Basal Stress Equations for Granular Debris Masses on Smooth or Discretized Slopes

Abstract

Knowledge of basal stresses is essential for analyzing slope stability and modeling the dynamics and erosive potential of debris flows and avalanches. Here we derive and test new algebraic formulas for calculating the shear stress τ and normal stress σ at the base of variable‐thickness granular debris masses in states of static or dynamic equilibrium on slopes. The formulas include a lateral pressure coefficient κ, but use of a fixed value κ = 0.7 yields predictions of σ that on average err by less than 3% and of τ that on average err by less than 13% in matching basal stresses measured in six large‐scale experiments involving wet debris masses with varying geometries and compositions. Much larger prediction errors result from use of infinite‐slope or shallow‐debris approximations. Specialized versions of the new formulas apply if basal topography is discretized and represented by a “staircase” function in a digital elevation model. Use of these formulas to assess static limiting equilibrium conditions shows that the apparent basal Coulomb friction angle ϕtread of debris that engages friction acting on the horizontal surfaces (or “treads”) of a staircase sloping at an angle θ is generally described by tanϕtread = tan (ϕ − θ)+κ tan θ, where ϕ is the true basal friction angle of the same debris in contact with a uniformly sloping bed. Differences between the values of ϕ and ϕtread can greatly influence the results of numerical simulations that use unsmoothed digital elevation model topography to calculate the stability or dynamics of debris masses on slopes.

Measuring Basal Force Fluctuations of Debris Flows Using Seismic Recordings and Empirical Green's Functions

“…The 10-m 3 sediment mass had a steeper surface slope (17°, compared to 9°), and a pond containing about 0.3 m 3 of water formed at the bluntly tapered upslope end of the debris. Iverson and George (2019) provide further details regarding these initial debris geometries, grain size distributions, and other debris physical properties. Journal of Geophysical Research: Earth Surface 3.1.1.…”

Impact Behavior of Dense Debris Flows Regulated by Pore‐Pressure Feedback

“…Depending on the state of the granular material, k s could be the coefficient of active earth pressure k a or the coefficient of passive earth pressure k p (Iverson & George, 2019). As λ deposit reaches unity, k H also approaches unity.…”

Landslide Disparities, Flume Discoveries, and Oso Despair

“…Other sets of debris flow flume experiments focused on a wide variety of topics, including debris flow motion through channel bends (Iverson et al, ), debris flow run‐up on vertical barriers and adverse slopes (Iverson et al, ), hydrologic triggering of landslides and debris flows (Reid et al, ), debris flow containment by flexible steel barriers (DeNatale et al, ), breaching of debris dams by rising water levels (Walder et al, ), basal stress states in static debris masses (Iverson & George, ), radiation of seismic energy by debris flows (Allstadt et al, ), and tsunami generation by debris flows entering bodies of water. Many additional topics await future experiments.…”