
==== Front
Sci Rep
Sci Rep
Scientific Reports
2045-2322
Nature Publishing Group UK London

39251638
71272
10.1038/s41598-024-71272-y
Article
Determining the debris flow yield strength of weathered soils: a case study of the Miryang debris flow in the Republic of Korea
Jeong Sueng-Won
Lee Seungjun
Oh Hyun-Joo
Kim Minseok minseok_kim@kigam.re.kr

https://ror.org/044k0pw44 grid.410882.7 0000 0001 0436 1602 Landslide Research Center, Geologic Hazards Division, Korea Institute of Geoscience and Mineral Resources, 124, Gwahak-ro, Yuseong-gu, Daejeon, 34132 Republic of Korea
9 9 2024
9 9 2024
2024
14 2097525 6 2024
26 8 2024
© The Author(s) 2024
2024
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Debris flow hazards are often interpreted through back-calculated simulation analysis or empirical methods. The mobility of a debris flow is greatly influenced by mechanical and hydrological parameters. The strength parameters play important roles in the debris flow initiation and flow stages. In particular, the rheological parameters of yield strength and plastic viscosity directly affect the debris flow runout distance and velocity. One of the most important parameters to consider when evaluating debris flow hazards is the shear strength. This strength is called the residual shear strength in the failure stage and the yield strength in the post-failure stage. The residual shear strength obtained from ring shear tests can be related to the initiation of mass movements; the yield strength obtained from rheological tests can be related to the mobilization of debris flows. The residual shear stresses obtained from ring shear tests of weathered soils typically range between 10 and 100 kPa and strongly depend on the normal stress and shear velocity. When progressive slope failure (i.e., strain-softening behavior) occurs at a relatively shallow slope depth (e.g., < 1 m), the soil strength ranges from approximately 5–10 kPa. If the liquid limit state (i.e., solid‒liquid transition) is reached, the shear strength of the soil is approximately 2 kPa. Once the soil fails and mixes with ambient water along the slip surface, the yield strength decreases dramatically, resulting in high mobilization. A suggestion on how strength parameters can be applied to estimate debris flow mobility is presented by considering the 2011 Miryang debris flow, which occurred in weathered soil deposits in Miryang city, Republic of Korea. The best approach for debris flow yield strength estimation would be to consider the residual shear strength in the initiation stage, the yield strength in the flow stage, and the reduction in yield strength with the entrainment effect of the flow in the rapid fluidization stage.

Keywords

Debris flow
Yield strength
Residual shear strength
Weathered soils
Entrainment effect
Subject terms

Natural hazards
Engineering
issue-copyright-statement© Springer Nature Limited 2024
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pmcIntroduction

Debris flows are fast-moving landslides with far-reaching runout distances that are comparable to those of creep, sliding, spreading, and toppling movements1–5. The high mobilization of debris flows lies in their constituent materials. Debris flows commonly consist of a mixture of soil and water, sometimes including rock and wood fragments and other debris. The incorporation of erodible bed and loose gully sediments into debris flows, called sediment entrainment, results in debris flows with large volumes6–9. To understand the related phenomenological characteristics, learnings from numerous research fields, such as geology, engineering geology, hydrology, geotechnical engineering, and rheology, must be combined. For this reason, debris flow research is multidisciplinary and convergent10,11.

Debris flows in mountainous areas are strongly influenced by several factors, such as slope, precipitation, pore fluid pressure, and vegetation. The main triggering factors are heavy rainfall, earthquakes, snowmelt, land use and human activities12. A variety of field and laboratory data are required for estimating debris flow risks. Among these data types, topography, geology, geotechnical and hydrological properties are often used. Static descriptions based on soil and rock mechanics are useful for theoretical considerations, but they are still difficult to link with fluid mechanics and include uncertainty11,13. In debris flow simulations, strength parameters, such as the shear strength, cohesion, and internal frictional angle, are often used to examine debris flow mobility14–18. In addition, the debris flow rheology, which can be characterized by the debris flow yield strength and viscosity, is paramount in estimating the debris flow runout distance and velocity because the debris flow runout distance and velocity are affected by the yield strength and viscosity, respectively19; considering the Voellmy rheology, the debris flow runout distance and velocity are also influenced by basal friction coefficients and turbulence terms13,20. All of these factors influence the strength parameters of debris flow dynamics. Most studies are based on back-calculations to estimate debris flow mobility. Sometimes empirical correlations are used21,22. According to many case studies of debris flows, these strength parameters can be assumed to be constant in debris flow simulations involving specific geological and geomorphological features. This can be established under the assumption that there is no change in the volume of the debris flow during the flow. This approach is suitable when there is no internal disturbance due to any external force. Additionally, the volume change of the debris flow due to erosion is ignored. The strength evolution and applicability of debris flow mobilization strategies for debris flow prevention are poorly understood.

