Analogue material with appropriate properties is of great importance to the reliability of geomechanical model test, which is one of the mostly used approaches in field of geotechnical research. In this paper, a new type of analogue material is developed, which is composed of coarse aggregate (quartz sand and/or barite sand), fine aggregate (barite powder), and cementitious material (anhydrous sodium silicate). The components of each raw material are the key influencing factors, which significantly affect the physical and mechanical parameters of analogue materials. In order to establish the relationship between parameters and factors, the material properties including density, Young’s modulus, uniaxial compressive strength, and tensile strength were investigated by a series of orthogonal experiments with hundreds of samples. By orthogonal regression analysis, the regression equations of each parameter were obtained based on experimental data, which can predict the properties of the developed analogue materials according to proportions. The experiments and applications indicate that sodium metasilicate cemented analogue material is a type of low-strength and low-modulus material with designable density, which is insensitive to humidity and temperature and satisfies mechanical scaling criteria for weak rock or soft geological materials. Moreover, the developed material can be easily cast into structures with complex geometry shapes and simulate the deformation and failure processes of prototype rocks.
Geomechanical model test is one of the most widely used approaches in field of geotechnical and geology research [
Analogue materials research started in Europe. In the 1960s, Fumagalli [
Generally, analogue materials can be divided into two types, organic cementitious materials and inorganic cementitious materials, and can be further subdivided into more than a dozen subclasses, shown in Figure
Classification of analogue materials for rock [
According to Indraratna’s suggestions [
Geomechanical model test is built on strict similarity law, which should satisfy simulated condition based on equilibrium equations, geometric equations, physical equations, boundary conditions, and displacement conditions [
Although scholars have tried many material preparation methods, most of them cannot satisfy mechanical scaling criteria for weak rock or soft geological materials, or some incur high cost, are complex, and offer low controllability of mechanical properties. Therefore, a new type of analogue material that meets excellent analogue material’s specifications should be developed.
In this paper, we present a type of material with high density, low strength and Young’s modulus, easy mouldability, and good stability, which can simulate weak rock or soft geological materials. In order to investigate the properties of the proposed material, orthogonal experiments are conducted and relationships between the physicomechanical properties of the analogue material and influencing factors are established by regression analysis.
Sodium silicate sand is a type of material used to make moulds and is widely used in the casting industry. However, the silicate content of sodium silicate cannot be accurately controlled and lead to a wide variation range of material properties. Therefore, sodium metasilicate solution is used here to allow control of the silicate content.
Sodium metasilicate often contains water of crystallisation and thus forms sodium metasilicate pentahydrate, or sodium metasilicate nonahydrate, but all these compounds have a low water solubility. Therefore, anhydrous sodium silicate powder was used as the raw material, because of its high water solubility. Sodium metasilicate can react with CO2 and harden, but the hardening process is slow, and what is worse is that a hardened layer will form on the surface and prevent the full reaction of the inner parts. Therefore, sodium fluorosilicate was used as a curing agent to accelerate the process.
The chemical formula for sodium fluorosilicate is Na2SiF6: which has a low water solubility and can be mixed with aggregate. Then it is stirred with the sodium metasilicate solution, after which it starts to harden. Specimens were made by casting the unset mixture into a mould and allowing it to harden.
The chemical reaction between sodium metasilicate and sodium fluorosilicate is
There are two reaction products: NaF and Si(OH)4. NaF will separate out from the solution. As shown in Figure
Growth of colloidal particle and gelatinization [
Analogue materials have different characteristics as a result of the differences in aggregates and cementitious materials used [
The raw materials were anhydrous sodium silicate, sodium fluorosilicate, quartz sand, barite sand, barite powder, and water. Anhydrous sodium silicate and sodium fluorosilicate are both pure granular materials; the sizes of quartz and barite and sand grains were 0.6 to 1.18 mm; and the sizes of the barite powder grains were 0.06 to 0.1 mm.
Therefore, material proportion can be determined by four coefficients:
Levels of each factor.
Level | Factor | |||
---|---|---|---|---|
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| |
1 | 40% | 0 | 1% | 1/4 |
2 | 50% | 1/3 | 3% | 2/4 |
3 | 60% | 2/3 | 5% | 3/4 |
4 | 70% | 1 | 7% | 4/4 |
The proportions of raw materials of each group.
