SEISMIC DAMAGE ASSESSMENT OF POTABLE WATER PIPELINES

4th International Conference on Earthquake Engineering Taipei, Taiwan October 1-13, 006 Paper No. 47 SEISMIC DAMAGE ASSESSMENT OF POTABLE WATER PIPELINES Chin-Hsun Yeh 1, Ban-Jwu Shih, Che-Hao Chang, W.Y. Walter Chen, Gee-Yu Liu 3 and Hsiang-Yuan Hung 4 ABSTRACT Seismic damage assessment of potable water systems is a very important task in proposing disaster mitigation plans. This paper adopts a traditional way to estimate the possible number of repairs of the buried pipelines under strong earthquakes, i.e., through regression analyses to obtain empirical formulas for estimating the repair rate of buried pipelines. Although peak ground acceleration, peak ground velocity, permanent ground ation, seismic intensity, etc., have been studied in the existing regression formulas of repair rate; however, these parameters are often taken into consideration separately. The existing regression formulas often over-estimate the damage of buried pipelines, especially in the region far away from seismic sources. This study aims to investigate the effects of ground shaking and permanent ground ation simultaneously in obtaining the regression formulas of repair rate. PGA is used to indicate the intensity of ground excitation and ground strain is used to indicate the degree of ground ation. The regression formulas will integrate with Taiwan Earthquake Loss Estimation System (TELES), which has been developed by the National Center for Research on Earthquake Engineering in Taiwan, to study their applicability and correctness. Keywords: seismic damage assessment, buried pipelines, repair rate, moving average method INTRODUCTION The catastrophic Chi-Chi earthquake with a main shock of Richter magnitude 7.3 took place in central Taiwan on September 1, 1999. Hundreds of aftershocks, several with Richter magnitude 6.5 or greater, occurred in the following days. The earthquake was caused by the rupture of Chelungpu fault with rupture length greater than 90 km and permanent displacement larger than 10 m. As a result, more than,400 people died, 11,000 wounded, and 100,000 were left homeless. The earthquake also caused severe damage and disruption to lifeline systems, especially the electricity and communications. Regarding the water supply systems, the damage to Shihgang Dam alone reduced 40% of water supply to Taichung metropolitan area. A major water-treatment plant at Fengyuan was severe damaged and a nearby main that crossed the fault was ed and blocked (Schiff et al., 000). The widespread damage to facilities and pipeline systems made water unavailable to many cities over a rather long period of time. A full restoration of the water supply in Taichung City took nine days. For some rural areas, it took an even longer time to resume. Observing the necessity, the principal objective of this study is to investigate the repair rate for buried water pipelines based on the repair (damage) data collected after the Chi-Chi earthquake. Regression models for the pipe repair rate with respect to seismic parameters, such as peak ground acceleration (PGA) and permanent ground ation 1 Research Fellow, National Center for Research on Earthquake Engineering, Taiwan, e-mail:chyeh@ncree.gov.tw Associate Professor, National Taipei University of Technology, Taiwan 3 Associate Research Fellow, National Center for Research on Earthquake Engineering, Taiwan 4 Assistant Research Fellow, National Center for Research on Earthquake Engineering, Taiwan

