Evaluation of the Nonlinear Seismic Response of an Earth Dam: Nonparametric System Identification

A system identification framework is proposed to investigate the nonlinear dynamic response of massive earth dams using the seismic motion recorded by a sparse array of accelerometers. The framework includes a methodical step of nonparametric analyses to characterize the involved loading conditions and response mechanisms. This nonparametric step provides essential information to reduce the indeterminacy of the associated parametric identificatin problem and ensure a proper model selection, calibration, and validation. The proposed framework was applied to the Long Valley earth dam (California) and benchmarked using records of a series of 1980 earthquakes. This article presents the conducted correlation, spectral motion reconstruction, and nonparametric stress-strain analyses. These analyses revealed a complex three-dimensional dynamic response marked by non uniform boundary conditions and a shear stress-strain behavior slightly less nonlinear than what was observed in triaxial tests of soil samples taken from the dam core.     

SYSTEM IDENTIFICATION OF LANDFILL SEISMIC RESPONSE

Assessment of landfill seismic response necessitates the availability of reliable dynamic material properties. During the past decade, geophysical surveys and computational studies have been conducted to investigate the seismic response of the Operating Industries, Inc. (OII) landfill in Southern California. In this paper, a survey and summary of available research results is presented. In addition, a set of Oil input-output seismic records during six earthquakes is thoroughly analysed. Spectral analyses are conducted to shed light on the landfill dynamic response characteristics. A simple shear beam model is found to be useful in modelling the landfill resonant behaviour. System identification techniques are employed to estimate the landfill stiffness and damping properties. These properties are defined by minimising the difference between computed and recorded acceleration response spectra at the landfill top. The identified stiffness properties are found to be near the lower bound of those documented through geophysical measure-ments. Identified damping of about 5% (at resonance) is within the range of earlier investigations. Comparisons of the computed and recorded accelerations show: (I) effectiveness of a linear viscous shear beam model in simulating the landfill dynamic behaviour, for the recorded small to moderate levels of dynamic excitation (up to 0.26 g peak lateral acceleration), and (ii) potential of the employed system identification procedure for analysis of input-output seismic motions.     

A COMPARATIVE STUDY ON THE ACTUAL AND ESTIMATED SEISMIC RESPONSE OF KIRALKIZI DAM IN TURKEY

Kiralkizi Dam, a 120 m high earthfill dam located in Diyarbakir city, Turkey, was shaken by a moment magnitude, M _w =4.6 earthquake at an epicentral distance of 8 km, on December 24, 2000, at 13:31 local time. The seismic response of the dam was assessed by using spectral ratios between (i) available crest and foundation records (C/F), (ii) horizontal and vertical components of the recorded motions (H/V), (iii) by performing 2 dimensional finite difference-based seismic response analyses (Flac-2D), and (iv) ID elastic shear beam solutions. First mode of vibration of the dam in the transverse direction by all four methods were estimated in the range of 0.55 to 0.62 second. Similar close agreement was not observed in higher modal periods estimated by H/V technique as compared to the predictions by C/F, Flac-2D, shear beam analysis techniques. Thus, H/V technique was concluded to be useful for the estimation of the fundamental resonance frequency of a soil structure, but not for its higher harmonics as consistent with available limited literature. In the longitudinal direction, natural period of the dam was estimated as 0.28 and 0. 82 second by H/V and C/F techniques, respectively. Such disagreement was explained by (i) differences in the definitions of the estimated periods, (ii) internal impedance contrast of the dam, (iii) contributions of 3D valley effects. Single seismometer record obtained from crest level was found to be inadequate for reliably assessing the response of a dam in the longitudinal direction, and it is recommended to install multiple seismometers both within dambody and the abutments. Last but not least, the results of these analyses were further compared by available accelograms recorded at three earthfill and rocknll dams from Japan. In general, it was concluded that the seismic response of Kiralkizi Dam is comparable and within the prediction ranges of available analyses methods and is consistent with the expected response of a dam this height.     

