Risk and the pavement design decision in developing countries by C. 1.Ellis TRANSPORT and ROAD RESEARCH LABORATORY Department of the Environment TRRL LABORATORY REPORT 667 RISK AND THE PAVEMENT DESIGN DECISION IN DEVELOPING COUNTRIES by Cl Ellis Any vievvs expressed in this report are not necessarily those of the Department of the Environment Overseas Unit Transport and Road Research Laboratory CroWhorne, Berkshire 1975 ISSN 0305–1293 CONTENTS Abstract 1. Introduction 2. me pavement design process 2.1 Traffic 2.2 Subgrade strengti 2.3 Pavement materials 2.4 Courses of action 3. Ftiure criteria 4. Decision analysis 4.1 Decision criteria 4.2 Decision trees 4.3 Discounted costs 4.4 Interpretation 5. Conclusions 6. Acknowledgements 7. References Page 1 1 1 2 2 3 3 4 4 4 5 5 8 9 10 10 @CROWN COPYMGHT 1975 Extracts from the text may be reproduced, except for commercial pu~oses, provided the source is acknowledged RISK AND THE PAVEMENT DESIGN DECISION IN DEVELOPING COUNTRIES ABSTRACT In this report the principles of simple decision analysis are applied to road pavement design in developing countries and the uncertainties in the pavement design process are described. Decision analysis is seen as providing a framework within which ‘engineering judgement’ may be exercised by the placing of subjective probabilities on the possible outcomes resulting from the use of different designs. It is proposed that pavement design should be considered not so much in terms of ‘success’ or ‘failure’ but more in terms of a satisfactory return on the investment of highway funds. In this way decisions may be based on an assessment of both technical and financial risks. 1. INTRODUCTION h common with most engineering decisions there is a risk element in decisions about pavement design. The purpose of thh Report is to put forward an ordered way of thinking about the pavement design decision to help the highway engineer and his client to choose the most reasonable course of action under the conditions of risk or uncertainty known to him at the time. Whilst not normally applied to highway engineering, the decision analysis approach is often used to advantage in the consideration of business decisions 1. Therefore, since the pavement design decision cannot be divorced from decisions about long-term financial investment, it seems appropriate that decision analysis should be considered in this context. This Report illustrates the use of the decision analysis approach in connection with pavement design, by means of simple examples showing the principles involved. For more detafled information on its use on specific engineering topics the reader is referred to Benjamin and Corne112, Burton and Walker3, and WU4. Any en~neering decision which involves uncertainty provides an opportunity for the use of ‘en~neering judgement’: that indefinable quality possessed by the professional engineer as a result of all his previous experience. Decision analysis provides a framework within wtich engineers can exercise judgement in their own specialist field and hence avoid the unneceswry expenditure which may result from a too rigid adherence to general specifications which may not be totally applicable to a particular project. Decision theory, as applied to pavement design in this Report, provides a way of using ‘engineering judgement’ more effectively. It does not replace this judgement. This Report has been written with a view to its particular apphcation in developing countries where the scope for substantial savings on project costs is known to be large. However, it is believed that the techniques described will also find application in developed countries. 2. THE PAVEMENT DESIGN PROCESS Modern methods for the thickness design of road pavements take account of three main factors: 1. Traffic 2. Subgrade strength 3. Pavement materials The elements of uncertainty in all three factors are discussed below. 