To answer this question, some typical pavement scenarios are analysed. This process involves the following steps:
Choose the pavement layer works to be investigated. (Section 6.1.1) Choose a UCS value typical for a stabilised material. (Section 6.1.1)
Obtain the horizontal strain at the bottom of the layer, for a particular loading scenario. (Section 6.1.2)
Determine the ITS using the relationships developed in Chapter 6 and calculate this for non-carbonated and carbonated material. (Section 6.1.3)
Use a fatigue relationship to determine the pavement life. (Section 6.1.4) Compare the different pavements and variables to analyse and understand the
sensitivity to variables in practical terms. (Section 6.1.5).
6.1.1 Typical pavements to be analysed:
A typical South African pavement is considered to evaluate the potential impact of different variables brought forward in this research study.
The pavement layers consist of a seal surfacing, G2 base, typical C3 subbase, G5 selected subgrade and a G7 in-situ subgrade. The thickness of the pavement layers are provided in Figure 6-1 and is representative of a typical pavement layer thickness as in the TRH4 (2013). The assumed stiffness values, presented in Figure 6-1, are typical values as suggested by
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Theyse (2000), however, no stiffness is allocated to the seal surfacing as it has no structural contribution. The G2 base layer is divided into three equal layers and an iterative process used to determine the Resilient Modulus (Mr) of these layers. The typical model, Mr = k1k2, is used
to determine the final Mr, before values are extracted for further calculations.
Figure 6-1: Pavement layer works, material properties and position of measurements
The standard axle configuration can be either a single or dual wheel load (SAPEM, 2014), for the purpose of this research study, a dual wheel load is selected. A typical standard axle load of 80kN is applied (i.e. 40kN per wheel) and the position of measuring the stresses and strains within the layer are shown in Figure 6-1. Generally, the horizontal and vertical stresses are critical at the centre position of a granular layer as this layer will fail in shear. For fatigue of the C3 cemented subbase, the horizontal strain is taken at the bottom of the layer.
Morton et al. (2004) suggests typical ranges of tyre pressures which has increased significantly over the years from the original 520kPa in previous years. For this reason, a tyre pressure of 800kPa was chosen as representative. Furthermore, a typical Road Category B, which coincides with a 90% Reliability, is considered for this analysis.
h = 50mm; Ei = 450MPa h = 50mm; Ei = 450MPa h = 50mm; Ei = 450MPa C3 Stabilised Subbase h=200mm E = 1000MPa G4 Selected Subgrade h=150mm E = 200 Mpa G7 Insitu Subgrade h = infinity E = 80 MPa G2 Base Course h=150mm Mr = interchanging* 40KN 40KN 1 2 3 4
Tyre Pressure = 800 kPa Wheel Contact area = 0,05m2
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6.1.2 Determine the Horizontal Strain
MePads, a software programme developed by the Council for Scientific and Industrial Research (CSIR) was employed to perform a linear elastic analysis on the pavement. An iterative process was followed in order to determine the stresses and strains at the identified positions.
The process involves assuming an initial Mr value for each of the 50mm base sub-layers.
Applying the chosen Mr model (in this case the k1k2 model), the reported horizontal and
vertical stresses are substituted and the results used to determined how different (% difference) this is from the seed value. This iteration process is continued until convergence is attained between the chosen and calculated Mr value. A value difference in Mr lower than
10% is acceptable for a Road Category B.
The k1 and k2 values, used to define the coefficients of the Mr model, are taken from research
done by van den Berg (2014). When this is reached two considerations is very important, that is the prescribed Modular Ratio as well as the maximum allowable Mr that may be used as boundary condition cap these values at a certain point due to the support given by underlying layers. The results of this analysis are provided in Table 6-1.
Table 6-1: Summary of MePads stresses and strains outputs
6.1.3 Determine the Indirect Tensile Strength using developed Relationships
Following the calculation of the stresses and horizontal strain, the resistance of the materials can be determined. This is determined by using the formulated UCS and ITS relationships together with the average drop or increase of UCS due to carbonation. The UCS and ITS relationship for curing period of 7 days is used in particular as a result of the challenges encountered with the specimens cured for 28 days. These challenges are discussed in previous chapters and include the low densities achieved for the gap grade specimens. Nonetheless, the outputs of these results can show insightful findings.
The choice of using ITS, rather that UCS, as the “strength parameter” emanates from the failure mode in cemented subbases being tension. There are many relationships available in literature that converts UCS values to direct tensile strength (DTS), but ITS results are
s1(kPa) s1(kPa) s1(kPa)
1 792,8 536,6 536,6 - 1866 25,6 0,485 987,72 -1 550 2 705,1 214,8 214,8 - 1135 775,99 -1 550 3 545 174,1 174,1 - 893 690,96 0 550 4 - - - 142 - - - - Mr (MPa) Mr Iteration (% Difference)
Iteration Position Cap
3
e
h MePads Values- 125 -
available after this has been developed and differ for non-carbonated and carbonated material, probably due to different variables having an influence on the UCS and ITS results.