Dynamic Characteristic Analysis of Two Adjacent Multi-grid Composite Wall Structures with a Seismic Joint by a Bayesian Approach

Field ambient vibration tests and modal identification using a Bayesian approach are conducted for a building made of multi-grid composite wall structure and divided into two adjacent parts by a seismic joint, to investigate the dynamic characteristics of the special structural type and the effects of the infilled seismic joint. It is found that dynamic interactions between the two structural parts exist possibly induced by the infill of the building separation. Natural frequencies obtained from other two modal parameter identification methods and modal analysis results of finite element models considering dynamic interactions agree with those identified by the Bayesian approach.     

Seismic Resistant Effects of Composite Reinforcement on Rockfill Dams Based on Shaking Table Tests

In this article, the seismic resistant effect of a new reinforcement measure on rockfill dams, the Composite Reinforcement, is investigated based on 1-g large-scale shaking table tests. A 1 m high rockfill dam, which is scaled from the Yele rockfill dam in China, is tested by inputting a series of motions designed from a realistic Wenchuan earthquake record. The model dam is divided into two sections, with one section representing a normal rockfill dam (RD) while the other section employing the Composite Reinforcement (composite reinforced rockfill dam (CRRD)). The seismic-resistant effect of the Composite Reinforcement is investigated by comparing the recorded dynamic response of the two dams, in terms of the peak acceleration amplification factor distribution along the dam core, the crest settlement, and the visualized failure pattern. Results show that the application of the Composite Reinforcement can effectively mitigate the seismically induced deformation of the rockfill dam by reducing the peak crest acceleration and residual crest settlement by 18% and 55%, respectively, when subjected to a 0.5 g input motion. The investigation of the captured failure pattern on the two dams further indicates the effective reinforcing effect of the Composite Reinforcement on preventing the sliding failures of rockfill materials in the top 20% height of the dam body.     

IDENTIFICATION AND VERIFICATION OF SEISMIC DEMAND FROM DIFFERENT HYSTERETIC MODELS

The goal of this paper is to develop a modified Bouc-Wen hysteretic model from cyclic loading test data for reinforced columns, including the behavior of stiffness degradation, strength deterioration, pinching and softening effects of RC members. Seismic demands on this inelastic single degree of freedom system when subjected to both near-fault ground motion and far-field ground motion excitations were examined.

The cyclic loading test of reinforced concrete columns was experimentally observed and a system identification computer program was developed to solve each control parameter of the hysteretic model. A least-squared method for identifying parameters of the model is proposed in this paper. The hysteretic constitutive law produces a smoothly varying hysteresis such as the control-parameters for strength deterioration, stiffness degradation, pinching and softening effects. Two implementations of (1) flexure damage and (2) shear damage were conducted to provide better understanding of hysteretic behavior of RC structural members. A pseudo-dynamic experiment was also developed to verify the model parameters.

Based on the developed hysteretic model, the seismic demand of this inelastic model was investigated by using both near-fault ground motion data and far-field ground motion data as input motion. An R-μT inelastic response spectrum from different hysteretic models was generated.     

Dynamic Analysis and Seismic Response of Planar Circular Arches with Variable Cross-Section

The aim of this paper is to investigate the dynamic response of planar circular arches with variable cross-section subjected to seismic ground motions. Arches have a wide range of application (e.g. bridges, roofs) thanks to their capacity to span large areas by resolving vertical actions into compressive stresses and confining tensile stresses. The full understanding of their dynamic response is a challenging technical and computational problem, especially when seismic loading is considered. For example, the assumption of axial inextensibility simplifies the differential equations but overestimates the vibration frequencies, especially those of shallow arches since axial forces are of paramount importance (as opposed to beams). In lieu of the above, our formulation incorporates the effect of axial extension, and the arches are modeled using a new generic curved beam model that includes both axial (tangential) and transverse (normal) to the arch centerline deformations, and is able to account for variable mass and stiffness properties, as well as elastic support or restraint. The resulting dynamic governing equations of the circular arch are formulated in terms of the displacements, and solved using an efficient integral equation method. Three circular arches with variable rectangular cross-section are analyzed in order to investigate their dynamic properties and seismic performance. Using both time history and modal analysis useful conclusions are drawn with regard to the contribution of each mode on the calculation of different response quantities.     

