Optimum axle loads of developing countries by J. Rolt commercial vehicles in TRANSPORT and ROAD . RESEARCH LABORATORY Department of the Environment Department of Transport TRRL LABORATORY REPORT 1002 OPTIMUM AXLE LOADS OF COMMERCIAL VEHICLES IN DEVELOPING COUNTRIES by J Rolt BSC PhD M lnst HE The work described in this Report forms pati of the programme @rried out for the Overseas Development Administration, but any views expressed are not ne~ssarily those of the Administration Overseas Unit Transport and Road Research Laboratory Crowthorne, Berkshire 1981 ISSN 0305–1 293 CONTENTS Abstract 1. Introduction 2. Method of analysis 2,1 Introduction 2.2 Factors included in the analysis 2.3 Method of computation – main series 2.4 Method of computation – subsidiary series 2,4.1 Terrain and subgrade 2,4.2 Pavement damage relationship 2.4.3 Price structure 2.4.4 Vehicle wastage 2.4.5 Construction poticy 2.4.6 Type of vehicle 2.4.7 Vehicle load condition 2.4.8 Road maintenance poticy 3. Road construction costs 3.1 Pavement design 3.2 Construction costs 3.2.1 PartiMy loaded vehicles 3.2.2 Increasing ule load 3.3 Stage construction costs 4. Vehicle operating costs 4.1 Introduction 4.2 &neral results 4.2.1 Vehicle wastage Page 1 1 3 3 3 3 4 4 4 4 5 5 5 5 5 6 6 7 7 7 7 8 8 8 10 5. 6. 7. 8. 9. 10. 11. 4,2.2 Vehicle load factor 4.3 Total vehicle operating costs Total transport costs 5.1 New road construction 5.1.1 5.1.2 5.1.3 5.1.4 5.1.5 Wmum total transport costs Terrain and subgrade Vehicle load condition Vehicles with high pavement damage factors Pavement damage relationship 5.2 Existing roads with strengthening overlays 5.2.1 Price structure 5.3 An example of mixed traffic on an existing road 5.4 Dscussion Other costs 6.1 Introduction 6,2 Bridges 6.3 Accidents 6.4 Ar pollution 6.5 Noise and vibration Summary Achowledgements References Appendix 1: Input data for model Appendix 2: Vehicle loading characteristics Page 10 10 11 11 11 12 12 12 12 12 13 13 13 14 14 15 16 16 16 17 17 18 32 35 @CROWN COPYRIGHT 1981 Extracts from the text may be reproduced, except for commercial purposes, provided the source is acknowledged OPTIMUM ~LE LOADS OF COMMERCIAL VEHICLES IN DEVELOPING COUNTRIES me Road Transport Investment Model for developing countries has been used to examine the effects of different tie loading characteristics on : the totrd costs of road transport. It is shown that the sum of vehicle operating costs, road construction costs and road maintenance and rehabfitation costs for a two lane highway irdtidy decrease rapidy as the tie load of the most heady loaded vehicles increases and passes through a sh~ow minimum at the optimum tie load. ” The vrdue of this optimum Me load was found to be stron~y dependent on the total freight tonnages carried by the heavily loaded vehicles, the load condition of these vehicles on the return trip, the exponent of the pavement damage – tie load relationship, and the relative prices of the major components of road transport cost. The optimum tie load was found to be virtudy independent of the road tignrnent and strength of the subgrade, but the road construction and strengthening poticy and the composition of the vehicle fleet had a sm~ but significant effect on ik value. It is shown that under most conditions there exists a traffic level above which the optimum tie load is above the current legal hrnits in force in most developing countries. me total road transport costs were usudy found to be relatively insensitive to tie load in the region of the minimum totrd trmsport cost, changes in tie loads of 10 per cent producing changes in the transport costs of less than 1 per cent. 1. INTRODUCTION The cost of operating a road transport system consists of two main components, namely the cost of operating the fleet of vehicles using the roads and the cost of constructing and maintaining the roads themselves. The cost of transporting a particular tonnage of freight decreases quite rapidy as the amount of freight which each veticle carries increases. ti the other hand the cost of providing and maintaining the roads increases as vehicle tie loads increase. The magnitude of these component costs and their variation with tie load ensures that under most circumstances the total cost of operating the transport system initidy decreases as tie load increases but passesthrough a minimum value at the optimum tie load before increasing again. Most developing countries spend a large proportion of their”scarce resources on road transport. It is therefore particularly desirable in such countries that the road transport system should operate under conditions which minimise the total cost. This report discussesthe relationship’ between tie load and road transport costs in developing counties and considers the ‘optimum’ tie load at which the total road transport costs are minimised. i The Iegd timits for We loads in industritised countries have increased slowly over the last few decades, but untfl relatively recently the economic justification for changes in these legaltimits has not been examined very closely. Formerly the basic data were not avtiable to enable either the cost of operating the vehicle fleet to be calculated or the estimation of the additiond pavement damage caused by the heavier tie loads to be made. This has been partiy rectified as a result of the AASHO Road Test in which the damaging effect of different tie loads on a variety of pavement structures was quantified. In addition severrdmajor studies2’3 of the factors which influence the cost of operating vehicles have been made and it is now possible to conduct incremental analyses to show the economic effects of increases in tie loads. Studies of this kind have been made in severalindustriahed countries4’5 with the conclusion that from a purely economic point of view,increases in present led tie load timits are justified under a tide variety of conditions. For example in a study completed about ten years ago in the United States of herica5 it was found that if legrdafle weight timits throughout the country were increased to 11.8 tonnes on a sin~e tie and 20.0 tonnes on a tandem tie on au federd-aid highways the toti benefit-cost ratio would be 12:1. To quote a recent report 6 ‘The magnitude of these figures was so stating and so contrary to the expectations of Mghway officiti that they were not reatiy accepted. A subsequent sensitivity analysis and assessment of the calculations indicated that the benefit-cost ratios were of such a magnitude as to be insensitive to any reasonable combination of possible errors’. The legaltirnits for de loads in developing countries differ widely from country to country ranging from 4 tonnes to 13 tonnes on a sin@etie and from 8 tonnes to 20 tonnes on a tandem tie. Indeed some countries have no legallimit on tie loads at W. To some extent these Wts reflect the different environmental and social conditions of each country but econotic analyses have rarely, if ever, been used to justify them. In many developing countries vehicles are often loaded above the Iegd load tirnits. In tie load surveys carried out in various countries 78‘ , It. has been found that up to 70 per cent of commercial vehicles are overloaded in this way, a typical figure being about 30 per cent. Not ody are the number, of vehicles which are overloaded large but the magnitude of the overloading is high. For example it has been shown that on one trunk road in Kenya the merage equivalence factor for comercird vehiclesis over five times the value wtich would be obtained if the vehicles were loaded to the current legal hmits. Mthough the damaging effect of these heatiy loaded vehicles on the pavement has been appreciated the over~ economic consequence of operating heavy vehicles with high tie loads has rarely been examined. h particular tie relationship between the optimum tie load, the legaltie load hmits and the spectrum of observed tie loads has not been studied in detti for a developing country. Recognizingthe magnitude of the benefits which can arise from operating the road transport system under conditions which give rise to a minimum total cost, some developing countries are now attempting to rationtise the operation of heir road transport system. An important step in this process is the selection of legal hrnits for de loads. This report Nustrates how the Road Transport Investment Modelg can be used to calculate the costs and benefits associated with different atie loads. The main factors which affect the value of the optimum tie load are identified and the sensitivity of the optimum to changes in these factors k examined. It is shown that under most conditions higher legal afle load tirnits than are currentiy in force h most developing countries are justified for a given vehicle fleet and the magnitude of the benefits which would be forgone if existing led fimits were genuinely enforced is very large indeed. This conclusion appfies whether new road construction or the strengthening of an existing road network is considered. 