*2.3.1 Structural model*

Many numerical and experimental studies have been carried out to clarify the inelastic behavior of RC columns. However, very few experimental studies have been carried out to date on the response behavior of the full structures in which few members may undergo extensive inelastic deformations. The inelastic deformations of the few members may significantly affect the overall response behavior and the structure integrity of the full structure. The unavailability of test records for the full viaduct structures can be attributed to the high cost and scale of conducting the associated large tests.

Sub-structured pseudo-dynamic test is a computer-controlled experimental technique in which direct numerical time integration is used to solve the equation of motion. By incorporating the sub-structuring concept, it is possible to test only the critical member effect on the inelastic seismic response of the whole structure.

The PC girder of the viaduct structure was considered as the experimental substructure. The PC girder was assumed to be composed of two identical cantilever

**147**

*Seismic Hazard of Viaduct Transportation Infrastructure*

members satisfying compatibility and equilibrium conditions at the center, and thus having only half of the girder as the experimental member (**Figure 1a**).

The sub-structured pseudo-dynamic testing technique was used for testing specimen B-2 of the viaduct model shown in **Figure 1b**. The load was applied quasi-statically during the test, and the dynamic effects were simulated numerically [8]. An analytical inelastic mechanical model and its restoring force-displacement model were used for all the RC members of the viaduct structure except for the PC girder [9]. The restoring force for the PC girder was measured directly from the

One component model [11] was employed for the inelastic member model. The one component model consists of a linearly elastic member with two equivalent nonlinear springs at the member ends (**Figure 4a**). The rotational deformation of the member due to the bending moment was expressed as the sum of the flexural deformation of the linear elastic member and the rotational deformation of the two equivalent nonlinear springs. The spring constants are known as KPA and KPB (**Figure 4a**) and are determined using Otani's method [12]. The inelastic momentrotation relationship of the spring was calculated by means of the ordinary flexural theory based on the assumption that the point of contra flexure was located at the center of each member. Furthermore, the rotations due to bond slip of the reinforcing bars as well as the prestressing tendons from the connecting joint were taken into consideration using Ohta's method [13] for all the members of the viaduct model. Takeda's et al. trilinear model [14] was used as the hysteretic restoring force model for the RC members (**Figure 4b**). Takeda's et al. model includes the characteristic behavior of concrete cracking, yielding, and strain hardening of the main reinforcement. Takeda's et al. model is a realistic and conceptual model that recognizes the continually degrading stiffness due to bond slip, shear cracks, and energy absorption characteristics of the structure during an earthquake excitation. The stiffness of Takeda's model during unloading (Kr) was defined by Eq. (1):

where α was the unloading stiffness parameter that was considered equal to 0.4 for the RC columns. The earthquake excitation during the sub-structured pseudodynamic test was the modified Hyogo-Ken Nanbu 1995 earthquake excitation (NS direction). The Hyogo-Ken Nanbu earthquake excitation was selected to represent a near-field excitation. The time scale was amplified to half the original time scale that was recorded during the original Hyogo-Ken Nanbu excitation. The maximum

The so-called mixed (explicit-implicit) integration method that was originally

Two percent damping was assumed for each mode of the modal damping until the member under consideration experience a rotation angle equal to the yield

ground acceleration that was considered during the sub-structured pseudodynamic test was kept as the original acceleration (818 gal) that was recorded

developed for finite elements analysis was found to be suitable for the substructured pseudo-dynamic test [10]. However, Nakashima et al. [17] found out that for the sub-structured pseudo-dynamic test, the constitutive operator splitting (OS) method is the most effective method in terms of both stability and accuracy. Consequently, the OS method was implemented in this study for the numerical integration of the equation of motion. The integration time interval was

0.0005 second, and the earthquake time interval was 0.005 second.

<sup>α</sup> (1)

*Kr* = (*Mc* + *My*)/(θ*<sup>c</sup>* + θ*y*) |θ*y*/θ*m*|

during the original excitation [15, 16] (**Figure 4c**).

*DOI: http://dx.doi.org/10.5772/intechopen.85700*

*2.3.2 Experimental procedures*

loading test system [10].

**Figure 3.** *Input displacements applied to specimen B-1 during the statically reversed cyclic loading test.*

members satisfying compatibility and equilibrium conditions at the center, and thus having only half of the girder as the experimental member (**Figure 1a**).
