After adding the fields and spatially joining the water pipes with land conditions, the collected Wellington pipe information was added to the Cousins VBA model. Various changes had to be made to the model’s calculations and VBA code, as it was not suitable for achieving the research objectives. Originally the code was used for calculating how long it would take to restore water to each Wellington reservoir. As the focus of this study is on how contextual factors impact repair times, having multiple endpoints would lead to confusing results, where the exact influence of each contextual factor would be hard to define. Also, the required calculations would become far too complex. Furthermore, by using one endpoint, the repair times from the four different Wellington sources can then be compared to determine the lowest total repair time, fulfilling the fifth research objective. Out of the many endpoints available, the Karori Reservoir was chosen because of its ideal location at the foot of bulk water pipe network where the multiple pipes, used for transporting water from each source, combine (Fig 2.3). By calculating repair times after this confluence, each water source was able to be included in repair time calculations as the endpoints were the same. Additionally, as most of the network and each source were included, the behaviour of the entire network could be easily understood. Finally, in the original Cousins Model, Karori was predicted to receive a repair time close to the median time for all Wellington
Chapter: 4 Data Collection and Analysis
69 reservoirs (Cousins, 2013). Thus, when used in calculations, Karori could represent the whole Wellington Region.
Including each water source involved firstly changing the number of assets the code could calculate. Then, anything that related to the multiple reservoirs quoted in Cousins (2013); Nayyerloo and Cousins (2014) was removed and replaced with references to the four different water sources. Each source was treated separately to reduce complexity, where all the pipes from each source to the final endpoint were included in the calculations. This separation meant that some pipes were addressed multiple times. For example, the ring south of Ngauranga Gorge was present in all four calculations (Fig 2.3). For ease of computation, the different sections involved in each calculation, such as the Ngauranga ring, and the line up to Kaitoke were modelled for damage and repair times individually, then added together to give the total for each source (Fig 2.3 & 2.4)
4.2.4.1 Shaking Intensity Calculations
Overall the main damage calculation created by Cousins was kept the same. Firstly, the damage was predicted by calculating likely shaking intensities expected from a Wellington Fault Mw 7.5 event. This prediction was accomplished by using the Dowrick and Rhaodes Model, to create Modified Mercalli (MMI) isoseismals, based on the type of faulting, faulting mechanism, and depth of rupture (Dowrick & Rhoades, 1999). Then shaking intensities were given to the pipes based on the isoseismal that they fell inside. Once the base MMI was calculated for each segment, the impact from the soil around each pipe was then incorporated. 4.2.4.2 Soil Amplification Considerations
Each soil type amplifies the shaking by a different amount. For example, softer soils increase the seismic amplitude or intensity, due to loose easily mobile structures. While more rigid soils or rock, decrease the amplitude (Cousins, 2013). This amplification effect decreases with magnitude, as the base shaking intensity becomes more dominant with increasing earthquake size. In the model, each soil type was given a different amplification number that waned with magnitude (Nayyerloo & Cousins, 2014)(Fig 4.8). The various equations and calculations for this amplification are explained below.
Chapter: 4 Data Collection and Analysis
70 Figure 4.8 The increments made to the Dowrick and Rhoades MMI because soft soil amplification. The diagram is based on Cousins (2013).
Three equations, based on the Cousins Model, were used to calculate this amplification. Slight changes were made to the original equations from Cousins (2013) based on a discussion with the author whom after doing more research found flaws in his original design. Unfortunately, this new research was never published.
1) The soil amplification for low MMI’s, smaller than seven, was:
(< 7) = 0.25 × ( − 3)
Where X is the soil base number (Table 4.2)
2) For pipes located in moderate MMI’s, from seven through to ten, the amplification equation was:
(7 − 10) = ((−0.166667 × ) + 1.666667) × − 3 2
Where mm is equal to the base MMI obtained from the isoseismals.
3) Finally, for MMI’s greater than 10, an amplification factor of zero was used.
(> 10) = 0
Once calculated, the amplification factors were then applied to the predicted MMI values. The resulting altered magnitudes were used in all further equations such as pipe break rates.
(Eq 4.1)
(Eq 4.2)
Chapter: 4 Data Collection and Analysis
71 4.2.4.3 Break Rate Estimations
To calculate the predicted break rates the Cousins Model was used. This model firstly calculates failure rates based on the MMI only, then applies amplifiers that increase or decrease the failure rate.
Average Fail_rate(s) = 1600 × 10 . ×
4.2.4.4 Redundancies
One of these multipliers specified in Eq (4.4) is the child number. The child number was placed on the end of the calculation and divides the fail rate by the total number of breaks that need to occur. By dividing by the child number, the likelihood of failure lowers, as each child pipe must break for the section fail. For example, if the child number is two, then the probability of failure is cut in half. This method of calculating the redundancy was used instead of the more widely used equation (4.5) from Opus International Consultants Ltd (2017), due to the fact that it is not known which pipe segments along the parallel or redundant pipe will break in an event. Therefore, it is hard to know what probabilities to include in the calculation (Fig 4.9).
= 1 − ((1 − 1)(1 − 2) … )
Where x stands for the probability of failure of one parallel pipe line or segment.
4.2.4.5 Other added amplifiers
Other amplifiers include material type and diameter influences, which were added together, and then included into the equation as the segment multiplier. The amplification factors for each pipe attribute are shown in Table 4.4) below.
Table 4.4 Pipe attribute multipliers. Each of these numbers adds towards the segment multiplier.
Nonductile
materials Old Couplings Diameter < 600mm Welded Steel Pipe
6 2 1.5 0.2
(Eq 4.4)
(Eq 4.5)
A B
Figure 4.9 The relationship between parallel or redundant water pipes and the segmented network. Each different colour represents a different 20m pipe segment.
Chapter: 4 Data Collection and Analysis
72 The landslide and liquefaction influences were then added, by placing them as exponents in equation (4.6) following the assumptions made in Nayyerloo and Cousins (2014), and the conclusions around liquefaction damage in Sherson et al. (2015).
LIQ = 2.5^X LS=2.5^Y
Where X is the liquefaction susceptibility value, and Y is the predicted landslide hazard value.
Finally, the equation is then multiplied by the segment length, to convert the fail rate into a probability. This probability then divided by 1000 to convert it into kilometre units. = × ( ( ) . ) × × × × ( )
Equation 4.6 was used for every single pipe segment, except for sections that crossed the Wellington Fault, or pipes that lay in potential landslide drop-out locations, as pipes in these sensitive areas were assumed to fail automatically. Once the fail probability had been calculated, each pipe segment was then given a random number between 0 and 1. If the random number fell in the range of the probability from 0 to 1, then pipe segment failed. If not, the pipe survived. The break rate was then calculated by dividing the number of failures over the total length.
Repair Time Calculations
After the damage was approximated, repair times to Karori were then estimated. Firstly prospect times were calculated, by assuming that 0.1 days per km of pipe, was needed for locating broken pipes from surface observations (Cousins, 2013; Nayyerloo & Cousins, 2014). Then base repair times were calculated by giving each segment that broke a different time based on the pipe’s diameter. Large pipes with a diameter greater than, or equal to 600mm were assumed to take between two (Eq 4.7) (Eq 4.6)
Chapter: 4 Data Collection and Analysis
73 and three days to repair, while a standard value of one day was used for pipes with diameters less than 600mm, following the procedures in Cousins (2013) & Nayyerloo and Cousins (2014).