and exposed to varying boundary conditions. It has been oten reported as industrial examples that many catastrophic disastrous pipeline accidents have been caused by the deect such as corrosion arisen by aging and/or environmental eects on pipelines. It is thus very important to investigate the eect o deect on the saety o buried pipelines or preventing heavy economical and social losses in advance, Choi[1]. The buried pipelines usually have the various types o deects such as corrosion and environment-assist-cracking. I these were operated under an excessive operating pressure in the corroded pipelines, it could produce larger stresses than saety designed one. It may be emphasized that the ailure analysis should be carried out with the help o the probability method than the conventional deterministic approach (CA) because the CA leads to uncertainties in the ailure analysis with random variables imposed on varying boundary conditions, ee et al.[], Hopkins and Jones[3]. In this paper, two ailure pressure models based on strength assessment methods were used to evaluate the ailure probabilities o the deect region in pipeline with internal operating pressure. For each model, using the FORM (irst-order reliability method) which is one o the probability analysis method with reliability index, the eects o varying boundary conditions on the ailure probability o pipeline are systemically investigated. Furthermore, the engineering results estimated by a ailure probability model are compared with those
estimated by the inite element analysis. At the end, the ailure probabilities corresponding to both normal and lognormal distributions o varying random variables are compared each other. Failure Pressure Models The major actors or the ailure o pipelines transporting the high-pressure gas are known to be mechanical damage and corrosion. Standards or a regular hydrostatic test and a corrosion assessment are generally used to assess the eect o the mechanical damage and corrosion on the integrity o the pipelines. To assess the integrity o corroded pipeline, we need to simpliy the geometry o the vicinity o corroded part. Fig. 1 shows a corrosion model and is generally urther simpliied as shown in Fig. to analyse the given geometric coniguration easily. FIGURE 1. A simpliication o a corroded surace law in a pipeline. (a) FIGURE. Section through an idealized corrosion deect. (a) Parabolic, (b) Rectangular (b) ASI/ASME B31G A ailure equation or the corroded pipelines is proposed by means o the data o bursting experiment and expressed with consideration o two conditions below. First, the maximum hoop stress can t exceed the strength o material. Second, relatively short corrosion is projected on the shape o parabola and long corrosion is projected on the shape o rectangular. The ailure pressure equation or the corroded pipeline is classiied by the shape o parabola and rectangular as shown below, Ahammed[4]. where P = 1.1 P P t 1 ( / 3)( d / t) 1 ( / 3)( d / t) / M t = 1.1 [ 1 ( d / t) is the ailure pressure, ] or or 0. 8 4 (Parabola) (1) t 0. 8 > 4 (Rectangular) () t is the outer diameter, M is the bulging actor, t is the thickness o pipelines, d is the maximum depth o corrosion region, is the deect length o corrosion region and is the strength.
The bulging actor (M) is deined as M = 1 + t or 0. 8 4 (3) t M = MB31G (Modiied B31G) Code or 0. 8 > 4 (4) t Kiener et al. pointed out some problems on the deinition o low stress = 1.1 ) and ( bulging actor, and proposed a new low stress such as 1.1 + 69 (MPa) and a new bulging actor as ollows, [4], Kiener and Vieth[5]. P ( = + 69) t 1 5( d / t) 1 5( d / t) / M The new bulging actor (M) is deined as, = (5) M = 1+ 75 03375 t t 4 or 50 t (6) M = 3.3 + 3 t or > 50 t (7) We initially assume that every variable is normal distribution and the probability distribution is determined by a mean and standard deviation. The ailure probability is calculated using FORM (irst order reliability method) that is one o the methods utilizing reliability index []. The FORM method is denoted rom the act that it is based on a irst-order Taylor series approximation o the perormance unctional or limit state unction (SF). A limit state unction is deined as below. = R (8) where R is the resistance normal variable, and is the load normal variable. Assuming that R and are statistically independent normally distributed random variables, the variable is also normally distributed. The event o ailure occurs when R<, that is <0. The probability o ailure (PF) is given as below 0 1 1 µ PF = P[ < 0] = exp = π d β 1 U exp du = Φ( β ) π where µ and are the mean and standard deviation o variable, respectively, new variable U is U = ( µ )/, Φ is the cumulative distribution unction or a standard normal variable and β is the saety index or reliability index denoted as below β µ µ µ R = = (10) R + (9)
