Toward more realistic formulations for the analysis of laccoliths

The published laccolith analyses are based on the linear plate bending theory and the a priori assumption that the width of the laccolith is fixed. This is not the case in an actual situation. The dimension of the laccolith in the horizontal plane has to result from an additional matching condition at the separation lines. The published analyses are generalized by dropping the a priori assumption that the width of the laccolith is prescribed, by assuming that the magmatic pressure is not constant, and by taking into consideration the vertical compressibility of the overburden “plate” and base in the contact region. In order to determine the magnitude of the magmatic pressure, a condition is postulated that equates the measured volume of the intruded magma in a laccolith with the corresponding analytical expression for the volume. The obtained closed-form solution appears to satisfy many of the intuitive expectations. It was evaluated numerically and the results are presented as graphs. It may be concluded that even very small laccoliths may exist, provided the magmatic pressure is sufficiently larger than the overburden weight. We also show the dependence of the laccolith size on its stratigraphic position; the thicker the overburden h the larger the size of the laccolith, for an overburden plate of given thickness, the larger the volume V of the intruded magma, the larger the laccolith width 2a and its height. The paper concludes by discussing a published analysis for laccolith with flexible underburden and overburden. It is shown that this analysis is based on a formulation that is of questionable validity.