4. Application of the MAST System for Collapse Experiments

One of the main goals of structural/earthquake engineering is to improve the resilience and performance of structures to withstand collapse due to extreme events. Recent devastating events including a number of large magnitude earthquakes around the world (e.g., Northridge 1994, Kobe 1995, Chile 2010, East Japan and Christchurch 2011) demonstrated that their intensity could reach to more than two times the design level according to the regional code provisions. In this context, it is becoming increasingly important to quantify the reserve capacity of structures against extreme events beyond the design level to the levels approaching collapse. Although there have been many advancements in the mathematical models employed in finite-element methods, many of these analytical models are calibrated using experimental observations. Therefore, experimental research remains critical toward better understanding and predicting the response of structures. However, there are also challenges in conducting laboratory tests for a number of reasons.

Firstly, actions on structures during extreme events such as earthquakes are generally multi-directional and continuously varying, due to the time-dependent nature of the input motion. For instance, variations of the axial loads during a seismic excitation may influence the response of the vertical structural components (e.g., bridge piers and building columns) since the response of such elements when combined with flexural, shear and torsional actions may differ from the cases when they are not subjected to the same axial load changes. Simulation of such highly coupled multi-directional loading conditions using conventional structural testing methods can be expensive, time-consuming and difficult to achieve. As a result, advanced and innovative experimental techniques and control strategies are under development by researchers (Nakata 2007; Wang et al. 2012; Hashemi et al. 2014; Hashemi and Mosqueda 2014).

Secondly, the experiments should be conducted large or full scale to accurately capture the local behavior of the elements. Certain types of local behavior such as bond and shear in reinforced concrete (RC) members, crack propagation, welding effects and local buckling in steel structures are well known to have size effects. Conducting large-scale experiments, however, may not be feasible due to the limited resources available in many laboratories including the number and capability of available actuators, the dimensions and load capacity of the reaction systems, difficulties in the actuator assemblies and testing configuration to reliably simulate the boundary conditions (Hashemi et al. 2016). Consequently, the specimen may be tested small scale or under uni/biaxial loading configurations, which do not necessarily represent the actual action or demand on the structural elements and the corresponding nonlinear response of the prototype system.

Finally, conducting multi-directional loading including axial load effects requires switched-/mixed-mode control strategy. The application of axial loads has been mainly considered by researchers using a combination of force-control actuators in the vertical direction that are decoupled from displacement-control actuators in the lateral direction of the specimen (Lynn et al. 1996; Pan et al. 2005; Del Carpio Ramos et al. 2015). In those tests, independent of lateral actuators, only the vertical force-control actuators apply the axial forces, while under large deformations, lateral actuators have a force component in the vertical direction that needs to be accounted for. Therefore, versatile and generally applicable switched-/mixed-mode control algorithms are required to take into account instantaneous three-dimensional coupling in the control systems.

In this chapter, the unique and powerful capabilities of the MAST system are presented in application for collapse assessment of reinforced concrete (RC) building components. The first experiment is a switched-mode quasi-static test of the RC wall subjected to pure axial demands through displacement-controlled tension and force-controlled compression loads. The next two experiments are conducted on two identical RC columns that are tested through mixed-mode quasi-static and hybrid simulation tests through collapse. In the quasi-static test, the specimen is subjected to constant axial load combined with bidirectional deformation reversal with increasing amplitude that follows a hexagonal orbital pattern. In hybrid simulation, the RC column serves as the first-story corner-column of a half-scale symmetrical 5 × 5 bay 5-story RC ordinary moment frame building that is subjected to bidirectional sequential ground motions with increasing intensities. Finally, to assess the effectiveness of the carbon fiber-reinforced polymer (CFRP) on rehabilitation of RC building columns, the earthquake-damaged RC column was repaired and retested under the same loading condition in hybrid simulation. A simplified collapse risk assessment study was then conducted to compare the response of the RC columns obtained from the quasi-static and hybrid simulation tests as well as the responses of the initial and repaired RC columns.

In the first experiment, the MAST system was used to assess the performance of an RC wall in a building that collapsed during the 2011 Christchurch earthquake. The building was a 5-story RC structure with a lateral load-resisting system comprised of RC walls forming a large shear core, centrally located in the floor plan. The collapse mechanism of the building was hypothesized to be an out-of-plane buckling instability of one of the RC core walls.

