مجله علوم و مهندسی زلزله
سال سوم شماره 1 (پیاپی 6، بهار 1395)

Tehran lies on the southern flank of the Central Alborz, an active mountain belt characterized by many historical earthquakes, some of which have affected Tehran itself. It is an arcuate fold and thrust belt, consisting of two major distinct structural trends: a NW-SE trend characterizing the west-central Alborz, and a NE-SW trend marking the east-central Alborz. The steep slopes of the Alborz on its southern flank adjoin the piedmont, which is covered by various units of post-orogenic alluvium. The border between the Alborz Mountain and the Tehran's piedmont (northern part of Tehran city) is marked by the North Tehran Fault (NTF) [1], dividing the Eocene rock formation from the alluvial units of different ages (Early Pleistocene to the recent alluvium). The oldest alluvial formation, named Hezardarreh is a folded and faulted conglomerate forming hills parallel to the mountain front. The age of this formation is difficult to determine accurately, due to the lack of datable features such as pollen, fossils or lithic industry [2]; however, it is mostly assumed to be Plio-Quaternary (the bottom of formation) to Early Quaternary (the upper part of formation). The formation overlying the eroded Hezardarreh Formation is very heterogeneous in composition, in particular to the north of Tehran and has been considered to be Mid-Pleistocene. The next following formation is widespread deposits named the “Tehran alluvium” have been assigned to Late Pleistocene [3]. The youngest mapped unit in Tehran City overlaying the Late Pleistocene alluvium is Holocene deposit, which is divided in younger part (4000 to 5000 years BP) and an older unit in age of 12000 years (BP) [4]. The assessment of seismic hazard depends upon the understanding of activity, mechanism and trends of faults affecting an area. The rapid urbanization of Tehran with remarkable concentration of people needs to be studied by new studies considering all possible active fault trends. The E-W-trending active faulting in Tehran is delineated by their morphological features recognized on aerial photos of 1955. This study examines the NW-trending faults as a possible seismic source. The measurement of 56 fault planes in 13 outcrops have shown that the morphological features associated with NW-directed faults are preserved in middle and late Pleistocene deposit of Tehran's piedmont. The length of these faults varies between 2.6 to 6.5 Km arranged in an en-echelon manner. The compressive faulting mechanisms of these trends are in accordance with the NE-directed present day stress direction. Morphological features of the NW-directed faults are controversial, because they appear as normal and compressive on aerial photos and in the outcrops. It means that the faulting mechanism in Tehran's piedmont cannot be explained by a single stress direction. In fact, two different stress directions have affected the alluvial plain, namely an older NW-directed prior to the NE-directed one, which explains the normal faulting mechanism along the NW-striking faults and was mapped as old normal fault, e.g. [5]. Thus the NW-trending faults are inherited fault affecting the Early and Mid-Pleistocene deposit as normal faults. According to the present day stress prevailing in the South Central Alborz obtained by P-axis of focal mechanisms and fault slip data in relative young alluvial deposits [6-7] a NE-directed stress explains the faulting mechanisms of active faults in this area. Although there is now field evidences proving the fault activity of NW-striking faults but the present day stress (NE-directed), it is reasonable to assume seismic activity along these faults.

