مجله علوم و مهندسی زلزله
سال پنجم شماره 3 (پیاپی 16، پاییز 1397)

In this research, perfectly matched layer has been implemented in the finite element method to simulate the radiation damping for soil-structure interaction analysis application. The perfectly matched layer (PML) has the ability to absorb and attenuate scattered waves under any angle of incidence and frequency, such that with the minimum dimensions of the modeling and the minimum amount of calculations, high-precision responses can be achieved. In order to time domain dynamic analysis by finite element method, a program is written utilizing MATLAB mathematical language, which is capable of analysis of different geometries, layering and dynamic/seismic loading in models with linear elastic behavior. The present program uses four-noded quadrilateral elements and uses the implicit Newmark method to solve the dynamic equation. The feature of theprogram is the implementation of PML, which can address the simulation of radiation damping in the finite element method correctly. This is done by rewriting the PML formulation, implementation in the finite element method, and step-by-step verifying the analysis of dynamic problems. First of all, to verify the dynamic analysis performance of the program, three simple examples have been solved, and the results show that theyare consistent with existing theories and the literature. Next, using PML, the problem of a rigid massless foundation vibration has been studied. Computing the impedance/compliance functions and comparing them with analytical or semi-analytical approaches existing in the technical texts, the efficiency and the precision of PML for surface loading conditions has been evaluated. In the frequency domain, the results are in good agreement with the previous studies. Besides, comparing the response from the reduced model (using PML) with the expected response from the extended mesh indicates that there is a complete match in the time domain. It is worth noting that this match is achieved while the model dimensions and the volume of data storage have been drastically reduced, but the accuracy of the answers has not varied. This reduction of dimension is such that if PML is located at a distance of up to a quarter of the foundation width, similar responses to larger models can be achieved.

Several analytical and numerical techniques have been developed for solving poroelastic governing equations; however, no closed-form solution in time domain for the general material case, even in simple one-dimensional geometry, has been yet introduced. Analytical solution for wave propagation in saturated porous media is limited and cannot be easily obtained for earthquake loading. The existence of such analytical solutions to simplified problems of seismic wave propagation is essential. In the present paper, a closed-form solution in time domain is obtained for saturated soil layer subjected to vertical component of earthquake acceleration. Saturated soil is assumed as a saturated poroelastic media and corresponding governing differential equations for earthquake loading are derived. In a poroelastic medium under the effect of seismic waves, solid phase displacement and pore pressure are coupledand interact with each other. If the ground surface and the boundaries between soil layers are horizontal, the lateral extent of the deposit has no influence on the response, and hence, the deposit can be considered as a one-dimensional confined column. The vibration modes, the modal shapes and their corresponding frequencies are obtained from the free vibration condition of the governing equation. By applying the method of separation of variables, the governing equation, which is a second order hyperbolicpartial differential equation, is separated into a Bessel equation in space and a single-degree-of-freedom vibration equation in time. The Bessel equation and the single-degree-of-freedom vibration equation are solved using the Bessel functions and Newmark's direct integration method, respectively. In order to examine the accuracy of the analytical response presented in this paper, acceleration values recorded in a saturated alluvial during one of the previous earthquakes are compared with the calculated values by the analytical method. A numerical example is presented to further analyze the analytical solution. The numerical example shows that a decrease in permeability has a damping effect on acceleration, whereas, amplifies the excessive pore pressure. The suggested solution can be used for dynamic analysis of wave propagation in saturated soils during earthquakes.

