Seismic Design Of Buildings Research Articles

Advanced ANN regularization-based algorithm for prediction of the fundamental period of masonry infilled RC frames

The fundamental period (TFP) of vibration is the time required for a structure to complete one full cycle of vibration, and it is one of the main features of the structural system. It highly influences the behavor of structures under earthquake excitation. Therefore, its determination is of highest importance for the seismic design of buildings. This is a complex task in a case of masonry infilled RC frames, due to high stiffness of infill walls and their interaction with the surrounding frame. In this study, using Artificial Neural Network (ANN) algorithms, the fundamental (natural) period of vibration of fully or partially masonry infilled Reinforced Concrete (RC) frame structures was evaluated. Accurate prediction of TFP has a key role in ensuring the safety and resilience of structures, which is particularly expressed in seismic-prone regions. The collected database from open literature contains 4026 samples which cover a wide range of RC frames. For practical reasons, the database is divided in the preprocessing phase into two parts that contain either bare frames or fully/partially infilled frames. The authors compared first and second-order ANN paradigms, and conducted feature importance analysis. The proposed models were validated and verified by comparison with the experimental data, seismic design codes, and derived equations by other researchers. In addition to the superiority that the BRA model has shown in comparison with other solutions, it also enables simpler approach for the calculation of TFP, unlike the proposals of other authors. Based on the results from best ANN model, multi-objective optimization genetic algorithm was employed for additional optimization of TFP which include investigation of the most optimal solutions between two conflicting objective functions.

Study on Damage Index for Beam–Column Joints with Flush End-Plate Connections

Experimental results from 109 flush end-plate (FEP) connections were analyzed to investigate the failure modes and damage index of FEP connections across various damage states. The present study was conducted in accordance with the performance design objectives specified in China’s GB50011-2010 Code for Seismic Design of Buildings. The observed rotation angles and corresponding rotation factors were systematically categorized using a probabilistic statistical approach, with the 95% confidence lower limit as the primary constraint. The damage states of FEP connections were classified as virtually undamaged, lightly damaged, moderately damaged, severely damaged, and joint failure. A minimum plate thickness of 12 mm and a minimum high-strength bolt diameter of 20 mm are recommended to be used for the FEP connections, in accordance with building codes in China, the United States, and Europe. Quasi-static tests of six FEP connections were conducted to validate the damage-state categorization. The results revealed that for connections undergoing moderate and severe damage, the mean rotation factor deviated from the theoretical values proposed in this study by 3.7% and 9.4%, respectively. Therefore, the damage state of FEP connections can be reliably predicted based on different rotation angles using the damage-state categorization presented herein.

Impact of Various High Intensity Earthquake Characteristics on the Inelastic Seismic Response of Irregular Medium-Rise Buildings

In the twenty-first century, the seismic design of buildings seems to have become a fully recognized topic. There are guidelines and standards which should be taken into account by designers in seismic areas. Designers using modern international guidelines have ascertained that the behavior of structures is not as expected. New challenges in the construction industry result in the construction of structures with new, unusual shapes. These are structures that do not meet the assumptions of safe construction in seismic areas. Contemporary buildings are also characterized by their irregular distribution of structural elements. Such solutions are not beneficial from the point of view of seismic engineering and can lead to reduced dynamic resistance and damage in such structures. In this paper, a five-storey, irregular-shaped reinforced concrete (RC) building model was subjected to different earthquakes with varying magnitudes, PGA (peak ground acceleration) and PGV (peak ground velocity) values, and durations of the intense shock phase. Once the model was verified using previous in situ measurements, the building model was subjected to five earthquakes. A numerical nonlinear analysis of the building was performed using a verified FEA (finite element analysis) model in the time domain through non-linear time history analysis with the Broyden–Fletcher–Goldfarb–Shanno (BFGS) method. The building’s dynamic properties were measured using various methods of excitation. The model was influenced, among others, by two far-field representative events caused by the last earthquake in Turkey, which resulted in strong ground motion. The analysis results identified the locations of structural damage and allowed for the assessment of the structure’s dynamic resistance. The results of the calculations prove that the duration of the intensive phase of extortion is one of the reasons for building damage in earthquake-prone areas. Building damage occurs with earthquakes that are characterized by an intensive phase of excitation with a long duration and high values of velocity in the earthquake components. The article highlights the inadequate dynamic resistance of the building, leading to excessive displacements and unfavorable structural solutions. Damage to buildings at this earthquake intensity caused damage to the load-bearing structure, which was not designed for such intensities. This paper is a research report with a specific case study of medium-rise irregular RC buildings.

