Critical Hydraulic Gradient Research Articles

Prediction Method for Fine Particle Loss Rate of Sandy Soil under Suffusion

In the process of seepage, the internally unstable fine particles of sandy soil are easy to be lost and form suffusion, which has a negative effect on the geotechnical building or foundation. The loss rate of fine particles is a key parameter for soil mechanical property degradation and stability analysis. In order to predict the loss rate of fine particles in sandy soil under suffusion, the internal stability evaluation criteria for determining whether soil will undergo suffusion is discussed first. Second this paper gives critical hydraulic gradient for erosion initiation and introduces the stress reduction factor. And then considering the difference of soil particles' forces, the stress reduction factor is modified, meanwhile the “erosion initiation probability of fine particles” is introduced to quantify the erosion initiation of fine particles. Next the migration process of fine particles in the pore network of soil is analyzed, and the probability of fine particles through constriction and the migration distance are given. Finally, the law of fine particle erosion and deposition are given according to the law of fine particle erosion initiation and migration, and the prediction method of fine particle loss rate was formed based on the law of mass conservation. The calculated results of fine particle loss by this prediction method are in good agreement with the numerical results, and the error is basically within 15%.

Physical observations of the transient evolution of the porosity distribution during internal erosion using spatial time domain reflectometry

A purpose-built permeameter was used to explore the transient evolution of porosity during the mixing process in filtration experiments. The experiments considered upward seepage flow and explored the influence of base and filter particle sizes, along with different hydraulic conditions. The permeameter acted as a coaxial transmission line enabling electromagnetic measurements based on spatial time domain reflectometry, from which the porosity profile was obtained using an inversion technique. Quantitative characteristics of the onset and progression of the mixing process were extracted from a porosity field map. The limiting onset condition was influenced by geometric and hydraulic factors, with the critical flow rate exhibiting a strong dependence on the base particle size, while the critical hydraulic gradient exhibited a stronger dependence on filter particle size. The progression of the mixing process was characterised by both the transport of base particles into the filter layer, as well as the settlement of the filter particles into the base layer due to the reduction of the effective stress at the base–filter interface leading to partial bearing failure. The rate of development of the mixture zone was strongly dependent on the hydraulic loading condition and the base particle size, but the final height of the sample after complete mixing was independent of the hydraulic loading path.

On fluid flow regime transition in rough rock fractures: Insights from experiment and fluid dynamic computation

The influence of roughness, aperture and asperity irregularity on fluid flow regimes in rough rock fractures was investigated by performing coupled triaxial water flow tests and fluid dynamic computation. Ten sets of fabricated curved wedges were developed to obtain different fracture surface roughness by splitting under compression. Three fluid flow regimes were identified in mated rock fractures: pre-linear flow at low flow velocity, linear Darcy’s flow at the medium flow velocity and post-linear flow at high flow velocity. In pre-linear flow regime, the increasing rate of flow rate increased with water pressure gradient, but it decreased in post-linear flow regime. The pre-linear flow is ascribed to the slippage effect of water-fracture interfaces, while the post-linear flow is mainly due to inertial effects. The critical hydraulic gradient for fluid flow regime transition from pre-linear to linear flow increased with the increase of confining stress. The numerical modeling shows that the asperity irregularity influences the flow regime. For low-speed flow in fracture under slip boundary condition, the slip flux per unit width in the fracture with triangular asperity is largest, while that of rectangular asperity is smallest. For high-speed flow in fracture with non-slip boundary condition, the rectangular asperity element causes more severe nonlinearity when compared to the fractures of trapezoidal and triangular asperity elements.

Research on a Critical Hydraulic Gradient of Piping in Noncohesive Soils

The critical hydraulic gradient of cohesive soil is an important condition for judging soil piping. For force analysis of movable particles in pore channels of soil, this study proposes to consider the influence of surrounding particles on the drag force of movable particles by water flow. According to the principle of relative motion, considering the interaction force between moving objects in still water, the value of the drag force of water flow that is affected by surrounding particles is calculated, to derive the method of the critical hydraulic gradient. This calculation method is suitable for the results of previous piping tests, and the method is accurate and concise.

