|7 A COST AND QUALITY OPTIMISED MODEL FOR
7.1 DESIGN AND MAINTENANCE CRITERIA
Unpaved roads, i.e. gravel surfaced or earth roads have been in use in Namibia much longer than bitumen surfaced roads which represent a quite recent development if one considers that the first modern paved road came into being only in 1959. Namibia's unpaved roads are named in Africa for their excellent shape and condition but it could never been proved whether the excellent quality of these roads are effective and optimised as far as costs and quality are concerned. Maintenance and regravelling were rather done on a empirical and emotional basis and less on the basis of a technically sound maintenance model with cost optimising properties. Nevertheless, in spite of the expanding network of paved roads in Namibia the unpaved roads still constitute the major part of the roads system. In Namibia 89,4% of the total road network were unpaved in 1986. According to statistics in the Department of Transport during September 1986 37.183 km of proclaimed trunk, main and district roads were unpaved against 4.402 km paved roads.
Some basic principles which have been developed in the previous section are also applicable for unpaved roads. The above mentioned continuous decrease in funding in real terms has the consequence that the available minimum funds must be applied with maximum effects. This can only be achieved with the use of a computerised pavement management system methodology. Chapter 9 attempts to develop an approach for evaluating unpaved road performance and the deterioration thereof. The basis for this approach is the extensive work in the Brazil pavement performance study . This study revealed equations for the prediction of roughness developments, rut depth and gravel losses. Furthermore, it gives criteria for the passability of unpaved roads as well as minimum gravel thicknesses to protect the road fill. The objective of all these input parameters is the development of a Maintenance Design System ' MDS' for unpaved roads which combines all these relationships together with user cost equations based on ' VOC' in a systematic manner which permits an evaluation of the interactive relations between all these parameters. One of the major results of the Brazil study was the fact that it has been proved that traffic had the greatest influence on regravelling and grading strategies as well as on the total cost of unpaved roads.
In 1986 a first attempt was made to test the 'MDS' system on selected roads with the objective to compare predicted and actual maintenance on the unpaved road network and to establish a cost and quality optimised maintenance model for unpaved Namibian roads. This was a real necessity, because to date, in spite of a treasure of accumulated experience in construction and maintenance of Namibian unpaved roads, no consistent and scientifically sound policy regarding the treatment of unpaved roads existed.
7.1.2 PROBLEM IDENTIFICATION
With the first improvements of the rough earth tracks in the late twenties and early thirties, after the advent of the first mechanically driven vehicles in Namibia shortly before and during the First World War, a beginning was made to accumulate experience in the construction, gravelling and maintenance of unpaved roads. It was quickly learnt that plastic binders had to be added to sandy roads to give them stability or that non-plastic sands or gravels had to be added to clay roads in order to prevent them from rutting and becoming sticky or even impassable in the rainy season. The clay acts as a binder to form a denser pavement while the sand and the gravel particles bear upon each other and resist traffic loads. The major maintenance of unpaved roads is still done with aid of mechanically driven graders, while some more sophisticated material specifications have been developed to use gravel materials with appropriate properties for the different types of earth roadbeds.
Grading of unpaved roads with aid of graders is still the principle method of maintaining gravel and earth roads. The policy regarding maintaining these roads is, however, not very consistent yet. There is no scientific method for maintenance frequency determination in existence. Currently the frequency determination is done on an empirical basis by the Roads Superintendents and Regional Engineers of the Namibian Department of Transport. The problem is clearly illustrated for some randomly selected unpaved roads in table 33:
TABLE 33 MAINTENANCE PARAMETERS OF SOME UNPAVED ROADS
Problem areas which cost money had to be identified. Twenty test sections in the Region of Windhoek established the following problems:
An isolated solution to one of the problems is a rock buster which started to crush large stones with the resulting lower IRI values. Other isolated solutions are improved, systematic prospectings for suitable gravel materials and the measurements of driving quality to identify problem sections. One of the main problems is to keep the water away from the road by appropriate drainage.
The maintenance predicament of Namibia's unpaved roads can, however, only be solved on a systematic basis. As has been outlined above one of the solutions is to know what is the state of the unpaved roads system. A systematic data collection effort like, for instance, the collection of riding quality data for all unpaved roads in order to compare these data with the predicted ones will have to form the basis of such a systematic approach. For such a task roughnesses of pavements are more important than pavement grips due to the dry nature of the Namibian climate. A 'MDS' system will create the basis for the rationalisation and optimisation of Namibia's unpaved road network. Simplified, a 'MDS' system corresponds as follows in figure 8 :
FIGURE 8 NAMIBIAN MAINTEMANCE DESIGN SYSTEM
- Resultant level of service: IRI = 3,3 or IRI = 6,5?
7.2 RESULTANT LEVEL OF SERVICE
In order to establish the resultant level of service an experiment to measure the public acceptability criteria of the riding quality of unpaved roads in Namibia was lodged by the Department of Transport during 1989 . Subjective evaluations of specific unpaved roads representing a wide spectrum of different riding qualities encountered in Namibia were investigated. Contingency table analysis was done to determine the relationship between subjective riding quality evaluation and objective roughness measurements by precise levelling or by profiling ( IRI). A regression analysis was used to develop a model. The dependent variable of the model is the subjective evaluation of the road by the road user.
A five point rating was used:
Table 34 shows the results of the field data:
TABLE 34 SUBJECTIVE RIDING QUALITY AS FUNCTION OF ROUGHNESS
| | | 1 2 3 4 5 | km/h |
| 2,20 | 59A- | 8,3% 50,0% 33,4% 8,3% 0,0% | 85 |
| 2,60 | 59A+ | 13,6% 54,6% 22,7% 9,1% 0,0% | 91 |
| 3,40 | 49C+ | 16,7% 58,3% 25,9% 0,0% 0,0% | 96 |
| 3,60 | 56 + | 0,0% 10,0% 56,6% 26,7% 6,7% | 93 |
| 4,00 | 56 - | 0,0% 25,0% 16,7% 58,3% 0,0% | 78 |
| 4,10 | 49C-*| 36,8% 36,8% 21,1% 5,3% 0,0% | 98 |
| 6,20 | 59B- | 0,0% 0,0% 30,0% 50,0% 20,0% | 80 |
| 6,70 | 55 - | 0,0% 8,3% 41,7% 41,6% 8,3% | 94 |
| 7,50 | 59B+ | 5,0% 0,0% 35,0% 45,0% 15,0% | 82 |
| 8,65 | 55 + | 5,9% 0,0% 29,4% 52,9% 11,8% | 84 |
NOTA: Department of Transport, 1989
* The road section of main road 49 in the negative direction
seems to be an outlier, therefore for the generalisation
of the model this section was ignored. The evaluation of the field data resulted in a model expounding the relationship between measured IRI and the road user's riding quality statistics according to the ratings. The regression equation for the model is :
Evaluation Estimate = 0,030918*Percentile + 0,025086*(14*IRI-10)
The model was fitted on the 95% confidence level and had an R-squared of 0,989% .
Table 34 shows the following tendencies:
IRI < 3,6
15% excellent, 35% good, 30% average: Sum = 80%;
The evaluation of table 34 is shown in figure 9:
FIGURE 9 ACCEPTABILITY CRITERIA AS FUNCTION OF ROAD ROUGHNESS
Figure 9 indicates the following trends (% for each rating):Warning: IRI = 6,00 (ratings 2 and 4)
Serious: IRI = 7,00 (ratings 1 and 2)
Acceptability Limit: IRI = 10,00 (ratings 4 and 5) The question arises whether these acceptability limits can be supported by a cost and quality optimised model? It must, however, be borne in mind that the Namibian road user has generally to travel long distances on unpaved roads. This psychological factor is aggravated by the fact that vehicle prices are relatively high related to average incomes and consequently this fact will push down the acceptable IRI level. To develop an interaction between the acceptability limits and an optimised maintenance model prediction formulae for different maintenance strategies have to be developed for unpaved roads in Namibia.
Some further interesting facts came to light during above acceptability/ rejection exercise. The observed average speeds in table 34 didn't reveal any statistical calculable pattern. It was, however, observed that for a test section with an IRI of 4,10 the average speed was 98 km/h and for an IRI of 7,50 82 km/h.