Dynamic performance of a 5-story full-scale prestressed precast space frame structure under edge and corner column failure scenarios

Progressive collapse resistance is more critical for precast concrete than cast-in-place structures. Most existing studies utilized scaled-down and quasi-static pushdown tests on substructures with rigid constraints under key member failure scenarios. However, the connection details, the spatial action of floors and the constraint stiffness of the remaining structure significantly affect the structure's progressive collapse resistance. Full-scale structural testing is the most direct method to evaluate the progressive collapse resistance of a new prefabricated structure, although it is difficult and costly to load and measure. A 2 × 2 bay 5-story full-scale frame structure was constructed according to the minimum requirements of the Code for Seismic Design of Buildings to investigate the progressive collapse resistance of a new precast, prestressed, efficiently fabricated frame (PPEFF) system. The structure's dynamic performance was analyzed by removing the 4th-floor edge column and bottom corner column. The slider and double micro-friction surface configuration proved suitable for the rapid removal of large axial force columns in a full-scale progressive collapse experiment. The layout of the full-scale structural test and the structure's dynamic responses are described. The effect of the lateral constraint stiffness and the duration of column removal on the dynamic response of the test structure were analyzed using finite element analysis. The progressive collapse resistance mechanism of the PPEFF structure was discussed. The PPEFF system remained in an elastic state and exhibited good progressive collapse resistance.

Educating non-specialized audiences about seismic design principles using videos and physical models

The prevalence of self-construction practices in Türkiye has resulted in a building stock whose earthquake resilience is highly uncertain. To mitigate the potentially devastating impact of anticipated large earthquakes, one viable approach is to increase earthquake awareness among builders themselves. However, these builders lack formal engineering training and are ordinary citizens. Therefore, the challenge lies in devising visual teaching methods, such as short videos, to explain complex seismic phenomena in a comprehensible manner. This paper introduces the use of educational media tailored for non-specialized audiences, encompassing regular citizens and students without engineering backgrounds. These videos are based on experiments conducted with physical models on a homemade shake table. They focus on key factors influencing the seismic response of multi-storey buildings and highlight common design and construction errors that lead to building damage. To assess the effectiveness of this approach, we conducted a workshop with junior architecture students, followed by post-workshop qualitative assessments through knowledge surveys and interviews. The findings indicate that while single-topic videos were effective learning tools for students without prior knowledge of seismic building design, students found models particularly useful for explaining specific concepts such as torsional behavior, the role of diaphragms, and the performance of non-structural components. However, despite positive feedback on the effectiveness of model testing, students generally did not perceive significant knowledge acquisition in model construction. Ultimately, the accessibility of freely available videos, coupled with their enhanced educational value, makes them effective tools for raising seismic awareness in communities vulnerable to future earthquakes.

Seismic design of buildings in the context of regions: A case study of a site in Semnan city, Iran

The seismic codes focus on single buildings and ignore the interdependencies between various sectors and infrastructure. This approach cannot ensure resilient communities and ignores essential aspects of seismic risk (e.g., exposure element). This paper proposes a regional-based design (RBD) method that considers the performance of individual components as well as the interactive consequences of their design on the communities. Unlike most studies, the proposed RBD method considers a dynamic behavior for a region/city and utilizes its master plan to model the stochastic variations in the future built environment. The method determines buildings' seismic design requirement (SDR) by considering the building-level and regional goals. Building-level goals address the most important performance objectives (e.g., safety in residential buildings) and should be satisfied for each structural system and occupancy. However, the method satisfies the regional goals for any structural system. This implies that if (hypothetically) all the buildings in a region/city were designed and constructed with only one structural system (e.g., special steel moment resisting frames, SMRFs), the regional goals should be satisfied. The method starts with the determination of the SDRs by satisfying equal building-level objectives for each occupancy in various locations of the region with one structural system. Then, to achieve the regional goals, the calculated SDRs are uniformly raised to improve the performance of the buildings (if required). The method also considers factors other than the buildings/facilities' performance that could affect the achievement of the regional goals (e.g., emergency response capacity). As a proof-of-concept, the proposed method is used in a site in Semnan City, Iran, to determine the SDR of steel SMRFs. The case study shows that there might be situations where elevating the seismic design requirements of the buildings could not guarantee the achievement of some regional goals. Moreover, the results indicate that factors like the design of the built environment could affect regional risks. Therefore, attention to factors other than the buildings' seismic performance is also essential in achieving the regional goals.

