# Application of Direct Shear Test to Analysis of the Rate of Soil Improvement with Polyester Fibres
## 3 Results
### Improvement of Soil Shear Strength Parameters
Figure 6: Shear stress versus normal stress in soil CS2. Differences in shear strength parameters for various amounts of fibres (i.e., improvement), considering all four specimens (case No. 1), are introduced in Table 7.  
The SEM images of fibres before testing can be seen in Figure 7a (\(50\times\) magnification) and Figure 7b (\(2000\times\) magnification). The SEM images of fibres mixed with soil CI in \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c} \hline \hline \multirow{3}{*}{**Soil**} & \multirow{3}{*}{**Case**} & \multirow{3}{*}{**Fibre**} & \multicolumn{3}{c}{**Strength**} & \multicolumn{6}{c}{**Expanded Uncertainty**} \\  & & & **Parameters** & \multirow{3}{*}{**R-**} & \multicolumn{3}{c}{**Without Covariance (A)**} & \multicolumn{3}{c}{**With Covariance (B)**} & \multicolumn{3}{c}{**Worst-Case (C)**} \\ \cline{4-14}  & & & **\(\varphi\)** & \(\varsigma\) & & **U(\varphi)** & **U(\varphi)** & **U(\varphi)** & **U(\varphi)** & **U(\varphi)** & **U(\varphi)** \\ \hline \multirow{4}{*}{CI} & & 0.0 & 27.469 & 48.963 & 0.99123 & 0.668 & 2.43 & 1.476 & 3.56 & 0.698 & 2.03 & 1.728 & 3.53 & 1.244 & 3.61 & 3.911 & 6.52 \\  & & 0.5 & 34.424 & 48.888 & 0.99703 & 0.704 & 2.04 & 1.742 & 3.56 & 0.698 & 2.03 & 1.728 & 3.53 & 1.244 & 3.61 & 3.971 & 7.76 \\  & & 1.0 & 39.172 & 32.197 & 0.99835 & 0.622 & 1.69 & 1.744 & 5.42 & 0.658 & 1.68 & 1.734 & 5.39 & 1.148 & 2.93 & 3.796 & 11.79 \\  & & 1.5 & 37.862 & 34.490 & 0.99953 & 0.662 & 1.75 & 1.706 & 4.95 & 0.660 & 1.74 & 1.698 & 4.92 & 1.162 & 3.07 & 3.746 & 10.86 \\ \hline \multirow{4}{*}{CS2 (3} & & 0.0 & 16.758 & 81.488 & 0.96632 & 0.648 & 3.27 & 2.313 & 2.84 & 0.630 & 3.76 & 2.268 & 2.78 & 1.108 & 6.61 & 4.568 & 5.61 \\  & & 0.5 & 28.047 & 71.832 & 0.99511 & 0.736 & 2.62 & 2.906 & 4.05 & 0.726 & 2.59 & 2.876 & 4.00 & 1.268 & 4.52 & 5.964 & 8.30 \\  & & 1.0 & 36.890 & 38.516 & 0.99588 & 0.683 & 1.85 & 3.087 & **5.02** & 0.61 & 1.85 & 3.080 & 8.00 & 1.192 & 3.23 & 6.646 & 12.25 \\  & & 1.5 & 36.672 & 40.012 & 0.99999 & 0.690 & 1.88 & 3.108 & 7.77 & 0.688 & 1.88 & 3.099 & 7.74 & 1.188 & 3.24 & 6.561 & 16.40 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Differences (improvement) in shear strength parameters for various amounts of fibres. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c} \hline \hline \multirow{3}{*}{**Soil**} & \multirow{3}{*}{**Case**} & \multirow{3}{*}{**Fibre**} & \multicolumn{3}{c}{**Strength**} & \multicolumn{6}{c}{**Expanded Uncertainty**} \\  & & & **Parameters** & \multirow{3}{*}{**R-**} & \multicolumn{3}{c}{**Without Covariance (A)**} & \multicolumn{3}{c}{**With Covariance (B)**} & \multicolumn{3}{c}{**Worst-Case (C)**} \\  & & & **\(\varphi\)** & & & **U(\varphi)** & & **U(\varphi)** & & **U(\varphi)** & & **U(\varphi)** & & **U(\varphi)** \\ \cline{3-14}  & & **(\%)** & **(\(\uparrow\))** & **(kPa)** & **(\(\uparrow\))** & **(\%)** & **(\(\downarrow\))** & **(\(\uparrow\))** & **(\(\uparrow\))** & **(\(\downarrow\))** & **(\(\downarrow\))** & **(\(\downarrow\))** & **(\(\downarrow\))** & **(\(\downarrow\))** & **(\(\downarrow\))** & **(\(\downarrow\))** \\ \hline \multirow{4}{*}{CS1 (4} & & 0.0 & 32.398 & 56.633 & 0.97043 & 0.8256 & 1.62 & 1.634 & 2.89 & 0.522 & 1.61 & 1.636 & 2.89 & 1.066 & 3.29 & 3.616 & 6.39 \\  & & 0.5 & 35.539 & 105.696 & 0.99886 & 0.634 & 1.78 & 2.245 & 2.12 & 0.622 & 1.75 & 2.250 & 2.13 & 1.276 & 3.59 & 4.953 & 4.69 \\  & 1, 2, 3  
various amounts after shearing under normal stresses of 50 kPa and 300 kPa are posted in Figure 8. The SEM images of fibres mixed with soil CS1 in various amounts after shearing under normal stresses of 50 kPa and 300 kPa are posted in Figure 10.  
As can be seen in Table 7 (blue coloured numbers), fibres in the amount of 1.0% increased the angle of internal friction of soil CI by 3.823\({}^{\circ}\) (11.94%) and also increased cohesion by 7.186 kPa (12.57%).