armin aziminejad

Civil structures inevitably undergo damage over time due to various reasons such as environmental changes, material aging, load variations, and insufficient maintenance. Monitoring these structures, especially aging ones, is crucial to detect damage early on and implement suitable retrofitting measures, ensuring their continued safe and reliable operation without unexpected failures. Consequently, there has been significant research in this field, focusing on damage detection in both simple and complex structures. Health monitoring of highway bridges is essential for achieving a reliable transportation system. The vibration-based damage detection method uses changes in the vibrational properties of structures to detect damages and ensure a healthy state. In this study, the absolute value of the modal flexibility damage index and the modal strain energy damage index simultaneously are utilized to prevent unsafe decisions. These absolute values of modal strain energy and flexibility damage indexes are utilized as the bases for training deep neural networks (DNNs). These indexes are applied to provide safe decisions and reliable damage evaluation in steel girder of the highway bridges. The convolution neural network (CNN) is utilized for damage quantification estimation. The CNN is one of the deep learning models that can currently be applied in 2D dominant approaches, such as pattern recognition and speech recognition. In addition, these networks can utilize the 1D time domain and vibrational signal data via the convolutional layer. The initial stage of CNN model comprises combined convolutional and pooling layers that apply different filters to extract features. Following this, fully connected layers, similar to a hidden layer of a multilayer perceptron are incorporated. Ultimately, these layers are classified together with a softmax layer. The convolution layer acts as a filter that convolutes the input layer with a set of weights, adding bias and applying an activation function to the outcome. Gradient descent momentum methods (SGDM) can be employed to optimize the parameters in CNN network architecture. SGDM estimates the gradient with high velocity in any dimension. This method mitigates issues such as jittering and saddle points by utilizing high-velocity inconsistent gradient dimensions and the SGD gradients, respectively. Additionally, when the Current gradient approaches zero, the SGDM provides some momentum. The convolution neural network is trained to utilize damage indexes obtained from numerical simulation of the validated finite element model of the bridge. The damage indexes as the inputs for the neural network, which are achieved from different damage scenarios. Once network training and validation are completed, a well-trained neural network is used to detect, localize, and quantify the intensity of unknown damages. The proposed method overcomes previous damage detection problems such as false positive indications, the unreliability of a single damage index, and insufficient precision in determining the intensity.  The results revealed that the presented method, based on the dual updated damage indexes and CNN, practically and accurately identified unspecified single damages' location and severity in multi-span beams. The new training method of deep neural network systems overcomes some shortcomings in ANN. Moreever, this deep neural network training scheme can reduce the need for huge amounts of input data and enhance the accuracy of network training. The method is capable in predicting single damage scenarios in steel beam.

Masonry arch bridges are built using masonry materials such as brick or stone with or without mortar. Their mechanical properties due to the variety of materials used, the quality of construction, and the effect of the passage of time can be inconstant and have significant uncertainties. Therefore, to ensure the ability and performance of the structure against the loads, especially earthquakes, adopting more accurate modeling methods and considering these uncertainties is fundamental issue of structural engineering. For a stone arch bridge of Iran's railway network, the mechanical properties of the materials including the normal and shear stiffness coefficient of the stone block joint as well as the internal friction angle of the joints were considered as quantities with uncertainty and as random variables. According to the discrete environment of the bridge, incremental dynamic analysis has been performed under the influence of eleven selected earthquake records using the discrete element method. After analyzing more than 2,600 bridge samples with different material properties, based on the response surface method, the limit state functions of the bridge failure in terms of three random variables have been determined for all records. Using FORM and MSC reliability methods, the reliability index and probability of bridge failure were calculated. The results showed that for the selected earthquake records, the spectral acceleration of the bridge collapse threshold were reduced by 30% to 50% considering the uncertainties compared to the case where the uncertainty in the materials is not considered.

