Chapter 2 LITERATURE REVIEW
Within this chapter an extensive literature review is presented related to Post-Tensioned (PT) precast concrete wall systems. A description of rocking behaviour is summarised followed by background relating to the use of concrete walls in seismic design. The founding research on self-centering precast concrete wall systems is discussed and a summary of the different systems that have been developed is provided. This is followed by a detailed review of the experimental testing and modelling on the dynamic behaviour of unbonded PT concrete wall systems. Lastly, the current codification and design procedures for unbonded PT precast concrete wall systems are discussed in detail.
The rocking mechanism has been of interest to the earthquake engineering community for some time. It can be shown that by allowing rocking motion to take place in a structure during a seismic event, the resulting accelerations, and hence forces can be reduced, due to the change in stiffness of the structure once rocking is initiated. It has been suggested that a rocking mechanism mayn have been deliberately used for seismic applications for Greek and Roman monuments . The interest of modern earthquake engineers in the rocking mechanism stems from Housner  who reported that during the 1960 Chilean earthquake a number of tall, slender structures survived while more stable appearing structures were severely damaged. Housner’s observations drew attention to the potential for a rocking mechanism to provide a form of seismic isolation to a structure. Two early New Zealand examples where the rocking mechanism was purposely used to provide seismic isolation to a structure were the South Rangitikei River Rail Bridge and a chimney at Christchurch Airport .
In Housner’s  1963 paper a Simple Rocking Model (SRM) was developed by analysing the dynamics of a rigid block resting on a rigid base excited into a rocking motion. Housner’s SRM makes two important assumptions, firstly, there is conservation of angular momentum about the point of impact, and secondly, impacts are considered to be point impacts with no bouncing or sliding. Housner initially developed an equation of motion as presented in Equation (2-1) for a rigid rocking block with the parameters defined in Figure 2.1. Equation (2-1) was then approximated as Equation (2-2) for tall slender blocks having an angle less than 20 °.
Housner also investigated the overturning potential of a rigid block subjected to constant acceleration, sinusoidal acceleration, and earthquake motion based on energy principles. The acceleration pulses in earthquake motion are random and once a block starts rocking in an earthquake there is an energy build-up in the system. The block is then able to overturn at much smaller peak accelerations than those predicted by the sinusoidal acceleration pulse. Housner showed the existence of a scale effect in the stability of two geometrically similar blocks. In other words, the larger of two blocks with the same aspect ratio, but of varying size, will be more stable against overturning.
Many studies have validated Housner’s rocking theory through experimental testing. Aslam et al.  confirmed the use of Housner’s SRM by conducting free vibration and forced vibration testing of concrete blocks using a shake table. A computer program was written to numerically solve the equation of motion of the block with the loss of energy due to impact represented by a coefficient of restitution. The coefficient of restitution was calculated by fitting an analytical solution to the experimental data for the free vibration tests. Aslam et al. demonstrated the rocking problems high sensitivity to the chosen coefficient of restitution, and highlighted the lack of understanding surrounding the energy dissipation mechanism associated with the impacts. The energy dissipation mechanism associated with the velocity reduction at impact is known as contact or radiation damping. Aslam et al. also introduced the concept of adding vertical prestressing to the blocks to increase the stability of the system. The addition of a vertical prestress force to a rocking system is often referred to as controlled rocking.
Concrete structural walls are often used as the primary lateral force resisting system in a building as they provide an efficient lateral load resisting system for both wind and seismic loading. Structural walls can be constructed from either cast-in-place or precast concrete. Precast concrete has advantages over cast-in-place construction, including high quality control, reduction in site formwork and site labour plus the bonus of rapid construction and optimised use of materials . However, the use of precast concrete in seismic regions was initially limited due to lack of research and the subsequent limits put in design codes .
Concrete structural walls have previously been found to perform well during earthquakes; including precast concrete walls designed to emulate cast-in-place Reinforced Concrete (RC) walls [42, 43]. Fintel  reported that concrete shear wall structures demonstrated the ability to fulfil the life safety requirements of seismic design and also suffered little damage. Typically precast concrete walls are constructed to emulate cast-in-place RC walls. Designing precast concrete walls to emulate cast-in-place RC walls requires in situ concrete joints during construction that limit the advantages provided by the use of precast concrete . A significant research effort has been undertaken to overcome the limitations of using precast concrete in seismic regions, this is discussed in section 2.4.
