Second, when the load is larger than the yield limit but smaller than the critical stress limit, plastic deformation will occur. Nevertheless, the plastic deformation tends to cease with the number of cycles. After numerous repetitions, the structure under this amplitude of load will respond purely elastically. If this material behavior will happen, then such a response is named shakedown, and the critical limit mentioned above is termed a shakedown limit or elastic shakedown limit. If the applied load is higher than the shakedown limit, the material will be plastically deformed during imposed cycles of load and would eventually fail due to fatigue or excessive plastic deformation. This phenomenon of variable material response leads to a desire for the rational criterion for design [28; 29; 30; 31]. The abovementioned phenomena are presented in Figure 1, where three stress limits are given. Therefore, we can divide the soil behavior into three zones of soil response, namely A, B, and C. In geotechnical engineering, the shakedown theory is useful for problems of foundations under cyclic loading [32] and under moving traffic loads [33; 34; 35; 36; 37; 27]. Deriving the exact shakedown limits in a three-dimensional stress state would be problematic, especially in cases of porous media, such as clayey soils. The engineering application of this concept would be provided by two fundamental shakedown theorems developed by [PERSON] [38] and [PERSON] [39]. A detailed description of this behavior is presented in Figure 1, where purely elastic behavior is displayed when the first point of the body does not reach the yield stress. The structure does not suffer any macroscopic plastic deformation, and damage does not occur at all. However, the load-carrying potential of the fabric is not entirely exploited [36; 40; 41]. During the soil's repeated loading, the hysteresis loop phenomena occur. Hysteresis loop shape depends on the stress level as well as on the physical parameters of the soil. Cyclic loading causes changes in the soil structure and, consequently, their properties. The analysis of the soil stress-strain response to cyclic loading will result in the hardening or softening process. The soil will experience cyclic hardening at most of the cyclic stress levels, despite the stress level being near to the failure point where the sample fails after a few cycles [41; 42; 43]. In other cases, the soil will decrease its strain amplitude in stress-controlled tests or increase its stress amplitude in strain-controlled trials. This relationship is depicted \[\log\bigl{(}\varepsilon_{a}^{p}\bigr{)}=a+b\cdot\log(N)=a\cdot N^{b}, \tag{2}\]1  
Nevertheless, the hysteresis loop on the stress-strain relationship can be simplified into the set of straight lines, which designate minimal and maximal strain in the range of stress amplitude. The loading and unloading in the one cycle will cause total axial strain \(\varepsilon_{a}^{T}\), which is compound from elastic \(\varepsilon_{a}^{E}\) and plastic \(\varepsilon_{a}^{P}\) axial strain parts as in Equation (12):  
\[\log\bigl{(}\varepsilon_{a}^{p}\bigr{)}=a+b\cdot\log(N)=a\cdot N^{b}, \tag{2}\]2  
The exact value of plastic and elastic strains in one cycle is easy to find in the stress-controlled tests. The energy stored and dissipated during one cycle of repeated loading describes a range of  
\[\log\bigl{(}\varepsilon_{a}^{p}\bigr{)}=a+b\cdot\log(N)=a\cdot N^{b}, \tag{2}\]3 Shema of stress-strain response of a material to cyclic loading, A—pure elastic response, B—shakedown, C—ratcheting during the cyclic loading. plastic strain occurring in one cycle. Dissipated energy during the following cycles decreases and the elastic response has a more and more substantial share in the total strain [41; 44]. Figure 3 presents such a classification of energy share during one cycle of repeated energy. In practice, the engineers and designers desire information about the settlement of the structure. The mathematical model, sophisticated enough and easy to use, is the solution to this problem.