2 2. METHOD OF ANALYSIS 2.1 Introdutiion To appreciate the relative irnportmce of the variables which affect the optimum atie load for a trunk road in a developing country and the interactions between them, the actual situation was initi~y simphfied. Asthe atiysis proceeded these simplifications were removed until fin~y an example of a complete analysis for a trunk road in a developing country is presented. No attempt has been made to conduct an rmdysis for the road network of an entire country for the reasons outhned in Section 6.1. InitiWy it was assumed that W the freight is transported by a fleet consisting of one type of vehicle and that d the vehicles are loaded to the particular tie load under consideration. The total transport costs for this simphfied situation were then calculated for a particular total freight tonnage carried over a fifteen year atiysis period. The calculations were then repeated for different tie loads to determine the tinimum total costs and the corresponding optimum afle load. This complete series of calculations was then repeated for different total freight tonnage ranging from 0.5 to 10.0 tihon tonnes. Further analyses were then performed to show how the minimum total costs and optimum tie loads depend on the other variables discussed below. The calculations themselves were d performed using the Road Transport Investment Model for developing countries (RTIM) wtich is described in detti elsewhere’ 1‘. 2.2 Fa~ors included in the analysis The analysis was designed to show how the optimum tie load depends on the following principal factors. 1) 2) 3) 4) 5) 6) 7) 8) 9) 1o) Total freight tonnage carried. Terrain and road ahgnment. Subgrade strength. Pavement damage relationship. Relative prices of the major components of road transport costs. Veticle waitage or wear rates. Stage construction poficy for the pavement. Type of vehicle and afle configuration. Vehicle load condition. Road maintenance poticy. 2.3 Method of amputation – main series The computational procedure is outtined in Figure 1. In this section of the report the ranges of the various parameters included in the analysis are described. The main series of calculations is defined by loops 1 and 2 in Figure 1. At the beginning of loop 1 the vehicle type or types have already been chosen and once the freight tonnage and rear atie load have dso been selected the total number of vehicle trips can be calculated (Section 2.4.7). It was assumed throughout this study that the growth rate of traffic (or freight) was constant at 5 per cent per year. Using this assumption the first year average dtiy traffic was calculated as required by the model input. Next the pavement was designed, according to the selected construction policy, using established pavement design procedures as described in Section 3.1. Findy the Road Transport hvestment Model was run to 3 obtain the road construction costs, vehicle operating costs and road maintenance costs. The rear tie load of the vehicles was then changed keeping the total freight tonnage constant and the sequence of operations repeated. For tandem Wes the totil rear afle load on the pair of ties was varied from 6 tonnes up to 32 tonnes and for sin#e afles from 4 tonnes up to 16 tonnes. The sequence of loop 1 was then repeated for different total freight tonnages (loop 2) and the results plotted as a series of graphs showing, for each freight tonnage, the dependence on rear tie load of a) Vehicle operating costs. b) Road construction and maintenance costs. c) Total transport costs. Graphs of this kind were produced for the complete range of the variables discussed in the foflowing sections. The model input data are summarised in Appendix 1. 2.4 Method of amputation - subsidiary series 2.4.1 Terrain and subgrade. Three types of terrain were selected namely flat, ro~ng and My and three vrduesof subgrade strength, defined by CBRvalues of 3, 7 and 15 per cent. The vertical tignment of the roads in the three terrain areas is shown in Appendix 1. The ody costs which are of interest in this analysis are those which depend on the load imposed by the main load-bearing ties of the vehicles. Thus the principal effect of the road tignment is on the vehicle operating costs which depend in a complex manner on vehicle weight and road geometry. The subgrade strength directly influences the structural design of the pavement which is extremely dependent on the tile loads imposed. The costs of the additiond earthworks associated with the rolhng and hi~y terrain are independent of afle load. 2.4.2 Pavement damage relationship. The structural damage to a pavement caused by static wheel loads is given by an empirical equation of the fo~owing form: (Pavement damage) a (tie load)n The value of the exponent, n, is genera~y taken to be about 4.5 but there is considerable uncertainty as to its exact value under different conditions. A partial reanalysis of the AASHO Road Testl is given in Reference 11 where it is shown that n can vary from 2.4 up to 6.6 under extreme conditions. It was concluded that. for heavy wheel loads on roads of medium or high strength, as measured by the structural number, the vahre of n wasin the range 3.2–5.6. In this study a value of 4.5 has been used for most of the calculations but a value of 6.0 has also been used to exafine the sensitivity of the results to the value of this exponent. 2.4.3 Price strutiure. Both the vehicle operating costs and pavement structural costs are stron~y dependent on the cost of products derived from crude od. In recent years these costs have risen rapidy in red terms hence the sensitivity of the value of the optimum tie load to the price structure, in particular the price of petrol and bitumen, has been examined. Ody two alternatives were studied namely the prices which appheJ in Kenya two years before and one yew after the large rise in the price of crude oil which took place in 1974. Details of the prices used in the analysis are contained in Appendix 1. 4 2.4.4 Vehicle wastage. Vehicle operating cost data were collected for the fleet of vehicles operating in Kenya as part of the study which lead to the production of the Road Transport Investment Mode13. In Kenya, as in most developing countries, vehicles are often heavily overloaded hence the vehicle operating costs which were obtained included data from vehicles which were habitually operated in this state. However data on the average working lives of vehicles were not obtained directly from the operators hence it was not possible to identify the dependence, if any, of this factor on vehicle load. To study the effect of reducing the average tife of vehicles the vehicle wastage equations in the model were changed to reduce the average life by 25 per cent, thus increasing the vehicle operating costs. 2.4.5 Construction policy. Two types of road construction policy were used. In the first policy the road was designed to carry the total traffic throughout the fifteen year analysis period without the need for additiond pavement strengthening. In the second policy the road was designed to carry the traffic expected during the analysis period assuming that the ade load fimit was 8 tonnes on a sin~e axle and 16 tonnes on a tandem afle. In these calculations as the axle load increased the total traffic load expressed in equivalent standard axles also increased although the number of vehicle trips needed to transport a given freight tonnage decreased. ~us the road needed strengthening at least once during the analysis period. Strengthening overlays were applied whenever the road reached a ‘failure’ condition. Road ‘fatiure’ is defined in RTIM by a critical level of roughness and since roughness has a considerable influence on vehicle operating costs it was important to ensure that in all runs of the model for which a particular maintenance policy was in use au vehicles experienced the same average roughness values. This was achieved by choosing the design thickness of the road or the thickness of strengthening overlays in such a wzy that the pavement reached the ‘faflure’ condition at the end of the analysis period. This method also ensured that the residual economic value of the road at the end of the analysis period was always the same and therefore did not need to be calculated. 2.4.6 Type of vehicle. Various types of vehicle were used in the analysis together with mixed vehicle fleets. The characteristics of these vehicles are based on the results of several afle load surveys conducted in Kenya7. ~assifications of vehicles based on afle configuration and udaden weight were used to define typical vehicles, details of which are given in Appendix 2. For each type of vehicle the relationship between tie load and payload and between afle load and pavement damage expressed in equivalent standard ties are known from the survey data. Using the first of these relationships the payload can be found for any given afle load and hence the total number of vehicle trips required to carry the selected freight tonnage can be found. Using this result the second relationship can be used to calculate the total number of ‘ standard ades for which the road must be designed. 2.4.7 Vehicle load condition. The average cost of transporting each tonne of freight depends on the level.of vehicle utifisation. For vehicles which are of interest in this study, namely those able to make use of the maximum allowed ade load, two extreme conditions were examined. In the first condition, here ctied the fu~ load condition, the vehicles were fufly loaded in both the outward and return directions. In the second or half-load condition the vehicles were fully loaded in one direction and empty in the other. 