A further very decisive part of above acceptability/rejection experiment for the development of optimised materials specifications was the establishment of the main contributing factors (factors from 1 to 5) to poor riding quality of the experimental road sections. Five factor were determined which are regarded as important under Namibian conditions:
Table 35 gives the results of this acceptability/rejection experiment:
TABLE 35 CONTRIBUTION FACTORS TO POOR RIDING QUALITY
| EXP.ROAD | IRI | AVERAGE |SMALL |LARGE | POT- |CORRU-|LOOSE | |
| SECTIONS | | EVALUAT.|STONES|STONES|HOLES |GATION|LAYER: | |
| | | | | | | |SAND | |
| 55 | 7,65| 3 - 4 | 6,9% | 0.0% | 3,4% |82,8% | 6,9% | 100% |
| 56 | 3,80| 3 - 4 |35,7% | 4,8% | 9,5% |40,5% | 9,5% | 100% |
| 49 | 3,80| 2 |61,3% | 6,5% | 0,0% | 0,0% | 32,2% | 100% |
| 59B | 6,80| 3 - 4 | 6,7% |33,3% | 3,3% |36,7% | 20,0% | 100% |
| 59A | 2,50| 2 |21,4% | 7,1% | 0,0% |14,3% | 57,2% | 100% |
| AVERAGE | | |26,4% |10,3% | 3,2% |34,9% | 25,2% | 100% |
NOTA: Department of Transport, 1989 The evaluation of above data revealed that a loose layer of sand is the main contributing factor to poor riding quality for roads with excellent to good IRIs (M.R.59A: IRI=2,50, average evaluation=2) while small stones are the main factor for roads with good to average IRIs (M.R.49: IRI=3,80, average evaluation=2) and corrugations for roads with average to bad IRIs (M.R.56: IRI=3,80 and M.R.55: IRI=7,65). Interesting is also that M.R.49 was judged with an average evaluation of 2 and M.R.56 with an average of 3-4 for same IRI values (3,80). Therefore it could be concluded that corrugation could have a more serious effect on acceptability than small stones. Large stones were judged as contributing factor on M.R.59B with IRI=6,80, but corrugation still played a greater role on this road. Pot-holes were not regarded as contributing factor to riding quality on all test sections. It was further concluded in the study that a significant relation between the evaluation and age of the driver, the load of the vehicles, the frequency with which the driver uses an unpaved road and the type of the vehicle driven could not be found .
These acceptability limits can be further replenished by performance values which are the result from personal experience gained from having travelled some 500.000 km on unpaved roads all over Namibia in 25 years as roads engineer. The performance acceptability criteria for small stones (stoniness), large stones, loose material and dust were based solely on a severity rating system used in above experiment. The criteria for pot-holes and surface drainage affected the performance of a unpaved road significantly, but to a lesser degree than the severity. The product of the square of the severity rating and the extent rating (see nota: table 36) was considered to be representative of the influence of the parameter on the performance. All of these criteria are unitless and are based on the ratings of severity and extent obtained during the personal monitoring and observations . Corrugation and the, under Namibian circumstances, much less important rut depth influences on performance are described by depth (mm) and roughness in terms of IRI. The criteria are pictured in table 36:
TABLE 36 PERFORMANCE CRITERIA FOR UNPAVED ROADS
| | | DESIRABLE | UNDESIRABLE | UNACCEPTABLE |
|Small Stones | Severity | < 3,5 | 3,5 - 4,5 | > 4,5 |
|Large Stones | Severity | < 3,5 | 3,5 - 4,5 | > 4,5 |
|Loose material | Severity | < 3,5 | 3,5 - 4,5 | > 4,5 |
| Dust | Severity | < 3,5 | 3,5 - 4,5 | > 4,5 |
| Pot-holes | Sev² * ext | < 30 | 30 - 35 | > 35 |
|Surface drainage | Sev² * ext | < 30 | 30 - 35 | > 35 |
| Corrugation | mm | < 20 | 20 - 30 | > 30 |
| Ruts | mm | < 25 | 25 - 35 | > 35 |
| Roughness | IRI | < 7,00 | 7,00 - 9,50 | > 10 |
NOTA: Extent Rating: From rating 1: extent of occurrence: 0-20% to
rating 5: extent of occurrence: 81-100%
The problem facing an appropriate Namibian maintenance model is twofold:
The basis for ' MDS' methodology is the prediction of different road performance mechanisms for cost/quality optimised models in order to establish optimal grading and gravelling/regravelling frequencies as well as the optimal point when an unpaved road has to be surfaced. Prediction of general road performance mechanisms leads also to optimal material specifications.
7.3 PREDICTING UNPAVED ROAD PERFORMANCE
There are four modes of traffic-induced deteriorations  which can be determined for unpaved roads:
The interaction of these four deterioration modes is illustrated as follows:
FIGURE 10 INTERACTION OF PAVEMENT DETERIORATION MODES
A pattern of the possible deterioration mechanisms and possible methods of analysis is discussed in the next sections.
7.3.1 DRY WEATHER DETERIORATION
Under Namibian conditions the most important deterioration mechanisms under dry weather circumstances can be summarised as follows :
At present these deterioration mechanisms cannot be analysed by a theoretical model. Only empirical methods are available to establish a predicting performance model for above deterioration mechanisms.
7.3.2 GENERAL WET WEATHER DETERIORATION
Where the shear strength of the surfacing and in-situ roadbed material is able to bear the induced traffic stresses the deterioration of the wearing course can normally be ignored. The dominant deterioration mechanisms under these conditions can be summarised as follows :
Analytical judgement of surface erosion cannot be done on a scientific manner yet. The formation of pot-holes is a function of the nature and frequency of depressions and the frequency of wheel load applications. At present the above deterioration mechanisms cannot be analysed by a theoretical model. Only empirical methods are available to establish a performance prediction model for general deterioration mechanisms under wet weather conditions.
7.3.3 WET WEATHER DETERIORATION FOR WEAK ROADS
The main criteria for a weak wearing course is insufficient shear strength to withstand traffic loads. For some time the road will be still passable under conditions of shear failure but the road can become impassable after relatively few wheel applications without prior warning. The only reliable yardstick to establish shear strength is the ' CBR' test while plasticity tests are only applicable to single wheel and not to the more realistic multi-wheel applications. Under wet weather conditions roughness and rut depth as well as gravel loss predictions have little meaning and can be ignored. The question remains whether traffic can use the road or not, and this can easily be established by empirical means. If overstressing of the subgrade occurs, the roadbed material will deform. This mechanism of deterioration is predominant in areas of poor subsoil drainage. For this type of deterioration empirical models have to be used, because minimum gravel layer thicknesses to avoid roadbed failure cannot be predicted by exact methods yet.
7.3.4 EVALUATION OF EMPIRICAL STUDIES
The basis for empirical relationships  to develop prediction models for pavement deteriorations of unpaved roads has been derived from the HDM3 Brazil study. The approach used in this study was to monitor existing unpaved roads under traffic. In this study roads have been selected which have been in service for many years with well compacted surfaces. The Brazil study used experiences gained in the "Kenya study". Variables used in the Brazil study like average daily traffic, grades, horizontal alignment and surfacing materials were selected from the Kenya study. The Brazil study used road sections of 320 m each in length with a total number of 48 test sections. The results of the Brazil study have been incorporated into the computer program HDM3, which predicts the riding quality of a pavement. The input data for HDM3 are the following:
1. Geometrics: road length, curves, terrain type;
These basic data for the HDM3 program have to be adjusted in order to be meaningfully used in the Namibian 'MDS' program. Topics like loss of gravel and optimised regravelling cycles, grading maintenance and the point in time when to surface an unpaved road have to be verified for Namibian conditions. Namibia, for instance, has many road building materials different to those used in HDM3. Further, it has been established that stoniness and compaction of an unpaved pavement are very important parameters, even more important than PI and CBR. These parameters which are not part of HDM3 have to be included into the ' MDS' system. The output data are the predicted riding quality for different levels of maintenance as well as the affordable pavement type.
