Geoscience Reference
In-Depth Information
Fluvial erosion at bank toes
The fluvial (particle-by-particle) erosion at bank toes directly influences channel bed
width and bank angle, and causes bank instability with respect to mass failure under
gravity. Arulanandan
et al
. (1980) proposed an empirical formula to compute the
fluvial erosion of cohesive bank material:
τ
−
τ
dw
dt
r
γ
ce
=
(5.170)
τ
s
ce
min
−
1
);
where
dw
/
dt
is the lateral erosion rate near the bank toe (m
·
τ
is the flow
cm
−
2
) applied on the bank toe, determined by
shear stress (dynes
·
τ
=
γ
RS
;
τ
ce
is
cm
−
2
) for bank toe erosion, related to water and soil
the critical shear stress (dynes
·
m
−
3
); and
r
is the initial rate of soil
properties;
γ
s
is the unit weight of the soil (kN
·
cm
−
2
min
−
1
), given by
r
erosion (g
.
The eroded bank material is treated as side inflow in sediment transport equations
(5.27), (5.28), and (5.34).
·
=
0.0223
τ
ce
exp
(
−
0.13
τ
)
ce
Bank mass failure
Depending on bank geometry, water table, surface runoff, seepage, vegetation, and
soil properties, channel banks may fail by various mechanisms, which may be planar
(e.g., Osman and Thorne, 1988; Simon
et al
., 2000), rotational (Osman, 1985), can-
tilever (Thorne and Tovey, 1981), or piping- or sapping-type (Hagerty, 1991). Planar
and rotational failures usually occur on the homogeneous, non-layered banks, whereas
cantilever failures usually happen on the layered banks. Piping- or sapping-type failures
most likely occur on the heterogeneous banks, where seepage flow is often observed.
A stability analysis of planar failures is introduced below, while those for other failure
types can be found in relevant references.
Osman and Thorne (1988) analyzed the planar failure shown in Fig. 5.17. It
is assumed that the failure plane intersects the bank toe. The factor of safety is
defined as
F
r
F
d
f
s
=
(5.171)
where
F
d
and
F
r
are the driving and resisting forces, respectively:
H
2
sin
y
d
−
H
2
tan
β
=
γ
s
2
F
d
=
W
t
sin
β
−
β
(5.172)
tan
α
H
2
cos
y
d
−
H
2
tan
=
(
H
−
y
d
)
C
+
γ
s
2
F
r
β
−
β
tan
φ
(5.173)
sin
β
tan
α
