Variation of hydraulic gradient in nonlinear finite strain consolidation

In the research field of ground water, hydraulic gradient is studied for decades. In the consolidation field, hydraulic gradient is yet to be investigated as an important hydraulic variable. So, the variation of hydraulic gradient in nonlinear finite strain consolidation was focused on in this work. Based on lab tests, the nonlinear compressibility and nonlinear permeability of Ningbo soft clay were obtained. Then, a strongly nonlinear governing equation was derived and it was solved with the finite element method.Afterwards, the numerical analysis was performed and it was verified with the existing experiment for Hong Kong marine clay. It can be found that the variation of hydraulic gradient is closely related to the magnitude of external load and the depth in soils. It is interesting that the absolute value of hydraulic gradient(AVHG) increases rapidly first and then decreases gradually after reaching the maximum at different depths of soils. Furthermore, the changing curves of AVHG can be roughly divided into five phases. This five-phase model can be employed to study the migration of pore water during consolidation.

Performance between the Hydraulic Gradient Method and the Perturbation Method for the Analysis of Water Supply Networks

The HGM(Hydraulic Gradient Method),it is used in most of the current commercial software,such as EPANET,WaterCAD,MikeNet,among others,the same that corresponds to an iterative method that depends on initial estimated parameters and programming structures that ensure convergence to obtain results with the highest precision,in addition to this the method makes use of non-linear equation systems.Likewise,the execution time for large extensions of water distribution networks is considerably high.On the other hand,the PM(Perturbation Method),is a new direct solution method,which makes use of principles of quantum mechanics to transform nonlinear equations into simpler linear systems.Obtaining a simple and robust optimization method that only requires simple and direct mathematical processes.Using the MathCad and Python programming languages as a verification tool,multiple tests were carried out,the results for the hydraulic parameters showing that the flow rates and pressures obtained by the HGM and the PM are extremely similar,in the same way the execution time(time run)have been 77.09%favorable to the PM.In other words,the PM presents efficiency to estimate the hydraulic characteristics such as the pressures at the nodes and the velocities in the pipes of the drinking water distribution networks.

Saint-Venant Fractional Equation and Hydraulic Gradient

The overall objectives to support analytically the mathematical background of hydraulics, linking the Navier-Stokes with hydraulic formulas, which origin is experimental but have wide and varied application. This, leads us study the inverse problem of the coefficients of differential equations, such as equations of the porous medium, Saint-Venant, and Reynolds, and accordingly with the order of derivatives. The research led us to see that the classic version suffers from a parameter that reflects the fractal and non-local character of the viscous interaction. Motivated by the concept of spatial occupancy rate, the authors set forth Navier-Stokes＇s fractional equation and the authors obtain the fractional Saint-Venant. In particular, the hydraulic gradient, or friction, is conceived as a fractional derivative of velocity. The friction factor is described as a linear operator acting on speed, so that the information it contains is transferred to the order of the derivative, so that the same is linearly related to the exponent of the friction factor. It states Darcy＇s non-linear law. The authors take a previous result that describes the nonlinear flow law with a leading term that contains a hyper-geometric function, whose parameters depend on the exponent of the friction factor and the exponent of the hydraulic radius. It searches the various laws of flow according to the best known laws of hydraulic resistance, such as Chezy and Manning.

Physically-based approach to analyze rainfall-triggered landslide using hydraulic gradient as slide direction

An infinite slope stability numerical model driven by the comprehensive physically-based integrated hydrology model(InHM) is presented.In this approach,the failure plane is assumed to be parallel to the hydraulic gradient instead of the slope surface.The method helps with irregularities in complex terrain since depressions and flat areas are allowed in the model.The present model has been tested for two synthetic single slopes and a small catchment in the Mettman Ridge study area in Oregon,United States,to estimate the shallow landslide susceptibility.The results show that the present approach can reduce the simulation error of hydrological factors caused by the rolling topography and depressions,and is capable of estimating spatial-temporal variations for landslide susceptibilities at simple slopes as well as at catchment scale,providing a valuable tool for the prediction of shallow landslides.

