Reformulated fractional plasticity for soil-structure interface
Introduction
Public infrastructures, e.g., tunnels, retaining wall and high-way embankments, are usually built in or on soils. Due to the significantly different stiffnesses of the soil and structure, it has been long recognized that there was a thin transition zone, i.e., interface, between the soil and structure [1]. The mechanical response of such soil-structure interface had a remarkable influence on the overall performance of the associated infrastructure [2]. In the past decades, great efforts had been devoted to the experimental and theoretical investigations on the complex stress-displacement behavior of soil-structure interface [3], [4], [5], [6], [7], [8], [9], [10], [11], [12]. It was found that the void ratio and applied normal stress significantly affected the strength and deformation of the interface. Similar to the state-dependent response of sand, normal-dilatancy and hardening/softening phenomena which often occurred in sandy soils could be also witnessed in the interface.
To capture the stress-displacement behavior of soil-structure interface with specific thickness (t) and void ratio (e), different constitutive models, using classical plasticity [13], generalized plasticity [7], two-surface plasticity [6], and hypoplasticity [14], [15], [16], [17], etc., were developed. To capture the stress-displacement behaviour of fine-grained interface, Stutz and Mašín [14] proposed a robust hypoplastic model by using reduced stress and strain rate vectors and redefined tensorial operations. To capture the three-dimensional (3D) behaviour of fine- and coarse-grained soil-structure interfaces, two advanced hypoplastic models were developed by Stutz and Wuttke [17] using intergranular strain concept, where good model performances were reported. In addition, Fang and Wang [3] proposed a 3D multishear model for granular soil-structure interface, based on the superposition of a series of orientated microshear responses in microshear structures. Inspired by the pioneering work of Sumelka [18], Sun et al. [19,20] developed a novel fractional plasticity approach, where the state-dependent plastic flow behavior of soil can be captured without using additional plastic potentials and classic state parameters (i.e., ψ [21] or Ip [22]). The magnitude and direction of the plastic strain increment were determined from the fractional gradient of the yielding function. Since then, the fractional plasticity has been applied and extended by researchers for capturing different mechanical problems of different soils, including true triaxial strength and deformation behavior of granular soils [23], and softening behavior of rock [24].
This study attempts to reformulate the original fractional plasticity approach for capturing the stress-displacement behavior of soil-structure interface. The paper is divided into four main parts: Section 2 presents the basic constitutive relations of fractional plasticity for interface. Section 3 provides the details of a fractional plasticity model for granular soil-structure interface. Section 4 presents the basic numerical schemes and model validation. Main conclusions are summarized in Section 5.
Section snippets
Constitutive relation for interface
The interface considered here is assumed to be homogenous and isotropic. Compressive deformations and stresses are positive and tensive ones are negative. Stress and strain notations associated with plane strain problems are used. Accordingly, the stress vector (σ) within the interface can be defined as:where σnand τ are the normal and tangential stresses, respectively. The corresponding displacement vector (U) can be defined as:where v and u are the normal and
Model formulation
This section develops one possible fractional plasticity model for soil-structure interface. The yielding function originated from the critical state soil mechanics [26] are used:where M is the ultimate stress ratio of the interface. σn0defines the size of the yielding function. Accordingly, the following expression for the plastic loading vector can be obtained:where the stress ratio μ = τ/σn.
In addition to m, n should be also defined. As
Basic numerical scheme
This section describes the basic numerical schemes for two common boundary conditions encountered in engineering practices, i.e., the shearing under constant normal load (CNL) and constant normal stiffness (CNS) conditions.
For tests under the CNL condition, and . So, recalling the elastoplastic relation shown in Eq. (11), the following relation can be derived:where i indicates i-th step of loading. For tests under the CNS condition, and , where K is the
Conclusions
This study presents a fractional plasticity approach for capturing the stress-displacement behavior of soil-structure interface. The main findings can be summarized as follows:
- (1)
A state-dependent non-associated plastic flow vector was proposed for capturing the normal-dilation and softening behaviors of the interface, without using additional plastic potential and state parameter (ψ or Ip).
- (2)
The developed model has eight constants, which can be all determined from traditional direct interface shear
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgement
The first author would like to thank Prof. Wen Chen for his lifelong inspiration. The financial support provided by the National Natural Science Foundation of China (grant no. 51890912), the Alexander Von Humboldt Foundation, Germany, and the National Science Centre, Poland (grant no. 2017/27/B/ST8/00351) are appreciated.
References (29)
- et al.
Unified modeling of monotonic and cyclic behavior of interface between structure and gravelly soil
Soils Found.
(2008) A simple critical state interface model and its application in prediction of shaft resistance of non-displacement piles in sand
Comput. Geotech.
(2017)- et al.
Constitutive modeling of soil-structure interface through the concept of critical state soil mechanics
Mech. Res. Commun.
(2006) - et al.
A three-dimensional state-dependent model of soil–structure interface for monotonic and cyclic loadings
Comput. Geotech.
(2014) - et al.
A general approach to model interfaces using existing soil constitutive models application to hypoplasticity
Comput. Geotech.
(2017) Fractional viscoplasticity
Mech. Res. Commun.
(2014)- et al.
Fractional order plasticity modelling of state-dependent behaviour of granular soils without using plastic potential
Int. J. Plasticity
(2018) - et al.
Elastoplastic modelling of mechanical behavior of rocks with fractional-order plastic flow
Int. J. Mech Sci.
(2019) - et al.
A critical state two-surface plasticity model for gravelly soil-structure interfaces under monotonic and cyclic loading
Comput. Geotech.
(2016) - et al.
A unified constitutive model for simulating stress-path dependency of sandy and gravelly soil–structure interfaces
Int. J. Non-Linear Mech.
(2018)
Tests of the interface between sand and steel in the simple shear apparatus
Géotechnique
A three-dimensional multishear bounding surface model of granular soil–structure interfaces under monotonic and cyclic loading
J. Eng. Mech.
Large-displacement interface shear between steel and granular media
Géotechnique
Testing and modeling of soil-structure interface
J. Geotech. Geoenviron. Eng.
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