Critical Gradient Research Articles

Experimental and numerical investigation on nonlinear flow behaviour through three dimensional fracture intersections and fracture networks

Abstract Fluid flow tests were conducted on four kinds of fracture intersections, namely straight fracture intersection, buckling fracture intersection, crossing fracture intersection and furcating fracture intersection. Corresponding numerical simulations were performed by solving the Navier-Stokes equations. The resultant flow force perpendicular to fracture walls were derived. The results show that at high hydraulic gradients the increased normal resultant force perpendicular to fracture walls will change the original flow direction and consequently cause the formation of eddies which triggers flow nonlinearity. Greater buckling angle and smaller crossing angle would result in the onset of nonlinear flow at a higher critical hydraulic gradient for the cases of buckling and crossing fracture intersections. The critical hydraulic gradient for the case of furcating fracture intersection depends on the absolute angle between furcating flow and the original flow direction. Based on the analyses, three nonlinear models for coefficient B in the Forchheimer law corresponding to three cases of fracture intersections are proposed, which are related to the fracture intersection angle and hydraulic aperture. These models are further validated using flow experimental data from a real fracture network created in a rock specimen with the corresponding fracture model constructed using the computed tomography (CT) method.

ANALYTICAL SOLUTIONS FOR PERMEABILITY OF A THREE-DIMENSIONAL FRACTAL-LIKE TREE NETWORK MODEL WITH FRACTURES HAVING VARIABLE WIDTHS

This study proposed analytical solutions for permeability of a fractal-like tree network model with fractures having variable widths, which has not been reported before, if any. This model is more realistic with natural fracture networks than the traditional constant width fracture network models. The results show that considering fracture width variations decreases the permeability. Taking the fracture width ratio that equals to 0.6 and the total number of branching levels that equals to 30 as an example, the permeability decreases by more than three orders of magnitude with respect to that of a constant width fracture network model. The fracture length ratio plays a more significant role in permeability when it is larger than 0.8 than that is less than 0.8. The permeability is more sensitive to the fracture aperture ratio that is less than 0.8. When the total number of branching levels is large (i.e. 30), the permeability changes significantly (i.e. more than three orders of magnitude); whereas when the total number of branching levels is small (i.e. 5), the permeability varies in a small range (i.e. less than one order of magnitude). When taking into account the relationships among fracture length ratio, fracture aperture ratio and fracture width ratio, the parameters can be easily obtained and analytical solutions for permeability can also be easily derived. The empirical function for predicting critical hydraulic gradient is proposed, which can be used to estimate whether the fluid flow is within the linear flow regime and whether the proposed analytical solutions are applicable in the present study.

Optimisation of microbially induced calcite precipitation protocol against erosion

Five strategies of microbially induced calcite precipitation (MICP) are suggested to improve the uniformity of treatment and enhance the erosional/hydraulic response of internally unstable and poorly graded soils. The treatment consisted of the injection of a bacterial suspension and a cementation solution. The volume of the injected bacterial suspension varied from 0·3 to one pore volume, while the concentration of the cementation solution (urea/calcium chloride (CaCl2)) varied from 0·35 to 0·75 M. The biotreatment of sand columns (ϕ = 160 mm and h = 100 mm) was conducted in either one, two or three stages, with or without a low-salinity fixation solution. The biotreated specimens were then submitted to an erosion test, and the results show that alternating injection of reagents in three stages enhances the uniformity of biomineralisation, as the hydraulic conductivity is constant from the top to the bottom of the specimens. This protocol also prevents internal erosion as the critical hydraulic gradient (i cr) is equal to 10 and the cumulative fine loss (M e) does not exceed 63 g/m2. Finally, the use of a fixation solution prevents any clogging near the injection point and stimulates the bacterial transport in the soil.

Non-darcian flow in loess at low hydraulic gradient

Determining the mechanism of water flow in loess involves many problems that are vital to science and engineering. Water flow through loess has usually been assumed to follow Darcy's law, but this has not been properly validated. The main objective of this study is to validate the applicability of Darcy's law for loess. For this purpose, we conducted constant-head permeability experiments and mercury injection porosimetry (MIP) on loess specimens of different dry densities. The results indicate that Darcy's law is not suitable for describing water seepage in loess at low hydraulic gradient, since there is a threshold hydraulic gradient (i0) below which no flow is observed and a critical hydraulic gradient (icr) below which the relationship between the hydraulic gradient (i) and seepage velocity (v) is non-linear. The MIP results show that variation in hydraulic conductivity is closely related to the pore size distribution (PSD) in loess specimens. i0 is positively correlated with the content of pores with diameters in the range of 0.01–1 μm and negatively correlated with the content of pores with diameters larger than 3 μm. The existence of bound water on loess is the main reason that its permeability deviates from Darcy's law. The mechanism of water movement in loess can be fully understood by considering the effect of bound water.

