Search results for: numerical range

Authors: N. Parandin, M. A. Fariborzi Araghi

Abstract:

in this paper, we propose a numerical method for the approximate solution of fuzzy Fredholm functional integral equations of the second kind by using an iterative interpolation. For this purpose, we convert the linear fuzzy Fredholm integral equations to a crisp linear system of integral equations. The proposed method is illustrated by some fuzzy integral equations in numerical examples.

Keywords: Fuzzy function integral equations, Iterative method, Linear systems, Parametric form of fuzzy number.

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Authors: Mostafa Jafarian Abyaneh, Khashayar Jafari, Vahab Toufigh

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The cost of experiments on different types of concrete has raised the demand for prediction of their behavior with numerical analysis. In this research, an advanced numerical model has been presented to predict the complete elastic-plastic behavior of polymer concrete (PC), high-strength concrete (HSC), high performance concrete (HPC) along with different steel fiber contents under uniaxial compression. The accuracy of the numerical response was satisfactory as compared to other conventional simple models such as Mohr-Coulomb and Drucker-Prager. In order to predict the complete elastic-plastic behavior of specimens including softening behavior, disturbed state concept (DSC) was implemented by nonlinear finite element analysis (NFEA) and hierarchical single surface (HISS) failure criterion, which is a failure surface without any singularity.

Keywords: Disturbed state concept, hierarchical single surface, failure criterion, high performance concrete, high-strength concrete, nonlinear finite element analysis, polymer concrete, steel fibers, uniaxial compression test.

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Authors: M. Zarebnia, R. Parvaz

Abstract:

In this paper the Kuramoto-Sivashinsky equation is solved numerically by collocation method. The solution is approximated as a linear combination of septic B-spline functions. Applying the Von-Neumann stability analysis technique, we show that the method is unconditionally stable. The method is applied on some test examples, and the numerical results have been compared with the exact solutions. The global relative error and L∞ in the solutions show the efficiency of the method computationally.

Keywords: Kuramoto-Sivashinsky equation, Septic B-spline, Collocation method, Finite difference.

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Authors: Abdelaziz Khernane, Naceur Khelil, Leila Djerou

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The aim of this work is to study the numerical implementation of the Hilbert Uniqueness Method for the exact boundary controllability of Euler-Bernoulli beam equation. This study may be difficult. This will depend on the problem under consideration (geometry, control and dimension) and the numerical method used. Knowledge of the asymptotic behaviour of the control governing the system at time T may be useful for its calculation. This idea will be developed in this study. We have characterized as a first step, the solution by a minimization principle and proposed secondly a method for its resolution to approximate the control steering the considered system to rest at time T.

Keywords: Boundary control, exact controllability, finite difference methods, functional optimization.

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Authors: Mohd Agos Salim Nasir, Ros Fadilah Deraman, Siti Salmah Yasiran

Abstract:

The Goursat partial differential equation arises in linear and non linear partial differential equations with mixed derivatives. This equation is a second order hyperbolic partial differential equation which occurs in various fields of study such as in engineering, physics, and applied mathematics. There are many approaches that have been suggested to approximate the solution of the Goursat partial differential equation. However, all of the suggested methods traditionally focused on numerical differentiation approaches including forward and central differences in deriving the scheme. An innovation has been done in deriving the Goursat partial differential equation scheme which involves numerical integration techniques. In this paper we have developed a new scheme to solve the Goursat partial differential equation based on the Adomian decomposition (ADM) and associated with Boole-s integration rule to approximate the integration terms. The new scheme can easily be applied to many linear and non linear Goursat partial differential equations and is capable to reduce the size of computational work. The accuracy of the results reveals the advantage of this new scheme over existing numerical method.

Keywords: Goursat problem, partial differential equation, Adomian decomposition method, Boole's integration rule.

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Authors: Ramy H. Mohammed

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In heat sinks, the flow within the core exhibits separation and hence does not lend itself to simple analytical boundary layer or duct flow analysis of the wall friction. In this paper, we present some findings from an experimental and numerical study aimed to obtain physical insight into the influence of the presence of the shield and its position on the hydraulic and thermal performance of square pin fin heat sink without top by-pass. The variations of the Nusselt number and friction factor are obtained under varied parameters, such as the Reynolds number and the shield position. The numerical code is validated by comparing the numerical results with the available experimental data. It is shown that, there is a good agreement between the temperature predictions based on the model and the experimental data. Results show that, as the presence of the shield, the heat transfer of fin array is enhanced and the flow resistance increased. The surface temperature distribution of the heat sink base is more uniform when the dimensionless shield position equals to 1/3 or 2/3. The comprehensive performance evaluation approach based on identical pumping power criteria is adopted and shows that the optimum shield position is at x/l=0.43.