Number | Factors | |||
---|---|---|---|---|
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|
|
| |
1 | 40% | 0 | 1% | 1/4 |
2 | 40% | 1/3 | 3% | 2/4 |
3 | 40% | 2/3 | 5% | 3/4 |
4 | 40% | 1 | 7% | 4/4 |
5 | 50% | 0 | 3% | 3/4 |
6 | 50% | 1/3 | 1% | 4/4 |
7 | 50% | 2/3 | 7% | 1/4 |
8 | 50% | 1 | 5% | 2/4 |
9 | 60% | 0 | 5% | 4/4 |
10 | 60% | 1/3 | 7% | 3/4 |
11 | 60% | 2/3 | 1% | 2/4 |
12 | 60% | 1 | 3% | 1/4 |
13 | 70% | 0 | 7% | 2/4 |
14 | 70% | 1/3 | 5% | 1/4 |
15 | 70% | 2/3 | 3% | 4/4 |
16 | 70% | 1 | 1% | 3/4 |
A four-factor, four-level test scheme was designed according to the orthogonal table
According to Tables
In order to ensure the repeatability of tests [ Weighing (shown in Figure Agitation (shown in Figure Casting (shown in Figure Stripping (shown in Figure Curing: The curing serves several purposes: to accelerate the development of material strength and to prevent cracking, shrinkage, and damage, which are caused by drying, temperature changes, and other natural factors. Specimens should be conserved under standard curing for 28 days.
Weighing.
Agitation.
Casting.
Stripping.
Mechanical testing programme was carried out on pressing machine with the rate of displacement 0.02 mm/min.
In order to investigate the uniaxial compressive strength (UCS) (Figure
Uniaxial compressive strength test.
The stress-strain curves from Group 3 are shown in Figure
Uniaxial compressive stress-strain plots: Group 3.
Besides, the curves of uniaxial compressive stress and strain from Group 7 are shown in Figure
Uniaxial compressive stress-strain plots: Group 7.
Young’s modulus can be calculated as the following:
In order to investigate the tensile strength, 16 groups of flattened Brazilian disk tests (Figure
Flattened Brazilian disk test or tensile splitting test.
According to Wang and Wu’s suggestions [
Flattened Brazilian disk specimen subjected to uniform diametral compression [
The load-time curves for the flattened Brazilian disk specimen used for the determination of rock tensile strength are shown in Figure
Load-time curve: Brazilian disk specimen used for the determination of rock tensile strength.
Experimental results including the data of density, Young’s modulus, uniaxial compression strength, and Brazil splitting strength were listed in the Appendix.
The total effect function of all factors can be expressed as the sum of each factor effect:
Regression coefficient
Using the following formula, the level of each factor is changed to a standard isometric point:
There were four level tests, and
The regression coefficients are calculated by using (
To establish the optimal regression equation and the effect of the factors on the significance of the decision and to determine the significance of the regression coefficients, first of all, the sum of the squares variation of regression coefficients was evaluated, followed by an
The numbers of degrees of freedom are
The density index results are listed in the Appendix (Tables
Test scheme and density index results.
