Introduction

With the rapid intensification of human engineering activities, engineering and geological hazards have occurred on an unprecedented scale. China, in particular, is at the forefront of the world’s hazards-prone countries due to its large land area, wide variations in topography, geomorphology and geological conditions, as well as its resource consumption and infrastructure construction intensity1. There are many types of natural and man-made hazards that are difficult to prevent and control. Water-sand inrush hazards encountered in various engineering constructions under water-rich sand layers are one of the representative hazards2,3,4,5. Water-sand inrush events involve the sudden and violent intrusion of high sand content mixtures into underground workspaces, this can lead to potentially catastrophic consequences for both property and human safety. Simultaneously, water-sand inrush also causes significant surface subsidence, destroying surface resources and threatening surface engineering facilities, as shown in Fig. 1.

Fig. 1
figure 1

Actual footage of the water-sand inrush hazards (a) Tertiary silty sand inrush at the Lan-Yu railway tunnel, (b) Water-sand inrush at the Zhongliang mountain 2# Tunnel, (c) Water and sand Inrush and subsidence at Yuan Datan Coal mine.

Full size image

In the 1970s, water-sand inrush incidents severely impacted several major tunnel projects, including the Jinshan Water Supply Tunnel in Shanghai, the Michigan Tunnel in the United States, and Line 1 of the St Petersburg Metro in the former Soviet Union. Zhou et al.6 analyzed 52 cases of subway station foundation pit accidents worldwide and found that water-sand inrush contributed to 62% of these incidents. Similarly, Dai7 analyzed 43 cases of water-sand inrush accidents in underground engineering, highlighting the severity of such events. A particularly notable case occurred at the LongDe coal mine8, where nearly 20,000 cubic meters of sand from a mountain disappeared into the mine in just 5 h due to the inrush. Zhang Bei et al.9 conducted a dedicated study on this type of hazard, they highlighted its rapid progression, high destructive power, and significant challenges in prevention and mitigation. These examples confirm that water-sand inrush events are fast, highly destructive, difficult to prevent, and cause extensive damage to both underground and surface structures10,11. These events, characterized by their intensity, hazardous nature, and unpredictability, pose significant challenges in prevention and control, impacting safety and economic sustainability.

Water-sand inrush involves the fluidization of the sand layer, the primary cause of this hazard is the interaction between stress and water pressure within the sand layer. Where sand formations typically contain mixtures of silt and clay particles (Fig. 2). Measurements indicate that the silt and clay content in original sand samples vary from about 0.9–5.3%, with some samples reaching up to 12%. This variation is particularly pronounced in the transition zone between the desert and loess plateau regions12,13.

Fig. 2
figure 2

Clayey sand samples from different boreholes in Yulin desert stratum (a) borehole k08, (b) borehole k12.

Full size image

Assessing, preventing, and controlling water-sand inrush are crucial for ensuring safety in underground construction in water-rich areas. The investigation of major scientific issues, including the inrush dynamics mechanism and the law of land surface subsidence of water-sand inrush in clayey sand layers under the hydraulic coupling effect, addresses strategic needs in the development and construction of underground engineering in such environments in China. A self-constructed water-sand inrush test system comprising 5 mm diameter conduits was employed to illustrate the characteristics of water-sand flow rates and variations in bottom water pressure in water-bearing sand layers under different water pressures, together with the impact of sand layer geostress14. By conducting simulated experiments on mining-induced roof strata water-sand inrush hazards, they investigated how fractures in the roof strata form and evolve. Guo et al.15 conducted an analysis of a mud-sand inrush at the ZF202 working face in the ZhaoJin Coal Mine, Huanglong coalfield. Their findings indicated that weakly cemented mudstone/sandstone formations also contribute to water-sand inrush following mud liquefaction and collapse under the coupling of water and geostress. Xu16 conducted an investigation into the permeability of overlying clay-sandy soils utilizing a modified ST-70 permeameter. Yuan et al.17 conducted laboratory experiments to investigate the dynamics of water-sand mixing inrush in viscous sand layers. In conclusion, previous studies have primarily concentrated on the circumstances surrounding water-sand inrush18 and the attributes of the fluid and migration patterns associated with this phenomenon. Further research is required to elucidate the mechanisms underlying surface subsidence caused by water-sand inrush. While the “Peck Formula” is widely employed to predict surface settlement curves, it fails to account for the influence of stratigraphic parameters and the dynamic outflow during an inrush19. Consequently, there is currently no agreed-upon formula for predicting the timing, extent, and volume of surface subsidence caused by water-sand inrush.

