Estimation of the Mechanical Properties of Igneous Rocks in Consideration of Seismic Effects

  • Zhen Cui
  • Qian ShengEmail author
  • Xianlun Leng
  • Zeqi Zhu
  • Yonghui Zhang
Original Paper


It is not widely accepted that the dynamic strain rate experienced by a rock mass during an earthquake is lower than that during a high strain rate scenario such as an explosion or a rock burst. The present study investigated the problem of determining the mechanical properties of rock considering earthquake effects using experimental tests and empirical formulas. First, to obtain the most concentrated frequency band of earthquake energy, a statistical analysis was conducted to obtain the response spectra of ground motion records near the example projects. The mean response spectrum was then fitted with a design response spectrum formula. The most concentrated frequency band of earthquake energy was then determined with the flat segment of the design response spectrum. Based on this frequency range, cyclic loading–unloading testing that simulated the earthquake effect was conducted on rock samples. The strain rate range experienced by rocks during an earthquake was then obtained. This strain rate range is between the quasi-static and intermediate strain rate ranges and is significantly lower than the high strain rate range. Based on this strain rate range, dynamic triaxial compression tests were conducted on igneous rock specimens from the case study areas. It is confirmed that the fit of the dynamic compression test results with the Hoek–Brown (HB) criterion is more accurate than that with the Mohr–Coulomb criterion. The HB strength envelope under static conditions can be used to predict the seismic strength behaviors, requiring an update of only the intercept of the envelope. Thus, the HB strength criterion considering the seismic effect was obtained. Moreover, the seismic modulus of the intact rock can be estimated with the values of the uniaxial compressive strength (UCS) under different strain rates and the modulus ratio, which was found to be independent of the strain rate. Hence, it is practical to estimate the mechanical properties of rock masses in consideration of seismic effects with the seismic HB strength criterion and the Hoek and Diederichs equation based on the UCSs under various strain rates. Ultimately, the rock mechanical properties in consideration of seismic effects were estimated via the proposed approach for the Baihetan hydropower plant project as an example.


Earthquake effect Mechanical properties Strain rate Igneous rocks Hoek–Brown strength criteria 

List of Symbols


Material constant for the rock mass in the HB criterion


Factors of \(c_{d}\) related to the rock type of the specimen


Factors of \(\sigma_{{{\text{ci}},d}}\) related to the rock type of the specimen


Baihetan hydropower plant




Cohesion obtained in the quasi-static test


Seismic dynamic cohesion


Disturbance factor in the HB criterion


Dagangshan hydropower plant


Intact rock modulus


Rock mass modulus


Geological strength index in the HB criterion

HB criterion

Hoek–Brown strength criterion


High strain rate


Intermediate strain rate


Material constant for the rock mass in the HB criterion

MC criterion

Mohr–Coulomb strength criterion


Local magnitude


Modulus ratio


Material constant for intact rock in the HB criterion


Material constant for rock mass in the HB criterion


Ordinate of the response spectrum


Sum of squared errors


Peak ground acceleration


Uniaxial compressive strength


Ordinate of the Chinese standard design spectrum for hydraulic structures

\(\beta_{\hbox{max} }\)

The maximum height of \(\beta\)

\(\dot{\varepsilon }\)

Strain rate in the quasi-static test


Internal friction angle


\(\varphi_{0}\) obtained in the quasi-static test


Seismic \(\varphi_{d}\)


UCS of the intact rock


\(\sigma_{\text{ci}}\) obtained in the quasi-static test


Seismic \(\sigma_{\text{ci}}\)



The study was financially supported by the National Key R&D Program of China (No. 2016YFC0401803), the National Basic Research Program of China (No. 2015CB057905), the National Natural Science Foundation of China (Nos. 51779253, 41672319), the Provincial Natural Science Foundation of Hubei (No. 2017CFB725), by the Key Laboratory for GeoMechanics and Deep Underground Engineering, China University of Mining & Technology (No. SKLGDUEK1912), and by Youth Innovation Promotion Association CAS. In addition, the first author expresses his personal gratitude to Dr CHEN Liujie of Guangzhou University for her continuous support and proofreading work for the current study.


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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  • Zhen Cui
    • 1
    • 2
    • 3
  • Qian Sheng
    • 1
    • 2
    Email author
  • Xianlun Leng
    • 1
    • 2
  • Zeqi Zhu
    • 1
    • 2
  • Yonghui Zhang
    • 1
    • 2
  1. 1.State Key Laboratory of Geomechanics and Geotechnical EngineeringInstitute of Rock and Soil Mechanics, Chinese Academy of SciencesWuhanChina
  2. 2.School of Engineering ScienceUniversity of Chinese Academy of SciencesBeijingChina
  3. 3.State Key Laboratory for GeoMechanics and Deep Underground EngineeringChina University of Mining and TechnologyXuzhouChina

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