The soil under footings is generally under cyclic loading, which causes that the footing operation becomes different from that in static loading condition. The change in the behavior corresponds to the bearing capacity and the settlement of the footing under cyclic loading. To compensate such limitations, it is common practice to improve the soil behavior by considering reinforcementlayers in depths under the footing region. By this approach, the reinforcement layers, which are able to resist tensile loads, decrease the soil settlements and consequently, cause to increase the tolerable applied pressure with respect to the condition where the soil is not reinforced with such layers. In the literature, there are several researches that studied and compared the behavior of non-reinforced and reinforced soils under both static and cyclic loads. It is noted that most of these studies were performed by considering small dimensions of footings by using dimensional analysis. Furthermore, all previous studies have only focused on the post-cyclic settlement of the footings and no investigation was done on the effectiveness of the bearing capacity or applied load under the footing. In the present study, the mechanical behavior of a footing under static and cyclic loading condition is investigated by paying attention to both the settlement and bearing capacity. It is also aimed to find the effect of loading frequency on the footing behavior. In order to have more effective results to be used as practice, experimental tests were performed by using an equipped plate load test (PLT) system. The diameter of the circular plate is 300 mm that is equal to traditional PLT equipment in common practice. The plate was thick to behave rigidly and it is equipped with monitoring system including LVDTs, load cells, pressure gauges and strain gauges installed in different parts of the plate. The test were done in a reservoir with diameter of 1400 mm and height of 900 mm. The soil inside the reservoir was uniform-graded sand whose relative density was 72%. In order to assure having a uniform-compacted soil in the whole reservoir, a portable curtain rain system was utilized. The loading equipment includes a loading steel frame with high capacity and a loading jack with 50-ton capacity. The loading system works hydraulically with closed-loop algorithm. In the experimental tests, only one layer of geogrid with the commercial name of CE121B was used, which was installed at 50 mm below the footing surface (equal to the ratio of the embedment depth to the plate diameter of 0.17). The ultimate bearing capacity of the footing (plate) was obtained experimentally for both non-reinforced and reinforced soil conditions. In order to investigate the footing behavior under cyclic loading, the footing was first loaded under static force equal to 33% of the corresponding ultimate bearing capacity and then, the cyclic loading was applied.The dynamic loading was harmonic with three different frequencies of 1, 2, and 4 Hz along with 1000 cycles with the amplitude of 20% ofthestatic ultimate bearing capacity of the footing. The results show that the variation of the cyclic settlement is almost linearwith the logarithm of number of cycles. In addition, comparison of the results shows that although the frequency has an increasing effect on the cyclic settlement, the effect of frequency is not so much. The cyclic settlement increases 18% if the frequency augments from 1 to 4 Hz. The applied load under the footing at the post-cyclic condition was also investigated for different footing settlements for all loading frequency levels. It was observed that generally, there is the same trend regardless of the level of footing settlement. There is a small increase in the loading (less than 10%) at the frequency of 2 Hz, such that it can be concluded that the frequency has very small effect on the pressure under the footing. The induced tensile strain in the geogrid layer was also investigated and it was found that for the applied loading conditions in this study, the loading frequency has no effect on it.

Due to the relative displacement of the earth crust micro plates, seismic waves and fault ruptures are formed, which shows different consequences on the ground surface. These effects vary according to fault depth, displacement value, type and sub-surface conditions. Although limited studies have been conducted on fault rupture propagation so far, studies have been accelerated following the occurrence of three earthquakes in Taiwan (Chi-Chi), and Turkey (Duzce and Kocaeli). Because of limited time to study the fault ground rupture after an earthquake, and the huge cost of performing large-scale tests (1 g conditions), it is important to perform studies on centrifugal model of fault rupture phenomena adopting accelerated gravity condition (Ng). In this study, a split box was designed and manufactured to simulate reverse and normal faulting. It was composed of a fixed and movable part designed to simulate footwall and hanging wall, respectively. The Firoozkuh sand No. 161 with a relative density of Dr=70% that is uniformly-graded fine clean sand with a mean grain size (D50) of 0.3 mm, maximum void ratio (emax) of 0.943 and a minimum void ratio (emin) of 0.548 was used in these tests. The tests were performed at the centrifuge facility of the University of Tehran, using Actidyn Systems C67-2 equipment and at a centrifugal acceleration of 60 g. Five initial tests were conducted to improve the boundary conditions of the models. The sidewalls of the model could create undesirable friction that could affect the test results; thus, different solutions were examined for reducing friction. Polyurethane sheets, double polyurethane sheets and silicon oil were used