The author has previously investigated the initial conditions, sensitivity of influencing factors and regularities of water-sand inrush17. This work represents an extension of the aforementioned study. The authors have developed a large model to specifically investigate the rules of land subsidence due to water-sand mixing inrush.

Experimentation

Aeolian sand and clay collection

Aeolian sand, collected from the Kubuqi Desert in Ordos, Inner Mongolia. It is light yellow in color and contains fine, relatively uniformly distributed particles interspersed with small black or white particles. Clay was obtained from Shenheyuan Q3 loess in Chang’an District, Xi’an, and was sieved through a 0.05 mm sieve. The grading and morphology of the aeolian sand and clay samples are shown in Figs. 3 and 4.

Fig. 3
figure 3

Morphology of the materials (a) Sampling site photograph, (b) Eolian sand, (c) Dry clay.

Full size image
Fig. 4
figure 4

The particle size distribution curves (a) Natural eolian sand, (b) Dry clay.

Full size image

Preparation of sand samples and its basic mechanical properties

Experimental sand samples with different clay contents (1%, 5%, 10%) were prepared by accurately weighing and mixing the sand and clay (Fig. 5). The shear strength of the sand at different clay contents was quantified by direct shear tests performed at a shear rate of 0.8 mm/min, as detailed in Table 1.

Fig. 5
figure 5

Photographs of sand samples with varying clay content (a) 1%, (b) 5%, (c) 10%.

Full size image
Table 1 Strength indices and permeability of sand samples with varying clay content.
Full size table

Design Idea of the model test

This study does not investigate fracture formation or evolution in the bedrock. Instead, its primary objective is to assess the patterns of land surface subsidence in the thick sand layer during inrush. This focus is driven by two main considerations: (1) The surface response during inrush in thick sand layers, which is a critical aspect for hazards prevention and management. (2) Fracture channel evolution in bedrock is influenced by lithology, cavity size, geostress, and construction intensity. Given this complexity and the broad scope of engineering geological modeling, our study focuses not on fracture evolution itself, but on its consequence: water-sand inrush-induced surface subsidence. This approach aligns with established research practices.

Experimental configuration

The model facility is made of transparent organic glass and has overall dimensions of 2200 mm (length) × 200 mm (width) × 1200 mm (height). It is equipped with an upper cover plate with a water inlet and a pressure gauge. These components are used to simulate the water pressure in the stratum by pressurization. At the bottom of the tank, a steel gate is controlled by a ball screw mechanism. This allows the crack width to be adjusted by manual rotation of a hand wheel. A photograph of the model is shown in Fig. 6.

Fig. 6
figure 6

Test model device (a) Physical drawing, (b) Design dimension drawing.

Full size image

Experimental design

The model facility is used to investigate the evolutionary patterns of water-sand inrush in aeolian sand with varying clay content under water pressure in a saturated environment. The experimental design aims to simulate and analyse the processes of surface subsidence and its evolution during inrush. Details of the experimental design are given in Table 2.

Table 2 Inrush test design table.
Full size table

Experimental procedure

The test consists of four stages: sample preparation, sample installation, inrush test and data collection, and data analysis. (1) Sample preparation: Approximately 240 kg of different clayey sand samples and 1 m3 of water are prepared in advance. (2) Sample installation: The clayey aeolian sand is methodically layered inside the model tank from bottom to top. Each 10 cm layer is compacted to ensure uniform density throughout the set-up. Sensors are installed at 30 cm intervals, resulting in a final sand layer thickness of 70 cm. (3) Initial test and data collection: Water is added to the sand layer until it is approximately 5 cm above the surface of the sand. The sand layer soaks for 1 h to achieve full saturation, with total water consumption recorded. (4) Data analysis: The sensors are connected to the data acquisition system and calibrated to zero. The sand-collecting container is placed on an electronic balance beneath the model tank, aligned with the tank's cracks, and connected to a computer for data acquisition, the scale being zeroed before use.

The inrush test is initiated by setting the lower crack gate to the predetermined width. A collection container is placed beneath the model tank to capture the inrush flow. Throughout the test, a high-resolution camera and a high precision electronic scale are used to monitor and record the water-sand inrush process. The camera is placed in front of the model facility and is set to automatically capture images every 5 s, documenting the morphology of the sand body inside the facility. At the same time, the electronic scale, connected to a computer, measures the mass of the water-sand mixture flowing out of the bottom fissure of the model tank at half-second intervals. During the test, the sand container on the electronic balance must be replaced periodically to avoid overloading. This procedure is continued until no further water-sand flow is detected, signaling the end of the test.

