## 1 Introduction  
The utilization of underground space has become quite important in urban areas due to the increasing demand for city infrastructure. Underground transportation systems and utility spaces can alleviate the increasing demand on infrastructure and would provide more open and green spaces for urban dwellers. Underground RC box culverts are widely adopted for utility tunnels for electricity power lines, water pipes, and communications lines. The underground box culverts constructed for the local electric company in this study have a very typical cross-section, as shown in Figure 1. The spans (internal distances between two walls) range from 2.0 m to 2.6 m generally, and the rises (internal distances between the top and bottom slabs) range from 2.0 m to 2.2 m. The earth fills over the top slabs are generally required to be greater than 1.2 m to prevent freezing damage. Most underground box culverts are constructed along existing urban highways. Haunches are constructed at the top two corners because the corner end moments of the bottom slab are not large due to the strengthened foundation under the bottom slab. The cover depth (the distance from the center of the rebar to the outside surface) of the outside main rebar is fixed at 80 mm, and it is 60 mm for the inside main rebar. Various probabilistic resistance models have been proposed and adopted to perform reliability-based code calibrations [1; 2; 3; 4; 5; 6; 7; 8; 9], mainly for buildings and bridges. [PERSON] et al. [1] proposed a probabilistic model of the flexural resistance of RC members in order to develop the load combinations and load factors for limit state design, in which the basic data were collected mainly from RC buildings and prestressed concrete beams. [PERSON] [2] developed a probabilistic resistance model of general bridge structural members based on the statistical models of the basic design variables proposed by [PERSON] et al. [1]. [PERSON], [PERSON], and [PERSON] [3] performed a reliability-based calibration of design codes for buried structures. However, the resistance model in this study [3] is adapted from previous works on bridge structures [10; 11]. [PERSON] et al. [4; 5] and [PERSON] and [PERSON] [6] proposed resistance models of building RC components, revised with new material test data. [PERSON] et al. [7] investigated the uncertainty of the flexural strength of an RC beam, in which the probabilistic model of rebar strength was only modified based on data collected from local (Italian) industries. All other models have been adapted from previous studies [1; 4; 12]. Similarly, [PERSON] et al. [8] studied the statistical characteristics of material properties as well as uncertainties in strength of RC members based on local data and local laboratory tests (Australia). [PERSON] et al. [9] proposed the probabilistic models for mechanical properties of materials including concrete, reinforcing steel, and prestressing steel to account for a recent improvement in production. Most studies [4; 5; 6; 7] adopted probabilistic models of geometric dimensions, as well as the experimental strength bias values in relation to flexural strength, from [PERSON]'s [1] models, in which geometric dimension errors were measured based on building members and the flexural strength biasness model was developed based on the experimental results obtained from RC beams and prestressed beams. Most underground utility culverts are constructed through a process involving open-excavation, concrete formwork, rebar assembly, concrete cast-in-place, field curing, earth refill, and pavement. Therefore, quality control for underground RC culverts has not been able to maintain constancy throughout the construction process in relation to the load-carrying capacity of RC culvert members. The variability of the member strength of RC culverts should be considered in the design process in order to achieve consistent structural safety as well as to ensure the construction of cost-efficient structures.