Critical Gradient Research Articles

Characterization of the I-phase regime at TCV

Abstract The I-phase is an H-mode confinement regime of tokamaks characterized by limit cycle oscillations, the so-called LCOs or bursts. These bursts are the manifestation of a periodic flattening of the plasma edge pressure profile. The profile flattening is caused by increased radial transport, driven by a high-frequency plasma edge mode that periodically appears. This short-living mode is intrinsically connected to each burst. It vanishes once the profiles are fully flattened, and it reestablishes during profile recovery once critical gradients are reached and a new cycle begins.
In this paper, we describe for the first time the unambiguous presence of the I-phase at the tokamak à configuration variable (TCV). As the I-phase confinement regime is found in the parameter regime between the L-mode and the fully developed H-mode, it is often confused with dithers between H-mode and L-mode. Therefore, we are highlighting the differences between these two phenomena. Furthermore, we show the two-dimensional dynamics of the I-phase mode and bursts and the associated filamentary transport, enabled by the outstanding capabilities of the 2D TCV Gas Puff Imaging (GPI) diagnostics.

A new flexible-wall triaxial permeameter for localized characterizations of soil suffusion

Suffusion involves the migration of fines within the soil matrix, which may cause many types of geohazards. Localized characterization of suffusion is necessary because suffusion is inhomogeneous. However, existing studies on localized characterization have primarily relied on rigid-wall permeameters, which prevent lateral soil deformation and might introduce preferential flow, biasing the experimental results. In this study, a new flexible-wall triaxial permeameter was developed for the localized characterization of suffusion. The permeameter testing system has four modules: a loading and permeating module, a pressurized water supply module, an outflow collecting module and a back pressure supply module. The local pore water pressure is captured by an invented perforation socket that connects transducers to the specimen through the flexible wall without water leakage. The local deformation is measured by photography. Three repeated suffusion tests on complete decomposed granite were carried out using the new permeameter. The results show that the maximum coefficients of variation of the initial seepage velocity, clogging hydraulic gradient, critical hydraulic gradient and total loss of fine particles are less than 4.9%, demonstrating satisfactory reliability. Soil suffusion is better characterized and understood since a localized indicator and a precursor for suffusion-induced failure are considered.

Quasi-continuous exhaust operational space

Abstract The IPED predictive pedestal code has been used to determine the critical gradients for the onset of 1) separatrix ballooning modes and 2) global peeling-ballooning modes as a function of plasma shaping. This results in a scaling of the onset threshold of separatrix ballooning modes as a function of elongation and triangularity αedge,crit = 0.64κ2.2(1+δ)0.9, while the critical gradient for global peeling-balloonig modes increases as αedge,crit 1.5. This implies that operational space for a ballooning unstable separatrix and stable peeling-ballooning modes exists at sufficiently high shaping. Applying a collisional broadnening based scaling of the separatrix gradients allows the critical separatrix density, required to drive the separatrix ballooning mode, to be derived from global plasma parameters for any operational scenario on any device. Evaluations for ASDEX Upgrade, JET, and the ITER 15 MA baseline plasma predict critical separatrix densities of 0.3-0.4 nGW for QCE access, making the QCE an attractive operational scenario for fusion devices.

Infiltration Characteristics and Hydrodynamic Parameters in Response to Topographic Factors in Bare Soil Surfaces, Laboratory Experiments Based on Cropland Fields of Purple Soil in Southwest China