Experiment results

Influence of water pressure on subsidence

The experimental results are shown in Fig. 7 for the case of inrush subsidence in saturated sand layers with 1% clay content under varying water pressures.

Fig. 7
figure 7

The sand inrush subsidence curves and real picture with 1% clay, 5 mm fissure width and different water pressure (a, b) When the subsidence range is extended to 200 mm, (c, d) When the subsidence range is extended to 400 mm, (e, f) When the subsidence range is extended to 600 mm (inrush finished).

Full size image

Figure 7 clearly shows that the magnitude of water pressure significantly affects the initial inrush rate and morphology (see Fig. 7a, b). Higher water pressures lead to faster inrush and subsidence rates, this is accompanied by greater deformation of the subsidence zone. However, in later stages, once the water pressure in the inrush damage zone has dissipated, the water-sand inrush flow rate and the morphology of the subsidence basin exhibits no significant variation. This is particularly true if internal channels within the sand layer extend to the surface (see Fig. 6c, d). The final forms of subsidence are relatively consistent, with variations in final subsidence measurements within 20%.

Influence of different clay content on inrush subsidence

The subsidence curves for saturated sand layers with clay contents of 1%, 5% and 10% under a 5 mm fissure width are shown in Fig. 8.

Fig. 8
figure 8

The sand inrush subsidence curves and final state diagrams for different clay contents with 5 mm fissure width (a, b) With 1% clay content, (c, d) With 5% clay content, (e, f) With 10% clay content.

Full size image

As illustrated in Fig. 8, an elevated clay content is associated with a reduction in inrush rates and an extension in the time required for the inrush to affect subsidence at a given radius. To illustrate, at a clay content of 1%, the duration of stable subsidence following an inrush is 20 min, compared to 40 min at a clay content of 5% and 70 min at a clay content of 10%. Moreover, higher clay contents lead to gentler subsidence basins. A 10% clay content produces a gradual slope without steep drops, forming a more uniform conical basin shape. In the case of a low clay content (1%), the subsidence basin exhibits a steep shape immediately following the cessation of the inrush. This is then succeeded by a gradual slope at the bottom, with the overall angle of the final slope of the subsidence basin being greater than that of the higher clay content sand layers.

Moreover, the measured subsidence basin curves presented in Fig. 8 demonstrate that the morphology of subsidence caused by water-sand inrush in water-rich sand layers significantly deviates from the parabolic shape typically associated with limited deformations from underground construction disturbances. This is in contrast to the estimates of surface settlement obtained using Peck’s method, which are in line with the aforementioned parabolic shape. The subsidence basin resulting from water-sand inrush typically exhibits a two-stage discontinuous deformation in lower clay content sand layers, characterized by steep outer edges and a gradual slope near the inrush channel. This distinctive feature of surface subsidence induced by water-sand inrush is illustrated in Fig. 9. The distinctive form of inrush-induced subsidence is influenced by the low cohesion of the sand layers and the drag force exerted by water outflow in sand. Further research should explore the morphology of inrush under varying geostress and coupled hydraulic pressures.

Fig. 9
figure 9

Surface subsidence profile diagram caused by sand inrush (a) Measured final subsidence curve, (b) Subsidence curve development and evolution with inrush.

Full size image

Under different caly content, the inrush and settling rates and subsidence troughs are different. The higher the viscosity content, the slower the rate, and the smaller the subsidence range. The main mechanisms include: (1) Interparticle Cohesion and Structural Stability. Clay particles possess higher cohesive forces compared to sand particles due to their plate-like structure and surface charge properties20,21. As clay content increases, these cohesive forces enhance the overall structural stability of the sand-clay mixture. This results in a more gradual and uniform settlement pattern, as observed in the gentler slopes of subsidence basins at higher clay contents (e.g., 10%). In contrast, lower clay content (e.g., 1%) leads to a weaker matrix structure, causing localized and abrupt subsidence with steeper slopes. (2) Permeability Reduction and Pore Water Pressure Dissipation22,23. The presence of clay significantly reduces the permeability of the sand layer. At higher clay contents, the slower dissipation of pore water pressure prolongs the time required for settlement stabilization, as evidenced by the extended duration of stable subsidence (e.g., 70 min at 10% clay content compared to 20 min at 1%). This delayed response allows for more uniform stress redistribution within the soil matrix, contributing to the formation of a conical basin shape with gradual slopes. (3) Drag Force and Particle Rearrangement23. During water-sand inrush, the drag force exerted by water outflow plays a critical role in particle rearrangement. In low clay content sand layers, the lack of cohesion allows sand particles to be easily transported, leading to rapid and discontinuous deformation. This results in the characteristic two-stage subsidence morphology with steep outer edges and a gradual slope near the inrush channel. In contrast, higher clay content increases the resistance to particle movement, mitigating the effects of drag force and promoting a more continuous deformation pattern.

