Study On The Propagation Law Of Pendulum-type Wave In Block-rock Mass

Rock mass is a complex geological body with the characteristics of discretness and heterogeneity.With the increase of underground mining depth,a new dynamic phenomenon of the rock mass,namely,pendulum-type wave,has been discovered.It propagates at low frequency and low speed in rock mass,and carries amounts of energy.Therefore,the pendulumtype wave can induces in deep rock engineering rockbursts and other disasters.For purpose of studying on the effects of heterogeneity and bimodulus characteristics of the block-rock mass,the dynamic equations of one-dimensional and two-dimensional block-rock mass are derived based on the model of spring-block.The dynamic equations are solved by the software of MATLAB.The law of propagation and frequency response of pendulum-type wave in the block-rock mass with heterogeneity and bimodulus characteristics are studied.Also studied is the law of pendulum wave propagation in the two-dimensional block-rock mass.The main research results of this thesis are as follows:(1)For the block-rock mass with heterogeneity,when the elasticity of the local weak interlayer decreases,the dynamic response of the block connected to this part is greatly affected by the elastic change,and the peak of acceleration increases.The influence of the change of elasticity or viscosity of the interlayer in different regions on the pendulum-type wave propagation is similar,but the degree of influence is different.The closer the position of viscoelastic change of intrlayer to the position of impact is,the stronger the influence is on the dynamic response of block-rock mass.(2)For the block-rock mass with the bimodulus characteristics,the compressive to tensile modulus ratio has little effect on the amplitude of the positive displacement of the block,but has a greater influence on the amplitude of the negative displacement.The amplitude of negative displacement increases with the increase of the compressive to tensile modulus ratio.Therefore,the traditional linear calculation method is at risk.With the decrease of the modulus ratio,in the acceleration response a phenomenon of “clustering” of the pendulum-type wave appears.Therefore,we should improve the traditional roadway support method with the consideration of anti-impact and fatigue measures in design of the supporting structure.(3)With the decrease of the compressive to tensile modulus ratio,the number of peaks of frequency response of block's acceleration increases obviously,the amplitude of peaks decreases and the position of peaks moves to low frequency range.The low-frequency characteristics of the pendulum-type wave in the block-rock mass with bimodulus characteristics are more obvious.(4)The natural frequency of the system can be inverted by the fact that the natural frequency of the system corresponds to the peaks of the frequency response.This approach provides a new idea for the determination and measurement of the natural frequency of the nonlinear system.(5)The acceleration response of a certain block in the two-dimensional block-rock mass decays rapidly with time,while the displacement response of the block decays slowly.In the two-dimensional block-rock mass of the infinite space,the displacement of the block is dominated by the positive displacement and the amplitude of negative displacement is small,but the reciprocating vibration about the original position has indeed occurred.The amplitudes of acceleration and displacement near the place where the impact load is applied are relatively large,and the amplitudes of acceleration and displacement decrease exponentially alone blocks.(6)The attenuation rate of the blocks' s acceleration is not only related to the viscosity coefficient of the interlayer,but also to the elastic coefficient between the blocks in the twodimensional block-rock mass.The smaller the elastic coefficient and the larger the viscosity coefficient of the interlayer between blocks is,the faster the attenuation velocity of the acceleration of the blocks is.The viscoelastic properties of the interlayer have important effects on the propagation and attenuation of the pendulum-type wave in the two-dimensional blockrock mass.