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Journal of Geology and Geoscience

J Geol Geosci Volume 2(1): 20181

ReseaRch aRticle

Mechanism of Suffusion Erosion Phenomenon In Porous MediaFarzad Ferdos1, Bijan Dargahi2, Luca Solari3

1Researcher, Division of Hydraulic Engineering, Department of Civil and Architectural Engineering, KTH Royal Institute of Technology, 100 44, Stockholm, Sweden.2Associate Professor, Division of Hydraulic Engineering, Department of Civil and Architectural Engineering, KTH Royal Institute of Technology, 100 44, Stockholm, Sweden.3Associate Professor, Department of Civil and Environmental Engineering, University of Florence, Florence, ITALY.

Abstract

A major cause of failure of embankment dams is internal erosion that is mostly driven by two different mechanisms, suffusion and concentrated leakage. Suffusion mechanism was studied for a cohesionless soil by laboratory experiments using an especially designed erosion apparatus which was capable of applying simultaneous hydraulic and mechanical loading while the erosion process was monitored.

The main novel outcomes of the work are

i) a new criterion for detecting the internal erosion initiation,

ii) a modified theoretical model, namely the Modified Hydromechanical Envelop (MHE), for encountering the soil in-situ stresses and seepage-induced shear stress on internal erosion initiation and its continuation and

iii) a semi-empirical constitutive law of internal erosion where the coefficients of this law were extracted experimentally. The MHE was proposed based on Mohr-Coulomb shear failure criterion. The constitutive law was defined as the rate of removal of mass due to the application of excessive shear stress higher than the material internal erodibility resistance. Importantly, both the initiation and the mass removal rate of suffusion are found to be dependent on the soil in-situ stresses.

Keywords: Constitutive law for internal erosion; Suffusion phenomenon; Initiation of erosion; Experimental studies; Porous media flow; Numerical modelling.

Correspondence to: Farzad Ferdos, Researcher, Division of Hydraulic Engineering, Department of Civil and Architectural Engineering, KTH Royal Institute of Technology, 100 44, Stockholm, Sweden, Tel: +46-(0)8-790 86 93; E-mail: ferdos[AT]kth[DOT]se

Received: Jan 29, 2018; Accepted: Feb 01, 2018; Published: Feb 03, 2018

IntroductionInternal erosion phenomena occur when soil particles are transported by seepage flow. These phenomena can seriously endanger the stability of water retaining structures [1] as well as slopes and channels [2]. They are concealed processes that occur deep inside the structure or its foundation and thus difficult to detect at their early stages of development. Here, an important consideration is the nature and characteristics of initiation of internal erosion. There are four different mechanisms: concentrated leakage, backward erosion, contact erosion, and suffusion [1]. Any of the foregoing mechanisms can lead to the formation of conduits, cavities and unstable zones within both the dam body and its foundation that can eventually cause dam failure. The understanding of these mechanisms requires insight knowledge of the material susceptibility of various soil types to internal erosion which are controlled by geometrical and hydro-mechanical parameters [3]. Geometrical parameters are soil mixture related constraints such as porosity, particle shape, pore constriction size distribution (CSD), and shape of the grain

size distribution (abbreviated as GSD). Hydro-mechanical parameters are related to the applied external loadings that consist of hydraulic loading (e.g. hydraulic gradient, seepage velocity) and mechanical soil stress conditions. Other parameters, such as soil saturation degree, temperature and viscosity of the seeping fluid are also potentially involved. The present study concerns suffusion phenomenon, which includes the processes that involve particle migration modes of finer soil particles through the voids of soil matrix by seepage flow. A short summary of main concepts of internal erosion that are related to the present study are presented first.

The pioneering work of [4] forms a common basis for studies on internal erosion where a set of granulometric criteria, well-known as filter criteria, were introduced for the first time. Based

Ferdos F (2018) Mechanism of Suffusion Erosion Phenomenon In Porous Media


on these filter criteria, various internal instability methods for erosion were developed [5-11]. An important finding from filter studies was the possibility of failure of a well-designed filter/base system due to internal erosion of the finer fraction of one of the compartments.

