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Effects of magma rheology changes and mechanical interactions with host rocks during magma ascent in volcanic conduits
Antonio Costa
INGV, Bologna, Italy
ERI, The University of Tokyo, Japan
IUGG 2015, Prague, 27 June 2015
Special thanks to O. Melnik
o Rheological changes and dynamics of magma ascent;
o Thermal regimes and validity of the Poiseuille law:
viscous heating vs conductive cooling
o Crystal kinetics and magma dynamics:
crystal growth and high crystallinity regimes
o Mechanical interaction with host‐rocks and controls of conduit‐
chamber geometry on eruption dynamics;
o Open issues.
Magma rheology
Magma (three‐phase system) viscosity depends on:
• Temperature
• Chemical composition (volatiles) • Crystal content
• Strain rate
• Bubble content
Non‐Newtonian visco‐elasto‐plastic behaviour
 A 
   ( ,Ca) (  ,  ) VTF exp 
T C
e.g., Giordano et al. (2008), Llewellin & Manga (2005); Costa et al. (2007;2009)
Eruption styles
Validity of common assumptions: e.g. the Poiseuille solution
1 D p
 L
 Incompressible magma (L/D>>1 OK)
 Steady‐state flow (Re<<1 OK)
 Constant viscosity
Sketch of the system: conduit + host rocks
Costa et al. (2007 c)
Governing equations v 0
  v  v  P  g  
c  c v  T  k T   : v
   v  v ;    ( )  VTF exp T AC 
(Rheology) Costa et al. (2007c)
Temperature evolution (low ΔP)
Costa et al. (2007c)
Temperature evolution (high ΔP)
Costa et al. (2007c)
Lubrication approximation Q  2
rv x dr
1   v x  P
r r  r  x
v x 
T k  T
 c p vx
   
 r 
x r r r
   ( )  R expbT  TR 
Costa and Macedonio (2003); Costa et al. (2007)
Thermal regimes
Na0 0 V 3 L
R  kc
‐ Thermal erosion of conduit wall; ‐ Strain localization (pumice texture);
‐ Friction factor for 1D models and effective viscosity: larger intensity eruptions can happen from volcanic conduits having significant smaller diameter (Vedeneeva et al. 2005);
Temperature profiles
for a given conduit diameter fragmentation can occur at much shallow depths (Vedeneeva et al. 2005).
Velocity profiles
(e.g. Polacci et al., 2001)
Crystal resorption effects
Costa et al. (2007)
Crystal kinetics: crystal content decrease as temperature increase; moreover high temperatures also inhibit crystal growth…
Viscosity of crystal‐rich magmas
Costa (2005); Costa et al. (2009a)
Nonlinear dynamics of magma flow in the conduit
Mount St. Helens Santiaguito
Lava dome eruptions have periods of high, low or no activity on timescales of hours to years. The most hazardous phenomena typically occur when magma discharge rates are high. •
During magma ascent pressure decreases and volatiles exsolve forming bubbles. This gas exsolution drives crystallization and, as a consequence, magma viscosity can increase by orders of magnitude.
These processes operate on different timescales.
Melnik and Sparks (1999;2005)
Governing Equation System Mass Conservation
Momentum Equations
Costa et al. (2007 a,b)
Pulses in discharge rate for an idealized cylinder conduit
Melnik and Sparks (2005)
Effects of wall‐rock elasticity:
multi‐week cycles
Costa et al. (2007 a,b)
Dual chamber conduit model: multi‐year cycles
Christopher et al (2014)
(Melnik & Costa, 2014)
Dual chamber conduit model: multi‐year cycles
(Melnik & Costa, 2014)
Stick‐slip mechanism: short term cyclicity
Costa et al. (2012; 2013)
Stick‐slip mechanism: short term cyclicity
Costa et al. (2012; 2013)
Potential causes and controls of stick‐slip in magma conduits
‐ Rheology (e.g. polymers)
‐ Viscous heating
‐ Magma fracturing ‐ Shear banding
‐ Frictional melting (e.g. Kendrick et al 2014; Lavallee et al 2012, Hornby et al 2015)
Deviation from Byerlees friction law due to frictional melting:
Effect of crystal shape and poly‐dispersity
Cimarelli et al. (2011)
Crystal interactions
Rognon et al. (2008)
Molecular dynamic simulations of concentrated cohesive particle systems
Changes in magma rheology due to viscous heating and heat loss, crystallinity and crystal changes, shear bandings, slip mechanisms, and mechanical response of host‐rocks can have a pivotal control in magma flows, such as: • drastically deform velocity, temperature and viscosity profiles;
• modify friction factor, reduce fragmentation depth, etc; • generate different strain‐rate and temperature regions in the conduits;
• promote crystal resorption and wall‐rock melting, etc.
Magma chamber‐conduit geometry and its sin‐eruptive variations
• control magma flow cyclicity in lava dome eruptions on different time‐scales, from hours (shallow conduit) to years (deep‐shallow connectivity).