JOURNAL OF TRANSPORTATION RESEARCH
Year:2008 | Volume:5 | Issue:2|Papers Count:12

In 2003, a process was developed in NCHRP Report 486 by TRB for allocating resources in Resurfacing, Restoration and Rehabilitation (3R) Projects after which the software called RSRAP was developed to execute such a process. In the said report, a set of impacts encountered after improving a network of road segments as 3R activities, and tradeoffs between them were introduced and quantified as the economic costs and benefits of the project, including:CC: Construction Costs,PSB: Present value of Safety Benefits,PNR: Penalty for Not Resurfacing,PRP: Present value of Resurfacing safety Penalty, and PTOB: Present value of Traffic-Operational Benefits.All these costs and benefits were incorporated in a Cost-Benefit Analysis as an economic evaluation method and in an optimization process using Integer Programming Model, in order to find the best alternative in each site of the network. The ten-step process to fulfill the analysis and optimization purpose contains the following components [changes and promotions implemented in this study, are described in brackets]:Identify the sites to be considered [no changes], Identify the improvement alternatives (and combinations of alternatives) to be considered for each site [crest vertical curves, narrow bridges and Permanent Raised Pavement Markers (PRPMs) are added to geometric features], Convert future costs and benefits to present values [discount rate are estimated for Iran], Estimate the construction cost of each improvement alternative [unit construction costs are estimated for Iran], Estimate the safety benefits for each improvement alternative [Accident Modification Factors (Ai\1Fs) are estimated and/or are considered for crest vertical curves, narrow bridges and Permanent Raised Pavement Markers; meanwhile, accident costs are also estimated for each Fatal, Injury and PD~ accident severity level in Iran],Estimate the penalty for not resurfacing [no changes],Estimate the safety penalty for each improvement alternative that involves resurfacing without other geometric improvements [no changes],Estimate the traffic-operational benefits for each improvement alternative [a new definition of vehicle speed increases is presented and is considered in quantified measure of PTOB; meanwhile, hourly time value is also estimated for each Iranian traveler.], Determine the net benefits for each improvement alternative [new measures of costs and benefits are used for determining the net benefits], and Select the most suitable improvement alternative for each site within the available budget by applying optimization logic [no changes in the model structure but the net benefit for each measure is estimated].In this paper, by introducing the process mentioned above, some correcting measures are proposed to expand the procedure and redraw a more comprehensive perspective due to the future economic status of the 3R projects. The two substantial modifications illustrated in this paper are:1. Estimating and/or considering Accident Modification Factors (Ai\1Fs) for crest vertical curves, narrow bridges and Permanent Raised Pavement Markers (PRPMs) to expand the measure of PSB.2. Estimating the impact of improvements in geometric features on vehicle speed increase, beside the 1 mph increase mentioned in the previous research due to resurfacing improvements, and accommodating the total increase in estimation of the PTOB benefit. In addition, referring to the scopes of this research and as a further expansion in the resource allocation process of 3R projects, a wider range of the other impacts rising from such projects are evaluated. The four components which are added to the existing process are: . Assessing the real vehicle speed increases both due to geometric and resurfacing improvements (DS);DS= DSg +1.6 DSg = ( fLs,1- fLs,2)+ ( fA,1- fA,2) DSg =g (fw,1 - fW,2)+ (fLc,1- fLc,2)+ (fM,1 - fM,2)+ (fA1- fA,2) Where:DS=total speed increase DSg = speed increase due to geometric improvements 1.6= speed increase due to resurfacing FLs=adjustment factor for lane and shoulder width on two-lane roads if adjustment factor for frequency of access points fLw=adjustment factor for lane width on multi-lane roads fA=adjustment factor for right-shoulder lateral clearance on multi-lane roads fLM=adjustment factor for median type on multi-lane roads Subscribes 1 and2: representative for before and after condition respectively Estimating the Present value of Benefits due to reduction of Vehicle Operating Costs (PBVOC) using the new definition of the vehicle speed increases; PBVOCjk = ADTx365x {1.93L/1000}x(0.2508Speed2 +219.775Speed-0.8681DS2 -715.3583DS -1.7362Speeedx DS+ 10930.48)x [(P| F,l) + (P|  F,i,2) +~(PI F,i,3)] Where: PBVOjk= present value of decreases in vehicle operating costs occurring through 30 months after road 3R improvements (Rials)ADT= average daily traffic (vehicle per day)L= road