Theexperimentalresultsof3-Dfractureundercompressionareintroducedinbriefandthetheoryofstresscriterionof3-Dfractureisstudied.Methodstoimitateinitialfracturesaredeveloped.Itispointedthatthereareimportantdefectsintheextremevalue(EV)methodeverproposedbyPalaniswamyandKnauss.ThemajordefectliesinthatonlytwoEulerangles(2EA)areconsidered,butanotheroneisneglected.IfthevariationofallthethreeEulerangles(3EA)areconsidered,onecangetbetterresultwhichisconsistentwiththeobservationoffaultingthatextendsoncurvedsurfacesbutnotonplanes.Themethodofevaluatingmaximalnormalstressdirectionvector(NSDV)isproposedandfurtherprovedtobeequivalenttothe3EAmethod.ItisprovedthattheNSDVmethodcanbefurtheroptimizedtothemethodofcompositionofthefirstprincipaldifferentialplane(CFPDP).TheresultsfromCFPDPmethodcanfitthecurvedsurfacesofinitialgrowthobservedintheexperimentsof3-Dfracture.TheCFPDPmethodcanalsobeusedtointerpretthe3-Dfracturesoftheslippingsectionbetweentheasperitiesintheburiedfaultplanethatismodeledasellipsecrack.Theresultsof3-Dfracturecanbeappliedtointerpretingtherelatedproblemsoffaultingincludingthemechanismofalotofshatterrockswithdifferentdimensions,thecauseofearthquakesoccurredattheedgeofplateunderlowshearstress,andthemechanismofanisotropycausedbytheextensivedilatancyanisotropy(EDA)cracks.
