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Trenchless Technology Research

Reliability based life cycle cost optimization for underground pipeline networks Kong Fah Tee ⇑, Lutfor Rahman Khan, Hua Peng Chen, Amir M. Alani Department of Civil Engineering, University of Greenwich, UK

a r t i c l e

i n f o

Article history: Received 8 November 2012 Received in revised form 5 April 2014 Accepted 9 April 2014

Keywords: Risk and cost optimization Probability of failure Genetic Algorithm Pipe renewal methods Life cycle cost Failure cost Condition index

a b s t r a c t The safety of underground pipelines is the primary focus of water and wastewater industry. Due to low visibility and lack of proper information regarding the condition of underground pipes, assessment and maintenance are frequently neglected until a disastrous failure occurs. The reduction of pipe thickness due to corrosion undermines the pipe resistance capacity which in turn reduces the factor of safety of the whole distribution system. Providing an acceptable level of service and overcoming practical difﬁculties, the concerned industry has to plan how to operate, maintain and renew (repair or replace) the system under the budget constraints. This paper is concerned with estimating reliability of non-pressure ﬂexible underground pipes subjected to externally applied loading and material corrosion during the whole service life. The reliability with respect to time due to corrosion induced deﬂection, buckling, wall thrust, bending stress is estimated. Then the study is extended to determine intervention year for maintenance and to identify the most appropriate renewal solution by minimizing the risk of failure and whole life cycle cost using Genetic Algorithm (GA). An example is presented to validate the proposed method with a view to prevent unexpected failure of ﬂexible pipes at the minimal cost by prioritizing maintenance based on failure severity and system reliability. Ó 2014 Elsevier Ltd. All rights reserved.

1. Introduction Underground pipeline network is a complex infrastructure system that has signiﬁcant impact on the economic, environmental and social aspects of all modern societies. The world is moving towards adopting more proactive and optimized approaches to manage underground pipeline systems for their short and long term renewal planning in a more sustainable way. These approaches mostly aim to maximize return on investment by optimizing the allocated budget. Return on investment includes higher asset performance, lower risk of failure and lower life cycle costs. Such decisions can range from determining the optimal maintenance or inspection interval to evaluating a proposed design change. The decisions involve deliberate expenditure in order to achieve reliability, performance and other beneﬁts. Costs involved are known but it is often difﬁcult to quantify the potential impact of risks, the efﬁciency or safety and structural life expectancy. Guice and Li (1994) suggested that not only are the beneﬁts difﬁcult to quantify but also the objectives often conﬂict with each other. Finding the optimal strategy is difﬁcult and the wrong maintenance strategy

⇑ Corresponding author. Tel.: +44 1634883141. E-mail address: [email protected] (K.F. Tee). http://dx.doi.org/10.1016/j.tust.2014.04.007 0886-7798/Ó 2014 Elsevier Ltd. All rights reserved.

will result in excessive costs, risks or losses. Optimization models for pipeline maintenance methodologies are still in their infancy condition when compared to those in bridges, buildings and other civil engineering structures although optimum design approaches for pipe structural systems are continuously evolving and improving (McDonald and Zhao, 2001; Tee and Li, 2011). Davies et al. (2001) pointed out that the Water Services Regulation Authority in England and Wales or OFWAT spent a huge amount of money every year on sewer replacement in the UK. According to Concrete Pipeline Systems Association (CPSA, 2008), OFWAT estimated that replacing or renovating the UK’s 309,000 km sewerage and drainage network required £200 billion. The consequences of failure are multiple and may include loss of life, injury, excessive maintenance costs, user costs, environmental impacts etc. It is clear that some of these consequences are incommensurable and cannot be evaluated in monetary terms. The concept that needs to clarify is the meaning of ‘optimum’. The word is often used in phrases such as the optimum maintenance strategy or the optimum performance. Woodhouse (2001) stated that in areas where there are conﬂicting interests, such as pressures to reduce costs at the same time as the desire to increase reliability or performance or safety, an optimum represents some sort of compromise between the demand and