Keywords: Shield, Fin array, Performance evaluation, Heat transfer, Validation.

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Authors: K. Boumediene, S. E. Belhenniche

Abstract:

This article presents a numerical analysis of a turbulent flow past DTMB 4119 marine propeller by the means of RANS approach; the propeller designed at David Taylor Model Basin in USA. The purpose of this study is to predict the hydrodynamic performance of the marine propeller, it aims also to compare the results obtained with the experiment carried out in open water tests; a periodical computational domain was created to reduce the unstructured mesh size generated. The standard kw turbulence model for the simulation is selected; the results were in a good agreement. Therefore, the errors were estimated respectively to 1.3% and 5.9% for KT and KQ.

Keywords: propeller flow, CFD simulation, hydrodynamic performance, RANS

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Authors: Hadi Rezghi Maleki, Babak Abazadeh

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In this paper, the effect of bolt clamping force on the fatigue behavior of bolted single lap joints of aluminum alloy 2024- T3 have been studied using numerical finite element method. To do so, a three dimensional model according to the bolted single lap joint has been created and numerical analysis has been carried out using finite element based package. Then the stress distribution and also the slip amplitudes have been calculated in the critical regions and the outcome have been compared with the available experimental fatigue tests results. The numerical results show that in low applied clamping force, the fatigue failure of the specimens occur around the stress concentration location (the bolted hole edge) due to the tensile stresses and thus fatigue crack propagation, but with increase of the clamping force, the fatigue life increases and the cracks nucleate and propagate far from the hole edge because of fretting fatigue. In other words, with the further increase of clamping force value of the joint, the fatigue life reduces due to occurrence of the fretting fatigue in the critical location where the slip amplitude is within its critical occurs earlier.

Keywords: Fretting fatigue, bolted single lap joint, torque tightening, finite element method.

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Authors: F. Esfandyari Darabad, Z. Samadi

Abstract:

Natural environments have always been affected by one of the most important natural hazards, which is called, the mass movements that cause instability. Identifying the unstable regions and separating them so as to detect and determine the risk of environmental factors is one of the important issues in mountainous areas development. In this study, the northwest of Sabalan hillsides overlooking the Meshkin city and the surrounding area of that have been delimitated, in order to analyze the range processes such as landslides and debris flows based on structural and geomorphological conditions, by means of using GIS. This area due to the high slope of the hillsides and height of the region and the poor localization of roads and so because of them destabilizing the ranges own an inappropriate situation. This study is done with the purpose of identifying the effective factors in the range motion and determining the areas with high potential for zoning these movements by using GIS. The results showed that the most common range movements in the area, are debris flows, rocks falling and landslides. The effective factors in each one of the mass movements, considering a small amount of weight for each factor, the weight map of each factor and finally, the map of risk zoning for the range movements were provided. Based on the zoning map resulted in the study area, the risking level of damaging has specified into the four zones of very high risk, high risk, medium risk, low risk, in which areas with very high and high risk are settled near the road and along the Khyav river and in the  mountainous district.

Keywords: Debris flow, environmental hazards, GIS, landslide.

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Authors: Yongxin Yuan, Jiashang Jiang

Abstract:

A new numerical method for simultaneously updating mass and stiffness matrices based on incomplete modal measured data is presented. By using the Kronecker product, all the variables that are to be modified can be found out and then can be updated directly. The optimal approximation mass matrix and stiffness matrix which satisfy the required eigenvalue equation and orthogonality condition are found under the Frobenius norm sense. The physical configuration of the analytical model is preserved and the updated model will exactly reproduce the modal measured data. The numerical example seems to indicate that the method is quite accurate and efficient.

Keywords: Finite element model, model updating, modal data, optimal approximation.