Modern damage-free systems are part of modern lateral seismic structures. These structures have minimal residual displacement and dissipate earthquake energy through replaceable fuses. self -centering rocking steel braced frame systems that have been investigated in this research are considered among these modern seismic systems. In self-centering rocking structures as well as other tall structures, the effect of higher modes can cause irreparable damages in the structure. In this research, an attempt has been made to reduce the effects of higher modes by using buckling restrained columns and braces (BRCs and BRBs) as energy dissipating fuses instead of standard columns and braces in self -centering rocking structures. Five 12-story structures were investigated, including;self -centering rocking steel braced frame system and four other structure with placement of BRBs and BRCs at the base, one-third, middle and three-quarter of the height. To investigate the seismic behavior of these structures, several analyses has been performed in OpenSees software under 22 far field records according to FEMA P695. Geometric and material nonlinearities is considered in the modeling. The results show the improvement of the seismic performance and the reduction of the effects of higher modes in the case of using BRBs and BRCs in the stories, compared to the case of the common self-centering rocking bracing system.

One of the important issues in the vibration analysis of rail structures is to investigate the effect of train movement and the variable location of the load. This research introduces a new model to provide the ability to investigate 3D stress during analyzing a linear model. This model includes 6 degrees of independent transitional and rotational freedom, and one dependent degree of freedom as Warping to analysis the effect of moving loads. So, the interaction of the independent degrees of freedom has been considered due to the asymmetry of the cross section, especially in the earthquake load conditions. Finally, using a numerical Mathcad programing model, some of the parameters that are effective in modelling and vibrational analysis of rails have been examined. One of the important achievements of this study is to prove the effect of rail vibration acceleration on the characteristics of the analysis model as well as the need to determine the length of the computational model based on the results of the rail vibrational acceleration and its processing at the end of the rail. According to the formulation performed, stiffness and damping matrix are asymmetric, because of the velocity and acceleration vector effect of the load, however the mass matrix remains symmetrical. Also, by creating initial sinusoidal displacement conditions on the system, the conditions of corrugation phenomena can be expressed. The seismic acceleration applied to the model to evaluate the relevant freedom degrees and determinate the permanent deformation is considered in the model. It indicates the presence of permanent twisting and warping values in the rail-beam model, is about 40-50% of the maximum value. According to this investigation, the determination of the boundary conditions based on the damping of the acceleration at the end of the rail is very effective in calculating the results more accurately.

In 1994, Northridge, California, an earthquake created brittle fractures and cracks near the beam-to-column connection welds in more than 170 steel MRF buildings. In many cases, these fractures and cracks were observed in the beam without any signs of plastic deformation. Since connections are one of the most important components of a building frame, a good understanding of the structural behavior of connections and sufficient knowledge of how it is transmitted is a prerequisite for designing a safe connection. Steel moment frame structures to resist the earthquakes are designed based on the assumption that they can resist yield or plastic deformation without reducing strength. The plastic deformation involves the plastic rotations of the beams at their connection to the columns and theoretically resulting in the loss of seismic energy applied to the structure. All the modifications proposed in recent years for the moment connections are aimed at shifting the maximum plastic capacity or ductility demand from the end of the beam or connection zone and transferring the ductility demand to an area within the beam and away from the column. On the other hand, the details of seismic moment connections provided in FEMA351 can be classified into two groups: a- Connection zone strengthening methods; b- Reduced beam methods. There are different types of the connections presented with the idea of ​​strengthening the connection zone; for example, we can refer to the connection with welded cover plates to the flange, the connection with the side plate, the connection with the screwed seat, the connection with the welding muscle, etc. However, the connections provided and used with the idea of ​​reducing the beam are more limited, such as RBS or reduced section beam connection, free-flange beam connection, sheared beam-to-web connection, and reduced beam-to-web connection. RBS connections form a plastic hinge outside the connections site and reduce force and moment at the connection, and is one of the pre-confirmed rigid connections after the 1994 Northridge earthquake. One method of building RBS connections is to use a connection of beam with a reduced section by replaceable links. The use of these replaceable links is one of the methods to increase the ductility and transfer the plastic hinge into the reduced area of ​​the beam. In these connections, the goal is to displace the plastic hinge into the reduced area of ​​the beam at a certain distance from the column, so in these connections, moving the plastic hinge away from the column reduces the concentration of strain in the welded zone. As a result, it reduces the weld cracking rate and thus reduces brittle failure in the connections.Connection of the reduced beam section was proposed after damage to structures in the 1994 Northridge earthquake. This connection reduces the damage caused to the panel zone by forming a plastic hinge outside the beam-to-column connection area. In this research, we investigate in a laboratory a new type of beam section connection, which in recent years has been named as replaceable links. Among the links designed in the first laboratory sample, the semicircular cutting method on the flange of the replaceable beam was used to reduce the finding, and in the second sample, circular holes in the flange of the sample were used to reduce the beam section. Studies have shown that high stress concentration occurs in the reduced area and other parts of the beam and column elements will remain without significant stress, which makes the beam replaceable after an earthquake. Analytical results show that the link with reduction by creating a hole in the flange has more energy absorption and ductility than the link with reduction by cutting a semicircle in the flange of the link beam. Also, according to the maximum amount of time recorded in the samples and referring to the existing regulations in the design of structures, it can be stated that both samples are among the allowable connections in a special moment frame.

