Environmental Engineering Reference
In-Depth Information
In the past decades much effort has been made to develop the constitutive equations and various
models have been proposed on the bases of the visoplastic and dilatant models, for the pseudo-one-phase
and two-phase debris flows (Julien and Lan, 1991; McTigue, 1982; Iverson and Denlinger, 1993, Shen
and Ackermann, 1982). The models were applied to study the velocity profiles of debris flows. The idea
to use a constitutive equation is to balance the shear stress created by the shear flow with the driving
shear created by gravity on the slope. Then a velocity distribution can be obtained if all the parameters
and the coefficients are known.
For pseudo-one-phase debris flow Johnson and Rohm (1970) and Yano and Daido (1965) postulated
that debris flow material behaves as a homogeneous viscoplastic continuum. Many scientists have applied
this model to study pseudo-one-phase debris flow (Chen, 1988; Shen and Ackermann, 1982). With the
constitutive equation of a viscoplastic fluid they explained the velocity profile with a plug of laminar
flow that is often observed in mudflows and viscous debris flows. The viscoplastic model can also interpret
the striking phenomenon of debris flow waves. Wang et al. (1990) and Wang (2001) experimentally and
theoretically studied the development of a viscoplastic fluid from continuous flow into intermittent
debris flow composed of a series of waves. They derived differential equations indicating that the yield
strength is the essential factor affecting the instability and development of the waves. Figure 4.32 shows
the stress-strain rate relation of the viscoplastic model and the dilatant model.
For two-phase debris flows Bagnold (1956) and Takahashi (1978, 1980, 1981) made the most prominent
early effort to construct a theory that accounts for particle interactions. The central feature of their theory
is the concept of grain flow dispersive stress, which was originally introduced by Bagnold (1954). The
theory postulates that the debris flow is a dilatant fluid but the shear stress is generated mainly by the
collision between the particles (Fig. 4.32). Scientists have applied this model to study two-phase debris
flows (Savage, 1984, Savage and McKeown, 1983). The theory provides the mechanism of supporting force
for the movement of gravel and stones, a velocity profile distinct from that of water flow, and high
resistance of debris flow, and seems to provide an explanation for the segregation of large and small particles
that lead to the debris flow head consisting of large stones and to inverse grading in debris flow deposits.
Fig. 4.32 The stress-strain rate relation of the viscoplastic model and the dilatant model for debris flows
Shortcomings exist in both the viscoplastic and dilatant models. The viscoplastic model does not work
well for the resistance of pseudo-one-phase debris flow. The model predicts the debris flow velocity to be
much lower than the flow of water because the viscosity and the yield shear stress of the debris mixture
is much greater than water. In fact, the velocity of pseudo-one-phase debris flows in the Jiangjia Ravine,
Yunnan Plateau of China, is sometimes even higher than the flow of water. The debris flow is composed
of high concentrations of fine material and the flow appears to be laminar, which means that the
resistance can be represented by the viscosity if it is really a kind of viscoplastic fluid. On the contrary,
drag reduction occurs in pseudo-one-phase debris flows and the rate of drag reduction is as high as 60%
(Wang et al., 2001). In other words, pseudo-one-phase debris flows move at 2 times higher velocities
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