K.F. Tee et al. / Tunnelling and Underground Space Technology 43 (2014) 32–40

performance. It is quite impossible to achieve the ideal – zero cost and at the same time total 100% reliability or safety. Structural reliability analysis of buried pipeline systems is one of the fundamental issues for water and wastewater asset managers. Methods of reliability analysis such as ﬁrst order reliability method, second-order reliability method, point estimate method, Monte Carlo simulation, subset simulation, gamma process, probability density evolution method, etc. are available in literature (Baecher and Christian, 2003; Sivakumar Babu and Srivastava, 2010; Tee et al., 2013b; Mahmoodian et al., 2012; Fang et al., 2013a, 2013b). Recently, considerable amount of attention has been given to reliability of underground pipeline networks in conjunction with the optimization to achieve maximum beneﬁts with the minimum cost (Moneim, 2011). The prediction of structural reliability throughout its life cycle depends on probabilistic modelling of load and strength of the system and on the use of appropriate analytical or numerical methods (Estes and Frangopol, 2001; Tee et al., 2013a). Knowing the age of a pipeline segment, the condition of the pipe and how a pipe of that type deteriorates over time makes it possible to estimate the remaining service life of speciﬁc pipe. Unfortunately few municipalities have sufﬁcient historical data to model the actual deterioration of underground pipes. Mailhot et al. (2000) used data from a Quebec municipality to simulate the deterioration of a sewer network from a good to poor state; Wirahadikusumah and Abraham (2003) modelled the deterioration of combined sewers using data from the city of Indianapolis; Ariaratnam et al. (2001) used data from the City of Edmonton to model sewer pipe deterioration and Micevski et al. (2002) modelled the deterioration of storm sewers for the Newcastle City Council in Australia. All the four models have predicted the pipe service life which is approximately 100–125 years. However, according to Newton and Vanier (2006), the estimated service life can range from 50 to 125 years depending upon the material and pipe diameter. In fact, the service life of a pipe can also be affected by other factors such as type of embedment soil, pipe thickness, pipe depth, pipe class (combined, sanitary, storm), level of maintenance, overburden, soil type, etc. (Ana et al., 2008; Wirahadikusumah et al., 2001). These elements are inherently conﬂicting, so an integrated multi-criteria approach is needed to develop renewal plans that satisfy these criteria in a balanced and optimized manner. The sustainable management and renewal of underground pipeline networks pose a wide range of difﬁculties due to increasing fear of failure risk and requirements to comply with environment and accounting regulations as well as limited renewal budgets. Many challenges have been faced by water industry during installation and maintenance of underground pipeline networks. Frequent change of weather, corrosion, shrinkage and crack may reduce the pipe service life even if repair is done and the initial strength may not be achieved. A vital failure criterion of pipelines subjected to both internal and external corrosion is that the loss of structural strength which is inﬂuenced by localized or overall reduction in pipe wall thickness. Ahammed and Melchers (1994) assumed that the loss of wall thickness through general corrosion which affects much of the circumferential wall thickness is uniform or near so. The size of the resulting pipe wall thickness undermines the pipe resistance capacity which in turn reduces the factor of safety of the whole pipeline distribution system. The decision to repair or replace existing pipes is typically based on past performance indicators such as annual number of failure in a given section of a pipe network. This approach is not robust because it depends largely on what has happened in the past and what is expected to happen in the future. A better approach to scheduling pipe maintenance is based on performance indicators such as structural integrity, hydraulic efﬁciency and system reliability (Khan et al., 2013).

33

The main objective of this study is to analyse the reliability of non-pressure ﬂexible underground pipes using First Order Reliability Method (FORM) and to present a reliability-based model of life cycle cost optimization in Genetic Algorithm (GA). Given the importance and high consequences of pipe collapse, a risk-based maintenance management methodology can be more effective by considering not only the probability of failure but also the consequences of failure. The optimization objective function of this study is the value of life cycle cost (LCC) which represents all the costs incurred throughout the life cycle of an underground pipe network, including the costs of design, construction, maintenance, repair, rehabilitation, replacement and expected costs of failure. The proposed maintenance strategy enables decision maker to decide when and how to renew the pipes (i.e. the most effective maintenance strategy, which could be replacement, structural, semi structural and non structural lining methods) at the minimum cost. 2. Corrosion of metal pipes Buried pipes are made of plastic, concrete or metal, e.g. steel, galvanized steel, ductile iron, cast iron or copper. Plastic pipes tend to be resistant to corrosion. Damage in concrete pipes can be attributed to biogenous sulphuric acid attack (Tee et al., 2011). On the other hand, metal pipes are susceptible to corrosion. Metal pipe corrosion is a continuous and time variable process. Under certain environmental conditions, metal pipes can become corroded based on the properties of pipe materials, soil surrounding pipe wall, water or wastewater properties and stray electric currents. The corrosion pit depth (DT) with respect to time can be modelled as shown in Eq. (1) or Eq. (2). Kucera and Mattsson (1987) ﬁrst proposed a widely accepted model, a power law equation to measure DT for atmospheric corrosion which can be expressed as follows.

