Earthquake Engineering Problems Research Articles

Higher-order thin layer method as an efficient forward model for calculating dispersion curves of surface and Lamb waves in layered media

The thin layer method (TLM) is an effective semi-discrete numerical tool for analyzing wave motion in stratified media. The TLM can calculate the eigenvalues and eigenvectors for both propagating and decaying waves, which is essential to simulate waves near the source. The eigenvectors are particularly useful in various applications, such as estimating modal contributions, calculating synthetic seismograms, determining Green’s function, analyzing site response, and solving wave amplification problems in earthquake engineering, to name a few. In practice, most engineering applications use linear element-based TLM. However, the overall performance of TLM depends upon the type of element and the number of thin layers. The linear element TLM requires relatively thin sub-layers to obtain an accurate solution, making it computationally expensive and time-consuming. This study explores the potential of using non-linear higher-order TLM (HTLM) for forward modeling. The mathematical framework of TLM is used to formulate the generalized HTLM in determining the multimodal dispersion curve of Rayleigh, Love, and Lamb waves. The convergence and computational efficiency of different orders of HTLM have been investigated on a diverse set of published soil profiles and plate-like structures. Since non-linear interpolation functions better capture the change in displacement and stress between the layers, the findings reveal that the HTLM consistently outperforms the linear element TLM in terms of accuracy. Furthermore, the computational efficiency of different order HTLM is analyzed by comparing the total degrees of freedom and CPU time. Remarkably, higher-order HTLMs exhibit improved accuracy without increasing the computational burden, making them an attractive option for practical applications such as global search-based inversion and full spectrum inversions where fast and economical forward modeling is essential. Therefore, the HTLM will become helpful in seismic wavefield modeling, dynamic soil characterization, non-destructive evaluation methods, wave propagation analysis through waveguides, seismic site response analysis, etc.

LC v-ST/FEM: a third-order accurate dissipation-controlled velocity-based space-time finite element method for solid dynamics and earthquake engineering problems

LC v-ST/FEM: a third-order accurate dissipation-controlled velocity-based space-time finite element method for solid dynamics and earthquake engineering problems

Constitutive Modelling of the Cyclic Response of Unsaturated Soils: A Discussion of the State‐of‐Art

Site response analysis (SRA) is an important aspect of seismic design that considers the impact of local site conditions on the ground response during earthquakes and plays a key role in the design of structures that interact or are made with soil. Although previous studies have demonstrated that factors such as the degree of saturation influence the site response, incorporating partial saturation into analysis has not been widely practiced. Numerical analysis tools exist; however, they are often unable to directly assess the influence of partial saturation, especially under seismic conditions. This is often caused by the missing implementation of constitutive models and finite elements able to account for partial saturation of soils under cyclic conditions. For this reason, a review of the most common constitutive models developed with a view to describing unsaturated soil behaviour subjected to cyclic loads is presented, followed by a critical discussion on their applicability to finite element frameworks, with the aim of providing a wide panorama of the available constitutive platforms suitable for implementation in numerical codes. Therefore, we present and discuss the mechanical and hydraulic properties of the constitutive models that can be applied to the analysis of boundary value problems, and specifically for SRA, focusing on partially saturated soils under cyclic loading conditions. It was observed that many constitutive model frameworks for cyclic loadings are based on the bounding surface or two‐surface theories, and some of them are coupled with hydraulic behaviour through the Soil Water Retention Curve (SWRC) or its variations. Two main approaches were identified based on the mechanical features, while regarding the hydraulic behaviour, the main distinction lies in the selected SWRC. Furthermore, certain constitutive models have been implemented in finite element software for numerical analysis of geotechnical earthquake engineering problems.