Effect of movability of water on the low-velocity pre-Darcy flow in clay soil

Water seepage in soil is a fundamental problem involving various scientific and engineering fields.According to the literature,low-velocity water seepage in low-permeability porous media,such as clay,does not follow Darcy's law,also known as pre-Darcy flow.The formation of immovable water due to water adsorption on the pore wall is believed to be responsible for the formation of pre-Darcy flow.However,this view lacks direct solid evidence.To investigate the pre-Darcy water flow in clay,head permeability experiments are conducted on six clay samples with different densities.The results indicate that water seepage in clay at low hydraulic gradients does not follow Darcy's law.A clear nonlinear relationship between flow velocity and hydraulic gradient is observed.Water flow in clay can be divided into the pre-Darcy flow and Darcy flow regions by the critical hydraulic gradient,which is 10-12 for the Albic soil with dry density between 1.3 g/cm^(3)and 1.8 g/cm^(3).According to the disjoining pressure theory,immovable water due to water adsorption on the pore wall is the primary reason for water flow deviating from Darcy's law in clay.The results indicate that the percentage of movable water ranges from 39.7%to 59.3%for the six samples at a hydraulic gradient of 1.As the hydraulic gradient increases,the percentage of moveable water also increases.Additionally,there is a strong correlation between the percentage of movable water and the variation in hydraulic conductivity with the hydraulic gradient.Furthermore,a quantitative relationship between the percentage of movable water and the hydraulic conductivity has been established.The results of this study suggest that water adsorption on the pore wall not only affects the water movability,but is also closely related to the pre-Darcy flow phenomenon in clay.

Experimental study on the effects of big particles physical characteristics on the hydraulic transport inside a horizontal pipe

This paper presents an experimental study of the physical characteristic effects of large particles on hydraulic transport in a horizontal pipe.The particles are spherical and are large with respect to the diameter of the pipe(8%,10%,16% and 25%).Experiments were done to test the important parameters in solid transport(pressure,velocity,etc.).As a result,the relationship between the pressure gradient forces and the mixture velocity was substantially different from the pure liquid flow.However,in a single-phase flow a monotonous behavior of the pressure drop curve is observed,and the curve of the solid particle flow attains its minimum at the critical velocity.The regimes are characterized with differential pressure measurements and visualizations.

Nonlinear Flow Properties of Newtonian Fluids through Rough Crossed Fractures

The nonlinear flow properties of Newtonian fluids through crossed fractures are estimated by considering the influences of length,aperture,and surface roughness of fractures.A total of 252 computational runs are performed by creating 36 computational domains,in which the Navier-Stokes equations are solved.The results show that the nonlinear relationship between flow rate and hydraulic gradient follows Forchheimer’s law–based equation.When the hydraulic gradient is small(i.e.,10^(−6)),the streamlines are parallel to the fracture walls,indicating a linear streamline distribution.When the hydraulic gradient is large(i.e.,10^(0)),the streamlines are disturbed by a certain number of eddies,indicating a nonlinear streamline distribution.The patterns of eddy distributions depend on the length,aperture,and surface roughness of fractures.With the increment of hydraulic gradient from 10^(−6) to 10^(0),the ratio of flow rate to hydraulic gradient holds constants and then decreases slightly and finally decreases robustly.The fluid flow experiences a linear flow regime,a weakly nonlinear regime,and a strongly nonlinear regime,respectively.The critical hydraulic gradient ranges from 3.27×10^(−5) to 5.82×10^(−2) when fracture length=20–100mmandmechanical aperture=1–5mm.The joint roughness coefficient plays a negligible role in the variations in critical hydraulic gradient compared with fracture length and/or mechanical aperture.The critical hydraulic gradient decreases with increasing mechanical aperture,following power-law relationships.The parameters in the functions are associated with fracture length.

Properties of Bentonite Enhanced Loess and Laterite

Loess and laterite distributed widely in the northern and southern China cannot be directly used as the natural barrier to isolate the solid waste because of their high hydraulic conductivity. In this paper, they are enhanced by bentonite to improve their hydraulic performance. The impact of bentonite content and water content on compressive strength of the compacted soil was investigated. The effects of bentonite content, water content, dry density and hydraulic gradient on the hydraulic conductivity were studied in detail. For the laterite and the laterite with 8% of bentonite, the experimental results of hydraulic conductivity can be applied in the engineering design. However, for the loess and the bentonite enhanced loess, those of hydraulic conductivity can not be directly applied in the engineering design because their hydraulic performance does not comply with the Darcy's law. These experimental results have to be carefully modified before application.

