Evaluation models for the assessment of the structural and operational condition of drain and sewer systems – Part III

5.4 STATUS_Sewer – Analysis of the actual situation based on an aging model

The analysis of the actual situation of the drain and sewer system object under consideration based on an aging model comprises the assessment of essential technical and statistical network parameters, taking into account their aging behaviour. This work step particularly serves to represent the condition data which have been captured at different points in time during the visual inspection on a uniform time horizon, i.e. the evaluation moment(s). In STATUS_Sewer, the forecast of the network situation at the point in time when the requirements list is created is done by means of network-specific aging models that are also used to predict future developments at any time (Section 5.4.4). Requirements lists that rely on a forecast of future developments at any time by means of network-specific aging models are the essential basis for medium- and long-term rehabilitation decisions as well as the development of differentiated rehabilitation and investment strategies for drain and sewer systems.

Rehabilitation planning that does not realistically capture the network-specific changes in conditions and prognosis for future performance, i.e. its remaining useful life, inevitably leads to a misinterpretation of both the rehabilitation and financial needs. In order to guarantee a long-term planning reliability in this respect, a comprehensive analysis of the characteristics of the local network aging process is indispensable, as that step creates the data basis for the subsequent and final step of STATUS_Sewer, namely “Strategy development and network development forecast” (Figure 1, 1^st part of the article).

 

5.4.1 Aging model STATUS_Sewer

Drain and sewer systems are subject to a constant aging process that is characterised by many influencing factors (Table 3) and object-specific influencing conditions or features and their combinations (age, actual structural condition, nominal size DN, depth of cover, material, etc.) and that process decisively determines the useful life of the facilities. This holds particularly true for drain and sewer systems that have developed historically and thus, are very heterogeneous with regard to their age or the material of their individual objects, for example. Of course, the network specific condition and fabric decay classes of the objects that were determined in the assessment process are also affected.

In practice, the term useful life is used differently depending on the specific approach. In accordance with [1] use is defined as the utilisation of a unit as intended and in compliance with good engineering practice, whereby the reduction of the performance reserve creates the need for special measures with regard to operation, maintenance and rehabilitation.

The physical life is defined as the period of time in which the utilisation of a unit as intended and in compliance with good engineering practice is possible without extraordinary maintenance. According to [1], the physical life of a unit can also be understood as the period of time until a reduction of the performance reserve caused by chemical, biological and/or physical processes sets in and the performance limit is reached (Figure 13).

In general, the physical life of a unit always ends at the point in time of defined failure. Depending on the local influencing conditions (water protection zone, relevance to the public right of way, relevancy of the sewer section for the drain and sewer network, etc.), an individual probability of failure can be defined as the criterion in the event of failure.

The economic life is the period of time in which the use of a unit is profitable, i.e. in which the accruing cost for its operation and maintenance are lower than the cost for its renovation or replacement. When measures have to be coordinated with other branches (gas, water, roads and other public works), the economic life is always notably shorter than the physical life.

The average useful life is the period of time in which the unit can be used with any certainty under usual stresses within the given structural, functional, economic and legal requirements.

The remaining useful life of drainage systems cannot be determined in advance due to the many influencing factors (Table 3), interactions, and the often many years of operation.

 

Table 3: Factors influencing the useful life of drain and sewer systems

Selected input parameters for the determination of the average useful life	Criteria for new constructions	Criteria for inventory assessment
Installation conditions	Acceptance criterion for structure and soil, check of the execution of construction work	Knowledge of the structural system pipe/soil
Execution of construction work	Open cut / semi-open cut and trenchless method of construction	Knowledge on the state of the art at the time of execution of construction work
Subsoil conditions	Foundation; good bearing soil, poor soil; groundwater conditions/-composition	E.g. changes in bedding conditions caused by Leakage combined with soil intrusion, Loosening of the soil in the embedment and cavity formation
Material used / Construction material	Technical characteristics	E.g. changes in the material characteristics due to aging
Operating conditions	Sewage composition; Discharge conditions Aeration,Cleaning	Cleaning frequency
Maintenance		Local repair or exchange of damaged piping or other structural components; Removal of deposits, obstacles, etc. in order to restore the hydraulic performance capacity; Maintenance of machines and equipment
Structure	Implementation of planning	Knowledge of The economic devaluation due to technical progress, The given performance reserve (fabric decay class) The actually given stability Individual circumstances

