Материал: Russian Journal of Building Construction and Architecture
Issue № 1(33), 2017 |
ISSN 2542-0526 |
data, i.e. values of Y obtained for experiments with different combinations of independent factors X1, X2, X3. The theory of experimental planning suggests that it is most reasonable to choose combinations of the parameters X1, X2, X3 called plans or points to be used for regression approximation of a function using experimental values of Y identified for the plans [5].
2. Experimental methods. A method of planning a complete factor experiment suplemented with a few plans in the centre of the variation area. Varying elements are the following factors: X1 is the content of a bituminous emulsion, %; Х2 is the content of cement, %; Х3 is the content of granular asphalt in the mineral part, % (Table 1). For all of the investigated characteristics of organic and mineral mixes, the mathematical model was searched for as a complete second-order polynomial of three variable with the removal of insignificant summands:
Y a0 b1x1 b2x2 b3x3 c1x1x2 c2x1x3 c3x2x3 d1x12 d2x22 d3x32 . (4)
In order to identify 10 initial parameters a0,bi,cj,dk for each of the characteristics Y three parallel series of 9 experiments were conducted. In each of the experiments there was a particular mix that was designed according to the guidelines of a complete factor experiment with three independent varying factors X1, X2, X3.
The plan of the experiment and levels of varying factors were determined using the results of the preliminary experiments.
As a response
Y Y(X1,X2,X3)
for each point (X1, X2, X3) of the plan of the experiment an arithmetic mean of the corresponding values of Y in three parallel series of the experiments. This improved the accuracy by 1.7 times. Changes in the factors of the experiment are ilustrated in Table 1.
Characteristics
Main level (X0i) Variation integral (Δi) Upper level (Хi max) 
Lower level (Хi min)
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Table 1 |
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Changes in three independent factors |
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Factors |
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Code |
X1, |
X2, |
X3, |
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content of a bitumi- |
content |
content of granular |
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nous emulsion, % |
of cement, % |
asphalt in the mineral part, % |
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0 |
5 |
3.5 |
35 |
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∆Х |
1.0 |
0.5 |
5 |
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Хi = +1 |
6.0 |
4.0 |
40 |
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Хi = 1 |
4.0 |
3.0 |
30 |
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The plan of the experiment and natural values of the variables in each point of the plan are presented in Table 2.
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Russian journal of building construction and architecture |
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Table 2 |
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Plan of the experiment and natural values of the variables |
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Number |
Plan of the experiment |
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Natural values of the variables |
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X1, |
X2, |
X3, |
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of the |
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Х1 |
Х2 |
Х3 |
content of a bitumi- |
content of ce- |
content of granular asphalt |
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plan |
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nous emulsion, % |
ment, % |
in the mineral part, % |
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1 |
–1 |
–1 |
–1 |
4.0 |
3.0 |
30 |
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2 |
+1 |
–1 |
–1 |
6.0 |
3.0 |
30 |
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3 |
–1 |
+1 |
–1 |
4.0 |
4.0 |
30 |
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4 |
+1 |
+1 |
–1 |
6.0 |
4.0 |
30 |
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5 |
–1 |
–1 |
+1 |
4.0 |
3.0 |
40 |
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6 |
+1 |
–1 |
+1 |
6.0 |
3.0 |
40 |
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7 |
–1 |
+1 |
+1 |
4.0 |
4.0 |
40 |
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8 |
+1 |
+1 |
+1 |
6.0 |
4.0 |
40 |
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9 |
0 |
0 |
0 |
5.0 |
3.5 |
35 |
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The major characteristics to be investigated were as follows:
–– the compressive strength limit at the temperature 20 ºС of dry samples following 7 days of solidification (R20, МPа) Y1;
––the compressive strength limit at the temperature 50 ºС of dry samples following 7 days of solidification (R50, МPа) Y2;
––the average density, g/сm3, Y3;
––swelling (Н, %) Y4;
––water saturation (W, %) Y5;
––the compressive strength limit at the temperature 20 ºС of water saturated samples follow-
ing 14 days of solidification (R20water, МPа) Y6;
––the compressive strength limit at the temperature 20 ºС of dry samples following 14 days of solidification (R20, МPа) Y7;
––the compressive strength limit at the temperature 50 ºС of dry samples following 14 days
of solidification (R50, МPа) Y8; –– water resistance (Кв) Y9.
The compositions of the mixes, investigated characteristics and their values obtained as a result of the experiments are presented in Table 3—4. In Table 4 in brackets there are the values identified according to the designed regression models.
The experiment found a range of the factors to obtain the compositions of the mixes with the best physical and mechanical properties: the content of granular asphalt is 40 % in the minral part, third-order bituminous emulsion is 4 %, and 3—4 % of cement in a complex binder. Ac-
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Issue № 1(33), 2017 |
ISSN 2542-0526 |
cording to these, the compositions were prepared to identify the properties of deformation and strength for road pavements.
