# Characterization of the Evolution of Energy Loss Rate in Cyclic Load Testing of Marine Soft Soil
## 6 Conclusions  
Research on energy evolution laws has primarily focused on geotechnical analyses of soft rocks and coal seams, while studies on marine soft soil have mainly concentrated on consolidation, shear behavior, and microstructural changes. However, systematic investigations incorporating the energy evolution laws of marine soft soil remain limited. This study, based on dynamic triaxial test data, explores the relationship between the energy loss rate and the number of cyclic loading cycles. By deriving and fitting the energy loss data, a mathematical expression for the energy loss rate is developed. The study introduces the energy loss rate ratio as a novel criterion for assessing the strength failure of marine soft soil. Additionally, the research examines the energy loss characteristics under different water content levels and confining pressures, providing valuable insights into the mechanisms of strength failure. These findings offer a new theoretical framework and practical tools for the rapid engineering strength evaluation of marine soft soil. The key research conclusions are as follows:  
1. A comprehensive method for calculating the energy dissipation rate of marine soft soil is proposed, accompanied by a derived mathematical expression. This method offers a precise and systematic approach for evaluating the energy dissipation behavior, providing a reliable means to assess the material's response under cyclic loading, and contributing to a deeper understanding of the dynamic properties of marine soft soil. 2. The study presents detailed envelope surfaces of the energy loss rate of marine soft soil, under various confining pressures and water content conditions, to assess its stability state. These envelope surfaces not only enhance the understanding of how marine soft soil behaves under different environmental and loading conditions but also offer a validated tool for practical engineering applications, ensuring more accurate stability assessments and facilitating the design of more resilient infrastructure. 3. Taking the subsea shield tunnel project traversing soft soil strata beneath an operational freight railway as a case study, this research systematically investigates the mechanical behavior of critical structural points through numerical simulation and analytical methods. A comprehensive stress-strain behavior analysis is conducted, followed by the development of a novel energy dissipation rate calculation model derived from the proposed methodology. The stability assessment is performed through comparative analysis with an innovative three-dimensional stability envelope, enabling quantitative evaluation of the point's dynamic equilibrium state under complex geotechnical loading conditions. The detailed envelope surfaces of the energy loss rate under various confining pressures and water content conditions can be employed to assess the stability of marine soft soil more effectively. These envelope surfaces can serve as a tool for real-time monitoring and stability evaluation. During the construction of subsea tunnels or other infrastructure in marine soft soil, these envelope surfaces can be used as a guide for continuous monitoring of soil conditions. When the energy loss rate exceeds certain thresholds, engineering interventions (e.g., additional grouting or reinforcement) can be triggered to prevent failure. In summary, the mathematical calculation method for the energy dissipation rate presented in this study aligns well with the overall trend of the experimentally calculated values, particularly in the low cycle number range. It is also demonstrated that using the proportion of energy dissipation rate as a criterion for evaluating the strength failure characteristics of marine soft soil is a feasible approach. These research findings provide valuable theoretical support for the development of theoretical models and engineering strength evaluations of marine soft soil. Conceptualization, K.W. and Y.Z. ; methodology, Y.L. ; formal analysis, Y.S. and H.Z. ; data curation, Y.S.