The development and evolution of a mechanistic-empirical design function for BSMs are discussed in this section. The failure mechanism for BSMs, permanent deformation (or rutting), is similar to that of granular materials as was determined in Chapter2. The starting point for the BSM transfer function to was to identify a transfer function that would describe the granular materials used in road construction. The transfer function for waterbound macadam was selected as a starting point in developing a transfer function for BSMs. This function calculates the bearing capacity in terms of the number of standard axle load repetitions that can be sustained before a certain level of plastic strain is induced in the layer. The development of the transfer function for waterbound macadam is discussed in Section 3.6.1.
Loudon International experimented with this transfer function, using the shear properties of BSMs and their extensive experience with the materials. The architecture of the waterbound macadam transfer function was used and coefficients were altered to better describe the unique properties of BSMs. This produced the preliminary transfer function for BSMs. The alterations included the replacement of the parameter for saturation (S) in the transfer function with retained cohesion (RetC). As the ”Loudon Transfer Function” has not been published, limited information is available regarding the calibration of this function. The heuristic approach followed and the alterations made to obtain the ”Loudon Transfer Function’ are discussed in Section 3.6.2. It is important to note that this function has not been published or calibrated and should not be used for design.
This research project aims to further adjust the ”Loudon Transfer function” and to calibrate this design function based on the long-term performance of pavements incorporating BSMs. A number of pavement structures that incorporated BSM layers were identified and analysed to obtain the input values for the transfer function at different stages in their design life. The number of standard axles obtained from the transfer function was compared to actual traffic data for the specific pavements.
The approach followed to calibrate the transfer function is discussed in Section 3.7.
The function was verified using other design methods which is discussed in Section3.8. Comparisons were made between the new transfer function, the ”Loudon Transfer Function”, the PN design method and actual traffic data. This approach ensures that the new transfer function would provide reasonable results. The transfer function was also calibrated to describe the life of a certain pavement given the level of reliability required for the design as per Section 3.7.5.
3.6.1 Waterbound Macadam
BSMs are similar to granular materials in that they fail in permanent deformation rather than cracking like cement stabilised materials. The transfer function for BSMs is therefore principally based on that of waterbound macadam. Equation 3.12 shows the formula for calculating the life, in terms of number of axle load repetitions (N), that the layer can sustain before a certain level of plastic strain is reached (Theyse et al.,2000). This model was based on triaxial and heavy vehicle simulator (HVS) test data for waterbound macadam material with crusher sand and natural sand filler.
log N = 1.891 + 0.075RD − 0.009S + 0.028P S − 1.643SR (3.12)
Where:
N = Number of standard axles that the layer can sustain before reaching the specified plastic strain limit
RD = Relative Density (%) S = Saturation (%)
P S = Plastic strain limit as a percentage of the layer thickness (%) SR = Stress ratio as given in Equation 3.13
The stress ratio used in this equation is a function of the load intensity, the shear properties of the materials as well as the overall pavement structure. The stress ratio for waterbound macadam can be calculated as per Equation3.13.
SR = (σ a 1 − σ3) σ3 h tan2 (45 +φ2) − 1 i + 2C tan45 +φ2 (3.13) Where:
σa1 = Applied major principal stress (kPa)
σ3= Minor principal stress acting in the middle of the granular layer (kPa)
C = Cohesion
φ = Angle of internal friction, calculated using Equation 3.14.
Theyse et al.(2000) obtained a model for the angle of friction of waterbound macadam material as shown in Equation3.14. This model describes the angle of friction as a function of relative density and saturation of the material. Relative density is expressed as a percentage of the apparent density, while saturation is expressed as a percentage of inter-particle voids (88% and 25% for example).
φ = −26.38 + 1.021RD − 0.171S (3.14)
3.6.2 Modified waterbound macadam transfer function (Loudon International) Loudon International adjusted the waterbound macadam transfer function to better describe the performance of BSMs. The ’Loudon Transfer Function’ was developed as a heuristic design tool based on known performance of pavement structures on five continents incorporating BSMs. Numerous BSM projects were taken into consideration before a function based on in-service performance was developed (Loudon International 2016, personal communication, August). The ’Loudon Transfer Function’ is shown in Equation 3.15. This function has not been published and minimal information regarding the calibration and verification thereof is available.
