@article { author = {Nasrollahnejad, Ali and Allamehzadeh, Mosafa and Javan Doloei, Gholam}, title = {Estimating Values of the Maximum Peak Ground Acceleration of a Strong Motion by Three Models of Artificial Neural Networks}, journal = {Bulletin of Earthquake Science and Engineering}, volume = {3}, number = {4}, pages = {1-19}, year = {2016}, publisher = {International Institute of Earthquake Engineering and Seismology}, issn = {2476-6097}, eissn = {2476-6100}, doi = {}, abstract = {Peak ground acceleration is one of the most important factors that needs to be investigated in order to predict the devastation potential resulting from earthquakes in reconstruction sites. Besides, the maximum level of shaking control is subjected criteria that can be worth considering. In this research, a training algorithm based on gradient descent and Levenberg-Marquart (Train LM) were developed and employed by using strong ground motion records. The Artificial Neural Networks (ANN) algorithm indicated that the fitting between the predicted PGA values by the networks and the observed PGA values were able to yield high correlation coefficients of 0.78 for PGA. From a deterministic point of view, the determination of the strongest level of shaking that is expected at a site has long been a significant consideration in earthquake engineering. Besides, knowledge of the maximum physically possible ground motions allows a meaningful truncation of the distribution of ground motion residuals, and as a result, leads to falling of the values computed in probabilistic seismic hazard analysis (Strasser and Bommer, 2009). The peak ground acceleration parameter is often estimated by the attenuation of relationships and by using regression analysis. PGA is one of the most important parameters, often analyzed in studies related to damages caused by earthquakes (Gullo and Ercelebi, 2007). It is mostly estimated by the attenuation of equations and is developed by a regression analysis of powerful motion data. Kerh and Chaw (2002) used software calculation techniques to remove the lack of certainties in declining relations. They used the mixed gradient training algorithm of Fletcher-Reeves’ back propagation error (Fletcher and Reeves, 1964). They applied three neural network models with different inputs including epicentric distance, focal depth and magnitude of the earthquakes. These records were trained and then the output results were compared with available nonlinear regression analysis. In this article, to estimate strong ground motion acceleration component in an area, four artificial neural networks with different algorithms were used, including General Regression Neural Network (GRNN), Nonlinear Auto Regression neural network (NARX), Feed-Forward Back-Propagation error (FFBP) and General Feed-Forward Neural Network (GFFNN). Input vectors of neural networks include four parameters, which have key effects in occurrence of an earthquake in an area. The parameters include magnitude of moment, rupture distance of earthquake center, mechanism of faults, and ranking of site. Output vector has only one component: maximum peak ground acceleration for an earthquake in an area is used as a target output. After different tests, GRNN network has maximum output correlation coefficient (0.87) and General Feed-forward Back-Propagation error neural network (FFBP) has the least (0.41). Besides, GRNN network had the least mean square error (0/014), and Back-Propagation network had 0.125. In this research, GRNN neural network is the best neural network, which can estimate possible peak acceleration more than 1g in an area. Artificial neural networks are a set of non-linear optimizer methods which do not need certain mathematical models in order to solve problems. In regression analysis, PGA is calculated as a function of earthquake magnitude, distance from the source of the earthquake to the site under study, local condition of the site and other characteristics that are linked to the earthquake source such as slippery length and reverse, normal or wave propagation. In non-linear regression methods, non-linear relations that exist between input and output parameters are expressed as estimations, through statistical calculations within a specified relationship (Douglas, 2003).