Due to the configuration of doorways and wall openings in the shear core, one of the walls at the ground floor had no adjacent return segments. It was theorized that this resulted in the wall being subjected to cyclic tension-compression axial loads due to the overturning moments on the shear core during the earthquake. Large cyclic axial loads eventually caused high enough tensile strains on the wall that it became extremely susceptible to out-of-plane buckling instabilities on the reversed cycle, where the wall was subjected to axial compression.

To simulate the out-of-plane buckling of the critical wall, a 3:4 scale model was constructed with a cross section of 1050 mm × 148 mm and a height of 2680 mm. The wall had a single central layer of longitudinal and transverse reinforcement, with, respectively, 0.25 and 0.35% reinforcement ratios. This resulted in two N16 (normal ductility with 16 mm diameter) longitudinal bars and 14-mm-diameter transverse bars placed at 300 mm centers. The reinforcement had a yield stress of 570 MPa and an ultimate stress of 670 MPa. The wall was cast using a Grade 40 concrete mix (i.e., a 40 MPa characteristic compressive strength at 28 days). Despite the concrete being a standard Grade 40 mix, the mean compressive strength on the test day, determined from 10 concrete cylinders with 100 mm diameter, was approximately 65 MPa.

To determine the approximate loading profile of the axial load on the wall, a finite-element model of the full building was built and subjected to the recorded ground motions. The loading profile was applied to the test specimen using switched-mode control. In this method, the applied loading automatically switches between force-controlled and displacement-controlled loading protocols. When the test specimen is being ‘pulled up’ in tension, the concrete cracks and the reinforcement yields and undergoes plastic deformation. Therefore, displacement-controlled loading is suitable to load the specimen up to the required tension displacement. When the test specimen is being ‘pushed down’ in compression, the concrete undergoes very small displacement increments for the associated amount of force, which sometimes are beyond the resolution of the measurement system. Therefore, force-controlled loading should be implemented to accurately reach to the desired level of compressive load. The loading protocol procedure is graphically illustrated in Fig. 4.1. Note that, when switching back and forth between force and displacement, the specimen is brought back to zero force to avoid any control instabilities.

Figure 4.2a shows the wall tested under the MAST system along the Z axis, while the remaining 5 DOFs (i.e., X, Y, Rx, Ry and Rz) are commanded to zero deformation to allow for pure application of axial load on the specimen. Figure 4.2b shows the out-of-plane failure of the RC wall occurred at the base. The command and measured signals are also presented in Fig. ‎4.3. The switching points can be seen in force time history, where the applied load changes from tension to compression and vice versa. Also, it can be seen that the measured displacement and force signals precisely matched the respective command signals in tension and compression. In terms of the specimen response, it is observed that the fracture of a longitudinal rebar (at ~1630 s) caused a sudden force reduction in tension, which was followed by the total failure of the specimen in compression.

The second experiment is a three-dimensional mixed-mode quasi-static cyclic test conducted on a large-scale limited-ductility RC column. Figure ‎4.4a and b, respectively, shows the design details of the column and the 6-DOF axes of crosshead movements. The specimen is attached to the strong floor from the base and to the crosshead from the top through rigid concrete pedestals. The RC column is 2.5 m high, has a square 250 mm × 250 mm cross section and is reinforced with four longitudinal bars of N16 and tied with R6 stirrups spaced at 175 mm with 30 mm cover thickness. The material properties of the specimen, obtained from laboratory tests, are also presented in Table 4.1.

The loading protocol consists of simultaneously applying a constant gravity load, equal to 8% of ultimate compressive load capacity in force control, while imposing bidirectional lateral deformation reversals in displacement control that follows the hexagonal orbital pattern suggested in FEMA 461 (Federal Emergency Management Agency 2007), as shown in Fig. ‎4.5‎. The sequence of loading in QS testing started with applying the gravity load on the specimen along Z axis. The specimen was then pushed to the initial uniaxial drift ratio toward point ‘a,’ followed by the orbital pattern ‘a-b-c-d-e-f-a.’ The reversal from point ‘a’ accompanies an orthogonal drift at points ‘b’ and ‘c’ equal to one-half the maximum drift ratios at points ‘a’ and ‘d.’ The entire loading cycle was then repeated at the same amplitude. Once the specimen reached point ‘a’ for the second time, the amplitude value for the next two cycles was increased and the next two biaxial load cycles were applied on the specimen. The process continued until the failure of the specimen. The remaining DOF axes (roll, pitch and yaw) were controlled in zero angle forming a double-curvature deformation of the column.

