## 1 Introduction  
As a flexible structure, steel corrugated pipe has many advantages, such as light weight, environmental protection, and rapid construction [1; 2]. Therefore, steel corrugated pipe is widely used in bridges, viaducts, highways, and underground passages [3; 4; 5; 6; 7; 8; 9]. Culvert is a common type of hydraulic structure that is mainly used to promote drainage through road systems and other barriers. Although culvert is made of a variety of materials, the most common types are steel corrugated pipes and reinforced concrete pipes, the former accounting for about 80% of the market [10]. Steel corrugated pipe culvert is a typical underground flexible structure. Compared with the traditional concrete culvert, this structure has less interference with the foundation and can better adapt to deformation. At the end of the 19 th century, steel corrugated pipes began to be used in culverts in Europe and North America. Since then, many researchers have conducted a lot of research on the construction and performance of steel corrugated pipe culverts. [PERSON] [11] carried out active load analysis of box culverts and arch culverts, and proposed a 2D analysis program for reducing surface load methods and load diffusion methods. [PERSON] et al. [12] established a three-dimensional finite-element model to simulate the behavior of buried steel corrugated pipe culverts during construction, and studied the stress characteristics with different filling heights within a certain wavelength range. [PERSON] et al. [13] studied the performance of eight single-steel corrugated pipe culverts under static load and dynamic load. [PERSON] et al. [14] carried out static loading tests on circular and arched steel corrugated pipe culverts, and the working performance of steel corrugated pipe culverts with different shapes was evaluated. [PERSON] et al. [15] conducted a three-dimensional numerical simulation and compared it with field measurement data to analyze the influence of backfill height, loading, size, shape, and other characteristics on culvert performance. [PERSON] et al. [16] established a three-dimensional finite-element model to simulate the mechanical properties of buried flexible pipelines under vehicle loads, and conducted field tests to evaluate the accuracy of the numerical model. Then, extensive parametric studies were conducted to examine the effects of burial depth, backfill type, and compaction level on the buried pipe. In all the above studies, the research on steel corrugated pipe culverts mainly focused on the behavior of a single-steel corrugated pipe culvert. However, multiple culverts in practical engineering are often used. It is necessary to study the behavior of multiple culverts. The behavior of multiple culverts in the construction and work stages has been studied by many scholars. [PERSON] et al. [17] studied the influence of multi-arch culvert spacing through dynamic finite-element analysis, and concluded that when the spacing between arch culverts is close, the increase in ground stress and volumetric strain is limited. [PERSON] et al. [18] studied the influence of multi-arch culvert spacing and mechanical behavior under seismic conditions through numerical analysis. The results show that when the element spacing is narrow, the overall stiffness of the ground and arch culvert is relatively increased. [PERSON] et al. [19] studied the structural mechanical behavior and surrounding soil arching state of multi-culverts in the backfill process by combining field testing, finite-element analysis, and theoretical analysis. These studies show that the interaction between culverts cannot be ignored in the analysis of multiple culvert structures. In summary, the behavior of multi-culverts in construction and operation stage still needs further study. In this study, two-dimensional and three-dimensional numerical models were established to analyze the behavior of multiple steel corrugated pipe arch culverts under construction and operation vehicle loads.