Considering the increasing use of dynamic analysis methods in structural design, the selection of appropriate design earthquake has been an important part of the design procedure. For intermediate and low importance structures, the design earthquake is typically provided by the seismic codes as a design spectrum. However, for important structures for which time-history analysis should be performed, the use of recorded ground motions as input is inevitable. On the other hand, the existing ground motions only show a small part of the reality. Experiences of past earthquakes indicate that sole reliance on existing data will never resolve all issues, and new damage problems have occurred recently. In order to overcome this problem, a new paradigm has to be used. The concept of “critical excitation” and the structural design based on this concept can become one of such new paradigms. In the present paper, the probabilistic critical excitation method is used to determine the critical excitations for three shear building models, which are modeled as MDF system. Selection of appropriate constraints is the main problem when using this method. It is shown that the upper bound of earthquake input energy per unit mass can be considered as suitable constraint for the critical excitation. This bound can be a reasonable benchmark to estimate the allowable range of possible energy in similar earthquake. Considering this bound as constraint, the method is used to determine the critical PSD functions and generating synthetic accelerograms. In order to demonstrate the effectiveness of the method, three real accelerograms are selected as benchmarks and linear dynamic analysis was conducted using these accelerograms and the generated critical excitations, and the key parameters of response including maximum displacement, drift and acceleration of stories are compared. Input base acceleration is defined as the product of an envelope function and a stationary Gaussian process with zero mean. Considering the sum of the mean-square interstory drift of the system as the objective function, the critical excitation problem is defined as follows: Given the mass, stiffness and the viscous damping matrix of a linear elastic MDOF system, as well as the envelope function, find the critical PSDF, so that the objective function is maximized under specific constraints. In order to solve this problem, first the constraints have to be selected. According to the concept of the constraints, there is no straight way to recommend a specific value of them. Thus that is very difficult to estimate that what value of one constraint is sufficient to make the final nonstationary input critical. Nevertheless, at least a reasonable assumption can be made for the ratio of constraints. Therefore, the method can be used to locate the rectangular function. Takewaki [1] by setting constraints on the acceleration and velocity time history of the ground motion determined an upper bound of total input energy per unit mass of a record for a damped linear elastic system. This bound is well defined by two curves that perfectly bound the actual input energy curve in the range of short and long periods. Investigations on the time-history of various ground motions indicate that even for the same level of energy bound for acceleration constraint, the maximum amount of actual energy is not constant. Moreover, this maximum value may occur in different periods. The upper bound of the total input energy for acceleration constraint can be used to estimate the possible range of energy in similar ground motions. This bound is only related to the area of the PSDF of excitation and the maximum value of it. These two parameters can define a class of ground motions that existing record is just one realization of them. As a result it is desirable to fix the upper bound of input energy and let the excitation to change in amplitude and frequency content in such a way that the objective function is maximized. By this mean, using a sample of ground motion, a synthetic accelerogram can be generated with the same upper bound but different energy content. In order to examine the effect of the critical excitations on the structures, a numerical simulation was carried out using the three typical shear building of 8, 14 and 20 stories. These buildings were designed as steel moment frames, using the ETABS commercial software, and then the mass and stiffness of stories were determined and the corresponding MDOF models were used for linear dynamic analysis. This study shows that the upper bound of the total input energy for acceleration constraint can be a reasonable benchmark to estimate the possible range of energy in similar earthquakes. This bound is only related to the area of the PSDF of excitation and the maximum value of it. By controlling these two parameters, the upper bound of input energy can be fixed and then by changing the amplitude and frequency content using the critical excitation method required accelerograms are determine so that the objective function is maximized. Comparison of linear dynamic analysis of three designed models under critical excitations and the corresponding actual records, which have been selected in such a way that the energy content of the record is the maximum in the natural frequency of the fundamental mode of structures, shows that the synthetic accelerograms can reasonably estimate the behavior of structures, including the maximum displacement, interstory drift and absolute acceleration of stories.

