مجله علوم و مهندسی زلزله
سال چهارم شماره 2 (پیاپی 11، تابستان 1396)

Earthquake is one of the major natural disasters that the current knowledge of the human kind is not able to predict it yet; however, it can be partly subjected to risk assessment and recognition of its pattern by using statistical methods. The Zagros region of Iran is known for its high seismic activity. This mountain belt is amongst the world’s most seismically active mountain ranges. This seismogenic zone is the result of the collision between the Arabian and Eurasian plates during the Cenozoic. Seismic activity in this zone is characterized by the occurrence of low to moderate magnitude earthquakes, most of which nucleate on blind (hidden) thrust faults. In this study, the temporal pattern of occurrence of earthquakes in the Zagros region for a period of more than 11 years, from the beginning of 2005 to the end of October 2016, have been examined using statistical methods. In this regard, the matching degree of the examined data with the Poisson distribution was evaluated and time series analysis of the data was carried out.
Methodology and Data Analysis: Randomness in time, space and size is the most obvious property of earthquake occurrence. At the same time, there are ample evidences to suggest that earthquakes do not occur in a completely disordered manner. The randomness of the occurrence of earthquakes in time or space can be evaluated by statistical methods such as Poisson distribution fitting test. In addition, time series analysis has been widely used in many applications, e.g. earthquake forecasting and the temporal pattern of earthquake occurrences, as a stochastic process, can be studied by this method. In this study, by using the goodness of fit test based on the chi-square statistic, the suitability of the Poisson distribution with λ parameter (the average rate of the earthquake occurrence) fitness to seismic data of the region with different ranges was assessed. Additionally, in this research, due to the low randomness degree of the data in time, the time series modeling of the data were carried out to find the productive time pattern model of the data. A sample of 150 data, covering the end part of the catalogue, was selected for the analysis and modeling of time series, and two main attributes of the earthquake data, magnitude and focal depth, as quantitative variables, were included in this modeling.
According to the obtained results, it can be said that temporal distribution of these data do not completely follow the Poisson distribution model, but with increasing the earthquake magnitude, the data probability distribution approaches to the Poisson distribution. Besides, the results of the time series analysis of data show that the temporal pattern of earthquake occurrence based on the magnitude variable has a good correlation with ARMA (1, 1) model. Similarly, considering the focal depth as variable in modeling, the time series models acceptably match ARMA (0, 1) and ARMA (0,2) models. These findings were verified by Box and Pierce method. According to the obtained results of this research, it is concluded that the earthquake occurrence in the Zagros region do not completely show a random pattern, and time series analysis modeling can be acceptably employed for finding the temporal behavior of seismicity in this region. However, the techniques used in this research are data driven and the reliability of the results obtained depends on the quality of the input datasets. Due to the insufficiency and inaccuracy of the studied data catalogue, it is expected that in future, more appropriate and reliable results could be achieved by reducing the seismic data errors and using the data with longer time periods.