UNBONDED PT CONCRETE WALL SYSTEMS
Self-centering concrete systems such as that shown in Figure 2.2 incorporate precast concrete elements with post-tensioning tendons. The use of precast concrete introduces dry connections that accommodate inelastic demand through opening and closing of an existing crack, introducing a rocking mechanism. The unbonded post-tensioning is designed to remain elastic during a design-level earthquake, and therefore provides a self-centering restoring force and the moment resistance for the system. The restoring force provided by the post-tensioning increases the stability of the rocking system against overturning. The combination of precast elements and unbonded post-tensioning generates a response that undergoes inelastic deformations with minimal damage. Unbonded PT precast concrete members have limited energy dissipation compared to a traditional RC structure due to the minimal damage sustained from a seismic event.
Figure 2.3 shows the idealised behaviour of concrete elements. The combination of precast concrete wall and post-tensioning produces the idealistic bilinear hysteresis shown in Figure 2.3. The decreased amount of hysteretic energy dissipation due to decreased damage is evident when you compare the bilinear hysteresis to a traditional full hysteretic (i.e. purely yielding) system. The low energy dissipation of the purely unbonded PT system typically leads to higher displacements during an earthquake and has led researchers to add further damping to the system, producing an idealised flag-shape hysteresis behaviour shown in Figure 2.3. The development of these systems is discussed in detail below.
The PREcast Seismic Structural Systems (PRESSS) research programme was initiated in 1991 in a joint effort by the United States and Japan to develop new technology that overcame the limitations associated with using precast concrete in seismic regions . The main focus of the PRESSS research programme was the use of unbonded post-tensioning to connect precast concrete structural elements. The concept was initially investigated analytically for use in concrete frames  and then extended to precast concrete walls . During the PRESSS programme four types of connections for PT frame were conceptualised and investigated. Concurrently, unbonded PT precast concrete walls were being investigated analytically at Lehigh University [4, 45].
The final phase of the PRESSS programme included the pseudo-dynamic testing of a 60% scale five-story precast concrete building that is shown in Figure 2.4. The test building used unbonded PT frames to resist lateral loads in the longitudinal direction while a jointed wall system was used to resist lateral loads in the transverse direction. The building was tested in both the frame and wall directions independently by subjecting the building to simulated seismic loads. The principal method of testing was pseudo-dynamic testing; this involves applying displacements in small increments to represent a seismic event based on an assumed stiffness matrix, and then updating the stiffness matrix at set intervals depending on the displacements and forces achieved in the previous step. The jointed wall system sustained minimal damage even when subjected to an earthquake 50% above the design level earthquake intensity. Minor crushing developed in each toe at the base of the wall, but this damage was essentially cosmetic and could easily be repaired without disrupting the normal operations of the building .
Chapter 1 Introduction
1.2 Rocking Walls
1.3 Current code provisions
1.4 Research motivation
1.7 Thesis outline
Chapter 2 Literature review
2.2 Rocking behaviour
2.3 Concrete walls
2.4 Unbonded PT concrete wall systems
2.5 Section analysis
2.6 Unbonded PT systems Dynamic behaviour
2.7 Evaluation of damping
2.9 Design procedures
2.10 Residual drift
Chapter 3 O-connector testing and design
3.2 Strength and stiffness equations
3.3 Experimental programme
3.4 Test Observations and results
3.5 Discussion of results
Chapter 4 Prototype and model design
4.2 Prototype Building
4.3 Seismic hazard
4.4 Displacement based design
4.5 Prototype wall design
4.6 Model scaling
4.7 Detailed model wall design and construction
4.8 Chapter summary
Chapter 5 Cyclic testing
5.1 Experimental programme
5.2 Test observations
5.3 Results and discussion
5.4 Influence of O-connectors
Chapter 6 Snap back testing
6.2 Experimental programme
6.3 Test setup
6.4 Test Procedure
6.5 Observations, results, and discussion
Chapter 7 Shake table testing
7.1 Design and construction of shake table test programme
7.2 Test setup and instrumentation
7.3 Testing procedure
7.4 Test observations and white-noise tests
7.5 Ground motion results and discussion
7.6 Harmonic motion results and discussion
Chapter 8 Evaluation of damping schemes
8.2 Damping scheme theory in current practice
8.3 SRW numerical analyses
8.4 PreWEC numerical analyses
8.5 Conclusions and recommendations
Chapter 9 Direct displacement based design evaluation
9.2 EVD in DDBD summary
9.3 Yield displacement and ductility
9.4 EVD recommendations
9.5 DDBD evaluation of EVD methods
9.6 Conclusions and recommendations
Chapter 10 Conclusions
10.1 Motivation and objectives
10.2 Summary of conclusions
10.3 Recommended research
GET THE COMPLETE PROJECT