Seismic Performance Assessment of Reinforced Concrete Box Culverts under Near and Far Fault Seismic Ground Motion Records

Studying the critical response characteristics of reinforced concrete box culverts with diverse geometrical configurations under seismic excitations is a necessary step to develop a reasonable design method. In this work, numerical analysis and assessment of reinforced concrete box culverts for seismic loading in addition to standard static loading from dead and live loads is conducted, aiming to highlight the critical difference in the seismic perfor-mances between two and three cell box culverts under near and far-fault ground motion. The results show how and where the seismic loading alters the responses of seismic loading of the models including the effect on safety and failure. The geometrical configurations of the culvert combined with the loading scenarios also significantly influence the magnitude and distribution of the seismic responses. The findings of this work shed light on the critical role of the geometrical configurations and shaking event in the seismic responses of reinforced concrete box culverts and this procedure can be applied as seismic assessment method to any culvert shape, size, and material.


Introduction
Given the relatively limited land resources in most metropolitan cities, much emphasis has been placed on the construction of more underground structures in order to ensure sustainable development. The resistance of these underground structures to natural hazards (such as earthquakes) deserves to be thoroughly investigated.
Road Box Culverts (RBCs) are typically designed on the basis of the Road Earthwork and Culvert Construction Guiding Principle hereinafter referred to as the guiding principle [1] [2]. The guiding principle refers to a culvert with a traditional structure as a conventional culvert and determines its application range [3]. Furthermore, this guiding principle states that conventional culverts satisfying these structural conditions are considered to exhibit a seismic performance, even without a seismic design; it is possible to determine these structural conditions solely with a static design. This is because when an earthquake occurs, RBCs are thought to behave in unison with the surrounding ground, and therefore, the lining is not subjected to large seismic forces [4]. Another reason is that past major earthquakes did not damage RBCs [5]. Even after earthquakes that have caused serious damage to geotechnical structures no significant damage to RBCs was reported [6].
In recent years, structures with enlarged sectional dimensions have become common. As a result, culverts are typically designed to withstand static loading without regard for seismic events. Prudence dictates, however, that large culvert projects installed in seismically active areas be designed to withstand structural damage caused by seismic events. As these structures do not meet the aforementioned structural conditions of conventional culverts, they require not only a static design but also a seismic design, creating the need for a method that can be applied to RBCs [7]. However, there is no standard seismic design methodology because of the absence of data regarding major damage caused by past earthquakes. Several seismic design methods have been applied to rectangular underground structures, e.g., cut-and-cover tunnels, which are structurally similar to RBCs, and various researchers have developed ways to evaluate their seismic behavior and seismic design [8] [9] [10] [11] [12]. It is presumed that the results of those studies are also applicable to the seismic design of RBCs because the cross-section of RBCs and the material of members of RBCs are similar to the underground structures described above. However, RBCs have unique structural features, e.g., no haunch at the bottom of the sidewalls and a wide cross-section.
Although there have been previous experimental studies [13] [14] and validation of dynamic analyses has been conducted in this area, these studies investigated RBCs under different seismic loading condition is still needed. Therefore, in the present study, seismic assessment of two models of RBC is conducted with near and far fault earthquakes loading to verify the seismic behavior of RBCs and establish a way to evaluate their seismic behavior. A numerical analysis using an elastoplastic finite analysis method is carried out and results were discussed.

Description of the Model
Analytical modeling of the reinforced concrete box culverts is achieved by using World Journal of Engineering and Technology  Table 1. Figure 3 shows the finite element models of the box culverts.
Embedded Element is a technique used to place embedded nodesat desired locations with the constraints on translational degrees-of-freedom on the embedded element by the host element [15] [16]. Both the rebar cages were modeled as the embedded region in concrete using constraints in the interaction module, and making the concrete the host. Thus, rebar elements can only have translations/rotations equal to those of the host elements surrounding them [17] [18].
The RBC sections were considered in the mesh generation, and it was regarded as a three-dimensional solid element for the box culverts, and three dimensional

Mechanical Parameters
Concrete grade C30 and reinforced with steel bars with nominal yield strength fy World Journal of Engineering and Technology = 500 MPa are considered. Beam-column connections are modeled as infinitely rigid links. The following analyses are carried out taking account of material nonlinearity. A rigid-perfectly plastic moment-rotation relationship is adopted as plastic hinge constitutive law. The nonlinear concrete and rebar model parameters are given in Table 2 and Table 3. The density, Poisson' ratio and elastic modulus of the materials are presented. The concrete damage plasticity model is employed to describe the inelastic behavior of concrete elements in the plastic stages, and the input parameters are presented. The tensile cracking and the compressive crushing

Input Earthquake Motion
In general, earthquakes have different properties such as peak acceleration, du- Kobe earthquake record can be treated as a typical, near fault, as its epicentral distance is near fault records with a distance to source of less than 5 km and El Centro earthquake with epicentral distance of 27 km was selected to illustrate far-fault ground motion characteristics. Ground motion parameters include the peak ground acceleration (PGA), peak ground velocity (PGV), peak ground displacement (PGD), frequency content, and response spectra. The shape of acceleration, velocity, and displacement time histories and their corresponding frequency content and response spectrum is shown in Figure 4.

