**3. Test results**

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

**148**

**Figure 4.**

*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

*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* 

## **3.1 Statically reversed cyclic loading test**

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

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 found (**Figure 5b**).

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 loaddeformation curve, was not the cause of the pinching.

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 the elastic recovery after considerable inelastic deformations.

#### **Figure 5.**

*Hysteretic load-displacement and backbone curves for specimen B-1 during the statically reversed cyclic loading test: (a) Hysteretic load-displacement curve; (b) experimental and analytical backbone curves.*

Specimen B-1 was a partially prestressed concrete specimen, and therefore the pinching was not significant. Consequently, a higher energy dissipation capacity than that of a fully prestressed concrete member was attained. The hysteretic loaddisplacement curve (**Figure 5a**) shows a stable behavior with a comparatively minor strength enhancement.

At early stages of loading and until a displacement of three times the yield displacement of the PC tendons, the residual tensile forces in the PC tendons were adequate to close previously opened cracks. At a displacement equal to four times the yielding displacement of the PC tendon, the concrete compression strains in the plastic hinge

**151**

**Figure 7.**

*end of the PC girder.*

**Figure 6.**

*centimeters).*

region exceeded the unconfined compression strain capacity, and concrete cover spalling was noticeable. Because of the existence of relatively close-spaced transverse hoops, crushing was delayed inside the concrete core as they act to restrain the lateral

*Load-time history of the actuator and experimental hysteretic moment-rotation curve of the left end of the PC girder: (a) Load-time history of the actuator; (b) experimental hysteretic moment-rotation curve of the left* 

*Cracking pattern of specimen B-1 at the end of the statically reversed cyclic loading test (heights are given in* 

*Seismic Hazard of Viaduct Transportation Infrastructure*

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

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

**Figure 6.**

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

Specimen B-1 was a partially prestressed concrete specimen, and therefore the pinching was not significant. Consequently, a higher energy dissipation capacity than that of a fully prestressed concrete member was attained. The hysteretic loaddisplacement curve (**Figure 5a**) shows a stable behavior with a comparatively minor

*Hysteretic load-displacement and backbone curves for specimen B-1 during the statically reversed cyclic loading* 

*test: (a) Hysteretic load-displacement curve; (b) experimental and analytical backbone curves.*

At early stages of loading and until a displacement of three times the yield displacement of the PC tendons, the residual tensile forces in the PC tendons were adequate to close previously opened cracks. At a displacement equal to four times the yielding displacement of the PC tendon, the concrete compression strains in the plastic hinge

**150**

**Figure 5.**

strength enhancement.

*Cracking pattern of specimen B-1 at the end of the statically reversed cyclic loading test (heights are given in centimeters).*

#### **Figure 7.**

*Load-time history of the actuator and experimental hysteretic moment-rotation curve of the left end of the PC girder: (a) Load-time history of the actuator; (b) experimental hysteretic moment-rotation curve of the left end of the PC girder.*

region exceeded the unconfined compression strain capacity, and concrete cover spalling was noticeable. Because of the existence of relatively close-spaced transverse hoops, crushing was delayed inside the concrete core as they act to restrain the lateral

#### **Figure 8.**

*Experimental hysteretic moment-rotation curves of the bottom and top ends of the RC column during the sub-structured pseudo-dynamic testing: (a) Experimental hysteretic moment-rotation curve of the bottom end of the RC column; (b) experimental hysteretic moment-rotation curve of the top end of the RC column.*

compression of the concrete that accompanies the onset of crushing, thus maintaining the integrity of the concrete core. It was not until a displacement of five times the yield displacement when the crushing began to penetrate inside the core concrete due to the large number of repetitions of the cycles. Additionally, the reinforcing bars experienced large increase in the tensile strains and buckling after cover spalling in the plastic hinge region. The cracking pattern of specimen B-1 after the test is shown in **Figure 6**.