on both sides of the split box to reduce the frictional resistance. These tests were conducted using polyurethane sheets along with silicon oil-covered surfaces, which were determined to be the best solution. The other two experiments were designed to simulate normal and reverse faulting after obtaining desirable and appropriate conditions. The results of simulation showed that the vertical movement of bedrock in reverse faulting dissipated throughout the soil layer, and amplificated throughout the soil thickness in normal faulting that the value of DDR (Dissipated Displacement Ratio) was 91% and ADR (Amplificated Displacement Ratio) was 124%, respectively. The required h/H ratios for complete development of a failure surface were 5.57% and 1.85% in reverse and normal faulting, respectively. The failure surface approached the ground surface at a smaller dip angle (50 ̊) than the fault dip angle at bedrock (60 ̊) in reverse faulting and it became increased (84 ̊) in normal faulting. The scarp fault in normal condition is sharper and higher than reverse faulting; therefore, the buildings located in this area suffer damages that are more drastic than reverse faulting. According to the conditions of this study, the width of deformation zone is almost equal in reverse and normal faulting, but its location with respect to bedrock fault tip is different in either types. The width of deformation zone is equal to the soil layer thickness, and its border moved toward hanging wall side almost one third of the soil layer thickness in normal faulting. Increases in the price of urban land and a shortage of land for construction make optimal determination of this zone of special importance. Therefore, for effective usage of land, it is suggested that complementary studies (field investigation or laboratory model testing) be performed.

Introduction Regarding to the efficiency of core-wall resisting system, it has become one of the most widely used structural resisting system. On the other hand, existence surrounding walls at subterranean levels together with diaphragm of grade level cause to comprise a stiff concrete box. This stiff box can create a large force at diaphragm of grade level whenever a lateral load is imposed to the structure. Due to a largeness of mentioned generated force, it may reverse the internal shear force of below grade in the core-wall. This phenomenon is often recognized as “Backstay Effect”. Some literatures such as PEER/ATC 72-1 have been prescribed various certain values for upper and lower bound of stiffness of effecting components. By utilization of these specified values, the aforesaid structural components must be designed for all the critical conditions. A study was performed by Karimi and Kheyroddin determined various limit states of backstay effect. These limit states were investigated by various boundary condition assumptions for core-wall support and ground level diaphragm. Another research was performed by these authors, presented a relationship for prediction of backstay effect; however, this relationship was not considering of shear deformation that may be important for mentioned investigation. Involving Shear Deformation This paper is focused on involving the shear deformation of the core-wall in backstay formulation. Large depth of section to the length ratio of a frame element causes to increase the contribution of the shear deformation in total deformation. Therefore, due to the largeness of the core-wall section dimensions relative to embedment length of structure in the ground, accounting of this aforementioned impact must be considered. In this research, the effect of shear deformation is comprised as a parameter named β. The β parameter is related to a shape of the element section and the length of that element, and can be calculated from the Elasticity of Material science. This parameter was obtained for a core with a shape of square thin walled section and then the aspect ratio of core width to the subterranean height is related to the generated force at the diaphragm of grade level. All the parameters exist in the presented formulas are dimensionless, that make convenient for the usage of them. Results and Discussion Obtained formula is depicted in the form of some curves as a function of an aspect ratio of the subterranean height to the core width at different individual stiffness ratios (the stiffness of a concrete box relative to the stiffness of a core-wall). Investigation of these curves (or main formula) shows when the value of stiffness ratios is very high; the result of obtained formula is closed to a limit state of the obtained results of the previous research. Results show that considering of shear deformation cause to decrease the core-wall stiffness and also decrease generated force at diaphragm of grade level. Furthermore, concerning shear deformation is quite important for a low ratio of the embedment length to the dimension of core-wall section. If this ratio is bigger than about 10, the effect of shear deformation is not considerable. Besides, for verification of the achieved formula, a numerical case study is performed. For this purpose, a building of 21 stories with a core-wall resisting system is investigated. This building has one story of basement and 20 stories of the superstructure with a quadrilateral typical plan (five bays of 6 m in each side). The core-wall section with a square shape of 6 by 6 m is placed at the centre of the plan. A notable point that must be considered at modelling time is not using the rigid diaphragm constraint at the diaphragm of grade level. Analysing of the explained mentioned building by ETABS program and comparing its result to the obtained result from the proposed formula showed a good acceptable match.