2.1 Traffic For pavement design purposes details are required of the commercial vehicles likely to use the road during the design life of the road. In the TRRL design methods5~ 6, the traffic is expressed in terms of a cumulative number of equivalent standard ades; this requires a knowledge of the following: a) present or initial flow of commercird vehicles b) future growth of commercial vehicle traffic c) ade-load distribution of commercial vehicles during the economic life of the road d) relative damaging effects of different afle loads. An estimate of the initial flow of commercird vehicles is usurdly based on traffic surveys on the existing route between the end points of the new project. On an existing route, there will be errors in estimating the present average dtiy flow of commercial vehicles, resulting from the counting methods used to obtain the data. Work by TRRL in Kenya7 suggests that estimated dafly traffic flows can rarely be expected to be better than *3O per cent of the true value averaged over the whole year. Although repeating counts at intervals throughout the year increases the accuracy of traffic estimates, this is achieved only at a disproportionate increase in cost. For new routes there is the additional problem of estimating generated, diverted or redistributed traffic. Estimation of future growth is rdso difficult and Howe8 has suggested that, although it is impossible to state precisely what the magnitude of the errors in estimating the future growth of commercial vehicles wfll be, a minimum confidence interval of +50 per cent seems likely. Howe therefore concludes that estimates of the cumulative number of commercial axles are subject to confidence intervals of the order oft 100 per cent. The axle-load distribution of commercial axles can only be determined accurately from axle-load surveys. Most designers assume that the axle-load distribution as initially determined will remain constant with time. This is certainly not the case at present in many developing countries where vehicle operators are taking advantage of larger vehicles and the difficulties of enforcing vehicle weight regulations, with a resultant steady increase in axle-loads. In addition, in many cases a new road is built to exploit development potential of a new kind and the vehicles which will use the new facility will probably be of different types from those previously using roads in the vicinity. There is also an element of uncertainty in the validity of the equivrdence factors used to relate afle-loads to the damaging effect of an equivalent standard tie (ESA). Whilst the factors quoted in TRRL design methods are believed to k the most appropriate in the light of up-todate research, they are not necessarily equ~y apphcable to all conditions. Having pointed out these limitations of the traffic estimating procedures, it is important to realise that in fact the pavement construction costs for new roads are relatively insensitive to small variations in traffic estimates, especially for pavements on the stronger subgrades. For example, for subgrade CBRS between 8 per cent and 24 per cent, Road Note No 316 recommends only an extra 50 mm of base thickness for a fifty-fold increase in traffic from say 0.05 x 106 repetitions to 2.5 x 106 repetitions of ESAS. This extra thickness may increase the pavement cost by about 15 per cent and the total road construction cost by as little as 5 per cent for a typical surface-dressed road, i.e., a 1 per cent increase in total costs for each ten-fold increase in traffic. For pavements on weaker subgrades, however, the cost increase would be greater. On the other hand, pavement life is measured in terms of traffic (i.e. ESAS). Therefore ‘life’ and pavement maintenance costs are much more sensitive to errors in traffic estimates. 2.2 Subgrade strength Estimates of subgrade strength are based on a knowledge of the sofl type and how that sofl reacts to changes in moisture content in a particular climatic environment and to compaction. From this knowledge an estimate is made of subgrade strength related to the moisture content and compaction state tikely to pertain in 2 the field. This is normally in the form of a CBR value at a specified level of compaction and equilibrium moisture content, as described in RN 316. Various methods are avafiable for estimating the equilibrium moisture content6. Errors are likely as a result of variability of the soil and in the assessment of relevant environmental conditions, eg depth to water-table. The degree of compaction achieved may also cause differences in the actual field density achieved during construction. These errors may be as a result of the level of supervision, the moisture content at the time of compaction or merely the differences between field and laboratory compaction techniques. The sensitivity of CBR vrdues to these variables is best demonstrated by means of an ISO-CBR chart of which Fig. 1 is an example. Since differences in estimated CBR values mainly affect the thickness of the cheaper sub-base materials, the effect of such uncertainties is likely to be less than 20 per cent of pavement costs. 