Department of Civil Engineering & Architecture

The work presents several dynamic analyses of an actual base isolation system previously identified by using a non-linear model and full scale free vibration tests. After a short introduction to the building and the base isolation system considered, reference is made to previous studies where the model used has been developed. The analytical model, originally derived for free vibration analyses and system identification applications, is extended in the present paper to earthquake response simulations. First a theoretical harmonic ground motion is considered in order to identify resonance conditions for the system and stress how these should be absolutely avoided in actual design by carefully studying the seismological and site conditions. The response of the system to a nearly harmonic natural ground motion is then predicted. Next the performance of the system under several significant ground motions from the Friuli 1976, Irpinia 1980 and L’Aquila 2009 earthquakes is considered and the reasons for its satisfactory or unsatisfactory behaviour are pointed out and explained. Means for correcting unsatisfactory performances are also suggested and implemented. Finally the behaviour of the system under near fault records from the L’Aquila 2009 earthquake is considered, the conditions leading to the maximum demands are highlighted and the reasons behind them are clearly explained.

An exact analytical solution is provided for the dynamic earthquake response of hybrid base isolation systems. A numerical formulation based on a Mixed Lagrangian approach is also provided where the solution at each time step is obtained by solving a constrained minimization problem. Numerical applications show that the two methods provide identical results with the exact solution requiring the least computational effort.

A mixed Lagrangian formulation for the 2D dynamic analysis and earthquake response of hybrid base isolation systems is presented. The governing equations of the system are derived and discretized in time by midpoint central differences. Algebraic manipulation of the discretized equations leads to a non-linear constrained optimization problem in terms of plastic and friction forces in the isolators. The formulation is implemented in a MATLAB computer program and its reliability is first checked against results obtained from a 1D analytical solution. Numerical applications are performed on a real base isolation system under a 2D resonant harmonic ground motion and a 2D earthquake ground motion. The results are shown in terms of the orbits described by individual isolators and significant force-displacement relationships at the isolator level.

A physical model composed of a tri-linear spring, a friction slider and a viscous damper is proposed for the simulation of the dynamic behaviour of hybrid base isolation systems (HBIS) composed of high damping rubber bearings (HDRB) and low friction sliding bearings (LFSB). After the introduction of the constitutive equations for each device composing the overall system, it is shown that the motion of the system consists of alternating linear phases. An analytical solution is provided in compact form for all possible phases of motion. The end conditions for one phase provide the initial conditions for the next one. The solution is applied to the dynamic identification of the HBIS of the Solarino buildings. A well established evolution  strategy (CMA-ES) is used as the dynamic identification algorithm. The estimated values of the physical parameters, together with simulated test responses, contribute to a better understanding of the behaviour of HBIS.

On the basis of a mechanical model for base isolation systems, a method is developed to derive upper and lower bounds for the system parameters. These are used to define a bounded search space from which feasible system parameter vectors can be selected. Starting points and penalty functions for the optimization procedures used to solve the dynamic system identification problem are established from these bounds. The CMA-ES method is used for the solution of two structural identification problems, an academic one and another concerning a real base isolated building. The results for the academic problem are correct to every significant digit and therefore better than those obtained in the literature by using the least squares method. Those obtained for the real problem are close, although not identical, to the ones evaluated by the least squares method.

An analytical model is derived for the simulation of the free vibration motion of hybrid base-isolation systems. The high damping rubber bearing component of the isolation system is modeled by a bi-linear spring while the low friction sliding bearing component is modeled by a linear Coulomb friction damper. After the formulation of the equation of motion of the combined system, an analytical solution is provided. A numerical application is then presented where the behavior of each component of the model is analyzed. The solution of the inverse problem is then considered whereby the system parameters must be evaluated given the acceleration response of the system being released after an initially imposed displacement. An evolution strategy has been used to solve a mathematically formulated inverse problem by using an imperfect model and a perfect one, demonstrating the importance of appropriate models in dynamic structural identification. Finally the model has been used for the identification of a hybrid base-isolation system in a real building, from acceleration records obtained in full scale free vibration tests on the building. The paper ends with a comparison of the results obtained by two different Coulomb friction models (constant and linear) and by quantifying the amount of energy dissipation in the various components of the system.

This work is an attempt to the dynamic identification of base isolation systems from earthquake response records. A very simple base isolation system is considered, composed of only four lead rubber bearings at the four corners of a building in the city of Kushiro in northern Japan. The acceleration of the building, recorded during the 2003 Tokachi-oki earthquake, is used for the identification. The identification procedure is based on the minimization of the distance between the acceleration of the building measured during the earthquake and the simulated one obtained by using a model presented at CUEE-12. A state-of-the art optimization algorithm (CMA-ES), based on the adaptation of the covariance matrix of a multivariate Gaussian probability distribution, is used to guide the identification process. The model parameters, obtained by identification from three laboratory tests performed in 1996 and in 2004, are used as a reference for the definition of the search space where the system parameters are expected to be. The optimal solution is given in probabilistic terms, namely the average value, standard deviation and coefficient of variation of the system parameters. The work is completed with a critical analysis of the minimal system response required to obtain a realistic prediction of the system parameters for the model considered.

