پژوهشگاه بین المللی زلزله شناسی و مهندسی زلزلهفصلنامه علوم و مهندسی زلزله2476-609711420241221Proposing a Collection of Selected Accelerometers for Near, Mid and Far Fields across Different Soils, Respecting the Diversity of Different Indexesپیشنهاد مجموعه شتاب‌نگاشت‌های منتخب حوزه‌های نزدیک، متوسط و دور برای خاک‌های متفاوت با رعایت تنوع بزرگا، پراکندگی فاصله‌ای، سرعت موج برشی ساختگاه و دوام لرزه ای12171438510.48303/bese.2024.2033870.1178FAهومنبرجویی روشن پوردانشجوی دکتری، گروه مهندسی عمران، واحد بوشهر، دانشگاه آزاد اسلامی، بوشهر، ایرانحمیدصفاریدانشیار، گروه مهندسی سازه و زلزله، دانشکده مهندسی عمران، آب و محیط زیست، دانشگاه شهید بهشتی، تهران، ایرانسید علیرضاکازرونیاناستادیار، گروه مهندسی عمران، واحد بوشهر، دانشگاه آزاد اسلامی، بوشهر، ایرانJournal Article20240630Nowadays, considering the diversity in construction, especially in tall and irregular buildings, the use of time-history analyses has become essential for designers. For this purpose, it is necessary to refer to available accelerogram databases and select those matching the site conditions. Accelerograms from near-field, mid-field, and far-field zones have distinct frequency content. Additionally, site conditions significantly affect the amplitude and period of seismic cycles. Another critical issue is the duration of earthquakes and their varying effects on structures. All accelerograms available in this database, caused by earthquakes with moment magnitudes ranging from 5 to 7.5, were collected and categorized based on distance into three groups: near-field (less than 20 km), mid-field (20 to 50 km), and far-field (more than 50 km). Subsequently, the records were classified according to the shear wave velocity of the site for each accelerogram and the standard soil classifications of the Iranian Standard 2800 code. Given the considerable number of records in various distance-soil type categories, proper selection while observing dispersion criteria is essential.<br />In this research, efforts were made to select, within each distance category, a representative sample covering all seismic magnitudes from 5 and above. Additionally, an attempt was made to cover the range of shear wave velocity within each category, from its lower to higher values. This process also accounted for variability in both distance and seismic duration. The distribution pattern based on each specified criterion is well illustrated in this study. Moreover, in the classification of accelerograms, factors such as earthquake focal depth were also examined. Focal depth is a key parameter in determining the intensity and distribution of seismic energy, which is evident when comparing the response spectra of accelerograms with the standard spectrum. Although deeper earthquakes typically transmit less energy to the surface, the frequency distribution of this energy can have diverse effects on structures. In this study, various earthquake acceleration records were extracted and analyzed from the database of the Earthquake Engineering Research Center at the University of California. The records were then categorized based on various criteria, including affected zone, magnitude diversity, distance, site soil conditions, and earthquake duration.<br />The database of this study includes 104 accelerograms for near-field earthquakes, 128 accelerograms for mid-field earthquakes, and 149 accelerograms for far-field earthquakes, whose distributions are presented based on different criteria. The response spectra of the selected accelerograms presented in this research were compared with the standard spectrum of the Iranian Standard 2800 code (fourth edition) for each distance zone and soil type. Some accelerograms showed significantly higher acceleration than Iran’s Standard 2800, while others showed lower values. This variation depends on the seismic potential of the source near the site, evaluated through hazard analysis. Additionally, the impact of the causative fault type and its kinematic characteristics were considered in this comparison.<br />This study presented the uncorrected accelerograms to provide a clearer representation of actual earthquakes occurring in different zones (near-field, mid-field, and far-field). However, in practice, scaling must be performed for seismic design as per regulations. As the distance from the seismic source increases in mid- and far-field zones, the acceleration reaching the site generally decreases, and the Iranian Standard 2800 acceleration spectrum provides more conservative values.