2.3 Pavement materials The selection of pavement materials is probably the aspect of pavement design where the biggest financial savings can be made in developing countries. This is because there is often a large difference in cost between a material that would probably be suitable and a material that would definitely be suitable. The decision maker should ask himself three questions: 1. Is the specification appropriate for the particular circumstances? 2. Does the material satisfy the specification for the pavement layer in question? 3. How much weight should be attached to the performance of alternative materials in similar circumstances? The first question hig~ghts the problem of choosing the correct specification and making sure that individud clauses of a specification are valid for a particular project. Perhaps the most obvious example of incorrect choice is the use in tropical areas of specifications written for temperate climates, with the possible result that a material may be rejected for use in a tropical country because it fails a strength criterion devised for an area in which frost has a serious effect. in general, practical cases will not be so clear cut. The uncertainty in the answer to the second question ~’does the materird satisfy the specification?”) ties in the identification of the conditions quoted in the specification: ie “what is the equfibriurn moisture content?” or “mat dry density corresponds to 95 per cent Mod AASHO compaction”. Perhaps the most difficult situation for the designer is that in which an unprocessed natural material (B) fafls to meet a specification but local experience suggests that it will be adequate. Should he use the cheap natural material or spend perhaps three times as much producing another material (A) to specification? Not unnaturrdly the designer W often choose the expensive material so that he can use the specification in his defence should problems subsequently arise. 2.4 Courses of action The possible courses of action in the design process maybe represented on a diagram, as shown in Fig. 2. For the purpose of this diagram, only two alternatives have been considered at each stage of the design process, ie a) the design traffic is estimated to be either 1.0x 106 ESA or 0.5 x 106 ESA b) the design CBR of the subgrade is either 4 per cent or 7 per cent c) use is made of either material A which meets the standard specification or material B which does not. This gives the designer a choice of eight possible courses of action. In practice there may well be more than two alternatives at any stage. 3 The purpose of this brief review of some aspects of the pavement design process has been to illustrate the uncertainties involved. 3. FAILURE CRITERIA Fadure is an emotive word which conjures up an image of poor quality and bad workmanship, attended by disastrous consequences such as the total collapse of a bridge or a dam, with severe loss of life or property. For this reason, quite righdy in many cases, ftiure is seen as something which must be avoided. However, to a road designer, ‘faflure’ is usudy associated with an arbitrary ‘standard, defined in terms of cracking and deformation of the new surfacing. Road ‘failures’ seldom result in a road being unusable by vehicles and rarely have disastrous econofic or social consequences. Therefore, perhaps it is appropriate to see the pavement design decision not so much in terms of ‘success’ or ‘ftiure’, but more in terms of a satisfactory return on the investment of highway funds. Decisions are thus based on an assessment of both technical and financial risks. 