Quantification of surface subsidence troughs due to water-sand inrush

The measurement data are employed to ascertain the maximum subsidence depth (Hmax) and the maximum influence radius (Rmax). Empirical formulas have been developed to estimate the evolution of the subsidence radius (R) and subsidence depth (H) at various times (t) following the water-sand inrush hazard, as well as to estimate the subsidence depth (hi) at different radii (ri). These formulas provide a theoretical foundation for assessing the extent and depth of surface subsidence caused by water-sand inrush. A diagram that quantifies the subsidence trough is presented in Fig. 10.

Fig. 10
figure 10

Diagram illustrating the quantitative relationship of subsidence trough.

Full size image

The following definition is provided: During inrush t, the inrush ratio \(\omega ={r_i}/{R_{\hbox{max} }}\) is defined as the ratio of the horizontal distance \({r_i}\) from any subsidence point \({P_i}\) to the maximum subsidence radius \({R_{\hbox{max} }}\) of the sand layer. The subsidence amount \({h_i}\) at a point \({P_i}\) to the maximum subsidence amount \({H_{\hbox{max} }}\) of the sand layer (which can be taken as the total thickness of the sand layer in the inrush zone) is defined as the subsidence ratio \(\delta ={h_i}/{H_{\hbox{max} }}\). A quantitative relationship between the inrush ratio \(\omega\)and the subsidence ratio \(\delta\) under varying clayey sand contents has been established by fitting, as demonstrated in Eq. (1).

$$\delta =a{\omega ^2}+b\omega +c$$
(1)

where: \(\delta ={h_i}/H{}_{{\hbox{max} }}\), \(\omega ={r_i}/R{}_{{\hbox{max} }}\), \(a,\;b,\;c\) are fitting coefficients. The coefficient fitting results for varying clay contents are presented in Table 3. The detailed experimental results and their corresponding fits are illustrated in Fig. 11.

Fig. 11
figure 11

Comparison of measured and fitted subsidence troughs for different clay content sand.

Full size image
Table 3 Table of fitted coefficients for the subsidence function at different clay contents.
Full size table

In practical applications, the maximum subsidence amount \({H_{\hbox{max} }}\) is typically considered to be the thickness of the sand layer in the inrush zone. Given the measured clay content within this layer, the coefficients (\(a,\;b\)) in the subsidence trough estimation function, as defined in Eq. (1), are determined by fitting. Consequently, the maximum radius (\({R_{\hbox{max} }}\)) of the subsidence profile can be calculated using the equation \(\delta ({h_i},{r_i})=\delta (0,{R_{\hbox{max} }})=a{\omega ^2}+b\omega +c=0\), as outlined in Eq. (1). Furthermore, the subsidence depth (\({h_i}\)) at various radial distances can also be computed using Eq. (1).

Although this fitting equation may not fully account for the two-stage characteristics of inrush-induced surface subsidence, it offers a practical means of estimating the extent and depth of subsidence at various points. Subsequently, actual data from an engineering project will be used to validate the function describing surface subsidence troughs caused by water-sand inrush.

Engineering verification

At approximately 23:30 on 29 August 2015, a water-sand inrush hazard occurred during the construction of an inclined shaft in the Yuyang District of Yulin City. The incident, which persisted for approximately 3 h, resulted in notable surface subsidence, as illustrated in Fig. 12a. The mine is located at the northern end of the Loess Plateau in northern Shaanxi province, in close proximity to the southeastern edge of the Mu Us Desert. The area is characterized by Quaternary aeolian sand deposits and is surrounded by abundant water sources, groundwater levels are typically 2–3 m below the surface. Subsequent to the incident, a detailed survey of the subsidence troughs was conducted, and a contour map of these troughs was created, as illustrated in Fig. 12b.

Fig. 12
figure 12

Isoline diagram of surface subsidence caused by water-sand inrush in an inclined shaft of a mine in Yulin (a) Real diagram of surface subsidence. (b) Measured isoline diagram of subsidence, which was created using Surfer, Version 17.0, the software is available at: https://www.goldensoftware.com/products/surfer.

