Research On Multi-parameter Inversion For Rock Mass Joint Using Reflected Wave

The joint has great effect on the strength and stability of rock mass, the effect degree directly relates to joint's geometry and mechanics parameters, including the joint's strike, dip angle, location, thickness, stiffness, strength et al. How to determine an underlying joint's characteristic parameters has been a key technical subject which concerned by rock mass engineers. Present rock mass engineering wave testing always only consider wave velocity or amplitude attenuation or spectrum characteristics when the tested signal be complained and analyzed, as a result, the cost is high or precision is low when the technique be used to detect a joint, furthermore, only one or two parameters can be acquired. So a research on multi-parameter inversion for joint through comprehensive and further analysis of signal reflected by joint indubitably has important theoretic meaning and engineering practical value.Through the analysis of stress wave's propagating process in the vertical direction at the joint, the expression of a series of echoes generated at the joint is achieved, then the combined vibration at the initial wave source is determined, finally a inverse model to detect the joint's characters based on signal process of the vibration is given.Based on the analytic geometry theory, a formula to calculate the reflected wave's traveling time can be deduced. The formula establishes a direct relationship between a joint's real dip angle, real dip direction and the traveling time of testing spots. The reflected wave's isotraveling time circle described by the formula has a clear conception and a definite meaning. Through complex signal analysis, a signal's instantaneous amplitude, phase and frequency can be presented. A simulating jointed rock masses, mortar to simulate rock and wet soil layer to simulate joint, be made and the complex signal analysis be applied to analyze the vibration signal at the testing spots on the upper rock surface. Despite the Rayleigh wave's serious interference, the initial arriving moment of the joint reflected wave can still be judged from instantaneous frequency efficiently. Using the complex signal analysis, the traveling time of several testing spots distributing around the source of vibration be get, a program based on MATLAB be written to search the center of the isotraveling time circle, then the joint's attitude be inversed in the end.In the other simulating joint model the testing plane is parallel to the joint, the receiving probe be set close to the sending probe to receive the vertical reflected signal. Applying complex signal analysis to analyze the signal, the initial arriving moment of every echo be showed clearly by instantaneous frequency figure. The signal's amplitude spectrum reveals that there are two main frequency, the higher is the probe signal's dominant frequency and the lower is the testing plane's free vibration frequency. The band-pass filter which be transformed from Littlewood-Paley wavelet can filter the two frequency signal separately, and the filtered signals display the change of the signal's amplitude that corresponding with the each echo's arrival.In order to separate initial echo from the tested signal, Duhamel integral be using to calculating the testing plane's forced vibration motivated by the probe's emitted signal. The forced vibration induces direct wave and Rayleigh wave which propagate along surface, with the help of LT and HT, the surface vibration be simulated. The forced vibration transmits downwards and induces incident wave for the joint, so the initial echo's waveform is same as the forced vibration's. A new signal can be get if initial echo be subtracted from the tested signal, set the new signal's instantaneous frequency's standard deviation as a assessment function, a program be designed on MATLAB to search the minimum, then the echo's amplitude be obtained.Through Hilbert transform, a signal's plane trace can be get. There are two frequencies in the tested signal, so the signal's plane trace may be looked as the track of the out pole's end when two poles rotate around parallel axles. Using the knowledge of motion synthesis in theory mechanics, a formula to describing the change of plane trace's step length and angle for two-frequency be get. So we may prolongate the tested signal's plane trace from the echo's initial arriving moment, and get a certain length of the signal's prolongation. If we subtract the prolongation from the real tested signal, the amplitude of 1st and 2nd echo be obtained.After the amplitude of every echo be obtained, we can use the inverse model to acquire the joint's thickness, quality factor, P-wave velocity for the simulating model.