ABSTRACT
The Mw6.2 22 February 2011 and Mw6.0 13 June 2011 earthquakes caused significant and wide-spread damage to the Christchurch infrastructure networks, including the Christchurch water networks (potable, waste, and storm). The transient and permanent ground deformations generated by these two earthquakes severely damaged buried pipes in some areas resulting in high repair rates (number of repairs per kilometre of pipe exposed), with many of the repairs in areas affected by liquefaction and lateral spreading.
It is demonstrated in this paper that by utilising ground motion maps in Modified Mercalli Intensity, the observed liquefaction maps and the water supply pipe repair record dataset for both the earthquake events, simple fragility models for buried pipes can be developed. The models require basic pipe characteristics (pipe size and material type) and shaking intensity to provide an estimate of repair rate for pipes in different ground conditions. Applying these models to other areas requires suitable liquefaction susceptibility maps. The basic input data requirements will allow the fragility models to be implemented in a risk modelling tool to rapidly evaluate the potential earthquake damage to buried pipe networks elsewhere in New Zealand in future earthquakes.
INTRODUCTION
Access to reliable and uninterrupted water and sanitation services is fundamental to creating healthy and safe societies. Physical damage to the infrastructure networks when exposed to a natural hazard such as an earthquake, and the resulting disruption to the services they provide, can result in multiple consequences (e.g. financial losses, impact on social well-being, impact on environment). The 2010–2011 Canterbury earthquakes severely damaged water, wastewater and storm water networks in Christchurch causing widespread interruptions to services provided by these networks in the months following the earthquakes. Many systems were classified as being on the brink of failure (Eidinger et al. 2012). A boil-water notice was imposed for two weeks following the MW6.2 22 February 2011 earthquake due to concerns about contamination of the fresh water sources and possible risk of breakouts of disease and sickness in the community. Damage to the wastewater treatment plant and other components in the network led to about 60 million litres of untreated wastewater being discharged directly into multiple local water bodies and streams, increasing the risk of contaminating the underground aquifers (Eidinger et al. 2012). To combat disrupted services, and to reduce potential health impacts on the community, hundreds of temporary fresh water tanks and pumps, along with about 10,000 portable toilets and 30,000 chemical toilets were distributed around the city. While the above response efforts were made, repairs on the damaged networks continued to restore the affected services. From October 2010 to February 2014, over 8,500 repairs on the water supply network, and over 1,700 repairs on the wastewater network, were undertaken. The damaged storm water network was also inspected and repaired, but at a much lower rate. A total of about 21,700 faults were discovered in the network up until March 2015, of which around 20,500 needed repair or some other attention. The exhaustive damage and repair data compiled, especially relating to the water supply pipes, provided an opportunity to develop empirical fragility functions for buried pipes, which will be the focus of this paper.
Fragility functions are an important component of risk and vulnerability assessments of assets exposed to natural hazards. A key characteristic associated with the Canterbury earthquakes was the strong shaking accompanied by widespread and severe liquefaction in many areas. This resulted in excessive and non-uniform ground deformation such as: large vertical and/or lateral displacements; cracks and fissures in the ground; ground distortion. It was observed that the buried pipes were generally subjected to transient ground deformations (from shaking) and permanent ground deformations (mostly due to liquefaction effects) often above the capacity of the pipelines to sustain such movements/loads, thereby resulting in widespread and numerous pipe faults (i.e. leaks and/or breaks) (Cubrinovski et al. 2014.). Utilising the pipe repair database many fragility functions have been derived (e.g. O’Rourke et al. 2014, Bouziou & O’Rourke 2017). However, if they are to be used for forecasting pipe damage, such formulations require calibration using input hazard parameters and these can be difficult to predict, can be highly variable or require significant effort to measure well (Toprak et al. 2019). In this paper, it is demonstrated that simple fragility models (originally developed as part of research work completed by Sadashiva et al. (2019)) can be developed. The steps taken to develop these models and their limitations are discussed in the following sections.