}, keywords = {Maximum Peak Ground Acceleration,Moment Magnitude,General Feed-Forward Neural Network,Ranking of Sites,Elman-Jordan Neural Network}, title_fa = {تخمین مقادیرحداکثر شتاب جنبش نیرومند زمین توسط سه مدل شبکه های عصبی مصنوعی}, abstract_fa = {در این تحقیق، برای برآورد بیشینه شتاب جنبش نیرومند زمین در یک منطقه، از سه نوع شبکه‌ی عصبی مصنوعی با الگوریتم‌های متفاوت استفاده شده است که عبارتند از: شبکه‌ی عصبی- فازی هم فعال، المان– جردن و پیشخور با الگوریتم پس انتشار خطا. بردارهای ورودی شبکه‌های عصبی، شامل چهار پارامتری هستند که تأثیرات مهمی در وقوع زمین‌لرزه در یک منطقه دارند. این پارامترها عبارتند از: بزرگی ممان زلزله، شعاع گسیختگی کانون زلزله، مکانیسم گسل و رده‌بندی ساختگاه. بردار خروجی نیز فقط یک مؤلفه دارد: حداکثر شتاب جنبش نیرومند زمین برای یک زمین‌لرزه رخ داده در یک منطقه که به‌عنوان خروجی هدف استفاده می‌شود. پس از انجام آزمایش‌های مختلف، از میان شبکه‌های عصبی طراحی‌شده، شبکه‌ی عصبی- فازی هم فعال (سی‌آنفیس) بالاترین ضریب همبستگی خروجی، برابر 82/0 و شبکه پیشخور با الگوریتم پس انتشار خطای عمومی، کمترین ضریب همبستگی 41/0 را نشان می‌دهد. همچنین شبکه سی‌آنفیس، کمترین میانگین مربعات خطای 075/0 و شبکه‌ی پیشخور، بیشترین میانگین مربعات خطای 125/0 را داشته است. در این تحقیق، شبکه عصبی – فازی هم فعال، بهترین شبکه‌ی عصبی است که می‌تواند حداکثر دامنه شتاب احتمالی بالاتر از g1 در یک منطقه را برآورد کند.}, keywords_fa = {حداکثر شتاب جنبش نیرومند زمین,بزرگی ممان زلزله,شبکه پیشخور پس انتشار خطا,رده بندی ساختگاه,شبکه المان جردن}, url = {http://www.bese.ir/article_240303.html}, eprint = {http://www.bese.ir/article_240303_d9e4bb7a0cb107ad5090be3b0a42f30f.pdf} } @article { author = {Askari, Faradjollah and Hassani, Ahmad}, title = {Seismic Displacement of Retaining Walls Using Limit Analysis Approach}, journal = {Bulletin of Earthquake Science and Engineering}, volume = {3}, number = {4}, pages = {21-30}, year = {2016}, publisher = {International Institute of Earthquake Engineering and Seismology}, issn = {2476-6097}, eissn = {2476-6100}, doi = {}, abstract = {Gravity walls are commonly used as earth retaining systems supporting fill slopes adjacent to roads and residential areas, especially to protect the transportation facilities and/or nearby structures in regions prone to earthquakes. Analysis of retaining walls behavior against earthquake is an important task for geotechnical engineers for reasons such as soil complex seismic behavior and inefficiency of quasi-static analyses. Seismic analysis and design of earth retaining walls is a difficult task, which traditionally requires the determination of the dynamic soil pressures induced by the soil seismic motion on the wall. Understanding the performance of a retaining wall during an earthquake is very important for an economical design and reducing the damages caused by large earthquakes. Calculated displacement of retaining walls has a key role in the optimal performance design of these structures under seismic loadings. The efficiency of a wall after an earthquake depends on its seismic displacement. Excessive displacements may not only cause the wall to collapse, but also cause to damage the adjacent structures. There have been numerous examples of this type of failure in recent earthquakes. Though the quasi static method for rational design methods of retaining structures has been performed for several decades, deformations ranging from slight displacement to catastrophic failure have been observed in many earth retaining structures during the recent major earthquakes. Many researchers have developed design methods for retaining walls during earthquakes by using different approaches. In this paper, an algorithm for calculation of permanent displacements of retaining walls in seismic conditions is presented. Formulation of this algorithm is based on the upper bound limit analysis. Displacement of the wall is calculated by obtaining its yield acceleration by limit analysis, and then combination of the proposed method with Newmark method. Effect of various parameters on the displacement of the walls is studied. For the upper bound theorem to be valid, the velocity field in the failure mechanism must conform to the normality flow rule (associated with the yield condition). The term normality rule originates from the geometric property of the potential law where the deformation rate vector