Simplified Mapping Rule for Bounding Surface Simulation of Complex Loading Paths in Granular Materials

Kan, Mojtaba E.; Taiebat, Hossein A.; Khalili, Nasser

doi:10.1061/(asce)gm.1943-5622.0000307

Cited by 36 publications

(17 citation statements)

References 21 publications

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“…However, the fractional derivative and integral do not commute as shown in the following Eq. (14) ( ) (14) 3 Connections between the fractional order and fractal dimension…”

Section: Definitionsmentioning

confidence: 99%

“…Some of the models [8,14,23] can simulate the real stress strain behaviour but are complex, whereas others [6,12] are relatively simple but cannot take into account the deformation and degradation of granular soils under complicated loading conditions. Most importantly, these models [7,16] can only simulate the cyclic behaviour of granular soils for very limited loading cycles, say less than 100 cycles.…”

Section: Introductionmentioning

confidence: 99%

“…Lots of experimental and theoretical studies have been performed [1][2][3][4][5][6][7][8][9][10][11][12][13][14] to investigate the mechanical behaviour of granular soils. For example, Xiao et al [15] conducted a series of true triaxial tests on the rockfill material under drained loading condition.…”

Section: Introductionmentioning

confidence: 99%

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Modelling long-term deformation of granular soils incorporating the concept of fractional calculus

et al. 2015

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Many constitutive models exist to characterise the cyclic behaviour of granular soils but can only simulate deformations for very limited cycles. Fractional derivatives have been regarded as one potential instrument for modelling memory-dependent phenomena. In this paper, the physical connection between the fractional derivative order and the fractal dimension of granular soils is investigated in detail. Then a modified elastoplastic constitutive model is proposed for evaluating the long-term deformation of granular soils under cyclic loading by incorporating the concept of factional calculus. To describe the flow direction of granular soils under cyclic loading, a cyclic flow potential considering particle breakage is used. Test results of several types of granular soils are used to validate the model performance. Abstract Lots of constitutive models exist to characterise the cyclic behaviour of granular soils but can only simulate deformations for very limited cycles. Fractional derivatives have been regarded as one potential instrument for modelling memory-dependent phenomena. In this paper, the physical connection between the fractional derivative order and the fractal dimension of granular soils is investigated in detail. Then a modified elasto-plastic constitutive model is proposed for evaluating the long-term deformation of granular soils under cyclic loading by incorporating the concept of factional calculus. To describe the flow direction of granular soils under cyclic loading, a cyclic flow potential considering particle breakage is used. Test results of several types of granular soils are used to validate the model performance.

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“…However, the fractional derivative and integral do not commute as shown in the following Eq. (14) ( ) (14) 3 Connections between the fractional order and fractal dimension…”

Section: Definitionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Modelling long-term deformation of granular soils incorporating the concept of fractional calculus

et al. 2015

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“…The plastic potential function for soils can be derived from consideration of the energy dissipated during plastic deformation by equating the total plastic work input with the energy dissipated in plastic deformation . This results in the following expression for the plastic potential function

g ((),,,, p^{'}, q, θ, p_{0}) = ({, \begin{array}{c} \overset{t}{true} q + \frac{A M_{cs} ((), θ) p^{'}}{A - 1} ((), {(p^{'} / p_{0})}^{A - 1} - 1) italicfor A \neq 1 \\ \overset{t}{true} q + M_{cs} ((), θ) p^{'} ln ((), p^{'} / p_{0}) italicfor A = 1, \end{array})

where p 0 controls the size of the plastic potential and A is a material constant dependent on the mechanism and amount of energy dissipation (not to be confused with the A parameter of the three‐point time discretisation scheme).…”

Section: Bounding Surface Plasticity Modelmentioning

confidence: 99%

Fully coupled elastoplastic hydro‐mechanical analysis of unsaturated porous media using a meshfree method