This report provides insight into the determination of strength parameters for estimating debris flow hazards. In the following section, we provide a general overview of debris flow events in the Republic of Korea and discuss the corresponding shear strength parameters in terms of their calculation methods and potential uses. To do this, ring shear tests (to obtain the residual shear strength) and rheological tests (to obtain the yield strength and viscosity) are performed. Two-dimensional debris flow simulations are conducted using different rheological models. The strength evolution of a debris flow, the residual shear strength obtained from ring shear tests and the yield strength obtained from rheological tests via a fully remolded process are emphasized. Finally, practical consideration of the strength parameters of debris flow dynamics is given.

Study area

In the Republic of Korea, debris flows are mostly triggered by rainfall events in weathered soil deposits23,24. The Miryang debris flow is adopted as a case study here to describe the dynamics of a debris flow (Fig. 1). The study area, Singok Mt., which is situated at 128° 49′ 0′′ E, 35° 35′ 45′′ N, is located in Singok-ri, Milyang city, Gyeongsangnam-do, Republic of Korea, and has an altitude of 560 m above sea level (Fig. 1a,b show before and after the debris flow). The geology of the debris flow area is characterized by intrusive rocks. The exposed formations in the study area range from late Cretaceous to Quaternary formations with various lithologies, including aphanitic andesite, vitric tuff, granodiorite, biotite granite, and alluvium. Most of the bedrock in the study area is composed of intrusive rocks (Fig. 1c). Slope failure started at the vitric tuff in the study area. This area had a mean temperature of 25.3 °C and a mean precipitation of 327 mm in July over 10 years (2002–2011). In particular, the precipitation in July 2011 was 512 mm. A total of 290 mm of rain fell in the study area for three days from July 8 to 10, 2011 (Fig. 1d); this was the highest rainfall recorded in 10 years. In particular, the maximum hourly rainfall in the study area was 40 mm at 1 PM on July 9, 2011 (ASOS, No. 288 Milyang station25). Thus, the studied debris flow event was the result of a combination of high-intensity and short-duration rainfall, which is common for debris flow disasters. The soil masses that failed were approximately 1 m thick and 6 to 16 m wide, with an average slope of 31–39° among the four source areas. Four debris flow source areas (F1–F4) have been estimated to cover 62–170 m2 based on field observation and DEM data. After heavy rainfall, the soil collapse in the mountain area occurred adjacent to a forest load added in 2007 on Singok Mt. behind Yangji village. No history of debris flows occurred before the addition of the forest load. After a 3-day rainy period, the debris flow struck the village of Yangji, killing four people and collapsing three houses. Reforestation and slope stabilization were performed after the debris flow event. Three check dam were constructed as a disaster prevention system. There was no eyewitness of the onset of debris flow, but the debris flow characteristics at the time of occurrence were inferred from the traces of the geological disaster area; it is highly likely that the initial slope failure immediately developed into a debris flow.Fig. 1 Study area: (a) before the debris flow event, (b) after the event, (c) geology, and (d) precipitation data.

Materials and methods

Geotechnical properties of weathered soils

The materials were collected from the debris flow source area in the Republic of Korea (Fig. 1). The geotechnical properties of the samples were examined according to ASTM standards. From the sieving analysis, the effective grain size (D10) and mean diameter (D50) in the grain size distribution are 0.003 mm and 0.6 mm, respectively. The coefficient of curvature (Cg = D302/D60∙D10) and the coefficient of uniformity (Cu = D60/D10) are 0.3 and 53, respectively. D10, D30 and D60 are the grain sizes corresponding to 10%, 30% and 60% finer, respectively, along the grain size curve. This means that the materials are well-graded sand-rich materials. According to the Unified Soil Classification System (USCS), the materials used are classified as CL: clay with low plasticity. It is well known that these materials are predominantly fine-grained soils, which are inorganic clays of low to medium plasticity, gravelly clays, and sandy and silty clays. The actual debris flow material contains a large amount of sands and gravels. However, in this study, we decided to conduct laboratory tests on in-situ soils containing fine-grained soils and some sands. This is because the debris flow mobility is greatly affected by the behavior of fine-grained soils. Natural water content was 14.1%. The dry density of soil is 1460 kg/m3. The specific gravity of the materials used is 2.6. The liquid limit and plastic limit are 27.8% and 19.8%, respectively. Thus, the plasticity index is equal to 8%. The cohesion and internal friction angle determined from the direct shear tests are 22 kPa and 39.4°, respectively. The permeability of the materials is 1.5 × 10–3 cm/s, which is a typical permeability for sand. Swedish fall cone tests (cone angle of 60° and weight of 60 g) were performed to measure the undrained shear strengths for different solid volumetric concentrations26. The undrained shear strength of soil is computed as K∙g∙m/P2. Here, K is fall cone coefficient (0.3), g is the gravity acceleration (9.81 m/s2), m is cone mass (g), and P is the cone penetration depth (mm).

