 A
area of the force sensor (used for calculations for the experimental and simulated drums)
 A_{1}
area corresponding to a region of the bed of the drum that spans the width of drum and is 1° long (A_{1} = (π/180) × D/2 × W)
 d
particle size
 d_{sys}
systemwide massaveraged particle size

local massaveraged particle size
 d_{50}
median particle size, i.e., the particle size compared to which 50% of the particles in the grain size distribution (by mass) are smaller
 d_{84}
the particle size compared to which 84% of the particles in the grain size distribution (by mass) are smaller
 d_{eff}
effective (reduced) particle size with explicit consideration of d of two objects in contact
 d_{j}
diameter of the particle j
 D_{e}
representative particle size (e.g., of the front of a debris flows, as in Stock and Dietrich [2006])
 D
diameter of drum
 E
modulus of elasticity
 E_{eff}
effective modulus of elasticity with explicit consideration of E and ν of two objects in contact
 e
coefficient of restitution
 f
the frequency of occurrence of debris flows in a particular location as defined in Stock and Dietrich [2006]
 f_{j}
the j^{th} contact between particle and drum bed at one time step

local average contact force between particles and drum bed
 f_{σ}
local standard deviation of contact force between particles and drum bed
 f_{max}
local maximum contact force between particles and drum bed

the average contact force between particles and drum bed for the entire system
 f_{σ,sys}
the standard deviation of contact force between particles and drum bed for the entire system
 f_{max,sys}
the maximum contact force between particles and drum bed for the entire system
 f_{c,max}
the maximum contact force for a single contact between a particle and a boundary such as a drum bed as obtained from the computational simulations
 f_{c,max,cm}
the maximum contact force for a single contact between a particle and a boundary such as a drum bed as predicted from the contact model

theoretical value of (equation (10))
 F_{n}
magnitude of the contact force between two particles (or a particle and a wall) in the direction normal to the plane of contact (equation (4a))
 F_{t}
magnitude of the contact force between two particles (or a particle and a wall) in the direction tangential to the plane of contact (equation (4b))
 k_{n}
stiffness coefficient relevant to compressive deformation of two particles (or a particle and a wall) in contact
 k_{t}
stiffness coefficient relevant to oblique deformation of two particles (or a particle and a wall) in contact
 K_{0}
scaling of excursion stresses with average inertial stress associated with dense granular flows over a bed as defined in Stock and Dietrich [2006]
 K_{1}
the relationship of rock resistance to incision rate of bedrock material associated with dense granular flows over a bed as defined in Stock and Dietrich [2006]
 L
the length of the snout of a debris flow as defined in Stock and Dietrich [2006]
 m_{j}
mass of particle j
 M
total mass of granular material
 n
an empirically determined exponent used by Stock and Dietrich [2006] in their relationship between Bagnold's expression for collisional stress and the incision rate of bedrock due by dense granular flows
 N_{c}
number of contacts between particles and drum bed used in a particular calculation
 N_{p}
total number of particles considered in a particular calculation
 N_{τ}
total number of time steps used in a particular calculation
 N_{c,4}
number of contacts between particles and the bed over a 4.3° region
 p
normal stress or pressure at a boundary (such as the bed of a drum)
 p_{4}
normal stress or pressure at the bed considering contacts over a 4.3° region

temporally averaged normal stress or pressure at boundary

p_{4} locally averaged over a 1° region

dimensionless p_{4}

the standard deviation of p_{4} considering a 1° region

lithostatic pressure on the drum bed
 R
the resistance of bedock to erosion, a consolidation of several parameters contributing to this as detailed in Stock and Dietrich [2006]
 t_{c}
duration of a collision
 v_{i}
impact velocity (velocity of a particle at initial contact between particle and another object, such as the bed of a drum)
 w
an empirically determined exponent used by Stock and Dietrich [2006] in their relationship between shear rate and the incision rate of bedrock by dense granular flows
 W
width of drum
 α
constant of proportionality relating the timeaveraged particle–bed force during a particular particle–bed contact to the maximum force of that contact

shear rate
 Γ
frequency of force data output
 δ_{n}
overlap (deformation) relevant to the contact between two particles (or a particle and a wall) in the direction normal to the plane of contact (equation (4a))
 δ_{t}
overlap (deformation) relevant to the contact between two particles (or a particle and a wall) in the direction tangential to the plane of contact (equation (4a))
 δ_{n,max}
maximum overlap (deformation) between contacting particles (or a particle and a wall) in the normal direction as obtained from the computational simulations
 δ_{n,max,cm}
maximum overlap (deformation) between contacting particles (or a particle and a wall) in the normal direction as predicted from the contact model

rate change of δ_{n}: d δ_{n}/dt

rate change of δ_{t}: d δ_{t}/dt
 η_{n}
damping coefficient relevant to compressive deformation of two particles (or a particle and a wall) in contact
 η_{t}
damping coefficient relevant to oblique deformation of two particles (or a particle and a wall) in contact
 θ
angular location along the drum bed, measured counterclockwise from vertically downward (e.g., Figure 2a)
 θ_{i}
angular location of the ith particle–bed contact considered along the drum bed, measured counterclockwise from vertically downward (e.g., Figure 2a)
 θ_{j}
angular location of the jth particle–bed contact considered along the drum bed, measured counterclockwise from vertically downward (e.g., Figure 2a)
 θ_{s}
position of the center of the force sensor
 Θ
the angle over which the sensor extends along the bed of the drum
 λ
linear concentration as in Bagnold [1954]
 μ
coefficient of friction
 ν
Poisson's ratio
 ν_{s}
solids volume fraction
 ν_{s,max}
maximum solids volume fraction (0.74 for monosized spheres)
 ρ
density of the material comprising the particles
 σ_{Bag}
collisional stress as defined by Bagnold [1954]
 ϕ
angle of inclination of surface over which granular materials flow, e.g., as in equation (3)
 Ω
speed of rotation of drum