Grooved fit joints, as shown in Figure 4, are a relatively new piping construction product that has gained popularity in earthquake prone areas because of the improved flexibility they provide to fire sprinkler piping systems. The grooved fit joint is composed of pipes with grooves, lathedog-plumbings, rubber gasket and bolts. Dimensions of 90° Elbow joint and Tee joint are presented in Figures 4B,C. Nominal size of 90° Elbow joint is 150 mm while the actual size is 165 mm. Nominal size of Tee joint is 150 × 80 mm while the actual size is 160 × 90 mm. Figures 4D,E present the deformation mechanism of the grooved fit joint. The gaps in the grooves and between the pipes make it possible to accommodate earthquake induced rotations. The lathedog-plumbings and pipe joints are made of cast iron and the water pipes are galvanized steel pipes. Detailed information of the materials and components can be found in Meide (2016).

Although this type of joint is massively used in piping construction in China, there's no sufficient investigation on its mechanical behavior, deformation capability, and failure mode. This study conducted three sets of quasi-static tests to examine the seismic performance of two types of grooved fit joints. The elbow joint employs a 90° elbow joint connected with two DN150 pipes, as shown in Figure 5A. The length of each pipe is 840 mm. The Tee joint uses a triplet connecting to two DN150 pipes and one DN80 pipe. The length of DN150 pipes is 840 mm, while the DN80 is 350 mm. Eight Tee joints are divided into two groups. One tests the rotation of DN150 pipes and the other tests the behavior of DN80, as shown in Figures 5B,C, respectively. In each group, there are one monotonic loading test and three cyclic loading tests.

Installation procedure of grooved fit joints is presented in Figure 6. Before the installation, lubricants are applied to the surface of rubber gasket. It is necessary to ensure that there is no gap between pipe end and joint. When tightening the bolts, take turns on both sides until the torque meets the installation requirements (60 Nm) and then the installation is completed.

The functionality examination is one of the objectives of the experiment. The joints shall be tested with the internal water pressure. The maximum working pressure of water pipeline is 1.2 MPa. According to requirements of GB 50084-2001 (2001) and GB 50261-2005 (2005), the test pressure shall be increased by 0.4 MPa when the designed working pressure is >1.0 MPa. Therefore, all specimens will be filled with water and pressurized to 1.6 MPa to capture the leakage during the test and simulate the working condition of pipes. To achieve a precise water pressure, each DN150 pipe is perforated and welded with a DN32 pipe. One DN32 pipe is used as the water injection orifice to the water pump, while the other for the air escape and equipped with a ball valve to shut off the orifice once all the air has escaped. Then the water pressure will increase. Once the target pressure, 1.6 MPa in this study, is reached, the valve close to the pump will be shut off to maintain the water pressure. The pipes full of pressurized water will be kept for 24 h before tests to examine the sealing performance.

The Tee joints are to be tested in two patterns, one examining the rotation capacity of the triplet connected to DN150 pipes, the other testing the capacity of the triplet to the DN80 pipe, as shown in Figures 8B,C, respectively. The test setup for Tee joints (DN150) is shown in Figure 7. One hydraulic-servo actuator is employed to realize the quasi-static tests at a low loading speed of 0.5 mm/s. One end of the actuator is fixed on the reaction beam which is securely fixed on the strong floor. The other end is attached to a load jig which is bolted on two linear bearing sliders. The sliders restrain the movement of the load jig in the axial direction only. The end of each DN150 pipe is pinned to one reaction pier fixed on the strong floor, while the end of DN80 is connected to the load jig along the loading direction (see Figures 7, 8B). Similar set-ups are used to test the Tee joints (DN80) and the elbow joints. When testing the DN80 connection of the Tee joints, the DN80 pipe is pinned to the load jig perpendicular to the loading direction (see Figure 8C). It is worth noting that the load jig is lengthened using a steel component as shown in Figure 8C. The elbow joints are pinned to the load jig at one end and to the reaction beam at the other, as shown in Figure 8A. The axes of the initial positions of the two DN150 pipes of the specimen are 45 degrees from the horizontal line. More details of the test setup are presented in Shang et al. (2018).

