پژوهشنامه زلزله شناسی و مهندسی زلزله
سال پانزدهم شماره 3 (پیاپی 57، پاییز 1391)

Slope stability analysis is routinely performed by engineers to evaluate the stability of embankment dams, road embankments, river training works, excavations and retaining walls. Slope stability analysis can be carried out by the limit equilib-rium method (LEM), the limit analysis method, the finite element method (FEM) or the finite difference method. By far, most engineers still use the limit equilibrium method with which they are familiar. Although the limit equilibrium method of slices does not consider the stress-strain relation of soil, it is widely used by engineers and researchers for slope stability analysis due to its simplicity and the related accumulated experiences. One of the main tasks in using the limit equilibrium method is the determination of the critical slip surface having the minimum factor of safety. Non-linear functions associated with the optimization of critical failure slip surface, a considerable number of local minimums during the process of optimization as well as, the need for a fast and efficient algorithm for generating the circular or non-circular trial slip surfaces, are the notable aspects of this complexity. In recent years, numerous modern global optimization methods have been proposed with success to solve the various types of problems, but very few of these methods have been applied to geotechnical problems. In this study, a Particle Swarm Optimization method (PSO) is developed to solve the factor-of-safety minimization problem. In this study by applying particle swarm optimization algorithm, circular and non-circular critical slip surfaces were determined in both homogeneous and non-homogeneous slopes under various static and seismic loadings. To locate the critical circular or non-circular failure surface, a trial slip surface generation algorithm is required. In this paper, the first section defines the generation of trial circular and non-circular slip surfaces and the safety factors of the general slip surfaces are calculated using a Bishop and Janbu methods. The second section briefly reviews the principle of the particle swarm optimization method as well as its specific initialization and convergence criterion. PSO is based on the simulation of simplified social models, such as bird flocking, fish schooling, and the swarming theory. This method is developed on a very simple theoretical framework and can be implemented easily with only primitive mathe-matical operators. This optimum position is usually characterized by the optimum value of a fitness function (e.g., factor of safety for the present problem). The third section applies the present method to four different types of slope analysis and compares the numerical results to previously published solutions and other famous software results. The proposed heuristic algorithm and generation of trial slip surfaces algorithm represents slip surfaces as circular and noncircular curves and solves for the optimal curve yielding the minimum factor of safety. To demonstrate its applicability and to investigate the validity and effectiveness of the algorithm, the obtained results are compared with the available softwares and the proposed algorithm is demonstrated to be effective and efficient in solving complicated problems with a high level of confidence. The calculation results show that the PSO has stronger adaptive ability, faster calculation rate and better global optimal character. The presented PSO algorithm method can be applied to find the non-circular failure surface with the lowest factor of safety very quickly compared to software’s or other methods and approaches.

Water supply system is one of the important lifelines in urban areas and its vulnerability has been proved in past earthquakes. These networks, due to their wideness of service area, and being located in various ground conditions, are subjected to several damages in the case of occurrence of major earthquakes. In addition to the direct damages of these networks, the lack of water for emergency usage like fire fighting and sanitary is an adverse consequence. These shortages lead, sometimes, in migration of affected people to other neighboring areas, which cause long lasting (months and even years) difficulties for them-selves and other people. Therefore, restoration of water systems is of great importance and any shortcoming in this regard results in dissatisfac-tion of the affected people. One of the main acts for restoration is rapid repair, and this is in turn dependent on having at hand a detailed program and action plan, without which the repair works will face delays. In this paper, by using the experiences gained from past earthquakes in Iran and worldwide, a suggested plan for undertaking the required actions for restoration of the water supply system in large cities has been discussed. At first different hazards which threat the water supply systems in earthquake prone areas, including strong ground shaking, surface faulting, landslide and lateral spread, large differential settlement, and liquefaction, have been briefly explained. Then, the performance of water systems subjected to earthquake excitations, and the causes of damages, based on the observations of the past seismic events, as well as various methods for seismic evaluation of water systems have been discussed. In the next stage, evaluation procedures, and damage indices and ratios, as well as the vulnerability models, which are used for seismic vulnerability evaluation of water supply systems, such as HAZUS model, have been explained. After that, the water supply system of Qum city, in central part of Iran, has been considered to be evaluated as a case study, and its specifications have been presented by using a GIS environment. Finally, based on the predicted condition of the city of Qum in the aftermath of a probable earthquake in this city, a detailed repair program has been suggested, in which all required phases from inspection of the network to repair the damaged parts of the system have been taken into consideration. Issues which are dealt with in this part of the paper include: a) the criteria and prerequisites for formation of the repair teams and their structures and duties, b) repair prioritization schemes for task allocation, c) establishment of repair bases in different parts of the city, d) estimation of the materials and machineries required for undertaking the repair works, and finally e) the interaction between various teams. It can be claimed that preparing repair programs based on the criteria and the procedure, given and discussed in the paper, is a crucial need for achieving a successful emergency management process in large and populated cities located in earthquake prone areas.

