# Assessing the State of Structural Foundations in Permafrost Regions by Means of Acoustic Testing
## 2 Methodology. Problem Statement
### Soil Model Selection
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Model** & **Parameter** & **Method** \\ \hline \multirow{4}{*}{Mohr–Coulomb} & \(E\) & Triaxial compression, pressuremeter tests \\  & \(\mu\) & Oedometer tests \\  & \(\varphi\) & In-plane shear tests \\  & \(c\) & \\ \hline \multirow{4}{*}{Hardening Soil} & \(E_{50}\); \(E_{ur}\) & Triaxial compression \\  & \(\mu\); \(\mu_{ur}\) & Triaxial compression \\  & \(E_{ood}\) & Triaxial compression \\  & \(\varphi\) & In-plane shear tests \\  & \(c\) & \\  & \(\Psi\) & Triaxial compression \\  & OCR & In-plane shear tests \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Methods of finding the parameters of soil models. The values of the stress tensor components take into account the interface between the soils and the pile (Figure 1). For the zone of seasonal thawing of soils and the pile freeze zone, [PERSON]'s solution [38] is applied. As for the soil compression zone, [PERSON]'s solution is used [39]. In both cases, the stress tensor components depend on the coordinates of the finite element and the resulting load:  
\[\{\sigma\}=f(P_{i},\ x,\ y,z,\ \mu) \tag{8}\]  
where \(P_{i}\) is the resulting load from the structure for different interaction zones (Figure 1), \(x,\ y,z\) are the coordinates of the elementary volume of soil, and \(\mu\) is Poisson's ratio. Let us find the resulting load for each pile-soil interaction zone:  
\[P_{1}=N-F_{p} \tag{9}\]  
\[P_{2}=N-\left(F_{p}+F_{a}\right) \tag{10}\]  
\[P_{3}=N-\left(F_{p}+F_{a}\right) \tag{11}\]  
\(F_{p}\) (Figure 1) depends on the depth of the layer of seasonal thawing \(h_{s}\)[25]. Therefore, with an increase in \(h_{s}\), \(F_{p}\) will also change. Similarly, when the soils of the adfreeze zone start thawing, the resistance of the soil along the lateral surface \(F_{a}\) will change. Consequently, the components of the stress tensor also depend on the state of the soils. Figure 1: The pile-soil system. 1—zone of seasonal thawing; 2—pile adfreeze zone; 3—soil compression zone; 4—pile foundation; \(F_{a}\)—shear strength in the soil along the lateral adfreeze zone; \(F_{p}\)—frost heaving force; \(N\)—load applied by the structure. Summarizing the above, the following conclusions can be made:  
* When condition monitoring a permafrost foundation, it is necessary to monitor not only changes in the deformation characteristics of the foundation, but also in the forces that interact within the pile-soil system. * In order to use DTP as the foundation of a model for monitoring permafrost foundations, it is necessary to monitor on site changes in \(E_{G}=E_{G}(\sigma)\), \(F_{p}\), \(F_{a}\). The use of DTP makes it possible to compensate for some of the shortcomings of the MC model, which expands its application range. However, it should be noted that DTP does not factor in rheological properties, which are strongly pronounced in frozen soils [40; 41; 42]. These properties need to be accounted for when making a long-term forecast of changes in the state of the foundation. Long-term forecasting of the state of permafrost is a complex problem that requires analysing a significant number of factors and parameters that can change over time, especially when climatic indicators fluctuate and change. In this regard, a question arises of whether it is possible or viable to make long-term forecasts. Therefore, the research we conducted was aimed at providing a rationale for a method that can be used for monitoring the current state of permafrost soils. The method implies analysing the state of soils at a given time and monitoring changes in soil characteristics over time.