m. hajiazizi
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پایدارسازی شیبهای خاکی کنار جادهها یکی از مسایل بااهمیت به منظور کاهش خطرات جانی و مالی جادهای میباشد. استفاده از راهکارهای مفید، ساده و مقرون به صرفه در پایدارسازی این شیبهای خاکی امری ضروری است. با توجه به پیشرفت و توسعه جادهای در نواحی شیبها، پایدارسازی شیروانیهای مشکوک و کسب اطمینان از پایداری آنها در برابر بارهای وارده یکی از چالشهای اساسی پیش روی مهندسان میباشد. استفاده از روشهای متداول پایدارسازی این مناطق بسته به شرایط محیطی، اهمیت محل مورد نظر و درجه ناپایداری آن، هزینههای مصرفی مصالح موجود، امکانات و غیره بسیار متنوع میباشد. یکی از روشهای مناسب و سازگار با محیط زیست برای مسلح کردن چنین شیبهایی استفاده از ستونهای سنگی میباشد. استفاده از ستونهای سنگی به عنوان یکی از روشهای پایدارسازی و افزایش ضریب اطمینان مطرح میشود که علاوه بر سادگی و راحتی اجرا، از نظر اقتصادی نیز مقرون به صرفه میباشد. هدف از انجام این پژوهش، ارایه نتایج مطالعات آزمایشگاهی و عددی پایدارسازی شیب خاکی با استفاده از ستون سنگی و بررسی مطالعات موردی انجام شده در زمینه استفاده از ستون سنگی برای پایدارسازی شیبهای کناری جادهها میباشد.
کلید واژگان: پایدارسازی, شیب جاده, ستون سنگی, مطالعه آزمایشگاهیRoad slope stabilization is one of the most common issues in reducing financial and life risks. Use of efficient and cost effective approaches for stabilizing earth slopes is a crucial matter. Due to Road growth, stabilizing of endanger slopes and insuring its safety is one of the basic concerns for engineers. With regard to regional condition, site importance, economical status, and many other factors, using common methods of stabilizing are diverse. One of these appropriate approaches for reinforcing earth slopes is the use of stone columns. Using stone columns, which, besides its simplicity and comfort implementation, is also very economical. The object of this research is presentation of experimentally and numerically investigates stone column stabilization of earth slopes, and investigates case studies about using stone columns in road slopes stabilization.
Keywords: Stabilization, Road slopes, Stone columns, Experimental Study -
تحلیل شیروانیهای خاکی از دیرباز مورد توجه پژوهشگران و محققان سراسر دنیا بوده است و راهکارهای متعددی برای تسلیح آنها (چه شیروانیهای طبیعی و چه مصنوعی) ارایه شده است. به طور کلی روشهای متعددی برای تسلیح و پایدارسازی شیبهای در خطر وجود دارد که یکی از شیوههای موثر، کارآمد و اقتصادی در این مورد، استفاده از ردیف ستون سنگی (یا شمع) به منظور تسلیح شیبهای خاکی و خاکریزهای جادهای و افزایش پایداری آنها میباشد. بهینهیابی مکان ستون سنگی یا شمع برای پایدارسازی شیبهای خاکی و خاکریزهای جادهای با استفاده از روشهای عددی و تحلیلی به وسیله پژوهشگران مختلف، منجر به نتایج متعددی شده است که این سوال را در ذهن طراح مطرح میکند که بهترین مکان واقعی برای نصب این المانهای سازهای در کجا قرار دارد؟ به نظر میرسد که جای مطالعات آزمایشگاهی برای تحقق این منظور خالی است که در پژوهش پیش رو، این موضوع از منظر مدلسازیهای آزمایشگاهی بررسی شده است. در این پژوهش به بررسی موقعیت بهینه و مناسب قرارگیری ستون سنگی و شمع به عنوان مسلحکننده در شیبهای خاکی و خاکریزهای جادهای و مقایسه نتایج روشهای تحلیلی در این زمینه پرداخته میشود.
کلید واژگان: شیب های خاکی, خاکریز جاده ای تسلیح, ستون سنگی, شمع, موقعیت بهینهEarth slope stability is one of the main issues on which researchers all around the world focus on and various methods proposed in order to reinforce slopes (both natural and man-made). There are lots of approaches for stabilization of slopes, among which using a row of stone columns (or piles) is the most effective and economical method in order to stabilize and reinforce earth slopes and road embankments. Researchers have used different numerical and analytical methods for optimal locationing of stone columns or piles for stability enhancements of earth slopes or road embankments, which were resulted in different outcomes. This issue brings the question that, where is the optimal location for inserting these structural elements? It seems that laboratory analysis and modeling in this issue is missing. In this paper, the problem is examined by laboratory modeling and optimal location of stone columns and piles as reinforcing elements in earth slopes and road embankments investigated and the results are compared.
