# 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
Once the soil undergoes \"initial compaction\" or \"initial reorganization,\" the amount of plastic deformation gradually decreases in subsequent cycles, leading to a reduction in corresponding energy consumption. In the later stage, as the number of cycles increases, the decrease in the energy dissipation ratio slows significantly and tends to stabilize. This indicates that, with cumulative plastic deformation, pore water pressure adjustments, and structural reorganization, the soil reaches a more stable state, where the area of the hysteresis loop no longer exhibits significant changes. The energy loss rate at this point reflects the stabilization of the internal structural adjustment of marine soft soil, which becomes stable at energy dissipation rates of 11.82%, 17.83%, and 38.29% for water contents of 40%, 50%, and 60%, respectively. (2) Exponential function fitting: The relationship curve between the energy dissipation rate of marine soft soil and the number of cyclic loadings can be effectively fitted using an exponential function, with R-squared values  
Figure 4: Fitted curve of the relationship between energy dissipation rate and the number of cyclic loadings in marine soft soil under 100 kPa surrounding pressure. greater than 0.93 indicating a high degree of fit. Based on this exponential function, the following relationship equation between the energy dissipation rate and the number of cyclic loadings is proposed:  
\[D=A+B\cdot e^{-\frac{N}{C}} \tag{7}\]  
where \(D\) is the energy loss rate, \(N\) is the number of cyclic loadings, \(A\) is the \"stabilized\" or \"residual\" value of the energy dissipation ratio when the number of cycles becomes large, \(B\) controls the initial energy dissipation amplitude, and \(C\) reflects the decay rate. Both \(A\) and \(B\) are nonlinear polynomial functions related to water content and confining pressure. This is due to the fact that, in soil mechanics research and practical engineering applications, water content and confining pressure are two key factors that significantly influence the mechanical behavior of soil and its cumulative strain under cyclic loading. The water content affects the physical state and mechanical properties of soil, such as density, porosity, and shear strength, all of which are critical for assessing the stability and safety of engineering designs. For example, rainfall and fluctuations in the water table can alter the water content, which in turn impacts the soil's bearing capacity. The confining pressure, on the other hand, determines the initial contact and interaction strength between soil particles and plays a decisive role in assessing the deformation modulus and strength parameters of the soil, particularly in deep foundations, tunnel excavations, and slope stability analyses. While the dynamic stress ratio is theoretically important as a parameter for describing soil behavior under dynamic loading, its changes and effects are often less direct or significant than those of water content and confining pressure in practical engineering applications. Moreover, determining and applying the dynamic stress ratio involves more complex factors, increasing the difficulty and uncertainty of engineering analysis. Therefore, this chapter focuses on the energy loss rate equation under varying water content and confining pressure conditions, excluding the influence of the dynamic stress ratio. This simplification aims to enhance the practicality and predictive accuracy of the energy loss rate equation, providing more direct theoretical support and technical guidance for engineering design and construction.