2.4.2. Gas Permeability

The foamed concrete is mainly used to isolate gas in the coal mine goaf, so the gas permeability is used as anther evaluation index, which can be tested by gas permeability measurement system (see Figure 3). First, 50 mm of the samples was cut off in dry density test, a layer of epoxy resin was applied on the outside of samples, and the sample was put into the concrete gas penetration tester, ensuring the airtightness of the device. Then the air pressure was controlled to be about 0.1–0.2 MPa at the inlet in the tester, so that the gas entered into the sample from the lower surface and exited from the upper surface. The air inlet pressure *P*<sup>1</sup> and air outlet pressure *P*<sup>2</sup> were recorded under different air supply pressures. Then, the gas permeability of the sample can be easily obtained from the apparent gas permeability *k*a, which can be calculated as follows:

$$k\_{\rm a} = \frac{Q}{A} \frac{2\eta h P\_1}{P\_1^2 - P\_2^2} \tag{2}$$

where, *k*<sup>a</sup> is the apparent gas permeability, m2; *Q* is the gas flow, mL/min; *A* is the cross section area of the sample, mm2; <sup>η</sup> is the viscosity of the compressed gas, Pa·s; *<sup>h</sup>* is the height of the test piece, mm; *P*<sup>1</sup> is the inlet pressure, bar; *P*<sup>2</sup> is the outlet pressure, bar.

**Figure 3.** Gas permeability measurement system.

#### 2.4.3. Compressive Strength

Although there is less requirement for the compressive strength of the foamed concrete, the higher the compressive strength, the more stable the whole goaf can be maintained, and the more conducive to the mining of the adjacent workface. Considering the short time filling effect and long time supporting effect, the compressive strength of 3 days and 28 days of the foamed concrete were selected as the other evaluation indexes, which can be tested by universal testing machine CSS-14100 (see Figure 4). Cube samples of 70.7 × 70.7 × 70.7 mm were taken, their dimensions measured, and the contact area *A*<sup>1</sup> was calculated. Then the sample was placed on the press plate center of the universal testing machine. The testing machine was started and controlled with a displacement loading speed of 0.02 mm/s. When the specimen cracks and reaches the complete failure state, the test is finished and the data as well as the maximum axial pressure *F* is recorded in the computer. Then the compressive strength σ of the foamed concrete can be obtained by the formula:

$$
\sigma = \frac{F}{A\_1} \tag{3}
$$

where, σ is the compressive strength of the sample, MPa; *F* is the maximum failure load of the sample, N; *A*<sup>1</sup> is the contact area of the sample, mm2.

As a result, the dry density, gas permeability, compressive strength of 3 days and 28 days, which were used as four test indexes according to the demands of the foamed concrete for gas isolation, were obtained by the methods above [17,18].

**Figure 4.** Universal testing machine.

#### **3. Results and Optimum Mix**

#### *3.1. Test Results and Analysis*

Average level is the average value of each factor at the same level. The average level of four indicators (dry density, gas permeability, compressive strength of 3 days and 28 days) under different factors can be seen in Figure 5a–d, and it can be noted that the foam is the main factor influencing the four indexes as mentioned above. The dry density and compressive strength drop and the gas permeability increases as the volume of foam increases. In order to further investigate the mechanism of this phenomenon, a microscope was used to magnify the samples with different foam content for 500 times, as shown in Figure 6.

When the foamed concrete sample is magnified by microscope, it can be seen that when the amount of foam is less, there are fewer pores in the sample, and these pores are small, airtight, and smooth. With the increase of foam content, both the number and the diameter of pores increase significantly. When the amount of foam reaches 2 L, the pores in the samples are denser and larger, and the connected pores are formed, which leads to larger gas permeability of the foamed concrete. At the same time, since the fact that foam helps to produce more pores, the increase of foam content can lead to a decrease in other solid materials in the unit volume, resulting in a decrease in density and strength.

**Figure 5.** *Cont*.

**Figure 5.** Average level of indicators under different factors: (**a**) average level of dry density; (**b**) average level of gas permeability; (**c**) average level of compressive strength of the 3rd day foamed concrete; (**d**) average level of compressive strength of the 28th day foamed concrete.

**Figure 6.** Pore structures of different foam content in 1 kg mass of solid powder: (**a**) 0.5 L foam; (**b**) 1.0 L foam; (**c**) 1.5 L foam; (**d**) 2.0 L foam; (**e**) 0.5 L foam (×500 times); (**f**) 1.0 L foam (×500 times); (**g**) 1.5 L foam (×500 times); (**h**) 2.0 L foam (×500 times).
