An extended displacement discontinuity method for analysis of stress wave propagation in viscoelastic rock mass

An extended displacement discontinuity method (EDDM) is proposed to analyze the stress wave propagation in jointed viscoelastic rock mass (VRM). The discontinuities in a rock mass are divided into two groups. The primary group with an average geometrical size larger than or in the same order of magnitude of wavelength of a concerned stress wave is defined as “macro-joints”, while the secondary group with a high density and relatively small geometrical size compared to the wavelength is known as “micro-defects”. The rock mass with micro-defects is modeled as an equivalent viscoelastic medium while the macro-joints in the rock mass are modeled explicitly as physical discontinuities. Viscoelastic properties of a micro-defected sedimentary rock are obtained by longitudinally impacting a cored long sedimentary rod with a pendulum. Wave propagation coefficient and dynamic viscoelastic modulus are measured. The EDDM is then successfully employed to analyze the wave propagation across macro-joint in VRM. The effect of the rock viscosity on the stress wave propagation is evaluated by comparing the results of VRM from the presented EDDM with those of an elastic rock mass (ERM) from the conventional displacement discontinuity method (CDDM). The CDDM is a special case of the EDDM under the condition that the rock viscosity is ignored. Comparison of the reflected and transmitted waves shows that the essential rock viscosity has a significant effect on stress wave attenuation. When a short propagation distance of a stress wave is considered, the results obtained from the CDDM approximate to the EDDM solutions, however, when the propagation distance is sufficiently long relative to the wavelength, the effect of rock viscosity on the stress wave propagation cannot be ignored.