Topography is an important factor that impacts the hydrological processes on sloping farmlands. Yet, few studies have reported the combined influences of slope gradient and slope position on infiltration characteristics and hydrodynamic parameters on sloping croplands in purple soil regions, an important area for agricultural productivity in Southwest China. Here, laboratory-simulated rainfall experiments were conducted in a steel trough (5 m long, 2 m wide, and 0.45 m deep), and rainfall lasted for 1 h at a rate of 90 mm h−1 to examine the variations in the infiltration rates and hydrodynamic parameters under varying slope gradients (i.e., 3°, 6°, 10°, 15°, 21°, and 27°) and slope positions (i.e., upper, middle, and lower), and explore the relationships between the infiltration rate and the soil detachment rate. The results showed that the infiltration rate decreased gradually with duration rainfall and ultimately approached a steady state in the six slope treatments. Cumulative infiltration ranged from 15.54 to 39.32 mm during rainfall, and gradually reduced with the increase of slope gradient. The Horton’s model outperforms other models for predicting the infiltration rate with an R2 value of 0.86. Factors such as Darcy–Weisbach friction, flow shear force, Manning friction coefficient, unit energy, and runoff depth varied in the following order: upper slope > middle slope > lower slope, whilst the Reynolds number and Froude number gradually increased along the slope transect from the upper to lower slope positions. A significant linear function was fitted between the soil detachment rate and the infiltration rate at the gentle slopes (3°, 6°, 10°), whereas an exponential relationship was observed at the steep slopes (15°, 21°, and 27°). Observation also suggested that 15° was the critical slope gradient of sediment detachment, infiltration characteristics, and hydrodynamic parameters. Our results provide theoretical insight for developing models that predict the impacts of topographic factors on hydrological characteristic and soil erosion in hilly agricultural landscapes of purple soil fields.

Prediction of Backward Erosion, Pipe Formation and Induced Failure Using a Multi‐Physics SPH Computational Framework

ABSTRACTSeepage‐induced backward erosion is a complex and significant issue in geotechnical engineering that threatens the stability of infrastructure. Numerical prediction of the full development of backward erosion, pipe formation and induced failure remains challenging. For the first time, this study addresses this issue by modifying a recently developed five‐phase smoothed particle hydrodynamics (SPH) erosion framework. Full development of backward erosion was subsequently analysed in a rigid flume test and a field‐scale backward erosion‐induced levee failure test. The seepage and erosion analysis provided results consistent with experimental data, including pore water pressure evolution, pipe length and water flux at the exit, demonstrating the good performance of the proposed numerical approach. Key factors influencing backward erosion, such as anisotropic flow and critical hydraulic gradient, are also investigated through a parametric study conducted with the rigid flume test. The results provide a better understanding of the mechanism of backward erosion, pipe formation and the induced post‐failure process.

Sediment size effects on non-Darcy flow: insights from Izbash equation and Forchheimer inertial coefficient analysis

The transition from Darcy to non-Darcy flow regimes was investigated using column experiments. This revealed key relationships between sediment characteristics and critical thresholds for the onset of the non-Darcy flow regime, as well as inertial flow parameters. An exponential dependence of the critical Reynolds number (Rec) on hydraulic conductivity (K) and a linear dependence on sediment size (d50) was found. The analysis revealed a potentially universal relationship between the critical hydraulic gradient (Ic) and K, with a power-law exponent of –3/2, consistent with previous investigations. Additionally, Ic was found to be inversely proportional to the power law of the square root of d50. Novel relationships are derived for estimating the Izbash equation inertial exponent (n) and the Forchheimer inertial coefficient (β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta$$\\end{document}) based on sediment characteristics. The exponent (n) was found to decrease with d50 and increase with K, following power-law relationships. A new equation is proposed, capable of predicting β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta$$\\end{document} with slightly improved accuracy, outperforming numerous and previously proposed empirical equations. Additionally, these data validate the works of Ergun and Irmay as an alternative for β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta$$\\end{document} estimation using porosity and sediment size. As the attainment of statistical significance in multiparameter curve fitting can be trivial, it has led to the proliferation of empirical equations for estimating β. This study highlights the limitations of existing empirical methods in determining β and emphasizes the necessity for a universal approach to predict this critical parameter, which will facilitate broader adoption of the Forchheimer equation.

An improved small-scale test setup for assessing backward erosion piping

Backward erosion piping is one of the erosion mechanisms that lead to embankment dam incidents, whereby foundation granular materials are transported to the downstream toe leaving a shallow pipe in place. Most previous studies have focused on secondary erosion as the responsible process for the pipe progression. On the other hand, a few experimental investigations have considered primary erosion by restricting the pipe pathway within a confined channel for easier monitoring of local gradients. This paper presents a modified small-scale setup with the hole-type exit configuration to capture local hydraulic conditions associated with the progression of the pipe in a realistic and unconstrained pathway. Horizontal compaction and a more accurate measurement and acquisition system are other improvements added to this setup. The test outcomes of the two fine sands have revealed that the scale factor of Sellmeijer’s model can be used to predict the critical global hydraulic gradient for the specific geometry of the small-scale setup with the hole-type exit. Moreover, the progression of the pipe remains unaffected by loading history. Results also confirm the previous findings regarding the mutual influence of local gradient and pipe tip progression.

