*2.3.2 Experimental procedures*

*Natural Hazards - Risk, Exposure, Response, and Resilience*

cylindrical concrete strength is 400 kgf/cm2

**2.2 Statically reversed cyclic loading testing**

**2.3 Sub-structured pseudo-dynamic testing**

conducting the associated large tests.

ing bars is 3400 kgf/cm2

*2.3.1 Structural model*

12,200 kgf/cm<sup>2</sup>

The specimens were fixed to a testing floor by the use of side supports, prestressed rods, and high-strength bolts. The loading was applied through an actuator that was fixed at a height of 150 cm from the bottom end of the PC girder of each specimen (**Figure 2**). The corresponding a/d ratio is 6.8. The average compressive

. Details of the specimens are shown in **Figure 2**.

Statically reversed cyclic loading test was carried out for specimen B-1. The objective of conducting this test was to clarify the load-displacement characteristics of the PC girders. The specimen was tested using the setup shown in **Figure 2b**. The setup consisted of the specimen, actuator, reaction wall, testing floor, data loggers, computer for data acquisition, and displacement measuring devices. The yield displacement was the measured displacement corresponding to the recorded yield load. The imposed displacements to the specimen through the actuator were multiples of the prestressing tendons yielding displacement. Ten repetitions of each cycle were considered. Typically, ten repetitions cannot be attained during a real severe earthquake, but they were planned to fully clarify the load-displacement characteristics.

**Figure 3** shows the input displacements that were applied to specimen B-1.

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

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

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

. The yield strength of the reinforc-

, and the yield strength of the prestressing tendons is

**146**

**Figure 3.**

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 loading test system [10].

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):

$$K\_r = \left(M\_c + M\_y\right) / \left(\Theta\_c + \Theta\_y\right) \left|\Theta\_y / \Theta\_m\right|^a \tag{1}$$

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 ground acceleration that was considered during the sub-structured pseudodynamic test was kept as the original acceleration (818 gal) that was recorded during the original excitation [15, 16] (**Figure 4c**).

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

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

#### **Figure 4.**

*One component model, Takeda's hysteretic restoring force model, and input ground excitation: (a) One component model, (b) Takeda's hysteretic restoring force model; (c) input ground excitation (Hyogo-Ken Nanbu Earthquake, 1995, Kobe city, NS direction).*

rotation angle. After reaching the yield rotation angle, the damping was assumed to become zero due to the fact that only the hysteretic damping is dominant after the displacement reaches the yield displacement. The system that was used in the

**149**

*Seismic Hazard of Viaduct Transportation Infrastructure*

sub-structured pseudo-dynamic test consists of the specimen, loading actuator, reaction wall, data loggers, personal computer for analyzing the inelastic response of the viaduct model and for controlling the input/output data, measuring devices, another personal computer for data acquisition, digital/analog (D/A) converter, and

1.The displacement of the girder at the first step was calculated analytically by the response analysis program that was based on Takeda's trilinear model.

2.By means of the digital/analog converter, the calculated displacement was converted from a digital value into an analog value that can be applied to the specimen

3.Immediately after the actuator applies the required displacement to the specimen, the restoring force was directly measured from the loading system. The computer records this restoring force after converting the data from analog to

4.The previous restoring force was used for the calculation of the displacement

5.The previous steps (steps 1–4) were repeated for the entire duration of the

The input cyclic wave, shown in **Figure 3**, was employed during the statically

The maximum displacement, in the two directions of loading, was about five times the yielding displacement of the prestressing tendons. The skeleton (backbone) curve for the specimen was experimentally obtained and shown in **Figure 5b**. The anticipated bond slip of the reinforcement and prestressing tendons was considered while predicting the analytical skeleton curve. A good agreement between the analytical and the experimental skeleton curves was

The flexural cracks were opened and closed, while almost no shear cracks were observed during the test. The hysteretic loops shown in **Figure 5a** show stiffness degradation and a change in stiffness during reloading which is known as pinching [19]. The pinching can be attributed to opening and closing of the cracks during the cyclic loading. Shear, which is generally responsible for the pinching of the load-

Prestressed concrete members usually show marked elastic recovery even after

considerable inelastic deformations, and thus leading to the occurrence of the pinching of the hysteretic loops. Energy dissipation capacities of the prestressed concrete members were less than those of reinforced concrete members because of

reversed cyclic loading testing of specimen B-1. **Figure 5a** shows the loaddisplacement curve for specimen B-1. The test was continued, after reaching the ultimate load, till a decrease of the load to 80% of the ultimate load was noticed. The 80% is a common acceptance criterion stipulated in the New Zealand standards

[18] and has been adopted by many prominent researchers [1].

deformation curve, was not the cause of the pinching.

the elastic recovery after considerable inelastic deformations.

analog/digital (A/D) converter. The test procedures were as follows:

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

through the actuator.

in the next step.

input excitation.

**3. Test results**

found (**Figure 5b**).

digital through the A/D converter.

**3.1 Statically reversed cyclic loading test**

#### *Seismic Hazard of Viaduct Transportation Infrastructure DOI: http://dx.doi.org/10.5772/intechopen.85700*

sub-structured pseudo-dynamic test consists of the specimen, loading actuator, reaction wall, data loggers, personal computer for analyzing the inelastic response of the viaduct model and for controlling the input/output data, measuring devices, another personal computer for data acquisition, digital/analog (D/A) converter, and analog/digital (A/D) converter. The test procedures were as follows:

