

Daniel MEGE
RESEARCH 



Scaling laws for dyke propagation
Length vs. maximum displacement
LENGTH VS. MAXIMUM DISPLACEMENT and implications for the maximum depth of LEFM applicability (at least in the study area)
For most fracture types a linear relation exists between length L and maximum displacement Dmax. Field evidence usually shows that
where a = 1 and g ranges between 0.1 and 0.001. This rule works surprisingly
well for a given fracture population that is not restricted by mechanical
discontinuities; the observed data scattering is explained by the difference
in linkage stage among the studied fracture population [1]. The value
taken by g depends on rock type, water content, and planetary size (gravity). Figure 1 : Location of the study area in Ethiopia
The exponent of this population is 0.48 (Figure 2). The behaviour of silicic and basaltic dykes is not significantly different; counting them in the same population improves the correlation coefficient (0.69) [2].
Figure 2: Length vs. maximum displacement for 39 studied Ethiopia dykes and other dykes and veins which dimensions were found in previous papers. These populations are better fit by a squareroot law (dashed lines) than a linear law (dotted lines) [2].
where KIC is fracture toughness in mode I (opening), n is Poisson's ratio, and E the Young's modulus of the basaltic rock mass, shows this squareroot dependence. However, this equation considers that dyke is infinitely tall. It is clear though that all the silicic dykes and many basaltic dykes should have erupted [3], and it can be shown that a more realistic fracture toughness is ~1/3 the value given by this equation [2], which gives 77 < KIC < 273 MPa.m1/2. Similar KIC values have been obtained in publications on other dyke populations.
Figure 3: Interpreted magmatic and magnetic fabric of dykes from the studied populations showing mixedmode emplacement. The diagram for mode I is to illustrate the theoretical patterns expected in case of dyke propagation in pure opening [2].
... which may help identify eruptive dykes!
In construction... See the paper by Mège and Korme in the publications list (JVGR n°131) for more information.
References[1] R.A. Schultz, R. Soliva, C. Okubo and D. Mège, 2009, Fault populations. In R.A. Schultz and T.R. Watters (Eds), Planetary Tectonics. Cambridge Univ. Press, 456509. [2] R.A. Schultz, D. Mège and H. Diot, 2008, Emplacement conditions of igneous dikes in Ethiopian Traps. J. Volc. Geotherm. Res., doi:10.1016/j.jvolgeores. 2008.08.012. [3] D. Mège, and T. Korme 2004, Fissure eruption of flood basalts from statistical analysis of dyke fracture length. J. Volc. Geotherm. Res., 131, 7792, doi:10.1016/S03770273(03)003172. [4] D. Mège and T. Korme, 2004, Dyke swarms in the Ethiopian Large
Igneous Province: not only a matter of stress. J. Volc. Geotherm. Res.,
132/4, 283310, doi:10.1016/S03770273(03)003184.
