Introduction

The rainfall-induced debris flows are the most common secondary geological hazards in the Wenchuan earthquake region. According to the research of Zhang and Matsushima (2016), loose solid materials in seismically active areas are easily entrained by runoff following heavy summer rain so that debris flow forms. After the earthquake, rainstorm debris flow activity can last for 5 to 10 years (Tang et al., 2009), even 30 years (Cui et al. 2008). Many researchers have tried to connect rainstorm debris flows to rainfall factors (Cannon and Savage 1988; Prete et al. 1998). Two types of debris flows were detected: runoff-generated and landslide-induced. Combined with the field observations, laboratory experiments, and theoretical analyses, Iverson et al. (1997) indicate that landslides mobilize to form debris flows by three processes: widespread Coulomb failure, liquefaction of the mass by high pore-fluid pressures, and conversion of landslide translational energy to internal vibrational energy. Coe et al. (2008) found that debris flows were initiated by water runoff from colluvium and bedrock that entrained sediment from rills and channels with slopes ranging from about 14° to 45°. The channelized debris flows can grow volumetrically because of bed-material entrainment transporting up to 1 × 105 m3 of sediments, and causing several victims (Reid et al. 2016; Gregoretti et al. 2018; Chen et al. 2019). Wieczorek et al. (1989) indicate that the requirements of antecedent rainfall and high-intensity rainfall apply to most areas where debris flows have been researched, but specific amounts vary regionally depending widely on soil thickness, the permeability of soil and bedrock, and topography. Besides, the researcher took into account a notion of seasonal threshold preceding a rainy event that triggered debris flow. After the Chi-Chi earthquake in Taiwan, the evaluation of factors controlling earthquake-induced landslides and initiation mechanisms of rainfall-induced debris flows were discussed (Shin 2001; Khazai and Sitar 2004). Gregoretti and Dalla Fontana (2007) collected historical rainfall data from twenty-eight debris flow events that occurred in six watersheds in the Dolomites and defined a threshold curve for the triggering of debris flows. Zhang et al. (2013) used rainfall conditions to study the prediction model of debris flows duration and runout volume. Okano et al. (2012) analyzed the debris-flow magnitude and flow characteristics using the fourteen sets of rainstorm and debris flow data from 1980 to 2005 at the Kamikamihorizawa Creek of Mount Yakedake. Combined with the precipitation conditions, Wu et al. (2020) established the sensitivity evaluation model for debris flows in the Longxi River area. The temporal frequency and scale of debris flows are related to the intensity and cumulative value of a single precipitation event (Gregoretti et al. 2016; Bogaard and Greco 2018). Zhuang et al. (2015) modeled the prediction of debris flows by analyzing the duration and intensity of post-earthquake rainfall and the thresholds. Staley et al. (2013) objectively defined the thresholds by maximizing the number of correct predictions of debris flow occurrence while minimizing the rate of errors. Van Asch et al. (2014) used hydro-mechanical numerical models to simulate the initiation, and run-out process, then established critical rainfall thresholds.

For the warning and forecast of a single debris flow, several factors that facilitate the triggering of debris flow are known, which included gully length, gully depth, ravines density, vertical slope, types of geological outcrops, surface runoff, channel erosion, pore water pressure, and instability index (Cui et al. 2009; Chen et al. 2011). Besides, the present research also includes some specific geotechnical index, in particular, the granularity and content of the materials in the potential source areas; available volumes of materials present on the slopes and in the gully likely to be mobilized (Ouyang et al. 2015; Yin et al. 2016). However, it is urgent to provide a quick and convenient early warning measure for mass debris-flow events in a small watershed. After the Wenchuan earthquake, massive debris flows occurred in the Longxi River watershed, Min River watershed, Subao River watershed, Mianyuan River watershed, and the Baishui River watershed. There are differences in the topographic, geological, and geotechnical parameters of these watersheds, even for specific watersheds. It is difficult to obtain detailed and reliable data on loose material distribution, triggering rainfall, and some physical factors that control the debris flow occurrence (Berti et al. 2020). However, we still hope to find a more accurate and applicable rainfall pattern to explore the role of rainfall in triggering debris flows. Thus, this paper carries out a study on the occurrence of debris flow under different rainfall patterns, depending on rainfall duration and intensity. The results will provide a fast basis for the prediction of debris flows in the Wenchuan earthquake area (Fig. 1).

Fig. 1
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The study map of the critical rainfall-induced debris flows in the Wenchuan earthquake region

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Study area

The Wenchuan earthquake on May 12th, 2008, Mw 8.3 was one of the most devastating earthquakes in China and induced a large number of post-quake disasters. Many debris flows under different rain patterns occurred in the Wenchuan earthquake-affected area, Southwest China. The number of debris flows, watershed area, and overall longitude and latitude information of the five study areas was included in Table 1. To reflect the distribution of debris flows and rain gauges in each study area, Figs. 2, 3, 4, 5, to 6 show the detailed interpretation results based on remote sensing images. At the same time, we made statistics on the morphological characteristics related to debris flow occurrence in each study area, such as drainage area, channel length, watershed relief, and channel gradient (Tables 2, 3, 4, 5, to 6).