<br />On the other hand, it was shown that as the soil becomes softer and the average shear wave velocity decreases, there is a risk of spectral acceleration amplification at longer periods. Therefore, specific structures with long dominant periods must undergo detailed time-history analyses using accelerograms corresponding to the relevant distance zones and site conditions to prevent potential damage. Furthermore, it was suggested that supplementary analyses be conducted to evaluate the sensitivity of structures to variations in input parameters.<br />Finally, the accelerogram tables presented in this study significantly assist structural designers in maintaining the necessary diversity when selecting accelerograms for time-history analyses. This ensures that the designed structure has sufficient resistance against various earthquakes and substantially reduces errors in accelerogram selection. Additionally, this method guarantees enhanced seismic design accuracy and minimizes the likelihood of structural damage caused by different earthquakes.امروزه با توجه به تنوع ساخت‌وساز، خصوصاً در ساختمان‌های مرتفع و نامنظم، استفاده از تحلیل‌های تاریخچه زمانی برای طراحان ضروری است. برای این منظور، باید به بانک شتاب‌نگاشت‌های موجود مراجعه و شتاب‌نگاشت‌های منطبق با شرایط ساختگاه را انتخاب کرد. شتاب‌نگاشت‌های حوزه‌های نزدیک، متوسط و دور دارای محتوای فرکانسی متفاوتی هستند. همچنین شرایط ساختگاه نیز تأثیر قابل توجهی بر دامنه و پریود سیکل‌های لرزهای دارد. یکی دیگر از مسائل مهم، دوام زلزله‌ها و اثرات مختلف آنها بر سازه‌ها است. در این پژوهش، رکوردهای مختلف شتاب زلزله از پایگاه اطلاعات مرکز تحقیقات مهندسی زلزله دانشگاه کالیفرنیا استخراج و بررسی شد. سپس رکوردها با توجه به معیارهای مختلف از جمله حوزه تأثیر، تنوع بزرگا، فاصله، شرایط خاک ساختگاه و دوام زلزله دسته‌بندی شدند. پایگاه اطلاعاتی این مطالعه شامل 104 شتاب‌نگاشت برای زلزلههای نزدیک، 128 شتاب‌نگاشت برای زلزلههای متوسط و 149 شتاب‌نگاشت برای زلزلههای دور میباشد که پراکندگی آنها بر اساس معیارهای مختلف آورده شده است. استفاده از جداول شتاب‌نگاشت‌های این تحقیق به طراحان کمک می‌کند تا با رعایت تنوع لازم در انتخاب شتاب‌نگاشت‌های مورد نیاز برای تحلیل تاریخچه زمانی، سازه‌ها را با اطمینان بیشتری در برابر زلزلههای احتمالی مقاوم سازند و خطا در انتخاب شتاب‌نگاشت تا حد زیادی کاهش یابد.https://www.bese.ir/article_714385_6fddc78bb90cadca0a8c4a4e019c5287.pdfپژوهشگاه بین المللی زلزله شناسی و مهندسی زلزلهفصلنامه علوم و مهندسی زلزله2476-609711420241221Seismic Performance Evaluation of Structures on Liquefied Soils Improved by Deep Mixing Method with a Grid Patternبررسی عملکرد لرزهای سازههای واقع بر خاک‌های روانگرای بهسازی شده به روش اختلاط عمیق با الگوی شبکه‌ای234671416310.48303/bese.2024.2032529.1175FAحمیدعلی الهیدانشیار، گروه مهندسی عمران، واحد زنجان، دانشگاه آزاد اسلامی، زنجان، ایران0000-0002-5761-0884سیدحمیدمدنیدانش آموخته کارشناسی ارشد ژئوتکنیک، گروه مهندسی عمران، دانشگاه علم و فرهنگ، تهران، ایرانJournal Article20240617The phenomenon of liquefaction can lead to significant damage to various structures, infrastructure, and superstructures situated on loose to medium dense saturated deposits during an earthquake. This occurs when the soil loses its resistance and transitions into a fluid-like state due to increased pore water pressure and decreased effective stress. Therefore, it is crucial to enhance the stability of such ground conditions before commencing any construction activities.<br />In recent years, the deep soil mixing (DSM) method utilizing a grid (lattice) pattern has emerged as one of the most widely adopted techniques for mitigating the effects of liquefiable soils. This method involves mechanically mixing stabilizing materials, such as cement and lime, with soil using either a dry method (in powder form) or a wet method (in slurry form) using hollow drills and mixing blades, depending on site conditions. This approach generates no vibrations in the soil or neighboring structures. The soil mixing process results in the formation of uniform soil-cement columns. Through the sequential and overlapping implementation of these columns before achieving full resistance, continuous walls and a grid structure are created beneath the ground surface, which are denser than the native soil. Consequently, these structures absorb maximum shear stresses induced by earthquakes, thereby preventing soil particle movement, reducing excess pore water pressure, and mitigating the effects of liquefaction.<br />Approximately half a century after the development of the DSM technique, its application has been limited in Iran due to technological constraints. The significance of employing this method is highlighted by the presence of coastal regions in both the northern and southern parts of the country. Given Iran's susceptibility to seismic activity and liquefaction in coastal zones, the implementation of deep soil mixing serves to mitigate liquefaction risks and avert associated challenges. However, very limited studies have been conducted on the performance of deep mixing column grid systems in the presence of structures during earthquakes. Most existing research has primarily focused on evaluating the performance of deep mixing grids in dealing with liquefaction without considering structural interactions. Consequently, there are currently no comprehensive guidelines for designing deep mixing columns with a grid pattern for liquefiable soils beneath structures.