length (kilometer)Speed= vehicles operating speed before improvements (kilometer per hour)DS=total speed increase (kilometer per hour)(PIF,i,n)= discount factor to change costs at the end of nth year to present values (n=I, 2 and 3) Estimating an approximate measure of the Present value of Benefits due to Economic Developments (PBED) as an indirect impact;PBEDjk = {S3i=1;. ai(k1 -1)}X [P| A, i, n] Where: PBEDjk=present value of benefits due to economic benefits (Rials) i= type of land use (1= industrial, 2= commercial, and 3= tourism) P1=number of units for economic activities on type i a1=average annual income for units acting in type i k1=indicator for influence of road improvement project on type i activities (P/A, i, n)= discount factor to change costs occurring annually through n years Estimating an approximate measure of the Present value of Environmental Impacts (PEI) as an indirect impact.PEIjk =íSdi´Ciý x(P| A,i,n) Where: PEIjk=present value of costs due to environmental impacts (Rials) d1=dimensions of environmental destruction type i C1= unit destruction fee for environmental destruction type i (P/A, i, n)= discount factor to change costs occurring annually through n yearsBy considering all these theoretical changes and modifications in the resource allocation process, promotional countermeasures are possible in RSRAP program as a further study.

Roller compacted concrete is distinct from ordinary concrete by virtue of its zero slump. Over the past several years, the increasing usage of RCC for pavement construction has been noted. The use of RCC for pavements is relatively a new technology and is still under development. However, early trials have proven the success of the use of RCCP, which encouraged engineers to apply it in various fields.Although roller compacted concrete pavement (RCCP) has enjoyed numerous applications of roads and large floors in Europe, Canada and United States since 1970s, it has not been used in Iran appropriately.According to ACI 325.1 OR, RCCP is defined as a relatively stiff mixture of aggregates, cementitious materials, and water, which is compacted by vibratory rollers and the use of aggregate fractions finer than the 75 micrometers (NO. 200) sieve, if non plastic, may be beneficial. Very fine aggregates (smaller than 75 mm)play an influential role in conventional concrete, but its effect on in both the fresh and hardened states of RCC was not investigated. Generally the presence of very fine particles limited in PCC for four main reasons:1. Reducing workability due to large surface area2. Preventing proper bond between cement paste and aggregates3. Absorbing water and reducing strength4. Increasing cracking resistanceAccordingly, most standards limit the very fines content to only a few percent. ASTM C33 limits the fines content in fine aggregate to 5%. The European standard for aggregates (EN 12620) permits four levels of fines content in fine aggregate (3, 10, 16 and 22%). In addition, specific limits can be established at different location according to different conditions.In the case of sand manufacturing, it is difficult to produce sand with very low fines content and to do so it requires modem washing system and a huge amount of water that is invaluable in hot and dry climates. Also as a result the amount of waste fines that accumulated annually for instance in the D.S alone is in excess of 100 million tons that have considerable environmental impact.In order to extend the usage of RCCP, a comprehensive laboratory investigation was carried out to evaluate the workability and mechanical properties of RCCP containing high-volume and low volume non-plastic aggregates fractions finer than the 75m. After determining the optimum percent of non-plastic natural filler, concrete mixtures were made with 2.5%, 7.5%, 10% and 15% nonplastic aggregates finer than sieve #200, in order to check the possibility of using unwashed aggregates and the effects of these very fine materials on mechanical properties of RCCP. Also the variables such as cement content and super plasticizer have been evaluated and discussed. Various plots and tables showing the interrelations between the studied variables were included in the paper.Results indicated that it is feasible to use unwashed aggregates in RCCP mixes but a few limitations should be carefully considered. Also natural filler caused to improve the mechanical properties of RCC. In addition one of the major findings was that the main factor that controlled most of hardened properties is achieving sufficient compaction and unlike conventional concrete increasing cement content may not result in strength increase. Based on the results, the optimum aggregates proportion and WIC ratio have been found in order to make RCC for pavement applications that meet all specified limits in the ACI 325.10 state-of-the-art report and ACI 211.3R-97. Finally the optimum percentage of super plasticizer was determined.

