of aggregate (VG), the excess paste (VPE) which covers aggregates
and the compact paste (VPC) which fill the voids of the skeleton that
can be extracted separately.
Hypothesis #2. The thickness of the excess paste layer is
negligible when compared to the size of the coarse aggregate.
Thus, the presence of this excess paste layer does not influence the
void volume among the grains of aggregate (intergranular air void).
This void will be filled with the compact paste (Fig. 2). Thus, the
volume of compact paste VPC is considered equally to the volume of
space between dry and compacted grains aggregate VV.
Considering a dry, compacted volume of aggregate Vtotal, the
volume of compact paste VPC can be calculated as:
VPC ¼ VV ¼ Vtotal VG ð1Þ
VPC ¼
VG
c VG ¼ VG
1 c
c ð2Þ
Eq. (2) allows determining the volume of compact paste from
the volume of gravel in the concrete matrix, which can also be
written as:
VPC ¼ Vtotal VG ¼
mG
qdry;compacted
mG
qspecify ð3Þ
VPC ¼
VG qspecify
qdry;compacted VG ¼ VG
qspecify
qdry;compacted 1! ð4Þ
On the other hand, it is noted that the sum of volumes of
cement paste VP, of granular solid VG, of the water retained by
the aggregate VW/G and of the voids VV form a unit volume of
pervious concrete:
VP þ VG þ VW=G þ VV ¼ 1 ð5Þ
where VP ¼ VPE þ VPC ð6Þ
Then VPE þ VPC þ VG þ VW=G þ VV ¼ 1 ð7Þ
For a given particle size, the volume of aggregates larger than
80 lm VG>80 is related to the total volume of the aggregate VG by
the factor ‘‘a’’:
VG>80 ¼ VG a ð8Þ
with a 6 1.
VG>80 is the volume of aggregates larger than 80 lm, which is
surrounded by the suspension consisting of cement paste and fine
smaller than 80 lm. In fact, the aggregate can be decomposed into
two parts depending on the size of the particles. The first part composes
the fines, smaller than 80 lm, and they are in the same order
size of the solid components in the cement paste (cement and filler).
The second part is thus formed by aggregates larger than
80 lm, denoted as G > 80. This threshold value (80 lm) allows considering
that smaller particles cover the larger particles. In the calculation
of the thickness of the paste in excess, it is assumed that
the paste consists only of particles of size smaller than 80 lm.
Thus the total volume of aggregates VG is written:
VG ¼ Vfines þ VG>80 ð9Þ
Similarly, the volume of water absorbed VW/G is proportional to
the total aggregate through an absorption coefficient of aggregate
‘‘b’’, and it is determined using Eq. (10):