is perpendicular (normal) to the yield surface. When dense sand is subjected to shear, it simultaneously exhibits volumetric changes (dilatancy). These changes, when described by the flow rule associated with the Mohr–Coulomb yield condition, tend to overestimate the true dilatancy. There are two distinct issues that need to be addressed: (1) How does the departure from the normality rule affect the yield acceleration of the structure; and (2) what flow rule should be used to obtain a reasonable estimation of the true displacements of a structure subjected to seismic excitation? The first question was addressed earlier by recent researchers who indicated that the yield acceleration of a soil structure built of “nonstandard" soil (“nonstandard” soil is one with deformation governed by the non-associative flow rule) can be obtained with sufficient precision by the kinematic approach if internal friction angle and cohesion of the soil is modified. For the second issue, the deformation description is described by the true dilatancy angle to conform the true material behavior and for prediction of the true (finite) displacements, Effect of various parameters on yield acceleration and the displacement of the walls is studied. Internal friction and dilatancy angles of the soils have the most important influence on the results.}, keywords = {Permanent Seismic Displacement,Retaining Walls,Limit Analysis}, title_fa = {محاسبه ی جابجایی لرزه ای دیوار حائل وزنی بر اساس روش آنالیز حدی}, abstract_fa = {در این مقاله، الگوریتمى جهت محاسبه‌ی جابه‌جایی ماندگار دیوارهاى حائل در شرایط لرزه‌ای ارائه شده است. در این الگوریتم که فرمولاسیون آن بر اساس روش مرز بالای آنالیز حدى پایه‌ریزی شده است، شتاب تسلیم با در نظر گرفتن چسبندگى و زاویه اصطکاک داخلى خاک و نیز لحاظ نمودن چسبندگى و اصطکاک بین خاک و دیوار محاسبه می‌شود. روش پیشنهادی در واقع توسعه‌ی روش میخالفسکی [1] از حالت شیروانی‌ها به دیوارهای حائل است و در آن فرمولاسیونی برای محاسبه‌ی شتاب تسلیم، شکل سطح گسیختگی و جابه‌جایی ماندگار دیوارهای حائل تحت بار زلزله به‌صورت دو بعدی پیشنهاد شده است. به‌علاوه اثر زاویه اتساع خاک، زاویه اصطکاک داخلی خاک، زاویه اصطکاک بین خاک و دیوار، بیشینه شتاب زلزله و ارتفاع دیوار بر میزان جابه‌جایی لرزه‌ای توسط روش ارائه شده مورد بررسی قرار گرفته است. نتایج در حالاتى خاص با دیگر محققان مقایسه شده که صحت اعتبار الگوریتم ارائه شده را به‌خوبی نشان می‌دهد. نتایج مطالعه‌ی انجام شده نشان می‌دهد انتخاب مقادیر زاویه‌ی اتساع خاک و زاویه‌ی اصطکاک بین خاک و دیوار از اهمیت بالایی برخوردار است و تأثیر زیادی بر روی شتاب تسلیم و جابه‌جایی می‌گذارد.}, keywords_fa = {تغییر مکان لرزه‌ای ماندگار,دیوار حائل وزنی,آنالیز حدی,مرز بالا,دو بعدی}, url = {http://www.bese.ir/article_240304.html}, eprint = {http://www.bese.ir/article_240304_6b3f654e64c606ea8c0e68143289805c.pdf} } @article { author = {Rajabi, Mohammad and Khosravi, Hossein}, title = {Comparison of Information Value Method and Analytical Hierarchy Process in the Earthquake-Induced Landslides Hazard Zonation (A Case Study)}, journal = {Bulletin of Earthquake Science and Engineering}, volume = {3}, number = {4}, pages = {31-42}, year = {2016}, publisher = {International Institute of Earthquake Engineering and Seismology}, issn = {2476-6097}, eissn = {2476-6100}, doi = {}, abstract = {Although many studies have been done on the landslide hazard zonation, landslide caused by the earthquake has received less attention. Analysis of features of landslides caused by the earthquake and their distribution is very important in recognizing landslide-prone areas for future earthquakes. The purpose of this study is to identify the effective factors and zonation of landslides caused by the earthquake through information value and Analytical Hierarchy Process (AHP) methods in the area near the epicenter of the Manjil earthquake with an area of 309.30 km. In this study, landslide hazard zonation caused by earthquake was performed by using bivariate regression (information value) and AHP, and the efficiency of these two methods were studied and compared. Hence, according to the landslides location, comparative studies and the results of other researchers, seven factors including Arias intensity, internal friction, cohesion, slope angle, aspect, direction, elevation and terrain rough, have been identified as the most important factors in the landslides caused