The results of the QS test, including the hysteretic behavior of the RC column in X and Y axes, axial load time history in Z axis, biaxial lateral drifts in X and Y axes and biaxial bending moments in Rx and Ry axes are presented in Fig. ‎4.6‎. The force relaxations observed in the hysteresis were due to pausing of the test in order to collect photogrammetry data at peak deformations in the X axis. The failure of the specimen occurred when the specimen was subjected to the maximum of 7.0 and 3.5% drift ratios in Y and X axes, respectively. These are large drifts for a limited ductile column, but effective of the relatively low axial loads applied to the column (Wibowo et al. 2014).

The third experiment is a three-dimensional mixed-mode hybrid simulation using an identical RC column to the one previously tested in the quasi-static cyclic experiment. For this purpose, a half-scale symmetrical 5-story (height of first story h₁ = 2.5 m, height of other stories h_typ = 2.0 m) 5 × 5 bay (column spacing b = 4.2 m) RC ordinary moment frame building is selected as the hybrid model. The physical specimen serves as the first-story corner-column of the building, considered as the critical element of the structure. The rest of the structural elements, inertial and damping forces, gravity and dynamic loads and second-order effects are modeled numerically in the computer. Figure ‎4.7‎ illustrates the components of hybrid simulation including numerical and experimental substructures.

The structure’s beams and columns were modeled using beam-with-hinges elements, where the nonlinear behavior is assumed to occur within a finite length at both ends based on the distributed plasticity concept (Scott and Fenves 2006) (Fig. ‎‎4.8a). The plasticity model follows a peak-ordinated hysteresis response based on the modified Ibarra–Medina–Krawinkler (IMK) deterioration model of flexural behavior (Ibarra et al. 2005; Zhong 2005). This model was chosen because it is capable of capturing the important modes of deterioration that participate in sidesway collapse of RC frames. The model requires the specification of a range of parameters to control the tri-linear monotonic backbone curve and different modes of cyclic deteriorations. As shown in Fig. ‎‎4.8b, these parameters include \(M_{\text{y}}\), \(M_{\text{c}} /M_{\text{y}}\), \(\uppsi_{\text{p}}\), \(\uppsi_{\text{pc}}\) and \(\uplambda\) that, respectively, represent yielding moment, a measure of maximum moment capacity, plastic curvature capacity, post-capping curvature capacity and cyclic deterioration. The model captures four modes of cyclic deterioration, including strength deterioration of the hardening region (\(\uplambda_{\text{S}}\)), strength deterioration of the post-peak softening region (\(\uplambda_{\text{C}}\)), accelerated reloading stiffness deterioration (\(\uplambda_{\text{A}}\)) and unloading stiffness deterioration (\(\uplambda_{\text{K}}\)). Based on the studies by Haselton et al. (2008), the strength deterioration of hardening region and the post-capping strength deterioration were assumed to be equal in the case study, while accelerated reloading and unloading stiffness deterioration were ignored. This reduced the calibration of cyclic deteriorations to one parameter. Table ‎4.2 presents the IMK parameters for beam and column elements.

After developing the numerical model, the elastic fundamental period of vibration and the corresponding first mode shape were obtained through eigenvalue analysis. A nonlinear static pushover analysis was then performed with the lateral force distribution proportional to the fundamental mode of vibration and with the consideration of second-order \({\text{P}} -\Delta\) effects. Figure ‎‎4.9 presents the results of the pushover analysis that show most of the energy dissipation occurs in the lower two stories.

For the HS test, the two horizontal components of the 1979 Imperial Valley earthquake ground motions recorded at El Centro station with peak ground acceleration of 0.15 g were used. Figure ‎‎4.10‎ shows the acceleration, displacement and acceleration–displacement response spectra for the two ground-motion components. Based on incremental dynamic analysis, four levels of intensities were considered to capture the full range of structural response from linear elastic range to collapse. The selected scale factors were 0.6, 4.0, 8.0 and 9.0, which pushed the structure to nearly 0.25% (elastic), 2, 4 and 6% inter-story drift ratios, respectively.

