Effects of gradation on sandy debris flow behavior

Abstract

A debris flow, a complex fluid situated between hyperconcentrated flows and granular flows, is recognized as a special natural hazard due to a combination of factors. In addition to parameters such as water content, solid volume concentration, particle shape, and mineral composition, the role of gradation (grain size distribution) on debris flow behavior warrants significant attention, yet it is often underemphasized. In this study, a modified material with discontinuous gradation was prepared by removing the sand (2–0.0625 mm) from Dongyuege debris flow sediments with gradation continuity. The effect of gradation continuity on debris flow behavior was investigated by conducting comparative tests with natural Dongyuege debris flow material. The experimental results indicate that sediments with grading discontinuities are more prone to initiate debris flows. The continuity of the gradation weakens the effect of the solid volume concentration in the slurry on its rheology and mobility. Additionally, debris flow slurries with discontinuous gradations have lower hydraulic conductivity than slurries with continuous gradations, which further inhibits the formation and dissipation of excess water pressure.

Introduction

Debris flows are fluids generated through the thorough mixing of water and solid particles of various sizes. The key factors influencing its behavior include water content, solid volume concentration, clast size and shape, mineral composition, and particle size distribution^1,2,3,4. As a result of these diverse contributing factors, debris flows are considered highly complex fluids^5,6,7,8.

Water plays a crucial role in initiating and transporting debris flows, as it provides stable flow conditions for the solid materials within the flow⁹. The water content also determines the competence of debris flows¹⁰. According to Zhou et al.¹¹ water content significantly influences the degree of liquefaction and energy dissipation in debris flows. The importance of water in debris flows is well established and recognized by numerous studies^12,13,14,15. Debris flows typically contain a substantial volume of solid material. Coussot and Meunier⁵ introduced the solid volume fraction as a key parameter to distinguish debris flows from other flow types and mass movements. A positive correlation exists between the solid volume concentration and the density of debris flows^16,17,18. The solid volume concentration in debris flows is markedly greater than that in floods and hyperconcentrated flows, leading to increased momentum and greater destructive potential. Moreover, the solid volume concentration significantly affects the yield stress and runout of debris flows^19,20,21,22. Extensive research has investigated the relationships between debris flow behavior and sediment characteristics^23,24,25. Interactions between particles in a debris flow can lead to changes in the shape of the particles, which in turn affects the flow behavior of the debris flow²⁶. Woźniak and Pisarska-Jamroży²⁷ reported that the erosive and internal erosion processes of debris flows contribute to the distinctive clast morphology of debris flow sediments in southern Poland. Similarly, Zhou et al.²⁸ conducted flume experiments with two different scales of debris flow sediments and reported that remolded debris flow slurries exhibited varied deposit morphologies. In natural debris flows, silt and clay particles, with diameters smaller than 0.0625 mm²⁹, are typically classified as mineral clasts. The role of these mineral clasts in debris flow behavior has been extensively recognized in the literature^30,31,32,33.

The above factors affecting debris flow behavior have been widely noted. Additionally, the close relationship between gradation (i.e. particle size distribution) and debris flow behavior is equally important. Commonly, wide grading^34,35 and poor sorting^1,36 describe the gradation characteristics of natural debris flow sediments. The variations in gradation can facilitate the transition of debris flow slurries between hyperconcentrated flows and granular flows³⁷. Hyperconcentrated flows look more like streams, and coarse particles cannot be suspended in them, which is one of the main differences between them and debris flows. Furthermore, the variations in gradation can influence the physical properties and rheological behavior of the slurry⁶. Debris flows with differing gradations exhibit varying levels of transport energy³⁸. In studies of natural debris flows, the gradation of debris flow sediments is commonly emphasized and reported. Li et al.³⁹ conducted flume tests with discontinuously graded sediments, and the results revealed that discontinuous grading weakened the entrainment capacity of debris flows. Roelofs et al.⁴⁰ prepared several sets of discontinuously graded sediments to study their effect on channel bed erosion mechanisms, and the results revealed significant differences in the outcomes caused by materials with different gravel and sand contents. Both entrainment and erosion lead to changes in the gradation of debris flows. Pastorello et al.⁴¹ investigated the soil matrix in three active debris flow regions and reported significant differences in gradation continuity, which resulted in different triggering mechanisms for debris flows in each of the three regions. Generally, discontinuous gradation refers to the absence or high content of particles within certain specific size ranges. Guo et al.⁴² conducted field studies on the slopes of debris flow gullies prone to continuous instability, where the soil on the slopes was almost free of clay and contained very few fine particles. Tian et al.⁴³ found that the two-level differentiation of fine particle content within the same region led to different debris flow behaviors. These studies focused on the effects of discontinuously graded debris flows on the external environment. However, few studies have focusing on how changes in the gradational continuity of debris flows affect their own physical properties and behavior. Our study can provide some references.

The debris flow sediments in Dongyuege, Nujiang Prefecture, Yunnan Province, China, exhibit a distinct continuity in terms of gradation. To examine the effect of grading continuity on debris flow behavior, four sets of experimental samples with varying maximum particle diameters (d_max = 5, 10, 20, and 30 mm) were prepared, including continuous and discontinuous gradations. Each set was remolded into debris flow slurries with different solid volume concentrations (C_v). Using a combination of slurrying tests, rheological tests, propagation tests, and excess water pressure monitoring, this study systematically assessed the impact of grading continuity on debris flow behavior.

Materials

Study site

The Dongyuege Gully (DYG, 27°38′9.20″N, 98°43′52.86″E) is located in Gongshan County, Nujiang Prefecture, Yunnan Province, where the peak rainfall occurs between June and August, with maximum precipitation ranging from 245.7 to 382.7 mm (source: China National Meteorological Data Center). This region is one of the most vulnerable areas to debris flow disasters in Southwest China. On August 18, 2010, a catastrophic debris flow occurred in DYG, causing enormous damage. Table 1 shows the main characteristics of the DYG gully area.