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Table 3 |
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Compositions corresponding with 9 plans of the experiment |
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Material |
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Composition of a mix |
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№ 1 № 2 № 3 № 4 № 5 № 6 № 7 № 8 № 9 |
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Crushed stone |
12.50 |
12.50 |
12.50 |
12.50 |
3.50 |
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3.50 |
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3.50 |
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3.50 |
3.50 |
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fraction 15—20 mm |
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Crushed stone |
12.50 |
12.50 |
12.50 |
12.50 |
8.50 |
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8.50 |
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8.50 |
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8.50 |
8.50 |
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fraction 10—15 mm |
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Crushed stone |
15.00 |
15.00 |
15.00 |
15.00 |
18.00 |
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18.00 |
18.00 |
18.00 |
18.00 |
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fraction 5—10 mm |
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Siftings |
30.00 |
30.00 |
30.00 |
30.00 |
30.00 |
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30.00 |
30.00 |
30.00 |
35.00 |
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Granular asphalt |
30.00 |
30.00 |
30.00 |
30.00 |
40.00 |
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40.00 |
40.00 |
40.00 |
35.00 |
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Cement |
3.00 |
3.00 |
4.00 |
4.00 |
3.00 |
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3.00 |
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4.00 |
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4.00 |
3.50 |
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Water |
1.50 |
1.50 |
1.50 |
1.50 |
1.50 |
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1.50 |
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1.50 |
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1.50 |
1.50 |
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Emulsion |
4.00 |
6.00 |
4.00 |
6.00 |
4.00 |
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6.00 |
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4.00 |
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6.00 |
5.00 |
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Total |
108.50 |
110.50 |
109.50 |
111.50 |
108.50 |
110.50 |
109.50 |
111.50 |
110.00 |
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Table 4 |
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Results of the tests of the compositions corresponding with 9 plans of the experiment |
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Property |
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Mix |
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(time of solidification) |
№ 1 |
№ 2 |
№ 3 |
№ 4 |
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№ 5 |
№ 6 |
№ 7 |
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№ 8 |
№ 9 |
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Strength limit at 20 ºС, МPа |
1.66 |
1.25 |
1.72 |
1.95 |
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2.77 |
2.01 |
2.25 |
1.75 |
2.35 |
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(7 days) |
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(1.61) |
(1.29) |
(1.77) |
(1.90) |
(2.81) |
(1.96) |
(2.2) |
(1.8) |
(2.35) |
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Strength limit at 50 ºС, МPа |
1.35 |
0.64 |
1.30 |
0.79 |
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1.43 |
0.66 |
1.56 |
0.68 |
1.15 |
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(7 days) |
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(1.30) |
(0.69) |
(1.36) |
(0.75) |
(1.47) |
(0.64) |
(1.54) |
(0.71) |
(1.06) |
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Swelling, % |
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–0.69 |
–0.38 |
–0.88 |
–0.88 |
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0.01 |
–0.03 |
–0.22 |
–0.18 |
–0.02 |
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(14 days) |
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(0.56) |
(–0.43) |
(–0.84) |
(–0.76) |
(0.03) |
(0.11) |
(–0.23) (0.16) |
(–0.36) |
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Water saturation, % |
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2.89 |
2.70 |
3.42 |
3.42 |
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3.06 |
3.69 |
3.82 |
2.93 |
3.43 |
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(14 days) |
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(2.64) |
(2.98) |
(3.60) |
(3.27) |
(3.22) |
(3.56) |
(3.56) |
(2.82) |
(3.26) |
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Strength limit at 20 ºС |
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2.82 |
1.90 |
2.88 |
1.88 |
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2.65 |
2.12 |
2.44 |
2.18 |
2.28 |
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in the water saturated state, |
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(2.87) |
(1.86) |
(2.87) |
(1.96) |
(2.64) |
(2.19) |
(2.54) |
(2.19) |
(2.39) |
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МPа (14 days) |
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Strength limit at 20 ºС, МPа |
1.99 |
1.44 |
2.48 |
1.98 |
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2.44 |
1.97 |
2.69 |
1.99 |
2.84 |
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(14 days) |
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(2.07) |
(1.51) |
(2.58) |
(2.03) |
(2.56) |
(2.0) |
(2.69) |
(2.14) |
(2.2) |
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Strength limit at 50 ºС, МPа |
1.61 |
0.77 |
1.85 |
0.86 |
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1.46 |
0.85 |
1.97 |
1.03 |
1.61 |
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(14 days) |
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(1.61) |
(0.88) |
(1.89) |
(0.93) |
(1.52) |
(0.80) |
(1.98) |
(1.02) |
(1.33) |
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Water resistance |
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1.42 |
1.32 |
1.16 |
0.95 |
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1.09 |
1.07 |
0.91 |
1.09 |
0.80 |
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(1.44) |
(1.29) |
(1.13) |
(0.97) |
(1.04) |
(1.12) |
(0.96) |
(1.04) |
(0.8) |
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Note: in brackets are the values found according to the designed regression models.
43
Russian journal of building construction and architecture
The results of the experiment are identified in Table 5.