Ring shear test: residual shear strength

A ring shear apparatus was developed for determining the residual shear strength27–29. Ring shear apparatuses are often used in landslide research because they allow unlimited shear deformation. Recently introduced ring shear apparatuses that offer a large ring shear cell and a high speed of rotation have made it possible to investigate the slope failure and post-failure behavior of landslides30–34. The ring shear device used in this work has a relatively large ring shear cell with an inner diameter of 110 mm and an outer diameter of 250 mm and a height of 75 mm. In the shear mode, the upper ring is fixed, and the lower ring is rotated. This makes it possible to study the ring shear characteristics of coarse-grained soils as well as fine-grained soils. In particular, a large cell can be used to observe changes inside a sample, such as changes in the shear zone35. The test program consists of sample preparation, saturation, consolidation, drainage control, and shearing. The soil samples were prepared by dry condition. It should be noted that it is difficult to collect weathered soils in an annular shape (i.e., ring shear cell) without soil disturbance. Thus, it is very important to reproduce the in-situ ground condition in the laboratory. A total of 4000 g of soil sample in a container of 2600 cm3 was placed in a ring shear cell. Five layers in a ring cell were created considering the in-situ density of debris flow outbreak areas. Each layer was tamped with a rubber hammer. For fully saturated soil condition, water was allowed to infiltrate the soil sample with a relatively low rate. The test was performed when the degree of saturation reached more than 95%, i.e., the ratio of increment of pore water pressure and normal stress greater than 0.9529. During testing, the normal stress, pore water pressure, displacement and torque were measured. For the landslide materials, normal stresses of 0, 50, 100, and 150 kPa were selected for shear velocities of 0.01, 0.1, 1, 10, and 100 mm/s, respectively. The shear velocity was kept constant until the residual shear state was reached. Drainage was achieved by controlling the upper and lower ring shear cells. Test was performed under undrained conditions by closing the drainage valve during shearing. A rough surface, e.g., with 32 and 72 blades in the inner and outer cells, respectively, was used to prevent slipping between the soil sample and the ring shear cell. Therefore, the normal stress- and shear velocity-dependent ring shear characteristics were examined. The detailed testing program is also described in Jeong et al.36.

Rheometric test: yield stress and viscosity

A vane geometry rheometer was used to examine the rheological properties of the debris flow materials. The rheometer (AntonPaar, RheolabQC with vane spindle) consists of a 500 cm3 container and vane spindle with a radius of 4 mm and a height of 40 mm. Ball-measuring or vane-geometry rheometers are often used for particles larger than 1 mm37,38. Therefore, a vane geometry rheometer is appropriate for debris flow materials. The soil samples were mixed with fresh water to the desired solid volumetric concentration and then put into containers. The vane penetrated into the soil sample in the container. The vane blade was set to shear 40 mm down from a fixed position of 50 mm over the bottom of the container. The shear rate-controlled mode was used to measure the shear characteristics, and the torque was measured automatically. The shear rate refers to the rate at which a soil sample is deformed against shear. The viscosity was measured with the shear rate to examine the shear thinning or shear thickening flow behavior. Based on the plot of shear stress and shear rate, Bingham yield strength and plastic viscosity were determined. The y-intercept and slope in the plot are the Bingham yield strength and plastic viscosity, respectively. The shear speed varied from 0.01 to 1200 min-1. The measurable shear stress and shear rate were 0.5–104 Pa and 10–2–4000 s-1, respectively. The water content was measured before and after the tests. In this study, it was assumed that the slip and temperature effects, particle settling, and edge effects during testing were negligible.