There have been considerable studies in recent years about evaluating the long-term conditional probability of the next strong earthquake (Mw>7) occurring on specific faults or fault segments which have experienced strong shocks. Also in these researches different kinds of recurrence-time distributions have been utilized in order to estimate these probabilities. In the shortage of a long term historical strong earthquake catalog, likely paleoearthquake observations provide possibility that can be used for probabilistic forecasting. In this paper, in order to gain dates of known recent ruptures of the fault, Paleoseismological observations are used. Uncertainties in input data and model parameter values have often ignored in hazard assessment that consequently causes less accuracy in results. Furthermore paleoseismic observations almost miss enough events at a given site to determine directly a probability density function for earthquake recurrence. So in access to more accurate outcomes, here a common statistical method that takes account of uncertainties in data and model parameter values are applied to estimate the time-varying hazard of rupture of the considered fault segment. The North Tabriz Fault is a major seismogenic fault in Northwest Iran where is defined by a high level of seismicity. This main right-lateral strike-slip fault with an average strike of Northwest-Southeast (NW-SE) has experienced strong and destructive earthquakes that the most destructive one is the 1780 AD. (Ms 7.4), rupturing the northwestern segment of the fault. Accordingly, the conditional probability of further rupture of the northwestern segment of this major fault is a significant subject. The recurrence interval of such earthquakes occurring on this fault segment based on paleosiesmological researches is 821±176year [1]. In order to evaluate the conditional probability, the basic statistical method adopted here is that of Rhoades et al. [2], with alterations clarified and applied by Rhoades & Van Dissen [3] and, recently, used by Van Dissen et al. [4].The purpose of this approach is to estimate the conditional probability of rupture of the fault as a single value which takes account of both input data and parameter uncertainties. Here we consider two different recurrence-time distributions, exponential as a time-independent model and weibull as a time-dependent model. The Exponential recurrence- time distribution commonly assumed in probabilistic seismic hazard analysis is the model just with one parameter called seismicity rate (λ). This model corresponds to a stationary Poisson process. The Weibull distribution is extensively assumed in failure time modelling for manufactured items. This time-dependent model which has been proposed as a model of fault rupture recurrence has two parameters called shape parameter (c) and scale paramer (β) [5]. Input data assuming in this methodology are based on assessments of the average single-event displacement and its uncertainties, the long-term slip rate and its uncertainties and the dates of known recent ruptures of the fault segment and its uncertainties [3]. Where the values of average single-event displacement and dates of recent ruptures of the fault are gotten from Paleoseismological investigations done by Hessami et al. [1] and preferred long-term slip rate is adopted from Rizza et al. [6]. In order to survey the sensitivity of the northwestern segment of the North Tabriz Fault conditional probability results to the reformed slip rate, conditional probabilities are estimated again with long-term slip rate value extracted from Hessami et al. [1]. As mentioned above, the methodology used here is the same as that described by Rhoades & Van Dissen [3]. In this approach parameter values as well as input data values are entered into analysis as probability distributions for considering data uncertainties. Lognormal distribution is assumed for the average single-event displacement and long-term slip rate, too [3-4]. In order to gauge the sensitivity of the considerable fault segment conditional probability outcomes to dates of rupture distribution than our uniform distribution, results are evaluated again with assumption of normal distribution for each date of rupture. Also, it requires determining prior distributions for the parameters of the recurrence time model. The prior distribution for the parameters of the exponential and weibull models are produced in the same way as those elaborated by Rhoades & Van Dissen [3]. The prior distribution of the mean recurrence times is specified from the considered probability distributions of the average single-event displacement and the average slip rate. The prior distribution of the coefficient of variation is taken to be uniform on (0, 1). Eventually, prior distribution for the parameters of the chosen models is obtained based on these two constructed prior distributions and relations given by Rhoades & Van Dissen [3]. By using prior distribution of parameters and equations presented [3], this procedure is carried out to compute time-varying hazard and conditional probability of rupture of the considered fault segment. By way of description [3], the above methods are performed to the northwestern segment of North Tabriz Fault, where strong events have been dated [1]. The mean hazard function under each of the models at any time between the year 2015 and 2330 , allowing for data and model parameter values uncertainties, has been figured. Over the 300 year, hazard rate under exponential model, although it is on decreasing tend, is almost static; whereas, the hazard rate under weibull is always increasing. The estimated conditional probabilities of rupture of northwestern segment of the North Tabriz Fault under the assumed models have been computed for time intervals 5, 10, 20, 50, 75, 100, 200 and 300 year. For the next 100 year the probability of rupture of the considered fault segment is15.88% and 10.28% under the exponential and Weibull models, respectively. Compared with the exponential model the conditional probability of rupture under the Weibull model is lower. As for results, the estimated conditional probability under these models is not similar. Although the exponential model is commonly used in hazard analysis but it is not suggested to be applied as a recurrence-time model to the faults or fault segments where large shocks occur [7]. So here, for the northwestern segment of North Tabriz Fault, the outcomes under time-dependent weibull model are preferred. Obtained results of the northwestern segment of North Tabriz Fault demonstrate that, assumption of the different types of prior distribution for dates of known ruptures has no significant effect on outcomes; however, these assessments are so sensitive to the values of the long-term slip rate and it’s uncertainties, causing in about 40% and 80% changes in values of probabilities for exponential and weibull recurrence-time distributions, respectively.