Self-centering controlled rocking steel braced-frame (SC-CR SBF) is an innovative seismic resistant system that reduces structural earthquake damages compared with conventional structural systems. In addition, the self-centering behaviour could reduce or eliminate building residual deformation and simplify the required repair after an earthquake. These benefits make this system an ideal alternative for conventional lateral force resisting systems such as moment-resisting frames or shear walls. Along with this issue, asymmetric structures are more vulnerable to earthquake excitations and require special seismic design considerations. Therefore, in this study, it is tried to improve the seismic behaviour of asymmetric SC-CR-SBF systems with proper distribution of strength. In this regard, the behaviour of low-rise uni-directional mass asymmetric SC-CR-SBF buildings is studied under bi-directional horizontal ground motions using OpenSEES software. The results show that the appropriate distribution of the strength of SC-CR SBFs in the plan reduced adverse torsional effects and based on these distributions, the proper configuration of mass and strength centers is introduced. Finally based on the results with appropriate arrangement of the centers, the maximum drift of the asymmetric structure decreases as much as roughly 14%. In other words, the maximum drift of the asymmetric SC-CR-SBF buildings of this study are acceptably close to the symmetric case.

Bridges are exposed to various micro and small damages during their service life. Due to the importance and role of these structures in transportation on roads, timely detection of damages in them has a special place. This research presents an innovative and efficient method for diagnosing and estimating micro and small damages to bridges. The proposed method is based on the combination of spectral finite element and modal strain energy-based damage index to determine the location of damages in the first step. Then the support vector regression technique is used to estimate the severity of damages in the second step. A new eight-node element with spectral finite element characteristics is defined in OpenSees software. Then, micro and small damages are modeled in a single-span beam and a double-span steel beam with spring supports. In the first step, after modal analysis of the structures, the modal strain energy-based damage index is calculated to determine the location of the damages. In the second step, using the modal strain energy-based damage indices calculated in the previous step, the support vector regression networks are trained to estimate the severity of the damages. The results show very high accuracy and optimal performance of the proposed method.