 

In STATUS_Sewer, the expected useful life of the objects within drain and sewer systems is considered as a random statistical parameter that can be assigned to an assumed probability distribution. Figure 14 (at the top) shows as an example an expected useful life described by means of a Weibull distribution function. The function describes the probability at which the object under consideration will survive a certain age. The probability at which this object will survive a certain age is described by means of the survival probability function (also called reliability function) (Figure 14, at the bottom). It is determined from the integral of the life expectancy distribution [2].

As the objects in a drain and sewer system are prone to a continuous deterioration of their condition, the standard approach of aging models with just two conditions (alive/dead or operable/inoperable) is much too limited and insufficient in this context. For that reason, the survival probability functions in the aging model have been categorised, analogously to the condition and prognosis class analyses. Consequently, clusters of so-called condition or system probability survival functions are the result (Figure 15). The course of the survival probability curves characterises the relative residence periods of the objects in the classes (Table 2, 1^st part of the article) and thus, provides information on their obsolescence rate in the system under consideration.

Some justified exceptional cases apart, age modelling is always done based on inspection data of the drain and sewer system under consideration without any subjective estimations. Normally, data from other networks, network-transcending data or experiential data from other modelling are not used because aging processes are primarily influenced and created locally. Each part of a drain and sewer system may show very individual aging behaviour.

The example in Figure 15 shows a comparison of the survival probability curves, on the one hand derived from the independent Kaplan-Meier-estimation method [4] (dots), and on the other hand derived from the Weibull-Accelerated-Failure-Time-Regression method [5] (continuous lines). As the results correlate well, it can be concluded that the use of the Weibull function turns out to be appropriate for the case at hand. In case that they do not, a new cluster parameters have to be chosen (Section 5.4.2).

Given that a significant amount of data can be provided for a statistical evaluation of different sewer section characteristics, the survival probability functions can also be mathematically determined for different sewer section groups (clusters) (Section 5.4.2).

 

5.4.2 Cluster analysis

The informative value of survival probability functions largely depends on the homogeneity of the objects that are used to determine the probability distribution. The cluster analysis is used in order to ensure the categorisation of objects into groups with either the same or similar aging characteristics. The groups of objects found that way are called clusters.

For drain and sewer systems, all object features with a direct or an indirect influence onto the aging behaviour can serve as separation criteria which are required in cluster formation. This does not mean that the respective features represent causes for aging, but rather that they stand for a clear distinction. Generally, it is assumed that the majority of defects in sewers are caused by planning, construction and operation errors. If, for example, the pipe material is considered to be an essential indicator in cluster formation, the defects are not necessarily a direct result of the chosen pipe material.

The selection of relevant clusters for modelling of aging is done in an iterative process and is largely based on the experience of the involved specialist engineers and their analyses of the given database. The results of such analyses are survival probability functions for a certain number of combined characteristics that illustrate the aging behaviour of the network with adequate accuracy. They are thoroughly checked for statistical and systematic relevance in each iteration step.

In STATUS_Sewer, amongst others, the following features are tested as separation criteria in the iteration process for cluster determination:

• Pipe material (vitrified clay, concrete, brickwork, plastic, other),
• Profile (circular profile, oval profile, other),
• Sewer utilisation (combined water, wastewater, surface water),
• Sewer type (gravity pipeline, other),
• Traffic load,
• Nominal size,
• Depth of cover,
• Number of connections,
• Year of construction.

