Estimations of Three Characteristic Stress Ratios for Rockfill Material Considering Particle Breakage

  • Wan-Li GuoEmail author
  • Zheng-Yin Cai
  • Ying-Li Wu
  • Zhi-Zhou Geng


The particle breakage during specimen shearing has a significant influence on the critical-state line (CSL) of the rockfill material. A series of large-scale triaxial compression tests on the rockfill material from Henan Province (HPR) were conducted in a wide range of initial void ratios and confining pressures. The influences of the particle breakage on the critical-state stress ratio \(M_{\mathrm{c}}\), the peak stress ratio \(M_{\mathrm{p}}\) and dilatancy stress ratio \(M_{\mathrm{d}}\) were investigated. The deviatoric stress and particle breakage of the HPR at the critical state increase with the increase in confining pressure, while the influences of the initial void ratio on these behaviors are too little to be considered. The gradient of the CSL in the \(q\hbox {-}p\) space of the rockfill, \(M_{\mathrm{c}}\), was found to be passively correlated with the particle breakage index \(B_{\mathrm{r}}\), rather than being a constant. Additionally, the observed values of \(M_{\mathrm{c}}\) at low confining pressures (low particle breakage occur) will be substantially undervalued if \(M_{\mathrm{c}}\) is estimated as a constant. In the critical-state-theory-based constitutive models, \(M_{\mathrm{p}}\) and \(M_{\mathrm{d}}\) are estimated as the combinations of \(M_{\mathrm{c}}\) and state parameter \(\psi \). It is believed that the simulations of \(M_{\mathrm{p}}\) and \(M_{\mathrm{d}}\) when \(M_{\mathrm{c}}\) is correlated with \(B_{\mathrm{r}}\) are obviously more favorable than those when \(M_{\mathrm{c}}\) is constant.


Rockfill Particle breakage Critical-state line Stress ratio 

List of Symbols


deviatoric stress, mean effective stress


void ratio


critical-state void ratio


initial void ratio

\(\sigma _{3}\)

confining pressure


critical-state stress void

\(q_{\mathrm{c}}, p_{\mathrm{c}}\)

deviatoric stress, mean effective stress at the critical state


dilatancy stress ratio

\(q_{\mathrm{p}}, p_{\mathrm{p}}\)

peak deviatoric stress, peak mean effective stress


peak stress ratio


atmospheric pressure

\(\psi \)

state parameter

\(\varepsilon _{\mathrm{a}}\)

axial strain

\(\varepsilon _{\mathrm{v}}\)

volumetric strain


particle size


the maximum particle size


the fractal dimension


particle breakage index

\(\phi \)

friction angle

\(M_{\mathrm{c0}}, \chi , \mu \)

material constants corresponding to \(M_{\mathrm{c}}\)

\(e_{\Gamma }, \lambda , \xi \)

material constants corresponding to the CSL in the \(e\hbox {-}(p/p_{\mathrm{a}})^{\xi }\) space

\(D_{0}, D_{\mathrm{c}}, D_{\mathrm{u}}\)

fractal dimensions of the initial PSD, current PSD and ultimate PSD



The authors gratefully acknowledge the research Grant from National Key R&D Program of China (2017YFC0405102), the financial support (GG201705) from Key Technologies R&D Program of Henan Water Conservancy, and the fund on basic scientific research project of nonprofit central research institutions (Y318005).


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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics 2019

Authors and Affiliations

  1. 1.Geotechnical Engineering DepartmentNanjing Hydraulic Research InstituteNanjingChina

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