# Study of Static and Dynamic Properties of Sand under Low Stress Compression
## 4 Conclusions  
This study highlights differences in the stress-strain behavior of four types of sand under low stress loading via the comparison of their stress-strain diagrams in two types of loading tools (an oedometer and a uniaxial compression machine), as well as their US and AE characteristics. A wide range of sand grain sizes (0.075-4.75 mm) was utilized for the study. Analysis of the sensitivities of different time domain AE parameters to the stress-strain changes was performed. By comparing the OD and UCD results for the US measurements, we conclude that the value of the HtD affected the results of the compression tests, primarily due to changes in the soil stiffness. The lower the HtD was, the stiffer the soil sample was due to the confining stress (triaxial stress mode), which implied restriction in the mobility of soil particles. The value of the confining stress can be estimated via the ratio of the lateral stress to the vertical stress, being \(K_{0}=1-\sin\phi\) (lateral stress factor at rest), where \(\phi\) is the friction angle. For quartz sand, \(\phi\) is generally in the range of 20-30\({}^{\circ}\) (\(\phi=-12.963\cdot d+29.778\), where \(\phi\) is expressed in degrees and \(\dot{d}\) is the particle size in mm, and the regression has been extracted from Figures 6-9. in [17]). The increase in the confining stress \(\sigma_{3}\) can be of the order of \(\sigma_{3}=\sigma_{1}\cdot K_{0}\), where \(K_{0}=0.5,\ 0.66\). The confining stress value under compression must be taken into account for the short samples (HtD < 2), while it is known to disappear in the middle part of the long cylindrical samples (HtD \(\geq\) 2). As we noted above, HtD < 1 in the OD experiments while it was \(\approx\)2 in the UCD and UCW tests, implying that the sand samples were much stiffer in the OD experiments (being under quasi-triaxial stress conditions) than in the UCD and UCW tests. The stiffer the soil was, the higher the value of the P wave speed was. This is the reason why similar P wave velocities were achieved at a much lower applied stress during the OD experiments in comparison with the UCD and UCW tests. By comparing the UCD and UCW results for the US measurements, we conclude that during both experiments, the range of the P wave speed was similar for all types of samples tested, while the value of the induced strain was much higher during experiments with wet sand samples relative to those using dry ones. The latest results can be explained by a decrease in friction between the soil particles with a subsequent increase in its compressibility (mainly due to the presence of a wide subzone a). Concerning the similarity of P wave speed values during the UCD and UCW experiments, it is known [36] that the value of the P wave speed of a wet medium can be estimated as follows:  
\[\frac{1}{\overline{V}_{p}}=\frac{n}{V_{w}}+\frac{1-n}{V_{p}^{dry}} \tag{2}\]  
where \(\overline{V}_{p}\), \(V_{p}^{dry}\) and \(V_{w}=1481\ m/s\) are values of the P wave speed in wet and dry soils and water, respectively, and \(n\) is the soil porosity value. Substitution of the values of porosity of our samples, of the P wave speed obtained by our experiments and of the P wave speed known for water into Equation (2) yields a difference between the values of the P wave speed in dry and wet sand samples of about 4%, which is generally consistent with the results of our observations. Regarding the AE measurement results, we conclude that the similarity of the changes in the AE hit number with a stress increase is consistent with the results noted by [15; 20; 21; 30]: the higher the stress level is, causing more friction between the sand particles, the more AE events there are during their movement. Comparison of the results of the OD and UCD tests was also consistent with the results observed by [17; 20; 21; 31], who noted that, at a similar stress level, stiffer specimens emit fewer acoustic signals due to the difference in compression modes.