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Authors: G. Tanapornraweekit, W. Kulsirikasem

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This paper presents the simulation of fragmentation warhead using a hydrocode, Autodyn. The goal of this research is to determine the lethal range of such a warhead. This study investigates the lethal range of warheads with and without steel balls as preformed fragments. The results from the FE simulation, i.e. initial velocities and ejected spray angles of fragments, are further processed using an analytical approach so as to determine a fragment hit density and probability of kill of a modelled warhead. In order to simulate a plenty of preformed fragments inside a warhead, the model requires expensive computation resources. Therefore, this study attempts to model the problem in an alternative approach by considering an equivalent mass of preformed fragments to the mass of warhead casing. This approach yields approximately 7% and 20% difference of fragment velocities from the analytical results for one and two layers of preformed fragments, respectively. The lethal ranges of the simulated warheads are 42.6 m and 56.5 m for warheads with one and two layers of preformed fragments, respectively, compared to 13.85 m for a warhead without preformed fragment. These lethal ranges are based on the requirement of fragment hit density. The lethal ranges which are based on the probability of kill are 27.5 m, 61 m and 70 m for warheads with no preformed fragment, one and two layers of preformed fragments, respectively.

Keywords: Lethal Range, Natural Fragment, Preformed Fragment, Warhead.

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Authors: Vaclav Dvorak

Abstract:

The article deals with experimental and numerical investigation of axi-symmetric subsonic air to air ejector with diffuser adapted for boundary layer suction. The diffuser, which is placed behind the mixing chamber of the ejector, has high divergence angle and therefore low efficiency. To increase the efficiency, the diffuser is equipped with slot enabling boundary layer suction. The effect of boundary layer suction on flow in ejector, static pressure distribution on the mixing chamber wall and characteristic were measured and studied numerically. Both diffuser and ejector efficiency were evaluated. The diffuser efficiency was increased, however, the efficiency of ejector itself remained low.

Keywords: Air ejector, boundary layer suction, CFD, diffuser.

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Authors: Raisa Kh. Bolotnova, Marat N. Galimzianov, Andrey S. Topolnikov, Uliana O. Agisheva, Valeria A. Buzina

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The paper presents the results of theoretical and numerical modeling of propagation of shock waves in bubbly liquids related to nonlinear effects (realistic equation of state, chemical reactions, two-dimensional effects). On the basis on the Rankine- Hugoniot equations the problem of determination of parameters of passing and reflected shock waves in gas-liquid medium for isothermal, adiabatic and shock compression of the gas component is solved by using the wide-range equation of state of water in the analitic form. The phenomenon of shock wave intensification is investigated in the channel of variable cross section for the propagation of a shock wave in the liquid filled with bubbles containing chemically active gases. The results of modeling of the wave impulse impact on the solid wall covered with bubble layer are presented.

Keywords: bubbly liquid, cavitation, equation of state, shock wave

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Authors: Taher M. Abou-deif, Mahmoud A. Fouad, Essam E. Khalil

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The present paper was concerned primarily with the analysis, simulation of the air flow and thermal patterns in a lecture room. The paper is devoted to numerically investigate the influence of location and number of ventilation and air conditioning supply and extracts openings on air flow properties in a lecture room. The work focuses on air flow patterns, thermal behaviour in lecture room where large number of students. The effectiveness of an air flow system is commonly assessed by the successful removal of sensible and latent loads from occupants with additional of attaining air pollutant at a prescribed level to attain the human thermal comfort conditions and to improve the indoor air quality; this is the main target during the present paper. The study is carried out using computational fluid dynamics (CFD) simulation techniques as embedded in the commercially available CFD code (FLUENT 6.2). The CFD modelling techniques solved the continuity, momentum and energy conservation equations in addition to standard k – ε model equations for turbulence closure. Throughout the investigations, numerical validation is carried out by way of comparisons of numerical and experimental results. Good agreement is found among both predictions.

Keywords: Air Conditioning, CFD, Lecture Rooms, Thermal Comfort

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Authors: Peristera A. Baziana

Abstract:

The idea of the asynchronous transmission in wavelength division multiplexing (WDM) ring MANs is studied in this paper. Especially, we present an efficient access technique to coordinate the collisions-free transmission of the variable sizes of IP traffic in WDM ring core networks. Each node is equipped with a tunable transmitter and a tunable receiver. In this way, all the wavelengths are exploited for both transmission and reception. In order to evaluate the performance measures of average throughput, queuing delay and packet dropping probability at the buffers, a simulation model that assumes symmetric access rights among the nodes is developed based on Poisson statistics. Extensive numerical results show that the proposed protocol achieves apart from high bandwidth exploitation for a wide range of offered load, fairness of queuing delay and dropping events among the different packets size categories.

Keywords: Asynchronous transmission, collision avoidance, wavelength division multiplexing.