OVERVIEW OF THE PIPE NETWORK
Information on the water supply network was collected from Christchurch City Council (CCC), Stronger Christchurch Infrastructure Rebuild Team (SCIRT 2013) and City Care Ltd. At the time of 2010-2011 Canterbury earthquakes, the pipe network was made up of mains and sub-mains, each about 1,750 km long (see Table 1). The pipes have also been classified based on the pipe material information that was available in the dataset; the summary of this is given in Table 2.
Table 1: Summary of Main (dia. ≥ 100mm) and Sub-Main (dia. < 100mm) water pipes in the network
| Pipe Type | Mains Length | Sub-Mains Length | ||
| km | % Total
Length |
km | % Total Length | |
| Asbestos Cement (ND*) – AC | 880.5 | 50.4 | 22.4 | 1.3 |
| Concrete Lined Steel (D*) – CLS | 56.5 | 3.2 | 0.0 | 0.0 |
| Ductile Iron (D*) – DI | 51.4 | 2.9 | 0.2 | 0.0 |
| Cast Iron (ND*) – CI | 208.5 | 11.9 | 18.7 | 1.1 |
| Modified Polyvinyl Chloride (D*) – MPVC |
141.7 | 8.1 | 0.6 | 0.0 |
| Polyvinyl Chloride (D*) – PVC | 203.2 | 11.6 | 69.2 | 3.9 |
| Steel (D*) – S | 49.5 | 2.8 | 1.0 | 0.1 |
| Unplasticised Polyvinyl Chloride (D*) – UPVC |
112.0 | 6.4 | 3.6 | 0.2 |
| Galvanised Iron – GI (ND*) | 2.1 | 0.1 | 210.0 | 12.0 |
| High Density Polyethylene (D*) – HDPE | 1.0 | 0.1 | 922.2 | 52.6 |
| Medium Density Polyethylene – MDPE80 (D*) |
2.8 | 0.2 | 458.9 | 26.2 |
| Other (also includes unknown pipe type)** | 36.5 | 2.1 | 46.9 | 2.7 |
| TOTAL | 1745.8 | 100.0 | 1753.5 | 100.0 |
| *Ductile (D) or Non-Ductile (ND) **mixed material ductility | ||||
Table 2: Pipe material distribution in the water network
| Pipe Type | Total Length (m) | Pipe Material (% total length) | ||
| Ductile | Non-Ductile | Unknown | ||
| Mains | 1745.8 | 36.9 | 62.5 | 0.6 |
| Submains | 1753.5 | 83.2 | 14.3 | 2.5 |
| Combined | 3499.3 | 60.1 | 38.4 | 1.5 |
EARTHQUAKES CONSIDERED
The MW7.1 earthquake on 4th September 2010 (primary event in the Canterbury Earthquake Sequence) was followed by several hundred aftershocks. This included two major aftershocks, the MW6.2 22 February 2011 and the MW6.0 13 June 2011 earthquakes (Figure 1), that caused significant and wide-spread damage to the pipe networks. We used pipe damage and hazard data relating to these two events to develop the fragility models.
Figure 1: Canterbury Earthquake Sequence (GNS Science 2014)
Estimating shaking intensities
Shaking intensities in terms of Modified Mercalli (MM) Intensity experienced at different parts of Christchurch were not fully available at the time of this study. Therefore, an existing ground motion prediction equation or attenuation model had to be used. These methods estimate the expected severity of ground motion intensity at any given place, due to an earthquake elsewhere. For this study we used the Dowrick & Rhoades model (Dowrick & Rhoades 2005, Smith 2002) to estimate the shaking intensity at each pipe location. For this, the pipes in the network were discretised into segments with a length equal to or less than 20m, and their centroid used as the location of each pipe segment. Since there are uncertainty parameters in the Dowrick & Rhodes model, e.g. inter-event and intra-event parameters, which are determined randomly within their predefined ranges, different intensity outcomes are possible. One of such realisations was used to develop a shaking intensity layer and correlate with damage to develop the repair rate models.
The Dowrick & Rhoades model considers not only the magnitude of the earthquake and its location, but also its focal depth, mechanism and the orientation of the fault source. It describes the attenuation of MM Intensity for New Zealand earthquakes by defining shaking intensity contours called isoseismals (which delineate zones of various strengths of shaking). An ‘intensity zone’ is then the area between two adjacent isoseismals; for example, the MM5 Zone is the area between the MM5 and MM6 isoseismals.
