Deformation Monitoring Model for Concrete Arch Dams Based on the Principle of Arch‐Beam Load Distribution

Traditional statistical models for arch dam deformation monitoring consider only functional equivalence between independent variables and deformation components (hydrostatic pressure, temperature, and time effects). However, they neglect the structural characteristic of compatible deformation between horizontal arch rings and cantilever beams under complex loading conditions. This study analyzes deformation mechanisms of arch dams under reservoir hydrostatic pressure and thermal loads based on arch‐beam load distribution principles. By examining load sharing and corresponding deformations of arch rings and cantilever beams within the dam system, we derive radial deformation expressions from the cantilever perspective, accounting for beam and foundation deformations. This establishes a mathematical formulation for radial deformation under hydrostatic pressure. Temperature loading is decomposed through the dam thickness into uniform temperature, equivalent linear temperature gradient, and nonlinear temperature gradient. Neglecting the nonlinear gradient (which primarily affects local surface deformation and stress), we develop separate radial deformation expressions for uniform temperature and linear temperature gradient. This yields a functional relationship for the temperature component of arch dam deformation. Building on these foundations, we construct a novel statistical model for analyzing concrete arch dam deformation behavior. Its validity and scientific rigor are demonstrated through engineering case studies.