Advanced general particle dynamics with nonlocal foundation for fracture analysis

Zhou, Xiaoping; Yao, Wu-Wen; Berto, Filippo

doi:10.1111/ffe.13777

Cited by 11 publications

(10 citation statements)

References 53 publications

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“…Correspondingly, according to the previous work by the authors, the continuity Equation 23 can be written as 47,48…”

Section: Bond Damage Model Of Gpd Algorithmmentioning

confidence: 99%

“…where ρ is density of rocks and the Kronecker delta, δ ij , values are 1 and 0, respectively, indicating whether the influence of hydrostatic pressure is considered. Considering a finite nonlocal influence domain, under the hydromechanical coupling condition, Equation 18 can be rewritten as 47,48…”

Section: Bond Damage Model Of Gpd Algorithmmentioning

confidence: 99%

“…Considering a finite nonlocal influence domain, under the hydromechanical coupling condition, Equation 18 can be rewritten as 47,48

ρ \frac{d boldv}{dt} goodbreak= boldb ((), boldx, t) goodbreak+ \int_{H} w ((),, boldy goodbreak- boldx, Δ) \cdot boldf ((),,, ξ, {boldξ}_{0}, t) d boldx

where w ( y ‐ x , Δ) is a kernel function, Δ is the radius of the influence domain, b ( x , t ) is the external force, and f is the nonlocal long‐range force under the hydromechanical coupling condition. In porous medium such as rocks, the nonlocal long‐force f considering the pore water pressure takes the following form based on Biot's theory 49 :

boldf ((),,, ξ, {boldξ}_{0}, t) goodbreak= c_{xy} H ((),,, ξ, {boldξ}_{0}, t) ([], s ((),,, ξ, {boldξ}_{0}, t) goodbreak- italicαγ \frac{P ((), boldy, t) + P ((), boldx, t)}{2})

where c xy is the micro‐elastic bond parameter,

H ((),,, ξ, {boldξ}_{0}, t)

is the state function of a bond, α is Biot's coefficient, γ is the coefficient of pore water pressure,

\frac{P ((), boldy, t) + P ((), boldx, t)}{2}

is the average pore water pressure on bond

ξ_{0}

between particles

boldx

and

boldy

bold-italics ((),, ξ, {boldξ}_{0})

is the stretch scalar vector, and

boldξ

and

ξ_{0}

are, respectively, the current and initial bond.…”

Section: Hydromechanical Coupling Model Of Gpdmentioning

confidence: 99%

“…Correspondingly, according to the previous work by the authors, the continuity Equation 23 can be written as 47,48

\frac{dρ}{dt} goodbreak= goodbreak- ρ \int_{H} w ((),, boldy goodbreak- boldx, Δ) \cdot ([], boldv ((), y) goodbreak+ boldv ((), x)) d boldx

where ρ [ v ( y ) + v ( x )] / 2 is defined as a nonlocal velocity divergence.…”

Section: Hydromechanical Coupling Model Of Gpdmentioning

confidence: 99%

“…Moreover, the critical stretch can be expressed as 48

s_{c} goodbreak= ({, \begin{array}{l} \sqrt{\frac{G_{c}}{([], ((), \frac{6 μ}{π} goodbreak+ \frac{16}{9 π^{2}} ((), boldκ goodbreak- 2 μ)) Δ)}} for 2 normalD \\ \sqrt{\frac{G_{c}}{([], ((), 3 μ goodbreak+ {(\frac{3}{4})}^{4} ((), boldκ goodbreak- \frac{5 μ}{3})) Δ)}} for 3 normalD \end{array})

where μ is shear modules, κ is bulk modules, and

G_{c}

is the critical energy release rate.…”

Section: Hydromechanical Coupling Model Of Gpdmentioning

confidence: 99%

See 4 more Smart Citations

Hydromechanical coupling model for mechanical and hydraulic behavior of fractured rock mass in the framework of advanced general particle dynamics

Zhou

Fan

et al. 2022

Fatigue Fract Eng Mat Struct

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In this paper, hydromechanical coupling model is proposed to study the mechanical and hydraulic behavior of fractured rock mass in the framework of advanced general particle dynamics (GPD), and the relationship between stress and seepage is determined. Then, the proposed model is employed to investigate one-dimensional seepage, and the numerical seepage field is in a good agreement with the analytical solution, implying the feasibility and accuracy of advanced GPD method. Finally, the proposed model is applied to analyze the mechanical and hydraulic behavior of surrounding rock mass around excavated tunnel under hydromechanical coupling conditions, and the numerical results obtained by the proposed model are in a good agreement with those obtained by PFC, which further verifies the correctness of the proposed model. K E Y W O R D S advanced general particle dynamics, fractured rock mass, hydromechanical coupling model, mechanical and hydraulic behavior

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“…Correspondingly, according to the previous work by the authors, the continuity Equation 23 can be written as 47,48…”

Section: Bond Damage Model Of Gpd Algorithmmentioning

confidence: 99%

Section: Bond Damage Model Of Gpd Algorithmmentioning

confidence: 99%

“…Considering a finite nonlocal influence domain, under the hydromechanical coupling condition, Equation 18 can be rewritten as 47,48