In recent years storage systems have extremely developed. These developments are in both hardware perspective like as storage cells design and automated storage and retrieval machines and software perspective like as travel-time model and equipment usage strategy. Automated storage and retrieval systems development is one of these efforts in industrial modernization.In this paper the process of storage and retrieve material in automated storage and retrieval system has been modeled according to orders including some items into a new model that has been introduced in this paper. The term 2-nested generalized traveling salesman problem (2-nested GTSP) has been coined for the model. The authors showed that the problem of picking an order's items could be modeled with 2-nested GTSP easily. Then a mathematical model of the problem was developed and solved with LINGO. Since the problem is NP-Hard, it was solved with a metaheuristic algorithm ACSrank. The algorithm ACSrank is a new version of ACO that was developed and have ASrank and ACS features. The results of mathematical model and ACSrank algorithm are compared. Both of them have the same answer in 8 test problems. In problems 9, 10 and 11 we found less than 4 percent error. In the last test problem, after 263 hours, we stopped the solver.

A major portion of energy consumption is in transport sector. At present over 800 millions motor vehicles are working in the world [1]. Gasoline and diesel as two main fuels used in motor-vehicles playa significant role in pollutant formation, such as HC, CO, NOx, SO2. CO2 as the main product of fossil fuel combustion, is the biggest challenge of human being today, because of global warming effect.Using hydrogen fuel eliminates the production of HC, CO, CO2, SO2. The only pollutant of hydrogen combustion is NOx and its amount depends on the combustion temperature and hence on the hydrogen-air mixture.The idea of using hydrogen as engine fuel was first expressed by Cecil in 1820. He was the first person used hydrogen as fuel in the internal combustion engine.Research on the hydrogen engine started at the end of 1970s. This research initially was based on the practically converting the engine and vehicle to hydrogen engine and hydrogen fuelled vehicle. It is followed by studying the performance of the engine experimentally and then theoretically. In the present paper, the performance of hydrogen engine and its only pollutant is theoretically investigated. A thermodynamic based model is used. General rate equations for temperature and pressure and also two relations for cylinder volume and combustion surface area are used. The mass flow rate of inflow and outflow through valves are also considered. Four processes, (Induction, Compression, Expansion and Exhaust) are considered and the above equations for each process are simplified.The computation starts with intake process. The mass and composition of the residual gases are initially guessed and it is assumed that no chemical reaction take place during this process. The mass inflow equation has to be solved simultaneously with simplified rate equations for temperature and pressure. Composition of the mixture has to be calculated as the fresh air-fuel mixture enters into the cylinder and for that composition the gas properties required in rate equations must be calculated at any temperature during intake process.During compression process, from the inlet valve closing time till the initiation of combustion with spark plug, the mixture composition is assumed to remain constant and only simplified rate equations for temperature and pressure are to be solved. Again the required properties for solving these equations are obtained at each temperature. For combustion process, turbulent flame is assumed and the cylinder volume is divided to two zones separated by flame front whose thickness is negligible. Combustion starts from spark plug position which is at the top and centre of cylinder head (a burned zone of 1 mm diameter is initially assumed.) and propagates till the whole mixture is burned. During the combustion, pressure is uniform in the cylinder, the temperature in the burned and unburned zone are also uniform. Mixture composition in the unburned zone is assumed to be constant and in the burned zone is obtained from the chemical equilibrium. During combustion process, the contact surface area of the burned and unburned zones with the combustion chamber walls, are also considered to determine the heat transfer rate. NO formation is also considered in this process.During expansion, as the temperature and pressure fall, NO formation calculation continues.During exhaust, equation of rate of change of temperature and pressure along with mass outflow rate are solved.The computation continues till at the end of the cycle, the assumed values of mass and composition of residual gases at the start are obtained with proper approximation.In the presentation of the results; 1- Parameters pertaining to the engine condition (maximum temperature, maximum pressure and maximum rate of pressure rise), 2-Emission characteristics (nitric oxide emission), 3- Engine performance (optimum spark timing, indicated power) and 4- Efficiency characteristics (indicated thermal efficiency) are given versus equivalence ratio.Fromthe first three curves, it is shown that the temperature, the pressure and the rate of pressure rise are high, at close to stoichiometric condition. From the curve of maximum rate of pressure rise, which is the indicative of knocking problem, the knock-limiting equivalence ratio for hydrogen engine under the specified condition is determined which is j=.6(by assuming that a pressure rise of 6 atmosphere per degree crank angle can cause knocking problem in the engine). So at this knock-limited equivalence ratio, the maximum temperature and maximum pressure attainable in