1-D Finite Element Artificial Boundary Method for Saturated Layered Half-Space Site Response under Obliquely Incident P-SV Waves

A novel finite element scheme is derived to evaluate the transient dynamic response of a multi-layered saturated porous half-space due to obliquely incident P or SV wave. The system consists of N − 1 layers with different thickness and properties that overlay on a saturated half-space from which the wave is input. Biot theory is utilized to describe the mechanism of saturated poroelastic media. In this method finite computational area is truncated from the infinite domain by a horizontal artifitial boundary introduced in the underlying half-space. Wave inputting effects and absorbing boundary condition at the bounday are derived. The spatial problem is then transformed approximatedly into a one-dimensional problem based on the Snell's law. The transient 1-D problem is descritized spacially by means of FEM and solved by the standard time intergration algorithm. Numerical examples show that the proposed 1-D finite element artificial boundary method can provide accurate results for seismic performance of saturated layerd half-space under obliquely incident waves with low values of permeability or frequency content. The method is applied in site response analysis of Hong Kong-Zhuhai-Macao immersed tunnel project. By comparison with the analytical solutions, it is demonstrated for geotechnic earthquake engineering problems, site response solutions with satisfactory accuracy can be achieved by the proposed method.

A novel peridynamic solution for modelling saturated soil-pore fluid interaction in liquefaction analysis

Saturated soil-pore fluid interaction under earthquake shaking can cause extensive damages to critical infrastructure systems. As such, accurate modeling of saturated soil-pore fluid interaction and its consequences (e.g., seismically-induced large deformation) are of particular importance for liquefaction analysis. Peridynamics (PD) has emerged as an effective method for solving large deformation problems by overcoming the disadvantage of finite element method caused by mesh dependency. However, the PD has not been extended to model soil-pore fluid interaction, limiting its application in liquefaction analysis. To bridge this gap, a novel solution strategy is presented for modeling soil-pore fluid interaction (i.e., the u-p equations herein) in liquefaction analysis of saturated granular soils, based on a hybrid PD (HPD) method recently proposed by the authors and co-workers. An explicit-explicit method is used to solve the coupled u-p equations. Liquefiable soil on level and sloped ground are analyzed and compared with experimental data and finite element simulations to validate availability and efficiency of the method, demonstrating the method to be effective in solving the soil-pore fluid equations and applicable to a broad range of geotechnical earthquake engineering problems associated with liquefaction.

Framework of a performance-based design for liquefaction resistance

Seismic liquefaction hazards remain a very challenging problem in geotechnical earthquake engineering and are one of the most important aspects currently to update the framework of the liquefaction resistance design from a performance-based perspective. In this paper, by investigating the characteristics of the seismic liquefaction hazard, as well as integrating the existing performance-based earthquake engineering (PBDEE) and advanced risk management theory, the connotation and key points of performance-based liquefaction hazard governance are proposed, and the framework of a performance-based design for liquefaction resistance (PBDLR) is constructed according to the technical system construction rules. The results indicate that the liquefaction hazard has its own characteristics in terms of the hitting target, hazard scale, occurrence mechanism, chain effect, treatment technology, and uncertainty of the influencing factors. Its technical system of hazard governance requires special consideration. The presented PBDLR integrates the advantages of both the advanced risk management theory and the existing performance-based earthquake engineering technology system, and the elements and structure consider the sociality of the target, the integrity of the function, the hierarchy of the composition, and the linkage of the elements and the completeness of the technology. The PBDLR takes the liquefaction hazard governance objective as the primary factor and performance analysis as the technical main body of the framework, and it is equipped with several new elements matching the characteristics of the liquefaction hazard and the requirements for the technical development of an anti-liquefaction design. The PBDLR presented in this paper can provide guidance and a reference for future research and technical development in liquefaction hazard governance.

Numerical investigation of energy dissipation when shear wave passing through interface in rock mass

The investigation of seismic wave propagation across discontinuous rock masses is of great importance for solving earthquake engineering problems. Although the parameters affecting the propagation of wave on the structural surface have been known to some extent, the influence of cohesion, inclination, and stiffness on the propagation of wave when passing through structural plane still needs further study. In the study of the incident wave simulation, we implemented FLAC3D to build the model with interface to measure the energy loss due to different parameters in the interface. The effect of cohesion, normal and shear stiffness, and dipping angle on characteristics of energy dissipation were investigated. Numerical results indicated that the cohesion as the adhesion of the material is playing an important role in energy dissipation. The normal and shear stiffness is not as obvious as what cohesion does, especially when they are at very low value. In addition, an increase in angle will bring about a decrease in the transmission coefficient and a decrease followed by an increase in the reflection coefficient.

