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I‌n t‌h‌e p‌r‌e‌s‌e‌n‌t s‌t‌u‌d‌y, t‌h‌e e‌f‌f‌e‌c‌t o‌f e‌a‌r‌t‌h‌q‌u‌a‌k‌e o‌n t‌h‌e c‌r‌a‌c‌k p‌r‌o‌p‌a‌g‌a‌t‌i‌o‌n o‌f S‌e‌f‌i‌d‌r‌u‌d d‌a‌m i‌s p‌r‌e‌s‌e‌n‌t‌e‌d u‌s‌i‌n‌g t‌h‌e c‌o‌n‌c‌e‌p‌t o‌f d‌y‌n‌a‌m‌i‌c f‌r‌a‌c‌t‌u‌r‌e m‌e‌c‌h‌a‌n‌i‌c‌s. A‌f‌t‌e‌r t‌h‌e i‌n‌t‌r‌o‌d‌u‌c‌t‌i‌o‌n o‌f d‌i‌s‌p‌l‌a‌c‌e‌m‌e‌n‌t a‌n‌d t‌r‌a‌c‌t‌i‌o‌n b‌o‌u‌n‌d‌a‌r‌y i‌n‌t‌e‌g‌r‌a‌l e‌q‌u‌a‌t‌i‌o‌n‌s, t‌h‌e d‌u‌a‌l b‌o‌u‌n‌d‌a‌r‌y e‌l‌e‌m‌e‌n‌t m‌e‌t‌h‌o‌d a‌n‌d m‌u‌l‌t‌i r‌e‌g‌i‌o‌n b‌o‌u‌n‌d‌a‌r‌y e‌l‌e‌m‌e‌n‌t m‌e‌t‌h‌o‌d a‌r‌e m‌i‌x‌e‌d t‌o s‌i‌m‌p‌l‌i‌f‌y t‌h‌e m‌o‌d‌e‌l‌i‌n‌g o‌f c‌o‌m‌p‌l‌i‌c‌a‌t‌e‌d c‌o‌n‌f‌i‌g‌u‌r‌a‌t‌i‌o‌n o‌f b‌u‌t‌t‌r‌e‌s‌s d‌a‌m‌s. S‌e‌i‌s‌m‌i‌c c‌r‌a‌c‌k p‌r‌o‌p‌a‌g‌a‌t‌i‌o‌n o‌f b‌u‌t‌t‌r‌e‌s‌s N‌o.15 o‌f S‌e‌f‌i‌d‌r‌u‌d d‌a‌m i‌s a‌n‌a‌l‌y‌z‌e‌d u‌s‌i‌n‌g t‌h‌e p‌r‌o‌p‌o‌s‌e‌d m‌i‌x‌e‌d m‌e‌t‌h‌o‌d. D‌i‌f‌f‌e‌r‌e‌n‌t p‌a‌r‌t‌s o‌f t‌h‌e d‌a‌m b‌o‌d‌y a‌n‌d d‌y‌n‌a‌m‌i‌c c‌r‌a‌c‌k p‌r‌o‌p‌a‌g‌a‌t‌i‌o‌n c‌a‌n b‌e m‌o‌d‌e‌l‌e‌d e‌a‌s‌i‌l‌y w‌i‌t‌h r‌e‌g‌a‌r‌d t‌o s‌i‌m‌u‌l‌t‌a‌n‌e‌o‌u‌s a‌p‌p‌l‌i‌c‌a‌t‌i‌o‌n o‌f b‌o‌u‌n‌d‌a‌r‌y e‌l‌e‌m‌e‌n‌t m‌e‌t‌h‌o‌d a‌n‌d m‌u‌l‌t‌i-d‌o‌m‌a‌i‌n d‌u‌a‌l b‌o‌u‌n‌d‌a‌r‌y e‌l‌e‌m‌e‌n‌t m‌e‌t‌h‌o‌d. A‌l‌s‌o, n‌e‌w e‌l‌e‌m‌e‌n‌t‌s a‌r‌e a‌d‌d‌e‌d t‌o t‌h‌e p‌r‌e‌v‌i‌o‌u‌s e‌l‌e‌m‌e‌n‌t‌s i‌n t‌h‌e c‌r‌a‌c‌k g‌r‌o‌w‌t‌h m‌o‌d‌e‌l‌i‌n‌g, w‌h‌i‌c‌h c‌a‌u‌s‌e‌s t‌h‌e r‌e‌d‌u‌c‌t‌i‌o‌n o‌f c‌a‌l‌c‌u‌l‌a‌t‌i‌o‌n t‌i‌m‌e. S‌e‌v‌e‌n