نشریه مهندسی عمران و محیط زیست دانشگاه تبریز
سال چهل و سوم شماره 4 (پیاپی 73، زمستان 1392)

1. In structural reliability analysis, we encounter parameters which do not possess constant determined values and are of random and vague identity in nature. Hence, we inevitably face a sort of uncertainty in the safety assessment of structures. The nature of uncertainties and the methods of their modeling in assessing safety of structures have been of researcher’s interest for many years [1]. A popular classification of uncertainty distinguishes between aleatory and epistemic uncertainty [2]. Probabilistic methods presuppose sufficient information for determining stochastic input parameters, such as, e.g. expected values, variances, and probability distribution functions. Thus they are only able to account for aleatory uncertainty. Inaccuracies, unreliable data, or uncertainty which cannot be described or insufficiently described statistically can thus only be accounted for approximately. Therefore, probabilistic methods may only be applied to a limited extent. Alternative methods based on fuzzy set theory [3] and the theory of fuzzy random variables [4] have only been applied in past few years which take into account epistemic uncertainty. The purpose of this paper is to determine fuzzy structural reliability index through modeling epistemic uncertainty arising from ambiguity in statistical parameters of random variables. The fuzziness of the computed safety level characterizes the new quality of the safety assessment compared with probabilistic methods. Meanwhile, the introduction of Fuzzy First Order Reliability Method (FFORM) and its application in evaluating the reliability of structures is under taken by three examples. The developed fuzzy probabilistic concept for the safety assessment of structures provides sophisticated algorithms to take account of uncertainty of different characteristics in a comprehensive way.2. In the proposed method, the form of limit state function is initially determined in the standard normal space. Then, the mean and standard deviation of random variables are modeled as fuzzy triangular numbers and are discretized to their α-cuts. The corresponding α-cuts of all variables constitute a spatial shape which is called the crisp subspace. The entire points inside this subspace are used as inputs to analysis algorithm in order to determine the corresponding interval of the respective fuzzy response for the same α-cuts. Assembling these intervals yields the membership function of fuzzy output. On the other hand knowing the smallest and largest elements, the above interval would be specified. There are two optimum points in the crisp subspace which yield the smallest and largest elements of the aforesaid interval, see Fig. 1. Thus determining these points turns into two simultaneous optimization problems according to Eqs. (1) and (2), aims finding the two optimums in the α-level Optimization technique. 3. Comparison of the defuzzificated fuzzy reliability indices with classical methods results presented the successful application of α-level optimization technique with verification of the proposed method. Survey results shown that the reliability index obtained from the existing methods only represents a special case of fuzzy method proposed in this paper. Furthermore, neglecting epistemic uncertainties of parameters influencing the structural performance in current probabilistic methods has caused a large error (about 10%) in the reliability index calculation. Hence, taking in to account, the epistemic uncertainty arising from statistical ambiguity in calculation of structural reliability index and correction of all available methods are necessary.4. In this paper, modeling the epistemic uncertainty of random variables via fuzzy triangular numbers in the FORM reliability method using the alpha level optimization method has been brought into focus. The proposed method is implementable in reliability problems in which all random variables are fuzzy sets and in reliability problems containing non-linear limit state functions and provides a precise acceptable response. The implementation of the proposed method leads to the definition of certain bounds of uncertainty for the reliability index, resulting in more realistic value compared to classic methods. Whiles this uncertainty interval is not taken into account in classic methods of reliability. The implementation of the proposed method with three examples demonstrates its capability in determining fuzzy reliability index. Investigation of results also indicates the accuracy of the proposed method and shows that the classic classic FORM method is only a special case of the proposed FFORM method.

