Reformulated fractional plasticity for soil-structure interface

https://doi.org/10.1016/j.mechrescom.2020.103580Get rights and content

Highlights

  • Fractional plasticity was modified for soil-structure interface.

  • Fractional dilatancy equation was developed for normal-dilatancy of interface.

  • State-dependent non-associativity was captured without using plastic potential.

Abstract

Correct representation of the non-associated state-dependent behavior of the soil-structure interface is important for geotechnical applications. The original fractional plasticity is reformulated in this study, by exploring the stress-displacement relation of the soil-structure interface under plain strain condition. Without using additional plastic potentials, a state-dependent non-associated plastic flow vector is developed for the interface, where plastic flow direction is governed by the fractional gradient of yielding function. The developed interface model has eight constants, which can be all determined from laboratory tests. Further validation against a series of test results of different soil-structure interfaces shows that the developed model can well capture the constitutive behavior of the interface subjected to different boundary conditions. The typical normal-dilatancy and strain hardening/softening responses of the interface can be reasonably reproduced.

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:σ=[σn,τ]Twhere σnand τ are the normal and tangential stresses, respectively. The corresponding displacement vector (U) can be defined as:U=[v,u]T=t[εn,εt]Twhere 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:f=τ2+M2σn2M2σnσn0where 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:m=[M2μ2(M2μ2)2+4μ2,2μ(M2μ2)2+4μ2]Twhere 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, σ˙n=0 and v˙0. So, recalling the elastoplastic relation shown in Eq. (11), the following relation can be derived:v˙i=D12epD11epu˙iwhere i indicates i-th step of loading. For tests under the CNS condition, σ˙n=Kv˙ and v˙0, 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.

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