In most current seismic codes, the stiffness and strength of seismic members are considered to be independent, so that a change in the strength of the members does not result in a change in the stiffness of the members. Recent studies show that these parameters are interdependent. Therefore, the way these parameters are calculated and the arrangement of centers of mass, stiffness and strength can be effective in determining the seismic response. In this research, buildings with different levels of normalized yield eccentricity (ed/A) were designed according to the ASCE/SEI 07-22 seismic code (Code Design models) and compared with the Balance-25% and Symmetric Strength models. The results of the nonlinear static analysis and incremental dynamic analysis showed that the average spectral acceleration at the level of collapse in the Balance-25% and Symmetric Strength models increased by approximately 18% compared to the Code Design model. Therefore, these models are safer than the Code Design model. In addition, the average of the peak rotation of floors and the maximum inter-story drift at the collapse level in the Balance-25% and Symmetric Strength models has decreased by 100% and 12% respectively compared to the Code Design model. Therefore, the Code Design model had the lowest and the Balance-25% and Symmetric Strength models had the highest dynamic seismic performance.

Because unreinforced welded connections (WUFs) were brittle and prematurely fractured in the 1994 Northridge earthquake in the area of penetrating welds in the beam-to-column connection, the researchers proposed RBS connections to improve the seismic behavior of rigid connections. The brittle failure of weld in the beam-to-column connection and the lateral buckling of the beam flange in the reduced sections of the beam flange led to the proposed modified forms of this type of connection. The new type of connection includes drilled flange connection (DFC) with parallel rows of holes. In order to improve the performance of these DFCs, in this study, beam flange drilling arrangements were used with an inclined arrangement of holes with different hole diameters. The study showed that in the inclined arrangement of a hole, the amount of plastic rotation is 0.059 radians, which is 7.3% more than the plastic rotation of the same RBS connection. Also, in the connection sample DFC7 with the most suitable oblique drilling arrangement, the equivalent plastic strain index in the center and corner of the penetration welding line has decreased to 92.3% and 87.7%, respectively, compared to conventional RBS connections. Mises index in this connection in the center and corner of the penetration welding line has decreased to 45.5% and 39.9% compared to RBS connections, respectively, indicating better performance and less sensitivity of this type of connection to the problems of the penetration welding area of the beam-to-column connection compared with conventional RBS connections and DFC connections with the parallel arrangement.

Seismic intensity measures (IMs) perform a pivotal role in probabilistic seismic demand modeling. Past studies investigated appropriate IMs for structures, including the vital component of the transportation system, the highway bridges. These studies were mainly focused on far-field earthquakes and did not consider the strong vertical component of ground motions in near-field earthquakes.  In order to evaluate the optimal IMs for the multi-span continuous concrete box girder bridges subjected to near-field earthquakes, ten sample bridges were modeled and then subjected to three-component records of 164  near-field earthquakes applying the OpenSees software framework. In the present research, 5 engineering demand parameters considering the most critical response parameters related to columns and deck were selected, along with 24  intensity measures considering the horizontal and vertical components of ground motions. Base on the optimality investigation method, parameters such as efficiency, practicality, proficiency, sufficiency, and relative sufficiency were considered. In total, 8200 nonlinear time-history analyses were conducted. The results presented that the peak ground velocity of the horizontal component (PGVH), velocity spectrum intensity of the horizontal components(VSIH), and Housner intensity of horizontal components (HIH) were the optimal intensity measures, and vertical component of ground motions in near-field earthquakes should be considered in optimality investigation.

Conventional earthquake-resistant systems, often experience inelastic behavior in a part of the structure during a large earthquake and eventually causing residual deformation and damage to the structure. Repairing these damages are unaffordable and often leads to structure destruction. Therefore, the use of structures with the ability to focus damage on interchangeable elements, which leads to reduced earthquake damage, is very important. Due to the importance of the performance of self-centering structures to reduce their damage against various earthquakes, in this study, the repairability index of buildings with post-tensioned self-centering connections has been developed. According to the 12 models of the studied building, a building that can be repaired, that the maximum rotation in its connection after the earthquake does not exceed the rotation of the immediate occupancy performance. Based on this, the output data of IDA analysis in OPENSEES were drawn according to the connection rotation-spectral acceleration. According to the predicted performance levels of Garlock for each acceleration level, the value of the connection opening is divided by the opening of the DBE level. The resulting curve shows the repairability index according to spectral acceleration, which if less than one, the repairability target is achieved. To evaluate the damage of angles, the failure index of the angle is determined according to the fragility curve and the intensity of damage in each building is expressed according to an equation.

