## 2 Methods and Materials
### Evaluation of Undrained Shear Strength From the Dilatometer Test  
#### 2.2.1 Single-Factor Relationships  
[PERSON] [3] proposed the following basic correlation between the normalized undrained shear strength and the horizontal stress index \(K_{D}\) for cohesive soils (for material index \(I_{D}<1.2\)):  
\[\frac{\tau_{fu}}{\sigma^{\prime}_{p}}=0.22\cdot(0.5\cdot K_{D})^{1.25} \tag{4}\]  
Figure 1: Dilatometer blade, measuring unit and seismic module of the seismic dilatometer test (SDMT). Analysis of the DMT results presented in the literature [10; 43; 44; 45; 47] indicates that for particular soils, the relationship between the overconsolidation ratio (\(OCR\)) and the horizontal stress index \(K_{D}\), as well as the normalized undrained shear strength and the horizontal stress index \(K_{D}\) differ from that proposed by [PERSON] [3] and can be modified as follows:  
\[\frac{\tau_{fu}}{\sigma_{v}^{\prime}}=S\cdot(n\cdot K_{D})^{m} \tag{5}\]  
where \(S=(\tau_{fu}/\sigma^{\prime}v)_{hc}\) is the normalized undrained shear strength for normally consolidated soil, and \(n\) and \(m\) are empirical coefficients. It has long been recognized that normalized undrained shear strength in normally consolidated soil depends on the mode of testing, boundary conditions, strain rate, and other variables [34; 35; 37; 44]. The different values of the \(S\), \(n\), and \(m\) parameters are shown in Table 1.  
[PERSON] et al. [38] proposed a relationship for estimating the undrained shear strength based on the corrected second pressure reading \(p_{1}\):  
\[\tau_{fu}=(p_{1}-\sigma_{ho})/N_{C} \tag{6}\]  
where \(\sigma_{ho}\) is the in situ horizontal total stress, and \(N_{C}\) is the dilatometer factor for clays that varies from about 5 to 9. The research carried out by [PERSON] et al. [38] and [PERSON] [42] indicates the values of \(N_{C}\) factor as shown in Table 1.  
A different relationship has been proposed by [PERSON] and [PERSON] [39], in which the undrained shear strength was a function of the corrected first pressure reading \(p_{o}\):  
\[\tau_{fu}=(p_{o}-\sigma_{ho})/N_{D} \tag{7}\]  
where \(N_{D}\) is the dilatometer bearing capacity factor, whose values are shown in Table 1. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Author** & **Equation** & \begin{tabular}{c} **Independent** \\ **Variable** \\ \end{tabular} & **Empirical Coefficients** \\ \hline \hline \multicolumn{4}{c}{Single-Factor Empirical Relationships} \\ \hline [PERSON] [3] & (4) & \(K_{D}\) & \begin{tabular}{c} [PERSON] [3] \\ cohesive soils \\ for \(I_{D}<1.2\) \\ \(S=0.22\), \(n=0.5\), \(m=1.25\) \\ \end{tabular} \\ \hline Modified Marchetti & (5) & \(K_{D}\) & \begin{tabular}{c} [PERSON] and [PERSON] [44] \\ marine clays \\ \(S=0.35\), \(n=0.47\), \(m=1.14\) \\ \end{tabular} \\ \hline [PERSON] et al. [38] & (6) & \begin{tabular}{c} [PERSON] et al. [38] \\ clays \(N_{C}=5\)–9 \\ [PERSON] [42] \\ Peliostoene and Pliocene clays \\ \(N_{C}=9.9\) \\ \end{tabular} \\ \hline [PERSON] and [PERSON] [39] & (7) & \begin{tabular}{c} [PERSON] and [PERSON] [39] \\ clays \(N_{D}=4\)–7 \\ [PERSON] [42] \\ Peliostoene and Pliocene clays \\ \(N_{D}=4.9\) \\ \end{tabular} \\ \hline \hline \multicolumn{4}{c}{Multi-Factor Empirical Relationships} \\ \hline [PERSON] [41] & (9) & \begin{tabular}{c} \(\sigma_{v}^{\prime}\) \\ (\(p_{u}-\sigma_{ho}\)) \\ \((p_{1}-\sigma_{ho}\)) \\ \end{tabular} & \begin{tabular}{c} [PERSON] et al. [51] \\ Pleistocene and Pliocene clays \\ \(\alpha_{0}=0.18\), \(a_{1}=0.14\), \(a_{2}=0.20\), \(a_{3}=0.15\) \\ \end{tabular} \\ \hline [PERSON] [42] & (10) & \
\begin{tabular}{c} \((p_{u}-\sigma_{ho})/N_{C}\) \\ \((p_{1}-\sigma_{ho})/\sigma_{v}\) \\ \end{tabular} &
\begin{tabular}{c} [PERSON] [42] \\ Pleistocene and Pliocene clays \\ \(\alpha_{0}=0.164\), \(a_{1}=0.345\), \(a_{2}=0.544\) \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Empirical coefficients in single- and multi-factor relationships to evaluate undrained shear strength \(\tau_{fu}\) from the dilatometer test.