Shear-induced depinning of thin droplets on rough substrates

Depinning of liquid droplets on substrates by flow of a surrounding immiscible fluid is central to applications such as cross-flow microemulsification, oil recovery and waste cleanup. Surface roughness, either natural or engineered, can cause droplet pinning, so it is of both fundamental and practical interest to determine the flow strength of the surrounding fluid required for droplet depinning on rough substrates. Here, we develop a lubrication-theory-based model for droplet depinning on a substrate with topographical defects by flow of a surrounding immiscible fluid. The droplet and surrounding fluid are in a rectangular channel, a pressure gradient is imposed to drive flow and the defects are modelled as Gaussian-shaped bumps. Using a precursor-film/disjoining-pressure approach to capture contact-line motion, a nonlinear evolution equation is derived describing the droplet thickness as a function of distance along the channel and time. Numerical solutions of the evolution equation are used to investigate how the critical pressure gradient for droplet depinning depends on the viscosity ratio, surface wettability and droplet volume. Simple analytical models are able to account for many of the features observed in the numerical simulations. The influence of defect height is also investigated, and it is found that, when the maximum defect slope is larger than the receding contact angle of the droplet, smaller residual droplets are left behind at the defect after the original droplet depins and slides away. The model presented here yields considerably more information than commonly used models based on simple force balances, and provides a framework that can readily be extended to study more complicated situations involving chemical heterogeneity and three-dimensional effects.

Experimental analysis of the thermo-hydro-mechanical (THM) coupling in freezing vertical shafts of unsaturated sandy soil

The evolutionary mechanism of frozen soil involves complex dynamic coupling among temperature, moisture and the stress field. However, existing research has struggled to adequately describe the interplay between these factors. To address this, we independently designed and developed a multifunctional loading system appropriate for geotechnical engineering experimentation and a corresponding loading technology. Using a model of vertical shaft freezing, we studied the spatiotemporal evolution of thermo-hydro-mechanical (THM) multi-field coupling. The research findings indicate that, compared to the freezing interface, the main section experiences not only more intense variations in the temperature field but also heightened activity in terms of in-situ freezing and moisture migration. Both the radial and circumferential characteristic faces exhibit wave-like variations in moisture gradient evolution. The circumferential face features a critical gradient at 3.8 m−1, whereas the moisture gradient curve of the radial face undergoes temporal elongation at the peak, resulting in no discernible extremities. Each characteristic position of the frost heave force growth undergoes three distinct phases: incubation, rapid increase and stabilisation. During the same phases, the response times for the growth of frost heave forces on the radial characteristic face are roughly equivalent. However, when moving outward along the equivalent freezing radius, the response time on the circumferential face becomes progressively delayed.

Effect of symmetry-breaking on the MHD edge stability limit of tokamak plasmas

We demonstrate for the first time that symmetry-breaking in tokamak plasmas reduces the window of stable edge operational space, leading to a lower achievable edge pressure gradient. Predictive simulations with the linear magnetohydrodynamic stability code CASTOR3D show a reduction of the critical pressure gradient by up to 30%, in agreement with experimental observations. The analysis has been extended to experimental plasmas considering, for the first time, ion diamagnetic drift effects in realistic non-axisymmetric (3D) tokamak geometry. The 3D geometry in plasmas with edge localised modes (ELMs) increases the growth rate of edge instabilities compared to the axisymmetric case. Further reducing the edge pressure gradient eliminates the instabilities corresponding to an experiment with suppressed ELMs, reproducing the empirically observed threshold for ELM suppression. Our findings highlight the importance of predictions of the ELM occurrence in full 3D geometry for future tokamak devices with intentionally and unintentionally broken axisymmetry.

