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Numerical analysis of submarine debris flow based on critical state soil mechanics

Kobayashi, T., Soga, K., & Dimmock, P. (2015). Numerical analysis of submarine debris flows based on critical state soil mechanics. In _Frontiers in Offshore Geotechnics III: Proceedings of the 3rd International Symposium on Frontiers in Offshore Geotechnics (ISFOG 2015) (Vol. 1, pp. 975-980). Taylor & Francis Books Ltd.

Paper

Keywords: #submarine #water-entrainment #bingham #cam-clay

Research questions

  • Why do submarine slides flow longer than subaerial despite the resistance due to surrounding water?

One hypothesis is the entrainment of water at the flow front resulting in a decrease in strength. The reduction of shear strength can explain the long run-out.

  • How do fine-grained sediments (clay-rich materials) affect the run-out?

  • Phase transition from solid to semifluid occurs due to shearing, mixing, and water entrainment beneath the flowing material - has this been proven?

Several assumptions have been made on how water entrainment influences the run-out and decrease in strength. More research is needed.

  • How do the mechanical properties of the sediments change at the sliding plane?

  • What is the proportion of water entrainment at the bottom vs. the rest of the sediments?

Future research / unanswered questions

  • How can the critical state be modified to accommodate higher water contents?

Can we use similarities with liquefaction to study this behavior?

  • Does the mechanical properties vary with the duration and the flow?

  • What range of liquidity index should be considered?

  • The assumptions of how water entrainment (occurs after reaching CSL, follows the path of CSL) affects the run-out behavior is not established.

  • What is the occurrence and magnitude of water entrainment in real debris flows?

  • How does the volume of sediment expand with run-out due to water entrainment? What is the impact of the specific volume on this behavior?

  • Can we relate the distance traveled with the amount of water entrainment, or is there a critical threshold?

  • Shear strength and viscosity change with water entrainment and run-out. What is the relationship?

Main findings

  • Non-newtonian fluid models do not accommodate for the transition in material properties by assuming constant rheological parameters throughout the flow.
  • Rheological flow models approximate the regime changes (solid to fluid-like) over the spatial and temporal domains and do not capture the real mechanics.
  • The undrained strength from critical state soil mechanics is found to change with liquidity index ($I_L$) as $S_u = 1.7 \times 100^{(1- I_L)}$
  • The original critical state assumption does not deal with high water content (where the water content is larger than the liquid limit).
  • A new power-law relationship is proposed between the liquidity index and undrained strength: $S_u = 1.07 I_L^{-0.258}$
  • Locat (1997) defined the Bingham viscosity as: $\mu = \left(\frac{9.27}{I_L}\right)^{3.3}$
  • Because of the proposed powerlaw relationship for critical state line, the algorithm of specific volume rather than the specific volume is used, as proposed by (Butterfield., 1979).
  • The modified Cam-Clay Bingham shear strength is proposed as $$ \tau = \tau_{cam}(I_L, \varepsilon_v^p, \varepsilon_d^p) + \mu(I_L)\dot{\gamma}$$ where $\tau$ is the shear strength, $\varepsilon_v^p$, and $\varepsilon_d^p$ are the plastic volume and deviatoric strains, $\mu$ is the viscosity, and $I_L$ is the liquidity index. The first term represents the shear resistance of the sediment and becomes less dominant on large shear strains. The second term represents the strain-rate-dependent resistance due to viscosity.
  • If the two terms $\tau_{cam}$ and $\mu(I_L)$ are constant, then the conventional Bingham fluid model is recovered.
  • Sensitivity of clay is considered by including a hardening parameter $p_d$ to the modified cam clay yield surface. Including sensitivity allows to model the measured peak strength and softening behavior.
  • To model the phase transition behavior due to water entrainment, the following assumptions are made:
    • water entrainment occurs after soil reaches the critical state
    • volume expansion happens along the critical state line
    • mean stress $p^\prime$ and $q$ decreases along CSL
  • The occurrence and magnitude of water entrainment in real debris flows are not well understood.
  • Instead, (2004) observed water entrainment mainly occurring at the bottom of the flow front.
  • Effect of water entrainment (strength reduction) is modeled as a function of the distance traveled by the material points.
    • The rate of volume expansion ($R_v$) against the travel distance and the maximum specific volume $V_{max}$ control the effect of water entrainment, but the factors and their relationships are unknown.
  • Numerical simulations matching the run-out observed showed the material parameters to be ($\mu$ of 600 pa.s and $\tau_y$ of 150 kPa) based on trial and error to match the run-out. Rheological measurements showed ($\mu$ of 1.5 pa.s and $\tau_y$ of 461 kPa at $I_L=1.16$).
    • There is an order of magnitude difference in viscosity
    • The equivalent fluid approximation using constant parameters does not capture the run-out response accurately.

Relation between $I_L$ and Su

Relation between $I_L$ and Su

Modeling of phase transition due to water entrainment

Modeling of phase transition due to water entrainment