## 2 Soil Remolding Toughness Measurement
### [PERSON] Thread Rolling Apparatus and Method
From the authors' independent analysis of the experimental data presented for 55 inorganic fine-grained soils reported by [PERSON] [8], their \(w_{\rm S}\) water contents corresponded to a liquidity index (\(I_{\rm L}\)) of \(\sim\)0.12 (standard deviation of \(\sigma\) = 0.05), with measurable toughness evident for \(I_{\rm L}<\) 0.43 (\(\sigma\) = 0.14). In other words, \(w_{\rm T}\) could be approximated as follows:  
\[w_{\rm T}=w_{\rm P}+0.43\ I_{\rm P} \tag{1}\]  
[PERSON] and [PERSON] [53] showed that \(w_{\rm T}\) shows a good correlation with the optimum water content for compaction. At all energy levels studied, they found that the maximum dry unit weight displayed a good correlation with the dry unit weight at the \(w_{\rm T}\) water content. Additionally, [PERSON] et al. [54] investigated \(w_{\rm T}\) and a soil state index parameter defined as SSI = \(w_{\rm T}\times e_{0}\), where \(e_{0}\) is the initial void ratio, as predictors of the compression index (\(\rm C_{c}\)) parameter. The inclusion of \(e_{0}\) means that the SSI takes into account the effects of several index properties, including the initial density and consistency of soils. They concluded that \(w_{\rm T}\) and, more so, the SSI are reasonable predictors of the \(C_{\rm c}\) parameter. Furthermore, the toughness coefficients, as given by the gradients of the bi-linear \(T\)-\(w\) relationship, the workability index \(I_{\rm W}\) (Equation (2)), and the toughness index \(I_{\rm T(B)}\) (\(=w_{\rm T}-w_{\rm P}\)), can be derived [8; 17; 18]. Here, the toughness index \(I_{\rm T(B)}\) simply gives the water content range over which the soil would be plastic and workable:  
\[I_{\rm W}=\frac{w-w_{\rm P}}{w_{\rm T}-w_{\rm P}} \tag{2}\]  
where \(w\) = soil water content, \(w_{\rm P}\) = plastic limit, and \(w_{\rm T}\) = toughness limit (i.e., water content at zero toughness). [PERSON] workability index \(I_{\rm W}\)[17] relates the soil's actual water content to its \"workable\" range of \(w_{\rm P}<w<w_{\rm T}\) (i.e., for \(w=w_{\rm T}\), \(I_{\rm W}=1\Rightarrow T=0\) and for \(w=w_{\rm P}\), \(I_{\rm W}=0\Rightarrow T=T_{\rm max}\)). In other words, this definition of a workability index does not really relate to the degree of workability (toughness) of the test soil, and, therefore, it does not allow one to discern between _silt_ and _clay_ materials, whose toughness are very different. Note, [PERSON] definition for the toughness index (i.e., \(I_{\rm T(B)}\)) is different from the \(I_{\rm T(C)}\) parameter, after [PERSON] [36], previously mentioned in the Introduction. Additionally, as presented in Table 1, [PERSON] [17] proposed a tentative classification of soil toughness (from \"very low\" to \"extremely high\" toughness) based on assigned ranges of \(T_{\rm max}\) values mobilized at the \(w_{\rm P}\) water content. \begin{table}
\begin{tabular}{c c} \hline
**Toughness Classification** & \(T_{\rm max}\) **(kJ/m3/100 r)** \\ \hline Very low & \(<\)5 \\ \hline Low & 5–10 \\ \hline Moderate & 10–20 \\ \hline High & 20–30 \\ \hline Very high & 30–50 \\ \hline Extremely high & \(>\)50 \\ \hline \end{tabular}
\end{table} 
Table 1: Proposed classification of soil maximum remolding toughness \(T_{\rm max}\) (mobilized at \(w_{\rm P}\)), as determined using [PERSON] thread rolling apparatus [17]. Note that [PERSON] definition of and measurement units for soil toughness represent one of many possible ways of quantifying toughness and, therefore, could be viewed as providing relative measures (based on the 100 reversals (i.e., 100 r) definition) of the soil's toughness properties/characteristics. [PERSON] could have chosen to base his work calculations on any set number of reversals (e.g., 20 r, 50 r, 120 r, etc. ), thereby giving a different definition and hence producing an altered value of \(T_{\text{max}}\) for investigating the same fine-grained soil. For instance, compared to the 100 r definition, a greater value of \(T_{\text{max}}\) would arise with the toughness calculation defined for a larger number of reversals.