Table 1 Summarizes the main characteristics of the DYG gully area.

Figure 1 depicts the geographical location of Dongyuege Gully, accompanied by satellite imagery of the entire watershed and localized close-up photographs. The slopes on both sides of the Dongyuege Gully watershed are steep, and the cross-section of the main gully displays a typical “V” shape (Fig. 1a). The watershed features numerous gullies with abundant loose debris deposits, many of which are perpetually covered with snow. This extensive catchment area provides ample water and sediment sources for debris flow activity, while the steep topography provides significant gravitational energy for the initiation of such flows.

Fig. 1

The location of the study area is marked with a red dot. (a) Satellite image (Google Earth Pro version 7.3.6 https://www.google.com/earth) of the DYG Gully watershed, with red lines indicating the water divide. (b) A photograph taken by investigators within the gully, clearly showing the steep slopes on both sides (taken by Lin Tian). (c) A boulder transported by the debris flow during the August 18 event (taken by Lin Tian).

Debris material

The DYG debris flow is representative of a typical sand-matrix debris flow. The clasts are primarily composed of granite, schist, gneiss, marble, and quartzite, with most coarse debris exhibiting an equiaxed shape. Fine particles smaller than 0.005 mm, predominantly consisting of clay minerals, are primarily composed of quartz (approximately 40%), mica (approximately 30%), and plagioclase (approximately 15%).

Samples of the DYG debris flow sediments were collected from 2015 to 2019, with a focus on particles smaller than 100 mm. Approximately 20 tons of these samples were stored in the laboratory without external interference following deposition, ensuring that they accurately represented the natural debris flow sediments. Considering the size effect and the existing experimental conditions. This study employed the wet sieving method to classify the sediments into eleven particle size ranges²⁹. These include 30–20 mm, 20–16 mm, 16–10 mm, 10–5 mm, 5–2 mm, 2–1 mm, 1–0.5 mm, 0.5–0.25 mm, 0.25–0.125 mm, 0.125–0.0625 mm, and < 0.0625 mm (Fig. 2a). Particles smaller than 0.0625 mm were further analyzed via a Beckman LS3320 laser particle sizer, resulting in a final grain size distribution for the DYG debris flow sediments (Fig. 2b).

Using the sieved sediment materials, four pairs of sediment samples were prepared with varying maximum particle sizes (d_max = 5, 10, 20, and 30 mm). Each pair consists of a natural sample (Crude Debris, CD) and a modified sample (Modified Debris, MD). CD represents continuously graded (well-graded) natural debris flow sediments. On the basis of our existing survey data and another ongoing study, the sand fraction (2–0.0625 mm) in the CD samples was removed to form the MD samples. The grading curves for the MD samples are shown in Fig. 2c. Compared with the CD samples, the MD samples exhibit a very distinct discontinuity in gradation.

Figure 2d shows the proportion of each particle group relative to the total mass and highlights the differences in gradation among these eight samples. In the absence of sand particles, there was an increase in the proportions of the other fractions in the MD samples. Nevertheless, the relative proportions of the particle groups remained unchanged in both the MD and CD samples. In this study, continuously graded samples (CD) were considered the control group, whereas discontinuously graded samples (MD) served as the experimental group.

Fig. 2

(a) Natural debris flow sediment samples with a maximum grain size of less than 100 mm collected from DYG gully. This figure accurately presents gradations of the CD samples with d_max = 5, 10, 20, and 30 mm. (b–c) Grain size distributions of the CD and MD samples. In contrast, the MD sample is discontinuous. (d) shows the percentage of each particle group relative to the total mass in different samples, visually reflecting the variation in content for each particle group.

Method

The influence of grading continuity on the behavior of debris flows was investigated through slurrying test, propagation test, rheological test, and excess water pressure test. To ensure the reproducibility and comparability of the results, consistent operational procedures and equipment were maintained for each pair of samples throughout the experiments. Given the considerable range of the maximum particle size (d_max) of the debris material, different sizes of equipment were employed in the experiments.

Slurrying test

Debris flows are specialized fluids that exist between granular flows and hyperconcentrated flows. They are typically distinguished by solid volume concentrations, C_v, which represents the percentage of solid materials in the mixture. Equation (1) is used to calculate the C_v of the mixture:

$$\begin{array}{*{20}{c}} {{C_v}~=~\frac{{{\rho _b} - {\rho _w}}}{{{\rho _s} - {\rho _w}}}} \end{array}$$

(1)

where ρ_b is the bulk density (g/cm³), ρ_w is the density of water (approximately 1 g/cm³), and ρ_s is the solid density (grain density) (g/cm³). The bulk density (ρ_b) is the controlling factor that determines C_v.

Cd v represents the upper limit of the solid volume concentration (C_v) of debris flows (i.e., the boundary between granular flows and debris flows)³⁷. When C_v exceeds Cd v, the debris–water mixture tends not to flow, a state referred to as granular flow. Conversely, Ch v represents the lower limit of the solid volume concentration (C_v) of debris flows (i.e., the boundary between debris flows and hyperconcentrated flows)^44,45. When C_v falls below Ch v, the coarse particles in the debris–water mixture settle, and the finer particles are carried away by the water. This state is referred to as hyperconcentrated flows. To visually express the slurrying potential of the sediment, the range of C_v during slurrying (i.e., the difference between Cd v and Ch v) is defined as the “slurrying index (I_d)”. A higher I_d indicates a greater slurrying potential, whereas a lower I_d indicates a reduced potential.