Similar to the granulometric criterion, [4] also formulated a theory about the onset of internal erosion (initiation) that included hydromechanical parameters into the soil susceptibility analysis and by introducing the critical hydraulic gradient concept. This concept accounts for the balance between the fluid pressure forces and the weight of the submerged soil particles. Internal stability of materials can also be affected by seepage and vibrations forces [12,13]. Another interesting concept is the stress reduction concept suggested by [14] which will be address later on in this article.

Despite the extensive previous works in addressing the suffusion process, most of the studies are mainly focused on geometrical parameters and their role in initiating suffusion. The studies that have investigated the destabilizing loads and the hydromechanical aspect tend to concentrate on the effect of hydraulic gradients as the only hydromechanical parameter. Only a few studies [3,15,16] consider the effect of mechanical loading. However, these studies do not include the dynamic forces induced by the flow and their effect on suffusion process. Additionally, much focus has been put on the potential for internal instability rather than describing the actual erosion process and thereby evaluating the mass erosion rate.

The present study investigates the physics of suffusion for a certain prescribed silty-sand mixture by using a combined experimental and theoretical approach. A specific geometrically susceptible soil mixture (i.e. soil sample “soil-A” from [14] tests) was used to study the effects of the hydromechanical loading, including the effect of flow velocities and the concept of stress reduction within each soil specimen for each test. The study examined the combined influence of soil stresses, hydraulic gradient and flow velocity on the initiation of seepage failure. The latter enabled the suggestion of a new approach that is based on a hydromechanical envelope using Mohr-Coulomb concept referred to as the modified hydromechanical envelope (hereafter MHE). By adopting MHE, the constitutive law of mass removal rate for internal erosion phenomena was suggested. The coefficients of that law were extracted empirically from the conducted experiments. Additionally, three-dimensional (3D) numerical simulations using Comsol Multi-physics modelling tool were also conducted to determine soil stresses and their distribution inside the erosion chamber.

The main study objectives can be summarized as:

• Conducting experiments to investigate the initiation of material instability “erosion initiation” as well as the continuation of the erosion “mass removal rate”.

• Theoretical formulating of a new approach based on the “hydromechanical envelope” in order to account for soil in-situ stress-dependency of internal erosion initiation and its continuation in soils.

• Defining a constitutive law governing the physical laws of internal erosion. The latter formed the basis of the numerical modelling of internal erosion in continuum mechanics’ framework.

BackgroundGiven the importance of granulometric criteria to evaluate the potential of soil internal instability, the main challenges ahead were to improve the understanding of internal erosion and to address the current knowledge gap.

Theoretical background on initiation of erosion and constitutive laws

A short survey of the related theoretical works on internal erosion that have severed as a base to formulate the new model is provided. Four important areas of approach (i.e. continuum- based approach), the choice of the closure model, granulometric and hydromechanical criteria, and the dynamics of erosion are covered. The survey is also intended to highlight the shortcomings and to suggest possible improvements.

Suffusion processes with the transport of particles and their mutual interactions within a soil media takes place at small scales (i.e. micro scale) which are difficult to replicate and hard to apply the physics of the random and complicated interaction between all the particles of a real large scale earthfill structure. Alternatively, a continuum-based methodology is more feasible for modelling internal erosion processes for large-scale soil structures. In a continuum-based multiphase framework, the internal erosion in soils can be described by the continuum mixture theory, which is based on the concept of porous media volume fractions. Vardoulakis [17] were the first to suggest a continuum-based approach to model the hydromechanical aspect of internal erosion processes involved for sand production. They introduced a three-component mixture theory for a representative volume element (RVE); consisting of a solid skeleton, fluidized particles and the flowing fluid. A system of partial differential equations (PDE) was derived based on balance equations for RVE. This continuum based internal erosion model was extended to other types of internal erosion mechanisms in porous media in by [18-29]. The outcome is a fully coupled and thermodynamically consistent approach that accounts for all the mass and momentum exchanges and for internal erosion to occur, at least one constitutive law for volumetric interaction (mass removal rate) is needed.