the hydrogen engine under the specified condition can be obtained, from other two curves which are 2400K and 5.2 MPa.Fromnitric oxide curve, it is shown that although NO formation is high for hydrogen engine at near stoichiometric condition due to existence of high temperature, but its maximum value occurs at equivalence ratio of j=.8. It is also shown that at equivalence ratio lower than knock limited equivalence ratio (j=.6) where the hydrogen engine is to be run, the NO formation is negligible. Hydrogen engine's performance is given by the curves of optimum spark timing and indicated power versus equivalence ratio. It is shown that although lower spark advance is required (because of higher flame propagation rate) near the stoichiomeric condition, but at knock free region of lower equivalence ratio higher spark advance is required. It is also shown from the indicated power curve that the power attainable from hydrogen engine is lowered because of the knocking problem. Hydrogen engine's efficiency curve indicates that, this avoidance of the knocking problem which forces the engine to be run at lean condition, and hence causes higher indicated thermal efficiency. Further, for presenting information on combustion, cylinder pressure and percent of mass burned are given in terms of the crank angle rotation, for limiting equivalence ratio of j=0.6.The start of the combustion and the end of the combustion can be identified from the cylinder pressure versus crank angle curve, but it does not provide information about the mass fraction burned. The curve of percent of mass burned versus crank angle gives this information and shows that high percent of the mass is burnt in the later part of combustion. This is because the flame front surface area increases as the combustion proceeds. From the present study, it is concluded that, because of the high combustion rate of hydrogen-air mixture, the maximum temperature, maximum pressure and maximum rate of pressure rise are high near stoichiometric condition. It is therefore necessary to have a mixture of lower equivalence ratio than knock-limited equivalence ratio (j=.6, under assumed condition of compression ratio 8, and rotational speed 2000 RPM) to be used in hydrogen engine. Under this lean limit condition, the nitric oxide emission as the only pollutant of the hydrogen engine is negligible, the performance and efficiency are high, but it's indicated power is low.

In an efficient transportation system, safety is the most important issue and is influenced by many factors. In a country similar to Iran, attention is mainly concentrated on engineering activities and with some physical adjustments, accident rates will reduce. Until recently, accident black-spots were identified and remedied by the experts' judgments and a handful of statistics without taking into accounts other important factors such as geometric and traffic conditions of the road network. This paper aims to define and identify the criteria for accident black-spots, then giving a value to each criterion in order to develop a model to prioritize accident black-spots.In this manner, experts are required to choose any criteria which they think is or are important and correlate to this study. Here are 15 criteria to choose from:1. Geometric Conditions,2. Traffic Conditions,3. Physical Conditions,4. Topography,5. Weather Conditions,6. Distance from Population Centers,7. Specific Places, like tunnels, bridges, intersections and foggy areas, 8. Type of Road (freeway, highway, arterial or access roads),9. Time Period (day or night),10. Accidents Costs,11. Maintenance Costs,12. Enforcements,13. Ratio of public transportation vehicles to all vehicles,14. State and Management Policies and15. Provision of radio communication and intelligent information systems.Then, experts are asked to choose some criteria for prioritization model. Having surveyed the experts' opinions, the most important criteria are achieved with regard to the responses of experts. After this process, regarding to number of responses to each criterion, importance of criteria was identified. In this way, geometric conditions, physical conditions, specific places, traffic conditions and distance from population centers, respectively had large number of responses. According to some experts' suggestions and some literature reviews, some of these criteria are more common than the others and they need to be considered in more detail such as geometric, traffic and physical characteristics. These main criteria, each have sub-criteria on which, the experts were asked to give their opinion about them. So, both main final criteria and sub-criteria are obtained at this stage. In addition, the experts are asked to give a weight coefficient based on Delphi method to each criterion, according to their experiences. These weights must be between I and 9.Then, final weights of each criteria and sub-criteria were identified. In some MADM problems where a decision matrix does not exist, the decision makers' judgments regarding the comparison each criterion is essential and needed. This matrix is a reciprocal matrix with positive components. Now it is time to form a dual comparative matrix for each criterion. At this stage, the "Geometric Mean Method" is used to calculate wi for each criterion. In this way, the geometric mean of each 1 row of the decision matrix will be calculated and the resulted vector must be normalized. At this stage the normalized weight values for each criterion, but according to the assumptions with structure of the prioritization models, each criterion and sub-criterion must be in the same level. So, to satisfy this stipulation, weight of sub-criteria must be multiplied by their correlate criteria weight.At last the final weight matrix which consists of 14 numbers was get. To do all these stages, the "Delphi" method has been used.