DT ¼ kT

n

ð1Þ

where k is multiplying constant (typical value 2.0), n is exponential constant (typical value 0.3) (Sadiq et al., 2004) and T is exposure time. Rajani et al. (2000) proposed a two-phase modiﬁed corrosion model to accommodate the self-inhibiting process as follows.

DT ¼ aT þ bð1 ecT Þ

ð2Þ

where a is ﬁnal pitting rate constant (typical value 0.009 mm/year), b is pitting depth scaling constant (6.27 mm) and c is corrosion rate inhibition factor (0.14 per year). Eq. (1) is normally used to predict DT for steel pipe whereas Eq. (2) is used for cast iron pipe. Due to reduction of pipe wall thickness caused by corrosion, the moment of inertia per unit length, I and cross-sectional area per unit length, As can be deﬁned as shown in Eqs. (3) and (4), respectively (Watkins and Anderson, 2000; Tee and Khan, 2012).

I ¼ ðt DT Þ3 =12

ð3Þ

As ¼ t D T

ð4Þ

where t is thickness of pipe. Eqs. (1)–(4) show that DT, I and As are time dependent variables. 3. Flexible pipe failure modes The dominating failure criteria of ﬂexible pipes are characterized by limit states as follows (a) Excessive deﬂection. (b) Actual buckling pressure greater than the critical buckling pressure.

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rb ¼ 2Df EDy y0 Sf =D2

(c) Actual wall thrust greater than critical wall thrust. (d) Actual bending stress greater than the allowable stress.

where Df is shape factor and y0 is distance from centroid of pipe wall to the furthest surface of the pipe.

3.1. Deﬂection The performance of ﬂexible pipe in its ability to support load is typically assessed by measuring the deﬂection from its initial shape. Deﬂection can be deﬁned as the change in inside diameter that results when a load is applied to a ﬂexible pipe. According to BS EN 1295:1 (1997) and BS 9295 (2010), deﬂection Dy can be calculated as

Dy ¼

KðDL W c þ P s ÞD ð8EI þ 0:061E0 Þ D3

ð5Þ

where K is deﬂection coefﬁcient, DL is deﬂection lag factor, D is 0 mean diameter, E is modulus of elasticity of pipe material and E is modulus of soil reaction. The loads acting on the pipe are governed by the term DLWC + PS where WC is soil load and PS is live load. Deﬂection is quantiﬁed in terms of the ratio of the horizontal increase in diameter (or vertical decrease in diameter) to the pipe diameter. The critical deﬂection for ﬂexible pipe, Dycr is determined as 5% of inside diameter of pipe (Hancor, 2009). 3.2. Buckling Buckling is a premature failure in which the structure becomes unstable at a stress level that is well below the yield strength of the structural material (Babu and Srivastava, 2010). The actual buckling pressure should be less than the critical buckling pressure for the safety of the structure. The actual buckling pressure, p can be calculated as follows (AWWA, 1999):

p ¼ Rw cs þ cw Hw þ PS

ð6Þ

where Rw is water buoyancy factor, cw is unit weight of water, Hw is height of groundwater above the pipe. The critical buckling pressure, pcr is calculated as follows (AWWA, 1999):

pcr ¼

1 Sf

ð10Þ

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ s ﬃ EI 32Rw B0 Es 3 D

ð7Þ

4. Risk and reliability analysis For acceptable value of probability of failure, USA Army Corps of Engineers suggested that the estimated reliability index should be at least 3.0 for above average performance and 4.0 for good performance (Babu and Srivastava, 2010). FORM is used in this study for estimating structural reliability of underground ﬂexible pipes. The limit state functions Z(X) for the aforementioned failure modes (deﬂection, buckling, wall thrust and bending stress) are deﬁned as the difference between actual and critical values. Z(X), with mean Z and standard deviation, r(Z) is a function of the random variables which are soil and pipe properties. The probability of failure for each limit state function can be evaluated by

