فهرست مطالب علیرضا غنی زاده

Application of different stabilizers and additives such as cement, lime, and fly ash is one of the solutions for improving weak and problematic subgrade soils. In this study, a clay soil was stabilized using different percentages of cement and lime (0, 3, 5, 7 and 9%) and with different moisture content (optimum humidity level, wet side and dry side) and unconfined compressive strength (UCS) test was conducted at different curing times (7, 14, 21, 28 and 60 days). Then, the gene expression programming (GEP) method was employed to model the UCS of cement-stabilized and lime-stabilized clay soil. In the developed models, three variables of additive percentage, curing time and moisture content are used as the input variables to predict the UCS. The results of this study showed that the coefficient of determination (R2) for the model developed to predict the UCS of cement-stabilized clay soil is 0.935 and 0.926 for training and testing data, respectively. The R2 value for the model developed to predict the UCS of lime-stabilized clay soil is 0.911 and 0.884 for training and testing data, respectively. The results of the parametric study showed that the UCS increases with the increase in the percentage of cement and lime and the curing time and decreases with the increase in the moisture content.

The resilient modulus (MR) of road materials is one of the most important parameters in the analysis and design of pavement. This parameter is used in both empirical methods and mechanistic-empirical methods as the main parameter for expressing the stiffness and behavior of road construction materials. To determine this parameter in the laboratory, it is necessary to perform a dynamic tri-axial loading test under various confining and deviator stresses, which is a time- and cost-intensive approach. In this paper, a wavelet neural network (WNN) hybridized with the teacher learning based optimization (TLBO) algorithm was used to model the MR of unbound subbase materials. The input variables included maximum dry density, uniformity coefficient, curvature coefficient, percent passing No. 200 sieve, confining stress, and deviator stress and output variable was resilient modulus of the unbound subbase materials. The results of this study indicate that increasing the number of neurons in the hidden layer to more than 20 neurons has little effect on increasing the accuracy of the wavelet neural network and the Mexican Hat wavelet function has the best result in predicting the resilient modulus. The results of this study also indicate that the WNN-TLBO method is more accurate than the ANN method in predicting the MR of unbound subbase materials. External validation results indicate that the WNN-TLBO method satisfy all the necessary criteria, which indicates the high predictive potential of this method. The results of sensitivity analysis indicate that the degree of importance of the confined stress is higher than other variables for predicting the resilience modulus. A parametric analysis was also done to study the effects of each input variable on the MR.

In road pavement design, soil resilient modulus is one of the factors that play a very important role in determining pavement thickness. In the past, determining the Resilient Modulus of soil directly from laboratory results has not always been practical due to its high costs, both in terms of equipment and labor. Therefore, it is possible to predict and determine this parameter based on past field data using artificial intelligence. Our goal in this paper is to develop a model for predicting the resilient modulus of stabilized clay soils using artificial neural networks. In this study, four different soil samples stabilized with additives, such as lime, fly ash, and cement kiln dust, were examined using the pavement design appendix of the AASHTO 2002 specification. By comparing the results to the laboratory data based on the statistical indicators such as regression coefficient (0.99), root mean square error (less than 6 percent), we found that the artificial neural network was highly accurate in predicting the resilient modulus..

In this study, the effect of adding different percentages of recycled concrete aggregates to aggregate base layer materials on the fatigue and rutting life of pavement has been investigated. In the performed analyzes, nonlinear analysis by NonPAS software has been used. To this end six four-layered pavement sections with different layers thickness were analyzed for three types of very soft, soft and medium clay subgrade soil. The behavior of asphalt layer materials was considered as linear elastic and the behavior of base, subbase and subgrade materials was considered as nonlinear elastic. In all sections of pavement, the use of 0 to 100% of recycled concrete aggregates for all subgrades, at least 61.6% and maximum 198.5% increases the fatigue life and at least -22.6% and maximum 88.4% increases rutting life. In very soft clay subgarde, in thicknesses above 20 cm for the base layer and thicknesses above 30 cm for the subbase layer, it is possible to use recycled concrete materials. In medium clay subgrades, in thicknesses above 15 cm for the base layer, thicknesses above 20 cm for the subbase layer and also thicknesses above 15 cm for the asphalt layer, it is possible to use recycled concrete materials. In hard subgardes, there is no special considerations in terms of the thickness of pavement layers for the use of recycled concrete materials.