(PGD), are proposed. The regression models may be used in the seismic scenario simulation and risk assessment of water-supply systems in Taiwan in the future. Fig. 1 depicts the analysis framework for studying seismic repair-rate of buried water pipelines in this study. At the beginning, the study area (Taiwan region) was split into uniform 0.5 km 0.5 km grid cells to create a grid system. The grid cells were employed as the basic geographic units for spatial analysis of pipe inventory, repair points, seismic parameters, and so on. Secondly, the strong-motion records, monitored during the Chi-Chi earthquake, from the Central Weather Bureau (CWB), Ministry of Transportation and Communication were used to estimate the distribution of peak ground acceleration (PGA). Similarly, the global position measurements at control points, before and after the Chi-Chi earthquake, by the Land Survey Bureau (LSB), Ministry of the Interior were used to estimate the distribution of permanent ground displacement (PGD). The attained PGD distribution was further used to estimate the distribution of ground strain. Finally, the water pipeline inventory and the associated repair data due to Chi-Chi earthquake were broken down into each grid cell. After partition of various kinds of data into grid cells, it became ready to carry out the spatial analysis of pipe repair rate and the further regression analysis. GIS Database Grid System Pipeline Length in Each Grid Cell Water Pipelines and Damage Data No. of Pipeline Repair Points in Each Grid Cell Displacements at LSB Control Points PGD Value at Each Grid Cell by Interpolation Ground Strain Value at Each Grid Cell by Numerical Differentiation Time Histories of Strong Motion at CWB Stations PGA Values at CWB Stations PGA Value at Each Grid Cell by Interpolation Repair Rate and the Corresponding Ground Motion/Displacement/Strain by Moving Average Method Regression Analysis Figure 1. The analysis framework for seismic repair rate of buried water pipelines It is worth noticing that, conventionally, the pipe repair rates were counted based on an equal interval value of ground motion intensity and/or ation. The defect of this approach, as has been pointed out Hwang et al. (004), is that the pipeline length may be quite different in each interval and the computed pipe repair rate may vary significantly depending on the selected interval value. In this study, a moving average method was proposed to deal with the ground motion intensity and/or ation. Conceptually, the moving average method is similar to the approach proposed by Hwang et al. in keeping an equal pipeline length in each interval. However, it has the merit to calculate the pipe repair rate at any desirable value of ground motion intensity and/or ation. The detail of the proposed method will be address later. THE STUDY AREA, WATER PIPELINE AND REPAIR DATA Water service in Taiwan (except Taipei City) is operated by the Taiwan Water Supply Corporation (TWSC). Of all the pipelines in the Chi-Chi earthquake-affected areas, there are 11 towns whose

pipeline inventory including location, diameter, material, etc., and the investigated pipe repair data had been collected, digitized and imported into a GIS-based database. These towns include Fengyuan, Jhuolan, Dongshih, Shihgang, Wufong, Lugang, Huatan, Fusing, Puli, Mingjian and Douliou. Fig. depicts the locations of these towns as well as the active faults in the neighborhood. The nominal diameters of water pipes in the database vary from 0 mm to,400 mm. Table 1 summarizes the diameter range, total length and number of repairs of large, medium and small pipes in the database. Fig. 3 illustrates the spatial distribution of water pipelines, repair points, the Chelungpu fault and grid cells around Fengyuan. Table 1. The pipeline information in the study area Pipe Type Diameter Range Length (km) No. of Repairs Large d > 150 mm 745 159 Medium 150 mm d 65 mm 1,989 854 Small d < 65 mm 740 * 1,801 * *: data might be incomplete Figure. The study areas, shown as shaded regions, include 11 towns in central Taiwan. The ruptured Chelungpu fault in Chi-Chi earthquake is also shown. It is noted in Table 1 that the average repair rate for small pipelines was several times larger than those of medium and large pipes. The small pipes, with nominal diameter less than 65 mm, are often used to connect distribution pipes to the customer ends. Many researchers do not include small pipes in their study as the corresponding data may be incomplete in the database. Furthermore, small pipes were usually discarded without repair if damaged and, as a result, won t be surveyed and documented after a major earthquake event. For this reason, small pipes are excluded from the analyses in this study. If required, the total length and the expected number of repairs of small pipes can be estimated from those of medium and/or large pipes.

After careful investigation of the pipeline inventory and repair-point database, more than 90% of the pipes and repair-points in the database belong to ductile pipes, such as PVC, PE, DI and steel pipes. Although the pipe material is one of the factors that influence the repair rate after earthquakes, we will not distinguish the pipe material for simplicity, in the following regression analysis. Figure 3. The spatial distribution of water pipelines, repair points, grid cells and the Chelungpu fault around Fengyuan DISTRIBUTIONS OF GROUND MOTION INTENSITY AND DEFORMATION Thanks to the completion of TSMIP (Taiwan Strong Motion Instrumentation Program) in 1997, CWB operated the densest modern digital strong-motion instruments in the world in the last century. More than 400 sets of three-component free-field ground motions were well recorded during the Chi-Chi earthquake. Here, the PGA value at each CWB strong-motion station referred to the geometric mean of PGA values at the two horizontal directions as PGA = PGA NS PGA EW (1) where PGA NS and PGA EW are the PGA values in the east-west direction and north-south direction, respectively. Then, the PGA value at each grid cell is calculated through numerical interpolation (and extrapolation). In order to prevent the undesired peaks and dips that might be artificially generated, the algorithm of minimum curvature is employed for the numerical interpolation. Fig. 4 depicts the attained PGA distribution caused by the earthquake as well as the CWB strong-motion stations which had successfully recorded the ground motion during the earthquake. While for the PGD, the database of high precision GPS survey of the LSB s position control points before and after the Chi-Chi earthquake has been got together by Chang et al. (004). This database serves as a good basis for finding out the actual change in topography in Taiwan caused by the earthquake. Similar to the numerical interpolation for attaining the PGA distribution, each component of the displacement field (u,v,w) can be separately estimated from the measured value at each LSB control points. The only difference here would be that the displacement field in the hanging wall area and the corresponding one in the footwall area have to be estimated separately to preserve its discontinuity along the Chelungpu fault. Finally, we may have the PGD distribution by calculating the magnitude of displacement vector at each grid cell, see Fig. 5.

