Sharif University of Technology
Scientia Iranica
10263098
23453605
24
5
2017
10
01
Investigating the experimental behavior of the reinforcements effect on the railway traverse under the dynamic load
2253
2261
EN
Alireza
Hajiani Boushehrian
Department
of civil engineering,
Shiraz Branch, Islmic
Azad University, Shiraz, Iran
ahajiani@gmail.com
A .
Vafamand
Master of science of geotechnical
engineering, Estahban Branch, Islamic Azad University, Iran
S .
Kohan
Master of science of highway
engineering, Shiraz Branch, Islmic
Azad University, Shiraz, Iran
10.24200/sci.2017.4149
An investigation into the causes of settlement and its control can place an obstacle to such hazards as derailing of a train due to the railway settlement. In this study, the effect of both geogrid and the geogrid anchor concerning the railway ballast layer settlement reduction has been taken into account. For this purpose, the ballast performance in the field conditions was simulated using a smallscale box test. In this experiment the static load was considered as the sum of the train and passenger weightand the dynamic load relating to the train vibration. Since this research aims at launching an investigation into the influence of utilizing geogrids in order to reduce the ballast settlement, this experiment has been carried out by considering the geogrid and geogrid anchor layer, the loading frequency variation, the amount of loading, the geogrid position, the number of geogrid layers and the related distances. Also, the results obtained from the empirical model have been analyzed and compared. A number of relations based upon the test results have been developed to estimate the permanent settlement relative to the dynamic load and the number of reinforcement layers.
Traverse,Dynamic load,Static load,geogrid,settlement,GridAnchor
http://scientiairanica.sharif.edu/article_4149.html
http://scientiairanica.sharif.edu/article_4149_90d18179f71d2143f938937b65263bb3.pdf
Sharif University of Technology
Scientia Iranica
10263098
23453605
24
5
2017
10
01
An Adaptive Relaxed Cellular Automata Method for ReliabilityBased Hydropower Operation of Reservoirs
2294
2306
EN
Mohammad
Azizipour
School of Civil Engineering, Iran University of Science and Technology,
Narmak, Tehran, Iran
m_azizipour@iust.ac.ir
M.H.
Afshar
School of Civil Engineering, Iran University of Science and Technology Narmak, Tehran, P.O. Box 16765163, Iran
mhafshar@iust.ac.ir
10.24200/sci.2017.4151
This paper presents a novel Cellular Automata approach for solution of reliabilitybased reservoir hydropower operation problems. The method is based on the observation that a low value of the penalty parameter would lead to partial enforcement of the constraints. In this method, therefore, the constraints of the chanceconstrained operation problem, namely operational and reliability constraint, are dealt differently. A high enough value of the penalty parameter is used for the first set while a lower than enough value is used for the second set leading to strong enforcement of the first set of the constraint and partial fulfillment of the second set. Since the proper value of the penalty parameter to be used for the reliability constraints is not known a priori, an adaptive method is, therefore, proposed to find the proper value. The proposed model is used for operation of Dez reservoir in Iran and the results are presented and compared with those of a Genetic algorithm. Hydropower operation is considered over short, medium and long term periods to demonstrate the efficiency and effectiveness of proposed method for problems of different scales. The proposed model is shown to produce superior results to the GA with much reduced computational effort.
Reliability,cellular automata,genetic algorithm,reservoir operation,hydropower
http://scientiairanica.sharif.edu/article_4151.html
http://scientiairanica.sharif.edu/article_4151_77c702c84c38e9a56067d133e81b8ddd.pdf
Sharif University of Technology
Scientia Iranica
10263098
23453605
24
5
2017
10
01
Attenuation Relation for Near Field Shallow Crustal Earthquakes Using NGAWest Database with MixedEffect Model in Comparison with Attenuation Relations for Iran
2183
2201
EN
Alirez
Shokran Neam
Department of Civil and Environmental Engineering, Amirkabir University of Technology, Tehran, Iran
alireza.shokran@aut.ac.ir
Touraj
Taghikhany
Department of Civil and Environmental Engineering, Amirkabir
University of Technology, Tehran, Iran
ttaghikhany@aut.ac.ir
10.24200/sci.2017.4152
This article presents a new empirical equation for the estimation of horizontal strong ground motions caused by shallow crustal earthquakes. This model is developed empirically by regression of the database which is used by the NGAWest2 GMPE developers with a fault rupture distance less than 60 kilometers. The data set consisted of corrected and processed accelerograms of 1545 strongmotion records of earthquakes between Mw 5.2 and 7.9. Model is a function of earthquake magnitude, distance from source to site, local average shear wave velocity, nonlinear soil response, sediment depth, rupture dip, faulting mechanism and hanging wall effect. This equation was derived by a stable algorithm for regression analysis called mixed effect model. The algorithm was used to develop PGA and PSA (T1) for periods from 0.01 to 10.0 seconds. Major differences between this model with recent developed attenuation relations for the world and Iran were observed for largemagnitude ground motions which were recorded at smalltomoderate distances from seismic source. The results showed that the nearfield affected the predicted values especially in soil sites. Moreover, comparison with the attenuation relations developed by Iranian data set confirmed that the equation in this region is sensitive more to distance than to other parameters.
