Tomodelthecumulativedeformationofgranularsoilsundercyclicloading,amathematicalmodelwasproposed.Thepowerlawconnectionbetweentheshearstrainandloadingcyclewasrepresentedbyusingfractionalderivativeapproach.Thevolumetricstrainwascharacterizedbyamodifiedcyclicflowrulewhichconsideredtheeffectofparticlebreakage.Allmodelparameterswereobtainedbythecyclicandstatictriaxialtests.Predictionsofthetestresultswereprovidedtovalidatetheproposedmodel.Comparisonwithanexistingcumulativemodelwasalsomadetoshowtheadvantageoftheproposedmodel.