# Assessing the State of Structural Foundations in Permafrost Regions by Means of Acoustic Testing
## 2 Methodology. Problem Statement
### Problem Statement  
The analysis of RP and acoustic tests presented above shows that it is promising to combine them for solving the problems of permafrost foundations condition monitoring. The use of complex multi-parameter testing is one of the key trends in the modern development of non-destructive testing, technical diagnostics and condition monitoring [46]. RP tests make it possible to find the values of the deformation modulus, and acoustic tests can be used to monitor how its values change. To do this, it is necessary to find the relationship \(E_{G}=f\left(E\right)\).  
There is a number of works that are devoted to the relationship \(E_{G}=f\left(E\right)\)[45; 47]. These works are similar in that they attempt to find a universal relationship for individual types of soils or rocks. The deformation properties of frozen soils depend on many factors, such as humidity, temperature, particle size distribution, and the chemical composition of water, etc. In addition, as mentioned above, the deformation modulus is not constant and depends on the load acting on the soil. Based on the above, we believe that for the purpose of condition monitoring of permafrost foundations, the relationship between \(E\) and \(E_{G}\) should be found for each individual object under study. In our work, we study the relationship \(E_{G}=f\left(E\right)\) for soils in a frozen state and the possibility of using this relationship to study thawing soils.  
To find the correlation between the deformation modulus and the dynamic modulus of elasticity on site, we propose to equip the standard measuring probe of the radial pressuremeter with a low-frequency transmitting transducer (Figure 2). This method makes it possible to find \(\varepsilon=f(\sigma)\) over the entire range \((\sigma_{min};\,\sigma_{max})\) for each soil layer (Figure 2) and ensures that there is contact between the transmitting transducer and the borehole wall, which is necessary. Based on the test results, \(V_{p}\), and \(\varepsilon=f(\sigma)\) are calculated for each soil layer over the entire range \((\sigma_{min};\,\sigma_{max})\).  
In addition, we propose a method for finding \(F_{a}\) based on the results of acoustic tests. A similar method is widely used for determining the strength characteristics of concrete by acoustic testing [48,49]. This method is standardized [50] and is based on finding \(R_{c}\ =f\ (V_{p})\) using standard samples, where \(R_{c}\) is the compressive strength of concrete, and \(V_{p}\) is the propagation velocity of the longitudinal wave. During testing, \(V_{p}\) is measured directly on the object being studied, after which \(R_{c}\) is found using the previously found \(R_{c}\ =f\ (V_{p})\).  
To find \(F_{a}\ =f\ (V_{p})\), we used acoustic testing and in-plane shear testing along the addreeze zone [51]. Tests were conducted on frozen, transient, and plastic-frozen states. When condition monitoring of permafrost foundations by observing the object under study, \(V_{p}\) is found, after which \(F_{a}\) is found using the relationship above.  
Based on the above, two key objectives were set for our experimental study, which will make it possible to draw preliminary conclusions about whether it is possible to use acoustic testing to solve the problems of condition monitoring of permafrost soils:  
1. To study the possibility of finding \(E_{G}\) during the thawing of soils by means of acoustic testing using the relationship \(E_{G}\ =f\ (E)\) found for the frozen state.
2. To study the relationship \(F_{a}=f\ (V_{p})\) on disturbed samples of frozen sand.