Soil Creep and Convex Upward Velocity Profiles

The movement of unconsolidated materials near the Earth’s surface is often driven by disturbances that occur at a range of spatial and temporal scales. The nature of these disturbances ranges from highly variable, such as tree turnover, to periodic and predictable, such as frost heave or creep. To explore the effect of probabilistic disturbances on surface processes, we formulated a granular creep model with analogy to rate process theory (RPT) used for chemical reactions. According to the theory, individual particles must be energized to a height greater than adjacent particles in order for grain dilation and transport to occur. The height of neighbouring particles (which is akin to activation energy in chemical reactions) varies with slope angle such that energy barriers get smaller in the downslope direction as slopes steepen. When slopes approach the friction-limited angle of repose, the height of energy barriers approaches zero and grains flow in the absence of disturbance. An exponential function is used to describe the probability distribution of particle excitation height although alternative distributions are possible. We tested model predictions of granular dynamics in an experimental sandpile. In the sandpile, acoustic energy serves as the disturbance agent such that grains dilate and shear in response. Particle velocities are controlled by the frequency of energy pulses that result in grain displacement. Using tracer particles, we observed a convex-upward velocity profile near the surface of the sandpile, consistent with predictions of our RPT-based velocity model. In addition, we depth-integrated the velocity model to predict how flux rates vary with inclination of the sandpile and observed non-linear flux–gradient curves consistent with model predictions. By varying the acoustic energy level in the experimental sandpile, we documented changes in the rate of grain movement; similar changes in modelled velocities were achieved by varying the exponent of the particle excitation probability distribution. The general agreement between observed and modelled granular behaviour in our simple laboratory sandpile supports the utility of RPT-based methods for modelling transport processes (e.g. soil creep, frost heave, and till deformation), thus enabling us to account for the probabilistic nature of disturbances that liberate sediment in natural landscapes. Copyright © 2004 John Wiley & Sons, Ltd.