# Crushing Performance of Ultra-Lightweight Foam Concrete with Fine Particle Inclusions
## 4 Results and discussion
### Loading Behavior  
The loading behavior of all the samples was investigated using the penetration test at the same testing ages as the vibrational frequency test. A demonstration of the loading responses of the control sample at the three ages is given in Figure 2, where the indentation stress was calculated by dividing the resistant force by the cross-section area of the cylindrical indenter. A preliminary test has confirmed that the friction between the indenter and sample is so small that such effect is negligible. All the indentation curves of the samples were curtailed on (1) the \(x\) axis at 160 mm as further penetration results in boundary effects and (2) the \(y\) axis at 5.7 MPa indentation stress as the loading capacity of the testing frame is reached.  
The trend of the indentation curve of the samples is consistent with the observation from several other studies on foam concrete [15; 36] and other cellular solids [37; 38]. As the test initiated, the material behaved in a linear-elastic manner with a steep increase of the indentation stress. After reaching a yielding point shortly at a few millimeters, the increment became substantially milder at a roughly constant rate. Due to the geometry of the indenter, the crushing plateau reported in our previous study was not captured in this test [15]; the material crushing strength, however, can still be quantitatively compared based on the indentation stress at the same indentation depth. In Figure 2, localized material cracking affected the 14- and 21-day loading curves of the controlled sample at around 30 mm, after which the curves returned to their normal trend lines. These events are considered as anomalies that can be generally neglected, and they were rarely observed in the other samples, as cracks could not propagate effectively in the weaker microstructure.  
Figure 2: General loading response from the penetration test at 7, 14, and 21 days for the control sample.  
The 7-, 14-, and 21-day loading behavior across different samples are compared in Figure 3. In general, the influence from sand ratio and sand size to the crushing strength follows the same trend as observed from the elastic modulus measurement. Comparing the results among the three ages, the strength gain is smaller for the samples with a larger sand ratio. This phenomenon should be mainly caused by the reduced cement usage in the high sand ratio samples. The slope of the load curves after the initial yielding is also relevant to inclusion of sand particles. There is a noticeable rise in the curve slopes of the controlled sample and those of a 0.15 sand ratio. As more sand was added into the mixture, this slope change becomes less pronounce. This observation should be associated with the reduced bulk modulus for samples of higher sand ratio, as the stress build-up underneath the indenter develops at a slower rate in weaker samples. This point is generally supported by data from the elastic modulus measurement.  
Figure 3: _Cont._  
At a low sand ratio of 0.15, the 7 day loading responses of Samples 0.15_300 \(\upmu\)m and 0.15_600 \(\upmu\)m are similar to Control, while the indentation stress of Sample 0.15_850 \(\upmu\)m is much lower during the entire crushing history. This evidence accords with an earlier study focusing on a higher foam concrete density and with coarser sand [22], which also shows that higher sand size reduces compressive and flexural strength of foam concrete. As a result of the reduced cement ratio, the indentation strength is consistently diminished for samples of the same sand size but higher sand ratio. At higher sand ratios of 0.3 and 0.5, however, it is still evident that the crushing strength is further reduced when larger sand particles are used. Another important observation is that no matter for which sand ratio, the relative strength reduction between the 850 \(\upmu\)m and 600 \(\upmu\)m samples is larger than that between the 600 \(\upmu\)m and 300 \(\upmu\)m samples, implying a profound influence from the 850-\(\upmu\)m sand.