The seismic damage of various structures has a significant impact on human production and life, to understand the seismic performance of typical structures and analyze their vulnerability characteristics, and achieve the objective of improving the seismic capacity of structures, and data from 18,480 empirical seismic damage samples from 33 cities and towns for the May 12, 2008, Wenchuan earthquake (China) are summarized and statistically analyzed. The reconnaissance results of the empirical seismic damage show that the structures of masonry structure, multistory reinforced concrete structure, bottom frame-seismic wall masonry and brick-timber and brick-masonry building have the characteristics of widespread application, a myriad of samples and typical failure, sample data for the categories of abovementioned structures are analyzed by statistics and numerical methods, and the empirical seismic damage probability matrix models are established. A nonlinear regression model for calculating the vulnerability grade and the number of samples damaged is proposed. Combined with the empirical sample data, the vulnerability regression function and the curve model of multiple structural types in the VI–X region are established. A mean vulnerability seismic index probability matrix model considering the empirical seismic vulnerability probability in the multiseismic region is proposed. The model is validated by using the above sample database, and the mean damage index matrix in the multiseismic zone is obtained. The analysis results can effectively evaluate the vulnerability characteristics of typical structures in multiseismic regions and provide a necessary reference for a view to a future revision of the building codes and seismic intensity scales currently in force.

Analysis of the probability matrix model for the seismic damage vulnerability of empirical structures

This study aims to consider the effect of soil–structure interaction (SSI) on the ductility and hysteretic energy demands of superstructures and propose empirical equations for demand prediction in soil–structure systems. To this end, the FEMA 440 procedure was considered to develop nonlinear single-degree-of-freedom oscillators with a period range of 0.1–3.0 s, as the representative of superstructures. The elastic-perfectly plastic and a moderate pinching degrading hysteretic models were considered for the nonlinear response of the superstructure. The model of the nonlinear soil–foundation system was developed through the Winkler method. In this regard, the type of soil beneath the foundation was assumed as D category, according to the site classification in ASCE 7-10. A wide range of key parameters, including the strength reduction factors (2 ≤ Rμ ≤ 8), the foundation safety factor (3 ≤ SF ≤ 7), the foundation-to-structure height aspect ratio (1 ≤ h/b ≤ 5), and the foundation length-to-width ratio (3 ≤ Lf/Bf ≤ 20) was introduced into the analytical models to conduct parametric studies. Results show the considerable effect of SSI on reducing the ductility and hysteretic energy demands in superstructures with short fundamental periods. More demand reduction can be achieved by providing the lateral sliding of the foundation on the soil surface, especially for systems with a small aspect ratio. The pinching–degrading hysteretic behavior of the superstructure remarkably modifies the level of demands. Moreover, predictive models were proposed for estimating the ductility and hysteretic energy demands in flexible base systems. These models modify demands in the rigid base structures based on their physical and mechanical properties. The developed models consider the effects of structural hysteretic behavior as well as foundation flexibility. The efficiency of the proposed model was assessed on a multi-story frame. Finally, the required ductility capacity of the systems was determined through the Park–Ang damage index and by using the developed predictive models. Results show the efficiency of the empirical models to reasonably estimate the required ductility capacity.

Estimation of the ductility and hysteretic energy demands for soil–structure systems

The structural damping ratio, structural quality, yield strength, and elastic modulus of section steel, compressive strength, elastic modulus of concrete, yield strength, and elastic modulus of steel bars play important roles in the stability of the steel-reinforced concrete (SRC) frame structure, which are usually uncertain. However, their importance influence on the different seismic demands of SRC is rarely investigated simultaneously. In order to investigate the effects of the above parameters on four seismic demands (i.e., the top displacement, the maximum floor acceleration, the base shear force, and the maximum interstory displacement angle) of SRC frame structures, the orthogonal polynomial estimation method is first applied to the importance analysis of structural seismic demand based on the moment-independent method. Two engineering examples are performed to verify the accuracy and efficiency of the proposed method. The results have the characteristics of fast convergence and are in good agreement with those obtained by the moment-independent method based on kernel density estimation. The variance importance index based on Monte Carlo (MC) method is also calculated for comparison. The influence of each random variable on the four structural seismic demands is basically the same. Therefore, the accuracy and efficiency of the proposed method are proved sufficiently.

