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The DOI for this manuscript and the correct format for citing the paper are given at the top of the online (html) abstract. Once the final, published version of this paper is posted online, it will replace the preliminary version at the specified DOI. Analytical Seismic Fragility Analyses of Fire Sprinkler Piping Systems with Threaded Joints Siavash Soroushian,a) S.M.EERI, Arash E. Zaghi,b) M.EERI, Manos Maragakis,a) Alicia Echevarria,b) Yuan Tian,c) and Andre Filiatraultc) For the first time, an analytical modeling methodology is developed for fire sprinkler piping systems and is used to generate seismic fragility parameters of these systems. The analytical model accounts for inelastic behavior constituents of the system including: threaded joints, solid braces, hangers, and restrainers. The model incorporates a newly developed hysteresis model for threaded tee joints that is validated by the experimental results of several tee subassemblies. The modeling technique at the sub-system level is validated using the experimental results of a sprinkler piping system. The methodology is used to obtain the seismic response of the fire sprinkler piping system of UCSF Hospital under a suite of ninety-six artificially generated tri-axial floor acceleration histories. After the component fragility parameters are obtained for the components of the system, three systemlevel damage states are defined, and a joint probabilistic seismic demand model is utilized to develop system fragility parameters. INTRODUCTION The seismic performance of critical facilities such as power plants, hospitals, and industrial units depends not only on the performance of the structural systems, but also on the functionality of their nonstructural systems, specifically fire sprinkler piping systems. Nonstructural systems are usually susceptible to the seismic damage because the shaking intensities that cause damage to them are lower than those that typically result in structural damage. In developed countries, the total loss due to the damage to nonstructural systems or damage resulting from the malfunction of nonstructural systems is much larger than what is related to the damage of a structure itself (Taghavi and Miranda, 2003). This is especially a) Dept. of Civil and Environmental Engineering, University of Nevada, Reno, MS 0258, Reno, NV 895570258 b) Dept. of Civil and Environmental Engineering, University of Connecticut, 261 Glenbrook Rd., Unit 3037 Storrs, CT 06269-3037 c) Dept. of Civil, Structural and Environmental Engineering, State University of New York at Buffalo, 222 Ketter Hall, Buffalo, NY 14260 true in the case of fire-following-earthquake scenarios when the fire sprinkler system fails to perform. Fire sprinkler systems are susceptible to several types of seismic damage. Fasteners and anchors connecting the system to structural members can be pulled out; sprinkler heads can break upon impact with adjacent structural or nonstructural components; couplings and pipe fittings may start leaking or break; pipes crossing separation joints in buildings that are not detailed for differential movement may undergo large deformation demands, as may pipes that are restrained at locations where they pass through rigid walls or floors (SEAOC, 2006). Nearly all of these failure types have been observed in past earthquakes in the United States including the 1964 Alaska Earthquake, the 1971 San Fernando Earthquake, the 1989 Loma Prieta Earthquake, and 1994 Northridge earthquake (Soroushian et al., 2011). In recent major earthquakes such as the 2010 Chile earthquake, most of the hospitals in the central south region of Chile were subjected to strong ground motion. A total of sixteen hospitals were inspected after the earthquake (Miranda et al., 2012). Four hospitals were closed due to excessive damage, and approximately 75% of function was lost in the remaining twelve (Gupta and Ju, 2011). In this earthquake, the damage to piping systems were mainly associated with the failure of pipe hangers, the braking of sprinkler heads due to impact with ceilings elements, leakage of threaded joints, etc. After the great 2011 Tohoku Pacific Earthquake, numerous structures were inspected. In the Tohoku Earthquake, damage to fire sprinkler systems and plumbing systems accounted for 10% and 27% of the entire cost of equipment damage to buildings, respectively (Mizutani et al., 2012). The percentage of cost of damage to the different components of fire protection systems is shown in a pie chart in Fig. (1.a). The damage to the piping adds up to approximately 50% of the total cost with Smoke outlets / duct 14% Others 4% Machinery 8% Dynamo 3% Water tank 4% Sprinkler heads 18% Piping 49% Water leakage 42% 0% 20% 40% (a) No water leakage 58% 60% 80% 100% (b) Figure 1. Damaged Parts of Fire Sprinkler System in the Tohoku Earthquake (Mizutani et al., 2012) 2 the damage to sprinkler heads second to that. Figure (1.b) shows that 42% of the piping systems with damaged parts exhibited water leakage (Mizutani et al., 2012). Over the last 20 years, several experiments have been conducted on piping systems; such as bending tests on sixteen simply supported pipe specimens (Antaki and Guzy, 1998), dynamic tests of twenty pipe specimens (Antaki and Guzy, 1998), shaking table experiments on four hospital piping assemblies (Zaghi et al., 2012), monotonic and cyclic tests on fortyeight pipe tee joints (Tian et al., 2012), dynamic test of full-scale piping systems (Soroushian et al., 2012), and dynamic tests of six piping subsystem configurations (Tian, 2012). The limited quantitative data collected from past earthquakes and the limitations of system-level experiments have resulted in a lack of knowledge in the modeling techniques of piping systems. A better understanding of the system-level response of these systems can be gained through reliable analytical models (Ellingwood and Wen, 2005) which incorporate effective probabilistic approaches, such as fragility analysis, to assist the technical community in assessing, managing, and reducing seismic risks. In this study, a hysteresis model is developed for threaded pipe joints. This model is validated using data generated after testing forty-eight piping tee joints at the University at Buffalo. This model was then used to simulate a piping subsystem that was tested at University at Buffalo. Afterwards, a fire sprinkler system layout incorporating a variety of commonly used sprinkler piping components (to make the outcome of this study being applicable for wide range of piping subsystems and systems) was adopted from the medical center building of the University of California, San Francisco (UCSF). A three-dimensional model of this piping system was built and subjected to ninety-six artificial tri-axial floor acceleration histories to assess the seismic demand placed on each piping component. Using a set of appropriate limit states, the piping component fragility curves are developed. Finally, system level fragility curves are generated by statistically combining the component fragility parameters. PIPING TEE JOINT TESTS AT THE UNIVERSITY AT BUFFALO Test Background A total of forty-eight tee joints, comprised of four different materials, diameters, and joint types, were tested at the Network for Earthquake Engineering Simulation (NEES) site at the University at Buffalo. A diverse database was developed on the cyclic response and damage 3 states of the tee joints; however, only the results comprising twenty experiments on the black iron threaded joints of the pipe diameters of 3/4 in., 1 in., 2 in., 4 in., and 6 in. are used in this study. Test Setup The test setup was composed of two pipe runs with a length of L on each side of the tee joint specimen (Fig. 2). One end of each arm was attached to the tee joint, and the other end was supported using a moment free connection to a load cell. One end of a perpendicular pipe segment, pointed by the arrows in Fig. 