# Application of Direct Shear Test to Analysis of the Rate of Soil Improvement with Polyester Fibres
## 3 Results
### Uncertainty of Shear Strength Parameters
Covariance between correlated input quantities (normal stresses and shear stresses) decreased the uncertainties of the angle of internal friction and increased the uncertainties of cohesion for all tested soils in the case of DST using all four specimens (see differences in expanded uncertainty \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline \multirow{3}{*}{**Soil**} & \multirow{3}{*}{\begin{tabular}{c} **Case** \\ **No.** \\ \end{tabular} } & \multirow{3}{*}{\begin{tabular}{c} **Fibre** \\ **Amount** \\ \end{tabular} } & \multicolumn{6}{c}{**Case B–Case A**} & \multicolumn{6}{c}{**Case C–Case A**} & \multicolumn{6}{c}{**Case C–Case B**} \\ \cline{3-14}  & & & \multicolumn{2}{c}{**\(\Delta\)U(\(\varphi\))**} & \multicolumn{2}{c}{**\(\Delta\)U(\(\varphi\))**} & \multicolumn{2}{c}{**\(\Delta\)U(\(\varphi\))**} & \multicolumn{2}{c}{**\(\Delta\)U(\(\varphi\))**} & \multicolumn{2}{c}{**\(\Delta\)U(\(\varphi\))**} & \multicolumn{2}{c}{**\(\Delta\)U(\(\varphi\))**} & \multicolumn{2}{c}{**\(\Delta\)U(\(\varphi\))**} \\ \cline{3-14}  & & & (\(\%\)) & (\(\%\)) & (\(\%\)) & (\(\%\)) & (\(\%\)) & (\(\%\)) & (\(\%\)) & (\(\%\)) & (\(\%\)) & (\(\%\)) & (\(\%\)) & (\(\%\)) & (\(\%\)) \\ \hline \multirow{2}{*}{\begin{tabular}{c} CS2 (4 \\ specimens; No. 1, 2, 3, and 4) \\ \end{tabular} } & \multirow{2}{*}{1} & 0.0 & \(-\)0.008 & \(-\)1.78 & 0.014 & 1.13 & 0.454 & 100.89 & 1.294 & 128.96 & 0.462 & 101.52 & 1.58 & 126.40 \\  & & 0.5 & \(-\)0.004 & \(-\)0.78 & 0.007 & 0.46 & 0.514 & 100.39 & 2.006 & 130.68 & 0.518 & 101.97 & 1.999 & 129.64 \\  & & 1.0 & \(-\)0.002 & \(-\)0.40 & 0.003 & 0.19 & 0.482 & 96.79 & 2.144 & 133.25 & 0.484 & 97.58 & 2.141 & 132.82 \\  & & 1.5 & \(-\)0.002 & \(-\)0.40 & 0.001 & 0.06 & 0.484 & 97.19 & 2.107 & 130.63 & 0.486 & 97.98 & 2.106 & 130.48 \\ \hline \multirow{2}{*}{\begin{tabular}{c} CS2 (3 \\ specimens; No. 1, 2, 3 and 3) \\ \end{tabular} } & \multirow{2}{*}{2} & 0.0 & \(-\)0.008 & \(-\)1.20 & \(-\)0.016 & \(-\)1.08 & 0.516 & 77.25 & 1.715 & 116.19 & 0.524 & 79.39 & 1.731 & 118.56 \\  & & 0.5 & \(-\)0.006 & \(-\)0.85 & \(-\)0.014 & \(-\)0.80 & 0.540 & 76.70 & 2.049 & 117.62 & 0.546 & 78.82 & 2.063 & 119.39 \\  & & 1.0 & \(-\)0.004 & \(-\)0.60 & \(-\)0.010 & \(-\)0.57 & 0.526 & 84.57 & 2.052 & 117.66 & 0.449 & 78.47 & 2.062 & 119.89 \\  & & 1.5 & \(-\)0.002 & \(-\)0.30 & \(-\)0.008 & \(-\)0.47 & 0.500 & 75.53 & 2.040 & 119.58 & 0.502 & 76.06 & 2.048 & 120.61 \\ \hline \multirow{2}{*}{\
\begin{tabular}{c} CS2 (3 \\ specimens; No. 1, 2, 3 and 4) \\ \end{tabular} } & \multirow{2}{*}{3} & 0.0 & \(-\)0.018 & \(-\)**2.78** & \(-\)**0.045** & \(-\)**1.95** & 0.460 & 70.99 & 2.255 & **97.49** & 0.478 & 75.87 & 2.300 & _101.44_ \\  & & 0.5 & \(-\)0.010 & \(-\)1.36 & \(-\)0.030 & \(-\)1.03 & 0.532 & 72.28 & 3.068 & 105.23 & 0.542 & 74.66 & 3.008 & 107.37 \\ \cline{1-1}  & & 1.0 & \(-\)0.002 & \(-\)**0.29** & \(-\)0.007 & \(-\)0.23 & 0.509 & 74.52 & 3.059 & 115.29 & 0.511 & 75.04 & 3.486 & 115.78 \\ \hline \multirow{2}{*}{
\begin{tabular}{c} CS2 (3 \\ specimens; No. 1, 2, 3 and 4) \\ \end{tabular} } & \multirow{2}{*}{3} & 0.0 & \(-\)0.002 & \(-\)0.29 & \(-\)0.010 & \(-\)0.32 & 0.498 & 72.17 & 3.453 & 111.10 & 0.500 & **72.62** & 3.463 & 111.78 \\ \cline{1-1} \cline{2-14}  & & & & & & & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Differences in expanded uncertainty between various cases (case A: without covariance; case B: with covariance; and case C: worst-case), soil CS2. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline \multirow{3}{*}{**Soil**} & \multirow{3}{*}{\ \begin{tabular}{c} **Case** \\ **No.** \\ \end{tabular}  } & \multirow{3}{*}{ \begin{tabular}{c} **Fibre** \\ **Amount** \\ \end{tabular}