This paper aims to investigate and compare the properties of highly plastic clay soil stabilized by geopolymers synthesized from various industrial residues and rice husk ash. To this end, steel slag, fly-ash and diatomite were used as the base material, and NaOH solutions of 8.68 M and Na2SiO3 solutions extracted from rice husk ash were used as an alkaline activator for stabilization. Stabilization was performed using 10, 20 and 30 percent of base materials by dry weight of soil. Samples were compacted at optimum moisture content and were cured for 7, 28 and 90 days. The results of the experiments show that the application of geopolymer as a stabilizer improve the compressive and tensile strength, increase Young's modulus and reduce the failure strain of the stabilized clay soil. The highest increase in the unconfined compressive strength (UCS) was related to stabilized clay with geopolymer synthesized using 30% of steel slag, its UCS was 25.2 times higher than the untreated clay soil. Also, the samples stabilized with geopolymer synthesized using 30% of fly-ash and 30% of diatomite showed the UCS of 4.05 and 12.72 times more than the untreated clay soil, respectively. The results of this study also showed that the stabilization of clay using geopolymer significantly increases the indirect tensile strength (ITS) of the samples, so that the samples stabilized with geopolymers based on the 30% of steel slag, 30% of fly-ash and 30% of diatomite, had an ITS of  23.14, 7.58 and 12.5 times more than untreated clay soil, respectively.

In the present study, Evolutionary Polynomial Regression (EPR) technique is employed to develop a mathematical model to estimate the USC of Full Depth reclaimed (FDR) materials stabilized with Portland cement. To this end, a dataset containing 62 records from experimental studies related to unconfined compressive strength of full-depth reclaimed (FDR) base stabilized with Portland cement were used. Percentage of cement, percentage of RAP, percent passing of #200 sieve, optimum moisture content, and curing time were considered as independent variables. The results show that EPR has a great capability for prediction of the UCS in case of FDR base stabilized with Portland cement.

There are several methods for analyzing flexible pavements, where the most widely used of which are the multilayerd theory and finite element method (FEM). In this study, two sections of four-layered pavement with assuming two temperatures for surface layer (25 and 40 °C) were analysed and five responses at radial distances obtained from nonlinear analysis using two methods of multilayered theory and finite element method were compared. NonPAS program is employed for nonlinear analysis of these two sections based on the multilayered theory and MICHPAVE program is used for nonlinear analysis of these two sections based on the finite element method. Also, 7 different methods have been used to determine stress points and correct stresses in the multilayered theory method. The results of the analysis showed that only for the vertical stress response on the subgrade, the results of the two programs are very different and for other responses, the difference between the two programs is reasonable. It was also found that the responses obtained from the NonPAS program for a thicker section were in better agreement with the results obtained from the MICHPAVE program. Among the 7 methods considered for determining the stress points in the multilayered method, method 7, which is based on sublayering the nonlinear layer and considering the stress points in the central depth of the sublayers and modifying the radial stresses based on the maximum tensile strength of the materials according to Mohre's failure criterion showed best conformity with the results of MICHPAVE program.

Rutting is among the most important distresses in flexible pavements, which is mainly influenced by asphalt mixes properties at high temperatures. There are different methods for measuring the rutting resistance of asphalt mixes. Flow number of asphalt mix, which is measured experimentally by dynamic creep test is one of the most commonly used rutting index, which requires advanced devices, notable cost and time. This paper aims to develop a simple model for predicting the flow number of asphalt mixes using Evolutionary polynomial Regression (EPR). The developed model can be used for predicting flow number based on Marshall mix design parameters including percentage of fine and coarse aggregates, bitumen content, filler content, air void content, void in mineral aggregate, Marshall stability, and flow. The coefficient of determination (R2) of model in case of training and testing set is 0.9714, and 0.969, respectively, which confirms the high accuracy of model. Comparison of the developed model with the existing models shows the superior performance of the developed model. In addition, the parametric analysis indicates the proper conformity of the developed model with the physical behavior of the asphalt mixtures.

