According to concept of van de Ven et al. (2003), an SMA mixture probably has no real stone skeleton immediately after compaction. A real skeleton in SMA is created during service under the effects of traffic and climatic loading when sand and filler grains between the coarse aggregates (skeleton) may be crushed or moved. Accordingly, at the design stage, the content of fine aggregate and filler must be determined.
Cause-and-effect relationships between the filler and the fine aggregate (crushed sand) have not been determined in a design method. Some Dutch research into this has led to establishing the optimal relationship between those elements. Research on sand-filler mixes and the filling and replacing effects occurring between them have been elaborated on in a Dutch publication (Voskuilen, 2000). This effect is shown in Figure 7.13; its description is as follows:
• The compacted fine aggregate (crushed sand) contains a quantity of air voids.
• As filler (particles smaller than 0.063 mm) is gradually added, it fills the air voids in the sand, and the voids in the sand-filler mix get smaller. This is the filling-stage; the existing skeleton of the mix is made of sand (the shaded area in Figure 7.13);
• The decrease of air voids continues until the voids in the sand are completely filled (reaching the minimum possible); then only air voids in the filler remain;
• The further addition of filler with a simultaneous decrease in the amount of sand causes a gradual increase of air voids in the mix. This is the replacement stage; the existing skeleton of the mix is made of filler (the clear area in Figure 7.13), and grains of sand are being shoved aside by filler particles.
We have found the root of the aformentioned effect—after all, it accompanies the supplementing of fine aggregate to coarse grains in SMA—from the gradual
decrease of air voids, through the void’s minimum, up to the gradual skeleton opening (as described in Chapter 6 in Section 6.2.3 on binary systems).
Looking at the form of the example in Figure 7.13, which shows the connection between the filler quantity and the content of air voids, we can observe that the rate of decrease of air voids is faster in the filling phase than its increase in the replacement phase. Thus, in the case of necessary adjustments to the content of air voids, a change in the sand fraction content will produce a stronger effect than will altering the filler content (leaving the chipping fraction unchanged) (Voskuilen, 2000).
According to Dutch research (Voskuilen, 2000), the recommended ratio of the quantity of fine aggregate (sand) to the quantity of filler amounts is 65:35 (m/m). If the filler density is about 2.700 g/cm3 and the density of crushed sand is about 2.650 g/cm3, this proportion may be employed without recalculation. Mass proportions should be converted into volume proportions in cases of significant deviations from these density values.
We were aware of air voids among coarse aggregate some time ago; now that we have set the sand-filler ratio, we can determine the total mastic volume in the SMA. The mastic volume is calculated according to the formula (Voskuilen, 2000)
pb pf ps pa
mb = Binder mass, % (m/m)
pb = Binder density, g/cm3
mf = Filler mass, % (m/m)
pf = Filler density, g/cm3
ms = Sand fraction mass, % (m/m)
ps = Sand fraction density, g/cm3
ma = Stabilizer (drainage inhibitor) mass, % (m/m)
pa = Stabilizer (drainage inhibitor) density, g/cm3
The filling ratio stone skeleton (FRs) is used in the Dutch method to determine the theoretical degree of filling of the air voids in the coarse-aggregate skeleton with mastic (i. e., for investigating whether the design mastic volume is an optimal one). FRs is defined with the formula
V — V
FRs = -^—^ -100%
Vs
FRs = Percentage ratio of filling the coarse-aggregate skeleton with mastic, % (v/v)
Vm = Mastic volume, % (v/v)
Vs = Air voids in the compacted coarse-aggregate skeleton, % (v/v)
Air voids in the compacted coarse-aggregate skeleton (Vs) are calculated using the formula
Vs = pg pg -100% pg
pg = Density of the coarse aggregate fraction, g/cm3
pb = Bulk density of the coarse aggregate fraction compacted in a gyratory compactor with a lubricating agent, g/cm3
The assessment of FRs ratio is as follows:
FRs < 0 implies that the air voids are not filled with enough mastic.
FRs = 0 implies that the air voids are filled with the mastic.
FRs > 0 implies that the air voids are overfilled with mastic.
For every SMA design, the FRs ratio should not exceed 0. One should remember that this is a theoretical factor and does not take into consideration the enlarging effect of the increasing air voids in the coarse-aggregate skeleton. Due to this, compacted SMA mixtures with air void contents of 4-5% (v/v) can all be marked by FRs = -4 (Jacobs and Voskuilen, 2004). It is easy to see that the content of the coarse-aggregate fraction and the size of air voids in the coarse-aggregate skeleton are dependent on the FRs level.