Floors as horizontal diaphragms and first element of lateral resisting system transfer the lateral forces to the vertical resisting elements. In conventional methods of analysis and design of structures, horizontal diaphragms are typically assumed to be rigid and distribute the horizontal forces to the vertical lateral load resisting elements in proportion to their relative stiffness. In addition, this assumption is often used to reduce the degrees of freedom and simplifies seismic analysis of buildings. Although this assumption may be justified for many structures, but for some types of structural systems, the effect of diaphragm deformability cannot be disregard and the floors behave as semi-rigid diaphragms and the actual force distribution between vertical lateral load resisting elements is not proportion to relative stiffness of vertical elements. In braced steel structures with block-joist floor, the vertical components consist of braces with high story stiffness and the floors in one direction may have less rigidity in their own planes. Furthermore, inaccurate modelling of flexibility of floor diaphragms leads to misestimating of building seismic response and unsafe design of vertical lateral load resisting elements such as braces. The main objective of this study is to evaluate the impact of in-plane diaphragm flexibility on the seismic response of steel braced buildings with block-joist floors in linear and nonlinear regions using a performance-based approach. In order to investigate the diaphragm effect on the seismic response of buildings; one story, three stories and five stories buildings are designed according to the Iranian Seismic Code procedures by assuming rigid diaphragm behaviour. In order to incorporate the flexible behavior of floor diaphragms, it is necessary that the building structural system be analysed as a three-dimensional system. The structural Software SAP2000 was used for the linear and nonlinear analysis procedures. For the linear and nonlinear analysis procedures, the instruction for seismic rehabilitation of existing buildings no.360 guidelines were used to determine the response and corresponding displacements and internal forces in building. Floors are modelled with SHELL element having four nodes in each element to consider in-plane flexibility of the diaphragm. The beams, columns and bracings were modelled by FRAME element and use of the diaphragm constraint and master joint to model a rigid floor assumption. By studying and comparison the results, it can be concluded that the design procedures in current codes, based on the assumption of rigid diaphragm, can not provide a reasonable estimate of the drift and brace ductility demand especially in lower stories of the building with large aspect ratio (aspect ratio greater than 3) and the flexible models produce more frame displacement and maximum drift relative to rigid models. Also, application of rigid diaphragm assumption for structures with aspect ratio greater than 3 causes significant errors in analysis results. Inclusion of diaphragm flexibility changed the natural period, maximum total base shear and dynamic response of structures. Also the results of studies indicate that the diaphragm flexibility change the distri-bution of forces between the vertical load resistance elements and causes the middle braced frames pick up additional lateral load.

Friction is one of the most natural phenomena which is applied vastly in earthquake engineering. Despite the imagination, recent researches have shown that the coefficient of friction is not constant and varies by instantaneous frequency and amplitude of movement in vertical direction. Chawdury and Helali [7, 10] have shown that the friction coefficient decreases by increasing the frequency (f) and amplitude (A) of the vertical direction, however it rises by relative velocity (V) of the contacting surfaces. They also showed that the presence of vibration affects the friction force considerably. The values of friction coefficient for the considered materials of above-mentioned research decreased with the increase of amplitude of vibration at different frequencies. The percentage reductions of friction coefficient under vibrating and non-vibrating conditions increased almost linearly with the increase of amplitude of vibration at different frequencies. But the percentage reductions of friction coefficient were different for different materials. The reduction of friction coefficient is also related with sliding velocity, surface roughness and normal load under vibration condition. In other words, the new finding of their research is that the friction coefficient depends also on V/A.f. They tested some material and determined their governing formula for calculating their coefficient of friction, relating to the frequency and amplitude. Despite the mentioned experimental tests, in which the frequency and amplitude of the vertical vibration was constant, these quantities are not constant during a real earthquake and vary time by time. Therefore, instantaneous frequency and amplitude of vertical component of the earthquake should be used to calculate the friction coefficient of the moment. Wavelet transform is applied here to calculate these instantaneous quantities. MATLAB was applied for such a purpose. It is worth noting that the coefficient of friction is constant and equal to static one, when the relative velocity of the contacting surface is zero. However, for other cases it should be calculated for every moment. The instantaneous quantities are determined by wavelet transform for the displacement function of the vertical component of the earthquake. The relative velocity is considered as the one in the previous iteration. It is worth mentioning that the vertical earthquake not only change the coefficient of friction, but also vary the normal load, and therefore it changes both governing parameters of the friction. In pure sliding bases, which are focused in this paper, variation of the friction coefficient is investigated in three earthquake records, including Bam, Tabas and Gazli earthquakes. The real friction coefficient, regarding influences of the vertical component of earthquakes is shown for the considered earthquake records in comparison with the constant value in Figures 13 to 15. As shown, the real friction coefficient is always less than the considered constant values. This relies that the maximum acceleration, applied to the superstructure, is overestimated when the variation of the friction coefficient is ignored.

Non-linear dynamic analysis is considered the most complete method for estimating seismic performance parameters of a structure. However, due to its complexity and time consumption, researchers and seismic code authorities suggest the use of non-linear static analysis (also called Pushover Analysis). With the development of the application of Pushover Analysis in recent years, more advanced types of Pushover analyses are proposed, attempting to take into account different important behavioral features of the structures during an earthquake, such as the effect of higher modes and/or the effect of changes in modal characteristics of the buildings during seismic excitations. Adaptive Pushover Analysis (APA) is one of these proposed methods in which the structural stiffness and the lateral load pattern change during a given step of the loading. Earthquake forces are usually a few times more than the value obtained from seismic codes. This decrease is enforced by response modification factor. In this paper, effective parameters in seismic design of dual structural systems have been explained by using the capacity curve obtained from Adaptive Pushover Analysis. Using Adaptive Pushover Analysis, seismic performance parameters such as response modification factor, over-strength factor and ductility ratio are evaluated for two different types of dual-structural systems: 1) RC moment resisting frames (MRFs) with steel braced frames, and 2) steel (MRFs) with RC shear walls. These two dual-structural systems have 5, 10 and 15 stories and are designed according to IRAN's seismic code (Std. No. 2800, Third Edition). For Adaptive Pushover Analysis, 22 far-field earthquake records recommended by FEMA-P695 are used. Mean value of response modification factors for different dual systems is obtained to be 7.22. Dual systems of RC MRFs with steel braced frames showed better seismic performance and are therefore highly recom-mended for rehabilitation of existing RC structures. According to the results obtained, the building height has significant impact on the response modification factor.