مجله علوم و مهندسی زلزله
سال نهم شماره 4 (پیاپی 33، زمستان 1401)

This study aims to investigate the analytical scheme of both the bi-normalized acceleration response spectrum and the bi-normalized tripartite response spectrum according to an ensemble of near-field strong ground motion records in the forward directivity conditions. For this purpose, the horizontal components of the ground acceleration time history were considered and a group of 16 ground motion pairs were selected, which have been recorded during two great earthquakes occurred in California, namely the Northridge (1994) and the Imperial Valley (1979). Also, the analytical scheme of the normalized acceleration response spectrum and the normalized tripartite response spectrum corresponding to a symbolic single-degree-of-freedom system have been compared with the related bi-normalized acceleration response spectra. It should be noted that the identification of near-field strong ground motion records is usually recognized by their physical characteristics such as peak ground acceleration (PGA), peak ground velocity (PGV), and the relatively short period process of energy release. Many strong ground motions have been recorded in less than 20 km from the fault rupture surface during intensive powerful earthquakes. In this case, the most famous earthquake tremors are the Imperial Valley (1979), Loma Prieta (1989), Landers (1992), and Northridge (1994) in California, plus the Kobe (1995) in Japan, Erzincan (1992), as well as Kocaeli (1999) in Turkey. Moreover, there are two very strong records, which were related to the Tabas (1978) and Bam (2003) earthquakes in Iran. The ensemble of the selected earthquake records in this research includes near-field ones that contain various tectonic occurrences. The main physical characteristics of the chosen records cover a wide range of the frequency content and strong ground motions duration as well as various high seismological amplitudes. The related values of the peak ground acceleration and velocity are numerically high. Generally, the peak ground velocity (PGV) is often viewed as a better indicator of the earthquake record damage potential than the peak ground acceleration (PGA). The large velocity pulses evident in the related plots can be viewed as damaging features. Moreover, the earthquake record damage potential also depends on how much dynamic ground displacement occurs during these velocity pulses. Referred to apparent physical influences caused by strong faulting mechanisms, the presence of high-amplitude velocity pulses is one of the most important characteristics of near-field records, which can be registered in a time-history domain. In general, these pulses appear as wave-shaped features with high amplitudes and long periods, which have a compound and continuous shape. Distinct powerful velocity pulses are resulted corresponding to high-amplitude acceleration pulses and spikes usually with a less than 1.5 second time-domain and also high-amplitude and short-time spikes with 0.2 to 0.3 second time-step in the spectral windows of the horizontal parallel and perpendicular components with respect to the fault rupture couture. These processes would essentially cause an enormous amount of the kinetic energy of strong ground motions to get released in the time-range of compound coherent and long-term velocity pulses in the related time history. In order to investigate these effects on the configuration of the aimed response spectrum, the velocity pulse time step, the ratio of corresponding kinematic energy of both two horizontal components, peak ground acceleration (PGA), and peak ground velocity (PGV) were considered.According to the performed computational assessments in this research, it was resulted that the bi-normalized response spectrum by the basic criterion of predominant period has a monotonous configuration and would get fewer effects due to variation of the notified spectral parameters.