The linked column frame (LCF) as a seismic resistant system with the ductile behavior using shear fuse will reduce the damage to other members of the structure at different hazard levels. In this paper, the seismic behavior of the LCF systems designed by Shoaib and Malakoutian procedures has been evaluated. In order to improve the seismic performance of the designed samples, a new and optimal system with the pattern of the double linked columns has been proposed. For this purpose, a 3-story model of SAC buildings with two linked beam bays and four- moment frame bays has been designed by the procedures. The studied models include: 1-The model designed by Malakoutian procedure (MaM), 2- The model designed by Shoaib procedure (ShM) and 3- The LCF with double-linked column pattern (DLCF). Models have been evaluated using incremental dynamic analyses according to FEMAP695 instructions in OPENSEES. The results show that the model designed by Shoaib procedure (ShM) has “50%” and 14% more capacity than the model designed by Malakoutian procedure and the DLCF model respectively. Also the average link beam capacity in the ShM model is “50%” higher than the MaM model. Finally the results show that compared to the MaM model the new pattern of the linked column in the DLCF model has considerably increased the structure’s capacity, the link beam capacity in energy absorption and base shear capacity by an average of 30%.

Traditional earthquake-resistant systems are dependent on the inelastic response of the building members. These systems experience significant residual displacements after major earthquakes due to seismic energy distribution all over the building and make their repair uneconomical. Self-Centering systems in steel frame buildings omit residual displacements and concentrate building damage on Self-Centering connection and reduce the cost of repair. Due to the dispersion of the response of Self-Centering systems against different earthquakes, it is necessary to determine an index to control sensitivity of these systems against various records. In this paper, developing an efficiency index of steel moment frame systems with Self-Centering connections using the dispersion index's methodology is discussed. After performing the time history dynamic analyses of two steel buildings with 3 and 9 floors, six types of self-centering connections for each frame with seven dispersion indices were evaluated. Decreased dispersion of responses indicate that the system is more efficient. Among these, under the optimization of indices, it is tried to select an index with a better performance which resulted to CV index (coefficient of variation). Finally, the structure with the least dispersion of responses is selected from the viewpoint of efficiency. The selected model of this research for 3 and 9 story buildings is model M5 which is the fifth model of Moradi models.*

Nonlinear time history analysis is recognized as the most appropriate tool for assessing the real behaviour of structures during seismic excitations. Validity rate of obtained results from this analysis significantly depends to the modeling, details and defined parameters. One of the main aspects of dynamic modeling is the consideration of natural viscous damping as well as value of damping ratio (ξ), which during last years evaluating the effects of these factors on nonlinear responses of moment-resisting steel frames has been limited, and Rayleigh damping model with ξ of 5% was used by researchers. Therefore, in this study attempt has been made to examine the impacts of value and modeling approach of natural damping on nonlinear responses of moment-resisting steel frames. For this purpose, a full scale 4 story steel structure which tested on shake table in 2007 has been considered as reference and modeled by OpenSees software. Natural damping has been defined with three methods; Rayleigh damping, mass-proportional damping and stiffness-proportional damping, for five different values of damping ratio (ξ=0.01, 0.02, 0.03, 0.04, 0.05). After conducting the nonlinear time history analyses, difference of obtained structural responses compared to the experimental responses has been investigated, and then errors of them have been extracted. Results indicate that reduce of damping ratio leads to the notable decrease of responses, specially, for story shear and overturning moment. The use of 5% damping ratio for nonlinear dynamic analysis of low rise moment-resisting frames is not appropriate and in most of cases leads to the underestimate and unreal results. Besides, it should be noted that the mass-proportional and Rayleigh damping models have higher accuracy in comparison with stiffness-proportional damping model, and these models show lower error.