Constitutive laws are specific to each material and approximate the response or the rate of response of that material to the external forces. The equations, need to be defined for internal erosion processes, should consider both the granulometric and hydromechanical criteria. Furthermore, they should include both the initiation of erosion and the continuous mass removal rate to get an appropriate solution for the internal erosion problem. The coefficients involved in this type of constitutive law need to be extracted experimentally for each soil type. Vardoulakis [17] adopted the constitutive law by Einstein and Sakthivadivel [30,31] for their erosion model. It reads:



𝑚 = 𝜔𝜌𝑠 (1 − 𝜑)𝜑|𝒗 [𝒑] − 𝒗 [𝒔]| (1)

in which, 𝑚 is the mass removal rate, 𝜔 is the erosion parameter of the material, 𝜌𝑠 is the solid constituent’s density, c is the concentration of the fluidized particles, 𝜑 is the porosity of the media and 𝒗 [𝒑] and 𝒗 [𝒔] are the relative velocities for the fluidized particles and the solid constituents. Steeb [32] formulated a similar constitutive law for their theoretical continuum based model. Their law reads:

𝑚 = (1 − 𝜑)𝑐(𝒗 [𝒑] − 𝒗 [𝒔] ). (𝒗 [𝒑] − 𝒗 [𝒔] (2)

Equation 2 has the same variables as in Einstein and Sakthivadivel’s models with the term for imbedded seepage velocity being presented in squared. In both equations 1 and 2, the mass removal rate is driven by the flow of the suspended solids relative to the stationary ones.

Suffusion erosion occurs in a soil mixture that violates the filter criteria that is the finer fraction of that soil mixture can migrate through the voids between the coarser fractions of the soil. Therefore, the soil pore structure has to be taken into account when defining the constitutive law for numerical calculation of internal erosion. There are many criteria introduced by various research groups, among which the major widely used granulometric criteria that define thresholds for soil internal susceptibility are given by [33,34] [13,35,36]. In these studies the soil internal stability limit is defined based on its skeleton and the shape of its GSD. Here, it should be noted that the soil mixture used in the present study (i.e. Soil-A from [14] was evaluated by all the aforementioned methods insuring the fulfilment of the granulometric criterion of internal erosion susceptibility. Consequently, the study focus is on determination of the hydromechanical criterion.

The dynamics of erosion concern the nature of initiation and the rate of erosion. The concept of the initiation or instability for suffusion erosion is defined differently in studies that concern seepage flow tests. The uncertainties in defining the initiation of suffusion is a key issue in most studies conducted. There are a number of different approaches that range from visual observations to the use of Shields critical shear stress diagram [37]. The use of turbidity measurements is also common for detecting suspended particle load and the detecting the initiation of erosion [38-41]. There are also some definitions that are based on visual inspection and observation of particle movement [14,39,3]. Among different definitions, two dynamic approaches are found more relevant. One considers a sudden change in the trend of the seepage velocity versus hydraulic gradient curve [i.e. 14]. The other takes a sudden variation in local hydraulic gradient as an indicator of local failure and therefore a sign of initiation of erosion (see recent works of [3,15,16]. For this purpose, the local instabilities were detected by monitoring the sudden changes in pressure readings of interior pressure transducers.

In this study, authors considered a new approach for definition of the initiation of internal erosion in addition to the method adopted by [3,15,16]. In this new approach, the continuous slope change, higher than the recorded data scatter amplitude

in the flux measurements curve versus time (constant hydromechanical loading) was considered as an indicator of erosion initiation. Implementation of this new criterion is motivated by the fact that any temporal change in flux under constant loading conditions is a result of a physical change in the soil porous structure. The latter is a consequence of particle migrations, either trapped by the adjacent downstream layer, leading to a decrease in flux (internal suffusion), or washed out, leading to an increase in the seeping flux (external suffusion), both are indications of particle migration and therefore a suffusion process.

The rate of erosion can be expressed as a volumetric content of eroded material (kg m-3s-1) or as a rate of that volumetric content leaving the interacting surface (kg m-2s-1), based on the how PDE systems are defined for the media. Here, the key point is that the coefficients for the constitutive law need to be carefully defined for consistency with the expected dimensions of the constitutive law to be used in the PDE system for the media. For suffusion mechanism, authors have adopted mass removal rate as a volumetric content in this study.