Test ID |
|
|
|
|
Density (g/cm3) | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Fine aggregate : coarse aggregates | Barite sand : quartz sand | Anhydrous sodium silicate : aggregates | Anhydrous sodium silicate : sodium fluorosilicate | 1 | 2 | 3 | 4 | 5 |
|
| |
1 |
|
2.0281 | 2.0411 | 2.0299 | 2.0288 | 2.0836 | 10.2116 | 2.0423 | |||
2 | 2.2802 | 2.2863 | 2.3439 | 2.2448 | 2.3126 | 11.4679 | 2.2936 | ||||
3 | 2.2938 | 2.4721 | 2.4567 | 2.4771 | 2.4946 | 12.1943 | 2.4389 | ||||
4 | 2.5172 | 2.5123 | 2.5198 | 2.5068 | 2.5051 | 12.5612 | 2.5122 | ||||
5 | 2.1153 | 2.1581 | 2.2020 | 2.1711 | 2.1674 | 10.8140 | 2.1628 | ||||
6 | 2.0465 | 2.0597 | 2.0800 | 2.0628 | 2.0517 | 10.3007 | 2.0601 | ||||
7 | 2.3080 | 2.3233 | 2.3008 | 2.3092 | 2.3218 | 11.5631 | 2.3126 | ||||
8 | 2.4797 | 2.4663 | 2.4623 | 2.4667 | 2.4930 | 12.3680 | 2.4736 | ||||
9 | 2.1763 | 2.1450 | 2.1829 | 2.1589 | 2.2079 | 10.8709 | 2.1742 | ||||
10 | 2.2912 | 2.2646 | 2.2476 | 2.2847 | 2.2481 | 11.3362 | 2.2672 | ||||
11 | 2.3146 | 2.3397 | 2.3352 | 2.3891 | 2.3533 | 11.7318 | 2.3464 | ||||
12 | 2.5032 | 2.4217 | 2.4908 | 2.4023 | 2.5109 | 12.3289 | 2.4658 | ||||
13 | 2.1848 | 2.1992 | 2.1698 | 2.1704 | 2.1606 | 10.8847 | 2.1769 | ||||
14 | 2.2467 | 2.2568 | 2.2963 | 2.2503 | 2.2876 | 11.3377 | 2.2675 | ||||
15 | 2.1576 | 2.1905 | 2.2248 | 2.2061 | 2.1538 | 10.9328 | 2.1866 | ||||
16 | 2.2303 | 2.2552 | 2.2518 | 2.2404 | 2.2814 | 11.2734 | 2.2547 | ||||
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46.4385 | 42.7810 | 43.5175 | 45.4525 |
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45.0570 | 44.4420 | 45.5440 | 46.4525 | |||||||
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46.2680 | 46.4340 | 46.7710 | 45.6180 | |||||||
|
44.4285 | 48.5315 | 46.3560 | 44.6655 |
Orthogonal polynomial regression analysis of variance: density index.
The source of variance | Square and variation | Degree of freedom | Variance estimate |
|
|
Level of significance | Remarks |
---|---|---|---|---|---|---|---|
|
5.8057 × 10−2 | 1 | 5.8057 × 10−2 | 28.70 | 4 |
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2.6220 × 10−3 | 1 | 2.6220 × 10−3 | 1.30 |
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7.9609 × 10−2 | 1 | 7.9609 × 10−2 | 39.36 |
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|
9.2578 × 10−1 | 1 | 9.2578 × 10−1 | 457.67 |
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2.3817 × 10−3 | 1 | 2.3817 × 10−3 | 1.18 |
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2.3729 × 10−1 | 1 | 2.3729 × 10−1 | 117.31 |
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|
7.4512 × 10−2 | 1 | 7.4512 × 10−2 | 36.84 |
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|
2.5528 × 10−2 | 1 | 2.5528 × 10−2 | 12.62 |
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|
4.7653 × 10−2 | 1 | 4.7653 × 10−2 | 23.56 |
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|
7.3659 × 10−3 | 1 | 7.3659 × 10−3 | 3.64 |
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||
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|||||||
Error | 1.3957 × 10−2 | 69 | 2.0228 × 10−3 |
According to (
The variance estimates of the error effect can be written as
As shown in Table
Regression analysis gives the optimal regression equation as
There were four levels (
Test scheme and Young’s modulus index results.
