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1、西 南 交 通 大 学本科毕业论文外文资料翻译年 级:2008级学 号:20080156姓 名:韩枫专 业:土木工程指导老师:杨庆华 2012年 6 月Reliability Engineering and System Safety 92 (2007) 12581266A physical probabilistic model to predict failure rates in buried PVC pipelinesP. Davis_, S. Burn, M. Moglia, S. GouldCSIRO Land and Water, Graham Road, Highett, Vi
2、c. 3190, AustraliaReceived 28 September 2005; received in revised form 28 July 2006; accepted 8 August 2006Available online 29 September 2006AbstractFor older water pipeline materials such as cast iron and asbestos cement, future pipe failure rates can be extrapolated from large volumes of existing
3、historical failure data held by water utilities. However, for newer pipeline materials such as polyvinyl chloride (PVC), only limited failure data exists and confident forecasts of future pipe failures cannot be made from historical data alone. To solve this problem, this paper presents a physical p
4、robabilistic model, which has been developed to estimate failure rates in buried PVC pipelines as they age. The model assumes that under in-service operating conditions, crack initiation can occur from inherent defects located in the pipe wall. Linear elastic fracture mechanics theory is used to pre
5、dict the time to brittle fracture for pipes with internal defects subjected to combined internal pressure and soil deflection loading together with through-wall residual stress. To include uncertainty in the failure process, inherent defect size is treated as a stochastic variable, and modelled with
6、 an appropriate probability distribution. Microscopic examination of fracture surfaces from field failures in Australian PVC pipes suggests that the 2-parameter Weibull distribution can be applied. Monte Carlo simulation is then used to estimate lifetime probability distributions for pipes with inte
7、rnal defects, subjected to typical operating conditions. As with inherent defect size, the 2-parameter Weibull distribution is shown to be appropriate to modeluncertainty in predicted pipe lifetime. The Weibull hazard function for pipe lifetime is then used to estimate the expected failure rate (per
8、 pipe length/per year) as a function of pipe age. To validate the model, predicted failure rates are compared to aggregated failure data from 17 UK water utilities obtained from the United Kingdom Water Industry Research (UKWIR) National Mains Failure Database. In the absence of actual operating pre
9、ssure data in the UKWIR database, typical values from Australian water utilities were assumed to apply. While the physical probabilistic failure model shows good agreement with data recorded by UK water utilities, actual operating pressures from the UK is required to complete the model validation.1.
10、 IntroductionPolyvinyl chloride (PVC) pipes have been used in Europe and Australia since the early 1960s and in North America since the late 1970s. They are currently used in 80% of the water reticulation market in North America. As described in a number of studies, PVC pressure pipes have exhibited
11、 relatively low failure rates in service compared to other pipe materials in use. For example, a Canadian study 1 indicated that un-plasticised polyvinyl chloride (PVC-U) pipes have fewer line breaks than traditional materials including ductile iron and a more recent extensive study confirmed the lo
12、w failure rate for PVC-U in the United States 2. In Australia, PVC-U pressure pipes installed in the early 1970s in a large rural water supply scheme have been exhumed and examined 3. The pipes were considered to represent Australian quality at that time and over a service life approaching 30 years,
13、 no failures occurred apart from those attributed to third-party damage or poorly manufactured solvent cement joints. However, in other instances premature field failures have been reported in PVC-U pipes, and have been attributed to poor installation, excessive operating conditions or third-party d
14、amage.In other cases, failures have been attributed to poorly manufactured pipes. Almost invariably, PVC-U pipe failures in the field occur by cracks initiating from stress concentrations in the pipe wall 4 and as PVC-U pipe usage increases, the economic, environmental and social consequences of the
15、se premature fracture failures also increases. Generally where failure data is plentiful, statistical methods are used to predict pipeline failure and as a first approximation, water main breakage rates are often described by fitting time-exponential functions to this recorded failure rate data. Alt
16、hough future failure rates can be extrapolated 5,6, forecasts are generally restricted to homogeneous groups of pipes (or cohorts) with similar attributes 7. While these statistical techniques continue to be widely used for water pipeline asset management, they also require large failure databases a
