Ideal Deterioration Model (IDM)

Section 2.2 clearly identified several major mechanisms leading to the deterioration of rigid sewers and stormwater pipes. These mechanisms are primarily attributed to many contributing factors (e.g. traffic load, static load, debris, tree roots, soil type, pipe size and buried depth). More importantly, a three-phase development of deterioration of combined sewers was considered in WRC (1983) and these three phases were translated into a ‘bath-tub curve’ for management planning by Davies et al. (2001a) for sewers

and by Kleiner and Rajani (2001) for water pipes.

Based on the above ideas, the present study considered an ideal deterioration model (IDM) using assumed deterioration curves for both structural and hydraulic deterioration of stormwater pipes. The IDM defined each pipe by a different deterioration curve because pipes in reality deteriorate differently from one to another due to many contributing factors. For example, some young pipes may experience structural or hydraulic failures in one area whilst older pipes still work well in other areas or even in the same area.

Before going into the details of the IDM, it is worth mentioning that the IDM for the structural deterioration should be constructed separately to the IDM for the hydraulic deterioration in the case that regular or longitudinal data are available. This is because the structural deterioration process is different with the hydraulic deterioration process and the effects of contributing factors on the structural deterioration process are different with those of contributing factors on the hydraulic deterioration process.

The IDM is shown in Figure 3-2 where individual pipes presumably have their own deterioration curve pattern as marked Pipe 1, Pipe 2,..,Pipe n. This figure also shows

how pipes change their condition over time represented by age from start-up phase to operation phase and until they reach the rehabilitation phase when structural or hydraulic failures are likely to occur if no maintenance is carried out. The ‘age’ is a unique factor that was used to express the change of pipe condition because ‘age’ complies with most M&R scheduling of asset management. It can be noted from this figure that a threshold line, which is at condition 3, defined the rehabilitation phase where pipes need rehabilitation or replacement, since they approach the condition that is considered not safe and economical to operate according to some criteria.

Phase 1 is called the start up-phase where any major defects identified during construction and system testing are fixed to bring pipes back to its original perfect condition (i.e. condition 1). Although some minor defects may not be detected when pipes step into the operation phase (phase 2), the condition of pipes at the beginning of phase 2 is assumed to be in condition 1. During the operation phase, pipes will deteriorate due to many causes such as chemical corrosion and mechanical loads in a way that deterioration rates of pipes may not be the same due to many contributing factors such as pipe size, pipe location and random damage events.

Age Start- up Phase Threshold Line Pipe 1 Pipe 2 Pipe n-1 Pipe n 120 90 60 30 0 3 2 1 Pipe Conditio n Operation Phase Rehabilitation Phase

Figure 3-2: Illustration of ideal deterioration curves

When M&R occurs in a drainage system, two age definitions can be used. The first is the absolute age, which shows the absolute change of age from its construction. The second is the reference age, which shows the adjusted age of the pipe that receives M&R and return to a perfect condition in order to make a consistent dataset for the management of pipes. For example, after receiving an M&R action, a pipe of age 30 in condition 3 will return to condition 1 with reference age of zero and absolute age of 30. By doing this, the pipe is treated as a new pipe given that all defects are fixed.

3.2.1 Condition Changes of Individual Pipes and Pipe Population

The IDM allows monitoring the condition changes of individual pipes over time. The condition changes of individual pipes show the condition of any particular pipe, as compared to the ‘like new’ condition, given the contributing factors (e.g. pipe size and pipe age) of the pipe. This monitoring allows correctly directing M&R actions on pipes that are considered as at risk. Furthermore, this IDM also allows monitoring the

condition changes of pipe population over time as shown in Figure 3-3. The curves in this figure show the proportions of pipes in each condition at any time during the expected life and thus are useful for budget planning and estimating of expected life of pipes. 0 0.2 0.4 0.6 0.8 1 0 20 40 60 80 100 120 Time (Years) P o rp or ti on o f pi pes Condition 1 Condition 2 Condition 3

Figure 3-3: Condition changes of pipe population (hypothetical data) 3.2.2 Construction of IDM with Real Data

The shape of each deterioration curve pattern in the IDM can be broadly identified when several points (i.e. inspected pipe condition) as ‘squares’ marked in the Figure 3-2 along the age axis are available. This is the case of having longitudinal data which could be collected using CCTV inspection or recently advanced inspection techniques like sonar and radar. However, collecting such real data for the construction of the IDM is an impossible task when technological restraints, the massive number of pipes and limited budget are considered. Instead of longitudinal data, the current practice is to obtain snapshot data (one inspection only during the pipe lifetime) of a sample set of pipes. These snapshot data are marked as ‘circles’ in Figure 3-2. Therefore, only a point of the deterioration curve can be seen.

The IDM is still the basis for the development of practical deterioration models in Section 3.3 for capturing condition changes of individual pipes and pipe population with snapshot data. The pipe condition and proportions of pipe in each condition are the two outputs from the deterioration models to be developed.

3.2.3 Input Factors to Practical Deterioration Models

A number of factors were identified in Section 2.2, which directly or indirectly affect the structural and hydraulic deterioration of sewers and stormwater pipes. However, it is expected that many more factors will emerge as the knowledge of the complex deterioration process is increased. A list of potentially contributing factors that affect the deterioration process of stormwater pipes are compiled and synthesized from literature review and expert opinion. These factors, which are classified to account for structural and hydraulic deterioration, are given in Table 3-1. These factors are categorized into two groups, namely, construction and operation factors and M&R factors.

Factors can also be viewed as static and non-static (time-dependent). However, the distinction between static and non-static factors is not always clear-cut. For example, the pipe slope can be viewed as a static factor but in reality there is a slight change of slope over time due to the settlement of bedding. The rationale for introduction of time- dependent property is to increase the accuracy in finding the underlying deterioration process (Kleiner and Rajani 2000). However, it is obvious that the use of time- dependent factors in any model requires longitudinal data (continuous data over a certain period) that are normally not available and costly to obtain in the future. Therefore all factors were considered static (time independent) as outlined in Section 1.4 (Scope and Assumptions) of this thesis. This excludes pipe age, structural condition and hydraulic condition. Furthermore, M&R factors were not used in the implementation of deterioration models due to lack of data.