4. DECISION ANALYSIS 4.1 Decision criteria In a decision between two dtemative designs, for example between Al and A2 in Fig. 2, there are two possible outcomes to each choice. The resulting road may either ‘fail’ or not ‘fail’. In the event of ‘failure’ the cost of rehabilitation must be borne; the cost of restoring the more expensive alternative would usually be less than the cost of restoring the cheaper design. We may distinguish between the ‘satisfactory’ cost of a design, ie the construction cost, and the ‘unsatisfactory’ cost, ie construction cost plus restoration cost. Table 1 shows an example of this. In the case of the cheaper design the figure for restoration cost (gl.5 mfl) is taken as equivalent to the construction cost for the more expensive design. TABLE 1 Example of possible outcomes of design decision Decision Outcome Satisfactory I Unsatisfactory Emil E mfl Bufld design Al 1.5 1.5 t 0.5 = 2.0 Butid design A2 1.0 l.Ot 1.5 = 2.5 A possible criterion for choosing between the two designs is to select the design for which the worst outcome is the least expensive. This is usudy ctied the ‘minimax loss’ approach 1 (ie minimum maximum loss) and is implemented by choosing that action for which the maximum possible cost is minimised. It is a very conservative approach since it assumes that whatever decision is made, the road til fd and require strengthening, The ‘unsatisfactory’ costs in Table 1 are then the maximum possible costs of the two designs and clearly the lowest maximum cost is that associated with design Al which is then the correct choice based on this criterion. ie From the example in Table 1: the maximum possible cost of buflding design Al is f2.O mfltion the maximum possible cost of budding design A2 is f2.5 mi~ion .. tie lowest maximum cost is 22.0 mfllion .. using this criterion we choose the design Al This dlustrates that the use of this criterion tends to avoid the worst outcomes but takes no account of opportunities for reducing costs or the probabilities of a particular outcome occurring. 4.2 Decision trees If we consider the situation in Table 1, the basic problem may be represented in the form of a simple decision tree (see Fig. 3). Up to now, no account has been taken of the probabilities of the different outcomes occurring as a result of a particular design decision. However, in practice, an enj,neer faced with a simdar problem would, as a result of his experience, be able to make a judgement on the relative merits of the two designs. He may say something like. . . “I think both designs would probably be satisfactory but Design Al is less fikely to faif than Design A2”. From this statement it is only a short step to putting numerical values to his judgement: for example . . ~’I think there’s a 90 per cent chance of Design Al being satisfactory”. In so doing, he has assigned personal probabilities to the likely outcome of his actions and these are normtiy expressed on a scale O to 1. Hence a 70 per cent chance of Design A2 being satisfactory may be expressed as a probability of 0.7 and consequendy a 0.3 probabdity (1.0 – 0.7) of it not being satisfactory. 1]1this way we can return to our simple decision tree and insert our estimated probabilities (Fig. 4). An engineer’s judgement wfil reflect his experience; so will his probability assignments. However, experienced engineers, given the same information, wfll tend to make similar probability assignments. For our basic problem (Fig. 4) we have placed a monetary value at the end of each branch of the decision tree. In this case the monetary value is the estimated totrd cost of any particular outcome. By multiplying a monetary value by its probability of occurrence, we can calculate the ‘expected monetary value’ of a design (in this case the ‘expected cost’). Thus, using the probabilities given in Fig. 4, we have Expected cost of design Al (0.1 x 2.0)+ (0.9x 1.5)= 0.20+ 1.35= ~1.55 mfl Expected cost of design A2 (0.3 X 2.5)+ (0.7 x.1.0)= 0.75+ 0.7 = &l.45 d Thus, if we use minimum ‘expected cost’ as our decision criterion, we would now choose design A2. Normally there is a range of possible outcomes for the two selected designs Al and A2. The example below shows how these can be considered. For each decision the basic outcome is stfll as before, ie either the road will be satisfactory or it Ml be unsatisfactory and therefore til require strengthening. However, if strengthening is required, there is a further range of possible outcomes to be considered. The strengthening layer will have tc) be designed on the basis of measurements of the residual strength of the pavement at the time. For simplicity, let us assume there are two, and ordy two, possible outcomes: either a 50 mm or a 100 mm layer of bituminous overlay. It is estimated that the probabdity of a 50 mm layer being required is 0.7 and hence, since we have assumed ody two possible outcomes, there is a 0.3 probability of a 100 mm layer being required. We dl also consider the probability of whether each of these overlays dl subsequently be satisfactory or not. The fu~ decision tree is given in Fig. 5 and an rdternative form of the tree is given in Fig. 6. 