Predicting natural vibration period of concrete frame structures having masonry infill using machine learning techniques

The natural period of vibration is one of the most significant factors used in the seismic design of buildings. Although the building design codes and previous studies provide some empirical methods to compute the natural period of vibration (T), their marginal accuracy and inability to incorporate the effect of masonry infill on vibration period significantly limits their use. Thus, researchers are constantly trying to find new and accurate methods to calculate T of concrete structures. To this end, this study presents the novel approach to predict T of reinforced concrete framed buildings (RC buildings) using Multi Expression Programming (MEP), Extreme Gradient Boosting (XGB), and Gene Expression Programming (GEP) machine learning algorithms. For this purpose, an extensive dataset of 569 points was gathered from previously published studies and split into training and testing sets for training and testing the algorithms respectively by using several error evaluation metrices like coefficient of determination (R2), Root Mean Squared Error (RMSE), and Objective Function (OF) etc. The results of error evaluation showed that XGB is the most accurate algorithm having the least OF value of 0.012 compared to 0.037 of MEP and 0.048 of GEP. Additionally, several explanatory analyses like sensitivity and shapley analysis were conducted on the XGB model which showed that number of storeys and opening ratio are the most contributing variables to prediction period of vibration. Thus, the models developed in this study can be practically utilized for determining natural vibration period of reinforced concrete frames with masonry infill.

Influence of the Vertical Load Bearing Status on the Seismic Performance of Weak-Joint-Type RC Frames Strengthened by the Wing Wall Installation Method

“Strong column–weak beam, strong joint–weak member” is a core concept for the seismic design of buildings. For existing reinforced concrete (RC) frame buildings that do not satisfy this concept, installing RC wing walls beside existing columns is a simple and effective method for strengthening both columns and joints to promote a beam-hinging mechanism. In this study, a numerical simulation method is used to analyze the seismic performance of weak-joint RC frames strengthened by additional wing walls considering the column axial force ratio and to determine whether to consider the secondary load as a variable. The results show that when the secondary load is not considered, i.e. existing columns do not bear a load during the strengthening process, the strength, stiffness and energy dissipation of the structure increase with increasing axial force ratio, but the ductility of the structure decreases. When the secondary load is considered, the strength and initial stiffness of the frame are the greatest when the column axial force ratio is 0.4. When the axial force ratio is less than 0.4, the secondary load has less influence on the strength, stiffness and energy consumption. When the axial force ratio is greater than 0.4, the secondary load has a significant impact on the seismic performance of the strengthened structure, and the strength, stiffness, energy consumption and ductility are significantly greater than those in the case in which the secondary load is not considered. Additionally, the larger the axial force ratio is, the more significant the difference is. It is revealed that in engineering seismic strengthening using the wing wall installation method, the influence of secondary load on seismic performance should not be ignored, especially when the axial force ratio is large.

A comparative study of SPT-based liquefaction potential estimation methods from three sites in India

ABSTRACT In the present study, four different SPT-based methods for liquefaction assessment namely Seed and Idriss (S–I), Tokimatsu and Yoshimi (T–Y), Japan Road Association (JRA), and Chinese code for Seismic Design of Buildings (CSDB) method has been discussed in detail. The present study compares the liquefaction potential estimation of S–I, T–Y, and JRA methods, respectively. The S–I method predicts 9.29 and 3.42 times higher liquefaction occurrence compared to JRA and T–Y methods respectively. Different damage indices such as liquefaction potential index (LPI), liquefaction risk index (LRI), and ground settlement have been evaluated for an earthquake magnitude of 7.5 on the Richter scale and peak ground accelerations varying in the range of 0.1–0.36 g respectively. LRI provides a more precise estimation of the liquefaction damages compared to LPI. The gradation of liquefiable soil has been presented and compared with the established limits of liquefiable soils.

Optimal Load Factors for Seismic Design of Buildings

This paper reviews the load combinations for the design of buildings established in the Federal District Building Regulations (RCDF-2004) and its Complementary Technical Standards (NTC-2004). New load factors are proposed to be specified in the next version of the RCDF. The combination of gravity load (dead load plus live load) and the combination of earthquake load (dead load, live load and earthquake load) are revised. A methodology is proposed to establish optimal load factors and combinations that guarantee the minimum expected total cost during the lifetime of the structure and that the probability of failure is at least equal to that implied in the RCDF-2004. Artificial Neural Networks are used to estimate structural reliability.