Prior to conducting the actual HS test with the physical subassembly in the laboratory, a series of FE-coupled numerical simulations (Schellenberg et al. 2009) was conducted to evaluate the integration scheme parameters for the actual experiments. Accordingly, Generalized Alpha-OS (Schellenberg et al. 2009) was used as the integration scheme, and the integration time step was optimized to preserve the accuracy and stability of the simulation, while allowing the completion of the entire test during the regular operation time of the laboratory. Five percentage Rayleigh damping was specified to the first and third modes of vibration, corresponding to the primary translational modes in X and Y directions. Additional damping was also assigned to free vibration time intervals between the forced vibrations in order to quickly bring the structure to rest.

The hybrid simulation started with applying the gravity load on the specimen, using a ramp function, followed by sequential ground motions. The entire sequence of loading was performed and automated using OpenSees. Considering the 117-ms delay in the hydraulic system, 500 ms was specified as the simulation time step in xPC-Target predictor-corrector to provide sufficient time for integration computation, communication, actuator motions and data acquisition. This scaled the 60 s of sequential ground motions to 6 h in laboratory time. Similar to the QS test, the rotational axes (roll, pitch and yaw) were controlled in zero angle, forming a double-curvature deformation of the column.

Figure ‎4.11‎ compares the responses of RC column including the hysteretic behavior of the RC column in X and Y axes, axial load time history in Z axis, biaxial lateral drifts in X and Y axes and biaxial bending moments in Rx and Ry axes for the QS and the HS tests. The specimen was pushed to a maximum of 6.4 and 2.7% drift ratios in Y and X axes, respectively. The maximum time-varying axial load applied on the specimen was 553 kN in compression and 161 kN in tension. By comparing the hysteresis plots from the HS test, it can be seen that the column was damaged as the structure progressively moved in one direction, while in the QS test the pattern of damage was symmetrical due to load reversals in cyclic deformations. Figure ‎‎4.12 shows the flexural failure of columns for both tests by comparing the plastic hinges developed at the top and the base of the columns from different angles.

The use of fiber-reinforced polymer (FRP) for the repair and rehabilitation of earthquake-damaged structures can be considered as a cost-effective and time-saving alternative to replacement. This is due to many advantages that FRP possesses over traditional materials for strengthening, including its high tensile strength, light weight, resistance to corrosion, durability and ease of installation. While numerous experimental studies have demonstrated the effectiveness of FRP strengthening for improving the seismic behavior of RC beam–column joints (Shan et al. 2006; Barros et al. 2008; Yalcin et al. 2008; Realfonzo and Napoli 2009; Wei et al. 2009; Gu et al. 2010; Ozcan et al. 2010; ElSouri and Harajli 2011; Realfonzo and Napoli 2012; Wang et al. 2012; Wang and Ellingwood 2015), few studies are available on the repair and rehabilitation of previously damaged column connections and the suitability of FRP as a post-earthquake strengthening solution (Ma and Li 2015; Jiang et al. 2016).

The fourth experiment aimed to evaluate the capability of CFRP repair on rehabilitating the earthquake-damaged RC column to its initial collapse resistance capacity. For this purpose, the damaged column was repaired using CFRP wraps in the plastic zones observed at both ends of the specimen. The damage contained localized zones of spalled and fractured concrete, horizontal and inclined cracking and bent longitudinal reinforcements.

The repair methodology involved: (1) removal of all spalled and fractured concrete; (2) epoxy injection of any cracks wider than 0.3 mm; (3) reinstatement of damaged concrete with a suitable repair mortar; and (4) wrapping of the column with CFRP. However, replacement of the yielded/buckled/ruptured rebars was not included in the repair process. Visual inspection and light tapping using a rubber hammer were used to identify and remove fractured concrete. Cracks that required injection were identified and labeled. Epoxy injection ports were drilled into the concrete directly over the crack and bonded to the surface with epoxy resin. The surface of the crack was sealed and the injection carried out using Sikadur^® 52 high-strength adhesive (see Fig. ‎4.20).