Ultrafast domain wall motion in ferrimagnets induced by magnetic anisotropy gradient

The ultrafast magnetic dynamics in compensated ferrimagnets not only provides information similar to antiferromagnetic dynamics, but more importantly opens new opportunities for future spintronic devices [Kim et al., Nat. Mater. 16, 1187 (2017)]. One of the most essential issues for device design is searching for low-power-consuming and high-efficient methods of controlling domain wall. In this work, we propose to use the voltage-controlled magnetic anisotropy gradient as an excitation source to drive the domain wall motion in ferrimagnets. The ultrafast wall motion under the anisotropy gradient is predicted theoretically based on the collective coordinate theory, which is confirmed by the atomistic micromagnetic simulations. The antiferromagnetic spin dynamics is realized at the angular momentum compensation point, and the wall shifting has a constant speed under small gradient and can be slightly accelerated under large gradient due to the broadened wall width during the motion. For nonzero net angular momentum, the Walker breakdown occurs at a critical anisotropy gradient significantly depending on the second anisotropy and interfacial Dzyaloshinkii-Moriya interaction, which is highly appreciated for further experiments including the materials selection and device geometry design. More importantly, this work unveils a low-power-consuming method of controlling the domain wall in ferrimagnets, benefiting to future spintronic applications.

Effect of Clay on Internal Erosion of Clay‐Sand‐Gravel Mixture

In this study, a one‐dimensional seepage test apparatus was used to investigate the effect of clay on the critical hydraulic gradient, hydraulic conductivity, migration of fine particles in soil, and percentage of fine particle loss during the internal erosion of clay‐sand‐gravel mixture, compared with clean gravel. The critical hydraulic gradient and fine sand loss percentage of the clay‐sand‐gravel mixture decreased, and critical flow velocity and the hydraulic conductivity increased. Six clay‐sand‐gravel mixture samples with different clay contents were used to evaluate the effect of different clay contents on internal erosion. As the percentage of clay mass to fine particle mass increases from 0% to 25%, the critical hydraulic gradient of soil samples decreases by nearly half and the fine sand loss percentage decreases from 13.73% to 3.48%. Overall, clay has a significant effect on the development of internal erosion of clay‐sand‐gravel mixture. And attention should be paid in engineering project; clay‐sand‐gravel mixture with a small amount of clay is more likely to be damaged than clean gravel.

Risk Assessment of Polluted Glass Insulator Using Leakage Current Index Under Different Operating Conditions

In this article, an innovative approach to assess the risk of uniform/non-uniform pollution and wet high voltage glass insulator is proposed. The assessment is based on a new index, named as $R_{hi}$ , which is derived from the $3^{\mathrm {rd}}$ , $5^{\mathrm {th}}$ and $7^{\mathrm {th}}$ harmonics of the leakage current. Two 33 kV strings of cap and pin glass insulators having three units with different profiles are employed to evaluate the risk level, based on measured critical voltage gradient ( Ec ). Critical voltage stress tests are executed on the contaminated insulators under different ratios of lower to upper surface ( $J$ ) and wetting rates. Furthermore, the effects of ratio of soluble deposit density ( ESDD ) to non-soluble deposit density ( NSDD ) on the flashover occurrence are analyzed. It was found that the insulator profile has significant influences on the likelihood of flashover which is estimated as 38% and 24% for type A and B insulators, respectively. From the results, it can be concluded that the proposed $R_{hi}$ index is able to predict the risk level of the insulator and the probability of flashover occurrence more accurately than the 5th/3rd index, which is widely published in literature.