Ghaffaripour

Esgandani

Khoshghalb

et al. 2019

Num Anal Meth Geomechanics

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Summary This paper presents the first application of an advanced meshfree method, ie, the edge‐based smoothed point interpolation method (ESPIM), in simulation of the coupled hydro‐mechanical behaviour of unsaturated porous media. In the proposed technique, the problem domain is spatially discretised using a triangular background mesh, and the polynomial point interpolation method combined with a simple node selection scheme is adopted for creating nodal shape functions. Smoothing domains are formed on top of the background mesh, and a constant smoothed strain, created by applying the smoothing operation over the smoothing domains, is assigned to each smoothing domain. The deformation and flow models are developed based on the equilibrium equation of the mixture, and linear momentum and mass balance equations of the fluid phases, respectively. The effective stress approach is followed to account for the coupling between the flow and deformation models. Further coupling among the phases is captured through a hysteretic soil water retention model that evolves with changes in void ratio. An advanced elastoplastic constitutive model within the context of the bounding surface plasticity theory is employed for predicting the nonlinear behaviour of soil skeleton. Time discretisation is performed by adopting a three‐point discretisation method with growing time steps to avoid temporal instabilities. A modified Newton‐Raphson framework is designed for dealing with nonlinearities of the discretised system of equations. The performance of the numerical model is examined through a number of numerical examples. The state‐of‐the‐art computational scheme developed is useful for simulation of geotechnical engineering problems involving unsaturated soils.

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“…The mapping rule adopted in the original model could not be efficiently applied in a boundary value problem with highly variable loading paths due to its complex mapping procedure and memory requirements. To tackle this problem, Kan et al [11] introduced a single stress point radial mapping rule which has a simpler procedure and is more amenable to complex loading paths. 3 In this paper a general method is presented for the treatment of overshooting.…”

Section: Introductionmentioning

confidence: 99%

On implementation of bounding surface plasticity models with no overshooting effect in solving boundary value problems

E-Kan

Taiebat

2014

Computers and Geotechnics

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Taiebat, H. (2014). On implementation of bounding surface plasticity models with no overshooting effect in solving boundary value problems. Computers and Geotechnics, On implementation of bounding surface plasticity models with no overshooting effect in solving boundary value problems AbstractThis paper presents a new scheme that can be used to overcome the overshooting effect, one of the well known problems occurs during application of bounding surface plasticity models in numerical analysis of boundary value problems. The scheme is based on definition of clouds of loading surfaces with a specific margin of strains within which unloading does not accompanied kinematic hardening. The basic concept of the scheme is introduced and the methodology and the relevant step by step algorithm to implement this scheme are presented. This scheme has been incorporated in the UNSW bounding surface model and implemented in a finite difference code and used to simulate cyclic triaxial tests as well as complicated monotonic and dynamic boundary value problems. The satisfactory performance of the scheme is demonstrated and its efficiency is discussed thorough these simulations. Abstract: This paper presents a new scheme that can be used to overcome the overshooting effect, one of the well known problems occurs during application of bounding surface plasticity models in numerical analysis of boundary value problems. The scheme is based on definition of clouds of loading surfaces with a specific margin of strains within which unloading does not accompanied kinematic hardening. The basic concept of the scheme is introduced and the methodology and the relevant step by step algorithm to implement this scheme are presented. This scheme has been incorporated in the UNSW bounding surface model and implemented in a finite difference code and used to simulate cyclic triaxial tests as well as complicated monotonic and dynamic boundary value problems. The satisfactory performance of the scheme is demonstrated and its efficiency is discussed thorough these simulations. Disciplines Engineering | Science and Technology Studies

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Simplified Mapping Rule for Bounding Surface Simulation of Complex Loading Paths in Granular Materials

Cited by 36 publications

References 21 publications

Modelling long-term deformation of granular soils incorporating the concept of fractional calculus

Modelling long-term deformation of granular soils incorporating the concept of fractional calculus

Fully coupled elastoplastic hydro‐mechanical analysis of unsaturated porous media using a meshfree method

On implementation of bounding surface plasticity models with no overshooting effect in solving boundary value problems

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