The slurrying experiment was conducted on a rigid inclined plane measuring 2.4 m in length and 1.2 m in width. This apparatus is referred to as a simplified tilting rheometer¹⁶, as illustrated in Fig. 3. The slope was set to 5°, which approximates the average slope of the DYG gully. Two sizes of thin-walled cylinders, hereafter referred to as “cylinders”, were employed in the experiment. A cylinder with a diameter of 10 cm and a height of 3.8 cm was used for samples with maximum particle sizes of 5 mm and 10 mm (Fig. 3b’, right). The maximum capacity of this cylinder on the inclined plane is approximately 265 cm³. A cylinder with a diameter of 20 cm and a height of 7.6 cm is also used for samples with maximum particle diameters of 20 mm and 30 mm (Fig. 3b’, left). The maximum capacity is approximately 2125 cm³. The thoroughly mixed debris‒water mixture was poured into the cylinder placed on the inclined surface, and the cylinder was then quickly lifted vertically to allow the mixture to propagate down the inclined plane.

Fig. 3

Process of determining the upper and lower slurrying limits for each sample via a simplified tilting plane rheometer. (a) A specific amount of water is used to fully saturate the dry debris, which is then stirred to create a slurry with the target solid volume concentration (C_v). (b) Schematic diagram of the slurrying test setup showing the slurry being poured into a cylinder and lifted at a uniform speed. (b’) A photograph of the cylinders used in the experiment is included. (c) This diagram illustrates the whole process of determining the upper and lower limits of slurrying using a CD-5 mm sample as an example. When the debris–water mixture no longer behaves as a solid, it is designated Cd v (c-3); when the solid and water mixtures no longer inextricably, it is designated Ch v (c-III).

The purpose of the slurrying experiments was to (a) confirm whether slurrying is possible for MD samples with discontinuous gradation. If so, to further determine the upper and lower limits of the solid volume concentration of the MD samples as slurries. (b) Upper and lower limits of the solid volume concentration of natural debris flow materials as slurrying. The slurrying test is a prerequisite for the subsequent experiments. In other words, if the sample cannot be remolded into a slurry, the subsequent tests cannot be conducted.

Propagation test

After the slurrying index (I_d) for each sample was determined, the flow capability of the remolded debris flows was visually demonstrated by treating each sample with different gradations as an experimental unit (a total of 8 units). For each experimental unit, the first sample was set at Cd v, and subsequent samples were remolded at intervals of ΔC_v = 0.01, with the final sample corresponding to Ch v. These samples were then subjected to propagation test.

The instruments used for the propagation experiments were the same as those employed in the slurry preparation experiments (Fig. 3b). These propagation experiments visually illustrate the impact of gradation continuity on the mobility of debris flow slurries with varying maximum particle sizes. The general steps for the propagation experiments are as follows:

• a. Mix a fixed mass of sediment with the required amount of water to achieve the corresponding C_v for 10 min. Then, the slurry is filled into a cylinder placed on the inclined plane, ensuring that it is filled to the standard level. For slurries with maximum particle sizes of 5 mm and 10 mm, a small cylinder (shoFig.  Fig. 3b’, right) with a capacity of approximately 265 cm³ is used. For slurries with maximum particle sizes of 20 mm and 30 mm, a larger cylinder (shoFig.  Fig. 3b’, left) with a capacity of approximately 2125 cm³ is utilized.

• b. Rapidly lift the cylinder while starting the timer, allowing the slurry to lose lateral constraints and diffuse to form a deposit on the inclined plane surface.

• c. Propagation tests were conducted on remolded samples with C_v = Cd v-0.1 via the same method, and the start time was recorded until C_v = Ch v.

• d. The clean water that escaped from each sample within 120 min of release was collected and weighed. Simultaneously, orthophotos of the deposit were taken via a high-definition digital camera. The completion of this step marks the end of the test and the sample is recovered.

This process ensures the comparability of all experimental units and clearly demonstrates the impact of gradation continuity on the spreading behavior of the slurry.

Rheometric test

Rheology experiments aim to evaluate the rheological properties of different slurries, with a primary focus on yield stress and viscosity^46,47. This experiment facilitates the exploration of the influence of gradation continuity on the yield stress and viscosity of debris flow slurries.

Given that the maximum particle sizes of the slurries involved in this study are 5 mm, 10 mm, 20 mm, and 30 mm, two different rheometers were employed to ensure suitability for the respective slurries. An Anton Paar MCR 52 rotational rheometer is used for slurries with maximum particle sizes of 5 mm and 10 mm (Fig. 4A). This instrument is equipped with a spherical measuring system and a sample container that can accommodate approximately 500 cm³ of slurry. A small ball rotates around the central axis at a set speed, and the shear rate and stress can be calculated from the speed and torque, which gives the yield stress and viscosity of the slurry.

For slurries with maximum particle sizes of 20 mm and 30 mm, a large two-point rheometer was utilized (Fig. 4B). The measurement system uses a two-point “H”-type paddle configuration and is capable of holding approximately 20.1 L of slurry. By monitoring the rotational speed and torque, the relationship between the shear rate and shear stress can be established. The Bingham model and the Herschel–Bulkley model are common rheological models, each with its own advantages and applicability^48,49. Based on the nearly linear relationship between shear stress and shear rate for all experimental samples, the Bingham’s model was used to fit the results. The yield stress and viscosity coefficient of the measured slurries were obtained. The formula is as follows:

$$\begin{array}{*{20}{c}} {\tau ={\tau _0}+\eta \cdot \gamma } \end{array}$$

(2)

where τ is the shear stress, τ₀​ is the yield stress, η is the viscosity coefficient, and γ is the shear rate.

Fig. 4

The rheometers used in the experiments. (A) The Anton Paar MCR 52 advanced rotational rheometer, which is suitable for slurries with d_max ≤ 10 mm: (a) Exterior view of the rheometer; (a’) dimensions of the measuring system; (a’’) the close-up photograph of the slurry being tested. (B) The especially designed large-scale ‘H’ paddle rheometer, which is suitable for slurries with d_max ≤ 30 mm: (b)The main part of the large rheometer, the data acquisition unit and the control unit are not displayed; (b’) dimensions of the container and the “H”-type paddle; (b’’) close-up photograph of the slurry being tested.

