Introduction
Debris flow is rapid, gravity-induced mass movement consisting of a mixture
of water, sediment, wood and anthropogenic debris that propagate along
channels incised on mountain slopes and onto debris fans (Gregoretti et al.,
2016). It has been reported in over 70 countries and often
causes severe economic losses and human casualties, seriously retarding
social and economic development (Imaizumi et al., 2006; Tecca and Genevois,
2009; Dahal et al., 2009; Liu et al., 2010; Cui et al., 2011; McCoy et al.,
2012; Degetto et al., 2015; Tiranti and Deangeli, 2015; Hu et al., 2016).
Rainfall is one of the main triggering factors of debris flows and is the
most active factor when debris flows occur, which also determines the
temporal and spatial distribution characteristics of the hazards. As one of
the important and effective means of non-engineering disaster mitigation,
much attention has been paid to debris flow early warning by researchers
(Pan et al., 2013; Guo et al., 2013; Zhou and Tang, 2014; Wei et al., 2017).
For rainstorm-triggered debris flows, the precipitation and intensity of
rainfall are the decisive factors of debris flow initiation, and a
reasonable rainfall threshold target is essential to ensure the accuracy of
debris flow early warning. However, if an extreme event
occurs, such as an earthquake, the rainfall threshold of debris flow may
change a lot. Tang et al. (2012a) analyzed the critical rainfall of Beichuan
city and found that the cumulative rainfall triggering debris flow decreased
by 14.8–22.1 % when compared with the pre-earthquake period, and the
critical hour rainfall decreased by 25.4–31.6 %. Chen et al. (2013) analyzed the pre- and post-earthquake critical rainfall for debris
flow in Xiaogangjian gully and found that the critical rainfall for debris
flow in 2011 was approximately 23 % lower than the value during the
pre-earthquake period. Other researchers, such as Chen (2008), Chen et al. (2009) and
Shied et al. (2009), have reached the conclusion that the post-earthquake
critical rainfall for debris flow is markedly lower than that of the
pre-earthquake period. The Guojuanyan gully, a small gully located in the
meizoseismal areas of a big earthquake, had no debris flows under the
annual average rainfall before 2008, but it became a debris flow gully after
the earthquake under the same conditions, even though the rainfall was smaller than
the annual average rainfall. This indicated that earthquakes have a big
influence on debris flow occurrence. The earthquake triggered many unstable
slopes, collapses and landslides that have served as the source material
for debris flow and shallow landslides in the years after the earthquake
(Tang et al., 2009, 2012b; Xu et al., 2012; Hu et al., 2016). Therefore, the
rainfall threshold of debris flow post-earthquake is an important and urgent
issue to study for debris flow early warning and mitigation.
As an important and effective means of disaster mitigation, debris flow
early warning has received much attention from researchers. The rainfall
threshold is the core of debris flow early warning, on which there is already a great deal of research (Cannon et al., 2008; Chen and Huang, 2010; Baum
and Godt, 2010; Staley et al., 2013; Winter et al., 2010; Zhou and Tang,
2014; Segoni et al., 2015; Rosi et al., 2015). Although the formation
mechanism of debris flow has been extensively studied, it is difficult to
perform distributed physically based modeling over large areas, mainly
because the spatial variability of geotechnical parameters is very difficult
to assess (Tofani et al., 2017). Therefore, many researchers (Wilson and
Joyko, 1997; Campbell, 1975; Cheng et al., 1998) have had to determine the
empirical relationship between rainfall and debris flow events and to
determine the rainfall threshold depending on the combinations of rainfall
parameters, such as antecedent rainfall, rainfall intensity and cumulative
rainfall. Takahashi (1978), Iverson and Lahusen (1989) and Cui (1991) predicted
the formation of debris flow based on studies of slope stability,
hydrodynamic action and the influence of pore water pressure on the
formation process of debris flow. Caine (1980) first statistically analyzed
the empirical relationship between rainfall intensity and the duration of
debris flows and shallow landslides and proposed an exponential
expression (I=14.82D-0.39). Afterwards, other researchers, such as
Wieczorek (1987), Jibson (1989), Hong et al. (2005), Dahal et al. (2009),
Guzzetti et al. (2008) and Saito et al. (2010), carried out further
research on the empirical relationship between rainfall intensity and the
duration of debris flows, established the empirical expression of rainfall
intensity–duration (I–D) and proposed debris flow prediction models.
