The open-pit mining slopes continue to become higher and steeper with the continuous exploitation of near-surface mineral resources. The blasting excavation exerts a significance influence on the slope stability. In fact, intact rock slopes do not exist and slope stability is controlled by the geological defects. In this paper, the stability of a rock slope imbedded with a fault is considered. The P-wave component of blasting seismic waves is focused on and the fault is simplified as a semi-infinite crack. In background of Daye iron mine, the peak particle velocity (PPV) threshold is determined based on the linear elastic fracture dynamics. The influence of frequency, Young's modulus, and Poisson's ratio is studied to modify the PPV threshold. Results show that (1) the PPV threshold decreases with the increasing Young's modulus and Poisson's ratio, but increases with the increasing frequency; (2) the initiation angle is immune to Young's modulus and the frequency, and only depends on the Poisson's ratio; (3) the PPV criterion is finally determined as 1.47 cm/s when the frequency
With the continuous exploitation of near-surface mineral resources in China, the open-pit mining slopes continue to become higher and steeper, whose stability is declining [
Dynamic stability has been extensively studied around the world. Ausilioe et al. studied the dynamic stability of reinforced slopes by considering different failure modes [
In fact, intact rock slopes do not exist. All the slopes contain geological defects, such as fault, potential sliding surface. Consequently, the slope stability is controlled by these geological defects. Some but insufficient studies on slope stability have been carried out in the recent years. Ouyang et al. [
In blasting engineering, the peak particle velocity (PPV) is always selected as the index for the dynamic stability of rock slopes [
A right-handed Cartesian coordinate system
Interaction between P-wave and fault.
In general, when the plane P-wave arrives at the crack, two diffracted waves will be generated. They are the diffracted P-wave
Due to that the incident P-wave is time-harmonic, the diffracted waves should be time-harmonic. Then the potentials of diffracted waves can be expressed as
The boundary condition on the crack can be written as:
Since
Integral path in
Let
Equations (
Because the incident wave will not cause the stress concentration near the crack tip, the stress field immediate near the crack tip is only determined by the diffracted waves. With the boundary conditions taken into consideration, the mode I stress intensity factor (SIF) is given by
The PPV normal to the wavefront of the incident wave can be expressed as
Substituting equation (
The stress field near the crack tip in the polar coordinate system can be expressed as [
In fracture mechanics, the maximum circumferential tensile stress criterion is always adopted to analyze fracture cracking. As a consequence, the safety criterion can be expresses as
Daye iron mine is located in Hubei Province, China. At its east open pit, the stability of the north slope is controlled by the faults F9 and F9′, as shown in Figure
Profit of engineering geological conditions of Daye iron mine.
It is obvious that the PPV threshold
Variation of
It can be seen from Figure
The variation of the initiation angle
Variation of
In order to get a more general and more applicable threshold, the influence of Young’s modulus
As mentioned before,
Variation of
It can be seen from Figure
The variation of the initiation angle
Variation of
As mentioned before,
Variation of
It can be seen from Figure
The variation of the initiation angle
Variation of
The following conclusions can be drawn: The PPV threshold decreases with the increasing Young’s modulus The initiation angle The PPV criterion is finally determined as 1.47 cm/s when The north slope is quite safe if the proposed PPV threshold is not violated due to the variation range of the initiation angle
The data used to support the findings of this study are included within the article.
The authors declare that there are no conflicts of interest regarding the publication of this article.
This work was supported by the Hubei Natural Science Foundation Project (Grant no. 2019CFB224), the scientific research project of Hubei Provincial Department of Education (Grant no. Q20191308), and the Jingzhou Science and Technology Project (Grant no. 2019Z18001).These grants are gratefully acknowledged.