A Unified View of Hybrid Seismic Simulation Algorithms

Hybrid simulation is a technique for examining the behavior of complex engineering structures. It involves creating a hybrid model of a structure that consists of two parts actively interacting during the test, (a) a physical subsystem – an experimental test piece representing a portion of a structure and (b) a computational subsystem – a computer model of the remainder of the structure. The interface conditions between the physical and computational subsystems are imposed by actuators and the resulting response of the physical subsystem is measured and fed back to the computer model. Several algorithms have been developed for hybrid simulation. In this paper, a unified viewpoint is developed for such algorithms. Many existing algorithms are derived as particular cases. Such an approach is valuable in understanding the precise working and limitations of a simulation and in meaningfully interpreting the results. It will also serve as a basis for more creatively utilizing such versatile dynamic testing facilities as provided by NEES. Introduction Hybrid simulation is a technique for examining the behavior of complex engineering structures. It involves creating a hybrid model of a structure that consists of two parts actively interacting during the test, (a) a physical subsystem – an experimental test piece representing a portion of a structure and (b) a computational subsystem – a computer model of the remainder of the structure. The interface conditions between the physical and computational subsystems are imposed by actuators and the resulting response of the physical subsystem is measured and fed back to the computer model. Hybrid testing has been widely used in seismic testing (Shing et al., 1996; Reinhorn et al., 2004) of structures and is recently being applied to testing structures exposed to fire (Korzen et al., 2000). The following examples illustrate the concept of hybrid simulation. Example 1: Figure 1 shows a multi-story building suffering damage from an earthquake. Suppose that it is known from analyses or from observations in past earthquakes that only a portion of the building could potentially suffer severe damage and needs to be understood better. Hybrid testing allows just this critical portion to be physically constructed and yet be tested as though it were part of the whole building. 1 Assistant Professor, Department of Civil, Environmental and Architectural Engineering, University of Colorado at Boulder, 428 UCB, Boulder, CO 80309. Email: [email protected] Figure 1. Example1 – Pseudo-dynamic Hybrid Testing Example 2: Figure 2 shows the setup to test a soil-structure interface. While the foundation system and the surrounding soil is physically constructed, the superstructure is simulated computationally. The earthquake excitation of the soil and the foundation system is provided by an earthquake simulator (shake table) while the interface conditions with the superstructure are imposed by an actuator. In both examples, since the whole structure need not be built, hybrid testing results in cost saving as well as requires less laboratory space and equipment. Figure 2. Example 2 – Dynamic Hybrid Testing Pseudo-dynamic vs. Dynamic Hybrid Simulation In example 1, the nature of the physical subsystem is to provide resistance to deformation. If the test is carried out in real-time, then it may also offer resistance to the rate of deformation. In example 2 however, besides the above two effects, the physical subsystem also has inertia effects, i.e. it offers resistance to deformation, to rate of deformation and to acceleration. Hence, hybrid experiments of the form of example 1 are referred to as pseudo-dynamic (since inertia effects of interest exist only in the computational system) while those of the type of example 2 are referred to as dynamic. Laminar Soil Box Acceleration Input: (Table introduces Inertia Forces) Soil Ph ys ic al S ub sy st em (w ith d is tri bu te d m as s an d st iff ne ss ) C om pu ta tio na l