Although I–D is the most used approach, other rainfall parameters have been
considered as well for debris flow thresholds. Shied and Chen (1995)
established the critical condition of debris flow based on the relationship
between cumulative rainfall and rainfall intensity. Zhang et al. (2014) developed a
model for debris flow forecasting based on the water–soil coupling mechanism
at the watershed scale. In addition, some researchers have highlighted the
importance of finding more robust hydrological bases to empirical rainfall
thresholds for landslide initiation (Bogaard and Greco, 2018; Canli et al., 2017;
Segoni et al., 2018). When data are scarce, a robust validation of a
threshold model can be based on a quantitative comparison with alternate
versions of the threshold (Althuwaynee et al., 2015) or with thresholds
calculated with completely different approaches (Frattini et al., 2009;
Lagomarsino et al., 2015). Wei et al. (2017) investigated a rainfall
threshold method for predicting the initiation of channelized debris flows
in a small catchment, using field measurements of rainfall and runoff data.
The location of the Guojuanyan gully.
![]()
The strata profile of the Guojuanyan gully (Jun Wang et al., 2017).
![]()
Overall, the studies on the rainfall threshold of debris flow can be
separated into two methods: the demonstration method and the frequency
calculated method. The demonstration method employs statistical analysis of
rainfall and debris flow data to study the relationship between rainfall and
debris flow events and to obtain the rainfall threshold curve (Bai et al.,
2008; Tian et al., 2008; Zhuang et al., 2009). The I–D approaches would be
this kind of method. This method is relatively accurate, but it needs a long-term rainfall database and disaster information; therefore, it
can be applied only to areas with a history of long-term observations. The
frequency calculated method, assuming that debris flow and torrential rain
have the same frequency and, thus, debris flow rainfall threshold, can be
calculated based on the rainstorm frequency in mountain towns that have
abundant rainfall data but a lack of disaster data (Yao, 1988; Liang and Yao,
2008). Researchers have also analyzed the relationship between debris flow
occurrences and precipitation and soil moisture content based on initial
debris flow conditions (Hu and Wang, 2003). However, this approach is rarely
applied to the determination of debris flow rainfall thresholds because it
needs series of rainfall data. Pan et al. (2013) calculated the threshold
rainfall for debris flow pre-warning by calculating the critical depth of
debris flow initiation combined with the amount and regulating factors of
runoff generation.
Most mountainous areas have little data regarding rainfall and hazards,
especially in Western China. Neither the traditional demonstration method
nor the frequency calculated method can satisfy the debris flow early warning
requirements in these areas. Therefore, how to calculate the rainfall
threshold in these data-poor areas has become one of the most important
challenges for the debris flow early warning systems. To solve this problem,
this paper developed a quantitative method of calculating rainfall threshold
for debris flow early warning in areas with scarcity of data based on the
initiation mechanism of hydraulic-driven debris flows.
Study site
Location and gully characteristics of the study area
The Guojuanyan gully in Dujiangyan city, located in the meizoseismal areas
of the Wenchuan earthquake, China, was selected as the study area (Fig. 1).
It is located at the Baisha River, which is the first tributary of the
Min River. The seismic intensity of the study area was XI, which was
the maximum seismic intensity of the Wenchuan earthquake. The Shenxi Gully
Earthquake Site Park is on the right side of this gully. The area extends
from 31∘05′27′′ to 31∘05′46′′ N
latitude and 103∘36′58′′ to 103∘37′09′′ E longitude, covering an area of 0.15 km2 with a population of
20 inhabitants. The elevation range is from 943 to 1222 m, the average
gradient of the main channel is 270 ‰ (the average slope
angle is 15.1∘), and the length of the main channel is
approximately 580 m.