#### **3.2 Sub-structured pseudo-dynamic test**

The used time history of the actuator load during the test is shown in **Figure 7a**. The resulting hysteretic moment-rotation curve for the left end of the PC girder is shown in **Figure 7b**. Pinching of the hysteretic loops is clear in **Figure 7b**. A maximum rotation angle of 0.045 rad. was observed and, the figure also indicates a considerable damage of the PC girder due to the input excitation.

**Figure 8a** shows the hysteretic moment-rotation curve of the bottom end of the left column of the viaduct model. It can be noticed from the curve that a considerable damage occurred during the input excitation. A maximum rotation of 0.036 rad. was observed. **Figure 8b** shows the hysteretic moment-curvature curve of the top end of the left column of the viaduct model. It can be observed from the curve that limited energy was dissipated in the plastic hinge that was expected

**153**

a seismic-resistant structure.

**Figure 9.**

**4. Response analysis results**

mum observed acceleration was 12.2 m/sec2

ment was 8.5 cm, which occurred at a time equal to 1.95 second.

*dynamic testing: (a) Acceleration time history; (b) displacement time history.*

*Seismic Hazard of Viaduct Transportation Infrastructure*

to form at the top of the left column of the viaduct model. Similar results were obtained for the bottom and top ends of the right column of the viaduct model. A comparison between the hysteretic moment-rotation curves in **Figures 7b** and **8a** shows that not only the reinforced concrete column but also the PC girder may undergo extensive damage during an earthquake excitation. As a consequence, adequate care should be given to the PC girder design to satisfy the requirements of

*Experimental acceleration time history and displacement time history during the sub-structured pseudo-*

The time history of the response acceleration (**Figure 9a**) shows that the maxi-

second. The time and direction of the maximum acceleration were consistent with the time and direction of the maximum input ground acceleration (**Figure 4c**). The time history of the response displacement (**Figure 9b**) shows that the maximum displace-

The results that were obtained from the reversed cyclic loading tests and the substructured pseudo-dynamic tests for the tested viaduct models show that not only the RC piers but also the PC girders may be damaged during earthquake excitations. This conclusion cannot be generalized without investigating to what extent changes in the viaduct model can influence the resulting response behavior and ductility

that occurred at a time equal to 1.25

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

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

#### **Figure 9.**

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

compression of the concrete that accompanies the onset of crushing, thus maintaining the integrity of the concrete core. It was not until a displacement of five times the yield displacement when the crushing began to penetrate inside the core concrete due to the large number of repetitions of the cycles. Additionally, the reinforcing bars experienced large increase in the tensile strains and buckling after cover spalling in the plastic hinge region. The cracking pattern of specimen B-1 after the test is shown in **Figure 6**.

*Experimental hysteretic moment-rotation curves of the bottom and top ends of the RC column during the sub-structured pseudo-dynamic testing: (a) Experimental hysteretic moment-rotation curve of the bottom end of the RC column; (b) experimental hysteretic moment-rotation curve of the top end of the RC column.*

The used time history of the actuator load during the test is shown in **Figure 7a**. The resulting hysteretic moment-rotation curve for the left end of the PC girder is shown in **Figure 7b**. Pinching of the hysteretic loops is clear in **Figure 7b**. A maximum rotation angle of 0.045 rad. was observed and, the figure also indicates a

**Figure 8a** shows the hysteretic moment-rotation curve of the bottom end of the left column of the viaduct model. It can be noticed from the curve that a considerable damage occurred during the input excitation. A maximum rotation of 0.036 rad. was observed. **Figure 8b** shows the hysteretic moment-curvature curve of the top end of the left column of the viaduct model. It can be observed from the curve that limited energy was dissipated in the plastic hinge that was expected

considerable damage of the PC girder due to the input excitation.