Durability Analysis of Concrete Cutoff Wall of Earth-Rock Dams Considering Seepage and Dissolution Coupling Effect

In this paper, a novel numerical model for characterizing the seepage and dissolution coupling effect on the durability of anti-seepage walls of earth-rock dams is proposed. The model considers the influence of hydraulic gradient-driven seepage on the non-equilibrium decomposition of the calcium dissolution in concrete, as well as the effects of seepage dissolution on pore structure, permeability, and diffusivity. The reasonableness of the model is validated by experimental and literature data, which is then applied to analyze the deterioration and failure processes of a concrete cutoff wall of an earth-rock dam in Zhejiang Province, China. On this basis, the seepage dissolution durability control indices of anti-seepage walls are identified. The findings demonstrate that the suggested method accurately explains the calcium leaching process in concrete. Under the seepage and dissolution coupling effect, calcium in the wall continuously decomposes and precipitates, leading to varying degrees of increases in structural performance parameters, which weaken the seepage control performance of the walls and consequently result in an increase in seepage discharge and hydraulic gradient. By proposing the critical hydraulic gradient as a criterion, the service life of the wall is projected to be 42.8 years. Additionally, the upstream hydraulic head, the initial permeability coefficient, and the calcium hydroxide (CH) content are three crucial indices affecting the durability of walls, and these indices should be reasonably controlled during the engineering design, construction, and operational phases.

Assessing core ion thermal confinement in critical-gradient-optimized stellarators

We investigate the core confinement properties of two recently devised quasi-helically symmetric stellarator configurations, HSK and QSTK. Both have been optimized for large critical gradients of the ion temperature gradient mode, which is an important driver of turbulent transport in magnetic confinement fusion devices. To predict the resulting core plasma profiles, assuming a fixed edge temperature, we utilize an advanced theoretical framework based on the gyrokinetic codes GENE and GENE-3D, coupled to the transport code TANGO. Compared to the HSX stellarator, both HSK and QSTK achieve significantly higher core-to-edge temperature ratios, partly thanks to their smaller aspect ratios, with the other part due to more detailed shaping of the magnetic geometry achieved during optimization. The computed core confinement time, however, is less sensitive to core temperature than the fixed edge temperature, simply due to the disproportionate influence, the edge has on stored plasma energy. We, therefore, emphasize the possible benefits of further optimizing turbulence in the outer core region, and the need to include accurate modeling of confinement in the edge region in order to assess overall plasma performance of turbulence optimized stellarators.

Segregation test—a standardisable test for suffusion assessment of granular soils

Suffusion is arguably the most complicated type of internal erosion. Although there are several popular assessment methods, the most realiable assessment is possibly still laboratory testing. However, there is not a standardised test for suffusion yet as different laboratories use different equipment and test configurations. Hence, a reliable comparison of outcomes across laboratories may not be able to achieve yet. This paper presents a new and simple, but very effective, way to test the susceptibility of soil to internal erosion using a novel segregation test. The test employs standard equipment which can be easily found in any geotechnical laboratory. There are some common characteristics of internal erosion and transport segregation, where fine particles are transported through the pore constrictions formed by the soil’s primary fabric. In segregation, particles are transported by gravitational/mechanical force to the bottom of the soil mass. Meanwhile, they are washed out of the soil mass by hydraulic force in internal erosion. Laboratory testing for internal erosion often requires specific equipment and a long duration. Meanwhile, segregation test could be undertaken with standardised sieving tower, which is available in any geotechnical laboratory. The approach was verified with an acrylic setup and some 3D-printed details. Later, the tests of 25 mixtures were undertaken with standard sieving sets. The correlation of laboratory results shows good agreement and prompts the common application of the new approach. The new test may not be able to completely replace the conventional suffusion test yet as it overlooks the critical hydraulic gradients at this stage, but it can be very useful if the research focuses on only the erodible mass and susceptibility to suffusion. In addition, it is a standardisable test with no specific requirements on equipment. The new approach may also be a starting point to study other types of internal erosion.

Experimental study on critical sand production pressure gradient at different production stages of high temperature and high pressure tight sandstone gas reservoir

AbstractSand production is a common issue in sandstone gas reservoir development, severely impacting the productivity of sandstone gas wells. In order to thoroughly investigate the sand production characteristics of high‐temperature and high‐pressure tight sandstone gas reservoirs, this study focuses on six core samples from tight sandstone gas reservoirs(three samples with fractures), under reservoir conditions (185 MPa, 160°C), sand production experiments were conducted to thoroughly investigate the sand production patterns in sandstone reservoirs under the combined influence of different effective stresses and production pressure differentials. The results indicate: (1) under the simultaneous increase of effective pressure and production pressure differential, sand production near the wellbore (r = 0.1 m) becomes more likely in the reservoir; (2) in actual reservoirs without fractures near the wellbore (r = 0.1 m), sand production phenomena do not occur; (3) reservoirs with fractures near the wellbore (r = 0.1 m) are more prone to sand production, under an effective stress of 90 MPa, with specimens containing fractures exhibiting a 76.48% lower critical sand production pressure gradient compared to those without fractures; (4) when the pore fluid pressure is 95 MPa, the maximum gas production rate for Well X without sand production is 12.4 × 104 m3/d. The experimental results have guiding significance for the rational production of gas wells in this type of reservoir.