4.3 Discounted costs The expected costs used as a criterion may be actual costs or discounted costs. In most pavement performance situations, the time interval between initial construction and subsequent pavement strengthening is large, and therefore discounted costs have been considered in our example. Table 2(a) gives example costslkrn for each of the ten possible outcomes considered in Figs. 5 and 6, and Table 2(b) @vesthese costs discounted at a rate of 10 per cent for a 20-year design fife. If the discounted costs of each possible outcome of a particular design are multiphed by the corresponding probabdity and then added together, we obtain the expected discounted cost. 5 TABLE 2(a) Ucision tree costs Years c1 ! C2 C3 C4 C5 C6 C7 C8 Cg I c~~ , 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 TotA costs (s) * tl 50rnm 00mm 4500* 4500* 27500 overlay overlay 4500* 23000 4500* 32000 9ooot 27500 18500 4500* 4500* 23000 4500* 18500 9ooo~ 4500* 27500 900G+ 23000 14000 . ,.,. .“, ..,, .“ . . ., .“. TABLE 2(b) Decision tree discounted costs – 10 per cent discount rate Discount Years c1 c~ c~ CQ C5 c~ CT Cg Cg Factor Clo o 0 18500 18500 18500 18500 18500 14000 14000 14000 14000 14000 0.90909 1 0.82644 2 0.75131 3 0.68301 4 0.62092 5 5588 5588 0.56447 6 2540 2540 0.51315 7 0.46650 8 0.42409 9 0.38554 10 1735 1735 0.35049 11 0.31863 12 0.28966 13 2607 2607 0.26333 14 0.23939 15 1077 0.21762 16 0.19784 17 890 0.17985 18 810 ----- O.lbj>u i9 0.14864 20 669 Total Discounted costs (~) 21125 20235 21776 21107 18500 17617 16540 20398 19588 14000 ,,, ., ,. ,. .,,., Thus the expected discounted cost per km for a decision to use design Al is: (&21 125 X 0.0018)+ (~20 235 X 0.0882) t ($21 776X 0.0) t ($21 107X 0.010)t(f18500 X 0.90) = ~38t1785t Ot211t 16650) = t18 684 per km The expected discounted cost per km for a decision to use design A2 is: (f17 617X 0.021)t(t16540 X 0.189) + (&20 398X 0.0018)+ (f19 588 X 0.0882)t(fi14000 X 0.70) = ~370 t 3126 t37 t 1728 t9800) = t15 061 perkrn 4.4 Interpretation The least expected discounted cost is thus$15 061 per km. Therefore, if least expected discounted costs are accepted as a vtid criterion, we decide to use Design A2. This does not mean that if we choose A2 the actual discounted cost W be fl 5061 per km. It could have any of the values C6 to Cl 0 in Table 2(b). However, Table 3 shows the probability of its having a particular value. An alternative method of presenting the same information is given in Table 4. TABLE 3 Expected costs a) Probability of a given discounted cost, design Al 90 per cent chance of scheme being satisfactory for a discounted costoff18500 per km 8.82 per cent chance of scheme being satisfactory for a discounted costofS20235 per km 1.0 per cent chance of scheme being satisfactory for a discounted cost of$21 107 per km 0.18 per cent chance of scheme being satisfactory for a discounted costof$21 125 per km O per cent chance of scheme being satisfactory for a discounted cost of221 776 per km I b) Probability of a given discounted cost, design A2 70 per cent chance of scheme being satisfactory for a discounted cost of $14000 per km 18.9 per cent chance of scheme being satisfactory for a discounted cost of gl 6540 per km 2.1 per cent chance of scheme being satisfactory for a discounted cost of fl 7617 per km 8.82 per cent chance of scheme being satisfactory for a discounted cost of $19588 per km 0.18 per cent chance of scheme being satisfactory for a discounted cost of 520398 per km TABLE 4 Expected costs (dtemative presentation) a) Probability of a given discounted cost, design A 1 90 per cent chance of scheme being satisfactory for discounted cost of &l 8500 per km 98.82 per cent chance of scheme being satisfactory for discounted cost of f20 235 or less per km 99.82 per cent chance of scheme being satisfactory for discounted costof$21 107 or less per km 100 per cent chance of scheme being satisfactory for discounted costof521 125 or less per km b) Probabtity of