Numerical Simulation Of Wavefield And Wave Dispersion Characteristics Analysis In Peridynamic Model

The subsurface rock has been subjected to complex geological process over a long geological time scale,and its internal structure is very complex,with a large number of fractures,joints,cavities and other discontinuous structural surfaces,making it an extremely discontinuous,inhomogeneous and anisotropic damage material..At a certain scale,the natural rock medium cannot be regarded as a continuum due to the existence of discontinuities and no longer fulfills the basic assumptions in classical continuum medium mechanics In seismic exploration,it is also necessary to consider the distribution of microfractures inside the rock medium,but it is difficult to identify the complex microstructure inside the rock at small scales within the wavelength scale of seismic waves,while millimeter-scale microfractures exist in practice,and there is also a complex interaction between wave propagation and fracture extension..Therefore,it’s necessary to establish a small scale medium model containing cracks and then analyse the characteristics of the wavefield distribution under the small-scale model.The equations of motion solved in the framework of classical theory of the continuum mechanics are partial differential equations.When discontinuities are encountered in the process of solving the equations,the basic differential equations are no longer applicable because the spatial partial derivatives do not exist,and the classical continuous medium mechanics encounters a challenge.As an emerging branch of solid mechanics in the continuum mechanics,peridynamics reconstructs the basic form of the kinematic equations in solid mechanics,which can effectively avoid the sharp singularity in solving the discontinuous problems.And peridynamics attempts to replace the partial differential equations in classical continuum mechanics with the integral form of the equations of motion and tries to unify the mathematical modeling of continuum,crack and particle in one framework,and realizes the unified description of the mechanical behavior of continuum model and discontinuous model,which makes it easy to deal with discontinuous modeling problems and has the ability to solve multiscale problems.This dissertation starts from the basic idea of peridynamics,and the basic integral form kinematic equations for the bond based and the ordinary state based peridynamics are derived,and the rock models are established at the same time.The numerical simulation and analysis of the deformation and pre-crack extension in different models are carried out by numerical calculation.The results show that there is a phenomenon of stress concentration at the tips of the both sides of cracks,and the uneven stress distribution easily leads to the crack initiation of rock materials.Meanwhile,the wavefield in the peridynamic models are further simulated in one-dimensional and twodimensional cases.When the wave propagates in the homogeneous model,the wave field appears as concentric circles,which is consistent with the simulation results in the linear elastic model;When propagating in the crack model,the stress wave is reflected on the crack surface and diffracted at the crack tip.The simulation results are consistent with the dynamic photoelastic experimental results and the finite element simulation results.In order to investigate the dispersion of wave propagation in the nonlocal model,the dispersion relation of the ordinary state-based peridynamic model is derived,and the effect of various peridynamic parameters,i.e.the radius of the horizon,the number of material points within the horizon and the parameters of the influence function,on the dispersion properties are analyzed.The results show that the effect of dispersion can be reduced by selecting a smaller the radius of the horizon and a larger shape parameter and peridynamic model is closer to the classical continuum model.The wave propagation characteristics in homogeneous and the cracked rock material model are studied using peridynamic theory,and further compared with the wavefield of the traditional linear elastic model,which verifies the effectiveness of the numerical computation and the peridynamic model.Peridynamic provides a certain theoretical basis and solution strategy for the study of the wave propagation in the discontinuous medium model and also provides a reference for analyzing the wavefield characteristics of cracked rock media from the microscopic point of view,and further broadens the research ideas for exploring the interaction between wave propagation and crack extension.