<br />This study investigates the most important influential factors in the design of deep mixing grids and their impact on the seismic response of structures situated on them. The research was conducted using Midas GTS NX, a three-dimensional finite element software, and the results were validated against centrifuge test data of Ishii et al. (2017). Liquefiable soil with a modified UBC sand behavioral model and deep mixing soil-cement columns was modeled with an elastic behavioral model. To investigate the seismic vulnerability of the structures, a conventional 10-story steel frame structure was designed and placed on the improved ground and then it was subjected to the Kobe (1995) and Northern California (1954) earthquakes..<br />The study reveals that increasing the diameter of soil-cement columns, the replacement area ratio, and the number of grids-while simultaneously decreasing grid dimensions-significantly reduces the generation of excess pore water pressure (r<sub>u</sub>). This reduction is achieved by enhancing the system’s stiffness and minimizing shear stresses. These improvements result in an average 35% in the shear applied to the enclosed, as well as a fourfold decrease in the relative displacement of structural floors compared to unimproved ground conditions due to applied earthquakes.<br />Finally, the study proposes an optimized triple-grid design with dimensions of 10.7 × 13 meters, a replacement area ratio of 20.1%, and DSM columns with a diameter of 0.9 meters. This configuration has been identified as the most effective solution for mitigating liquefaction effects and reducing the seismic vulnerability of structures.پدیده روانگرایی، عامل تخریب بسیاری از سازه‌ها، تأسیسات زیربنایی و روبنایی واقع بر نهشته‌های سست تا نیمه‌متراکم اشباع در هنگام زلزله است که بهسازی این‌گونه زمین‌ها قبل از هرگونه اقداماتی جهت ساخت‌وساز امری ضروری و حائز اهمیت است. روش اختلاط عمیق خاک با الگوی شبکه‌ای به علت محصور نمودن خاک و کنترل تنش‌های برشی ناشی از زلزله به یکی از روش‌های کارآمد در بهسازی خاک‌های روانگرا تبدیل شده است. در این تحقیق به بررسی عددی مهم‌ترین عوامل تأثیرگذار در طراحی شبکه‌های اختلاط عمیق و اثر آن بر پاسخ لرزهای سازههای واقع بر آن با کمک نرم‌افزار اجزای محدود سه‌بعدی Midas GTS NX پرداخته و نتایج حاصل با استفاده از اطلاعات آزمایش سانتریفیوژ اعتبارسنجی شده است. نتایج حاصل از مطالعه پارامتریک و ارزیابی پاسخ لرزهای خاک و سازه نشان می‌دهد که با افزایش قطر ستون‌های خاک-سیمانی، نسبت مساحت جایگزینی، تعداد شبکه‌ها و کاهش ابعاد شبکه، از نرخ تولید اضافه فشار آب حفره‌ای به دلیل افزایش سختی سیستم و کاهندگی بیشتر تنش‌های برشی وارده به خاک محصور توسط دیوارهای شبکه، به‌طور متوسط تا 35 درصد نسبت اضافه فشار آب حفره‌ای و همچنین تغییر‌مکان نسبی طبقات سازه به دلیل جلوگیری از روانگرایی و نشست زمین، به‌طور متوسط تا 4 برابر نسبت به زمین فاقد بهسازی برای زلزلههای اعمالی، کاهش می‌یابد.https://www.bese.ir/article_714163_5c862abe4d1f98569e40fd820d2766b0.pdfپژوهشگاه بین المللی زلزله شناسی و مهندسی زلزلهفصلنامه علوم و مهندسی زلزله2476-609711420241221Steel Damper Made of Two Square Tubes for Bracing with Similar Behaviors in Tension and Compressionمیراگر فولادی ساخته شده از دو لوله مربع شکل برای مهاربندی با رفتارهای مشابه در کشش و فشار476371747910.48303/bese.2024.2012334.1137FAلیلامنتظریاندانشجوی دکتری، گروه عمران، واحد چالوس، دانشگاه آزاد اسلامی، چالوس، ایرانحیدردشتی ناصرآبادیاستادیار، گروه عمران، واحد چالوس، دانشگاه آزاد اسلامی، چالوس، ایرانمرتضیجمشیدیاستادیار، گروه عمران، واحد چالوس، دانشگاه آزاد اسلامی، چالوس، ایرانمحمودحسینیاستاد، گروه مهندسی عمران، دانشکدۀ فنی- مهندسی، دانشگاه مدیترانه شرقی (EMU)، فاماگوستا، قبرس شمالی0000-0003-3142-4087Journal Article20231002The convergent bracing system has served as a lateral load-bearing mechanism in buildings for many decades. Despite its widespread application, it exhibits two significant weaknesses: low energy dissipation capacity and susceptibility to buckling under high compressive loads. To address these issues, yielding dampers have been introduced in recent decades. These dampers enhance the energy dissipation capacity of bracing elements in convergent bracing frames and help prevent buckling. Numerous types of yielding dampers have been proposed; however, most suffer from one or more of the following drawbacks: they exhibit different behaviors in tension and compression, they are complex and difficult to manufacture, and they lack a straightforward design methodology.
