Hazard assessment of debris-flow-prone watersheds in Cubatão, São Paulo State, Brazil

In Brazil, research related to the occurrence and prevention of debris flows is incipient when compared to the extent of the impacts caused by the phenomena. There is a need for further studies that consider susceptibility and hazard, especially in areas that are environmentally and socioeconomically vulnerable. This study aimed at assessing debris-flow hazard in the Rio das Pedras watershed, in Cubatão (State of São Paulo, Brazil), based on a set of different physiographic parameters (geomorphological, morphometric, geological) and in the application of empirical models. The hazard assessment was based on: (1) the evaluation of the history of events in the region; (2) the identification of the geomorphic controlling factors; (3) the estimation of the magnitude of a potential event; and (4) the identification of the elements at hazard. The results show that a debris-flow event in Rio das Pedras would more severely impact the Anchieta Highway (SP-150), the gas pipeline GASAN, the oil pipeline OSSP and the districts Pinhal do Miranda and Cota 95. These results highlight the relevance of geomorphological and geological parameters when estimating the extent of debris runoff, which is essential when defining the hazard in a debris-flow-prone watershed.


Introduction
The occupation of areas prone to natural disasters is a recurrent process in human history, especially in regions with high population density (Alcántara-Ayala 2002, Kahn 2005;Alvalá et al. 2019). In mountainous regions, the record of natural disasters is frequent, especially hydrogeomorphic processes, which main controlling and initiation factors in tropical areas are relief and rainfall, respectively (Rickenmann and Zimmermann 1993;Takahashi 1991;Yang et al. 2021).
Debris flows are one of the most destructive hydrogeomorphic processes in Brazil and worldwide (Kahn 2005;Álvala et al. 2019). These phenomena are initiated by heavy precipitation events and behave like dense flows, transporting large amounts of material (from soil to large rocky blocks) along drainage paths in areas characterized by steep slopes and high amplitude, resulting in great impact power and large radius of destruction (Varnes 1978;Takahashi 1991;Rickenmann and Zimmermann 1993;Hungr et al. 2014;Bernard and Gregoretti 2021).
The increase in the recurrence and magnitude of debris flow events on a global scale (Winter and Shearer 2014;Borga et al. 2014) is directly associated with the increase in the number of extreme rainfall events (Giorgi et al 2011;Borga et al. 2014;Westra et al. 2014). In Brazil, this increase can also be noted by the high number of deaths related to the occurrence of debris flow in the last century, totaling 5771 fatalities and 45 events, which are distributed mainly in the south and southeast region, mostly concentrated in the Serra do Mar mountain range (Cabral et al. 2022a).
Serra do Mar is a mountain range that extends for about 1500 km on the south and southeast coast of Brazil (Vieira and Gramani 2015), which are the regions with the highest population densities in the country, with an average of 100 inhabitants per km 2 (IBGE 2011), and also host important logistical infrastructures for the country's economy (ports, highways, railways, oil pipelines, refineries). Due to this importance, more debris flows studies and hazard zonation methodologies are needed in Brazil, as highlighted by recent studies (Kobiyama et al. 2015;Cabral et al. 2022b).
Analyses based on morphometric and geomorphological parameters are generally more accurate and are based on investigations carried out directly in the field . These analyses are also fundamental to understanding the dynamics of debris flows in watersheds (Gaume and Borga 2008;Borga et al. 2014;Lucia et al. 2018). However, difficulties in access and high costs related to field campaigns can represent a challenge for studies in greater detail Destro et al. 2018). As an alternative, empirical statistical methods were developed to estimate the magnitude of debris-flow events (Takahashi 1991;Bianco and Franzi 2000;Massad 2002;Takahashi 2009;Kanji et al. 2007, Chang et al 2011, based on the analysis of past events that occurred in a certain region or catchment, thus generally being site-specific (Takahashi 1991;Massad 2002).
When trying to estimate the magnitude of a debris-flow event by using empirical equations in hazard zonation, some parameters are fundamental for an effective analysis, such as peak discharge, runout and velocity (Rickenmann 1991;Takahashi 1991;Kanji et al. 1997Kanji et al. , 2003Massad 2002;Pak and Lee 2008;Medina et al. 2008;Reid et al. 2016;Gregoretti et al. 2019;Calista et al 2020;Cabral et al. 2022a). Some attempts to estimate the magnitude of debris flows have been made in the region of Cubatão, São Paulo state, with the purpose of dimensioning structures to contain debris flows, such as sabo dams, or to establish methodologies for hazard zonation (Kanji et al. 1997;Massad et al. 1997;Massad 2002;Cabral et al 2022b).
In this work, a hazard zonation methodology is proposed in the Rio das Pedras watershed, in Cubatão (Serra do Mar), at a 1:25,000 scale, based on the analysis of previous events, identification of the main geomorphological factors, estimation of the magnitude of possible events through empirical equations and the identification of the elements at hazard, by mapping of the most critical areas. The aim of this methodology is also to validate the effectiveness and applicability of contingency plans currently in place in the region. The watershed selected for this study stands out due to hosting several industrial, logistical and residential complexes within its limits, in an area with great social and environmental vulnerability and a high recurrence of landslide events.