Natural Frequency of Single Pier Bridges Considering Soil-Structure Interaction

Because of the crucial role of free vibration frequency of a structure (e.g., a bridge) in design procedure, more realistic estimation of the frequency ends up in safer and more optimized design. As obtaining the free vibration frequencies of a bridge, considering soil-pile group-structure interaction, provide more realistic values, development of an analytical model to obtain such free vibration frequencies is studied in this research work. Most researchers have studied models with a single pile foundation. The purpose of this study is to assess soil-structure interaction (SSI) effects on dynamic performance of pile group supported bridges. A new analytical model is proposed to predict seismic analysis of these bridges. Applying the dynamic equations of motion for the system, SSI effects have been estimated. Based on the suggested analytical model, a new approximate equation is proposed for calculating natural frequency of pile group supported bridges. Equation accuracy has been investigated by comparing the results with those achieved by previous studies. Most periods calculated by the approximate equation are similar to those given for other case studies, indicating that the model could be applicable to other projects. Since the proposed model is very similar to real soil-pile-pier systems, this approximate equation can be used in preliminary seismic design of bridges.     

Shaking table tests on a stone masonry building: modeling and identification of dynamic properties including soil-foundation-structure interaction

This article presents the identification of dynamic properties of a stone masonry building, followed by numerical simulation of its dynamic response accounting for soil-foundation-structure interaction. The first part regards numerical simulations of the earthquake response of a two-story building prototype with timber floors, made of three-leaf stone masonry without laces. This 1:2 scale prototype was tested on a shaking table in its as-built state and after strengthening, at the National Technical University of Athens. Afterward, the building prototype was modeled with flat shell elements and equivalent frames (common frames and macro-elements), for an investigation of its linear and nonlinear seismic response, assuming base fixity. Numerical results were compared to the experimental ones, which yielded conclusions on the considerations of each employed modeling strategy, as well as its efficiency and applicability. The second part considers the effect of soil-structure interaction using appropriately modified foundation stiffness values to account for the foundation soil flexibility. Comparison of the numerical results with and without SSI effects showed how the flexibility of the soil-foundation system and the soil-structure interaction modified the system’s modal characteristics and response within the elastic range, in terms of both seismic loads and deformations, and produced conclusions about its consequences on the overall structural stability.     

Unusual Overshooting in Steady-state Response for Structure-dependent Integration Methods

It is numerically illustrated that an unusual overshooting phenomenon might occur in the solution of a forced vibration response if a structure-dependent integration method is applied to conduct the analysis, such as Chang explicit method [2002] and CR explicit method [2008]. This overshooting may occur in the steady-state response of a high frequency mode and it becomes significant as the natural frequency of the mode increases. This unusual overshooting behavior can be successfully detected by using a local truncation error derived from a forced vibration response rather than a free vibration response. A missing loading term in the difference equation for displacement increment is responsible for this unusual overshoot. It is analytically and numerically verified that the unusual overshooting behavior will automatically disappear after introducing the missing loading term into the difference equation for displacement increment.     

Dome of the Basilica of Santa Maria Degli Angeli in Assisi: Static and Dynamic Assessment

This study presents the results of the static and dynamic assessment of the dome of the Basilica of Santa Maria degli Angeli in Assisi, designed by Galeazzo Alessi. The first section is devoted to an overview of the masonry domes designed by the Italian architect and focuses on the structural solutions adopted in the several cases described to better understand Alessi’s designing skills. In the second part, the drum-dome system is analyzed in order to attain a structural assessment. The static assessment is performed by means of limit analysis and finite element model approaches with non-linear mechanical behavior. The obtained results are consistent with the detected crack pattern and confirm the suitability of the reinforcement steel rings applied to the drum. The seismic assessment has been performed by response spectrum analysis. Due to the lack of specific information, a probabilistic approach for the material mechanical properties was used. The results obtained highlight an adequate seismic response of the structure that can be attributed to the dynamic properties of the slender drum-dome system. This finding justifies the good performance of the structure during the seismic events of 1832 and 1997.     

