Multiscale cumulative damage and compaction behavior in deep-sea and deep-earth energy engineering

The safe operation of offshore wind power foundations, deep geothermal systems, and subsurface energy-storage infrastructure depends on cementitious materials retaining mechanical integrity after environmental deterioration and pressure-dominated loading; however, this state-dependent transition remains insufficiently described in existing constitutive frameworks. To address this issue, a pore-evolution-governed multiscale constitutive framework is established, in which cumulative damage and compaction are incorporated within a unified description. A cumulative damage function is formulated from characteristic pore size, porosity, and connectivity to quantify irreversible degradation of the solid skeleton, while a compaction state function characterizes the progressive closure of pores, microcracks, and weakened interfacial defects during continued compression. These two mechanisms are embedded into a state-dependent plastic-damage formulation and transferred to equivalent stochastic elements through a two-step Mori-Tanaka homogenization strategy, enabling coupled evolution of stiffness, strength, peak strain, and post-peak response. For FT-induced cumulative damage, representative of deep-sea infrastructure deterioration, the model captures enlargement of the compaction-dominated regime: peak strain increases by 116.7%, the strain at 40% of peak stress by 234.7%, and the secant modulus decreases by 76.8%. For hydrostatic pressure-induced compaction, representative of deep-earth energy engineering, the model reproduces the transition from damage accumulation to compaction-sensitive compression with an average normalized pre-peak deviation of 7.2%. The results show that weaker porous skeletons exhibit stronger compaction sensitivity, affecting not only strength loss, but also stiffness recovery and the deformation demand required to re-establish stable load transfer, thereby providing a mechanics-based basis for integrity assessment and service prediction in offshore, geothermal, and subsurface energy systems.