Solving the wheel/rail contact problem is one of most important issues in a rail vehicle dynamic simulation. For instance, the wear rate and pattern of the wheel/rail profiles can affect the vehicle stability. This effect is usually considered virtually in computer simulations rather than a real life condition. Also, obtaining an optimal wheel profile is mainly carried out using dynamic simulation packages. At the first stage, the wheel and rail contact point location is found, and then followed by its contact point shape and size. For this purpose, researchers simulate a quasi-static condition of a 2-bogie coach during its curving by the use of measured rail and wheel profiles to extract the required parameters.The authors of this paper describe various contact theories, and the geometrical contact equation within the wheel and rail interface is then presented. The results of a code developed in this study arecompared with the output data of a commercial software tool such as ADAMSlRail. 1. WheellRail Contact TheoriesA convenient method to find the wheel/rail contact point location is to assume that the contact patch is rigid (a non-elastic mode). Using this theory finds the minimum vertical distance between the wheel and rail profiles, and nominates corresponding points within the profiles as the possible contact point. In this method the wheel profiles moves laterally against the rail profile and contact point locations are found as a function of the wheelset lateral movement.After finding the contact points, the curvature of the profiles within the contact points is calculated and the contact location is achieved using Hertz formula. The outputs discontinuity is the major deficiency of the rigid contact model. Since the results of contact model will later be used in the softwaretool, it leads to a numerical instability of the dynamic simulation. This discontinuity occurs in the presence of a multi point contact model within the contact patch. The smoothing process of such discontinuities is one of the solutions by use of the splines. For instance, ADAMSlRail smoothesthe output results using Bezier-Splines. 33 To address this problem, multi point contact models were developed by the researchers. By taking into account the deformation of the first contact point, further contact points will come into the simulation process. Meanwhile, the deformation of the profiles at the first contact points make it possible to approaching two profiles and appearing new contact points. The contact points will be obtained in such a manner to satisfy the force equilibrium. 2. WheellRaii Geometrical Contact Equations in a Rigid One-Point ContactContact equations were given for an unconstrained wheelset in a curve. Using these equations result in four final relationships as follow:tan dwr=dxwr/dhwr, tan dwt= dxwl/dhwl, tan drr= dxrr/dhrr, tan drl= dxrl/dhrlwhere xw and hw are the x and y coordinates of the wheel profile, and xr& hr stand for x and y coordinates of the rail profiles, 1 is the second index for the left profiles, and r is the second index for the right profiles. d is the gradient of the profile at the contact point. If the shape of profiles is known as mathematical functions, the Newton-Raphson equation can be used to solve these relationships. In most cases the shape of profiles is given by the x and y values, and the Newton- Raphson method is not thereafter applicable. Note that a geometrical solving method was used in this study.For this reason, the profiles are initially estimated using 3rd order splines so the curvature of the profiles at any point of the contact can be calculated. It is possible to smooth the profiles in this manner to decrease the discontinuity of the output results. A MATLAB code to solve these equations was developed. This code is capable to take into account the horizontal and vertical irregularities of rails as inputs into the simulation process. The output results of the code are contact points, the gradient within contact points, rolling radius of wheels and the contact areas. The profiles can have different shapes. The generality character of the code makes it possible to simulate wheel set movement along a track with a variable rail gauge, and the rail and wheel profiles.To find a solution, the code moves the wheel profiles laterally to a specified magnitude and then generates some artificial points on the wheel and rail profiles to obtain a better convergence rate and accuracy. The code then finds the shortest distance between the wheel and rail profiles. If the differential distance lies within the given range, the points will be recorded as contact points.Nevertheless, the wheel profiles will be rotated. These stages will be followed until the given range will be satisfied.The simulation results were compared with the two well-known commercial software tools such as ADAMS/Rail and VAMPIRE. All comparisons show an excellent agreement between the code developed in this study and the mentioned software outputs.

