Rheology of welding: inversion of field constraints

At present the mechanisms and rheological behaviour of pyroclastic deposits during welding and compaction are poorly understood. Here, we explore the extent to which the rheological properties of pyroclastic deposits are constrained by physical property distributions in welded ignimbrite. Physical properties of samples from a 20-m section of the Bandelier Tuff, New Mexico are used as proxies for strain. The observed strain (εT) is ascribed to a combination of a time-dependent viscous compaction (εv) and a time-independent mechanical compaction (εm) described by: ε T = ( 1 − ϕ o ) α ln { 1 + α ⁢ σ ⁢ Δ ⁢ t η o ( 1 − ϕ o ) exp α ϕ o ( 1 − ϕ o ) } + σ E ( 1 − ϕ o ) where ϕo is the original porosity, σ is load, and ηo and E are the viscosity and Youngʹs modulus of the deposit at zero porosity, respectively. The quantity α is an experimentally determined parameter used to relate the viscosity and porosity of porous aggregates. Simple conductive heat transfer models are used to generate cooling curves for individual samples; these curves dictate times of residence (Δt) at temperatures above the glass transition temperature. We adopt an inverse model approach whereby the observations on the natural material and model cooling curves are used to constrain the values of ηo (1014.5 Pa s) and E (3–7 MPa). Our optimization also predicts the relative components of viscous and mechanical compaction throughout the welded ignimbrite. Viscous compaction dominates the lower two thirds of the section (εv: εm>1.0); the maximum in εv is coincident with the observed peak in welding intensity. Lastly, we present two dimensionless numbers (QA and QB) which are used to create a map of welding potential for pyroclastic deposits. The map has four quadrants which coincide with (i) no welding, (ii) welding and compaction driven by temperature (εv>εm) or (iii) by gravitational loading (εm>εv), and (iv) welding aided by temperature and load (εv≌εm).