## 1 Introduction  
As one of the components of lifeline infrastructure systems for civil engineering, long-distance water diversion projects have been established around the globe for decades to reduce the disparity between the water supply and demand. In general, hydraulic tunnels (HTs) are the most common subterranean constructions for water conveyance infrastructure, whose primary advantage is to reduce engineering distances and circumvent geographical limitations. However, some practical engineering sites are inherently positioned in high-intensity areas due to the requirement to cross mountains and rivers, which imposes higher seismic design standards on HTs. Note that a considerable proportion of tunnels, particularly those crossing fault fracture zones, still suffer from severe damage during strong seismic events. More specifically, the seismic performance of underground structures located in the fault fracture zone is significantly poorer than that of underground structureswith good geological conditions, due to the circulation dislocation and shear deformation of the fault fracture zone. For example, the severe damage to the Dagang CFHT during the Chi-Chi earthquake demonstrates that seismic activity is more common in regions with poor surrounding rock characteristics and abrupt shifts between surrounding rock masse layers [1]. By reviewing different case histories [2; 3; 4; 5; 6], it also can be inferred that the significant task for the civil engineering community is to ensure the long-term and safe operation of CFHTs in every country and society. In light of this information, it can be concluded that civil engineers and property owners must pay full attention to the seismic performance of CFHTs in regions with frequent seismic activity during seismic design. With the widespread application of fragility analysis in civil engineering, the cloud analysis [7], incremental dynamic analysis (IDA) [8], and multiple stripe analysis [9; 10] methodologies are gradually being accepted and playing irreplaceable roles in establishing robust seismic fragility curves after selecting the optimal intensity measure (IM). All three typical analytical methods require a large number of structural response results to derive the statistical seismic IM-demand measure (DM) relation [11]. In particular, several thousand heavy nonlinear time history finite element (FE) numerical simulations using a series of ground motions (GMs) are required to directly obtain the engineering demand parameters (EDPs) of underground structures. However, the long computational time and great effort required for dynamic analysis make the approach inefficient and difficult to adopt in practice [12]. In order to tackle these issues, the simple linear regression of the IM-DM relation in the logarithmic space is commonly utilized to reduce the computational costs and develop appropriate probabilistic seismic demand models (PSDMs) for underground structures, based on the work of [PERSON] et al. [8]. Notably, the normal distribution condition of the structural response and the linear function of IM-EDP in the logarithmic space are the primary sources of error in seismic fragility analysis [13]. Furthermore, a structure under strong GM excitation will experience nonlinear behavior, resulting in a less efficient simple linear regression. In modern civil engineering problems, another way to improve the computational efficiency is to calibrate the statistical relationships between seismic inputs and EDPs using data-driven deep learning (DL) algorithms. There is a tendency to use DL algorithms as a valuable alternative to alleviate the computational burden in seismic safety assessment. Recently, [PERSON] et al. [14] implemented artificial neural networks (ANNs) into the probabilistic framework for FRP-strengthened RC columns to esimtate the seismic resistance, demonstrating that the values predicted by ANNs have the potential to evaluate the structural performance. [PERSON] et al.