General analytical solutions for one-dimensional diffusion of degradable organic contaminant in the multi-layered media containing geomembranes

• Derives general analytical solutions for one-dimensional diffusion of degradable organic contaminants in multi-layered media containing geomembranes under time-varying boundary conditions. • Solutions are validated against experimental data, existing analytical solutions, and finite-difference methods, confirming their accuracy and reliability. • Application to composite cutoff walls reveals key factors affecting service performance, providing scientific guidance for barrier design and evaluation. • The analytical solutions serve as a benchmark for verifying complex numerical models in contaminant transport studies.