Response Modification Factor of High-Strength Steel Frames with D-Eccentric Brace Using the IDA Method

The design innovation of high-strength steel frames paired with D-eccentric bracing exhibits remarkable resistance to plastic deformation during seismic events. This method strategically combines regular steel connections (with yield strengths below 345 MPa) and high-strength steel beams and columns (such as Q460 or Q690, with yield strengths over 460 MPa), effectively reducing cross-sectional sizes while preserving the elasticity of non-energy-dissipating members. This configuration results in substantial ductility and superior energy dissipation capabilities. The response modification factor (R) is vital for achieving both effective and economical seismic resilience, particularly in the development of efficient and cost-effective seismic designs. However, the 2016 edition of the Code for Seismic Design of Buildings (GB50011-2010) fails to incorporate the concept of R, opting instead to apply a uniform value to all structural systems. This oversight is fundamentally flawed, necessitating a comprehensive investigation into the R value specifically for the high-strength steel frame with a D-eccentric brace. This research primarily aims to improve structural performance design, provide guidance for future projects, and encourage the adoption of this advanced seismic performance structure in earthquake-prone areas. To achieve these objectives, a performance-based seismic design approach is employed. This method involves designing structures with varying numbers of stories (4, 8, and 12), different link lengths (900, 1000, and 1100 mm), and various steel strengths (Q460 and Q690). This study uses the Incremental Dynamic Analysis (IDA) method to determine the R values for each prototype. The derived performance coefficients act as crucial references for the development of future innovative structural designs. This research greatly enhances seismic design practices and facilitates the wider adoption of high-strength steel frames with D-eccentric braces due to their outstanding seismic performance.

Post-earthquake building services downtime distribution: a case study of the 2016 Kumamoto, Japan, earthquake

Seismic damage to building services systems, that is, mechanical, electrical, and plumbing systems in buildings related to energy and indoor environments, affects the functionality of buildings. Assessing post-earthquake functionality is useful for enhancing the seismic resilience of buildings via improved design. Such assessments require a model for predicting the time required to restore building services. This study analyzes the downtime data for 250 instances of damage to building services components caused by the 2016 Kumamoto earthquake in Japan, presumably obtained from buildings with minor or no structural damage. The objectives of this study are (1) to determine the empirical downtime distribution of building services components and (2) to assess the dependence of the downtime on explanatory variables. A survival analysis, which is a statistical technique for analyzing time-to-event data, reveals that (1) the median downtime of building services components was 90 days and, 7 months after the earthquake, the empirical non-restoration probability was approximately 32%, (2) the services type and the building use are explanatory variables having a statistically significant effect on the downtime of building services components, (3) the log-logistic regression model reasonably captures the trend of the restoration of building services components, (4) medical and welfare facilities and hotels restored building services components relatively quickly, and (5) the 7-month restoration probability was observed to be highest for electrical systems, followed by sanitary systems, then heating, ventilation, and air conditioning systems, and finally life safety systems. These results provide useful information to support the resilience-based seismic design of buildings.

INELASTIC DISPLACEMENTS MACHINE-LEARNING-BASED ESTIMATIONS FOR THE RC-BUILDINGS SEISMIC DESIGN CONSIDERING SSI EFFECTS

Over the past few decades, scientists have dedicated considerable attention to investigating the impact of soil-structure interaction (SSI) on buildings’ performance. It is now widely recognized that these interaction effects can either positively or negatively influence a building's response to seismic events. Regarding the seismic design of buildings following standard prescriptions and accounting for SSI effects, ASCE 7, for example, guides through the modification process of the design forces obeying the interacting soil-structure system (SSS) behavior in an oversimplified manner. Nevertheless, no recommendations are made for adequately estimating inelastic displacements (IDs) focused on the design process. In an effort to rectify these limitations, this study examines the inelastic displacement response of ductile RC buildings while incorporating the influence of SSI. In that sense, a database of 3D-model structures with varying in-plan and elevation geometries as well as different supporting soil characteristics were generated and later assessed using OpenSeesPy as the modeling and analysis engine. Nonlinear dynamic analyses were executed accounting for flexible-base and fixed-base conditions as per ASCE 41, and their inelastic displacements are used to generate estimation models. The Gradient Boosting Regression Tree (GBRT) technique from machine learning (ML) is used in accomplishing this aim. It was observed that the wave parameter σ, along with the flexible-to-fixed base design shear force ratio, V*, are enough to explain up to 90% of the variation in IDs in the estimation model.