2,4.8 Road maintenance policy. The options in the model allow different road patching and surface dressing pohcies to be adopted. The effect of these different policies on the total costs was ne~igible in comparison with the different costs of the stage construction pohcies and is not discussed further. 5 3. ROAD CONSTRUCTION COSTS 3.1 Pavement design The relationship between the modified structural number of a pavement and its traffic carrying capacity which is used in the model is an extension of Road Note 31 12!13. The total thickness of pavement is always less than that recommended in the design curves of Road Note 29 14 but the tfickness difference is almost constant hence both design curves give the same variation in thickness, and therefore construction costs, with ade load. The road structure assumed consists of a cement stabilised sub-base, a crushed stone base and a bituminous surfacing. Comparisons of thickness design charts has shown that the defined terminal condition of a road has a major influence on the recommended pavement thicknesses. Thus although a design based on Road Note 29 does not alter the variation in pavement costs with afle load it does affect the vehicle operating costs through the’influence of road surface condition and could therefore affect the optimum afle load. By ensuring that the average roughness experienced by dl vehiclesin a series of model runs is always the same, the effect of roughness on vehicle operating costs is dso the same and therefore not dependent on afle load. This is guaranteed by ensuring that the road reaches the terminal condition at the end of the analysis period. [t can be shown from most pavement design charts that the traffic carrying capacity of a road is related to the structural number 1 by an equation of the form: Traffic Carrying Capacity a (Structural Number)m The value of the parameter ‘m’obtained from the AASHTO design charts 15, which recommend larger values of structural number than most design charts in current use, is approximately 6.3; for other design charts ‘m’is greater than 6.3. In general “fora low traffic design (less than 2.5 mi~ion standard ties) the value of ‘m’is greater than for a high traffic design. In the design chart used here ‘m’varies from 10.0 for low traffic to about 7.5 for high traffic (more than 10.0 million standard ties). If this equation is considered together with the pavement damage equation above it can be seen that an increase in structural number of 15 per cent increases the traffic carrying capacity by about 200 per cent. This is equivalent to an increase in sin$e axle load from 8.0 tonnes to just over 10.0 tonnes even assuming the number of vehicle trips remains unaltered. A 15 per cent increase in structural number is also equivalent to an increase in pavement costs of about 15 per cent (Section 3.2) and an increase in total construction costs of considerably lessthan this. This example illustrates the extreme importance of the power indices in the above equations. Unfortunately the only systematic study of the relative damaging effects of different axle loads was undertaken during the AASHO Road Test. The conclusions bf this study have been criticised for a variety of reasons but principally because (a) the test was conducted on only one type of subgrade, (b) much of the pavement deterioration occurred during the spring thaw making it difficult to isolate the deterioration which took place during the dry, warm periods of the year and (c) the study was an accelerated test leading to road fadure within two years. Nevertheless this is the ody full scale study from which it has been possible to derive a relationship between axle load and pavement deterioration and therefore the results are widely used. In this study the traffic has been defined by the equivalent number of standard afles calculated by using either the standard 4.5 power law approximation to Liddle’s original equation developed during the AASHO Road Test or by using a 6.0 power law as described in Section 2.4.2 above. 6 3.2 Construtiion costs The unit costs used in the construction submodel of RTIM are shown in Appendix 1. The results of the model runs show that the cost of construction is hnearly dependent on the structural number provided the structural number, SN, is above the lower hmiting value SNO. The costs can be expressed as follows: Costs = a t (b x SN), SN > SNO where the constant ‘a’depends principally on the vertical geometry and therefore the quantity of earthworks but not on SN, the constant ‘b’is independent of vertical geometry and SNOis the value of SN which is required for the lowest traffic levels. 3.2.1 Partially loaded vehicles. Fi~re 2 shows the cost of constructing a road in ro~ing terrain on a subgrade with a design CBR of 3 per cent as a function of traffic. The curve indicates that the marginal cost of construction decreases quite quictiy as the design traffic increases. The importance of this becomes apparent when the traffic which does not increase its tie load in accordance with the increasing hmits is taken into account. Generally throughout this study it has been assumed that all the vehicles make full use of the axle load hrnits imposed. Certainly the results of tie load surveys in developing countries has shown that overloading above the legal hmits is so frequent and of such a magnitude that virtually dl pavement damage is often attributable to these vehicles. The effect of vehicles which do not make use of the afle load hmits under consideration is twofold. The effect on the total vehicle operating costs as tie load increases is constant since no changes take place to these vehicies but the effect on pavement construction costs is not constant. The graph shows that when the atie load tirnit is low and the total construction costs are dso low the marginal cost of design for the partly loaded vehiclesis high whereas when the afle load hmit is raised the total construction costs are also raised but the marginal cost of design for the partly loaded vehicles decreases. The effect of this on the relationship between road construction costs and tie load is to flatten the rising curve and thereby to increase the optimum ade load. 3.2.2 Increasing axle load. The results of a series of runs of the model showing the relationship between construction costs, ade load, and total freight tonnage are shown in Figure 3. The effect of the different terrain categories is simply to raise or lower the cost curves by fixed amounts depending on the differences in the fixed earthworks costs. 3.3 Stage mnstru~ion rests The relationship between the cost of structural overlays and traffic is similar in shape to Figure 2. An example of such a relationship is shown in Figure 4 for a road witi an initial structural number of 3.05. The costs shown are the sum of normal maintenance costs and overlay costs. Indicated on the graph are the points corresponding to various thicknesses of overlay and the number of overlays which have been apptied during the analysis period. Various rdternative poticies are possible witlrin the constraints of the assumptions. ~enever the number of overlays required is greater than one t!~ereare rdways poticies available which require thicker but less frequent overlays. These poticies will usua~y be more expensive as a result of the discount procedure built into the model. The maintenance costs themselves excluding the cost of overlays are smti and m2ny of the component costs of maintenance are independent of tie load. The costs of patching failed areas of pavement and the costs of surface dressing are crdculated in the model and included in the total cost summations but are not andysed in detafl. 7 4. VEHICLE OPERATING COSTS 4.1 Introdutiion The estimation of vehicle operating costs within the model is based on the results of studies carried out in Kenya, Ethiopia and elsewhere9’13. Data were co~ected in terms of quantities rather than prices so that the model user is able to apply up to date prices in his calculations. Two sets of input cost data were used in this study. These are summarised in Appenti 1 and apply to Kenyan conditions. 