"

# 0Z ¼ UðbÞ Pf ¼ P½ZðXÞ < 0 ¼ U rðZÞ

ð11Þ

where U is the cumulative standard normal distribution function (zero mean and unit variance) and b ¼ Z=rðZÞ is known as safety index or reliability index. There are basically two models of system reliability. One is known as series system in which the occurrence of one failure mode constitutes the failure of the whole system. The other is known as parallel system in which the system fails only when all failure modes occur. For a pipe, the occurrence of either failure mode will constitute its failure. Therefore a series system (also called a weakest link system) is more appropriate for its assessment of failures. The correlation between the failures events is estimated and the value is within the range from 0 to 1. Thus, the probability of failure for a series system, Pf,s can be estimated as follows (Fetz and Tonon, 2008)

Max½Pf ;i 6 P f ;s 6 1

n Y ½1 Pf ;i

ð12Þ

i¼1

where Sf is safety factor and B is empirical coefﬁcient of elastic support.

where Pf,i is the probability of failure due to ith failure mode of pipe and n is the number of failure modes considered in the system.

3.3. Wall thrust

5. Reliability based LCC optimization

Thrust or stress on the pipe wall is determined by the total load acting on the pipe including soil, trafﬁc and hydrostatic loads. The actual wall thrust can be calculated as follows

Evolutionary strategies, such as Genetic Algorithm (GA), Ant Colony Optimization Algorithm and Particle Swarm Optimization Algorithm have received considerable attention in many areas of water resource management including pipeline network design problems. This paper proposes a new step-wise integrated approach in developing optimized plans using GA that would identify the most appropriate compromise of renewal solutions while simultaneously optimizing life cycle cost, condition state and risk of failure of pipeline networks. The proposed approach deﬁnes a systematic procedure to quantitatively assess the risk, optimise life cycle cost and evaluate renewal options which help to reduce the subjectivity typically involved in decision-making process. The problem is treated as a multi-objective problem characterized by a technical objective deﬁned by risk measure and an economic objective deﬁned by total life cycle cost. In this paper, GA has been selected as an optimization technique in maintenance strategy because GA has been proven to be a robust and powerful algorithm for arriving at the global optimum. There are no mathematical limitations on the type and number of decision variables, formulation of objective functions and constraints, which is an important factor considering the complexity of optimization process.

0

T ¼ 1:3ð1:5W A þ 1:67PS C L þ P w ÞðDo =2Þ

ð8Þ

where Do is outside diameter and CL is live load distribution coefﬁcient. The loads acting on the pipe considered in wall thrust analysis are soil arch load WA, live load PS and hydrostatic pressure Pw. The critical wall thrust is calculated as follows

T cr ¼ F y As /p

ð9Þ

where Fy is the minimum tensile strength of pipe and /p is capacity modiﬁcation factor for pipe. 3.4. Bending stress For the safety of pipe, the bending stress should not exceed the long term tensile strength of the pipe material. Therefore, checking the bending stress is important to ensure that the value is within material capability. Bending stress rb can be calculated as follows (Gabriel, 2011)

K.F. Tee et al. / Tunnelling and Underground Space Technology 43 (2014) 32–40

The implementation of a quantitative assessment and riskbased life cycle maintenance is a very complex task due to the difﬁculties of assessing quantitatively the probability and the consequences of failure, especially for a large network of pipe structures. For a given pipeline distribution network, huge number of solutions can be selected through a range of decision variables and in such cases, probabilistic methods are used instead of mathematical models to search for the best solution. The whole life cycle cost (LCC) has been used as an objective function in maintenance optimization. The effects of corrosion are included in the pipe failure models. In this study, the LCC consists of initial cost or installation cost, maintenance cost and expected cost of failure. The total life cycle cost CLCC can be presented as follows (Hinow et al., 2008)