7.3.5 PREDICTION FOR COST/QUALITY OPTIMISED MODELS
The objectives of the development of a "Namibian Performance Model" was the validation of the "Brazil Model" and to establish an 'MDS' system for Namibian traffic as well as ' VOC' patterns and Namibian materials and their specific properties. Further it is envisaged to establish theoretical values for gravel losses and to predict IRI values as yardstick for the roughness of unpaved roads in order to establish optimised blading frequencies and the point of surfacing. The input parameters are besides traffic loads and material properties the Namibian climatic conditions. As has been outlined before the Namibian climatic conditions have not a very distinct influence on the performance of the prediction model because most parts of the country are situated in regions with a N>10 value in the average with minimal climatic influences on road building materials. To achieve above outlined objectives 19 test sections @ 300 m length each in the districts of Windhoek and Gobabis have been established and are represented in table 37:
TABLE 37 UNPAVED ROAD SECTIONS FOR NAMIBIAN 'MDS' SYSTEM
126.96.36.199 PREDICTION MODEL FOR ROUGHNESS
In chapter 5 it has been shown that roughness is the principal measure of pavement condition that can be directly linked to vehicle operating costs. The Namibian roughness experiment  revealed that each period between blading cycles can be differentiated as three distinct stages: After blading, the initial roughness is relatively low and stays nearly constant. The second stage is a steep deterioration in roughness under traffic. In the final stage the roughness is relatively constant at its maximum until the next blading. Consequently, the rise in roughness can be seen as a function of the number of days since the last blading. Both studies, the Brazil and the Namibian ones, proved clearly that the roughness after blading is varying, which will have to be considered in any prediction equation. This was not possible to achieve to date because these three deterioration stages as functions of the traffic couldn't be incorporated into the prediction equation. This is the reason why the prediction model for roughness doesn't coincide with the measured results as well as the gravel loss prediction equation. However, it has been experienced that in the average there is a good correspondence between predicted and measured IRI-values on different roads.
The form of the deterioration model is a function of the interaction of traffic with the road surface. As the first irregularities develop under the influences of traffic and weathering, the dynamic forces imposed on the road are increasing with resulting increases of pavement deterioration and roughness which again impose higher dynamic forces until a relatively balanced state of maximum roughness has been reached, with corrugations as most serious form of roughness. At the upper end of the roughness scale the deterioration level is so serious that traffic is slowing down with the resulting smaller changes in roughness. Due to the relatively good performance of Namibian unpaved roads, very little data exist in the IRI range of 11,0 and higher. This and the non-linear deterioration curve are the reasons that the exact modelling of the roughness development was not feasible to date. Seasonal factors and other variables must still be incorporated into this model. Therefore, an empirically developed exponential curve has been used for the development of the Namibian roughness prediction equation . The Namibian prediction model for the change of roughness 'R' for different times since the last blading for different 'ADT' is the following and is pictured in figure 11:
FIGURE 11 PREDICTION: ROUGHNESS CHANGE AS FUNCTION OF 'ADT'
-0,016*PI): Change in nat.logarithmic value of QI (counts/km)
D = time period considered, in days per 100
The Namibian roughness prediction model has an R-squared value of 0,38, and the sample size was 1.476 observations. The standard error was 0,153 in terms of the logarithmic transformation. Thus, if the roughness equation predicts a change in a roughness of 100 (QI), the true value of change should fall between 74 and 134 with 95% confidence. Figure 11 shows that for shale wearing course the change in roughness climbs from IRI=2,6 for 100 'evu' to IRI=5,2 for 500 'evu' within a time period 'D' of 365 days.
188.8.131.52 PREDICTION MODEL FOR GRAVEL LOSSES
Regravelling of an unpaved road is a major maintenance operation and it is analogous in importance to an reseal of a bitumen-surfaced road. The establishing of a predicting model for gravel losses is an important tool to know when a road has to be regravelled. Gravel loss can be defined as a time-dependent reduction of the thickness of a gravel layer by the mechanical removal ( wear and abrasion) of gravel material from the road prism to the immediate surrounding of the road. The predicting gravel loss formula has to be verified by measuring the change in elevation of a grid of points on the test section relative to a bench mark with level and rod, at successive times. The major factors causing gravel loss are traffic-related influences like whip-off and friction from the vehicles and weathering influences as for instance wind and rain. These factors have to be used as input parameters into any prediction formula. Other input parameters in any gravel loss predicting model are materials, like PIs, LLs and other material constants, road alignment and road grades as well as influences caused by the number of bladings or the point of time of the last regravelling since the testing started.
From the first preliminary tests on the 19 Namibian test sections, mentioned in table 37, the following gravel loss prediction formula for Namibia was developed :
Gravel Loss: GL=D*(-0,0346*G-0,1288*PI+0,0242*ADT+0,39*T7+0,548) (mm)
D = time period considered, in days per 100
FIGURE 12 PREDICTION: GRAVEL LOSS AS FUNCTION OF 'ADT'
Above Namibian equation for gravel losses has a correlation factor: R-squared of 0,81. The approximate 95% confidence intervals are the gravel loss +/- 8,2 mm. The sample size was 112. The Brazil formula has been proved to be a good predictor for gravel losses but it seems that the Namibia gravel loss prediction formula is giving lower values than the Brazil formula as has been proved for test sections 903 ( quartz) and 914 ( calcareous mix) (see table 37).
Figure 12 shows that the gravel loss (mm/year) climbs for calcareous and non-calcareous wearing course materials from 5 mm/year to 40 mm/year for an ADT increase (evu) from 50 to 450.
It was learnt from the Brazil research project  that good compaction of the gravel wearing course decreases the initial gravel loss as has been proved on the Namibian test section 911 (main road 39). Proper compaction to at least 93% Mod. AASHO is very important for the good performance of a gravelled road over its life time. Improper compaction and misuse of compaction water, like for instance crust compaction by watering and compacting the top 30 mm of the wearing course only, is a major cause for bad performance of an unpaved road. The gravel loss equation doesn't take compaction into account yet, because the compaction role traffic is playing is difficult to quantify and test data regarding the role of proper compaction are lacking. Empirically it has been established that proper compaction is a key issue in the proper performance of an unpaved road.
The prediction models for roughness and gravel losses form the basis for the establishment of an economically defendable regravelling and black-topping cycle which is based on cost-optimised arguments, in other words to establish certain set standards before any road improvement or maintenance is due (so-called trigger values). Cost/quality optimised models can be used to determine the optimal point when to grade or to gravel an unpaved road. They can also be used to determine the cost-optimal point of time when an unpaved road has to be bitumen-surfaced.
7.3.6 PREDICTION EQUATIONS FOR GENERAL PERFORMANCE
At this moment prediction models for general performance like rut depth, corrugations, dust, pot-holes, cracks, loose material and surface drainage parameters can be used for the establishment of optimal materials specification while at present only roughness and gravel loss predictions are part of a cost/quality optimised model.
184.108.40.206 PREDICTION MODEL FOR RUT DEPTH
On Namibian unpaved roads ruts are normally not very deep and don't cause a lot of problems for the road users in contradiction to the Brazil study  where it has been claimed that deep ruts affect the safe operation of vehicles and prominent ruts can act as drainage channels and can prevent water from running off the roadway. In Namibia rut depth tests have, therefore, been carried out for one dry season only.
The depression in the road, transverse to its centre line, under a 1,22 m long straight edge, was measured as rut depth. The Namibian prediction equation for rut depth has been established as follows: change in rut depth 'RD' with time :
where: See values for 'LnR' and 'GL'
The relationship between rut depth and average daily traffic is shown in figure 13:
FIGURE 13 PREDICTION: RUT DEPTH AS FUNCTION OF 'ADT'
Figure 13 shows an increase of rut depth from less than 1 mm per year for calcretes and calcareous materials to approximately 5 mm per year for an increase in average daily traffic from 20 to 500 evu (see table 36: ruts < 25 mm are not serious).
Due to the fact that in case of the Brazilian prediction formula for rut depth three different equations for three different seasonal periods and a fourth one for fresh rut depth direct after blading have been developed, no direct comparison with the Namibian rut depth prediction is possible. The Namibian rut depth prediction model has an R-squared value of 0,65, and the sample size was 755 observations. The standard error was 5,95.
In Namibia, however, a prediction model for corrugations ( longitudinal roughnesses) is more important than lateral roughnesses as, for instance, wheel tracks (rut depth) which are of great concern in developed countries.
220.127.116.11 PREDICTION MODEL FOR CORRUGATIONS
The most important parameter to influence riding quality and acceptability of unpaved roads are corrugations which appear on nearly all Namibian gravel and earth roads, the road surface being composed of granular material in heaps transverse to the direction of traffic at different wave lengths. They can cause considerable damage to vehicle suspension systems . Corrugations also lead to intermittent loss of contact between tyres and pavement, reducing the effectiveness of steering and braking, thus reducing considerably effective vehicle control .