In order to mitigate the environmental impact of iron ore tailing (IOT) and also to reduce the use of natural aggregates, these materials can be used as road materials after stabilization with chemical additives. In this research, the feasibility of using Golgohar IOT, stabilized with 4, 6 and 8% of Portland cement as road base materials, has been investigated. To this end, modified Proctor compaction test, unconfined compressive strength (UCS) test and durability against freezing and thawing (F-T) cycles test were conducted on IOT samples stabilized with different percentages of Portland cement. Results of compaction testing on the samples showed that increasing the percentage of cement increases the optimum moisture content (OMC) and decreases the maximum dry density (MDD). In the next stage, IOT were stabilized using 4, 6 and 8% of Portland cement and UCS samples were fabricated with three different compaction moistures (dry side, optimum moisture content and wet side) and cured for 7, 28 and 56 days. The results showed that with increasing the percentage of cement from 4 to 8% for all curing times, the UCS increased between 1.45 to 2.15 times. Also, the 28-day UCS and 56-day UCS are about 1.73 times and 2.34 times the 7-day UCS, respectively. It was also found that the UCS increases with decreasing moisture content. The results of durability tests against (F-T) cycles on the samples showed that with increasing the percentage of cement, the durability of stabilized materials increases, so that in samples with higher percentage of cement, the lowest percentage of weight loss and volume reduction is observed. Finally, it was found that IOT stabilized with at least 4% of Portland cement provides the necessary strength and durability criteria for use as stabilized base layer.

Accurate determination of resilience modulus (Mr) of pavement subgrade soil is one of the important factors for successful design of pavement structure. This parameter is usually measured using a dynamic triaxial test, which is a complex and expensive experiment. In this study, the evolutionary polynomial regression (EPR) method has been used to develop a model for predicting the resilient modulus of clay subgrade soils based on the results of cone penetration test (CPT). By means of the developed model, the resilient modulus of subgrade soils can be estimated by having the parameters of cone tip resistance (qc), slave friction resistance (fs), moisture content (w) and dry density (γd). The results of this study show that the model developed by the exponential function is the best model constructed. Based on the developed model, the coefficient of determination (R2) for training set, testing set and total set was 0.9808, 0.9714 and 0.9785, respectively. The sensitivity analysis performed also showed the very good agreement of the developed model in predicting the resilient modulus of subgrade soil. The results of sensitivity analysis showed that the moisture content is the least important parameter for predicting the resilient modulus of fine-grained soils and the importance of other parameters is almost the same. In this study, the effect of different parameters on the resilient modulus of subgrade soil has also been evaluated using parametric analysis.

High plasticity clay soil is one of the soils that can be found in most regions of Iran. This soil is known as a problematic soil and as subgrade soil for transportation infrastructures, its characteristics must be improved. The purpose of this study is to evaluate the strength characteristics of high plasticity clay soil stabilized with industrial waste, which in addition to soil stabilization, also has environmental benefits. In this research, steel furnace slag, fly ash and diatomite have been used as stabilizer agents. Stabilization was performed using with 10, 20 and 30% of stabilizer agents by dry weight of soil and samples were compacted at optimum moisture content. In the present study, compaction as well as unconfined compressive strength (UCS) were conducted to compare the strength parameters of soil before and after stabilization. The results showed that the steel furnace slag had a much better performance as a stabilizer than fly ash and diatomite. Samples stabilized with 10% of steel furnace slag with a UCS of 2.16 MPa has a better performance in comparison with other stabilized samples and is the optimum sample. This sample shows a 3.92 times increase in UCS compared to the untreated clay soil. Treated samples with 30% of fly ash and 30% of diatomite with UCS of 0.9 and 1.03 MPa, show 49% and 88% increase in UCS compared to untreated samples, respectively.

One of the Practical solutions for improving subgrade soil is the utilization of additives for soil stabilization. Generally, the unconfined compressive strength (UCS) and indirect tensile strength (ITS) tests are employed for quality control of stabilized materials. These tests are time- consuming due to the time needs for curing of samples, and can also be costly if the number of samples increases. In this study, we have employed two methods including artificial neural network (ANN) and adaptive neuro-fuzzy inference system (ANFIS) to predict UCS and ITS of clayey subgrade soil stabilized with Portland cement and iron ore mine tailing (IOMT). To this end, cement content, IOMT content, optimum moisture, and curing time were considered as input parameters, and unconfined compressive strength, as well as indirect tensile strength, were considered as output parameters and in each case a dataset consisting of 100 data points were used for developing computational intelligence models. Modeling by means of these three methods confirmsthe superiority of the artificial neural network model over ANFIS model. Also, the sensitivity analysis showed that the Portland cement content and IOMT Content have the greatest and lowest effect on the predicted compressive and tensile strength, respectively.