For each experimental sample, the first monitored slurry had a C_v of Cd v. Then, a remodeled sample with C_v = Cd v-0.1 was used as the second monitored sample until the last sample with C_v = Ch v was monitored to complete the experiment. In the end, 70 sets of experimental results were obtained. To ensure the reproducibility of the test results and the consistency of the results, each sample was tested twice.

Measurement of excess water pressure

Monitoring the excess water pressure of the slurry enhances the understanding of the influence of continuous grading on the mobility of debris flows. The testing containers for slurries with upper particle diameters of 5 mm and 10 mm differed from those used for slurries with upper diameters of 20 mm and 30 mm (Fig. 5). The piezometer is made of a hollow acrylic tube, with scales marked on the surface and a gauze-screened bottom end (inlet). Its inner diameter is 5 mm, with lengths of 20 mm and 30 mm, respectively. For each sample with varying gradations, three slurries of different C_v values were monitored within the slurrying potential.

Fig. 5

Two experimental setups that are structurally and materially identical but differ in size. A device with a diameter of 10 cm and a height of 13.5 cm is used for slurries with d_max = 5 mm and 10 mm. A device with a diameter of 18 cm and a height of 26.5 cm is used for slurries with d_max = 20 mm and 30 mm. h_s0, h_e0, and h_p represent the hydrostatic pressure (the depth at which the pressure sensor is embedded), the excess water pressure (0.6 times the hydrostatic pressure), and the height of the liquid column in the pressure sensor, respectively.

The method for monitoring excess water pressure is based on the methods of Pierson³⁶, Zhou et al.⁵⁰, and Tang et al.⁵¹, with appropriate modifications. The specific operational steps are as follows:

• a. The pre-prepared debris‒water mixture is saturated for 24 h, followed by thorough stirring for 10 min to reshape it into a debris flow slFig. (Fig. 3a).

• b. The reshaped slurry is then poured into a pre-prepared container, and the volume concentration, volume, density, and water content of the slurry are recorded.

• c. A piezometer is inserted vertically into the center of the slurry surface, with an embedment depth of 6 cm (or 12 cm), to serve as the initial hydrostatic pressure head (h_s0). Rhodamine B solution is then injected into the piezometer to a height (h_p) equal to 1.6 times the embedment depth (h_s).

• d. Once the above steps have been completed, a timer is started, and the liquid column height (h_p) and hydrostatic head (h_s) are recorded every 5 min. Once the excess water pressure reached its peak (indicated by the change in liquid column height from rising to falling), the liquid column height and hydrostatic pressure head were recorded every 10 min. During each recording, a pipette was used to extract the decant water⁵² from the slurry surface, and the cumulative decant water mass was measured and recoFig. (Fig. 5).

The monitoring duration for slurries with upper particle diameters of 5 mm and 10 mm is 600 min, whereas for slurries with upper particle diameters of 20 mm and 30 mm, the monitoring time is 750 min.

Equation (3) is used to calculate the relative excess water pressure, expressed as follows:

$$\begin{array}{*{20}{c}} {R~=~\frac{{{h_p} - {h_s}}}{{{h_s}}}~} \end{array}$$

(3)

where R represents the relative excess water pressure, h_p is the height of the liquid column in the piezometer, and h_s is the embedment depth of the piezometer. Using this calculation, a curve of R-T (time) can be plotted to analyze the trend of the excess water pressure over time.

In this work, three different slurry samples with varying C_v values were tested for each gradation. These slurries correspond to C_v1 = 0.75Cd v + 0.25Ch v(i.e., Cd v-0.25I_d), C_v2 = 0. 5Cd v + 0.5Ch v (i.e., Cd v-0. 5I_d), and C_v3 = 0. 25Cd v + 0.75Ch v (i.e., Cd v-0. 75I_d).

Results

The natural sediments of DYG and those with sand removed were remolded, and a series of experiments were carried out on the remolded slurry. The operational procedures for all samples in each experiment were kept identical to ensure comparability. Overall, the experimental results aligned with our expectations, demonstrating that gradation continuity plays a crucial role in debris flows characterized by a sandy matrix.

Slurrying potential

The slurrying test determined the upper and lower limits of slurrying (Cd v and Ch v​), as well as the slurrying index (I_d​), for the eight different gradations of DYG debris flow materials. Figure 6 shows the variation in the slurrying potential for these eight materials.

Fig. 6

The slurrying potential and slurrying index for the eight remolded materials. Rectangles with the same background color indicate that the remolded slurry has the same upper particle size limit. The legends with black grid lines represent samples with continuous gradation, whereas those without grid lines represent samples with discontinuous gradation. Above each legend, the upper limit of slurrying (Cd v) is marked, and below it, the lower limit of slurrying (Ch v) and the slurrying index (I_d) are indicated.

As the maximum particle size (d_max) increases, both the upper limit (Cd v) and the lower limit (Ch v) of slurrying show a positive correlation with d_max for both CD and MD samples. In contrast, the slurrying index (I_d) decreases gradually, suggesting a negative correlation with d_max. Notably, for samples with the same d_max, the Cd v​ and Ch v values for the CD samples are significantly higher than those for the MD samples, with the Cd v values of the MD samples even falling below the Ch v values of the CD samples. For example, when the upper limit particle size is 5 mm, the Cd v and Ch v values for the CD samples are 0.568 and 0.484, respectively, and I_d = 0.084. In comparison, the corresponding values of C_v for the MD samples are 0.466 and 0.369, and I_d = 0.097. The Cd v and Ch v values for the CD samples decrease by 21.9% and 31.2%, respectively. When the upper limit particle size increases to 30 mm, the Cd v and Ch v for the CD samples increase to 0.648 and 0.598, respectively, resulting in an I_d of 0.050. Moreover, the Cd v and Ch v values for the MD samples decrease to 0.612 and 0.545, respectively, and I_d = 0.067, representing decreases of 5.9% and 9.7%, respectively, compared with those of the CD samples. Each pair of samples with the same upper limit particle size demonstrated a similar significant trend.