1. Access to safe drinking water is an important factor for human life. Presence of both chemical and microbial contaminants in water can lead to different types of disease. In areas which groundwater is contaminated to fluoride via dissolution from geological formations and earth crust, drinking water can be considered as a major source of exposure to fluoride. Dental fluorosis and skeletal fluorosis are health outcomes of exposure to high concentration of fluoride via drinking water. World Health Organization (WHO) guidelines [1] suggested that in areas with warm climate, the optimal fluoride concentration in drinking water should remain below 1 mg/L (1 ppm or part per million), while in cooler climates it could go up to 1.2 mg/L. The differentiation derives from this fact that we perspire more in hot weather and consequently drink more water. The guideline value (permissible upper limit) for fluoride in drinking water was set at 1.5 mg/L, considered a threshold where the benefit of resistance to tooth decay did not yet shade into a significant risk of dental fluorosis. It has long been known that excessive fluoride intake carries serious toxic effects. But scientists are now debating whether fluoride confers any benefit at all or no. There are different options for overcoming to fluoride problem in drinking water including replacement of contaminated water resources with safer one or removal of excessive fluoride from water through application of different treatment methods. Those methods are generally based on chemical absorption, chemical precipitation, ion exchange and physical removal [reverse osmosis (RO) and electrodialysis process (ED)] [2]. Present study aimed to investigate the efficiency of a modified activated alumina for removal of fluoride from aqueous solution. 2. Methodology2.1. Batch experiments:Modified Activated Alumina (MAA) by iron compounds was used in current study which was a commercial product of Alcan Company, Canada [3]. During batch absorption experiments, effects of solution pH (5-9), initial fluoride concentration (1-10 mg/L), adsorbent dose (1-50g/L), contact time (15-180min) and shaking rate (100-400rpm) on fluoride removal was investigated in the laboratory temperature (20±1ºC). 2.2. Fluoride measurement:SPADNS method was used for the measurement of fluoride based on standard methods for the examination of water and wastewater. The SPADNS colorimetric method is based on the reaction between fluoride and a zirconium-dye lake. Fluoride reacts with the dye lake, dissociating a portion of it into colorless complex anion (ZrF62-) and the dye. As the amount of fluoride increases, the color produced becomes progressively lighter. Spectrophotometer (Model: Jenway 6105 UV/Vis) was used at 570 nm for measurements [4]. 3. 3.1. Effect of absorbent dose, contact time, pH and shaking rate on fluoride removalAbsorbent dose of 1, 5, 10, 25 and 50 g/L removed respectively 70, 91, 95, 97 and 98 of fluoride with initial concentration of 10 mg/L during 120 minutes. Optimum dose of absorbent was determined 5 g/L in 120 minutes. Fluoride level was decreased from 10 mg/L to 0.8 mg/L by 5g/L MAA (as optimum dose). This concentration is in the range of national guideline for fluoride in drinking water. Results of the study indicated that fluoride removal efficiency increased by increasing the contact time. Removal efficiency in 15, 30, 60, 120, and 180 minutes were 70, 80, 88, 92 and 93 percent using optimum dose, respectively. The best removal efficiency was observed at neutral pH in which removal efficiency was 90-92%. The best removal performance was observed in both shaking rate of 300 and 400 rpm (93%). 3.2. Absorption isotherm:Langmuir and Freundlich isotherms were investigated for absorption model. Fig. 1 and Table 1 show achieved results of batch experiments for absorption models. As can be seen in the figure, the equilibrium isotherm for fluoride uptake corresponds closely to the Langmuir model.Table 1. Absorption isotherm parameters for removal of fluoride by MAAModel qm (mg/g) B (L/mg) Kf N R2Langmuir 8.23 0.147 - - 0.85Freundlich - - 5.16 5.22 0.434. According to observed removal efficiencies during the study, MAA used in the study can be considered as an efficient absorbent for the removal of fluoride from drinking water. However, conducting more research using real water samples and column experiments is highly recommended before filed application of the method.

1. Unreinforced concrete canals are one type of sensitive and important water conveyance structures. Whereas these structures are inevitably constructed on different types of soils, investigation of geotechnical issues related to the interaction of soil and concrete lining is important for reducing damages to the canals. These damages in the hydraulic canals are observed in the forms of cracking in the concrete lining and their large displacement. Due to numerous cases observed in Iran, construction of irrigation canals on the problematic soil has led to serious damage to the structure of canals and finally losses a lot of costs. One of the most common types of problematic soils is expansive soils. Every year many of new structure are constructed on the swelling soils, over 60% of these structures suffered minor damages such as cracking and approximately 10% of these structures are heavily damaged that cannot be repaired.In a comprehensive definition, expansive soils are referred to the soils which have the potential of swelling and shrinkage and show significant volumetric changes and eventually lead to serious damages to different structures, especially light structures. These damages in the hydraulic canals are observed in the forms of cracking in the concrete lining and their tuck. Over time and with the