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Analysis of the Stress Wave Effect During Rock Breakage by Pulsating Jets

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Abstract

Formation, propagation and attenuation of stress waves during rock breakage by pulsating jets are simulated by introducing the Johnson–Holmquist-Concrete nonlinear constitutive model, and using the smoothed particle hydrodynamics approach. The curve of stress over time at different locations of the rock surface under the action of high-velocity pulsating jets is obtained, as well as relationship curve between amplitude of stress wave and distance to jet action spot. Based on the computational results, breakage behavior of rocks under stress wave effect, and impacts of jet velocity and rock properties on stress wave effect are analyzed. The results show that the stress wave effect of pulsating jets is rather strongly localized, and the amplitude of stress wave decreases sharply with increasing distance to jet action spot. The intensity and effect range of stress wave are in direct proportion to jet velocity; besides, there is a threshold velocity regarding macroscopic failure of rocks. Rocks of different lithologies have somewhat different failure modes under stress wave action of pulsating jets; failure mode of low strength rocks like sandstone is mainly crack propagation under tensile stress during rock loading and unloading processes, whereas the failure mode of hard brittle rocks such as limestone and granite is mainly longitudinal failure caused by stress concentration.

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Abbreviations

a :

First-order volume correction to \(\gamma_{0}\)

A :

Dimensionless viscous strength

B :

Dimensionless pressure hardening coefficient

c :

Sound velocity in aqueous medium

C :

Dimensionless strain rate effect coefficient

C 0 :

Intercept of relationship graph between stress wave velocity and particle velocity

C w :

Shock wave velocity

D :

Dimensionless damage factor

D 1 :

Damage constants

D 2 :

Damage constants

\(e_{i}\) :

Energy of particle i

\(f^{\prime}_{c}\) :

Quasi-static uniaxial compressive strength of the material

\(K_{1}\) :

Material constants

\(K_{2}\) :

Material constants

\(K_{3}\) :

Material constants

m j :

Mass of particle j

N :

Total number of particles

N′:

Pressure hardening exponent

p :

Pressure

P*:

Normalized pressure

P w :

Pump pressure

S 1 :

Constant

S 2 :

Constant

S 3 :

Constant

T*:

Maximum dimensionless tensile volumetric stress of material

t :

Particle movement time

v :

Jet velocity

\(v_{i}^{\alpha }\) :

Velocity of particle i in α direction

\(v_{ij}^{{^{\beta } }}\) :

Velocity between two particles in β direction

\(W_{ij}\) :

Smooth kernel function with B-spline type

x :

Location vectors in different positions

α :

Contravariant indexes

β :

Contravariant indexes

γ 0 :

Gruneisen coefficient

Δε p :

Equivalent plastic strain increment

Δθ p :

Plastic volumetric strain increment

\(\varepsilon_{i}^{\alpha \beta }\) :

Stress of particle i

\(\varepsilon_{j}^{\alpha \beta }\) :

Stress of particle j

\(\dot{\varepsilon }^{ * }\) :

Dimensionless strain rate

\(\dot{\varepsilon }\) :

Strain rate

\(\dot{\varepsilon }_{0}\) :

Reference strain rate

μ :

Viscosity coefficient of fluid

\(\bar{\mu }\) :

Amended volumetric strain

μ lock :

Locked volumetric strain

ρ :

Actual density

ρ 0 :

Initial density

ρ w :

Density of water

ρ i :

Density of particle i

σ :

Actual equivalent stress

\(\sigma_{i}^{\alpha \beta }\) :

Stress of particle i

\(\sigma^{\prime}_{ij}\) :

Shear stress

\(\varepsilon^{\prime}_{ij}\) :

Shear strain

ϕ :

Medium parameter

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Acknowledgments

This paper is jointly Supported by Program for Changjiang Scholars and Innovative Research Team in University (IRT1235), National Program on Key Basic Research Project (973 program, 2012CB723103), Chinese Ministry of Education (213022A), and supported by Scientific Research Foundation of State Key Lab. of Coal Mine Disaster Dynamics and Control (2011DA105287—FW201204).

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Authors and Affiliations

  1. State Key Laboratory Cultivation Base for Gas Geology and Gas Control, Henan Polytechnic University, Jiaozuo, 454000, Henan, China

    Yong Liu & Jianping Wei

  2. CME, EIS, University of Wollongong, Wollongong, NSW, 2500, Australia

    Jianping Wei & Ting Ren

  3. The Collaborative Innovation Center of Coal Safety Production of Henan Province, Jiaozuo, 454000, Henan, China

    Jianping Wei & Ting Ren

  4. School of Safety Science and Engineering, Henan Polytechnic University, Jiaozuo, China

    Jianping Wei

Authors
  1. Yong Liu
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  2. Jianping Wei
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  3. Ting Ren
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Correspondence to Jianping Wei.

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Liu, Y., Wei, J. & Ren, T. Analysis of the Stress Wave Effect During Rock Breakage by Pulsating Jets. Rock Mech Rock Eng 49, 503–514 (2016). https://doi.org/10.1007/s00603-015-0753-7

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  • DOI: https://doi.org/10.1007/s00603-015-0753-7

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