2, was attached to the tee joint and the other end connected to a hydraulic actuator, which applied a mid-span point load. To capture the leakage during the test, all of the specimens were 40 psi pressurized with water. The moment demand of the tee joints was calculated by multiplying the force measured by the shear load cells by the length of the lever arm, L. The cord rotation was obtained by dividing measurements the displacement using linear potentiometers attached to each side of the tee joint, by the length, L. Figure 2. Tee Joint Experimental Set-Up (Tian et al., 2012) Additional details of the test setup are presented in Tian et al. (2012). Summary of the Moment-Cord Rotation Responses Tee-joint subassemblies were subjected to a cyclic loading based on a study performed by Retamales et al. (2008, 2011). The subassemblies were subjected to increasing cycles of displacements to capture significant leakage of the tee-joint. This leakage occurred when the pipes slipped at the threads, and the sealant (Teflon tape) degraded causing a significant threaded damage. Due to the displacement limitation of the actuator, complete failure was not achieved (Tian et al., 2012). For each pipe diameter, three subassemblies were tested. Considering the left and right sides of the tee-joints, a set of six moment-rotation relationships was obtained for each pipe size. Figure 3 shows the examples of momentrotation hysteresis responses of tee-joints for different pipe diameters. This figure illustrates that the pinching is more pronounced in the larger diameter pipes. 4 Moment (kips-in) Black Iron Threaded- 3/4in. 2 10 0 5 -2 0 Black Iron Threaded- 1in. Black Iron Threaded- 2in. 40 20 0 -0.04 -0.02 Moment (kips-in) -4 -0.06 0 200 -5 0.04 -0.2 0.02 20 -0.1 0 Black Iron Threaded- 4in. -0.03 -0.02 -0.01 0 0.01 0.02 Black Iron Threaded- 6in. 400 200 100 0 0 -100 -200 -200 -0.02 40 0.2 -0.04 0.1 -0.01 0 0.01 0.02 0.03 -400 -0.015 -0.01 -0.005 0 0.005 0.01 0.015 Rotation (rad.) Figure 3. Moment-Rotation Hysteresis Response of Tee Joint Subassemblies with Different Diameters (Tian et al., 2012) THE DEVELOPMENT OF A HYSTERESIS MODEL FOR THREADED TEEJOINTS The experimental data from tee-joint subassemblies is utilized to develop an adaptable hysteresis material model using OpenSees (OpenSees, 2012) for the threaded joint of different pipe diameters. The “Pinching4" uniaxial material along with a "zeroLength" element are used to simulate the moment-rotation response of a threaded tee-joint. The “Pinching4” material enables the simulation of complex pinched force/momentdeflection/rotation hysteresis responses accounting for degradations under cyclic loadings similar to those shown in Fig. 3. This material model requires the definition of thirty-nine parameters as presented in Fig. 4.The key parameters of this material in the positive (P) and negative (N) directions: 1) points defining the backbone curve e(P-N)di, e(P-N)fi, 2) the ratio Force (dmax,f(dmax)) (ePd2,ePf2) (ePd3,ePf3) (ePd1,ePf1) (rDispP.dmax, rForceP.f(dmax)) (ePd4,ePf4) (*,uForceP.eNP3) Deformation (*,uForceN.eNF3) (eNd4,eNf4) (rDispN.dmin, rForceN.f(dmin)) (eNd1,eNf1) (eNd2,eNf2) (eNd3,eNf3) (dmin,f(dmin)) Figure 4. Pinching4 Material Properties (OpenSees, 2012) 5 of reloading/maximum historic deformation rDisp(P-N), 3) the ratio of reloading/maximum historic force rForce(P-N) 4) the ratio of negative (positive) unloading/maximum (minimum) monotonic strength uForceP(N), and 5) ratios defining the unloading stiffness degradation gKi. A detailed description of these parameters can be found in the OpenSees Manuals (OpenSees, 2012). Validation of the Hysteresis Model with Experimental Data for Tee-Joints "Pinching4" material model was calibrated using the tee-joint moment-rotation relationships of all the pipe diameters. For each pipe diameter, the moment-rotation hysteresis response, the value of cumulative hysteresis energy, and moment histories were used in the calibration process on a visual basis. Moreover, the parameters were calibrated in such a way that the maximum cumulative hysteresis energy stays within the ±10% range of the experimental values. The cord rotation histories were used as the inputs for the model. Due to the malfunction of some of the potentiometers, the moment-rotation relationships were not available on both sides of all the tee-joints, but a set of at least three momentrotation relationships were available for each pipe diameter. Figure 5 shows the aforementioned characteristics of the calibrated hysteresis model for one of the 3/4"-diameter Dissipated Energy (kip-in-rad.) Moment (kips-in) tee-joints. 0.75" Dia.-Specimen #2-Left End-Hysteresis Behavior 2 Analytical 1 Experimental 0 -1 -2 -3 -0.06 -0.04 -0.02 0 0.02 0.04 Rotation (rad.) 0.3 0.2 0.1 0 -0.1 0 0.2 0.4 0.6 0.8 1 Cumulative Rotation (rad.) 0.75" Dia.-Specimen #2-Left End-Moment History 2 Moment (kip-in) 0.75" Dia.-Specimen #2-Left End-Dissipated Energy 0.4 1 0 -1 -2 -3 0 2000 4000 6000 8000 10000 12000 14000 Steps Figure 5. Analytical-Experimental Comparison of Second 3/4" Specimen on Left Side of Tee Joint 6 After performing a sensitivity analysis (in such a way that the maximum cumulative hysteresis energy stays within the ±10% range of the experimental values) on the material parameters, ten parameters out of thirty-nine parameters were assigned a fixed value independent of the pipe diameter. The material parameters gK1 to gK4, and gKLim, all of which define the unloading stiffness degradation characteristic of the material, were set to the same value of gK (Table 1). The “cyclic damage” was used to determine stiffness and strength degradations. Thus, the values of gD and gF were assumed to be zero. The other twenty-nine parameters were used to match the shape of the analytical hysteresis curves to those obtained from experiments. Table 1 presents the values of important material parameters for different pipe diameters. Figure 6 illustrates the comparisons of analytical and experimental data for four different pipe diameters. Each material parameter has a relationship with the pipe diameter. This allows for the determination of these parameters for other pipe diameters through interpolations and extrapolations. Table 1. Sample Calibrated Pinching4 Parameters for Various Pipe Diameters Component ePf1 ePf2 ePf3 ePf4 eNf1 eNf3 eNf4 rDispP rForceP uForceP Name ePd1 ePd2 ePd3 ePd4 eNd1 eNd2 eNd3 3/4" Pipe Diameter eNd4 rDispN rForceN uForceN Specimen #3 Left End ... 0.32 0.001 0.7 0.005 1.8 0.015 1.85 0.023 -2.1 -0.028 0.30 0.30 0.80 0.80 ... -0.80 0.15 Specimen #3 Left End 1.5 0.001 -0.5 -0.95 -1.87 -0.001 -0.002 -0.010 ... 1" Pipe Diameter 3 -1.5 -6.1 -7.45 0.030 -0.001 -0.005 -0.020 ... 2" Pipe Diameter 0.5 0.8 -0.5 0.0001 24.34 0.023 -8 -13.5 -18 -0.001 -0.005 -0.010 ... 4" Pipe Diameter -19.5 0.023 -60 -105 -115 -0.001 -0.004 -0.010 ... 6" Pipe Diameter 210 -100 -200 -225 0.023 -0.001 -0.005 -0.010 ... -116 -0.020 3.34 0.008 4.3 0.025 ... Specimen #2 Left End ... 15 0.001 Specimen #3 Left End ... 60 0.001 Specimen #2 Right End ... 100 0.001 22 0.003 130 0.003 190 0.005 24 0.01 131 0.013 205 0.010 eNf2 125 0.013 -5 -0.035 0.2 0.2 -230 -0.023 0.4 -0.2 0.4 -0.1 0.60 ... ... 0.1 0.1 gK 0.50 ... 0.4 -0.1 ... 0.01 -0.25 0.001 0.15 ... 0.0001 0.0001 0.1 0.05 ... 0.0001 0.0001 0.7 ... 0.60 ... 0.30 ... Throughout the calibration process, a total of twenty sets of twenty-nine parameters for the "Pinching4" material were optimized based on all available experimental data. Although the results for each set of experiments were quite similar, there were minor discrepancies between the material parameters for the individual experiments of each set. Therefore, for the simplicity of the future analytical studies of the sprinkler piping systems (not only limited to 7 5 1" Dia.-Specimen #3-Left End 27 Analytical Experimental 2" Dia.-Specimen #2-Left End 15 0 0 Moment (kips-in) -5 -15 -10 -0.04 150 -0.02 0 0.02 -25 -0.035 0.04 4" Dia.-Specimen #3-Left End 250 -0.02 -0.01 0 0.01 0.02 6" Dia.