Debris flow simulation method

To analyze the 2011 Miryang debris flow, we utilized the fluid dynamics-based Deb2D numerical model developed by An et al.39. The debris flow model Deb2D was designed based on the Navier–Stokes equations, which interpret fluid flow through a hyperbolic conservation form of two-dimensional shallow water equations. In the program, the shallow water equations are discretized based on the finite volume method to ensure the stability of the hydrodynamic numerical method. A detailed definition and calculation method for discrete terms is explained by An et al.39. The processes of erosion, entrainment, and deposition (called the entrainment effect in this paper) that occur due to friction with the ground during a debris flow are designed to be simulated using an erosion parameter40. In this report, the terms residual shear strength and yield strength are determined from ring shear tests and rheological tests, respectively.

Results

Determination of residual shear strength

A series of ring shear tests were carried out. This research focused primarily on the shear stress characteristics of weathered soils depending on their normal stress and shear velocity. The movement rates of weathered soils are sensitive to changes in porosity41,42. The shear strength of soils during failure can be affected by the changes in normal stress and shear displacement35. In addition, drainage conditions are directly related to the movement stages of soil failure. Drained test conditions are suitable for studying slow-moving landslides, and undrained test conditions are suitable for studying fast-moving landslides. When slope conditions due to heavy rainfall reach a sufficiently wet state, undrained test conditions are judged to be reasonable. Figure 2 presents the results of ring shear tests. The shear stress measurements were performed for normal stresses ranging from 0 to 150 kPa and shear velocities ranging from 0.01 to 100 mm/s under undrained conditions. The shear stress is strongly affected by the given shear velocity and increases as the shear velocity increases. In most cases, there are peak and residual shear stresses for a given shear velocity, indicating a typical strain-softening behavior. The residual shear strength was determined from the last part that reached steady state in the shear stress-time plot. The shear stresses appear after a certain time at shear velocity less than 0.1 mm/s. This is due to the time delay in reading the torque. It is believed that there is no problem to determine the residual shear strength. Both the peak and residual shear stresses increase with increasing normal stress. Figure 3 shows how to determine the peak and residual shear stresses. The plot of the shear stress and shear displacement shows that the residual shear stress can be determined at the final stage of the test, with no further change in the shear stress (Fig. 3a). Under a relatively low shear velocity of 0.01 mm/s, the peak and residual shear stresses appear to depend on the normal stress (Fig. 3b). As the given normal stress and shear velocity decrease, the deviation of the shear stress also decreases. Both the peak and residual shear stresses gradually increase with increasing normal stress for a given shear velocity. The peak and residual shear stresses are sensitive to the change in shear velocity (Fig. 4). Similar ring shear tests were performed for the rainfall-induced Shiraishi landslide, Tokushima Prefecture, Japan43. The difference between the peak and residual shear stresses was found to be 9–12 kPa at a shear velocity of 0.01 mm/s for the applied normal stress; this different was much greater (57–68 kPa) at a shear velocity of 100 mm/s. According to previous studies29,30,44, the residual shear stress of sandy materials varies by up to 100 kPa. The change in shear stress in the residual state is relatively small compared to that in the failure state, particularly for shear velocities less than 10 mm/s. When the shear velocity is increased to 10 mm/s, the maximum increase in the peak stress reaches 99 kPa, and the residual shear stress is approximately 32 kPa. Except for the case in which the shear velocity is 100 mm/s, the differences in the peak and residual shear stresses are approximately 25 kPa and 9 kPa, respectively. The values obtained in the residual state consistently fall within a much smaller range than those obtained at the peak point. The apparent internal friction angle of the material at the residual shear stress varies from 3.5° to 24.5° for given shear velocities. Similar results were obtained from Wang et al.31. According to Tika and Hutchinson45, the residual friction angle are greatly influenced as function of clay fraction and plasticity index. In particular, the residual friction angle dramatically decreases when the clay fraction (< 2 μm) and plasticity index are approximately larger than 30%.Fig. 2 Ring shear tests: normal stress- and shear velocity-dependent shear stresses: NS is the normal stress (kPa), and V is the shear speed (mm/s).

Fig. 3 Peak and residual shear stress as a function of the normal stress from the ring shear tests.

Fig. 4 Measurement of shear stresses as a function of shear velocity: (a) peak shear stress and (b) residual shear stress.