Some aspects of the causes of corrugations have, however, come to light already in earlier research works. It has been discovered that three different types of materials regarding their corrugation susceptibility must be differentiated :
Further susceptible areas of corrugations are areas of cornering, braking and acceleration.
The root cause of corrugations would appear to be the loss of soil binder from the wearing course material. Corrugations are further caused by the impact of traffic loads imposed on the road surface. The cure for corrugation is to prevent the drying out of the soil binder which prevents the loss of fines by paving the road or to retain the road surface in position by regular grading. Empirically it can be derived that corrugations are a function of cohesion, plasticity, specific gravity, the percentage of stones in the gravel wearing course as well as the speed and mass of vehicles.
A prediction model for corrugations was developed , based on experiments done on Transvaal (RSA) and Namibian test sections (see table 37). The severity of corrugations was rated for all sections in the Transvaal (not Namibia) on the following basis:
The mean corrugation depth ( amplitude) recorded for all test sections was 16,9 mm and the mean spacing was 759,0 mm. The maximum amplitude and wave length were 28,4 mm and 1.198,0 mm respectively. It is interesting to note that the corrugation depth appears to have a maximum value , which is reached fairly quickly after maintenance, after which no further increase occurs even if maintenance is delayed. This observation must, however, be investigated by further research.
The main variables affecting the corrugation depth were the percentage Heavy Vehicles HV (average: 15% in Namibia), Dust Ratio (DR: (P075/P425)), Grade (GRADE) (%), Mean Annual Rainfall (RAIN) (mm), Weinert N-value (N), Plastic Limit (PL), percentage smaller than 0,075 sieve (P075), Optimum Moisture Content (OMC)(%), Maximum Dry Density (MDD)(kg/m3) and CBR at Optimum Moisture Content ( CBR). The predicted corrugation rating 'CR' was developed as :
CR = 93,2 - 37,7*DR - RAIN(0,07 + 0,007*GRADE + 0,001*CBR)- 0,81*CBR - PL(0,37*GRADE + 0,25*N) - 0,39*OMC*N (rating)
The prediction model had an R-squared of 0,57 and a standard error of 12,4. Further significant factors to the rating of corrugations are the percentage of heavy vehicles and the quartz content which are difficult to determine and fit into the model.
It was also established that the wave lengths of corrugations are a function of the ' PI' of the surfacing material, of the over size of stones in this material, of insufficient cohesion and the sand blanket over the bearing course. A wave length between corrugations of 900 mm for average Namibian conditions was established as derived from the 19 test sections (see table 37). Shorter wave length corrugations also tend to have smaller depth.
It was further found that it appears that wave length is directly proportional to the speed of vehicles. Shorter wave lengths of 500 to 600 mm with speed restrictions of 60 km/h were established on game reserve roads in the Etosha Pan. In the Kalahari Gemsbok Park wave lengths were measured from between 450 and 550 mm for a speed restriction of 50 km/h. Wave lengths of 800 to 900 mm on unpaved roads for average travelling speeds of 80-90 km/h and 1.000 to 1.200 mm on unpaved sections with favourable performance parameters with average speeds of 100 to 120 km/h were measured. It can thus be concluded that the following prediction model for wave length (mm) is a realistic assumption with the average travelling speed (km/h) as variable whereby the inclusion of material coefficients have to be ascertained by further research:
WL = 10 (AV.SPEED)(mm)
Both the horizontal and vertical components of wheel movements increase with increasing vehicle speed  resulting in longer wave lengths and deeper troughs which would fit in with the " forced oscillation theory". The speed-dependency of wave lengths  could explain the movements of corrugations, whether they move in the same direction than the traffic  or in the opposite direction. Empirical observations at bridge decks in Namibia, however, revealed that normally corrugations move in direction of traffic. With a change in speed the corrugation space will change, with a concomitant movement of corrugations (forward for increased average speeds, backwards for decreased speeds). In summary, it seems that wave lengths of corrugations are mainly speed dependent while their depths are both speed and material dependent.
Fixed corrugations with wave lengths of about 900 to 1.000 mm (even up to 2.500 to 3.000 mm and troughs up to 150 mm)  are not normally removed by routine grader maintenance. Where fixed corrugations occur heavy cutting and re-working and re-compaction by the grader is necessary to remove them.
Material factors influencing corrugations will be included into the proposed materials specification for unpaved roads which follows below.
18.104.22.168 PREDICTION MODEL FOR DUST
Dust is of major concern for travelling on unpaved roads, although the performance ratios are difficult to quantify. The following dust-dependent factors are influencing the performance rating of unpaved roads:
Only limited research on the effect of materials properties on dust emission from unpaved roads has been lodged so far . A five-point rating system was developed by which the dust was rated during roughness readings at 80 km/h. The severity of the dust visible in the interior rear-view mirror was rated as follows:
About 50 ratings were obtained for each section in Namibia and 30 in Transvaal/RSA. The average dust severity of all sections was 3,9 with a minimum of 2,0 and a maximum of 4,97. Ratings of less than 2 were excluded from the model because it was assumed that the pavement was moist at the time of the experiment. Multiple regression analysis was used to establish a best-fit equation. Variables which influence the severity rating for dust were the following: Gravel Index GI (1-ratio P200/P2650), Plastic Limit PL, Felspar Content FC, soaked CBR, the percentage of heavy vehicles HV and the fraction smaller than 4,75 mm (P475). The predicted dust rating 'DUST' was developed as  with an R-squared of 0,43:
DUST = 6,7 - 4,03*GI - 0,16*PL - 0,11*FC + 0,28*GI*PL +
0,0003*CBR*HV - 0,0002*CBR*P475
Further variables influencing the dust rating were not included into the Namibian model as yet: fraction smaller than 6,7 and 2,0 mm, the Dust Ratio DR and the Laboratory Maximum Size (LABMAX) whereby it is felt that the 6,7 mm sieve passing is the most highly correlated grading parameter for dust.
Dust collected  behind vehicles consists mainly of material finer than 0,075 mm with only between 15 and 25% being finer than 0,002 mm (silt). The material adhering to the back of a vehicle under wet conditions is slightly finer than normal dry dust with about 30% less than 0,002 mm. It seems thus that dustiness ratings are highly dependent on the relative portion of silt-sized particles and not so much the clay-sized fraction whereby it has to be considered that the general paucity of this fraction in test samples of dust is due to the very low settling velocity of these very fine particles and to loss into the atmosphere.
Felspar is a strong parameter in the development of dust and was therefore included into the dust prediction model although it cannot easily be quantified without specialised equipment which currently is not obtainable in Namibia. At the present point of time no direct correlation can be established between dust and a proposed materials specification for Namibian unpaved roads.
22.214.171.124 PREDICTION MODEL FOR POT-HOLES
Pot-holes are not a very important factor influencing riding quality according to above acceptability criteria. Personal experiences revealed that the reasons for the forming of pot-holes are normally a weak subgrade combined with weak drainage of the road prism with the material types being only of a minor contributory factor. These observations were strengthened by the prediction model for pot-holes .
Pot-holes were rated by severity and extent on a standard 5-point scale and the depth and diameter of the pot-hole which appeared to affect roughness was measured. The severity of pot-holes was rated according to the following criteria:
The average pot-hole severity and extent for each test section was calculated from all the results. The average severity was 2,13 with a minimum of 1 and a maximum of 4,1 while the extent was 1,25. The average pot-hole depth was 35,5 mm and diameter was 776 mm.
The following prediction model  for pot-hole severity 'PS' with the grade of the section G, Weinert's N-value, the Maximum Dry Density MDD, the Dust Ratio DR and the Optimum Moisture Content OMC as variables and with an R-squared value of 0,45:
PS = 4,2 - 0,185*G - 0,00004*N*MDD - DR(3,10 - 0,257*OMC) - 0,12*OMC (rating)
If all factors which lessen the porthole severity from a maximum of 4,2 would be 0, a pot-hole rating of 4,2 would still prevail which proves the doubtfulness of this prediction model. Pot-holes are, however, an inherent feature of any unpaved road with the additional proviso that under Namibian climatic conditions with very high N-values in most parts of the country pot-holes are not a severe performance factor as also proved by the acceptability test above.