Study of the seismological aspects of major earthquakes occurred in California, Japan and New Zealand indicates that the structures located in regions with high level of seismicity, experience aftershocks with different intensities in addition to the mainshock. Multiple earthquakes create inelastic response in structures and lead to the accumulation of considerable damage in the structural and non-structural elements. The aim of this research is to determine the effect of aftershocks on the response parameters of a 10-story steel bundled tube frame structure. According to the analytical results of this study, the occurrence of severe aftershocks following the near-field earthquakes does not have a significant contribution to the changing maximum inter-story drift parameter. Additionally, by increasing the intensity of the aftershocks, the residual inter-story drift does not indicate a clear trend height-wise, obviously. Moreover, when the dominant period of the mainshock is close to the fundamental period of the structure, and the dominant period of the aftershock is close to the fundamental period of the damaged structure, then the occurrence of the aftershock increases the amplitude of the nonlinear response of structural elements. The response parameters studied in the current paper include maximum interstory drift, residual inter-story drift, plastic hinge mechanism and induced forces due to shear lag effect . It should be noted that the maximum inter-story drift in all stories of the studied structure subjected to the fault normal component of the Bam 2003 mainshock record has exceeded the allowable value prescribed by the Iranian seismic code 2800. This is due to the dominant period of the Bam record that is very close to the fundamental period of the studied structure. The findings of this study display that the occurrence of the aftershocks following the mainshock does not change the maximum inter-story drift considerably. Moreover, the strong aftershock (PGAas/PGAms=1.0) occurring after the Cape Mendocino 1992 mainshock i.e. PET record, increased the maximum inter-story drift at the middle and upper stories. Results apply that by changing the aftershock intensities, no clear trend in residual drift values is emerged. The reason could be attributed to the fact that the damaged structure may not have the more maximum displacement when it stops oscillating. However, the Bam mainshock record caused maximum residual drift equal to 0.024, which according to FEMA356 is beyond the Life Safety (LS) performance level.

Roughly since the 1990s, the model updating problem in fields such as design, construction, repair and maintenance of mechanical systems and civil structures has been a very important, challenging, and developing subject. In general, in the model updating methods, an analytical model of a structure, which is usually formed based on its as built data by using of the finite element method, is corrected considering a set of experimental measured data obtained from vibration of the concerned structure. In fact, the main purpose of the model updating methods is to correct some structural parameters such as mass, stiffness, and damping, in order to achieve a better compromise between analytical and experimental data. We expected that a correctly updated analytical model of a structure predict dynamic behaviour of the real structure better and more accurately than its initial model. In this way, considering the structural model changes with respect to a previously constructed reference model would be measurable. On the other hand, if a structure suffers damages through some extraordinary loadings, this will also be recognizable through comparing the difference between the updated model and its reference model. In this view point, the model updating methods may be a good substitution for traditional methods of damage detection and be generally applied methods for the structural health monitoring, also seismic control and performance/behaviour evaluation of civil structures. Many methods have been developed so far in order to update finite element model of civil structures, which are generally categorized in two main groups including direct and indirect or iterative methods. In the direct methods, mass and stiffness matrices of the structure are directly updated during one step. In these methods, there is no direct relation between elements of the structural matrices and structural physical parameters. Therefore, although the updated matrices obtained from these methods have a relatively acceptable accuracy in predicting linear structural behaviour, todays they are rarely used in updating the model of real structures. On the other hand, among the researchers, the iterative methods, because directly use of sensitivity