A classical approach to soil-structure interaction problems includes three analysis stages. The first is the estimation of free field motion (FFM). The second stage accounts for the effect of excavation on FFM alternations in the perimeter of excavated part. The third and final step deals with soil-structure interaction, usually in two sub-parts, i.e. kinematic and inertial interactions. For the case of underground systems, the first two stages and also the first sub-part of the third stage, govern the forces imposed to embedded structures. To implement the above analysis plan, FFM is usually considered as shear waves with upward propagation direction. Such assumption has formed the popular simplified seismic design method of underground structures [1-6]. Though, this common assumption may not be valid for topographic urban areas were wave fields reach surface through different incident angles. Such inclination would lead to various states of confrontation between embedded cavities and wave fields. The state variety, in turn, cause underground openings to experience different stress fields and hence dissimilar void-wall deformations. The tractions that affect embedded structures are the results of such deformations. Therefore, there is a serious need to uncover the role of wave field-cavity face-off orientation on void-wall distortions. Here, the effect of face-off angle, between shear wave field and rectangular cavities, on semi-local distortions is investigated. For this purpose, a 2D isotropic soil model including homogeneity is included under statically simulated seismic shear deformations. The analysis was performed through the finite element method regarding different aspect ratios for cavity and subsequently global distortions were reported. To drive semi-local distortions, in the analyzed model, the cavity junctions were initially connected by strait lines. Then, the divergences from perpendicularity between adjacent edge lines of the opening were calculated. This approach would provide the same results for different corners of perfect rectangular cavities. However, this is not the case for imperfect rectangles were the responses would not take similar values for different junctions. The first part of this research examines the performance of perfect cavities against different incident angles. The second part deals with the samples of semi-rectangular sections. With an overview on results for perfect rectangles, it can be figured out that the traditional formulations for cavity distortion estimation just cover special incident angles, which are close to zero value and also specified to square sections rather than general rectangular shapes. However, as the incident angle varies from zero to 45 degrees and also sections tend to more slender shapes, usual suggestions would become in many cases conservative and also in a number of occasions unconservative. For instance, in the case of 45 and -45 incident angles, global distortion of sections vanishes in spite of existence of local arching shapes. This means that wall deformations are totally different from what is expected in the case of zero confrontation angle. Furthermore, the above investigation is extended to two of semi-rectangular sections. The selected cases, which belong to different metro stations in Kobe and Athens metropolitans, possess rectangular sub-parts at the bottom. These sub-parts make deviations from perfect rectangles. In the former case, the added part is placed in the middle length with which one of two symmetry axis is removed and the other one still remains. In the later one, the added part is placed at an arbitrary position that removes both symmetry axes. In this second round of analysis, as distortions vary from node to node, each nodal distortion is reported separately. Due to the results, it is seen that by approach to the position of added parts, deformations become more different from perfect states. This difference may result in more than 50% increase in corner angle adjustments. That is while far regions from added inclusions experience approximately the similar responses to perfect rectangles. It is worth mentioning that to reach a comprehensive influence map on the effect face-off angle, further investigation is required. Besides, it is important to note that this document has focused on edge junctions for the calculation of nodal distortions. Other local deformations were out of the scope of this paper.

Nowadays, it is highly conspicuous that the problems of urban transportation are failed to be resolved on the ground, thus the best and quickest remedy is using underground facilities in metropolises. Especially, in congested urban areas, shallow depth underground structures (tunnels, subways and metro stations) are frequently built. Besides, the geometrical aspects, these box-shaped structures have some characteristics that are different from those of the mined circular tunnels. For example, the dimension of the box-type tunnels is, in general, greater than those of circular tunnels. This characteristic along with the potential of large seismic ground deformations that are typical for shallow soil deposits increase interaction effects of these shallow tunnels with their surrounding medium and adjacent structures [1]. Therefore, investigating the effect of these shallow underground structures on the seismic response of surface structures is of great importance [2-5].  In the current study, the effects of single and twin box-shaped underground structures on the amplification patterns and seismic response of ground surface are parametrically examined.