Rheological and propagation characteristics

Rheological data for a total of 70 remolded slurries derived from eight materials were obtained via two rheometers with different application conditions. Each remolded sample was fitted via the Bingham model to determine its yield stress and viscosity coefficient. Additionally, the samples used in the propagation experiments were identical to those used in the rheological tests, ensuring consistency in terms of the solid volume concentration (C_v), water content, and density. Each sample corresponds to a set of rheological parameters (yield stress and viscosity coefficient), propagation data, and clean water escape data.

Viscosity coefficient and yield stress

Yield stress refers to the minimum stress that must be overcome before debris flow begins to move. The viscosity coefficient represents the fluid’s viscosity and determines the resistance encountered by the debris flow during its runout. Figure 7a–d shows the yield stress of slurries with varying gradations and solid volume concentrations (C_v) for the eight samples, whereas Fig. 7a’–d’ displays the corresponding viscosity coefficients. Overall, the rheological properties of the DYG debris flow slurries (yield stress and viscosity coefficient) exhibited a well-defined power-law relationship with C_v. As C_v increased, the growth rates of both the yield stress and viscosity coefficient intensified significantly. This result follows a consensus. In contrast, increasing the maximum particle size (d_max) did not significantly enhance the yield stress or rheological characteristics of the debris flow slurries.

Fig. 7

Rheological test results of four pairs of remolded slurries. (a–d) show the variation in yield stress with solid volume concentration (C_v) for samples of different gradations, whereas (a’–d’) represent the relationship between the viscosity coefficient and solid volume concentration (C_v) for the same samples. On the right side of each panel, the yield stress and viscosity coefficient ranges for the MD and CD slurries with the same maximum particle size (d_max) are displayed, providing a clearer comparison of the differences between the two slurries.

The yield stress of the discontinuously graded MD slurries covers a wider range than that of the CD slurries. As the maximum particle size (d_max) increases from 5 mm to 30 mm, the yield stress range for the MD slurries expands by 15.8%, 24.1%, 15.8%, and 67.7% compared with the range for the CD slurries. The difference in viscosity coefficients decreases as the maximum particle size increases. To compare the similarity between the two sample sets, the Jaccard index was calculated for slurries with the same d_max. The formula for calculating the Jaccard index is as follows:

$$\begin{array}{*{20}{c}} {Jaccard~Index\left( {{R_{{\text{CD}}}},{R_{{\text{MD}}}}} \right)=\frac{{\left| {{R_{{\text{CD}}}} \cap {R_{{\text{MD}}}}} \right|}}{{\left| {{R_{{\text{CD}}}} \cup {R_{{\text{MD}}}}} \right|}}~} \end{array}$$

(4)

where: R_CD and R_MD represent the sets of yield stress or viscosity coefficients of the CD slurry and MD slurry, respectively, for the same d_max value. |R_CD∩R_MD| denotes the range of the intersection of the two sets, and |R_CD∪R_MD| represents the range of the union of the two sets Table 2 presents the Jaccard indices for yield stress and viscosity coefficients between the CD and MD slurries with the same d_max.

Table 2 Jaccard index of rheological properties of slurries with the same upper limit particle size.

Inundation area and escaping clear water

The results of the inclined plane propagation test visually demonstrate the impact of continuous gradation on the flowability and water retention capacity of debris flows. The boundary conditions for each series of slurries were uniform and consistent before their complete loss of lateral confinement. Figures 8 and 9 show the orthographic images of all remolded slurries after propagation on the inclined plane. Additionally, the mass of clear water escaping from each slurry over two hours was collected and recorded.

Fig. 8

(a) Orthographic images of the test slurries with d_max = 5 mm and 10 mm. The C_v values for each slurry are labeled above the orthographic images. (b) Line plot shows the inundation area of each slurry and the quality of clean water escaping within 120 min for each series. A-CD, A-MD, Mcw-CD, and Mcw-MD represent the inundation areas of each CD slurry and MD slurry, as well as the quality of escaping water collected within 120 min for each CD slurry and MD slurry.

The inundation area ranges for CD slurries with four different maximum particle sizes (d_max = 5, 10, 20, and 30 mm) are as follows: 120.6 to 456.2 cm², 114.8 to 415.7 cm², 493.0 to 1414.0 cm², and 486.7 to 1194.3 cm², respectively. After removing the sand fraction and remolding into discontinuously graded MD slurries, the corresponding inundated areas ranged from 115.3 to 476.7 cm², 121.0 to 409.3 cm², 510.5 to 1581.2 cm², and 445.5 to 1145.8 cm², respectively. Further calculations of the Jaccard index for CD slurries and MD​ slurries with the same d_max show values of 0.93, 0.96, 0.83, and 0.88 as d_max increases from 5 mm to 30 mm. Overall, when d_max​ is the same, there is no significant difference in the range of inundation areas between the CD slurries and MD slurries, and they are even quite similar. In other words, their sets of inundation areas have a large overlap. This result aligns with the findings from the rheological tests.

Fig. 9

(a) Orthographic images of the test slurries with d_max = 20 mm and 30 mm. The C_v values for each slurry are labeled above the orthographic images. (b) Line plot shows the inundation area of each slurry and the quality of clean water escaping within 120 min for each series. A-CD, A-MD, Mcw-CD, and Mcw-MD represent the inundation areas of each CD slurry and MD slurry, as well as the quality of escaping water collected within 120 min for each CD slurry and MD slurry.

