# Assessing the State of Structural Foundations in Permafrost Regions by Means of Acoustic Testing
## 2 Methodology. Problem Statement
### Methods for Finding Soil Parameters  
As mentioned above, when condition monitoring of permafrost soils, it is necessary to conduct on-site measurements of the parameters included in the model. Moreover, it is important to measure them directly in the zone of the structure's influence on the soils. Let us consider methods for finding \(E_{G}=E_{G}(\sigma)\), \(F_{p}\), \(F_{a}\). \(F_{p}\) is found using the value of settlement \(h_{s}\)[25]. To monitor \(h_{s}\), a lot of methods and instruments have been developed, which is why we do not discuss here the issue of finding \(F_{p}\). As a method of finding \(E_{G}=E_{G}(\sigma)\), let us consider radial pressuremeter (RP) tests. This method is suggested in [43], and it has a number of advantages and disadvantages. The main advantage is that when soils form different layers, which is typical for the Arctic zone of the Russian Federation, the use of RP makes it possible to find \(E_{G}=E_{G}(\sigma)\) for each type of soil. Condition monitoring of permafrost soils implies ongoing monitoring of the deformation and strength parameters of soils. The use of RPs implies loading the soil in a range of stresses \((\sigma_{max};\sigma_{min})\) during each observation. Soils are characterized by such properties as hysteresis and hardening/softening, as a result of which the deformation moduli found during initial loading and after repeated loading will not be equal. In our opinion, this is the biggest limitation to using RP tests for solving problems of condition monitoring of permafrost soils. Another limitation is that the stresses produced by the pressuremeter chamber are transmitted through soils at distances no longer than 500 mm. The lateral adfreeze force \(F_{a}\) is determined at the stage of design and engineering surveys. Currently, there are no direct monitoring methods for this parameter. \(F_{a}=f\) (\(A_{t}\)) is found, where \(A_{t}\) is the soil thawing coefficient that is based on the freezing temperature of soils, which is not constant [14; 15; 16]. In our opinion, to solve the problems of condition monitoring of permafrost foundations, acoustic testing can be used. This method is currently quite widely used to study the physical and mechanical properties of soils. However, similar to RP tests, acoustic testing has a number of limitations. In acoustic tests, soil is loaded in the elastic range. As a result of the elastic effect [44], no residual deformations are observed in soils, which, in contrast to RP tests, allows for repeated studies. The elastic wave passes through the mass of the soil being studied, making it possible to directly study the deformation parameters of soils in a much larger volume of soil compared to RP tests. At present, distances can reach 100 to 150 m. However, when choosing the dimensions of the volume of soil, it must be understood that an increase in them leads to the averaging of the resulting indicators. Studying mechanical properties of soils by acoustic testing is based on the mathematical methods of the theory of elasticity. However, in real conditions, soils are not absolutely elastic; the foundations of structures operate in the elastic-plastic range of loads, which is clearly demonstrated by the results of plate load tests [45]. This fact is the biggest limitation for the use of acoustic testing. An indicator of the deformation properties of soils is the deformation modulus (12):  
\[E_{G}=\frac{\sigma}{\varepsilon_{G}}=\frac{\sigma}{\varepsilon_{e}+ \varepsilon_{p}} \tag{12}\]  
where \(E_{G}\) is the deformation modulus, \(\varepsilon_{G}\) is the relative normal total strain, \(\varepsilon_{p}\) is the relative normal plastic strain, \(\sigma\) is the normal stress, and \(\varepsilon_{e}\) is the relative normal elastic strain.