Based　on　the　discrete　element　particle　flow　software　PFC3D,　four　irregular　particles　with　the　same　aspect　ratio,　convexity,　and　sphericity　as　the　binary　pictures　are　constructed.　To　examine　the　influence　mechanisms　of　particle　shape　on　mechanical　properties,　microstructure,　and　critical　characteristics,　an　index　F　characterizing　the　regularity　of　the　particle　shape　is　introduced.　By　examining　the　link　between　the　regularity　index　and　the　constitutive　parameter,　a　statistical　model　is　developed　to　predict　the　peak　friction　angle　while　considering　the　impacts　of　relative　density　and　particle　shape.　The　findings　demonstrate　that　decreasing　the　value　of　the　regularity　index　always　causes　an　increase　in　the　stress　ratio,　shear　dilatancy,　and　void　ratio.　In　p＇-q,　e-logp’,　and　MCN-logp’　spaces,　the　distribution　pattern　of　critical　state　lines　is　affected　by　the　particle　shape.　At　the　same　strain　instant,　when　the　particle　becomes　more　irregular,　the　distribution　direction　of　the　maximum　contact　force　of　irregular　particles　tends　to　be　more　horizontal　to　resist　the　greater　external　loads.　In　comparison　to　spherical　particles,　the　Δq/p＇　and　Δφp　of　irregular　particles　increase　linearly　with　the　increase　of　ΔF.　The　measured　and　predicted　values　of　the　peak　friction　angle　for　the　statistical　model　are　essentially　consistent.　The　critical　parameters　ecs、ηcs、φcs、MCNcs　decrease　linearly　with　the　increase　of　the　regularity　index.　The　above　conclusions　serve　as　a　guide　for　revising　the　empirical　formula.　©　2024　Elsevier　Ltd