4.2 General results Tables 1 and 2 show typical vehicle operating cost components. Table 1 shows that although price of fuel increased by more than 100 per cent between 1972 and 1975 the total costs increased the by 63 per cent. In this example the proportion of total costs attributable to fuel thereby increased from 10.0 per cent to 12.4 per cent. Table 2 illustrates how sensitive the costs per tonne payload are to the tie load selected. Detded comparisons of the vehicle operating cost components obtained using the model tith the results of other studies have been discussed elsewhere3. TABLE 1 Effect of price structure on vehicle operating costs (Prices expressed in Kenyan s~ngs per b) VeMcle type 3 tie Udaden wei~t 7.5 toMes BHP 177 had condition Payload (tonnes) Fuel Oil Spares Wintenance Tyres Depreciation Interest Crew wages Overheads Total Total/tonne h FuU 11.6 1972 0.34 0.02 0.71 0.41 0.33 0.21 0.11 0.60 0.68 3.41 0.294 % 10.0 0.6 20.8 12.0 9.7 6.2 3.2 17.6 20.0 Road roughness 3,000 mm/h Annual tiometrage 75,000 Futi 11.6 1975 0.69 0.04 1.26 0.54 0.49 0.43 0.20 0.80 1.11 5.55 0.469 % 12.4 0.7 22.7 9.7 8.8 7.7 3.6 14.4 20.0 1975, 1975 0.77 0.54 0.04 0.04 1.26 1.26 ‘ 0.54 0.54 0.61 0.39 0.43 0.43 0.20 0.20 0.80 0.80 1.16 1.05 D 5.80 5.25 0.356 0.644 8 TABLE 2 Typical vehicle operating costs (1975 prices expressed in Kenyan shilfings per km) Vehicle type Unladen weight BHP 2 ade 5.5 tonnes 150 5.0 2.0 0.39 0.04 1.16 0.54 0.19 0.39 0.19 0.80 0.93 4.63 2.31 Road rou~ess 3000 mm/km , Annual kilometrage 75,000 9.0 7.4 0.57 0.04 1.16 0.54 0.33 0.39 0.19 0.80 1.00 4.97 0.672 10,0 8.8 0.60 0.04 1.16 0.54 0.37 0.39 0.19 0.80 1.01 5.10 0.580 11.0 10.0 0.63 0.04 1.16 0.54 0.40 0.39 0.19 0.80 1.03 5.13 0.513 12.0 11.2 0.65 0.04 1.16 0.54 0.43 0.39 0.19 0.80 1.05 5.25 0.469 7.0 5.0 0.50 0.04 1.16 0.54 0.27 0.39 0.19 0.80 0.97 4.86 0.972 Rear axle (tonnes) Payload (tonnes) Fuel oil Spares Maintenance Tyres Depreciation Interest Crew wages Overheads TOTAL TOTAL/TONNE Vehicle type 3 axle Unladen weight 7.5 tonnes BHP 177 Road roughness 3000 mm/km Annual kilometrage 75,000 Rear afle (tonnes) 1 10.0 14.0 Payload (tOMW) 6.8 11.6 Fuel 0.59 0.69 oil 0.04 0.04 Spares 1.26 1.26 Maintenance 0.54 0.54 Tyres 0.37 0.49 Depreciation 0.43 0.43 Interest 0.20 0.20 Crew wagea 0.80 0.80 Overheads 1.05 1.11 TOTAL 5.27 5.55 TOTAL/TONNE 0.775 0.479 18.0 20.0 22.0 18.7 21.1 24.0 16.3 23.5 0.77 0.04 1.26 0.54 0.61 0.43 0.20 0.80 1.16 5.80 0.356 0.81 0.04 1.26 0.54 0.67 0.43 0.20 0.80 1.19 5.93 0.317 0.85 0.04 1.26 0.54 0.73 0.43 0.20 0.80 1.21 6.05 0.287 0.88 0.04 1.26 0.54 0.80 0.43 0.20 0.80 1.23 6.17 0.263 Vehicle type 3 tie + 2 tie trailer Urdaden weight 12.0 tonnes Road roughness 3000 mm/km BHP 177 Annual tiomctrage 75,000 Rear afle (tonnes) Payload (tonnes) 10.0 12.3 0.78 0.04 1.57 0.54 0.62 0.53 0.25 0.80 1.29 6.43 0.523 14.0 21.1 O.gl 0.04 1.57 0.54 0.85 0.53 0.25 0.80 1.37 6.87 0.326 18.0 20.0 34.2 22.0 38.6 24.0 29.8 43.0 Fuel oil Spares Maintenance Tyres Depreciation Interest Crew wages Overheads TOTA.L TOTAL/TONNE 1.02 0.04 1.57 0.54 1.07 0.53 0.25 0.80 1.46 7.28 0.244 1.07 0.04 1.57 0.54 1.19 0.53 0.25 0.80 1.50 7.49 0.219 1.11 0.04 1.57 0.54 1.30 0.53 0.25 0.80 1.54 7.69 0.199 1.16 0.04 1.57 0.54 1.41 0.53 0.25 0.80 1.58 7.89 0.183 9 4.2.1 Vehicle wastage. Vehicle wastage is taken into account in the model as part of depreciation costs. Table 1 shows that depreciation costs are less than 8 per cent of total vehicle operating costs and hence total costs are not very sensitive to this factor. The difference in vehicle operating costs when the high wastage equations were used was always less than 2 per cent and made no significant difference to the resulting optimum axle load, 4.2.2 Vehicle load factor. Table 2 indicates that for the example shown vehicle operating costs per tonne of payload for the half load condition are increased by about 80 per cent over the full load condition. This figure increases to nearly 100 per cent for low values of a~e load, as might be expected. 4.3 Total vehicle operating costs The dependence of total vehicle operating costs per tonne kilometre on gross vehicle weight is i~ustrated for three types of vehicle in Figure 5. These costs are total running costs plus standing charges for the vehicle in question but do not include costs associated with loading and urdoading. It is assumed that these latter costs are dependent only on payload and can therefore be expressed as an extra cost per tonne. Naturally this will vary for different types of cargo but for any particular cargo it is assumed constant and therefore cannot affect the optimum afle load. Detafled comparisons with veticle operating costs obtained in other studies have proved difficult for several reasons. Firstly the operating conditions in developed countries where dl the comprehensive studies have taken place are quite different. For example the cost components which are of interest in this study, namely those which depend on vehicle load condition, represent a completely different proportion of total runting costs. Furthermore there are no other studies in which the relationship between these costs, expressed in terms of costs per vehicle kilometre, and vehicle load condition has been isolated. Costs are usually expressed as average costs per tonne kilometre for different types of vehicles obtained under average load conditions. The decrease in costs with gross vehicle weight therefore represents a mixture of effects. First of all the decrease in costs per tonne is attributable to the increased load factor even though the average trip cost is assumed to be the same. Secondly as the gross vehicle weight increases so generally does the size of vehicle used in the calculations. Thus the basic relationship between the cost of a vehicle-kilometre and the payload (or gross vehicle weight) for a particular type of vehicle cannot be obtained. A further major disadvantage of other studies is that costs are usually obtained in money terms with the result that they are soon out of date. In the Road Transport Investment Model quantities are used where possible for dl the components of vehicle operating costs. Thus different price structures can be used to assessthe effects of, for example, the rise in price of any component cost. Finally it is not always clear in reports of other studies which of the component costs have been included and which excluded from the total vehicle operating costs. In particular the treatment of interest charges, depreciation and crew wages often varies from author to author. Despite these difficulties a comparison between a sample of the vehicle operating costs used in this study and several other studies is shown in Figure 6. The data have all been norrnafised to the vehicle operating costs obtained for a vehicle of 14 tonnes gross vehicle weight. The data for this figure were obtained from Figure 5 by drawing a smooth curve through the lowest sections of the three separate curves representing the 2-axled vehicle, the 3-axled vehicle and the 5-axled vehicle trtier combination in the full load condition. This is the same approach used by the other authors and represents a sensible choice of vehicle by the vehicle operators. It would be expected that since many operators in developing countries overload their vehicles the change over between vehicle sizes would take place further along the gross 10 vehicle weight scale resulting in lower costs per tonne payload in comparison with the studies conducted in Sweden16 and the USA2. This is confirmed in Figure 6. 5. TOTAL TRANSPORT COSTS 5.1 New road instruction In this series of runs of the model the road was assumed to be designed and constructed to carry the total traffic expected during the design life at various tie loads and freight tonnages without the need for any structural strengthening, Thus surface dressings and other normal maintenance costs were included but overlays were not required. A typical set of results is shown in Figure 7. In the AASHO Road Test the highest tandem tie load used to determine the de load – pavement damage relationship was about 22 tonnes. Extrapolation of the base data much beyond this is unrehable. In addition it is apparent from the histograms shown in Appendix 2 that rdthough a 24 tonne load on a dual-dud tandem tie is the value below which 95 per cent of axle loads he there are many individud ties on both the 2-axled vehicles and on vehicles and trailers with a sin~e-durd tandem wfich exceeds 12 tonnes. The 95 percentile appears to be about 16 tonnes for a sin~e tie. This would correspond to 24 tonnes on the singe-dud tandem tie provided the dud wheeled tie carried two-thirds of the load and the sin@ewheeled tie one-third, as would be expected for a properly designed tie. Thus 24 tonnes appears to be the 95 percentile for boti types of tandem axle and 16 tonnes for a singe tie. Few vehiclesincluded in the vehicle operating cost study3 exceeded these limits. N results for tandem tie loads above 24 tonnes must therefore be considered an extrapolation of both the vehicle operating cost data and the pavement damage data. For this reason graphical results are rdwaysshown as broken tines above 24 tonnes. 5.1.1 Minimum total transpoti rests. fie results in Figure 7 show that for each freight tonnage the total transport costs initi~y decrease very rapidy as afle load increases, pass through a very shallow minimum and then increase slowly thereafter, Over a wide range of afle loads the total costs are relatively insensitive to tie load. This pattern appfies to au total cost curves discussed in this report. However the tie load at which the minimum occurs depends very stron~y on the total freight tonnage carried by the fully loaded vehicles. The insensitivity of the total costs to Ae load in the region of the minimum is an important factor to be considered when pohcy decisions about Iegd fimits and enforcement are being made. As a measure of this insensitivity the atie load at which total costs are 2% per cent higher than the minimum has been plotted in Figure 7. In this example an increase in costs of 2%per cent is equivalent to a decrease in tandem aAe load of between 5 and 6 tonnes, ie a decrease of between 17 and 33 per cent in the afle load as total freight tonnage varies from 10 down to 0,5 milhon tonnes. Figure 7 has been plotted for a particular fleet of vehicles using 1972 prices on a new road in rolling terrain constructed on a subgrade of CBR 3 per cent. The lowest freight tonnage (0.5 mfllion) corresponds to an initial dtiy traffic of about 10 fufly loaded vehicles per day in each direction. The optimum tie load for tMs tonnage agrees reasonably wefl with the current Iegd hmit in many developing countries. However for any higher levels of freight tonnage carried on fu~y loaded vehicles the optimum rises appreciably, In addition the effect of additiond freight carried on vehicles which are not loaded to the tie load limit is to increase the optimum tie load as discussed in Section 3.2.1 above. 