-Specimen #2-Right End 100 50 100 0 0 -50 -100 -100 -150 -0.025 -0.018 -0.01 0 0.01 -250 -0.012 0.018 -0.005 0 0.005 0.012 Rotation (rad.) Figure 6. Sample Analytical-Experimental Hysteresis Comparisons of Different Pipe Diameters this study), one suite of material parameters was defined as the generic (representative) parameters for each pipe diameter, called generic model hereafter. To develop this generic model the following assumptions were made. 1) A symmetric moment-rotation hysteresis behavior was used, 2) the first point of the backbone curve, ePd1 (Fig. 4), was defined as 0.001 rad. This enabled the use of the average experimental moment values corresponding to 0.001 rad., 3) the rest of the three nonlinear rotation points of the backbone curve of the generic model, ePd2, ePd3, ePd4 (Fig. 4), were set to 0.005, 0.01, and 0.023 rad., respectively based on the calibrated backbone curve parameters of each set, 4) a linear interpolation was used to find the moment corresponding to the above mentioned rotations where the moment values at the calibrated backbone curves are unavailable. The average of these moment values for each set were used for ePf2, ePf3, and ePf4 (Fig. 4) to define the backbone curve, 5) the average calibrated values were used for the rest of the parameters needed to define the generic hysteresis response. Figure 7 shows the comparison of the generic model using the aforementioned procedure with sample experimental data from each set. It should be noted that the inconsistency between the experimental results of the three sets for each pipe diameter is much larger for pipes of smaller diameter. Therefore, larger error in the hysteresis behavior is present between the generic model and each of the three experimental sets. This error can be seen by comparing the generic analytical model and sample experimental results 8 of 1in. and 6in. pipe diameters. Table 2 also shows the generic model parameters obtained using the previously mentioned assumptions. 1" Dia.-Specimen #2-Right End-Hysteresis Behavior 5 2" Dia.-Specimen #4-Right End-Hysteresis Behavior 30 Generic-Analytical Experimental 20 10 0 0 -10 Moment (kips-in) -5 -0.06 -20 -0.04 -0.02 0 0.02 -30 -0.15 0.04 4" Dia.-Specimen #4-Left End-Hysteresis Behavior 200 50 100 0 0 -50 -100 -100 -200 0.01 0 0.06 300 100 0 -0.05 6" Dia.-Specimen #4-Right End-Hysteresis Behavior 150 -150 -0.015 -0.008 -0.1 -300 -0.007 0.02 0.025 -0.004 -0.002 0 0.002 0.004 0.007 Rotation (rad.) Figure 7. Sample Generic Analytical-Experimental Hysteresis Comparison of Different Pipe Diameters Based on pipe location and required water pressure, a wide range of pipe diameters is commonly used in sprinkler piping layouts. The test matrix of the University at Buffalo did not include all the pipe diameters that are typically found in a system. Thus, a procedure is proposed to fill this gap in the experimental data and enable estimation of the parameters of the generic hysteresis model for the missing pipe diameters. This methodology is explained in the following steps. First, the parameters of the generic models were plotted against the pipe diameter based on the experimental data (the average of three moment values obtained from the database of the component tests). The values of the moments corresponding to 0.001, 0.005, 0.01, and 0.023 rad. can be plotted against the pipe diameter because these rotations were kept constant for all diameters as shown in Figure 8. Then, the best polynomial curve was fit to the data for each parameter. Using these algebraic functions of pipe diameter, the modeling parameters were obtained for those pipe diameters that were not tested at the University at Buffalo. Also, for each proposed pipe diameter, linear interpolation between the two closest pipes diameters, which were obtained from the experiment was performed for the parameters except those that defined the backbone curves. Table 2 shows 9 the values of the modeling parameters obtained from this methodology for the missing pipe diameters. Figure 8 shows the trends of the modeling parameters for the “Pinching4” material (OpenSees, 2012) with respect to the pipe diameter. Table 2. Generic Pinching4 Calculated Parameters Pipe Name e(P-N)f1 e(P-N)f2 3/4" 1" 2" 4" 6" 0.47 1.50 9.75 63.83 105.00 1.19 3.37 20.18 114.03 224.38 1.25" 1.5" 2.5" 3" 3.5" 5" 1.04 2.96 20.91 34.15 48.78 90.24 8.24 14.30 44.54 63.27 84.41 162.29 e(P-N)f3 e(P-N)f4 rDisp(P-N) rForce(P-N) uForce(P-N) gK(P-N) 0.62 0.49 0.15 0.08 0.07 -0.27 -0.30 -0.03 -0.10 0.00 0.50 0.53 0.58 0.34 0.25 0.40 0.32 0.13 0.11 0.09 0.07 -0.23 -0.16 -0.05 -0.06 -0.08 -0.05 0.54 0.55 0.52 0.46 0.40 0.29 TEST SETS 2.00 2.36 0.07 4.07 5.08 0.03 22.81 23.43 -0.04 121.51 125.17 0.04 254.38 258.13 0.13 PROPOSED COMPONENTS 8.83 9.66 0.009 14.70 15.78 -0.008 46.10 48.07 -0.022 66.55 68.91 -0.003 90.17 92.88 0.017 180.03 183.59 0.081 First Moment of Backbone Curve at 0.001 Rad. 120 3 2 M1= -1.444D + 15.792D 100 27.533D + 13.606 Second Moment of Backbone Curve at 0.005 Rad. 250 2 M2= 4.8166D + 10.975D - 13.003 200 80 150 60 100 Moment (kip-in) 40 50 20 0 1 2 3 4 5 0 6 Third Moment of Backbone Curve at 0.01 Rad. 250 200 200 150 150 100 100 50 50 2 3 4 5 4 5 6 2 M3= 6.336D + 6.0535D - 8.636 1 3 300 2 0 2 Fourth Moment of Backbone Curve at 0.023 Rad. 300 250 1 0 6 M4= 6.2625D + 7.2411D - 9.1762 1 2 3 4 5 6 Nominal Pipe Diameter (in.) Figure 8. Sample Fitted Curves on Backbone Curve Parameters of the Generic Model VERIFICATION OF TEE-JOINT MODEL IN A PIPING SUBSYSTEM The piping subsystem tested at the University at Buffalo was used for verification of the developed tee-joint components. In this section a summary of the test setup is presented. 10 Test Background A two-story, full scale sprinkler piping subsystem was tested under dynamic loading using the University at Buffalo Nonstructural Component Simulator (UB-NCS). The UBNCS is a two level shake table that simulates the seismic motions of two adjacent floors (Fig. 9a). This equipment subjects its content to large magnitudes of acceleration, velocity, and interstory drifts. A more detailed description of the UB-NCS can be found in Mosqueda et al. (2008). The tested piping subsystem consisted of two 30 ft. by 11 ft. layouts over two adjacent floors. These two floor layouts were connected by a 15 ft.-long vertical pipe riser (Fig. 9b). To detect leakage, the specimen was filled with water under a typical city pressure of 40 psi. To simulate the interactions between the ceiling system and sprinkler heads, six of the sprinkler heads were placed in common ceiling tiles made up of acoustic material and gypsum drywall using thru-ceiling fittings that were suspended 2 ft above from the UB-NCS deck or outrigger beam (Fig. 9b). At the end of the branch lines of the first floor, 0.49lb additional weights were added to replicate the mass of longer branch lines. (e,f) (b,c) (d) (a) (b) (a) Figure 9. Test Set-Up for Sprinkler Piping Subsystem Testing (Tian et al. 2012b). The piping subsystem was hung from and braced to the UB-NCS per NFPA 13 (NFPA, 2011). The layout of the piping system, location of hangers and braces, and diameter of the pipes are shown in Fig. 10 for both floors. The hangers consisted of 3/8-in, 22- and 24-inlong threaded rods on the first and the second floors, respectively. Sway bracing was provided on the main run of pipe near the riser using1-in diameter pipes in both longitudinal and lateral directions. At the end of the main run of pipe on the first floor, a lateral brace was installed using the same 1-in diameter brace pipe (Fig. 10). On the second floor, the ends of 11 the branch lines were restrained with two diagonal 12-gauge splay wires, however no end braces were utilized on the branches of the first floor. Longitudinal sway brace Longitudinal sway brace Lateral sway brace Hanger 4in dia. Second floor Connection 2in dia. Hanger 2in dia. 4in dia. Lateral sway brace 2in dia. 1in dia. Hanger Wire restrainer Sprinkler head 2in dia. Hanger Hanger