ARCHIVES OF MECHANICS Arch. Mech. 71 (1), 23–47, 2019, DOI: 10.24423/aom.3084 State-dependent fractional plasticity model for the true triaxial behaviour of granular soil Y. SUN 1) , W. SUMELKA 2) 1) Key Laboratory of Ministry of Education for Geomechanics and Embankment Engineering, Jiangsu Research Center for Geotechnical Engineering Technology, Hohai University, Nanjing 210098, China e-mail: sunny@hhu.edu.cn 2) Institute of Structural Engineering, Poznan University of Technology, Piotrowo 5, 60-965 Poznań, Poland e-mail: wojciech.sumelka@put.poznan.pl The fractional plasticity was proposed to model the stress-strain be- haviour of granular soils, but only within the scope of classical triaxial loading condition. In this study an attempt is made to develop a 3D fractional plasticity model for granular soils subjected to true triaxial loads by using characteristic stress, where all the fractional-order and integer-order derivatives can be easily obtained. Without using a plastic potential, the non-associated plastic flow rule is achieved by performing fractional derivatives of the yielding function in the characteristic stress space. The obtained plastic flow direction is found to be influenced by the fractional order, characteristic stress parameter and intermediate stress ratio. To further val- idate the proposed model, a series of true triaxial test results of different granular soils are simulated, from which good agreement between the model predictions and the corresponding test results is found. Key words: fractional plasticity, characteristic stress, true triaxial test, granular soil. Copyright c  2019 by IPPT PAN, Warszawa 1. Introduction Granular soils, such as the rockfill materials used in hydraulic engineering and unbound materials in pavement engineering, usually suffer from complex loading conditions where the three principal stresses are distinct from each other. In these engineering practices, the plastic deformation behaviour of granular soil is usually considered as one of the most important mechanical properties that needs to be investigated thoroughly. However, due to the limita- tions of the laboratory techniques, classical triaxial test [1–4], biaxial test [5–7] and plain strain test [8] were usually used to study the strength and deforma- tion behaviour of granular soil. However, the stress conditions in those tests were