In this research, using a finite difference approach, the effects of parameters such as; depth, horizontal space, lining stiffness of tunnels and input excitation frequency on the seismic response of the ground surface have been parametrically studied. Numerical analyses are performed through using the FLAC 2D software. Moreover, analytical results of Luco and De Barros [6] and numerical result of Yiouta-Mitra et al. [7] are chosen for the validation of the numerical approach. 
To investigate the variations of frequency-dependent ground surface response, first, Ricker wavelets have been utilized as seismic excitations. Then the model subjected to seven real earthquake records and accordingly accelerations response spectra (spectral accelerations) have been presented.

This section exhibits the important results obtained from the parametric study. The results demonstrate that in the presence of twin tunnels, the maximum value of amplification always occur in center of the ground surface (x/a=0) while for case of single tunnel it occurs in the sides. Moreover, it can be deduced that the presence of the twin tunnels creates more serious condition with respect to the single tunnel. Furthermore, several real earthquake excitations were selected for further investigation about the effect of box-shaped tunnels on the ground surface acceleration. The results show that the presence of box-shaped underground structures has considerable influence on the seismic amplification patterns of the ground surface and characteristics of acceleration response spectrum. This issue is particularly evident in the case of shallow and twin underground tunnels. The main reasons of this occurrence may be related to significant wave sweeping effects due to the waves scattering by the shallow structures, which increase interaction effects of the shallow tunnels with their surrounding medium and adjacent structures. 

In the current study, the effects of single and twin box-shaped underground structures on the amplification patterns and seismic response of ground surface are parametrically examined. For this purpose, using a verified numerical approach, the effects of crucial parameters, such as depth, horizontal spacing, lining stiffness of tunnels and frequency content of wave excitations on the ground surface response are evaluated. In the next stage, seven real earthquake excitations are selected for further investigation about the effect of box-shaped tunnels on the seismic response spectra of ground surface and the results are compared with the free-field condition. The main important conclusions drawn from the present study are as follows:1. The box-shaped underground structures have considerable influence on the seismic amplification of the ground surface and characteristics of acceleration response spectrum.2. The presence of twin tunnels creates more serious condition with respect to single tunnel.3. The presence of the tunnel resulted in deamplification in short periods (high frequencies) and amplification in long periods with respect to the free-field model.4. The significant wave sweeping effects due to the waves scattering by shallow structures, increase interaction effects of the shallow tunnels with their surrounding medium and adjacent structures.

The use of urban tunnels is increasing to accommodate lifelines such as roads, railroads, subways, sewer systems and high-voltage electrical cables. Many cities sit on sedimentary deposits and faulting zones, which presents challenges for the construction of these tunnels. One type of probable damage is that caused by permanent ground displacement (PGD). Severe earthquakes can cause such displacements to appear at the ground surface and cause fractures called surface faulting. The interaction of surface faulting at ground structures such as bridges, dams, and buildings or underground structures such as tunnels and pipelines can result in major damage to them. Comprehensive studies have been conducted to fully understand this phenomenon [1-11]. The building codes of many countries recommend avoiding construction in the vicinity of active faults, but at times the construction of a tunnel intersecting a fault is inevitable [4]. It is not always possible to avoid the construction of a tunnel near an active fault. Tunnels are at the risk of faulting due to their long length. This can affect the design of the tunnel lining. Such a tunnel must be capable of resisting fault displacement so that it will suffer only minor damage. When designing tunnels located in the areas with the potential for surface fault rupture, it is necessary to consider the effects of loads caused by fault rupture in addition to other types of seismic loads [12]. Researchers have developed specific criteria to account for the effect of seismic wave loading. However, the effect of fault rupture loads has not been considered in comprehensive design methods. Highly active faults can cause significant damage to a tunnel. Fault displacement can produce extreme stresses on the lining of the tunnel. The study of tunnel behavior passing through a fault zone during an earthquake is practically unknown because it has been experienced less study and investigations. Physical modeling by the use of geotechnical centrifuge provides the possibility of investigating the up-mentioned geotechnical phenomenon. The current study investigated the effects of normal faulting on shallow segmental tunnels using physical modeling in a geotechnical centrifuge. This article describes the details of physical modeling of a normal fault, a segmental tunnel in a centrifuge, and the results of six centrifuge tests. One