4.1 Determination of erosion characteristics based on newly
developed model
As illustrated in Fig. 2(b), the soil specimens were eroded
approximately axisymmetric during a HET. Although irregular eroded hole
in the HETs was observed in the previous studies (Benaissa et al. 2012;
Říha and Jandora 2015; Lachouette et al. 2008; Xie et al. 2018), it was
still reasonable to utilize a linear erosion law and homogeneity
assumption to predict erosion enlargement (Benaissa et al. 2012). Hence,
the results were presumptively reasonable to conduct further analyses.
Figure. 3 presented the observed erosion rate and extended radius in the
erosion hole under six flow rates. The soil sample was subjected to
erosion with a fixed flow rate. It is expected that erosion rate
achieved is highest in the beginning. Erosion rate decreased gradually
with time during the tests. The radius of the soil hole was continually
increased until erosion rate became negligible. The results showed that
eroded hole enlargement was nonlinear with time, which is in agreement
with the previous studies of Sterpi (2003), Cividini and Gioda (2004),
Wilson (2009), and Jiang and Soga (2019). The developed equation
[21] was applied for explanation of the temporal variation of
erosion in the tests. The data of radius was successfully fitted by
equation [21]. In general, the fitted equation indicated that\(R(t)\) did follow the function of time, with an exponent of 0.25. As
explained in equation [14], erosion rate could be reviewed to obey
the first derivative equation of \(R(t)\). Thus, equation [33] was
used to fit the data of erosion rate over time. Although both equations
are describing the same erosion process, it should be noted that the
goodness-of-fit of equation [21] is higher than equation [33].
As indicated in Fig. 4, proposed equations (equation [21] and
[36]) fitted considerably with the temporal variation of erosion.
Eroded depth was found to reduce with time. It can be also visualized
that rate of change of hole size (as indicated in Fig. 2(b)) gradually
becomes negligible at the end of test. It was found from Fig. 4 that
eroded depth and cumulative soil loss increased with flow rate. Based on
the corresponding deformation of the soil pipe, the mechanical
characteristics (i.e. hydraulic shear stress and water pressure) were
obtained and interpreted in the soil pipe, as documented in Fig. 5. The
variation of hydraulic shear stress and pressure drop showed a similar
trend with erosion rate over time. The decline of hydraulic shear stress
led to the decrease of erosion rate and eroded depth as also observed
from erosion law (Wall and Fell 2004). As observed from equation
[12], hydraulic shear stress decreased with an enlargement of hole
over time. A higher flow rate resulted into higher hydraulic shear
stress and pressure drop. Interestingly, at the latter half of tests,
hydraulic shear stresses of different flow rates became constant, which
is defined as equilibrium shear stress in the current study. The
equilibrium shear stress (\(\tau_{e}\)) will be further discussed in the
next section. The recorded profile of pressure drop is consistent with
that of Benahmed and Bonelli (2012). The pressure drop was balanced in
the final phase of the experiment, which was referred as the
semi-equilibrium condition in the study of Wilson (2009). This result
supports the opinion that the generated pore water pressure from a high
hydraulic gradient would be dissipated attributed to the enlargement of
the soil pipe (Hicher 2013; Ouyang and Takahashi 2016). Hydraulic
non-equilibrium within soil pipes would be exhausted by soil erosion and
the hydraulic potential energy would be diminished during the process of
sediment detachment and transport (Wilson et al. 2009; Sang et al. 2015;
Nguyen and Indraratna 2020).
To interpret erosion characteristics, the \(R^{4}-t\) curves were
plotted based on equation [32]. As indicated in Fig. 6 (a),
proportional relationship between \(R^{4}\) and time was found in each
experiment for different flow rates. Table 2 summarized the
interpretation of erosion characteristics. Equation [32] was used to
fit the data of HET. The slopes of the best-fit lines reflected the
values of \(\lambda\). Equation [25] was used to determine erosion
coefficient based on the results from equation [32]. Fig. 6 (b)
proves that \(\lambda^{4}\) is proportional to flow rate for a given
soil as indicated in Equation [25]. This theoretically suggests that
the erosion coefficient is likely to remain constant under different
experimental conditions (Indraratna et al. 2008).