The range of residual shear strength is relatively small for a given normal stress, except for the case with a shear velocity of 100 mm/s, which resulted in the greatest residual shear strength range. Interestingly, the shear stress continuously increases from the initial shear stress, which is at least twice as high as that of the previous normal stress of 10 mm/s, when the maximum normal stress is applied. This result may be due to the fragmentation effect of particles during shearing through rolling and particle interlocking with rapid shear rotation (Fig. 5). Changes in grain size distribution during ring shear tests can provide clear evidence of this (Fig. 5a). A large amount of fine particles, such as silty and clay-sized particles, may be produced, especially at the bottom of the ring shear box (Fig. 5b). Coarser particles move to the top of the ring shear box. Similar test results have been reported by numerous researchers23,29,32,33. It has been found that the peak and residual shear stresses are not significantly affected under low normal stress (e.g., less than 50 kPa) and shear velocity (e.g., 0.01 mm/s) conditions; thus, the peak and residual shear stresses can be used as a prediction metrics for the mobilization of slow-moving landslides, such as creep motion18. These results can be considered the shear strength characteristics at the initial time of landslide occurrence when the soil depth is generally shallow (e.g., generally less than 1 m) under weathered soil conditions in the Republic of Korea.Fig. 5 Grain size distribution before and after shearing.

Rheological properties of weathered soils

The rheological properties of soils are important to consider in the estimation of debris flow mobility. A vane rheometer (AntonPaar Series, RheolabQC) can be used to measure the yield strength and viscosity of non-Newtonian fluids with vane spindles. Figure 6 presents the test results obtained from the vane-rotated rheometric system for the weathered soils taken from the debris flow source area. To increase the accuracy of the results, each soil sample underwent three tests with different initial shear rates of 0.001, 0.01, and 0.1 s-1. The relationships between the shear stress and shear rate were plotted for a given solid volumetric concentration (cvs). cvs refers to the ratio of solid volume/the total volume (solid and water) of sample46. As debris flow materials behave as Bingham-like fluids (Fig. 6a, an existence of yield strength and plastic viscosity), the ideal plastic Bingham yield strength and plastic viscosity are determined for different water contents (or volumetric concentrations of the solid) with an easy and common way to measure the yield strength. The flow curve indicates that the material behaves as a typical shear thinning effect during flow; thus, the viscosity, which is equal to the shear stress/shear rate, decreases with increasing shear rate (Fig. 6b). As shown in Fig. 6b, the viscosity can decrease (i.e., shear thinning) or remain constant (i.e., ideally viscous) with increasing shear rate. The viscosity of Bingham-like materials tends to decrease up to a certain shear range and then become constant. Eight soil samples were tested with the desired liquidity index, which is often used to describe the moisture condition of soil consistency47, of 1.9–7.1, corresponding to a solid volumetric concentration of 33%–52% (Fig. 6c). Similar flow behaviors were observed in most of the test results, but it was confirmed that the inflection point gradually decreases as the water content increases. The yield strength varies from 63 to 2200 Pa, and the plastic viscosity varies from 0.8 to 6.2 Pa∙s. The largest value is similar to the value at the liquid limit, which is the water content where the solid starts to act as a liquid48. The viscosity before yielding in the biviscosity rheological model49,50 seems to disappear as the water content increases (Fig. 6d). These results make it easier to determine the ideal Bingham yield strength and viscosity.Fig. 6 Rheological characteristics of landslide materials with different solid volumetric concentrations ranging from 33 to 52%: (a) flow curve of cvs = 39.5%, (b) viscosity–shear rate relationship, (c) shear stress–shear rate relationships for all materials, and (d) viscosity–shear rate relationships for all materials. The y-intercept value is the Bingham yield strength and the slope is the plastic viscosity in the inserted figure. To determine the yield strength and plastic viscosity, the linear section of shear stress and shear rate plot was considered.