11 The relationship between the optimum tandem tie load and freight tonnage is summarised in Figure 8. 5.1.2 Terrain and subgrade. The optimum tandem afle loads for each freight tonnage were found to be almost independent of the vertical alignment of the road. No differences were distinguishable between flat and roUng terrain but the values for hi~y terrain were about 0.5 tonnes lower for low freight tonnages. Simflarly the effect of subgrade strength was sm~, the curves representing subgrades of CBR value 3, 7 and 15 per cent all falling within 0.5 tonnes of each other. The only likely exception to this general result occurs if the design charts which are used to determine the thickness of the pavement layers do not require a continuously increasing ttickness as traffic loading increases. Some design charts recommend a fixed design for a considerable range of traffic loads thereby proviting a slight overdesign for traffic at the low end of the range and possibly a slight underdesign for traffic at the high end. Under these circumstances the pavement costs do not increase continuously with atie load and unique minima in the total cost curves do not always exist. In ttis study the pavement design thicknesses always increase 13 continuously with traffic loading . 5.1.3 Veilicle load rendition. The model runs described above were dl for vehicles fully loaded in both directions. The other extreme condition in which vehicles are empty on the return trip has a significant effect on the minima in the cost curves. The relationship between the optimum tie load associated with these minima and freight tonnage is shown in Figure 8. The optima are always higher than for the fill load condition, the difference varying from 2.0 tonnes at a total freight tonnage of 0.5 mflhon to over 6.0 tonnes at freight tonnages greater than 3.0 milfion. However for tonnages greater than 1.5 mflfion the tandem axle optima are always above 24 tonnes and therefore in the area of data extrapolation. 5.1.4 Veklicles with Iligll pavement damage factors. Vehicles with tandem axles consisting of one dual wheeled axle and one sin#e wheeled axle have been shown to be particularly damaging to the roads (Appendix 2). Such a veticle does more than three times as much damage to the road as a sitiarly loaded vehicle with two dud wheeled ties making up the tandem set. Unfortunately vehicles of this type are very common in East Africa. Figure 8 shows that the optimum tandem tie load for a fleet of vehcles of this type is between 2 and 4 tonnes less than that for vehicles with dud wheels on both axles. 5.1,5 Pavement damage relationship. The effect of changing the pavement damage-atie load. relationship from a 4.5 to a 6.0 power law is dso shown in Figure 8. The optimum tandem axle load is about 1 tonne less than obtained using the 4.5 power law at low freight tonnages but this difference increases to more than 6 to~es as the tonnage increases to 10.0 mflhon. 5.2 Existing roads with strengthening overlays [n this series of runs the roads were designed assuming that the total freight tonnage was carried on 3-axle vehicles whose tandem tie load was 16.0 tonnes. As the ade load increased for each tonnage, overlays were appfied to the road as described in Section 2.4.5. The cost of the original road construction was therefore identical for each ade load and did not affect the optimum aAe load. Typical results are shown in Figure 9 and the relationship between the optimum tandem afle load and the freight tonnage is shown in Figure 10. It can be seen that the optima are between 1 and 2 tonnes lower than obtained for the new road construction poticy. This difference is not significant in view of the insensitivity of total costs to axle loads near the minima. 12 5.2.1 Pria strutiure. me model runs were repeated using 1975 prices thus enabhng the effect of prices before and after the od crisis to be determined. me prices used are shown in Appendix 1. fie relationship between the optimum atie loads and freight tonnage is shown in Figure 10. me minima in the total cost curves are lesssh~ow than before, the difference in tandem tie load between the opttia and the tie load corresponding to tin increase in the minimum costs of 2.5 per cent being between 2 and 3 tonnes instead of between 4 and 5 tonnes. me optima themselves are dso between 1 and 3 tonnes lower than obtained using 1972 prices. 5.3 An example of mixed traffic on an existing road me results of the tie load survey on the main Al 09 trunk road in Kenya ae shown in Appendix 2. A series of model runs was made using a mixed fleet of vehicles sifiar to the fleet operating on this road. me actual pavement details were dso used as input together with an overlay pohcy designed to Wow the road to reach ftiure after fifieen years. A growth rate of 5 per cent for traffic and a discount rate of 12 per cent (appropriate in 1975) were used as before. It was assumed that the vehicles were d loaded so that the main load bearing tie for each type of vehicle and trder always carried the selected tie load as in the previous examples. me afle load which most closely resembles the average operating conditions encountered in practice is about 19 tonnes on a tandem ade but this varies with each vehicle type. me runs were made using 1975 prices. me cost curves are shown in Figure 11 for different total freight tonnages carried in one direction. me actual tonnage on the road is close to 20 mWon tonnes 7. me optimum tandem tie load is wefl above 24 tonnes. me optimum tie load for lower freight tonnages have been plotted in Figure 10 where it can be seen that they he close to the line for 3-tied vehicles with the 1975 price structure. me total costs for vehiclesin the hdf load condition show that the minima ford tonnages greater than 5.0 Won are greater than 24 tonnes. 5.4 Discussion me results described here indicate that for any combination of variables there is a freight tonnage above which the optimum tandem afle load exceeds 24 tonnes. For any reasonable combination of variables (Section 2.2) this tonnage is fikely to be between 5 and 10 mifion tonnes transported in one direction during a 15 year period provided it is carried by fu~y loaded vehicles which are rdso able to make a return trip in the fu~y loaded condition. ~s tonnage is equivalent to an initial dtiy traffic flow of less than 100 fu~y loaded veticles in each direction. me existence of other vehicles wMch are not fufly loaded increases the optimum tie load and consequently decreases the traffic level of fufly loaded vehicles at which the above statement is true. In addition if the veticles are only partitiy loaded on the return trip the optimum atie load rises further implying that at even’lower traffic levelsthe optimum tandem tie load exceeds 24 tonnes. In Kenya under conditions where the optimum is clearly greater than 24 tonnes its dependence on the factors considered here is unimportant because vehicle operators are unable or unwi~ng to exceed this weight with their current fleet of vehicles; 24 tonnes on a tandem tie is the value below which 95 per cent of d tandem afle loads he. Under conditions where tie optimum is below 24 tonnes, the optimum is found to be independent of terrain or subgrade and relatively independent of whether the road is designed initially to carry the fu~ load or is inititiy designed to carry a lower load with subsequent strengthening. It is extremely dependent 13 on whether the veticles can be fu~y loaded on both the outward and return trips and also on the total tonnage actuWy carried. However udess the number of fully loaded vehicles fds below about 5 per day the optimum is urdikely to be below the relatively common legaltirnits of 8 tonnes on a sin~e tie and 16 tonnes on a tandem tie. Under most conditions it appears that the total operating costs are insensitive to tie load near to the optimum. Thus costs increase only by 2.5 per cent as the de load is reduced below the optimum by 3 or 4 tonnes. Comparison with the work of other authors is difficult because conditions vary so much from country to country, however it is interesting to note that from Btick’s comprehensive study 16 for Swedish conditions using a 6.5 metre wide highway, a traffic growth of 6 per cent and a 20 year design fife, the freight tonnage at which a tandem atie load of 24 tonnes or more becomes justifiable is about 4.5 tion tonnes carried on the fu~y loaded vehicles. BrincYs results are shown in Figure 10. The relationship between optimum tie load and tonnage is steeper than obtained here but leads to the same conclusions for heavily trafficked roads. Results obtained by Motomura 17 for the Sultanate of Oman showed that under almost dl conditions the optimum tandem tie load was greater than 24 tonnes. The ody exceptions occurred at low traffic levek (less than 100 heavy vehicles per day) under conditions of no traffic growth coupled with high discount rates. Under conditions of more retistic traffic growth it was found that the optimum tandem afle load