Empirical attenuation relationship,NGA,Mixed effects model,Nonlinear model,Iran plateau
http://scientiairanica.sharif.edu/article_4152.html
http://scientiairanica.sharif.edu/article_4152_fd30514feeb6594638e99aed86fc0005.pdf
Sharif University of Technology
Scientia Iranica
10263098
23453605
24
5
2017
10
01
Optimization of Hedging Rules for Hydropower Reservoir Operation
2242
2252
EN
K.
Sasireka
School of Civil Engineering, SASTRA University, Thanjavur 613401, India
sasireka@civil.sastra.edu
T.R.
Neelakantan
Associate Dean (Research) and L&T ECC Chair Professor Centre for Advanced Research in Environment, School of Civil Engineering SASTRA University, Thanjavur 613401 India
trneelakantan@civil.sastra.edu
10.24200/sci.2017.4153
Reservoir operation plays an important role in economic development of a region. Hedging operations were used for municipal, industrial and irrigation water supplies from reservoirs in the past. However, hedging operation for hydropower reservoir operation is very rare. Practically simple and useful new form of Standard Operation Policy and new form of hedging rules for hydropower production are introduced in this paper and demonstrated with a case study for hydropower reservoir operation of Indirasagar reservoir system in India. The performances of optimal hedging rules were compared with that of a new standard operation policies and the superiority (reliability increases by about 10%) of the hedging rules are presented. When the number of decision variables is increased from 5 to 15, the energy production is increased by 0.7 %, the spill is reduced by 16.8 % while the reliablity is decreasing slightly by 2.1 %. A bilevel simulationoptimization algorithm was used for optimizing the hedging rules. For optimization, Genetic Algorithm, artificial bee colony algorithm and imperialistic competitive algorithms were attempted. The results indicate that all the three algorithms are competitive and artificial bee colony algorithm is marginally better than the other two.
Hedging rule,reservoir operation,hydropower,Optimization,genetic algorithm,artificial bee colony algorithm,imperialistic competitive algorithm
http://scientiairanica.sharif.edu/article_4153.html
http://scientiairanica.sharif.edu/article_4153_4c2bd3ed32b21bdf1c8ad02f6b135a07.pdf
Sharif University of Technology
Scientia Iranica
10263098
23453605
24
5
2017
10
01
Uncertainty analysis of open channel flow: stochastic approach to Advection–Diffusion equation
2262
2270
EN
hossein
khorshidi
Department of Civil and Environmental Engineering, Shiraz University, Shiraz, Iran
khorshidi@shirazu.ac.ir
N.
Talebbeydokhti
Civil and Environmental Engineering Department, Environmental Research and Sustainable Development Center, Shiraz University, Shiraz, Iran
taleb@shirazu.ac.ir
Gholamreza
Rakhshandehroo
Civil and Environmental Engineering Department, School of Engineering, Shiraz University, Shiraz, Iran
rakhshan@shirazu.ac.ir
10.24200/sci.2017.4154
In fluid mechanics applications, transport occurs through the combination of advection and diffusion. This paper presents a stochastic approach to describe uncertainty and its propagation based on AdvectionDiffusion Equation. To assess the uncertainty in initial water depth, random initial condition is imposed on the framework of 1D open cannel flow. Karhunen–Loeve Expansion is adopted to decompose the uncertain parameter in terms of infinite series containing a set of orthogonal Gaussian random variables. Eigenstrucures of covariance function associated with the random parameter, which play a key role in computing coefficients of the series, are extracted from Fredhulm’s equation. The flow depth is also represented as an infinite series of its moments, obtained via polynomial expansion decomposition in terms of the products of random variables. Coefficients of these series are obtained by a set of recursive equations derived from the ADE. Results highlight the effect of various statistical properties of initial water depth. The mean value and variance for the flow depth are compared with Monte Carlo Simulation as a reliable stochastic approach. It was found that when higherorder approximations are used, KLE results would be as accurate as MCS, however, with much less computational time and effort.