Rackwitz and Fiessler proposed a method to estimate the reliability index using the procedure as shown in Fig. 3. In this paper, we iterated the loop to estimate a reliable reliability index until it is converging to desire value ( β 0. 001), Mahadevan and Haldar[6]. Where the coeicient o variation (C.O.V) is denoted as below with the standard deviation, and the mean, µ. C OV µ.. = (11) FIGURE 3. Processing o computing the reliability index. Rackwitz-Fiessler Transormation Method For the case o another distribution o random variables, Rackwitz and Fiessler proposed the µ equivalent normal distribution with and, by imposing two conditions: The cumulative distribution unctions and the probability density unctions o the actual variables and the * x equivalent normal variables should be equal at the checking point ( ) on the ailure surace. Considering each statistically independent non-normal variable individually and equating its cumulative distribution unction with an equivalent normal variable at the checking point, we obtain as below[6]. F x * x µ Φ * ) = µ x * Φ 1 F ( x * ) ( ( ) = (1) where Φ is the cumulative distribution unction o the standard normal variable, µ and are the mean and the standard deviation o the equivalent normal variable at the checking point, and F ( * x ) is the cumulative distribution unction o the original non-normal random variables. Equating probability density unctions o the original variable and equivalent normal variable at the checking point, we obtain as below. * 1 * * 1 x µ [ Φ ( F ( x ))] = ( x ) φ = φ (13) * ( x ) where φ is the probability density unction o the standard normal variable and ( * x ) is the probability density unction o the original non-normal random variables. The non-normal variables can be treated as normal distributed variables through the transormation o Eqs. (1) and (13).
Finite Element Analysis In this paper, we analyse the corroded pipelines based on ASI/ASME B31G code with a groove modelled as a parabolic using a inite element code ABAQUS V6.3, ee and Kim[7]. Fig. 4 shows a modelling shape o groove used in the FEM analysis. The material used in the analysis is API grade 60 ( = 43MPa, E = 193. GPa ). We evaluate ailure pressure o corroded pipelines with varying groove widths o 60mm, 80mm and lat groove as shown in Fig. 4. Fig. 5 shows the 3- modelling coniguration used in the inite element analysis and a representative result. We analyse or a quadrant cylinder shape and symmetric corroded groove in the FEM analysis. In this paper, according to the von Mises ailure criterion the ailure probability o corroded pipelines is assessed using the FEM results. The SF used in this probabilistic analysis is deined as below. = (14) where is the result o FEM analysis. FIGURE 4. Geometries o varying grooves. FIGURE 5. ocal details o 3- FE model and a result. Case Study The random variables listed in Table 1 have been utilized to investigate the ailure probability and inite element analysis o the corroded pipeline. TABE 1. Random variables and their parameters used in the example. Variable Mean C.O.V Variable Mean C.O.V P a 8MPa 0.1 t 10mm 5 43MPa 67 d 3mm 0.1 00mm 5 600mm 3
Results and iscussion Fig. 6 shows variation o ailure probability with exposure period o corroded pipelines using variables in Table 1. It can be recognized in Fig. 6 that the ailure probability increases with increasing o exposure periods or each ailure pressure model. It is noted that the FEA model has the largest increasing rate o ailure probability and B31G model has relatively small increasing rate. And it is also noted that the ailure probability or MB31G model is the largest or less than 5-year exposure periods and the ailure probability or FEA model is the largest or more than 5-year exposure time. 0. FEA MB31G B31G 0 5 10 15 0 5 30 35 40 FIGURE 6. Relationship between ailure probability and exposure period or several ailure pressure models. Fig. 7 shows a relationship between ailure probability and reliability index. As expected, the reliability index decreases with increased exposure period and the nominal ailure probability increases with increased exposure period accordingly. 0. B31G.5.0 0. MB31G.5.0 0 5 10 15 0 5 30 35 40 0 5 10 15 0 5 30 35 40 (a) (b) 0. FEA.5.0 0 5 10 15 0 5 30 35 40 (c) FIGURE 7. Relationship between ailure probability and reliability index or several ailure pressure models. (a) B31G, (b) MB31G, (c) FEA.