Hydromechanical Envelope Model

In soil mechanics, failure envelopes are common concepts in engineering practice for determination of limiting resistance of material. The envelopes are defined based on a certain limiting behaviour that combines various soil parameters where the initiation is governed by reaching the borders of the envelopes. The present study hypothesis is the possibility of applying the failure envelop concept to internal erosion processes that can account for soil stresses and also flow-induced shear stress. Prior to presenting the proposed model, some background information is provided that contributes to the better understanding of the model. Moffat [3] was the first to introduce the limiting envelope method to study internal instability for porous material based on the effective stress concept of [4]. He demonstrated that the combined effects of hydraulic gradient (i) and vertical effective stress (𝜎𝑣’ ), govern the initiation of internal instability. A hydromechanical path was defined as the variation of normalized mean vertical effective stress (vertical effective stress divided by hydrostatic pressure i.e.𝜎’𝑣⁄𝜌𝑓𝑔𝑧) ) with local hydraulic gradient across the specimen for each test and for each loading increment. The plot of this hydromechanical path for each test ended at a critical hydraulic gradient (icr). The latter was found to be bounded by an envelope that was described by a linear relation between normalized effective vertical stress and the hydraulic gradient.

Li [15] later modified the aforementioned conceptual model and a new stress reduction concept of [14] was added to the model introduced by [3]. This updated model recognises the effect of mean soil normal stress and relates the critical hydraulic gradient to this stress. Experimental works conducted by [3,15,16] validate the model and show how this critical gradient to initiation the instability increases by increasing the normal effective stress. However, the forces induced by the



seepage flow on the soil particles as well as the lateral soil stresses and their effects are not considered in neither of the models.

Effective stress distribution in porous media and its effect on initiation of erosion was first addressed in [14]. They discovered that the initiation of internal instability of cohesionless soils occurs at hydraulic gradients three to five times smaller than the theoretical gradient for a uniform granular material with the same porosity. They attributed this behaviour to the stress distribution within the porous matrix and the differences in load-bearing of various grain size fractions. Based on their observations, the finer fraction received less of the applied mechanical stresses when sufficient numbers of coarse particles were present. They defined this attribute as a stress reduction concept and suggested the use of a stress reduction factor (i.e. α). Based on this conceptualization, a well graded or a uniformly graded soil mixture [34] has≅ 1 where the applied loading is distributed evenly among the particles. For gap graded soil mixtures 𝛼 < 1 where only awhere only a proportion of the applied mechanical loading is taken by the finer fraction therefore the effective stresses in the finer fraction (which are prompted for internal erosion) are lower.

In present study, authors introduce a modified model to the hydromechanical envelope model (i.e. MHE) which is conceptualized on Mohr-Coulomb failure envelope concept and incorporates all principal stresses, hydraulic gradients as well as the flow-induced shear stress on the soil. It fills the previous knowledge gap of not considering flow-induced shear stress and lateral soil stresses on the initiation of instability of the finer fraction. The MHE model is also incorporate the [14] stress reduction factor concept.

Methods Methods include a modified theoretical method, a new hydromechanical susceptibility criterion for initiation of internal erosion. Combined experimental and numerical approaches were used to verify the proposed presented theoretical model.

Modified hydromechanical envelope (MHE) model

The need for defining a new failure envelope model that could account for the effects of flow- induced shear stress and lateral soil stresses on the initiation of erosion within the finer soil fraction was stated earlier.

Particularly, not considering the flow-induced shear stress on the soil grains results in small values for the stress reduction factor that does not explain the small gradients needed for initiate material instability. However, adaptation of these small stress factors cannot explain the particle motion in the porous media with such small gradients (i.e. too small to move a single soil particle when the force balances is considered for just a free single particle within the porous media). The literature values of these critical gradients (i.e. for Soil-A there are, 0.20 [14], 0.4 [15] and 0.28 [16]) is not enough to make a single soil grain to move against the gravity when the flow-induced shear forces are not considered.

