Influence of Higher Modes on Strength and Ductility Demands of Soil-Structure Systems

Due to the inherent complexity, the common approach in analysing nonlinear response of structures with soil-structure interaction (SSI) in current seismic provisions is based on equivalent SDOF systems (E-SDOF). This paper aims to study the influence of higher modes on the seismic response of SSI systems by performing intensive parametric analyses on more than 6400 linear and non-linear MDOF and E-SDOF systems subjected to 21 earthquake records. An established soil-shallow foundation-structure model with equivalent linear soil behaviour and nonlinear superstructure has been utilized using the concept of cone models. The lateral strength and ductility demands of MDOF soil-structure systems with different number of stories, structure-to-soil stiffness ratio, aspect ratio and level of inelasticity are compared to those of ESDOF systems. The results indicate that using the common E-SDOF soil-structure systems for estimating the strength and ductility demands of medium and slender MDOF structures can lead to very un-conservative results when SSI effect is significant. This implies the significance of higher mode effects for soil-structure systems in comparison with fixed-based structures, which is more pronounced for the cases of elastic and low level of inelasticity

Performance-based seismic design of flexible-base multi-storey buildings considering soil–structure interaction

A comprehensive parametric study has been carried out to investigate the seismic performance of multi-storey shear buildings considering soil–structure interaction (SSI). More than 40,000 SDOF and MDOF models are designed based on different lateral seismic load patterns and target ductility demands to represent a wide range of building structures constructed on shallow foundations. The cone model is adopted to simulate the dynamic behaviour of an elastic homogeneous soil half-space. 1, 5, 10, 15 and 20-storey SSI systems are subjected to three sets of synthetic spectrum-compatible earthquakes corresponding to different soil classes, and the effects of soil stiffness, design lateral load pattern, fundamental period, number of storeys, structure slenderness ratio and site condition are investigated. The results indicate that, in general, SSI can reduce (up to 60%) the strength and ductility demands of multi-storey buildings, especially those with small slenderness ratio and low ductility demands. It is shown that code-specified design lateral load patterns are more suitable for long period flexible-base structures; whereas a trapezoidal design lateral-load pattern can provide the best solution for short period flexible-base structures. Based on the results of this study, a new design factor RF is introduced which is able to capture the reduction of strength of single-degree-of-freedom structures due to the combination of SSI and structural yielding. To take into account multi-degree-of-freedom effects in SSI systems, a new site and interaction-dependent modification factor RM is also proposed. The RF and RM factors are integrated into a novel performance-based design method for site and interaction-dependent seismic design of flexible-base structures. The adequacy of the proposed method is demonstrated through several practical design examples

Pushover analysis for seismic assessment and design of structures

The earthquake resistant design of structures requires that structures should sustain, safely, any ground motions of an intensity that might occur during their construction or in their normal use. However ground motions are unique in the effects they have on structural responses. The most accurate analysis procedure for structures subjected to strong ground motions is the time-history analysis. This analysis involves the integration of the equations of motion of a multi-degree-of-freedom system, MDOF, in the time domain using a stepwise solution in order to represent the actual response of a structure. This method is time-consuming though for application in all practical purposes. The necessity for faster methods that would ensure a reliable structural assessment or design of structures subjected to seismic loading led to the pushover analysis. Pushover analysis is based on the assumption that structures oscillate predominantly in the first mode or in the lower modes of vibration during a seismic event. This leads to a reduction of the multi-degree-of-freedom, MDOF system, to an equivalent single-degreeof- freedom, ESDOF system, with properties predicted by a nonlinear static analysis of the MDOF system. The ESDOF system is then subsequently subjected to a nonlinear timehistory analysis or to a response spectrum analysis with constant-ductility spectra, or damped spectra. The seismic demands calculated for the ESDOF system are transformed through modal relationships to the seismic demands of the MDOF system. In this study the applicability of the pushover method as an alternative mean to general design and assessment is examined. Initially a series of SDOF systems is subjected to two different pushover methods and to nonlinear-time-history analyses. The results from this study show that pushover analysis is not able to capture the seismic demands imposed by far-field or near-fault ground motions, especially for short-period systems for which it can lead to significant errors in the estimation of the seismic demands. In the case of near-fault ground motions the results suggest that pushover analysis may underestimate the displacement demands for systems with periods lower than half the dominant pulse period of the ground motion and overestimate them for systems with periods equal or higher than half the dominant pulse period of the ground motion. Subsequently a two-degree-offreedom, 2-DOF, is studied in the same manner with specific intention to assess the accuracy of the different load patterns proposed in the literature. For this system pushover analysis performed similarly as in the SDOF study. Finally the method is applied on a four-storey reinforced concrete frame structure. For this study pushover analysis was not effective in capturing the seismic demands imposed by both a far-field and a near-fault ground motion. Overall pushover analysis can be unconservative in estimating seismic demands of structures and it may lead to unsafe design