C LCC ðTÞ ¼ C A þ

T T X X C M ðiÞ þ C f ðiÞ Pf ;s i¼1

ð13Þ

35

a high, medium, or low scale according to soil type and groundwater level as shown in Table 2 (Halfawy et al., 2008). The condition index (CI) can be calculated from the regression model (Newton and Vanier, 2006) as follows:

CI ¼ 0:0003T 2 0:0003T þ 1

ð14Þ

where T = age of pipe (in year) which corresponds to the intervention year obtained from the life-cycle cost optimization. Once the condition index and possible scenarios of soil loss have been determined, renewal methods can be selected. For example, a pipe with condition index 3 and high possibility of soil loss will require replacement or the use of a structural liner to carry loads and stabilize deformation. At a minimum, a semi structural liner that can withstand hydrostatic pressure is required. 7. Worked example

i¼1

where CA is capital cost, CM is maintenance cost, Cf is system failure cost and i = 1, 2, 3 . . . T year. Failure probability of series system, Pf,s is determined using Eq. (12). The cost terms in the right-hand side of the Eq. (13) are the costs in the year they actually occur. The (1 + r)T factor is used to convert the cost into its present value discounted by the discount rate of r, for the T year period. The discount rate depends on the prevailing interest rate and the depreciation of the currency or inﬂation rate. This rate is not a constant term and may vary over the life of the pipeline structure. From an economical point of view, the ideal goal of risk and cost management of pipe network should be minimizing the total LCC of the network. In this study, the problem of identifying the optimal intervention year is transformed into minimization of total LCC (Eq. (13)). A poor maintenance policy often leads to early failure. On the other hand, a conservative maintenance policy may result in excessive costs. The underground pipeline network will require rehabilitation or replacement several times during the system design life. 6. Selection of renewal methods The pipeline renewal technologies are growing rapidly and becoming more efﬁcient and cost-effective. Different renewal methods exhibit different capabilities, limitations, costs and beneﬁts. The particular characteristics of the pipe (e.g., material, diameter, etc.) and site conditions (e.g., soil, water table, trafﬁc etc.), along with other operational, social and environmental factors determine the applicability of different renewal methods in a particular situation. In any given scenario, applicable and cost effective renewal methods should be determined based on a systematic procedure. The renewal methods are grouped into four main categories: replacement, structural, semi structural and non-structural lining methods. Structural liners are deﬁned to be capable of carrying hydrostatic, soil and live loads on their own. Structural liners are expected to be independent i.e., bonding with original pipelines is not required. Semi structural liners are designed to withstand hydrostatic pressure or perform as a composite with the existing pipelines. Semi structural liners could be designed as interactive or independent (Halfawy et al., 2008). Semi structural liners typically are not used for gravity pipelines. Non-structural liners are used mainly to improve ﬂow, resist corrosion, or to seal minor cracks in gravity pipelines (Heavens, 1997). In this study, the proposed underground pipeline maintenance strategy complements the aforementioned life cycle cost optimization by identifying applicable renewal categories based on condition index and the possibility of surrounding soil loss as shown in Table 1. The possibility of surrounding soil loss is assessed on

An underground pipeline network under a heavy roadway subjected to hypothetical operating conditions is taken as a numerical example to validate the proposed life cycle cost optimization maintenance strategy. The pipeline network consists of approximately 860 km of sanitary pipes and 755 km of storm pipes. The sanitary pipes of length 500 km and 360 km were constructed in 1989 and 1994, respectively whereas the storm pipes of length 255 km and 500 km were constructed in 1999 and 2003, respectively. A schematic layout of the whole network is shown in Fig. 1. The sanitary pipes were constructed on clay whereas the storm pipes were built on sand and the whole underground pipes were above the groundwater level. For simplifying the problem, all the pipes in the network (both sanitary and storm) are presumed as large size steel pipes with an outside diameter of 1.21 m and initial wall thickness of 0.021 m. The pipeline network is subjected to corrosion and its corrosion rate is modelled using Eq. (1). The pipe and soil parameters are listed in Table 3. There are 9 random variables (elastic modulus of pipe, soil modulus, soil density, live load, deﬂection coefﬁcient, corrosion coefﬁcients, pipe wall thickness and height of the backﬁll) where the mean and coefﬁcient of variation (COV) are listed in Table 4 (Ahammed and Melchers, 1994; Sadiq et al., 2004; Sivakumar Babu et al., 2006). All of them are considered as normally distributed, except deﬂection coefﬁcient which is log-normal distributed. It is assumed that the capital cost or initial cost is £1.2 million ($1.98 m), maintenance cost is £0.15 million ($0.25 m), expected failure consequence cost is £2 billion ($3.3 m) and discount rate is 4.2%. 8. Results and discussion The structural reliability of the underground pipeline network is ﬁrst estimated and then life cycle cost optimization is performed to predict the optimal maintenance or renewal time which takes into account the reliability analysis and total cost. The proposed maintenance strategy enables decision maker to choose a feasible renewal method based on the calculated optimal renewal time. 8.1. Probability of failure The probabilities of failure due to corrosion induced deﬂection, buckling, wall thrust and bending stress with respect to time are estimated based on the parameters and basic variables given in Tables 3 and 4. The occurrence of either failure mode of the pipe will constitute its failure. Therefore the probability of failure of the underground pipeline network is determined using Eq. (12) and the result is shown in Fig. 2. As all the random variables are considered as normally distributed, except deﬂection coefﬁcient