The hydromechanical paths for developing the MHE are defined in accordance with the Mohr-coulomb failure envelope, and plotted similar to the plots produced from the Triaxial test results. At no flow condition (hydrostatic), the stresses at any point within the specimen can be expressed in terms of the effective principal stresses (i.e. 𝜎1, 𝜎’2 and 𝜎3). Applying additional upstream water head to this soil sample at rest, results in an increase in pore water pressure within the soil matrix that will induce seepage. The hydraulic loading causes the principal effective stresses to change (i.e. decreases for an upward flow condition). It changes from (𝜎11, 𝜎13) state to (𝜎21, 𝜎23) considering a case with lateral principal stresses of 𝜎2 > 𝜎3 and additionally, a flow-induced shear forces are inserted which results in an upwards shift of the Mohr-Coulomb circle by τf2, as illustrated in the Figure 4. In which τ1 and τ2 are the maximum shear stresses that the specimen can take before instability occurs, and τb1 and τb2 are the total induced shear stress on the specimen. In both cases the applied shear stress (i.e. τb1 and τb2) are lower than the total shear stress needed for initiation of erosion (i.e. τ1 and τ2) and therefore no soil particle would get detached to be transported.

The increase in loading with stepwise increase of the hydraulic gradient, causes the principle stress circles to move to the left on the principal stress axis at each loading increment due to the increase of pore water pressure and also upwards due to the increased velocity and seepage-induced shear stress. The initiation of erosion occurs at the ith loading step where the combined total induced shear stress reaches the limit of internal stability of the soil. At that specific condition, internal instability occurs as illustrated in Figure 5. The difference between τi and τbn is due to considering the flow-induced shear stress affecting the initiation of internal instability. Thus, the model shows that the combined destabilizing effects of both the hydraulic gradient and flow-induced shear reduce the threshold for instability from τ1 to τb1.

Laboratory experiments

The laboratory experiments were specifically designed to investigate the phenomenon of internal erosion (e.g. suffusion phenomenon) that can occur in various soil types that are subject to various types of mechanical and hydraulic loadings. The main challenges were the measurements of continues small rates of erosion and the application of a wide range of mechanical and hydraulic loads. In this respect, a number of new approaches and methodologies were adopted. The specific objectives of the tests were to study the initiation of material instability i.e., erosion initiation as well as the characteristics of the phenomenon defined by the mass removal rate. A detailed account is provided that highlights the main aspects.

Apparatus and setup: The set-up consisted of the erosion rig, water supply system and instrumentation. A schematic illustration of the erosion rig is given in Figure 1. The erosion rig assembly consisted of an inlet, an erosion chamber, an outlet and a sedimentation tank which all were made of Plexiglas and were framed by stainless steel for reinforcement.



The erosion chamber had inner dimensions of 350×200×150 mm and a wall thickness of 50 mm for inlet, erosion chamber, outlet sections and 8mm for the sedimentation tank.

The test specimen was laterally partially confined by the rigid walls of the rig and a vertical mechanical load cane to the top of the specimen by means of a perforated top plate; the plate was 15 mm in thickness with 96 holes each 20mm holes and was pressed by a piston rod. An inlet port in the inlet section allowed water flow to be introduced to the rig which passed through a chamber of plastic balls that diffused the flow prior entry into the erosion chamber. The chamber ensured smooth uniform flow through the perforated plate with 96 holes, each 10 mm in diameter, located at the bottom of the erosion chamber. A plastic filter mesh was placed between the specimen and the perforated rigid bottom plate that only permitted water flow. The opening size of the mesh was selected based on the GSD of the tested specimen to prevent finer particles to pass into the inlet section during specimen placement, packing and saturation. However, the top of the sample was left free to allow easy passage of finer particles detached due to the internal erosion. Material flowing out of the outlet section was captured in the sedimentation tank (Figure 1).

The rig dimensions restricted the maximum grain size of a material that could be tested. The Gradient Ratio standard test method (ASTM D5101) prescribes the maximum particle size to be less than 1/10 the diameter of the permeameter cell which is confirmed by [42]. Head [43] suggests instead a value of

1/12. The maximum grain size was restricted to 15 mm to keep the ratio to be equal or less than 1 to 10.

