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Effect of shear bond failure on the strength ratio in DEM modeling of quasi-brittle materials

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Abstract

Displacement softening has shown to be an effective ingredient to overcome common deficiencies associated with DEM modeling based on bonded spherical particles (Ma and Huang in Int J Rock Mech Min Sci 104:9–19, 2018b). By incorporating a softening path in the normal force–displacement contact law, we show that the softening contact model can not only yield a realistic compressive over tensile strength ratio as high as about 30, but also capture the highly nonlinear failure envelope at the confined extension stress range, typical for quasi-brittle materials such as rocks and concretes. In our previous model, bond breakage at the particle scale is governed by the normal bond strength only. Here, we generalize the model by removing the restriction on the shear bond failure. Formulation of the displacement-softening model is first introduced. Novel features from modeling the behaviors of Berea sandstone without considering shear bond failure are summarized. How material behaviors at both the micro- and macroscale are affected by the inclusion of shear bond failure is then analyzed. Finally, implications of the numerical results in the context of how to calibrate material properties for DEM modeling in general is discussed.

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Abbreviations

\(\beta \) :

Reciprocal of the softening coefficient \(\chi \)

\(\chi \) :

Softening coefficient

\(\chi _{*}\) :

Critical value of \(\chi \)

\(\eta _{\mathrm{{sc}}}\) :

Percentage of shear micro-cracks at 80\(\%\) of the post-peak loading level in the uniaxial compression test

\(\eta _{\mathrm{{st}}}\) :

Percentage of shear micro-cracks at 80\(\%\) of the post-peak loading level in the direct tension test

\(\eta _{\mathrm{{s}}}\) :

Percentage of shear micro-cracks at the peak stress level

\(\kappa \) :

Normal over shear stiffness ratio of the point contact

\(\mu \) :

Coulomb’s friction coefficient

\(\omega \) :

ratio between the limiting confining stress where the tension cutoff ends and the uniaxial tensile strength

\({\overline{\delta }}_{*}\) :

Normal bond stretch when the bond breaks (m)

\({\overline{\delta }}_{\mathrm{{c}}}\), \({\overline{\delta }}_{2}\) :

Critical stretch (m)

\({\overline{\delta }}_\mathrm{{n}}\) :

Normal bond stretch (m)

\({\overline{\kappa }}\) :

Area contact (bond) stiffness ratio

\({\overline{\sigma }}_{\mathrm{{c}}}\) :

Normal bond strength

\({\overline{\tau }}_{\mathrm{{c}}}\) :

Shear bond strength

\({\overline{\theta }}\) :

relative angle of rotation between the particles

\({\overline{E}}_{\mathrm{{c}}}\) :

Area contact (bond) modulus (GPa)

\({\overline{F}}_{n\text {max}}\) :

Maximum normal bond force (N)

\({\overline{F}}_\mathrm{{n}}\) :

Normal bond force (N)

\({\overline{F}}_{\mathrm{{s}}} \) :

Shear bond force (N)

\({\overline{k}}_{\ell }\) :

Normal bond stiffness of the elastic loading path (N/m)

\({\overline{k}}_\mathrm{{u}}\) :

Normal bond stiffness of the softening path (N/m)

\({\overline{M}}^{n}\) :

Twisting moment (N m)

\({\overline{R}}\) :

Bond radius (m)

\({\overline{U}}_\mathrm{{b}}\) :

Nominal energy loss density associated with one bond breakage (MPa)

\(\sigma _1\) :

Maximum principal stress (MPa)

\(\sigma _3\) :

Minimum principal stress (MPa)

\(\sigma _{\mathrm{{c}}}\), UCS:

Uniaxial compressive strength (MPa)

\(\sigma _t\), UTS:

Uniaxial tensile strength (MPa)

\(\varpi \) :

Shear over normal bond strength ratio

A :

Cross-sectional area of the bond (\({\hbox {m}}^2\))

D :

Diameter of the cylindrical assembly (mm)

\(E_{\mathrm{{c}}}\) :

Point contact modulus (GPa)

H :

Height of the cylindrical assembly (mm)

J :

Polar moment of inertia (\({\text {m}}^4\))

N :

Total number of micro-cracks at the peak stress

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Authors and Affiliations

  1. Department of Civil and Architectural Engineering, Lawrence Technological University, Southfield, MI, 48075, USA

    Yifei Ma

  2. School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, GA, 30332, USA

    Haiying Huang

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  1. Yifei Ma
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Ma, Y., Huang, H. Effect of shear bond failure on the strength ratio in DEM modeling of quasi-brittle materials. Acta Geotech. 16, 2629–2642 (2021). https://doi.org/10.1007/s11440-021-01220-x

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