Considering the results of the continuous and gap grade RCA material, the developed relationship between UCS and ITS is expressed as follows (as determined in the Chapter 5):
Continuous: Non-Carbonated: 𝑈𝐶𝑆 = 0.007 𝑥 𝐼𝑇𝑆 + 1.56 (6-1) Carbonated: 𝑈𝐶𝑆 = 0.007 𝑥 𝐼𝑇𝑆 + 0.59 (6-2) Gap: Non-Carbonated: 𝑈𝐶𝑆 = 0.0076 𝑥 𝐼𝑇𝑆 + 0.97 (6-3) Carbonated: 𝑈𝐶𝑆 = 0.0059 𝑥 𝐼𝑇𝑆 + 1.20 (6-4) Continuous (7 day): Non-Carbonated: 𝐼𝑇𝑆 = (𝑈𝐶𝑆 − 1.56 0.007 ) (6-5) Carbonated: 𝐼𝑇𝑆 = (𝑈𝐶𝑆 − 0.59 0.007 ) (6-6) Gap (7day): Non-Carbonated: 𝐼𝑇𝑆 = (𝑈𝐶𝑆 − 0.97 0.0076 ) (6-7) Carbonated: 𝐼𝑇𝑆 = (𝑈𝐶𝑆 − 1.20 0.0059 ) (6-8) It should also be noted that the ITS is an indirect test and the TRH13 (1986) suggests that:
𝐷𝑇𝑆 = 𝐼𝑇𝑆 1.5
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This relationship is considered when calculating the tensile strain resistance. The results of the steps involved in calculating this are presented in Table 6-2 (Steps 1-3). In addition, for sensitivity analysis, a range of UCS values (3-5.5MPa) are chosen as indicated taking cognisance of the fact that these higher UCS values are not typical for a C3 material and this should be considered further.
Table 6-2: Calculating the Pavement Life of the Cemented Subbase
To determine the pavement life, the typical fatigue relation for cemented materials (stipulated in the SAMDM) is used as the failure mechanism under consideration. The failure mechanism for the C3 layer is cracking at the bottom of the material layer due to horizontal tensile forces. Therefore, the tensile strain, positioned at the bottom of the layer, is used as the critical parameter for the subbase.
Non-Carbonated Carbonated Non-Carbonated Carbonated
3 205,71 182,86 267,25 27,75 3,5 277,14 254,29 333,04 93,54 4 348,57 325,71 398,83 159,33 4,5 420,00 397,14 464,62 225,12 5 491,43 468,57 530,41 290,91 5,5 562,86 540,00 596,20 356,70
Non-Carbonated Carbonated Non-Carbonated Carbonated
3 137,14 121,90 178,17 18,50 3,5 184,76 169,52 222,03 62,36 4 232,38 217,14 265,89 106,22 4,5 280,00 264,76 309,75 150,08 5 327,62 312,38 353,61 193,94 5,5 375,24 360,00 397,46 237,80
Non-Carbonated Carbonated Non-Carbonated Carbonated
3 0,82 0,62 1,34 0,00 3,5 1,42 1,23 1,85 0,06 4 1,96 1,79 2,30 0,44 4,5 2,43 2,29 2,69 0,98 5 2,83 2,71 3,02 1,53 5,5 3,17 3,06 3,31 2,02 UCS (MPa)
Step 2: Direct Tensile Strain (Microstrain) Grading Type
Step 3: Pavement Life (N x 10^6) Grading Type Continous Gap Continous Gap UCS (MPa) Continous Gap UCS (MPa)
Step 1: Indirect Tensile Strength (kPa) Grading Type
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The Fatigue relationship, for a Road Category B, is presented as follows:
𝑁 = 𝑆𝐹 𝑥 106,84(1−
𝜀
7.63𝜀𝑏) (6-10)
Where,
N = Estimated Design life for a Road Category B Sf = Shift factor due to layer thickness
e
= Tensile strain at bottom of the layer (calculated as142 microstrain) e
b = Strain at break, in this case as calculated for each scenarioIn the current exercise, the impact of carbonation on the pavement life of the subbase layer is considered only. Although a pavement structure should be considered in its entirety when calculating the pavement life, the objective of calculating these results is only to compare the subbase life in its “bound phase” of the non-carbonated versus carbonated RCA material. Therefore, the pavement life (reported in Step 3 of Table 6-2) should not be taken as absolute values but rather as comparative against each other and unique to the results of this research study. These results are illustrated in Figure 6-2 below, where “NC” represents non- carbonated and “C” represents carbonated.
Figure 6-2: Pavement Life of Non-Carbonated and Carbonated RCA Material of Subbase Layer These results indicate a significant drop in the pavement life for the gap grade RCA material as opposed to the continuous grade RCA material. In addition these results substantiate the findings of the lab results as well as in literature by Li (2012) which alludes to lightly cemented
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materials being more susceptible to carbonation. Assuming of course that a lower UCS is indicative of lighter cementing. These results suggest that the choice of grading of RCA material is imperative and that good controls should be implemented to ensure maximum packing of the particles in order to provide resistance as far as possible against carbonation.