Because of the way in which the MM intensity scale is defined, the intensity values are constrained to be integer numbers; they are discrete variables. In reality, the attenuation of shaking is a gradational process, and for attenuation modelling the intensities are regarded as continuous variables – that is, they are regarded as having fractional values. To this end, the MM5 isoseismal is defined as being intensity 5.0 in the attenuation model, MM6 as 6.0, and so on. The intensity at the point midway between the MM5 and MM6 isoseismals is 5.5. Note that the model predicts the radii of continuous-variable isoseismals, rather than integer-variable ones.
Observed liquefaction severity
As mentioned earlier, a key characteristic associated with the Christchurch earthquakes was the strong shaking accompanied by widespread and severe liquefaction in many areas. The liquefaction severity maps (Figure 2) utilised in this study were produced by Tonkin & Taylor Ltd using information collected from drive-by surveys where evidence of liquefaction and its effects was mapped, including visible lateral spreading and sand and water ejection from the ground surface (Canterbury Geotechnical Database 2013).
Based on the severity of the manifestation observed, liquefaction was divided into six classes as shown in Figure 2. These observed liquefaction severity classes were then mapped (see Table 3) to liquefaction susceptibility classes (Dellow et al. 2003), which are used for formulation of pipe fragility models in this study. By spatially joining the pipe segment centroid locations with the observed liquefaction severity maps, the liquefaction classes were assigned to the pipe segments.
Figure 2: Observed liquefaction severity maps from Tonkin & Taylor Ltd for the February (on left) and June earthquakes (on right). The dots represent pipe faults identified in the water supply network
Table 3: Liquefaction severity and susceptibility class mapping
| Observed liquefaction severity class | Liquefaction susceptibility class |
| Not observed, presumed no liquefaction | None-to-Low |
| No land damage observed | |
| Minor land damage but no observed liquefaction | |
| Moderate liquefaction but no lateral spreading | Moderate |
| Severe liquefaction but no lateral spreading | High |
| Moderate to major lateral spreading | Very high |
| Severe lateral spreading |
PIPE DAMAGE DATA
Pipe damage information was determined using water supply pipe repair data supplied by City Care Ltd. Location of damaged pipe sections was found to be primarily from surface observations and pressure changes. From the repair data it was observed that various contractors who worked on pipe repairs often used different terminologies (e.g. ‘AC pipe replaced’, ‘3 m pipe repaired’) when recording the repair processes. The repair notes typically contained limited information about the type of repair or cause (i.e. leak or break), repair date and length of pipe repaired. However, despite above challenges relating to the data, the dataset still contained valuable information that provided insight to understand the performance of the buried pipes during the earthquakes and the opportunity to develop the fragility models for buried pipes.
The damaged water network was repaired (as much as practical) after each event. The pipe repair dataset generally contained the inspection dates (or repair request dates). This information was helpful to relate an earthquake to an observation of damage and subsequent repair. To calculate the time taken to restore the network after each event, or the period within which all reported damage could be associated with the event and was not pre-existing damage or damage caused by the previous event in the sequence, O’Rourke et al. (2014) suggest that as the network is restored the cumulative rate of repair (repairs per day) follows a pattern of initial high rate of repair, followed by a transient state with an intermediate repair rate, and finally a steady state of repair with a rate close to the pre-earthquake rate of repairs (i.e. ‘business as usual’). The beginning of the steady state of repair shows where the repair period associated with the event ends. Such a tri-linear trend was possible to be established from the repair data. For the 22nd February 2011 earthquake, the change to a steady state of repair occurs around 15th April 2011 therefore repairs identified in the inspection process before 15th April 2011 were considered pipe faults directly related to the February earthquake. For the June event, the onset of transition to the steady state occurred two months after the earthquake in mid-August 2011.