Topography can have significant effects on the seismic ground response during an earthquake. Fortunately, the topography effect on the seismic motion is considered more in recent years and seismic design regulations and guides include this factor; however, study about many aspects of this complicated factor is essential to reduce unforeseen damages caused by earthquakes or any seismic motion in topographical areas. A single topographic irregularity (a canyon or a hill) has been studied by many researchers, and many realistic applications are also found. Nevertheless, to the best of our knowledge, few studies deal with the interaction of topographic irregularities. The aim of this study is to determine how a series of irregularities interact as compared to a single irregularity. When a seismic motion happens in a topographical area, seismic waves are trapped and reflected between the topographic features because of the surrounding topography. Therefore, the interaction between topographies can amplify the seismic ground response. In order to reveal how the interaction between topographies influence on seismic response, several numerical finite element studies have been performed by ABAQUS program, the results of which are presented in the form of the time history and dimensionless graphs. Due to the evaluate effect of geometry type, height, length and angle of slope on the seismic response; rectangular, trapezoidal and triangular topographies are studied with different heights (20-100 m) and different angles (15-75 degrees). As the result of these simulations, although seismic ground motion amplification of the various geometries (rectangular, trapezoidal and triangular topography) is different, the total trend is similar. It means that increasing slope height, length and angle of all types of geometry has a greater effect on seismic response amplification. In order to study the interaction of topographic irregularities, several models with different numbers of topographies are evaluated. Models are series of triangular topographies with the height of 100m and slope angle of 30°. Distance between each of the topographies is 10 m, and the total length of topographic irregularities is about 1079.2 m. Shear Wave Velocity (V_S) is 560 m/s. In this study, different numbers of topography in different distance of seismic source are evaluated. Applied Seismic motion is the record of Manjil earthquake in horizontal direction. Besides, models are two-dimensional and flexible. In many studies, different kinds of energy absorbing boundaries have been investigated and results show that the best boundary conditions is infinite element method. ABAQUS infinite elements can be used to define infinite boundaries in the dynamic problems. These elements have Elastic behavior and absorb the wave energy so that they act as absorbent boundaries. Researchers such as Nielsen, Preisig and Jeremic Have examined the performance of these elements. Modal analysis in Abaqus software has been done to determine the natural frequencies of the soil site. Soil damping is related to strain and differs in the diverse strain levels. Therefore, average of the soil critical damping ratio is assumed 5%. Application of the critical damping ratio is depreciation of the seismic waves reflected from the model boundaries. When the natural frequencies of the soil site are determined, α_R and β_R (Riley damping coefficients) can be calculated. The results show that site seismic response is very different when there is no topographic irregularity between the seismic source and the site; in comparison with several topographic irregularities exist between them. Further topographic features between the seismic source and the site would cause further seismic motion amplification and is so tangible for the hills far away from the source and the ridges. Importance of this issue is because the greater number of topographic irregularities are caused the greater value of seismic motion amplification and in reality, there is a series of topographic irregularities together. Although changes rate of the acceleration dimensionless graphs is greater than velocity and both are greater than displacement dimensionless graphs, their trend changes are similar to each other. It means that surroundings topography (topographies interaction) have effects on site acceleration more than site velocity and displacement. Finally, it is concluded that topographies interaction factor (surrounding topography) should be considered as an effective and independent parameter of a single topography, while the seismic regulations has not paid enough attention to this problem.

Horizontal to vertical spectral ratio technique on single station ambient noise data, is a well-known technique in study of site effect. Recently, this technique is introduced as a tool for identification of shear wave velocity profile of soil beside its normal usage.
Many studies in recent years showed that the ellipticity of the fundamental mode of Rayleigh waves can be obtained by reducing the Love and Body waves effects from the H/V spectral ratio. Based on the relation of the H/V curves and the ellipticity of Rayleigh waves and dependency of ellipticity to the shear-wave, this method can retrieve the S-velocity structure in a thick alluvial deposit.
In this paper, HVTFA and RayDEC methods are used to retrieve the ellipticity curves for more than 140 single-station ambient noise measurements. The HVTFA technique based on time-frequency analysis with Continuous Wavelet Transform tries to reduce the SH-wave influence that is possible by identifying P-SV wavelets along the signal and computing the spectral ratio from these wavelets. It is assumed that the energetic points in time-frequency representation of the vertical signal is related to a single Rayleigh wave wavelet. The average over all wavelets defines as ellipticity.
Based on random decrement technique, the Ray DEC method uses the vertical component as a master trigger and stacks a large number of horizontal and vertical signals from three-component records of seismic noise to obtain ellipticity curves.
The right flank of ellipticity curves (from the first peak of curves to the next trough) were used in inversion, because numerical studies show that the right flank is the most reliable part of ellipticity, and the energy of the Rayleigh-wave fundamental mode strongly dominates in these frequency ranges.
In the following, ellipticity curves were classified based on the f0 peaks and the right flanks in two ways; visual observation of similarities and k-means clustering statistical approach.
Inversions process performed using the Neighborhood Algorithm based on the partition of the parameter space into Voronoi cells. The Voronoi decomposition of the parameter space is the base of an approximation of the misfit function, which is progressively refined during the inversion. The method uses prior information (initial parameterizations) and try to optimize the computation at the different stages of inversion.
The results of inversion show the existence of the thick alluvial deposits in the northern and eastern parts of the city. For the southern parts, the method shows higher velocity and lower depth of bedrock. These results are in agreement with geological situation of the region, existence of mountainous area at the southern and western parts, and extensive alluvial plains at northern and eastern parts.