The determined influences of the separation criteria on the aging model partly coincide. Thus, the pipe material is an excellent starting point in the clustering process also because it is, de facto, a multiple indicator. As certain material groups have noticeably been used only either up to a specific point in time (brickwork) or from a specific point in time onwards (plastic), influences of construction periods are thereby modelled as well. Likewise, a certain pipe material has been / is used either up to specific nominal sizes or from specific nominal sizes onwards for different sewer types and utilisations or profiles.

Under the assumption that a significant amount of data for different feature combinations (e.g. material types, nominal size, depth of cover, etc.) is available for the statistical evaluation, the survival probability functions and aging prognosis can be created separately for the respective sewer section types (e.g. sewers made of vitrified clay in a defined nominal size range (Figure 16). The modelling of the aging behaviour is done based on the available condition and fabric decay class analyses of each inspected object. The results are the respective condition and fabric decay survival probability functions.

 

5.4.3 Condition and fabric decay survival probability functions

The fabric decay survival probability functions describe the likelihood at which a cluster forms part of a certain fabric decay class and thus, shows a specific performance reserve. The course of the fabric decay survival probability curves indicates the relative residence periods of the sewer sections in the fabric decay classes and thus, gives information about the deterioration speed of the sewer sections for the network under consideration.

The fabric decay survival probability functions are derived from the Weibull distribution of the objects in the respective fabric decay class. The parameters of the Weibull distribution are calculated for the individual fabric decay classes from the objects’ fabric decay classes by means of a regression method, assuming an accelerated failure time model. The set of curves is interpreted on the basis of a vertical (Figure 17) that is crossed by the fabric decay survival probability curves. The partial lengths of the verticals result in the time-dependent probability vector for the allocation of a sewer section and its curve related clusters into individual fabric decay classes.

Figure 17 shows an example for a cluster as to how the object fabric decay survival probability curves are interpreted for a sewer section after a period of 50 years. Based on the example, the sewer section still has its full performance reserve potential with a probability of 37 % (no fabric decay FDC=0) and a depleted performance reserve with a probability of 5 % (FDC=5). As, adapted from the inspection data, the fabric decay can only be determined at the time of inspection, it is required to forecast the aging behaviour or the fabric decay deterioration individually for every sewer section and every chosen point in time based on the fabric decay survival probability curves of the respective clusters (Section 5.4.4). In the event that there are no inspection data available, the forecast can rely on the initial values of the clusters, e.g. year of construction, and thus, still provide for a proper evaluation of the probable fabric decay class development.

Figure 18 shows fabric decay survival probability curves differentiated according to the performance objectives of stability, leaktightness, operational safety, and for all performance objectives as a whole. Their trends indicate the different aging behaviour. Based on the transition pace to the next, lower-ranking fabric decay class, and the residence time in it, general statements can be made initially with regard to the aging process, which can then be verified in a comparison with the experience of the network operator. Diverse, widely spaced fabric decay survival probability curves indicate long residence times in the corresponding fabric decay classes. In the illustrated example, this holds true for the performance objective “stability”. When the survival probability curves follow each other in a rather tight spacing, a high deterioration speed is to be assumed, as in the example of the performance objective “leaktightness”.

The condition survival probability functions describe the likelihood at which a cluster forms part of the individual condition classes and thus, shows a specific rehabilitation urgency. Basically, with increasing age, the likelihood of an urgent or immediate need for action increases, too.

The determination of the condition survival probability functions is done analogously to the approach of determining the fabric decay survival probability functions. The mathematical correlations are identical.

Figure 19 shows that an average sewer section of a cluster for which these condition survival probability functions were generated is still free of damage at an age of 50 years with a probability of 9 %, while it has a 15 % probability of being in need of immediate rehabilitation measures. As the inspection data only reveal the condition at the time of inspection, it is required to forecast changes in the condition or the increase of a rehabilitation urgency individually for each sewer section based on the condition survival probability curves of the respective clusters for each selected point in time. For sewer sections that have not been inspected or sewer sections where the inspection results cannot be analysed, the forecast can rely on the initial values of the corresponding cluster, e.g. year of construction, and still provide for a proper evaluation of the probable condition development.