occurring of melting and freezing cycles, lining fine micro cracks are become larger and provide a situation for water penetration and plant growth then these factors eventually lead to changes of hydraulic canal characteristics and finally its destruction. Since the repair and rehabilitation of damaged structures impose huge costs on project, doing research for understanding the mechanism of interaction between the soil and canal lining seems necessary.Therefore, by considering the presented introduction, construction of canals on problematic soils such as expansive soils is inevitable and appropriate procedures should be followed to reduce the damages.For this purpose, in this study the section of trapezoidal canal with real dimensions has been modeled by Geo-Studio (2007) software and interaction of the soil-concrete lining and the effect of considering filter layer under canal have been studied in the impounding conditions and finally the result of numerical analyses have been compared to in-situ observations. Since the soil of canal bed is in the unsaturated condition and has a swelling potential, firstly it is necessary to mention the background of previous studies for numerical modeling of unsaturated soil behavior and efforts have been done by researchers to implementation presented theories2. The behavior of an unsaturated expansive soil can be formulated using the theory of unsaturated soils, using two independent stress variables, the constitutive relationships for the soil structure and water phase, and flow laws for the water phase [1-4]. The two stress state variables are net normal stress, (σ-ua), and matric suction (ua-uw), where σ is total normal stress, ua is pore-air pressure, and uw is pore-water pressure. Changes in the void ratio and degree of saturation of an unsaturated soil can be expressed as functions of the stress state variables to form two three-dimensional constitutive surface [5]. Approximate volume change (and water content) coefficients should be adequate for most engineering analyses. Procedures for the approximation of the volume change coefficients assist in the implementation of unsaturated soil mechanics into geotechnical engineering practice. The primary interactive processes involved with a volume change analysis of an unsaturated expansive soil are stress deformation and water flow. The stress-deformation process is governed by static equilibrium, while the water flow is governed by water continuity equation. Solutions for volume change require that both the equilibrium equation and the continuity equation be solved. The solutions can be obtained using either a coupled or an uncoupled approach.As mentioned, the behavioral models of unsaturated soils are complex. In addition a large number of parameters required for analysis and there are many problems related to measuring or calculating the values of these input parameters. Because of that, these behavioral models are rarely used by geotechnical engineers.According to the conducted surveys, these behavioral models are not applied to common software of geotechnical engineering. Therefore, some geotechnical engineers have wrongly assumed these kinds of soils as a saturated soil and used the related behavioral models such Cam-Clay or Modify Cam-Clay. In recent years, many attempts have been made by researchers to apply behavioral models of unsaturated soils and using these models in geotechnical engineering softwares. For applying these models, simplifying assumptions are made but these should not undermine the accuracy of the results. Based on the review of the available technical resources, the behavioral models of unsaturated soils are applied only to the two pieces of geotechnical engineering software so far which are Plaxis2D 2010 and GeoStudio 2007. In this research, GeoStudio 2007 software package is used for modeling. The basis of this software for modeling of unsaturated expansive soils is the behavioral model and presented equations by Vu and Fredlund [4]. For verifying the accuracy of the results, presented example by these researchers was modeled by the software and the proposed behavioral model for unsaturated soils was assigned to it. By comparing the results, accuracy and precision of the software can be realized and the software gives a close agreement between the results by application of both coupled and uncoupled analysis methods, which has been previously described. It should be noted that the input parameters of the software and the solution of the equations are simplified as much as possible toward the method of Vu and Fredlund to be applicable for geotechnical engineers. Thus, SIGMA/W software can be used to estimate the amount of swelling with appropriate accuracy in unsaturated expansive soils that are affected by changes in wetting conditions and consequently caused negative pore pressures. SIGMA/W, which is in the GeoStudio software package, is based on the finite element method for stress-deformation analysis of earth structures. Its comprehensive formulation makes it possible to solve any kind of simple and complex problem. For instance, by using this software, both simple linear-elastic deformation analysis and complicated effective-stress analysis based on non-linear elastoplastic behavior can be conducted. When this software is used together with other products of GeoStudio package, changes in pore pressure and its distribution in soil mass due to the external loading can be computed by using coupled and uncoupled formulation. In addition, SIGMA/W can be used for modeling of soil interaction with beam or bar elements.In this study Tabriz Plain Canal is selected as a case study. The irrigation and drainage network of Tabriz plain is under construction in six regions and 