was greater than 24 tonnes even when the number of heavy veticles per day fe~ below 20. The report17 uses 1978 prices but does not give a detded breakdown of U component COSS. It must be assumed that in Oman the cost of oil based products such as bitumen and petroleum is low with the result that the optimum tie load is high in comparison with most countries. In almost dl other studies which have considered the effects of changing tie load limits the calculations have been done on an incremental basis. GenerWy the results confirm that increases in vehicle axle load limits are justified economica~y and that quite large increases in load are beneficial for a heatiy trafficked network5,1 8,19,20 6. OTHER COSTS 6.1 Introdudion There are two classes of costs which cannot be included in the Road Transport Investment Model and which therefore have to be considered separately. First of W there are those costs which although quantifiable cannot be generalised sufficiently precisely for inclusion in the model. These costs include M major structures such as bridges and major culverts. Secondy there are those costs which are difficult or impossible to quantify and include the social costs of transport such as air po~ution, accidents, traffic delays and noise. This report is concerned primarily with the dependence of the optimum axle load on those factors which can be included in the model. The report would, however, be incomplete without some discussion of these other costs, some of which are not very dependent on the tie load and hence have fittle or no influence on the optimum. These additional costs must afl be included if a complete cost-benefit analysis for a countrywide road network or even a principal trunk road is attempted. Table 3 summarises aflthe important factors which 14 need to be included in such an analysis. me probable response of vehicle operators and freight shippers to changes in axle load fimits, levels of enforcement, taxes and duties and related legislation need to be determined before a fu~ analysis can proceed. Vehicle operations other than the long distance haulage considered in this report need to be included and this will require a study of the operating charactetitics of the whole veticle fleet. A summary of the incremental cost benefit analysis necessary for a developed country is given in Reference 2 and a summary of the additional problems encountered in developing countries has been given by Fossberg21 , Some of these factors are discussed in ttis section with particular reference to the hkely effect on the optimum axle load. It should be borne in mind throughout this section that ody those vehicles which are loaded to the specified limit have any major influence on the optimum tie load. TABLE 3 . Principal factors to be included in a complete cost-benefit analysis of the effects of changing vehicle axle loading practice 6.2 1. 2. 3. 40 5. 6. 7. 8. 9. 10. 11. 120 13. 14. 15. 16. 17. 18. ~anges in taxation, licensing, duties and other revenue collection by Government Cost of enforcement Cost of operating vehicles Ganges in loading practice of vehicles ~anges in operators choice of veficle Ganges in the number of vehicle trips mange in total freight costs and transport charges Impact on other transport modes due to change in modd spht Additiond cost of new tighway construction including bridges Additiond cost of road strengthening including bridges Addtiond cost of road and bridge maintenance ~nges in the timing of the construction of additional highway capacity Additiond cost of road realignment Ganges in traffic accidents ~anges in noise and vehicle induced vibrations Changesin levels of air poflution Ganges in the price and avtilabihty of goods ~anges in travel time due to the impact of heavy vehicles on traffic operations Bridges Bridgesrespond differently to loads depending mainly on the dimensions of the structure, the strength of the materials used in fabrication, the type of bridge and the basic design. For any increase in axle loads or gross vehicle weights some bridges will require strengthening whereas others wi~ not. For some of the former category strengtherdng wifl be found to be economically unjustified and complete reconstruction wiu be necessary. A method of calculating these costs has been proposed in Reference 2 but each bridge has 15 to be treated separately and generalisations are not possible. In a case study completed for Sweden16 Brinck has estimated that the cost of constructing bridges to carry vehicles with a 24 tonne tandem tie load is about 26 per cent higher than for a 16 tonne load. He does not, however, calculate the cost of strengthening existing bridges. With an average of one 28 metre span bridge for every 10 Wometres of highway Brinck estimates that bridge construction costs are about 12 per cent of road construction costs. The incremental cost of bridges designed for the higher afie load therefore makes a sma~ but significant difference to total transport costs and therefore to the optimum ade load. In those developing countries with a much lower density of bridges than Sweden the incremental cost of bridge strengthening and construction wifl make tittle difference to the optimum atie load. For those countries with a M@ density of bridges the calculation of the optimum tile load is not possible until a complete study of dl the bridges has been made. 6.3 Accidents The effect of increases in afle loads on the number and severity of road accidents is controversial and difficult to assessfrom published data even for industriafised countries. In the United Mngdom the involvement rate (accidents per kilometre travefled) for heavy goods vehiclesin serious accidents is simflar to that for cars but the severity of accidents is greater22. The causes of those accidents are difficult to determine but it is tikely that the dimensions and mass of the vehicle and its mode of use are faciors. The effect on accident rates of increasing vehicle afle loads is unknown, but for the same freight tonnage transported accident involvement may increase as a result of increases in vehicle weight. This W be offset by a reduction in the number of kilometres travelled. The operating conditions in developing countries are so different from industridised countries that even broad genertisations are not possible. Vehicle maintenance is much poorer, vehicle testing often non existent, restrictions on driving hours are not enforced or are non existent, training of drivers is less effective and road conditions are very different. Detailed accident studies are necessary before a relationship between accidents and vehicle afle loading can be established. 6.4 Air pollution In the USA transportation causes serious air poflution giving rise to nearly dl the carbon monoxide and about hdf of the nitrous oxides and hydrocarbons present as pollutants in the air. Diesel engines have been shown to be considerably cleaner than petrol engines in dl respects except in the emission of particles of unburnt carbon (smoke) 23. These particles, while smeWngunpleasant and being visually obvious, are less of a health hazard than the other pollutants. The dependence of the quantity of pollutants on vehicle load condition is unknown but possible incremental increases caused by increases in axle load are likely to be offset by the reduction in vehicle trips necessary to carry the same amount of freight. 6.5 Noise and vibration Both the level of noise and the vibrations caused to structures near the road by heavy vehicles are tikely to increase with axle load but as with pollution this is offset by the decrease in vehicle trips. Neither noise nor vibrations are important in the context of most developing countries where population densities in rural areas are genera~y low. 16 7. SUMMARY The Road Transport Investment Mode19has been used to show that for a typical developing country the sum of vehicle operating costs and road construction, maintenance and strengthening costs for a two lane highway decrease rapidy as the afle load of the fu~y loaded vehiclesincreases, passesthrough a relatively shdow minimum value at the optimum afle load, and then increases gradu~y thereafter. The vahre of the optimum tandem de load was found to be virtua~y independent of the vertical alignment of the road and the strength of the subgrade. The choice of road construction and strengthening pohcy and the composition of the vehicle fleet had a small effect on the optimum tandem tie load; the variations considered here making less than 3 tonnes difference in the optimum provided that tandem ties consisting of one dud wheeled tie md one singe wheeled tie are treated as two singe sties for the purpose of defining the tie load hmits. The most important variables which influenced the optimum axle load, listed in order of importance, were found to be the total freight tonnage carried by the fully loaded vehicles,the !oad conditions of these vehicles on the return trip, the exponent of the pavement damage-tie load relationship and the relative price of the major components of road transport cost. For total freight movements of lessthan one lfion tonnes transported in one direction over 15 years by fully loaded vehicles the optimum tie load is close to or below the common tandem afle legal hmit of 16.0 tonnes which is found in many countries. However under most conditions there exists a freight tonnage above which the optimum tandem tie load exceeds the 95 percentile found in Kenya of 24 tonnes. This tonnage is generdy lessthan 10.0 fi~on tonnes, a figure wfich is equivalent to an initial average &fly traffic of about 100 heavy vehicles making fufl use of the 24 tonne tandem afle load. The effect of additiond vehicles which are not fu~y loaded is to increase the vahre of the optimum afle load stfll further and thus to reduce the average dtiy traffic of the fu~y loaded vehicles at which the optimum tandem tie load exceeds 24 tonnes. The minimum in the total cost curves is such that quite large decreasesin the tie load of the fully loaded vehicles below the optimum increases the total transport costs ordy by smd amounts. For example decreasesin tandem afle loads of 3 or 4 tonnes usudy increase the total costs by less than 2.5 per cent. Finally the report shows how the Road Transpbrt Investment Model can be used for a complete cost-benefit analysis of a proposed change in axle load Wts for a developing country and indicates the data which need to be obtained for the calculations to be completed successfully. 