126.96.36.199 PREDICTION MODEL FOR CRACKS
Personal experience reveals that cracks are not a very serious performance parameter for Namibian unpaved roads except for materials with high ' PI'. For the much wetter regions of South Africa, with low N-values, sections with serious cracks broke up badly under heavy traffic and formed pot-holes. Although cracks are not regarded a problem factor on Namibian unpaved roads the prediction model  will be included for completeness. The following severity criteria were used:
1. No visible cracks.
Severity values were established for the wet and dry seasons with an average severity of 2,3 for the rainy and 3,7 for the dry season. Weinert's value, the Grading Modulus 'GM', the Plastic Limit 'PL' and the Liquid Limit 'LL' were used as variables in the model for crack severity 'CS':
CS = 4,50 - 0,16*N - 1,26*GM - 0,076*PL + 0,08*LL (rating)
188.8.131.52 PREDICTION MODEL FOR SMALL STONES
Small stones (loose material) are after corrugations the second important aspect which influences the performance of unpaved roads, as indicated in above acceptability study (for roads with good to average IRI). The generation of small stones by traffic result in a general loss of gravel skid resistance with the resulting reduction of traffic safety. Normally the wheel tracks have the least amount of small stones with concentrations of loose material along the edges of the road and in the centre of the lane (Afrikaans: Middelmannetjie). Thick layers of small stone layers (usually more than 100 mm) are responsible for many accidents due to a total loss of control over the vehicle. Although no systematic statistics for this kind of accident cause exist it can be empirically stated that thick, loose berms of small stones are maybe the principal cause of accidents on unpaved roads, especially for drivers not used to this type of road. It can also be empirically derived that small stone layers on unpaved roads will affect the rolling resistance significantly with a resulting increase in fuel consumption.
In Namibia no systematic research on small-stone-performance of unpaved roads was undertaken as yet. A study was undertaken in Transvaal/RSA  where average small stones material for unpaved test sections was analysed in terms of pointed properties. A rating system was established with the objective of identifying those materials which were particularly prone to ravelling under traffic and would thus require frequent grader blading and regravelling. The following severity rating system was used:
Small stones material can be defined as cohesionless surface material which could easily be moved with a shoe or stick . Sections with more than 5% small stones of the total test section area were included into the experiment. The average small stone severity for all the sections was 3,0.
The major factors influencing the formation of small stones material were the Dust Ratio DR, Weinert's value and the Maximum Dry Density MDD. An R-squared value of 0,59 with standard error of 0,44 was obtained for the prediction severity rating formula for loose stones 'LSS' :
LSS = 0,68 - 14,9*DR + 0,09*N + 0,0013*MDD (rating)
The small stones material is mainly dependent on the climatic Weinert's N-value. The cohesion of loose stones material plays also an important factor influencing the generation of small stones blankets. This is accounted for by the dust ratio and density parameters. These parameters will be accounted for in the proposed material's specification which is developed in the next sections.
184.108.40.206 PREDICTION MODEL FOR SURFACE DRAINAGE
Wet weather passability is equivalent to good or bad drainage of the road prism. The Plasticity Index ' PI', the percentage of material passing the 0,075 mm sieve and the soaked laboratory ' CBR' are parameters for wet season conditions . It is essential to avoid any ponding of water on the road surface, because ponding is causing sections, even constructed with excellent materials, to become impassable.
A severity rating system for surface drainage of unpaved roads was developed  in order to establish the erosion susceptibility of the experimental sections. The surface drainage and erosion were evaluated according to the following severity rating criteria:
The significant variables for the prediction model were Weinert's N-value, the Average Daily Traffic ADT, the Plastic Limit PL, the Laboratory Maximum Size LABMAX (mm), % passing the 4,75 mm sieve (P475), the Grading Modulus GM, the Gravel Index GI, the Aggregate Pliers Value APV (a simple field test to establish an aggregate crushing value in the field) and the Relative Compaction COMP (density established in the field relative to the density in the laboratory). The average severity rating revealed a rating of 3,23 for all sections with an R-squared value of 0,40 with a standard error of 0,55. The prediction model for surface drainage severity 'SDS' is as follows :
SDS = GM(5,63 - 0,18*PL - 0,02*P475) + LABMAX(0,15 - 0,001*COMP)+ N(0,06 - 0,002*APV) - GI(17,32 - 0,81*PL) + 0,04*P475 + 0,06*COMP + 0,002*ADT - 6,9 (rating)
It has, however, to be observed that the main factor influencing road drainage and erosion properties are the crossection of the road and not so much above environmental and materials variables. The crossection of a road is controlled by factors which fall outside an optimised materials specification for unpaved roads.
7.3.7 GENERAL PERFORMANCE WITHOUT PREDICTION MODELS
There are further research projects without prediction formulae which are barely touched yet. These projects will contain aspects like large stones and skid resistance under wet weather conditions of unpaved roads.
220.127.116.11 LARGE STONES
The Namibian acceptability study revealed that large stones were the second least contributing factor to poor riding quality. Large stones which are sticking out of the road surface are responsible for car bouncing, stone initiated corrugations and bad grading effectivity. The more they stuck out of the wearing course the more serious are the consequences which in a negative sense influence the riding quality.
Most material's specifications for unpaved roads in southern Africa provide for the exclusion of oversize material. But, very seldomly completely over-size free sections of unpaved roads will be encountered. Many of these sections are acceptable with respect to riding quality as was proved in above acceptability/rejection experiment. The complete exclusion of oversize material would be unnecessarily harsh and uneconomic but a limit on the quantity and dimensions of large stones is surely warranted and will be included into the proposed material's specification for Namibian unpaved roads.
The severity rating for large stones is as follows :
The average large stones severity for all the sections was 3,0. The average maximum stone size was 322,5 mm with a minimum of 139 mm and a maximum of 674 mm. No prediction model was developed because the large stone parameter could easily be established from grading analysis from the borrow pit.
18.104.22.168 SKID RESISTANCE
Skid resistance and wet weather trafficability are not very serious under Namibian conditions and are more important from the safety point of view than for cost/quality optimised performance criteria. A driving test with 80 km/h is a satisfactory empirical measure for skid resistance during wet weather. Main contributing factors for skid resistance are fine materials (materials passing the 26,5 and 0,075 mm sieves), the Plastic Factor PF (product of percent finer than 0,075 mm and plastic limit), the Mean Annual Rainfall and the Dust Ratio DR.
7.4 OPTIMAL MATERIALS SPECIFICATION
To minimise the performance problems which were dealt with in the previous sections the following empirical measures have to be applied:
Furthermore the experiences learnt from the prediction models for general performance will have a bearing on the development of revised, optimal materials specifications for unpaved roads.
7.4.1 NORMAL GRAVEL AND EARTH ROADS
Revised, optimal material specifications for normal gravel and earth roads can be developed on empirical grounds of a relationship between different performance parameters like riding quality on the one side and material properties on the other, on the basis of visual-sensitive methods. Thereafter the material parameters influencing the riding quality with consideration of the lessons learnt from the prediction models for general performance have to be established and evaluated.
Prospecting for suitable gravels and laboratory testing is the first step to ensure the utilisation of the best available gravel sources in order to achieve better wearing courses for unpaved roads . The final step will be, of course, consistent compaction control.
Empirically it can be stated that an ideal wearing course for unpaved roads will have a good grading (not too coarse) and will have sufficient binding qualities (in terms of PI). To establish an optimal material specification the Department of Transport decided during 1982 to launch a country-wide effort to obtain field data of existing wearing courses in order to compare actual riding quality and general behaviour of these pavements with laboratory test results. The idea was to obtain acceptance-samples as well as rejection-samples which had to be taken on a prescribed manner. These samples had to be representative of road sections with definitive acceptable or definitive unacceptable riding qualities. It was also requested to do the sampling together with a standard questionnaire with information on grading frequencies, gravelling or regravelling history, traffic counts and road user complaints. 308 samples from all over Namibia were received and the necessary evaluations took until 1986 in order to take the specifications to the final test. This effort can only be regarded as first iteration in a long process of analysing gravel wearing courses.
