## 3 Results and Discussion  
The evaluation of strain gauge measurements and all related analyses showed that the stress increments detected on the pipeline just before entering the support foot were negligible during the sheet pile hammering. The recorded stress changes were comparable to the measurement made in the resting state and did not exceed the value of \(\pm 2\) to 3 MPa. In the case of monitoring the response of the pipeline to pressure changes in it, it was necessary to understand the stresses detected by the measurement as increments of their values \(\Delta\sigma\), which are related to increments of pressure \(\Delta p\) compared to its reference value at \(p_{ref}\) = 6,0972 MPa. The largest stress increases were recorded by the strain gauge located at the top of the arch above the river. Based on the correlation analyses performed on the resulting regression dependences of \(\Delta\sigma_{t}\) and \(\Delta\sigma_{m}\) on \(\Delta p\), it was found that from a statistical point of view, the quadratic polynomial model is slightly more representative than the linear polynomial model. However, this was particularly true for a range of measured values. In case of need for extrapolation of these dependencies and reverse reconstruction of the total values of stresses \(\sigma_{t}\) and \(\sigma_{m}\) and their dependence on the input (primary) quantity, i.e., pressure \(p\) in its wide range of 0 to 6 or 7 MPa, was required, the quadratic models provided unrealistic or distorted results. Therefore, paradoxically--a slightly less representative from a statistical point of view, but far more realistic from a technical point of view--a linear model was chosen for extrapolation purposes. The increments of shear stresses in the pipe wall in the monitored locations were small, and the calculated values are smaller or comparable to the resolution or tolerance of the measuring chain; it is, therefore, possible to assume that the directions of the principal normal stresses are identical to the circumferential and axial directions of the pipe; these small values of shear stress increments correspond to a lower value of both the correlation coefficient and the coefficient of determination; it follows that with small shear deformations, the influence of measurement inaccuracy, given by the resolution of the measurement chain as well as the physical nature of the measurement method, is more pronounced. This model showed that the increase in pressure \(\Delta p\) by 1 MPa corresponded to the approximate increases in normal stress in the circumferential direction \(\Delta\sigma_{t}\) = 61.5 MPa and in the axial direction \(\Delta\sigma_{m}\) = 46.0 MPa. The analysis showed that this pair of stresses is also a pair of principal stresses. Therefore, they could also be used to determine the corresponding unit value of the equivalent stress \(\sigma_{eq}{}^{VIM}\) according to the [PERSON] theory at a level of 55.4 MPa. Further, with the application of this linear regression model for the reference value of pressure at the level of \(p_{ref}\) = 6.0972 MPa, it was then possible to further express the corresponding absolute values of the stresses \(\sigma_{t}\) and \(\sigma_{m}\) at the level of 374 and 280 MPa and the corresponding level of the equivalent stress \(\sigma_{eq}{}^{VIM}\) at the level of 337 MPa. At the same time, for stress increments above 10 MPa, a significant dependence of their values on the pressure in the pipeline was observed. Moreover, from a mutual comparison of the curves of stress increments \(\Delta\sigma_{t}\) and \(\Delta\sigma_{m}\) and at the same time against pressure changes \(\Delta p\) from the curves in Figure 13, a weak geometric nonlinearity of the pipeline