The　fracture　behaviors　of　quasi-brittle　materials　such　as　concrete　were　evaluated　based　on　the　crack　propagation　criterion,　and　among　all　criterions　reported　in　the　literature,　the　toughness-based　crack　initiation-propagation　(TCIP)　criterion　capable　of　capturing　simultaneously　the　crack　initiation　and　propagation　was　widely　used.　Recently,　a　modified　fracture　parameter　was　introduced　to　ensure　the　energy　balance　relationship,　however,　the　use　of　the　modified　parameter-based　TCIP　criterion　was　limited　only　to　mode-I　fracture　of　quasi-brittle　materials.　In　the　context　of　mixed-mode　fracture　problems,　an　extra　effort　was　made　in　this　paper　to　extend　the　modified　parameter-based　TCIP　criterion　previously　developed　for　the　mode-I　fracture　to　the　mixed　mode　I-II　fracture.　Application　of　the　extended　criterion　was　performed　on　three-point　bending　beams　with　offset　and　multi-segment　notches　through　finite　element　analysis,　in　which　the　cohesive　force　at　the　fracture　process　zone　was　applied　through　nonlinear　spring　elements.　On　concrete　materials,　the　full　crack　trajectories　for　mixed　mode　I-II　fracture　and　nonlinear　mechanical　responses　such　as　P-delta,　P-CMOD,　and　P-CMSD　curves　were　numerically　obtained　in　the　present　paper.　With　the　modified　fracture　energy　parameter,　good　consistency　was　found　between　the　numerical　results　given　by　the　reported　model　and　experiments.　Nevertheless,　it　must　be　admitted　that　the　use　of　TCIP　criterion　with　the　modified　fracture　energy　parameter　on　concretes　was　bounded,　it　would　be　more　prominent　on　other　geomaterials　such　as　rocks,　for　both　static　and　dynamic　analysis.