Implications of Thrown-Out Boulders for Earthquake Shaking

In the source areas of some large shallow earthquakes, we have found many dislodged boulders struck by severe ground shaking. Some boulders were located at quite distances from the former sockets, which remained undisturbed with surrounding clear edges. This fact indicates the possibility that vertically upward seismic acceleration exceeded the earth's gravity (1g). This phenomenon of upthrown boulders is investigated herein by examining the effects of waves, which emanate deep in the ground due to an earthquake, propagate through the ground and boulder, and reflect back to the ground, involving a variety of their interaction. An elastic dynamic analysis is carried out on the basis of a one-dimensional continuum model consisting of the ground and boulder. It is subjected to the input of the Ricker wave, which is intended to simulate an earthquake-generated wave, emanating from the bottom of the model ground. The upthrow of a boulder is taken to occur when the dynamic response at the bottom of the boulder satisfies certain conditions. It turns out that the possibility of upthrow occurrence is high when the period of the Ricker wave coincides with the fundamental period of the ground vibration. It leads to the conclusion that the upthrow takes place due to resonance in the response of the system of the ground and boulder to the external wave input. The upthrow possibility increases as the input acceleration increases. Trial is made of predicting the maximum acceleration and velocity of an earthquake, based on this consideration of the up throw phenomenon.     

Finite Element Analysis of Dam-Foundation Coupled System Considering Cone-Type Local Non-Reflecting Boundary Condition

This article deals with the seismic analysis of the dam-foundation coupled system considering direct coupling approach using displacement based finite element method. A cone-type local non-reflecting boundary condition (NRBC) is adopted to model the semi-infinite soil domain. The reservoir effect adjacent to dam body has also been incorporated in the analysis. The results depict the superiority of the proposed NRBC in absorbing spurious wave reflections over the traditional viscous boundary conditions. The analysis results show that the dynamic response of the dam gets highly affected due to the consideration of the elastic foundation domain at its base.     

COMPLEX MODE SUPERPOSITION ALGORITHM FOR SEISMIC RESPONSES OF NON-CLASSICALLY DAMPED LINEAR MDOF SYSTEM

This paper deals with a complex mode superposition method for the seismic responses of general multiple degrees of freedom (MDOF) discrete system with complex eigenvectors and eigenvalues. A delicate general solution, completely in real value form, for calculat-ing seismic time history response of the MDOF system which cannot be uncoupled by normal modes, is deduced based on the algorithms of the complex superposition method. This solution comprises of two parts which are in relation to the Duhamel integration to sine and cosine function respectively. The related term of the Duhamel integration to sine function is actually the displacement response of the oscillator with corresponding modal frequency and the damping ratio. The other can be transferred into a combina-tion of the displacement and velocity responses of the same oscillator. In order to meet the practical needs of seismic design based on code design spectra for various kinds of structures equipped by viscous dampers, the complex complete quadratic combination (CCQC) method is deduced following similar procedures such as the well-known CQC method, in which a new modal velocity correlation coefficient, together with a new modal displacement-velocity correlation coefficient are involved besides the modal displacement correlation coefficient in normal CQC formula. The new algorithm of CCQC is not only as concise as that of the normal CQC but also has explicit physical meaning. The results obtained from complex mode superposition approaches are discussed and verified in some examples through step by step integration computation under a prescribed earth-quake motion input. From these examplary analyses, it may be pointed that the CCQC algorithm normally yields conservative outcome and that the forced mode uncoupling approach has good approximation even the discussed examplary structures are strongly non-proportional.     

Numerical Evaluation of Seismic Soil Pressures on Rigid Walls Fixed to the Bedrock

Seismic soil pressures developed on a 7 m rigid retaining wall fixed to the bedrock are investigated using a finite element model that engages nonlinear soil intended materials available in OpenSees. This allows incorporation of the inelastic behavior of the soil and wave propagation effects in the soil-wall system seismic response. The nonlinear response of the soil was validated using the well-stablished, frequency-domain, linear-equivalent approach. An incremental dynamic analysis was implemented to comprehensively examine the effect of soil nonlinearity and input motion on the induced seismic pressures and to evaluate current code equations/methodologies at different levels of earthquake intensity. The results show that soil nonlinearity and seismic wave amplification may play an important role in the response of the soil-wall system. Therefore, methodologies that rely only on peak ground acceleration may introduce large bias on the estimated seismic pressures in scenarios where high nonlinearity and site amplification are expected.     