Table 38 contains the sample source statistics for the four Namibian regions and includes personal observations and testings with acceptance and rejection samples :
TABLE 38 RIDING QUALITIES STATISTICS OF SAMPLE SOURCES
In determining the test procedure, the following material properties and combinations have been thought to have a direct effect on the performance of wearing courses of unpaved roads:
These properties must be compared with the actual performance of a road by means of visual riding quality establishments:
The tests revealed that plasticity plays an important role in predicting the riding qualities of a gravel wearing course. It has been established that if the 'PI' of the wearing course material is below 4 then there is a 48% chance of success while for a 'PI' of between 4 and 8 this percentage increases to 67%. With a 'PI' above 8 even a 76% chance of getting a satisfactory riding quality can be expected with a slight drop in 'RQ' if the 'PI' exceeds a value of 12. Thus it can be derived that high plasticity is positively influencing riding quality while a low plasticity will be disadvantageous for the riding quality of a wearing course.
The investigations also established the relationship between riding quality and soil fines. It was found that if the 0,075 sieve passing percentage was below 10% then there would be only a 41% chance of a satisfactory riding quality while it increased to 70% for a percentage of between 10 and 20% with a slight decrease in riding quality from 20% to 40% passing. It can be presumed that a passing of more than 50% will have an adverse effect on riding quality but due to lacking samples in this category this could not be verified yet.
Furthermore the relationship between riding quality and the Fineness Index was investigated. It was established that wearing course material with a value of below 50 had a chance of only 48% to achieve a satisfactory riding quality. The riding quality increased to 69% when the Fineness Index lied between 50 and 100 and the success rating increased further to 73% for values between 100 and 200. For values in excess of 200 the riding quality showed an insignificant decrease.
As mentioned earlier the particle distribution had not a very heavy bearing on riding quality except for the case where a malratio between 'PI' and coarseness existed. It seems, therefore, that it would serve no purpose to determine a relationship between riding quality and maximum size or grading modulus. It has to be noted, however, that with evaluating the overall materials statistics in table 39 it can be established that a rated unacceptable 'RQ' of between 13% and 67% for the cases on record could be attributed to grading alone. By grading alone it is implied that the 'GM' was either above or below and/or the maximum aggregate size was above the specified values as shown in table 40:
The comparison effort between riding quality and specific materials properties has, not surprisingly, proved that specific anomalies could not be avoided. These anomalies could be attributed firstly to the subjective character of this study. For example, it was found that some samples complied with all aspects of the specifications but were unacceptable. Besides personal and subjective judgement criteria, this could be attributed to the fact that the field evaluation was, for instance, undertaken toward the end of a grading cycle, or the wearing course material was poorly compacted, or grading frequencies were too low for this type of material. The contrary was also found to be true and could be attributed to low traffic volumes or field evaluations shortly after a grading cycle. A small number of samples performed poorly for no apparent reason at all. But, it can be stated that due to the absence of scientifically established field data this visual evaluation method was a good start to obtain a more realistic optimal materials specification for unpaved roads.
TABLE 39 MATERIAL PROPERTIES STATISTICS
Table 39 can be evaluated as follows:
(i) Plasticity Index (PI)
In the Windhoek and Otjiwarongo regions over 40% of all samples with a good RQ had PI values below the present minimum specified value of 6. In the other regions it varied from 16% to 27% with a total mean of all regions of 26%. This implies that the minimum PI value could be reduced from 6 to 4.
Good RQ where the PI values exceeded the maximum specified value got a mean value of only 5% and ranged from 0% to 13%. Due to the fact that PI values have no significant influence on poor riding quality with a mean value of 11% it could be considered to increase the allowable PI to 25 for regions with N>10 and 15 for N<10 for empirical reasons.
(ii) Grading Modulus (GM)
In most parts of Namibia where the riding quality performed well, but the 'GM' was below the specified value, percentages of between 0% and 17% could be observed, except for the East Caprivi which is situated in a N<10 area with rather fine calcareous sand-clays where a 43% success rate was established. No change should be envisaged here and the minimum 'GM' should be retained with 1,3 for N<10 and 1,1 for N>10.
The upper limit 'GM' gave higher success ratings ranging from 45% to 79% with a mean value of 55%. The existing upper 'GM' of 1,7 for all areas in Namibia could be increased to 1,9.
(iii) Maximum Size
Between 23% and 58% with a mean of 39% success ratings were observed in the case of maximum size. Theoretically it can be derived that the maximum size could be increased in the proposed specifications but one would be hesitant to recommend this, because oversize stones have empirically be proved to be one of the main causes for poor riding quality a has been shown earlier.
Two other important material parameters, minimum ' CBR' and minimum percentage compaction were not investigated due to the fact that a lowering of the specification in this case could not be recommended. The disastrous effect of rain on a gravel wearing course with a sub-standard 'CBR' is well documented. Two examples are the failures on trunk road 14/2 on Büllspoort and the dune section on main road 91 between Gobabis and Makam. Other derivations could be made, for instance, that a wearing course material with all three properties ( PI, GM and maximum size) outside the specifications has only a 10% chance to be acceptable. The success rate climbs to 37% with two properties outside and to 53% with only one property outside the specification . Less than 7% of the poor 'RQ' sections complied with the full specifications. In summary it can be stated that Grading Modulus 'GM' and Plasticity Index 'PI' are the most important quality parameters for gravel wearing courses.
7.4.2 ATLANTIC COAST SALT-GRAVEL ROADS
This section describes the development of a material's specification for Namibia's unique "Atlantic coast salt-gravel roads" based on acceptance and rejection criteria. The excellent and dust-free riding quality of the salt-gravel roads is not only a function of the specific gravel materials used in this technique but also one of the moist conditions of the coastal mist. During the absence of the hygroscopic moisture during east wind conditions, rutting or ravelling in the wearing course of the salt-gravel pavement with a resulting deteriorating riding quality is the consequence. The contrary effect is achieved if isolated rainfalls are occurring with resulting slipperiness and, after the drying-out process of the wearing course a very uneven, rough road surface .
In order to find optimal material properties for salt-gravel roads, a correlation between the riding quality and adjacent material properties had to be established. Altogether 44 sample points were identified, 23 representing a good and 21 a poor, visual riding quality . Material testing of these samples identified those soil properties which can be expected to have some degree of influence on the level of riding quality and the maintenance performance of salt-gravel wearing courses. The following material properties have been identified:
Summarising it can be stated that poor riding quality salt-gravel wearing courses are manifested by corrugations, roughness, ravelling and potholing as well as slipperiness followed by rutting or pick-up . Corrugations will normally appear in the top approximately 50 mm of the wearing course in cohesionless materials. The cohesion in salt-gravels is a function of the hygroscopic soluble salts, possibly the gypsum and the PI. Ravelling on larger scale and potholing on lesser scale are resulting in increased roughness of road surface. Ravelling and potholing are caused by materials with high 'GM' and/or too much oversize aggregates whereby inadequate soluble salts or low PIs are unable to keep the material together. Under moist conditions traffic with its compacting effect has a favourable influence on the riding quality of a salt-gravel road. Slipperiness is mainly caused by rains on sections with high-plasticity materials and/or high soluble salt contents. This situation is further worsened by picking-up of material under high traffic loads resulting in a "cobblestone-like-surface" after drying out. Depending on the physical and chemical properties of the salt-gravel materials severe and dangerous rutting of the road surface can occur .
In conclusion it can be summarised that at least two beneficial material properties are needed to achieve a favourable performance. It has been further proved that salt-gravel roads are only successful in an approximately 10 km radius from the Atlantic coast line in order to enable the hygroscopic salt-gravel materials to make use of the beneficial effects of the coastal mist.
7.4.3 THE MATERIAL SPECIFICATION FOR UNPAVED ROADS
Above experiences and conclusions from the prediction models for general performance of unpaved roads lead to revised, optimal materials specifications. It is, however, not practical to have only one standard specification for the whole of Namibia as the performance of any gravel wearing course is greatly affected by the volume and class of traffic and by environmental conditions. In the arid areas of Namibia with high N-values and in many cases low traffic volumes it is possible to construct a satisfactory gravel wearing course using calcrete surfacings with plasticity indexes as low as 'SP' (slightly plastic: <4) and up to 25 whereas in areas with high rain fall and N-values less than 10 a wearing course with 'SP' plasticity may form corrugations within a few days and any gravel with a 'PI' of more than 20 and a fine grading can become dangerously slippery during the rainy season. This is the reason that in the proposed materials specification for wearing course material two different climatic regions, i.e. for N<10 and for N>10 are specified. Region 2 with N > 10 is consisting of the Namib Desert and the whole Namibian south, south of the Tropic of the Capricorn. The rest of Namibia will be Region 1.