In recent decades, several destructive earthquakes resulted in extensive structural and non-structural damage in structures, which was produced by lateral displacements. Therefore, it reveals the necessity for the accurate estimation of the lateral displacement of structures in the design procedure.Present seismic codes using structural overstrength and the ability of energy dissipation capacity of the structures allow a structure to be designed for reduced seismic design forces with force reduction factor. As a result of this, the response of the structure lies beyond the elastic region in the event of strong ground motions; thus, simple linear analyses procedures fail to predict the structure deformations accurately. On the other hand, due to complexity and time consuming nonlinear dynamic analysis, this type of analysis has not been acknowledged as an applicable method for structural engineers. Efforts in the direction of finding a procedure to estimate the maximum lateral inelastic displacement began years ago.According to present seismic design provisions, displacement amplification factor (Cd) is being applied to elastic lateral displacements in order to assess inelastic displacements due to ground motions. Although, the factor of Cd in the codes are not in accordance with the actual behavior of the structure, the empirical does, based on the structural performance observed in the past earthquakes and should be corrected according to the effect of height and number of stories. In this paper, the effect of Cd on seismic performance of steel special moment frames is evaluated. In this regard, six types of buildings are designed with different values of Cd (i.e., 4, 5, 5.5, 6, 7, and 8); and, in order to investigate low to high-rise buildings, 5 heights (i.e., 5-, 10-, 15-, 20- and 25-stories) are considered in two regular and irregular states. Irregularity is considered to be a mass irregularity in the first floor, so that the mass of the first floor is 50% higher than the mass of the adjacent floor. The numerical finite element models are developed in OpenSEES software. Incremental dynamic analysis (IDA) and nonlinear static analysis are performed to quantify structures’ seismic performance; Nonlinear static analyzes are performed to determine overstrength and ductility factors of buildings. Also, the effect of earthquakes on buildings is investigated using incremental dynamic analysis that is accomplished with 22 far-field earthquake record pairs proposed in FEMA P695. Eventually, the effect of different values of Cd on seismic performance of the buildings are quantified and investigated using FEMA P695 methodology and fragility curves in terms of the adjusted collapse margin ratio (CMR) and the probability of collapse (Pf).The results demonstrate that the probability of collapse (Pf) of short and medium-rise buildings with Cd equal to 5.5 is higher than 10%, which is the targeted value of Pf according to design codes; therefore, considering Cd equal to 5.5 in the design of these buildings does not provide real displacement and leads to underestimated design of buildings. In irregular buildings, although the Pf values increased compared to regular buildings, a similar trend was observed in general. In short, the amount of Cd that leads to an acceptable performance of collapse in the structures is equal to 8, 8, 7, 6 and 5.5 in regular 5, 10, 15, 20 and 25 story buildings, respectively; moreover, similarly in 5, 10, 15, 20 and 25 story buildings with mass irregularity are equal to 7, 7, 6, 5.5 and 5.5, respectively. Based on these values, relations are proposed to correct the displacement amplification factor in regular and mass irregular steel special moment frames.Also, comparison of Pf and weight of structures designed with ASCE 7-10 and ASCE 7-16 regulations revealed that design of structures according to ASCE 7-10 criteria with modified values of Cd that is presented in this paper will be economical in addition to achieve the intended collapse performance.

As one of the most common lateral load-resisting systems, X-braced Frames have low energy dissipation. In this study, performance of a new energy dissipation system in X-brace frames (XBFs), which can be thought of as a passive control system, is investigated. The Rubber-Fuse Damper (RFD) is a new damper with a rubber core, steel plates, adhesive, and four bolts. The use of a rubber core for energy dissipation is a key feature of the damper's. The monotonic and cyclic behavior of a single-span and single-story XBF with varying frame height-to-span ratios equipped with the proposed RFD is investigated using finite element modeling and validated with experimental data. The RFD is either single or in pairs in each XBF specimen. In addition, the ductile damage method (DDM) revealed damage to the main structural components, such as bracing members. The results revealed that X-braced frames with single and double rubber-fuse dampers (XBF-RFDs) performed better under cyclic and monotonic loading than X-braced frames without rubber-fuse dampers (XBFs). Furthermore, because the bracing members did not buckle in the XBF-RFD specimens, there was no rapid loss in the stiffness and strength of the X-braced frames.The monotonic loading reduced the stiffness of the XBF-RFD specimens by 93% to 98% to XBF specimens at various height-to-span ratios. In comparison to the XBF specimens, the yield and ultimate base shear of the XBF-RFD specimens dropped as well, with the highest reductions of 91% and 82%, respectively. When compared to XBF specimens