*2.2. Testing*

All the specimens were tested after 28 days of curing. Before testing was carried out, the bulk density of each sample was measured.

The compressive tests of the cylinders were performed using a FORM + TEST Prüffsysteme MEGA3 Testing Machine for compression testing at a loading speed of 0.1 kN/s. Strains were measured with two groups of strain gauges of length 10 mm, orthogonally adhered to the side surface of the cylinder (Figure 2a). Measurements were recorded using a Z-TECH 64-channel Wheatstone bridge.

**Figure 2.** Samples during the test: (**a**) flexural test of the beam; (**b**) cylinder compressive test.

The tests of the beams were carried out according to EN 196-1:2016, and the flexural strength was determined for each type of beam. In addition, for the pure geopolymer, compressive strength tests were done using the cube samples that remained after the bending test. The tests were performed with a Controls 65-L27C12 Universal Testing Machine at a loading speed of 0.05 kN/s. During each test, the deformation of the reinforced samples was measured using the DIC (digital image correlation) method. Pictures were taken at one-second intervals using a Canon EOS100D camera (Figure 2b). Strains and displacements were computed with GOM Correlate software.

## **3. Experimental Results and Analysis**

#### *3.1. Mechanical Properties of Foamed Geopolymers*

The results of the cylinder tests are shown in Table 4, which gives the mean values for the three cylinders. The modulus of elasticity and Poisson's ratio are defined as secant values within 40% of the strength.


**Table 4.** Average results of cylinder tests.

Geopolymers synthesized from fly ash obtained from anthracite coal combustion (the Jaworzno power plant) had the best strength properties. The cylinder (uniaxial) compressive strength of geopolymer made of fly ash from Jaworzno was on average 114% higher than the values obtained for geopolymers synthesized using suspensions from lignite coal-fired power plants (Turow and Belchatow). An even greater difference was seen in the modulus of elasticity, which was on average 213% higher, and in the case of geopolymer foamed with 3% H2O2 content, up to 370% higher. These results were gained for geopolymer made from Jaworzno fly ash, despite the average lowest density in the comparison group for the same quantity of foaming agent.

The modulus of elasticity for the foamed geopolymers based on fly ash from the Jaworzno power plant was comparable to those of foamed OPC concretes. Figure 3 shows a comparison with test results for foamed concrete of different densities published by Kozłowski [55] and Drusa [56].

**Figure 3.** Secant modulus of elasticity vs. bulk density of tested samples: comparison with the results of foamed ordinary Portland cement (OPC) concrete tests performed by Kozlowski and Kadela [55] and Drusa et al. [56].

Figures 4–6 show the stress-strain relationships for geopolymers synthesized from the three different types of fly ash.

**Figure 4.** Stress-strain relationship for samples based on Jaworzno fly ash.

**Figure 5.** Stress-strain relationship for samples based on Turow fly ash.

**Figure 6.** The stress-strain relationship for samples based on Belchatow fly ash.

By analogy with OPC concrete, the stress-strain relationship can be described by the following function:

$$
\sigma = \sigma\_{\mathcal{U}} \left[ 1 - \left( 1 - \frac{\varepsilon}{\varepsilon\_{\mathcal{U}}} \right)^{n} \right], \tag{1}
$$

where *σ<sup>u</sup>* and *ε<sup>u</sup>* are the average strength and the corresponding ultimate strain obtained during the tests. The function in (1) was adjusted to the test results by determining the value of the power exponent *n*. The results of these analyses are summarized in Table 5. A value of *n* = 2 gives the parabolic relationship recommended for concrete, while *n* = 1 gives a linear relationship. Figures 4–6 show the curves corresponding to the functions described by the parameters listed in Table 5. The fit of the functions was verified by maximizing the determination coefficient. The results obtained for R-squared are presented in the last column of Table 5.

**Table 5.** Parameters for the function in (1) describing the stress-strain relationship for the

**Strength MPa Ultimate Strain ‰ Exponent** *n* **Correlation with Test Results (R2)** J\_1% 9.14 3.93 1.2 0.993 J\_2% 6.36 3.14 1.2 0.994 J\_3% 2.42 1.98 1.24 0.986 T\_1% 4.27 3.64 1.09 0.996 T\_2% 2.44 4.12 1 0.990 T\_3% 1.55 3.96 0.9 0.964 B\_1% 4.33 5.56 1.6 0.985

B\_2% 2.37 4.71 1.35 0.973 B\_3% 0.68 2.15 1.08 0.993

The strengths obtained in the cylinder tests were confirmed by the beam tests, and these are summarized in Table 6, which shows the density, cube compressive strength, and tensile flexural strength. In additional, to enable further comparisons with the reinforced beams, it shows the failure force for which the flexural strength was calculated. The results were similar to those of the cylinder tests, as the average cube compressive strength was 73% higher and flexural strength 29% higher for the fly ash from Jaworzno than for those from the other two power plants.


foamed geopolymer.


The foaming caused a severe drop in strength. For example, the compressive strength of a plain (not foamed) geopolymer, based on fly ashes from Jaworzno, is on average 40 MPa. Strength decreases with decrease of geopolymer density. Similar relationships of strength and density were obtained in studies published by other authors [23,27]. Moreover, to a similar extent, foaming affects the strength of concretes based on Portland cement [46,55,56].