Test ID |
|
|
|
|
Young’s modulus (MPa) | ||||
---|---|---|---|---|---|---|---|---|---|
Fine aggregate : coarse aggregates | Barite sand : quartz sand | Anhydrous sodium silicate : aggregates | Anhydrous sodium silicate : sodium fluorosilicate | 1 | 2 | 3 |
|
| |
1 |
|
21.8962 | 27.963 | 19.646 | 69.5052 | 23.1684 | |||
2 | 61.9473 | 93.1975 | 77.4981 | 232.6428 | 77.5476 | ||||
3 | 120.2802 | 100.0844 | 103.2362 | 323.6007 | 107.8669 | ||||
4 | 159.9495 | 173.4145 | 174.1913 | 507.5553 | 169.1851 | ||||
5 | 22.2968 | 27.2367 | 21.1451 | 70.6785 | 23.5595 | ||||
6 | 23.5181 | 15.346 | 15.5944 | 54.4584 | 18.1528 | ||||
7 | 74.0988 | 65.8336 | 72.6667 | 212.5992 | 70.8664 | ||||
8 | 69.1296 | 56.8568 | 98.6768 | 224.6631 | 74.8877 | ||||
9 | 102.5573 | 111.2596 | 68.2513 | 282.0681 | 94.0227 | ||||
10 | 89.7668 | 100.6273 | 123.138 | 313.5321 | 104.5107 | ||||
11 | 16.2539 | 8.0914 | 9.5063 | 33.8514 | 11.2838 | ||||
12 | 11.1586 | 11.443 | 11.9502 | 34.5519 | 11.5173 | ||||
13 | 37.2454 | 50.4401 | 38.6258 | 126.3114 | 42.1038 | ||||
14 | 19.3454 | 16.8179 | 12.8439 | 49.0071 | 16.3357 | ||||
15 | 30.0612 | 35.9429 | 34.9628 | 100.9671 | 33.6557 | ||||
16 | 10.7866 | 10.395 | 10.6829 | 31.8645 | 10.6215 | ||||
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1133.304 | 548.5632 | 189.6795 | 365.6634 |
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||||
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562.3992 | 649.6404 | 438.8403 | 617.4687 | |||||
|
664.0035 | 671.0184 | 879.339 | 739.6758 | |||||
|
308.1501 | 798.6348 | 1159.998 | 945.0489 |
Orthogonal polynomial regression analysis of variance: Young’s modulus index.
The source of variance | Square and variation | Degree of freedom | Variance estimate |
|
|
Level of significance | Remarks |
---|---|---|---|---|---|---|---|
|
2.3480 × 104 | 1 | 2.3480 × 104 | 138.39 | 4.13 |
|
|
|
9.6348 × 102 | 1 | 9.6348 × 102 | 5.68 |
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5.3201 × 103 | 1 | 5.3201 × 103 | 31.36 |
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2.4806 × 103 | 1 | 2.4806 × 103 | 14.62 |
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1.4674 × 101 | 1 | 1.4674 × 101 | 0.09 |
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1.4405 × 102 | 1 | 1.4405 × 102 | 0.85 |
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4.6801 × 104 | 1 | 4.6801 × 104 | 275.85 |
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2.0670 × 101 | 1 | 2.0670 × 101 | 0.12 |
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5.1386 × 102 | 1 | 5.1386 × 102 | 3.03 |
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1.4421 × 104 | 1 | 1.4421 × 104 | 85.00 |
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4.4916 × 101 | 1 | 4.4916 × 101 | 0.26 |
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1.8862 × 102 | 1 | 1.8862 × 102 | 1.11 |
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|||||||
Error | 5.9382 × 103 | 35 | 1.6966 × 10−2 |
To establish the optimal regression equation, it was important to judge the significance level of each factor, and to determine the significance of the regression coefficient, firstly, the regression coefficient of the variation of the squared sum was found, and then an
According to (
The results are listed in Table
Regression analysis gives the optimal regression equation as
The UCS results are listed in the Appendix (Tables
Test scheme and compressive strength index results.
Test ID |
|
|
|
|
Compressive strength (MPa) | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Fine aggregate : coarse aggregates | Barite sand : quartz sand | Anhydrous sodium silicate : aggregates | Anhydrous sodium silicate : sodium fluorosilicate | 1 | 2 | 3 | 4 | 5 |
|
| |
1 |
|
0.2949 | 0.2984 | 0.2188 | 0.1995 | 0.2912 | 1.3028 | 0.2606 | |||
2 | 0.5785 | 0.5832 | 0.7068 | 0.5723 | 0.6511 | 3.0918 | 0.6184 | ||||
3 | 2.5366 | 2.7429 | 2.4855 | 2.6060 | 2.7399 | 13.1110 | 2.6222 | ||||
4 | 4.1403 | 3.6729 | 4.7884 | 4.0876 | 4.5456 | 21.2348 | 4.2470 | ||||
5 | 0.5408 | 0.4813 | 0.6027 | 0.4228 | 0.5529 | 2.6005 | 0.5201 | ||||
6 | 0.1228 | 0.1549 | 0.1706 | 0.2080 | 0.1592 | 0.8155 | 0.1631 | ||||
7 | 1.7678 | 1.5183 | 1.5102 | 1.4143 | 1.9126 | 8.1232 | 1.6246 | ||||
8 | 0.9976 | 1.0144 | 1.0713 | 0.8484 | 0.9594 | 4.8912 | 0.9782 | ||||
9 | 1.3242 | 1.1996 | 1.9182 | 1.9821 | 2.0006 | 8.4247 | 1.6849 | ||||
10 | 2.3129 | 1.6285 | 1.8888 | 2.4849 | 1.3878 | 9.7029 | 1.9406 | ||||
11 | 0.2654 | 0.1876 | 0.2182 | 0.2508 | 0.2150 | 1.1370 | 0.2274 | ||||
12 | 0.2049 | 0.1392 | 0.2293 | 0.1864 | 0.2427 | 1.0026 | 0.2005 | ||||
13 | 0.8433 | 0.8210 | 0.7965 | 0.8615 | 0.8251 | 4.1475 | 0.8295 | ||||
14 | 0.3936 | 0.3880 | 0.3782 | 0.3416 | 0.3835 | 1.8849 | 0.3770 | ||||
15 | 0.3292 | 0.4720 | 0.5058 | 0.3780 | 0.4433 | 2.1284 | 0.4257 | ||||
16 | 0.2533 | 0.1871 | 0.2265 | 0.2256 | 0.2369 | 1.1294 | 0.2259 | ||||
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38.7404 | 16.4755 | 4.3847 | 12.3135 |
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16.4304 | 15.4951 | 8.8233 | 13.2675 | |||||||
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20.2672 | 24.4996 | 28.3118 | 26.5438 | |||||||
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9.2902 | 28.258 | 43.2084 | 32.6034 |
Orthogonal polynomial regression analysis of variance: compressive strength index.
The source of variance | Square and variation | Degree of freedom | Variance estimate |
|
|
Level of significance | Remarks |
---|---|---|---|---|---|---|---|
|
1.7856 × 101 | 1 | 1.7856 × 101 | 245.48 | 4 |
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1.6055 × 100 | 1 | 1.6055 × 100 | 22.07 |
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4.1944 × 100 | 1 | 4.1944 × 100 | 57.66 |
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4.9177 × 100 | 1 | 4.9177 × 100 | 67.61 |
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2.8070 × 10−1 | 1 | 2.8070 × 10−1 | 3.86 |
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5.7996 × 10−1 | 1 | 5.7996 × 10−1 | 7.97 |
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4.6213 × 101 | 1 | 4.6213 × 101 | 635.31 |
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1.3671 × 10 | 1 | 1.3671 × 10 | 18.79 |
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9.6450 × 10−1 | 1 | 9.6450 × 10−1 | 13.26 |
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1.3744 × 101 | 1 | 1.3744 × 101 | 188.95 |
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3.2584 × 10−1 | 1 | 3.2584 × 10−1 | 4.48 |
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9.5443 × 10−1 | 1 | 9.5443 × 10−1 | 13.12 |
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|||||||
Error | 4.8736 × 100 | 67 | 7.2740 × 10−2 |
To establish the optimal regression equation, it was important to judge the significance level of each factor, and to determine the significance of the regression coefficient, firstly, the regression coefficient of the variation of the squared sum was evaluated, and then an
According to (
The results are listed in Table
Thus the optimal regression equation was
Tensile strengths and the regression coefficients are listed in the Appendix, Table
Test scheme and tensile strength index results.
Test ID |
|
|
|
|
Tensile strength (MPa) | |||||
---|---|---|---|---|---|---|---|---|---|---|
Fine aggregate : coarse aggregates | Barite sand : quartz sand | Anhydrous sodium silicate : aggregates | Anhydrous sodium silicate : sodium fluorosilicate | 1 | 2 | 3 | 4 |
|
| |
1 |
|
0.0973 | 0.0976 | 0.0895 | 0.0949 | 0.3793 | 0.0948 | |||
2 | 0.1949 | 0.1903 | 0.1917 | 0.2078 | 0.7847 | 0.1962 | ||||
3 | 0.7546 | 0.6716 | 0.7655 | 0.7924 | 2.9841 | 0.7460 | ||||
4 | 0.9333 | 0.8623 | 0.8947 | 0.8466 | 3.5370 | 0.8842 | ||||
5 | 0.1382 | 0.1207 | 0.1675 | 0.1755 | 0.6019 | 0.1505 | ||||
6 | 0.0459 | 0.0407 | 0.0492 | 0.0406 | 0.1763 | 0.0441 | ||||
7 | 0.6694 | 0.5585 | 0.4850 | 0.5193 | 2.2322 | 0.5581 | ||||
8 | 0.2910 | 0.2140 | 0.2459 | 0.2622 | 1.0132 | 0.2533 | ||||
9 | 0.4919 | 0.5025 | 0.5248 | 0.4561 | 1.9752 | 0.4938 | ||||
10 | 0.6960 | 0.5942 | 0.5703 | 0.5589 | 2.4193 | 0.6048 | ||||
11 | 0.0945 | 0.0891 | 0.0888 | 0.0932 | 0.3656 | 0.0914 | ||||
12 | 0.0698 | 0.0647 | 0.0597 | 0.0624 | 0.2565 | 0.0641 | ||||
13 | 0.2543 | 0.2770 | 0.2880 | 0.2876 | 1.1069 | 0.2767 | ||||
14 | 0.1137 | 0.1052 | 0.1032 | 0.1177 | 0.4397 | 0.1099 | ||||
15 | 0.1404 | 0.1426 | 0.1388 | 0.1406 | 0.5625 | 0.1406 | ||||
16 | 0.0603 | 0.0680 | 0.0558 | 0.0651 | 0.2492 | 0.0623 | ||||
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7.6851 | 4.0633 | 1.1704 | 3.3077 | ||||||
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4.0236 | 3.82 | 2.2056 | 3.2704 | ||||||
|
5.0166 | 6.1444 | 6.4122 | 6.2545 | ||||||
|
2.3583 | 5.0559 | 9.2954 | 6.251 |
To establish the optimal regression equation and the effect of the factors on the significance of the decision and to determine the significance of the regression coefficient, firstly, the regression coefficient of the variation of the squared sum was evaluated, and then an
Orthogonal polynomial regression analysis of variance: tensile strength index.
The source of variance | Square and variation | Degree of freedom | Variance estimate |
|
|
Level of significance | Remarks |
---|---|---|---|---|---|---|---|
|
7.0194 × 10−1 | 1 | 7.0194 × 10−1 | 438.56 | 4 |
|
|
|
1.5725 × 10−2 | 1 | 1.5725 × 10−2 | 9.82 |
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|
2.1558 × 10−1 | 1 | 2.1558 × 10−1 | 134.69 |
|
|
|
|
8.7854 × 10−2 | 1 | 8.7854 × 10−2 | 54.89 |
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|
1.1162 × 10−2 | 1 | 1.1162 × 10−2 | 6.97 |
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|
1.1177 × 10−1 | 1 | 1.1177 × 10−1 | 69.83 |
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|
2.5528 × 100 | 1 | 2.5528 × 100 | 1594.97 |
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5.3361 × 10−2 | 1 | 5.3361 × 10−2 | 33.34 |
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6.3135 × 10−2 | 1 | 6.3135 × 10−2 | 39.45 |
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|
4.3616 × 10−1 | 1 | 4.3616 × 10−1 | 272.50 |
|
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|
1.7851 × 10−5 | 1 | 1.7851 × 10−5 | 0.01 |
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||
|
1.1284 × 10−1 | 1 | 1.1284 × 10−1 | 70.50 |
|
|
|
|
|||||||
Error | 8.1629 × 10−2 | 51 | 1.6006 × 10−3 |
For the tensile strength, the order of importance (decreasing) was
Thus the optimal regression equation was
This analogue material was applied in a model test that investigated the reinforcement effect on the upper part of the tunnel. In the model, the parameters of analogue material were determined by surrounding rock that was weak or soft rock in the prototype.
According to the method of analogue material preparation and the similarity laws for geomechanical models, analogue materials may be prepared by controlling the mechanical parameters of the materials.