under monotonic loading, the reduction in base shear and stiffness avoided buckling, resulting in more stable behavior and smaller nonlinear deformations of the XBF-RFD specimens.Furthermore, the XBF-RFD specimens showed no sudden stiffness or strength drop. The results of the cyclic loading of the XBF-RFD specimens demonstrated that no rapid drop in stiffness or strength was detected due to no buckling of the bracing members under the cyclic loading, as was the case with the monotonic loading. Additionally, in comparison to the XBF specimens, the drifts corresponding to the first plastic hinges of the XBF-RFD specimens show that the bracing members experienced nonlinear deformation at greater drifts, with the plastic hinges created in them at bigger displacements.The RFD also reduced Von Mises stress and damage in the bracing members of the XBF-RFD specimens, according to the cyclic loading results. At height to span ratios of 0.5, 1, and 1.5, the ultimate Von Mises stress reduction in the bracing members was 26%, 42%, and 36%, respectively, and this decrease was a reason to prevent the buckling phenomenon. Unlike the XBF specimens, which lost seismic functionality at low drifts, the XBF-RFD specimens maintained their seismic functionality up to a 4% drift of the cyclic loading, and they dissipated a greater quantity of energy.

Seismic risk assessment of structures is an important and practical tool for seismic safety assessment, earthquake consequence analysis, seismic strengthening planning and post-earthquake crisis management. This assessment consists of various parts including seismic hazard analysis, exposure evaluation, vulnerability analysis, and risk estimation. One of the most important parts of this process is the development of structural fragility functions or curves for undesired performance. Various methods have been used to determine fragility functions. In most of these methods, a general limit state such as maximum relative displacement of the floors is considered as failure mode, while in older buildings, more failure modes such as shear failure mode of structural members are usually prevailing.In this paper, a framework for determining the fragility functions of structural collapse based on different failure modes of structural members using fault tree analysis is presented. This method includes developing the fault tree of the undesired performance of the structure (through possible failure modes in members), preparing a suitable computer model of the structure according to failure modes, selecting earthquake acceleration records for IDA analysis, determining the capacity and limit mode of failure modes based on laboratory results or standards, performing IDA analysis for the structure and forming a fragility table, calculating the fragility parameters using a suitable statistical distribution and plotting the seismic fragility curve for each of the base events in fault tree and quantifying the fault tree, and finally deriving the fragility curve of the structure.This method was applied on a reinforced concrete building frame made in Europe according to the design criteria of the 50s and 60s, and then the results were compared with the conventional method of developing fragility functions, which is based on the general limit state of maximum relative displacement of floors. Because the main reason for the weakness of the frame under study is the weakness in shear of the columns due to the lack of seismic transverse reinforcement details at the time of their design and construction, in next stage, the fragility function of the studied frame is determined by observing the criteria of seismic transverse reinforcement and is compared with the fragility function of the existing frame without observing these criteria. The results show a much lower median estimate of the capacity of the fragility function due to the shear weakness of the old frames in the proposed method compared to the conventional method. The fragility curves derived from conventional methods match very well with the failure mode causing weak-storey on the first floor. This observation is in good agreement with the results presented in the references in which the main collapse mode for this frame is the failure of the weak floor in the first floor. Another observable result in the proposed method is the reduction of the dispersion of the results using this method compared to the conventional method because the fragility curve obtained from this method covers a narrower range than the conventional method.Considering the criteria of transverse reinforcement, it was observed that in many columns, the philosophy of designing new regulations, which is flexural failure before shear failure, has occurred, which shows the high importance of transverse reinforcement in column sections. By observing the criteria of transverse reinforcement of sections, the most vulnerable part of this frame are the columns of row 2 in shear failure mode, due to the significant difference in the cross-sectional height of the columns of this row compared to other rows. This difference in the height of the sections leads to high absorption of shear force in the section, which causes the force to pass through the capacity much faster and as a result, its high vulnerability. Finally, comparing the fragility curves of frame collapse in two cases with considering the seismic shear reinforcement criteria and without considering it shows the significant effect of cross-section reinforcement criteria on the seismic fragility function of structures.