For the flow regulations, it is well recognized that energy losses through hoses and connections reduce the efficiency of permeameters [43]. To evaluate the hydraulic efficiency of the erosion rig a series of tests were run with empty erosion chamber. Pressure and flux data analysis confirmed that a seepage velocity greater than 0.01 ms-1 yielded a significant reduction in efficiency, implying nearly half of the energy loss occurred in the hoses and connection of the device. To ensure efficiency greater than 90%, flow velocity within the erosion rig were limited to 0.002 ms-1 for the tests. The latter was in agreement with the limit in [44] findings. The maximum velocity limit of 0.002 ms-1, for all the conducted experiments, was considered.

Municipality water was used to supply the inlet tank with pure water. Hydraulic loading of the test specimen was applied by means of water head control, using inlet and outlet tanks. An overflow on the inlet tank bypassed the excess flow to the reservoir in the laboratory to maintain a constant water head at the bottom of the test specimen. In addition, to maintain a constant water head at the top of the specimen and the outlet section an overflow piano key weir, installed on the sedimentation tank, was used. The height of the inlet tank above the outlet section established the applied differential water head. The specimen length and available head room of the laboratory yielded a maximum average applied hydraulic gradient of 10 when the full length of the chamber was used.

Sedimentation tank

25mm 25mm 25mm 25mm 150 mm

25mm

25mm

15 mm

200 mm

150 mm

50 mm 200 mm 450 mm

8mm

60 mm

450 mm

250 mm

100 mm

200 mm

100 mm

50 mm

75 mm

Flow

Flow

Out�ow section

Port C

Port B

Port A Eros

ion

cham

ber

In�o

w s

ectio

n

Figure 1: Sketch of the apparatus for internal erosion experiments.



The water head distribution along the length of specimen was determined using three pressure transducers (PTs) at Port A, Port B and Port C in Figure 1. Port A was located 20 mm higher than the bottom plate on the wall of the erosion chamber to monitor the water head at the “head “of the specimen. Port B was located in the centre of the specimen and port C was located 20 mm lower than the top plate at the “tail” of the specimen on the wall of the erosion chamber. Additionally water head was monitored by a PT at the inlet section on the inlet pipe and water elevation levels at the inlet and outlet tanks. The resolution of the transducers was ±1.0 mm of water head. Local and global hydraulic gradients (i) were computed from measured differential water pressures, knowing the spacing between the ports.

Mechanical loading was applied to the specimen through the piston rod to impose a target value of normal stress vertical direction (i.e z direction). It was measured using a compression load cell.

Eroded material from the soil specimen was captured in the sedimentation tank located beside the erosion rig, which was mounted on an online digital weighing scale with a resolution of ± 0.001grams. The output signals of weighing scale were directly read by the data logger. This setup allowed for continuous monitoring of accumulation of finer particles during the tests and for an online eroded mass monitoring.

Water flux was measured by using a magnetic flow meter appropriate for low flows. Fluxes smaller than the lower detectability limit for the flow meter (0.01 ls-1) were measured by intercepting the collected outflow level in a rectangular tank using a magneto strictive level transmitter for a specific time interval. The flux was then used to deduce the changes in the soil matrix of the reconstituted soil and its evolution with time during each test.

An electronic data logger system was used to record all outputs from the pressure transducers, magnetic flow meter, thermometers, the load cell and the weighing scale. LabVIEW software was used to operate and controlled the tests.

Prior to the erosion tests, the erosion rig was tested for several choices of different fluxes and various magnitude of hydraulic loading to obtain rig specific parameters. Results from these runs were used for the device and sedimentation tank weight measurements calibration.

Soil material and preparation: Test soil specimens were mixed and prepared by processing to get the same grain size distribution as “Soil-A” used by [14]. This gap graded susceptible Test soil specimens were mixed and prepared by processing to get the same grain size distribution as “Soil-A” used by [14]. This gap graded susceptible soil, originally used in [14] experiments, was also used by [15,16]. Soil mixture grading and properties are presented in Figure 2 and Table 1. The rationale for performing tests on this specific soil was that the soil fulfilled the granulometric criteria for the internal instability [i.e. 33,34,13,35]. Furthermore, using this specific soil enabled the possibility of comparing the results with other studies conducted on the similar soil mixtures. Water was added to the blended dry soil mixture to reach 10% of moisture content. This facilitated the packing of the specimen in the erosion chamber and prevented segregation. The weight of the soil, packed in erosion chamber, was measured and used for evaluating the mean initial porosity and density of the specimen. The mean initial porosity was also monitored by measuring the water needed for saturating the soil specimen prior to the start of each experiment.