 

5.4.4 Forecast model

The forecasts and strategies provide information about future network developments under certain preconditions and thus, can illustrate the medium- and long-term consequences of decisions made today.

The forecast model in STATUS_Sewer is based on the condition and fabric decay survival probability functions (Section 5.4.3). In this context, the curves derived from these functions are called aging curves.

For a forecast of the network development, STATUS_Sewer makes use of the Semi-Markov-chains model. The model allows for an aging simulation of a drain and sewer system as a stochastic process across a larger time span and thus, for predictions about the future development of each object.

For that purpose, the conditions the object might possibly be in are listed and the corresponding residence in or transition probabilities to the individual conditions are described. It is typical for Markov-processes that the future development of the system is only subject to the lastly inspected condition, but not to any prior conditions [6]. The aging forecast of drain and sewer systems based on Markov chains additionally requires the subsequently explained specifications.

In principle, when considering mere aging processes without rehabilitation interventions (repair, renovation or replacement), unidirectional Markov-chains are to be assumed. That means that both the condition and the fabric decaystate of a sewer section or any other object can only change for the worse. Consequently, it is a unidirectional development. From a mathematical point of view, the aging process is finally over, when the worst fabric decay class, i.e. a definite failure, is reached. This condition is called “absorbing”, as, once reached, it is not left again. An absorbing condition can only be reversed by a replacement, which is the basis for a new aging object.

Based on statistical evaluations of object inspection data by means of time-dependent Semi-Markov-processes, different residence times can be proven within the individual condition and fabric decay classes (Figure 20).

The transition probabilities of the aging curves to the next inferior class are subject to the point in time under consideration, the corresponding age, and the condition / fabric decay class (if available) determined during the last inspection of the object. These facts result in age-dependent and network-specific estimations of transition probabilities from one class to the next. The accuracy of the forecast correlates with the quality and the extent of the available inspection data. The forecast includes the following differentiations:

• Object not inspected;
• Object inspected;
• Object inspected multiple times

Further object-individual differentiations result from specific survival probability functions for different clusters.

In addition, the forecast model allows for an analysis of the residual useful life for each object. The analysis includes the determination of the changes in both the condition and fabric decay over time as well as the point in time where an object will have to be replaced (failure).

 

Case Example: Sewer section inspected once

In the following, it is assumed that the same sewer section from the previous example has been inspected once and thus, inspection data on its current condition are available. For the forecast calculation based on fabric decay class classification, a membership of 50 % each is assumed in the fabric decay classes “FDC 1” and “FDC 2”. This classification forms the starting vector for further forecasting (Figure 21). Compared to the uninspected sewer section, the knowledge about the sewer section’s fabric decay class at the point of inspection essentially increases the accuracy of the forecast, particularly in the short term.

In Figure 21, the forecast of the fabric decay class development for the exemplarily chosen sewer section is illustrated in five-year-steps. The initial distribution represents the fabric decay class distribution at the point of analysis (foremost column group). The probability of failure (FDC 5) increases continuously. After 30 years (age of the sewer section: 40 years), the sewer section is assumed to form part of the fabric decay classes FDC 3 and FDC 4 with a probability of 20 % each, whereas the risk of a final failure (FDC 5) already amounts to about 56 %.

In general, the physical life ends at the time of definite failure. Depending on the local influencing conditions (water protection zone, relevancy to the public right of way, relevancy of the sewer section for the drain and sewer system, etc.), an individual probability of failure can be defined as the criterion that denotes failure. Basically, it can be assumed that sewer sections with a probability of failure of more than 50 % no longer meet the minimum requirements [7].

An additional increase of the forecast quality can be achieved by including repeated inspections. In that case, both a starting vector and a subsequent vector are available for the forecast calculation.

Condition classes and condition survival probability functions are used for the forecast of sewer section conditions as the second structural assessment parameter (Section 5.4.3). The further course of action is analogous to that of the fabric decay class forecast.