Keywords: Earth Slopes, Road Embankments, Stone Column, Pile, Optimal Loc -
به کارگیری ستون های سنگی یکی از راهکارهای موثر در افزایش ظرفیت باربری خاک ها و کاهش میزان نشست است. در شرایطی که بستر خاکی به محصورکنندگی بیشتری نیاز داشته باشد، استفاده از غلاف هایی از جنس ژیوتکستایل و ژیوگرید یکی از روش های بهبود عملکرد این اعضای باربر محسوب می شود. هدف از انجام این پژوهش مقایسه ی رفتار غلاف های ژیوتکستایل و ژیوگرید در مسلح کردن ستون های سنگی در آزمایش سه محوری در شرایط تحکیم یافته ی زهکشی نشده است. در آزمایش ها از ستون سنگی در ماسه استفاده شده است. در این پژوهش یک سری آزمایش های سه محوری در حالت زهکشی نشده انجام شده است. نتایج نشان داد که در شرایط یکسان، غلاف ژیوگرید نسبت به ژیوتکستایل عملکرد بهتری دارد؛ به طوری که در کمترین تنش محصورکننده، افزایش ظرفیت باربری برای ستون مسلح به ژیوگرید و ژیوتکستایل به ترتیب 1٫31 و 1٫18 برابر است.
کلید واژگان: ماسه, ستون سنگی, غلاف ژئوسنتتیکی, آزمایش سه محوریThe use of stone columns is one of the effective ways to increase the bearing capacity of soils. An alternative system that can provide sufficient lateral confinement to support stone columns and increase bearing capacity is geosynthetic encased stone columns. These methods have been well utilized in Europe and South America. If the soil bed requires excessive confinement, the use of geotextile and geogrid encase around the stone columns is one way to improve the performance of these load-bearing members. This study aims to compare the behavior of geotextile and geogrid layers in reinforcing stone columns in standard Ottawa sand. In this study, a series of triaxial experiments in the undrained state was used. In the lowest confining pressure case, the load-bearing capacity for the geotextile reinforced column will be 1.18 times higher. Whereas for the geogrid-reinforced stone column, the load-bearing capacity is 1.31 times higher. In this study, standard Ottawa sand, gravel with a unit weight of 17 kN/m3 and a friction angle of 47.8°, geotextile and geogrid layers, and triaxial test apparatus are used. Triaxial specimens were 10 cm in diameter and 20 cm in height. Stone column dimensions of 2 cm in diameter and 20 cm in height are selected, respectively. Due to the limitations in the laboratory and the simulation of natural conditions, the unit weight of sand samples and stone columns made in triaxial test molds were selected as 15 and 17 kN/m3, respectively. Precipitation is used to fabricate cylindrical sand samples for triaxial testing. In this method, firstly attach the membrane to the underside of the triaxial apparatus and fasten the detachable bifurcation mold to the membrane and attach the membrane to the detachable mold walls by suction pumping about 2 bars. The aim is to create a homogeneous sample with uniform rainfall velocity to obtain a sample with evenly possible porosity. The method of precipitation depends on two parameters, one is the intensity of rainfall (amount of sand poured in a given volume at a specified time), and the other is the height of the sand fall, which is the distance between the sand outlet from the precipitation tank to the sand bed. The important point is that to achieve the same porosity, and this distance must be kept constant throughout the precipitation process. After construction, the test is performed according to ASTM D7181-11. Triaxial CU experiments on Ottawa sand were carried out in three cases: unreinforced, reinforced using geotextile encased stone column and reinforced using geogrid encased stone column. In triaxial experiments, three confining pressures of 200, 300, and 400 kPa were used.