This paper introduces a novel yield-based energy damper known as the double square tube steel damper. This system is designed for installation in bracing elements and demonstrates consistent behavior under both compression and tension, making it simple to manufacture and design. The proposed damper dissipates energy through two square tubular sections, which are integrated with the bracing element, in such a way that when subjected to axial force, one section experiences tension while the other experiences compression.
The paper initially presents the hysteretic load-displacement behavior of the damper through laboratory testing and finite element analysis. The laboratory samples and finite element models provide insights into the damper’s performance, confirming its capacity for stable and efficient energy dissipation. Based on the results of the finite element analysis for the double square steel damper, which considers various sizes and thicknesses of the square parts, two simple formulas are derived. These formulas relate the initial stiffness and yield strength of the damper to the mechanical and geometric characteristics of the yielding components, providing a straightforward method for design.
To further demonstrate the effectiveness of the proposed damper in reducing the seismic response of buildings, its performance is evaluated in a five-story building equipped with chevron bracing. This evaluation is conducted through a series of nonlinear time history analyses that simulate the building's response to seismic events. The results of these analyses reveal that the implementation of the proposed dampers, with appropriate stiffness and strength, can significantly mitigate seismic impacts. Specifically, the maximum roof acceleration and the maximum base shear of the building can be reduced by approximately 30% and 20%, respectively, compared to a building utilizing conventional bracing systems.
The force-displacement hysteresis diagram of the double square tube steel damper exhibits symmetrical geometry and an optimal width, which indicate its stability and high energy absorption capacity. This symmetrical behavior in both tension and compression presents a significant advantage over the buckling-prone behavior of conventional braces. The consistent performance under different loading conditions ensures that the damper can reliably dissipate energy, enhancing the overall resilience of the structure during seismic events.
Another significant advantage of the proposed damper is its replaceable nature within the bracing system. This feature not only facilitates maintenance and replacement but also offers substantial economic benefits. By allowing easy replacement of the damper after a seismic event, the overall cost of structural maintenance and repair are reduced.
Moreover, the improved performance characteristics of the damper elevate the structure's performance level from Life Safety (LS) to Immediate Occupancy (IO), offering improved protection for both the building and its occupants.
In conclusion, the double square tube steel damper addresses the critical weaknesses of conventional convergent bracing systems by offering improved energy dissipation and resistance to buckling. Its simple design, ease of manufacturing, and reliable performance under both tension and compression make it a practical and effective solution for enhancing the seismic resilience of buildings. The positive results from both experimental testing and finite element analysis, coupled with its successful application in a five-story building, underscore the potential of this innovative damper to enhance safety and economic efficiency of seismic design.سیستم مهاربندی همگرا به دلیل ظرفیت پایین در اتلاف انرژی و کمانش تحت بارهای فشاری، با چالش‌هایی مواجه است. در سال‌های اخیر، استفاده از میراگرهای تسلیم شونده برای بهبود این سیستم‌ها پیشنهاد شده است، اما این میراگرها معمولاً دارای معایبی همچون رفتار متفاوت در کشش و فشار، پیچیدگی در ساخت، و نبود روش طراحی ساده هستند. در این مقاله، میراگر انرژی جدیدی به نام میراگر فولادی لوله مربع شکل دوبل معرفی شده است که برای نصب در المان‌های مهاربندی طراحی شده است. این میراگر رفتار مشابهی در فشار و کشش دارد، ساخت آن آسان است، و طراحی آن به راحتی انجام می‌شود. عملکرد این میراگر با استفاده از آزمایش‌های آزمایشگاهی و تحلیل اجزا محدود بررسی شده و دو فرمول ساده برای سختی اولیه و مقاومت تسلیم آن ارائه شده است. نتایج نشان می‌دهد که استفاده از این میراگر در ساختمان‌های با مهاربندی شورون می‌تواند حداکثر شتاب سقف و برش پایه را به ترتیب حدود 30 و 20 درصد کاهش دهد. رفتار هیسترزیس پایدار و متقارن این میراگر، نشان‌دهنده قابلیت جذب انرژی بالا و عملکرد بهتر در مقایسه با مهاربندهای مرسوم است. همچنین، این میراگر به دلیل قطعات قابل تعویض، صرفه اقتصادی بالایی دارد و سطح عملکرد سازه را از LS به IO ارتقاء می‌دهد.https://www.bese.ir/article_717479_ea369768b27a0807d496ecd73ecc2afe.pdfپژوهشگاه