Mechanical response of sediments to bubble growth

Abstract

Modeling the process of bubble growth in sediments requires an understanding of the physics that controls bubble shape and the interaction of the growing bubble with the sediment. To acquire this understanding we have conducted experiments in which we have injected gas through a fine capillary into natural and surrogate sediment samples and have monitored pressure during bubble growth to provide information about stress and strain. In gas injection studies with natural sediment samples, we have observed two modes of bubble growth behavior. One of these modes, characterized by a saw-tooth record of pressure as the bubble grows, is consistent with fracture of the medium. Observations indicate that bubble growth by fracture should correspond to bubbles that are coin- or disk-shaped. This shape is confirmed in observations of bubbles in natural sediments and in our studies of bubble injection into gelatin, a surrogate sediment material. Interpretation of the stress–strain results for bubble growth also required that we measure Young’s modulus, E. The measurements show E to be near 0.14 MN m 2, which differs by more than 4 orders of magnitude from values that have been reported in the literature. Our measurements of E give substantially better estimates of bubble shape than are predicted using the literature values. Our data are interpreted with linear elastic fracture mechanics (LEFM) which predicts that the critical pressure for bubble growth will depend on the bubble volume, V raised to the −1/5 power. While evidence of substantial heterogeneity in sediment properties is apparent in our results, this V −1/5 dependence is confirmed. Through application of LEFM theory, we have determined the critical stress intensity factor, K 1c, a material property and the principal determinant of bubble shape and growth by fracture. Our values of K 1c range from ∼2.8×10 −4 MN m −3/2 to ∼4.9×10 −4 MN m −3/2 for our natural sediment samples from Cole Harbor, Nova Scotia. We have also estimated the critical stress intensity factor for Eckernförde Bay samples by analyzing published images of natural bubbles. The K 1c obtained in this way is similar to our Cole Harbor results and is ∼5.5×10 −4 MN m −3/2.