1. 0. Groove Width=Through Groove Width=80mm Groove Width=60mm 1. 0. FEA(P=10MPa) FEA(P=8MPa) MB31G(P=10MPa) MB31G(P=8MPa) B31G(P=10MPa) B31G(P=8MPa) 0 5 10 15 0 5 30 35 40 0 5 10 15 0 5 30 35 40 (a) FIGURE 8. Relationship between ailure probability and exposure period. (a) varying groove widths, (b) varying internal operation pressures. Fig. 8(a) shows the variation o ailure probability with varying groove width o corroded deects in the inite element analysis. We analyse the ailure probability o buried pipelines with varying groove width o corroded deects as 60mm, 80mm and lat groove as shown in Fig. 8(a). It is noted that the ailure probability becomes larger with narrow groove width like 60mm. And it can be recognized that the ailure probability o groove width, which is lat groove and 80mm, is larger about 0.38 than those o groove width, which is 60mm. Fig. 8(b) shows the variation o ailure probability or varying internal operation pressure. It is noted that the ailure probability increases or all models with increasing internal operation pressure. Especially, it is noted that the amount o increasing o FEA model is the largest about when the exposure period is 0 year, whereas the amount o increasing o B31G model is the smallest. (b) 0. B31G (lognormal) (normal) (normal) (lognormal).5.0 0. MB31G (lognormal) (normal) (normal) (lognormal).5.0 0 5 10 15 0 5 30 35 40 0 5 10 15 0 5 30 35 40 (a) (b) 0. FEA (lognormal) (normal) (normal) (lognormal).5.0 0 5 10 15 0 5 30 35 40 (c) FIGURE 9. Eect o normal and lognormal distribution o random variable on ailure probabilities or several ailure pressure models. (a) B31G, (b) MB31G, (c) FEA. Fig. 9 shows relationships between the ailure probability and the reliability index or two dierent statistical distributions o the random variables such as the normal and lognormal
distribution. For the B31G model, it is noted that the reliability index o lognormal distribution is larger than that or normal distribution, whereas the ailure probability or lognormal distribution is smaller than that or normal distribution. However, or the MB31G model and FEA model, it is noted that reliability index and ailure probability or lognormal distribution is larger than that or normal distribution at some range o exposure periods, whereas it is reversed at a certain range o exposure periods. The eects o dierent statistical distributions o random variables on the reliability index are larger than those o ailure probability. Conclusion In this study, FORM (irst order reliability method) and inite element analysis model are utilized to extract useul technical inormation in carrying out the eective ailure control or the corroded pipeline. Using B31G, MB31G and FEA models, the eect o the corrosion depth, the corrosion length, the thickness, the diameter, the inner luid pressure and the stress o pipeline on the ailure probability is systematically studied and the ollowing results are obtained: 1. It is recognized that the ailure probability increases with increasing o exposure periods or ASI/ASME B31G model, MB31G model and inite element analysis model. The results by FEA model show, however, the highest increasing rate o ailure probability.. It is noted that the increasing rate o ailure probabilities or the narrower groove width is higher than that o the wider groove width. 3. It is ound that the eect o the statistical distribution o random variables such as normal and lognormal on the reliability index and ailure probability is not big. However, the reliability index and ailure probability or lognormal distribution is larger than that or normal distribution at some range o exposure periods, whereas it is reversed at a certain range o exposure periods. Acknowledgment The authors are grateul or the support provided by a grant rom the KOSEF and Saety and Structural Integrity Research Center at the SungKyunKwan University. The authors wish to thank all the members concerned. Reerences 1. S. C. Choi, Gas Saety Journal, Vol.6, o.5, 5-33, 000.. O. S. ee, J. S. Pyun and. H. Kim, Int. J. o KSPE, Vol. 4, o. 6, 1-19, 003. 3. P. Hopkins and. G. Jones: In Proceedings o the 11th International Conerence on Oshore Mechanics and Arctic Engineering, ASME, Vol. V, Part A, 11-17, 199. 4. M. Ahammed, Int. J. Pressure Vessels and piping, Vol. 75, 31-39, 1998. 5. J. F. Kiener and P. H.Vieth, Oil and Gas Journal, 88(3), 56-59, 1990. 6. S. Mahadevan and A. Haldar, Probability, Reliability and Statistical Method in Engineering esign, John Wiley & Sons, 000. 7. O. S. ee and H. J. Kim, Proceeding o KSPE, Vol. 3, o. 11, pp. 096-101, 1999.