An application of Evolution Strategies (ESs) to the structural identification of base isolation systems in earthquake engineering is presented. The analysis of a test problem considered in the literature clearly shows the effectiveness of ESs for the problem. Simple ESs outperform the previously used methods while state-of-the-art ones, such as the CMA-ES, provide practically exact solutions. The application of the CMA-ES to the real data recorded in 2004, when releasing imposed displacements on a building in Solarino, leads to improved identification results and gives hints of limitations in the model available in literature. Improved models of higher dimensionality are introduced to overcome such limitations. The application of the CMA-ES with the new models leads to improvements of up to 53% compared to the previous solutions in literature. Thus, ESs are shown to be a very powerful tool for the dynamic identification of structural systems and an important aid in the design and evaluation of models of high dimensionality for structure identification.

This work presents a Mixed Lagrangian Formulation for the dynamical response of base isolated buildings to earthquake excitations. After the formulation of the equations of motion, compatibility equations, constitutive laws and flow rules, a Lagrangian functional and a dissipation function are provided from which the governing equations can be derived as Euler-Lagrange equations. The mid-point difference method is used for the time discretization of the governing equations and after some algebraic manipulations the solution within the time step is provided in the form of constrained non-linear optimization problem. Some numerical applications simulating release tests on a real base isolated building are used to show the performance of the proposed formulation.

A three-story reinforced concrete  building in Augusta (IT), isolated at the base and designed according to the provisions of the latest Italian seismic regulations, was subjected to a series of push and sudden release tests  in March 2013. The Augusta isolation system is hybrid, consisting of 16 High Damping Rubber Bearings (HDRB) and 20 Low Friction Sliding Bearings (LFSB). The tests were characterized by a long quasi-static phase, where the building was pushed slowly to the desired displacement amplitude (sliding velocity $\approx 0.1mm/sec$, strain bearing demand $\gamma=0.39-0.78$), and a  dynamic phase where the building was left free to oscillate. The duration of the dynamic phase was utmost $1 \%$ the duration of the static phase. The recordings included the displacements at the isolation level and the floor  accelerations. A baseline fitting scheme was developed for the removal of the low frequency noise in the records. Application of the adjustment scheme provided reliable estimates of the floor velocities and displacements. The advantage of the proposed signal processing method other than its simplicity, is its ability to account for boundary conditions, for instance initial and residual displacements. Once the signals obtained from all eight tests performed were adjusted, they were used in the identification of the non-linear isolation system and the flexible superstructure (linear in the range of interest). The identification was performed in the time domain using the Covariance Matrix Adaptation Evolution Strategy, a stochastic algorithm for difficult, non linear black-box optimization. The identification of the isolation system provided the mass of the rigid block, the bi-linear properties used in the mechanical representation of the rubber bearings and the sliding coefficient of friction for the Coulomb model used in the modelling of the sliders. The obtained parameters, showed that rubber bearing properties were closer to the corresponding static laboratory properties, therefore implying that after the long quasi-static phase the HDRBs did not have time to recover their dynamic properties. The identified sliding coefficient of friction was in average $1\%$, leading to significant energy dissipation. The identified superstructure properties were the distribution of the floor masses, the modal frequencies, damping ratios and mode shapes. The identified data for the isolation system and the superstructure were input in a synthesized model of the isolated Augusta building, for the dynamic response simulation of the structure. A constrained optimization algorithm was developed ad hoc for the  time-step solution of the  coupled equations of motion. The obtained simulated response of the Augusta building matched the experimental response, in terms of displacements, velocities and accelerations.

A three-story reinforced concrete  building in Augusta (IT), isolated at the base and designed according to the provisions of the latest Italian seismic regulations, was subjected to a series of push and sudden release tests  in March 2013. The Augusta isolation system is hybrid, consisting of 16 High Damping Rubber Bearings (HDRB) and 20 Low Friction Sliding Bearings (LFSB). The tests were characterized by a long quasi-static phase, where the building was pushed slowly to the desired displacement amplitude (sliding velocity $\approx 0.1mm/sec$, strain bearing demand $\gamma=0.39-0.78$), and a  dynamic phase where the building was left free to oscillate. The duration of the dynamic phase was utmost $1 \%$ the duration of the static phase. The recordings included the displacements at the isolation level and the floor  accelerations. A baseline fitting scheme was developed for the removal of the low frequency noise in the records. Application of the adjustment scheme provided reliable estimates of the floor velocities and displacements. The advantage of the proposed signal processing method other than its simplicity, is its ability to account for boundary conditions, for instance initial and residual displacements. Once the signals obtained from all eight tests performed were adjusted, they were used in the identification of the non-linear isolation system and the flexible superstructure (linear in the range of interest). The identification was performed in the time domain using the Covariance Matrix Adaptation Evolution Strategy, a stochastic algorithm for difficult, non linear black-box optimization. The identification of the isolation system provided the mass of the rigid block, the bi-linear properties used in the mechanical representation of the rubber bearings and the sliding coefficient of friction for the Coulomb model used in the modelling of the sliders. The obtained parameters, showed that rubber bearing properties were closer to the corresponding static laboratory properties, therefore implying that after the long quasi-static phase the HDRBs did not have time to recover their dynamic properties. The identified sliding coefficient of friction was in average $1\%$, leading to significant energy dissipation. The identified superstructure properties were the distribution of the floor masses, the modal frequencies, damping ratios and mode shapes. The identified data for the isolation system and the superstructure were input in a synthesized model of the isolated Augusta building, for the dynamic response simulation of the structure. A constrained optimization algorithm was developed ad hoc for the  time-step solution of the  coupled equations of motion. The obtained simulated response of the Augusta building matched the experimental response, in terms of displacements, velocities and accelerations.

