The Study Of P-wave Across A Joint Set With Semi-numerical Method

P-wave propagation characteristics in the joints rock are closely related to thestress-strain relationship of rock and joints. In addition to that they alone can impacton stress wave propagation, their common role or part of nature can enable the stresswave to produce a new wave phenomena. Scholars are concerned about the focus ofstress wave propagation characteristics related to the amplitude and energycharacteristics.From the two aspects, the systematical analysis of properties of P-wave anddevelopment, applications of new calculation method, we launched our research. Atfirst, based on the fracture model of improved nonlinear normal deformation behavior,finite difference solutions of vibration velocity of transmission wave are obtainedwith semi-numerical method. The amplitude, energy, spectrum, and time delay ofdifferent wave’s first-arrival pulses across multi-fracture with large gap isinvestigated. Using the theory of P-wave across a group of large spacing joints inelastic rock, after the data processing of seismic waves, the transmission of seismicwaves in the group of large spacing joints is analysised. The relationship betweenwaveform, higher harmonic, time delays and the number of joints is investigated.Then, we use two calculation methods to consider P-wave across a dual non-linearjoint. The first one is bese on nonlinear wave equation and its approximate solutionand. The second one is based on the model of the flexible nonlinear rock and finitedifference method. On this basis, by using characteristic equation of P-wave, thesemi-numerical solutions of transmitted wave are obtained. Computational programsare compiled and parameter studies are conducted to get an insight into transmittedwaveform, frequency spectra and transmission coefficient under the influence of dualnonlinear, in terms of joint, wave source, nonlinear coefficient of soft rock, positionof joint. At last, joints rock is divided into many imaginary linear joints with smallspacing and large stiffness, and some nonlinear joints is inserted. Method ofsemi-numerical solutions of P-waves across a group of dual nonlinear joints is obtained by using semi-numerical analysis. Then relationship between the parametersof P-wave and joints, the nonlinear coefficient of rock and waveform of the first waveand the follow-up wave, transmission coefficient of first wave, energy of the firstwave and the follow-up wave is investigated. Some new wave phenomena are found.