Response of Steel Moment and Braced Frames Subjected to Near-Source Pulse-Like Ground Motions by Including Soil-Structure Interaction Effects

Most seismic regulations are usually associated with fixed-base structures, assuming that elimination of this phenomenon leads to conservative results and engineers are not obliged to use near-fault earthquakes. This study investigates the effect of soil–structure interaction on the inelastic response of MDOF steel structures by using well known Cone method. In order to achieve this, three dimensional multi-storey steel structures with moment and braced frame are analysed using non-linear time history method under the action of 40 near-fault records. Seismic response parameters, such as base shear, performance of structures, ductility demand and displacement demand ratios of structures subjected to different frequency-contents of near-fault records including pulse type and high-frequency components are investigated. The results elucidate that the flexibility of soil strongly affects the seismic response of steel frames. Soil–structure interaction can increase seismic demands of structures. Also, soil has approximately increasing and mitigating effects on structural responses subjected to the pulse type and high frequency components. A threshold period exists below which can highly change the ductility demand for short period structures subjected to near-fault records

Modal pushover analysis for high-rise buildings

Thesis (M. Eng.)--Massachusetts Institute of Technology, Department of Civil and Environmental Engineering, 2013.Cataloged from PDF version of thesis.Includes bibliographical references (pages 50).Pushover analysis is a nonlinear static analysis tool widely used in practice to predict and evaluate seismic performance of structures. Since only the fundamental mode is considered and the inelastic theorem is imperfect for the conventional pushover analysis, a modified Modal Pushover Analysis (MPA) is proposed by researchers. In this thesis, the theories of dynamics for single-degree-of-freedom (SDOF) and multiple-degree-of-freedom (MDOF) are introduced, including elastic analysis and inelastic analysis. The procedures and equations for time history analysis, modal analysis, pushover analysis and modal pushover analysis are discussed in detail. Then an 8-story height model and a 16-story height model are established for analysis. The pushover analysis is conducted for each equivalent SDOF system, and by combination of the distribution of 1 mode, 2 modes and 3 modes, the responses of modal pushover analysis are obtained. The results of pushover analysis and modal pushover analysis are compared with those of time history analysis. The results of the analysis show that the conventional pushover analysis is mostly limited to low- and medium-rise structures in which only the first mode is considered and where the mode shape is constant. The modal pushover analysis is shown to have a superior accuracy in evaluation of seismic demands for higher buildings, especially for story drift ratios and column shears. With this in mind, some design recommendations and areas of future work are proposed in the conclusion.by Ming Zheng.M.Eng

Estimation of Earthquake Input Energy, Hysteretic Energy and its Distribution in MDOF Structures

Current seismic codes for building design often utilize a force or a displacement-based approach in their implementation. In a force-based approach, a structure is designed to ensure it possesses sufficient strength to resist the maximum forces imparted to it by an earthquake. In a displacement-based approach, a target displacement is calculated or identified and the structure is proportioned to achieve a specified performance level, defined by strain or drift limits, under a specified level of seismic intensity. A third approach, which has gained momentum in the earthquake engineering community, is the energy-based approach. In this approach, a design is considered satisfactory if the capacity of a structure to absorb or dissipate energy exceeds its energy demand from an earthquake. In the present research, a new energy-based approach is proposed in which velocity index (VI), obtained as the product of two ground motion indexes - peak ground velocity (PGV) and cumulative absolute velocity (CAV), is used to normalize input energy spectra. The use of VI as a normalization factor not only allows for the creation of dimensionless input energy spectra, but can result in smaller values of coefficients of variation when compared to other normalization factors currently being used. Earthquake input energy spectra for four site classes (Site Class B, C, D and E as per IBC 2012 soil classifications) and four hysteretic models (bilinear plastic, stiffness degradation, bilinear flag and bilinear slip) are developed for five ductility levels (=1, 2, 3, 4, 5) using ground motion ensembles of 38, 42, 38 and 26 recorded at site classes B, C, D and E, respectively. For purpose of design, the normalized input energy spectra are divided into three regions - short period, intermediate period and long period - that are consistent with the customary design response spectra contained in various seismic codes and standards. A close examination of these spectra has shown that regardless of the hysteretic models used, the normalized seismic input energy decreases as ductility increases, and increases as the soil gets softer. For each site class, empirical ductility dependent input energy expressions are developed, and hysteretic to input energy ratio relationships are formulated. The proposed design input energy spectra are validated using six major earthquakes and are found to reasonably match the spectra generated using time history analysis. Since the input energy spectra are developed for single-degree-of-freedom (SDOF) systems, to facilitate the implementation of the proposed method in the design of multi-degree-of-freedom (MDOF) systems, simple expressions that relate earthquake input and hysteretic energies for MDOF system to its equivalent single-degree-of-freedom (ESDOF) systems are formulated. The energy relationships are verified using four (a three story, a five story, a seven story and a nine story) frames each subjected to six earthquakes wherein a very good estimate for the three- and five- story and a reasonably acceptable estimate for the seven-, and nine-story frames were obtained. A new method for distributing hysteretic energy over the height of moment resisting frames is also proposed. The new distribution scheme was used in determining the energy demand (hysteretic energy) component of an energy-based seismic design (EBSD). EBSD is a story-wise optimization design procedure developed using the relationship that exists between energy dissipating capacity and plastic analysis/design of structures. Finally, the entire process of determining the input energy for ESDOF systems to the distribution of hysteretic energy over the height of MDOF structures using the proposed EBSD design procedure is demonstrated using two design examples: a three-story one-bay frame and a five-story two-bay frame