Evaluation of hydrogen/ammonia substitute fuel mixtures for methane: Effect of differential diffusion

One strategy for utilizing ammonia as an energy vector is to replace conventional hydrocarbons with hydrogen-enriched ammonia in existing or retrofitted combustors. However, the strong differential diffusion effect of hydrogen can significantly alter the combustion properties and cause challenges in combustor operability. Therefore, this numerical study performs a systematic investigation on the effect of differential diffusion on fundamental combustion properties of ammonia/hydrogen fuel blends. The investigated combustion properties span from the initiation of combustion, i.e., ignition, to stretched flame propagation and ultimately to flame stabilization mechanisms. The objective is to evaluate the feasibility of hydrogen/ammonia/air mixtures as substitutes for methane/air particularly considering the implications of differential diffusion effects. To this end, four fuel blends with similar unstretched burning properties are selected: fuel lean ammonia/hydrogen (AH-L), fuel rich ammonia/hydrogen (AH-R), fuel lean methane (M-L) and fuel lean methane/hydrogen (MH-L). First, the forced ignition and stretched flame propagation are evaluated. It is found that the AH-L (AH-R) mixture has a large negative (positive) Markstein length, and thereby among the selected fuel blends, AH-L (AH-R) has the lowest (highest) minimum ignition energy. Then flame stabilization mechanisms are investigated. For a stable flame, AH-L (AH-R) has an intensified (weakened) flame base and a weak (strong) flame tip, which shows a higher flashback (blow-off) propensity. Based on the critical gradient theory, a novel stability regime diagram is proposed. With the regime diagram, the flame stabilization limits (central flashback, boundary layer flashback, stable, and blow-off) and flow conditions can be determined for burners of different sizes.

Reduction of electrostatic turbulence in a quasi-helically symmetric stellarator via critical gradient optimization

We present a stellarator configuration optimized for a large threshold (‘critical gradient’) for the onset of the ion temperature gradient (ITG) driven mode, which achieves the largest critical gradient we have seen in any stellarator. Above this threshold, gyrokinetic simulations show that the configuration has low turbulence levels over an experimentally relevant range of the drive strength. The applied optimization seeks to maximize the drift curvature, leading to enhanced local-shear stabilization of toroidal ITG modes, and the associated turbulence. These benefits are combined with excellent quasi-symmetry, yielding low neoclassical transport and vanishingly small alpha particle losses. Analysis of the resulting configuration suggests a trade-off between magnetohydrodynamic (MHD) and ITG stability, as the new configuration possesses a vacuum magnetic hill.

Hydraulic breakthrough of clay smears due to technical and natural actions

We outlined earlier in this journal by means of finite element simulations how patterns of normal faults arise by a synsedimentary tectonic extension, and how clay smears evolve therein. In the present paper, we show how hydraulic breakthroughs of clay smears can arise so that water, gas and mud rise in faults. Mechanical properties of sand and clay are introduced first for the stable range and then for rupture and internal erosion. Our numerical simulations for the evolution of normal faults and clay smears are discussed in light of critical phenomena. Water assembled in an open-cast mine about 20 years ago as the critical hydraulic gradient in a clay smear dropped to the actual one due to the rapid excavation-induced deformation. The latter led to a critical point under an excavation the slope of which was parallel to a nearby normal fault. Clay smears can also break by earthquakes so that the critical hydraulic gradient drops to the actual one caused by methane with an excess pressure. This can lead to hydraulic breakthroughs and cold eruptions at outcrops of faults.

