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Due to the distinct integral definitions of the fractional derivatives for compression and extension, a generalised state-dependent fractional plasticity model suitable for both loading cases is derived analytically to simulate the drained and undrained behaviour of granular soils. A series of triaxial tests on different granular soils are then used to validate the model. It is found that material responses, such as hardening and softening, contraction and dilation, liquefaction and steady state flow, etc., under compressive and extensive loads is well described by the proposed model. [ABSTRACT FROM AUTHOR]