Centrifuge Modeling Study of Backward Erosion Piping with Variable Exit Size

This study presents the results from a series of centrifuge modeling tests conducted to investigate the backward erosion piping across a sandy foundation underlying an impervious cohesive layer with a defined exit hole. Different levels of centrifuge gravitational acceleration and various exit hole sizes were tested. The behavior at different phases of erosion was analyzed based on in-flight video recordings and posttest observations, along with local and global pressure loss measurements. Results showed that the overall mechanism that was modeled was similar to the mechanism described in previous small-scale experimental studies. The results showed that the exit hole size had minimal impact on the critical hydraulic gradient but affected the characteristics of the piping path and the amount of eroded material. The critical hydraulic gradient that initiated the erosion decreased slightly as the centrifuge gravitational acceleration increased. The values of the critical hydraulic gradient, which was studied locally and globally, ranged between 0.15 and 0.40, and fell within a range of estimates from typical analytical methods. This study provides a means to improve the testing protocol and analysis of centrifuge modeling of internal erosion mechanisms, which currently is limited in the literature.

Linear and nonlinear fluid flow responses of connected fractures subject to shearing under constant normal load and constant normal stiffness boundary conditions

Linear and nonlinear fluid flow behaviors of connected fractures during shearing under constant normal load and constant normal stiffness boundary conditions are numerically characterized solving the Navier-Stokes equations. The model consists of three fractures having an identical length of 200 mm and a width of 100 mm, among which the bridge fracture is sheared. Both smooth and rough-walled fracture surfaces are generated to investigate the effect of surface roughness on flow streamline distributions and the ratio of flow rate to hydraulic gradient. The results show that the permeability monotonically increases during shearing under constant normal load conditions, due to the shear-induced dilation of fractures. Under constant normal stiffness conditions, the permeability either increases or decreases during shearing, controlled by the competing role played by the shearing fracture and nearby fractures. As shear advances, the shearing fracture dilates and increases the permeability, whereas the surrounding fractures are compressed that decrease the permeability. The flow rate of rough-walled models is overestimated by approximately 45 ∼ 80% comparing to the smooth parallel plate model. For smooth models, the critical hydraulic gradient dramatically decreases with increasing the shear strain from 0.015 to 0.025 and then slightly fluctuates with the increment of shear strain from 0.025 to 0.05. The critical hydraulic gradient monotonically decreases during the shearing process for rough-walled models. The range of critical hydraulic gradient is between 0.001 and 0.02.

Nonlinear fluid flow through three-dimensional rough fracture networks: Insights from 3D-printing, CT-scanning, and high-resolution numerical simulations

Nonlinear flow behavior of fluids through three-dimensional (3D) discrete fracture networks (DFNs) considering effects of fracture number, surface roughness and fracture aperture was experimentally and numerically investigated. Three physical models of DFNs were 3D-printed and then computed tomography (CT)-scanned to obtain the specific geometry of fractures. The validity of numerically simulating the fluid flow through DFNs was verified via comparison with flow tests on the 3D-printed models. A parametric study was then implemented to establish quantitative relations between the coefficients/parameters in Forchheimer's law and geometrical parameters. The results showed that the 3D-printing technique can well reproduce the geometry of single fractures with less precision when preparing complex fracture networks, numerical modeling precision of which can be improved via CT-scanning as evidenced by the well fitted results between fluid flow tests and numerical simulations using CT-scanned digital models. Streamlines in DFNs become increasingly tortuous as the fracture number and roughness increase, resulting in stronger inertial effects and greater curvatures of hydraulic pressure-low rate relations, which can be well characterized by the Forchheimer's law. The critical hydraulic gradient for the onset of nonlinear flow decreases with the increasing aperture, fracture number and roughness, following a power function. The increases in fracture aperture and number provide more paths for fluid flow, increasing both the viscous and inertial permeabilities. The value of the inertial permeability is approximately four orders of magnitude greater than the viscous permeability, following a power function with an exponent α of 3, and a proportional coefficient β mathematically correlated with the geometrical parameters.

Evaluation of the internal stability of well-graded silty sand through the long-term seepage test

Suffusion is the phenomenon responsible for internal erosion, and is the process by which finer soil particles are moved through the constrictions between the larger soil particles by seepage forces. Generally, gap-graded soil is known to be susceptible to suffusion. Meanwhile, suffusion of well-graded silty sand and the resulting soil behavior are not well understood. Moreover, the previous researches on laboratory suffusion tests focused on the study of the critical hydraulic gradient, which triggers the internal instability of the soils within a short period of time. Therefore, in this study, long-term suffusion tests were conducted on well-graded silty sand under a hydraulic gradient lower than the critical value. As a result, abrupt increases in permeability and amount of soil discharged were observed due to the progressive migration of the soil particles, resulting in suffusion even at a relatively low hydraulic gradient.

