Seismic margin assessment of a reinforced concrete skewed bridge in a nuclear power plant

This paper presents the seismic margin assessment of a reinforced concrete (RC) bridge using the high-confidence-of-lowprobability-of-failure (HCLPF) value. An existing RC skewed bridge built in a nuclear power plant (NPP) in Korea was selected for studying objective. Finite element modeling of the bridge is developed in OpenSees, an open system for earthquake engineering simulation. The reference earthquakes applied for the probability analysis are selected from the set of generated ground motions that using for designing NPP structures in Korea. The HCLPF value is calculated based on the fragility method associated with the approximate second moment approach. The effect of randomness and uncertainty in demand and capacity variables is taken into account in the fragility analysis procedure. Based on the calculated HCLPF values, the seismic fragility assessment of the bridge can be readily implemented.


Introduction
The seismic safety assessment of the infrastructures is important, particularly the structures within nuclear power plants. In recent time, earthquakes have been occurred in South Korea with a higher level of intensity, such as the 2016 Gyeongju earthquake and the 2017 Pohang earthquake which lately struck Korea in November. Therefore, a seismic fragility assessment of structures in the region is needed. Fragility analysis is a crucial phase and its fragility parameters, obtained from this process play a momentous role for the seismic risk assessment of structures.
Generally, nuclear power plants (NPP) have been designed for the Safe Shutdown Earthquake (SSE) level. In South Korea, the developed response spectrum with the peak ground acceleration (PGA) 0.3g is normally selected for designing the SSE. The conservative design criteria are established. Therefore, the NPPs have additional seismic margin to withstand earthquake motion larger than Design Basic Earthquake (DBE) ground motion. For seismic margin assessment, the high confidence of low probability of failure (HCLPF) is utilized to represent the capacity of structures and relays. The HCLPF is defined as the PGA with a 95% confidence that the probability of failure is less than 5% point on the fragility curves for a component [1]. There are two methods for computing the HCLPF capacity, the fragility method and the conservative deterministic failure margin method.
For this study, a bridge structure constructed within an NPP in South Korea, is selected for seismic margin assessment. This paper presents the fragility method in terms of approximate second moment approach to calculate the HCPLF of the bridge pier, which is considered as the most crucial member of the bridge structure. The procedure proposed in EPRI (1994) [2] is adopted. The investigated bridge is described in detail in the next section.

Description of the investigated bridge
The investigated bridge includes 11 spans with the RC slab girder and 10 RC circular threecolumn bent type. The length of all spans is 14.   In this research, the finite element program, OpenSees, is applied for modeling the bridge structure [3]. There are various models for concrete and steel materials in OpenSees. For this research, the concrete02 model, which adopted the Kent-Park model [4] is applied for confined and unconfined concrete of the bridge piers. The steel02 model, which adopted the Menegotto-Pinto model [5] is used for modeling of reinforcing bars. These two models have taken into account the nonlinear characteristics of materials. Fig. 3 shows the stressstrain relationship of the concrete and steel material models. The pier elements are modeled as nonlinear beam column elements in terms of fiber sections. Fig. 4 illustrates the fiber section model for the bridge piers and the moment-curvature relationships of all pier sections.
The girder slab is assumed to be elastic behavior during seismic excitations. Hence, the elastic section namely, ElasticMembranePlateSection, is adopted to model the bridge slab elements. Additionally, the piles are also considered elastic beam elements connected to soil medium through the soil springs. The soil springs are modeled in terms of zerolength elements. The force-displacement relationship of the zerolength is represented by the p-y curves [6]. Fig. 5 shows the 3D finite element model of the bridge in OpenSees.  The approximate second moment approach proposed in the EPRI (1994) is adopted to develop fragility parameters of the pier columns. The procedure for fragility analysis of the bridge piers is presented in Fig. 6.  Fundamental frequency, f 2.222 Hz 10 Elastic damping,  0.05 A list of the basis demand and capacity variables of fragility analysis is given in Table 1 and Table 2, respectively. Each of these variables and recommended procedures for obtaining their parameter values can be referred in EPRI (1994). Particularly, the drift limit is estimated based on the moment-curvature relationship, in which the curvature of 0.08 (i.e. at the concrete crushing) is considered as the failure state of the piers. The drift limit can be evaluated by following equation according to FHWA (2006) [7], where  is curvature and L is the pier height. Table 3 gives a summary of the deterministic properties of the pier for analysis.  The results of seismic fragility analysis of all the bridge piers are summarized in Table   4. Note that  c in Table 4 is the composite standard deviation and defined as a combination of the randomness ( r ) and uncertainty ( u ) standard deviations. It can be observed that the minimum value of HCPLF is 0.5g, larger than the SSE design value, so that the bridge may be safe under earthquakes with PGA less than 0.5g. Moreover, the piers at the middle area of the bridge (i.e. from P5 to P7) show a higher probability of failure than the ending parts. This is due to the reason that the shear forces induced by the seismic load at the center area of the bridge is larger than those at the others. The composite fragility curves of the bridge piers at the ultimate state are shown in Fig. 7.

Conclusions
This paper presents a seismic margin assessment of the bridge structure which was built in an NPP in Korea. The HCPLF capacity values of the bridge piers are calculated by