Figure 4. The estimated PGA distribution in the Chi-Chi earthquake is shown. The CWB strong-motion stations around the study areas are also shown as circles. From the attained distribution of PGD values in three directions, the strain can be derived through direct calculation. Consider the horizontal displacement field ( u, v) as a function of spatial variables x and y only, the components of strain tensor at the ground surface of any grid C, see Fig. 6, can be calculated by the central difference method as: u 1 ε x = = ( U E UW ) () x v 1 ε y = = ( VN VS ) (3) y 1 u v 1 ε xy = + = ( U N U S + VE VW ) y x (4) 4 where ( U E, VE ), ( U W, VW ), ( U N, VN ) and ( U S, VS ) are the horizontal displacements of the four adjacent grids, and is the width of grid cells. Once the strain tensor is calculated, the corresponding principal strains ( ε 1, ε ) can be obtained, too. Finally, the ground strain ε * of the grid C can be defined as the maximum magnitude of ε 1 and ε. Fig. 7 depicts the distribution of the attained ground strain.

Figure 5. The estimated PGD distribution in the Chi-Chi earthquake is shown. The LSB position control points around the study area are also shown as triangles. V N N U N V W W U W C V E E U E V S S U S Figure 6. The horizontal displacement components of the four adjacent grid cells for deciding the ground strain at grid C. PIPE REPAIR RATES AND REGRESSION ANALYSIS Based on the previous calculation, several spatial features, such as the total pipeline length and the number of repairs in each grid cell, the estimated PGA, PGD and ground strain at each center of grid cell in the Chi-Chi earthquake, were obtained. Overlaying these layers, it is ready to obtain the empirical relationship between pipe repair rate and various kinds of seismic parameters. The pipe repair rate is defined as the number of repairs divided by the pipeline length. Some researchers calculated the pipe repair rate and the seismic parameters in each grid cell and used the pairs of data directly in the regression analysis. Some researchers calculated the pipe repair rate by using pipelines determined from an equal interval value of the seismic parameter. They then performed simple regression analysis to establish a seismic vulnerability function. As was pointed out by Hwang et al. (004), these approaches are mathematically flawed, because the pipeline length may be quite different in each grid cell or within an equal parameter-value interval and the data points should have

different weights depending on the pipeline length in regression analysis. To overcome the defect, Hwang et al. proposed an alternative approach to determine the pipe repair rate. The pipe repair rate of each data point in the regression analysis is computed from the repair points with approximately equal pipeline length, which may associate with different interval values of seismic parameters. Then, a simple regression analysis is utilized to establish seismic vulnerability function, since approximately the same pipeline length is used in the calculation of pipe repair rate. Figure 7. The estimated ground strain in the Chi-Chi earthquake is shown. As an example, we selected the grid cells with ground strain less than 0.001 in the Chi-Chi earthquake and performed regression analysis of pipe repair rate with respect to PGA using Hwang's approach. Since the permanent ground ation in these grid cells were very small (see Fig. 7), the results can be deemed as empirical formulas of pipe repair rate due to ground shaking If each data point in the regression analysis covered 100 km pipeline length, the results are shown in Fig. 8 for both midsize and large-size pipes. As shown in the figure, the data points are unevenly spaced along the axis of PGA. Most of the data points are centered on the small PGA interval, thus they are sometimes insufficient to describe the seismic vulnerability function in the range of large PGA. Three models, i.e. power, logarithmic and linear models, were used in the regression analyses and the R value, which is normally used to measure the fitness of regression model, for each model was shown in the right-hand side of Fig. 8. It is noted that all of the R values were greater than 0.86 and the power model was the most suitable one in this case. In order to describe the trend of seismic vulnerability function in the range of large parameter-value and to facilitate selection of proper regression model, a moving average method was used in this study. An equal interval value of seismic parameter was selected at the beginning. The pipe repair rate of each data point was computed from the repair points with approximately equal pipeline length, as in the approach of Hwang et al.; while kept the average parameter value close to the specified one. The step-size along PGA axis was 10 cm /sec and the pipeline length per data point was 00 km in obtaining Fig. 9. A simple regression analysis was utilized to establish the seismic vulnerability functions. Comparing Figs. 8 and 9, which use the same pipeline inventory and repair data in the Chi- Chi earthquake, the trend of data points in Fig. 9 is clearer than that in Fig. 8. Furthermore, a larger