Sprinkler head 2in dia. 2in dia. 4in dia. Sprinkler head Hanger First floor Connection Hanger 2in dia. Sprinkler head 1in dia. Hanger Hanger Hanger 1in dia. 2in dia. Sprinkler head Lateral sway brace 1in dia. Sprinkler head Wire Restrainer (a) Wire restrainer Sprinkler head 1in dia. Hanger Hanger Wire Restrainer (b) (c) Figure 10. Piping System Plan View of (a) the First Floor (b) the Second Floor (c) and the Elevation View of the Riser Pipe (Tian, 2012) Bottom Displacement History D (in) 20 20 0 -20 0 50 V (in/sec) Top Displacement History Max = 23.2 in 0 Min = -23.7 in -20 5 10 15 20 25 30 35 40 45 50 55 60 0 Bottom Velocity History 50 Max = 33.8 in/sec 0 -50 0 1 A (g) Min = -27.7 in 5 10 15 20 25 30 35 40 45 50 55 60 Top Velocity History Max = 40.4 in/sec 0 Min = -36.1 in/sec -50 0 5 10 15 20 25 30 35 40 45 50 55 60 Bottom Acceleration History 1 Max = 0.76 g 0.5 Min =-40.5 in/sec 5 10 15 20 25 30 35 40 45 50 55 60 Top Acceleration History Max = 0.8 g 0.5 0 0 -0.5 -0.5 -1 0 Max = 27.2 in Min = -0.58 g -1 0 5 10 15 20 25 30 35 40 45 50 55 60 Min = -0.69 g 5 10 15 20 25 30 35 40 45 50 55 60 Time (sec) Figure 11. Sample of Achieved, Displacement, Velocity, and Acceleration Histories at Maximum Considered Earthquake (MCE) Level (Tian, 2012) 12 The loading history protocols used in this experiment were developed specifically for the qualification of nonstructural systems (Retamales et al., 2011). Figure 11 shows a sample of achieved loading histories corresponding to the Maximum Considered Earthquake (MCE). The experimental results of the piping subsystem under these excitations were used for validating the analytical OpenSees model. Further information about the test setup and loading protocol is provided in Tian (2012). Validation of the Analytical Model The pipes including the riser, main runs, branch lines, and sprinkler drops were modeled with “Force-Based Beam-Column” (OpenSees, 2012) elements with elastic gross section properties of the pipes. The threaded fittings of the branch lines and drop pipes were modeled using one "zeroLength" element on the either end of the pipes. These elements were defined using the nonlinear “Pinching4" material for the rotational degrees of freedom (DOFs) based on the specified characteristics of Table 2, while an elastic material with properties of the pipe cross section was used for the other DOFs. The hangers were modeled using “ForceBased Beam-Column” elements with a fiber-section consisting of the Giuffre-MenegottoPinto steel material (CEB, 1996), which is implemented in OpenSees as "Steel02" material. A modulus of elasticity of 29,000 ksi, yield strength of 85 ksi (Goodwin et al., 2007), and hardening slope ratio of 1% were assigned to the hangers. These hangers had pin connection to the pipes. The wire restrainers were modeled using pinned "truss" elements along with a tension only "Elastic-Perfectly Plastic (EPP) Gap" material with the modulus of elasticity of 29,000 ksi and tensile strength of 80 ksi (USG, 2010). The rigid seismic braces were modeled with “Force-Based Beam-Column” elements using elastic section properties of the 1-in. pipe. The connection of the seismic braces was assumed to be rigid at both ends. The schematic of the elements and materials are presented in Fig. 12. The mass of the piping system was determined using the wet weight of the pipes. An additional mass of 0.2 lb was used for each sprinkler head. The mass and weight of the system were concentrated at the nodal points. 13 Hanger Wire Restrainer 24 or 22" 24 or 22" Tee - Joint 3/8" Steel Threaded Adjustable ZeroLength + Pinching4 4 tight rap in 1.5" Fiber-Section + Steel 02 Hanger Gauge #12 Wire Truss + Tension EPP Gap Parameters Based on Table 2 Figure 12. Schematic of the Analytical Models for Main Components Data collected from the experiments was comprised of the displacement of the piping sub system measured relative to the reaction wall, the rotations at critical tee joints, the accelerations of the sprinkler heads at critical locations on the pipes, and the axial forces of the vertical hangers and wire restraints. The detailed instrumentation plan is reported in Tian (2012). The first three vibration periods of the piping subsystem based on experimental data are 0.58, 0.53, 0.46 sec, respectively. The corresponding periods obtained from the analytical model are 0.58, 0.55, 0.42 sec. A Rayleigh damping with a 3% damping ratio set to the first and the third modes of piping system was obtained from the calibration process. Considering the fact that the groove fit connections of the main runs and the riser pipes were modeled as rigid connections, the correlation between the dynamic characteristics of the analytical model and experimental data is acceptable. The responses of the elements labeled “a” through “f” in Figure 9 were used to compare the analytical and experimental results. They were selected because of the limited effect that the flexibility of the groove fit joints have on the response of these elements. Figure (13a-13f) compares the results obtained from the experiment and the analytical model. 14 x 10 -3 Experimental Analytical Rotation (rad.) 2 1 (a) 0 -1 Displacement (in.) 15 20 25 30 Time (sec) 35 40 45 50 2 6 (b) (c) Acceleration (g) Spectral Acceleration (g) -2 10 1 4 0 2 0 -1 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 -2 10 2 15 20 25 30 Time (sec) Period, T 40 (d) 20 0 -20 -40 10 15 20 25 30 Time (sec) Force (kips) 0.05 40 45 50 0.06 (e) 0.025 (f) 0.04 0 0.02 -0.025 0 -0.05 15 35 20 25 30 35 40 45 -0.02 15 20 25 30 35 40 45 Time (sec) Figure 13. Comparison of Experimental and Analytical Results: a) Tee Joint Rotation History at Location “a”, b) 5% Damped Spectral Acceleration at the Tip of the Branch Line Labeled “b”, c) Acceleration History at the Tip of the Branch Line Labeled “c”, d) Absolute Displacement History at the Tip of the Branch Line Labeled “d”, e), f) Axial Force in the Hanger Labeled “e”, and f) Axial Force at the Wire Restrainer Labeled “f” FRAGILITY STUDIES Seismic fragility curves are conditional probability statements describing the vulnerability a system under seismic loading on a statistical basis. This vulnerability is generally expressed in terms of some level of capacities (known as damage states) that have physical meaning in terms of repair costs and/or the system functionality in terms of the 15 down time. The conditioning parameter of these probabilistic statements is often a single measure of a seismic event such as peak floor acceleration (PFA). Incorporating a probabilistic assessment approach in piping systems, leads to a better understanding of the seismic vulnerability of these elaborate systems. This knowledge enables achieving less seismically vulnerable buildings in design. After the modeling methodology and the nonlinear properties of the elements were validated using the subsystem experimental results, the same modeling technique was used to complete fragility studies of typical sprinkler piping components and systems. The essential steps for generating the fragility curves are: 1) develop an analytical model, 2) generate a ground motion suite, 3) determine capacity estimates, 4) create probabilistic seismic demand models, and 5) fragility formulation (component and system level). Each of these steps will be presented in the following sections. Specifications of Hospital Fire Sprinkler Piping System The dimensions and layout of fire protection piping systems are individualized for each building and vary based on the architecture and occupancy of the building. Therefore, selecting a generic fire piping system is, to some extent, arbitrary. Slight modifications were implemented on the original design by redesigning the hangers and braces to meet the minimum spacing requirement of NFPA 13: Standard for the Installation of Sprinkler Systems (NFPA, 2011). In addition, the bracing system was changed from cable bracing to the solid sway bracing type that is commonly used in construction. In this study the geometric uncertainties were incorporated by using the large UCSF piping system which includes a variety of commonly used components such as main runs and branch lines of various diameters, hangers, seismic braces, wire restraints, tee joints, elbow joints, and sprinkler drops and heads. It also contains a sufficiently large quantity of each component which enables a better statistical evaluation of the seismic performance of each component within the system. It should be noted that due to the uncertainty of material properties and other parameters such as damping ratio, variability in many of the modeling parameters such as steel yield strengths, wire restrainers and pipe hanger failure forces, pipe hanger clip breakage force, and different anchorage ultimate strengths can be incorporated in piping systems. However, this model was developed using the same modeling technique and variables that were calibrated based on the experiments in University at Buffalo. 