An appropriate solution for dealing with low-resistance and problematic soils is stabilization of the soil. Also, exploitation and use of mineral resources generates a lot of mine tailings. Increasing the production of these tailings has created a significant concern for the mining authorities, regarding to achieve more depot space and environmental issues caused by waste deposits. The purpose of this research is to stabilize red clay with hydrated lime and iron ore mine tailings. For this purpose, samples with 0, 2, 4 and 6% lime and 0, 10, 20 and 30% of iron ore tailings dense and prepared in three percent moisture content (optimum, wet side and dry side). In order to perform unconfined compression strength (UCS), the specimens were treated for 7, 28 and 56 days. Unconfined compressive strength test showed that by increasing lime content up to a specific value, the UCS increases, and increasing the amount of lime content to more than it will reduce the UCS of samples when the content of iron ore mine tailing remains constant. In addition, the UCS and elastic modules decrease with increasing moisture content and vice versa. The UCS of the 7-day, 28-day and 56-day samples increses 84 to 259%, 97 to 290% and 110 to 342%, respectively, in terms of lime percentage, Iron ore mine tailing percentage and moisture content. Also, the freezing and thawing test showed that by increasing the iron ore mine tailing up to a specific value (2 to 4%), reduces the weight and volume loss of samples, and after that the weight and volume loss increase. Results of this study confirms that the optimum percentage of hydrated lime is 2 and 4%, regrading to 20 and 10 percentage of tailing, respectively by considering both UCS and freezing and thawing criteria.

Due to the economic and environmental issues, utilization of mineral wastes, e.g. iron ore mine tailing (IOMT), as road materials can be recommended as a sustainable alternative. In the present work, the mechanical properties as well as the resistance to freezing and thawing (F-T) cycles of low plasticity clay soil stabilized with different percentages of Portland cement (0%, 6%, 9%, 12%, and 15%) and different percentages of IOMT content (0%, 10%, 20%, 30 %, and 40%) are investigated. To this end, the unconfined compressive strength (UCS), initial elastic modulus (E0), and indirect tensile strength (ITS) at different curing times of 7, 14, 18, and 56 days for different admixtures are determined to select the optimum mix design for stabilization of clayey subgrade soil. This work shows that with increase in the percentage of cement, the strength parameters such as UCS, E0, and ITS increase, while increasing IOMT does not show a specific trend to increase the strength parameters. Evaluation of the strength parameters at different curing times shows that in the short-term curing times (7 and 14 days), the iron ore mine tailing has a positive effect on the strength parameters, while in the long-term curing times (28 and 56 days), the iron ore mine tailing has a negative effect on the strength parameters. In total, it was found that 12% of the Portland cement and 10-40% of IOMT passes the UCS and F-T criteria for stabilization of low plasticity clay soils, while clay soil (without IOMT) requires at least 15% of Portland cement for stabilization.

In this paper, two models have been developed to predict the resilient modulus of asphalt mixtures reinforced with Korta fiber subjected to square and haversine waveform, based on the response surface methodology. To this end, the asphalt mix samples were fabricated with three different percentages of bitumen and four different percentages of Korta fiber and then the resilient modulus was measured at five temperatures, five loading frequencies and two loading waveforms (squared and haversine), using UTM 30 apparatus. In this study, temperature, loading time, bitumen percentage and fiber percentage were considered as inputs variables and the resilient modulus under haversine and square loading waveforms was considered as output variable. The results of this study show that the response surface methodology is able to predict the resilient modulus of fiber reinforced asphalt samples with high accuracy, so that the regression coefficient of the developed equations for the haversine and square loading waveforms is 0.9795 and 0.9777, respectively. Also, the results of the sensitivity analysis show that increasing fiber percentage to a certain amount increases the resilience modulus and increasing the fiber content to more than this percentage, decreases the resilient modulus. This study also shows that the optimum percentage of Korta fiber depends on the bitumen content in the asphalt mix. So that in asphalt mixtures with higher bitumen percentages, the optimum fiber percentage was less (about 1 kg/ton) and in mixtures with lower bitumen percentage, the optimum fiber percentage was higher (about 1.5 kg/ton).

Design of vertical alignment with minimum earthwork cost can effectively reduce the construction costs of highways. In most past researches, the objective function has been considered as the sum of the absolute value of difference between the vertical alignment and the existing ground and due to the complexity of earthwork calculation, real costs of earthwork have been ignored. Also, to deal with constraints just the static penalty functions are employed. In case of static penalty functions, if one of the constraints is violated, a relatively large coefficient is multiplied by the objective function and as a result, many early populations are removed in the next iteration and the convergence time increases. This paper aims to compare different penalty functions for problem of vertical alignment optimization. To this end, station, elevation and vertical curve length in case of each point of vertical intersection (PVI) were considered as decision variables. The objective function was considered as earthwork cost and constraints were assumed as the maximum and minimum longitudinal slope, minimum elevation of compulsory points, and the minimum length of vertical curves. For solving of this optimization problem, the accelerated particle swarm optimization (APSO) and the colliding bodies optimization (CBO) algorithm were employed. The results illustrate that the selected penalty function greatly affects the convergence speed as well as the optimum solution (earthwork costs). This study also showed that the effective optimization of highway vertical alignment can be achieved using annealing penalty function and CBO algorithm.