Internal erosion: critical hydraulic gradient in one-dimensional vertical seepage and its relation to soil gradation

A hydromechanical envelope that governs the onset of soil erosion by seepage-induced internal instability is examined with reference to theoretical and laboratory stress-gradient paths for one-dimensional upward and downward seepage flow. The method is validated from permeameter test results on glass ballotini. Using the theory, analysis of a database of 22 gradations establishes a semi-empirical relation between attributes of a grain size distribution curve and a stress-reduction factor governing potential for internal erosion. The semi-empirical relation provides a screening tool for susceptibility of a soil to seepage-induced internal instability.

ANTI-EROSION CAPACITY OF A GRANULAR FILTER SUBJECTED TO A PERIODICALLY VARIABLE HYDRAULIC GRADIENT

The instability of a filter system is a significant cause of seepage failure in embankment projects. The filter system in the earth-rock embankment is mainly composed of graded cohesionless soil. To uncover the performance of the granular filter in resisting the internal erosion, a set of experiments was carried out with an improved experimental apparatus, considering different hydraulic loading scenarios. The movement of graded cohesionless soil, the seepage velocity and the hydraulic gradient were monitored in the experiments. It was found that during the process of increasing the hydraulic gradient, the failure of the granular filter mainly experienced three stages: the first one was the dynamic equilibrium stage; the second was the critical start stage; and the third was the failure stage, in which a sudden change in the seepage velocity was the precursor of seepage failure. The critical hydraulic gradient and destructive hydraulic gradient decreased with the water level amplitude. Moreover, the experiments revealed that the loading modes of the hydraulic gradient significantly influenced the anti-erosion capacity of the granular filter. Compared with the stepwise loading mode, the cyclic reciprocating loading mode greatly weakened the anti-erosion capacity of the granular filter under the same water level amplitude. The destructive hydraulic gradient of the latter was only 71.8 % of the former under a higher water level amplitude, indicating that the corresponding measures should be considered to avoid the occurrence of a periodically variable hydraulic gradient.

Random finite element analysis of backward erosion piping

Backward erosion piping (BEP) is a type of internal erosion that threatens the integrity of dams and levees. BEP has been shown to be highly sensitive to spatial variations in soil properties; however, there are presently no assessment methods that permit incorporating spatial variation in soil properties into BEP analysis. The Random Finite Element Method (RFEM) is a numerical approach for incorporating spatially variable properties into finite element analysis. In this study, an RFEM approach to simulating BEP was developed to assess pipe progression through variable soils. The soil hydraulic conductivity and critical hydraulic gradient for pipe progression were treated as log-normal random variables. Analyses were conducted for a range of hydraulic conductivity and critical gradient random fields with varied spatial correlation lengths, distribution parameters, and field correlations. Results indicate that the probability of failure increases with increasing spatial correlation length. Additionally, increased variance in soil permeability was shown to increase the probability of failure for large correlation lengths and decrease the probability of failure for short correlation lengths. Regardless of correlation length, increasing values of the mean critical hydraulic gradient led to decreased failure probabilities, and increasing values of critical hydraulic gradient variance led to increased failure probabilities.

Effects of Contact Area and Contact Shape on Nonlinear Fluid Flow Properties of Fractures by Solving Navier-Stokes Equations

Abstract The influences of contact shape and contact area on nonlinear fluid flow properties through fractures are investigated by solving Navier-Stokes equations. The evolutions of nonlinear relationships between flow rate and hydraulic pressure drop, Forchheimer coefficients, nonlinear factor, critical hydraulic gradient, distributions of flow streamlines, and tracer flow paths at different times are systematically estimated. The results show that the nonlinear relationships between flow rate and hydraulic pressure drop can be well described by Forchheimer’s law, in which the nonlinear term coefficient b is approximately three orders of magnitude larger than the linear term coefficient a. The smaller contact area corresponds to smaller variations in many aspects such as flow rate, critical hydraulic gradient, flow streamlines, and tracer flow paths. The critical hydraulic gradient decreases with the increasing degree of contact shape variations while the contacts have the same mean area. The increase in hydraulic pressure drop can induce significant eddies and decrease the permeability and/or conductivity of fractures. However, the distributions of streamlines and tracer flow paths are not dramatically disturbed under a large hydraulic pressure drop.

