Abstract
We explore the impact of roughness in crack walls on the P-wave modulus
dispersion and attenuation caused by squirt flow. For that, we
numerically simulate oscillatory relaxation tests on models having
interconnected cracks with both simple and intricate aperture
distributions. Their viscoelastic responses are compared with those of
models containing planar cracks but having the same hydraulic aperture
as the rough wall cracks. In the absence of contact areas between crack
walls, we found that three apertures affect the P-wave modulus
dispersion and attenuation: the arithmetic mean, minimum and hydraulic
apertures. We show that the arithmetic mean of the crack apertures
controls the effective P-wave modulus at the low- and high-frequency
limits, thus representing the mechanical aperture. The minimum aperture
of the cracks tends to dominate the energy dissipation process, and
consequently, the characteristic frequency. An increase in the confining
pressure is emulated by uniformly reducing the crack apertures, which
allows for the occurrence of contact areas. The contact area density and
distribution play a dominant role in the stiffness of the model and, in
this scenario, the arithmetic mean is not representative of the
mechanical aperture. On the other hand, for a low percentage of minimum
aperture or in presence of contact areas, the hydraulic aperture tends
to control de characteristic frequency. Analysing the local energy
dissipation, we can more specifically visualise that a different
aperture controls the energy dissipation process at each frequency,
which means that a frequency-dependent hydraulic aperture might describe
the squirt flow process in cracks with rough walls.