As time progressed, the deposits experienced clear water drainage. Despite identical preparation steps for each deposit, significant differences in the volume of clear water expelled within two hours were observed between CD slurries and MD slurries with similar inundation areas at the same maximum particle size (d_max​). For example, at d_max = 5, the CD slurry inundation area was 387.7 cm³ and collected 2.54 g of escaping water, whereas the MD slurry with an inundation area of 383.3 cm³ collected only 1.00 g of escaping water. Similarly, for the CD slurries with inundation areas of 378.2 cm³ (d_max = 10, C_v = 0.512), 1414.0 cm³ (d_max = 20, C_v = 0.585), and 1194.3 cm³ (d_max = 30, C_v = 0.598), the corresponding volumes of escaping water collected were 2.71 g, 13.38 g, and 5.77 g, respectively. In contrast, the MD slurries with inundation areas of 376.8 cm³ (d_max = 10, C_v = 0.429), 1420.9 cm³ (d_max = 20, C_v = 0.512), and 1145.0 cm³ (d_max = 30, C_v = 0.545) collected only 1.08 g, 6.71 g, and 3.18 g of escaping water, respectively. Overall, the amount of clear water expelled by the continuously graded remolded slurries within two hours was significantly greater than that expelled by the discontinuously graded remolded slurries.

Excess water pressure and decanting of water

Two different sets of measurement containers and graduated piezometers (Fig. 5) were used to monitor the variation in excess water pressure in all the CD and MD slurries over time. The results of these tests are presented in Fig. 10. The peak positions of the relative excess water pressure for each slurry are indicated by triangular markers. Variations in grading led to significant differences in the development and dissipation of excess water pressure.

Fig. 10

Curves of the relative excess water pressure (R) over time for remolded slurries with different gradations. Slurries with the same maximum particle size are plotted in the same panel. The solid lines represent continuous gradation slurries, whereas the dashed lines indicate discontinuous gradation slurries.

Excess water pressure of continuously graded slurry

Each continuously graded CD material was remolded to prepare slurries with three different solid volume concentrations (C_v1, C_v2, and C_v3). A total of 12 slurries were monitored for changes in relative excess water pressure (R) over time (as shown by the solid lines in Fig. 10). Overall, the R − T curves generally tend to increase, reach a peak, and then decrease.

During the rising phase, the relative excess water pressure (R) increased from the initial value of R₀​ (equal to 0.6) to the peak value of R_max. The time required to reach R_max​ for samples with maximum particle sizes (d_max) of 5 mm, 10 mm, 20 mm, and 30 mm ranged from 165 to 255 min, 215–245 min, 315–405 min, and 435–450 min, respectively. The corresponding R_max values ranged from 0.86 to 0.90, 0.92–0.97, 0.94–0.99, and 0.95–0.99, respectively. Out of the 12 remolded slurries, eight samples exhibited a clear descending phase after reaching the peak. The remaining four remolded slurries (d_max = 5 mm, C_v = 0.526 and C_v = 0.505; d_max = 10 mm, C_v = 0.550; d_max = 30 mm, C_v = 0.623) entered the descending phase after durations ranging from as long as 13 monitoring cycles (55 min) to 3 cycles (15 min).

For the remolded slurries with d_max = 5 mm and 10 mm, R decreased by 0.1–0.16 and 0.21–0.25, respectively, after a total monitoring duration of 600 min. Moreover, for slurries with d_max = 20 mm and 30 mm, the excess water pressure decreased by 0.06–0.12 and 0.05–0.08, respectively, after a total monitoring duration of 780 min.

Overall, the remolded slurries with continuous gradation exhibited the following characteristics throughout the entire monitoring sequence: a rapid increase in R, a shorter duration at the peak, and a faster rate of decline.

Excess water pressure of discontinuous graded slurry

Similarly, the discontinuously graded MD slurries were remolded under each d_max​ condition with three different C_v samples, resulting in a total of 12 remolded slurries. Throughout the entire monitoring period, the water pressure development in these slurries significantly differed from that in the CD slurries.

In Fig. 10, the R–T curves of the 12 MD slurries generally exhibit a slow increase, followed by a plateau at the peak and a slight (or nearly negligible) decline. During the rising phase, all the MD slurries took a longer time to reach R_max than did the CD slurries. Specifically, the times required for slurries with d_max = 5 mm, 10 mm, and 20 mm to complete the rising phase were 185–510 min, 240–335 min, and 460–660 min, respectively. For the slurries with d_max = 30 mm, the shortest time to reach the peak R was 505 min, and for the slurry with C_v = 0.595, R still slowly increased at the end of the 780-minute monitoring period.

Compared with the CD slurries, the MD slurries not only presented a longer time to reach the peak but also presented a significantly lower R_max. The ranges of R_max​ for the four slurries with different upper particle size limits were as follows: 0.71–0.77, 0.73–0.82, 0.85–0.88, and 0.88–(no peak observed). Although the slurry with C_v = 0.595 (d_max = 30 mm) did not reach a peak by the end of the monitoring period (R = 0.92), the rising trend was very slow (nearly stopping). It took 155 min for R to increase from 0.91 to 0.92.

Moreover, the decline in R after reaching the peak was very slow for the other 11 slurries. The R values of slurries with d_max ​= 5 mm, 10 mm, and 20 mm decreased by only 0.01–0.04, 0.03–0.05, and 0.01–0.02, respectively, over the remaining monitoring time. The R values for the other two slurries with d_max = 30 mm decreased by only 0.03 and 0.04, respectively.

Notably, as the upper particle size limit (d_max​) increases, the relative excess water pressure (R) of the remolded slurry also increases. This trend can also be observed in remolded slurries with continuous grading. However, for remolded slurries with the same d_max ​, the variations in excess water pressure appear to be insensitive to changes in the solid volume concentration (C_v).