Study area
The Rio das Pedras watershed has an area of 1.39 km 2 , an altimetric amplitude of 650 m and main channel length of approximately 1.7 km (Fig. 2C). The watershed is chosen as the test-site due to the morphometric characteristics, recurrence of landslide events and the large volume of in-channel material (rock boulders, woody debris) (Fig. 1).
Moreover, the Anchieta highway (SP-150), pipelines (GASAN and Petrobras OSSP) and residences are located within the watershed's limit, which can be impacted by potential future events.
Cubatão is home to a large industrial and petrochemical complex, extending along the valleys of the Mogi and Cubatão rivers. The industrial facilities, especially those located near the foothills of the mountain range, are frequently at risk of being affected by periodic events of landslides, debris flows and flash floods. The slopes in the region show clusters with high population density, mainly consisting of irregular occupation with precarious building standards ).  (Cabral et al 2022b), most notably at the oil refinery region in 1985, 1994 and 1996. The 1994 event halted the refinery's activities for a week, causing U$ 40 million in losses (Massad 2002;Massad et al. 2003;Kanji et al. 2007).
The watershed is located in the geomorphological province denominated "Coastal," in the Serra do Mar subzone (Fig. 2B), in the subsystem of festooned scarps with concave amphitheaters (Hasui and Sadowsky 1976). The geology of the Rio das Pedras watershed is comprised of the Precambrian rocks, consisting predominantly of ophthalmic and stromatitic migmatites, schists, phyllites, quartzites, and granites (Tatizana et al. 1987) (Fig. 3A).
The Cubatão fault zone extends along the southeastern coast of the Mogi and Cubatão river valleys (Hasui and Sadowsky 1976). The Cubatão Lineament separates two distinct blocks: in the North, the Juquitiba block with a predominance of stromatitic migmatites, with SW dip direction (where the Rio das Pedras watershed is located); in the South, the Coastal Block is comprised of ophthalmic migmatites, with NE dip direction (Hasui and Sadowsky 1976).

Material and methods
The methodology used in this work is based on the application of four steps: (1) survey of the history of recurrence of events in the study area, (2) mapping of geomorphological conditions, (3) estimation of the magnitude of a possible event in the watershed and, finally, the (4) identification of the elements at hazard.

3
The first step in the hazard assessment was to collect data regarding debris-flow events in the study area, to estimate the recurrence of these events, assuming that the factors that caused events in the past may generate new ones in future (Van Westen 1993; Guzzetti et al. 1999). The second stage concerns the geomorphological analysis of the watershed, to identify and characterize the main triggering agents of debris flows. The third step is the estimation of the magnitude based on the application of empirical equations of volume, run-out distance, velocity and time of arrival in the depositional area (Rickenmann 1991;Takahashi 1991;Massad 2002;Kanji et al. 2003). The fourth step is hazard recognition, where the elements that are susceptible to damages related to debris flows are identified.