40000 hectares in the northwestern part of Iran. The length of the main canal is 29 km, the width of floor is between 2.5 to 5.0 m, and its height is between 2 to 2.75 m. The slope of canal walls is 1 (vertical) to 1.5 (horizontal). The canal lining is made of unreinforced concrete. In the construction phase of first 10 km, due to a heavy rain and flooding, a part of canal was filled with water. After the water was emptied out, cracks and heave were observed in some parts of the canals. In order to investigate this phenomenon, an undisturbed soil specimen was obtained from heaved zone and a free swelling test was performed.3. The results of laboratory tests show that the surface soils of Tabriz plain are composed of silt and clay. In this research, standard methods are used to predict swelling potential of these soils. Generally there are two indirect methods for anticipating the swelling potential in references, Seed et al. method (1962) [6] and Van der Merve method (1964) [7]. The result show that the swelling potential of soil samples vary from low to high and the result of free swelling test show that the free swell height and the swelling pressure of undisturbed sample are about %5.4 and 40 kPa respectively. These values show that the soil heave should be considered in lightweight structure designing such as Tabriz plain canal.As observed in in-situ investigation, the swelling phenomenon has led to cracking and relative displacement of canal panels in joint locations from few to 30 mm. To prevent the occurrence of this phenomenon, using a filter layer with 30 cm thickness was proposed in this project. Application of filter layer doesn’t have direct effect on soil heave but the properties of filter material lead to reduce the swelling potential. The filter is composed of granular material so it can uniformly transfer the local pressure of canal bed soils to lining and lead to reduce the relative displacement of adjacent panels. Another parameter is the weight of filter layer. This layer applies about 5 kPa additional pressure to expansive canal bed soil although this pressure isn’t more than the swelling pressure but it can compensate that amount of swelling pressure.This proposed method was tentatively performed in 50 m length of real canal. For evaluation the efficiency of this method, surveying points were observed on canal section and displacement of these points were measured.The in-situ surveying records showed that the performance of filter layer led to reducing the swelling potential and the relative displacement of panels decreased from 30mm to 5 mm. As mentioned before, in this research the actual dimensions of the under construction water canal of the irrigation and drainage network of Tabriz plain, which is located on the expansive soils, is used for numerical modeling. Three series of joint are considered in canal section, two joints in canal walls in the level of 0.5 meter from floor and one joint in canal floor. As a real condition for modeling of joint, two centimeter space is vertically considered in lining surface. For the simulation of the initial conditions (local conditions), it has been assumed that the canal bed soil is somewhat dried and a constant suction is established in the soil. For modeling the infiltration into the soil, water level inside the canal is applied as a water head to the lining elements. The lining has been modeled by beam elements. Generally, it is assumed that in the initial conditions, a suction equal to 200 kPa was available in the environment. In the first step of analysis, the initial in-situ stress conditions are applied to the model and primary balance is obtained. In this step linear elastic behavior is considered for the soil and concrete lining and the environmental suction of -200 kPa is considered in the computation. For analysis of heave coupled case, the soil behavior is considered elastoplastic and the proposed model by Vu and Fredlund [4] is used to predict the behavior of unsaturated expansive soils. This should be considered that all equations used in the computations and the mechanism of soil behavior are functions of time.Since the aim of the presented research is to study the soil-lining interaction behavior in various moisture conditions and also the effect of implementation of filter layer to control the swelling of canal bed soil by using site investigation and numerical methods and comparing the results of two methods, two types of analyses are done in this research. In the first case, the filter layer has not been considered under the lining and calculations have been performed and in other case, the filter layer has been considered and all calculations have been repeated. In any of cases, the water level in the canal is assumed as constant and 2 meter above the floor.4. The results of numerical analyses and in-situ observations have acceptable consistent in prediction of the deformation shape of panels, the values of displacement and the effect of filter layer on these phenomenon. The use of a filter layer under the concrete lining leads to the relative reduction of general heave in unsaturated expansive bed soil and also prevents the lining cracking.The intersection point of the canal wall with floor, the upper corner of the canal wall and middle point of lining length are considered as the locations of concentration of internal forces in the canal section. The joints along the wall act as a hinge, the values of moment in these points are zero and they have a functional role to control the cracking in the canal wall. The optimization of the location of joints and the modification of the geometric properties of canal section are others ways to reduce the lining damages in canals which are constructed on expansive soils.