The gravel and sand used for the soil mixture for testing were purchased with varying specific grain size ranges. A sample of each soil type was sieved to get the GSD of each material type.

0

20

40

60

80

100

0,001 0,01 0,1 1 10 100

Perc

ent �

ner b

y w

eigh

t

Grain size (mm)

Soil Mix Soil-ASkempton and Brogan (1994)

Figure 2: GSD curve of the soil mix produced for suffusion tests compared to the GSD of Soil-A of Skempton and Brogan (1994).

Soil Name USCS

Speci�c weight

of the mixtures

(GS)

Natural dry

density (γd)

Moisture

content (w)

Average porosity

(samples before tests)

Soil -A GP -SP 2.58 (g cm-3) 1.73 (g cm-3) 10 (%) 0.27-0.28

Table 1: Soil mix properties for the suffusion tests.



These materials were used to produce the specific soil mixes for the erosion tests. Test specimens were prepared by mixing different size ranges to obtain the target gradation curve. The specific gravity of all materials was also measured separately as well as for the soil mixtures blended for the erosion tests.

Procedures for suffusion tests: The test procedure for suffusion tests comprised of two main phases: consolidation and multi stage seepage flow. The purpose of the former was to obtain the target vertical stresses on the specimen. The purpose of latter was to increase the hydraulic loading stepwise and monitor the initiation of internal instability as well as the mass removal rates. Three types of tests were done under 4 different mechanical loadings (i.e. equivalent to 0, 10, 25 and applied 50 kPa normal stress in z-direction on the top of the specimen). These test types were:

a) Determination of the initiation of the internal erosion: this was done under a constant mechanical loading and stepwise increasing the hydraulic head in the upstream tank until the initiation of internal erosion was detected. This test group is referred as Test 1.1 to Test 4.2 in the text.

b) Suffusion erosion under constant hydraulic loading: where the specimen was loaded until the initiation of erosion was observed and after the detection of initiation, the mechanical load and the upstream water head was kept constant. During these tests the mass removal from the specimen was monitored. This test type is referred as Test A-1 to Test A-4 in the text.

c) Suffusion erosion under varying hydraulic head: where in contrast to test type (A), after the erosion initiation and under constant mechanical loading, the upstream hydraulic head was increased stepwise. At each step the head was kept constant for a certain period of time while the mass removal was monitored. This test type is referred as Test B-1 to Test B-4 in the text.

16 sets of experiments were done; 8 tests for initiation of erosion (Test 1.1-Test 4.2), 4 tests with constant hydraulic head (Test A-1-Test A-4), and 4 with stepwise incremental hydraulic heads for evaluating the mass removal rate (Test B-1-Test B-4). Summaries are presented in Tables 2, 3 and 4 in the results section of the article.

The mechanical vertical loading by a piston which inserted an axial load on the sample. The mechanical vertical loading was applied gradually until reaching the target load by increments steps of 5 kPa and maintaining each loading step until the local hydraulic gradients created by the mechanical loading were dissipated. The required time for this specific soil mixture varied between a few seconds to a few minutes. Hydraulic loading was applied and controlled by raising the upstream tank with the help of a cable lift.

Suffusion erosion was monitored by the online sedimentation tank weight recordings, where the submerged accumulative eroded mass weight was extracted from the recordings. At the end of each test, the eroded mass was collected from the sedimentation tank and then 19 dewatered and oven-dried. The dried soil weight was used for calibrating data to compare it with the measurements from the sedimentation tank weight

Test ID

Reconstituted sample Initiation of internal erosion - Local

Initiation of internal erosion- continues

Load Length Dry Unit weight Porosity

Local critical

gradient initiation zone

Applied water head

Flux

Average critical

gradient

Applied water head

Flux

F (kPa) L (mm) γd (gcm-3) n icr H (mm) Q (ls -1) cr H (mm) Q (ls -1)