Study on Critical Hydraulic Gradient Theory of Flow Soil Failure in Cohesive Soil Foundation

The current formula of critical hydraulic gradient is not adapted to solve critical hydraulic gradient of cohesive soil. Assume that the seepage failure mode of the cohesive soil foundation was cylindrical or inverted circular truncated cone, based on the calculation formula of the critical hydraulic gradient of Terzaghi, the analytical formula of the critical hydraulic gradient considering the influence of the shear strength of the soil was derived. Then, the seepage failure process of the clay layer was simulated numerically, and the effects of the clay layer thickness, failure radius, and shear strength indexes on the critical hydraulic slope were analyzed. The comparison results show that the numerical test results are in good agreement with the calculated results of the new formula. In addition, the critical hydraulic gradient of sandy loam and loess under different working conditions was studied severally by a self-made permeation failure instrument. The results show that the critical hydraulic gradient decreases with the increase of soil thickness and failure radius, and the maximum error between the test and the corresponding formula results is no more than 16%.

2-D coupled fluid-particle numerical analysis of seepage failure of saturated granular soils around an embedded sheet pile with no macroscopic assumptions

The present paper reports the application of a 2-D coupled fluid-particle simulation model with no macroscopic assumptions to the seepage failure of saturated granular soils. The basic problem of the seepage failure of a horizontal ground with an embedded sheet pile, where the system size is set to be 200 × 100 mm and the average diameter of the soil particle is 550 μm, is numerically investigated. Both the seepage flow and the motion of the soil particles are directly solved by coupling the lattice Boltzmann method and the discrete element method. The goal of this study is to confirm that the 2-D direct simulation can be performed on the scale of a model experiment with soil particles that correspond in size to that of real sand. As a result of the analysis, it is shown that a typical series of behavior for seepage failure, where boiling and heaving initially occur on the downstream side near the sheet pile and finally lead to quicksand, can be seamlessly reproduced. Comparing the cases with different initial void ratios, it is found that the deformation area and the rates of the failure process can be varied according to the packing state. By tracking the velocity of each soil particle, it is visually shown that seepage failure begins to occur in the corner areas of the sheet pile much earlier than the onset of quicksand. By focusing on the fluid force acting on that particle, it is seen that the relatively large values for the hydrodynamic forces are concentrated on the upstream side before the beginning of uplift. In addition, by a comparison with two theories for the critical hydraulic gradient, the current limitations and problems of the proposed method are also summarized.

A vertical layered theoretical model to predict the suffusion-induced heterogeneity of cohesionless soil

Suffusion is a typical form of the internal erosion, which leads to worldwide failures of embankment dams. Extensive investigations have been carried out to characterize suffusion process. However, less research has been focused on the lasting heterogeneity development by suffusion physically and quantitatively, despite the phenomenon been found in literatures. This paper proposes a vertical layered theoretical model based on the force balance of movable particles under one-dimensional upward seepage on gap-graded specimens. In the model, the finer particles loss was deduced respectively in every layer, combined with the coupled calculation including the seepage flow, the soil particles movement and the soil structures changes. The model was verified with experiments and showed a good consistency in the critical hydraulic gradient, layered water head, seepage velocity, finer particle loss and hydraulic conductivity. Finally, suffusion induced soil grading changes and the implications to the suffusion development are discussed quantitatively. The results indicate that the theoretically modeled soil heterogeneity changes are consistent with the suffusion phenomenon and the experimental observations. The outlet and inlet are more sensitive to suffer suffusion under upward seepage, as the two layer have more violent fine particles loss and soil grading coarsening. The layered model can theoretically simulate the development of suffusion with the sequential changes of the soil structures and serves as a new approach to understand the process in cohesionless soil.