1. Generally, prediction and calculation of the settlement of piles are complicated due to soil change during pile construction and many uncertainties inherent in the load distribution along the shaft and base of the pile. Therefore, most of the suggested relations about the settlement of piles are empirical. The results of some load tests in sand are available in reports. The empirical and semi-empirical relations have been used for the calculation of pile settlement previously by researchers. However, nowadays, calculation of pile settlement is carried out by load-transfer, elasticity theory and numerical (such as finite element) methods. Pile load test is one of the accurate methods for evaluation of pile settlement that is generally applied for important projects. In this study, settlements of piles were measured by performing compression load tests on 12 small scale cast-in-situ concrete piles in sandy soils and the obtained results were compared with the results of some other settlement calculation methods. 2. Methodology2.1. Site characterization:The area of study is located in Sorkhroud city. The soil of this region consists of coastal deposits. The groundwater table was below the base of piles. Therefore, the effect of groundwater on piles was not considered in this study. Then, laboratory and in-situ tests were carried out.2.2. Load tests on piles:The compression load tests were carried out using constant rate of penetration (CRP) method and in accordance with ASTM D 1143-81[1]. In this study, 180*80*80 cm concrete blocks were used to provide reaction for the applied load. The weight of each block was about 2.7 ton. The blocks were placed on a 6-m long beam. The piles were loaded by utilizing a 50 ton capacity hydraulic jack having a stroke of 15 cm, placed below the beam. Figs. 1-3 show the equipment.2.4. Pile settlement calculation In the present research, the settlements of piles were calculated by Meyerhof’s empirical and Vesic’s semi-empirical methods [2, 3]. On the other hand, recently, computer programs can numerically model piles and evaluate their settlements. In the numerical modeling, selection of soil modulus of elasticity is usually difficult considering soil’s elastic behavior. Therefore, different relations have been suggested for estimation of this parameter. The study shows that by performing pile load test and considering soil’s elastic behavior, the soil modulus of elasticity can be estimated using back analysis. For this purpose, the piles were numerically modeled using the computer program PLAXIS 2D and the obtained load-settlement curves were compared with the corresponding curves obtained by pile load tests.3. The load-settlement curves of piles were determined by performing pile load tests. The settlement calculation was performed for the selected piles using empirical and semi-empirical methods. The results show that empirical and semi-empirical methods are in a good agreement with the results obtained by pile load tests. Since soil behavior is modeled using Mohr-Coulomb elastic-plastic model, the settlements of piles depend on soil modulus of elasticity significantly. In this paper, soil modulus of elasticity was determined using back analysis and trial and error methods for the selected piles considering their allowable loads. 4. In this study, the settlements of piles in sandy soils were evaluated by performing pile load tests. At first, soil modulus of elasticity was estimated using finite element method. The results depict that the obtained soil modulus of elasticity is in a good agreement with Schmertmann method [4]. The obtained sand modulus of elasticity with medium relative density is about 12000 kPa. Vesic’s semi-empirical and Meyerhof’s empirical methods [2, 3] evaluate the settlements of piles acceptably which can be used for practical purposes. However, Meyerhof [2] method was more accurate. The results show that by selecting an acceptable empirical coefficient Cp in the Vesic [3] method, pile settlement can be predicted more accurately. The disturbance of soil during pile construction greatly affects this coefficient. In the present study, the empirical coefficient (Cp) was estimated 0.035 for in-situ piles constructed in slightly disturbed sandy soils with medium relative density.

1. Multidimensional modeling of ground motions for seismic response analysis of structures needs the principal axes of earthquakes to be detected. This principal axes show the energy situation in the orthogonal directions. This paper reviews the characteristics of earthquakes recorded in various stations in August 2012, Varzeghan- Ahar’s twin earthquakes along the principal directions and compare the angles of principal axes of the two earthquakes to find out which direction have a greatest energy.2. Principal axes of ground motion:The computation of the principal axes of earthquake accelerograms has been the subject of a number of studies [1, 2]. Principal axes can be computed in a manner analogous to the computation of eigenvectors of an eigenvalue problem. Three different sets of principal axes can be computed by diagonalizing the following matrices (1) the total energy matrix, (2) the covariance matrix, and (3) the cross spectral matrix of three wave components.The most commonly used method to compute the principal axes is by diagonalizing the covariance matrix of ground accelerograms. Applying a procedure similar to the orthogonal transformation of three-dimensional stress, an orthogonal set of principal axes can be determined for three-dimensional ground motions. Along these principal axes, the components of motion have minimum, intermediate and maximum values of variance and have zero values of covariance. This property suggests that components of earthquake motion do not need to be cross-correlated statistically if they are directed along the principal axes.If the ground motions are assumed to be Gaussian with zero mean values, the three-dimensional ground motion process can be completely characterized in probabilistic terms by the covariance matrix as follows Where each term of the covariance matrix can be expressed as follows In which E denotes the ensemble average.By diagonalizing the covariance matrix, the off-diagonal terms in the covariance matrix are zeros because the ground motion components along the principal axes are fully uncorrelated with respect to each other.Let and represent a set of orthogonal horizontal components of ground acceleration. The correlation coefficient between these two components over the time interval Results And Discussion