بین المللی زلزله شناسی و مهندسی زلزلهفصلنامه علوم و مهندسی زلزله2476-609711420241221Limit State Analysis of Barrel Vault Supported by Walls against Constant Horizontal Ground Accelerationبررسی حد نهایی پایداری تاق آهنگ بر روی پایه در برابر شتاب افقی ثابت زمین موازی صفحۀ قوس658771429210.48303/bese.2024.1995821.1132FAفرزینایزدپناهمربی، گروه مهندسی معماری، دانشکدۀ معماری، دانشگاه شهید باهنر کرمان، کرمان، ایرانالهام الساداتعلمداریپژوهشگر آزاد، کرمان، ایرانJournal Article20230804A significant portion of Iran's traditional architecture can be observed in areas that are vulnerable to earthquakes. Conservation involves knowledge of this heritage, as well as appropriate analysis and design. This underscores the need for careful study of these numerous structures and their risk of collapse during earthquakes. On the other hand, there are many such structures with unknown material properties, making analysis expensive, time-consuming, and unreliable. Therefore, it is necessary to understand the overall structural behavior of such structures. The current research aims to quickly study a structure type based on general assumptions in order to understand its behavior in relation to its geometric features in the context of Iranian vernacular architecture and allow for primary judgment in design and analysis. This article focuses on the behavior of a barrel vault supported by walls in its arch plane and addresses the question: what is the stability threshold of this type of structure to constant horizontal ground acceleration for different geometrical proportions? The problem is investigated by a limit state analysis using thrust line, based on Heyman’s assumptions. The results are verified with the tilt table method and 48 physical models. The influence of various factors on the stability threshold of a structure is discussed. These factors include the ratio of the thickness of the semicircular arch to its radius, the height of the brick infill interlocked with the haunch of the arch, which changes the embracing angle, and the ratio of the width of the wall to the radius of the arch. The results show that as the embracing angle of the arches decreases and the thickness of the arch increases, the arch stability threshold increases. By selecting a suitable geometrical proportion for arches, the vault, despite its 2D behavior, can withstand lateral acceleration very well. Therefore, in most cases, the weakness of the wall determines the lateral stability threshold of such a structure. In some cases, by increasing the thickness of the semicircular arch, a more economical design can be achieved for the arch and wall complex, but this strategy is only useful for areas with low earthquake risk. As it requires a huge wall in the high-risk areas, it makes the structure more expensive to build. Thus, using an arch with a small embracing angle is advised. Moreover, using a thick arch leads to a more destructive mode of collapse: overturning of the wall. The negative effect of cracks in walls also decreases using arches with small embracing angles. Furthermore, the experience of assembling physical models shows that this method makes the structure easier to build. This validates the traditional strategy employed by master builders of designing thin vaults with small embracing angles. The brick filling of the arch haunch up to a certain threshold significantly increases the lateral stability of the structure consisting of the arch and wall; however, increasing the filling level more than this threshold reduces the overall stability. Because this reduction in the studied proportions is not significant, removing the extra filling cannot be considered an effective technique for increasing the overall lateral stability of existing buildings. In addition, cracks in the wall reduce the stability threshold. This problem, especially with a slender wall, leads to a significant reduction in the lateral stability threshold. In some proportions of arch, e.g., when the embracing angle is 90 degrees, the negative effect of cracking walls is controlled to some extent. Physical models show that in the case of a thin semicircular arch, an analytical model based on an ideal mathematical model cannot be reliable. In other cases, with a small embracing angle, physical models can withstand lower lateral loads, around 50% of the nominal threshold of lateral stability, than analytical models. The data from this study can inform decisions on the stabilization and design of masonry structures.با توجه به قرارگیری بخش بزرگی از میراث معماری ایران در مناطق لرزه خیز، توجه به بررسی سازمان یافته رفتار این سازه ها در زلزله حائز اهمیت است. هدف پژوهش حاضر بررسی سریع و پارامتریک گونه ای از این سازه ها جهت یک دریافت کلی از رفتار آنها در برابر زلزله بر اساس مشخصات هندسی آنها بوده است. این نوشتار، با تمرکز بر روی رفتار موازی صفحۀ قوس در سازۀ متشکل از تاق آهنگ بر روی پایه، به این پرسش پرداخته که حد نهایی پایداری این‌گونه سازهای، در تناسبات مختلف هندسی در اثر شتاب افقی ثابت زمین به چه میزان است؟ در این مسیر، اثر تغییر نسبت ضخامت به دهانۀ قوس و میزان چیدن پای قوس نیم دایره و نسبت ضخامت پایه به دهانه، برای یک ارتفاع مشخص، بر پایداری سازه بررسی شده است. تحلیل، در حالت حد نهایی و با استفاده از خط رانش انجام شده و نتایج با استفاده از روش دوران صفحۀ زمین بر روی مدل فیزیکی اعتبارسنجی شده است. نتایج نشان می دهند می توان با چیدن شانۀ قوس تا ارتفاعی مشخص و انتخاب ضخامت مناسب، پایداری تاق را در برابر شتاب افقی زمین به سطح مطلوبی رساند و پس از آن، میزان پایداری سازه وابسته به نسبت عرض به شعاع می باشد. افزایش چیدن شانۀ قوس پس از یک میزان مشخص، باعث کاهش میزان حد نهایی پایداری سازه می شود. افزایش غیر ضروری ضخامت قوس، نیز، احتمال فروریختگی پایه را در نتیجۀ وقوع مکانیسم قوس قوی- پایۀ ضعیف افزایش می دهد.https://www.bese.ir/article_714292_de511f1ffe56066d1d1cc5561e413830.pdfپژوهشگاه بین المللی زلزله شناسی و مهندسی زلزلهفصلنامه علوم و مهندسی زلزله2476-609711420241221Quantitative Investigation of the Accuracy of Cubic Spline Interpolation Compared to Linear Interpolation for Earthquake Recordsبررسی کمّی میزان دقت درون‌یابی اسپلاین مکعبی نسبت به درون‌یابی خطی؛ مطالعه موردی: رکوردهای زلزله8910671416710.48303/bese.2024.2023815.1151FAمسعودمحمودآبادیاستادیار، دانشکده فنی مهندسی، دانشگاه قم، قم، ایرانمحمد علیامامیدانشجوی کارشناسی، دانشکده فنی و مهندسی، گروه عمران، دانشگاه قم، قم، ایرانJournal Article20240226Given that the accelerograms recorded in various earthquakes are in the form of numerical data measured at short time intervals, the numerical evaluation of the dynamic response of structures is of great importance. In addition, during severe earthquakes, structures enter the nonlinear behavior range, and it is necessary to calculate the nonlinear behavior of structures using conventional numerical methods. Due to the small distance between the accelerogram points, the points are usually connected to each other by line segments. As a result, at the junction of the line segments, their slopes are not necessarily equal, and only the function values at their junctions are equal. Given that linear interpolation of excitation is one of the simplest interpolation methods, if the time intervals between the points are small compared to the natural period of the structure, linear interpolation is acceptable and provides sufficient accuracy. However, if the structure in question is highly rigid with a very small period–in other words, a very high frequency–the use of the linear excitation interpolation method can be challenging.
There are various methods for interpolating a function over an interval, each with its own advantages and disadvantages. Approximating an arbitrary function over a closed interval can be very inaccurate due to the oscillatory nature of polynomials. Furthermore, a small change in the function over a subinterval can have a large effect on the interpolating polynomial. For this reason, in practice, it is preferable to divide the interval into small subintervals and reduce the degree of the interpolating polynomial as much as possible. This approach is called piecewise polynomial approximation. The simplest of these polynomials are linear polynomials (degree one). The graph of these functions is a broken line connecting the set of points (x<sub>0</sub>,y<sub>0</sub>), (x<sub>1</sub>,y<sub>1</sub>), ... and (x<sub>n</sub>,y<sub>n</sub>). One of the disadvantages of this method is the lack of differentiability at the ends of the subintervals. The geometric interpretation of this is the non-smoothness of the graph. To overcome this problem, in the cubic spline method, third-degree polynomial functions are used for each subinterval. By setting the values of these functions and their first and second derivatives equal at the connection points, equations are obtained for calculating the unknown coefficients of these polynomials. Of course, at the beginning and end points of the interval, the values of the function must also be substituted to obtain two other equations in terms of the unknown coefficients of the third-degree polynomials. Additionally, at the beginning and end points of the interval, free boundary conditions (setting the second derivative of the third-degree functions to zero at the beginning and end of the interval) or restricted boundary conditions (setting the first derivative of the third- degree functions to zero at the beginning and end of the interval) must be used to obtain two other equations in terms of the unknown coefficients of the third- degree polynomials. By considering all these equations, the unknown coefficients of the third-degree polynomials are calculated. It should be noted that free boundary conditions were used in this study.