ρ \frac{d boldv}{dt} goodbreak= boldb ((), boldx, t) goodbreak+ \int_{H} w ((),, boldy goodbreak- boldx, Δ) \cdot boldf ((),,, ξ, {boldξ}_{0}, t) d boldx

boldf ((),,, ξ, {boldξ}_{0}, t) goodbreak= c_{xy} H ((),,, ξ, {boldξ}_{0}, t) ([], s ((),,, ξ, {boldξ}_{0}, t) goodbreak- italicαγ \frac{P ((), boldy, t) + P ((), boldx, t)}{2})

where c xy is the micro‐elastic bond parameter,

H ((),,, ξ, {boldξ}_{0}, t)

is the state function of a bond, α is Biot's coefficient, γ is the coefficient of pore water pressure,

\frac{P ((), boldy, t) + P ((), boldx, t)}{2}

is the average pore water pressure on bond

ξ_{0}

between particles

boldx

and

boldy

bold-italics ((),, ξ, {boldξ}_{0})

is the stretch scalar vector, and

boldξ

and

ξ_{0}

are, respectively, the current and initial bond.…”

Section: Hydromechanical Coupling Model Of Gpdmentioning

confidence: 99%

“…Correspondingly, according to the previous work by the authors, the continuity Equation 23 can be written as 47,48

\frac{dρ}{dt} goodbreak= goodbreak- ρ \int_{H} w ((),, boldy goodbreak- boldx, Δ) \cdot ([], boldv ((), y) goodbreak+ boldv ((), x)) d boldx

where ρ [ v ( y ) + v ( x )] / 2 is defined as a nonlocal velocity divergence.…”

Section: Hydromechanical Coupling Model Of Gpdmentioning

confidence: 99%

“…Moreover, the critical stretch can be expressed as 48

s_{c} goodbreak= ({, \begin{array}{l} \sqrt{\frac{G_{c}}{([], ((), \frac{6 μ}{π} goodbreak+ \frac{16}{9 π^{2}} ((), boldκ goodbreak- 2 μ)) Δ)}} for 2 normalD \\ \sqrt{\frac{G_{c}}{([], ((), 3 μ goodbreak+ {(\frac{3}{4})}^{4} ((), boldκ goodbreak- \frac{5 μ}{3})) Δ)}} for 3 normalD \end{array})

where μ is shear modules, κ is bulk modules, and

G_{c}

is the critical energy release rate.…”

Section: Hydromechanical Coupling Model Of Gpdmentioning

confidence: 99%

See 3 more Smart Citations

Hydromechanical coupling model for mechanical and hydraulic behavior of fractured rock mass in the framework of advanced general particle dynamics

Zhou

Fan

et al. 2022

Fatigue Fract Eng Mat Struct

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Modeling Brittle Failure in Rock Slopes Using Semi‐Lagrangian Nonlocal General Particle Dynamics

Yin,

Zhou,

Pan

2024

Num Anal Meth Geomechanics

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The nonlocal general particle dynamics (NGPD) has been successfully developed to model crack propagation and large deformation problems. In this paper, the semi‐Lagrangian nonlocal general particle dynamics (SL‐NGPD) is proposed to solve brittle failure in rock slopes. In SL‐NGPD, the interaction between particles due to deformation is calculated in the initial configuration, while the friction contact interaction from discontinuities is calculated in the current configuration. The Van der Waals force model is utilized for friction contact. The bond‐level energy‐based failure criterion is developed to predict tensile/compressive‐shear mix‐mode cracks. The artificial viscosity and damage correction are used to enhance the numerical stability and accuracy when modeling brittle failure. The SL‐NGPD paradigm is numerically implemented through adaptive dynamic relaxation and predictor–corrector schemes for stable numerical solutions. The stability and accuracy of SL‐NGPD are verified by simulating compression tests. Thereafter, the crack coalescence patterns of double‐flaw specimens are investigated to understand the triggering failure mechanism of jointed rock slopes. Finally, the progressive failure process of the rock slope with step‐path joints is simulated to demonstrate its validity and robustness in modeling brittle failure in rockslides. The numerical results illustrate that the proposed SL‐NGPD is promising and performant for analyzing brittle failure problems in geotechnical engineering.

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Optimization of working slope configuration in seasonal operations of cold regions open-pit mine

Liu,

Huang,

Cao

et al. 2024

Alexandria Engineering Journal

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Advanced general particle dynamics with nonlocal foundation for fracture analysis

Cited by 11 publications

References 53 publications

Hydromechanical coupling model for mechanical and hydraulic behavior of fractured rock mass in the framework of advanced general particle dynamics

Hydromechanical coupling model for mechanical and hydraulic behavior of fractured rock mass in the framework of advanced general particle dynamics

Modeling Brittle Failure in Rock Slopes Using Semi‐Lagrangian Nonlocal General Particle Dynamics

Optimization of working slope configuration in seasonal operations of cold regions open-pit mine

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