AdvectionDiffusion equation,Karhunen–Loeve expansion,Monte Carlo simulation,Open channel flow,Stochastic solution
http://scientiairanica.sharif.edu/article_4154.html
http://scientiairanica.sharif.edu/article_4154_d919e51c5aa17be737cf3f8cf4946fcb.pdf
Sharif University of Technology
Scientia Iranica
10263098
23453605
24
5
2017
10
01
Axisymmetric active lateral earth pressure for cΦ soils using the stress characteristics method
2332
2345
EN
Amin
Keshavarz
School of Eng.
Persian Gulf University
Bushehr, Iran
amin.keshavarz@gmail.com
Mohsen
Ebrahimi
School of Eng.
Persian Gulf University
Bushehr, Iran
mohsenebrahimi01@gmail.com
10.24200/sci.2017.4155
The slip line or Stress Characteristics Method (SCM) is used to analyze the active lateral earth pressure in the axisymmetric case. In this paper, in addition to the retaining walls in the axisymmetric and plane strain conditions that studied in the past, a new model of the retaining wall in the axial symmetry is considered, which widely used in the design of grain silos, buildings and road constructions. The effects of the various parameters, including cohesion and friction angle of the soil, wall and backfill slopes and soilwall interface adhesion and friction angle on the lateral earth pressure have been evaluated for all cases of the retaining walls. Based on the proposed theory, a computer code has been developed for the plane strain and axisymmetric cases. Also, finite element modelling is used to verify the results of the SCM. Comparison of the results indicated the accuracy of the proposed method. Furthermore, the effect of the plastic critical or tension crack depth has been evaluated and indicated that neglecting the plastic critical depth is not conservative.
lateral earth pressure,Axisymmetric,stress characteristics,slip lines,Finite element
http://scientiairanica.sharif.edu/article_4155.html
http://scientiairanica.sharif.edu/article_4155_f10322e40b022aec36be7d1df6f0823f.pdf
Sharif University of Technology
Scientia Iranica
10263098
23453605
24
5
2017
10
01
Assessment of Collapse Modes in Reinforced Concrete Frames Considering RecordtoRecord and Modeling Uncertainties
2213
2226
EN
Ehsan
Tafakori
Department of Civil Engineering, Engineering Faculty, University of Guilan, P.O. Box 416353756, Rasht, Iran
ehsan.tafakori@gmail.com
Saeid
Pourzeynali
Dept. of Civil Eng., the University of Guilan, Rasht, I. R. Iran
pourzeynali@guilan.ac.ir
Homayoon
E. Estekanchi
Department of Civil Engineering, Sh
arif University of Technology,
P.O. Box 111559313, Tehran,
Iran.
stekanchi@sharif.edu
10.24200/sci.2017.4156
Dominant collapse mechanisms (DCMs) have been reported to play an important role in collapse capacity of structural systems and the seismic losses consequent to it. Therefore, DCMs of Reinforced Concrete (RC) frames have been studied, in this article, considering RecordtoRecord (RTR) and modeling uncertainties. Two sets of RC frames have been designed, in this regard, that share the design assumptions but contain different levels of overstrength. Each set contains 26, 4 to 20story nonlinearly modeled frames. Initially, Incremental Dynamic Analysis (IDA) was used to identify frames’ DCMs. The RTR variability reflected through IDA was next combined with spectral shape and pulse effects of the ground motion records. Modeling uncertainties were introduced finally to the study using a response surface based Monte Carlo method. The study results reveal that the degree to which DCMs are affected by the associated uncertainties is a function of the overstrength provided to the frames. This affection is found to be generally important and particularly remarkable for especially detailed ductile structures.