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The Moment-Independent Importance Analysis of Structural Seismic Requirements Based on Orthogonal Polynomial Estimation

Displacement is a better indicator of building damage than force; therefore, performance-based seismic design methodologies aim at controlling damage through limiting lateral inelastic displacement of structures. This study aims at predicting the inelastic displacement demand of structures through utilizing artificial neural networks and Bayesian regularization algorithm. A large set of inelastic displacement ratios was computed using nonlinear time history analyses of single-degree-of-freedom oscillators subjected to ground motions recorded on soft soils. Four types of hysteretic models were utilized to cover a wide range of structures, namely flag-shaped, elastic-perfectly plastic, small-Takeda, and large-Takeda hysteretic models. The inelastic displacement ratios were correlated with displacement ductility and structure period normalized to ground motion record predominant period. The study offered insight on inelastic displacement ratios of structures built on soft soils, the effect of structure period, ground motion predominant period, ductility level, and hysteretic model. The inelastic displacement ratios exceeded one for periods less than the record predominant period, while for periods more than 1.5 the predominant period, it was almost equal to one. Furthermore, in the vicinity of the ground motion record predominant period, inelastic displacement demands are smaller than elastic displacement demand. Dispersion of inelastic displacement ratio increases as the inelastic displacement demand increases, while larger dispersion was evident for structures with period ranges between 1.5 and 2.0 times the ground motion predominant period. Finally, the study provided the necessary parameters needed for artificial neural network models to regenerate inelastic displacement ratio models needed in designing structures built on soft soils.

Artificial neural networks prediction of inelastic displacement demands for structures built on soft soils

Earthquake is a regular phenomenon causing enormous damage in different corners of the world. A large number of masonry buildings in various countries, which contain unreinforced masonry (URM) walls are particularly at high risk. These structures are primarily designed to resist vertical load that makes them more susceptible to in-plane or out-of-plane shear forces resulting from lateral loads. Besides, shear resistance of these URM walls decreases due to the deterioration of mortar joint because of aging. Hence, retrofitting of these old buildings has become an important issue. Among several techniques, ferrocement retrofitting can be a low-cost technique in the context of the economic condition of different developing countries. This study aims at investigating the behavior of ferrocement retrofitted unconfined URM walls under both partially reversed cyclic loading and cyclic compression loading. Six 725 mm × 725 mm masonry wall units were prepared with bricks. To compare the effectiveness of ferrocement, two types (18 gauge and 20 gauge) of 12.5 mm × 12.5 mm square opening woven wire meshes were tested. Mix proportion of cement and sand for masonry mortar and ferrocement used were 1:4 and 1:2, respectively with 0.45 w/c ratio. The results showed that the ultimate load-carrying capacities of ferrocement retrofitted specimens were 35–58% and 27–46% greater than the reference specimen under partially reversed cyclic loading and cyclic compression, respectively. Deformations of ferrocement retrofitted specimens before failures were 43%-58% and 33%-46% greater than those of the reference specimens under partially reversed cyclic loading and cyclic compression, respectively.

Experimental study on behavior of ferrocement retrofitted unconfined URM wall under cyclic loading

This study evaluates the seismic vulnerability of an existing URM building which is currently used as a city hall of one of the biggest cities in the east part of Algeria called Constantine. In order to avoid serious damages, in the future, a seismic vulnerability and damage investigation of this kind of buildings are must. A seismic vulnerability study has been considered. Structural analysis is performed based on the site investigation (including inspection of the building and materials characteristics). An analytical procedure for the derivation of fragility curves is proposed. Different tools regarding the determination of capacity curves of the structural system by using a nonlinear analysis are implemented and four damage states are defined. The earthquake action is expressed in terms of spectral values; the probabilities of the damage states are obtained considering a lognormal probability distribution.