The dynamic identification of a four story reinforced concrete building retrofitted by base isolation is performed on the basis of push and release tests performed on the building. The identification is performed in two stages. In the first stage, the superstructure is considered rigid and the isolation system is identified by using a tri-linear model for the high damping rubber bearings and a constant Coulomb friction model for the low friction sliding bearings. In the second stage, the motion recorded just above the isolation system is considered as the input of a detailed free-body SAP2000 model of the superstructure. For identification purposes, a condensed model is derived from the detailed model. This is used in combination with the Covariance Matrix Adaptation-Evolution Strategy (CMA-ES) optimization algorithm for the identification of the structural parameters consisting of a multiplier of the stiffness matrix and a parameter specifying stiffness proportional damping. The identified model parameters are used for the simulation of the experimental recorded accelerations and the match is quite satisfactory. The use of the identified parameters for the isolation system and for the superstructure in the detailed SAP2000 model produces results that match the general trend of the isolation mode but fail to reproduce the high frequency response exhibited by the experimental results. The reaction history of the isolation system on the superstructure is evaluated by using both the rigid superstructure model and the one considering deformation of the superstructure. It is shown that while the former does not exhibit high frequency content, the latter shows considerable high frequency response. Application of the reaction containing high frequency components to the detailed SAP2000 model results in accelerations that match reasonably well the experimentally measured ones. Finally, the identified stiffness parameters point towards a significant reduction of the modulus of elasticity of concrete for the evaluation of the cross section rigidities when using gross section second order moments of inertia. The significant identified damping ratios appear to be considerably large consistent with the large released force and resulting initial acceleration and subsequent rapid attenuation.

A three-story reinforced concrete building in Augusta (Sicily, Italy), isolated at the base and designed according to the provisions of the latest Italian seismic regulations, was subjected to a series of push and sudden release tests in March 2013. The isolation system consisted of 16 high damping rubber bearings and 20 low friction sliding bearings. The release tests were performed at low amplitudes to ensure that no damage would occur in the building; the imposed displacements varied from 5.8cm to 11.7cm (isolator demand γ max =0.39-0.78). During the tests, the displacements at the isolation level were measured along with the accelerations at each floor of the building. Once the tests were completed, the observed structural response was used for the assessment of the properties of the isolation system. Before input in analyses, the signals were treated for the removal of low frequency noise using a simple baseline fitting scheme. The developed signal processing scheme consists in defining the duration of the main event, removing the background noise and using polynomial curves for the adjustment of the signal reference baseline. The method does not require significant computational effort and accounts for boundary conditions, provided that these are known. The polynomial coefficients used in the baseline fitting of the signals are determined from the boundary conditions; namely the initial and end accelerations, velocities and displacements. The deterministic definition of the polynomial coefficients and the recovery of permanent displacements enforces the reliability of the method and makes it an attractive alternative to high pass filtering, which instead requires proficient users and includes a lot of subjectivity in the filter parameter selection. The proposed baseline scheme is applied herein for the adjustment of the absolute and relative acceleration signals obtained from test 9, one of the tests with the highest initial input (u0=10.1cm). Implementation of the method provides the adjusted response in terms of absolute and relative floor accelerations, velocities and displacements. The processed absolute accelerations and velocities are zero when the motion starts and when the motion ceases; while the absolute ground floor displacement equals the experimental (measured) initial displacement at the beginning of motion and the experimental residual displacement at the end of motion. The predicted ground floor displacement matches very satisfactorily the displacement measurement. The developed method is implemented moreover on the relative to the base acceleration signals, for the evaluation of the relative displacement and velocity response of the superstructure. The method assures that the relative response is zero at the beginning and end of motion, since the superstructure remains elastic under such small excitation. The relative response is evaluated in two ways: (i) subtracting the adjusted ground floor response from the adjusted upper floor response and (ii) processing the raw relative motions. The implementation of methodologies (i) and (ii) provides identical relative accelerations and velocities, enforcing the reliability of the method. The relative displacements are high pass filtered to remove the effect of long period noise in the second half period of motion, where the signal amplitude is significantly small and the noise is probably predominant.