Geologically, the Guojuanyan gully is composed of bedrock and Quaternary
strata. The bedrock is upper Triassic Xujiahe petrofabric (T3x), the
lithology of which is mainly sandstone, mudstone, carbonaceous shale belonging to
massive layered structures, and semi-solid petrofabric. The Quaternary
strata are alluvium Q4el+pl, alluvial materials
Q4mathrmpl+dl, landslide accumulations and debris flow deposits
Q4sef+del. The thickness of the Quaternary strata ranges from 1 to 20 m and varies greatly.
The strata profile of the Guojuanyan gully is shown in Fig. 2.
Geographically, the study area belongs to the Longmen Mountains. The
famous Longmenshan tectonic belt has a significant effect on this region,
especially the Hongkou–Yingxiu fault. The study area has strong tectonic
movement and strong erosion, and the main channel is “V” shaped. The area
is characterized by a rugged topography, and the main slope gradient
interval of the gully is 20 to 40∘, accounting for
52.38 % of the entire study area.
Climatically, this area has a subtropical and humid climate, with an average
annual temperature of 15.2 ∘C and an average annual rainfall of
1200 mm (Wang et al., 2014).
Materials and debris flow characteristics of the study area
The Wenchuan earthquake generated a landslide in the Guojuanyan gully,
leading to an abundance of loose deposits that have served as the source
materials for debris flows. A comparison of the Guojuanyan gully before and
after the Wenchuan earthquake is shown in Fig. 3. According to the field
investigation and field tests, the 3-D landslide characteristics induced by
the earthquake and the infiltration characteristics of the loose materials
are shown in Tables 1 and 2 (Wang et al., 2016). They indicate that the
volume of materials is more than 20 × 104 m3, and the
infiltration capability of the earth surface has increased significantly. Therefore,
the triggering rainfall for debris flow decreased greatly. The Guojuanyan
gully had no debris flows before the earthquake because of the lack of loose
solid materials; however, it became a debris flow
gully after the earthquake, and debris flows occurred in the following years
(Table 3). The specific conditions of these debris flow events were
collected through field investigations and interviews. The field
investigations and experiments determined that the density of the debris
flow was between 1.8 and 2.1 g cm-3. Unfortunately, there were no
rainfall data before 2011, when we started field surveys in the Guojuanyan
gully.
The Guojuanyan gully
before (a) and after (b) the Wenchuan earthquake (from Google Earth).
![]()
The landslide 3-D characteristics induced by the earthquake in the
study area.
Average length
Average width
Average height
Average depth
Slope
Volume
(m)
(m)
(m)
(m)
(∘)
(× 104 m3)
160
80
180
15
30
20
The infiltration characteristics of solid materials in the study
area.
Infiltration curve
Infiltration rate
Initial infiltration
Stable infiltration
(cm min-1)
(cm min-1)
f= 0.6529 × exp(-0.057×t)
3.52
0.34
The specific conditions of debris flow events in the Guojuanyan
gully after the earthquake.
Time
Volume
Surge
Rainfall data
(104 m3)
record
24 September 2008
0.6
1
No
17 July 2009
0.8
1
No
13 August 2010
4.0
3
No
17 August 2010
0.4
1
No
1 July 2011
0.8
1
Yes
17 August 2012
0.7
1
Yes
9 July 2013
0.4
1
Yes
26 July 2013
2.0
2
Yes
18 July 2014
1.5
1
Yes
Debris flow monitoring and stream bed survey of the study area
After the Wenchuan earthquake, continuous field surveillance was undertaken
in the study area. A debris flow monitoring system was also established in
the study area. To identify the debris flow events, this monitoring system
recorded stream water depth, precipitation and real-time video of the gully
(Fig. 4). The water depth was measured using an ultrasonic level meter, and
precipitation was recorded by a self-registering rain gauge. The real-time
video was recorded onto a data logger and transmitted to the monitoring
center, located in the Institute of Mountain Hazards and Environment,
Chinese Academy of Sciences. When a rainstorm or a debris flow event occurs,
the real-time data, including rainfall data, video record and water depth
data, can be observed and queried directly in the remote client computer in
the monitoring center. Figure 5 shows images taken from the recorded video.