17、s a basis for analysis. Assuming good quality data, this does not pose problems for older pipeline materials such as cast iron and asbestos cement. However, for newer pipeline materials such as PVC-U, there is much less recorded failure data available and valid statistical models are difficult to ge
18、nerate. A common problem with statistical analysis of pipeline materials such as PVC-U is that many recorded failures in PVC-U pipes can be attributed to manufacturing problems that have since been rectified (i.e. manufacture with poor processing levels or manufacture on a non-vacuum extruder). Cons
19、equently, unless these influences are identified and considered in the assessment, extrapolated failure rates are based on these transient influences, which no longer apply to newer pipes installed in the network. To support the statistical techniques developed over the past decade, this paper descr
20、ibes a physical probabilistic model to estimate failure rates in PVC-U pipes.2. Fracture mechanics analysis of PVC pipe failureLinear elastic fracture mechanics (LEFM) theory can be applied to analyse brittle fracture failures in plastic pipelines 8. The brittle fracture process can be envisaged as
21、a balance between an applied stress intensity factor (SIF) and the plane strain fracture toughness of pipe material.The process is split into three stages:(1) An incubation period between load application and crack initiation.(2) A period of slow crack growth.(3) Fast brittle fracture, when the appl
22、ied SIF exceeds the material fracture toughness.Fig. 1 illustrates how failure may occur from a defect at the pipe inner surface. Provided that point loads are avoided during installation, this represents a worst-case scenario for a buried pipe. The applied SIF is determined by the in-service loadin
23、g conditions and the installed condition of the pipe. Service loading can be split into contributions from internal pressure, diametrical deflection and residual stress. As described by Williams 8, for a defect of radial depth a (in m) in the pipe wall, an applied SIF KI (in MPam0.5) can be defined
24、in terms of the applied stress s (in MPa) K1=Y （1）where Y is a dimensionless geometric correction factor, which accounts for the influence of pipe size and loading type on KI. As described by Lu et al. 9, the total SIF for a pipe in service can be defined asKITOT=KIP+KID+KIR （2）where KIP is the SIF
25、due to internal pressure, KID is the SIF due to in-plane diametrical deflection loads and KIR is the SIF due to processed-in residual stresses. As detailed inEq. (2), the individual SIFs are described in terms of remote stresses and geometry factors 9. After crack incubation ends, a period of slow c
26、rack growth occurs. Under a static load, K can be related empirically to crack growth rate da/dt (in m/s) in the form 8 （3）where D and m are constants obtained from laboratory testing 10. At some stage, a propagating crack will attain a critical size and fast brittle fracture will occur 8. The crite
27、rion for brittle fracture failure is expressed as （4）where KIC is the material plane strain fracture toughness (in MPam0.5) and can be measured using a range of different test methods 11.3. Applied SIFs for pressure, deflection and residual stressLu et al. 9 previously used finite element analysis t
28、o determine crack tip displacements and SIFs for plastic pipes under a range of loading conditions. For a pipe subjected to internal pressure only, the SIF associated with an internal defect is written as 9 （5）where a is the radial depth of a defect from the pipe inner surface (in m), and b is the p
29、ipe wall thickness (in m). Following LEFM notation, YP is the geometric correction factor for this geometry and loading type. sIP is the hoop stress at the pipe inner surface (in MPa). Similarly, the SIF solution for external soil deflection loading is 9 （6）In this case, sID is the remotely applied
30、membrane hoop stress at pipe inner surface (inMPa). According toWatkins and Anderson 12, this is given by （7）where D is the diametrical deflection (in), and Dm is the mean diameter of the pipe (in m). E is the time-dependant Youngs modulus of the pipe material (in MPa). In practise, D is usually unk
31、nown, but can be determined from the magnitude of external loads due to soil backfill, and any live surface load applied 12. As described by Lu et al. 9, the applied SIF associated with residual stress is （8）where sIR is the residual stress at the pipe inner surface.4. Net section collapse criterion
32、 Whilst some failures in PVC-U pipe are purely brittle, examination of fracture surfaces from field failures indicate that local plastic deformation can also occurred during fracture 2. According to Marshall et al. 4, a defect or growing crack also reduces the cross-section of the pipe wall and sinc