The linear quadratic regulator algorithm (LQR) is one of the common algorithms in control engineering that is used in many studies due to its simplicity. This controller is used to achieve optimal system performance by minimizing the cost function related to the state vector and the control input vector. In LQR control, the control gain is determined based on the weight matrices Q and R. One of the main issues in using this algorithm is adjusting the values of its weight matrices, which are determined based on trial and error or the use of meta-heuristic optimization algorithms. The improper determination of the weight matrices can reduce the performance of the controller. For example, increasing Q or decreasing R leads to a larger control gain matrix, which ultimately increases the control force and decreases system states (or responses). Therefore, if the control gain is designed using a very large Q matrix and its value remain constant during the simulation process, the possibility of producing a control force with the maximum capacity is very high. If this happens, the force generated by the actuator during the simulation process may be more than the required force, and the differences between the designed control force and the applied control force can in some cases reduce the control performance significantly or consume more energy than required. On the other hand, it is appropriate to assume the values of these two matrices to be constant in the case of sensors without noise and structure without uncertainty, and LQR control has the ability to reduce the response of the structure under various external vibrations. However, when the information coming from the sensors include noises and the system has uncertainty, the LQR control with constant gain has little ability to reduce the system response properly. In order to solve this problem in this study, a hybrid Fuzzy-LQR controller is proposed in which a fuzzy supervisor is used to change the LQR gain matrix online. In general, fuzzy logic has the ability to deal with noise and system uncertainty due to the lack of need for an accurate mathematical model of the system. Therefore, by combining LQR control and fuzzy control, the advantages of both controllers can been used. This fuzzy supervisor adjusts the pre-designed initial gain according to the created conditions by changing R weight matrix, so that the control force applied to the structure is proportional to the required control force and does not exceed the allowable actuator capacity. This change is implemented also with the aim of minimizing the amount of energy consumed by the actuator. To evaluate the performance of the proposed controller, three-story and eight-story buildings are used, all stories of which are equipped with the active tendon actuator. This structure has been subjected to the vibrations of two artificial earthquakes with a risk level of 10% and 2% in 50 years and different responses of the structure including the maximum value of responses and root of their mean squares have been determined. Then, the high capability of the Fuzzy-LQR controller, which even in the presence of parametric uncertainty and noise in the sensors can reduce the response by up to 90%, can be proved by comparing the results of the proposed controller and LQR controller based on different meta-heuristic algorithms. For example, the responses of displacement, velocity and acceleration of stories are reduced by an average of 81%, 83% and 71%, respectively using the proposed controller and under earthquake with a risk level of 10%. While using only the LQR controller, these values are 71%, 72% and 64%, respectively. The following results show that the root mean square of the responses has decreased more than their maximum value, which indicates the proper performance of the proposed algorithm during the excitation. Finally, it can be concluded that the proposed controller has a robust and stable behavior against various vibration and system uncertainties.