a given discounted cost, design A2 70 per cent chance of scheme being satisfactory for discounted costoff14000 per km 88.9 per cent chance of scheme being satisfactory for discounted cost of216 540 or less per km 91.0 per cent chance of scheme being satisfactory for discounted cost of fl 7617 or less per km 99.82 per cent chance of scheme being satisfactory for discounted cost of gl 9588 or less per km 100 per cent chance of scheme being satisfactory for discounted cost of g20 398 or less per km 8 Expected costs are not always an accurate indicator of a decision maker’s feelings about a situation. This is particularly true where possible losses or gains are large compared with the decision maker’s resources. In the pavement design situation this may arise, for instance, where the possible extreme values are widely different from the expected value. For example, consider two possible extreme cases: Case 1 There is a 0.75 probability of total cost being fl mfl but, owing to the use of a marginal base material, there is a 0.25 probability of total cost being gl Omfl, where the additional f9 mfl is reconstruction and extra maintenance costs. Expected cost = (0.75x 1) t (0.25 x 10)= 0.75 + 2.5 = S3.25 md Case 2 There is 0.50 probability of total cost being 53.5 md and 0.50 probabdity of total cost being f5.O mil Expected cost = (0.50x 3.5) t (0.5 x 5.0)= 1.75 t 2.5 = U.25 mfl Using the least expected cost as a criterion, the decision would be made in favour of Case 1. However, the decision maker may feel that he is not prepared to take the risk of Case 1 costing f5 mfl more than the maximum possible cost of Case 2. On the other hand, if the decision maker is responsible for a very large road maintenance organisation with an annual budget which is very large relative to the possible S9 mfl additiond (expenditure, he may be prepared to accept tie risk and make his decision on the basis of expected costs. Since most roads are buflt for local or national governments with large financial resources relative to the costs of a particular project, it may be argued that least expected costs are a valid criterion for pavement design decisions. This paper illustrates the use of the decision tree approach in connection witi~ pavement design, but it is equ~y apphcable to a host of other engineering decisions. ~atever the find decision, this approach to the pavement design situation provides a useful guide to the engineer and decision maker dike. 5. CONCLUSIONS There are many areas of uncertainty in decisions relating to the design of road pavements for an agreed economic life. It is believed that the process of placing subjective probabilities on the possible ol~tcomes resulting from the use of different designs provides a numerical framework which enables enginet>ring judgments to be taken into account in making the final decision. The main steps in analysing such a decision are: a) Describe the possible outcomes of each design proposal in the form of a decision tree b) Place a cost value on each possible outcome c) Assign subjective probabilities to the occurrence of each possible outcome. (The sum of probabdities of ti the outcomes of any one decision must be 1.0). d) Crdculate the expected discounted cost of each design proposal. It is not suggested that decisions should be made automatically on the basis of ‘least expected cost’. However, it is recommended that this information should be avtiable, so that it can be considered along with political and financial criteria by the decision maker. In this paper, the aim has been to give a simple introduction to the possible use of decision analysis in pavement design problems, and hopefu~y in other tighway engineering problems too. 6. ACKNOWLEDGEMENTS This report was prepared in the Overseas Unit of the Transport and Road Research Laboratory. (Head of Unit Dr E D Tin~e). 1. 2. 3. 4. 5. 6. 7. 8. 7. REFERENCES MOORE PG. Risk in business decision. London, 1972 (Longman). BENJAMIN J R and C A CORNELL. Probability, statistics and decision for civfl engineers. New York, 1970 (McGraw-~1 Inc). BURTON R W and R N WALKER. A method of deting with the uncertainties involved in the consideration of various alternatives in the provision of asphalt overlays. NIRR IntemQl Report RE14172. (National Institute for Road Research, South Africa). 