Seismic design of buildings: Where to next?

This paper critically reviews the current building seismic design approach based on the observed performance of modern building stock in recent earthquakes, highlights the inability of the current design approach in controlling seismic damage and losses, and proposes a conceptual framework for next generation seismic design codes that is likely to meet public expectations. In addition to ensuring life-safety in rare earthquakes, the proposed loss-optimization seismic design approach also aims to ensure quick functional recovery and minimum loss (i.e. repair, downtime, and injury/fatality) in moderate-strong earthquakes by limiting damage to building’s structural and non-structural components. Based on comparison of performances of building stock in some recent major earthquakes in different countries, the paper presents some simple strategies to render buildings more resilient and suffer significantly less seismic damage (and consequentially incur less loss). Finally, the paper scrutinizes the efficacy of some commonly used low-damage technologies in minimizing building seismic losses.

A Comparative Study of Seismic Performance Evaluation of Reinforced Concrete Frame Structures Using Chinese and African Seismic Codes

The evaluation of various earthquake codes, it is one of the significant challenges in the study area of earthquake engineering. However, according to the literature review, most research works have not addressed comparing Chinese and African seismic codes. Therefore, the purpose of this study is to identify each code’s advantages by comparing assessment of the seismic efficacy of moment resistance frame reinforced concrete (MRF-RC) frames using four different codes: the Ethiopian Building Code Standard (EBCS-8), the Egyptian Code for Design and Construction of Reinforced Concrete Structures (ECP-201), the Algerian Seismic Regulations (RPA-99), and the Chinese Code for Seismic Design of Buildings (GB-50011), the first three are the major codes used in Africa. The seismic provisions of these codes are compared and evaluated using nonlinear time-history analysis (NL-THA) and nonlinear static pushover to validate the results. These analyses are performed on four MRF-RC frame models with different heights. The results include various parameters that reflect the seismic performance of the structures. The study revealed that the Chinese code is more conservative and overestimates seismic performance compared with African codes. However, the Chinese code can be applied in African projects considering the African soil classifications, and seismic weight are adjusted to meet the African design criteria.

Shaking Table Tests of Chuandou-Type Timber Structure Building for Seismic Fortification High-Intensity Area

ABSTRACT This study investigated the seismic performance of Chuandou-type timber structure buildings intended for seismic fortification in a high-intensity zone. An earthquake simulation shaking-table test was conducted on a two-layer Chuandou-type structure constructed in Yunnan, China. The El Centro, Kobe, and artificial waves were used as input excitations. The natural frequency, stiffness, acceleration response, and displacement response to the earthquake events were determined. The experimental results indicate that as the acceleration intensity of the earthquake increases, the natural frequency and stiffness of the model structure decrease. The acceleration amplification coefficient of each layer varied from 0.47 to 1.95. The energy dissipation of column foot slip, mortise-tenon joint friction and extrusion were visible, and the dynamic amplification coefficient of the first layer was less than one except for Kobe wave excitation. When the input peak acceleration is 0.63 or 0.95 g, the model shocks violently and exhibits a spectacular whiplash effect, with the model’s maximum inter-story drifts being 1/23 and 1/26, respectively. However, the model did not tilt or collapse, which displays that the Chuandou-type structure had an overall good deformation and self-centering ability. Additionally, it satisfies the standards of the Chinese Code for Seismic Design of Buildings (GB2011–2010).

Shape function-based multi-objective optimizations of seismic design of buildings with elastoplastic and self-centering components

Although the current seismic design of buildings ensures collapse resistance, repairs after disasters are time-consuming and costly. High performance structures and reliable design methods that consider repairability are required for resilient communities. This paper proposes a shape function-based framework and adopts a flexural-shear multi-degree-of-freedom model for seismic design optimization. The proposed framework has fewer parameters and higher portability, and provides better results than a component-based framework. Multi-objective particle swarm optimization is adopted to determine feasible structures for multiple requirements. The optimization provides well-designed elastoplastic and self-centering components of 10–60 floor structures and generates suitable maximum displacement, residual displacement, and cost. A simplified calculation method based on the optimized result is proposed and is verified to guarantee a good performance. Additional optimization of the re-centering ratio and hybrid damping of the self-centering component provides a triangular distribution of the re-centering ratio with values of 1.14–1.26 on the lower floor and a viscous damping ratio of 0.04 to 0.07 for each floor. The maximum acceleration is controlled by 0.8 g after the incorporation of hybrid damping.

