مجله علوم و مهندسی زلزله
سال دهم شماره 1 (پیاپی 34، بهار 1402)

One of the main tools in seismic hazard analysis is Ground Motion Prediction Equations (GMPEs). Selection of appropriate GMPEs is an important step in hazard evaluation, which can cause accurate seismic design of structures. The GMPEs have been developed based on the local or regional or global data. Iranian plateau is a shallow crustal environment except the Makran region in south-east Iran in which the subduction events can happen. Due to the tectonic characteristics of the Makran subduction zone, different categories of GMPEs are required for seismic hazard assessment including GMPEs for shallow crustal events and subduction zone earthquakes (both in-slab and interface events). Taking into account that most of GMPEs in Iran have been provided for shallow crustal earthquakes, development of a GMPE model is needed for this subduction zone. Therefore, a new ground motion prediction model (GMPE) is developed based on Makran interface subduction events in this study. Due to the lack of recorded data in the Makran zone, this study is based on records of strong ground motions in other subduction zones, including events in Japan and Mexico from 1985 to 2018, as well as a database compiled by Atkinson and Boore (2003) including events recorded in Japan, Mexico, Alaska, Peru and Chile from 1968 to 1998. The database contains 1424 records of interface subduction events with Mw 5 to 9, distances less than 300 km and focal depth   less than 40 km. Since all records should be the same in terms of magnitude and measured by Mw, records that were reported with Mb and Ms were separated. Then, by examining the relationships and relevant articles and the conditions of this database, these values were eventually converted to Mw. Soil type of some records was reported according to geological characteristics of the region. The soil type of some others, due to the lack of geological characteristics information, using the information of the stations in that area, Vs30 values were extracted in different depths of the soil and using the studies, coefficients and relationships provided, the Vs30 value for each station was obtained. The soil type of some others was determined according to NEHRP classification. Finally, using presented studies by previous researchers to match this available information, this unification has been done. Existing records are categorized by soil type, Mw and focal length, and diagrams representing them are also plotted. The soil type of the records is A, B, C, D and E according to NEHRP classification. Processing of the database have been performed and the spectral accelerations in different periods have been obtained. In this work, some functional forms have been tested to understand the best model according to the most possible accuracy to fit our dataset. Then, using regression analyses, the ground motion prediction model is developed. Therefore, based on the comparison of the models, the dispersion of residues and the standard deviation of the models, best model has been selected for development. The intra-event and inter-event residuals for the proposed model have been obtained. Since the intra-event residual values are different for each earthquake record, it has been investigated in several different periods and also the fitting line is plotted in the diagrams. Inter-event residues have constant values in each earthquake. The residual value in each earthquake is considered average between the residues of different periods, the corresponding diagram is plotted and the fitting line is plotted in these diagrams. Spectral values ​​in the proposed model and the value of standard deviation are compared with other models in the world that shows that the proposed model has good accuracy for predicting spectral values and it is consistent with other models available.

A growing body of evidence suggests that the possibility of nonlinear rocking oscillations can protect the structure from serious damage. One of the potential concerns about this design approach is the magnitude of residual settlement and maximum rotation. Several improvement techniques have been proposed to ameliorate the nonlinear behavior of rocking foundations based on the vertical factor of safety. Rocking systems with a large factor of safety against vertical load are more prone to toppling collapse under severe ground motions. This research explored the effectiveness of using soft walls next to a rocking foundation for mitigating seismic risk. The vital advantage of this improvement technique is that it is a feasible strategy for both new construction and existing structures.
The soil-foundation-structure system has been analyzed using the numerical finite element (FE) method that takes the material and geometric nonlinearities into account. In this case, the nonlinear response mainly involves the interaction between footing uplift and soil failure, which may induce additional (gravitational) aggravating moment (P-Δ effect).
In the first step, a three-dimensional (3D) numerical model has been constructed for the rocking foundation-soil system experiment. In order to verify the accuracy of the simulation, the numerical modeling and the experimental test results have been compared. The results of the centrifuge physical testing conducted were used to validate the numerical simulation. All FE analyses were performed in Abaqus software. This software has been utilized by a number of researchers to study complex soil-foundation–structure interaction phenomena.
