Simulated Portfolio for the Seismic Risk Assessment of Composite Structures
Assessment of damage costs due to an earthquake is an important issue for the insurance industry, yet it currently lacks real damage data for realistic pricing of individual risks. Sophisticated numerical tools, which are widely used to assess structural behavior in great detail (like FEM), may be used with confidence in modeling damage and therefore, they may be suitable in seismic risk assessment for insurance purposes. To produce a virtual damage database, the “Simulated Building Portfolio”-Tool (SBP-Tool) was developed at the University of Kassel in cooperation with the Munich Re. This paper presents the first virtual portfolio for steel-concrete composite frame structures. The SBP-Tool uses beam elements for the composite columns and steel girders, and shell elements for the concrete slabs. Shear springs are automatically created to model the composite action between concrete slabs and steel beams. Rotational springs model the semi-rigid beam-column connections. INTRODUCTION The assessment of damage losses due to an earthquake is an important issue for the insurance and reinsurance industry, but it currently lacks the level of detail that is required for realistic pricing of individual risks. Once again, the recent earthquakes that stroke Chile (Maule, Mw 8.8, February 6, 2010), New Zealand (Darfield, Mw 7.0, September 3, 2010 and Lyttelton, Mw 6.1, February 21, 2011) and Japan (Honshu, Mw 9.0, March 11, 2011) in the last three years proved the strategic importance of this kind of industry and renewed the crucial question of how to develop a resilient concept for society. Any further advancement in that respect is strictly related to the capabilities of creating reliable models to predict seismic risk. This process implies a better understanding of the hazard, of the vulnerability and of the exposure that is involved. Even if important on-going projects, like the Global Earthquake Model (GEM), are aiming at sharing and improving our knowledge, the “state-of-the-art” of the empirical data-set regarding earthquake’s economic losses presents a severe non-uniformity. The worldwide information available is extremely different from both the quality and the geographical points of view. Since earthquakes are rare events, the situation will not likely change significantly in the foreseeable future. It is therefore necessary to further investigate the development of innovative concepts based on consolidated numerical simulation techniques. This paper presents how to simulate a first portfolio consisting of steel-concrete composite structures, which can be used in combination with detailed wave propagation models to estimate the damage and the resulting damage costs. [Mazzieri 2013] shows how to describe a spatial variability of strong-ground motions through large-scale 3D simulations of wave propagation in near-surface soils. He developed complex 3D FE-models for a region of 1 km x 1 km and a depth of 50 m. More than 1.000.000 Finite Elements are typically required to simulate the wave propagation in a particular soil system. Using these complex soil models, Mazzieri assessed the response of buildings due to the simulated wave propagation by modeling them as rigid bodies (Figure 1). This neglects the dynamic characteristics and the non-linear structural behavior of buildings despite being the controlling factors for the response of buildings under seismic actions. Fig.1 Left: 3D-model of the soil and the buildings in Christchurch CBD, [Mazzieri 2013] Right: Snapshots of the simulated displacement of the buildings of the Christchurch CBD, [Mazzieri 2013] A combination of such detailed wave propagation models with sophisticated structural models for the buildings in question is required, if reliable data for seismic risk analysis is to be provided. THE SBP-TOOL FOR GENERATING A VIRTUAL PORTFOLIO To create this kind of building models, the so-called “Simulated Building Portfolio-Tool” (SBP-Tool) was developed at the University of Kassel in cooperation with the Munich Re, [Mühlhausen 2011, 2012]. It provides a virtual portfolio of realistic buildings by using a set of global building criteria provided by the user in a configuration file. A statistical process automatically generates each individual building for the portfolio using the given range for each criterion. Fig. 2 Import new routines to generic SBP-Tool The program is written in ISO C99 and features a modular design (Figure 2). This allows for easy adaptation to different structures (masonry, steel frames, rc-frames with masonry infill, etc.) and inclusion of additional building features, like stairs or penthouses. Currently, the SBP-Tool is used to generate 3D linear FE-models of masonry buildings (Figure 3) and as a recent addition, steel-concrete composite frame structures. A detailed description of how to generate the sophisticated steel-concrete composite frame structures with the predesign (static) module is given in the following chapter. Fig. 3. A regional portfolio of 3D FE-models for masonry buildings simulated with the SBP-Tool. This can be combined with any seismic input, e.g. wave propagation models Whereas the first file (a configuration file) does not depend on any particular FE-software, the second one, the output, must be adapted to its specific commands. This allows the use of other FE-software (Ansys, Open Quake, SLang etc.) without interfering with the initial generation process of the buildings. SLang imports the ASCII files and, by executing the commands, it creates the mass and stiffness matrices. They are exported as two additional output files. Furthermore, SLang creates a file with all the information associated with each DOF. Thus, a set of 4 files is created for each building generated containing all the necessary information to perform a dynamic analysis, and in particular a time history analysis. In general (e.g. non-linear