Falling Weight Deflectometer (FWD) is one of the common methods for determining the bearing capacity of pavement. The inverted pavement system developed in 1970 in South Africa. This type of pavement is constructed as a sandwich structure, so that a crashed stone base layer is placed between two layers with high stiffness (asphalt concrete layer and cement treated base layer). The main purpose of this research is developing a method for predicting the moduli of the inverted pavements based on the measured deflection bowl using the FWD. Since, the nonlinear modeling of aggregate base is very important in case of inverted pavements, to stablish a dataset, about 38,000 inverted pavement sections have been analyzed by the non-linear finite element program, MICHPAVE. Then, using a hybrid artificial neural network and the colliding body optimization algorithms (ANN-CBO) method, a procedure was developed for backcalculation of inverted pavements assuming nonlinear behavior of aggregate base. The results of this study indicate that the results of MICHPAVE program are very close to the results of the KENLAYER program as well as field data. This study also showed that the artificial neural network is able to predicted the surface deflection bowl of the inverted pavements accurately (R2> 99.99%). In addition, it was found that the hybrid ANN-CBO has superior accuracy and speed in comparison with the hybrid ANN-GA for nonlinear backcalculation of inverted pavements.

In the past few years, with the advances made in the production of geosynthetic products, the use of these products in the pavement reinforcement has increased dramatically. Among the geosynthetic products, geocell improves the performance of the pavement due to the proper 3D confining of aggregates materials inside its cells. In order to investigate the effect of base layer reinforced with the geocell, six different geometries with reinforced and unreinforced base layer were simulated in ABAQUS finite element software. The behaviour of aggregate base and subbase layers were consirdered nonlinear which is implemented in ABAQUS by a FORTRAN subroutine. In the next stage, the results of the ABAQUS program as well as FORTRAN subroutine were validated using the results of KENLAYER and MICHPAVE programs as well as a full scale test. The results showed that the results of the ABAQUS program are consistent with results of other programs and also with the results of the fieled test. According to this research, by reinforcement of base layer using geocell, the surface deflection responses decreases betwen 5 to 10.28%, the tensile strain responses at the bottom of the asphalt decreases between 7.15 to 12.24% and the vertical compression strain on the top of subgrade decreases between 5.1to 9.19%. Also, the damage analysis was conducted based on the Asphalt Institute relations and results showed that the reinforcement of base layer increase asphalt fatigue life by 21.68-34.94% and subgrade rutting life by 20.89-35%.

This research aims to develop a mathematical model for continuous modeling of the pavement deflection basin based on the measured deflections using FWD device. Another purpose of this research is determining the optimal distance of the geophones for measurement of deflections. For this purpose, 10000 different flexible pavement sections were analyzed using multi-layered elastic theory and then a database containing deflection at nine different distances in case of each pavement section was established. The results show that the coefficient of determination for fitting the proposed equation to the pavement surface deflection basin in all cases is more than 0.99, which confirms the ability of proposed equation for mathematical modeling of pavement surface deflection basin. In order to determine the optimal radial distance of geophones, all scenarios with 4, 5, 6, and 7 geophone were examined and five best scenarios were selected in each case. The results of this study showed that the best radial distance for six geophones is 1830, 1220, 915, 457, 203, and 0 mm and the best radial distance for seven geophones is 1830,1220, 915, 457, 305, 203 and 0 mm.

Unconfined Compressive Strength (UCS) test is commonly employed to determine the strength and quality control of the stabilized layers. This method is time consuming due to the needed time for curing of samples. Also, this method can be costly if the number of samples is increased. In this paper, the group method of data handling (GMDH) was used to develop simple models with sufficient accuracy to predict the UCS of clayey subgrade stabilized with Portland cement and lime. To this end, after stabilization of samples with different percentages of Portland cement and lime at three different moisture contents (dry, wet and optimum moisture content) and curing times of 7, 14, 21, 28 and 60 days, the UCS tests were conducted to establish a comprehensive database including 150 records. In the next step, two different UCS prediction models for clayey subgrade soil stabilized with Portland cement and lime were developed by using the GMDH method. The R2 value for training and testing sets for samples stabilized with Portland cement was 0.9294 and 0.94522, respectively, while the R2 value for training and testing sets for samples stabilized with lime was 0.8897 and 0.880, respectively. In addition, the sensitivity analysis of each model showed that the cement percentage and moisture content have the most impact on the predicted UCS, respectively.