Dynamic Response and Reliability Analysis of Stochastic Multi-Story Frame Structures under Random Excitation

In earthquake engineering problems, uncertainty exists not only in the seismic excitations but also in the structure's parameters. This study investigates the influence of structural geometry, elastic modulus, mass density, and section dimension uncertainty on the stochastic earthquake response of a multi-story moment resisting frame subjected to random ground motion. The North-south component of the Ali Gharbi earthquake in 2012, Iraq, is selected as ground excitation. Using the power spectral density function (PSD), the two-dimensional finite element model of the moment resisting frame's base motion is modified to account for random ground motion. The probabilistic study of the moment resisting frame structure using stochastic finite element utilizing Monte Carlo simulation was presented using the finite element program ABAQUS. The dynamic reliability and probability of failure of the stochastic and deterministic structure based on the first passage failure were checked and evaluated. Results revealed that the probability of failure increased due to randomness in stiffness and mass of the structure. Generally, natural frequencies for the lower modes of vibration and relative displacements for the lower stories were more sensitive to the randomness in system parameters.

Retraction Note: An Implicit Unconditionally Stable Integration Method for Nonlinear Structural Dynamics and Earthquake Engineering Problems

Retraction Note: An Implicit Unconditionally Stable Integration Method for Nonlinear Structural Dynamics and Earthquake Engineering Problems

Causal inference on observational data: Opportunities and challenges in earthquake engineering

Collecting and analyzing observational data are essential to learning and implementing lessons in earthquake engineering. Historically, the methods that have been used to analyze and draw conclusions from empirical data have been limited to traditional statistics. The models developed using these techniques are able to capture associative relationships between important variables. However, the intervention decisions geared toward seismic risk mitigation should ideally be informed by an understanding of the causal mechanisms that drive infrastructure performance and community response. This article advocates for a paradigm shift in earthquake engineering where the language, tools, and models that have been (and continue to be) developed to draw causal conclusions from observational data are adopted. Several categories of data-driven earthquake engineering problems that can benefit from causal insights are examined. Two widely adopted frameworks from the broader causal inference literature are presented and linked to hypothetical earthquake engineering problems. The critical role of semi-parametric models and sensitivity analysis in justifying causal claims is also discussed. The article concludes with a discussion of specific opportunities and challenges toward the widespread use of causal inference as a tool for knowledge discovery in earthquake engineering. The ability to leverage the underlying physics of a problem within a causal inference framework is identified as both an opportunity and challenge for earthquake engineering researchers.

Aftershock Probabilistic Seismic Hazard Analysis of Major Earthquakes in Western Zagros in Iran and Verification of Two Applied Methods

ABSTRACT Aftershock probabilistic seismic hazard analysis (APSHA) is essentially useful for various earthquake engineering problems. In this paper, a series of aftershock seismic hazard analyses were conducted in western Zagros region in Iran using different approaches. The results were obtained in terms of exceedance probabilities of peak ground accelerations within different time intervals following the mainshock. The results were generally compatible with the recorded data; however, the accuracy depended on the causative fault geometry and spatial distribution of aftershocks. The accuracy decreased in shorter time intervals after the mainshock and also in longer time spans especially when strong aftershocks occurred.

On the Interpretation of Conditional Ground-Motion Models

ABSTRACT Recently, a number of conditional ground-motion models (CGMMs) have been developed for intensity measures (IMs) other than pseudospectral acceleration (PSA) values that are particularly useful for geotechnical earthquake engineering problems. In a CGMM, a non-PSA IM is conditioned on PSA IMs, and other earthquake parameters (e.g., magnitude Mw, rupture distance Rrup) as well as site conditions (e.g., the time-averaged shear-wave velocity in the top 30 m VS30). Even though CGMMs are useful in engineering practice, their interpretation in the context of traditional (non-CGMM) has not been discussed to the authors’ best knowledge. In this study, we provide an interpretation of CGMMs in terms of the scaling difference between the spectral and nonspectral IMs used in the formulation of a CGMM and the coefficient of correlation of these spectral and nonspectral IMs. In addition, the interpretation can derive into an alternative procedure for calculating correlation coefficients between PSA IMs and non-PSA IMs, which is illustrated.