**3.2 Sub-structured pseudo-dynamic test**

**152**

**Figure 8.**

*Experimental acceleration time history and displacement time history during the sub-structured pseudodynamic testing: (a) Acceleration time history; (b) displacement time history.*

to form at the top of the left column of the viaduct model. Similar results were obtained for the bottom and top ends of the right column of the viaduct model. A comparison between the hysteretic moment-rotation curves in **Figures 7b** and **8a** shows that not only the reinforced concrete column but also the PC girder may undergo extensive damage during an earthquake excitation. As a consequence, adequate care should be given to the PC girder design to satisfy the requirements of a seismic-resistant structure.

The time history of the response acceleration (**Figure 9a**) shows that the maximum observed acceleration was 12.2 m/sec2 that occurred at a time equal to 1.25 second. The time and direction of the maximum acceleration were consistent with the time and direction of the maximum input ground acceleration (**Figure 4c**). The time history of the response displacement (**Figure 9b**) shows that the maximum displacement was 8.5 cm, which occurred at a time equal to 1.95 second.

#### **4. Response analysis results**

The results that were obtained from the reversed cyclic loading tests and the substructured pseudo-dynamic tests for the tested viaduct models show that not only the RC piers but also the PC girders may be damaged during earthquake excitations. This conclusion cannot be generalized without investigating to what extent changes in the viaduct model can influence the resulting response behavior and ductility

factor. A parametric study that includes parameters such as the yielding ratio (Py/mg), the elastic natural period, and the strength ratio between the PC girder and the RC columns is required to verify the conclusion.

The accuracy of any parametric study is dependent on the accuracy of the available analytical hysteretic restoring force models for prestressed and reinforced

#### **Figure 10.**

*Analytical hysteretic moment-rotation curve of the left end of the PC girder and the bottom and top ends of the RC column: (a) Analytical moment-rotation curve of the left end of the PC girder; (b) analytical momentrotation curve of the bottom end of the RC column; (c) analytical moment-rotation curve of the top end of the RC column.*

**155**

*column.*

**Figure 11.**

*Seismic Hazard of Viaduct Transportation Infrastructure*

concrete members of the viaduct model. Therefore, response analyses were carried out for the same viaduct model that was tested using the sub-structured pseudodynamic test in the previous section. The response analysis results were compared

The one component model proposed by Giberson [11] was employed during the response analyses. Takeda's trilinear restoring force model was used for the RC columns, and the modified Takeda's model was used for the PC girders. The modified Takeda's model [7] accounts for the partial prestressing that was applied to the girders. Zatar et al. [20, 21] presented and verified the accuracy of another restoring force model for prestressed and partially prestressed members. The model by Zatar

**Figure 10a** shows the hysteretic moment-rotation curve analytically obtained for the left end of the PC girder. The maximum moment was −5.15 × 10–4 Nm, and

**Figure 10b** and **c** shows the hysteretic moment-rotation curves for the bottom and the top ends of the RC column, respectively. Little energy was dissipated at the top end of the column. Conversely, considerable damage was observed at the plastic hinge that existed at the bottom end of the RC column. The maximum moment in

A comparison was made between the experimental and analytical hysteretic moment-rotation curves for the left end of the PC girder and for the bottom and

*Experimental versus analytical moment time history for the left end of the PC girder and the top and bottom ends of the RC column: (a) Experimental moment time history for the left end of the PC girder; (b) analytical moment time history for the left end of the PC girder; (c) experimental moment time history for top end of the RC column; (d) analytical moment time history for top end of the RC column; (e) experimental moment time history for the bottom end of the RC column; (f) analytical moment time history for the bottom end of the RC* 

Nm, and the corresponding rotation was

with the experimental results of the sub-structured pseudo-dynamic test.

et al. incorporated modifications for Takeda's restoring force model.

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

the corresponding rotation was −0.043 rad.

the bottom end of the column was 1.3 × 105

−0.042 rad.

