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Study on the Characteristic Energy Factor of the Deep Rock Mass Under Weak Disturbance

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Abstract

This study aims to investigate the characteristic energy factor of the deep rock mass deformation subjected to the disturbance induced by excavation or explosion. Based on the well-known rock hierarchical structure, the equivalent average kinetic energy of the deep rock mass under weak disturbance is first introduced. The characteristic energy factor that reflects the instable deformation of the deep rock mass is derived using the principle of variation. The relationship between the characteristic energy factor and the energy hierarchical sequence of the deep rock mass deformation and failure has also been illustrated. We believe that the characteristic energy factor is closely related to the characteristic scientific phenomena of deep rock mass in essence, which can provide a new approach for the study of deep rock mass in the fields of nonlinear mechanics, statistic physical mechanics, and mechanics of explosion and geophysics.

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Abbreviations

\( A,B,n,m \) :

Coefficients measured in the test

\( C_{p} \) :

P-wave velocity, m/s

\( C_{R} \) :

The cohesive strength between blocks and surface, MPa

\( f \) :

Disturbing force, N

\( f_{1} ,f_{2} \) :

Vibration amplitude, functions of coordinates, N

\( F_{\delta } \) :

The applied force provided by the surrounding rocks, N

\( F_{\tau } \) :

Shear force, N

\( F_{\text{s}} \) :

Resistance of the surface against the rock movement, N

\( i \) :

Level of rock blocks (tectonic elements)

\( I \) :

The impact energy factor

\( k \) :

Dimensionless energy conditions for the appearance of quasi-resonance and pendulum-type waves

\( k{}_{\delta } \) :

Stiffness coefficient of the surrounding rock, N/m

\( L_{i} \) :

Characteristic size of rock blocks at the ith level, m

\( L_{*} \) :

Characteristic size of dissipative structures, m

\( M \) :

Mass of the rock mass at the center of explosion-center, kg

\( M_{i} \) :

Mass of the rock blocks with size of \( L_{i} \), kg

Q :

Explosion equivalent, kt TNT

\( r \) :

Coordinate, m

\( R(t) \) :

The stable motion, m

\( R_{c} \) :

Denotes the strength of the rock under the action of initial geostress \( \sigma_{0} \), MPa

\( R_{*} \) :

The irreversible deformation region radius under large-scale underground explosion, m

\( R_{\text{cavity}} \) :

The radius of the cavity for a large-scale underground explosion, m

\( R_{\text{crush}} \) :

The radius of the crushing zone for a large-scale underground explosion, m

\( R_{\text{crack}} \) :

The radius of the radial cracking zone for a large-scale underground explosion, m

\( S \) :

The interface area, m2

\( T \) :

Compression duration of the compression wave, s

\( T^{\prime} \) :

Period of motion in the stationary field U, s

\( U \) :

Stationary field of high-geostress, J

\( U_{\text{total}} \) :

Denotes the total energy of the system, as shown in Fig. 1b, J

Fig. 1
figure 1

Illustration of the simplified calculation of the rock shear stability

Full size image
\( U_{\text{eff}} \) :

The effective potential energy, J

\( U_{\text{s}} \) :

The work done by the shear force, J

\( W \) :

Disturbance energy, the average value of the vibration kinetic energy, J

\( W_{L} \) :

The work done by the surrounding rocks, J

\( \chi \) :

Number of the contact surfaces

\( \delta_{0} \) :

Displacement of the surrounding rocks, m

\( \varepsilon \) :

Effective strain

\( \varepsilon_{*} \) :

The critical effective strain as the irreversible deformation appears on the slip surface

\( \bar{\varepsilon } \) :

Equivalent average strain

\( \mu_{0} \) :

Friction coefficient

\( \mu_{\text{s}} \) :

The static friction coefficient

\( \mu_{\text{d}} \) :

The dynamic friction coefficient

\( \rho \) :

Density of the rocks, kg/m3

\( \sigma_{f} \) :

Dynamic stress, MPa

\( \sigma_{\text{n}} \) :

The normal stress perpendicular to the interface, MPa

\( \sigma_{0} \) :

Initial geostress, MPa

\( \tau \) :

Shear strength between rock mass and slip surface, MPa

\( \upsilon \) :

Particle vibration velocity, m/s

\( \upsilon_{0} \left( r \right) \) :

The maximum velocity of the particle vibration velocity, m/s

\( \upsilon_{*} \) :

The maximum velocity of the particle vibration velocity at \( r = R_{*} \)

\( \omega \) :

Frequency of the disturbing force, s−1

\( \xi (t) \) :

Micro-vibration function, m

\( \varGamma \) :

Displacement of the rock block, m

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Acknowledgments

The authors would like to acknowledge the financial support from the National Natural Science Foundation of China (Grant No. 51527810, No. 51309233, No. 51309234) and the National Basic Research Program of China (973 Program, No. 2013CB036005), which is greatly appreciated by the authors.

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Authors and Affiliations

  1. State Key Laboratory of Disaster Prevention and Mitigation of Explosion and Impact, PLA University of Science and Technology, Nanjing, 210007, China

    Mingyang Wang, Jie Li, Linjian Ma & Houxu Huang

  2. School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing, 210094, China

    Mingyang Wang, Jie Li & Linjian Ma

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  1. Mingyang Wang
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  2. Jie Li
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Correspondence to Mingyang Wang.

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Wang, M., Li, J., Ma, L. et al. Study on the Characteristic Energy Factor of the Deep Rock Mass Under Weak Disturbance. Rock Mech Rock Eng 49, 3165–3173 (2016). https://doi.org/10.1007/s00603-016-0968-2

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  • DOI: https://doi.org/10.1007/s00603-016-0968-2

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