Wave propagation through discontinuous media in rock engineering

The analysis of wave propagation in jointed rock masses is of interest for solving problems in geophysics, rock protective engineering, rock dynamics and earthquake engineering. At present, more than in the past, analyses of underground structures in seismic conditions need be considered. The aim of the present thesis is to contribute to the understanding of wave propagation in rock masses and of its influence on the stability of underground structures. The research is focused first on the analysis of the phenomenon through analytical, numerical and experimental methods. Then, static and dynamic stability analyses of a real case study such as the water storage cavern of the Tel Beer Sheva archaeological site in Israel (Iron age 1200-1700bc) are carried out. An analytical method such as the Scattering Matrix Method (SMM) is developed for the study of wave propagation through rock masses. This method (SMM) is based on the scattering matrix and is borrowed from electromagnetic wave propagation theory of transmission lines such as coaxial cables, optical fibres, strip-lines, etc. The scattering matrix is composed of reflection and transmission coefficients of a single joint or a set of parallel joints. Dry, fluid filled or frictional joints are considered. The computation can also be performed with material damping. Both P, SV or SH-waves can be applied to the model with any oblique angle of incidence. The analytical solution is obtained in the frequency domain and allows one to consider multiple wave reflections between joints. The analytical results obtained with the SMM are compared with other analytical methods and with the Distinct Element Method (DEM) by using the UDEC and 3DEC codes (from Itasca Consulting Group). The results obtained with the SMM applied to different joint models are compared with those obtained experimentally with the Hopkinson pressure bar (SHPB) tests. Resonant column laboratory tests are also performed to investigate the effects of fractures on wave propagation in a soft rock. A three-dimensional DEM model is implemented to simulate the resonant column test. Numerical and experimental results are compared. The stability of the water storage cavern of the Tel Beer Sheva archaeological site in Israel, excavated in a jointed chalk is assessed by means of static and dynamic DEM analyses in two and in three dimensional conditions. A back analysis of both the roof collapse during construction and of the cavern in its present configuration with a pillar installed in the centre is also carried out. Finally dynamic analyses are performed to evaluate the influence of wave propagation on the stability of the cavern with a deconvoluted motion produced by the Nuweiba earthquake (1995) being applied as input. Additional numerical analyses are performed to evaluate the dependence of the damage on the amplitude, duration, frequency and direction of the input wave.