pipeline length per data point was used in the moving average method. If the same pipeline length per data point was used in the Hwang's approach, only very few data points could be obtained, the PGA range of data points would be smaller, and the results would be ambiguous in selection of a proper regression model. 10 1 0.1 Regression analysis of PGA The mid-pipe +++ data point power model (R = 0.987) logarithmic model (R = 0.914) linear model (R = 0.878) The Large-pipe data point power model (R = 0.965) logarithmic model (R = 0.867) linear model (R = 0.938) 0.01 0 00 400 600 800 Pga Figure 8. The grid cells with ground strain less than 0.001 in the Chi-Chi earthquake were selected and the regression analysis of pipe repair rate with respect to PGA (in unit of cm /sec ) was conducted using the approach of Hwang et al. (004). THE PROPOSED REGRESSION MODEL Since seismic damage to buried pipelines is affected by many factors such as site conditions, intensity of ground shaking and ation, and pipe parameters including pipe diameter, pipe material, joint mechanical property, etc., it is not easy to estimate the pipe repair rate analytically. Regression analysis is often required to obtain the relationship between pipe repair rate and influence factors based on the observed data. For simplicity, besides pipe diameter, we assume that the pipe repair rate was mainly affected by the intensity of ground shaking and the level of permanent ground ation. Furthermore, the two factors are assumed to be uncorrelated and the repair rates caused by these two factors can be added up. In other words, the pipe repair rate can be expressed as = + (5) where and are the pipe repair rates caused by the ground shaking and the permanent ground ation, respectively. It is noted that although other parameters such as peak ground velocity, Arias intensity and spectral intensity may be used in estimation of, only PGA is adopted in this study for some reasons. First, PGA is the most popular ground-motion intensity parameter and its attenuation form and site effect have been well studied in the literature. Secondly, it is easy to incorporate the regression formula in terms of PGA with seismic scenario simulation. As far as is concerned, the ground strain obtained in the previous section may be a good choice.

The Chelungpu fault is a thrust fault and its fault plane has a small dip angle (about 30 degrees). As a result, the ground motion and the permanent ation patterns in the hanging wall area were quite complicate and different from those in footwall area (see Figs. 4, 5 and 7). To avoid confusion in evaluation of Eq. 5, the regression analysis was divided into two stages. In the first stage, since the effect of permanent ground ation is significant only in the neighborhood of ruptured fault and in the hanging wall area, we excluded these regions to derive. After deducting the value of from the observed data, is derived using the rest part of the data in the second stage. In other words, we selected regions with ground strain less than 0.001, which was referred to as PGAdominate region, to evaluate the coefficients in the first term of Eq. 5. After deducting the repair rate due to ground shaking from those of observed data, the second term of Eq. 5 was calibrated using the rest part of data. 10 (number / km) 1 Regression analysis of PGA Mid-size pipe ++ Repair rate Point = 1.103 10-5 PGA 1.768 (R = 0.905) Large-size pipe Repair rate Point = 8.637 10-5 PGA 1.38 (R = 0.93) 0.1 0.01 0 100 00 300 400 500 600 700 800 Pga (gal) Figure 9. Using the same data in Fig. 8, the data points in the regression analysis of pipe repair rate with respect to PGA (in unit of cm /sec ) were obtained by the proposed moving average method. Several regression models, such as power, logarithmic and linear models, have been used in previous studies on the vulnerability function of buried pipelines. As shown in Figs. 8 and 9, a power model generally has good R value. Thus, a power model was adopted in the following study and it can be b expressed as y = ax, where y is the pipe repair rate (e.g.,, or ); x is the seismic parameter (e.g., PGA, PGD or ground strain); and a, b are unknown regression coefficients. The regression results of term has been shown in Fig. 9 and the estimated repair rates for largesize and mid-size pipes in the PGA-dominate region can be expressed as follows: Large-size pipe Mid-size pipe 5 1.38 = 8.637 10 PGA = 0. 93 5 1.768 = 1.103 10 PGA = 0. 905 R (6) R (7) The R values in the regression analyses of Eqs. 6 and 7 were greater than 0.9; thus, PGA is a suitable parameter to estimate the seismic vulnerability of buried pipelines in the PGA-dominate region.