8. ACKNOWLEDGEMENTS This study was carried out by the Werseas Unit (Head of Unit: J N Bulman) of the Transport and Road Research bboratory, United Kingdom. Much of the work described in this report was carried out in conjunction with the Kenyan Ministry of Works. The author is indebted to the Engineer in ~ef, Mnistry of Works and Msstaff without whose consistent cooperation the work could not have been successful. 17 9. REFERENCES 1. HIGHWAYWSEARCH BOARD. The AASHO Road Test. Report 5. Pavement Research. Highway Research Board Special Report 61E. Washington DC, 1962 (National Research Council). 2. STEVENS, H. tine haul tructing costs upgraded, 1964. Highway Research Record No. 127. Washington DC, 1966 (National Research Councfl). 3. HIDE, H, S WABAYNAYAKA,I SAYER and R WYATT. The Kenya Road Transport Cost Study: research on vehicle operating costs. Department of the Environment, T~L Report LR 672. Crowthorne, 1975 (Transport and Road Research hboratory). 4. BNNCK, C E. Benefits of increased afle loads. Roceedings 94. StocWolm, 1968 (The National Road Research Institute, Sweden). 5. WHITESIDE, R E, TING Y CHU,J C COSBY,R L WHITAKER and R WINFREY. Changesin le@ vehicle weights and dimensions: some economic effects on highways. National Cooperative H&hway Research fiogram Report 141. Washington DC, 1973 (Natioml Research Councfl). 6. FREITAS, M D and M L REISS. Safety performance of large truck in the United States of America. Symposium on Heavy Freight Vehicles and their Effects 1977. Pan’s, 1977 (Organisation for &onomic Cooperation and Development), pp 67–82. 7. JONES, T E. tie loads on paved roads in Kenya. Department of the Environment Department of Transport, TRRL Report LR 763. Crowthorne, 1977 (Transport and Road Research bboratory). 8. ELLIS, C I. Ale load distribution on roads overseas. Survey on roads in West Mrdaysia 1967. Ministry of Transport, RRL Report LR 187. Crowthorne, 1968 (Road Research hboratory). 9. ROBINSON, R, H HIDE, J WHODGES, S WABAYNAYAKAand J ROLT. A road transport investment model for developing countries. Department of the Environment, TRRL Report LR 674. Crowthorne, 1975 (Transport and Road Research hboratory). 10. ROBINSON, R. Road transport investment model: draft user manuaL Department of the Environment, T-L Report SR 224 UC. Crowthorne, 1976 (Transport and Road Research bboratory). 11. ADDIS, R R and R A WHITMARSH. Relative damaging power of wheel loads in tied traffic on pavements of different strengths. Department of the Environment Department of Transport, TRRL Report LR 979. Crowthorne, 1981 (Transport and Road Research Laboratory). 12. TRANSPORT AND ROAD RESEARCH LABORATORY. A guide to the structural design of bitumensurfaced roads in tropical and sub-tropical countries. Department of the Environment Department of Transport, Road Note No. 31. hndon, 1977 (H M Stationery Office). 13. ROLT, J and S WABAYNAYAKA. Revision 1 of the Road Transport Investment Model. Department of the Environment, TRRL Report SR 246. Crowthorne, 1976 (Transport and Road Research bboratory). 18 14. TRANSPORT AND ROAD RESEARCH LABORATORY. A guide to the structural design of pavements for new roads. Department of the Environment, Road Note No. 29. hndon, 1970 (H M Stationery Office). 15. AMENCAN ASSOCIATION OF STATE HIGHWAYAND TRANSPORTATION OFFICIALS. AASHTO interim guide for the design of pavement structures 1972. Washington DC, 1974 (American Association of State Highway and Transportation Officials). 16. BMNCK, C E. Optimum ade loads. Proceedings 92. Stoctiolm, 1966 (The National Road Research Institute, Sweden). 17. YUICHIRO MOTOMURA. Optimum tie load tit. The 58th Annual Meeting of the Transportatwn Research Board 1979. Washington DC, 1980 (National Research Councd). 18. SHEEDY, J P M. The implications in relation to road pavements of increasing the permitted sin#e tie load from 10 tons to 13 tons (12.8 tons). The National Institute for Physical Pbnning and Construction Research RC 81. Dubhn, 1971 (me National Institute for Physical Manning and Construction Research). 19. PHANG, W A Vehicle weight regulation and the effects of increased loadings on pavements. Department of .Zighways Ontario Report RR 151. Ontario, 1969 (Department of Highways Ontario, Canada). 20. FRY, AT, G R EASTON, I R KER, J McL STEVENSON and J R WEBBER. A Study of the konornics of Road Vehicle Limits. National Assoctitwn of Australian State Road Authorities. Sydney, 1975 (Natiod Association of Austrtian State Road Authorities). 21. FOSSBERG, P E. Road freight transport problems with special reference to developing countries. Symposium on Heavy Freight Vehicles and their Effects 197Z Pans, 1977 (Organisation for fionomic Cooperation and Development). 22. NEILSON, I D, R N KEMPand H A WLKINS. Accidents involving heavy goods vehicles in Great Britain; frequencies and design aspects. Department of the Environment Department of Transport, TRRL Report SR 470. Crowthome, 1979 (Transport and Road Research bboratory). 19 Notes: ----= ----= -—— 4 Select price str”ct”re I -—— Selectvehicle wastege 1 m ---- + Select maintenance -—— policv for road I ~ Selectfreight tonnage I P Design road and overlavs Calculate construction costs, vehicla operating 1- c Plot total costs versus rear axle load and obtain optimum Repeat for changas in parameters I Flat, rolling or hillv various subgrades Used to test sensitivity to critical component prices Including mixed vehicle fleets 0.5–10.0 million tonnes over 15 year period 6-32 tonnes tandem axle 4-16 tonnes single axle Designsbased on structural number methods Fig. 1 Metiod of analysis 1.0 0.9 0.8 0.7 . . . 0 1 2 3 4 5 6 7 8 9 10 Traffic (mill ions of standard axles) Fig. 2 me cost of a new road in rolling terrain as a function of traffic (1972 prim) 1.5 1.0 0.5 0 Total freight carried (millions of tonnes in 15 years) 100 7.5 . 5.0 2.5 1.5 0.5 . 0 4 8 12 16 20 24 28 32 36 Tandem axle load (tonnes) Fig. 3 Pavement construction costs for a new road in rolling terrain as a function of axle load and freight tonnage 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 . Number and thickness of overlavs 3 x 75mm i 3 x 50mm 2 x 50mm 90mm 37mm I . 25mm I Initial SN = 3.o5 . Initial SN = 3.60 1 I 1 I I I 1 1 0 4 8 12 16 20 24 28 32 Traffic (millions of standard axles) Fig. 4 Total costs of overlays and maintanan- as a function of traffic (1975 prim) 2.1 1.( o I I 1 I I I 11 10 ,1 ,1 ,1 El II \l \\ b\ ● Two axle Three axle o Three axle + 2 axle trailer _ Full load ==== Half load .— t\ \ \ ‘, \\ \ h. ‘\\ \\ b \\ t\ \ \L\. o 10 20 30 40 50 60 Gross vehicle weight (tonnes) Fig. 5 Vehicle operating costs as a function of gross vehicle weight for three ~pes of vehicle (1975 prices) 90 8C 70 60 50 40 30 20 . . . . This studv . . I I ~ 0’ 1 1 I I 1 I 10 15 20 25 30 35 40 45 Gross vehicle weight (tonnes) Fig. 6 Comparison of vehicle operating costs 2.5 2.0 1.5 1.0 0.5 0 0, II .I-otal freight carried (millions of tonnes in 15 years ,_ _ _ -, ~.o -__c. -l.5 Minimum Minimum + 2y2% costs 4 8 12 16 20 Tandem axle load (tonnes) 24 28 32 Fig. 7 Total transport costs for a fleet of 3~xled vehicles on a new road under full load conditions using 1972 prims c.- [ \ 3\ \ \ \ \\ o \ \. 2.5 2.0 1.5 1!.0 0.5 a . . . . Total freight carried (millions of tonnes in 15 years ~+ N -- 10.C / W--””*5 Minimum Minimum + 2Y2% costs 1 1 1 1 1 1 1 . 0 4 8 12 16 20 24 28 32 Tandem axle load (tonnes) Fig. 9 Total transport costs for a fleet of 3-axled vehicles on an existing road strengthened with overl~s under full load conditions using 1972 prim \ \ \ \ \ ( ‘; ‘; \\\ \\\ \ \ \ ‘\ \\ \\ \ \ .= E.- m 2 I \ \ \ \ \ \ \ \ \ \ \: \ 0 m 0 0 (SUUO1)peoI alxe wi~puel wnw!ldo I . . . Total freight carried (millions of tonnes in 15 years) 20 15 10 5 0 4 8 12 16 20 24 28 32 Tandem axle load or 2 x single axle load (tonnes) Fig. 11 Total transport costs as a function of axle load for a mixed vehicle fleet, overl~ poli~, full load conditions using 1975 prices. 60 40 20 0 a) 2-AXLE VEHICLES PULLING TRAILERS (Trailers not included) . 0 4 8 12 16 20 24 c) 3-AXLE VEHICLES. DUAL/DUAL TANDEM Legal limit . + . 0 4 8 12 16 20 24 e) 3-AXLE VEHICLES. SING LE/DUAl. TANDEM Legs’’imit+ % o 4 8 12 16 20 24 60 40 20 0 b) 2-AXLE TRAILERS . Lega,,imitl l=] O 4 8 12 16 20 24 60 40 20 0, 60 40 20 0 d) 3-AXLE TRAILERS. DUAL/DUAL TANDEM . 