Historical events in the catchment
The debris-flow events that have occurred in the watershed are shown in Table 1, based on Gramani (2001) and Massad (2002). Moreover, based on these events, as well as others in Cubatão, Tatizana et al. (1987) established rainfall thresholds (Fig. 4) for debrisflow initiation. According to Tatizana et al. (1987), a debris flow is triggered when the 72-h accumulated rainfall is over 120 mm, and the peak intensity is over 40 mm h −1 .

Mapping of the geomorphological and geological conditions
Fieldwork was carried out in September 2019 to investigate evidences of past debrisflow events in the watershed, as well as to characterize the controlling factors of the phenomenon. The past occurrence of debris flows has very specific geomorphological and Regarding the characterization of the controlling factors, the debris flows can be of primary origin (initiating in the slopes), usually triggered by translational landslides on steep slopes, which provide unconsolidated material that reached the main drainage system and is, then, transported (Cruden and Varnes 1996). Debris flows can also be of secondary origin (initiating in the channel), triggered by the collapse of material accumulated in natural dams or loosely accumulated along the channel bed (Takahashi 1981).
The evaluation of geomorphological parameters such as the altimetric gradient of the watershed, degree of carving, volume of material in the main channel, slope and the occurrence of talus deposits in the depositional area is important in the evaluation of the occurrence of future debris flows, as well as being applied as input parameters in empirical Table 1 Selection of debris flows events in the Rio das Pedras watershed (Cubatão-SP). Source: adapted from Gramani (2001) and Massad (2002) Location Year Area (km 2 ) Triggering rainfall Velocity (m/s) Volume (m 3 )  Fig. 4 Correlation between precipitation and landslides (Tatizana et al. 1987) equations for hazard assessment. The geomorphological parameters were acquired during field campaigns and GIS software.

Magnitude estimation
The empirical equations applied in the estimation of the physical parameters of debris flows at Serra do Mar are based on Takahashi (1991), Kanji et al. (1997), Massad et al. (1997) and Rickenmann (1999). The estimated parameters are peak discharge, magnitude, and run-out distance.

Peak discharge
The peak discharge equation (Eq. 1) that best fits the study area is the one from Kanji et al. (1997) and Massad (2002), developed based on Takahashi (1991): where A is the watershed area (km 2 ), I 1 is the intensity of the rainfall (mm/h) accumulated in the hour before the event initiation and c is the concentration of solids per unit volume (Eq. 2), based on Takahashi (1991): where θ is the average slope, ρ 0 is the specific weight of the slurry (water + sediments), δ is the specific weight of the granular material, and ϕ is the angle of internal friction of the granular material.

Magnitude
Based on past events at Serra do Mar, Massad (2002) proposed the magnitude equation for the mountain range: where V s is volume of solids transported, η is the average porosity of the soil of the hillslopes, A e corresponds to the landslide area in relation to the total watershed area (A′, in m 2 ), and p is the percentage of remobilized material from the riverbeds in relation to the total volume of solids (V s ). For these parameters, Massad (2002) proposed that for debris flow at Serra do Mar, on the coast of the São Paulo state, the average depth of landslides (e) is 1 m (Tatizana et al. 1987;Wolle 1988;Cabral et al. 2022c), η of 40%, p of 15% and A e of approximately 9%, according to Massad (2002). Kanji et al. (2003) established the upper limit of the distance covered by the debris run out using the following equation:

Run-out distance
where H is the altimetric gradient of the ramp covered by the debris run out (in meters), L is the horizontal distance covered by the debris run (in meters), and Q is the volume of material mobilized during the event (in cubic meters).

Velocity
The peak velocity is estimated using the equation suggested by Rickenmann (1991), as it is independent from the flow height variable (h), which is an information that is not available for our study area: where U = flow velocity (in ms −1 ); θ = mean channel slope (°); g = acceleration due to gravity (m/s 2 ); d50 = mean diameter (m) of the granular phase, defined according to tests on soils in the natural slopes and the material deposited along the river bed (Massad 2002); q˳ = is the flow of water only (Fig. 5).