by Manjil earthquake. Then, these factors were prepared in a Geographical Information System (GIS). All information and data for the initial analysis were imported into GIS, and zonation maps of the landslide caused by the earthquake were prepared with regard to the above-mentioned methods. For this purpose, in the information value method, the inventory map has been initially integrated with the maps of effective factors in the landslides occurrence. After calculating the weight of each subclass of factors and finally adding the results of the previous stage in the information layer table in the Arc GIS, landslide hazard zonation map was obtained by this method. Through using the expert opinions and the tables used in the AHP method, the effective criteria and sub-criteria in the occurrence of landslide caused by earthquakes in the study area were compared. Afterward, the results of these comparisons were placed in Expert Choice software, and the relative weights of each criteria and sub-criteria was obtained. Then, the obtained final weights were added to the effective factors information layer table. Finally, hazard zonation map of landslide caused by earthquake in the study area was obtained by this method. According to the results of AHP method, Arias intensity and terrain rough factors had highest and lowest impact on the landslide occurrence. The greatest impact for sub-criteria 10–11.54 is related to the Arias intensity, and minimum impact is related to the smooth sub-criteria of terrain rough factor. Further, according to the zonation maps obtained by these two methods, the models obtained from AHP and the information methods, high risk and very high risk zones have respectively constituted 73 and 52 percent of the region. After reviewing the efficiency of procedures employed in this study by using two quality sum (QS) and precision (P) indicators, the results showed that bivariate regression model is more appropriate than AHP method and its results are more consistent with reality.}, keywords = {Manjil Earthquakes,Landslides Caused by Earthquake,hierarchical analysis,Value of Information}, title_fa = {مقایسه روش‌های ارزش اطلاعاتی و تحلیل سلسله مراتبی در پهنه‌بندی خطر زمین‌لغزش‌های ناشی از زلزله (مطالعه موردی)}, abstract_fa = {امروزه روش های مختلفی برای پهنه بندی خطر زمین لغزش ها وجود دارد. در خصوص زمین لغزش های ناشی از زلزله اما تحقیقات محدودتری انجام شده است. بررسی و تحلیل مشخصات زمین‌لغزش‌های ناشی از زلزله و نحوه توزیع آن‌ها در شناخت مناطق مستعد زمین‌لغزش در زلزله‌های آینده اهمیت بسزایی دارد. هدف از این مطالعه شناسایی عوامل مؤثر و پهنه‌بندی زمین‌لغزش‌های ناشی از زلزله به روش‌های ارزش اطلاعاتی و تحلیل سلسله مراتبی در محدوده ای در نزدیکی رومرکز زلزله منجیل به مساحت 30/309 کیلومترمی باشد. در این مطالعه با استفاده از دو مدل رگرسیون دومتغیره (ارزش اطاعاتی) و تحلیل سلسله مراتبی پهنه بندی خطر زمین لغزش های ناشی از زلزله انجام شده و کارایی این دو روش مورد بررسی و مقایسه قرار گرفته است. به این منظور، ابتدا با توجه به موقعیت زمین‌لغزش‌های به وقوع پیوسته، بررسی‌های تطبیقی و نتایج سایر محققین، 7 عامل شامل شدت آریاس، زاویه اصطکاک داخلی، شیب، چسبندگی، جهت شیب، ارتفاع و انحنای دامنه به عنوان مهمترین عوامل وقوع زمین لغزش های ناشی از زلزله منجیل شناسایی شده و لایه‌های رستری عوامل مذکور در محیط سامانه اطلاعات جغرافیایی (GIS) تهیه گردید. نقشه فهرست زمین‌لغزش‌ها نیز با استفاده از عکس‌های هوایی و مشاهدات میدانی تهیه و درکنار سایر اطلاعات قرار گرفت. تمامی اطلاعات و داده‌های تهیه شده جهت آنالیز اولیه وارد محیط GIS شد و نقشه های پهنه بندی خطز زمین لغزش های ناشی از زلزله با در نظرگرفتن روش های مذکور انجام شد. سپس کارایی دو روش مورد بررسی با استفاده از دو شاخص جمع کیفیت‌ها (QS) و دقت روش (P) مورد بررسی قرار گرفت. نتایج نشان می‌دهد که مدل رگرسیون دومتغیره (روش ارزش اطلاعاتی) نسبت به روش تحلیل سلسله مراتبی روش مناسب‌تری بوده و نتایج آن با واقعیت تطابق بیشتری دارد.