concrete moment frame,collapse modes,Uncertainties,Performancebased Earthquake Engineering,Incremental Dynamic Analysis
http://scientiairanica.sharif.edu/article_4156.html
http://scientiairanica.sharif.edu/article_4156_9d36e3dee782bc9a53af6ed22e6209be.pdf
Sharif University of Technology
Scientia Iranica
10263098
23453605
24
5
2017
10
01
Comparison of three dimensional and two dimensional axisymmetric finite element analyses of a corner section of a tailings dam
2320
2331
EN
Muhammad Auchar
Zardari
0000000231974786
QuaideAwam University of Engineering, Science and Technology, Nawabshah
muhammad.auchar@quest.edu.pk
Hans
Mattsson
Department of Civil, Environmental and Natural Resources Engineering
hans.mattsson@ltu.se
Sven
Knutsson
Luleå University of Technology, SE97187 Luleå, Sweden
sven.knutsson@ltu.se
Linda
Ormann
Fortum, Power Division, Renewable Energy, Våxnäsgatan 10,
Karlstad, Sweden
linda.ormann@fortum.com
10.24200/sci.2017.4157
This paper presents three dimensional (3D) and two dimensional (2D) axisymmetric finite element analyses of a corner of a tailings dam. The analyses were performed to: (i) locate tension and/or low compression zones and to evaluate slope stability during sequential raising of the dam corner, and (ii) find whether the results of 2D axisymmetric analyses can be reliable for the dam corner. The corner is a potentially weak section of the dam where tension and/or low compression zones may develop. Development of such zones inside the dam corner can lead to cracks and initiation of internal erosion. The results of both the 3D and 2D axisymmetric analyses indicated that (i) tension and/or low compression zones were located in vicinity of surface of the dam corner mainly above the phreatic level, and (ii) the dam corner is stable up to the planned height if it is gradually strengthened with rockfill berms on the downstream side. The results of 2D axisymmetric analyses showed a fairly good agreement with those of 3D analyses. It is concluded that 2D axisymmetric analyses are appropriate for this dam corner. This implies that significant computational time can be saved by utilizing 2D analyses instead of 3D analyses.
Tailings dam,Corner,Finite element analysis,Internal erosion,Consolidation, Slope stability
http://scientiairanica.sharif.edu/article_4157.html
http://scientiairanica.sharif.edu/article_4157_4758112a9fb02a6f3c6c7520fd45a459.pdf
Sharif University of Technology
Scientia Iranica
10263098
23453605
24
5
2017
10
01
A OneParameter Controlled Dissipative Unconditionally Stable Explicit Algorithm for Time History Analysis
2307
2319
EN
ShuennYih
Chang
Department of Civil Engineering
,
National Taipei University of Technology
changsy@ntut.edu.tw
Ngoc  Cuong
Tran
Department of Civil Engineering
,
National Taipei University of Technology
Tsui  Huang
Wu
Department of Civil Engineering
,
National Taipei University of Technology
Yuan  Sen
Yang
Department of Civil Engineering
,
National Taipei University of Technology
10.24200/sci.2017.4158
A new family of onestep integration methods is presented herein. A free parameter is used to control the numerical properties and it can be considered as an indicator of numerical dissipation for the high frequency modes. This family method can have unconditional stability, explicit formulation and desired numerical damping, which implies that the low frequency modes can be accurately integrated while the spurious growth of high frequency modes can be suppressed or even eliminated. In addition, a zero damping ratio can be achieved. Since the unconditional stability and explicit formulation are integrated together for the proposed family method, it can drastically reduce the computational efforts when compared to the traditional integration methods.