Keywords: Ottawa Sand, Stone column, Geosynthetic Encasement, Triaxial test -
Among the methods used to design the tunnel, the Q-system is a comprehensive method that has attracted the attention of many researchers today. However, the limitations of the Q-system make it impossible to access all the required parameters as well as the time and cost of them, which has made it impossible to classify the rock mass using the Q-system. This paper attempts to predict the value of Q by parameters that have the highest coefficient of importance in the value of Q, using the Gene Expression Programming (GEP) technique. The most effective parameters involved in the Q value have been identified using Pearson correlation analysis (PCA), and then three different input models have been used to obtain Q value so that they are more closely related to experimental values. A total number of 159 experimental data were used for training and testing of the models, respectively. The innovation of this paper is that instead of 6 parameters, only three influential ones were used for determining the value of Q. Using the three parameters RQD, Jn and Ja, which have been determined as the most effective parameters and applying Pearson correlation analysis method, the value of Q can be determined with an acceptable approximation. In the suggested relation, the coefficients of determination (R2), root mean square error (RMSE), BIAS and the scatter index (SI) obtained were 0.917, 2.31, 1.74 and 0.43, respectively that show the new equation presented by GEP, can be undoubtedly used to predict the value of Q.
Keywords: Gene Expression Programming, Q-System, Rock Mass Classification, Pearson correlation analysis -
ارتفاع روباره تونل، تاثیر قابل توجهی در پایداری و یا ناپایداری تونل های سطحی دارد. در این پژوهش تاثیر ارتفاع روباره ی تونل سطحی در سنگ های مقاوم در حالت استاتیکی و شبه استاتیکی مورد بررسی قرار می گیرد. تحلیل تنش-کرنش برای تونل های سطحی در سنگ های مقاوم و در حالت شبه استاتیکی با استفاده از روش تفاضل محدود موضوع جدیدی است که در این مقاله مورد بحث و بررسی قرار گرفته است. با توجه به زلزله خیز بودن کشور ایران، تحلیل شبه استاتیکی تونل ها به جای تحلیل استاتیکی، ضرورت دارد؛ و در این مقاله نتایج به دست آمده از تحلیل شبه استاتیکی نسبت به تحلیل استاتیکی قابل تامل می باشد. با توجه به سطحی بودن تونل، تراز آب زیرزمینی پایین تر از کف تونل در نظر گرفته شده است. نتایج به دست آمده از تحلیل استاتیکی علاوه بر روش تفاضل محدود (FLAC2D) به کمک روش اجزای محدود (PLAXIS2D) نیز مورد بررسی قرار گرفته است که نتایج حاصل شده از هر دو روش از نزدیکی و تطابق قابل قبولی برخوردار می باشند. تغییر مکان افقی در کناره تونل در حالت شبه استاتیک در حدود 5 برابر تحلیل استاتیک بدست آمده است و تغییر مکان قایم در تاج تونل در دو حالت استاتیکی و شبه استاتیکی تقریبا به یکدیگر نزدیکند. علت این نتایج را می توان اینچنین توجیه کرد که شتاب افقی اعمال شده به تونل، تغییر مکان افقی کناره های تونل را تحت تاثیر خود قرار داده است و این شتاب افقی در تغییر مکان قایم تونل تاثیر قابل توجهی نداشته است.کلید واژگان: تونل, تنش-کرنش, روش های عددی, تحلیل شبه استاتیک, ارتفاع روبارهThe tunnel overburden height has considerable effect on stability or instability of surface tunnels. In this research, effects of overburden surface tunnel in strong rocks in both static and pseudo-static states investigated. In this paper, the results of pseudo-static analysis comparing to static state analysis are outstanding. Due to superficiality of tunnel, the water table line considered lower than tunnel bottom. The static analysis performed by Finite Element Method (FEM) and Finite Difference Method (FDM) and both results are close and acceptable. Results of static analysis indicated that by increasing in overburden height, horizontal displacement in sidewalls of tunnel and vertical deformation of tunnel crest would decrease. The stress amounts in sidewalls and crest of tunnel in pseudo-static state are higher than static condition.Keywords: Tunnel, Stress-Strain, Numerical methods, Pseudo-Static Analysis, Overburden Height
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کلید واژگان: شیروانی های خاکی, تقویت توسط تایر, ظرفیت باربری, جابجایی جانبی
In recent years, the number of waste tires around the world is increasing rapidly and has become an environmental and economic problem. Today, accumulation of waste tires in the environment is one of the biggest problems to the environment and recycling waste tires is the best strategy to solve this problem. The use of waste tires in construction and geotechnical projects is one of the effective strategies in this regard. In this paper, experimental tests of earth slope reinforced with waste tires based on horizontal displacement (25 experiments) has been performed. During incremental loading, digital images were taken from the models and the particle image velocity (PIV) method was used. Parameters such as tire layer length, number of layers and tire layer position are considered as variable. The results show that the use of tire reinforcement has a significant effect on reducing horizontal displacement under the foundation and slope surface. Horizontal