Exceptional grain refinement induced by dispersed MgO particles in TIG-welded AZ31 alloy

Due to the low content of alloying elements and the lack of effective nucleation sites, the fusion zone (FZ) of tungsten inert gas (TIG) welded AZ31 alloy typically exhibits undesirable coarse columnar grains, which can result in solidification defects and reduced mechanical properties. In this work, a novel welding wire containing MgO particles has been developed to promote columnar-to-equiaxed transition (CET) in the FZ of TIG-welded AZ31 alloy. The results show the achievement of a fully equiaxed grain structure in the FZ, with a significant 71.9% reduction in grain size to 41 µm from the original coarse columnar dendrites. Furthermore, the combination of using MgO-containing welding wire and pulse current can further refine the grain size to 25.6 µm. Microstructural analyses reveal the homogeneous distribution of MgO particles in the FZ. The application of pulse current results in an increase in the number density of MgO (1-2 µm) from 5.16 × 104 m−3 to 6.18 × 104 m−3. The good crystallographic matching relationship between MgO and α-Mg matrix, characterized by the orientation relationship of [112‾0]α−Mg//[01‾1]MgO and (0002)α−Mg//(111)MgO, indicates that the MgO particles can act as effective nucleation sites for α-Mg to reduce nucleation undercooling. According to the Hunt criteria, the critical temperature gradient for CET is greatly enhanced due to the significantly increased number density of MgO nucleation sites. In addition, the correlation with the thermal simulation results reveals a transition in the solidification conditions within the welding pool from the columnar grain zone to the equiaxed grain zone in the CET map, leading to the realization of CET. The exceptional grain refinement has contributed to a simultaneous improvement in the strength and plasticity of welded joints. This study presents a novel strategy for controlling equiaxed microstructure and optimizing mechanical properties in fusion welding or wire and arc additive manufacturing of Mg alloy components.

Hydraulic heave in granular soils under hypergravity conditions

A series of discrete element method (DEM) simulations have been conducted to investigate the initiation and development of hydraulic heave for granular soils under hypergravity. During the development of hydraulic heave, local failure can occur when the stress-reduction factor (α) is less than 0.8, in which the particles are reorganized by the fluid and subsequently regain stability as particles settle down. However, if α is greater than 0.8, global failure occurs, causing the mobilization of the entire soil. The triggering mechanism of the hydraulic heave is the force equilibrium between the contact force and critical fluid force, which scales up proportionally with g-level. The non-linear variation of critical hydraulic gradient (icr) with g-levels is attributed to the non-linear relationship between fluid force and hydraulic gradient. Finally, an analytical model along with a fitting formula, is proposed to predict this non-linear relationship between icr and g-level.

Overburden failure and water–sand mixture outburst conditions of weakly consolidated overlying strata in Dananhu No.7 coal mine

This study presents a case of weakly consolidated strata developed in Dananhu No.7 coal mine. Using a combination of numerical simulation, field measurement comparison, and the critical hydraulic gradient criterion, we investigate the overburden failure and the risk possibility of water–sand mixture inrush during excavation. The following are the principal findings: (1) Weakly consolidated rocks have poor physical characteristics, particularly when they are mudded and disintegrated after encountering water, which may become a favorable source of water–sand inrush; (2) The water-conducting zone develops to a height of 160.5 m with a crack-mining ratio of 15.29 times, extending upward to Toutunhe Formation aquifer. The predictions are consistent with measurements in adjacent mines with similar geological conditions; (3) Cracks without larger subsidence are developed at the front edge of the mining direction, and some parallel stepped cracks behind the goaf could be easily observed. Ground subsidence along the goaf center finally displays a symmetrically wide-gentle U shape; (4) The critical hydraulic gradient of Toutunhe Formation aquifer, aquifer above 3# coal seam, and aquifer of 3#–7# coal seam in Xishanyao Formation is 1.314, 1.351, and 1.380, the actual value is 0.692, 2.089, and 7.418 accordingly. It is inferred water–sand mixture outburst will not occur in Toutunhe Formation aquifer, while the potential risk exists in the aquifers of Xishanyao Formation. Through drainage and depressurization projects, a water–sand mixture outburst accident does not occur during excavation. This study reveals the overburden failure characteristics and the initiation mechanism of water–sand inrush in weakly cemented strata, as well as the internal relationship between them, which provides new research ideas for safe operation in other mining areas with similar geological conditions. The research work has certain practical guiding significance.