and variations of structural physical parameters to update structural models are more acceptable. Modal parameters of the structure including the natural frequencies and mode shapes are one of the most widely used data in these methods. However, since there is always a non-linear relationship between the modal data and physical parameters, the updating problem in this method is turned into a nonlinear least squares problem that must be solved using the iterative optimization methods. In these methods, the errors between the numerical results and the measured ones are considered as the objective function of the optimization problem. By minimizing the objective function by changing some pre-determined physical structural parameters of the initial analytical finite element model, through an iterative updating method, location and severities of damages are detected, as well as the correct physical parameters. This study aims at updating the finite element model of 3D structures performed through a sensitivity-based iterative optimization method known as the trust region Gauss-Newton method. This is done through finding the best values for the elemental stiffness parameters in analytical model through minimizing the difference between the frequencies and mode shapes of the real and damaged structure. Moreover, in order to reduce the number of updating parameters and avoid singularity problems due to usual numerical errors in the process of solving large-scale optimization problems, a new updating process has been implemented through several iterative stages via sequential analysis to find unknown correction factors. This process continues until the results from the two final analyses are very close during an acceptable accuracy. In order to examine performance of the proposed procedure, it is implemented for detection of several damage scenarios of a 3D three-story steel dual system of an MR structure equipped by a bracing system. Extensive analyses show that, the proposed method is a powerful model updating method to detect location and severity of sparse/minor damages of large-scale structures with the minimum possible error.

Previous earthquakes have shown that a strong ground motion is followed by some aftershocks that are smaller than the main shock, but often produce moderate to high aftershocks in the affected areas. Hence, the structures constructed in seismic areas are not only affected by a single seismic event, but this event also includes foreshocks, main shock and aftershocks. For example, the 2012 East Azerbaijan earthquake (August 21, 2012), with a magnitude of Mw = 6.4 occurred in the northeast of Tabriz, had an aftershock with a magnitude of Mw = 6.3 that happened approximately 11 minutes later. It is known that aftershocks can cause significant failure to the structures damaged by mainshock ground motions. In other words, during aftershocks, there are structures that have already been damaged by an earthquake and have not yet been repaired, which may be damaged or collapsed under the aftershock seismic event. Literature review shows that most existing codes are limited to choose a single event called "design earthquake", while the effects of aftershock earthquakes have been ignored. Despite the qualitative knowing of this issue, limited studies have been reported in the past studies on sequence earthquakes. The plastic hinge area in reinforced concrete buildings is an area where an RC member experiences a moderate to severe plastic deformation under the moderate to strong ground motions. The occurrence order and position of plastic hinges plays a key role in the seismic rehabilitation of old buildings as well as the design of new structures. Contrary to the subject importance, most studies have been limited to the steel structures, and no studies have been conducted on the occurrence order and position of plastic hinges in the reinforced concrete buildings under the mainshock-aftershock seismic sequences. Therefore, in this paper, three-dimensional models with 4, 7, 10, 13, 16, and 20 stories are evaluated under the seven single and seven mainshock-aftershock earthquake records by nonlinear time-history analysis. The formation and average rotation of plastic hinges as well as the performance level of the structures are calculated and compared by nonlinear time history analysis. The results show that the buildings suffered serious damage under the aftershock earthquakes. Number of plastic hinges that pass through LS level increase significantly, so that this number is 31 times in the 13-story building and the building collapse after mainshock earthquake. In all the structures except the 4-story building, under the mainshock-aftershock earthquake records, plastic hinges are formed in the columns of some stories.