Deep convolutional generative adversarial networks for the generation of numerous artificial spectrum‐compatible earthquake accelerograms using a limited number of ground motion records

AbstractDeep learning (DL) methodologies have been recently employed to solve various civil and earthquake engineering problems. Nevertheless, due to the limited number of reliable data in the field of earthquake engineering, it is not convenient to obtain accurate results using DL. To tackle this challenge, the generative adversarial network (GAN) approach may be considered a reliable possible candidate. GANs have been introduced as an efficient way to train generative models. GANs exhibited their capabilities as well as versatility in the field of image production. For nonlinear dynamic analyses of structures, artificial ground accelerograms that are compatible with a target response spectrum are usually generated. In this paper, an efficient algorithm is proposed by which numerous artificial spectrum‐compatible earthquake accelerograms are generated using a few ground motion records. For this purpose, a specific well‐established generative model, namely, the deep convolutional GAN (DCGAN), is adopted for the first time and used. It is shown that DCGAN can easily generate desirable artificial ground accelerograms by having a limited number of seismic records as input to train the network. To quantitatively demonstrate the quality of the artificial ground accelerograms generated by the DCGAN, several computer experiments are presented, among which the robustness and feasibility of the proposed method are examined by using only four earthquake accelerograms as the worst scenario. Moreover, the efficiency of the DCGAN is illustrated by comparing various seismic parameters and the spectral response of the generated accelerograms with those of the actual accelerograms. The outcomes illustrate the efficiency and robustness of the presented DCGAN.

RETRACTED ARTICLE: An Implicit Unconditionally Stable Integration Method for Nonlinear Structural Dynamics and Earthquake Engineering Problems

A novel time integration procedure is designed in order to solve the differential equation of motion of dynamics and earthquake engineering problems. The procedure is constituted on the principle of impulse-momentum, leading to a lesser number of assumed fields. The algorithmic properties of the procedure are determined by stability and accuracy analyses. Overshooting tendency, which is not related to stability and accuracy characteristic of a method, and order of accuracy are also examined. It is displayed that the new method is unconditionally stable and non-dissipative. Also, the numerical dispersion of the proposed algorithm appears to be much less than the commonly used integration methods. The method has no tendency to overshoot both the displacement and velocity response solutions. Its order of accuracy is around four as compared to two of the other methods considered in the study. A few numerical examples consisting of both single and multi-degree of freedom systems with linear and nonlinear characteristics are performed to see the overall behavior of the method in various practical problems. The numerical results of the proposed method obtained from these examples coincide well with the simulated exact results.

Development of a general‐purpose parallel finite element method for analyzing earthquake engineering problems

AbstractA parallel finite element method (FEM) based on high‐fidelity models for solving diverse earthquake engineering problems is presented. Its key feature is a parallel solver that is tuned to solve large‐scale wave equations. Tensorial material constitutive relations of concrete and soil and sophisticated nonlinear joint elements are implemented to broaden the applicability of the parallel FEM. The performance of the proposed parallel FEM is demonstrated for three examples; namely, seismic response, liquefaction, and surface earthquake fault analyses. A high‐fidelity model was constructed for each analysis, and the numerical results were validated against observed data. The performance of the proposed parallel FEM approach was evaluated in terms of the resolution of the simulated results. Ensemble computing based on approximately a hundred high‐fidelity models is useful for cases where there are considerable uncertainties regarding the material properties.

Research and Assessment of the Seismic Risk of Strong and Destroying Earthquakes on the Territory of Tajikistan

The area of Tajikistan is 143.1 thousand km2, while about 93% of its territory is occupied by mountains, the maximum heights of which reach more than 7000 m above sea level. The rest of the country (7%) is plains and valleys with heights from 300 to 1000 m above sea level. Such a significant range of heights is explained by the location of the study area in the junction zone of the Tien Shan fold system and the Alpine-Himalayan belt and leads to a wide variety of geological, hydrogeological, landscape-climatic and seismic conditions, analysis of the consequences of destructive earthquakes is of great importance for solving scientific and practical problems in the field of seismology, as well as problems of earthquake-resistant construction. The analysis of consequences of destructive earthquakes is important for solving scientific and practical tasks in the field of seismology and problems of earthquake engineering. One of the main sources of seismic resistance assessment of buildings and structures, along with theoretical and experimental studies, is engineering analysis of the consequences of strong earthquakes. This article deals with the effects of earthquakes on the earth's surface. The example of the following devastating earthquakes that occurred in Tajikistan, the impact of these seismic events on various types of residential buildings built from local materials is considered, and the main reasons for the observed nature of deformations and destruction are discussed.

