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Dynamic Modelling of Seismic Wave Propagation due to a Remote Seismic Source: A Case Study

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Abstract

Rockbursts are some of the most dangerous phenomena encountered in underground mines. They can be triggered by an abrupt ground disturbance from a remote seismic source. In this paper, the mechanism of remotely triggered rockbursts around a coal mine drift is analyzed using the synchro-squeezing transform (SST) method and dynamic modeling. Based on seismic monitoring data, the seismic waveform at the source is estimated through empirical scaling law and calibrated in the model. Then, with the SST seismic waveform decomposition codes, the P and S waves are separated and filtered, and then applied in orthogonal oscillating directions at the source simulating their inherently diverse radiation mechanism. A three-dimensional numerical model was constructed with FLAC3D for a case study rockburst of a mine drift at Wudong Coal Mine. The static simulation results show that stress concentration occurs in the roof and rock pillar near the production level, and that the rock mass around the drift is already damaged due to the upper unloading effect and the bending deformation of the roof and pillar. Dynamic modeling confirmed that weak materials cause greater attenuation of particle vibration than hard materials. The rock mass around the drift experienced a significant strain energy release of 2.1 × 108 J and maximum displacements in the working face of 129 mm. The P wave showed a larger contribution to the dynamic disturbance in the horizontal direction than in vertical direction, while the S wave has a predominant proportion in the vertical direction. As expected, particle vibration velocity and displacement on the north side of the drift are greater than those on the south side—under incidents waves propagating from the north side. Based on model results and peak particle velocity (PPV), it was deemed that the computed released energy is large enough to threaten the drift integrity, resulting in drift damage for up to 200 m from the working face. The predicted failure characteristics and potential damage range are consistent with field observations. The proposed approach of synchro-squeezing transform (SST) and dynamic modeling could prove useful in the assessment of damage in rockburst-prone areas—it could further help assess the need for and design of dynamic rock supports.

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(reproduced from Tarasov and Potvin 2012)

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Abbreviations

SST:

Synchro-squeezing transform

PPV:

Peak particle velocity

FEM:

Finite-element method

FDM:

Finite-difference method

BSR:

Brittle shear ratio

UCS:

Uniaxial compressive strength

RMR:

Rock mass rating

a :

Scale factor

Ak(t):

Instantaneous amplitude

b :

Translation of the mother wavelet

C p :

P wave velocity

C s :

S wave velocity

C ϕ :

Constant related to the selected wavelet

E :

Elastic modulus

E S :

Energy released

f max :

Highest frequency

fk(t):

Instantaneous frequency of the component k is estimated from the instantaneous phase

G :

Shear modulus

H :

Depth below the ground surface

K :

Number of components

l :

Frequency band

M o :

Seismic moment

N :

Local model attenuation ratio

PPVa :

Peak particle velocity measured by the field sensor

PPVb :

Peak particle velocity at the event source estimated by empirical scaling law

PPVb′:

Calibrated peak particle velocity at the event source

PPVc :

Peak particle velocity measured at the receivers arranged in the path from the source to the sensor in the model.

PPVc′:

Calibrated peak particle velocity measured at the receivers arranged in the path from the source to the sensor in the model.

R :

Source-to-target distance

s(t):

Seismic signal wave

t :

Time

Va(t):

Wave velocity recorded by the field sensor

Vb(t):

Wave velocity at the event source estimated based on the scaling law

Vb′(t):

Calibrated wave velocity on the event source

Ws(a, b):

Coefficients which are used to compute the instantaneous frequency

σ s :

Static stress

σ d :

Dynamic stress caused by incident seismic waves

σ c :

Critical stress required for rockburst occurrence

ϕ :

Potential function

∇2 :

Laplacian operator

η(t):

Additive noise

θk(t):

Instantaneous phase of the component k

ψ * :

Complex conjugate of the mother wavelet

ωs(a, b):

Instantaneous frequency

ℜ :

Real part of the discrete SST

Δl :

Model mesh size

Δσ:

Stress drop

λ :

Wavelength

ρ :

Material density

μ :

Poisson's ratio

σ 0 zz :

In situ stress component in the vertical direction

σ 0 xx :

In situ stress component in the X-horizontal direction

σ 0 yy :

In situ stress component in the Y-horizontal direction

σ 1 :

Maximum principal stress

σ 3 :

Minimum principal stress

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Acknowledgements

Special thanks are due to Wudong Coal Mine for the microseismic data and other relevant data. This work was supported and financed by the State Key Research Development Program of China (No. 2016YFC0801408), the National Natural Science Foundation of China (No. 51634001, No. 51774023, No. 51904019), and the Fundamental Research Funds for the Central Universities (No. FRF-TP-18-081A1).

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Authors and Affiliations

  1. School of Civil and Resources Engineering, University of Science and Technology Beijing, Beijing, 100083, China

    Shengquan He, Xueqiu He & Dazhao Song

  2. Department of Mining and Materials Engineering, McGill University, Montreal, H3A 0E8, Canada

    Shengquan He, Tuo Chen, Isaac Vennes & Hani Mitri

  3. Zhong-an Academy of Safety Engineering, Beijing, 100083, China

    Xueqiu He

  4. Shenhua Xinjiang Energy Company Limited, Urumqi, 830027, China

    Jianqiang Chen

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  1. Shengquan He
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He, S., Chen, T., Vennes, I. et al. Dynamic Modelling of Seismic Wave Propagation due to a Remote Seismic Source: A Case Study. Rock Mech Rock Eng 53, 5177–5201 (2020). https://doi.org/10.1007/s00603-020-02217-w

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