Although the CBR cover-curve approach has generally been superseded by a mechanistic approach, there are some design cases where it would still be appropriate. The USBM - CBR design criteria has been extended to accommodate wheel loads generated by typical ultra-class six- wheeled rear-dump trucks. The USBM work only extended to a 55-mt (300 mtGVM) truck size and does not incorporate the effects of tire pressure, which influence the bearing pressure and contact radius. The approximate CBR values of various in-site or sub-grade (unimproved) soil types are defined by the Unified Soil Classification (USCS), following Test Designation D-2487 of the American Society for Testing and Materials (ASTM) and the American Association of State Highway and Transportation Officials' (AASHTO) systems.

The equivalent single wheel load (ESWL) is the single wheel load having the same contact pressure, which produces the same value as the dual wheel loads at any depth in the layerworks. In the original USBM work, it was suggested that to accommodate the effects of dual rear wheel assemblies, single wheel loads should be increased by 20%. However, as will be seen later, when using the semi-rational ESWL approximation, a more realistic estimation can be made.

As an example, using USBM (1977) data for a 40,000 lb (18.2 mt) (single) wheel load, with a sub-grade (in-situ) CBR of 5%, at least 700-mm cover is required above this material. When a sub-base layer of CBR 15% material is placed above sub-grade, this layer should have 350-mm cover, in other words, the sub-base should be 350-mm (700-350) thick. Using a base layer CBR of 60% above this, the layer thickness will be 200 mm (350-150). A material of CBR of 100% would form the remaining 150 mm, to give total cover of 700 mm (350 + 200 + 150). When calculating the ESWL cover, a 20% increase in wheel load equates to approximately 790 mm of cover.

Alternatively Equation 1 can be used to estimate the thickness of cover (ZCBR (m)) required above a material of California Bearing Ratio (CBR %).

In Equation 1; tw is the truck wheel load (mt), P is tire pressure (kPa) and CBR is the California Bearing Ratio of the material (%). To replicate the tandem rear axle, the ESWL (ZESWL (m)) cover can be estimated using Equation 2.

The above equations have been developed for truck wheel loads in the range of 15 to 105 mt (equivalent to a GVM of 90 to 630 mt) and a tire pressure ranging from 700 to 900 kPa. Applying the above equations to the previous example yields an ESWL cover of 950 mm and a sub-base thickness of 500 mm. The base layer could then be placed at 330 mm thickness, followed by the wearing course at 120 mm thickness. Using the semi-rational ESWL approximation therefore yields a slightly more conservative estimate of layer thickness requirements.

Mechanistic Design Methodology

Figure 2—Haul road classification and associated mechanistic structural design limiting strain criteria.

The applied load is calculated according to the mass of the vehicle and the rear dual wheel axle load distributions, from which the single wheel load is found. The load application is determined from dual wheel geometry and together with tire pressure, the contact stress is calculated. Figure 1 summarizes the layered elastic model and data requirements.

The strains induced in a road are a function of the effective elastic (resilient) modulus (Eeff) values assigned to each layer in the structure. Other correlations are published by Thompson and Visser and AUSTROADS from where Equation 3 is taken, which, when used in conjunction with layer CBR values, determines the modulus values (Eeff, MPa).

In each case however, care should be taken to ensure that the general correlations presented here are consistent with soil properties not directly assessed in the derivation of the equation. In several instances, the Eeff values actually measured in mine haul roads have been found to be well in excess of those predicted by Equation 3, especially on laden carriageways where traffic-induced compaction has occurred following construction.

Highway vertical compressive strains are limited through design to about 1,000 to 1,500 microstrain, but for mine haul roads, higher limits can be applied since:
• Load repetitions are much lower (albeit at higher wheel loads) than for highways;
• Design life may be much shorter; and
• Blading can be easily undertaken; and combined with occasional re-sheeting, can be used to correct permanent deformations in all but the most inadequately designed roads.

Figure 3—Comparison of CBR and mechanistic design equivalents using 18.2 metric ton wheel load.