33、e less intact material is able to sustain the applied pressure, the stress required to cause failure will decrease. This will eventually produce yielding and plastic collapse of the remaining un-cracked ligament in the pipe wall. The competition between brittle fracture and ductile yielding mechanis
34、ms is described in terms of a net section yield locus 4 as shown schematically in Fig. 2. In contrast to LEFM theory, the dependence between failure stress and crack size for net-section yielding is linear. Different failure mechanisms will be observed, depending on which failure stress is lowerthe
35、net section yield stress or the stress required for brittle fracture. Whilst net section yielding may be observed for small cracks, there is clearly a critical size above which brittle failure is observed (point ac in Fig. 2) 4. For crack sizes larger than a (Fig. 2), ductile failure would again be
36、observed as the net-section yield stress falls below the stress required for brittle fracture. In addition to the failure equation for brittle failure Eq. (4), a failure criterion for ductile fracture can be written as 4 （9）whereis the net-section yield stress (in MPa) and is the total applied stres
37、s under service loads (in MPa). is the time-dependent material yield stress (MPa), a is defect size and b is the pipe wall thickness (both in m) 13.5. Accounting for uncertainty in pipe failure modelsModelling of individual pipe assets using fracture mechanics theory can provide information on the p
38、erformance of a specific asset. However, water utilities usually require performance predictions for their complete pipe network. If operating conditions and defect sizes were available for all assets in the network, service lifetimes for each asset in the network could be calculated based on the mo
39、dels detailed above. However, since the majority of water utilities possess data for only a limited number of assets, network wide predictions in this manner are impractical. A useful alternative is to model uncertainty in each of the key variables that govern the failure process. This can allow the
40、 probability of failure to be estimated for assets where precise data is unavailable. The first step in such a probabilistic failure analysis is to formulate a limitstate failure criterion in terms of the load (L) and resistance (R) variables. As defined previously, the criterion for brittle fractur
41、e is when the total applied SIF exceeds the material fracture toughness and the criterion for ductile failure is when the total applied stress exceeds the net section yield stress. （10）where brittle fracture is defined to occur when m10 and ductile yielding when m20.Although probabilistic models hav
42、e been developed for water pipeline failure, they often rely on approximations14. For example, Level II first-order second-moment (FOSM) methods are often used to account for uncertainty in limit state models 14,15. In all probabilistic analyses,the basic variables in Eq. (10) are no longer single-v
43、alued but are treated as stochastic with mean values and variances. The limit-state equations are reformulated in the form M f eZT, where M is the stochastic limit state variable and Z is a random vector of the stochastic basic variables that comprises the limit state function. In FOSM methods, M is
44、 assumed to be approximately Normal distributed. Because of this assumption, there is a direct translation between the shortest distance, b from the failure region in variable space to the origin, and the probability of failure 14,15. However, in reality, stochastic variables of the limit state form
45、ulation (such as defect sizes) may not be Normally distributed. Complex loading conditions also mean that limit state failure models are rarely linear and M is often a non-linear function of stochastic variables. This causes some degree of non-Normality in M. Furthermore,iterative methods to calcula
46、te b require linear approximations to the failure surface, resulting in over-simplification.As a consequence of all assumptions, realistic physical failure mechanisms can be lost in order to obtain a solution.A more straightforward way to estimate the lifetime probability functions (discrete probabi
47、lity density functions) of PVC pipes is to use Monte-Carlo simulation in conjunction with the limit state formulations of pipe failure in Eq. (10). The Monte-Carlo simulation samples lifetimesby repeatedly generating random numbers and uses these to calculate and evaluate the limit state equation. F
48、or a simulated hypothetical network of pipes, a number of failures are recorded over time, which allows the lifetime distribution to be estimated. In contrast to FOSM methods, Monte Carlo simulations allow the details of the physical failure mechanism to be preserved with no linearisation required. Also, no