Short wavelength ion temperature gradient mode in tokamak plasmas with hollow density profiles

By the gyrokinetic integral eigenmode equation, we numerically investigate the short-wavelength ion-temperature-gradient (SWITG) mode in tokamak plasmas with hollow density profiles. This paper finds that the critical ion temperature gradient (ITG) R/LTiC exists for the hollow density profile. Over such a gradient, the SWITG mode is unstable. The R/LTiC for a hollow density profile is slightly lower than that for a peaked density profile, though far away from the threshold, the mode in the latter case is more unstable. Furthermore, the scaling of the ITG threshold increasing with ion-to-electron temperature ratio Ti/Te has been calculated, suggesting that the SWITG mode is more difficult to excite in hot ion plasmas as compared with that in hot electron plasmas. For the slightly hollow density profiles, it is shown that in the case of flat (peaked) electron temperature profiles, the SWITG modes are destabilized (stabilized) by the trapped electrons. For the steep hollow density profiles, however, the trapped electrons reduce the growth rate substantially, and thus, the SWITG stability threshold is raised significantly. In addition, the dependence of the threshold on local plasma parameters is analyzed in detail. It is found that the SWITG modes become more unstable for the high safety factor, small Larmor radius, weak magnetic shear, and high electron-to-ion temperature ratio.

Examination of the Size and Morphology of Austenite Grains in Lamellar Graphite Cast Iron

There is a current discussion concerning the austenite grains of lamellar graphite irons and its growth at different carbon equivalent contents. The term “grain” is often employed to refer not only to the primary austenite, but also to the colonies or cells formed during the eutectic solidification. This investigation applies advanced experimental methods to study the solidification of lamellar graphite iron. A better understanding of the solidification process should lead to the design of better casting procedures. Samples of lamellar graphite iron were cast and directly austempered after solidification in order to reveal their solidification macrostructure. A typical ingot structure was found, with a narrow columnar-to-equiaxed transition. Electron backscatter diffraction technique was applied to confirm these macroscopic observations. Color etching was employed to determine the size of eutectic colonies at the columnar and equiaxed regions. The EBSD results confirm previous proposals, revealing that the solidification grains result from the growth of austenite dendrites. These grains include several eutectic colonies or cells inside, all these colonies or cells having the same crystalline orientation as the primary austenite dendrite. An analysis of the critical gradient for columnar-to-equiaxed transition could be developed. The size of the eutectic colonies at the columnar zone was found to be smaller than the size of the eutectic colonies at the equiaxed zone. Besides, the size of equiaxed grains strongly decreased with the increase in cooling rate, while no evident differences were obtained when the size of the columnar grains was measured.

Prediction of Alfvén eigenmode energetic particle transport in ITER scenarios with a critical gradient model

A reduced 1D, local, critical-gradient model of energetic particle (EP) transport by Alfvén eigenmodes (AEs)—the TGLF-EP+Alpha model—is applied to a much-studied ITER base case and variations with lower plasma current and lower current penetration. The TGLF-EP+Alpha model is a highly reduced and computationally inexpensive model of EP transport. Such a reduced critical-gradient model, while inapplicable to transport driven by strongly nonlinear or non-local abrupt events, is a valuable tool for scoping studies needed in scenario optimization for ITER and beyond. It relies on the assumption of critical-gradient AE transport with the critical EP density gradient determined by linear AE stability calculations in the TGLF gyro-Landau fluid code automated with the parallel-processed TGLF-EP wrapper. EP transport is treated with simultaneous drive of AEs by fusion-born alpha particles and fast ions born from a MeV neutral beam injection heating. The effect of simultaneous drive creates about 50% increased particle transport in both EP channels. High magnetic safety factor and low shear are generally destabilizing to AEs, but low shear tends to be more important. A tailored q-profile, steady-state-relevant scenario can reduce AE-induced EP redistribution by more than 25% over the ITER base case despite having half the total current.

Estimating the disequilibrium in denudation rates due to divide migration at the scale of river basins