c‌a‌s‌e‌s b‌a‌s‌e‌d o‌n t‌h‌e l‌e‌v‌e‌l a‌n‌d l‌e‌n‌g‌t‌h o‌f i‌n‌i‌t‌i‌a‌l c‌r‌a‌c‌k‌s i‌n t‌h‌e b‌o‌d‌y o‌f t‌h‌e d‌o‌w‌n‌s‌t‌r‌e‌a‌m w‌a‌l‌l i‌s c‌o‌n‌s‌i‌d‌e‌r‌e‌d. T‌h‌e t‌i‌m‌e d‌o‌m‌a‌i‌n a‌n‌a‌l‌y‌s‌i‌s f‌o‌r s‌t‌a‌b‌l‌e c‌r‌a‌c‌k c‌o‌n‌d‌i‌t‌i‌o‌n i‌s c‌o‌n‌s‌i‌d‌e‌r‌e‌d i‌n t‌h‌e c‌a‌s‌e A. I‌n o‌t‌h‌e‌r c‌a‌s‌e‌s (B, C, D, E, F a‌n‌d G), a‌n‌a‌l‌y‌s‌i‌s a‌r‌e p‌e‌r‌f‌o‌r‌m‌e‌d f‌o‌r d‌i‌f‌f‌e‌r‌e‌n‌t u‌n‌s‌t‌a‌b‌l‌e c‌r‌a‌c‌k c‌o‌n‌s‌i‌d‌e‌r‌i‌n‌g t‌h‌e c‌r‌a‌c‌k g‌r‌o‌w‌t‌h a‌n‌d c‌r‌a‌c‌k f‌a‌c‌e‌s c‌o‌n‌t‌a‌c‌t. T‌h‌e e‌f‌f‌e‌c‌t o‌f i‌n‌i‌t‌i‌a‌l c‌r‌a‌c‌k l‌e‌n‌g‌t‌h o‌n t‌h‌e c‌r‌a‌c‌k p‌r‌o‌p‌a‌g‌a‌t‌i‌o‌n i‌n t‌h‌e S‌e‌f‌i‌d‌r‌u‌d d‌a‌m c‌a‌n b‌e o‌b‌s‌e‌r‌v‌e‌d b‌y c‌o‌m‌p‌a‌r‌i‌s‌o‌n o‌f c‌a‌s‌e‌s B, C a‌n‌d D. W‌h‌e‌n l‌a‌r‌g‌e‌r i‌n‌i‌t‌i‌a‌l c‌r‌a‌c‌k l‌e‌n‌g‌t‌h i‌s c‌o‌n‌s‌i‌d‌e‌r‌e‌d, t‌h‌e c‌r‌a‌c‌k r‌e‌a‌c‌h‌e‌s t‌o t‌h‌e b‌o‌d‌y o‌f u‌p‌s‌t‌r‌e‌a‌m w‌a‌l‌l b‌e‌f‌o‌r‌e t‌h‌e m‌a‌i‌n s‌h‌o‌c‌k o‌f a‌c‌c‌e‌l‌e‌r‌a‌t‌i‌o‌n r‌e‌c‌o‌r‌d‌s. F‌o‌u‌r c‌a‌s‌e‌s D, E, F a‌n‌d G a‌r‌e a‌n‌a‌l‌y‌s‌e‌d f‌o‌r c‌a‌m‌p‌a‌r‌i‌s‌o‌n o‌f i‌n‌t‌i‌a‌l c‌r‌a‌c‌k l‌e‌v‌e‌l. T‌h‌e r‌e‌s‌u‌l‌t‌s o‌f t‌h‌e p‌r‌e‌s‌e‌n‌t s‌t‌u‌d‌y a‌r‌e i‌n g‌o‌o‌d a‌g‌r‌e‌e‌m‌e‌n‌t w‌i‌t‌h t‌h‌e o‌b‌s‌e‌r‌v‌e‌d c‌r‌a‌c‌k p‌r‌o‌f‌i‌l‌e‌s o‌f t‌h‌e d‌a‌m a‌f‌t‌e‌r t‌h‌e e‌a‌r‌t‌h‌q‌u‌a‌k‌e. B‌u‌t i‌t i‌s w‌o‌r‌t‌h t‌o m‌e‌n‌t‌i‌o‌n t‌h‌a‌t a 3D a‌n‌a‌l‌y‌s‌e‌s i‌s p‌r‌e‌f‌e‌r‌r‌e‌d f‌o‌r a b‌e‌t‌t‌e‌r s‌i‌m‌u‌l‌a‌t‌i‌o‌n.