An undisturbed network aging forms the basis for the forecasts illustrated in Figure 21, i.e. no intervening rehabilitation measures are taken. From an analytical point of view, this assumption is of essential importance, as this is the only way the network-specific deterioration speed can be clearly described.

 

5.4.5 Conclusion

The structural condition analysis according to STATUS_Sewer provides accurately defined assessment parameters for each sewer section, i.e. the condition class as a criterion for the rehabilitation urgency, and the fabric decay class as a criterion for the performance reserve. Their determination can be traced back right to the individual defects.

By means of the condition class, the network operator gets information on the temporal ranking of required rehabilitation measures. The fabric decay class provides insights on the type and extent of the required rehabilitation measures. Thus, the consideration of both assessment parameters in parallel represents an essential planning aid in creating a requirements list for rehabilitation measures and a corresponding investment plan.

Against the background that available inspection data are often in part many years old, STATUS_Sewer provides a present time forecast using an aging model, whereby the condition status data are updated in relation to the time of assessment.

For all objects with a sufficiently large database, the forecast model yields both an overview of the fuzzified condition and fabric decay classes at the time of assessment in tabular form as well as a chronological forward projection, e.g. for the next 40 years to come. A graphic illustration of these results, for the condition and fabric decay classes of example sewer sections in a drain and sewer network at the time of assessment, can be found in Figure 22 and Figure 23. A huge number of the drain and sewer sections in the drain and sewer network shown here have rankings in the condition classes CC 4 and CC 5 and thus, have a high rehabilitation urgency (Figure 22).

If, however, the fabric decay classes of the sewer sections in the exact same drain and sewer system (Figure 23) are considered, the result is less dramatic. This example highlights the difference between the condition and fabric decay class, which, in addition to the potential severity of defect (PSD), also considers the defect concentration value (DCV). The requirements list that takes both the condition and fabric decay classes into account would, in this case, considerably differ from a requirements list that is simply based on the determined condition classes.

The chronological forward projection of the condition and fabric decay class changes under the assumption that, for the considered drain and sewer system, no changes are to be expected for future operation, maintenance and rehabilitation decisions (action principle “Current Strategy”) is shown in Figure 24 and Figure 25. Effects of a changed/optimised strategy can also be illustrated.

The development of the condition classes in Figure 24 shows how defects that should be fixed in the short term and that are currently estimated at 24 % double to more than 50 % over a period of 40 years. The development of the fabric decay classes (Figure 25) in the same time frame shows an increase of the sewer sections with a low or depleted performance reserve from 35 % up to about 80 %.

Thus, the network operator is provided with useful information which helps to reveal and quantify risks with the current course of action even at an early stage. It forms the basis for strategy optimisation.

The informative value of such long-term forecasts largely depends on a detailed analysis of all mentioned aspects from the point of view of an engineer. It is absolutely indispensible to ensure a proper forecast quality. On the one hand, the forecasts must provide similar results for similar data and thus, be stable; on the other hand, the results must illustrate the actual network aging process as precisely as possible.

The forecast model from of STATUS_Sewer was checked with the help of available repeat inspections using ex-post forecasts. In the process, the forecasted values derived from the initial inspection were contrasted with the actual values determined in the repeated inspections in order to verify the fabric decay class development.

As a result, the average deviation for a forecasted period of time of 10 to 15 years amounted to 0.14 fabric decay classes. In relation to a scale of five fabric decay classes, this results in an average deviation of 2.8 %. Against the background of a long time frame in the forecast, this rather small deviation can be classified as being negligible. Furthermore, that slight insecurity is fully offset by the significant increase in knowledge about the future network development and, thus, a clear increase in planning reliability. A better forecast quality can be achieved for repeatedly inspected sewer sections as, in these cases, both an initial distribution (inspection result #1) and a subsequent distribution (inspection result #2) are provided [8].

The following links will take you to the first and second part of the article:

• "Evaluation models for the assessment of the structural and operational condition of drain and sewer systems – Part I"
• "Evaluation models for the assessment of the structural and operational condition of drain and sewer systems – Part II"
   

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