PIPE FRAGILITY MODELS
The repair data relating to the February and June earthquakes were geospatially joined to the pipe network data. Then, the repair rates (or pipe fault rates) for each pipe class (combination of material type and size), MMI bin and liquefaction susceptibility class were calculated by dividing the number of repairs over the total length of the pipes exposed within the pipe class, MMI bin and liquefaction susceptibility class. Finally, to remove extreme repair rates that arose from low sample sizes (i.e. short total lengths), the calculated pipe repair rates were put through a screening criterion using a screening process proposed by O’Rourke and Deyoe (2004). This screening process removed all repair rates that were based on a total length less than the minimum length specified by the criteria. The repair rates left after this screening process were determined to be within 50% of the true rate with 90% confidence. The screening process initially limited the number of fragility models we could develop because of the large variety of pipe types and sizes leading to a limited number of data points passing the screening criteria and becoming available for constructing the repair rate equations. To overcome this limitation, the available repair data were combined into fewer pipe classes. These pipe classes were defined by diameter (i.e. Mains or Sub-Mains), and material ductility (i.e. Ductile or Non-Ductile). To provide additional data for the Non-Ductile Mains category, repair rates for the asbestos cement and cast-iron pipes from the literature (ALA 2001) were included. Some of the other categories still lacked data which affected the statistical robustness of the fragility models developed; this can be seen in below section.
Results
A total of twenty fragility classes were defined (see Table 4). For each class and earthquake event, the repair rates were calculated for each MM intensity bin and subjected to the screening process. The ‘passed’ repair rates were then used to formulate the fragility models. Where repair rates from a different event for the same intensity bin passed, an average repair rate was calculated for the intensity bin and used.
Repair rates seem to increase with liquefaction severity (as expected). For most of the ‘None-to-Low’ liquefaction susceptibility related classes, repair rates increase with shaking intensity. Relationship between repair rate and MM intensity was possible to be established for such cases. However, for higher liquefaction severity cases (i.e. Moderate, High and Very High categories), limited data in most cases restricted our ability to draw relationships between repair rate and shaking intensity. From the passed repair rate data points, a flattening trend was generally observed. Although repair rates increased with changing MMI, they increased more as the level of liquefaction susceptibility increased. Once liquefaction has occurred in an area, the extent and severity of pipe damage does not change appreciably as the shaking intensity increases. This makes the threshold intensity at which damage from liquefaction occurs important. For areas vulnerable to liquefaction-induced ground damage, the damage can be reported through average repair rates when MM intensities are above the threshold for liquefaction to occur. In this study this threshold was observed to be at MM8.
Best-fit curves developed for some of the pipe classes for the ‘None-to-Low’ liquefaction susceptibility category are shown in Figure 3 and Figure 4. Only two repair rate data points were available for ductile mains in areas with little or no liquefaction; therefore, a fragility curve for the ductile mains in this liquefaction category was produced by using the best-fit curve for the non-ductile mains and scaling it to pass through the mean of the two ductile mains repair rate points (y-axis) and the respective MM intensities (x-axis). Figure 3 shows these curves.
A large proportion of the non-ductile sub-mains in the network (see Table 2) are represented by Galvanised Iron (GI) pipes. The repair rates for such pipes were found to be much higher (~5 to 9 times) when compared with the repair rates for the ductile sub-mains. The same ratio in the mains category was found to be ~2.6 (2 to 3.5 times lower). Therefore, the GI pipes were excluded from the non-ductile submains category and a separate class was defined for them. The high repair rates for GI pipes could be attributed to their small size (mostly of dia. ≤ 25mm) and their age (mostly old and possibly also corroded).
The repair rate curve for the non-ductile sub-mains (excluding GI pipes) was developed by scaling up the ductile sub-mains curve assuming the same 2.6 ratio, as in the mains category, applies. A similar approach was taken to calculate the repair rate parameters for such pipes in areas with higher liquefaction susceptibilities.
The calculated repair rate (RR) parameters are summarised in Table 4.