In this article, three accelerograms–El Centro, Tabas and Naghan–were considered and their velocity and displacement records were obtained by numerical integration. The time interval between the points of these three accelerograms was 0.02 seconds. Then, the number of points of records in the acceleration, velocity and displacement records was reduced with reduction rates of 1, 2, 3, 4 and 5. In the next step, the deleted data were calculated using linear interpolation and cubic spline interpolation, and the root mean square error (RMSE) of the calculated values was computed by comparing them to their actual values for both interpolation methods.
Subsequently, 21 records of acceleration, velocity and displacement from different earthquakes were downloaded from the PEER website. Unlike the previous three records, these records had varying time steps.
Similar to the previous three records, the RMSE was calculated for data reduction rates of 1, 2, 3, 4 and 5 using both linear interpolation and spline interpolation. The comparison of these errors showed that the linear interpolation error for displacement records is higher than the spline interpolation error for the corresponding velocity records. Additionally, it was observed that the linear interpolation error for velocity records is higher than the spline interpolation error for the corresponding acceleration records. Moreover, with the increase in data reduction rate, the ratio of linear interpolation error to the corresponding error of spline interpolation had a decreasing trend.
Finally, power relationships were developed for the average ratio of the linear interpolation error to the spline interpolation error as a function of the data reduction rate. These relationships showed a strong correlation with their actual corresponding values.در این مقاله، ابتدا تعدادی شتاب‌نگاشت مصنوعی که از مجموع امواج سینوسی با فرکانسهای مختلف و با درصد نوفه‌های مختلف تشکیل شده بودند، در نظر گرفته شدند. با انتگرال‌گیری متوالی از آنها رکوردهای سرعت و تغییر مکان به دست آمد. با حذف یک‌درمیان نقاط این رکوردها، تعداد نقاط آنها کاسته گردید. سپس، نقاط حذف شده با استفاده از درون‌یابی خطی و درون‌یابی اسپلاین محاسبه شدند و با داشتن مقادیر واقعی نقاط حذف شده، جذر میانگین مربعات خطای این دو روش درون‌یابی محاسبه شدند و با یکدیگر مقایسه گردیدند. در گام بعدی، 21 رکورد شتاب، سرعت و تغییر مکان زلزلههای مختلف از سایت PEER دانلود گردید. جذر میانگین مربعات خطا به ازای نرخ کاهش دادههای برابر با 1، 2، 3، 4 و 5 با استفاده از درون‌یابی خطی و درون‌یابی اسپلاین برای این رکوردهای واقعی محاسبه شد. مقایسه این خطاها نشان داد که خطای درون‌یابی خطی برای رکوردهای تغییر مکان بیشتر از خطای درون‌یابی اسپلاین برای رکوردهای متناظر سرعت میباشد. همچنین، مشاهده شد که خطای درون‌یابی خطی برای رکوردهای سرعت بیشتر از خطای درون‌یابی اسپلاین برای رکوردهای متناظر شتاب میباشد. همچنین، با افزایش نرخ کاهش دادهها، نسبت خطای درون‌یابی خطی به خطای متناظر درون‌یابی اسپلاین روندی کاهشی داشت.https://www.bese.ir/article_714167_024023c441bb8058bd2359eeb2a42f91.pdfپژوهشگاه بین المللی زلزله شناسی و مهندسی زلزلهفصلنامه علوم و مهندسی زلزله2476-609711420241221A Study on Destroyed and Damaged Buildings in Zindajan Earthquakes; Case Study: Earthquake Affected Villages of Zindajan District,
Herat Province-Fall 1402بررسی ساختمان‌های تخریب شده و آسیب‌دیده زلزله زنده‌جان؛ مطالعه موردی: روستاهای زلزله‌زده ولسوالی زنده‌جان ولایت هرات- پاییز ۱۴۰۲10711971748110.48303/bese.2024.2016044.1144FAنظام الدینتیموریرئیس دانشکده مهندسی دانشگاه جامی، هرات، افغانستانالف شاهاحسانمدیر گروه بخش عمران دانشکده مهندسی دانشگاه جامی، هرات، افغانستانJournal Article20231120The recent earthquakes in Herat city in the Zindajan district, occurred between October 7 and 15, with a series of tremors reaching a magnitude of 6.3. The hypocenter of these earthquakes was located in the Zindajan district of western Afghanistan, resulting in widespread destruction. These earthquakes and their aftershocks have left thousands of already-vulnerable populations living in underserved (white areas) in urgent need of humanitarian and health assistance. To date, nearly 43,400 people across this district have been directly affected, with almost 23% being children under the age of five. Significant damage has been reported in the area, with casualties including at least 2000 deaths and more than 