Mechanics of growth of some laccolithic intrusions in the Henry mountains, Utah, II: Bending and failure of overburden layers and sill formation

Abstract

Deformation of host rocks during growth of a laccolithic intrusion is analyzed using the theory of bending a stack of thin elastic plates. The theoretical model suggests that magma spreading laterally in the form of a sill will eventually gain sufficient leverage on the overlying strata to deflect them upward and form a laccolith. The amount of bending increases as the fourth power of the distance the magma spreads, whereas the overburden resists bending as the third power of its effective thickness. Effective thickness is the thickness of a single layer which has the same resistance to bending as a multilayer of similar length and elastic modulus. The effective thickness of overburden in the Henry Mountains is estimated as between 1 7 and 2 3 of the actual thickness. The form of bending is similar for Newtonian, pseudoplastic, and Bingham magmas. The magnitude of the bending depends upon the total upward force and its distribution and is not simply related to magma viscosity as has been suggested by several previous investigators. After elastic bending strata should fail over the periphery of an intrusion, the site of maximum bending strain and differential stress predicted by the theory. Field observations described in Part I correlate well with these predictions. Because bending strains are proportional to layer thickness, strata of comparable strength but different thicknesses fail at different stages of laccolith development. This leads to the different cross-sectional forms of laccoliths observed in the field. The effect of host rocks on sill form and growth is analyzed using the elastic solution for an elliptical hole under uniform pressure. The theory suggests that sill thickness increases in proportion to length. The concentration of high stresses near the sill termination should induce permanent deformation and account for the blunt terminations described in Part I. This blunting is most likely to occur in relatively ductile rocks whereas sills simply split brittle rocks and maintain sharp terminations. The driving pressure in sills can be calculated from measurements of length and termination radius of curvature, if the yield strength of the host rocks can be estimated. This driving pressure must be greater than the overburden pressure, but sills apparently do not form or propagate by lifting their overburdens. Instead they propagate by locally deforming the host rock. After spreading over a distance about three times the effective overburden thickness, the overlying layers begin to bend upward significantly. This stage marks the transition from a sill to a laccolithic intrusion.