Abstract. Basin-averaged denudation rates may locally exhibit a wide dispersion, even in areas where the topographic steady state is supposedly achieved regionally. This dispersion is often attributed to the accuracy of the data or to some degree of natural variability of local erosion rates which can be related to stochastic processes such as landsliding. Another physical explanation of this dispersion is local and transient disequilibrium between tectonic forcing and erosion at the scale of catchments. Recent studies have shown that basin divide migration can potentially induce such perturbations, and they propose metrics to assess divide mobility based on cross-divide contrasts in headwater topographic features. Here, we use a set of landscape evolution models assuming spatially uniform uplift, rock strength and rainfall to assess the effect of divide mobility on basin-wide denudation rates. We propose using basin-averaged aggressivity metrics based on cross-divide contrasts (1) in channel χ, an integral function of position in the channel network; (2) in channel local gradient; and (3) in channel height, measured at a reference drainage area. From our simulations, we show that the metric based on differences in χ is the most reliable to diagnose local disequilibrium. The other metrics are more suitable for relatively active tectonic regions such as mountain belts, where contrasts in local gradient and elevation are more important. We find that the ratio of basin denudation associated with drainage migration to uplift can reach a factor of 2, regardless of the imposed uplift rate, erodibility, diffusivity coefficient or critical hillslope gradient. A comparison with field observations in the Great Smoky Mountains (southern Appalachians, USA) underlines the difficulty of using the metric based on χ, which depends on the – poorly constrained – elevation of the outlet of the investigated catchment. Regardless of the considered metrics, we show that observed dispersion is controlled by catchment size: a smaller basin may be more sensitive to divide migration and hence to disequilibrium. Our results thus highlight the relevance of divide stability analysis from digital elevation models as a fundamental preliminary step for basin-wide denudation rate studies based on cosmogenic radionuclide concentrations.

Test Study on the Suffusion Process of Sand-Rock Mixtures by NMR Systems

Test results on the suffusion of sand-rock mixtures (SRMs) in one-dimensional laboratory seepage tests are reported with details regarding the experimental setup and procedures. The nuclear magnetic resonance (NMR) systems were successfully applied to track fine-particle migration through pores and detect the pore size distribution of SRMs during suffusion. This article discussed the changes of pore size distribution and fine-particle migration and its effect on the suffusion mechanism at 0, 15, 30, 60, 90, and 120 min under the critical hydraulic gradient. Then, the mesostructural changes of mixtures—such as pore distribution, curvature coefficient, and pore fractal dimension—were analyzed to reveal the suffusion mechanism, and an original suffusion evaluation model was proposed. The results showed that the pore connectivity and fine-particle migrations as two controlling factors for suffusion are an interactive process. Furthermore, the pore size range was narrowed and mostly concentrated in large pores with an increase of pore volume, resulting in fine-particle migration and structural deterioration. Moreover, the suffusion evaluation model was divided into four stages by the mesostructural parameters variation.

Modelling seepage flow near the pipe tip

Backward erosion piping is an important failure mechanism in both dikes and dams where uniform silts and sands are covered by a cohesive layer. It is an internal erosion mechanism during which shallow pipes are formed at the interface of the aquifer and the cohesive top layer in the direction opposite to the flow. The hydraulic conditions near the pipe tip determine the onset of erosion near the pipe tip, which causes pipe lengthening. The seepage field near the pipe tip was analysed using the analytical solutions. The two-dimensional (2D) analytical solution available for calculating the seepage field at the vertical section of the pipe tip in three-dimensional (3D) groundwater flow has been validated on the basis of experiments with 3D configurations. The motion characteristics of particles at the pipe tip were explained on the basis of the analysis of the effect of the ditch at the toe of the pipe tip on the hydraulic conditions near the pipe tip. The equilibrium of the soil in front of the pipe tip was analysed to determine the pressure distribution on the top of the sand layer in front of the pipe tip. The unified method for calculating the local critical hydraulic gradient at the pipe tip in both 2D and 3D experiments was proposed. The local critical hydraulic gradients at the pipe tip were analysed for the available experiments, indicating that the influences of grain diameter and scale on the local critical hydraulic gradient are limited, a finding that is essential for the development of a new model.

Exploring the interaction of surface roughness and slope gradient in controlling rates of soil loss from sloping farmland on the Loess Plateau of China

