## 3 Results  
The TSHC tests allowed the values of undrained shear strength to be obtained at selected angles of principal stress rotation for undisturbed clay, undisturbed and reconstituted sandy silty clay, as well as reconstituted clayy sand (Table 2). To determine these parameters, the maximum deviator stress was used as the failure criterion. All obtained values of undrained shear strength were normalized based on the vertical effective stress, \(\sigma^{{}^{\prime}}v\), to obtain comparable values of normalized undrained shear strength. Based on research carried out by [PERSON] [41] in a torsional shear hollow cylinder apparatus, a relationship was proposed to evaluate undrained shear strength at any angle of principal stress rotation [45]. The proposed relationship differs from the commonly known equation proposed by [PERSON] [9], because undrained shear strengths at \(\alpha\) values of \(0^{\circ}\) and \(90^{\circ}\) are determined based on strength tests. This allows a more accurate determination of undrained shear strength for \(\alpha\) values between \(0^{\circ}\) and \(90^{\circ}\). The undrained shear strength at any angle of principal stress rotation, \(\tau_{fu}^{\alpha}\), can be evaluated as [45]:  
\[\tau_{fu}^{\alpha}=\tau_{fu}^{90^{\circ}}+\eta_{\tau_{fu}}\Big{(}\tau_{fu}^{0 ^{\circ}}-\tau_{fu}^{90^{\circ}}\Big{)}, \tag{3}\]  
where \(\eta_{\tau_{fu}}\) is the index of change in undrained shear strength, \(\tau_{fu}^{90^{\circ}}\) is the undrained shear strength at \(\alpha=90^{\circ}\), and \(\tau_{fu}^{0^{\circ}}\) is the undrained shear strength at \(\alpha=0^{\circ}\). The index of change in undrained shear strength due to a change in angle of principal stress rotation is defined as:  
\[\eta_{\tau_{fu}}=\left(\tau_{fu}^{\alpha}-\tau_{fu}^{90^{\circ}}\right)/ \left(\tau_{fu}^{0^{\circ}}-\tau_{fu}^{90^{\circ}}\right). \tag{4}\]  
Figure 3: Selected soil samples after the TSHC tests. Figure 2: An example of a soil sample in the shape of a hollow cylinder. Based on the TSHC test results, the following relationship between the indexes of change in undrained shear strength at any angle, \(\alpha\), was proposed by [PERSON] [41]:  
\[\eta_{\tau_{fus}}=1-(sin\alpha)^{exp[a_{o}+a_{1}(\frac{a}{90})^{n}]}, \tag{5}\]  
where \(a_{o}\), \(a_{1}\), and \(n\) are empirical coefficients. The obtained relationship in Equation (5) for over-consolidated clayey sand (clSa(R)), tested by [PERSON] [40], is presented in Figure 4. The coefficient of determination, \(R^{2}\), for the relationship determining the change in undrained shear strength for clayey sand was equal to 0.93. The values of empirical coefficients \(a_{o}\), \(a_{1}\), and \(n\) for all tested soils are shown in Table 2. Test results showed that the values of empirical coefficients in Equation (5) depended on the type and structure of the soil, and its stress history. The proposed equation was derived on the basis of tests performed on over-consolidated clays with a low impact of glaciotectonic disturbances on the soil structure. Figure 5 presents the undrained shear strength of clayey sand, clSa(R), based on Equation (3), with the index \(\eta_{\tau_{fus}}\) obtained from Equation (5), and empirical coefficients presented in Table 2. In Figure 5, undrained shear strength evaluated based on Bishop's relationship is also presented. The undrained shear strength at \(\alpha=90^{\circ}\) determined in the TSHC test was different from the result based on [PERSON]'s relationship. In this case, the relative error was equal to 0.82. Using [PERSON]'s relationship to determine undrained shear strength for clayey sand clSa(R), the biggest relative error was at an \(\alpha\) value of \(30^{\circ}\), and was equal to 4.19%. However, when using the proposed method, the error was equal to 0.38%. Figure 4: Relationship describing the index of change in undrained shear strength for clayey sand clSa(R). Figure 5: Undrained shear strengths based on Equation (3), Equation (5), and Bishop’s relation for clayey sand clSa(R).