Due to the lack of surface space, most structures are heading underground. The box culvert is underground infrastructure and serves to protect the buried structure from the underground environments, but it has a different characteristic from other structures in that the inner space is empty. Therefore, in this study, the vertical earth pressure which is the most significant effective stress acting on a box culvert was measured by conducting a geotechnical centrifuge model test. A box culvert was installed following the embankment installation method, and the vertical earth pressure acting on it was measured considering the cover depth, gravitational acceleration, and loading and unloading conditions. The soil pressure measured was greater than the existing theoretical value under high cover depth and the unloading condition, which is considered as the variability of many soils or the residual stress acting under the loading condition. Finally, a goodness-of-fit test was conducted as a part of variability analysis. The measured earth pressure was found to be considerably larger than the existing theoretical value, and the variability was large as well. This means the existing theoretical equation is under-designed, which should be reflected in future designs.

Crack control for slabs and beams in current design practices in Korea are based on the Frosch’s model, which is adapted in ACI 318. It is more difficult to have consistent quality control in underground construction sites, such as the RC box culverts used for electric power distribution built below the ground level. There are more discrepancies between the as-built dimensions and the design dimensions provided in drawings in these structures. Due to this variability in construction error, the crack widths measured in such structures have higher potential to have more differences than the calculated values. Although crack control is a serviceability concern, if the owner chooses to have a target crack width that needs better control, crack width estimations can be improved by considering such construction variability. The probability-based crack width model suggested in this study will allow minimizing the discrepancies between the measured and calculated crack widths and provide reliable estimations of crack widths. Typical size of slabs and beams ranging between 300 mm (12 in.) to 500 mm (20 in.) used in underground RC box culverts in Korea were tested under the four-point bending test program. The thicker specimens had smaller bar spacings which created more cracks with smaller crack widths. However, with smaller crack widths generated in these specimens, there were more errors between the measurements and calculated values. From site investigations in Korea, the thickness of slabs in underground box culverts varied the most among all parameters. As a result, the bottom concrete covers had the highest variability. Bottom concrete covers and bar spacings are the two most important parameters in concrete crack control. A probability-based crack width estimation model for flexural members was developed in this study to consider this construction variability. Monte Carlo simulations were performed to evaluate the probabilistic characteristics of the design surface crack widths with a target width of either 0.3 mm (12 mils) or 0.5 mm (20 mils). The probabilistic models of design variables included in the crack width estimation model were generated based on field-collected information from construction sites in Korea. Because the surface crack widths in RC flexural members are sensitive to the construction errors of concrete cover depths, and since there are differences between the assumed and actual stress distribution closer to the reinforcing bars, the probability of having surface cracks of 0.3 mm width (12 mils) is found to be quite high, such as 89% at the positive moment region (mid-span, bottom surface) of the top slab in RC box culverts and 45% for the negative moment region (support area, top surface) of the top slab with current design practice. In order to ensure crack widths to be smaller than the design target width, probability-based crack width factors are recommended in this study to improve estimations depending on the selected target reliability levels.

This study was performed to evaluate the probabilistic characteristics of the flexural strength of reinforced concrete (RC) flexural members adopted for underground box culverts. These probabilistic models were developed to be adopted for the development of limit state load combination formats for underground RC box culverts. The probabilistic models of uncertainties inherent in the basic design variables were developed to evaluate flexural strength using field material test data as well as field survey data collected from various domestic construction sites of underground box culverts in Korea. The basic design variables include concrete strength, steel rebar strength, and section dimensions, such as slab thickness and rebar locations. Some design variables are assumed to have inherent construction error characteristics, which may be different from those inherent in the RC members for buildings and bridges. The bias models on flexural strength were evaluated based on the experimental results of four-point flexural tests on one-way RC slabs, which were fabricated following the general practice adopted in the local underground box culvert construction process. Based on the probabilistic models of basic design variables, as well as the bias models of flexural strength, Monte Carlo simulations were performed to examine the probabilistic characteristics of both ultimate flexural strength and yield moment strength of RC slab members. Some sensitivity analyses were performed to confirm the soundness of various probability models and the assumptions adopted in the development procedure. The proposed procedure may be applied to develop probabilistic resistance models for structural members, in which the construction error characteristics are assumed to be different from other practices.