These data can be used to analyze the rainfall or other characteristics,
such as the 10 min, 1 and 24 h critical rainfall. The recorded video is
usually used to analyze the whole inundated process of debris flow events
and to identify debris flow events as well as the data from rainfall, flow
depth and field investigation.
Debris flow monitoring system in the study area.
![]()
Real-time images from video taken during the debris flow movement.
![]()
Data collection and the characteristics of rainfall
The Wenchuan earthquake occurred in the Longmenshan tectonic belt, located
on the eastern edge of the Tibetan plateau, China, which is one of three
rainstorm areas of Sichuan Province (Longmen Mountains rainstorm area, Qingyi
River rainstorm area and Daba Mountains rainstorm area). Heavy rainstorms and
extreme rainfall events occur frequently. Because there were few data in the
mountainous areas, we collected the rainfall data from 1971 to 2000 and from 2011 to 2012
(from our own on-site monitoring); the characteristics of the rainfalls are
as follows:
The average monthly precipitation of the Guojuanyan gully from
1971 to 2000 and the monthly rainfall of 2011 and 2012.
![]()
Abundant precipitation. The average annual precipitation was 1177.3 mm
from 1971 to 2000, and the average monthly precipitation is shown in Fig. 6.
From 1971 to 2000, the minimum annual precipitation of 713.5 mm occurred in
1974, and the maximum annual precipitation of 1605.4 mm occurred in 1978.
The total precipitation in 2012 is 1148 mm, in the trend range of the
historical data.
Seasonality of the distribution of precipitation. From Fig. 6 we can
observe that rainfall is seasonal, with approximately 80 % of the total
rainfall occurring during the monsoon season (from June to September) and
the other 20 % in other seasons. The laws of monthly rainfall in 2011
and 2012 coincide with the historical data. For instance, in 2012, the total
annual rainfall in this area was approximately 1148 mm, and rainfall in the
monsoon season from June to September was 961 mm, accounting for 83.7 % of
the annual total.
Great differences in rainfall intensity. From 1971 to 2000, the
maximum monthly rainfall was 592.9 mm, the daily maximum rainfall was 233.8 mm, the hourly maximum rainfall was 83.9 mm, the 10 min maximum rainfall
was 28.3 mm and the longest continuous rainfall time was 28 days.
Debris flow field monitoring data and on-site investigation data were used
to identify the debris flow events and to analyze the characteristics of the
rainfall pattern and the critical rainfall characteristics. Analyzing the
typical rainfall process curves (Fig. 13), we find that the hourly
rainfall pattern of the Guojuanyan gully is the peak pattern, displaying
the single peak and multiple peaks, a characteristic of short-duration
rainstorms. Through the statistical analysis of the 10 min, 1 and 24 h
critical rainfall of debris flow events after the earthquake, their
characteristics can be obtained, as shown in Fig. 7.
The critical rainfall of debris flows in the Guojuanyan gully.
![]()
According to the Sichuan Hydrology Record Handbook (Sichuan Water and Power
Department 1984), during 1940–1975, the annual average of maximum 10 min
rainfall of the study area is approximately 15.1 mm, the maximum 1 h
rainfall is 45.0 mm and the annual average of maximum 24 h rainfall is 132 mm. Figure 7 shows that the majority of the debris flow events in 2011–2014
occurred in a rainfall below the annual average values. This can be a
consequence of the Wenchuan earthquake, which explicitly lowered the triggering
rainfall threshold in the test site.
Materials and methods
This study makes an attempt to analyze the trigger rainfall threshold for
debris flow by using the initiation mechanism of debris flow, firstly to
analyze the rainfall characteristics of the watershed by using the field
monitoring data and then to calculate the runoff yield and concentration
progress based on field observation. Additionally, the critical runoff depth
to initiate debris flow was calculated by the initiation mechanism with the
underlying surface condition (materials, longitudinal slope, etc.) of the
gully. Then, the corresponding rainfall for the initiation of debris was
back-calculated based on the stored-full runoff generation. At last, these
factors were combined to build the rainfall threshold model. This method can
be applied to the early warning system in the areas with scarcity of
rainfall data.