Structural vibrations caused by earthquakes, wind or other factors can be controlled by various methods. The conceptual approach of structural control includes changes in member stiffness, structural mass and damping to deal with forces passively, semi-actively and actively. Until today, a number of these structural control methods have been successfully used and researchers are promoting methods to increase their applicability and scope by improving performance.In recent years, researches have significantly been focused on the development and expansion of structural control methods and equipment. Also, in the last three decades, many efforts have been made to transform the conceptual approaches of structural control into usable and practical technologies in structures. It has been clarified that the structural control is one of the important and key points in the design of new structures and a suitable solution for improving structures against wind and earthquake loads. However, until today, most of the existing programs and strategies have led to the use of passive mass dampers or isolation of vibrations from the base. Over the past years, various control equipment and algorithms have been proposed, each of which has its own advantages according to the required performance and the part used.Semi-active control systems are a separate and emerging example, similar to active control systems. In this control system, the required external energy is much less compared to the energy controlled by the structure. Basically, the semi-active control system does not introduce external energy into the structural system, so the output band of the structure's seismic response is guaranteed [1].The resistive force or energy dissipation is determined by the internal mechanism of the system members based on the feedback of external or internal sensors. Therefore, this system has combined the advantages of passive and active control systems. Studies have clearly shown that the use of semi-active control equipment and systems has been significantly better than passive control systems in reducing the seismic response of structures, and this system has the ability and potential of this has the ability to perform at the same level or even better than active control systems [2].In this study, the use of electromagnetic force in the friction damper has been considered and a controllable friction damper has been introduced. In this damper, electric current changes are used to change the force perpendicular to the sliding surfaces of the friction plates. In this method, by using powerful electric magnets that require little electrical energy and by controlling the intensity of the passing current, the function of the friction damper is controlled. For this purpose, taking into account the magnetic behavior of the material and using computer modeling, in addition to validating the analytical results, the behavior of this electromagnet was analyzed parametrically and the test results confirmed the proper behavior and controllability of this damper. To change the force perpendicular to the surface of the electromagnets, using electronic circuits, the current passing through them was changed from zero to 1.5 amps, and the maximum force produced by the damper reached about 1200 N. The electric power needed to create the maximum power capacity was measured to be 8.5 watts. Also, the response time of power generators to current changes was measured to be maximum 56 milliseconds to reach the maximum capacity and 68 milliseconds to reset the damper force. The results of this study showed that this type of power generator has the ability to be used in the direction of semi-active structural control. The analytical and experimental results of electromagnets showed that the maximum tension perpendicular to the surface that this type of power generator can create is around 10 kg/cm [22].

The direct displacement-based design (DDBD) method is one of the most powerful and efficient performance-based design procedures. This method has the ability to consider the nonlinear behavior of structures under seismic excitation with acceptable accuracy. The methodology of this method is based on substituting a multi-degree of freedom (MDOF) system into a single degree of freedom (SDOF) system associated with the peak displacement response. The SDOF system is defined by implementing equivalent parameters such as effective mass and height, design displacement, yield displacement, ductility, effective damping, and effective period. Up to now, the DDBD method has been applied and developed by many researchers and the last version of the model code for DDBD was published as DBD12.Over the past three decades, using fluid viscous dampers as a manner for more reliable and safer design of structures, particularly in seismic regions, has steadily increased. Consequently, the equivalent lateral force (ELF) procedure as an allowable method for designing structures equipped with dampers has been presented by ASCE-7. However, the DDBD method also suggests the procedure to design structures equipped with dampers. Previous studies showed that although structures equipped with viscous dampers designed by the DBD12 approach can satisfy the target performance limit states, a significant overestimation may be seen between the performance target limit and inert-story drift ratios (IDRs) obtained from nonlinear time-history analyses. In other words, the structures are not economically designed.To solve this drawback, the present study proposes modifications for low to mid-rise steel moment-resisting frames (MRFs) with dampers in the DDBD method. In doing so, the effect of interaction between ductility demand and added extra damping related to the viscous damper is considered to calculate effective damping. Moreover, a velocity modification factor is also applied for calculating damper constants. In order to compare the proposed modifications with the conventional DBD12 approach, 3-, 6- and 9-story steel MRFs are designed by each of mentioned procedures separately. Furthermore, linear and nonlinear dampers with velocity exponent values equal to 0.35, 0.5, 0.7, and 1 are used. To investigate the seismic performance of the structures designed, nonlinear time-history analyses are performed under the ground motions that the average of their pseudo-acceleration response spectra is matched with 2800 standard design spectrum. Then, the IDRs and displacement profiles of the structures are compared at the maximum considerable earthquake (MCE) hazard level. The results obtained from the analyses of the structures designed by DBD12 confirm the overdesign of this approach. On the other hand, the obtained results of structures designed via proposed modifications validate the efficiency of these modifications. Low-rise MRFs in all of the velocity exponent values can significantly decrease the difference between the peak IDR and target limit. Also, implementing the proposed modifications for mid-rise MRFs with linear damper and damper velocity exponent values equal to 0.7 can acceptably match the peak IDR and target limit. In addition, the seismic behavior of structures designed by the proposed modifications at the MCE hazard level is also checked at the design earthquake (DE) hazard level. The results show the satisfaction of life safety performance level for these structures. It is worth to mention that the peak IDRs in the mid-rise MRFs with damper velocity exponent values equal to 0.5 and 0.35 designed by the proposed modifications exceed the target limits at both the MCE and DE levels. Therefore, more studies are suggested for mid-rise MRFs with nonlinear dampers.Finally, comparison between two mentioned procedures reveals that using the proposed modification in the DDBD method leads to about 8% decrease for used steel and about 30% decrease for damper constants.