Based on the scaling criterion, the scale factors for stress, length, and bulk density of a material have a determinate relationship [
Given the scale factor for bulk densities is unity, the relationship can be transformed to [
Therefore, the scales of mechanical parameters match the geometrical scale.
The geometric similarity ratio can be set based on the relevant scale of the model and the prototype: a value of 100 was chosen here. Therefore, the corresponding mechanical parameters of the model or analogue materials can be calculated according to the similarity law and the parameters of the prototype material.
Then the range of each mechanical parameter of the objective material was calculated (Table
The range of mechanical parameters of objective and prototype materials.
Density (g/cm3) | Young’s modulus (GPa) | Compressive strength (MPa) | Tensile strength (MPa) | |
---|---|---|---|---|
1# prototype material | 2.800~2.900 | 20~35 | 500~1000 | 140~150 |
1# objective material | 2.800~2.900 | 0.20~0.35 | 5~10 | 1.4~1.5 |
1# prototype material | 2.100~2.200 | 3~4 | 20~40 | 10~20 |
2# objective material | 2.100~2.200 | 0.03~0.04 | 0.2~0.4 | 0.1~0.2 |
According to the raw material configuration (Table
Raw material configurations and the measured mechanical indices of analogue materials.
Material ID | Raw material configuration | Measured mechanical index | |||||
---|---|---|---|---|---|---|---|
|
|
|
Density |
Young’s modulus |
Compressive strength (MPa) | Tensile strength | |
1# analogue material | 30% | 50% | 3% | 2.855 | 0.286 | 6.058 | 1.469 |
2# analogue material | 65% | 00% | 3% | 2.181 | 0.035 | 0.315 | 0.180 |
Note: the mass ratio of sodium fluorosilicate to anhydrous sodium silicate was 3 : 4 (this was the optimal value).
Subsequently, number 2 analogue material was applied in a geomechanical model test which investigated the antistrike property of reinforcement layer on the top of tunnel. Some photographs of the specimens made of number 2 analogue material have been shown in Figure
Some specimens made of number 2 analogue material.
Scaling tunnel model without reinforcement layer
Scaling tunnel model within reinforcement layers
Since it is an example of our material used in application, more details and data of the scaling tunnel model tests are not convenient to disclose.
Generally, the properties of the developed analogue materials can be predicted according to the proportions. The experiments and applications indicate that it is a type of excellent analogue material which satisfies mechanical scaling criteria for weak rock or soft geological materials, and it will have broad application prospects.
A new type of analogue material is developed, which is composed of coarse aggregate (quartz sand and/or barite sand), fine aggregate (barite powder), and cementitious material (anhydrous sodium silicate). It is a type of low-strength and low-modulus material with designable density, which is insensitive to humidity and temperature and satisfies mechanical scaling criteria for weak rock or soft geological materials. In order to establish the relationship between parameters and factors, the material properties including density, Young’s modulus, uniaxial compressive strength, and tensile strength were investigated by a series of orthogonal experiments with hundreds of samples. According to the orthogonal experimental method, a four-factor, four-level test scheme is designed for the new material according to the orthogonal table The relationship between parameters and factors was obtained. For the density index, the most important factor is Regression equations of the parameters including density, Young’s modulus, compressive strength, and tensile strength were obtained by using orthogonal polynomial regression analysis. The experiments and applications indicated that the properties of analogue materials were stable and predictable. It was easy to obtain objective material from the regression equations and trial test.
See Tables
The authors declare that there is no conflict of interests arising from the work reported in, or the publication of, this paper.
Songlin Yue, Yanyu Qiu, and Pengxian Fan conceived and designed the study. Songlin Yue, Pin Zhang, and Ning Zhang performed the experiments. Songlin Yue and Pengxian Fan wrote the paper. Yanyu Qiu, Pin Zhang, and Ning Zhang reviewed and edited the paper. All authors read and approved the paper.
The authors acknowledge the financial support from the Natural Science Foundation of China (Grants 51308543 and 51304219), the China Postdoctoral Science Foundation Funded Project (Grant 2015T81074), and the Open Fund Project of State Key Laboratory of Coal Resources and Safe Mining, CUMT (Grant 14KF02).