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Qualitative Method and Case Study for Ground Vibration of Tunnels Induced by Fault-Slip in Underground Mine

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Abstract

To evaluate tunnel ground vibrations induced by fault-slip in underground mine, it is crucial to resolve the peak ground velocity (PGV) and the peak ground acceleration (PGA). To quantify PGV and PGA in three-dimensional space, the forces acting on the fault and the seismic wave radiation pattern were investigated. A qualitative method for ground vibration of tunnels induced by fault-slip in underground mine was proposed and applied to the Yongshaba Phosphate Mine, China. Firstly, the moment tensor of the significant fault-slip event was obtained using a full waveform source inversion method based on the recorded seismograms. It describes the forces acting on the fault and the seismic wave radiation pattern. Then, the inverted source was used as a reference to evaluate the ground vibrations under possible larger seismic magnitudes and probable slip models. The vibrations along the tunnels resulted from different slip models were calculated using the representation theorem by the convolution of the Green’s function and the corresponding moment tensor. The velocity series and the acceleration series were obtained. Results show that the spatial distribution of the ground motions are closely related to sensor-source distance, the sensor-source azimuth, as well as the strike, dip, and rake configuration of the slip model. The seismic magnitude has an exponential effect on the distribution of the PGVs and PGAs. The PGV and PGA have similar spatial distribution patterns. The PGV values of the north and vertical components show nearly 5 times higher than the east component. The vertical vibrations affect the widest area. The ground support principles were suggested considering the parameters including the PGVs, the PGAs, the rock mass rating, and the dynamic loads.

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Abbreviations

PGV:

Peak ground velocity (\(m/s\))

PGA:

Peak ground acceleration (\({\text{m}}/{{\text{s}}^2}\))

MT:

Moment tensor

MTI:

Moment tensor inversion

\(\alpha\) :

Strike of the fault plane, defined as the angle from North

\(\beta\) :

Dip of the fault plane, defined as the angle from the horizontal

\(\lambda\) :

Rake of the fault plane, defined by the movement of the hangingwall relative to the footwall

\({M_0}\) :

The scalar seismic moment, \(~{M_0}=\mu A\bar {u}\) (\({\text{N}}\;{\text{m}}\))

\({M_{11}}\) :

The 1st independent element of the moment tensor, \({M_{11}}= - {M_0}(\sin \beta \cdot \cos \lambda \cdot \sin 2\alpha +\sin 2\beta \cdot \sin \lambda \cdot {\sin ^2}\alpha )\)

\({M_{22}}\) :

The 2nd independent element of the moment tensor, \({M_{22}}={M_0}(\sin \beta \cdot \cos \lambda \cdot \sin 2\alpha - \sin 2\beta \cdot \sin \lambda \cdot {\cos ^2}\alpha )\)

\({M_{33}}\) :

The 3rd independent element of the moment tensor, \({M_{33}}={M_0}\left( {\sin 2\beta \cdot \sin \lambda } \right)\)

\({M_{12}}\) :

The 4th independent element of the moment tensor, \({M_{12}}={M_0}(\sin \beta \cdot \cos \lambda \cdot \sin 2\alpha +0.5\sin 2\beta \cdot \sin \lambda \cdot \sin 2\alpha )\)

\({M_{13}}\) :

The 5th independent element of the moment tensor,\({M_{13}}= - {M_0}(\cos \beta \cdot \cos \lambda \cdot \cos \alpha +\cos 2\beta \cdot \sin \lambda \cdot \sin \alpha )\)

\({M_{23}}\) :

The 6th independent element of the moment tensor, \({M_{23}}= - {M_0}(\cos \beta \cdot \cos \lambda \cdot \sin \alpha - \cos 2\beta \cdot \sin \lambda \cdot \cos \alpha )\)

\({u_n}\) :

The Displacement \(u\) of the \(n\)th component, recorded at position \(x\) and time \(t\), \({u_n}(x,~t)={M_{pq}}(t) \times {G_{np,q}}(x,~t)\)

\({M_{pq}}\) :

The force couple in the direction \(pq\)

\({G_{np,q}}\) :

The spatial derivatives of the \(n\)th components of the Green’s functions

\(*\) :

The asterisk indicates convolution

\({v_n}\) :

The vibration velocity of the \(n\)th component at a particular site, \({v_n}(x,~t)={\text{d}}u/{\text{d}}t\)

\({a_n}\) :

The ground acceleration of the \(n\)th component at a particular site, \({a_n}(x)={\text{d}}v/{\text{d}}t\)

\({\text{RMR}}\) :

Rock mass rating

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  1. School of Resources and Safety Engineering, Central South University, Changsha, 410083, China

    Ju Ma, Longjun Dong, Guoyan Zhao & Xibing Li

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  1. Ju Ma
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  2. Longjun Dong
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  3. Guoyan Zhao
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Correspondence to Longjun Dong.

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Ma, J., Dong, L., Zhao, G. et al. Qualitative Method and Case Study for Ground Vibration of Tunnels Induced by Fault-Slip in Underground Mine. Rock Mech Rock Eng 52, 1887–1901 (2019). https://doi.org/10.1007/s00603-018-1631-x

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