unconditional stability,numerical dissipation,explicit method,Nonlinear dynamic analysis,accuracy,structuredependent integration method
http://scientiairanica.sharif.edu/article_4158.html
http://scientiairanica.sharif.edu/article_4158_c7f44f60222eb72eeef90bd1828604b6.pdf
Sharif University of Technology
Scientia Iranica
10263098
23453605
24
5
2017
10
01
Effect of Steel and Concrete Coupling Beam on Seismic Behavior of RC Frame Accompanied with Coupled Shear Walls
2227
2241
EN
Habib
Akbarzadeh Bengar
Department of Civil Engineering, University of Mazandaran,
Babol
sar, Iran
h.akbarzadeh@umz.ac.ir
Roja
Mohammadalipour A ski
Department of Civil Engineering, Shomal University, Amol, Iran
10.24200/sci.2017.4159
Construction of diagonal reinforcement in concrete coupling beam is difficult so its replacement is steel coupling beam. Literature shows that a few studies have been done on seismic behavior of RC coupled wall with steel coupling beam. In this paper, the influences of increase in building height on the seismic nonlinear behavior of dual structural systems in forms of RC frames accompanied with RC coupled shear walls once with concrete then with steel coupling beam have been investigated. Therefore the buildings with 7, 14 and 21 story and containing RC coupled wall systems with concrete and steel coupling beams used to perform the pushover analysis having different load patterns. Some seismic parameters such as ductility factor, response modification factor due to ductility, overstrength facto, response modification factor (R) and displacement amplification factor (Cd) have been studied. Regarding the results, the response modification factor for the mentioned structural system is higher than the values which are used in Codes of practice for seismic resistant design of buildings. Also, the displacement amplification factor and the response modification factor increased as the structure height decreased and the value of these factors at steel coupling beam structures are higher than concrete coupling beams.
RC coupled Shear wall,Concrete and steel coupling beam,seismic behavior,Nonlinear analysis,Response modification factor,Displacement amplification factor
http://scientiairanica.sharif.edu/article_4159.html
http://scientiairanica.sharif.edu/article_4159_15dbe9025b4f5c5954b11256bd4e93fc.pdf
Sharif University of Technology
Scientia Iranica
10263098
23453605
24
5
2017
10
01
An Anisotropic Multiplane ElasticDamage Model with Axial and Shear Damage and Its Application to Concrete Behavior
2202
2212
EN
S.A.
Sadrnejad
Civil Engineering Faculty,
K. N. Toosi University of Technology
M.R.
Hoseinzadeh
Civil Engineering Faculty,
K. N. Toosi
University
of
Technology
10.24200/sci.2017.4160
The prediction of material response is necessary for the analysis of structure under static or dynamic loading. Mathematical modeling of the nonlinear tridimensional mechanical behavior of quasibrittle materials like concrete caused by damaging and plasticity effects are one of the most serious classical challenges we face in the engineering science. Among phenomena of different orientation, the microplane models, like multiplanes models which use a constitutive equation in a vectorial form rather than tensorial form by means of capturing interactions, can serve this goal adequately. This paper presents a simple realistic and robust damage based model in the multiplanes framework accomplished with a few parameters for calibration and suitable for engineering purposes without volumetricdeviatoric split of strain tensor and its problems. This damage formulation has been built on the basis of two types of fundamental damage, axial damage and shear damage, that essentially can be occurred on each microplane and based on this concept two new axial and shear damage functions are presented. By comparing between the results of the proposed model and experimental data, model verification has been examined under different loading/unloading/reloading stress/strain paths.
MultiPlanes,MicroPlane,ElasticDamage Model,Nonlinear Behavior,QuasiBrittle Materials,Concrete
http://scientiairanica.sharif.edu/article_4160.html
http://scientiairanica.sharif.edu/article_4160_a6dbac4736835bf628b8b50933545baa.pdf
Sharif University of Technology
Scientia Iranica
10263098
23453605
24
5
2017
10
01
Innovative Analytical Solutions to 1, 2 and 3D Water Infiltration into Unsaturated Soils for InitialBoundary Value Problems
2346
2368
EN
Hamed Reza Zarif
Sanayei
Department of Civil and Environmental Engineering; Shiraz University, Iran
hzarif63@gmail.com
G. R.
Rakhshandehroo
Department of Civil and Environmental Engineering, Shiraz University, Iran
N.
Talebbeydokhti
Department of Civil and Environmental Engineering, Head of Environmental Research and Sustainable Development Center; Shiraz University, Iran
taleb@shirazu.ac.ir
10.24200/sci.2017.4161
Fluid infiltration into unsaturated soil is of vital significance from many perspectives. Mathematically, such transient infiltrations are described by Richards' equation; a nonlinear parabolic Partial Differential Equation (PDE) with limited analytical solutions in the literature. The current study uses separation of variables and Fourier series expansion techniques and presents new analytical solutions to the equation in one, two, and three dimensions subject to various boundary and initial conditions. Solutions for 1D horizontal and vertical water infiltration are derived and compared to numerical finite difference method solutions, whereby both solutions are shown to coincide well with one another. Solutions to 2 and 3D vertical water infiltration are derived for constant, noflow, and sinusoidal boundary and initial conditions. Presented analytical solutions are such that both steady and unsteady solutions may be obtained from a single closed form solution. The solutions may be utilized to test numerical models that use different computational techniques
Richards’ equation,Analytical solution,Infiltration,unsaturated soil,Initial  Boundary Value Problems
http://scientiairanica.sharif.edu/article_4161.html
http://scientiairanica.sharif.edu/article_4161_aba210701dfa4d6b971d241fb1fb5770.pdf
Sharif University of Technology
Scientia Iranica
10263098
23453605
24
5
2017
10
01
An experimental study of the seismic behavior of infilled RC frames with opening
2271
2282
EN
H.