The flow chart of the research.
![]()
The flow chart of the research is shown in Fig. 8.
The main influence factors for the formation of debris flow event include
three parts: a steep slope of the gully (served as potential energy
condition), abundant solid materials (source condition) and water source
condition (usually is rainfall condition for rainstorm debris flow). For
rainstorm debris flow events, the precipitation and intensity of rainfall
are the decisive factors of debris flow initiation. If there are no
earthquakes or other extreme events, the topography of the gully can be
considered relatively stable. In contrast, rainfall conditions and the
distribution of solid materials that determine the occurrence of debris
flows can display temporal and spatial variation within the same watershed.
Therefore, it is common to provide warning of debris flows based on rainfall
data after assessing the supply and distribution of loose solid materials.
In Takahashi's model, the characteristics of soil, such as the porosity and
the hydraulic conductivity of soils, are not considered, and the
characteristic particle size and the volume concentration of sediment are considered, while
the characteristics of topography are mainly represented by the longitudinal
slope of the gully. Furthermore, in the stored-full runoff model, the
maximum storage capacity of watershed, which is mainly decided by the porosity
and permeability of the soil, may represent the characteristic of the
hydraulic conductivity of solid material to a certain extent. Therefore,
this study does not consider the hydraulic conductivity.
Rainfall pattern and the spatial–temporal distribution
characteristics
Mountain hazards such as debris flows are closely related to rainfall
duration, rainfall amount and rainfall pattern (Liu et al., 2009). Rainfall
patterns affect not only the formation of surface runoff but also
the formation and development of debris flows. Different rainfall patterns
result in different soil water contents; thus, the internal structure of the
soil, stress conditions, shear resistance, slip resistance and removable
thickness can vary. The initiation of a debris flow is the result of both
short-duration heavy rains and the antecedent rainfall (Cui et al., 2007;
Guo et al., 2013). Many previous observational data sets have shown that the
initiation of a debris flow often appears at a certain time that has a high
correlation with the rainfall pattern (Rianna et al., 2014; Mohamadi and Kavian, 2015).
The precipitation characteristics affect not only the formation of runoff but
also the formation and development of the debris flow. Different
rainfalls result in different soil water contents, and thus the internal
structure of the soil, stress conditions, corrosion resistance and slip
resistance can vary (Pan et al., 2013). Based on the rainfall
characteristics, rainfall patterns can be roughly divided into two kinds,
the flat pattern and the peak pattern, as shown in Fig. 9. If the rainfall
intensity has little variation, there is no obvious peak in the whole
rainfall process; such rainfall can be described as flat pattern rainfall.
If the soils are characterized by low hydraulic conductivity, this kind of
rainfall cannot trigger a debris flow separately; they
will mainly be triggered by the great amount of effective antecedent
precipitation. When the rainfall intensity increases suddenly during a
certain period of time, the rainfall process will have an obvious peak and
is termed peak pattern rainfall. If the hydraulic conductivity is high
enough, the rainfall can infiltrate the soil completely and mass can move easily.
These debris flows are mainly controlled by the short-duration heavy rains.
Peak pattern rainfall may have one or more peaks (Pan et al., 2013).
The diagram of rainfall patterns.
![]()
Through analyzing the rainfall data of the Guojuanyan gully, the rainfall
pattern and the spatial–temporal distribution characteristics can be
obtained.
The calculation of the antecedent precipitation index (API)
The rainfall factor influencing debris flows consists of three parts:
indirect antecedent precipitation (IAP) (Pa0 in this paper),
direct antecedent precipitation (DAP) (Rt in this paper) and
triggering precipitation (TP) (I60 in this paper). The
relationships among them are shown in Fig. 10. Obviously, IAP increases
soil moisture and decreases the soil stability, and DAP saturates soils and
thus decreases the critical condition of debris flow occurrence. Although TP
is believed to initiate debris flows directly, its contribution amounts to
only 37 % of total water (Cui et al., 2007). Guo et al. (2013) analyzed the
rainstorms and debris flow events during June and September in 2006 and
2008: there were 208 days with antecedent rainfall more than 10 mm,
approximately 57 % days of the rain season. Among them, there were 66 days
with antecedent rainfall between 10 and 15 mm, with 1 debris flow event;
53 days between 15 and 20 mm, with 4 debris flow events; 28 days between
20 and 25 mm, with 4 debris flow events; 30 days between 25 and 33 mm, with 5
debris flow; and 35 days more than 33 mm, with 9 debris flow events. So this group of data can specifically illustrate the importance
of the antecedent rainfall to the debris flow events.