}, keywords_fa = {زلزله منجیل,زمین‌لغزش‌های ناشی از زلزله,تحلیل سلسله مراتبی,ارزش اطلاعاتی}, url = {http://www.bese.ir/article_240305.html}, eprint = {http://www.bese.ir/article_240305_3d71b6ca009e95250541f6f1306e104d.pdf} } @article { author = {Esmaeil Abadi, Reza and Bahar, Omid and Aziminezhad, Armin}, title = {Hysteretic Damping Capacity of Steel Moment-Resisting Frames in Life Safety Performance Level Required in Direct Displacement-Based Design Method}, journal = {Bulletin of Earthquake Science and Engineering}, volume = {3}, number = {4}, pages = {43-59}, year = {2016}, publisher = {International Institute of Earthquake Engineering and Seismology}, issn = {2476-6097}, eissn = {2476-6100}, doi = {}, abstract = {In recent years, interests in utilizing performance-based design to achieve earthquake-resistant structures have grown. One of a robust procedure in this category, which is presented in 1993 by Prof. Priestley, is Direct Displacement-Based Design (DDBD) method. Extensive and developed researches have shown that DDBD has a great potential to overcome existing shortcomings of the force-based design method. During last decade, DDBD, which was initially proposed for designing RC buildings and bridge piers, are developed for steel structures. DDBD has two main factors: hysteretic damping capacity and yield displacement of the building. Accurate estimation of these parameters is very important to determine proper value of design base shear of the building under consideration. These factors were firstly estimated experimentally for concrete structures but now, they are intensely studied analytically by many researchers for various forms of steel structures. In this regard, this paper attempts to consider more realistic estimation of equivalent viscous damper capacity of moment resisting steel frame structures and its influence on determined base shear values. In this paper, 30 different moment-resisting frames with various numbers of stories (3, 6, 9, 12 and 15) and spans (3 and 6) are studied. For each frame, different analysis methods are carried out: (1) nonlinear static or pushover analysis, (2) nonlinear time history analysis employing synthetic accelerograms, (3) nonlinear time history analysis employing two sinusoidal protocols with different excitation frequencies: initial and effective frequencies, (5) nonlinear static cyclic analysis using an incremental sinusoidal displacement protocol, (6) simple linear analysis of an equivalent single-degree-of-freedom (SDOF) model of the structure subjected to a sinusoidal load, and finally (7) the proposed relation in the Model Code for the Displacement-Based Seismic Design of Structures, DBD12. Comparing the results shows that the equivalent damping ratio obtained using DBD12 relation for life-safety (LS) level is significantly lower than the values obtained by the analyses conducted in this study. This means that the determined base shear for designing such steel building is much more than values for a safe building. In other words, steel buildings using relations of DBD12 tend to be stiffer and stronger than needed. Hence, a new relation is derived to determine the hysteretic damping of MR steel frame structures in the LS performance level as a function of a ductility coefficient. Furthermore, using the relationship between the initial and effective period mentioned in ATC40, another practical relationship is proposed as a ratio of the effective period over the initial period of the considered building.}, keywords = {Direct Displacement-Based Design (DDBD) Method,Equivalent Viscous Damping,Nonlinear Static Analysis,Effective period,Sinusoidal Loading Protocol}, title_fa = {ارائه‌ی روابط جدید ظرفیت میرایی هیسترزیس قاب‌های خمشی فولادی در سطح عملکرد ایمنی جانی مورد نیاز روش­­ طراحی مستقیم مبتنی بر تغییر مکان}, abstract_fa = {هدف اصلی این مقاله، ارائه‌ی رابطه‌ی مناسبی برای محاسبه‌ی نسبت میرایی هیسترزیس برای قاب­های خمشی فولادی و مقایسه‌ی آن با رابطه‌ی ارائه شده در روش طراحی مستقیم مبتنی بر تغییر مکان است. نکته‌ی کلیدی در روش طراحی مستقیم بر اساس تغییر مکان، مدل کردن میرایی هیسترزیس به‌وسیله‌ی نسبت میرایی ویسکوز معادل (EVD) 1 با استفاده از روابط و فرمول­های مبتنی بر شکل­پذیری می­باشد. خطا در برآورد میرایی ویسکوز معادل می­تواند به خطا در محاسبه‌ی نیروها و برش پایه در این روش منجر شود. در این مطالعه برای به دست آوردن این نسبت، مدل‌های مختلف قاب­های خمشی فولادی با بهره‌گیری از تحلیل­های متنوعی مورد مطالعه قرار گرفته است. 30 مدل‌ قاب­ خمشی، با تعداد طبقات 3، 6، 9، 12 و 15، به دو شکل 3 دهانه و 6 دهانه، و تحلیل‌ها شامل: تحلیل استاتیکی غیرخطی، تحلیل دینامیکی غیرخطی با استفاده از هفت شتاب­نگاشت ساختگی، تحلیل تاریخچه زمانی دینامیکی بر اساس دو پروتکل رکورد سینوسی یکنواخت، یکی مبتنی بر زمان تناوب اولیه و دیگری مبتنی بر زمان تناوب در سطح عملکرد ایمنی جانی و در نهایت