Suffusion response of well graded gravels in roadbed of non-ballasted high speed railway

The suffusion mechanism of well graded gravels in the application of high speed railway roadbed is still not fully understood. Field inspections of high speed railway show that suffusion of well graded gravels can result in mud pumping and affect the normal operation of high speed trains. This paper reports a total of 12 laboratory suffusion tests on well graded gravels typically used in Chinese high speed railway roadbed under three different degrees of compaction (93%, 95% and 97%). The influence of degree of compaction and initial fines content on the critical hydraulic gradient of roadbed materials and the characteristics of suffusion is systematically investigated. The results show that well graded gravels suggested by the design code can experience suffusion once the hydraulic gradient reaches a critical value. The critical hydraulic gradient generally increases with the degree of compaction and the initial fines content. An empirical equation is proposed to predict the eroded mass of fine particles, which can reasonably reproduce the experimental measurements for well graded gravels under different failure hydraulic gradient.

Impacts of Consolidation Time on the Critical Hydraulic Gradient of Newly Deposited Silty Seabed in the Yellow River Delta

The silty seabed in the Yellow River Delta (YRD) is exposed to deposition, liquefaction, and reconsolidation repeatedly, during which seepage flows are crucial to the seabed strength. In extreme cases, seepage flows could cause seepage failure (SF) in the seabed, endangering the offshore structures. A critical condition exists for the occurrence of SF, i.e., the critical hydraulic gradient (icr). Compared with cohesionless sands, the icr of cohesive sediments is more complex, and no universal evaluation theory is available yet. The present work first improved a self-designed annular flume to avoid SF along the sidewall, then simulated the SF process of the seabed with different consolidation times in order to explore the icr of newly deposited silty seabed in the YRD. It is found that the theoretical formula for icr of cohesionless soil grossly underestimated the icr of cohesive soil. The icr range of silty seabed in the YRD was 8–16, which was significantly affected by the cohesion and was inversely proportional to the seabed fluidization degree. SF could “pump” the sediments vertically from the interior of the seabed with a contribution to sediment resuspension of up to 93.2–96.8%. The higher the consolidation degree, the smaller the contribution will be.

Experimental study on internal erosion and seepage in the foundation of a dike under variable water head

Internal erosion is one of the main causes of dike failures. Their failure mechanism is related to the physical characteristics (distribution of particle size, permeability characteristics, clay content, etc.), stress state, and hydraulic conditions of the soil around the dikes. In this study, a series of erosion tests under different rising rates of the water head were conducted to study the internal erosion mechanism of a dike foundation under varying hydraulic conditions. It was found that different water head rising rates resulted in different internal erosion failure modes; furthermore, two critical values of water head rising rate were observed that decided whether erosion or piping occurred, and influenced the failure destructiveness of the internal erosion. Under the action of a continuous water head, the continuous failure through internal erosion occurred primarily in four stages. Moreover, under different water head rising rates, the change rules of the water head, seepage flow, and Jx–Q (average horizontal hydraulic gradient–seepage flow) curve were different. The mechanism of internal erosion and the critical hydraulic gradient could be determined based on the Jx–Q change characteristics. The backward erosion piping, based on the well flow model, suggested that the water head changing rate influenced the piping process.

Analytical solution of startup critical hydraulic gradient of fine particles migration in sandy soil

Analytical solution of startup critical hydraulic gradient of fine particles migration in sandy soil

Evaluation of Water Retention Capacity of Bulkheads in Underground Coal Mines

The mechanism of water flow in and around the bulkheads and the surrounding rock is studied for Panel No. 21102 in the Sanhejian coal mine in Xuzhou, China. Based on an analysis of the properties of the bulkheads and the surrounding rock, three types of water conducting pathways are identified: (1) a water conducting pathway at the interface between the bulkhead and the surrounding rock; (2) a water conducting pathway in the faults of the rock; and (3) a water conducting pathway in the fractures of the rock. The possibility of these three pathways for water flow at Panel No. 21102 is analyzed, and the connectivity coefficient of the water conducting pathway is determined. The expression for calculating the critical hydraulic gradient of the rock by using the connectivity coefficient in the water conducting pathways is presented which is based on the permeability and integrity of the rock. The ratios of the critical hydraulic gradient to the steady state hydraulic gradient are calculated for 13 mines in China. An acceptable safety factor in controlling the water flow for the bulkhead is found to be 1.68. When the safety factor is less than 1.68, water leakage has occurred in a number of cases. Finally, changes in the water pressure in the bulkheads with time and changes in the seepage flow with time in the surrounding rock are analyzed. It is found that there is a good correlation between the rate of water flow and water pressure which confirms that water pressure plays a decisive role in controlling seepage from the rock in and around the bulkheads.