Full size image

The maximum subsidence depth (Hmax) was determined to be 4.01 m based on the measured data, while the maximum diameter (Rmax) of the subsidence troughs was calculated to be 65.15 m. The subsidence troughs resulting from the water-sand inrush in this engineering project were simulated using the previously established Eq. (1) and the fitting parameters for 1% clay sandy soils from Table 3, as illustrated in Fig. 13.

Fig. 13
figure 13

Comparison of measurements and calculated subsidence troughs caused by water and sand inrush in an inclined shaft of a mine in Yulin.

Full size image

Figure 13 demonstrates that the simulated subsidence distance and depth within the subsidence troughs due to a water-sand inrush in an actual engineering project align closely with the measured data when the experimental fitting Eq. (1) and its associated fitting parameters are utilized. The calculated maximum subsidence depth exhibits an error of only 2.9 cm in comparison to the actual measurements. This accuracy serves to reinforce the established relationship between the extent of the hazard and the duration of subsidence caused by the inrush.

Discussion

Water-sand inrush hazards are influenced by multiple factors: geological conditions, hydrogeological conditions, and engineering interventions24,25. In the context of experimental investigations into the evolution of overburden fractures and the mechanisms governing water-sand inrush phenomena, physical model tests26,27,28 were conducted with the objective of analyzing the development of water-conducting fractured zones and examining the failure mechanism in overburden strata during shallow buried thick seam mining. Jiang et al.29 investigated the evolution mechanism of tunnel water-sand inrush, considering the potential hazard posed by water-rich sandy dolomite structures. They employed fluid-solid coupling model tests to identify the different types of water-sand inrush mechanisms and the factors affecting the inrush hazards. Zhao et al.25 investigated the process of water-sand inrush through vertical karst conduits, employing a simulated testing system to study the migration and inrush of water-sand mixtures. Their findings revealed the dynamic behaviour of water stress and flow rate in relation to conduit size. Evaluation of surface subsidence due to water-sand inrush is insufficient. Additionally, there is no readily available commercial equipment for such experimental research. Most of the equipment used is self-developed and self-produced, and there is a lack of research on the coupling of hydraulic and ground stress. Additionally, the scale of the model tests is relatively limited30,31,32,33, with a notable absence of model test systems at the scale of meters.

The previous research on formation subsidence focuses on the excavation of subway and other tunnels, coal mining and groundwater extraction29,34,35,36,37. The test and research on the rule of surface subsidence and the estimation of subsidence caused by water-sand inrush hazards are not extensive enough20,38,39.

Conclusion

Given the limited research quantifying surface subsidence due to water-sand inrush in water-rich sand layers, this study employed large-scale visualized model experiments. These experiments were conducted across three sandy soils with varying clay contents. The analysis of subsidence evolution due to inrush yielded the following conclusions:

  1. (1)

    Water pressure predominantly influences the initial rate of sand inrush, exerting minimal impact on the final subsidence morphology. At 0.15 MPa water pressure, the initial subsidence rate was significantly higher compared to lower pressures. This indicates that higher water pressures accelerate the initial inrush but do not significantly alter the final shape of the subsidence trough.

  2. (2)

    The clay content within the sand layers significantly affects both the rate of sand inrush and the final morphology. As clay content increases, the sand-water inrush rate decreases due to enhanced particle cohesion, and there is a corresponding reduction in the range and extent of inrush as well as the total volume of sand displaced. The stabilization time for the inrush also lengthens, leading to variations in the final shape of the subsidence trough. Specifically, increasing clay content from 1 to 10% reduced the maximum subsidence depth from 57.5 cm to 42 cm and extended the stabilization time from approximately 20–70 min. At low clay contents, the subsidence trough displays a two-stage characteristic with an abrupt transition followed by a slope, while at higher clay contents (10%), the trough exhibits only a sloped profile without a pronounced steep section.

  3. (3)

    A quantitative function for predicting surface subsidence troughs due to water-sand inrush was developed, and the parameters of this function for sand layers with different clay contents were determined, achieving high fitting accuracy (R2 > 0.92). This function was validated through practical engineering scenarios of inrush hazards, demonstrating robust applicability. The predicted maximum subsidence depth (4.04 m) and the subsidence radius (65.15 m) was accurately captured.

Further research should evaluate the effects of fissure channel characteristics (length, roughness, angle) on water-sand inrush. More theoretical and numerical simulation studies are also needed.