4.2 Difference in erosion characteristics as determined from
traditional and new model
The interpretation of erosion characteristics from traditional model
(Equation 1) was based on the relationship of erosion rate with
hydraulic stress, as depicted in Fig. 7 (a). Erosion coefficient and
critical shear stress can be inferred from the slope and horizontal
intercept of curve, respectively. In the current study, the\(\dot{\varepsilon}-\tau\) curves were also presented, as shown in
Fig. 7 (b). However, the temporal variation of the two curves is
reversed so that the physical definition of the horizontal intercept is
changed. Critical shear stress is the hydraulic shear stress when the
erosion happens initially (Wall and Fell 2004b). However, the horizontal
intercept in the current study is the hydraulic shear stress at the end
of experiment. Therefore, this quantity is newly defined as equilibrium
shear stress. Critical shear stress was proposed to formulate the
criteria of hydraulic earth construction to prevent erosion (Arulanandan
and Perry 1983). Similarly, equilibrium shear stress would be suggested
to the consideration of post-construction risk assessment. As indicated
in Table 3, the determination of equilibrium shear stress also showed
the stability of the measurement approach with a nearly constant value
of 0.08 Pa.
Even though erosion characteristics could be obtained from the\(\dot{\varepsilon}-\tau\) curves, some errors of the interpretation
from the curves happened due to the theoretical discretization of model
application. As described in Fig. 6, erosion coefficient could be
deduced from the continuous \(R^{4}-t\) curves. This approach is
recommended by the current study. Only after \(R(t)\) is known from
experiments, other quantifies can be calculated. The model of \(R(t)\)has no issue of discretization since the instantaneous data of \(R(t)\)is collected and analyzed. In contrast, the measurement of erosion rate
considering the average soil loss at a time interval results into the
deviation induced by discretization. Besides, equation [22] and Fig.
4 suggest that variation of erosion rate with time should follow the
concave function. Therefore, it implies that the instantaneous erosion
rate should be theoretically and slightly higher than the measured
erosion rate.
The comparison between the traditional and new model for obtaining
erosion characteristics was analyzed, as shown in Fig. 8. Traditionally,
erosion characteristics can be developed from the\(\dot{\varepsilon}-\tau\) curves based on equation [1]. The\(\dot{\varepsilon}-\tau\) curves plotted with measured data should be
fitted by linear relationships. However, some subtle fluctuations
appeared in curves due to the problem of
discretization.
With the interpretation from \(R^{4}-t\) curves, the theoretical\(\dot{\varepsilon}-\tau\) curves were predicted. Measured\(\dot{\varepsilon}-\tau\) curves generally coincided with the
prediction model. Table 4 summarized the outcomes of the two models. The
values of erosion coefficient provided from \(R^{4}-t\) model were
slightly higher than those developed from the\(\dot{\varepsilon}-\tau\) curves. However, the performance of fitting
of \(R^{4}-t\) model is better than the traditional model, as shown in
the comparison of the determination coefficient (R2).
Besides, the results from traditional model showed higher variance among
the HETs.
Comparison between predicted and measured erosion behavior (from Fig. 8)
can be generalized as shown in Fig. 9. Erosion process during HET can be
categorized into three phases, namely initial phase , normal
phase , and final phase . At the initial phase, the measurement is
lower than the idealization of the model because it needs some time to
initiate erosion with the existence of critical shear stress. The second
phase is expected as the erosion variation is almost close to the
theoretical model. At the final phase, the erosion coefficient is
strengthened, which results into the rapid failure of the soil body and
achieves the equilibrium of hydraulic shear stress and erosion
resistance of the soil. Fell et al. (2003) also categorized the erosion
process of infrastructure failure into four phases, includinginitiation , continuation , progression , andformation . These two distinction methods are similar and
complementary to each other. The initial phase and final phase share the
same definition with the first and fourth phases in the study of Fell et
al. (2003), respectively. The normal phase is parallel to the combined
phases of continuation and progression. The concept of three phases is
suitable for small-scale experiments, while the four-phase analysis is
used in large-scale tests. Both two models are necessary to understand
the erosion process from laboratory tests to field surveillance. Results
from both current experiments and previous studies suggested that the
erosion coefficient would slightly increase with elapsing time. This
weakness of erosion resistance is attributed by the reduction of Young’s
modulus and possible enhancement of permeability during the HETs (Parron
Vera et al. 2014; Jiang and Soga 2019). Progressive internal erosion
reduces the sliding resistance at interparticle contact, triggering
macroscopic deformations and even failure of the soil specimen (Hicher
2013). This explains the nonlinear relationships between applied shear
stress and the erosion rate in the study of (Khanal et al. 2016).
Therefore, it is significant to understand the stage of the erosion
variation to react the erosive responses.