Because the initial conditions play an important role in simulating geotechnical problems, a staged analysis procedure has been adopted. In the dynamic analysis stage, an incremental-iterative procedure was used to integrate the equations of motion. The Hilber-Hughes-Taylor algorithm was used to conduct the transient analysis phase. The modified Newton–Raphson method was employed to decrease the calculation cost needed for the great number of degrees of freedom of the model.
Finely refined 3D FE mesh was used to precisely reproduce the mechanism of bearing capacity failure and the rocking behavior. The soil medium and foundation were discretized into eight-node hexahedral continuum elements (C3D8 element type). Two-node linear beam elements were used to model the superstructure (B31 element type). A special surface-to-surface contact formulation between the foundation and soil was used for the realistic simulation of possible uplift and sliding of the foundation. Surface-to-surface contact can calculate contact stresses accurately by reducing the possibility of large-localized penetration of the two surfaces. The properties of the contact element were defined by the interface stiffness in the normal and the tangential directions.
Nonlinear soil behavior was modeled using a kinematic hardening model with the Von Mises failure criterion and associated plastic flow rule. This simplified constitutive model is applicable for the prediction of the undrained behavior of clay as normal pressure independent. In contrast to soil, the behavior of the structure-foundation model is assumed to be linear elastic. A parametric study was carried out to explore the sensitivity of the geometric design variables of the diaphragm wall, such as height and thickness on the behavior of the isolated foundation-soil system.
It should be mentioned that the values of model parameters were determined based on their practical feasibility. The distance of walls has been determined far from the edge of the foundation to avoid static bearing capacity failure.
The results showed that the placement of vertical soft walls next to the foundation could limit the transmitted forces onto the superstructure. This could be lessened the maximum motion of the structure and the following overturning moment of the foundation. Hence, adequate safety margins against toppling collapse could be easily achieved under strong motions.

In a case study, behavior of an underground-railway tunnel of the Tehran metro subjected to tremendous explosive load was explored by numerical analysis. Blast wave propagation in the soil is studied by effective stress analysis in PLAXIS 2D finite element code. To assure reliability of the code in performing a robust dynamic calculation, Lamb Problem was modeled by the code and results were compared with analytical solutions, which was satisfactory. Due to the significant effect of the soil type and layering on the dynamic response of the buried structures in an explosive loading, care was taken in the study to resemble the real soil layering, relying on the available geotechnical investigations in the area. Based on the available data and also semi-empirical relations, HS Small soil model was calibrated to resemble soil behavior. In this regard, five parameters of density, elastic modulus, Poisson’s ratio, damping ration and layer thickness were carefully defined for each layer. Semi-empirical relationships were used to calculate soil dynamic shear modulus, which were larger than the static shear modulus. HS Small model has the ability to resemble the cyclic behavior of the soil by applying Masing’s rules in a load-unload-reload cycle. PLAXIS updates the stiffness matrix of the soil mass at each step of the analysis according to the strain and deformations that have been created in the soil, which increases the precision of the calculations. In this study, the Unified Facilities Criteria (UFC 3-340-03) manual was used to calculate the blast pressure. The weight of TNT explosive (charge weight) was considered 510 pounds (230 weight) in this regard. The type of explosion is assumed as an unconfined explosion, i.e., a surface burst. According to the UFC 3-340-03, the graph of changes of explosive pressure with time which is presented as a triangular pulse in the time domain, was defined in applied to the model geometry in the finite element code. Appropriate mesh dimensions relative to the transmitted wave-length in the numerical simulation play an important role in the precision of the results. Consequently, the frequency content of the pressure-time signal was probed in the frequency domain using the Fourier transform technique. To reduce the reflection of the waves from the model boundaries, viscous absorbent boundaries were defined in the model, as well as enlarging the model dimensions to reduce unwanted and unreal reflections from the boundaries of the model as much as possible.