The test results can be expressed as a correlation between the rheological properties and the solid volumetric concentration (Fig. 7). In general, the yield strength increases with decreasing water content or increasing solid volumetric concentration. There is a clear linear relationship between the yield strength (τy) and plastic viscosity (ηh) for debris flow materials, i.e., ηh = 0.003 τy + 0.8. A similar relationship was reported by Locat51. Therefore τy/ηh = 1 can be set for debris flow materials. Here, τy is in kPa, ηh is in Pa∙s, respectively. This equation can take into account the grain size effect by increasing the plastic viscosity term52. Both rheological properties are correlated with the solid volumetric concentration (cvs) and show similar behavior for a given concentration, with similar ranges of inflection points. When the solid volumetric concentration (cvs) is greater than 44%, the yield strength increases significantly, and when the solid volumetric concentration (cvs) is less than 44%, the yield strength decreases dramatically and tends to disappear completely. This inflection point is considered the point (i.e., 44%) at which the landslide materials are completely fluidized and converted into fluidized debris flows. For a solid volumetric concentration of 44%, the yield strength is approximately 300–500 Pa, and the plastic viscosity is 1.5 Pa∙s. As a result, the shear strength in the residual state has a range of 2–10 kPa (ring shear test), the shear strength in the liquid limit state has a value of approximately 2 kPa (Atterberg limits test), and the fully fluidized flow has a range of 0.3–0.5 kPa (rheological test), which can be generated by the change in the solid volumetric concentration. The lowest value is estimated to be critical limit at which bonding force between particles is broken. Based on these test results, a numerical analysis of the debris flow was performed by dividing the event into the onset of soil failure, the transition from solid to liquid, and occurrence of high fluidization.Fig. 7 Rheological properties (yield strength and viscosity) obtained with different solid volumetric concentrations: (a) yield stress and viscosity, (b) cvs and yield strength, and (c) cvs and viscosity.

Debris flow simulation results

In the 2011 Miryang debris flow, there were a total of four outbreak areas (F1–F4), and the outbreak areas mainly transitioned into two main flow channels (P1 and P2 in Fig. 8). The debris flow sources were considered to have initiated at the same time and have influenced the two flow channels. The simulation results for each case considered, dependent on the rheological parameters, i.e., yield strength and viscosity only, are shown in Fig. 8. Four cases were considered: Case 1, the shear strength taken as the value at the residual state (10 kPa); Case 2, the shear strength taken at the fully remolded state (the liquid limit state, 2 kPa); Case 3, the shear strength taken at the transition from solid to liquid (0.5 kPa), which is resulted from the rheological tests; and Case 4, the shear strength taken at the fluidization state (0.1 kPa), which is the lowest yield strength of debris flow materials. For the shear strength smaller than this, it behaves like a flash flood. In Case 3, the flow state was characterized by a solid volumetric concentration of 44% of the debris flow material (Fig. 7). In the debris flow simulation, the mass density of the debris flows was uniformly set at 2000 kg/m3, referencing debris flow events in the Republic of Korea53–55. The input parameters for the cases considered were based on the range of shear strengths determined by laboratory testing, e.g., 10 kPa, 2 kPa, 0.5 kPa, and 0.1 kPa. The viscosities were determined from the relationship between the yield stress and plastic viscosity, τy/ηh = 1, as proposed by Locat51 and Jeong et al.52.Fig. 8 Simulation results for the maximum flow height of the Miryang debris flow event according to each parameter case considering the shear strength obtained from the residual, liquid limit, solid‒liquid transition, and fully liquefied states.

The flow behavior is strongly influenced by the rheological parameters; in general, a low yield strength and viscosity result in a high flow mobility (i.e., long travel distance and high speed). However, when a low yield strength is applied, debris flow materials sometimes deviate from the main flow path. In particular, for the lowest yield strength (i.e., 0.5–0.1 kPa), the flow behavior closely resembles that of pure water rather than a debris flow, allowing it to surmount topographical obstacles easily (Fig. 8c,d). In Cases 1 to 3, the debris flow cannot reach the actual runout distance. Since erosion, entrainment, and deposition can increase the initial volume of a debris flow by 10–50 times and significantly influence its flow momentum, it is essential to consider these processes in debris flow simulations9,56,57. Figure 8 focuses on the effect of rheological parameters without incorporating erosion, entrainment, and deposition processes, which explains why all the cases fail to simulate the runout distance. This study employed the erosion–entrainment–deposition algorithm presented by Lee et al.40 to simulate the debris flow more realistically. The governing equations and input parameters for the erosion–entrainment–deposition process are summarized in Table 1. The entrainment effect also affects the flow distance, height and velocity. Figure 9 presents the simulation results with and without the entrainment effect. As expected, when the entrainment effect is accounted for, a much greater mobility is expected than when the entrainment effect is not considered. In the case of main flow P1, the debris flow runout distance is smaller than that in the case of main flow P2. Notably, we divided the debris flows into two main flow types, F2–P2 and F3–P2 (Fig. 10), with respect to the maximum flow heights and velocities. Two main starting points (F2 and F3) appear to affect the main flow channel P2. However, there was a large difference of approximately 4 times the flow height and approximately 3 times the flow velocity after confluence. When estimating debris flow hazards, selecting a constant yield strength may lead to inaccurate simulation results. To compensate for these shortcomings, the reduction in yield strength with the entrainment effect along the flow path should be considered.Table 1 Governing equations of the Bingham law and entrainment effect in the debris flow model.