16 The piping system shown in Figure 14 covers an area of approximately 17000 sf. It is 250 ft long and 176 ft wide and has more than 900 threaded joints (649 1-in., 185 1.25-in., 28 1.5in., 7 2-in., 41 2.5-in, 34 3-in, and 29 4-in diameter joints). A plenum height (the distance between the supporting structural floor and the ceiling system) of 4 ft is used. The piping system is suspended 2.5 ft below the supporting floor, thus the sprinkler drops are1.5-ft long. The sprinkler piping system is connected and braced to the supporting floor with 1-in diameter longitudinal and lateral pipe sway braces, 3/8-in all-threaded hangers, and 12-gauge wire restraints. The sway braces and wire restraints are oriented at 45 degree angles with respect to the plane of the supporting floor. Area 1 Area 2 Area 4 Area 3 Figure 14. 3-D View of UCSF Medical Center Sprinkler Piping System The piping layout was composed of 4 major areas. Area 1 is composed of main run pipes with total length of 154 ft with diameters varying from 2.5- to 4-in. These pipes feed 23 1.25in. and 1-in diameter branch lines and 61 sprinkler heads. In Area 2, main run pipes are 97 ft long with 4-in diameter. This pipe supplies the water for 4 1.25-in. and 1-in. branch lines and 15 sprinkler heads. Area 3 integrates 97 ft of 3- and 2.5-in. diameter main runs with 15 branch lines ranging in diameter from 1.5- to 1-in., and a total of 44 sprinkler heads. Area 4 consists of 82 ft of main distribution line varying in diameter from 4 to 2 in. The main distribution line feeds 16 1.5- to 1-in. branch lines. In this area, the main line and branch line supply 47 sprinkler heads. 17 According to the NFPA 13 (NFPA, 2011), flexible couplings shall be used on riser pipes passing through the structural floors allowing piping systems to accommodate inter story drifts. Therefore, riser pipes were not modeled, and their damage were not included in this study. In addition, the solid braces in longitudinal and lateral directions near the riser-main run intersections are required by the NFPA13 (NFPA, 2011). This will isolate the dynamic response of the piping system of each floor from that of the adjacent floors. Therefore, in this study, only the piping layout for of one floor is analytically modeled. However, it should be noted in piping systems without solid braces near the riser, the overall response and performance of the system may significantly be different, and the results of this study may not hold true. Analytical Model of Sprinkler System The modeling assumptions are the same as those described for the subsystem model, except the weight of sprinkler heads is assumed to be 0.5 lb which is larger than those tested at the University at Buffalo. The real time element removal algorithm was incorporated in the analyses to capture the progression of damage to the piping system during seismic excitations. The element removal algorithm enables the model to redistribute the forces after failure occurs in an element using the "remove element" command in OpenSees software (OpenSees, 2012). This algorithm was set to remove the wire restrainers after reaching their rupture capacity, 0.4 kips from USG (2010). Due to the large spectrum of hanger clip details, the failure force of the pipe hangers was calculated based on the minimum NFPA 13 (NFPA13, 2011) requirements. NFPA 13 mandates that the hangers shall be designed to support five times the weight of the water-filled pipe plus 250 lb at each point of support. The hanger axial forces were calculated after the dead load analysis was concluded. During the response history analyses the program triggered the "remove element" command when the axial force of a hanger reached the five times the recorded axial force plus 250 lb. A Rayleigh damping matrix was used in the piping model and 3% damping was assigned to the first and third modes of vibration. The first five vibration modes of the model were obtained as 1.22, 1.2, 1.19, 1.17, and 1.16 sec, respectively. Generation of the Input Motions An uncertainty in the nature of floor motions is present due to the inherent randomness of the seismological mechanisms and variations of structural systems. The uncertainty of the ground motions are elaborated by using a set of 96 triaxial acceleration histories which are 18 artificially generated using the spectrum-matching procedure. As stated by Gupta and Ju (2011), piping systems have many localized modes. Therefore, this approach was used to generate motions that cover a wide range of frequencies and excite most of the localized modes of piping systems as the consequence. However, using this approach may lead to conservative results due to the large energy content of the generated motions. SIMQKE software (VanMarcke et al., 1976) was used to generate the artificial acceleration histories. The target response spectrum was input in the form of a spectral velocity spectrum, and the output was obtained in the form of acceleration histories with a specified peak acceleration value. Acceleration spectra were produced for the horizontal directions following ICCAC156 (ICC, 2010) parameters (Fig.15a). The z/h parameter is the story height ratio, and SDS is the design spectral response acceleration at short periods. The target horizontal floor spectra were developed by combining a uniform distribution of SDS values varying from 0.1 g to 3 g and four height ratios of 0, 0.33, 0.67, and 1.0. The minimum and maximum periods for the horizontal accelerations were defined as 0.03 and 3.0 sec, respectively. The above procedure was executed once for the x-direction and once for the y-direction with the same SDS and z/h values generating a total of 192 frequency independent horizontal acceleration histories. To generate the vertical component of the acceleration history sets, the vertical acceleration response spectrum introduced in ASCE/SEI 7-05 New Chapter 23 (ASCE, 2005) was adopted. The SDS value used to determine the vertical response spectrum for each set was the same as that of the horizontal spectra. (a) (b) Figure 15. Design Response Spectra, (a) Horizontal Response Spectrum, (b) Vertical Response Spectrum 19 ASCE Chapter 11 (ASCE, 2005) was used to relate the parameters of the vertical acceleration spectra to the horizontal motion by determining SMS, FA, and SS. The vertical coefficient, CV, is then determined from Table 23.1-1 of ASCE/SEI 7-05 (ASCE, 2005). Site Classes D, E, and F were used to define the values of CV. Figure 15b displays the vertical response spectrum from the new Chapter 23 of ASCE/SEI 7-05 (ASCE, 2005). The minimum and the maximum periods for the vertical accelerations were defined as 0.02 and 2.0 sec, respectively. Table 3 presents the sample target response spectrum parameters used to generate the synthetic horizontal and vertical acceleration histories. Table 3. Sample Desired Response Spectra Parameters Vertical Parameters Horizontal Parameters Case No. SDS (g) AFLX-H (g) z h = 0 z h = 1 z 3 h = ARIG-H (g) 2 z 3 h z =1 h =0 z h = 1 z 3 