In　the　present　paper　the　author　investigates　the　global　structure　stability　of　Riemann　solutions　for　general　quasilinear　hyperbolic　systems　of　conservation　laws　under　small　BV　perturbations　of　the　initial　data,　where　the　Riemann　solution　contains　rarefaction　waves,　while　the　perturbations　are　in　BV　but　they　are　assumed　to　be　C-1-smooth,　with　bounded　and　possibly　large　C-1-norms.　Combining　the　techniques　employed　by　Li-Kong　with　the　modified　Glimm＇s　functional,　the　author　obtains　a　lower　bound　of　the　lifespan　of　the　piecewise　C-1　solution　to　a　class　of　generalized　Riemann　problems,　which　can　be　regarded　as　a　small　BV　perturbation　of　the　corresponding　Riemann　problem.　This　result　is　also　applied　to　the　system　of　traffic　flow　on　a　road　network　using　the　Aw-Rascle　model.　(C)　2013　Elsevier　Inc.　All　rights　reserved.