Application of Particle Motion Technique to Structural Modal Identification of Heritage Buildings

Determining the behavior of a structure estimated by means of finite elements analysis requires not only an in-depth knowledge of its geometry and dynamic properties but also an experimental validation to corroborate the adequacy of the characteristics of the structure. Most of the current structural identification techniques are based on linear methods that call for many measurement points and/or a relative simple structure. Complex structures are somewhat still an unexplored field due to the difficulties with the finite element method and the experimental corroboration of its results. This study presents the use of particle motion computation applied to each structural vibration mode to improve the identification of its dynamic properties, and its application to the Gothic Cathedral of Palma de Majorca (Spain).     

NONLINEAR SHAKE TABLE IDENTIFICATION AND CONTROL FOR NEAR-FIELD EARTHQUAKE TESTING

The primary focus of a structural shake table system is the accurate reproduction of acceleration records for testing. However, many systems deliver variable and less than optimal performance, particularly when reproducing large near-field seismic events that require extreme table performance. Improved identification and control methods are developed for large hydraulic servo-actuated shake table systems that can exhibit unacceptable tracking response for large, near-field seismic testing. The research is presented in the context of a 5-tonne shake table facility at the University of Canterbury that is of typical design. The system is identified using a frequency response approach that accounts for the actual magnitudes and frequencies of motion encountered in seismic testing. The models and methods developed are experimentally verified and the impact of different feedback variables such as acceleration, velocity and displacement are examined.

The methods show that shake table control in testing large near-field seismic events is often a trade off between accurate tracking and nonlinear velocity saturation of the hydraulic valves that can result in severe acceleration spikes. Control methods are developed to improve performance and include both acceleration and displacement feedback to reduce the acceleration spikes, and record modification, where the reference signal is modified to conform to the shake table's operational parameters. Results show record modification gives exact tracking for near-field ground motions, and optimal system response for reference signals with velocity components greater then the system capabilities. Overall, the research presents a methodology for simple effective identification, modelling, diagnosis and control of structural shake table systems that can be readily generalised and applied to any similar facility.     

Stochastic Quantification of Soil-Shallow Foundation-Structure Interaction

This article highlights soil-structure interaction (SSI) effects on the seismic structural response accounting for uncertainties in the model parameters and input ground motions. A probabilistic Monte Carlo methodology was used to conduct approximately six million dynamic time-history simulations using an established rheological soil-shallow foundation-structure model. Considering the results yields outcomes that contradict prevailing views of the always beneficial role of SSI. In other words, the likelihood of having amplification in structural response due to SSI is large enough that it cannot be readily ignored. This research provides a significant first step towards reliability-based seismic design procedures incorporating foundation flexibility.     

Definition of Seismic Input for Out-of-Plane Response of Masonry Walls: I. Parametric Study

Response of masonry walls to out-of-plane excitation is a complex, yet inadequately addressed theme in seismic analysis. The seismic input expected on an out-of-plane wall (or a generic “secondary system”) in a masonry building is the ground excitation filtered by the in-plane response of the walls and the floor diaphragm response. More generally, the dynamic response of the primary structure, which can be nonlinear, contributes to the filtering phenomenon. The current article delves into the details and results of several nonlinear dynamic time-history analyses executed within a parametric framework. The study addresses masonry structures with rigid diaphragm response to lateral loads. The scope of the parametric study is to demonstrate the influence of inelastic structural response on the seismic response of secondary systems and eventually develop an expression to estimate the seismic input on secondary systems that explicitly accounts for the level of inelasticity in the primary structure in terms of the displacement ductility demand. The proposed formulation is discussed in the companion article.     

The SAFE Experimental Research on the Frequency Dependence of Shear Wall Seismic Design Margins

The SAFE experimental programme consists of a series of 10 specimens of shear walls, with different reinforcement ratios, tested until their ultimate capacity under seismic input motion by the pseudo dynamic method. A unique input signal is used, calibrated for controlling the seismic demand. Its input central frequency is selected so that for some specimens it is lower than their eignenfrequency, while for other ones it is the opposite. In conclusion there is clear experimental evidence that design margins are much larger in the second case (input central frequency larger than structure eignenfrequency) than in the first one.