Abstract
This work elucidates dynamic control equations of the anchoring system and the derivation of displacement equations and corresponding vibration modes. Furthermore, the anchoring system is found to be composed of three different vibration modes: (1) when ω < (k1/ρ1A1)1/2, the vibration mode of the anchoring section is an exponential function; (2) when ω = (k1/ρ1A1)1/2, the vibration mode of the anchoring section is a parabolic function; (3) when ω > (k1/ρ1A1)1/2, the vibration mode of the anchoring section is a trigonometric function, while all the free sections are trigonometric functions. With an increase of frequency, the amplitude of the bolt exhibits multipeak distribution characteristics and an intermittent amplification phenomenon. When the frequency reaches a certain value, the bolt of the free section exhibits only the amplified state. Under dynamic load, the amplitude of the bolt increases from end of bolt to the maximum in the root. On the other hand, when the frequency is low, the peak position of the roof bolt is stable, and the excitation wave component is the main influencing factor of the peak value of axial force at the root of the bolt, independent of frequency. When the frequency is relatively high, the peak value of the axial force is stable at the interface, and the higher the frequency, the greater the peak value of axial force. Axial force of the bolt has responded strongly to the frequency at the interface, and the farther away from the interface, the weaker the response.
Highlights
Anchor bolts’ anchoring and failure mechanism have become the focal point of current anchoring technology because the standard static support system does not always face extreme dynamic load effects, and the roadway has a certain level of seismic resistance [1, 2]. erefore, the static support design can often achieve the stability control of the surrounding rock under dynamic load
As the dynamic load acting on the roadway is generally dominated by low-frequency excitation, the dynamic response of the bolt has an optimal frequency corresponding to the vibration amplitude of the bolt under certain conditions, which is the best frequency between 300 and 500 rad/ s in this example
In addition to the root of the bolt, a reduction in axial force of varying degrees occurs at any cross-sectional location of the bolt, the first appearance of a neutral point in the anchored section. erefore, it may be onesided, even invalid, and futile to attempt to obtain a better roadway control effect by increasing the length of bolt or anchoring section without considering the influence of the main frequency effect of dynamic load
Summary
Anchor bolts’ anchoring and failure mechanism have become the focal point of current anchoring technology because the standard static support system does not always face extreme dynamic load effects, and the roadway has a certain level of seismic resistance [1, 2]. erefore, the static support design can often achieve the stability control of the surrounding rock under dynamic load. Since the mechanical effects of acceleration, velocity, frequency, and time on the bolt members are rarely considered in support design, the resulting dynamic response of the bolted surrounding rock structure is often the main inducing factor for roadway failure and instability [4, 5]. In the early 1980s, a joint research project was undertaken at the University of Aberdeen to study the mechanical response of bolted anchoring systems under transient impact loading [10], involving measurements at the active construction site and reinforced by laboratory and computer models It is a preliminary research of the dynamic response characteristics of the bolts. Ivanovic et al [17] established a model of the dynamic response of rock bolts under impact forces, performed simulation experiments and numerical analysis, and analyzed the effect of displacement and stress response of rock bolts under impact loads and frequencies. By defining the axial force amplification coefficient, the dynamic response characteristics of the axial force of the bolt under multifactor coupling conditions are discussed
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