AbstractSurface roughness and slope gradient are two important factors influencing soil erosion. The objective of this study was to investigate the interaction of surface roughness and slope gradient in controlling soil loss from sloping farmland due to water erosion on the Loess Plateau, China. Following the surface features of sloping farmland in the plateau region, we manually prepared rough surfaces using four tillage practices (contour drilling, artificial digging, manual hoeing, and contour plowing), with a smooth surface as the control measure. Five slope gradients (3°, 5°, 10°, 15°, and 20°) and two rainfall intensities (60 and 90 mm/hr) were considered in the artificial rainfall simulation experiment. The results showed that the runoff volume and sediment yield increased with increasing slope gradient under the same tillage treatment. At gentle slope gradients (e.g., 3° and 5°), the increase in surface roughness prevented the runoff and sediment production, that is, the surface roughness reduced the positive effect of slope gradient on the runoff volume and sediment yield to a certain extent. At steep slope gradients, however, the enhancing effect of slope gradient on soil erosion gradually increased and surpassed the reduction effect of surface roughness. This study reveals the existence of a critical slope gradient that influences the interaction of surface roughness and slope gradient in controlling soil erosion on sloping farmland. If the slope gradient is equal to or less than the critical value, an increase in surface roughness would decrease soil erosion. Otherwise, the increase in surface roughness would be ineffective for preventing soil erosion. The critical slope gradient would be smaller under higher rainfall intensity. These findings are helpful for us to understand the process of soil erosion and relevant for supporting soil and water conservation in the Loess Plateau region of China.

Outflows from inflows: the nature of Bondi-like accretion

ABSTRACT The classic Bondi solution remains a common starting point both for studying black hole growth across cosmic time in cosmological simulations and for smaller scale simulations of active galactic nuclei (AGN) feedback. In nature, however, there will be inhomogeneous distributions of rotational velocity and density along the outer radius (Ro) marking the sphere of influence of a black hole. While there have been many studies of how the Bondi solution changes with a prescribed angular momentum boundary condition, they have all assumed a constant density at Ro. In this Letter, we show that a non-uniform density at Ro causes a meridional flow and due to conservation of angular momentum, the Bondi solution qualitatively changes into an inflow–outflow solution. Using physical arguments, we analytically identify the critical logarithmic density gradient |$\partial \ln \rho/\partial \theta$| above which this change of the solution occurs. For realistic Ro, this critical gradient is less than 0.01 and tends to 0 as Ro → ∞. We show using numerical simulations that, unlike for solutions with an imposed rotational velocity, the accretion rate for solutions under an inhomogeneous density boundary condition remains constant at nearly the Bondi rate $\dot{M}_\mathrm{ B}$, while the outflow rate can greatly exceed $\dot{M}_\mathrm{ B}$.

Toward an Integrated View of Ionospheric Plasma Instabilities: 4. Behavior in the Transitional Valley Region

AbstractBehavior of unstable plasma waves generated by the Farley‐Buneman instability (FBI) and the gradient drift instability (GDI) is analyzed in the transitional valley region near 120 km in altitude. The analysis is based on the expression for the FBI/GDI growth rate γ that has been recently generalized to include ion inertia effects for arbitrary altitude and wavelength, within the limits imposed by the fluid and local approaches. It is found that the ion inertia leads to a different instability behavior when the convection component is between the two critical values determined by the ion acoustic speed Cs and the ratio ri between the ion collision and gyrofrequency. The most interesting case occurs near 120 km, just below where ri=1. From analysis of electron density gradients G=∇n/n that result in marginal instability condition γ=0 (i.e., critical gradients G0), there exists a critical scale where G0=0 and below which all waves are unstable to FBI. Above this scale, G0>0 and gradients need to be sufficiently strong G>G0 for the plasma to become unstable through GDI. There also exists a maximum in dependence , which refers to the least unstable scale and gradient. For convection outside of the specified range, no critical or least unstable scale exists, which is a typical situation outside of the transitional valley region. Overall, this analysis shows that the FBI convection thresholds and the GDI critical gradients are modified by the ion inertia and that the effects are most pronounced in the transitional valley region near 120 km.

Study on Water-Sand Inrush Mechanism for Mining Under Pore Water in China

In China, pore water is one of the major water hazards of coalmines, accountable for severe pit flooding and human casualties. This article introduced the two types of water-sand conducting channels, primary and man-made, contributing to water-sand inrush when mining under pore aquifer of the bottom Quaternary loose strata; the four situations of water-sand inrush mechanism caused by man-made channels channelling pore aquifer, man-made channels involving pore aquifer via primary channels, and waterproof coal pillar caving when mining on steep-slope coal seam; as well as analysis of the correlation between the critical hydraulic gradient and the coarse particles ratio based on results from penetration test. It is to provide references for countries confronting similar problems and to facilitate international discussions on pore water control.

