Purpose

This article concentrates on the block-hierarchical structures of rock masses and investigates the dynamic problem and dispersion relation of pendulum-type waves caused by the low-frequency vibrations of rock blocks in blocky rock masses, and determines the effect of block-hierarchical structures.

Methods

The blocky rock masses composed of granite blocks and rubber interlayers are simplified into the block–spring model and the wave motion model. Based on Bloch theorem and d’Alembert’s principle, the dispersion relation and equations of motion of blocky rock masses with complex block-hierarchical structures are determined, respectively.

Conclusion

With the increase of the rock size and geomechanical invariant, the initial frequency of the first attenuation zone gradually decreases, and only the low-frequency waves lower than that frequency can propagate in the blocky rock masses, which reveals the mechanism of low-frequency characteristics of pendulum-type waves theoretically. Research on the two models with different block-hierarchical structures indicates that the equivalent substitution of the two models is not universal and unconditional. The larger the stiffness ratio, or the higher the order of block-hierarchical structures, the smaller is the effect of ignoring the high-order hierarchical structures.

Applications

The research will be of interest to a wide range of experts in the fields of stress wave propagation, earthquake engineering and rock bursts, as well as those working to reduce the engineering vibrations of underground structures and process monitored wave packet data for structures.

中文翻译：

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复杂块状层状结构块状岩体低频振动引起的摆式波的色散关系及动力特性

目的

本文针对块状岩体的块状层次结构，研究了块状岩体中岩块低频振动引起的摆式波的动力问题和频散关系，并确定了块状层次结构的效应。

方法

将由花岗岩块和橡胶夹层组成的块状岩体简化为块-弹簧模型和波动模型。基于布洛赫定理和达朗贝尔原理，分别确定了具有复杂块状层状结构的块状岩体的频散关系和运动方程。

结论

随着岩石尺寸和地质力学不变性的增大，第一衰减区的初始频率逐渐降低，只有低于该频率的低频波才能在块状岩体中传播，揭示了低频特性的机理理论上的摆型波。对两种具有不同块层次结构的模型的研究表明，这两种模型的等价替代不是普遍的、无条件的。刚度比越大，或者块层次结构的阶数越高，忽略高阶层次结构的影响越小。

应用领域

这项研究将引起应力波传播、地震工程和岩爆领域的广泛专家以及致力于减少地下结构工程振动和处理结构监测波包数据的专家的兴趣。