h = 2 z 3 h =1 AFLX-V (g) ARIG-V (g) 1 0.12 0.12 0.19 0.19 0.19 0.05 0.08 0.11 0.11 0.07 0.03 2 0.24 0.24 0.38 0.38 0.38 0.10 0.16 0.22 0.22 0.14 0.05 3 0.36 0.36 0.58 0.58 0.58 0.14 0.24 0.34 0.34 0.27 0.10 … … … … … … … … … … … … 22 2.64 2.64 4.22 4.22 4.22 1.06 1.76 2.46 2.46 3.17 1.19 23 2.76 2.76 4.42 4.42 4.42 1.10 1.84 2.58 2.58 3.31 1.24 24 2.88 2.88 4.61 4.61 4.61 1.15 1.92 2.69 2.69 3.46 1.30 For the acceleration histories, a trapezoidal intensity envelope with a rise time, level time, and total duration of 5, 20, and 30 seconds, respectively, was specified for both the horizontal and vertical motions. A 4th order low-pass Butterworth filter with a cut off frequency of 50 Hz was applied to the acceleration histories using Matlab (MathWorks, 2010). Afterward, the motions were baseline corrected using the linear curve fitting method. The statistical distribution of the peak floor accelerations and the median, 16th, 84th, and 97th percentiles of the 5% damped elastic spectrum for the horizontal and vertical components are presented in Fig. 16. This figure shows that the PFAs vary from 0.05g to 2.67g in the horizontal direction and from 0.03g to 1.3g in vertical direction. The maximum frequency of occurrence for a given range of PFA is 11 in horizontal direction while it is a constant number of 8 in vertical direction. In this study, only one set of tri-axial motions was used for a given SDS and z/h. This may result in a slight underestimation of the dispersion of demand parameters as the variations in the time and frequency contents of different sets of acceleration histories is not accounted for. However, the large number of input motions used 20 in the study has minimized this effect. The nonlinear analytical model of the UCSF piping system was subjected to the described 96 sets of triaxial motions. The maximum responses of the piping system, including joint rotations, hanger and brace forces, and nodal displacements Horizontal Spectral Acceleration (g) were recorded. (a) Frequency Max = 2.67 g Min = 0.05 g Peak Horizontal Floor Acceleration (g) (c) 5 Percentile 97 Percentile 84 Median 16 Percentile (b) 4 3 2 1 0 0 0.5 1 1.5 4 Min = 0.025 g Max= 1.3 g 2.5 3 Percentile 97 Percentile 84 Median 16 Percentile (d) 3.5 3 2.5 Frequency 2 Period (sec.) 2 1.5 1 0.5 0 0 0.5 1 Period (sec.) 1.5 2 Figure 16. (a) Distribution of Peak Horizontal Floor Acceleration , (b) Horizontal Spectral Floor Acceleration, (c) Distribution of Peak Vertical Floor Acceleration, (d) Vertical Spectral Floor Acceleration Fragility Analysis An analytical fragility curve-generation methodology was used in this study to assess the seismic vulnerability of the piping systems. This methodology utilized the nonlinear timehistory analyses of the mentioned UCSF piping system to estimate the seismic demands on piping components, known as engineering demand parameters (EDPs). A fragility statement shows the probability that the seismic demand on a piping component, EDP, goes beyond some level of its capacity or damage state that is the representative of some performance level. This statement is conditioned on the value of some seismic intensity measure (IM) such as peak floor acceleration (PFA) in this study. The relationship of the demand and floor acceleration, IMs, can be approximately represented with the standard normal cumulative distribution function shown in Equation (1) (Nielson and DesRoches, 2007): 21 ln(S d / S c ) P(EDP ≥ C | IM ) = Φ β d IM 2 + β C 2 (1) Where Sd is the median of the demand estimate as a function of IM, Sc is the median estimate of the capacity, βd|IM is the logarithmic standard deviation of the demand with respect to the intensity measure, βc is the logarithmic standard deviation of component capacities, and Φ[·] is standard normal cumulative distribution. Pipe Joint Capacity Parameters The capacity of each pipe diameter was determined from the median rotational threshold corresponding to the first significant leakage of the joint, θ leak . For the pipe diameters that were tested at the University at Buffalo, θ leak and βC were borrowed from the work done by Tian et al. (2012) and are presented in Table 4. For the rest of pipes, θ leak (rad.) was calculated using Equation (2) (Tian et al., 2012). θ leak = 2s D0 (2) In this equation s (average axial slip, analogous to strain in bending assuming plane section of pipes remain plane) is a constant value of 0.019in. for threaded pipe joints and D0 (in.) is the outside pipe diameter. Table 4 shows that the values of θ leak calculated using Equation (2) correspond very well with the experimentally determined values; therefore, this equation provides a good approximation for the median rotational capacity at first significant leakage for those pipe diameters that were not previously tested. Also for each pipe diameter in this group, values of βC were calculated by linear interpolation between two adjacent Table 4. Rotational Capacities of Piping Joint Components Pipe Name 3/4" Pipe 1" Pipe 2" Pipe 4" Pipe 6" Pipe 1.25" Pipe 1.5" Pipe 2.5" Pipe 3" Pipe 3.5" Pipe 5" Pipe Experiment βc θleak Eq. (2) θleak TEST SETS 0.040 0.206 0.037 0.031 0.146 0.029 0.014 0.094 0.016 0.010 0.216 0.009 0.006 0.204 0.006 PROPOSED COMPONENTS NA NA 0.023 NA NA 0.020 NA NA 0.013 NA NA 0.011 NA NA 0.010 NA NA 0.007 22 Interpolation βc NA NA NA NA NA 0.133 0.120 0.125 0.155 0.186 0.210 previously tested diameters. The βC values obtained from experiments were calculated based on limited number of tests (3 specimens per diameter) (Tian et al., 2012). Component Damage States A damage state is a metric that describes the post-earthquake functionality or the level of damage experienced by a component or system subjected to a certain intensity measure. The individual damage states are characterized by representative values for the median, SC, and dispersion, βC, for the component damage states distributions which are also assumed to be lognormal akin to the demands. A continuous range of damage were assumed to exist, though the damage state definitions are discrete. This assumption enables the closed-form computation of the component fragility curves. Moment While only a single capacity may exist for certain components within a piping system, Extensive (Leakage) θN components and entire system. Three damage Moderate (Dripping) Slight multiple damage states can be defined for the θM=(θN+θLeakage)/2 θLeakage states were defined for pipe components named "Slight", "Moderate", and "Extensive". Rotation Figure 17. Schematic Definition of Pipe Joint Damage States The damage states of pipe joints were defined based on the extent of their plastic rotations. The second point on the generic backbone curve, θN, was assumed as the start of nonlinear behavior. The likelihood of any leakage in this level is low; however, there is a possibility of the permanent rotation of joints. The "Moderate" damage state was selected as the average value between "Slight" and "Extensive" rotations. The latter damage state corresponds to the observation of the first significant leakage rotation (θleak). The moderate rotational damage state, θM, was defined as the dripping and spraying condition of the threaded joints (Fig. 17). The dispersion values were set to βC for all damage states. However, βC values obtained from experiments were calculated based on limited number of tests (3 specimens per diameter) (Tian et al., 2012). Consequently, the dispersion values used for defining damage states may be considered an approximate. The parameters for the damage states of pipe joint are presented in Table 5. 