Civil Engineering Reference
In-Depth Information
Total volume V2
¼
8
1
1
1
¼
8m3
ðÞ
Total surface area S2
¼
8
6
1
1
¼
48 m3
ðÞ
Calculation result V2
¼
V1
S2
¼
2S1
Thus, if the side length of a cube is reduced by half, the total volume is the same,
but the total surface area increases by one time.
Similar calculations have also been conducted to other polygons and spheres,
and the results are the same, which are good supplement to SSA theory. However,
Professor Ding Kangshe had proven that this method is only suitable for cube and
sphere rather than cuboid and other irregular objects. Therefore, if it is to be used in
practical engineering, further studies are needed to be conducted by others [
1
].
1.1.2 Maximum Density Method
The core of this method is that the sand and stone consisting the concrete should
firstly have reasonable grading so as to obtain the maximum density and minimum
void content for content. Lots of voids would be caused within concrete if the
particle grading of coarse aggregate,
fine aggregate, and cement is unreasonable. As
a result, the optimum grading and maximum density of various particles comprising
the concrete should be determined to guarantee the minimum void content in
concrete. How to guarantee the maximum density and the minimum void content?
The answer is mainly according to continuous grading theory of Fuller; the equation
can be expressed as Formula (
1.1
):
p
d=D
P ¼
100
ð
1
:
1
Þ
In Formula,
P
Percentage passing certain sieve, %;
D
Maximum particle size, mm; and
D
Pore size of sieve, mm
The Fuller grading curve can be expressed by Formula (
1.1
). Although the Swiss
scholar Bolomey and France scholar Feref had adjusted it according to practical
situation, the grading curve did not change radically.
In order to meet optimum grading requirement of
fine and coarse aggregate for
high-performance concrete and self-compacting concrete, Italian scholar Talbot
modi
ed the Fuller continuous grading formula to the form of Formula (
1.2
):
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