# Damping Ratio of Sand Containing Fine Particles in Cyclic Triaxial Liquefaction Tests
## 2 Materials and Methods
### Experimental Programme  
According to field investigations [5; 6; 18], liquefied soils are generally composed of a coarse sand matrix containing a few fine particles in relatively limited quantities. To get closer to this in situ condition, the density index of sand matrix \(I_{\text{Dmat}}\) was set as the controlled parameter to prepare all triaxial specimens:  
\[I_{\text{Dmat}}=\left(e_{\text{max}}-e_{\text{mat}}\right)/\left(e_{\text{max}}- e_{\text{min}}\right) \tag{1}\]  
where \(e_{\text{mat}}\) is the void ratio of sand matrix, \(e_{\text{max}}\) and \(e_{\text{min}}\) represent the maximum and minimum void ratio of the clean HN31 sand, respectively. The clear benefit of using such a concept is its ability to conserve the prevailing role of the coarse sand matrix, irrespective of the amount of fine particles [19]. A very loose state of \(I_{\text{Dmat}}=0.00\) was adopted to favour the triggering of sand liquefaction [20] since a high contractiveness was believed helpful in analysing the subsequent dynamic characteristics. Under the circumstance, the fines content \(F_{\text{c}}\) was defined as the dry mass of added fines divided by that of the base sand. Three relatively low values (5.0%, 10.0% and 15.0%) were used, more consistent with filed surveys. For further analysis, different intensities of shearing were applied by varying the cyclic shear ratio (\(CSR\)) so as to establish the relevant cyclic shear resistance curves. The detailed test programme is summarised in Table 2.  
In the present work, the entire setup for cyclic triaxial tests consists of (i) a reaction frame, (ii) a confining chamber, (iii) CO\({}_{2}\), de-aired water tanks and (iv) an overhead crane. Figure 4a displays the schematic layout of the essential reaction frame and the confining chamber. A novel auto compensation system [21] was used to obtain the test specimen and the loading piston connected (Figure 4c). The primary function of the system was to avoid disturbing the fragile soil fabric as much as possible for improving the quality and repeatability. Cylindrical specimens with 100 mm in diameter and 200 mm (Figure 4b) in height were reconstituted with ten layers using the dry tamping technique [22]. After mixing base sand and fine particles through stirring and shaking in an enclosed container, all mixtures were divided into ten identical parts. Each part was carefully introduced into a split mould with a spoon, followed by slight compaction efforts to achieve the required \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Ref.** & \(F_{\text{c}}\) **(\%)** & \(CSR\) [1] & \(f\) **(Hz)** & \(\sigma^{\prime}{}_{\text{c}}\) **(kPa)** \\ \hline CTT01 & 5.0 & 0.120 & & \\ CTT02 & 5.0 & 0.105 & & \\ CTT03 & 5.0 & 0.090 & & \\ CTT04 & 5.0 & 0.075 & & \\ CTT05 & 10.0 & 0.120 & & \\ CTT06 & 10.0 & 0.105 & & \\ CTT07 & 10.0 & 0.100 & 0.10 & 200 \\ CTT08 & 10.0 & 0.090 & & \\ CTT09 & 10.0 & 0.075 & & \\ CTT10 & 15.0 & 0.120 & & \\ CTT11 & 15.0 & 0.105 & & \\ CTT12 & 15.0 & 0.090 & & \\ CTT13 & 15.0 & 0.075 & & \\ \hline \hline \end{tabular} Note: [(1)] \(CSR=\tau_{\text{cyc}}/\sigma^{\prime}{}_{\text{c}}\).  
\end{table} 
Table 2: Cyclic triaxial test programme. thickness of 20 mm using a hand tamper. The confining pressure was then increased to 100 kPa to hold the test specimen properly, and the conventional three-step saturation was initiated. Carbon dioxide was first flushed (about 15 kPa) through the dry specimen for about 15 min with the purpose of replacing air, followed by the injection (about 9 kPa) of de-aired water. The final steps involved the application of a back pressure. Namely, the back pressure and confining pressure were alternatively increased in small steps of about 20 kPa until the Skempton's \(B\) value was at least equal to or greater than 0.98. This criterion can be believed to be fair enough to achieve a full saturation for sandy deposits.