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Authors: Prodromos E. Atlamazoglou

Abstract:

The method of moments combined with the method of symmetrical components is used for the analysis of interstitial hyperthermia applicators. The basis and testing functions are both piecewise sinusoids, qualifying our technique as a Galerkin one. The dielectric coatings are modeled by equivalent volume polarization currents, which are simply related to the conduction current distribution, avoiding in that way the introduction of additional unknowns or numerical integrations. The results of our method for a four dipole circular array, are in agreement with those already published in literature for a same hyperthermia configuration. Apart from being accurate, our approach is more general, more computationally efficient and takes into account the coupling between the antennas.

Keywords: Hyperthermia, integral equations, insulated antennas, method of symmetrical components.

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Authors: Sing-Wu Liou, Yin-Fu Huang

Abstract:

For identifying the discriminative sequence features between exons and introns, a new paradigm, rescaled-range frameshift analysis (RRFA), was proposed. By RRFA, two new sequence features, the frameshift sensitivity (FS) and the accumulative penta-mer complexity (APC), were discovered which were further integrated into a new feature of larger scale, the persistency in anti-mutation (PAM). The feature-validation experiments were performed on six model organisms to test the power of discrimination. All the experimental results highly support that FS, APC and PAM were all distinguishing features between exons and introns. These identified new sequence features provide new insights into the sequence composition of genes and they have great potentials of forming a new basis for recognizing the exonintron boundaries in gene sequences.

Keywords: Exon-Intron Discrimination, Rescaled-Range Frameshift Analysis, Frameshift Sensitivity, Accumulative Sequence Complexity

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Authors: J. J. Cetina-Denis, R. M. López-Gutiérrez, R. Ramírez-Ramírez, C. Cruz-Hernández

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This work addresses the problem of designing an algorithm capable of generating chaotic trajectories for mobile robots. Particularly, the chaotic behavior is induced in the linear and angular velocities of a Khepera III differential mobile robot by infusing them with the states of the H´enon chaotic map. A possible application, using the properties of chaotic systems, is patrolling a work area. In this work, numerical and experimental results are reported and analyzed. In addition, two quantitative numerical tests are applied in order to measure how chaotic the generated trajectories really are.

Keywords: Chaos, chaotic trajectories, differential mobile robot, Henons map, Khepera III robot, patrolling applications.

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Authors: Ilya Popov, Steven Hulshoff

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A numerical investigation of the effects of nanosecond barrier discharge on the stability of a two-dimensional free shear layer is performed. The computations are carried out using a compressible Navier-Stokes algorithm coupled with a thermodynamic model of the discharge. The results show that significant increases in the shear layer-s momentum thickness and Reynolds stresses occur due to actuation. Dependence on both frequency and amplitude of actuation are considered, and a comparison is made of the computed growth rates with those predicted by linear stability theory. Amplitude and frequency ranges for the efficient promotion of shear-layer instabilities are identified.

Keywords: NS-DBD, plasma, actuator, flow control, instability, shear layer

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Authors: Y. Hu, X. Zhao, T. Yamaguchi, M. Sasajima, Y. Koike

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To focus on the vibration mode of a cone loudspeaker, which acts as an electroacoustic transducer, excitation experiments were performed using two types of loudspeaker units: one employing an impulse hammer and the other a sweep signal. The on-axis sound pressure frequency properties of the loudspeaker were evaluated, and the characteristic properties of the loudspeakers were successfully determined in both excitation experiments. Moreover, under conditions identical to the experiment conditions, a coupled analysis of the vibration-acoustics of the cone loudspeaker was performed using an acoustic analysis software program that considers the impact of damping caused by air viscosity. The result of sound pressure frequency properties with the numerical analysis are the most closely match that measured in the excitation experiments over a wide range of frequency bands.

Keywords: Anechoic room, finite element method, impulse hammer, loudspeaker, reverberation room, sweep signal.

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Authors: jianhua Hou, Changqing Yang, and Beibo Qin

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A numerical method for solving nonlinear Fredholm integral equations of second kind is proposed. The Fredholm type equations which have many applications in mathematical physics are then considered. The method is based on hybrid function  approximations. The properties of hybrid of block-pulse functions and Chebyshev polynomials are presented and are utilized to reduce the computation of nonlinear Fredholm integral equations to a system of nonlinear. Some numerical examples are selected to illustrate the effectiveness and simplicity of the method.

Keywords: Hybrid functions, Fredholm integral equation, Blockpulse, Chebyshev polynomials, product operational matrix.