In this research the stability of slopes, made of unsaturated soils, constructed by compacted layers has-been studied. The properties of unsaturated soils such as the stability of slopes made of them and shear strength have been investigated, and the priory theoretical backgrounds have been cited from the related literature.In this study the program "UDAM" (which have been already developed by Gatmiri and Nanda for the unsaturated soils) has been specially applied.As the development of pore water pressure and also pore air pressure developed during (and after that) the embankment construction and the major effective factors on the stability, so the computations of the quantities of these pore pressures were one of the main purposes of this research.In order to evaluate the stability of unsaturated slopes, it was necessary to a computer program which be suitable for analyzing the unsaturated soils. Because of this, the program CASSAP which has already been developed by Syrous Aryani, has been modified to be able to catch the pore water pressure and the suction of the soil and compute the stability safety factor.The results of these two mentioned programs (UDAM & MCASSAP) have illustrated in different diagrams and figures the final conclusion revealed some new and interesting results.Following is a brief description of UDAM program: The main concepts in the computations are based on the differential equations governing the equilibrium equations for unsaturated porous media. These equations which represent the relationships between the different conditions are as follows:d/dt(nSrPW)+ d/dxi(nSr.pw.uwi)=0d/dt(nSapa)+ d/dxi(nSr.pw.uai)=0pb+sij.j-pui=0where n is the porosity; Sr the degree of water saturation; Sa the degree of air saturation; P, Pa,Pw are the densities of soil, water and air respectively; Uiw and uia are the velocities of water and air respectively; and Ui is the acceleration.affecting parameters of soil, air and water in equilibrium Furthermore, since the variations of void ratio and saturation degree are functions of some physic mechanical properties of the medium, these variations should be expressed inside a three dimensional space, which is named as the state surface. In UDAM program, the equations of state surface for void ratio and saturation degree are as follows: (Gatmiri and Delage, 1995; Gatmiri et al., 1993). e=1+e0/exp{[a/(s-ua)/pam+b(1-/(s-ua)/ s)(ua-uw)_/patm]1-m/kb(1-m)} sr=1-[as+bs(s-ua)]{1-exp[-cs(ua-uw)]}where ua and Uw are the air and water pressure respectively; (s - ua) and (ua - uw) are the net normal stress and matric suction respectively; patm is the atmospheric pressure; a, b, m, kb are parameters.Then the permeability coefficients of water and air calculated by the following relationships, respectively: kw=a 100ea(sr-sru/a-sru)3 ka=b ga/ma[e(1-sr)]b

To make the slippery roads surfaces safe during the winter, highway authorities usually must either apply rock salt (NaCl) or other chemical de-icers to melt ice and snow or spread sand to provide traction. Since usage of these materials may have negative environmental and physical impacts, therefore, their properties must be known to provide adequate space for improvement and to compensate for any short comes.In this research we are only concerning with the physical impact of the issue which is lowering skidding resistance of the surface as a result of applying rock salt to melt the snow and ice.Road surface type snow and ice melt more rapidly on a concrete surface because it gives up heat more rapidly. Since asphalt absorbs more solar radiation, it is therefore have more heat available for melting snow. This is why snow melts rapidly next to bare asphalt pavement areas. Even when the temperature of the pavement is below freezing point, it holds some heat and can help melting snow and ice.Changing ice or snow into water (brine) requires heat from the air, the sun, the pavement, or traffic friction. The surface temperature of a snow- or ice-covered road determines de-icing salt amounts and melting rates. As temperatures go down, the amount of salt needed to melt a given quantity of Ice creases significantly. U sing salt brine to pre-wet is becoming more common because of its lower cost. In this research it was established that the presence of salt brine on the surface will lower down the skidding resistance of the surface considerably. It is necessary to have adequate drainage system on the roads that enables the melted snow and ice which have concentration of high amount of salt contentto be clear off the surface as soon as possible. It is better to apply salt as needed than to over-treatinitially.It has been established that on the location in which the harsh maneuvering, acceleration and deceleration is needed aggregate of higher Polished Stone Value (PSV) be used than it was believed to be used before.

