# Characterization of the Evolution of Energy Loss Rate in Cyclic Load Testing of Marine Soft Soil
## 3 Envelope Surfaces of Energy Dissipation Rates for Marine Soft Soil in Dynamic Triaxial Tests
### Calculation Method for Energy Loss Rate  
When constructing urban subway systems in marine soft soil, the strength of the soil gradually degrades under the cyclic loading caused by subway train operations. However, existing strength theories and damage criteria are often insufficient for accurately analyzing and assessing this type of strength failure or damage. Therefore, this paper adopts an energy-based approach to study the internal energy evolution behavior of the soil under cyclic loading/unloading. By analyzing energy changes, a criterion based on sudden shifts in strength is established to evaluate failure. This method can be used to determine whether the strength failure occurs in marine soft soil, providing a reference for assessing the overall stability of subway tunnels [15; 16]. Under cyclic loading, the internal structure of the soil continuously adjusts and deteriorates. The relationship between elastic strain energy and plastic dissipation energy (hysteretic energy loss) reflects the deterioration of soil stiffness and the accumulation of structural damage. Based on the stress-strain data obtained from the dynamic triaxial tests of marine soft soil with varying water contents, a Python 3.11 program was developed to calculate the elastic strain energy, plastic strain energy, and energy dissipation rate during each loading and unloading cycle. The results yielded the change curve of the energy dissipation rate with the number of loading cycles in marine soft soil under different water content conditions, as shown in Figure 3. From the figure, the following observations can be made: (1) Effect of circumferential pressure and cyclic loading: Under the same water content conditions, the energy dissipation rate of marine soft soil increases with higher circumferential pressure, while it decreases as the number of cyclic loadings increases. The curve fluctuates but eventually stabilizes, meaning that the energy dissipation rate reaches a stable value after a certain number of loading cycles. This stable value can be used as an indicator of potential failure in marine soft soil. (2) Effect of water content: Under different water content conditions, the energy dissipation rate of marine soft soil increases as the water content rises at a given circumferential pressure. This can be explained by two factors: (1) during the overall cyclic loading phase of marine soft soil, the proportion of elastic strain energy is largest, while dissipated energy remains relatively small. This suggests that most of the input energy is stored as elastic strain energy. (2) As the perimeter pressure increases, the proportion of dissipated energy decreases, but the proportion of elastic strain energy remains dominant. This indicates that the energy transformation behavior across specimens under different pressures is similar, with energy accumulation as the dominant process. To better illustrate the energy dissipation characteristics of marine soft soil, an exponential function was used to fit the relationship curve shown in Figure 3, resulting in the fitting curve for the energy dissipation rate of marine soft soil versus the number of cyclic loadings, as shown in Figure 4.  
Figure 3: _Cont_. Figure 4: \(Cont\). Figure 3: Variation in energy dissipation rate with the number of cyclic loadings in marine soft soil under different water content conditions. From Figure 4, the following observations can be made: (1) Initial and stabilization stages of energy dissipation: In the initial decay stage, the energy dissipation ratio remains high, regardless of the water content. During the first few cycles, the energy dissipation ratio decreases rapidly as the number of cycles increases. This is because the initial cyclic loading induces substantial plastic rearrangement, microfracture expansion, or pore structure adjustments within the soil, resulting in significant energy consumption per cycle.