# Application of Direct Shear Test to Analysis of the Rate of Soil Improvement with Polyester Fibres
## 1 Introduction
The measured values of the internal friction angle ranged from 8.66\({}^{\circ}\) to 32.16\({}^{\circ}\), with mean and median values of 18.73\({}^{\circ}\) and 17.70\({}^{\circ}\), respectively. The cohesion value ranged from 1.74 to 38.95 kPa, with a mean of 20.77 kPa and a median of 20.91 kPa. Since the reliability of the predicted values of the shear strength parameters obtained from the models depended on the reliability of the above-mentioned values of the shear strength parameters, their uncertainty should be taken into account. In our opinion, there is a big limitation to DST that is not addressed by many researchers: a large amount of DST is carried out in accordance with ASTM D3080/D3080M [12], STAS 8942/2-82 [13], AASHTO T 236-08: 2008 [14], BS 1377: Part 7:1990 [15], and ISO 17892-10:2018 [16], where only three specimens are sufficient and no limit value of the correlation coefficient between shear stresses and normal stresses is prescribed. One can propose that, in such cases, different combinations of three normal stresses (e.g., the combination 50 kPa, 100 kPa, and 200 kPa and the combination 100 kPa, 200 kPa, and 300 kPa) can provide different DST results (but are valid for the same common interval of normal stress from 100 kPa to 200 kPa). In contrast to the mentioned standards, STN 72 1030: 1988 [17] prescribes at least four specimens and PN-88/B-04481 [18] requires at least five specimens. Even in cases where researchers applied DST using four specimens, the improvement of shear strength parameters is small in some cases, but no uncertainty of the DST results is provided, so the improvement could not be confirmed. DST was also applied in the evaluation of soil improvement using PES fibres TEXZEM PES 200 [19; 20; 21]. [PERSON] et al. [19] reported the results of DST of soil improved by the mentioned fibres, TEXZEM PES 200, in amounts of 0.5%, 1.0%, and 1.5% of soil dry mass. Soil SC was used. DST was carried out using a fully automatic large shear box apparatus, SHEARMATIC 300 (Wykeham Farrance, CONTROLS Group, Milan, Italy). It was found that the optimal amount of fibres was 1%, at which the increase in the angle of internal friction measured was 6.1\({}^{\circ}\) (from 45.2\({}^{\circ}\) to 51.3\({}^{\circ}\), corresponding to 13.5%) and the increase in cohesion obtained was 17.5 kPa (from 0 kPa to 17.5 kPa). The results of DST of soil CS mixed with the previously mentioned fibres, TEXZEM PES 200, can be also seen in the study by [PERSON] [20]. DST was carried out using the above-mentioned large shear box apparatus, SHEARMATIC 300. The results showed that fibres in the amount of 0.5% significantly increased the angle of internal friction (by 8.7\({}^{\circ}\), corresponding to 28.8%) as well as cohesion (by 14.4 kPa, corresponding 48.2%). [PERSON] [21] also introduced a significant improvement of soil CS mixed with the previously mentioned fibres, TEXZEM PES 200. DST was carried out using the previously mentioned large shear box apparatus, SHEARMATIC 300. The results showed that fibres in the amount of 0.5% increased both the angle of internal friction by 16.1\({}^{\circ}\) (corresponding 86.0%) and cohesion by 32.3 kPa (corresponding 211.2%). [PERSON] et al. [22], after analysing various possible methods for the estimation of DST uncertainty, came to the conclusion that a hybrid ordinary least squares method, denoted as HOLS, which they presented, provided better results in both cases of ho moscedastic and heteroscedastic data compared to the ordinary least squares (OLS), iterative weighted least square (IWLS), and weighted line of organic correlation (WLOC) approaches, as OLS largely overestimated measurement uncertainties (MUs) while IWLS and WLOC strongly underestimated MUs. The HOLS simulations of the MU values of the DST outcomes, depending on the correlation coefficient values of the DST measurands, clearly showed that when these correlations were stated as zero, then the MUs were underestimated.