Slope conditions
In the study area, characteristics and factors favorable to destabilization processes (shallow landslides, rock fall, erosion) were verified. The vegetation in the area is mostly preserved or in the process of regeneration, which indicates that the state of degradation is not directly responsible for destabilization processes, as the upper third of the watershed is preserved without signs of anthropic activities. Deposits characteristic of past debris flow events are found, characterized by granulometric inversion (Fig. 6A), in addition to relatively resistant exposed bedrock (migmatites, quartzites, granites) (Fig. 6C). The metric fracturing pattern in the bedrock could potentially indicate a large supply of material that could be entrained by future debris-flow events.

Drainage conditions
Drainage channels have a direct influence on the process of formation and development of a debris flow. The material mobilized in a debris flow does not come only from the slopes, but a significant portion, especially the course fraction, is incorporated by the flow along the channel (talus, colluvium, alluvium, river terraces and old deposits from past debris flows) through entrainment.
In the study area, the mobilizable material observed along the main channel can be divided into the following types of deposits: (a) thin alluvial terraces, with thickness that varies from 1 to 2 m, distributed mainly in the final third of the channel, between the transport and deposition zone. In this portion, there is a predominance of gravel and coarse-sand matrix. Toward the headwaters' region, the increase in grain size is noticeable, where terraces start to show a predominance of metric rock boulders; (b) colluvium and residual soils; (c) coarse alluvium ( Fig. 7A-C) covering the channel bed; and (d) metric rock blocks that vary in diameter between 1 and 5 m, forming dams in the upper third of the channel (Fig. 8A, B).
In-channel debris is more susceptible to remobilization, forming an abundant source of material along the channel. Figure 9 shows the main channel profile, representing the different debris-flow development and movement zones, following the premises of Vandine (1996) and Simoni et al. (2020).
The slope inclination in the headwater's region shows values close to 70°, decreasing to approximately 30° near the bottom limit of the deflagration zone. In the transport zone, slope varies from 25° to 15° and, finally, in the area of deposition, slope is generally under 15°.

Natural dams
The natural dams are an important geomorphological indicator in watersheds and consist of an aggravating element in the initiation of debris flows, with their observation in the field being fundamental for the estimation of future scenarios. The origin of these Fig. 6 Front view of the slope side tank. A Eroded deposit with granulometric inversion typology, typical of debris flows; B Frontal and partial view of an elongated straight slope; C Highly altered granite and migmatite/slope with signs of recent movement dams is conditioned to the accumulation of woody and stony debris, responsible for totally or partially blocking the river flow (Gregoretti et al. 2010;Kean et al. 2013).
Whether in the main channel or in the tributaries, these dams behave in a way that partially retains the water flow, forming a temporary "reservoir." The increase in the water table during a rain event causes the rupture of these dams, releasing suddenly the flow and resulting in numerous debris pulses.
In the study area, out of the 17 points that were mapped during field campaigns in the main channel (Fig. 10), 3 of them correspond to partial or breached dams (Fig. 11A) and 14 of them are closed dams (Fig. 11B), i.e., they block the entirety of the main channel. Fig. 7 Main drainage characterization. A alluvial terraces with coarse material, ranging from 0.5 to 2 m and with the presence of residual colluvium; B coarse alluvium covering the drainage; C alluvial terraces with coarse material, ranging from 1 to 2 m

Peak discharge and magnitude
Adopting a solids concentration (c) of 37.6%, based on Kanji et al. (1997), a watershed area of 1.39 km 2 and an I 1 of 40 mm/h, the peak discharge is estimated at 538.46 m 3 /s  using Eq. 1, which is similar to those estimated by Massad (2002) for other watersheds in the region, with estimated values between 630 and 780 m 3 /s. The volume of solids that can be transported by a debris-flow event (i.e., the magnitude) in the watershed, based on a precipitation scenario under the aforementioned conditions, is estimated at approximately 168,000 m 3 .

Run-out and average velocity
The debris-flow runout distance in the Rio das Pedras basin is estimated at 1856 m, considering the upper third of the main channel as the starting point, where the main deflagration zone is located. (Fig. 12).

