# Study of the Effect of Cutting Frozen Soils on the Supports of Above-Ground Trunk Pipelines
## 3 Results
### Development of Above-Ground Trunk Pipeline Support Design
These experiments aimed to simulate the loads created by soil frost heave forces and to determine the stress of fracture of the frozen soil, depending on soil type and temperature, as a result of the continuous spread of permafrost in the region. Figure 4: Instrumentation to determine the characteristics of frozen soil: (**a**)—flask: Volumetric Flasks with screw caps 25 mL, accuracy 50 mm; (**b**)—installation for testing frozen soil by single-plane shear along the freezing surface: GEOTEC STANDARD, vertical load up to 10 kN, accuracy \(\pm\) 1%; (**c**)—stabilometer: automated GT 1. 3.8, vertical load up to 5 kN lateral pressure up to 0.6 MPa, accuracy \(\pm\) 1%; (**d**)—unit for soil compression tests: KPR-1, pressure up to 1 MPa, accuracy 0.001 MPa. Figure 5: Refrigerators for soil freezing: (**a**)—refrigerator for lower temperatures BIND_6056, temperature up to 5 \({}^{\circ}\)C, accuracy 0.1 \({}^{\circ}\)C; (**b**)—refrigerator for lower temperatures UT-7400, temperature range 0–65 \({}^{\circ}\)C, the accuracy of maintaining temperature \(\pm\)0.1; (**c**)—temperature value for experiments at \(-\)4 \({}^{\circ}\)C; (**d**)—temperature value for experiments from \(-\)5 \({}^{\circ}\)C to \(-\)10 \({}^{\circ}\)C.  
At the outset of the experiment, it was determined that a fracture stress of 3.5 kN was necessary for the destruction of frozen soil at \(-4\)\({}^{\circ}\)C using a sharp edge with an angle of 45 degrees. The results indicated that the required fracture stress was higher for the 45-degree sharp edge compared to the use of a sharp edge with an angle of 30 degrees. Consequently, a 30-degree sharp edge was employed for subsequent experimentation. The measurements were recorded and displayed on the computer screen as graphs and values, as exemplified by the fracture stress plots of frozen soil at the minimum low temperature of \(-10\)\({}^{\circ}\)C in Figure 8.  
The loads acting on the support of the aboveground pipeline were calculated by determining the fracture stress of frozen soil, at which the soil undergoing frost heaving  
Figure 6: Experimental unit with built-in refrigerating chamber: load limit of 150 tons, limit of relative error \(\pm\) 1%: (**a**)—press with the closed refrigerating chamber; (**b**)—press with an open refrigerating chamber (created by the authors). Figure 7: Frozen soils in the state of fracture stress: (**a**)—frozen sand; (**b**)—frozen loamy sand; (**c**)—frozen clay. Source: from the authors. was severed from the sharp edge of the supporting structure under the influence of frost heave forces. Determination of the Convergence of Calculation Results Based on the Proposed Experimental Model with the Results of Finite-Element Modeling of the Process of Cutting Frozen Ground  
In this section, we developed a finite-element model of the cutting process of frozen soil using the PLAXIS software. To this end, a three-dimensional model was constructed to represent a loaded baseplate cutting through the frozen soil. The calculations were performed using the Mohr-Coulomb module, a mathematical model that describes the response of brittle materials, such as concrete, to both shear stress and normal stress. Utilizing the results of the in-situ experiment, the soil characteristics were employed as the initial simulation data for a baseplate with frozen soil, as depicted in Figure 9.  
Figure 8: Fracture stress diagram of frozen sand, sandy loam, and clay at \(-10\)\({}^{\circ}\)C.  
Figure 9: Model of a loaded base plate cutting bloated frozen soil. Model parameters: length—150 mm, width—80 mm, height—170 mm, angle of sharp edge—30 degrees. Ground cutting occurs as a result of plastic deformation when the relative shear stress reaches a value of 1 (depicted in red) on all side faces. This is shown in Figures 10-12.