The 2023 US 50-State National Seismic Hazard Model: Overview and implications

The US National Seismic Hazard Model (NSHM) was updated in 2023 for all 50 states using new science on seismicity, fault ruptures, ground motions, and probabilistic techniques to produce a standard of practice for public policy and other engineering applications (defined for return periods greater than ∼475 or less than ∼10,000 years). Changes in 2023 time-independent seismic hazard (both increases and decreases compared to previous NSHMs) are substantial because the new model considers more data and updated earthquake rupture forecasts and ground-motion components. In developing the 2023 model, we tried to apply best available or applicable science based on advice of co-authors, more than 50 reviewers, and hundreds of hazard scientists and end-users, who attended public workshops and provided technical inputs. The hazard assessment incorporates new catalogs, declustering algorithms, gridded seismicity models, magnitude-scaling equations, fault-based structural and deformation models, multi-fault earthquake rupture forecast models, semi-empirical and simulation-based ground-motion models, and site amplification models conditioned on shear-wave velocities of the upper 30 m of soil and deeper sedimentary basin structures. Seismic hazard calculations yield hazard curves at hundreds of thousands of sites, ground-motion maps, uniform-hazard response spectra, and disaggregations developed for pseudo-spectral accelerations at 21 oscillator periods and two peak parameters, Modified Mercalli Intensity, and 8 site classes required by building codes and other public policy applications. Tests show the new model is consistent with past ShakeMap intensity observations. Sensitivity and uncertainty assessments ensure resulting ground motions are compatible with known hazard information and highlight the range and causes of variability in ground motions. We produce several impact products including building seismic design criteria, intensity maps, planning scenarios, and engineering risk assessments showing the potential physical and social impacts. These applications provide a basis for assessing, planning, and mitigating the effects of future earthquakes.

Analysis and Application of Double Steel Plate Concrete Composite Shear Wall in the R&D Building of Zhanjiang Bay Laboratory

The R&D Building of Zhanjiang Bay Laboratory is a high-rise structure with multiple irregular items exceeding the specification limit, employing a steel frame-shear wall structural system. The outer frame consists of square steel tube concrete columns and solid-web steel beams, while the core shear wall uses a double steel plate concrete composite shear wall. This paper employs the architectural structural calculation software YJK-EP to perform a dynamic elastic-plastic time-history analysis under rare earthquake action. The shear and bending resistance of the shear wall at the maximum shear force and bending moment are checked to meet the requirements of the “Technical Specifications for Concrete Structures of High-rise Buildings”. The maximum inter-story displacement angle meets the requirements of the “Code for Seismic Design of Buildings”. The double steel plate concrete composite shear wall Wall-1, connected to a large-span and heavy-load transfer truss, was verified under significant seismic action using the ABAQUS software. The results indicate that Wall-1 can meet the design target requirements under major earthquake conditions. Finally, a dynamic nonlinear analysis method was employed using MIDAS-GEN software to study the structure’s anti-progressive collapse performance. The results show that under seven different scenarios, the maximum rotational angle of the remaining structural horizontal members is 2.02°, far less than the limit set by GSA, indicating that a progressive collapse did not occur. In the scenario where the corner column is removed, both the maximum shear and bending moment values for Wall-1 are far below its shear and bending resistance capacities, satisfying the load-bearing requirements. The removal of the corner column has a significant impact on the displacement of the columns on the same level nearby, with the peak displacement change rate reaching 702.65%.

The threshold value of ground motion acceleration characterizing the nonlinear response of sites

Assessing the nonlinearity of a site plays a crucial role in earthquake engineering. For some building structures and lifeline projects that need safety assessment after earthquakes, the analysis of nonlinear degree of sites can help accurately revealing the amplification effect of sites and evaluating the damage degree of buildings which is convenient for subsequent reinforcement and demolition work. The quantitation of nonlinear threshold of sites is an important method to evaluate the degree of site nonlinearity. In this paper, a nonlinear characteristic index reflecting the degradation of shear modulus is proposed based on the instantaneous frequency of the site calculated by using the vector auto-regression moving average (VARMA) model. Then, seismic records of class Ⅰ, Ⅱ, Ⅲ and Ⅳ sites specified as per code for seismic design of buildings in China are selected from the KiK-net network in Japan, and the threshold value of ground motion acceleration characterizing the nonlinear response of sites are provided. Finally, the variation of the nonlinear characteristic index (shear modulus degradation) vs. different (peak ground acceleration) PGA for four types of sites are presented.