Navier‒Stokes equations and Bingham law	Entrainment effect	
ht+hux+hvy=ehut+hu2+gh2gh222x+huvy=Sgx-Sfxhvt+huvx+hv2+gh2gh222y=Sgy-Sfy

Sfx=3ρ12τy+ηhuh,Sfy=3ρ12τy+ηhvh

	e(x,y,t)=dzdteif)τ>τe-dzdtdelse if)τ<τd

hmaxx,y,0=dzdττ-τe=dzdτρghs-τeif)τdf>τe0else

	
Note: t = time; x and y = Cartesian coordinates; h = depth of the debris flow mixture; u and v = depth-averaged velocity components in the x and y directions, respectively; g = acceleration of gravity; e = entrainment (e > 0) or deposition rate (e < 0); Sgx and Sgy = gravitational acceleration in the x and y directions; Sfx and Sfy = driving friction in the x and y directions, respectively; ρ = mass density; τy = yield strength; ηh = viscosity; dz/dte = erosion-entrainment rate (m/s); dz/dtd = deposition rate (m/s); hmax(x,y,0) = maximum potential erosion depth; τ = shear stress; τe and τd = critical shear stress of erosion and deposition (kPa); dz/dτ = average potential erosion depth (m/kPa); and s = channel slope. For simulating the debris flow with entrainment, τy = 1 kPa, ηh = 5 Pa∙s, dz/dte = 0.03, dz/dtd = 0.01, dz/dτ = 0.1, τe = 1 kPa and τd = 0.5 kPa.

Fig. 9 Simulation results for the maximum flow height of the Miryang debris flow: (a) without the entrainment effect and (b) with the entrainment effect.

Fig. 10 Flow height and velocity profiles of the Miryang debris flow: (a, c) F2–P2 and (b, d) F3–P2.

Discussion

Landslides can be classified into a wide range of mass movement types, such as slides, slumps, spreads, topples, and flows1,3,4. Among these movement types, debris flows are among the fastest. In weathered soil deposits, the transition from slide to flow may occur due to the degradation of the weakly bonded matrix. Figure 11 illustrates a typical mass movement process from sliding to fluidizing via remolding (Fig. 11a). The change in the mobilized shear strength of weathered soils may be significant when dividing the failure and post-failure stages at the end of slumping or sliding. In these stages, the strength is referred to as the residual shear strength, remolded strength, or yield strength (Fig. 11b). At the onset of failure, the strongly connected particles exhibit robust flocculation during structural bond breakage, but they may break into the many pieces of a subflocculation system through particle rearrangement, including rolling, interlocking and fragmentation58. The development of the shear zone during shearing indicates a reduction in grain size and a decrease in porosity. When water flows into such a shear zone, new fluidization can occur59. In the residual state of the slide plane, the infiltrated water may fill in between loose soil particles, thereby weakening the strength and accelerating the movement of the failed mass (Fig. 11c). Depending on the grain sizes of the natural slope, the slip surface seems to form as a jagged or arc-shaped shear zone. Mechanically, the increase in pore water pressure during shearing directly leads to changes in plastic shear strains and soil structures60,61. As previously mentioned, the strength of intact soil is always greater than that of remolded soil because intact soil has not yet experienced bond breakage. Thus, it is necessary to discuss how such a rapid change in the shear strength occurs. With respect to landslide events, more rapid and larger deformations can be triggered by a reduction in shear strength and an increase in water content. In shallow landslide-prone areas, the vertical stress is almost constant, but the pore water pressure increases (or the effective stress decreases), and the shear strength gradually decreases after experiencing strong resistance along the slip surface as shear deformation progresses (Fig. 3). The shear strength at this time can be regarded as the residual shear strength. The residual state is a state in which a landslide can occur with the minimum shear strength (Fig. 11d). If the method of determining residual shear strength is applied to the rheological concept, the residual shear strength may depend on the water content. In other words, the correlation between the shear stress and shear rate, that is, the flow curve, can be determined through the variation in water content under conditions where a landslide can occur. In the flow curve, the y-intercept is the yield strength, and the slope is the plastic viscosity (Fig. 11e). In addition, the change in viscosity can be determined by considering the solid volumetric concentration or water content (Fig. 11f).Fig. 11 Landslide transition from slide to flow: (a) landslide with failure and post-failure from the sliding stage through the remolding stage to the fluidization stage; (b) shear strength development from residual to remolded to yield strength; (c) strength loss and fluid particles in the shear plane during sliding; (d) determination of residual shear strength; (e) yield strength with viscosity; and (f) viscosity with as a function of solid volumetric concentration (cvs). H is the height, L is the length, sf is the slide plane and failure process, cvs is the volumetric solid concentration, and τr is the residual shear strength.