Rainfall index classifications.
![]()
As in Fig. 10, take 1 h rainfall (I60), obtained from the
observed data of the Guojuanyan gully, as the TP. The API includes IAP and DAP, calculated as the
following expression (Zhao et al., 2011; Guo, 2013; Zhuang et al., 2015):
API=Pa0+Rt,
where Pa0 is the effective antecedent precipitation (mm) and Rt is
the direct antecedent precipitation (mm), which is the precipitation from
the beginning of the rainfall that triggers debris flow to the 1 h before
the debris flow.
It is difficult to study the influence of antecedent rainfall to debris flow
as it mainly relies on the heterogeneity of soils (strength and permeability
properties), which makes it hard to measure the moisture. Usually, the
frequently used method for calculating antecedent daily rainfall is the
weighted sum equation as below (Crozier and Eyles, 1980; Glade et al., 2000):
Pa0=∑1nPi⋅Ki,
where Pi is the daily precipitation on the ith day preceding the
debris flow event (1≤i≤n) and Ki is a decay coefficient due to
evaporation and geomorphological conditions of the soil. The value of the
K is typically 0.8–0.9 and can be determined by the test of soil moisture
content based on Eq. (2) in the watershed. The effect of a rainfall event
usually diminishes with the time going forward. Different patterns of storm
debris flow gullies require different numbers of previous indirect rainfall
days (n), which can be determined by the relationship between the triggering
rainfall and the antecedent rainfall of a debris flow (Pan et al., 2013).
If the rainfall is sharp and heavy, the initiation of debris flow would
mainly be determined by DAP and TP, while the influence of the antecedent
precipitation would be decreased, and vice versa.
The rainfall threshold curve of debris flows
The initiation mechanism of hydraulic-driven debris flows
When the watershed hydrodynamics, which include the runoff, soil moisture
content and the discharge, reach a certain level, the loose deposits in
the channel bed will initiate movement and the sediment concentration of the
flow will increase, leading the sediment-laden flow to transform into a
debris flow. The formation of this kind of debris flow is a completely
hydrodynamic process. Therefore, it can be regarded as the initiation
problem of debris flow under hydrodynamic force. The forming process of
hydraulic-driven debris flows is shown in Fig. 11.
The typical debris flow initiate model.
![]()
According to Takahashi's model, the critical depth for hydraulic-driven
debris flows is
h0=C∗(σ-ρ)tanϕρtanθ-C∗(σ-ρ)ρ-1dm,
where C∗ is the volume concentration obtained by
experiments (0.812); σ is the unit weight of loose deposits (usually
2.65 g cm-3); ρ is the unit weight of water (1.0 g cm-3); θ is the channel bed slope (∘); ϕ is the internal friction
angle (∘) and can be measured by shear tests; and dm is the
average grain diameter (mm), which can be expressed as
dm=d16+d50+d843,
where d16, d50 and d84 are characteristic particle sizes of
the loose deposits (mm), whose weight percentages are 16, 50 and
84 %, respectively.
Takahashi's model has become one of the most common for the initiation of debris
flow. A great deal of related studies were published
based on Takahashi's model. Some discussed the laws of debris flow
according to the geomorphology and the water content (Sassa et al., 2010;
Wang et al., 2016), while others examined the critical conditions of debris flow
with mechanical stability analysis (Cao et al., 2004; Jiang et al., 2016).
