Numerical Modeling of Stalagmite Vibrations

Recently, it has been argued that natural, intact stalagmites in caves give important constraints on seismic hazard since they have survived all earthquakes over their (rather long) life span. This suggests that the pattern of oscillation should be fully understood, including the splitting of eigenfrequencies that has occurred in recent cave observations. In the present study, we simulate the oscillation of a given stalagmite by setting up four simplified models of the stalagmite. The dimensions of the intact stalagmite were measured in situ, and the geo-mechanical and elastic parameters of broken stalagmite samples, determined in geo-mechanical laboratory, have been taken into account. The eigenfrequencies of the stalagmite are then calculated numerically, by the finite element method, and compared with the measured in situ values. The latter have shown splitting of eigenfrequencies, which we were able to reproduce by the numerical model calculations taking into account the asymmetric shape of the stalagmite.