After careful definition of the model geometry and loadings, both static and dynamic calculations were performed. The former simulated the construction of the underground tunnel, and the latter simulated the surface burst after tunnel construction, ignoring the crater caused by the explosion on the surface. The results show that the peak stress at the crown and bottom of the tunnel decreases as the soil density of the first layer increases, irrespective of static or dynamic values of the soil modulus. However, the stress values corresponding to the static parameters are greater than those of dynamic parameters. This comparison shows that if the static shear modulus values are preferred, the tunnel should be designed regarding larger stresses, which is not economical. Despite the decreasing effect of the first layer density on the stress magnitudes, the increase of the density of the second layer -that surrounds the tunnel- increases the stresses at the crown and bottom of the tunnel. The results also revealed that the effect of Poisson’s ratio of the soil on the tunnel's stresses are very small, but with the increase in the damping ratio, the amount of stress in the tunnel crown decreases dramatically. As the soil layers thicknesses increase, stress at the crown of tunnel decreases. These findings are useful to plan a safer design for crowded subway stations, regarding proper soil layering and properties

The Welded Unreinforced Flange-Welded (WUF-W) connection is one of the most applicable rigid connections used in moment frames. On the other hand, applying built-up box columns is conventional in Iran and Asian countries. Considering the challenges of installing the continuity plates inside the built-up box columns, developing the seismic design equation of minimum face thickness of box column in the connections without continuity plates and trying to reach some creative solutions for eliminating the continuity plates have always been hot topics for researchers, designers, and steel structure industries. It is worth mentioning that due to the lack of use of built-up box columns in European and American countries, European and American standards have not dealt with the criteria of the seismic design of the continuity plates in built-up box columns. Although the AIJ code has proposed a pair of through diaphragms instead of continuity plates to solve the challenges of installing the continuity plates in built-up box columns, and this method has been considered by Iranian researchers, it seems that because of the risk of completely cutting the column section and protruding the continuity plate from column face level, this method has low chance to be widespread used. Regarding the fact that the behavior of the panel zone of H section and box section columns are different, developing the seismic design equations for minimum thickness of column face in built-up box columns without continuity plates have been advised in AISC 341-16. The motivation of developing the seismic design equation of box column face thickness increases when considering that 5th draft edition of the 10th part of the Iranian National Building Code (Steel Building Design and Construction) clarifies that all rigid connections of I beam to box columns, regardless of the column face thickness, must have continuity plates which seems strict. On the other hand, by converting the beam extreme moment to a compression-tension couple force, it seems that the depth of the beam has influence on the nominal capacity of column face resistance.Therefore, in this numerical study, 18 samples have been modeled to investigate the behavior of WUF-W rigid connection to built-up box columns as well as the probable effect of beam depth on the behavior of WUF-W rigid connection of I beam to box columns. The models have been loaded under cyclic loading and monotonic loading corresponding to the AISC 341-16 protocol. The loading has been continued up to 0.06 radian rotation and the frames have been simplified to a console beam and a column. To verify the modeling, the experimental study of Saniee Nia et al. has been used.The results show that although all the models without continuity plates apparently pass the provisions of AISC 341-16 and the 4th edition of the 10th part of the Iranian National Building Code, more attention to details displays some problems. In all samples without continuity plates, the column thickness has been almost 25% over designed, to guarantee the appropriate behavior. But focusing on the equivalent plastic strain at the beam flange edge at loading steps shows the disproportionate spread of plastic strain along the beam flange edge. The plastic hinge is located at the end of beam at the intersection of beam and column face and the column face is partially deformed, which is not desirable. The models without continuity plate have lack of enough rotational stiffness, which does not represent rigid connections but semi-rigid joints. It seems that, unlike what was expected, the beam depth has no obvious effect on the pattern of hysteresis carves of the models without continuity plates like Eurocode 3. However, by 46% decreasing in beam depth, the equivalent plastic strain at the beam flange edge becomes more uniform up to  55% and the rigidity increases up to 23%. Finally, it seems that increasing the thickness of the box column face will lead to increase the rigidity and therefore, it is recommended to develop the seismic design equations to determine the minimum face thickness of the box column in the connection without continuity plates. Finally, it is suggested to address semi-rigid connections in the AISC 341 and in the Iranian National Building Code, 10th part.