Figure 3: Mean pipe repair rate curves for Mains: ‘None-to-Low’ liquefaction susceptibility case
Figure 4: Mean pipe repair rate curves for Sub-Mains: ‘None-to-Low’ liquefaction susceptibility case
Table 4: Pipe fragility models
| Pipe Class | Liquefaction Susceptibility Class | Fragility Class | RR [km-1] = a × MMI b | RR [km-1] | ||||
|---|---|---|---|---|---|---|---|---|
| a | b | R2 | Median | Mean | Std. Dev. | |||
| Ductile
Mains |
None-to-Low | DM-LL | 3.10e-11 | 10.116 | – | – | – | – |
| Moderate | DM-ML | – | – | – | 0.55 | 0.55 | 0.18 | |
| High | DM-HL | – | – | – | 0.61 | 0.61 | – | |
| Very High | DM-VHL | – | – | – | 2.58 | 2.59 | 0.06 | |
| Non-Ductile
Mains |
None-to-Low | NDM-LL | 8e-11 | 10.116 | 0.903 | 0.35 | 0.39 | 0.34 |
| Moderate | NDM-ML | 6e-6 | 5.688 | 0.768 | 1.40 | 1.52 | 0.70 | |
| High | NDM-HL | 2e-10 | 10.773 | 0.815 | 2.79 | 3.00 | 2.31 | |
| Very High | NDM-VHL | – | – | – | 5.42 | 6.21 | 5.33 | |
| Ductile
Sub-Mains |
None-to-Low | DSM-LL | 3e-9 | 8.339 | 0.991 | 0.18 | 0.22 | 0.18 |
| Moderate | DSM-ML | 2e-9 | 8.966 | 0.895 | 0.46 | 0.42 | 0.23 | |
| High | DSM-HL | – | – | – | 0.61 | 0.61 | 0.53 | |
| Very High | DSM-VHL | – | – | – | 1.91 | 1.90 | 0.36 | |
| Non-Ductile
Sub-Mains (excluding Galvanised Iron) |
None-to-Low | NDSM-LL | 7.75e-9 | 8.339 | – | – | – | – |
| Moderate | NDSM-ML | – | – | – | 1.19 | 1.18 | – | |
| High | NDSM-HL | – | – | – | 2.79 | 3.02 | – | |
| Very High | NDSM-VHL | – | – | – | 4.02 | 4.55 | – | |
| Galvanised Iron Sub-Mains | None-to-Low | NDSM-LL | 2e-9 | 9.441 | 0.893 | 1.78 | 1.88 | 1.18 |
| Moderate | NDSM-ML | – | – | – | 6.36 | 6.11 | 1.56 | |
| High | NDSM-HL | – | – | – | 8.51 | 8.50 | 0.37 | |
| Very High | NDSM-VHL | – | – | – | 10.85 | 10.86 | 3.30 | |
CONCLUSIONS
Fragility models are an important component of risk and vulnerability assessments of assets exposed to natural hazards. This paper demonstrated how simple fragility models for pipes can be developed by utilising the water supply pipe repair data and earthquake hazard relating to the Mw6.2 22 February 2011 and Mw6.0 13 June 2011 Christchurch earthquakes (one realisation used to develop shaking intensity layer). The models developed following the approach taken require basic pipe characteristics (pipe size and material type), shaking intensity and suitable liquefaction susceptibility maps.
Simple relationships between repair rate (i.e. number of pipe repairs per km of exposed pipe length) and MM intensity was established for pipes buried in ‘None-to-Low’ liquefaction susceptible ground. For pipes in a ground with higher liquefaction susceptibilities, average repair rates have been proposed. Simplicity of the models from this study allows them to be easily implemented in a risk modelling tool to rapidly evaluate the potential damage to similar buried pipe networks elsewhere in New Zealand and overseas in future earthquakes. The models may not be appropriate for use in detailed assessments and caution must be exercised due to the limitations/assumptions behind the derived models as explained in the paper.
ACKNOWLEDGEMENT
The funding provided by the New Zealand Ministry of Business, Innovation and Employment (MBIE) that enabled this research is gratefully acknowledged. The authors are also thankful to many individuals and industry bodies for their input to this study, the supports of SCIRT, City Care Ltd and WSP (formerly Opus Research) have been particularly valuable. Funding support to present the work at this conference is from GNS Science research project: Built Environment & Performance, Social Vulnerability, Evolving Landscapes Project.
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