The purpose of this study is to provide a model for predicting the dry density of the clayey subgrades stabilized with Portland cement and iron ore mine tailing (IOMT) materials. For this purpose, Portland cement with 0, 6, 9, 12 and 15% and iron ore mine tailing with 0, 10, 20, 30 and 40% was added to clay soil, and then the compaction test was performed using modified proctor method on 25 different compounds and a database of 125 records was prepared. Then, using a response surface method (RSM), a model was proposed to predict the density of the clay subgrade stabilized with IOMT and Portland cement. Input variables in this model include moisture content, percentage of iron ore mine tailing and percentage of Portland cement, and the output variable is dry density of the stabilized clay soil. The regression coefficient of the developed model was 0.9634 which indicates the high accuracy of this model. Also, the predicted R2 (0.9416) indicates its logical compatibility with the adjusted R2 value (0.9551), with respect to a difference less than 0.22 among them. Finally, based on the developed model, two diagrams were developed to predict the maximum dry density and the optimum moisture content of clay subgrade stabilized with Portland cement and iron ore mine tailing. Regarding the results of this study, it is possible to predict the optimum moisture content as well as maximum dry density of the clay subgrade with low plasticity stabilized with Portland cement and iron ore mine tailing.

Reclaimed asphalt pavement material (RAP) that are known as reconstruction and asphalt milling debris, constitute a major part of the waste materials. One of the applications that have been considered recently, is the use of these materials (RAP) in mixes such as roller-compacted concrete (RCC). Therefore, in this study, after experimental studies and making 141 concrete samples, 47 unique data of the compressive strength of RCC containing RAP was obtained. Then, response surface methodology (RSM) was used to build a model to predict the compressive strength. The regression coefficient (R2) of 0.9668 for the developed model, indicated the accuracy of the model. The model showed that in addition to all the basic variables other than fine aggregate, interaction between cement and fine RAP, coarse aggregate and curing time, fine RAP and curing time, curing time square and temperature square, can also be effective in predicting the compressive strength values. Also according to the results of the sensitivity analysis, it was observed that the amount of compressive strength will be increased by increasing the amount of cement and the slope of this increasing in higher amounts of fine RAP was far less. In addition, decreasing the fine RAP or increasing the curing time in a fixed amount of coarse aggregate, will lead to an increase in compressive strength. And also, curing time will have a greater effect on the compressive strength in lower percentage of fine RAP.

In road design, pavement has detailed design and its cost is inevitable. But, in the infrastructure, the costs can be considerably reduced by optimizing the position of vertical alignment. One of the most expensive parts of the infrastructure is earthwork costs, which is highly dependent on the project vertical alignment. Therefore, the aim of this study was to evaluate various meta-heuristic methods for proposing a method for vertical-alignment optimization to have the lowest cost of earthwork operations. In this study, first, the objective function and constraints of the problem were formulated and then the distance, height, and length of the vertical curve in every point of vertical intersection (PVI) were considered as decision variables. Initial vertical alignment and position of the PVIs were defined according to the guidelines and demands. The objective function was defined as the sum of absolute difference of the vertical alignment height and ground surface. Meanwhile, the constraints were defined as minimum and maximum longitudinal slope, minimum height of the bridges, avoiding interference of the curves, and minimum length of the vertical curve. For optimization of the problem, Genetic Algorithm (GA), Accelerated Particle Swarm Algorithm (APSA) and Firefly Algorithm (FA) were used in the MATLAB software. For better evaluation of the developed method, three different topographies (plain, rolling, and mountainous) were designed and the original vertical alignment was optimized by each algorithm. In addition to the difference of vertical alignment and ground surface, comparison of the ratio of volume of fill to volume of cut, and earthwork costs, was carried out. Results showed that the highest optimiztion percentage for the three topographies belonged to FA, APSA and GA, respectively. Therefore, application of FA highly reduced the costs of road infrastructure. In addition, the time and replications needed to solve the problem show that the necessary time for optimization and obtaining the optimum solution is ignorable in comparison to the achieved cost saving.