1972. WU TIEN H. Uncertainty, safety and”decision in sofl engineering. JOUMQ1 of the Geotechnical Engineering Division, Boceedings of the American Socie~ of Civil En~.neers, Vol. 100, No. GT3, March 1974. ROAD RESEARCH LABORATORY. A guide to the structural design of flexible and rigid pavements for new roads. Department of the Environment, Road Note 29. London, 1970 (HM Stationery Office), 3rd Edition. TRANSPORT AND ROAD RESEARCH LABORATORY. A guide to the structural design of bitumensurfaced roads in tropical and sub-tropicrd countries. fioposed revision of Road Note 31. Crowthorne, 1974 (Unpublished). HOWE J D G F. A review of rurrd traffic< ounting methods in developing countries. Department of the Environment, RRL Report LR 427. Crowthorne, 1972 (Road Research Laboratory). HOWE J D G F. The sensitivity to traffic estimates of road planning in developing countries. Department of the Environment, TRRL ReportLR516. Crowthorne, 1973 (Transport and Road Research bboratory). 10 10[ ‘$ 2 104 1Oc > .; c : 96 ~ n 92 88 84 1.8 ‘E c 2 1.7 1.6 1.5 1.4 1.3 B.S. compaction (Heavy) <&i \ ./ / 8.S. compaction / ‘/ ,’ /; ‘ ~~ // / a ‘Norma’)~ ,// / ,’ /: ,/ / I / ~\ // / / C.B. R. (per cenl 4 8 12 16 20 24 28 32 110 85 Moisture content (per cent) Fig. 1 DRY DENSITY-MOISTURE CONTENT–C.B. R. RELATIONSHIPS FOR A SANDY-CLAY SOIL I TRAFFIC I i SUBGRADE STRENGTH i I MATERIALS f DEsl GN I I I I ..1. A~A1 I I I I I I I I i I I I I I I I I I 1 I I I I I I I I ;\ I I I I I I I ~v I I I I I I I I I I I I I I I I I I I I I I - I I I I I I I I 1 I I I I I I I I I I I ? A8 Note:- Inthisparticular figure no interdependence of actions should be inferred from the ‘tree’ structure of the diagram. Design decisions relating totraffic, subgrade strength and materials maybe taken independently. Fig. 2 EXAMPLE OF POSSIBLE COURSES OF ACTION IN THE PAVEMENT DESIGN PROCESS I I I I ACTION I I I OUTCOME I COST (f million) I I I / I I I I I I I I I I I I i I I I I I I I I I I I I / I I 2.0 1.5 2.5 1.0 Fig. 3 DECISION TREE – BASIC PROBLEWi I I ACTION OUTCOME / I I I ~ I I I I I 1 / I I I I I I I I I i E COST (f million) 2.0 1.5 2.5 1.0 Fig. 4 BASIC PROBLEM WITH PROBABILITIES ACTION I OUTCOME ~ OUTCOME t OUTCOME I COST / I Id c’ I I I I I ~ : G4 / I I I I .—. —.— .—. - r I .-. —. —.—.—. ~ C5 i I I I I I c, ~ I I I I I I I I I I 10I J Fig. 5 DECISION TREE FOR PAVEMENT DESIGN i ACTION I I I I I I I I OUTCOME I i I I I I I I I I I I I I I / Q I I I I / I I I I I I I I I I ..6+ I I I I I I I I I / I I I I w I I I ~ I I I I I I I I I .+ I I I I I I I 10 c~ c, C* I * I I Probabilities Ii %! Fig. 6 ALTERNATIVE TO FIG. 5 (1896) Dd209410 2,050 12/75 HPLtd So’ton G1915 PRINTED IN ENGLAND ABSTRACT Risk andthepavement design decision in developing countries: CIEI.LIS: Department of the Environment, TRRLbboratory Report 667: Crowthorne, 1975(Transport and Road Research hboratory). In this report the principles of simple decision analysis are applied to road paveme]lt design and the uncertaim ties in the pavement design process are described. Decision analysis is seen as providing a framework within which ‘engineering judgement’ may be exercised by the placing of subjective prob:~bilities on the possible outcomes resulting from the use of different designs. It is proposed that pavement design should be considered not so much in terms of ‘success’ or ‘failure’ but more in terms of a satisfactory return on the investment of highway funds. In this way decisions maybe based on an assessment of both technical and financial risks. ISSN 0305–1293 ABSTRACT Risk and the pavement design decision in developing countries: C I ELLIS: Department of the Environment, TRRL bboratory Report 667: Crowthorne, 1975 (Transport and Road Research bboratory). In tfi report the principles of simple decision analysis are applied to road pavemerlt design and the uncertainties in the pavement design process are described. Decision analysis is seen as providing a framework within which ‘engineering judgement’ may be exercised by the placing of subjective prob:~bilities on the possible outcomes resulting from the use of different designs. It is proposed that pavement design should be considered not so much in terms of ‘success’ or ‘failure’ but more in terms of a satisfactory return on the investment of highway funds. In this way decisions maybe based on an assessment of both technical and financial risks. ISSN 0305–1 293