Considering the high importance of energy-carrying buried pipelines in lifeline network, it is vital to understand this kind of structures against seismic dynamic excitations. In this paper, seismic behavior in some part of a buried pipe with horizontal bend under Bam earthquake record effect (2003, Iran) is studied experimentally and numerically using ABAQUS software. In the numerical model, the pipe is modelled via a three-dimensional four-node shell system, and the soil is modeled using elastoplastic properties.As non-linear dynamic analysis, with applying Bam earthquake record effects, a thorough parametric studied are performed on different pipe diameter and thicknesses, and then the axial strain and plastic strain values obtained from the strain gauges along the horizontally-bent pipe are compared with the numerical model results.Also, a correlation is obtained which relates the location of plastic hinge formation point on the pipe to the pipe diameter and thickness. The comparison of numerical model and experimental results show that in buried horizontally-bent pipes, the most axial strain, plastic strain, and stress in the pipe take place in the fixed wedge and near to the fault line. In the buried horizontally-bent pipes, with increasing the pipe diameter to thickness ratio this location will get more distance from the fault line.Also, the pipelines with larger diameters have lower pipe-soil strain ratio (εp/s) values causing lower axial and plastic strains.

Due to the lack of access to the data of three rotational components of earthquakes, seismic analysis of new buildings as well as assessment of the vulnerability of existing structures are usually carried out only by applying the translational components of earthquakes. Iranian Standard 2800 proposed an accidental eccentricity for considering the earthquake rotational component effect in the seismic analysis of building structures. The present investigation is focused on the effects of earthquake rotational excitation on the seismic response of buildings having various dynamic properties which situated on a rigid foundation. In addition, adequacy of the accidental eccentricity of 5% recommended by seismic design code for inclusion of the earthquake rotational component impact in the non-linear time history analysis of buildings is studied, as well. To achieve this, a large number of one-story torsionally stiff and flexible building models with a wide range of lateral vibration periods (T=0.05 to 2sec) and three different values of inherent eccentricity of 0, 15 and 25% were modeled. These models were once excited by the translational components of ground motions and once again by both translational and rotational components of ground motions. The building models were re-analyzed after applying the 5% accidental eccentricity based on the procedure presented by Standard 2800 (shifting the center of mass in the negative and positive directions by 0.05 of the plan dimension). For conducting the non-linear time history analyses, a number of earthquakes were selected and the rotational records for these events were generated by use of an indirect single station method based on the seismic wave propagation in an elastic and homogeneous medium. In total, over than 2600 nonlinear dynamic analyses have been conducted in this numerical research. In order to determine the role of earthquake rotational excitation in the seismic behavior of  buildings, the variations of displacement response for the left and right sides of diaphragm and the torsion of diaphragm about the mass center due to the effect of rotational component were evaluated. By comparing the results obtained in this study, it is found that the rotational component has a substantial influence on the structural responses, which this effect is a function of the fundamental dynamic characteristics of system such as uncoupled rotational to translational frequency ratio, lateral vibration period and irregularity. The displacement of diaphragm can be increased up to 50% when the rotational component of ground motion is included in the seismic load combinations. Decreasing the frequency ratio leads to increase of the rotational component effect for the stiff buildings with short periods, while in the other cases reduces the growth of displacement due to the rotational component. Furthermore, results indicate that the accidental eccentricity of 5% cannot increase the seismic responses as much as the earthquake rotational motion, and leads to unreal and underestimate results for the most of lateral vibration periods. Thus, the current Standard 2800 approach cannot be considered as an appropriate alternative for considering the accidental torsion induced by the rotational component of ground motion, and it seems that this approach needs to be re-evaluated.