The injection ports were cut after hardening of the Sikadur^® 52. A repair mortar, BASF MasterEmaco^® S 5300, which is a polymer-modified structural repair mortar, was then used to replace the damaged concrete (see Fig. ‎4.21). The average compressive strength of the repair mortar was 41.9 MPa, based on the results of three 50 mm × 50 mm cubes obtained on the test date. The mortar was tested in accordance with ASTM C109 (American Society for Testing and Materials 2011).

The CFRP wrapping was applied over a 600-mm length at each end of the column in regions corresponding to the maximum moment, three days after the crack injection was performed. The concrete in these regions was confined using three layers of MBrace CF130 unidirectional carbon fiber sheet. The CFRP was expected to provide a passive confinement pressure, thereby increasing the compressive strength of concrete. Furthermore, the orientation of the fibers was arranged parallel to the existing steel stirrups, and this was expected to significantly increase the shear capacity at the column ends. The total increases in axial and shear capacity of the column as a result of the CFRP wrapping were estimated as 35 and 250%, respectively, when calculated in accordance with ACI440.2R-08 (American Concrete Institute 2008). A summary of the material properties of the CFRP (MBrace CF130) and adhesive (MasterBrace^® P 3500 Primer) used in the repair is given in Tables ‎4.5 and 4.6.

Prior to the application of the CFRP to the concrete surface, the corners of the column were rounded to achieve a minimum radius of 25 mm. A mechanical abrasion technique was used to remove the weak layer of cement laitance adhering to the surface of the concrete and achieve a surface roughness similar to 60 grit sandpaper (see Fig. ‎4.22). The surface was cleaned to remove any dust prior to application of the FRP. The FRP was applied using a wet layup technique, and each layer was thoroughly impregnated with resin prior to application to the column. The repair process was performed while the column was still under the MAST system and supporting an axial load of 130 kN, in order to mimic the actual gravity load in a real structural repair scenario. The CFRP was cured at 50 ℃ for 7 days using heat lamps prior to testing (see Fig. ‎4.23).

The repaired column was tested under the same hybrid testing conditions as for the initial column. The intensity levels in hybrid simulation included the same previous four scale factors of 0.6, 4.0, 8.0, 9.0, as well as an additional scale factor of 10.0, in order to push the structure to ~0.25% (elastic), 2.0, 4, 6 and 8% maximum inter-story drift ratios, respectively.

Hybrid simulation was completed with no rupture observed in the CFRP sheets. A detailed comparison of hybrid simulation test results for the initial and repaired columns is presented in Fig. ‎4.24. The results include the hysteretic response in X and Y axes, the axial force time history in Z axis, energy dissipation computed from lateral force deformation in X and Y axes and the biaxial bending moments in Rx and Ry axes.

Figure ‎4.25a shows a closer view of the hysteretic response of the initial and repaired columns in Y axis, along which the column experienced maximum deformation. Two main significant changes can be observed in the behavior of the repaired column. First, the CFRP repair was not able to restore the flexural strength of the initial column, as the maximum resisting force was 32% less in the repaired column. This is mainly due to the fact that the repair process did not include replacement of the yielded, buckled or ruptured rebars, and as a result the loss of strength could not be fully compensated. Second, the repaired column showed significant improvement in ductility due to the confinement effects of the CFRP wraps. As observed in Fig. ‎‎4.25a, the hardening branch of the plastic deformation response of the repaired column is extended to much larger drifts compared to the initial column. Specifically, while applying the maximum compressive axial load on the initial column (553 kN = 23.35% ultimate capacity), a rapid drop occurred immediately after reaching the peak resisting force. However, the repaired column remained in the hardening region while being subjected to the same level of axial load. This is also evident by comparisons of other corresponding cycles from the two experiments. For instance, Fig. ‎4.25b shows, respectively, the capping points ‘A’ and ‘B’ for the initial and repaired column from the same corresponding cycles. The initial column shows stiffness hardening up to 3% drift (point ‘A’), while this value has been extended to 4.5% drift (point ‘B’) for the repaired column. In addition, by comparing the behavior of the RC columns after point ‘C,’ which is located on the same corresponding cycle and at the same level of drift, it is observed that the initial column entered the post-capping negative stiffness region, while the repaired column was still in the stiffness hardening region.