Tekeli
Department of Civil Engineering, Suleyman Demirel University, Isparta, Turkey
A.
Aydin
Department of Civil Engineering, Suleyman Demirel University, Isparta, Turkey
10.24200/sci.2017.4554
In fill walls are not generally taken into account in structural analysis due to their complex behavior at seismic actions. As it is known, they increase the stiness as well as the lateral load capacity of the system. Sometimes, inll walls may have window and door openings in their planes. In the present study, behavior of Reinforced Concrete (RC) frames with inll walls, which have openings, is investigated under cyclic lateral loadings. Location and size of the openings in the inll wall are selected as investigation parameters.Test specimens are constructed and experimentally analyzed. The inll wall changes the behavior of the frames under cyclic lateral loads signicantly. Location and size openings in the inll wall are two main parameters that aect the behavior of the inll walls as well as the frame. The test results clearly show that the contribution of the inll wall to the behavior of RC frame diminishes signicantly when the opening ratio is larger than 9%.Therefore, the eect of the opening in the inll wall must be taken into account in thestructural modeling when the opening ratio is larger than 9%.
In Fill wall,Opening,Reinforced concrete buildings,Cyclic lateral loading,Location and size of the openings
http://scientiairanica.sharif.edu/article_4554.html
http://scientiairanica.sharif.edu/article_4554_b58a9f2c4389657af6e0e8be07903492.pdf
Sharif University of Technology
Scientia Iranica
10263098
23453605
24
5
2017
10
01
Reliable seismic collapse assessment of shortperiod structures using new proxies for ground motion record selection
2283
2293
EN
M.
Yakhchalian
Department of Civil Engineering
and Surveying
, Islamic Azad University, Qazvin Branch
,
P.O.
Box
34185

1416,
Qazvin, Iran
m_yakhchalian@alumni.iust.ac.ir
Gholamreza
Ghodrati Amiri
Center of Excellence for Fundamental Studies in Structural Engineering, School of Civil Engineering, Iran University of Science &Technology, Tehran, Iran
ghodrati@iust.ac.ir
Mahdi
Eghbali
School of Civil Engineering, Iran University of Science & Technology, P.O. Box
16765

163,
Tehran, Iran
m_eghbali@iust.ac.ir
10.24200/sci.2017.4162
One of the important steps in seismic collapse assessment of structures by using nonlinear dynamic analyses is the appropriate selection of ground motion records. Epsilon (εSa), eta (η), and gamma (γ) for longperiod structures, are proxies that have been recently proposed for Ground Motion Record Selection (GMRS). In this study, two parameters, named γs, are proposed, which have considerable correlation with the collapse capacity of shortperiod structures having fundamental period less than 1 s. One of these parameters is a linear combination of εSa, epsilon of Pseudo Spectral Acceleration (PSA) at 1.5 times of the fundamental period of the structure (εSa(1.5T1)) and εPGV. The other one is a linear combination of εSa, εSa(1.5T1) and epsilon of spectrum intensity, εSI. To obtain and optimize γs, the Particle Swarm Optimization (PSO) algorithm is applied. Since the parameters proposed as γs have significant correlation with the collapse capacity of shortperiod structures, they can be used as efficient proxies for GMRS in seismic collapse assessment of shortperiod structures. The results show that GMRS using γs leads to reduction in the dispersion of structural collapse capacity in comparison with GMRS based on εSa or η.
ground motion record selection,shortperiod structures,reliable seismic collapse assessment,Epsilon,gamma,Fragility Curve
http://scientiairanica.sharif.edu/article_4162.html
http://scientiairanica.sharif.edu/article_4162_c2a1941cc56d7cd698b230f0a96db9d6.pdf