Decanting water

Decreasing water, i.e., phase separation between particles and water^53,54, was observed in all 24 remolded slurries during the excess water pressure monitoring experiments. However, significant differences were evident between CD (continuous grading) slurries and MD (discontinuous grading) slurries within the same time scale. Table 3 presents the mass, volume, water content, and drainage amount at the end of the experiment and the percentage of drainage relative to the total water volume for each monitored remolded slurry.

Table 3 Physical parameters of different slurries and collected decanting water quality.

An analysis of the statistical results in Table 3 clearly reveals that variations in C_v significantly impact the drainage of water in debris flow slurries. Under the same d_max conditions, both the CD and MD slurries presented a marked increase in the volume of decanted water per 100 cm³ as C_v decreased (i.e., as the moisture content increased). Interestingly, for the same d_max conditions, the decanted water from the MD slurries with higher moisture contents was significantly lower than that from the CD slurries. This characteristic is clearly reflected in the value of m_d.

Discussion

Control of the gradation continuity on the slurring potential

The design of the slurry test simplifies the complex conditions involved in the formation of debris flows in natural environments. While these simplifications may limit the applicability of the research findings to natural settings, they also highlight the effect of gradation continuity on debris flow behavior.

As the maximum particle size (d_max) increases, both the Cd v and Ch v​​ of the continuously graded (CD) slurries and discontinuously graded (MD) slurries gradually increase. A higher C_v value indicates a smaller proportion of water in the slurry, resulting in a higher density of the slurry. This trend is consistent with previous research findings^18,50.

A higher I_d indicates a greater slurrying potential and greater potential to form debris flows. Although discontinuously graded MD samples can also be remolded into debris flow slurries, the experimental results indicate that discontinuous grading significantly affects the conditions for debris flow formation. For the same d_max, the Cd v and Ch v values of the MD samples when remolded into debris flow slurries are lower than those of the CD samples. However, the I_d values of the MD samples are generally greater than those of the CD samples (Fig. 6). This suggests that discontinuously graded loose deposits are more likely to develop into debris flows during rainfall events. Under equivalent conditions, their transition into granular flows and hyperconcentrated flows is less probable than that of continuously graded deposits.

Influence of the gradation continuity on the rheological properties and propagation ability

In previous studies, the rheological parameters of debris flow slurries have often been closely correlated with their propagation characteristics^55,56,57. Therefore, the results of rheological and propagation tests are discussed together in this study.

For the same maximum particle size (d_max), the Jaccard index of the rheological properties between the CD samples and MD samples is relatively high (Table 3), yet there is a significant difference in the range of the solid volume concentration (C_v) between the two samples. The C_v of the MD samples is notably lower than that of the CD samples, indicating that the density of the MD slurry with similar rheological properties is lower than that of the CD slurry. Thus, under the same conditions, the competence and destructive potential of the MD slurry are lower than those of the CD slurry. Moreover, for the same d_max, the C_v of the MD slurry is significantly lower than that of the CD slurry under similar inundation areas. This suggests that while the MD slurry has a higher water content, it does not exhibit greater mobility. Iverson et al.⁶ discovered through large-scale flume experiments that excess water pressure is one of the controlling factors for the spreading distance of debris flows. However, due to the limitations of the experimental scale, the results of the spreading tests did not highlight the impact of excess water pressure on slurry mobility⁵⁸. For this reason, differences in gradation have become the focal point in analyzing this phenomenon.

Currently, there is no universal standard to clearly define Cd v and Ch v, leading to a degree of subjectivity in their determination. This affects the maximum and minimum values of the yield stress and viscosity coefficients for the eight materials. This factor also directly influences the results of the Jac card index. In the absence of such subjective influences, the Jaccard index for CD and MD slurries with the same d_max would be closer to 1 in both the rheological and propagation tests. Notably, the Jaccard index for the rheological parameters of the d_max = 30 mm slurry differs from those of the other samples, primarily for this reason.

The rheological and propagation tests demonstrate that the rheological properties and mobility of the slurry are highly sensitive to changes in the solid volume concentration (C_v). When C_v approaches the upper limit for slurrying, the changes in these characteristics are particularly pronounced. Conversely, as C_v approaches the lower limit for slurrying, the changes in mobility become even more evident. Related studies^19,59 have revealed similar trends. However, when sediment grading is discontinuous, the impact of the solid content on the rheological properties and mobility of the slurry is significantly reduced.

The impact of graded pairs on water channels in debris flows

Peak and dissipation of excess water pressure

After the saturated debris‒water mixture is thoroughly mixed, the particle skeleton of the mixture undergoes reorganization (i.e., the mixture is liquefied). Meanwhile, excess water pressure is generated. The excess water pressure then causes the particles in the debris flow slurry to become suspended, and the previously isolated pores become interconnected, forming a water-supported structure. Water surrounds the fine particles, forming a suspension, which further suspends silt and sand particles, followed by gravel suspension, ultimately resulting in a debris flow slurry. When the debris flow slurry is no longer subjected to external disturbances (i.e., mixing stops), The suspended particles deposition under their own weight. Meanwhile, the excess water pressure in the slurry begins to dissipate.

The sedimentation of debris flows occurs through the time-dependent consolidation of a fluid-saturated porous medium under load⁶⁰. Both the solid materials and the water within the debris flow slurry are well known to be incompressible. Figure 11 illustrates the dissipation mechanism of excess water pressure in both the CD slurries and the MD slurries. During the deposition process, the excess water pressure drives the water between the pores to the surface of the slurry, where it accumulates to form decanting water. When complete consolidation occurs, it means that the excess water pressure has fully dissipated. The dissipation of excess water pressure is the process in which the water within the slurry undergoes changes in load-bearing. The structure of the water-supported framework influences the rate of water movement between the pores. However, the gradation of the sediment determines the structure of the water-supported framework.

