## 4 Analysis of Mechanical Properties and Energy Absorption Performance of Confined Compression
### Analysis of Volume Strain and Compressibility  
The energy absorption characteristics of the EPP concrete under external load are reflected in various forms such as deformation, crushing, collapse of internal porous structure and mutual friction of concrete fragments at the micro level. At the macro level, it is reflected in the compression of the overall volume of the specimen. According to the compression characteristics of confined compression of EPP concrete, a reasonable index dense strain \(\theta_{m}\) is proposed to evaluate the compression performance of the concrete according to the stress-volume strain relationship diagram of the confined compression of concrete. According to Figure 11, the lateral compression stress-volume strain relationship curves of each group of concrete specimens are segmented. The final value of compressive strain in the linear elastic stage is defined as \(\theta_{cc}\), the final value of compressive strain in the ultimate failure stage is defined as \(\theta\)d and the final value of compressive strain (dense strain) in the confined compression platform stage is defined as \(\theta_{m}\). Therefore, during the compression process, the EPP concrete first enters the linear elastic stage (\(0<\theta_{cc}\)). At this stage, the EPP concrete does not change significantly. After reaching the end point, it enters the ultimate failure stage (\(\theta_{cc}<\theta_{d}\)). The test block cracks and structural damage occurs, with an obvious stress drop phenomenon, and then enters the compression platform stage (\(\theta_{d}<\theta_{m}\)). At this stage, pore wall collapse and pore filling occur continuously in the EPP concrete. On the curve, it shows that with the increase in strain, the stress increases slowly. After the internal pores of the EPP concrete are filled, it enters the dense hardening stage (\(\theta>\theta_{m}\)). At this stage, minimal strain growth occurs and the stress increases sharply. The result shown in the actual test is that after the strain reaches a certain \(\theta_{m}\) value, the stress \(\sigma\) value is close to the vertical rise and the strain \(\theta\) is almost unchanged. In the test instrument, the abscissa points of the value corresponding to the instantaneous change point are read as the compression performance characteristic value of the EPP concrete material and the ordinate point is read as the ultimate stress value of the EPP concrete material. Therefore, it is reasonable to use \(\theta_{m}\) as the compression limit value of EPP concrete materials with different mix ratios to calculate the limit value of the EPP concrete's energy absorption. As shown in Figure 12, when the ultimate strain is reached, for the A3 group of the EPP concrete materials, the corresponding stress is 40 MPa and the strain is 0.35. The specific absorption energy calculation is shown in Section 4.3. Therefore, it can be considered that at this point, the EPP concrete (A3) specimen becomes completely dense under pressure, and the cement mortar fragments that become dense after recombination bear the load. Therefore, the volumetric strain value corresponding to a stress value of 40 MPa is defined as the \"ultimate compressive strain\" \(\theta_{m}\). The curves of each group from A1 to A6 \(\theta_{d}\) and \(\theta_{m}\) are extracted. See Table 4.  
Figure 11: Sectional schematic diagram of stress–volume strain relationship curve. In this section, we only analyze the dense volume strain \(\theta_{d}\) and the ultimate compressive strain \(\theta_{m}\). This is because the compressive failure strain of the EPP concrete specimen is influenced by both the elastic modulus and the uniaxial compressive strength, which mainly reflect the deformation performance of the specimen before failure.