Throughout history, earthquake mitigation has always been of vital importance for the humans. Nowadays, by growing technology and computer sciences, several approaches including empirical, analytical and numerical methods are developed and used by researchers to attempt for reducing some possible damages of this phenomenon. Although the responses of analytical methods have high accuracy, various types of arbitrarily shaped topographic features cannot be applied for modeling in reality. It results in the development of numerical methods which have good flexibility. Technically speaking, numerical methods were generally divided into two types, volumetric and boundary methods. Although volumetric methods have advantages such as high accuracy, simple formulation and wide covering range of problems, they have high computations and complex models in the problems with infinite and semi-infinite boundaries. Thus, the field is prepared for the presence of boundary approaches such as Boundary Element Method (BEM). In this method, only the boundaries of the media need to be discretized in order to analyze an elastic continuous media. Considering the automatic satisfaction of the wave’s radiation conditions in the formulation, it is an appropriate method for dynamic analysis.
Two BEM formulations have been proposed to be used in modeling, including full-plane and half-plane. In this paper, the half-plane time-domain BEM was applied to obtain the amplification pattern of the homogeneous ground surface in the presence of unlined horseshoe-shaped tunnels, subjected to propagating obliquely incident out-of-plane SH-waves. In the use of the proposed method, the boundary around the tunnel was only required to be discretized. The Ricker wavelet was assumed as incident wave function. The geometrical properties of the first part from second line of the Karaj metro tunnel were considered as the case study. A sensitivity analysis was carried out on the responses with considering some intended parameters including depth ratio, horizontal location ratio, and angle of incident wave. It should be noted that, to obtain acceptable responses and in order to achieve the dimensionless results, the scale of 50 times was applied in the modeling. The response of the ground surface and the amplification patterns were presented in the time/frequency domains and the synthetic seismograms were obtained.
The results showed that making the meshes to focus only on the tunnel surrounding boundary and leaving the discretized ground surface reduces not only the analysis time, but also the input data and calculations compared to traditional BEM approaches. The verification of the responses versus existing analytical results showed that the used method had great accuracy for modeling underground tunnels. Simple modeling of actual underground structures and obtaining accurate responses through the use of time-domain half-plane BEM were main purposes of this paper. Besides, the presence of metro tunnels was effective on the formation of different seismic patterns of ground surface. The general pattern of responses in the frequency domain showed that, when subjected to vertically propagating incident SH-waves, the isolation effect of the presence of the tunnel was quite pronounced on reducing the ground surface response.

Considering the fact that the computational cost of Nonlinear Time History Analysis (NLTHA) has been reduced significantly, specially, during last decade, this type of analysis has been promoted among civil engineering society. On the other hand, basic shift from conventional design approach to the performance-based method highlights the essential need for the estimation of different engineering demand parameters (EDPs) with as highest reliability as possible. Focusing on the selected set of strong ground motions (SGMs) as an important source of uncertainty on the results, there are a variety of studies in the earthquake engineering literature the purpose of which is to introduce a standard scheme for efficient selection and preparation of appropriate SGMs as the input of NLTHA. A part of existing differences, most of the methods suffer from a common limitation that is the application of simplifying assumptions in their contextual framework that may not always be correct. For example, there are several structure-specific scaling and selection methods using an equal SDOF as the representative of the target structure that must be analyzed. Although the use of such simplifications is unavoidable, their effect on the reliability of the results estimated by performing NLTHA under proposed set of SGMs by the method must be evaluated.
In this paper, a recently proposed structure specific record selection method is investigated in terms of its ability to keep the efficiency in case of structures that may challenge the assumption of reducing a MDOF nonlinear system to an equal SDOF. The investigated method have proposed an a priori set of SGMRs selected from a commonly used general set, which is introduced for collapse assessment. The method first utilizes the statistical exploration of a collapse capacity database that is constructed by analyzing numerous SDOF systems each of which represents specific combination of structural features such as ductility and period. Then, by defining a quantitative similarity measure, the whole database is refined to find the optimum subset representing the general set fairly good for any predetermined structural characteristics.
For a comprehensive study, a group of 2-D one-bay vertically regular frames of five different heights (i.e. 3, 6, 9, 12, and 15 stories) has been used in this study. The height-wise distribution of stiffness was tuned to achieve equal drifts in all stories that are calculated using the Iranian code of practice for seismic resistant design of buildings forces (Standard 2800). The yield strength distribution was chosen such that the yielding is observed almost simultaneously at all plastic hinges under the lateral force distribution, which is determined by Standard 2800. To cover a variety of ductility values, nonlinear response spectra with constant ductility equal to 1, 2, 4, and 6 have been utilized as the design spectra. Thus, eight different designs (two values of T1 and four values of μ) are considered for each fixed height, leading to a total of 40 frames. A set of 22 pairs of horizontal SGMRs selected from a specific far-field set, which was used in the FEMA P. 695 as the suggested SGMs for NLTHA.
The most important results that can be concluded from the comprehensive evaluation of the mentioned selection method can be listed as;
• The proposed selected subsets, in most cases underestimate seismic demands of regular frames compared to the estimations by using the reference set of 44 SGMs. This can be attributed to the fact that many of steel frames do not experience severe levels of nonlinearity or side-sway collapse.
• The application of the proposed subsets by the selection method does not necessarily result in the reduction of the statistical dispersion in the estimated EDPs.
• Comparing the estimated EDPs by the proposed subset with those of other potential subsets, almost in all cases there is no significant superiority of the selection method in terms of accuracy and reliability. This can be interpreted by noting to the fact that the goal of selection method is the reliable collapse simulation of the structures and it cannot easily be generalized to the other performance levels.
The results confirm that the ductility plays an important role in the SGMs selection output. Therefore, it is suggested that the provision of a new selection process involving ductility of target structure is investigated as a future complementation of the current method.