Table 1 Detailed information on the study area
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Fig. 2
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Distribution map of twenty-one debris flows in the Min River watershed

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Fig. 3
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Distribution map of twenty debris flows in the Mianyuan River watershed

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Fig. 4
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Distribution map of fourteen debris flows in the Subao River watershed

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Fig. 5
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Distribution map of twelve debris flows in Longxi River watershed

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Fig. 6
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Distribution map of twelve debris flows in the Baishui River watershed

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Table 2 Geomorphological parameters of the Min River watershed
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Table 3 Geomorphological parameters of the Mianyuan River watershed
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Table 4 Geomorphological parameters of the Subao River watershed
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Table 5 Geomorphological parameters of the Longxi River watershed
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Table 6 Geomorphological parameters of the Baishui River watershed
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Method and data

For exploring the rainfall patterns triggering debris flows in these river watersheds, the rainfall intensity and the antecedent rainfall are selected as essential analysis parameters. After careful study of the existing literature and previous research results, this paper adopted the method by Jan and Lee (2004) to define the event with continuous rainfall. The start of a rainfall event is defined when the intensity reaches 4 mm/h. The end of the rainfall event is defined when the intensity is lower than 4 mm/h during 6 continuous hours (Jan and Lee 2004; Chang et al. 2011). In this paper, the antecedent rainfall is defined as the total amount of rainfall before the debris flow occurs during the accompanying rainfall events. According to Chow et al. (1988), the rainfall depths previously precipitated were named antecedent rainfall. Some rain gauge stations and mud level measurement monitoring devices have been installed in the field and could provide data in real-time when a debris flow event occurred. With the weather forecasts provided by the weather bureau, the following rainfall data were obtained: ➀ hourly rainfall intensity, which is the amount of rainfall in mm per hour; ➁ cumulative rainfall, which is the total amount of one continuous precipitation event; ➂ rainfall duration, which is the duration of one precipitation event; ➃ the starting time of debris flows, which can be defined from field surveys and the data of mud level measurement monitoring devices.

In some specific seasonal rainfall events, the rainfall threshold may play an important role in the initiation of debris flow, such as influencing the saturation degree of soil or loose rock mass. However, the effect of rainfall may be different under different rainfall events. Through the field investigation and previous study, we obtained rainfall data for the five river watersheds and then studied the occurrence characteristics of debris flows under different rain patterns. The occurrence time, rainfall intensity, antecedent rainfall, rainfall duration, and corresponding rainfall pattern of debris flow in five river watersheds are listed in Table 7.

Table 7 Rainfall data of typical debris flow events in the Wenchuan seismic region (S, short-term sudden rainfall patterns; M, medium-term persistent rainfall patterns; L, long-term intermittent rainfall patterns)
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Results

In this paper, the detailed rainfall data and the cumulative value of antecedent rainfall of all debris flow events above are plotted in Figs. 7, 8, to 9. Through comparative analyses of the different rainfall diagrams, this paper distinguishes three types of triggering rainfall patterns: short-term sudden rainfall pattern, medium-term persistent rainfall pattern, and long-term intermittent rainfall pattern.

Fig. 7
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Short-term sudden rainfall patterns at the origin of the triggering of debris flow in the Wenchuan earthquake area (yellow star: the occurrence time of debris flow)

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Fig. 8
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Medium-term persistent rainfall patterns at the origin of the triggering of debris flow in the Wenchuan earthquake area (yellow star: the occurrence time of debris flow)

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Fig. 9
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Long-term intermittent rainfall patterns at the origin of the triggering of debris flow in the Wenchuan earthquake area (yellow star: the occurrence time of debris flow)

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Short-term sudden rainfall pattern

A “short-term sudden rainfall pattern” is characterized by a rapid increase of rainfall intensity so that debris flows are triggered in a short time interval. One important sign of this pattern is that the antecedent rainfall duration is not exceeding more than 5 h. Depending on the data measured in the field, the duration of antecedent rainfall is short, usually less than 5 h. There could be little rain in the first few hours but with a quick rise of the rainfall intensity, and the debris flow will occurrence immediately. Figure 7 shows the rainfall is relatively small due to the short duration of antecedent rainfall. The yellow stars in Figs. 7, 8, to 9 show the timing of debris-flow occurrence. With high-intensity rainfall conditions, the intensity of rain exceeds the seepage intensity to form slope runoff (Kean et al. 2013; Simoni et al. 2020). The generated flash floods entrain abundant loose materials in the channel that can quickly convert into debris flows. The representative events with this type of rainfall pattern are as follows: the “8.13” debris flows in the Longxi River watershed, the “7.31” debris flows in the Mianyuan River watershed, the “9.23” debris flows in the Subao River watershed, and the “7.31” debris flows in Baishui River watershed.