Water tanks as vital structures play an important role in drinking water supply and safety after an earthquake. Therefore, studying and understanding the behavior of these structures against earthquake load in order to accurately design these structures is important to engineers. The use of numerical modeling to solve such problems has many applications. Despite the high accuracy of methods such as the finite element method, these methods impose a high computational cost on users. In fact, one of the main challenges in solving problems related to the vibration behavior of water tanks against earthquakes is the high cost of its calculations. In this paper, a method called the method of fundamental solutions with pressure formulation is used to analyze this category of problems. The method used in this paper has a much lower computational cost than the finite element method. Another feature of this method is the possibility of using a large time step in calculations. For this purpose, discrete wavelet transform, which has been proposed in recent years as a suitable method for the down-sampling of discrete waves, is used. This means that in this method, in tanks with real dimensions, sometimes the solution time step can be considered with acceptable accuracy up to 0.16 seconds. For this purpose, first, the proposed method for laboratory results is validated and then the structure of a tank with real dimensions under the load of 10 earthquake records is analyzed. In this regard, each earthquake wave is filtered up to five stages. At each stage of the filter, two waves of approximation and detail are obtained. The number of points of each wave of approximation and detail is half the wave of the previous stage. Due to the fact that previous studies have shown that the frequency content of the main wave is closer to the approximate wave, so at each stage of the filter, the wave of details is omitted. In this way, the number of records in each stage of the filter is half of the previous stage. This means that in the first to fifth stages, the number of discrete points is halved, a quarter, an eighth, a sixteenth, and a thirty-second, respectively. Based on the results obtained from the analysis of the tank with real dimensions, it is determined that the error of base shear of the tank (as an important parameter in the design) can be ignored in all approximate waves. This error was less than 7% for all earthquake records and all approximate waves. Also, based on the results of this article, it can be said that in order to obtain the maximum height of the fluid, care must be taken in using approximate waves with more than two levels of the wavelet filter. Because the error created for this parameter increases dramatically with the increase in the number of wavelet filters. However, this increasing trend in earthquake records is very different. Of course, the approximate wave with one filter stage introduces a negligible error in almost all earthquake records. Also, approximate waves are successful in predicting the change in fluid height. Therefore, it can be concluded that if parameter of the base shear is required for analysis, the wavelet method can work well with an error of less than 5% by reducing the calculations by 32 times. On the other hand, based on the results obtained from this article, it seems that the wavelet method has limitations in obtaining the fluid height, especially at high levels of decomposition (A2 to A5). Finally, to summarize, it can be said that if the base shear is the desired parameter from the analysis, the results presented in this paper show that the use of this method can reduce the cost of calculations with appropriate accuracy in some earthquake records by more than 90%.

Height of the buildings directly affects the seismic performance and behavior of the structure during the earthquakes. This parameter is also significant when the structure is excited by two consequent ground motions. This paper presents the results of a study on the effect frame height on the seismic performance under two successive strong ground motions. It has been shown that, when the consequence of the first event remain in the structure as damage, the building often shows different dynamic characteristics as well as more vulnerability during the second seismic event. Three RC moment resisting frames with 4, 8 and 15 stories are designed based on the latest version of Iranian code of seismic design of buildings referred as Standard No. 2800 (STD 2800). The frames are then simulated in OpenSees software to perform nonlinear dynamic analysis. Twenty natural ground motion sequences each including two seismic events were selected from previous studies for the purpose of nonlinear incremental dynamic analysis. Maximum inter-story drift was employed as a damage index, to capture the performance of the RC frames under sequences. The accepted performance level for collapse level was taken from Iranian instruction for seismic rehabilitation of existing buildings, PBO-Publication No. 360, 2007, which is similar to ASCE 41-13. Seismic fragility values are calculated for the buildings under the second event when being damaged in first event. Assuming a log-normal distribution for failure probability function, corresponding values of median, μ and standard deviation, β, for each case are calculated and discussed for frames with different heights. The results indicate how the main parameters of the seismic fragility function may differ with frame height.

