TY - JOUR
T1 - Segment tip geometry of sheet intrusions, I
T2 - Theory and numerical models for the role of tip shape in controlling propagation pathways
AU - Walker, Richard J.
AU - Stephens, Tara L.
AU - Greenfield, Catherine
AU - Gill, Simon P. A.
AU - Healy, David
AU - Poppe, Sam
N1 - This study was conducted without allocated funding. Catherine Greenfield is a Daphne Jackson Trust Research Fellow funded by NERC and the University of Leicester. Simon Gill is supported by a Royal Society Apex Award. Sam Poppe was supported by a frs-FNRS postdoctoral fellowship while at UlB and currently by a ULAM scholarship (NAWA Poland) and NCN Poland grant 2020/37/K/ST10/02447 at SRC PAS. The au- thors thank Tim Davis and Steffi Burchardt for discussions that benefitted the formulation of this paper, and thank the three anonymous reviewers and Editor—Jamie Farquharson—for review commentary that helped to improve the clarity of this paper.
PY - 2021/10/18
Y1 - 2021/10/18
N2 - Inferences about sheet intrusion emplacement mechanisms have been built largely on field observations of intrusiontip zones: magmatic systems that did not grow beyond their observed state. Here we use finite element simulationof elliptical to superelliptical crack tips, representing observed natural sill segments, to show the effect of silltip 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. Super elliptical tips concentrate maximum tensile stress pσmaxqand shear stress out-of-plane of the sill, which may promote non-coplanar growth, vertical thickening, or coplanar viscous indentation. We find that σmax“Pep1`2? aκmaxq, where Peis 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.
AB - Inferences about sheet intrusion emplacement mechanisms have been built largely on field observations of intrusiontip zones: magmatic systems that did not grow beyond their observed state. Here we use finite element simulationof elliptical to superelliptical crack tips, representing observed natural sill segments, to show the effect of silltip 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. Super elliptical tips concentrate maximum tensile stress pσmaxqand shear stress out-of-plane of the sill, which may promote non-coplanar growth, vertical thickening, or coplanar viscous indentation. We find that σmax“Pep1`2? aκmaxq, where Peis 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.
KW - Igneous sill
KW - Igneous dike
KW - Superellipse
KW - Curvature
KW - Stress
U2 - https://doi.org/10.30909/vol.04.02.189201
DO - https://doi.org/10.30909/vol.04.02.189201
M3 - Article
VL - 4
SP - 189
EP - 201
JO - Volcanica
JF - Volcanica
SN - 2610-3540
IS - 2
ER -