Experimental Studies on Extraction of Modified Suction Caisson (MSC) in Sand by Reverse Pumping Water

A suction caisson can be extracted by applying reverse pumping water,which cannot be regarded as the reverse process of installation because of the dramatically different soil−structure interaction behavior.Model tests were first carried out in this study to investigate the extraction behavior of the modified suction caisson(MSC)and the regular suction caisson(RSC)in sand by reverse pumping water.The effects of the installation ways(suction-assisted or jacking installation)and the reverse pumping rate on the variations of the over-pressure resulting form reverse pumping water were investigated.It was found that neither the RSC nor the MSC can be fully extracted from sand.When the maximum extraction displacement is obtained,the hydraulic gradient of the sand in the suction caisson reaches the critical value,leading to seepage failure.In addition,the maximum extraction displacement decreases with the increasing reverse pumping rate.Under the same reverse pumping rate,the final extraction displacements for the RSC and MSC installed by suction are lower than those for the RSC and MSC installed by jacking.The final extraction displacement of MSC is almost equal to that of the RSC with the same internal compartment length.Based on the force equilibrium,a method of estimating the maximum extraction displacement is proposed.It has been proved that the proposed method can rationally predict the maximum extraction displacement and the corresponding over-pressure.

On the Influence of Vortex-Induced Resistance on Oil-Shale Particle-Slurry Flow in Vertical Pipes

The transportation in vertical pipelines of particle slurry of oil shale has important applications in several fields(marine mining,hydraulic mining,dredging of river reservoir,etc.).However,there is still a lack of information about the behavior of coarse particles in comparison to that of fine particles.For this reason,experiments on the fluidization and hydraulic lifting of coarse oil shale particles have been carried out.The experimental data for three kinds of particles with an average size of 5 mm,15 mm and 25 mm clearly demonstrate that vortices can be formed behind the particles.On this basis,a vortex resistance factor K is proposed here to describe this effect.A possible correlation law is defined by means of a data fitting method accordingly.This law is validated by an experiment employing particles with an average size of 3.4 mm.The vortex resistance factor K results in a reduction of the speed of solid particles and an increase in the sliding speed as well as a decrease in the hydraulic gradient.As a result,using this factor,the calculation of the solid particle speed and hydraulic gradient can be made more accurate with respect to measured values.

Development of a simple method for determining the influence radius of a pumping well in steady-state condition

Influence radius of a pumping well is a crucial parameter for hydrogeologists and engineers. Knowing the radius of influence for a designed drawdown enables one to calculate the pumping rate required to layout a project foundation that may need lowering of groundwater level to a certain depth due to dewatering operation. In addition, this is important for hydrogeologists to determine ground water contamination flow paths and contributing recharge area for domestic water supply and aquifer management purposes. Empirical formulas that usually neglect vital parameters to determine the influence radius accurately have been traditionally utilized due to lack of adequate methods. In this study, a physically based method, which incorporates aquifer hydraulic gradient for determining the influence radius of a pumping well in steady-state flow condition, was developed. It utilizes Darcy and Dupuit laws to calculate the influence radius, where Darcy’s law and Dupuit equation, in steady-state condition, represent the inflow and the outflow of the pumping well, respectively. In an untraditional manner, this method can be also used to determine aquifer hydraulic conductivity as an alternative to other pumping test methods with high degree of accuracy. The developed method is easy to use;where a simple mathematical calculator may be used to calculate the influence radius and the pumping rate or hydraulic conductivity. By comparing the results from this method with the MODFLOW numerical model outputs with different simulated scenarios, it is realized that this method is much superior and more advantageous than other commonly used empirical methods.