23 Table 5. Damage State Definitions of Pipe Joint Components Pipe Diameter Slight 3/4" Pipe 1" Pipe 2" Pipe 4" Pipe 6" Pipe 0.005 0.005 0.005 0.005 0.005 1.25" Pipe 1.5" Pipe 2.5" Pipe 3" Pipe 3.5" Pipe 5" Pipe 0.005 0.005 0.005 0.005 0.005 0.005 Moderate Extensive Median (rad.) TEST SETS 0.023 0.040 0.018 0.031 0.094 0.014 0.010 0.010 0.006 0.006 PROPOSED COMPONENTS 0.014 0.023 0.013 0.020 0.009 0.013 0.008 0.011 0.008 0.010 0.006 0.007 Dispersion βc 0.206 0.146 0.094 0.216 0.204 0.133 0.120 0.125 0.155 0.186 0.210 The damage states of the pipe hangers and wire restrainers were determined from the median percentage of failed hangers or wire restrainers, θ break , and the logarithmic standard deviation of the rotational capacity, βC. A constant value of 0.4, the most frequently used value in nonstructural components (ATC 58, 2009), was assigned to βC for pipe hangers and wire restrainers. Three damage states (DS) were defined for the percentage of failed hangers and wire restrainers. DS1 represents 5% loss of hangers and 10% loss of restrainers, DS2 represents 10% loss hangers and 20% loss of restrainers, and DS3 represents 15% loss of hangers and 30% loss of restrainers. Component Demands The power-law regression and a single value for dispersion were used for characterizing the median demand which are assumptions that are often made. However, they are not necessarily the only possible models to represent the seismic demand as a function of an IM (Ramanathan, 2012). A regression analysis of this data is used to estimate the parameters (Sd and βd|IM) of the probabilistic seismic demand models using Equation (3, 4) (Cornell et al., 2002): Sd = aIM b β d|IM ≅ iN=1 ln(d i ) − ln(aIM (3) b )) 2 N −2 (4) In Equations (3) and (4), Sd and βd|IM are the median estimate of the demand and the logarithmic standard deviation of the demand, respectively. The parameter di is the peak demand corresponding to ith floor motion (out of total N motions). 24 The response of a piping system can significantly vary due to its geometry. As an example, for the same pipe section, the rotational demands on long (more than 2-ft long) armovers are generally larger than on straight drops (Soroushian et al., 2012). Therefore, it is necessary to categorize the EDPs to better represent the physical damage. To do so, EDPs of branch line pipes were categorized based on the pipe diameter and the type of branch line (with or without armovers). The demand parameters of the piping system were defined as: 1) percentage of failed wire restrainers, 2) percentage of broken hangers, 3) the rotation at the tee armovers and elbow armovers, 4) the maximum of the rotations at the joints of a branch line (for a given pipe diameter) which is considered as the representative for the performance of that branch line , and 5) rotation of fittings on the main runs. Table 6. Engineering Demand Parameter Table 7. Engineering Demand Parameter Estimations for Pipe Joint Components Pipe Name Estimations for Hanger and Wire Restrainers a b βd|IM ARMOVERS 0.018 1.69 0.51 0.010 1.45 0.43 BRANCH LINES 0.009 1.53 0.53 0.011 1.41 0.55 0.010 1.45 0.60 MAIN RUNS Armover-Tee Joint Armover-Elbow Joint 1" Pipe 1.25" Pipe 1.5" Pipe 0.005 0.001 0.001 0.001 2" Pipe 2.5" Pipe 3" Pipe 4" Pipe 1.70 0.87 1.01 1.38 0.67 0.36 0.48 0.50 Component Name a 0.06 0.14 Hangers Wire Restrainers b 1.68 1.46 βd|IM 0.55 0.39 As mentioned previously, piping systems have many localized modes instead of few fundamental modes. Therefore, the spectral acceleration at a specific period was not considered as the intensity measure. Component demands were considered with respect to the PFA of the floor motion that generated the demand. Tables 6 and 7 present the regression parameters a and b along with βd|IM for piping 0 Armover-TeeJoint Rotation (rad.) 10 1.46 Sd= 0.14PFA Ratio of Failed Wires βd|PFA= 0.39 10 -1 (a) -2 10 -1 10 10 0 10 1 10 -1 1.69 Sd= 0.018PFA βd|PFA= 0.51 10 -2 10 -3 (b) -4 10 -2 10 10 -1 10 0 Peak Floor Acceleration (PFA), g Figure 18. Median Sample Probabilistic Seismic Demand on Piping Components 25 10 1 components and hanger-wires, respectively. Figure 18 shows the demand plots for the failed wire restrainers and the rotational demands for the Armover-Tee pipe joints. This figure demonstrates that the linear logarithmic regression analysis may underestimate or overestimate the actual demands under the small or large intensities. This error can be eliminated using a more elaborate regression analysis. Component Fragility Curves After calculating estimated demand and capacity parameters, the fragility curves of different piping components can be obtained from Equation (1). Figure 19 shows the piping component fragility curves using this equation. The curves show that the response of teearmovers is the most dominant component in the vulnerability of piping systems in nearly all damage states. The dominancy of larger diameter branch line pipes (1.5 and 1.25 in.) on overall vulnerability of piping system increases in higher damage states. In higher damage states the pipe hangers start to yield, and more wire restrainers fail. As a result, the branch 1 0.9 0.9 0.8 0.8 0.7 0.7 0.6 0.6 0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 0 0 0.5 1 1.5 Wires Hangers Tee-Armover Elbow-Armover 1in Branch Line 1.25in Branch Line 1.5in Branch Line 2in Main Run 2.5in Main Run 3in Main Run 4in Main Run System 2 (b) Moderate Damage 0 0 2.5 0.5 1 1.5 2 2.5 (c) Extensive Damage 1 0.9 0.8 0.7 P[DS|PFA] P[DS|PFA] (a) Slight Damage 1 0.6 0.5 0.4 0.3 0.2 0.1 0 0 0.5 1 1.5 Peak Floor Acceleration (PFA), g Figure 19. Component Fragility Curves for Piping Systems 26 2 2.5 lines behave like cantilevers, and the demand on these pipe diameters, which usually only have connections to the main runs, increases. In this study the general trend is that the demand on the largest and smallest main runs (4in and 2in) is higher. Because these pipes are mainly located at the beginning and end of branch lines in addition to the existence of solid sway braces, the bending demand at these locations is generally higher than at other locations. Table 8 shows the median and dispersion values for the seismic fragility curves of the piping components. Table 8. Medians and Dispersion Values for Piping Component Fragilities States Component Name Slight Armover-Tee Joint Armover-Elbow Joint 0.48 0.60 1" Pipe 1.25" Pipe 1.5" Pipe 0.68 0.57 0.61 2" Pipe 2.5" Pipe 3" Pipe 4" Pipe 0.99 NA* NA* 2.64 Hangers Wire restrainers 0.91 0.81 Moderate Extensive Median PFA(g) ARMOVERS 1.01 1.40 1.41 2.11 BRANCH LINES 1.57 2.23 1.17 1.67 1.15 1.59 MAIN RUNS 1.44 0.94 NA* NA* NA* NA* 3.54 4.38 SUPPORTS 1.38 1.75 1.30 1.71 Dispersion 0.53 0.45 0.55 0.56 0.61 0.67 0.38 0.50 0.55 0.68 0.56 * Estimated median values are much larger than can be appropriately extrapolated from regression analyses. System Level Fragility Studies The assessment of seismic vulnerability for the entire piping system must be made by combining the effects of the various piping system components. Three system damage states "Slight", "Moderate", and "Extensive" were defined by combining the previously defined component damage states. For a given system level damage state, the series system assumption is used to generate fragility curves. In this study, the terms of repair time, repair cost, and the effect on the overall functionality of the system were considered constant for all pipe joint components. A valid consideration is that significant leakage of small and large pipe diameters may not have the same consequence on overall functionality of a piping system. Defining a robust scenario for the contribution of the damage to a component on the functionality of the piping system is complex and is not included in this study. However, four different system level fragilities will be developed later by removing the different categories of component damage from the system level fragilities. 