Probability-based seismic fragility analysis provides a quantitative evaluation of the seismic performance exhibited by structures. This study introduces a framework to perform seismic fragility analysis of utility tunnel and internal pipeline system considering wave passage effect of the ground motion spatial variation. The numerical model of a double-beam system resting on a nonlinear foundation is established to simulate the soiltunnel-pipeline interactions. 17 pairs of earthquake records are chosen and scaled as inputs at the outcrop. One-dimensional (1D) free-field analyses are conducted to obtain the ground motion time histories at the bottom slab of the utility tunnel, and then incremental dynamic analysis (IDA) is performed for the utility tunnel-internal pipeline system. The damage states (DSs) are defined by the maximum joint opening for the utility tunnel and maximum strain for the internal pipeline, and the peak bedrock velocity (PBV) is determined to be the most representative intensity measure (IM) for developing the seismic fragility curves. The seismic fragility curves of the system are constructed using the joint probabilistic seismic demand model (JPSDM) and Monte Carlo sampling method. The research findings indicate that: (1) the framework proposed in this study is suitable for the fragility assessment of long-extended utility tunnel-internal pipeline system; (2) the utility tunnel and internal pipeline as a system exhibit greater fragility compared to either one of the components, and the JPSDM and Monte Carlo sampling method for the system fragility analysis is more precise than the first-order bound method; (3) the proposed fragility curves in this study provide quantitative damage probabilities for the individual components and system under different seismic intensity levels. (4) The IM values corresponding to 50% exceedance failure probability of the whole system is 1%-3% lager than that of the upper bounds, and it is 3% to 5% less than that of the lower bounds. The conservative upper bound is a more suitable approximation for system fragility. (5) It should be noted that the obtained fragility curves are valid for the considered tunnel-pipeline structure and site conditions. For different tunnel structures and site conditions, the fragility curves can be constructed following the same steps outlined in this study.

Seismic intensity measures (IMs), which are closely related to both earthquake hazards and structural responses, play a critical role in the performance-based earthquake engineering (PBEE) framework. This paper aims to investigate and define the most representative IMs for probabilistic seismic demand model (PSDM) for the longitudinal utility tunnel and internal pipeline system. Similar to the requirements by the Chinese Code for seismic design of urban rail transit structures, the utility tunnel in this study is assumed being buried in four typical engineering site classes for the analyses. Soil-tunnel-pipeline interactions are simulated using a doublebeam system resting on a nonlinear foundation. Soil-tunnel interaction, tunnel-pipeline interaction and joint connections are modeled as nonlinear springs with different mechanical properties. A series of 17 pairs of outcrop ground-motion records and 27 commonly used IMs are selected in the analyses. Engineering demand parameter ( EDP ) is defined based on the maximum joint opening and the maximum strain of the utility tunnel and internal pipeline, respectively. The selected IMs for predicting the seismic responses of tunnel-pipeline systems are tested using different criteria, i.e., correction, efficiency, practicality, and proficiency. The final decision-making procedure employs a fuzzy multi-criteria decision method. The numerical results indicate that: (1) The velocity-related IMs are the most representative IMs based on the four criteria for structures buried in four sites of different conditions; (2) The optimal seismic IMs vary with different criteria, site classes and structure types. According to the fuzzy multi-criteria decision approach, optimal IMs for the tunnel-pipeline system are PGV , PGV , EPV and HI for site classes I - IV, respectively. The proposed optimal IMs can be utilized to construct seismic fragility curves of utility tunnel, internal pipeline and tunnel-pipeline systems in four different site classes.