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Authors: Pradeep M., N. S. Mahesh, Raja Hussain

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Resistance spot welding (RSW) has been used widely to join sheet metals. It has been a challenge to get required weld quality in spot welding of dissimilar thickness materials. Weld parameters are not generally available in standards for thickness beyond 4mm. This paper presents the welding process design and parameter optimization of RSW used in joining of low carbon steel sheet of thickness 0.8 mm and metal strips of cross section 10 x 5mm for electrical motor applications. Taguchi quality design was adopted for weld current and time optimization using L9 orthogonal array. Optimum process parameters (current- 3.5kA and time- 10 cycles) were obtained from the Taguchi analysis and shear test results. Confirmation experiment result revealed that the weld quality was within acceptable interval. Further, numerical simulation of RSW process was carried out with selected weld parameters to quantify the temperature at faying surface and check for formation of appropriate nugget. The nugget geometry measured after peel test and predicted from numerical validation method were similar and in accordance with the standards.

Keywords: Resistance spot welding, dissimilar thickness, weld parameters, Taguchi method, numerical modeling.

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Authors: A. Ghafouri, N. Pourmahmoud, I. Mirzaee

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In this numerical study, effects of using Al2O3-water nanofluid on the rate of heat transfer have been investigated. Physical model is a square enclosure with insulated top and bottom horizontal walls, while the vertical walls are kept at different constant temperatures. Two appropriate models are used to evaluate the viscosity and thermal conductivity of nanofluid. The governing stream-vorticity equations are solved using a second order central finite difference scheme, coupled to the conservation of mass and energy. The study has been carried out for the nanoparticle diameter 30, 60 and 90 nm and the solid volume fraction 0 to 0.04. Results are presented by average Nusselt number and normalized Nusselt number in different range of φ and D for mixed convection dominated regime. It is found that different heat transfer rate is predicted when the effect of nanoparticle diameter is taken into account.

Keywords: Nano-fluid, nanoparticle diameter, heat transfer enhancement, square enclosure, Nusselt number.

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Authors: M. Abdollahi, S. N. Moghaddas Tafreshi

Abstract:

Expanded polystyrene (EPS) geofoam is often used in below ground applications in geotechnical engineering. A most recent configuration system implemented in roadways to protect lifelines such as buried pipes, electrical cables and culvert systems could be consisted of two EPS geofoam blocks, “posts” placed on each side of the structure, an EPS block capping, “beam” put atop two posts, and soil cover on the beam. In this configuration, a rectangular void space will be built atop the lifeline. EPS blocks will stand all the imposed vertical forces due to their strength and deformability, thus the lifeline will experience no vertical stress. The present paper describes the results of a numerical study on the post and beam configuration subjected to the static loading. Three-dimensional finite element analysis using ABAQUS software is carried out to investigate the effect of different parameters such as beam thickness, soil thickness over the beam, post height to width ratio, EPS density, and free span between two posts, on the stress distribution and the deflection of the beam. The results show favorable performance of EPS geofoam for protecting sensitive infrastructures.

Keywords: Beam, EPS block, numerical analysis, post, stress distribution.

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Authors: M. G. Murtaza, E. E. Tzirtzilakis, M. Ferdows

Abstract:

Biomagnetic fluid dynamics is an interdisciplinary field comprising engineering, medicine, and biology. Bio fluid dynamics is directed towards finding and developing the solutions to some of the human body related diseases and disorders. This article describes the flow and heat transfer of two dimensional, steady, laminar, viscous and incompressible biomagnetic fluid over a non-linear stretching sheet in the presence of magnetic dipole. Our model is consistent with blood fluid namely biomagnetic fluid dynamics (BFD). This model based on the principles of ferrohydrodynamic (FHD). The temperature at the stretching surface is assumed to follow a power law variation, and stretching velocity is assumed to have a nonlinear form with signum function or sign function. The governing boundary layer equations with boundary conditions are simplified to couple higher order equations using usual transformations. Numerical solutions for the governing momentum and energy equations are obtained by efficient numerical techniques based on the common finite difference method with central differencing, on a tridiagonal matrix manipulation and on an iterative procedure. Computations are performed for a wide range of the governing parameters such as magnetic field parameter, power law exponent temperature parameter, and other involved parameters and the effect of these parameters on the velocity and temperature field is presented. It is observed that for different values of the magnetic parameter, the velocity distribution decreases while temperature distribution increases. Besides, the finite difference solutions results for skin-friction coefficient and rate of heat transfer are discussed. This study will have an important bearing on a high targeting efficiency, a high magnetic field is required in the targeted body compartment.

Keywords: Biomagnetic fluid, FHD, nonlinear stretching sheet, slip parameter.