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K.F. Tee et al. / Tunnelling and Underground Space Technology 43 (2014) 32–40

Table 1 Selection of renewal categories based on condition index and soil loss possibility (Halfawy et al., 2008). Condition Index

2 3 4 and 5

Possibility of soil loss Low

Medium

High

Non-structural or semi-structural Non-structural or semi-structural Structural or replacement

Non-structural or semi-structural Semi-structural or structural Structural or replacement

Semi-structural, structural or replacement Semi-structural, structural or replacement Structural or replacement

Table 2 Possibility of soil loss based on soil type and groundwater level (Halfawy et al., 2008). Soil Type

Groundwater level

Clay Gravels and low plasticity clay Silt and sand

Below pipe

Same line with pipe

Above pipe

Low Low High

Medium Medium High

High High High

Fig. 1. Layout of pipeline network (not to scale).

Table 3 Parameter values of worked example. Symbol description

Value

Buoyancy factor, Rw Trench width, Bd Outside pipe diameter, Do Inside pipe diameter, DI x-Sectional area of pipe wall per unit length, As Shape factor, Df Capacity modiﬁcation factor for pipe, /p Safety factor for bending, Sf Tensile strength of pipe, Fy Safety factor for buckling, Sf Poisson ratio, t Allowable strain, ecr

1.00 2.00 m 1.231 m 1.189 m 0.021 m2/m 4.0 1.00 1.5 450 MPa 2.5 0.3 0.2%

Table 4 Statistical properties of random variables. Material properties

Mean (l)

COV (%)

Distribution

Elastic modulus of pipe, E Backﬁll soil modulus, Es Unit of weight of soil, cs Wheel load (live load), Ps Deﬂection coefﬁcient, K Multiplying constant, k Exponential constant, n Thickness of pipe, t Height of the backﬁll, H

213.74 106 kPa 103 kPa 18.0 kN/m3 80.0 kPa 0.11 2.0 0.3 0.021 m 3.75 m

1.0 5.0 2.5 3.0 1.0 10.0 5.0 1.0 1.0

Normal Normal Normal Normal Lognormal Normal Normal Normal Normal

which is log-normal distributed. Thus Rackwitz–Fiessler algorithm has been applied to transform its distribution from log-normal to normal in this study.

The study shows that the probability of pipe failure at the beginning is zero and it remains unchanged until about 40 years of service life, then it gradually changes as time increases and after 50 years, the probability of failure rises drastically. When the thickness of the pipe is reduced due to corrosion, the moment of inertia and the cross-sectional area of pipe wall are decreased with a resulting reduction in pipe strength as shown in Eqs. (3) and (4). The upper limit of the failure probability obtained from Eq. (12) has been used for the subsequent total life cycle cost optimization as the worst case scenario. 8.2. Optimal cost and time to renew As shown in Eq. (13), the expected cost of failure is calculated by multiplying system failure cost with the probability of failure. Once the probability of failure has been calculated, the optimal time to repair or replace and the associated life cycle cost can be obtained from life-cycle cost optimization using GA. Fig. 3 shows the convergence of total LCC obtained from life-cycle cost optimization and the optimal value is about £25 billion ($41.25b). The optimal LCC cost is associated with the ﬁrst maintenance after 62 years of service. The maintenance cost and expected cost of failure for the whole underground pipeline network are shown in Figs. 4 and 5. Based on the given data, the sanitary pipe of 500 km is required to renew in 2051, while 360 km in 2056. Similarly, the storm pipe of 255 km is required to renew in 2061 and 500 km in 2065 in order to achieve the minimum life cycle cost which takes into account the reliability of the underground pipe network. Next, the proposed maintenance strategy is extended to determine an applicable and feasible renewal method using Tables 1 and 2. The recorded database shows that the sanitary pipes are