tire rows are the best reinforcement location in terms of improved bearing capacity and lateral displacement. When four layers of 60 cm long reinforcement tire are placed in the upper half of the slope, the bearing capacity increases 3 times and the lateral displacement under the foundation decreases by 3.1 times. When three layers of tires with a length of 60 cm are placed in the upper third of the slope, the bearing capacity increases by 2.3 times and the lateral displacement under the foundation increases by 1.3 times. When six, eight, and nine layers of reinforcing tires with a length of 60 cm are placed into the slope, lateral displacement under the foundation is reduced more than 3.5 times. In Iran, eight largest tire factories produce 13.5 million tires in a year. It also imports 4 million tires a year. Therefore, 17.5 million tires are the annual consumption of the country. More than 100,000 tires are the product of factory production line waste, as well as used tires. Waste tires have been used to strength retaining walls, foundations, improve soil properties, embankments and etc. Therefore it is believed that soil reinforced with waste tires become a wider application in the future, especially in countries with low worker costs. In this paper, the test was performed in a box with length, width and height of 2, 1, 1 m, respectively. The test material used in this study is sand in the dry state. The maximum and minimum dry sand densities are 19.43 and 16.36 kN/m, respectively. Internal friction angle and cohesion were measured by direct shear test at 38 degree and about 0 kPa, respectively. Digital images taken from the front of the test box during the experiment. Images were processed using GeoPIV software developed at the University of Cambridge. The results of this study are as follows:1. The best position in terms of bearing capacity and lateral displacement is to use four layers of reinforcing tire in the upper half of the slope.2. As the length of the reinforcement layer increases, the bearing capacity increases significantly and the lateral displacement decreases. Especially when the length of the reinforcement tire is 60 cm and the length of the reinforcement passes through the rupture wedge, the improvement in bearing capacity and lateral displacement of the foundation is noticeable.3. The best position in the three layers of reinforcement tire on the slope in terms of bearing capacity and lateral displacement is one-third of the upper slope.4. The presence of a tire in the lower third of the slope has little effect on improving the bearing capacity, lateral displacement of the foundation and the slope surface compared to the slope without reinforcement.
Keywords: Soil Slopes, Tire Reinforcement, Bearing Capacity, Lateral Displacement -
Utilization of numerical and analytical methods to stabilize earth slopes applying piles or stone columns is subject commonly discussed by numerous researchers. Various researchers have practiced optimization of the location of pile or stone column, to stabilize earth slope through numerical and analytical approaches. Their efforts have led to various results raising the question of what the optimal place for installation of a pile or stone column is. It is look like that no experimental studies are conducted in this regard; the point which is discussed in this article. Experimental study conducted in this article is new topic and it can solve the problem caused by varying and sometimes contradictory results of numerical analyses to find the optimal pile (or stone column) location. In this article, an experimental study is conducted for two-layer sand earth slope, which is saturated through precipitation and failure after saturation over time. Installing stone columns in different locations and saturating the earth slope through precipitation, rational acceptable results were obtained that can appropriately assist designers. All of the experimental models were modeled and compared using the 3D finite difference method (3D FDM), which are compliant with each other.Keywords: Stabilization, Sand slope, Stone column, optimal location, Experimental test
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In the present study, shear displacements were calculated for all failure surface slices in earth slopes using the limit equilibrium method. To this end, the hyperbolic shear stress-strain constitutive law was applied. Local factors of safety were determined for the slices based on stress and displacement values. In order to calculate the displacement of earth slopes using the proposed method, a numerical model was developed satisfying the equilibrium of forces by a trial and error approach. A comparison between shear displacements obtained from this study in examples 1 and 2, with those obtained from FEM analysis which has yielded the normal errors of about 1.066% and 0.52%, respectively. Eventually, the effects of failure ratio ( ), and hyperbolic stiffness parameters (n and k) on displacement of earth slopes were examined.