27 The probability that the piping reaches or goes beyond a particular damage state (Failsystem) is the union of the probabilities that each of the components will reach that same damage state (Failcomponent–i ), as shown in Equation (5) (Nielson and DesRoches, 2007) : [ ] n [ P FailSystem = P FailComponent − i i =1 ] (5) Joint Probabilistic Seismic Demand Model A joint probabilistic seismic demand model (JPSDM) was used to estimate the piping system level fragility (Nielson and DesRoches, 2007). A JPSDM is developed by assessing the demands placed on individual components (marginal distribution) through regression analysis. A covariance matrix is calculated by estimating the correlation coefficients between the demands placed on the various components. Using the capacity parameters and the JPSDM, Equation (5) can be evaluated using a Monte Carlo simulation. A Monte Carlo simulation is used to compare some level of correlation realizations between component demands using the JPSDM defined by a conditional joint normal distribution in the transformed space and statistically independent component capacities to calculate the probability of system failure. This procedure is applied for each damage state for various levels of IMs. As previously stated, armovers contribute to the vulnerability of the piping system more than the other components. A simple approach was used to estimate the relative change in the median values of the fragility curves. The median values of the system fragility curves were calculated without considering the armover component demands in the JPSDMs. Then the armover component demands were added to the JPSMs, and the percent change in the median value of system fragility curves with and without considering the armovers was calculated. A positive change indicates a less vulnerable piping system. Also the use of other pipe connections like groove fitting connections with a greater leaking rotational capacity or over braced main runs may reduce the vulnerability of main runs. To see the difference between all of the optional configurations, 4 different system level fragility curves were developed, namely, "All" (considering all the components), "w/o Armovers" (Removing armover demands from JPSDMs), "w/o main runs" (Removing main run demands from JPSDMs), and "w/o main runs & Armovers " (Removing both main run and armover demand from JPSDMs). Table 9 shows the lognormal parameters (median, λ, and logarithmic standard deviation or dispersion, ζ) that characterize the piping system fragility from 28 regression analysis based on all 4 different cases. As the piping system fragility curves are approximately the envelope of component fragility curves, the dispersion values in Table 9 are smaller than the values presented in Table 8. Table 9 shows that armover drops can increase the median value of the fragility curve in the slight damage state by 16%. In the other damage states, damage is not only limited to the armovers. Therefore the median values increased by only 6% and 5% for the moderate and extensive damage states, respectively. In all damage states the contribution of main run damage is negligible compared to the rest of components. Figure 20 shows the piping system fragility curves for the four different cases. (a) Slight Damage 0.9 0.9 0.8 0.8 0.7 0.7 0.6 0.6 0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 0 0 0.5 1 1.5 (b) Moderate Damage 1 2 2.5 1 0 0 0.5 1 1.5 2 2.5 (c) Extensive Damage 0.9 0.8 All 0.7 P[DS|PFA] P[DS|PFA] 1 w/o Armovers w/o Main Runs w/o Armovers & Main Runs 0.6 0.5 0.4 0.3 0.2 0.1 0 0 0.5 1 1.5 Peak Floor Acceleration (PFA), g Figure20. System Fragility Curves for Different Piping System Conditions 29 2 2.5 Table 9. Medians and Dispersions for 4 Different Piping System Conditions System Name ALL w/o Armovers w/o Main Run w/o Main Run & Armovers Slight Median λ 0.46 0.54 0.46 0.54 Difference (%) NA 15.78 0.04 15.85 Moderate Dispersion ζ 0.33 0.39 0.33 0.39 Median λ 0.93 1.00 0.94 1.00 Difference (%) NA 6.20 0.42 7.03 Extensive Dispersion ζ 0.34 0.38 0.34 0.38 Median λ 1.26 1.32 1.27 1.34 Difference (%) NA 5.02 1.13 6.94 Dispersion ζ 0.34 0.36 0.34 0.37 SUMMARY AND CONCLUSIONS A series of nonlinear threaded joint hinges were developed for various pipe diameters based on a previous component experiment. An analytical model was developed and validated using subsystem experimental data. Following the validation of the analytical model, a full fire sprinkler system layout incorporating a variety of common sprinkler piping systems was adopted from the University of California, San Francisco (UCSF) medical center building and was analytically simulated in OpenSees. Seismic fragility curves were generated using this comprehensive three-dimensional model including approximately 900 inelastic members modeling threaded joints, main distribution lines, pipe branches, braces, hangers, wire restrainers, and sprinkler heads subjected to a suite of artificial ground motions. A real time element removal algorithm was incorporated in the analyses to capture the progressive damage of the piping system during seismic excitation. The conclusions made are listed below: • Among the component fragility curves, long armovers with tee joint connections to the branch lines were the most vulnerable components of the piping system, while long armovers with elbow attachment to the branch lines experienced less damage compared to the other branch line components. • The dominancy of larger diameter branch line pipes (1.5in and 1.25in.) on overall vulnerability of the piping system increases at higher damage states. This increase can be attributed to the progressive damage during an earthquake. At higher damage states the pipe hangers start to yield, more wire restrainers will fail, and as a result, the branch line will behave like a cantilever. Therefore, the demand on these pipe diameters which mainly have connections to main runs, will increase. • The smallest and largest main run pipe diameters experienced more damage compared to the other pipe diameters. The largest and smallest pipe diameters are generally located at 30 the beginning and end of main run line, respectively. In these locations the rotational demand is higher because of the sway braces required by code. • The system fragility curves show that the existence of armover drops can increase the median value of the fragility curve in the slight damage state by 16%. At the other damage state levels, the leaking is not only limited to the armovers, therefore, the increase in median values in the moderate and extensive damage is 6% and 5%, respectively. • In all damage states the contribution of main run leaking is negligible compared to the rest of components. ACKNOWLEDGMENTS This material is based upon work supported by the National Science Foundation under Grant No. 0721399. This Grand Challenge (GC) project to study the seismic response of nonstructural systems is under the direction of M. Maragakis from the University of Nevada, Reno and Co-PIs: T. Hutchinson (UCSD), A. Filiatrault (UB), S. French (G. Tech), and B. Reitherman (CUREE). Any opinions, findings, conclusions or recommendations expressed in this document are those of the investigators and do not necessarily reflect the views of the sponsors. The input provided by the Practice Committee of the NEES Nonstructural Project, composed of W. Holmes (Chair), D. Allen, D. Alvarez, and R. Fleming; by the Advisory Board, composed of R. Bachman (Chair), S. Eder, R. Kirchner, E. Miranda, W. Petak, S. Rose and C. Tokas, has been crucial for the completion of this research. The authors are especially grateful to A. Gupta for providing the piping plan . REFERENCES Antaki, G. and Guzy, D. ,1998. Seismic testing of grooved and threaded fire protection joints and correlation with NFPA seismic design provisions, ASME Proceedings, Pressure Vessels and Piping Division, PVP-Vol. 364, Seismic Engineering, 69-75 American Society of Civil Engineers. (2005). ASCE/SEI 7-05, American Society of Civil Engineers Cornell, A. C., Jalayer, F., Hamburger, R. O., and Foutch, D. A., 2002. Probabilistic basis for 2000 SAC Federal Emergency Management Agency steel moment frame guidelines, J. Struct. Eng. 128, 526–532. Comite Euro-interational du Beton. RC elements under cyclic loading, state of the art report. Thomas Telford Publications, London, England, 1996. 31 Ellingwood, B. R., Wen, Y.-K. 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