Comparative Analysis: CBR Cover-Curve vs. Mechanistic Design
To compare the two design methodologies, a range of layerworks materials and wheel loads are required. Initially, the previous example is adopted (18.2 metric ton wheel load) with similar in-situ and layer strengths. Tandem wheel geometry for a CAT 773F (16.4-mt wheel load similar to the required 18.2 mt) is used and an 800-kPa tire pressure is applied.

Using the MePADS software to solve the 4-layer model with the depth to base of sub-grade set at 5-m below the surface of the road gives the comparative results shown in Figure 3. For the layer thicknesses determined from the CBR cover-curve design methodology, the highest strain value was 2,160 microstrain at the top of the subbase, while the sub-grade strain was limited to 1,400 microstrain. By redefining layer thicknesses to meet the 2,000 microstrain limit, a new mechanistic structural design was determined (See Table 1 and Figure 3). A 200-mm reduction in layer thickness was achieved, which, when combined with a haul road construction width of 27 m, would achieve a savings in material placement and compaction of approximately 5,400 m3/km or 21%.

Figure 4—Comparison of CBR and mechanistic design equivalents using 104 metric ton wheel load.

Using the MePADS software to solve the 4-layer model, with depth to base of sub-grade set at 5-m below the surface of the road, a tandem wheel geometry for a CAT 797B (104 mt wheel load) is used and an 800 kPa tire pressure are applied. The CBR cover-curve design results in strains in excess of the 2,000 microstrain limit being developed in the base and sub-base, which will compromise road serviceability and performance. The mechanistically-derived equivalent design reduces base and sub-base thickness by 850 mm, and increases wearing course thickness by 190 mm. The overall savings in material volumetric and compaction requirements is 660 mm. When combined with a haul road construction width of 34 m, this would achieve a savings in material placement and compaction of approximately 22,440 m3/km or 27% and also provides a better response to the applied wheel loads.

Equation 3

For the larger wheel loads in this example, the CBR cover-curve ESWL-based approach leads to significant under-design of Category I and II roads compared to the mechanistically-derived equivalent structure. While the method could be appropriate for Category III roads, the excessive material volumetric and compaction requirements indicate the method is also inappropriate under these circumstances too.

In the foregoing analysis, it is also important to recognize the role of layer compaction in the development of the design and if different layer material resilient moduli are used, the comparative design results will also vary. Additionally, the mechanistic design approach is also sensitive to the assumed depth to base of sub-grade material. In this analysis, the depth was limited to 5 m. Critically, should this depth reduce (and the thickness of the sub-grade layer reduces), the stresses and strains induced in this layer by the applied wheel load will increase, requiring a change to the layerworks design.

Conclusions
The structural design specification of a mine haul road is a critical component in the overall road design process. Poor design often leads to premature failure of the road, safety is often compromised and productivity and equipment service-life will certainly decrease. With the advent of autonomous trucks, any structural design deficiency would be exacerbated and its impact on operations more problematic to address.

Table 1—Comparative analysis of CBR and mechanistic structural designs for 18.2 and 104 metric ton wheel loads

Two approaches are available to the design engineer; the CBR cover-curve methodology, derived and updated from the seminal USBM work in 1977 and more recently, a mechanistic design methodology utilizing a multi-layered elastic model to represent the response of the haul road layerworks to an applied load.

When comparing the two design techniques, it is seen that for smaller truck wheel loads, the CBR cover-curve ESWL-based design yields a slightly underdesigned result compared to the mechanistic design. Therefore, the CBR cover-curve design method could be used to design Category III roads, albeit at the expense of a potential 21% saving in layerworks volumetric and compaction requirements that a mechanistic design would deliver.

When much larger wheel loads are considered, in conjunction with the channelized traffic paths typical with autonomous trucks, the CBR cover-curve ESWL-based approach leads to significant under-design of Category I and II roads. While the method could be appropriate for Category III roads, the excessive material volumetric and compaction requirements indicate the method is inappropriate and a mechanistic approach is required under these circumstances.