Keywords: Displacement of slope, Limit equilibrium method, Earth slope, Safety factor, Hyperboli model -
در نوشتار حاضر، به بررسی آثار طول و ضخامت سگمنت های بتنی اجرا شده در تونل در نشست های عرضی و طولی سطح زمین پرداخته شده است. در انجام آنالیزها از روش اجزاء محدود (F E) با استفاده از نرم افزار A B A Q U S استفاده شده است. در پژوهش حاضر، ابتدا نتایج به دست آمده از مدل ساخته شده در نرم افزار A B A Q U S جهت صحت سنجی با نتایج تجربی و مشاهده های محلی برای قطعه ی 28−5S از خط 1 متروی میلان مقایسه شده است. درنهایت، اثر ضخامت و طول سگمنت های بتنی که به کمک دستگاه E P B T B M نصب شده اند، در نشست سطحی بررسی شده است. نتایج به دست آمده نشان می دهند با افزایش ضخامت و نیز افزایش طول قطعات و به تبع آن افزایش طول گام های حفاری در روش ذکر شده از تونل زنی، هم در راستای طولی و هم راستای عرضی تونل، مقدار نشست های سطحی کاهش می یابند که به دلیل افزایش سختی محیط به علت اجرای پوشش تونل است. همچنین با افزایش ضخامت و طول سگمنت ها، افت حجمی ایجاد شده در اثر حفاری تونل کاهش می یابد.
کلید واژگان: نشست, E P B T B M, سگمنت بتنی, تونل, اجزاء محدودIn recent years, the need to make greater use of urban spaces on the one hand and the lack of these spaces in comparison with the ever- increasing demand of urban society are reasons for optimum utilization of available spaces with underground constructions such as tunnels. Most of these excavations with large volume of drilling are located at shallow depths and close to surface which cause displacements in the groundand effect of these movements can be seen as surface settlements in the soil. Surface settlements can be very influential in surface structures such as buildings and facilities that are located in densely populated urban areas and the vicinity of the excavated tunnels. The control of these settlements in order to protect surface structures during tunnel excavation, is the most important issue considered by design engineers. Analytical, experimental, and numerical methods for estimating these settlements were studied and presented by several researchers. However, experimental and semi-experimental methods are not able to include all parameters; so they cannot perform detailed calculation in complex problems. For this reason, the use of numerical methods was developed in order to accelerate and increase the accuracy of calculations, beside methods was developed.In the present work, the effect of tunnel support on surface settlement has been studied by using finite- element method after verification of the model results made with ABAQUS software along with the experimental results and observations of sections s5-28 of the Milan underground line1. As the thickness and length of the concrete lining as geometric parameters that affect the support system stiffness, they can affect the surface settlements caused by tunnel excavation. Therefore, it is important that the support have the optimum size to have the greatest effect on reducing the settlements. Finally, in the present work, the effect of thickness and length of concrete segments installed with EPB-TBM ,has been studied. Keywords: settlement, EPB-TBM, concrete segment, tunnel, finite element.
Keywords: S?E?T?T?L?E?M?E?N?T, E?P?B-T?B?M, C?O?N?C?R?E?T?E S?E?G?M?E?N?T, T?U?N?N?E?L, F?I?N?I?T?E E?L?E?M?E?N?T -
در پژوهش حاضر، یک روش تعادل حدی جدید ارائه شده است که کلیه ی شرایط تعادل را ارضا می کند. در روش پیشنهادی، شکل سطح لغزش به صورت دایره یی و غیردایره یی و قطعات در امتداد شعاع سطح لغزش و یا خطوطی در نظر گرفته شده اند که به یک نقطه هم گرا می شوند. همچنین معادلات تعادل نیروها و گشتاور، بدون هیچ گونه فرض ساده کننده یی استفاده شده اند. نوآوری پژوهش حاضر در شکل قطعات به صورت قطاع است که موجب حذف شدن فرضیات متداول در روش تعادل حدی می شود. بنابراین انتظار می رود که روش مذکور در تعیین ضریب اطمینان، خطای کمتری داشته باشد. به منظور محاسبه ی ضریب اطمینان با استفاده از روش پیشنهادی، یک مدل عددی توسعه داده شده است، که جهت ارضاء هم زمان معادلات تعادل نیرو و گشتاور، از روش تکراری (سعی و خطا) استفاده می کند. همچنین روش ارائه شده می تواند مقدار نیروهای قائم و برشی را در بین قطعات محاسبه کند. به منظور ارزیابی روش پیشنهادی و کارایی مدل توسعه داده شده، چند مثال با شرایط مختلف حل شده است که نتایج حاصل از آن ها تطابق خوبی با نتایج روش های دیگر دارد.