Numerical Simulation Results
Strong earthquakes could make geometric nonlinearity of the structure enhanced, which leads to large deformation under the excitation of rare seismic intensity. The seismic analysis has been fulfilled using finite element software Abaqus. The earthquake wave propagates along x direction. The main results obtained from the numerical analyses carried out will be summarized. The acceleration and displacement response of the box culverts, as well as the bending moments, shear forces, axial forces and stress-strain responses of the box culverts were studied. In particular, the responses of the two box culvert structures will be compared and used to describe and discuss the global and local behavior of their seismic resisting systems, when subjected to near and far fault earthquake excitations. A general overview of their prevailing characteristics is given here, and specific aspects are referenced when needed to explain key points. Particular care is paid to the response of the side wall and slab element, showing their influence on the global structural performance of these two box culvert prototypes. Figure 5 shows the visualization of the Jobs at the end of the shaking events step.

Displacement Responses
RBCs are short-span structures, and their mechanical properties are affected by side walls. On the one hand, side walls constrain vertical deformation of top slab, and on the other hand, they bear the lateral pressure of the soil to RBC. The displacement results of the side walls of various RBC structures are graphically drawn in Figure 6 in order to compare and analyze the simulated values. In Figure 6, a positive value of the X-axis indicates that the side wall is deformed outward, and a negative value indicates that the side wall is deformed inward.
Side wall in rotated and horizontal direction is deformed due to vertical downward displacement of top slab under load. The horizontal displacement of four

Seismic Bending Moment
Bending moments are required for design purposes. Figure 8   other, with curvy distribution in between. All bending moment responses of top slab and side wall from the near fault shaking represent the maximum responses of the axis compared to the obtained bending moment responses from the bending moment responses due to far fault excitation. Thus, comparing the total bending moment responses from different models, the moment at the center of top slab reduces tremendously in a triple cell box culvert as compared to that in a double cell culvert. The reduction in central moment is of the order of 36% under far fault event and 34% under near fault excitation. However, the side wall moments reduce by 55% under far fault event and 41% under near fault shaking event. It can be observed that, the increase in cell of culvert leads to substantial decrease in bending moment at the center of all the members and particularly at the side walls. Considering all the models and compared the top slab with the side wall bending moment results, it can be clearly seen that the responses from the top slab are on higher side than the side wall moments. On the other hand, in a double and triple cell box culvert the top and bottom slabs are continuous therefore; the support moments are on higher side than the central moment. These observations suggest that the seismic bending moments are significant and the total bending moments should be considered in the design as a loading combination case. This is particularly impor-World Journal of Engineering and Technology tant for culverts situated in areas with high seismicity, as the seismic bending moment will increase as the PGA increases.

Axial Force Responses
Regarding the axial-force distribution, Figure 9 shows the total axial forces developed in the top slab and side wall elements under the two different seismic scenarios. The distribution of axial force in the elements isn't symmetrical. The effects of the application of near fault seismic load increase considerably the axial loads in the top slab members to, but don't show highly impact on the side wall. The maximum axial-force distribution occurs in the three cell box culvert top slab under near fault shaking event and is 12 percent increase over the maximum under far fault shaking event, moreover the locations of maximum response under the two events are nearly same. It should be stated here that the variation of the force gives rise to reduction in the model shear strength due to reduction or even loss of the concrete contribution. Moreover, this variation has a significant effect on the moment-curvature and axial load-bending moment interaction diagram of the R.C. element. Findings from recent researches indicated that the section capacity could be significantly reduced, especially for the exterior and inferior element.

Stress-Strain Behavior Responses
In this section, seismic load effects on stress and strain of box culverts were also The result is shown in Figure 11. Analysis of the stress distribution in Figure 11 shows the distribution law of the principal stress. Figure 12 and Figure 13 show that the stresses in the horizontal direction (S11) and in the vertical direction (S22) for each configuration. The strain variation law of the section is obtained by sorting and summarizing the strain data of measurement points. A positive strain indicates that the concrete is being pulled, and a negative value indicates that the concrete is under pressure. After the RBC structure cracking, the strain distribution of the section shows the nonlinear distribution law, and the position of the neutral axis increases in the vertical direction with the increase of the load, indicating that the bending and tensile action of the concrete under the section is more obvious. As shown, in Figure 11, the amplitudes of the peaks increased gradually not at the same rate, but in the analysis, the peak amplitude at the positive side exceeded that at the negative side. This phenomenon may have occurred because of the following: in the analysis, the amount of displacement on the positive side was larger than that on the negative side during one period, which generated discrepancy of displacement.
By comparing the two shaking events on the integral RBC structures, the responses of the two models components show significant large differences under the different seismic waves with the same model and standard. It can be found

Conclusions
This study developed the finite element analysis of the differential settlement World Journal of Engineering and Technology prediction for adjacent longitudinal precast box culvert and subject to different loading conditions including different loading area. To verify the seismic behavior of the RBCs and establish a method for evaluating their seismic behavior numerical analyses under near and far-fault ground motions were carried out.
Two models of two and three cell reinforced concrete box culvert were considered. Based on interpretations and discussions of the simplified results, the major findings were summarized as follows: 1) A model for reinforced concrete box culvert subjected to both static and seismic loadings can be used to demonstrate the complete step-by-step methodology for evaluation of seismic behavior of reinforced concrete box culvert. The working state of RBCs could be divided into elastic stage and plasticity state [19] [20]. 4) The present study confirms that dynamic analysis can be used to evaluate the seismic behavior of RBCs under near and far fault earthquakes and the proposed method is rational, easy to apply, and fulfills engineering need heretofore unfulfilled for a reinforced concrete box culvert installation.

Conflicts of Interest
The authors declare no conflicts of interest regarding the publication of this paper.