Topography magnification effects and the surroundings of structures had has an important role in their destruction after earthquakes. In this article, dynamic interaction of morning glory spillway of Barzu dam placed in Shirvan has been investigated in the frequency domain. Due to the position of structure, the earthquake occurrence is possible in the time when no water exists around the structure. Therefore, it is an important issue to consider the dynamic interaction between the spillway and its foundation. The solving method is based on boundary element method. First the formulation of boundary element method in the frequency domain is presented and then three examples are considered for verification of the results. The first example is a cantilever beam which is presented for verification of 3D elastodynamic finite medium problems. The second example is one layered valley which is presented for verification of one layered infinite medium. The third example is alluvial valley which is presented for verification of wave propagation in multi-layered infinite domains. After the verification, the foundation domain which is placed around some part of the structure has been modeled and analyzed separately, and then a model which has 2 sub domains has been presented. In order to have a realistic analysis, the problems have been modeled and analyzed three-dimensionally. In this study, the effect of some parameters such as shape irregularities, mechanical properties of materials (density, Poisson coefficient, shear modulus), stimulation frequency, incident wave type (P, SH, SV), azimuth and angle of incident wave on dynamic analysis result of the mentioned structure is investigated. The results of dynamic interaction analyses

This paper is concerned with the investigation of the interaction of a vertically-loaded disc embedded in a transversely isotropic half-space. By virtue of transform methods, the generalized mixed boundary-value problem is formulated as a set of dual integral equations, which, in turn, are reduced to a Fredholm equation of the second kind. In addition to including existing solutions for zero and infinite embedment as degenerate eases, the present analysis reveals a severe boundary-layer phenomenon which is apt to be of significance to this class of problems in general. The present solutions are analytically in exact agreement with the existing solutions for a half-space with isotropic material properties. To confirm the accuracy of the numerical evaluation of the integrals involved, numerical results are included for cases of different degree of the material anisotropy and compared with existing solutions. Further numerical examples are also presented to elucidate the influence of the degree of the material anisotropy on the response.

Experience of the past earthquakes indicates that topographic magnification and surroundings of structure contribute to the destruction of structures after the earthquake. In this article, the dynamic interaction formulation of structures is presented. The method is based on the boundary element method in frequency domain. In order to assess the accuracy and efficiency of the proposed formulations for the dynamic interaction of structures, several problems are considered. Also, the structural analysis of morning glory spillway of Barzu dam located in Shirvan was investigated. For this purpose, every domain placed around the structure was modeled and analyzed separately, and then a model incorporating all the domains was presented.For realistic analysis, the problems were modeled and analyzed three-dimensionally. In this study, the effects of parameters such as shape irregularities, mechanical properties of materials (density, Poisson coefficient, shear modulus), stimulation frequency,incident wave type (P, SH, SV), azimuth and angle of incident wave on dynamic analysis of mentioned structure were considered.The results show that the foundation flexibility causes stiffness reduction and thus reduction of frequency vibrational modes of the system. The fluid-structure interaction brings about a high change in seismic response of the system in a way that the values of the displacements increase at frequencies lower than the 1.5 times of the first vibration mode and decrease at higher frequencies. The fluid in contact with structure increases the effective mass and reduces vibration frequencies of the system.

The formulation of simultaneous analysis of dynamic crack growth and contact of its faces in two-dimensional domain is introduced. Displacement and traction boundary integral equations and additional contact equations are used simultaneously in one region in the time domain. The proposed method has the capability of automatic modelling of crack propagation and contact of crack faces in mixed mode fractures by adding only new elements in front of crack tips. This automatic capability of simultaneous analysis of dynamic discrete crack propagation and contact problem is not enhanced in any of available commercial softwares. In order to verify the proposed method and so as to show the versatile features and capabilities of the method, dynamic crack growth of edge cracks and contact of crack faces in a T shaped plate is analysed

Due to the development of urban areas, underground structures are increasingly needed. Therefore, not only it is likely to have two tunnels located close to each other, but also it happens frequently.Because of the complexity of realistic problems, closed form analytical solutions are not accessible for them. However, latest advances in computational techniques have made numerical approaches more practical for realistic problems. Boundary element method (BEM) is one of such approaches. This technique formulates the problem in terms of boundary values. The main advantage of BEM, especially in comparison with finite element and finite difference methods, is that the discretization is only applied to the boundary, thus reducing the volume of modeling and the number of unknown variables. Moreover, the radiation condition at infinity is exactly satisfied in this method which is very striking for wave propagation problems. First the formulation of boundary element method in the time domain is presented and then a parametric study on the dynamic response of unlined circular tunnels subjected to internal explosion is done. Depth of tunnels, vertical and horizontal distance between two tunnels, diameter of tunnels, and other parameters related to geometry are important factors which can affect displacements and stresses of tunnels under explosive loading. In the present study, effect of two parameters has been investigated: changing the depth of the tunnel that is subjected to internal explosion (case A) and changing the horizontal distance between two shallow tunnels subjected to explosion (case B). Radial displacements and circumferential stresses are the results obtained. Case A- Tunnel depth: The tunnel behavior in depth of H=50R is alike to behavior of same tunnel in infinite depth. Also, radial displacement in upper point of tunnel in depth of H=2R is about 2.7 times of the same tunnel in infinite depth. Circumferential stress in points placed on horizontal diameter of tunnel in depth of H=2R is about 1.8 times of the same tunnel in infinite depth. Case B- Tunnels distance: Two tunnels with horizontal distance of greater than L=50R don’t affect each other. When horizontal distance parameter of two tunnels is L=2.5R then the maximum normalized displacement of the side point of the loaded tunnel, is approximately 2.15 times of the same tunnels with distance of infinite. Also, when horizontal distance of two tunnels is L=2.5R, circumferential stress in lower point of the loaded tunnel, which is normalized with static stress, is approximately 1.2 times of the same tunnels with distance of infinite. Normalized results calculated here display the importance of the geometric parameters on the behavior of unlined tunnels subjected to internal explosion and provide suitable criteria for displacement design of shallow tunnels that are subjected to internal explosion. The accuracy of the present study for the computation of radial displacements and circumferential stresses is verified by solving several problems.