Hazard mapping
The mapping of the elements at hazard in the immediate radius of debris flow deposition zone was carried out based on the use of aerial photographs and field investigations, in which a scenario of a high level of hazard was identified related to three main elements: a 100 m stretch of the Anchieta Highway (SP-150), the gas and oil pipeline line that crosses the downstream stretch of the watershed and the neighborhoods also located downstream (Fig. 13).
Based on the mapping carried out in the main channel, on the in-channel debris deposits and on the magnitude estimation with the radius of potential destruction, two residential districts located in the downstream portion of the watershed are interpreted Fig. 11 Characterization of dams in the main channel. A Front view of the partial dam, with rock boulders that vary from 1 to 3 m and its schematic profile on the right (Point 16); B frontal view of the total dam in the main channel, with rock boulders that vary from 2 to 4 m and schematic profile on the right (Point 17) to be on the impact route of a debris-flow event, as well an oil and gas pipeline and the Anchieta Highway (SP-150).
The geomorphological mapping carried out in the watershed allowed us to observed evidences of past debris-flow event and, considering the increase in the frequency of intense rain events in the region (Marengo et al. 2021), there is a strong possibility of new debris-flow events in this watershed. As a result, a hazard zonation map is proposed for the watershed, based on the geomorphological analysis.
The hazard zonation map shown in Fig. 14 features two main categories: Red and Yellow Zone, to represent the different hazard levels that takes into consideration the potential destruction degree (total or partial). The Red Zone is classified as a very high hazard zone or a total destruction zone, interpreted as an immediate impact area with high levels of damage to infrastructures, such as the highway, the pipeline network and residences. The Red Zone covers mostly the depositional area of a debris flow, and its delimitation obeyed the topographic characteristics of the terrain, the runout distance and the estimated magnitude.
The Yellow Zone is classified as a high hazard zone, with the partial destruction of structures. In the study area, this zone covers mainly the region after the highway, as most of the sediments are interpreted to be deposited in the Red Zone, with the Yellow Zone receiving mostly a slurry laden with fine-grained sediments.

Conclusions
The hazard zonation conducted in our study is based on the identification of the main infrastructures and communities at hazard, on the estimation of kinematic parameters using empirical equations and on the geomorphological investigation of the debris-flow-prone watershed proved to be satisfactory. The hazard zonation helped to delineate the main zones of impact and destruction, contributing to the development of programs that can support the definition of the guidelines that should be in place during emergency situations in case of a strong likelihood of a debris-flow event. It should be noted, however, that the empirical mathematical relationships applied in this study can show relative dispersion, as they simplify a complex phenomenon (Costa 1984;Takahashi 1991;Massad 2002).
More studies focused on the dynamics of debris flows in Brazilian mountain regions are needed and their comparison with other countries can support the development of new models and approaches for a better understanding of the phenomenon and how to prevent future disasters. Studies based on numerical modeling, such as Medina et al. (2008), Gregoretti et al. (2019), Marchi et al. (2019), Zhou et al. (2019), Cabral et al. (2022b), demonstrate how much further we can advance in debris-flow hazard assessments and that local-scale studies are important to a more in-depth analysis. Finally, due to the fact that the study area shows a high socioeconomic and environmental susceptibility and vulnerability to debris flow events, it is recommended in the short and medium term the adoption of non-structural measures, such as monitoring systems and automated alerts, and structural measures, such as the installation of Sabo dams, to reduce the potential negative impacts of a debris-flow event.
Author contributions Mr. VQV worked on the development and writing of the manuscript, organized and collected fieldwork data. Dr. FAVGR organized the fieldwork campaign, contributed to the development and organization of the manuscript. Mr. VC contributed to the fieldwork and writing of the manuscript. Dr. JEZ contributed to the writing and organization of the fieldwork and data collection. Dra. CVdSC aided the collection of fieldwork data and data processing. Mrs. MFG aided in the fieldworks, collection data and writing the manuscript. Mr. Ogura aided in the fieldworks, collection data and organization of the manuscript. Mr. CEK aided the organization and writing of the manuscript.
Funding This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior-Brasil (CAPES).

Data availability
The datasets generated during our study are available from the corresponding author upon request.