Theoretical Methods for Wave Propagation across Jointed Rock Masses

Different methods are presently available for the analysis of wave propagation across jointed rock masses with the consideration of multiple wave reflections between joints. These methods can be divided into two categories. One is based on the displacement discontinuity model for representing rock joints, where the displacements across a joint are discontinuous and the tractions are continuous, and the other is the equivalent medium method. For the first category, there are three methods, i.e., method of characteristics (MC), scattering matrix method (SMM) and virtual wave source method (VWS). MC solves the equation of motion by using the theory of characteristic curves. SMM is based on the definition of the scattering matrix in which the reflection and transmission coefficients of a set of joints are stored. VWS method replaces the joints in the rock mass with a virtual concept. For the second category, equivalent medium model treats the problem in the frame of continuum mechanics and simplifies it from an explicit wave propagation equation. The objective of this paper is to review and compare these theoretical methods. The comparison shows that the four solutions agree very well with each other. Some additional considerations about the advantages and disadvantages of these methods are also given in the pape

Infarto estriatocapsular na infância: relato de quatro casos

Os autores apresentam o estudo de quatro crianças que manifestaram hemiparesia desproporcionada de instalação súbita, sem perda da consciência. O diagnóstico de infarto estriatocapsular foi confirmado pela tomografia computadorizada do crânio (TCC) e ressonância magnética (RM). Discutem os achados clínico-neurológicos e de exames complementares. História familiar de migrânea foi relatada em dois dos pacientes. Constatou-se migrânea em dois, trauma craniano, miocardite e prolapso de válvula mitral em um. Hemiparesia esquerda, com predomínio bráquio-facial em três e braquial em um. A TCC demonstrou comprometimento do núcleo lenticular e da cápsula interna nos quatro casos; da cabeça do núcleo caudado em três e da substância branca em dois. A RM foi realizada em dois e confirmou os achados da TCC. O eletrencefalograma, obtido na fase aguda em três, se mostrou alterado nos quatro casos

Wave Propagation in Discontinuous Media by the Scattering Matrix Method

Propagation of elastic waves in discontinuous media is studied in this paper by the scattering matrix method (SMM). An electromagnetic transmission line analogy is also used to set up the mathematical model. The SMM operates in the frequency domain and allows for all wave polarizations (P, SV and SH). Rock masses are examples of discontinuous media in which the discontinuities (fractures or joints) influence wave propagation. Both elastic and viscoelastic joints are considered and the latter are described by Kelvin-Voigt, Maxwell and Burgers models. Rock joints with Coulomb slip behavior are also analyzed, by applying the averaging principle of Caughy (J Appl Mech 27:640-643, 1960). The evaluation of the effects of periodic discontinuities in a homogeneous medium is presented by introducing the concept of Bloch waves. The dispersion curves of these waves are useful to explain the existence of frequency bands of strong attenuation, also in the case of lossless (perfectly elastic) structures. Simple expressions of transmission and reflection coefficients are obtained. Finally, the SMM results are compared with those computed via the distinct element method (DEM). The comparisons are performed on a medium with joints with Coulomb slip behavior and the agreement is satisfactory, although the SMM must be applied in conjunction with the equivalent linearization technique. Even if the DEM is much more general, the SMM in these simple cases is extremely faster and provides a higher physical insigh