The specimens were subjected to a cyclic loading following loading protocol suggested by FEMA 461 (2007), as shown in Figure 9. This protocol is commonly used for the seismic performance assessment of non-structural components and equipment, as it allows all damage states to be quantified to develop the corresponding fragility models. The loading protocol consists of repeated cycles with an amplitude that steadily increases by 1.4 times at each step. Two cycles of loading are conducted at each amplitude level. At least six cycles must be performed before any damage can be observed.

The bending moment of the Tee joints (DN150), M, was calculated using Equation (1), where F is the load applied by the actuator, and D_i is the distance from the pin end of the pipe to the center of the triplet. The bending moment of the Tee joints (DN80) and the Elbow joints can be calculated in a similar way:

Full field displacement and strain measurement with high speed 3D digital image correlation (DIC) system is used for the measurement of strain and rotation in this study. DIC method is a powerful digital image correlation technique that gives the full-field strain distribution across a specimen (Reedlunn et al., 2011). The pipe surface is sprayed with black and white speckle. The measurement system tracks the speckle changes and uses the optimized 3D DIC algorithm to calculate the displacement and strain. The measured strain using DIC method can cover the range from 0.005 (50 micro-strains) to 2,000%. During the loading process, water leakage will first happen at one end of the joints. Therefore, the rotations of all pipes connected to the joints are measured and the one with the first damage will be adopted to quantify the damage states. The rotation is defined as the relative rotation angle between the joint and the pipeline and can be obtained in the post-processing software of the high speed 3D digital image correlation (DIC) system.

Meanwhile, four strain gauges are pasted on each pipe of the specimen, as shown in Figure 10. The curvature of each section is measured by two strain gauges respectively attached to the top and bottom of the pipes, as formulated in Equation (2), where, κ represents the curvature of the measured section, ε₁ and ε₂ are the strains measured from the strain gauges, and s is the interval between two strain gauges (pipe diameter in this study). The moment M of the section is then calculated with Equation (3), where E is the young's modulus, and I is the moment of inertia of the concerned section. The distribution of bending moment along the pipe is assumed to be linear. The calculated bending moments of the two measuring points on the failure side are used to obtain that at the pipe joint section by linear assumption. The data measured from strain gauges will be used to calibrate the optical measurement and compared with the bending moment calculated using the method of Equation (1).

The observed damage at first leakage was consistent for all specimens tested. Table 1 lists and shows photographs of the observed damages. The main failure modes were the fracture of coupling flanges and the pulling-out of pipes. Slight wear at interface between pipes and joint can be observed at DN150 pipes and heavy wear can be observed at DN80 pipes but the wear didn't cause any leakage and did no harm to the functionality of the pipes, which implies a good sealing performance of the improved joint.

Three damage states (DS) of grooved fit joints are defined based on the test results. DS₁ represents the case in which pressure in the pipe drops to 85%, DS₂ represents massive leakage when the water pressure drops to 0 MPa, and DS₃ represents complete damage of the joints, including the resistance force dropping to 85% of the peak force, visible cracks, and the pipe pull-out. The rotations corresponding to different damage states for each specimen are compared in Figure 11, both monotonic and cyclic test results are given. All types of joints exhibit large rotational capacities ranging from 0.054 to 0.274 rad before massive leakage. Rotational capacity of the DN80 Tee joint is much larger than that of the DN150 Tee joint and the Elbow joint. The monotonic rotational capacities of massive leakage (DS₂) are larger than their corresponding cyclic rotational capacities. This result is consistent with the results of Tian et al. (2014).

The measurement scheme provides two methods to obtain the bending moment of the concerned sections. Figure 12 shows the measured hysteretic curves from DIC and strain gauges, respectively. The moment of DIC curve is calculated using the method of Equation (1), while that of strain gauge is calculated using the method of Equations (2, 3). They measured generally well. And in the following discussion, the data measured from DIC will be used. Typical moment vs. rotation hysteretic curve of each type of grooved fit joint is shown Figure 13. The occurrence of massive leakage (DS₂) is indicated by a solid red dot on each plot. After massive leakage, the tests were continued up to complete damage (DS₃) of the test specimens. It can be observed from the hysteretic loops that the moment values would keep increasing even at a large rotation around 0.1 rad. And a pinching effect was introduced by the gaps in the improved configuration. As soon as the load intensity was increased, during the load-inversion phase, the gap generated caused relative rotations with near-zero force variation. Furthermore, reduction of the reloading stiffness can be observed after each loading step because the response could be highly influenced by the cumulative damage.