Lightweight steel structures (LSFs), which are manufactured dry and manufactured using industrial production and cold rolling (CFS). For carrying the side loads in cold-rolled structures, belt braces or shear walls are used. . Considering that the weight of the materials, the preparation and implementation of the wall is a limiting factor for its use in the repair of the frames. Determining the proper makeup that reduces the use of wall panels can be a significant factor in improving the performance of the frames in improving and framing the frames. The sample of the laboratory chosen to examine the performance of the LSF lightweight steel frame system and the accuracy of the modeling in the ABAQUS software includes a LSF light steel frame system, tested by Bin Liu et al. (2016). For this purpose, the frame reinforced samples were categorized in three general categories, including a non-reinforced sample, a braided braid, a double-row braid, and a 45-degree reinforced sample under a monotonic loading, comparing the results obtained from the sample analysis With non-reinforced specimens, it was found that the bearing capacity of the reinforced frame with double-row double-row multi-row bricks was close to the full 45-degree frame. Use of higher yielding steel increased the static strength and earth-impact resistance of the bracing, but the ability The energy absorption reduces it. Use of 45 ° steel sheets adds an extra Its shape is framed.

Moment-resisting frames have extensive usage in earthquake-prone areas and high ability in energy dissipation.After the earthquake in Northridge 1994,Kobe 1995 fixed connections of steel structures have shown poor performance and generally they were caught brittle fracture of beam flange weld to the column.In order to remedy to avoid similar situations in future earthquakes,researchers introduced connection with reduced beam section in name of RBS(Reduced Beam Section),that stress concentration at the junction can be prevented by reducing the local section of beam in the vicinity column and location of plastic hinge transferred from connection to the distance from the column.
In this research, firstable the three special steel moment-resisting frames of three-dimension 5,10 and 15 story with seismic compressed sections as RBS was analyzed as time history by using SAP software at the near and far field earthquakes with and without considering the effect of vertical component,then a critical connections in each of the frames was modeled by ANSYS software and it was analyzed as dynamic under obtained loads from each record(in SAP).
The study results showed that the vertical component put negative effects on the performance of this type of connection in terms of concentration of stress, strain and ductility.It is necessary to say that the negative effect of the vertical component on the connections at near field earthquakes was comparatively more than at far field earthquakes.

In this paper، a new method is presented to find tunnel target racking displacement in the earthquake considering nonlinear behavior of lining and soil and also soil- structure interaction. In the next step tunnel racking reduction factor has been evaluated for an incomplete ellipse tunnel located in two soil types، A and B، with overburden depth of 5 and 20 m by performing nonlinear static analysis. Finally، to verify the values of racking reduction factors، tunnel responses obtained by linear static analyses reduced by the calculated values of racking reduction factor are compared with responses obtained by nonlinear dynamic analyses. Design and analysis of the underground structures such as tunnels are performed on the basis of structure and ground deformations because the seismic response of such structures is very sensitive to the imposed ground deformations. In recent years، Several researches have indicated the importance of the harmful effects of earthquakes on tunnels and underground structures. Methodology and Approaches: In this paper، by combining Wang (1993) and Hashash (2000) methods in determination of tunnel target racking displacement and using the trial and error method to correct tunnel structure stiffness، possibility of redistribution of the forces and deformations became possible and it was tried to present a comprehensive method to determine the tunnel target racking displacement. In the next step، by using the force-racking displacement curve and applying the existing equations of reduction factors of the structures and their generalization for tunnels and underground structures and considering the soil-structure interaction، tunnel racking reduction factor is estimated. Then، using ABAQUS software، a comparison has been performed between dynamic and static forces in the tunnel lining. Results and Comparison of lining force (bending moment and axial force) between linear static analyses modified by tunnel racking reduction factors and nonlinear time history analyses shows that the accuracy of achieved tunnel racking reduction factors is acceptable. The studies also show that implementing linear static analyses without tunnel racking reduction factor leads to very conservative results of lining force in tunnel. Nonlinear time history dynamic analyses are time consuming and complicated in modeling procedure and analysis duration. Thus، By using the proposed racking reduction factors، Linear static analyses could be an alternative for nonlinear dynamic analyses with a suitable accuracy.