In the case of different materials from different geological sources, calcretes should always receive preference. In the case of non-availability of calcrete or other suitable gravels, sand-clays or fine materials derived from weathered dolerite or decomposed granites may be acceptable. The 'PI' should in this case be between 4 and 8. Materials with high ' PI' values should be used only in conjunction with a high grading modulus. It could be disastrous if for instance a gravel with a maximum allowable 'PI' and minimum 'GM' is used in the N<10 area with high traffic volumes. The research on this topic has to be intensified in the future because in the moment the experience in this field is rather vague.
Another very important " Namibia-Adapted Technology" is represented by the unique west coast salt-gravel roads as reported above. The most important materials properties which will assure the forming of a stable pavement for these salt roads are the presence of soluble salts and high plasticity or a combination of these two properties. Gypsum is also beneficial for these roads. Other properties like maximum aggregate size, the shape of the aggregate and the percentage fines (-0,075 mm) are of lesser importance. The coarseness of the aggregate is of importance in those cases only where a unbalance between the content of soluble salts and the plasticity exists. In cases where the plasticity and/or the soluble salt content are low, coarse round aggregates will be quickly stamped out under the influence of traffic and will form pot-holes and even bad corruga tions.
The major problem in the evaluation of salt-gravel roads is to find the critical boundaries between different materials properties because the performance of the pavement of these roads will be interdependent of a combination of all decisive materials properties. Experience gained so far with satisfactory performances of salt-gravel roads have resulted in a materials specification in table 40.
The proposed materials specification for unpaved roads should serve as a guide only and should not be too rigidly applied. The most important aspect is, however, to combine the two decisive parameters for the performance of a gravel wearing course namely grading ( Grading Modulus 'GM' as function of coarseness) and Plasticity Index (PI) with the climatic conditions of the area where such gravel pavements are to be applied. The following materials specification for gravel wearing courses and salt-gravel pavements is proposed :
TABLE 40 MATERIALS SPECIFICATION FOR GRAVEL WEARING COURSES
7.5 COST AND QUALITY OPTIMISED MODELS
Cost and quality optimised models compare the future flow of benefits of a facility with the initial cost of construction as a basis. Therefore it is necessary to consider the time value of money. This is done by discounting the future costs and benefits to a present value ( Present Worth 'PW' of the Costs and the Present Worth of the Future Benefits) by using the discount rate or the opportunity cost of capital (OCC). For investments OCC is assumed to be an average of the short-term and long-term rates of interests. When the effect of public investment in highways is considered, the interest rate must reflect the return on investment in the national economy. In this thesis an OCC of 10% was used to illustrate the effect of the OCC on a comparison of the alternatives. Such cost/quality optimised models are assisting the establishment of the Net Present Worth ( NPW) for gravel-surfacing and bitumen-surfacing of roads which are based on real cost-optimised justifications and not on guess-work. The NPW of a given investment is obtained by subtracting the present worth of the costs from the present worth of the future benefits. The benefits as well as the costs are discounted at the OCC interest rate. The investment is feasible if the NPW is positive.
7.5.1 DETERMINATION OF OPTIMAL GRADING FREQUENCIES
The standard maintenance of an unpaved road is done by a blading device such as a motor grader. Grading frequencies are in Namibia currently mainly established by empirical means. In formulating an optimum maintenance strategy the total costs between blading and road user costs have to be minimised. The basis for such a cost optimised maintenance model is again the Brazil study, as adapted to Namibian circumstances. It was experienced during this study and confirmed by Namibian maintenance experiences that any maintenance model has to differ between dry and wet cycles because both require different maintenance methods. During the dry season, for instance, the gravel bearing course should never be touched but a thin gravel blanket should be graded over it. During the wet season, however, the gravel bearing course can be compacted under moist conditions effectively by grading. But, it must also be stated that Namibian experiences have shown that this empirical rule is in many cases not applied, with consequent detrimental effects regarding costs and maintenance.
The Brazil study revealed that every specific unpaved road has its own minimum between blading and user costs. The optimal maintenance state can be seldom achieved and it will be a realistic objective to achieve 60-80% of the optimum. Following this course the total optimised maintenance costs on a district level can be achieved. Another sound empirical rule is that for each spent US $ for grading maintenance three US $ in saved user costs have to be returned. On this basis the maintenance budget can be established including the road nodes, the road lengths, the total number of bladings per year, the dry blading frequency and the wet blading frequency.
Another important parameter for this optimisation program is the establishment of a sound IRI service level. For each road the low, the medium and the still acceptable high IRI value has to be established. The Brazil study proved that the predicted IRI values compared very well with the actual measured IRI values. During a validation effort of the Brazil study the average predicted IRI of one of the test sections was 5,4 and the actual measured one was 5,2. The same experience was made on several test sections in Namibia. An ideal IRI service level has to be established on ground of user costs. During the Brazil study  it was revealed that IRI is climbing steeply if the frequency of blading will be cut, for instance, to half. If, on the other hand, the frequency will be determined too high with a resulting very low IRI, a very unfavourable economic balance will be the consequence.
The Namibian model for the change of roughness (change in IRI of 2,6 for shale and ADT=100 (evu) after 365 days since last blading, for instance) (see figure 11) could not be linked to the model for optimal grading frequencies, due to the non-linear deterioration curve for different materials under traffic.
On the empirical basis (Brazil study) of one spent US $ for three saved US $ in ' VOC' the Namibian optimised roads model regarding the optimal point of grading unpaved roads, dependent on costs, roughness IRI and ADT was established. Figure 14 pictures the accumulated 'VOC' for unpaved roads with different roughnesses from an excellent road with IRI=3,0 to an unacceptable road with IRI=10,5 in dependence of the average daily traffic. The total vehicle operating costs 'VOC' were used as developed in figure 4 for Namibian conditions, for cars (85%) and heavy trucks (15%). This traffic composition 85% light and 15% heavy mirrors average Namibian traffic conditions. For an excellent unpaved road with an average IRI=3,0 a 'VOC' of US$ 6.460/km/year for 100 vehicles (85% light/15% heavy); US$ 7.600/km/year for 100 vehicles for a good unpaved road (IRI=5,0), US$ 9.400/km/year for a bad unpaved road (IRI=7,5), US$ 10.400/km/year for an undesirable bad unpaved road (IRI=9,0) and US$ 11.400/km/year for an unacceptable unpaved road (IRI=10,5) was established. (See tables 26 and 27 and table 36).
Table 36 established that an unpaved road with roughnesses between IRI=7,00 and 9,00 is regarded as undesirable. Therefore, for this cost/quality optimised model, it was decided to take a road with an IRI=7,50 as an offset point which is extreme under Namibian conditions. With average grader maintenance costs of US$ 36/km (US $ 6,00/blade km: 6 blades wide) and with savings of vehicle operating costs for an improvement of an unpaved road from IRI=7,50 to IRI=5,00 it can be derived from figure 14 that for an 'ADT' of 100 (85% light, 15% heavy) a grading of 17 times/year is cost/ quality optimised. ( VOC-Savings=US $ 9.400 - US $ 7.600/km/year = US $ 1.800; with 3:1 principle US $ 600/km/year can be spent: US $ 600/36 results in a grading cycle of 17 times per year). However, it has to be stated that under Namibian conditions a VOC-saving/maintenance relationship of a 3:1 ratio represents a rather low level of maintenance. To date the Namibian road user is used to a higher maintenance level of 3:1 for such traffic load (ADT=100) under average conditions which probably is too high to be cost/quality optimised (see table 33).
FIGURE 14 OPTIMAL POINT OF GRADING OF UNPAVED ROADS
7.5.2 DETERMINATION OF OPTIMAL GRAVELLING FREQUENCIES
Any unpaved road is subject to loss of gravel due to traffic and environmental factors like for instance wind. This gravel loss has to be replaced. In Namibia approximately 30-50% of the total gravelling effort is currently used to compensate for gravel losses. The balance of gravelling is done to provide for new gravel surfaces or to replenish existing gravel surfaces. The ' MDS' system gave a prediction for a total gravel loss for all unpaved roads of the Windhoek district of 160.000 m3 for 1984/85. The total gravel used for all unpaved roads in this district was for the same period 370.000 m3. This represents a gravel loss replacement of approximately 43%. In the Bronkhorstspruit district in South Africa  the total gravel loss on the 677 km long unpaved road network has been predicted by means of the South African prediction formulae with 129.000 m3 and the actual loss has been established with 138.500 m3.