The experimental results of the cyclic tests were processed to develop the seismic fragility models for grooved fit joints. The cyclic behavior of the piping joints was governed primarily by joint rotation, and this is the only engineering demand parameter (EDP) considered. The three damage states were considered in the seismic fragility analysis, i.e., pressure dropping, massive leakage, and complete mechanical failure, corresponding to DS₁, DS₂, and DS₃, respectively. Based on the method proposed by Porter et al. (2007), experimental fragility curves were defined for the three joint types based on the measured rotational capacities given in Figure 11. The median rotational capacity, θ_m, and associated logarithmic standard deviation, β_t, were computed by Equations (4, 5).

where θ_i denotes the i-th measured rotational capacity and M is the number of cyclic tests conducted for this type of joints (M = 3 in this study). Considering the fact that the specimen number is <5 and all specimens experienced the same loading history, a correction factor β_u = 0.25 is introduced in the calculation of logarithmic standard deviation and the modified logarithmic standard deviation β is calculated by Equation (6). Table 2 summarizes the median rotational capacity and logarithmic standard deviation obtained for each type of joint. Figure 14 compares all the fragility curves derived from the experimental data. The fragility curves of water leakage damage state (DS₂) are further compared with the results of Tian et al. (2014) in Figure 15, where GFC50.8 (3.8) represents the pipes with diameter of 50.8 mm and the pipe wall thickness is 3.8 mm. It can be found that the rotation capacities of Chinese style joints are quite larger than those of American style joints. It is worth noting that more tests are needed for detail comparison to consider the influence of pipe diameter and pipe wall thickness.

A probabilistic seismic demand model (PSDM) can be obtained through regression analysis using the computed responses. The relationship between the interstory drift ratio (IDR) of each story and ground motion intensity was estimated using a standard power function, as presented by Li and Ellingwood (2007):

which can be rewritten in the logarithmically transformed space as:

where S_D is the conditional median interstory drift ratio demand, a and b are unknown regression coefficients which can be found from linear regression in the log space, and IM is the ground motion intensity measure [S_a(T₁) in this study]. A conditional logarithmic standard deviation, β_D|IM, was estimated based on the calculated data to consider the uncertainty associated with the demand model (Li and Ellingwood, 2008; Tavares et al., 2012):

where N is the number of simulations and d_i is the calculated maximum interstory drift ratio. Figure 18 shows the result of the probabilistic seismic demand analysis for first floor of the 10-story building. R² is the coefficient of determination which can be used to indicate the robustness of the regression. Parameters used to define the probabilistic seismic demand model of the case study building are given in Table 3.

It is assumed that the pipe joints of vertical pipes are installed at the ends of the pipe, nearly at the same level of the floor slab, as presented in Figure 19. We assumed that the rotation on vertical pipes imposed by building deformation (drift) is only concentrated at end joint rotations, so that the joint rotation is equal to the interstory drift ratio (IDR) (Soroushian et al., 2014a). The following assumptions have been made in this study:

With the developed PSDM of the interstory drift ratio of each story and the capacity as defined by component fragility curve (section Experimental Fragility Analysis of Grooved Fit Joints), the exceedance probability that the pipe joint demand (D) would be larger than the capacity (C) at a given earthquake intensity measure was computed by Equation (10) for the three damage states. It can be rewritten as Equation (11) by substituting the demand median S_D in the form of Equation (8) (Tavares et al., 2012):

Figure 20 shows fragility curves of grooved fit joints (DN150) used for vertical pipes using S_a(T₁) as an intensity measure, where F_i (i = 1,2,…,10) represents the fragility curve of i-th floor. The damage probability of grooved fit joints (DN150) used for the vertical pipe under 0.07, 0.20 and 0.40 g [corresponding S_a(T₁) are 0.0498, 0.1424, and 0.2847 g] corresponding to the service level earthquake (SLE), design-basis earthquake (DBE), and maximum considered earthquake (MCE) in the Chinese codes (GB50011–2010) is nearly zero. The large deformation capacity of the improved grooved fit joints would ensure the functionality of fire protecting after a rarely occurred earthquake.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.