# Application of Direct Shear Test to Analysis of the Rate of Soil Improvement with Polyester Fibres
## 2 Materials and Methods  
Soil from a cut slide and excavated soil at the highway construction site near Zilina, Slovakia, and soil from a cut slide in Przybedza, Poland, were used, see Figure 1.  
BS 1377: 1990. Part 2 [29] was applied to obtain soil particle size distribution, water content (w), liquid limit (w\({}_{\rm L}\)), and plastic limit (w\({}_{\rm P}\)), and British Standard BS 5930:2015 [30] was applied to classify the soils. The grain size distribution of the soils is presented in Figure 2 and the soil properties can be seen in Table 1.  
Figure 1: Highways under construction near Zilina, Slovakia and in Przybedza, Poland. (**a**) Location No. 1: cut slide (soil CI), near Zilina, Slovakia; (**b**) Location No. 2: excavated soil, about 360 m from location No. 1 (soil CS1); (**c**) Location No. 3: cut slide (soil CS2), Przybedza, Poland [28]. Polyester fibres TEXZEM PES 200 were used and the fibre properties are presented in Table 2. A picture of the fibres is presented in Figure 3a. Slovak technical standard STN 72 1030: 1988 on DST [17] was applied to determine the shear strength parameters of the soil and soil mixed with fibres. DST was carried out using a fully automatic large shear box apparatus, SHEARMATIC 300 (Wykeham Farrance, CONTROLS Group, Milan, Italy), presented in Figure 3b. The fibres were mixed with soils of optimum water content and maximum dry density in amounts of 0.5%, 1.0% and 1.5% (ratio of fibres to dry soil) and compacted in a box of size 0.3 m \(\times\) 0.3 m \(\times\) 0.08 m. The consolidation time was 5 h, and the shear speed was 0.05 mm/min. Normal stresses of 50 kPa, 100 kPa, 200 kPa, and 300 kPa were applied and tests were terminated at a horizontal displacement 35 mm (11.6% of the width of the specimen). A picture of a specimen of soil and fibres in the amount of 0.5% after testing under a normal stress of 50 kPa can be seen in Figure 3c. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Soil Parameters** & **CI** & **CS1** & **CS2** \\ \hline Water content (\%) & 18.1 & 21.6 & 10.2 \\ Plastic limit (\%) & 20.6 & 27.8 & 19.7 \\ Liquid limit (\%) & 44.2 & 54.7 & 40.2 \\ Plasticity index (\%) & 23.6 & 26.9 & 20.5 \\ Optimum water & 18.6 & 21.0 & 13.7 \\ content (\%) & & & \\ Maximum dry & 1717 & 1630 & 1925 \\ density (kg\(\cdot\)m\({}^{-3}\)) & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Soil properties. \begin{table}
\begin{tabular}{c c} \hline \hline
**Polyester Fibre Parameters** & **TEXZEM PES 200** \\ \hline Length (mm) & 70 \\ Colour & White \\ Density (g\(\cdot\)cm\({}^{-3}\)) & 1.38 \\ Mass density (dtex) & 2200 \\ Tensile strength (cN/dtex) & 7.77 \\ Elongation at break (\%) & 10.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Properties of polyester fibre [20]. Figure 2: Grain size distribution diagram of soils: Full line is applied for Cl; long dash line is applied for CS1; dotted line is applied for CS2. The shear strength parameters were calculated using formulae:  
\[\tan\phi=\frac{n\Sigma\tau\sigma_{ef}-\Sigma\tau\Sigma\sigma_{ef}}{n\Sigma \sigma_{ef}^{2}-\left(\Sigma\sigma_{ef}\right)^{2}} \tag{1}\]  
\[c=\frac{\sum\tau\Sigma\sigma_{ef}^{2}-\Sigma\sigma_{ef}\Sigma\tau\sigma_{ef}}{ n\Sigma\sigma_{ef}^{2}-\left(\Sigma\sigma_{ef}\right)^{2}} \tag{2}\]  
where \(\tau\) and \(\sigma_{ef}\) (kPa) are the pair of stresses obtained from each specimen and \(n\) is the number of specimens. STN 72 1030: 1988 requires the test to be carried out with at least four specimens for the test of peak strength and requires the value of the correlation coefficient \(r\) calculated using Formula (3) to be larger than 0.9500:  
\[r=\frac{n\Sigma\left(\tau\sigma_{ef}\right)-\sum\tau\Sigma\sigma_{ef}}{\sqrt{ \left[n\Sigma\sigma_{ef}^{2}-\left(\Sigma\sigma_{ef}\right)^{2}\right]\cdot \left[n\Sigma\tau^{2}-\left(\Sigma\tau\right)^{2}\right]}} \tag{3}\]  
Determination of uncertainty was carried out in accordance with EUROLAB Technical Report 1/2006 [31]. Here, only the most important issues are presented.