In simulating the post-failure phenomenon, the rheological strength is used as the input parameter. Rheologically, it is difficult to explain the initial strength of a landslide and the mobilized strength that causes the debris flow. Imran et al.19 indicated that debris flow mobility is strongly dependent on changes in yield strength and plastic viscosity. However, this approach does not provide information on the input parameters for simulating debris flows via numerical analysis. In most cases, arbitrary values or values measured from rheological approaches are selected. Many well-known debris flow models perform numerical simulations by treating parameters as constants under specific conditions. Representative rheological models include the Bingham, Herschel–Bulkley, power law, and Voellmy functions. Among the rheological parameters in these models, uncertainties in the input parameters may lead to significant errors in debris flow assessment. Although the simplistic debris flow approach may not accurately represent the complex behavior of debris flows, some flow models remain popular because of their simplicity and efficiency. Considering these points, this study proposes a method for determining the yield strength of a debris flow. First, it is recommended to determine the yield strength for the major (or representative) grain sizes that drive the debris flow behavior. Therefore, one method is to divide the behavior of the debris flow into fine-grained soil and coarse-grained soil. The probability of debris flow in both groups may be high because mobility is dependent on the wetting, shearing and fragmentation processes during the flow. In addition, the shear rate should consider field conditions with varying movement rates when considering the one-point method. The second method is to find the critical point of change from the solid state to the liquid state. In geotechnical engineering, when the liquidity index is equal to unity, that is, at the liquid limit (called Atterberg limits), a phase transition occurs. In fact, this phase transition has a range of 1.5–1.8 kPa for clayey soils when using a fall cone apparatus26. A phase transition occurs at approximately 2 kPa for fully remolded soils, which appear to gradually fluidize as the water content increases. This value is smaller than the residual shear strength of the reconstituted weathered soil ranges from 5 to 10 kPa. In practice, this value corresponds to the maximum shear strength applicable in commercial test equipment. In the third method, the gradual reduction in shear strength, such as a decay function, can be considered at the minimum shear strength obtained in the field; for example, the intact and remolded shear strengths measured manually in vane shear tests can be used as an initial value of landslide movement.

Conclusions

Debris flows sometimes cause unpredictable disasters because they occur suddenly and without warning. Therefore, first-order predictions methods and remedial measures for debris flows should be developed. In this case, the determination of strength parameters is a valuable tool for estimating debris flow hazards and developing effective mitigation strategies. However, there is no effective method for selecting or determining the input parameters. The present study focused on determining the yield strength with respect to the strength evolution during debris flow motion. Ring shear tests and rheological tests were performed to determine the shear strength of debris flow materials. The determination of shear strengths (i.e., the residual shear strength and yield strength) and understanding of the strength evolution process of weathered soils may be applied to create a preliminary debris flow hazard map. From the perspective of the strength evolution, the shear strength can change from the residual state through the remolded state to the fluidization stage. The strength determined at each stage gradually decreases due to mixing with the ambient water and entrainment of the soils along the flow path. The analysis of the applicability of a two-dimensional model indicated that the residual shear strength and yield strength can be considered the shear strengths at the initiation and flow stages of a debris flow. In most debris flow models, the rheological properties, e.g., yield stress and plastic viscosity, are treated as constant values. As a way to compensate for this limitation, the most widely used approach is to consider the effect of sediment entrainment, even though sediment entrainment is strongly dependent on the grain size distribution, pore water pressure, and depth of erodible bed along the debris flow path. Additional related research on the mechanics of yield strength reduction should be conducted.

Acknowledgements

This study was supported by the KIGAM research project (24-3412-1). The authors appreciate the valuable comments made by the editor and reviewers to make a substantial improvements to this manuscript.

Author contributions

S.W.J. wrote the main manuscript text; S.W.J. tested and analyzed the laboratory data; H.J.O. analyzed the debris flow events, geologic characteristics, and precipitation data; and S.L. and M.K. performed and analyzed the debris flow simulations. All the authors participated in the interpretation of the results and have read and commented on the manuscript.

Data availability

The datasets used and analyzed during the current study are available from the corresponding author upon reasonable request only.

Competing interests

The authors declare no competing interests.

Publisher's note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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