In general, if a region suffers from large ground strain, it is normally near the ruptured fault or in the hanging wall areas, and is accompanied with large PGA. Thus, the effect of PGA could not be neglected and should be deducted from the pipe repair rate when calibrating the term of Eq. 5 using data in the large-strain region, i.e., non PGA-dominate region. The regression results of pipe repair rate with respect to ground strain (ε ) are shown in Fig. 10 and can be expressed as follows: Large-size pipe Mid-size pipe ε 0.701 = 7.849 ( = 0. 85 = 6.634 ε 0.381 ( = 0. 71 R ) (8) R ) (9) 10 (number / km) 1 Regression analysis of Strain Mid-size pipe ++ Repair rate Point = 6.634 Strain 0.381 (R = 0.71) Large-size pipe Repair rate Point = 7.849 Strain 0.701 (R = 0.85) 0.1 0.01 0 0.00 0.004 0.006 0.008 Strain Figure 10. Using data of the grid cells with ground strain greater than or equal 0.001, the pipe repair rate due to ground ation was obtained by regression analysis and moving average method. The R values in the regression analyses of Eqs. 8 and 9, though less than those in Eqs. 6 and 7, are both greater than 0.7. In view of the randomness caused by deducting ground shaking effect, the pipe repair rate is strongly correlated with the ground strain. The step size of moving average was 0.00 and the regression region included all the study area in obtaining Fig. 10. The pipeline length used to calculate the repair rate of large-size and mid-size pipe is approximately 150 km and 00 km, respectively. Combining Eqs. 6-9 in Eq. 5, the resultant regression model in terms of PGA and ground strain can be expressed as follows: Large-size pipe Mid-size pipe = 8.637 10 = 1.103 10 5 5 PGA PGA 1.38 1.768 + 7.849 ε + 6.634 ε 0.701 0.381 (10) (11) CONCLUSIONS Based on the high-resolution GPS measurements before and after Chi-Chi Taiwan earthquake at LSB control points, the permanent ground displacement and the associated ground strain were obtained at

each center of grid cell by interpolation. Combining information of permanent ground ation and ground shaking intensity makes it possible to study repair rate of buried pipelines due to the dual effects after strong earthquakes. In this study, the water pipeline inventory and the repair data in 11 towns around Chelungpu fault after the Chi-Chi earthquake were carefully analyzed. The study region covers wide ranges of PGA and ground strain; therefore, the regression results can be utilized in other applications without extrapolation. To fully utilize the investigation data, which is often rare and sparse in space, after strong earthquakes to calculate the pipe repair rate, a modified approach of Hwang et al. (004) together with a moving average technique is proposed to increase the resolution of data points in regression analysis. Regression formulas of pipe repair rates, classified by pipe diameters and in terms of PGA and ground strain, were obtained. Observing the R values in the regression analyses, PGA and ground strain are suitable parameters to assess the repair rate of buried pipelines. ACKNOWLEDGMENTS The authors thank the Central Weather Bureau, MOTC and the Land Surveying Bureau, MOI for providing the strong-motion records and the GPS measurements, respectively, in Chi-Chi Taiwan earthquake. The authors also thank the Taiwan Water Supply Corporation for providing the blueprints of water pipelines and the pipe repair sheets in several towns in central Taiwan after the Chi-Chi earthquake. Without these valuable data, it is impossible to conduct this study. REFERENCES Chang, C.-H., Y.M. Lin, W. Chen and B.J. Shih (004). "The Damage Ratio Estimation of Water Pipelines Due to Earthquake by Permanent Ground Deformation," Proc. 3rd Taiwan-Japan Workshop on Lifeline Performance and Disaster Mitigation, Taipei, Taiwan, NCREE-04-006, pp. 45-51. Hwang, H., Y.H. Chiu, W. Chen and B.J. Shih (004). "Analysis of Damage to Steel Gas Pipelines by Ground Shaking Effects during the Chi-Chi, Taiwan Earthquake," Earthquake Spectra, 0(4), pp. 1095-1110. Schiff, A. J. and A. K. Tang, eds. (000). Chi-Chi Taiwan Earthquake of September 1, 1999 Lifeline Performance, EIC, TCLEE Monograph 18, ASCE.