However, Takahashi's relation was determined for debris flow propagating
over a rigid bed – hence, with a minor effect of quasi-static actions near
the bed. Lanzoni et al. (2017) slightly modified the Takahashi formulation
of the bulk concentration, which considered the long-lasting grain
interactions at the boundary between the upper inertial grain layer and the
underlying static sediment bed and validated the proposed formulation with
a wide set of experimental data (Takahashi, 1978; Tsubaki et al., 1983;
Lanzoni, 1993; Armanini et al., 2005). The effects of flow rheology on the
basis of velocity profiles are analyzed with attention to the role of
different stress-generating mechanisms.
The grain grading graph of the Guojuanyan gully.
![]()
Critical water depth of debris flow triggering in Guojuanyan gully.
C∗
σ
ρ
tanθ
d16
d50
d84
dm
ϕ
tanϕ
h0
(g cm-3)
(g cm-3)
(mm)
(mm)
(mm)
(mm)
(∘)
(mm)
0.812
2.67
1.0
0.333
0.18
1.9
10.2
4.1
21.21
0.388
7.04
The calculated process of the rainfall threshold.
Watershed
h0
B
V
Q
Δt
F
R
Im
R+Im
(mm)
(m)
(m s-1)
(m3 s-1)
(h)
(km2)
(mm)
(mm)
(mm)
Guojuanyan
7.04
20.0
1.5
0.197
1
0.11
6.9
100
106.9
The rainfall process of debris flow events in the Guojuanyan
gully from 2011 to 2014 (a 1 July 2011; b 17 August 2012; c 9 July
2013; d 26 July 2013; e 18 July 2014).
![]()
This study aims to the initiation of loose solid materials in the gully
under surface runoff; the interactions on the boundary are not involved.
Therefore, Takahashi's model can be used in this study.
Calculation of watershed runoff yield and concentration
The stored-full runoff, one of the modes of runoff production, is also
called the super storage runoff. The reason for the runoff yield is that
the aeration zone and the saturation zone of the soil are both saturated. In
the humid and semi-humid areas where rainfall is plentiful because of the
high groundwater level and soil moisture content, when the losses of
precipitation meet the plant interception and infiltration, the stored-full runoff would not increase anymore with continued rain. The Guojuanyan gully is located
in Dujiangyan city, which is in a humid area. Therefore, stored-full runoff
can be used to calculate the watershed runoff. That is, it can be supposed
that the water storage can reach the maximum storage capacity of the
watershed in each heavy rain event. Therefore, the rainfall loss in each
time I is the difference between the maximum water storage capacity Im and
the soil moisture content before the rain Pa. The water balance equation
of stored-full runoff is expressed as follows (Ye et al., 1992):
R=P-I=P-(Im-Pa),
where R is the runoff depth (mm), P is the precipitation of one rainfall
(mm), I is the rainfall loss (mm) and Im is the watershed maximum
storage capacity (mm) for a certain watershed (a constant for a
certain watershed that can be calculated by the infiltration curve or
infiltration experiment data). In this study, Im comes
from the Sichuan Hydrology Record Handbook (Sichuan Water and Power
Department 1984) and Pa is the API,
referring to the total rainfall prior to the 1 h peak rainfall leading to
debris flow initiation.
Equation (5) can be expressed as follows:
P+Pa=R+Im.
The precipitation intensity is a measure of the peak precipitation. At the
same time, the duration of the peak precipitation is generally brief,
lasting only up to tens of minutes. Therefore, 10 min precipitation
intensity (maximum precipitation over a 10 min period during the rainfall
event) is selected as the triggering rainfall for debris flow, which is
appropriate and the most representative. However, it is difficult to obtain such
short-duration rainfall data in areas with scarcity of data. Therefore, in
this study, P and Pa are replaced by I60 (1 h rainfall) and
API, respectively; thus, Eq. (6) is
expressed as
I60+API=R+Im.
In the hydrological study, the runoff depth R is
R=W1000F=3.6∑Q⋅ΔtF=3.6QF,
where R is the runoff depth (m); W is the total volume of runoff
(m3); F is the watershed area (km2); Δt is the duration
time, in this study it is 1 h; and Q is the average flow of the watershed
(m3 s-1), which can be expressed as follows:
Q=BVh0,
where B is the width of the channel (m), V is the average velocity (m s-1)
and h0 is the critical depth (m).