On Cohesive Soil Damping Estimation by Free Vibration Method in Resonant Column Test

Abstract Measurement of soil properties under cyclic and dynamic loading conditions is a critical task in the solution of most geotechnical earthquake engineering problems. The main dynamic properties of soils are usually expressed in terms of shear modulus and damping ratio that are generally obtained from laboratory tests. To date, the resonant column test is considered one of the most accurate ways to determine dynamic soil properties at low to medium-strain levels. Because it allows for investigation of a wide range of strain amplitudes, it is a valuable tool for characterizing the shear soil behavior for a large number of practical geotechnical problems. One of the approaches followed in estimating the damping ratio from the resonant column test is the free vibration method (also called logarithmic decrement or amplitude decay method). It consists of analyzing the time history of the damped free vibrations of the specimen once harmonic loading is cut off after reaching the resonant conditions. The soil damping ratio is determined measuring the logarithmic ratio of the amplitude of any two successive peaks of the system damped motion (logarithmic decrement). In this article, the influence on the damping ratio of the shear strain level, the plasticity index, the confining pressure, and the time interval between the peaks selected in calculating the logarithmic decrement is evaluated from the results of resonant column tests performed on 51 undisturbed isotropically consolidated fine-grained soil specimens.

An archive of data from resonant column and cyclic torsional shear tests performed on Italian clays

Measurement of soil properties under cyclic and dynamic loading conditions is a critical task in the solution of most geotechnical earthquake engineering problems. The main dynamic properties of soils are usually expressed in terms of shear modulus, G, and damping ratio, D, and they are generally obtained from laboratory tests at different strain levels. Dynamic geotechnical problems often require a site-level or territorial approach involving a considerable number of dynamic laboratory tests that might be too expensive and time-consuming. Thus, it is a common practice to use empirical relationships between dynamic parameters and measurements from routine geotechnical tests. Therefore, the availability of a large and reliable archive of multiple testing results constitutes a fundamental step for geotechnical earthquake engineers and researchers. To this aim, a large data-set of the index and dynamic parameters measured from 170 undisturbed clay samples obtained from 90 sites in Central and Northern Italy is made available, and its use and application are further described and discussed.

A frequency-dependent absorbing boundary condition for numerically solving u-U elastic wave equations in layered and fluid-saturated porous media

An accurate absorbing boundary condition (ABC) is proposed to incorporate in the frequency-domain finite element simulation for numerically solving u-U elastic wave equations in horizontally multilayer fluid-saturated porous media. The u-U elastic wave equations are first discretized only along the depth direction in which the material properties are heterogeneous, analytical method using in the remaining coordinate direction. A general eigenvalue problem on the horizontal wavenumber is then solved with the frequency as known parameter. Dynamic stiffness on the artificial boundary of finite domain is finally obtained as ABC based on the solution to the above eigenvalue problem. The proposed ABC is mathematically derived without introducing any approximate assumptions, and the only approximation comes from the finite-element discretization of the fluid-saturated porous medium in the depth direction. The proposed ABC can also be coupled seamlessly with the finite element method (FEM). Numerical examples of wave radiation problems are given to demonstrate the effectiveness of the proposed ABC and its coupling with FEM. Finally, a practical application of proposed ABC to assess the topography effects of the fluid-saturated porous basin-type site is presented to show that the proposed ABC can also be used to solve wave scattering problems in geotechnical earthquake engineering.

Applicability of Bouc-Wen Model to Capture Asymmetric Behavior of Sand at High Cyclic Shear Strain

Abstract Seismic response evaluation of the site of interest subjected to a bedrock motion is one of the most important problems in earthquake geotechnical engineering. For one-dimensional (1D) non...