Segment tip geometry of sheet intrusions, I: Theory and numerical models for the role of tip shape in controlling propagation pathways

Abstract

Inferences about sheet intrusion emplacement mechanisms have been built largely on field observations of intrusion tip zones: magmatic systems that did not grow beyond their observed state. Here we use finite element simulation of elliptical to superelliptical crack tips, representing observed natural sill segments, to show the effect of sill tip shape in controlling local stress concentrations, and the potential propagation pathways. Stress concentration magnitude and distribution is strongly affected by the position and magnitude of maximum tip curvature κmax. Elliptical tips concentrate stress in-plane with the sill, promoting coplanar growth. Superelliptical tips concentrate maximum tensile stress (σmax) and shear stress out-of-plane of the sill, which may promote non-coplanar growth, vertical thickening, or coplanar viscous indentation. We find that σmax = Pe(1+ 2(√[aκmax]), where Pe is magma excess pressure and a is sill half length. At short length-scales, blunted tips locally generate large tensile stresses; at longer length-scales, elliptical-tipped sills become more efficient at concentrating stress than blunt sills.

Segment tip geometry of sheet intrusions, II: Field observations of tip geometries and a model for evolving emplacement mechanisms

“…bedding planes) to cause bedding plane slip and buckling of strata [Pollard et al 1975;Rubin 1993]. Pollard [1973] proposed two end-member models to account for wedge-shaped zones of faulted host rock ahead of rounded segment tips: brittle-shear failure and ductile-shear failure, both of which resemble Hencky-relation slip line solutions for Segment tip geometry of sheet intrusions, II Stephens et al, 2021 a pressurised hole in an infinite plate [e.g. Nádai 1950;d'Escatha and Mandel 1974].…”

“…Notably, the segment tip geometry controls the location of shear stress concentrations about the tip [e.g. Obert and Duvall 1967;Walker et al 2021]. Shear stress will concentrate at the segment tip maximum curvature; in the case of a circular tip this is a single concentration distributed around the tip [e.g.…”

“…Pollard 1973;Souche et al 2019], but in the case of a superelliptical or rectangular tip geometry [e.g. Merle and Donnadieu 2000;Walker et al 2021], this is not the case.…”

“…Pollard et al 1975;Delaney and Pollard 1981;Hutton 2009;Schofield et al 2010;Kavanagh and Sparks 2011;Walker et al 2017;Healy et al 2018;Galland et al 2019;Kjøll et al 2019]. Lobate or blunt tips cannot Segment tip geometry of sheet intrusions, II Stephens et al, 2021 form via linear elasticity, which has led to the development of various non-brittle propagation models, including viscous indentation and bulldozing [e.g. Spacapan et al 2017], host rock fluidisation [e.g.…”

“…Currier and Marsh 2015;Mattsson et al 2018;Burchardt et al 2019]. Such modifications are also likely to occur in segmented sheet intrusions, and since late-stage processes have the potential to overprint early structures, segment geometries as observed in the field, may be representative only of the final stage of emplacement, rather than the emplacement process as a whole [Walker et al 2021].…”