# Characterization of the Evolution of Energy Loss Rate in Cyclic Load Testing of Marine Soft Soil
## 1 Introduction  
Marine soft soil is a typical soil type characterized by high water content, high compressibility, and low strength. It is commonly found in soft foundation projects in coastal areas, such as seaports, airports, subways, and cross-sea bridge constructions. Due to its unique genesis and structure, marine soft soil exhibits notable energy conversion and dissipation behaviors when subjected to external loads. Therefore, investigating the energy evolution laws of marine soft soil holds significant theoretical and engineering value in understanding its mechanical behavior and informing its use in engineering applications. As is well known, energy evolution laws are central to understanding the entire process of soil behavior, from elastic deformation and yielding to failure. By studying the energy conversion mechanisms in marine soft soil under stress--such as elastic energy storage, energy dissipation, and plastic energy dissipation--more accurate constitutive relationships can be developed. This provides a foundation for constructing refined constitutive models, contributes to the development of soil mechanics theories based on energy concepts, and offers new perspectives for enhancing nonlinear soil mechanics. According to thermodynamics, the transformation of matter and energy is a fundamental characteristic of physical changes in materials, and material failure occurs when there is instability in its physical state during energy conversion. [PERSON] et al. [1] investigated the effects of freezing and thawing temperatures and confining pressures on soil stress-strain and strength characteristics through monotonic and cyclic loading tests. They examined changes in total work, elastic deformation energy, dissipated energy, energy dissipation rates, residualstrain, and destructive variables. [PERSON] et al. [2] conducted uniaxial compression tests on Genhe silty permafrost at different temperatures, exploring the effects on mechanical and energy indices, and established quantitative relationships between elastic-plastic strain energy, stress/strain, and temperature. [PERSON] et al. [3] proposed a new energy-based criterion for slope failure and analyzed its applicability in slope stability analysis with spatially varying soil properties. [PERSON] et al. [4] analyzed the energy evolution and strength characteristics of coarse-grained soil using shear tests, derived energy balance equations, and developed a theoretical model linking energy and strength parameters. [PERSON] et al. [5] explored the Brazilian splitting test's applicability in determining the tensile strength of expansive soil, considering the effects of water content and dry density on tensile strength and energy evolution during loading. [PERSON] et al. [6] studied energy evolution in coal specimens under graded cyclic loading/unloading and established an energy evolution model based on dissipation behavior. [PERSON] et al. [7] quantified the strength characteristics of permafrost using an energy-based approach, incorporating damage variables into a viscoelastic constitutive model. [PERSON] et al. [8] conducted triaxial tests on marble to study energy evolution during rock deformation and developed a nonlinear energy evolution model. [PERSON] et al. [9] proposed a one-dimensional sharp interface model for active layer evolution and permafrost thaw. [PERSON] et al. [10] introduced a variational model of pressure plasticity to construct cohesive energy in a dissipative system. [PERSON] et al. [11] performed UCS tests on soft soil reinforced with different binder contents and polypropylene fibers to assess the impact of cyclic loading on elastic and plastic deformation energies. In summary, while the study of energy evolution laws has been extensively applied in the geotechnical analysis of soft rocks and coal beds, research on marine soft soil has primarily focused on consolidation, shear properties, and microstructural evolution. Systematic studies based on energy evolution laws remain limited.