کلید واژگان: پایداری شیروانی خاکی, ضریب اطمینان, روش تعادل حدی, سطح لغزشSlope stability analysis is used in a wide variety of geotechnical engineering problems such as embankments, road cuts, open-pit mining, excavations, canals, landfills, etc. The limit equilibrium method is the most popular approach in slope stability analyses. In this study, a new limit equilibrium method is proposed that can satisfy the forces and moment without any assumptions. In this method, circular or non-circular slip surface has been considered and slices are intended along the radius of the slip surface. Innovation of this research is in the form of slices in circle sector which could eliminate the common simplifying assumptions in the equilibrium equations. The forces and moment equilibrium equations have been applied without any simplifying assumptions and expected that this method can achieve lower error in determining the safety factor. In order to calculate the safety factor using the proposed method, a numerical model has been developed. In this model, the soil slope characteristics such as slope geometry, soil strength properties, seismic coefficient and also water level are considered as input. Then sliding wedge is introduced and on the basis of number of divisions that the user defines, sliding wedge is discretized. In the next step, the coordinates of each node of these slices are determined. To compute the safety factor, a process should be taken that satisfies the force and moment equilibrium equations simultaneously. To achieve this goal, the iterative method (trial and error) is used in this study. In order to evaluate the proposed method and the efficiency of the developed model, several tests with different conditions are solved. The mentioned test results are in good agreement with the results of other methods that satisfy all of the equilibrium equations.
Keywords: E?A?R?T?H S?L?O?P?E S?T?A?B?I?L?I?T?Y, F?A?C?T?O?R O?F S?A?F?E?T?Y, L?I?M?I?T E?Q?U?I?L?I?B?R?I?U?M M?E?T?H?O?D, S?L?I?P S?U?R?F?A?C?E -
به دست آوردن تغییرمکان های اطراف تونل، یکی از موضوعات مهم در تونل سازی است. در نوشتار حاضر، به کمک روش های تفاضل محدود و اجزاء محدود و همچنین داده های اندازه گیری شده به ارائه ی روابطی جدید برای مقایسه ی تغییرشکل تونل در حالت های دوبعدی و سه بعدی و برای توده سنگ های سالم و درزه دار پرداخته شده است، که نتایج متفاوت آنها قابل توجه است. با توجه به اینکه در بسیاری از تحلیل های عددی، مدل سازی دوبعدی انجام می شود، روابط ارائه شده در نوشتار حاضر می تواند منجر به نتایج واقعی شود. مطابق با نتایج حاصل از تحلیل های مختلف در توده سنگ های سالم، مقدار تغییرمکان اطراف تونل در حالت دوبعدی بزرگ تر از حالت سه بعدی است، اما در توده سنگ های درزه دار مقدار تغییرمکان اطراف تونل در حالت دوبعدی کمتر از حالت سه بعدی است. همچنین نتایج حاصل از پژوهش حاضر، از طریق تونل سد گاوشان تایید شده است.
کلید واژگان: تونل, تغییرمکان, روش های عددی, تحلیل دوبعدی, تحلیل سه بعدیTo obtain the displacements of a tunnel is one of the major issues in the tunnel. In this paper, using the finite difference and finite element methods and measurements data, new relationships are presented between the 2-D and 3-D deformation of a tunnel. This comparison was performed between competent rock and jointed rock mass where different results are considerable. Empirical, numerical and analytical methods are regarded as different tools for design of tunnel. Nowadays, due to the advancement of technology, limitation on surface spaces, and political and security issues, many developed and developing countries focus on constructing underground structures for civil and military applications. Underground road and highways, tunnels, urban subway networks, power plants, nuclear waste repositories, oil reservoirs, shelters, and warehouses are structures which are rapidly under construction in different countries. It should be noted that these achievements have been made over a long time, accompanied by different problems. In order to predict the displacement of a tunnel with regard to its 2-D deformation, the new equations are proposed in this paper in 3-D case that can be employed. Due to the fact that in many numerical analyses, modeling is done in 2-D case, the relationships presented in this article can be real results. According to the results of the various analyses of intact rock mass, displacement of tunnel in 3-D is less than that in the 2-D case. But, in the jointed rock mass the displacement of tunnel in 2-D is less than that in the 3-D case. The results of this research have been verified by tunnel of Gavoshan's dam. After comparing and analyzing the results, relationships have been proposed for the coloration between 2-D and 3-D in intact rock mass and jointed rock mass. The solved examples give reasonable and acceptable results.
Keywords: T?U?N?N?E?L, D?I?S?P?L?A?C?E?M?E?N?T, N?U?M?E?R?I?C?A?L M?E?T?H?O?D?S, 2D A?N?A?L?Y?S?I?S, 3D A?N?A?L?Y?S?I?S
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