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

columns is required to verify the conclusion.

factor. A parametric study that includes parameters such as the yielding ratio (Py/mg), the elastic natural period, and the strength ratio between the PC girder and the RC

The accuracy of any parametric study is dependent on the accuracy of the available analytical hysteretic restoring force models for prestressed and reinforced

*Analytical hysteretic moment-rotation curve of the left end of the PC girder and the bottom and top ends of the RC column: (a) Analytical moment-rotation curve of the left end of the PC girder; (b) analytical momentrotation curve of the bottom end of the RC column; (c) analytical moment-rotation curve of the top end of the* 

**154**

**Figure 10.**

*RC column.*

concrete members of the viaduct model. Therefore, response analyses were carried out for the same viaduct model that was tested using the sub-structured pseudodynamic test in the previous section. The response analysis results were compared with the experimental results of the sub-structured pseudo-dynamic test.

The one component model proposed by Giberson [11] was employed during the response analyses. Takeda's trilinear restoring force model was used for the RC columns, and the modified Takeda's model was used for the PC girders. The modified Takeda's model [7] accounts for the partial prestressing that was applied to the girders. Zatar et al. [20, 21] presented and verified the accuracy of another restoring force model for prestressed and partially prestressed members. The model by Zatar et al. incorporated modifications for Takeda's restoring force model.

**Figure 10a** shows the hysteretic moment-rotation curve analytically obtained for the left end of the PC girder. The maximum moment was −5.15 × 10–4 Nm, and the corresponding rotation was −0.043 rad.

**Figure 10b** and **c** shows the hysteretic moment-rotation curves for the bottom and the top ends of the RC column, respectively. Little energy was dissipated at the top end of the column. Conversely, considerable damage was observed at the plastic hinge that existed at the bottom end of the RC column. The maximum moment in the bottom end of the column was 1.3 × 105 Nm, and the corresponding rotation was −0.042 rad.

A comparison was made between the experimental and analytical hysteretic moment-rotation curves for the left end of the PC girder and for the bottom and

#### **Figure 11.**

*Experimental versus analytical moment time history for the left end of the PC girder and the top and bottom ends of the RC column: (a) Experimental moment time history for the left end of the PC girder; (b) analytical moment time history for the left end of the PC girder; (c) experimental moment time history for top end of the RC column; (d) analytical moment time history for top end of the RC column; (e) experimental moment time history for the bottom end of the RC column; (f) analytical moment time history for the bottom end of the RC column.*

the top ends of the RC column, respectively (**Figures 7**, **8**, and **10**). The comparison included the observed damage, the hysteretic behavior, the maximum moment, and the associated rotation. An overall good agreement was found between the substructured pseudo-dynamic test and the response analysis results. The unloading stiffness of the hysteretic moment-rotation curve of the PC girder that was obtained from the response analyses was different from the unloading stiffness that was found during the sub-structured pseudo-dynamic test. However, the total dissipated energy that was obtained from the response analyses was found to be almost similar to the experimentally dissipated energy during the excitation.

The moment time history curves that were obtained from the sub-structured pseudo-dynamic test for the left end of the PC girder and the bottom and the top ends of the RC column are shown in **Figure 11a**, **c** and **e**, respectively. The corresponding moment time history curves that were obtained from the response analyses are shown in **Figure 11b**, **d** and **f**, respectively. The comparison between the experimental and analytical moment time histories shows good agreement, thus verifying the accuracy of the used analytical hysteretic restoring force models for both the prestressed and the reinforced concrete members of the viaduct model. Consequently, the restoring force models can be further employed in a parametric study that includes the yielding ratio (Py/mg), the elastic natural period, and the strength ratio between the PC girder and the RC columns. A parametric study that included these parameters is carried out in order to verify the study conclusions as well as to fully understand the response behavior of the viaduct structures during severe earthquake excitations. Because of space limitations, the results of the parametric study are not included in this paper. However, all the results can be found elsewhere [22].