0 4 8 12 16 20 24 f) 3-AXLE TRAILER. SINGLE/DUAL TANDEM . I I L Legal limit . 0 4 8 12 16 20 24 Weight categories per axle (Itonnes) (Tandems treated as two singles) Fig. 12 Resul@, of weighing suwey 10. APPENDIX1 INPUT DATA FOR MODEL The originrd input data were based on the costs derived for the Yala–Busia road in Kenya described in Appendix 1 of Reference 9. These are summarised below. The new prices are based on a survey of prices in Nairobi in 1975 and are dso shown. 1. 2. 3. 4. Road cross section &rriageway width Carriageway slope Shoulder width Shedder slope at slope FWslope Ditch depth Ditch bottom width Ditch bottom slope Ditch side dope ~earing width Road tignment 7.00 metres 1 in 40.00 2.50 metres 1 in 10.00 1 in 1.00 1 in 3.00 1.00 metres 2.50 metres lino,oo linl.so 20.00 metres Road type Totrd rise Total fd Curvature (m/h) (m/h) degrees/h Level road 3.2 2.8 15 RoWng road 25.5 5.4 75 my road 34.0 17.0 150 The costs of earthwork, culverts and headwtis are independent of tie load and are therefore not reproduced here, Pavement costs (Kenyan sti~ngs) hproved subgrade per cubic metre StabWsed subbase per cubic metre Crushed stone base per cubic metre Surface dressing per square metre Asp~tic concrete per cubic metre Shoulder gravel per cubic metre T 1972 1975 15.5 20.0 71,1 90.0 122.4 159.7 11.1 16.8 260 525 21.3 25.0 32 5. Wintenance costs (Kenyan shi~ngs) Mterids loaded Uquid bitumen at source Surface dressing stone at source Base patch material on site Surface patch *on site Water at source Diesel fuel detivered bbour (Kenyan s~ngs per hour) Common labour Truck driver Hant operator Foreman Per titre Per cum Per cum Per cum Per cum Per titre Rant hire (Kenyan mgs per hour) 4500 titre self prope~ed bitumen distributor 0.25 tonne vibrating ro~er Grader (3.7m blade) 10 tonne self prope~ed rofler Tractor mower (1.8m wide) Water truck (6 cu metres) Tipper truck (4 cu metres) 6. Vehicle costs (Kenyan shi~ngs) Petrol per titre Diesel per htre hbricants per titre ~ntenance labour per hour Tyres Crew wages per hour Vehicle type A @urchase price in Kenyan s~gs) B~= 150 ULW= 5.5 tonnes Vehicle type B @urchase price in Kenyan ~n,gs) B~= 177 ULW= 7.5 tonnes Vehicle type C @urchase price in Kenyan Wn8s) B~= 177 ULW= 12.0 tonnes Vehicle type D @urchase price in Kenyan ~ngs) B~= 177 ULW= 12.5 tonnes 1972 1975 0.80 1.00 78.00 90.00 1.50 3.00 71.00 175.00 1.25 1.50 1.16 1.84 1.60 1.90 2.40 3.00 4.00 5.00 6.00 8.60 20.0 40.00 5.0 10.00 34.3 70.00 20.0 40.00 15.0 25.00 15.0 25.00 18.00 35.00 1.10 2.65 0.90 1.84 4.70 9.20 30.00 40.00 500.0 2200.0 9.50 12.00 — 234000 142000 253000 — 317000 — 357000 N heavy vehicles travel 75000 Wometres per year and the crews work for 5000 hours per year. m 7. Mntenance package units Light (surface) patchi~ 0.25 tonne tibrating rofler Tipper truck(4 cu metres) 6 labourers 1 foreman Roductitity of unit is 19 sq m/h He@y (base) patching 0.25 tonne tibrating ro~er Tipper truck(4 cu metres) 7 labourers 1 foreman Roductitity of unit is 3 cu m/ti Surface dressing 4500 htre self prope~ed bitumen distributor 10 tonne self propefled rofler Tipper truck (4 cu metres) 23 labourers 1 foreman Roductitity of unit is 1600 sq m/ti Mowing of shoulders Tractor mower (1.8m wide) 1 labourer Oforeman Roductitity of unit is 5000 sq m/k Grading of shoutiers Grader (3.7m blade) 1 labourer Oforeman Roductitity of unit is 7000 sq m/h Drainage maintenance Tipper truck (4 cu metres) 10 labourers 1 foreman Productivity of unit is 10 cu mm 11. APPENDIX2 VEHIC~ LO~ING CHWCTENSTICS me loading characteristics of the majority of the vehicles used in this study were taken from tie load surveys conducted in Kenya during 1972-19747. Fi#lre 12 shows the results of surveys at one site on the Al 09 trunk road from Mombasato Nairobi. The resudtsare forthe heatiy loaded directionwhichis towardsNairobi. Amore detied ehation of the histogramsshowsthat there is a sharpcut off as tie load increases. For eachtype of vehicleor ttier the highest5 per cent of tie loadsspansless than 1.5 tonnes. The tie loadsbelowwhich95 per cent of W valuestie for eachtype of tie confi~ration aregivenbelow. a) 2-tied vehicles — 16 tonnes b) 2-tied trders 14.5toMes c) 3-tied vehicles(dti-dti tandem) – 10 tonnes pertie or 20 tonnes per tandemset d) 3-tied vehicles(sin@e-dudtandem) – 16tonnes per dud tie or 24 tonnes pertandemset e) 3-tied trders (dud-dud tandem) – 12tonnes per tie or 24 tonnes per tandemset O 3-tied trders (sin@e-durdtandem) - 14 tonnes per dti tie or 21 tonnes pertandemset Amore detded adysis of the surveysisshowrIin Tables4 and 5. From these tablesthe payload, pavementdamageand mainload carryingtie weightfor d vehiclesusedin the study can be obtained by interpolation. Veficles Trders TABLE 4 Wractenstics of 3-Wed veficlesand trders Udadenwei@t (tonnes) 6.5 7.5 . 8.5 10,0 5.0 Payload (tonnes) ,6 10 14 18 22 26 30 6 10 14 18 22 26 30 6 10 14 18 22 26 30 6 10 14 18 22 26 30 8.3 13.6 19.0 21.7 24.3 27.0 Rear afle load (toMes) 8.9 12.3 15.7 19.0 22.2 25.4 28.6 9,0 12.6 16.1 19,5 22.8 26.0 29.1 10.3 13,7 17.0 20.3 23.6 26.8 30.0 11.8 15.1 18.5 21.7 25.0 28.1 31,3 10.0 14.0 18,0 20.0 22.0 24.0 Equivalent standard ties 0.15 0.60 1.7 4.0 8.1 14 25 0.16 0.71 ~ 2.0 4.6 9,2 17 28 0.30 0.98 2.5 5.3 10.7 19 32 0.51 1.48 3.6 7.4 13.8 23 38 0.19 0.85 2.7 4.3 6.6 9.8 Sin~e-dud tie 0.30 1.3 4.1 10,0 ~ 21 39 68 0.31 1.4 4.6 11.4 24 43 75 0.58 2.2 5.9 13.7 28 51 86 1.1 3.4 8.9 19 37 63 103 0.42 1.92 6,0 9.7 14.9 22 \ ‘\ Veticles Trders . . . . .. ‘~ TABLE5 “ - x.. Garacteristics of 2-tied veticlesand trders 5.0 4.5 4.00 6.65 9.25 11.75 14.20 16.55 18.80 20.90 5.5 9.5 13.5 15.5 17.5 19.5 War tie load (tOMW) 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0 5.0 7.0 9.0 10.0 11.0 12.0 ~uivdent standardties \ .. 0.26 . . 0.92 2.5 5.6 11.3 20 35 55 0.22 1.00 3.1 5.0 7.7 11.3 (1461) Dd8041301 1,400 a/81 HPLtd So’ton G1915 PRINTED IN ENGLAND A=TRACT Optimum axle loads of mmmercial vehicles in d(~veloping muntries: J ROLT PhD MInst HE: Department of the Environment Department of Transport, TRRL Laboratory Report 1002: Crowthorne, 1981 (Transport and Road Research Laboratory). The Road Transport Investment Model for developing countries has been used to examine the effects of different axle loading characteristics on the total costs of road transport. It is shown that the sum of vehicle operating costs, road construction costs and road maintenance and rehabilitation costs for a two lane highway initially decrease rapidly as the axle load of the most heavily loaded vehicles increases and passes through a shallow minimum it the optimum axle load. The value of this optimum axle load was found to be stron~y dependent on the total freight tonnages carried by the heavily loaded vehicles, the load condition of these vehicles on the return trip, the exponent of the pavement damage – z~le load relationship, and the relative prices of the major components of roadl transport cost. The optimum axle load was found to be virtually independent of the road alignment and strength of the subgrade, but the road construction and strengthening poticy and the composition of the vehicle fleet had a small but significant effect on its value. It is shown that under most conditions there exists a traffic level above which the optimum axle load is above the current legal linnits in force in most developing countries, The total road transport costs were usudl~~ found to be relatively insensitive to axle load in the region of the minimum total transport cost, changes in axle loads of 10 per cent producing changes in the transport costs of less than 1 per cent. ISSN 0305– 1293 A~TRACT Optimum axle loads of wmmercial vehicles in developing muntries: J ROLT PhD MInst HE: Department of the Environment Department of Transport, TRRL Laboratory Report 1002: Crowthome, 1981 (Transport and Road Research Laboratory). The Road Transport Investment Model for developing countries has been used to examine the effects of different axle loading characteristics on the total costs of road transport. It is shown that the sum of vehicle operating costs, road construction costs and road maintenance and rehabilitation costs for a two lane highway initially decrease rapidly as the axle load of the most heavily loaded vehicles increases and passes through a slhdlow minimum it the optimum axle load. The value of this optimum axle load was found to be stron~y dependent on the total freight tonnages carried by the heavily loaded vehicles, the load condition of these vehicles on the return trip, the exponent of the pavement damage – axle load relationship, and the relative prices of the major components of road transport cost. The optimum axle load was found to be virtually independent of the road alignment and strength of the subgrade, but the road construction and-strengthening poficy and the composition of the vehicle fleet had a small but significant effect on its value. It is shown that under most conditions there exists a traffic level above which the optimum axle load is above the current legal limits in force in most developing countries. The total road transport costs were usually found to be relatively insensitive to axle load in the region of the minimum total transpc)rt cost, changes in axle loads of 10 per cent producing changes in the transport costs of less than 1 per cent. ISSN 0305– 1293