ABSTRACT
If | | ≥ | | ,c b g uσ δtan⇒ =τ h( )r− ( )2 2 0 (2)
If | | < ⇒ = .c u2 0 (3)
where σ δc g( ) )2 0( , being δ0 the Coulomb friction angle.
Observe that the presence of the term ( ) in the definition of the Coulomb friction term is due
1 INTRODUCTION
Let us consider a simplified two-layer Savage-Hutter type system that can be use to model tsunamis generated by landslides. This model is a simplified version of the one introduced in (Fernández et al. 2008): a layer composed of fluidized granular material is assumed to flow within an upper layer composed of an inviscid fluid (e.g. water). The sediment layer is modelled by a Savage-Hutter type model where buoyancy effects have been considered:
∂ ∂
+ ∂ ∂
= ,
∂ ∂
+ ∂
∂ +
∂ ∂
−
h t
q x
q t x
q h
g g= −h h
h x
gh
2 db dx
h t
q x
q t x
q h
g h rgh
i+ , ∂ ∂
+ ∂ ∂
= ,
∂ ∂
+ ∂
∂ +
2 ∂ ∂
−
−
⎧
⎨
⎪⎪⎪⎪⎪⎪
⎩
⎪⎪⎪⎪⎪⎪
h x
gh db dx
r i bτ τ−
(1)
In these equations, index 1 makes reference to the upper layer (water) and index 2 to the lower one
to the buoyancy effects, that must be taken into account only in the case that the sediment layer is submerged in the fluid, otherwise this term must be replaced by 1.
