Rayleigh wave propagation in intact and damaged geomaterials

Abstract

Abstract An analytical model of an elastically deforming geomaterial with microstructure and damage is assumed to be a material where the second spatial gradients of strain are included in the constitutive equations. Based on this assumption, a linear second gradient (or grade-2) elasticity theory is employed, to investigate the propagation of surface waves in either intact or weathered—–although homogeneous and isotropic at the macroscale—materials with microstructure such as soils, rocks and rock-like materials. First, it is illustrated that in contrast to classical (grade-1) elasticity theory, the proposed higher-order elasticity theory yields dispersive Rayleigh waves, as it is also predicted by the atomic theory of lattices (discrete particle theory), as well as by viscoleasticity theory. Most importantly, it is demonstrated that the theory: (a) is in agreement with in situ non-destructive measurements pertaining to velocity dispersion of Rayleigh waves in monumental stones, and (b) it may be used for back analysis of the test data for the quantitative characterization of degree of surface cohesion or damage of Pendelikon marble of the Parthenon monument of Athens.