Analytical　solutions　for　coupled　problems　are　very　significant　for　both　understanding　the　physical　mechanism　and　verifying　the　numerical　methods.　However,　existing　solutions　usually　focus　on　advection-dispersion　models　without　considering　the　coupling　effect　of　contaminant　transport　or　partial-coupled　models　with　the　zero　initial　concentration　(ZIC)　condition,　which　are　impractical　in　many　engineering　applications.　This　paper　proposes　novel　analytical　solutions　to　solve　the　non-zero　initial　concentration　(NZIC)　problem　for　a　fully-coupled　hydraulic-mechanical-chemical　(HMC)　model　by　Fourier　transform.　The　proposed　analytical　solutions　are　highly　competent　and　efficient　compared　with　existing　solutions　from　the　literature.　The　solutions　are　applied　to　investigate　the　long-term　contaminant　transport　behavior　and　consequent　deformation　of　clay　liner　under　NZIC　conditions.　Results　show　that　the　presence　of　NZIC　greatly　promotes　contaminant　ions　migration　and　shorten　breakthrough　time.　The　higher　the　initial　concentration,　the　shorter　the　breakthrough　time.　When　the　initial　concentration　is　increased　by　3　and　5　times,　the　corresponding　breakthrough　time　is　reduced　by　23.9　and　27.1　years,　respectively.　In　practical　engineering,　neglecting　the　NZIC　of　contaminant　can　lead　to　an　overestimation　of　performance　efficiency　of　clay　liners.