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Authors: Sang-Youl Lee

Abstract:

This study deals with an advanced numerical techniques to detect tensile forces in cable-stayed structures. The proposed method allows us not only to avoid the trap of minimum at initial searching stage but also to find their final solutions in better numerical efficiency. The validity of the technique is numerically verified using a set of dynamic data obtained from a simulation of the cable model modeled using the finite element method. The results indicate that the proposed method is computationally efficient in characterizing the tensile force variation for cable-stayed structures.

Keywords: Tensile force detection, cable-stayed structures, hybrid system identification (h-SI), dynamic response.

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Authors: Marian Gaiceanu, Emil Rosu

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In this paper the optimal control strategy for Permanent Magnet Synchronous Motor (PMSM) based drive system is presented. The designed full optimal control is available for speed operating range up to base speed. The optimal voltage space-vector assures input energy reduction and stator loss minimization, maintaining the output energy in the same limits with the conventional PMSM electrical drive. The optimal control with three components is based on the energetically criteria and it is applicable in numerical version, being a nonrecursive solution. The simulation results confirm the increased efficiency of the optimal PMSM drive. The properties of the optimal voltage space vector are shown.

Keywords: Matlab/Simulink, optimal control, permanent magnet synchronous motor, Riccati equation, space vector PWM

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Authors: S. Housseno, A. Simonet, M. Simonet

Abstract:

Semantic query optimization consists in restricting the search space in order to reduce the set of objects of interest for a query. This paper presents an indexing method based on UB-trees and a static analysis of the constraints associated to the views of the database and to any constraint expressed on attributes. The result of the static analysis is a partitioning of the object space into disjoint blocks. Through Space Filling Curve (SFC) techniques, each fragment (block) of the partition is assigned a unique identifier, enabling the efficient indexing of fragments by UB-trees. The search space corresponding to a range query is restricted to a subset of the blocks of the partition. This approach has been developed in the context of a KB-DBMS but it can be applied to any relational system.

Keywords: Index, Range query, UB-tree, Space Filling Curve, Query optimization, Views, Database, Integrity Constraint, Classification.

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Authors: H. Mohammadiun, A. Kianifar, A. Kargar

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Nowadays, there is little information, concerning the heat shield systems, and this information is not completely reliable to use in so many cases. for example, the precise calculation cannot be done for various materials. In addition, the real scale test has two disadvantages: high cost and low flexibility, and for each case we must perform a new test. Hence, using numerical modeling program that calculates the surface recession rate and interior temperature distribution is necessary. Also, numerical solution of governing equation for non-charring material ablation is presented in order to anticipate the recession rate and the heat response of non-charring heat shields. the governing equation is nonlinear and the Newton- Rafson method along with TDMA algorithm is used to solve this nonlinear equation system. Using Newton- Rafson method for solving the governing equation is one of the advantages of the solving method because this method is simple and it can be easily generalized to more difficult problems. The obtained results compared with reliable sources in order to examine the accuracy of compiling code.

Keywords: Ablation rate, surface recession, interior temperaturedistribution, non charring material ablation, Newton Rafson method.

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Authors: L. Nikakhtar, S. Zare

Abstract:

One of the main practical difficulties attended with tunnel construction is related to underground water. Uncontrolled water behavior may cause extra loads on the lining, mechanical instability, and unfavorable environmental problems. Estimating underground water inflow rate to the tunnels is a complex skill. The common calculation methods are: empirical methods, analytical solutions, numerical solutions based on the equivalent continuous porous media. In this research the rate of underground water inflow to the Tabriz metro first line tunnel has been investigated by numerical finite difference method using FLAC^2D software. Comparing results of Heuer analytical method and numerical simulation showed good agreement with each other. Fully coupled and one-way coupled hydro mechanical states as well as water-free conditions in the soil around the tunnel are used in numerical models and these models have been applied to evaluate the loading value on the tunnel support system. Results showed that the fully coupled hydro mechanical analysis estimated more axial forces, moments and shear forces in linings, so this type of analysis is more conservative and reliable method for design of tunnel lining system. As sensitivity analysis, inflow water rates into the tunnel were evaluated in different soil permeability, underground water levels and depths of the tunnel. Result demonstrated that water level in constant depth of the tunnel is more sensitive factor for water inflow rate to the tunnel in comparison of other parameters investigated in the sensitivity analysis.

Keywords: Coupled hydro mechanical analysis, FLAC2D, Tabriz Metro, inflow rate.

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