structures) around 500 time histories are required to determine the standard deviation of a local variable with an accuracy of greater than 99 % according to the central limit theorem. That means for a given portfolio like the one in figure 4 with 65 buildings and approximately 1.700.000 DOFs, 8.500.000 time histories are required. To compute 8.500.000 time histories in a short period of time, the use of an efficient algorithm in combination with parallel computing is necessary. In the case of linear structures, the use of power spectra provides an efficient way to calculate the required statistical values of local variables, which can be obtained by multiplying the transfer function of the local variable with the power spectrum of the input process (ground motion). STEEL-CONCRETE COMPOSITE FRAME STRUCTURES WITHIN THE SBP-TOOL A composite structure combines two or more materials with each other and is a widely used structural system in buildings and bridges. Nowadays, a wide range of materials can be used in composite structures, like wood and concrete (especially ultra high performance concrete), but the most common way is combining steel and concrete for manufacturing composite columns, composite beams and composite slabs. The main purpose of combining different materials is to take advantage of the strengths of each material despite the different mechanical properties and their individual weaknesses; for example while one material can be efficient in tension (e.g. steel) the other one (like concrete) would be efficient in compression. Further advantages of using steel-concrete composite structures are that concrete provides a good protection against corrosion and high temperature (fire). The use of steel-concrete composite structures can result in a more efficient design in comparison with steel or concrete structures alone. Usually, larger spans can be reached when a concrete-steel composite system is chosen [Bode,1998, Huber, 2000]. Fig. 4 – A sketch of a steel-concrete composite slab, [Duowei webpage] Concrete Slab Profiled steel decking Shear studs
Large Numerical Models in Continuous Hybrid Simulation
Hybrid simulation is a technique that combines experimental and numerical testing and has been used for the last decades in the fields of aerospace, civil and mechanical engineering. During this time, most of the research has focused on developing algorithms and the necessary technology, including but not limited to, error minimisation techniques, phase lag compensation and faster hydraulic cylinders. However, one of the main shortcomings in hybrid simulation that has prevented its widespread use is the size of the numerical models and the effect that higher frequencies may have on the stability and accuracy of the simulation. The first chapter in this document provides an overview of the hybrid simulation method and the different hybrid simulation schemes, and the corresponding time integration algorithms, that are more commonly used in this field. The scope of this thesis is presented in more detail in chapter 2: a substructure algorithm, the Substep Force Feedback (Subfeed), is adapted in order to fulfil the necessary requirements in terms of speed. The effects of more complex models on the Subfeed are also studied in detail, and the improvements made are validated experimentally. Chapters 3 and 4 detail the methodologies that have been used in order to accomplish the objectives mentioned in the previous lines, listing the different cases of study and detailing the hardware and software used to experimentally validate them. The third chapter contains a brief introduction to a project, the DFG Subshake, whose data have been used as a starting point for the developments that are shown later in this thesis. The results obtained are presented in chapters 5 and 6, with the first of them focusing on purely numerical simulations while the second of them is more oriented towards a more practical application including experimental real-time hybrid simulation tests with large numerical models. Following the discussion of the developments in this thesis is a list of hardware and software requirements that have to be met in order to apply the methods described in this document, and they can be found in chapter 7. The last chapter, chapter 8, of this thesis focuses on conclusions and achievements extracted from the results, namely: the adaptation of the hybrid simulation algorithm Subfeed to be used in conjunction with large numerical models, the study of the effect of high frequencies on the substructure algorithm and experimental real-time hybrid simulation tests with vibrating subsystems using large numerical models and shake tables. A brief discussion of possible future research activities can be found in the concluding chapter.
Utilization of multi–axial shaking tables for the modal identification of structures
A multi–axial shaking table is normally used for earthquake simulation and the dynamic qualification of structures. In most cases the same set–up can also be used for a modal identification of the tested structure. However, this requires the application of suitable modal identification methods. Here, the theory and the basic principles of modal identification by multi–axial base excitation are described. Starting with the relative kinematics and the fundamental dynamic relationships, the specifics of base excitation are explained. Equations for the structural responses and the dynamic forces at the interface are presented and discussed. A survey of identification approaches developed at DLR, Gottingen is given. A frequency– and a time–domain method are described in more detail and illustrated by their application to a laboratory structure. The frequency–domain method is best suited for a general and reliable modal identification, whereas the time–domain method is capable of analysing transient vibrations. Also, the frequency–domain identification of a larger structure is outlined.