Bounding surface plasticity for sand using fractional flow rule and modified critical state line
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O R I G I NA L
Yifei Sun
· Wojciech Sumelka · Yufeng Gao
Bounding surface plasticity for sand using fractional flow rule and modified critical state line
Received: 23 December 2019 / Accepted: 19 June 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Bounding surface plasticity has been widely used for capturing the stress–strain behaviour of geomaterials. However, it may require multiple sets of model parameters for constitutive modelling of sands with a wide range of initial states, because of the distinct critical state characteristics under low and high densities or pressures in the e − ln p plane. In this study, an enhanced bounding surface plasticity approach for sand with a wide range of initial material states is developed. A fractional plastic flow rule and a modified critical state line are suggested, which ensures that without using any predefined state indices, the developed model can consider the state-dependent dilatancy and hardening behaviours of sand subjected to low and high pressures/densities. The approach is validated by simulating the well-documented test results of Toyoura sand and Sacramento River sand. For comparison, the original state-dependent dilatancy approach in Li and Dafalias (Géotechnique 50(4):449–460, 2000. https://doi.org/10.1680/geot.2000.50.4.449) is also adopted and implemented. It is found that the two approaches can reasonably capture the typical stress–strain behaviour, e.g. hardening/contraction, softening/dilation, liquefaction, quasi-steady state flow, and non-flow, of sands with different initial material states, by using a single set of model parameters. However, compared to the current work, Li and Dafalias (2000) model relied on a predefined state parameter, for capturing the state-dependent behaviour of sand under a wide range of initial states Keywords Fractional order · Critical state · State dependence · Constitutive relation · Sand 1 Introduction Sand is widely distributed in the field. Due to different deposition conditions, it could have distinct initial densities even at the same initial consolidation pressure; however, it could also have the same initial densities Y. Sun Key Laboratory of Ministry of Education for Geomechanics and Embankment Engineering, Hohai University, Nanjing 210098, China Y. Sun Faculty of Civil and Environmental Engineering, Ruhr-Universität Bochum, 44801 Bochum, Germany E-mail: [email protected] W. Sumelka Institute of Structural Analysis, Poznan University of Technology, Piotrowo 5, 60-965 Poznan, Poland E-mail: [email protected] Y. Gao (B) Key Laboratory of Ministry of Education for Geomechanics and Embankment Engineering, College of Civil and Transportation Engineering, Hohai University, Nanjing 210098, China E-mail: [email protected]
Y. Sun et al.
Fig. 1 CSL and current stress state
but experience different initial pressures. The initial density associated with the initial pressure defines the initial state of sand. It has been widely recognised that such initial state has significant
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