In recent years, sandwich panels have become one of the common infill panels in the moment resisting frame systems. The behavior of these infill panels has always been discussed by researchers. Based on seismic design, for prevention of structures collapse during the severe earthquake, it is necessary to absorption of energy by plastic deformation. In fact, the seismic applied load to structures is greater than applied force to it during design. This reduction of design applied loads is by behavior factor. Behavior coefficient depends on parameters such as ductility coefficient, structural damping coefficient, soil characteristics, earthquake characteristics, over strength coefficient and design reliability coefficient. Therefore, estimating the behavior of structures is always of particular importance in order to understand their response to earthquakes. In the present study, the behavior factor of moment resisting frames with the sandwich infill panel has been investigated. Also, an equation has been established to calculate the behavior factor, based on various effective parameters. In this regard modeling and nonlinear analysis of moment resisting frames models with the sandwich panels were performed in ETABS 2017. Nonlinear analysis is necessary for determining the effect of earthquake force in during design and nonlinear dynamics analysis is time consuming so usually designers use the nonlinear static analysis. Nonlinear static analysis is one of the nonlinear analysis methods that the lateral load represents the earthquake load and is applied statically and increasingly to the structure. Estimating behavior factor prior to the starting of the design process is an important help to designers. For the process of analysis and design of the researched structures, the national building regulations and also ACI 318-14 have been used in loading, analyzing and designing process. In this paper, we have examined behavior factor of the reinforced concrete (RC) frame with sandwich infill panels using gene expression programming. Gene expression programming is very successful in this case. The success of an issue depends largely on how well it works. Gene expression programming is a genetic algorithm that uses the population of individuals and selects them according to fit and introduces genetic changes using one or more genetic operators. In this modeling, some effective parameters in the performance of moment resisting frames with the sandwich infill panels have been considered in various and variable ways. These parameters include: the number of stories (2, 4, 6, 8, 10, 12, and 15), the ratio of span length to story height (1, 1.5, and 2), the design base acceleration (0.35 and 0.3), ratio of concrete compressive strength to the longitudinal reinforcements yield stress (0.08 and 0.075). After calculating the behavior factor using valid methods, a database was created by using the behavior factors obtained from the models. A mathematical equation was conducted by GeneXproTools software to obtain the behavior factor. The main purpose of this research is to establish an equation to obtain the behavior factor of the moment resisting frames system with the sandwich infill panel based on effective parameters. The obtained equation has resulted in a regression coefficient of 93%. After extracting the relevant functional equations, the sensitivity and parametric study of the behavior factor concerning the parameters of the mentioned variable have been studied.  The result shows that the parameters of the number of stories and the ratio of span length to story height, are the most influential on the behavior factor. In this regard, with increasing the number of stories, the coefficient of behavior increases, and with increasing the ratio of span length to story height, the value of behavior factor decreases.