Pore characteristics and nonlinear flow behaviors of granite exposed to high temperature

This paper experimentally investigates the role of high temperature treatment on pore characteristics, permeability, critical Reynolds number, and flow nonlinearity of granite exposed to temperatures of 100~800 °C. First, variations in pore characteristics, porosity, and pore fractal dimension of granite were analyzed using the mercury intrusion method. Then, a number of water flow tests were conducted on the samples with confining pressures varying from 10 to 30 MPa. The results show that (i) the cumulative pore volume of granite shows an increase with temperatures, which first increases gradually in the range of 100~400 °C, and increases significantly in the range of 400~800 °C. The pore structure becomes developed gradually; (ii) as the temperature increases from 100 to 800 °C, the pore fractal dimension decreases by 12.09%, indicating gradually weaken complexity of pore distributions. An exponential function is used to evaluate the increasing porosity of rock based on the temperature levels; (iii) the relations between volume flow rate and pressure gradient can be well described using the Forchheimer’s law. Both linear and nonlinear coefficients increase with the confining pressure. The equivalent permeability experiences an exponential increase with the temperature due to thermally induced defects; (iv) by defining a critical nonlinear effect factor of 10%, the critical pressure gradient was calculated, which increases with the confining pressure. The critical Reynolds number shows a decrease of 25.49%~67.74% with confining pressure due to more isolated contact areas and tortuous flow paths but increases by a factor of 5.97~17.24 with the temperature. A three-order polynomial function is used to analyze the decrease in transmissivity versus the pressure gradient. The Forchheimer’s law results are evaluated by plotting the normalized transmissivity against the pressure gradient, and an increase in the temperature generally shifts the fitted curves downward.

Reservoir quality and expected fluids for the Ordovician Hawaz sandstone in the NC186 Concession, Murzuq Basin, Libya

The present work evaluates the Middle Ordovician Hawaz sandstone reservoir in four wells (A25-NC186, A30-NC186, H2-NC186 and H4-NC186) distributed in the NC186 Concession of Murzuq Basin, Libya. The available well log data set for each well includes: gamma ray, calliper, spontaneous potential, resistivity, density, neutron, sonic, density correction and photoelectric logs. These data have been qualitatively interpreted using Interactive Petrophysics (IP) software and quantitatively analysed by calculating different petrophysical parameters comprising; water saturation, minimum bulk volume of water, absolute permeability, critical water saturation, pressure gradient and fluid density for the promising horizons. The quantitative interpretation has revealed that three horizons (H4, H5 and H6) are suitable for further quantitative interpretation. The calculated petrophysical parameters for these horizons show that all of the studied zones represent oil reservoirs in an irreducible state (i.e. water-free oil production). This finding indicates that the remaining water is located on the pore surfaces as thin films and will not move through the production process. The results reflect excellent reservoir quality for all examined zones, including high porosity (10–26%), high permeability (42–2824 mD), low water saturation (12–43%) less than the critical water saturation (31–45%) and low BVW (0.02–0.06) less than BVWmin (0.07).

Experimental Investigation of Grout Nonlinear Flow Behavior through Rough Fractures

This research experimentally analyzed the impacts of various water cement (W/C) ratios of ultrafine cement grout material and normal loads FN applied to fractures on grout nonlinear flow behavior through a rough plexiglass fractured sample. An effective self-made apparatus was designed and manufactured to conduct the stress-dependent grout flow tests on the plexiglass sample containing rough fractures. At each W/C ratio, the grout pressure P increased from 0 to 0.9 MPa, and the normal loads FN ranged from 666.3 to 1467.8 N. The results of the experiments indicate that (1) the Forchheimer’s law can be used to express the results of grout nonlinear flow through rough fractures. Moreover, both nonlinear coefficient a and linear coefficient b in Forchheimer’s law decreased with the increase of the W/C ratio, but increased with the increase of the FN value. (2) For normalized transmissivity, with the increase of Re, the decline of the T/T0–Re curves means that the grout flow behavior through the fracture mainly went through three stages: the viscosity effect, then the weak inertia effect, and finally the strong inertia effect. The three stages showed that with the increase of Re, the grout flow state changed from linear to nonlinear. Moreover, with the increase of the W/C ratio, the Forchheimer coefficient β decreased. (3) At a given FN, the critical grout hydraulic gradient Jc decreased, but the critical Reynolds number Rec increased as the W/C ratio increased; at a given W/C ratio, Jc increased, but Rec decreased as FN increased.