Equation (7) is the expression of the rainfall threshold curve for a watershed,
which can be used for debris flow early warning. This proposed rainfall
threshold curve is a function of the API
and 1 h rainfall (I60), which is a line with a negative slope.
Discussions
The trend of the debris flow events as well as the debris flow thresholds
were analyzed in Fig. 14 by using the monitoring rainfall data. A comparison
between the thresholds and the calculated threshold curve indicates that
they have the same laws. Therefore, the threshold calculated method proposed
in this work is reasonable and can be used in areas with scarcity of
data. The proposed rainfall threshold curve is a function of the API and the 1 h rainfall (I60), which has been
validated by rainfall and hazard data. It should be noted that the proposed
approach is based on a procedure that can be exported elsewhere only if a
site-specific calibration is used to develop specific thresholds for other
test sites. Therefore, the specific value of the threshold should be
calculated by the initiation conditions of the debris flow in a specific
gully.
However, this work still has two limitations. In Fig. 14, there are two
points above the curve that did not trigger debris flow at all. Although we
have highlighted the significance and interconnection of antecedent rainfall,
critical rainfall and 1 h triggering rainfall, as well as their accurate
determination before the hour of debris flow triggering, it should be
noted that the rainfall is only the triggering factor of debris flows. A
comprehensive warning system must contain more environmental factors, such
as the geologic and geomorphologic factors and the distribution of material
source. In addition, the special and complex formative environment of debris
flow after an earthquake caused the rainfall threshold is much more complex and
uncertain. The rainfall threshold of debris flow is influenced by the
API, rainfall characteristics, amount of
loose deposits, channel and slope characteristics, and so on. Therefore, we
should further study the characteristics of the movable solid materials, the
shape of gully, and so on to modify the rainfall threshold curve. In contrast, if the two rainstorms were under the threshold, all the
debris flow event points would still be located above the threshold and there
would be no missed alarms. Therefore, the threshold established in this
work is convenient and relatively safe.
Restricted by the limited rainfall data, this study was
validated by only five debris flow events. Another limitation of this work is
that the approach proposed in this study has not been validated by
gullies other than the Guojuanyan gully so far. Figures 13 and 14
indicated that only five debris flow events were triggered by high-intensity and short-duration rainfalls. In the future, the value of the
curve should be further validated and continuously corrected with more
rainfall and disaster data in later years.
Conclusions
First, in the areas affected by the Wenchuan earthquake, loose deposits are widely
distributed, causing dramatic changes to the environmental development of debris flow; thus, debris flow occurrence increased
dramatically in the subsequent years. The characteristics of the 10 min, 1 h
and 24 h critical rainfalls were represented based on a comprehensive
analysis of limited rainfall and hazard data. The statistical results show
that the 10 min and 1 h critical rainfalls of different debris flow events
have minor differences; however, the 24 h critical rainfalls vary widely.
The 10 min and 1 h critical rainfalls have a notably higher correlation with
debris flow occurrences than the 24 h critical rainfalls.
Second, the rainfall pattern of the Guojuanyan gully is the peak pattern, both
single peak and multi-peak. The API was
fully explored by the antecedent effective rainfall and triggering rainfall.
Third, as an important and effective means of debris flow early warning and
mitigation, the rainfall threshold of debris flow was determined in this
paper, and a new method to calculate the rainfall threshold was put forward.
Firstly, the rainfall characteristics, hydrological characteristics and
some other topography conditions were analyzed. Then, the critical water
depth for the initiation of debris flows was calculated according to the
topography conditions and physical characteristics of the loose solid
materials. Finally, according to the initiation mechanism of
hydraulic-driven debris flow, combined with the runoff yield and
concentration laws of the watershed, this study promoted a new method to
calculate the debris flow rainfall threshold. At last, the hydrological
condition for the initiation of a debris flow is the result of both
short-duration heavy rains (I60) and the API. The proposed approach resolves the problem of debris flow
early warning in areas with scarce data and can be used to establish warning
systems of debris flows for similar catchments in areas with scarce data,
although it still needs further modification. This study provides a new
point of view of debris flow early warning in mountainous areas.