A hypoplastic constitutive model for debris materials

Guo, Xiaogang; Peng, Chong; Wu, Wei; Wang, Yongqi

doi:10.1007/s11440-016-0494-0

Cited by 34 publications

(16 citation statements)

References 37 publications

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“…Its simplicity and robustness make it an ideal basic model to build more sophisticated models, e.g., critical state model and high-order model [5,8,9,13,30,31]. The failure surface is derived from the constitutive equation and likes that of DruckerPrager.…”

Section: Discussionmentioning

confidence: 99%

A basic hypoplastic constitutive model for sand

Lin

Wang

2017

Acta Geotech.

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Hypoplastic constitutive models are based on nonlinear tensor functions and are characterized by simple formulation and few parameters. In its early stage, mainly basic hypoplastic constitutive equations were concerned, where the stress tensor is assumed as the only state variable. There followed some enhanced models based on the basic constitutive equation by including void ratio as an additional state variable. In this paper, we first show that the widely used hypoplastic model by Wolffersdorff is seriously flawed because the underlying basic equation does not perform properly. We proceed to develop a basic hypoplastic constitutive equation by introducing a new tensorial term, which preserves the critical state at large strain. The model performance is demonstrated by parameter study for some element tests. This simple and robust basic equation is well suited to build more sophisticated models.

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Section: Discussionmentioning

confidence: 99%

A basic hypoplastic constitutive model for sand

Lin

Wang

2017

Acta Geotech.

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“…With the additional term I e , we ensure that both dense and loose sands can be modeled with only 1 set of material parameters. It is noteworthy that the original structure of I e in previous studies has 7 parameters. However, only 4 parameters are needed in the present form.…”

Section: Constitutive Modelmentioning

confidence: 99%

“…Owing to their simple formulation with few model parameters, hypoplastic model makes a unified description of inviscid and viscous behaviour feasible. Recently, rate dependency has been incorporated into hypoplasticity to describe the time‐dependent behaviour of frozen soil, debris flow, and soft clay . We proceed to develop the hypoplastic model for the non‐isotach behaviour of granular soils.…”

Section: Introductionmentioning

confidence: 99%

Modelling the time‐dependent behaviour of granular material with hypoplasticity

Wang

Yin

et al. 2018

Num Anal Meth Geomechanics

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Summary This paper presents a constitutive model for time‐dependent behaviour of granular material. The model consists of 2 parts representing the inviscid and viscous behaviour of granular materials. The inviscid part is a rate‐independent hypoplastic constitutive model. The viscous part is represented by a rheological model, which contains a high‐order term denoting the strain acceleration. The proposed model is validated by simulating some element tests on granular soils. Our model is able to model not only the non‐isotach behaviour but also the 3 creep stages, namely, primary, secondary, and tertiary creep, in a unified way.

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“…The viscous hypoplastic model proposed by Guo et al [1] is used as the basis for the hypoplastic model proposed in this work, which is characterized by an additive structure,…”

Section: Hypoplastic Viscous Modelmentioning

confidence: 99%

Extended hypoplastic model incorporating the coordination number for the simulation of granular flow

Bal

Dang

Meschke

2019

Proc Appl Math and Mech

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In this contribution, a hypoplastic viscous soil model incorporating viscous and grain-inertia rate effects observed in granular flows is enhanced by means of the coordination number, which allows to characterize the evolution of the microstructure of the granular material. Near a critical solid volume fraction and critical coordination number there exists a transition from a solid-like (rate-independent) to a flow-like (rate-dependent) behavior of granular materials. This information is used to calibrate a so-linear concentration factor, which controls viscous and grain-inertial rate effects in terms of the rate dependent evolution of the coordination number. The influence of this proposed hypoplastic model considering the coordination number is investigated in this paper by means of a simple undrained shear test . The viscous hypoplastic model proposed by Guo et al. [1] is used as the basis for the hypoplastic model proposed in this work, which is characterized by an additive structure,where σ H and σ D are the static and dynamic contributions to the total Cauchy stress tensor σ, respectively. The dynamic partdepends on the second invariant of the rate of deformation gradient II d , on the deviatoric part of the rate of the deformation gradient d dev and on the viscous and grain-inertia scaling factorswhere µ is the dynamic viscosity of the interstitial fluid surrounding the grains, C is the mean solid volume fraction, ρ s the density of the solid grains, and d is the mean diameter. λ N is the proposed linear concentration factor given bywhereN max is the maximum coordination number corresponding to the maximum possible volume fraction C max , N * is the rate dependent coordination number N , which is computed using a Prandtl-type equation [2], and α, β are parameters that are calibrated according to experiments. It should be noted that in Bagnold's theory [3], the linear concentration factor is written as λ = Cmax C 1 3 − 1 −1 . Figure 1 a) displays λ N − C plots for different values of α (β = −1). Coordination number and evolution of soil microstructureDiscrete Element Method (DEM) simulations of steady and unsteady shear flows performed by Vescovi et al. [4] show, that there exists a critical volume fraction C c and critical coordination number N c below which the granular material exhibits a rate dependent (flow-like) behavior , whereas a rate independent (solid-like) behavior is found above these critical values. A curve fitting (performed by the authors) of the N -C plots obtained from DEM simulations for steady shear flows [4] at different shearing rates is shown in Figure 1 b). Steady state values provided by DEM results are subsequently combined with the model proposed by Rothenburg et al. [5], describing the strain-driven evolution of the coordination number. This allows its determination for a given strain level. The proposed non-linear equation relating the shear strain γ and N is given bywhere c is a constant independent of the coordination number, N 0 is the initial value of the coordination num...

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A hypoplastic constitutive model for debris materials

Cited by 34 publications

References 37 publications

A basic hypoplastic constitutive model for sand

A basic hypoplastic constitutive model for sand

Modelling the time‐dependent behaviour of granular material with hypoplasticity

Extended hypoplastic model incorporating the coordination number for the simulation of granular flow

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