| The instability and failure of dangerous rock mass of slope has the characteristics of spatial location randomness,time uncertainty and sudden events.The current monitoring method is difficult to meet the needs of collapse prevention and control of dangerous rock mass.In this paper,the falling dangerous rock mass of slope was taken as the research object,and the correlation model between the stability factor of the falling dangerous rock mass and the first-order natural frequency was established.The theoretical analytical algorithm of the first-order natural frequency of the falling dangerous rock mass of slope was derived.Based on the laboratory experiment,the stability identification method of the falling dangerous rock mass of slope based on the natural frequency under the condition of constant micro-motion was analyzed,and the whole method is applied in practice.The conclusions can be given as follows:(1)Based on the theoretical analysis,the stability coefficient of the dangerous rock mass is related to the natural frequency,damping ratio and the relative depth of the trailing edge crack.Based on the laboratory experimental analysis,the natural frequency of the dangerous rock mass is sensitive to the change of the depth of the trailing edge crack.It showed that the main control parameter of the stability coefficient of the dangerous rock mass-the relative depth of the trailing edge crack can be characterized by the dynamic parameters of the dangerous rock mass,and the stability evaluation model of the falling dangerous rock mass of slope based on the natural frequency was established.(2)For the tensile fractured dangerous rock mass,considering the parameter inertia of the overall rigid body motion of the dangerous rock mass,combined with the equivalent continuous stiffness model of the fracture and the dynamic foundation half-space theory,the constraint stiffness of the cantilever dangerous rock mass was derived,which provided the boundary conditions for solving the motion equation of the dangerous rock mass.Combined with the vibration mode function of dangerous rock mass,the analytical algorithm of the first-order natural frequency of cantilever dangerous rock mass was derived,and the correctness of the analytical algorithm was verified based on numerical simulation.The average relative error between the theoretical value and the simulated value was 1.93%,and the minimum relative error was 0.44%.The computability of the first-order natural frequency of the cantilever dangerous rock mass was realized,which provided the necessary dynamic parameters for the stability evaluation model of t cantilever dangerous rock mass.(3)For the shear fractured dangerous rock mass,the separation part of the dangerous rock mass and the bedrock was compared to a cantilever beam,and the motion deformation characteristics of the unseparated part of the dangerous rock mass and the bedrock were analyzed.Combined with the dynamic foundation halfspace theory and the motion deformation characteristics of the non-cantilever beam part of the dangerous rock mass,the motion constraint stiffness of the dangerous rock mass was derived,which provided the boundary conditions for the motion equation of the dangerous rock mass.Combined with the vibration mode function of the dangerous rock mass,the analytical algorithm of the first-order natural frequency of the dangerous rock mass was derived,and the correctness of the analytical algorithm was verified based on the numerical simulation.The average relative error between the theoretical value and the simulated value was 2.95%,and the minimum relative error was 0.52%.The computability of the first-order natural frequency of the shear fractured dangerous rock mass was realized,which provided the necessary dynamic parameters for the stability evaluation model of the shear fractured dangerous rock mass.(4)Considering the practical application,the dangerous rock mass is often in the high and steep slope,and its volume is often huge,through the way of artificial excitation is not feasible.In this paper,through the combination of laboratory experiments,based on the relative amplitude spectrum method and the equivalent amplitude spectrum method,the first order natural frequency calculation method of the falling dangerous rock mass of slope was proposed,so that the stability evaluation model of the falling dangerous rock mass based on the natural frequency can be measured and calculated in real time.On this basis,the stability evaluation model of dangerous rock mass of falling slope based on natural frequency was applied to practical engineering,and good application results were obtained. |