Post-Earthquake Fire (PEF) is an incident that can lead to a crisis and can be more critical than the earthquake itself due to the problems of passing vehicles and providing aid and assistance to the residents after the earthquake, and it can cause a lot of human and financial losses. Despite the large history of post-earthquake fires, the design regulations do not take into consideration the simultaneous effect of fire load and earthquake. On the other hand, in design based on the performance of structures, structural members should be designed for a specific level of performance that depends on the importance of the structure, which in the event of a post-earthquake fire, the performance level of the structure can change .Structures that are designed according to the regulations for the level of life safety performance may deviate from the desired level in the event of a fire after an earthquake. In this research, Post-Earthquake Fire was modeled in a moment steel frame. In this modeling, various levels of ground motion intensity and several time intervals were considered to extinguish the fire in the event of a post-earthquake fire. Three-story moment steel frame structures were modeled using OpenSEES software and studied to the performance level of life safety. Considering 44 different accelerograms, first, a scale of these accelerograms was applied to the structure. Then, assuming 60 seconds of free vibration to damping of the structure, the thermal load was applied to the members exposed to heat under the nine-point heat gradient, taking into account the ISO834 standard fire curve. Considering the maximum relative displacement between floors of 2.5% for the safety performance level, the quasi-acceleration spectrum component in the period of the first mode of the structure (Sa(T1)) was determined for this maximum relative displacement between floors under earthquake alone. Then, for different durations of post-earthquake fires, the maximum relative displacement between the floors under post-earthquake fires was determined and  Sa(T1) of a scale of the accelerogram applied was determined so that the structure under earthquake alone can have a maximum relative displacement between floors equal to the maximum displacement between floors under post-earthquake fire, and finally with this ratio Sa(T1) to Sa(T1) of the accelerogram scale, which had produced a maximum relative displacement of 2.5% between floors in the structure, a coefficient was obtained to modify the base shear to provide the performance level of life safety for various durations of post-earthquake fire.

Physical modelling experiments at 1 g via shaking table or augmented gravitational field (Ng) with geotechnical centrifuge are powerful tools that have been widely used to investigate the seismic behaviour of various earthquake-related problems in recent decades. It is an established method for verifying design hypothesis, realization failure mechanisms, and gaining an insight into complex geotechnical problems including liquefaction-induced phenomena and their mitigation techniques, level or inclined grounds, problematic soils, retaining walls and embankments, and soil-structure systems such as shallow or pile foundation system through the use of appropriate similitude laws. While element tests are frequently used to obtain dynamic soil parameters, they fail in providing realistic observations of how soil and structures interact in reality. Thus, physical modelling is a better approach to understanding the behaviour of a wide range of geotechnical problems where large deformations occur such as liquefaction, lateral spreading, or landslide. However, geotechnical models cannot be directly mounted on shaking tables due to the requirements of confinement. To properly model the ground in full or reduced-scale physical modelling tests, a model container is required to hold the soil in place and provide confining stresses. Replication of the semi-infinite extent of the ground in a finite dimension model soil container could raise challenging issues; the undesirable effects of the container’s artificial boundaries could affect the obtained results by altering the stress-strain field of the soils through reflected P-waves along other superfluous waves within the model.
In the current study, a comprehensive literature review on the advancement of physical modelling in geotechnics has been carried out. In this regard, a brief historical development of shaking tables and geotechnical centrifuge apparatus was outlined. Further, different types of developed model containers were explored. Additionally, vital criteria and requirements of an ideal container for carrying out seismic model tests at 1 g shaking table or Ng centrifuge experiments were thoroughly discussed. In particular, the development of laminar shear beam (LSB) containers as well as key properties in terms of detail design, construction, and particular usage in designated projects was presented in this paper. In the end, the recently fabricated LSBs were examined nationwide providing key properties and features in their design procedures.
Among all types of developed model containers, LSBs are the most common containers due to their accuracy in reproducing one-dimensional (1D) ground response in seismic conditions. The LSB allows free movement of soil column during shaking without imposing significant boundary effects and is able to maintain 1D soil column behaviour. Moreover, the use of LSBs enables the modelling of large strain modelling problems. Comparative studies by numerous researchers have confirmed that LSBs are the most advanced and efficient type of soil container in modelling soil-structure systems.