تحلیل بار افزون رفت و برگشتی با استفاده از پروتکل جابه‌جایی سینوسی فزاینده انجام شده است. استنتاج حاصل از محاسبات نسبت میرایی در سطح عملکرد ایمنی جانی بر اساس روابط یاکوبسن و جنینگز، مقادیر حاصل از روابط میرایی معادل در دستورالعمل FEMA-440 و نیز مدل‌سازی سازه‌ی یک درجه آزاد، اختلافاتی را با فرمول تجربی پیشنهاد شده در پیش‌نویس دستورالعمل DBD2012 نشان می‌دهد. لذا، در محدوده‌ی شکل‌پذیری سازه‌های مورد مطالعه، به جای فرم رابطه‌ی موجود برای محاسبه‌ی نسبت میرایی هیسترزیس، از فرم رابطه‌ی نمایی استفاده شد که با نتایج به دست آمده هماهنگ‌تر است. در انتها نیز با برقراری ارتباط بین زمان تناوب اولیه و معادل سازه، رابطه‌ی جدیدی برای محاسبه‌ی نسبت میرایی هیسترزیس مبتنی بر نسبت زمان تناوب معادل به زمان تناوب اولیه در سازه‌های قاب خمشی فولادی پیشنهاد گردیده است.   }, keywords_fa = {روش طراحی مستقیم مبتنی بر تغییر مکان,نسبت میرایی ویسکوز معادل,تحلیل استاتیکی غیرخطی,پروتکل بار سینوسی}, url = {http://www.bese.ir/article_240306.html}, eprint = {http://www.bese.ir/article_240306_13238e09d0c5249a28d1c62dc6d9202c.pdf} } @article { author = {Meshki, Hossein and Joghataie, Abdolreza}, title = {Decoupling of Variables in Optimal Seismic Design Using Spherical Interpolation}, journal = {Bulletin of Earthquake Science and Engineering}, volume = {3}, number = {4}, pages = {61-72}, year = {2016}, publisher = {International Institute of Earthquake Engineering and Seismology}, issn = {2476-6097}, eissn = {2476-6100}, doi = {}, abstract = {In this paper, a method is presented based on approximating the objective function and constrains in optimization problems in conjunction with Lagrange multiplier method. Besides, an algorithm is developed in this relation. Instead of linear or parabola terms employed in Taylor expansion to proceed cautiously with short step lengths, in the method presented here, an arc with constant curvature is used that makes it possible to proceed with relatively longer step lengths. For an n-dimensional optimization problem, the spheres are n-dimensional too. The radius of curvature and center of spheres can be determined at the tangent point between each function and its corresponding sphere. For the objective function, the parameters of sphere are determined at the reference point obtained by Lagrange equations, but for the constraints, first the reference point is returned to the surface of all the active constraints, then at the points on the constraints, the approximate parameters are calculated. Hence every computational step includes two parts: the determination of the reference point and returning it to the surface of active constraints. The criterion for returning to the active constraint is based on the shortest distance of the reference point from each of the active constraint, because the reference point is the output of optimization represented by Lagrange equations and so is the basis of the calculations. For returning the reference point to the active constraint, only one scalar variable is involved in the calculations. The introduction of the n-dimensional spheres both reduces the number of and simplifies the form of equations that need to be solved simultaneously to determine the optimum point and Lagrange multipliers at each optimization step, because the unknowns are now the Lagrange multipliers. This results in a significant reduction in computation time. Separating the design variables from Lagrange equations, the time of calculations may be saved for the loops of time-history analysis in the optimal seismic design. The method is applied to the optimization of two major parts of the lateral resistance systems, and the results are compared with those from penalty method. Considerable reduction of solution time is observed.   Conclusions The following remarks and conclusions are pertinent with regard to the formulation and the results presented in the paper: (1) The structural examples solved by the method presented here have also been solved by the exterior penalty method where both methods have provided exactly the same optimum solutions.  (2) The proposed method does not depend on the convexity or the concavity of the constraints or the objective function, because the radius of sphere that indicates the curvature is directly utilized at each computational step.  (3) Similar to the other optimization methods, the convergence behaviour and success of the proposed method depends on the starting point. (4) Separating the design variables from Lagrange equations, the time of calculations may be saved for the loops of time-history analysis in the optimal seismic design. (5) In this method, the criterion for the returning to the active constraint was utilized that is based on the shortest distance of the reference point from each of the active constraint (residual error); however, the methods based on Taylor expansion do not consider the minimization of residual error in every computational step. (6) Lagrange multipliers related to the constraints of lower and upper bound in the structural optimization problems can be decoupled from the others by the proposal method.  (7) Though of the time of computation to converge, the final solution is of great importance and should be discussed in detail. The space limitation does not let a proper comparison of convergence behaviour between the presented method and the exterior penalty method. Hence this issue has been postponed to a follow-up paper, but just qualitatively, the presented method has shown the convergence faster.}, keywords = {N-Dimensional Sphere,Radius of Curvature,Reference Point,Lagrange Multipliers,Contrained Problems}, title_fa = {جداسازی متغیرها در بهینه یابی طرح لرزه ای به کمک درون‌یابی کروی}, abstract_fa = {در این مقاله روش بهینه­یابی جدیدی با بهره­گیری از تقریب در تابع هدف و قیدها جهت استفاده در معادلات لاگرانژ ارائه شده است. همچنین برای این مدل، الگوریتمی در قالب فرایند حل عددی به‌منظور نزدیک کردن جواب تقریبی به جواب دقیق بهینه برای مسائل واقعی مهندسی و به‌طور خاص مسائل سازه­ای ارائه شده است. تقریب ارائه شده در این مدل عددی به فرم کره در فضای n‌ بعدی بوده که با بیان جدیدی از تعریف عمومی انحناء و شعاع انحناء ارائه شده است. این تقریب باعث جدا شدن متغیرهای طراحی از هم شده به‌طوری‌که تنها مجهول در دستگاه معادلات بهینه، ضرایب لاگرانژ می­باشند. متغیرهای طراحی به کمک روابط استخراج شده برحسب ضرایب لاگرانژ مستقیماً بدون تحلیل هیچ‌گونه معادله­ای حاصل می­شوند. هر گام محاسباتی شامل دو بخش، یکی به دست آوردن جواب تقریبی بهینه و دیگری برگرداندن جواب تقریبی بر روی قیدهای فعال به‌منظور انجام تقریب مجدد می­باشد. با جداسازی متغیرهای طراحی از معادلات لاگرانژ، زمان محاسبات به‌خصوص برای تحلیل‌های تاریخچه­-زمانی مورد نظر در طرح‌های بهینه‌ی لرزه‌ای می­تواند ذخیره شود. با استفاده از این روش دو مثال سازه­ای به‌عنوان بخش اصلی سیستم مهار جانبی قاب خمشی بتنی و مهاربندی مورد بررسی قرار گرفته که نتایج آن کاملاً منطبق با نتایج حاصل از روش پنالتی خارجی می­باشند. در این روش به دلیل کاهش تعداد متغیرها و طول گام بلند در محاسبات، سرعت همگرایی بالا می­باشد.   }, keywords_fa = {کره n بعدی,شعاع انحناء,نقطه مرجع,ضرایب لاگرانژ,مسائل مقید}, url = {http://www.bese.ir/article_240307.html}, eprint = {http://www.bese.ir/article_240307_fb738daa8911cd30c2d12ec97dfdffc9.pdf} } @article { author = {Motalebian, Masoud and Hajialilue Bonab, Masoud and Davoodi, Mohammad}, title = {Evaluation of Stone Columns Installation on Fundamental Frequency of Site with Finite Elements Method}, journal = {Bulletin of Earthquake Science and Engineering}, volume = {3}, number = {4}, pages = {73-84}, year = {2016}, publisher = {International Institute of Earthquake Engineering and Seismology}, issn = {2476-6097}, eissn = {2476-6100}, doi = {}, abstract = {Installation of stone columns is one of the proper and known methods for the improvement of weak soils. Stone column construction are employed to improve the bearing capacity, slope stability, and drainage rate, as well as reducing the settlement and liquefaction potential of the soft soil. In geotechnical earthquake engineering, stone columns are generally used to control the liquefaction potential of loose granular soils. However, the seismic performance of these inclusions has been partially studied and requires more researches. On the other hand, it is important to estimate a fundamental frequency of site for the seismic design of buildings and infrastructures and considers the basis of site classifications in seismic codes. In this paper, the effects of stone column construction on the fundamental frequency of the sites are studied numerically. Finite element analysis was performed using ABAQUS. The analysis is a modal analysis through the calculation of eigenvalues. Analyses was carried out in 3D