The connection with reduced beam section was proposed after the 1994 Northridge earthquake. Until then, it was generally believed that connections with complete groove welding can withstand large plastic deformations. However, the cracks and brittle failures taken place in connections revealed that the actual ductility in these connections might be lower than what was predicted by design codes. By forming a plastic hinge outside the joint, this connection reduces the damage inflicted upon the panel zone. It has to be mentioned, however, that due to the concentration of damage in the reduced area, the entire beam has to be replaced after average earthquakes that is practically impossible. The aim of this study is to experimentally investigate the use of the reduced section in a replaceable fuse. The column and the beam were chosen to be made of sections equivalent to IPE 240 and IPB 180 wide flange profiles and the cyclic quasi-static load was applied until a drift of about 9 percent. The hysteresis moment-drift diagram was drawn. The first sample was a reduced beam section with end plate and stiffeners (RBS). Under loading, this sample satisfied the criteria for the ductility of special moment resisting frame. However, due to the fact that after an average or strong earthquake damage concentrates in the beam and replacing it after earthquake is either extremely difficult or not possible at all, it was tried to use a short replaceable fuse at the end of the beam in the second and third samples. The second sample incorporated a fuse with the length of 35.5 cm and a beam with a reduced flange (RBS-F). Since the ratio of the width of the flange to the height of the beam is directly correlated to its resistance against lateral-torsional buckling, cutting the beam in RBS connections causes different types of buckling to occur faster. To overcome this problem, in the third sample, only the height of the beam was decreased and the dimensions of the flange were not altered. Therefore, the third sample included a 35.5 cm long fuse and a beam with a reduced web (RWS-F). All of the samples satisfied the required drift for the rigid connection special moment resisting frames and using different types of RBS connections reduces the damage inflicted upon the column and the panel zone. The results showed that in addition to having very suitable ductility, the RBS-F and RWS-F samples can be very good post-earthquake replacements for conventional RBS connections

Structural control is considered as an efficient method to improve seismic behavior of buildings. Control methods are divided into passive, active, hybrid and semi-active due to adaptability and need to external energy. Semi-active control methods have the reliability of passive systems, and at the same time maintain the consistency and variability of active systems. In this method, structural responses decrease based on the change in damping properties or stiffness of the system. Tuned Liquid Damper, TLD, has a dual operation: it can be used as a damper and water tank. It has low manufacturing, installation and maintenance costs. In this damper, water sloshing reduces the vibration of the structure. In the recent years, researchers have tried to use the baffles and perforated plates in the damper tank to increase the energy dissipation. In this study, the variable baffles previously presented by Zahrai et al. are used. The objective is to examine the behavior of TLD with variable baffles and feasibility of its usage in semi-active control of structural responses due to near and far field earthquakes. Therefore, in this research, an experimental model of the proposed damper is used to passively control responses of a 2D frame. In this study, a benchmark 5-story building structure utilized in the Sydney Technological University, Australia and adopted by the International Association for Structural Control is used. The structure can have a maximum of five stories with different heights. According to the study by Zahrai et al. to tune the TLD, it is enough to adjust the structural frequency between the frequencies of the damper when the TLD baffles are fully open and fully closed concluding that the damper in this situation has the best performance. It should also be mentioned about the re-adjustment of the damper after rotation of baffles that since the period of the structure is between the damper periods in fully open and closed baffle situations, significant changes will not happen in initial tuning. In fact, if the TLD is tuned properly at first, the baffle rotation does not make too much change in its initial tuning. The study by Sun et al. is used to model the fluid damper in OpenSees. For each orientation, equivalent stiffness, mass and damping are determined. The mass and the viscous spring defined in OpenSees are utilized according to each baffle angle. The stiffness and damping of viscous spring are equal to the equivalent stiffness and damping values. In this paper, the behavior of TLDs with variable baffles under four near-field and four far-field earthquakes is evaluated. The liquid depth inside the damper was considered to be 42 mm, which is equivalent to mass percentage of 1%. Damping of structural models can be changed using an efficient semi-active control algorithm, which acts by changing the angles of baffles. The investigation of the numerical results shows that the rotation of the baffles during the excitation improves seismic behavior of the structural models and reduces the roof displacement. The results show that higher reduction is observed under the near-field earthquakes than the case under far-field earthquakes. However, this reduction is lower for the baffle angles of 50 and 70 degrees due to the curving of the streamlines inside the damper and increase of the damping coefficient in these angles.