Behavioural Factors Effect On Drift Demand For Tall Reinforced Concrete Buildings Subjected To Repeated Far-Field Earthquakes

Real earthquake event does not appear in single tremor but actually lead to appearance of several tremors consecutively. It is found that the sequences of ground motions have a significant effect on the response of reinforced concrete (RC) frames building. Previous research done mostly ignored the importance of the effect of repeated far-field earthquake (FFE) event. This thesis presents a seismic response evaluation of two tall building models in term of drift demand subjected to single and repeated FFE records at various behavioural factors, qo using linear and nonlinear analysis. Analysis was performed in bi-directional horizontal components of the building by subjecting the RC structural model to FFE in single, double and triple of 20 strong earthquake events. The performances of both tall building models were evaluated based on seismic action towards the stiffness and strength of the building model. From all results obtained, drift demand drastically increases with 18m different in height between top floor of twelve (N=12) RC storey and 17th floor of eighteen (N=18) RC storey building models with same structural element properties

Surrogate probabilistic seismic demand modelling of inelastic single-degree-of-freedom systems for efficient earthquake risk applications

This paper proposes surrogate models (or metamodels) mapping the parameters controlling the dynamic behaviour of inelastic single-degree-of-freedom (SDoF) systems (i.e., force-displacement capacity curve, hysteretic behaviour) and the parameters of their probabilistic seismic demand model (PSDM, i.e., conditional distribution of an engineering demand parameter [EDP] given a ground-motion intensity measure [IM]). These metamodels allow the rapid derivation of fragility curves of SDoF representation of structures. Gaussian Process (GP) regression is selected as the metamodelling approach because of their flexibility in implementation, the resulting accuracy and computational efficiency. The metamodel training dataset includes 10,000 SDoF systems analysed via cloud-based non-linear time-history analysis (NLTHA) using recorded ground motions. The proposed GP regressions are tested in predicting the PSDM of both the SDoF database (through ten-fold cross validation) and eight realistic reinforced concrete (RC) frames, benchmarking the results against NLTHA. An application is conducted to propagate such modelling uncertainty to both fragility and vulnerability/loss estimations. Error levels are deemed satisfactory for practical applications, especially considering the low required modelling effort and analysis time. Regarding single-building applications enabled by the proposed metamodel, this paper presents a first attempt at a direct loss-based design procedure, which allows setting a target loss level for the designed structure (shown for a realistic RC frame). An earthquake risk model involving dynamic exposure and vulnerability modules is illustrated as an example of building portfolio applications. Specifically, the proposed application considers a retrofit-based seismic risk-reduction policy for a synthetic building portfolio, for which it is possible estimating the loss evolution over time

Impact of ground-motion duration on nonlinear structural performance: Part I: spectrally equivalent records and inelastic single-degree-of-freedom systems

In current seismic performance-based assessment approaches, nonlinear dynamic analysis of structures generally relies on ground motions selected based on their pseudo-spectral accelerations, with little or no consideration for ground-motion duration. Part I of this study, presented in this article, attempts to comprehensively quantify the impact of ground-motion duration on the nonlinear structural performance of case-study inelastic single-degree-of-freedom systems for shallow-crustal seismicity conditions. The effect of duration is decoupled from that of ground-motion amplitude and spectral shape by assembling sets of spectrally equivalent long- and short-duration records. Such sets are employed in incremental dynamic analyses of a wide range of computational models incorporating in-cycle and cyclic strength and stiffness deterioration. The structural response is quantified in terms of peak- and cumulative-based engineering demand parameters. Formal hypothesis testing is used to assess the statistical significance of duration’s impact on the median structural capacity of the considered structural systems. Furthermore, the derivation of duration-dependent fragility and vulnerability relationships demonstrates that ground-motion duration effectively impacts the nonlinear structural performance of various systems, and it should be accounted for in current practice. The fragility median values for highly deteriorating structural systems under long-duration ground motions are found to be up to 21% or 34.0% smaller than the short-duration counterpart if a peak- or cumulative-based engineering demand parameter is adopted, respectively