Fig. 11

Panels (a) and (b) illustrate the dissipation of excess water pressure in continuously graded slurries and discontinuously graded slurries, respectively. The blue arrows in the figures indicate the downward deposition of suspended coarse particles under the influence of gravity, whereas the yellow arrows represent the movement trend of water being displaced during the sinking of particles. In panel (a), the lengths of the yellow arrows are generally greater than those in panel (b), highlighting the significant differences in hydraulic conductivity and the rate of excess water pressure dissipation between the two types of slurries.

Variations in the contents of clay, silt, and gravel can lead to different soil structures³⁶. A continuously graded mixture indicates excellent hydraulic conductivity among water, clay, silt, sand, and gravel within the slurry. As a result, the excess water pressure in continuously graded (CD) slurries dissipates more readily through efficient drainage pathways than discontinuously graded (MD) slurries do. In Fig. 10, the slope of the R-T curve represents the dissipation rate of the relative excess water pressure. Clearly, the dissipation rate of the relative excess water pressure in the CD slurry is significantly faster than that in the MD slurry.

Major⁶⁰ demonstrated that an increase in the clay content leads to a significant change in the propagation rate of the slurry, subsequently affecting the formation and dissipation of excess water pressure. Zhang et al.⁶¹ reported that during the deposition of debris flows, a relatively high concentration of fine particles results in relatively slow dissipation of the pore water pressure. The presence of silt and clay components leads to a considerable amount of water being adsorbed onto the surfaces of soil particles, forming a water film that cannot move freely. This portion of water provides some buoyancy to the fine particles while simultaneously restricting their settling and consolidation. Consequently, the dissipation of excess water pressure in discontinuously graded (MD) slurries occurs at a slower rate.

This phenomenon explains why, under the same d_max conditions, the excess water pressure in the CD slurries rises faster, peaks higher, has shorter maintenance times, and descends more quickly than that in the MD slurries.

Influence of gradation on the water holding capacity of debris flow slurries

In MD slurries with a relatively high proportion of fine particles, the drainage pathways for water are relatively easily obstructed by these fine particles³⁶. Moreover, fine particles have a larger specific surface area than coarse particles do, leading to a greater amount of water being adsorbed onto the surfaces of the fine particles, which diminishes their ability to move freely. This means that there is less free water rising to the surface of the slurry. Consequently, the increase in fine particles contributes to a greater water retention capacity in debris materials⁶². On the other hand, compared with CD samples, MD samples exhibit changes in their sediment skeleton that result in smaller interparticle voids. This leads to significantly different hydraulic conductivities between MD slurries and CD slurries. This phenomenon explains why, within the slurry potential, the water content of the MD slurries is notably greater than that of the CD slurries (Table 3), yet the amount of decanting water (clear water) released is far lower than that of the CD slurries (Table 3; Figs. 8b and 9b). While debris flow sediments rarely or never lack sand particles under natural conditions, this experimental design is intended to highlight the influence of gradation continuity on debris flow behavior.

In conclusion, the discontinuous grading caused by an increase in fine particle content leads to sediments exhibiting a greater water retention capacity. The variation in moisture content within debris materials plays a critical role in controlling the initiation and magnitude of debris flows⁶³. Chen et al.⁶⁴ concluded that soils with higher water retention capacities are more prone to trigger debris flow initiation. Additionally, Thomas et al.⁶⁵ reported that differences in soil water retention significantly affect the soil moisture content and pore water pressure, making monitoring these changes beneficial for landslide early warning systems. Inspired by these findings, further exploration of the control exerted by discontinuous grading on the initiation of debris flows is warranted on the basis of the existing experimental results.

Conclusion

Using debris flow sediments from the Dongyuege (DYG) deposit in Southwest China, four pairs of remolded slurries with different gradation characteristics (continuous grading and discontinuous grading) and a maximum particle size of 30 mm were prepared. A comparative analysis was conducted through slurrying tests, rheological tests, propagation tests, and excess water pressure monitoring to investigate the effect of grading continuity on sandy matrix debris flows. The results provide important insights into how gradation continuity influences the occurrence and movement processes of debris flows. Although the maximum particle size of the experimental samples is only 30 mm, which may not fully represent natural debris flows, the results from the four samples with different maximum particle sizes are consistent. This largely strengthens the generality and applicability of the conclusions. With the increasing with the popularity of numerical simulations, these results also contribute to improving the models.

The effect of gradation continuity on the potential and runout characteristics of debris flow initiation is significant. The I_d​ (slurrying index) value reflects the slurrying potential. Discontinuously graded samples exhibit a higher slurry index, indicating that such materials are more prone to forming debris flows. However, their lower solids volume concentration (C_v) than continuous graded samples indicate that their competence and destructiveness are also reduced.

It is well known that as the solids volume concentration (C_v) of a slurry increases, its yield stress and viscosity increase, whereas its mobility decreases. However, when the rheological properties and inundated areas of CD slurries and MD slurries are similar, the solid volume concentration (C_v) in MD slurries is usually lower. This suggests that in slurries with discontinuous gradation, the effect of the C_v on their rheological characteristics and mobility is reduced.

The higher hydraulic conductivity of the water-supported structure in continuously graded slurries provides more effective drainage pathways. Continuously graded slurries present higher excess water pressures than discontinuously graded slurries do, and their dissipation rates are faster. In contrast, discontinuously graded slurries lack effective hydraulic conductivity within the water-supported structure, causing most of the water to remain trapped inside the slurry. As a result, discontinuously graded slurries have lower excess water pressures, but they persist for a longer duration.

In conclusion, the continuity of gradation significantly influences the initiation and flow behavior of sandy debris flows. Although debris flows generated from discontinuously graded sediments exhibit longer deposit consolidation times, their competence and destructiveness are significantly reduced. Therefore, it is essential to consider the impact of gradation characteristics in the prevention and early warning of debris flows.