log N = 1.55 + 0.1(RD) + 0.05(RetC) + 0.1(P S) − 22.333(SR) (3.15)
Where:
N = Number of axle repetitions to reach a rut depth of P S× layer thickness of BSM RD = Relative Density (%)
RetC = Retained cohesion (%) SR = Stress Ratio
3.6.3 New BSM transfer function
This research aims to further adjust the ”Loudon Transfer Function” to better describe BSM behaviour. Adjustments were made to develop a preliminary design function for BSMs. The major adjustments made to this function were to replace the term for RD with Mod AASHTO density, saturation with retained cohesion (RetC) and to increase the significance of deviator stress ratio within the function. The terms which describe the influence of density and moisture resistance were incorporated into a single term, the effect of which is described by a single constant. The preliminary new transfer function is given in Equation3.16.
log N = A − B(DSR)3
+ C(Pmod.RetC) + D(P S) (3.16)
Where:
N = Number of axle repetitions to accumulate deformation in the BSM layer of P S× layer thickness of the BSM
DSR = Deviator Stress Ratio (-)
Pmod= BSM density expressed as a percentage of 100% Mod.AASHTO density (%)
RetC = Retained Cohesion (%)
P S = Permanent Deformation allowable before failure in the BSM as % of BSM layer thickness (%)
The letters A, B, C and D in Equation 3.16 represent constants used to calibrate the transfer function. Seed values for each of the constants were estimated at the start of this study and calibrated using laboratory and field results. The initial values for the 4 constants are:
A = 1 B = 60 C = 0.001 D = 0.1
The first adjustment made to the ”Loudon Transfer Function” was to replace the term for relative density with density as a percentage of Mod AASHTO density. The compaction achieved during construction plays a vital role in all aspects of material behaviour.
The next significant adjustment to the waterbound macadam transfer function was the replacement of the term for saturation (S) with retained cohesion (RetC). As a result of bitumen treatment, BSMs have superior moisture resistance and are able to retain a greater percentage of cohesion when compared to granular materials. Monotonic triaxial testing on BSM samples that were conditioned
with moisture exposure using the Moisture Induced Sensitivity Test (MIST), provide the means to a more reliable measure of the moisture susceptibility of the material. Therefore, the material’s moisture susceptibility, rather than the degree of saturation, was used in the transfer function.
In Equation 3.12 the term defining the influence of saturation has a negative symbol. Therefore, an increase in saturation of the material reduces the number of axles obtained from the transfer function. This is reasonable as an increase in moisture reduces the shear properties and consequently the life of the material.
In Equation3.16 the term defining the influence of retained cohesion (which replaces the term for saturation), has a positive symbol. This indicates that an increase in retained cohesion increases the number of axles the material can sustain before failure. This is also reasonable as an increase in moisture resistance reduces the degree of damage to a material when exposed to moisture under repeated loading. The increase in the number of axles the material can sustain before failure, as a result of the increase in retained cohesion, as per the new design function, is shown in Figure3.28.
Figure 3.28: Increase in number of standard axles the material can sustain with an increase in retained cohesion according to the new design function
The new transfer function increases the significance of the deviator stress ratio on the life of the pavement. The term describing the effect of DSR has a negative symbol, indicating that an increase in DSR would shorten the life of the pavement.
power 3. The significance of this power and the investigation of its value are discussed in Section
3.7. The deviator stress ratio, measured at 25% of the BSM layer thickness from the top of the BSM layer, is dependent on a number of factors:
1. The load applied to the pavement: an increase in load increases the DSR. The transfer function was developed for a standard axle load of 80 kN. The effect of overloading was investigated as per Section 5.3.
2. The shear properties of the BSM: an increase in either cohesion or friction angle increases the failure envelope. For each corresponding confining stress, the larger failure envelope increases the failure stress and in turn reduces the DSR for a specific load.
3. The resilient modulus of the material controls the load spreading ability thereof. An increase in resilient modulus of a single layer attracts more stress to that layer, while offering better support to the layers above.
4. The overall pavement structure, the support under the BSM layer as well as the materials covering the BSM all have a large influence on the DSR in the BSM. Improved support for the BSM layer increases the confinement of this material under loading, reducing the DSR. The cover on the BSM layer determines the stress experienced by the BSM layer under loading. An increase in the cover depth and resilient modulus of the cover reduces the stress in the BSM and in turn the DSR.