2,500 injuries. As of October 19, aftershocks continue to occur, leaving communities in a state of fear and unease. Furthermore, over 3,330 homes have been completely destroyed, and extensive damage to infrastructure, including the water supply network, has been reported. This has forced many people to live in tents, open areas, and other temporary shelters. According to seismologists, the epicenters of these earthquakes were situated between the Siakhubulak Fault in the north and the Herat Fault in the south. According to satellite data from Sentinel-1A, an area measuring 30 km by 15 km, extending east to west around the location of these earthquakes, experienced uplift. Meanwhile, the satellite detected subsidence in a small area to the east of the uplifted zone. The seismologists added that the ground deformation was diffuse and inferred that the earthquakes were associated with a blind thrust fault. The fault responsible for the disaster is likely a structure located between the Herat and Siakhubulak faults. From a technical perspective, what is significant in the impacted area is the construction of buildings with steel and concrete structures, as well as houses made of earth and unreinforced materials that lack design considerations to withstand the forces of an earthquake. According to survey data from the affected villages in the Zindajan district, the buildings can be categorized into four types: steel structures, concrete structures, unreinforced structures, and houses built of earth. In this research, over 95 percent of houses built of earth were destroyed due to their insufficient strength to withstand seismic loads, resulting in the highest number of casualties. Unreinforced structures were identified as the second most vulnerable causing significant damage; however, fortunately, fewer roofs collapsed onto residents, thereby saving lives. The studied areas also included concrete and steel structures, some of which sustained serious damage, while a few managed to maintain their stability. This research examined the pathology of buildings and houses, as well as the causes of the damages. The findings from this study are presented below. The lack of proper monitoring and evaluation of constructed structures and buildings, particularly those lacking design and proper connections, has resulted in significant damage. A major issue in this disaster was not only the construction of earth-based structures but also other buildings that were not designed to withstand lateral and seismic loads. This deficiency led to the destruction and damage of most buildings during the first earthquake. The results show that despite experiencing four powerful earthquakes measuring above 6.2 on the Richter scale, steel structures, concrete structures, and even unreinforced structures collapsed far less frequently than earth-built houses. These more resilient structures maintained their stability and helped save human lives, according to the statistics. It has been said that if houses were built from earth instead of other materials, approximately 95 percent of causalities could be reduced.بروز زلزلههای اخیر ولسوالی زنده‌جان ولایت هرات در پاییز 1402 باعث تلفات بیش از ۲۰۰۰ نفر انجامید و بیشتر خانه‌ها و ساختمان‌ها در روستاهای فوق تخریب و ویران شدند. آنچه در این فاجعه از دید فنی قابل توجه است ساخت‌وساز به شیوه سنتی و نامناسب، شکل‌گیری ساختمان‌هایی با اسکلت فلزی، بتنی و دیوار باربر بدون طراحی در مقابل نیروی زلزله است. در مناطق فوق، ساختمان‌ها به چهار دسته تقسیم‌بندی می‌شود. خانه‌های با ساخت و سازه سنتی (گلی)، ساختمان‌های بنایی، ساختمان‌های بتنی و سازههای فلزی. خانه‌های گلی به خاطر عدم استحکام در مقابل نیروی زلزله بیشتر از 95 درصد تخریب گردیده که بیشترین تلفات را از خود به‌جای گذاشته‌اند. ساختمان‌های بنایی در رده دوم قرار گرفته که بیشترین آسیب را بعد از خانه‌های گلی از خود به‌جا گذاشته‌اند ولی سقف‌های کمتری بر سر ساکنان فرود آمده است. در روستاهای فوق نیز ساختمان‌های بتنی و سازههای فلزی به چشم می‌خورد که بعضی از این سازه‌ها آسیب جدی دیده و تعدادی بدون آسیب پایداری‌شان را حفظ نمودند. اینکه در این زلزله کمتر ساختمانی بدون آسیب باقی مانده است، بدون تردید نقص در برنامه‌ریزی، طراحی، محاسبات اجرا و نظارت هر یک به‌نوبه خود می‌توانند در این حادثه بزرگ نقش داشته باشند.https://www.bese.ir/article_717481_b5488595f0a7be6521833802847616d1.pdf