Numerical　simulations　become　a　necessity　when　experimental　approaches　cannot　cover　the　required　physical　and　time　scale　of　interest.　One　of　such　area　is　a　simulation　of　long-term　host　rock　behaviors　for　nuclear　waste　disposal　and　simulation　tools　involved　in　the　assessment　must　go　through　rigorous　validation　tests.　The　DECOVALEX　project　(Development　of　COupled　models　and　their　VAlidation　against　EXperiments)　is　dedicated　to　this　purpose　by　international　participants.a　This　work　is　part　of　the　ongoing　phase　DECOVALEX-　2023　(D-2023,　Task　G)　particularly　aiming　to　simulate　fracture　behaviors　under　various　conditions.　Here,　we　cross-verified　a　variety　of　numerical　methods　including　continuous　and　discontinuous　approaches　against　four　benchmark　exercises　with　emphasis　on　numerical　accuracy　and　parameterization　of　the　various　numerical　approaches.　The　systematic　inter-comparisons　of　test　cases　highlight　advantages　and　disadvantages　of　the　different　numerical　models.　Numerical　details　on　discretization　effects　(e.g.　mesh　density　and　orientation)　and　domain　size　were　investigated　in　detail　for　practical　applications.　It　became　evident　that　meticulous　attention　to　mesh　resolution　and　domain　size　is　imperative　for　achieving　accurate　numerical　simulations,　even　for　static　cracks.　Moreover,　when　comparing　numerical　methods　to　closed-form　solutions　for　static　cracks,　all　models　successfully　reproduced　the　maximum　crack　opening　but　encountered　challenges　near　the　crack　tips.　Finally,　the　paper　discusses　how　to　convert　between　and　therefore　compare　parameters　of　various　numerical　approaches.　Our　benchmark　studies　reveal　that　each　model　necessitates　a　distinct　number　of　parameters,　even　in　simple　scenarios　like　static　crack　aperture　benchmarks.　It　is　generally　more　practical　to　employ　fewer　parameters　to　mitigate　model　over-parameterization　and　enhance　experimental　feasibility.