Medium-term persistent rainfall pattern

Antecedent rainfall is an important indicator of the classification of the medium-term persistent rainfall pattern. The debris flow is preceded by a period of antecedent rainfall. For medium-term persistent rainfall events, the antecedent sufficient rain duration time is about 7 h, and the total duration will continue more than 10 h but less than 1 day. As shown in Fig. 8, although the rainfall intensity at the time of these debris flow occurrence was relatively small, the antecedent rainfall had resulted in the saturation of loose materials and accelerated surface runoff. The representative events with this type of rainfall pattern are as follows: the “8.18” debris flows in the Longxi River watershed, the “8.13” and “8.19” debris flows in the Mianyuan River watershed, and the “8.21” debris flows in the Min River watershed.

Long-term intermittent rainfall pattern

The long-term intermittent rainfall pattern is mainly characterized by prolonged antecedent rainfall. The rainfall may continue 2 or 3 days, with one or sometimes more short breaks. Generally speaking, the first rainfall period has a clear maximum, while the second rainfall period does not exceed 10 h. The long antecedent rainfall period can increase the overland flow and moisture of the soil. The increasing high discharge can saturate loose materials and transport them to the channel. Figure 9 shows during the antecedent period, a repetition of separate rain events with moderate rain intensities. These rain events have a long antecedent duration that leads to the high moisture content in materials. Massive erosion occurs in the channel by entrainment of material from both sides of the channel. With the passing of the peak rainfall, the water level drops, and erosion in the channel gradually stops. As the rain continues and the flow increases, the immature flow will move downstream with increasing sediment concentration and volume until it becomes a fully formed debris flow (Berti et al. 2020). On the whole, compared with the conditions of debris flow induced by short-term sudden rainfall pattern and medium-term persistent rainfall pattern, the time stage of the generation and triggering of long-term intermittent rainfall pattern-induced debris flow is relatively later and the peak rainfall required is also lower. The representative events with this type of rainfall pattern are as follows: the “8.14” and “7.11” debris flows in the Min River watershed, the “9.24” debris flows in the Subao River watershed, and the “7.10” debris flows in the Mianyuan River watershed.

ID rainfall threshold analysis

According to the above rainfall database of the five river watersheds, the intensity-duration curve (ID curve) of three rainfall patterns was constructed to describe the critical rainfall conditions for debris flow initiation. The intensity-duration rainfall threshold of the most common type has the form of I = αD-β (Guzzetti et al. 2007, 2008; Saito et al. 2010; Zhou et al. 2014). To plot the ID curve, all the rainfall intensity I and duration D data of debris flow events were noted in a graph of a rectangular coordinate system (D on the x axis, I on the y axis). Based on the rainfall data, the ID curve for the debris flow events in the Wenchuan earthquake region was drawn by the Origin software. The threshold curve and the formula in different rainfall patterns are shown in Fig. 10.

Fig. 10
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ID thresholds for the debris flow events under three rainfall patterns (a example of rainfall data; b ID threshold curve)

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On August 19th, 2019, a heavy rainstorm occurred at about 0:00 in the Min River watershed. More than eight debris flows occurred after 26 h. According to the characteristics of rainfall, these debris flow events belong to the long-term intermittent rainfall pattern. The triggering rainfall intensity and antecedent rainfall were 24.2 mm/h and 121.1 mm, respectively (Fig. 10a). Using the intensity-duration model to carry out verification, the results show that it can predict this debris flow event (Fig. 10b).

Conclusion and discussion

Debris flows were frequently induced by rainfall after the Wenchuan earthquake, causing substantial economic losses and heavy casualties. Correctly classifying rainfall patterns and precisely setting up a prediction rainfall threshold of post-seismic debris flows based on rainfall data can help to enhance disaster prevention and mitigation. Although there are differences in the topographic, geological, and geotechnical parameters of these watersheds, we still want to get a more accurate intensity-duration threshold curve for different rainfall patterns. In this paper, the relationship between the characters of rainfall patterns and the debris flow occurrence was analyzed. Five river watersheds in the Wenchuan earthquake region were selected because according to the field investigation, all the debris flows of this region were triggered by rainfall. The pattern of rainfall triggering debris flows in the Wenchuan earthquake region can be divided into three types: short-term sudden rainfall pattern, medium-term persistent rainfall pattern, and long-term intermittent rainfall pattern. In the short-term sudden rainfall pattern, heavy rainfall can lead to the enhancement of surface runoff, and thus bring a large amount of loose sediment into the debris flow in a short period. In the case of medium-term persistent rainfall patterns, both the flow runoff erosion and slope failure mechanisms can play a vital role in initiating debris flows. The long-term intermittent rainfall pattern with the lowest intensities and long duration are favorable for the initiation and reactivation of landslides, which can transform into debris flows, especially when failure at the end is accompanied by a lot of rain. According to the three rainfall patterns, the ID curve for the debris flow events in the Wenchuan earthquake region was established and verified.

As the introduction explains, the excitation condition of debris flow in seismic zones is influenced by many factors, such as geologic structure, geomorphology, rock kind, vegetation, and precipitation. For example, the lithology of outcrops or rock type distributions directly influence the quantity and quality of available loose materials for the generation of rainstorm debris flows. However, due to the lack of lithological data, this paper only considers the prediction of threshold under one variable of rainfall. In the future, we will further collect relevant data and carry out the study on the rainfall threshold of debris flow using a multivariate approach.