Effects of pore-fluid pressure on the motion of debris flows

ABSTRACT

Pore-fluid pressure mediates the shear strength between soil particles and significantly controls the movement of debris flows. This study analyzes the effects by proposing a numerical model to solve the pore-fluid diffusion equation coupled to changes in surge motion of debris flows. The model was established by combining a Lagrangian method solving the depth-averaged one-dimensional equations for the debris-flow motion and a Fourier-series solution for the pore-fluid diffusion equation. Owing to the source term related to the change in surge depth, the Fourier-series solution shows that the excess pore-fluid pressure near the bed dissipates faster and exhibits a non-monotonic profile. The results of numerical calculations reveal that the diffusivity of excess pore-fluid pressure and the liquefaction condition have significant impacts on the depth profiles and velocities of debris-flow surges.

CO EDITOR-IN-CHIEF:

• Ou, Yu-Chen

ASSOCIATE EDITOR:

• Ou, Yu-Chen.

KEYWORDS:

• Debris-flow surge
• pore-fluid pressure
• lagrangian method
• fourier-series solutions

Nomenclature

AK, $B_k$	=	coefficients of Fourier series
$c_1,$ $c_2$	=	coefficients in the correction factor to diffusivity
$D_v$	=	pore pressure diffusivity
$\mathit{d}$	=	total distance of surge
$d_s/\mathit{dt}$	=	total time derivative with solid-grain velocity
$\bar{d}/\mathit{dt}$	=	time derivative with mean streamwise velocity
$\mathit{g}$	=	gravitational acceleration
$\mathit{H}$	=	typical height of slide
$\mathit{h}$	=	depth of debris flow
$\mathit{k}$	=	permeability
$k_{\mathit{act}/p\mathrm{ass}}$	=	active or passive earth pressure coefficient
$\mathit{L}$	=	typical spread of slide
$N_p$	=	number of meshes
$\mathit{p}$	=	pore fluid pressure
$p_w$	=	hydrostatic pressure
$\mathit{T}$	=	total normal stress
Tf(xx), Tf(yx), Tf(xy), Tf(yy)	=	fluid stresses
Ts(xx), Ts(yx), Ts(xy), Ts(yy)	=	soil stresses
$\mathit{t}$	=	time
$\mathit{u},$ $\mathit{v}$	=	streamwise, vertical velocity component
$\bar{u}$	=	depth-averaged velocity
${\mathit{v}}_s$, $\left(u_s,v_s\right)$	=	velocity of solid grains
$\mathit{x},$ $\mathit{y}$	=	spatial co-ordinates
$x_i,x_j$	=	center, boundary points of mesh
$\mathit{\alpha }$	=	mixture compressibility
$\mathit{\beta }$	=	correction factor to diffusivity
$\mathit{\delta }$	=	internal friction angle
$\mathit{\delta t}$	=	time step
$\mathit{\epsilon }$	=	aspect ratio of debris flow
$\mathit{\zeta }$	=	inclination angle of slope
$\mathit{\eta }$	=	normalized depth variable
$\mathit{\mu }$	=	viscosity of interstitial fluid
$\mathit{\xi }$	=	distance to the tail of surge
$\mathit{\rho }$	=	density of mixture
${\rho }_w$	=	density of water
$\mathit{\varphi }$	=	bed friction angle
${\phi }_0$	=	ratio of actual and theoretical excess pore fluid pressure
$\mathit{\psi }$	=	excess pressure
${\psi }_0$	=	initial excess pressure
${\psi }_b$	=	excess pressure at bed

Acknowledgments

The authors express their gratitude to the John Su Foundation for the financial support and extend their appreciation to the anonymous reviewers and the editor for their valuable comments.

Disclosure statement

No potential conflict of interest was reported by the author(s).