Groundwater Waves in a Coastal Fractured Aquifer of the Third Phase Qinshan Nuclear Power Engineering Field

Tidal fluctuations of Hangzhou Bay produce progressive pressure waves in adjacent field fractured aquifers, as the pressure waves propagate, groundwater levels and hydraulic gradients continuously fluctuate. The effect of tidal fluctuations on groundwater flow can be determined using the mean hydraulic gradient that can be calculated by comparing mean ground and surface water elevations.Tidal fluctuation is shown to affect the piezometer readings taken in a nearshore fractured aquifer around the nuclear power engineering field. Continuous monitoring of a network of seven piezometers provided relations between the tidal cycle and the piezometer readings. The relations can be expressed in times of a time and amplitude scaling factor. The time lag and the tidal efficiency factor and wavelength are calculated using these parameters. It provides significant scientific basis to prevent tide and groundwater for the nuclear power engineering construction and safety run of nuclear power station in the future.

Experimental and Numerical Investigation of Stress Condition in Unstable Soil

In unstable soils, a special erosion process termed suffusion can occur under the effect of relatively low hydraulic gradient. The critical hydraulic gradient of an unstable soil is smaller than in stable soils, which is described by a reduction factor α. According to a theory of Skempton and Brogan (1994) [1], this reduction factor is related to the stress conditions in the soil. In an unstable soil, the average stresses acting in the fine portion are believed to be smaller than the average stresses in the coarse portion. It is assumed that the stress ratio and the reduction factor for the hydraulic gradient are almost equal. In order to prove this theory, laboratory tests and discrete element modelings are carried out. Models of stable and unstable soils are established, and the stresses inside the sample are analysed. It is found that indeed in unstable soils the coarse grains are subject to larger stresses. The stress ratios in stable soils are almost unity, whereas in unstable soils smaller stress ratios, which are dependent on the soil composition and on the relative density of the soil, are obtained. A comparison between the results of erosion tests and numerical modeling shows that the stress ratios and the reduction factors are strongly related, as assumed by Skempton and Brogan (1994) [1].

Seepage behavior of soil mixed with randomly distributed recycled plastic materials

Seepage through embankment fill materials is crucial issue in the construction of embankments for irrigation and drainage projects.Proper ground improvement methods should be used to improve the strength and stability characteristics of soil used as fill material.Utilization of waste plastic materials to enhance the engineering properties of soil is a sustainable approach.Additionally,the use of raw products directly from plastic recycling units in the form of flakes and pellets as soil additives has the potential to further enhance the economic benefits of this method.This study randomly mixed plastic materials with soil for use in the construction of earth embankments,such as river levees,dykes,and canal diversion structures,and evaluated the effectiveness of these materials in reducing seepage failures in hydraulic structures.To achieve these goals,this study collected high-density polyethylene(HDPE)plastic from plastic recycling units and used soil mixed with HDPE plastic in the form of flakes and pellets in different contents as embankment fill materials,then evaluated how these materials affected the piping features.Laboratory experiments were conducted to determine the seepage velocity and critical hydraulic gradient of soil mixed with plastics in various contents and to compare the values with those of plain soil.The results showed that random distribution of waste plastics in the form of flakes and pellets in soil is an effective method for improving the piping resistance of soil.

Causes of the Abnormal Seepage Field in a Dam with Asphaltic Concrete Core

Asphaltic concrete core（ACC） dams are widely built in China. Many ACC dams perform well, but others have experienced significant leakage including the case in western China studied herein. A numerical model of saturated-unsaturated water flow was adapted to simulate the seepage through the dam. By comparing the normal and abnormal seepage fields under different conditions, the main causes for the actual abnormal seepage field were identified and attributed to a defect in the ACC and an unintended, low permeability layer（LPL） in the transition zone（TZ） and the downstream dam shell. These conclusions are consistent with the situation and performance of the dam. Inadequate ACC construction processes might have caused defects in the ACC. An abrupt change of the ACC thickness probably induced stress concentrations and caused the ACC to fail. Material sources for the TZ and dam shell were complex and varied from specifications, and soil gradation for the TZ was inadequately controlled. In particular, tests show that the permeability varies over large ranges in these two parts of the dam. An unexpected LPL probably exists in both areas, and extends continuously.