Based on the AASHTO provisions, the equivalent static and dynamic method of analysis are the two methods used for the seismic analysis of bridges. These methods are selected for the bridge analysis depending on the bridge type and its seismic performance category (SPC). There are four methods of analysis in AASHTO for seismic analysis of the bridges among which the single mode method is used for the analysis of the regular bridges classified as SPC B, CorD with 2 to 6 spans. The piers height effect is not regarded as a criterion in the selection of the above methods of AASHTO. In the single mode method the earthquake load is evaluated by applying a uniform load over the total length of the bridge, and calculating the static displacements of the bridge deck. Based on these displacements, the bridge period is obtained and used in the calculation of the seismic coefficient and seismic design loads. In the present paper, the effects of the bridge piers height on their seismic performance is studied and the results reveal that the procedure mentioned above is not able to accurately estimate the internal forces developed, due to earthquake motions, in the bridges with high piers .To demonstrate this deficiency, 6 sample bridges, with 4 uniform 25m length spans, are selected. The height of piers is the same in each bridge but varies from 5m to 45m in samples. The bridges are analyzed by the single mode method, and the internal forces of the piers are compared with those obtained from the multimode analysis method by including 25 modes in the analysis. The results of the multimode analysis are used as the reference to calculate the errors in the single mode method. The axial and shear forces, as well the bending moments in the piers are compared with the reference solutions. The fundamental natural period of the bridges are also obtained by using the multimode analysis and compared with those obtained from the single mode method. These comparisons indicate that the single mode method is not able to accurately predict the natural period of the bridges, as well the internal forces of the piers. The results of the present study show that the discrepancy of the results from the reference values are mainly due to the distribution and applying the equivalent loads, and partially due to the equation used for the evaluation of periods. To reduce these errors, it was proposed in this paper, that the piers need to be included effectively in the analysis procedures. For this purpose, it is found that the following modifications have to be made on single mode method:1. The uniform loading, which is the first step in the single mode method, should be extended to the piers also.2. The piers weight need to be properly included in the calculation of period. 3. The effective weight of piers needs to be included in the calculation of equivalent seismic loads.4. In calculating the internal forces caused by the earthquake motions, the equivalent seismic loads should be calculated associated with all individual piers and also bridge deck. The above modifications are implemented in the single mode method and the 6 selected sample bridges are analyzed again. The results of the fundamental periods and internal forces are obtained and compared with the reference solutions. The comparison of the results shows that the proposed modifications highly improve the accuracy of the single mode method in predicting the seismic behavior of bridges with high piers. The main conclusions of the present work can be summarized as follows:The accuracy of the single mode method in calculating the fundamental period of bridges with pier-height/span ratio different to 0.5 is not good.The single mode method is not accurate to predict the internal forces of the piers. This is more visible in the prediction of pier axial forces of the bridges with small pier-height/span ratio. This lack of accuracy is mostly due to the presence of vertical vibration modes in the seismic vibration of such bridges which is not considered in the single mode method. The accuracy of the single mode method for the prediction of internal forces of the piers is deteriorated by differentiation of pier-height/span ratio from 0.5. Hence, this ratio can be considered as criteria such that for bridge with pier-height/span ratio differs to 0.5, the proposed method can be considered to obtain accurate estimates.The accuracy achieved in the proposed method reveals the necessity of inclusion of piers weight in the analysis and also reveals how the distribution of equivalent seismic load can affect the results.