The Brazil model to predict gravel losses is based on traffic data, materials data and geometrical data input which can be used to compare the predicted losses with the real ones. The Brazil prediction values compare very well with those from the Kenya study. Figure 12 summarises the prediction formula developed for gravel losses for Namibian conditions. The data compiled in this figure estimate for average Namibian gravel loss conditions for an average daily traffic of 300 vehicles per day a gravel loss of 25 mm/year which has to be replaced. This means a regravelling cycle of 6 years for an average 150 mm gravel layer for this relatively high traffic number. For a more realistic 'ADT' of 100 vehicles a gravel loss of 8 to 10 mm/year can be expected, with a regravelling cycle of more than 15 years for a 150 mm gravel layer. The optimal point of regravelling has to be established for each individual material and traffic dependent case. Cost/quality optimised systems can, for instance, be used to prove that it can be economical to bring better material over larger haul distances to get the cost optimum. Laterite gravel needs less blading maintenance than quartzitic gravel, whereby the blading costs are increasing from fine laterites to coarse quartzites. This example can be used to prove that larger haul distances for more expensive gravelling materials can be compensated by lesser maintenance and road user costs.
It has also be borne in mind that above gravel loss is only caused by traffic action and no environmental factors were taken into account. Consequently the optimised point of regravelling could even be reached for considerable smaller traffic numbers.
7.5.3 DETERMINATION OF THE OPTIMAL SURFACING POINT
The developed cost/quality optimised system can be used to investigate the optimal point of surfacing an unpaved road. This point is a function of the traffic load and the net present worth ( NPW) of the investment as well as the riding quality in terms of roughness.
The minimum required discount rate which is needed to calculate the time value of money would normally be the true or real rate of interest in the long term (opportunity cost of capital: OCC). This is because all economic calculations are prepared using constant prices and make no allowances for future general inflation which is assumed to affect costs and benefits equally. For Namibian average conditions, taking into account the true rate of interests of internal and foreign loans, an OCC of 10% will be used in the model.
To establish this point two economic comparison criteria can be used, both being basically the same:
CCp + MCp + VOCp < CCu + MCu + VOCu or PWp < PWu
p = paved (conventional surface treatment: see: 10.3.3.2); u = unpaved; (Accident and time related costs are not included due to lack of data).
CC = Initial construction costs per km + Present Worth
of replacement for 20 years and 10% discount
rate p.a. (OCC) with a salvage value of the project of 50% of the initial
The second principle will be followed in the development of the optimised roads model. It has to be considered that apart from the vehicle operating costs argument, road users can also take account of generally higher speeds and improved road safety on paved roads against unpaved roads. This was, for instance, argued in the section about performance criteria for dust where it was stated that dust can force the surfacing of an unpaved road long before cost/quality optimised levels have been reached. The developed cost/quality optimised Namibian roads model is only cost and performance related as far as roughness is concerned, but not speed, time, accidents and other performance parameters like, for instance, dust related. Generally it can be stated that high traffic volumes will increase the benefit cost ratio of surfacing unpaved roads.
In the development of the model an economic analysis period for paved roads with different initial construction costs and short and long term maintenance costs for an average paved road in Namibia for 20 years will be given. Realistic unit costs as obtained from the Department of Transport for December 1989 and recalculated into US $ (1 US $=R 2,63) to avoid the high South-African/Namibian inflation factor were used to show the relative cost components. The "Present Worth" of replacement of the total construction costs and the revenue accrued by the "Present Worth" of salvage value after 20 years at 10% interests per annum for an assumed salvage value of 50% of the initial construction costs were taken into account.
Initial costs for paved roads in Namibia can fluctuate from US$ 25.000/km for appropriate low cost roads (example: spoorbaan roads as shown in chapter 8) to US$ 250.000/km dependent on the following aspects:
The average initial construction prices CCp currently applicable in Namibia are US$ 138.000/km for a new conventional paved road in average terrain with normal drainage structures, 12 m wide and 8,00 m surfacing width; US$ 82.500/km for a new paved road under very favourable conditions (terrain and drainage structures); US$ 55.000/km for appropriate low-volume paved roads or the surfacing of existing gravel roads with adequate geometrical and drainage properties and US$ 25.000/km for the concrete-paved spoorbaan road which (performance and construction considerations will be dealt with in chapter 8). The current, average initial construction prices for unpaved roads CCu fluctuate from US$ 12.000/km (for an average IRI=7,50) to US$ 20.000/km (for an average IRI=5,00), with the exclusion of deep excavations, high fills and major drainage structures. In order to develop boundary conditions these four classes of paved roads and two classes of unpaved roads will be investigated in the model. In all cases an average salvage value of 50% of the initial construction costs was assumed and brought into the model. The initial construction costs were based on the assumption that average construction prices for construction lengths of 50 km for December 1989 were used.
The short term maintenance costs for paved roads MCp are US$ 250/km/year for routine minor maintenance and US$ 14.000/km for a reseal (average once in 20 years) as well as US$ 50/km/year for overhead administrative costs. The maintenance costs for unpaved roads MCu are US$ 800/km/year (average IRI=5,00 for good unpaved roads) and US$ 900/km/year (average IRI=7,50 for bad unpaved roads) for grading and small maintenance works and US$ 550/km/year (IRI=5,00) and US$ 650/km/year ( IRI=7,50) for regravelling costs (average once in 15 years) as well as US$ 50/km/year for overhead administrative costs for both, good and bad unpaved roads. The maintenance costs were based on current realistic machine hire rates, climbing with increased traffic loads for December 1989.
The total vehicle operating costs ' VOC' were used as developed in figure 4 for Namibian conditions, for cars (85%) and heavy trucks (15%). For a paved road with an average IRI=2,5 a 'VOC' of US$ 6.300/km/year for 100 vehicles (85% light/15% heavy); for a low-cost paved road with an average IRI=3,00 US$ 6.460/km/year for 100 vehicles; for a spoorbaan type appropriate road with an average IRI=4,30 (see figure 16) US$ 7.210/km/year for 100 vehicles; for a good unpaved road with an average IRI=5,00 US$ 7.600/km/year for 100 vehicles and for a bad unpaved road with an average IRI=7,50 US$ 9.400/km/year for 100 vehicles were established.
All costs have been discounted to the " Present Worth" for an estimated rate of interest of 10% per annum and for 20 years. The analysed cost/quality optimised roads model to establish the optimal point of surfacing an unpaved road is pictured in figure 15:
It can thus concluded that it would be advantageous to improve a bad unpaved road (IRI=7,50) to a good gravel road (IRI=5,00) (US$ 20.000 /km) for a traffic load of more than 40 vehicles per day, for instance by adding a gravel wearing course to an earth road. In the absence of suitable natural road building materials for such a road it would be advantageous to pave such a road (IRI=7,50) to an appropriate "Spoorbaan"-level (IRI=4,30) (US$ 25.000/km) for a traffic load of more than 70 vehicles per day or to another appropriate low-volume paved level (US$ 55.000/km) for more than 125 vehicles per day. It would be advantageous to improve a bad unpaved road to a paved road level with favourable geometric and drainage properties (US$ 82.500/km) for more than 190 vehicles per day while it will be not cost/quality optimised to surface a good unpaved road (IRI=5,00) carrying less than 110 vehicles per day, even for appropriate low-volume spoorbaan road level. To build a full-scale conventional paved road (US$ 138.000/km) will only be cost/quality optimised for a bad unpaved road carrying more than 330 vehicles per day or a good gravel road carrying more than 500 vehicles per day, events which so far were seldomly encountered in Namibia. Aspects like timing and accident costs as well as performance factors like dust and all-year-trafficability and social factors like labour-intensiveness ( Spoorbaan roads) are difficult to quantify, but these factors play a role to justify the construction of a paved road at levels below above cost/quality optimised levels ( shadow-pricing). It should also be borne in mind that above criteria are broad boundaries only. Every project has to be investigated individually to establish the real individual optimal point of surfacing an unpaved road, taking into account all factors.FIGURE 15 OPTIMAL POINT OF SURFACING UNPAVED ROADS