Records in the near-fault areas indicate the strong vertical ground motion. Near-fault earthquakes are different from far-fault earthquakes due to the adverse effect of their vertical component, which can be very destructive for long span frames. The Vertical Component of earthquake is different from the horizontal component. Vertical component of earthquake occurs when the compression P waves separate. Whereas the horizontal component occurs as the shear S waves separate. The frequency content of vertical component of earthquake is higher than the horizontal component. The natural frequency of structures in the vertical direction is more than that of the horizontal direction. These factors may cause the resonance in the structures. The first step in the examination of the effects of vertical component of an earthquake on structures is identifying the stimulating source of vertical component of the earthquake, response spectrum of the vertical component and affecting parameters on the vertical component. In this research, the effect of horizontal and vertical components of earthquakes has been investigated in long span building frames by modeling two types of such structures with various openings sizes in a powerful finite element software. For this purpose, in the first phase of the study, the structures have first been evaluated under the effect of horizontal component of earthquake alone, and then, the vertical component of earthquakes has been added and performance of the structures has been evaluated again. To evaluate the performance of structures, both linear and nonlinear as well as static and dynamic analyses according to the seismic rehabilitation of structures guidelines have been performed. In the second phase of the study, for more confident evaluation, the reliability indices as suitable tool, recommended in recent researches, have been used. For this purpose, the amounts of moment, shear force, axial force of columns, and deflection of the long span beams have been calculated, and the corresponding reliability indices have been obtained by using an appropriate statistical software.

Fiber Reinforced Polymer (FRP) composites are widely used in retrofitting and strengthening of Reinforced Concrete (RC) structures. FRP composites are applicable for strengthening various structural elements including beams, columns and plane elements such as floor slabs and shear walls. Despite their broad usage, available guidelines typically do not contain a comprehensive procedure for retrofitting design of RC elements under general loading conditions. As RC columns are essentially subjected to simultaneous axial force and bending moment in monolithic construction, their evaluation and retrofit under such combined effects are of major importance in the retrofit design process. It appears that available expressions in most design guidelines merely accounts for the possible increase in the compressive strength of concrete due to the enhanced confinement on the concrete core provided by the FRP jackets. Theoretical and experimental studies on the behavior of columns confined by FRP composites subjected to axial force and bending moment are available in the literature. Those studies have demonstrated that FRP jacketing enhances the elements behavior in term of both strength and ductility. Most of studies are primarily devoted to the strengthening of RC elements under pure axial force. In recent years, however, studies have been conducted on response of RC elements under combined effects of axial load and uniaxial bending. Rocca (2009), among others, conducted a very precise and valuable practical study on the effects of bending moments on retrofitting of RC columns using FRP composite. He introduced the interaction curves of retrofitted RC columns with FRP jackets based on the principles of equilibrium and strain compatibility. Moreover, results of various experimental tests are found in the literature emphasizing the behavior of RC elements under eccentric loading conditions. Such tests have investigated the effects of various parameters including the strength of FRP composites, number of FRP layers, orientation of FRP layers, etc. on both strength and ductility of the retrofitted members.
The present paper deals with the retrofitting and strengthening of RC columns under combined effects of axial force and biaxial bending moment using FRP composites. The study is essentially the extension of the work conducted by Rocca (2009) to the more general biaxial case. Longitudinal, transverse and combined fiber-sheets are considered as alternatives of retrofitting RC columns using FRP composites. The proposed design procedure is then explained via a case study by which advantages and disadvantages of longitudinal, transverse and combined fiber composite sheets are investigated and discussed according to the interaction curve of the retrofitted column. Results demonstrate that the proposed procedure is appropriate for practical retrofitting applications, and different fiber-sheet layouts are effective in enhancing the load bearing capacity of both the compression- and tension-controlled columns.