## 4 Analysis of Mechanical Properties and Energy Absorption Performance of Confined Compression
### Stress-Strain Curve Analysis  
Based on the results obtained from the analysis of the stress-strain curve, the deformation of the specimen was observed to be caused by the compression of the pores in the EPP concrete. Accordingly, the deformation parameters were expressed by the volume strain. Moreover, as the compression specimen was laterally restrained by the steel sleeve, as well as the fact that the cross-sectional area of the specimen was basically unchanged, the volume strain can be simplified as the vertical strain of the specimen (Formula (1)). \[\theta=\frac{\Delta V}{V}=\frac{\Delta a}{a} \tag{1}\]  
where \(\theta\) stands for the volume strain value, \(\Delta V\) denotes the volume compression (mm\({}^{3}\)), \(V\) represents the volume of the EPP concrete cube specimen (10\({}^{6}\) mm\({}^{3}\)), \(\Delta a\) is the vertical compression deformation value and \(\alpha\) is the side length of the EPP concrete cube specimen (100 mm). The stress-volume strain curve obtained from the test is shown in Figure 7.  
Figure 6: Relationship between uniaxial and confined compressive strengths and EPP volume replacement. Figure 7: \(Cont.\)As can be seen in Figure 7, the compressive stress-volume strain curves of the six groups of EPP concrete specimens (A1-A6) display the characteristics shown in Figure 8. Moreover, the curves can also be divided into three stages, namely, the elastic-plastic stage, the compression platform stage and the strain hardening stage. Furthermore, the higher EPP particle content was found to result in the more obvious boundary points of the compression platform stage and the dense compression stage. Figure 8: _Cont._  
Figure 7: Stress–volume strain curves of concrete specimens with different EPP volume contents under lateral confinement conditions. (**a**) A1 group: EPP volume content of 28%. (**b**) A2 group: EPP volume content of 35%. (**c**) A3 group: EPP volume content of 42%. (**d**) A4: EPP volume content of 50%. (**e**) A5 group: EPP volume content of 57%. (**f**) A6 group: EPP volume content of 64%. Elastic-plastic stage: From the beginning of the loading to the first peak stress, the EPP concrete specimen was compressed. As a consequence, the increase in the volume strain was observed to lead to a rapid increase in the stress. Moreover, the relationship between the stress and the volume strain first increased linearly on the curve. Later, as a typical structural failure phenomenon of brittle materials, the curve increased with a decreasing slope until the compressive stress reached its peak strength. Compression platform stage: An obvious unloading phenomenon was observed when the structure of the concrete specimen was entirely destroyed. Moreover, an obvious stress drop phenomenon was also noticed on the stress-strain curve, on which the strain and the stress rapidly increased and decreased, respectively. Contrary to the results obtained from the ordinary uniaxial compression test, as the EPP concrete specimen was placed in the steel sleeve, the concrete fragments after the failure surface were confined to the steel sleeve. Consequently, the stress-strain curve began to increase after falling to a certain extent. This is when the pores inside the specimen began to collapse. Subsequently, the stress increased and fell several times, which resulted in the stress-strain curve displaying a long plateau stage. The curve was not horizontal at this stage. However, as the whole concrete structure was gradually broken and the internal pores of the specimen were compressed and collapsed layer by layer, the curve slowly rose in the shock. This can be also seen in the multiple fluctuation points of the curve until most of the pores were compressed and compacted. At the same time, the higher the EPP particle content, the longer the compression platform section and the more fluctuation points.