of the most important and applicable results obtained from the faulting tests is an understanding of the failure modes. It was possible to discern vulnerable areas in the segmental tunnels by determining the failure modes and designing methods to mitigate tunnel damage. The present study conducted a series of centrifuge model tests on segmental tunnels subjected to normal faulting. Results indicate the probable rupture mechanisms. Results show that segmental tunnels can tolerate superficial faulting. However, as the faulting displacement increases, oval shapes in segmental ring occur in the faulting zone and finally tunnel collapse happen. However, the results indicated the absence of sudden collapse of segmental tunnels under normal faulting and improvement of function in response to an increase in the overburden of the tunnel. The angle of the fault affected tunnel behavior. Despite large displacement faulting, structural damage to the segments was very low because of the adequate geometric functioning of the segments and their joints. The length of the zone affected by faulting in the tunnel decreased as the overburden increased, but the severity of damage increased in response to localization of fault displacement. Sinkhole formation upon the collapse of soil into the tunnel is likely at the ground surface. Special attention must be paid to the effect of sinkholes on ground structures in the vicinity of the tunnel. The results of this paper can be used to determine the pattern of rupture where a tunnel intersects a fault. Obviously, the pattern derived from this modeling can play an important role in developing analytical analysis and numerical methods. The results can be used for better understanding of segmental tunnel behavior where it intersects a fault zone; it can also be used to specify the locations affected by the faulting and to adopt preventive strategies as well.

Seismic design and performance assessment of structures require employing earthquake loadings and determining the responses of structures using nonlinear analysis. Among the structural analysis methods, nonlinear time history analysis (NTHA) is the best option for this purpose because it demonstrates realistic behavior of structures against earthquake loadings. However, nonlinear time history analysis of structures involves still some problems related with assembling the suitable set of accelerograms that can properly represent the desired seismic level. Then, in order to perform a nonlinear time history analysis, appropriate record selecting and scaling strategy is required. Because of probabilistic specifications of ground motions, the identification of records to be applied in the evaluation of structural responses is a critical task. Furthermore, record selection directly influences both the median estimation and the dispersion about the median. The literature for selecting a pre-defined number of recordings within a ground-motion data set is developing consistently due to the recent intention of earthquake or structural engineering practice. Therefore, the characteristics of the selected ground-motion records and scaling strategies are more important for estimation of seismic responses and affecting the accuracy of structural responses are depended to the records selection [1-4]. In this research, a probabilistic based method has been utilized for optimum selecting and scaling of acceleration ground-motion records, which could be led to the reduction of dispersion in nonlinear structural responses. The utilized methodology in this research constrains the scaling to the differences between each individual record and corresponding estimation from the ground-motion prediction equation (GMPE) model. The record selecting and scaling are such that in addition to minimizing the dispersion of nonlinear responses, the median linear responses will be matched to the target spectrum. Furthermore, the applied method will preserve the seismic essence of the selected ground-motion records [4]. In addition, the method emphasizes the significance of preserving the basic seismological features of the ground-motions after being scaled. The final selection of the recording set is accomplished by estimating the standard deviation of all combinations resulting from an available accelerogram data set. In this study, by investigation of responses of MDOF steel moment resistant frames, the accuracy of the implemented method is verified. Because of the lack of accelerograms data for our country (Iran), the mean spectrum of relatively severe earthquakes has been produced as the design spectrum. The mentioned spectrum has been provided using 11 records (each record with two horizontal components) for soil type-2 with shear wave velocity between 375-750 m/s, minimum PGA equal to 0.3 g and minimum Mw equal to 5.30. In this investigation, selections of ground motions are managed at two stages. At first stage, 20 records with considering the design earthquake are selected. For second stage, among 20 ground motions, 10 records are selected for performing the nonlinear time history analysis. For nonlinear time history analysis, 4-story and 12-story 2D steel frames have been investigated. Designing of the mentioned frames have been carried-out using ETABS commercial software, and evaluation of seismic behavior of the frames has been performed using SeismoStruct framework [5]. For nonlinear modeling of steel material, Menegotto-Pinto constitutive modeling has been utilized in the finite-element procedure. The obtained results show that the dispersion of responses using the present study is less than the responses obtained from 2800[6].