Deformation and strength properties of the compositions of organic and mineral mixes |
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Component composition of a |
Cement — 3 %, |
value |
Cement — 4 %, |
value |
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complex binder |
bituminous emulsion — 4 % |
bituminous emulsion — 4 % |
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Failure load, N |
3.5 |
3.6 |
3.7 |
3.9 |
4.4 |
4.0 |
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Average |
Average |
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Height of the sample, сm |
7.2 |
7.1 |
7.1 |
7.2 |
7.2 |
7.2 |
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Diameter of the sample, сm |
7.1 |
7.2 |
7.1 |
7.2 |
7.2 |
7.1 |
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Crack resistance using the |
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tensile for a crack at the tem- |
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perature |
0.69 |
0.70 |
0.73 |
0.71 |
0.75 |
0.85 |
0.78 |
0.79 |
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0 °С and deformation speed |
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50 mm/min, МPа |
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Failure load at 50 оС, N |
19.5 |
18.2 |
22.6 |
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18.4 |
20.4 |
17.3 |
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Time of loading, sec |
5 |
5.5 |
6.1 |
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6 |
5.5 |
7 |
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Loading speed, mm/min |
50 |
50 |
50 |
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50 |
50 |
50 |
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Average performance of the |
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deformation of the samples in |
2442.50 |
2502.50 |
3451.08 |
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2755.50 |
2807.75 |
3031.00 |
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the test using the Marshall |
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scheme, J |
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Failure load at 50 оС, N |
4.91 |
5.27 |
6.43 |
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9.5 |
8.5 |
8.5 |
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Time of loading, sec |
5 |
4.4 |
4 |
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4 |
3.9 |
3.9 |
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Loading speed, mm/min |
50 |
50 |
50 |
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50 |
50 |
50 |
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Average performance of the |
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deformation of the samples in |
613.75 |
579.70 |
643.00 |
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950.00 |
828.75 |
828.75 |
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the test for one-axial compres- |
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sion, J |
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Coefficient of the internal |
0.90 |
0.91 |
0.93 |
0.91 |
0.85 |
0.88 |
0.89 |
0.87 |
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friction |
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Compressive strength limit at |
1.23 |
1.32 |
1.61 |
1.39 |
2.38 |
2.12 |
2.12 |
2.21 |
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50 оС, МPа |
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Shear adhesion, МPа |
0.25 |
0.26 |
0.31 |
0.27 |
0.52 |
0.44 |
0.43 |
0.46 |
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Considering the influence of the components of a complex binder in the range of optimal values of the characteristics of organic and mineral mixes on the shear resistance, note that the coefficient of internal friction is insignificantly higher than for a smaller content of cement in a complex binder. As the content of cement in a complex binder goes up by 3 to 4 % per 100 % of the mineral part, the shear adhesion increases by 1.7 times. Crack resistance using the strength limit with a crack at the temperature 0 °С and the deformation speed of 50 mm/min in the range of optimal values of the characteristics of the compositions of organ-
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Issue № 1(33), 2017 |
ISSN 2542-0526 |
ic and mineral mixes is within 0.7—0.8 МPа. The effect of an extremely high content of cement per a unit is insignificant.
Conclusions
1.Water saturation of compositions in the investigated area ranges from 2.80 to 3.80 %, which corresponds with the range specified in the GOST (ГОСТ) 30491-2012. Smaller water saturation corresponds with a high content of a bituminous emulsion and an extremely low content of cement in a complex binder as well as granular asphalt in the mineral part.
2.The density of the samples in the investigated area of factors is within 2.35—2.38 g/secm3. Deviations of the characteristics are not significant. A smaller average density corresponds with compositions containing the upper boundary of granular asphalt. Thus a higher density corresponds with compositions containing the lower boundary of granular asphalt in the mineral part of a mix.
3.All of the investigated compositions are prone to swelling in the entire range of changes of the factors.
4.The strength of the compositions in the water saturated state is within 1.9—2.9 МPа. It is mostly affected by a composition of a complex binder and least by a content of granular asphalt in the mineral part of the mix. The best value of a characteristics corresponds with the investigated factors as follows:
–– content of granular asphalt is 40 % in the mineral part, –– that of third-class bituminous emulsion is 4 %,
–– that of cement is 3—4 % in a complex binder.
5.The major factor that influences the strength characteristics of an organic and mineral mix in the range of normal temperatures is the amount of a bituminous emulsion in the composition of a complex binder in the entire range of the investigated recipe characteristics allowing the strength to change from 1.4 to 2.7 МPа. This is also true following 7 as well as 14 days of solidification of the samples. A higher content of cement in a complex binder with a minimum content of an emulsion improves the characteristics. A higher content of granular asphalt in the mineral part has a more insignificant effect on changes in the characteristics.
6.The strength characteristics of an organic and mineral mix at higher temperatures depend on the amount of a bituminous emulsion in a complex binder in the entire range of the investigated factors, which changes the strength at the temperature 50 ºС of dry samples I nthe range of 0.8 to 2.0 МPа. A higher value of the characteristics corresponds with the upper boundary of a content of cement in a complex binder as well as a higher amount of granular asphalt in the mineral part of an organic and mineral mix.
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