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K.F. Tee et al. / Tunnelling and Underground Space Technology 43 (2014) 32–40

Fig. 2. Probability of failure for underground pipelines.

11

3.5

x 10

Best: 25055561526.833, Mean: 25061454916.4899

Life Cycle Cost (Present Value), £

3 2.5

Best values Mean values

2 1.5 1 0.5 0

0

20

40

60

80

100

120

140

160

Generation Fig. 3. Convergence of total life cycle cost for pipeline network from GA.

Fig. 4. Maintenance cost for pipeline network.

180

200

38

K.F. Tee et al. / Tunnelling and Underground Space Technology 43 (2014) 32–40

Fig. 5. Expected cost of failure for pipeline network.

Fig. 6. Life cycle cost with different soil densities.

built on clay and the soil type of the storm pipes is sand. In addition, both types of pipes are above the groundwater level. Based on this information and according to Table 2, the possibility of soil loss for sanitary pipes is low whereas for storm pipes, the

possibility of surrounding soil loss is high. The condition index (CI) for the pipe network is estimated as 2.13 using Eq. (14) by substituting the identiﬁed optimal time to renew (62 years) from the life-cycle cost optimization. Applicable renewal categories are

Fig. 7. Life cycle cost with different soil heights.

K.F. Tee et al. / Tunnelling and Underground Space Technology 43 (2014) 32–40

39

Fig. 8. Life cycle cost with different discount rates.

then selected from Table 1 based on the pipe CI and the possible scenario of soil loss. The sanitary pipes of 500 km and 360 km are required to renew using non-structural or semi-structural lining method based on the estimated CI of 2 and low possibility of soil loss. On the contrary, due to high possibility of soil loss and the pipe CI of 2, the storm pipes of 225 km and 500 km are renewed using semi-structural or structural liners. Alternatively replacement is recommended when the repair cost is greater than the cost of replacing the pipes. 8.3. Parametric study A parametric study has been carried out to analyse the effects of different parameters on reliability and life cycle cost of the underground pipeline network. For example, if soil properties (such as soil modulus or soil density) changes, this will affect probability of failure and hence reliability and life cycle cost of the pipeline network. As shown in Fig. 6, the life cycle cost increases drastically when soil density is increased from 16 kPa to 20 kPa. The parametric study also demonstrates that with increasing soil height above pipeline decreases service life and increases life cycle cost of the pipeline network as illustrated in Fig. 7 for soil height from 3.0 m to 3.75 m. Due to increment of soil height, overburden pressure is increased and therefore failure probability is also increased which leads to higher total life cycle cost with respect to time. Fig. 8 shows that when discount rate varies from 5% to 7%, the whole life cycle cost also varies signiﬁcantly. Similarly, other factors such as pipe dimension including pipe thickness and diameter, live load, inﬂuence pipe failure probability and consequently affect its life cycle cost. 9. Conclusions This paper presents a novel integrated approach for systematizing the maintenance of underground pipeline networks. The approach integrates two main criteria in the planning process: structural reliability and whole life cycle cost. The probability of failure due to corrosion induced deﬂection, buckling, wall thrust and bending stress is estimated and then the study is extended to minimize the risk and life cycle cost optimization using GA. It follows that a rigorous decision process should ﬁnd a balance between the risk of failure and the cost to mitigate it. The proposed maintenance strategy also enables decision maker to select appropriate renewal method based on the identiﬁed optimal time to renew, pipe condition index and the possibility of surrounding soil loss. A numerical example is presented to validate the proposed

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