# 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
### Energy Dissipation Rate Envelope Surfaces  
Based on Equation (7) and the trends of parameters \(A\), \(B\), and \(C\) observed in Figure 5, the energy loss rate equation for marine soft soil in dynamic triaxial tests, with water contents between 40% and 60% and confining pressures between 50 kPa and 200 kPa, can be derived using the linear interpolation method. This allows for the determination of the energy dissipation rate at which the internal structure of marine soft soil stabilizes under varying water content and confining pressure conditions.  
Figure 5: Trends of parameters \(A\), \(B\), and \(C\) of the energy loss rate equation under different water content and surrounding pressure conditions.  
Figure 6 shows the envelope surface diagram of the energy dissipation rate of marine soft soil during the dynamic triaxial test at 100 kPa. Figure 5(a) illustrates the envelope curves of energy dissipation rates under various water content conditions. Additionally, Figure 5(b) presents the three-dimensional envelope surface, plotted in a 3D coordinate system, where the X-axis represents the number of cyclic loadings, the Y-axis denotes different water content levels, and the Z-axis corresponds to the energy dissipation rate. Applying the same reasoning, Figure 7 is obtained.  
Figure 6: Envelope surface of energy dissipation rate of marine soft soil during dynamic triaxial test at 100 kPa surrounding pressure. Different colors represent different values of energy dissipation rate, from blue to red represents the gradual increase of energy dissipation rate in marine soft soil.  
Figure 7 presents the envelope surface diagram of the energy dissipation rate of marine soft soil during the dynamic triaxial test under confining pressures of 50 kPa, 100 kPa, and 200 kPa. Figure 7a shows the two-dimensional envelope curves of energy dissipation rates under various water content conditions, plotted with an enclosing pressure of 50 kPa as an example. Similarly, envelope curves for energy dissipation rates at perimeter pressures of 100 kPa and 200 kPa can also be constructed. These curves are then plotted in a three-dimensional coordinate system, resulting in a three-dimensional envelope surface, as shown in Figure 7b.  
From the figures, the following conclusions can be drawn: (1) Energy dissipation characteristics: Under different water contents and cycle times, the energy dissipation of marine soft soil shows a gradual increase. (2) Stability assessment: In similar dynamic triaxial test conditions found in engineering applications, this envelope diagram can be used to assess the stability of marine soft soil. Specifically, if the energy dissipation rate  
Figure 7: Envelope surface of energy dissipation rate of marine soft soil during dynamic triaxial test at 50 kPa, 100 kPa, and 200 kPa surrounding pressure. (**a**) Two-dimensional envelope curve of energy dissipation rate at 50 kPa. Different colors represent different values of energy dissipation rate, from blue to red represents the gradual increase of energy dissipation rate in marine soft soil.  
of the marine soft soil in the project falls below the range of the envelope surface, the soil is considered to be in a stable state; if it exceeds the range, the soil is in an unstable state. (3) Effect of confining pressure: As the confining pressure increases, the envelope surface of the energy dissipation rate of marine soft soil shows an upward trend. While the envelope surfaces at confining pressures of 50 kPa, 100 kPa, and 200 kPa follow a similar shape, the range of the envelope expands with increasing confining pressure.  
In summary, the stable state of marine soft soil in practical engineering applications can be assessed by converting the actual stress state of the soil into dynamic triaxial test conditions. The energy dissipation rate of marine soft soil is then calculated using Equations (6) and (7) and compared with the envelope surface diagram of the energy dissipation rate for marine soft soil at different confining pressures.