and 2D in some cases. According to the modal analysis of the problem, the behavior of the soil and stone column are considered linear elastic. Additionally, the shear wave velocity and density of the soil and stone columns are assumed constant in depth. The results demonstrated that stone columns construction can increase the fundamental frequency of the site to four times. The fundamental frequency amplification factor of the site (α) can be defined according to the dimensionless parameters including stone column to soil shear wave velocity, height to diameter, distance to diameter, and stone column arrangements. The results indicated that α decreased with a rise in the ratio of the stone column height to diameter. Stone column arrangements are either square or triangle. When the triangle and square arrangements is used, zones of influences by each column as a regular hexagon and square, respectively. A comparison of the stone column arrangements demonstrated that, in triangle arrangement, α was greater than the corresponding value in square arrangement. The reason behind this is that in triangle arrangements, the zones of influence of each column is greater than the similar value in the square arrangement. Depending on the height of the column and depth of the bedrock, stone columns can be constructed as end bearing with their end on the bedrock or as floating with free end in the soil. The results indicate that, in floating stone columns, the effects of stone columns on α with respect to the condition where the stone column was end bearing, was considerably insignificant. In the following, tri-variant relation was determined for α. This relation was achieved using the Evolutionary Polynomial Regression (EPR). This method utilizes multi-objective genetic programming to derive regression equations by constructing symbolic models. Two-thirds of the data chosen to operate as training data and the other was used as testing data. The statistical parameters showed the good correlation and high accuracy of the derived relation for training and    testing data. In the following, the problem is done in plane strain condition (2D). For this purpose, stone columns which were in a row, were assumed as equivalent strips and these strips were supposed as a set of considerable rigid retaining walls in the soil profile. Similar to the 3D case, α can be presented by the values of dimensionless parameters. Finally, a 2D equivalent method for simplification of the 3D actual problem will be presented by examining the various cases. The results suggest that in the case the inertial moment of stone columns in 3D equal to 2D, relatively good approximation exists between the actual 3D and the equivalent 2D results.}, keywords = {Stone Columns,Fundamental Frequency,FEM,EPR Genetic Algorithms,Soil Improvement}, title_fa = {بررسی تأثیر احداث ستون‌های سنگی بر فرکانس اصلی ساختگاهی به روش اجزای محدود}, abstract_fa = {به‌کارگیری ستون‌های سنگی، از جمله­ روش­های مناسب و شناخته ­شده­ در بهسازی خاک­های سست محسوب می‌شود. این مقاله، به بررسی تأثیر احداث ستون‌های سنگی بر فرکانس اصلی ساختگاهی با تحلیل عددی    می­پردازد. برای بررسی مسئله، نرم­افزار اجزای محدود ABAQUS با تحلیل مودال به‌کار رفته است. نتایج نشان می‌دهد احداث ستون‌های سنگی، می‌تواند فرکانس اصلی ساختگاه را تا چهار برابر افزایش دهد. ضریب بزرگنمایی فرکانس اصلی ساختگاه () بر اساس پارامترهای بدون بعد، شامل نسبت­های سرعت موج برشی ستون سنگی به خاک، ارتفاع به قطر و مساحت به سطح بارگیر ستون سنگی، بیان شده است. نتایج نشان می‌دهد با افزایش نسبت ارتفاع به قطر ستون و لاغر شدن ستون،  کاهش می­یابد. مقایسه‌ی آرایش­های مختلف ستون‌های سنگی بیان می­دارد که  در آرایش مثلثی بیشتر از مقدار متناظر در آرایش مربعی می‌باشد. بر اساس تحلیل­های صورت گرفته، ستون‌های سنگی شناور برخلاف ستون‌های سنگی اتکایی تأثیر چندانی بر فرکانس اصلی ساختگاه نخواهد داشت. در ادامه با کمک الگوریتم ژنتیک بر مبنای رگرسیون چندجمله­ای تکاملی (EPR)،  به شکل رابطه­ای سه متغیره بر پایه­ی پارامترهای بدون بعد و با همبستگی مناسبی بیان شده است. در پایان، یک روش معادل دوبعدی با فرض کرنش مسطح برای ساده‌سازی مسئله‌ی سه‌بعدی ارائه گردیده است.}, keywords_fa = {ستون‌های سنگی,فرکانس اصلی,روش اجزای محدود,ABAQUS,الگوریتم ژنتیک EPR,بهسازی خاک}, url = {http://www.bese.ir/article_240308.html}, eprint = {http://www.bese.ir/article_240308_5afb089efdd5f2e3e7b4363ff4193e0a.pdf} }