Seismic Vulnerability and Damage Assessment of an Existing URM Building

Methods for the seismic demands evaluation of structures require iterative procedures. Many studies dealt with the development of different inelastic spectra with the aim to simplify the evaluation of inelastic deformations and performance of structures. Recently, the concept of inelastic spectra has been adopted in the global scheme of the Performance-Based Seismic Design (PBSD) through Capacity-Spectrum Method (CSM). For instance, the Modal Pushover Analysis (MPA) has been proved to provide accurate results for inelastic buildings to a similar degree of accuracy than the Response Spectrum Analysis (RSA) in estimating peak response for elastic buildings. In this paper, a simplified nonlinear procedure for evaluation of the seismic demand of structures is proposed with its applicability to multi-degree-of-freedom (MDOF) systems. The basic concept is to write the equation of motion of (MDOF) system into series of normal modes based on an inelastic modal decomposition in terms of ductility factor. The accuracy of the proposed procedure is verified against the Nonlinear Time History Analysis (NL-THA) results and Uncoupled Modal Response History Analysis (UMRHA) of a 9-story steel building subjected to El-Centro 1940 (N/S) as a first application. The comparison shows that the new theoretical approach is capable to provide accurate peak response with those obtained when using the NL-THA analysis. After that, a simplified nonlinear spectral analysis is proposed and illustrated by examples in order to describe inelastic response spectra and to relate it to the capacity curve (Pushover curve) by a new parameter of control, called normalized yield strength coefficient (). In the second application, the proposed procedure is verified against the NL-THA analysis results of two buildings for 80 selected real ground motions.

Simplified procedure for seismic demands assessment of structures

Modern seismic codes rely on performance-based seismic design methodology which requires that the structures withstand inelastic deformation. Many studies have focused on the inelastic deformation ratio evaluation (ratio between the inelastic and elastic maximum lateral displacement demands) for various inelastic spectra. This paper investigates the inelastic response spectra through the ductility demand µ, the yield strength reduction factor Ry, and the inelastic deformation ratio. They depend on the vibration period T, the post-to-preyield stiffness ratio α, the peak ground acceleration (PGA), and the normalized yield strength coefficient η (ratio of yield strength coefficient divided by the PGA). A new inelastic deformation ratio Cη is defined; it is related to the capacity curve (pushover curve) through the coefficient (η) and the ratio (α) that are used as control parameters. A set of 140 real ground motions is selected. The structures are bilinear inelastic single degree of freedom systems (SDOF). The sensitivity of the resulting inelastic deformation ratio mean values is discussed for different levels of normalized yield strength coefficient. The influence of vibration period T, post-to-preyield stiffness ratio α, normalized yield strength coefficient η, earthquake magnitude, ruptures distance (i.e., to fault rupture) and site conditions is also investigated. A regression analysis leads to simplified expressions of this inelastic deformation ratio. These simplified equations estimate the inelastic deformation ratio for structures, which is a key parameter for design or evaluation. The results show that, for a given level of normalized yield strength coefficient, these inelastic displacement ratios become non sensitive to none of the rupture distance, the earthquake magnitude or the site class. Furthermore, they show that the post-to-preyield stiffness has a negligible effect on the inelastic deformation ratio if the normalized yield strength coefficient is greater than unity.

Seismic structural demands and inelastic deformation ratios: Sensitivity analysis and simplified models

Seismic structural demands and inelastic deformation ratios: A theoretical approach

In recent years, a new interest has in fact arisen in the displacement based seismic design, especially in tall buildings. Several contributions have already been submitted for the development of different procedures based on displacements with the aim to simplify the evaluation of seismic demands of structures. In this paper, an improved procedure based on displacements applicable to the analysis and design of tall buildings is presented and illustrated by examples. It is considered as a new procedure for estimating the seismic deformation of Multi-Degree-of-Freedom systems. An example of a calculation that highlights the steps involved in applying this inelastic response evaluation approach is included to demonstrate the simplicity of the method. The accuracy of the proposed procedure is verified against the Nonlinear Time History Analysis (NL-THA) results and Uncoupled Modal Response History Analysis (UMRHA) of a 9-story steel building subjected to El-Centro 1940 (N/S) as a first application. In the second application the accuracy of the improved procedure is verified against the nonlinear time history analysis results of two tall buildings. The comparisons showed that the new method gives accurate deformations.

Benazouz Chikh

Papers

Seismic Vulnerability and Damage Assessment of an Existing URM Building

Simplified procedure for seismic demands assessment of structures

Seismic structural demands and inelastic deformation ratios: Sensitivity analysis and simplified models

Seismic structural demands and inelastic deformation ratios: A theoretical approach

Seismic Demands Assessment of Tall Buildings: Theoretical Approach and Applications