# Application of Direct Shear Test to Analysis of the Rate of Soil Improvement with Polyester Fibres
## 3 Results
### Uncertainty of Shear Strength Parameters  
Values of the expanded uncertainties of the shear strength parameters are introduced in Table 4 (for soil CI), Table 5 (for soil CS1), and Table 6 (for soil CS2). In the mentioned tables, for every column, maximal absolute values of uncertainties are marked as red underlined numbers, maximal relative values of uncertainties are marked as italic red underlined numbers, minimal absolute values of uncertainties are marked as blue underlined numbers, and minimal relative values of uncertainties are marked as italic blue underlined numbers. As can be seen in the tables, the lowest uncertainties were applied for DST with four specimens (case No. 1) and the highest uncertainties were applied for DST with three specimens (case No. 3). This fact supports the recommendation to not carry out DST with only three specimens, especially in the case of using DST to evaluate the rate of shear strength parameter improvement by various materials. The values of the uncertainties of the shear strength parameters in case B (with covariances) were closest to the real uncertainties since covariances between correlated input quantities (normal stresses and shear stresses) were taken into account. In this case, for soil CI (see Table 4), the maximal absolute value of the uncertainty of the angle of internal friction \(\max U(\varphi)\) was 0.876\({}^{\circ}\) (3.67%) and the minimal absolute value of the uncertainty of the angle of internal friction \(\min U(\varphi)\) was 0.520\({}^{\circ}\) (1.62%). The maximal absolute value of the uncertainty of cohesion \(\max U(c)\) was 3.466 kPa (2.77%) and minimal absolute value of the uncertainty of cohesion \(\min U(c)\) was 1.604 kPa (2.81%). For soil CS1 (see Table 5), \(\max U(\varphi)=0.926^{\circ}\) (3.57%), \(\min U(\varphi)=0.522^{\circ}\) (1.61%), \(\max U(c)=4.050\) kPa (3.59%), and \(\min U(c)=1.636\) kPa (2.89%). For soil CS2 (see Table 6), \(\max U(\varphi)=0.726^{\circ}\) (2.59%), \(\min U(\varphi)=0.442^{\circ}\) (2.13%), \(\max U(c)=3.098\) kPa (7.74%), and \(\min U(c)=1.250\) kPa (2.00%). So, generally, in this study, the uncertainties of the angle of internal friction were under 1\({}^{\circ}\) and 4% and the uncertainties of cohesion were under 5 kPa and 8%. These values are not negligible and should be taken into account since, when evaluating improvement rate, the difference (improvement) in shear strength parameters should be larger than the uncertainties. The uncertainties of the shear strength parameters in case C (worst-case estimated uncertainties) were very high. For soil CI (see Table 4), \(\max U(\varphi)=1.506^{\circ}\) (4.46%) and \(\max U(c)=7.105\) kPa (8.70%). For soil CS1 (see Table 5), \(\max U(\varphi)=1.684^{\circ}\) (6.49%) and \(\max U(c)=8.132\) kPa (7.20%), and for soil CS2 (see Table 6), \(\max U(\varphi)=1.268^{\circ}\) (4.52%) and \(\max U(c)=6.646\) kPa (17.25%). Therefore, it is not recommended to apply the worst-case estimation of uncertainty. For easier comparison, differences in expanded uncertainty between various cases (case A: without covariance; case B: with covariance; and case C: worst-case) were calculated and are presented in Table 11 (for soil CI), Table 12 (for soil CS1), and Table 13 (for soil CS2). The manner of marking and colouring the numbers is the same as in the case of the numbers in Tables 4-6. As can be seen, for all soils, differences in expanded uncertainty between case B and case A were minimal, so covariances between correlated input quantities (normal stresses and shear stresses) had a negligible influence on result uncertainty. On the contrary, differences in expanded uncertainty between case C and case A and also between case C and case B  
It was found that, in this study, correlation coefficient \(r(\sigma_{i},\sigma_{j})\) had a value of 0.80095, \(r(\sigma_{i},\tau_{j})\) had a value of 0.42487, and \(r(\tau_{i},\tau_{j})\) had a value of 0.22537.