Test-1.1 0 187 1.66 0.387 0.075 BC 42 0.023 0.262 81 0.052

Test-1.2 0 199 1.76 0.307 0.258 BC 105 0.013 0.271 171 0.042

Test-2.1 10 196 1.86 0.302 0.267 AB 101 0.019 1.137 274 0.038

Test-2.2 10 197 1.91 0.285 0.295 BC 111 0.014 1.286 294 0.017

Test-3.1 25 196 1.83 0.310 0.719 AB 178 0.054 1.81 712 0.117

Test-3.2 25 195 1.85 0.300 0.725 BC 189 0.046 1.64 681 0.103

Test-4.1 50 193 1.88 0.280 1.034 BC 258 0.029 3.24 943 0.089

Test-4.2 50 190 1.87 0.292 1.021 BC 247 0.036 4.160 1118 0.106

Table 2: Result summary from tests for determination of initiation of erosion.

Test name

Comulative dried

eroded mass

Experiment time

Logistic Function Natural logaritmic function Maximum

erosion rate from the curve Δm/Δt(kgs-1)

Maximum erosion rate

from the Smoothed data

Δm/Δt (kgs-1)

a/[1+e(-b(t-c))] -Ae(-Bt)+C

m (g) t (s) a b c t < A B C t > Span =60s

Span =600s

Test-A-1 432.68 92000 0.371 1.597 3.03 31060 1.36 0.533 0.456 31060 1.39E -05 2.44E -05 1.99E -05

Test-A-2 417.63 160000 0.235 3.358 1.837 20730 0.55 0.353 0.43 20730 1.93E -05 3.68E -05 2.03E -05

Test-A-3 214.87 200000 0.099 8.588 0.433 9076 0.16 0.052 0.247 9076 2.13E -05 7.50E -05 2.41E -05

Test-A-4 379.61 346000 0.291 4.229 0.195 4750 0.18 0.191 0.383 4750 3.05E -05 2.20E -04 3.43E -05

Table 3: Result summary from suffusion tests type (A) where the mass removal rates evaluated with two methods.



recordings. Additionally, the remnants of specimen in the erosion chamber was collected, dewatered and oven dried and weighed to be compared to the initial weight as an additional measurement for evaluating the mean volumetric changes of the soil density due to suffusion.

Numerical Modelling

The estimation of vertical and horizontal stresses induced by application of mechanical loads on the packed soil specimen was of crucial importance for the application of the proposed MHE model and considering the mechanical loading on suffusion mechanism.

Mechanical loading is defined as the applied force on the soil

surface, which can be translated to principal stresses and the stress field within the soil body. As illustrated in Figure 3, for a two-dimensional soil element in a continuum framework, the stresses acting on its surfaces can be expressed as principal stresses by Eqs. 3 and 4. These principal stresses, σ1 and σ 3, are the maximum and minimum normal stresses, respectively. These stresses are used for evaluating the state of the induced shear stresses within the soil material.

221

1 12 4x y xy x y (3)

To evaluate the principal soil stresses around the erosion hole a 3D numerical model of the erosion rig, that contained the soil sample, was developed in COMSOL Multiphysics software.

Test name

Loading step

Force F

(kPa)

Height L

(m)

Porosity Φ

(-)

Density γsat

(gcm-3)

Flux Q

(ls -1)

Super�cial Velocity

U (ms-1)

Reynolds number

Re (-)

Average gradient

i (ΔH/L)

Average mass

removal rate

Δmav/Δt (gs-1)

Test B -1

1 0.00 0.187 0.307 2.097 0.052 0.019 34.7 0.271 0.0035 2 0.00 0.187 0.307 2.097 0.072 0.045 80.25 0.371 0.0066 3 0.00 0.187 0.307 2.097 0.088 0.055 98.16 0.600 0.0077 4 0.00 0.187 0.307 2.097 0.106 0.066 118.60 0.753 0.0107 5 0.00 0.187 0.307 2.097 0.121 0.075 134.98 0.819 0.0081 6 0.00 0.187 0.307 2.097 0.137 0.085 153.04 0.872 0.0101 7 0.00 0.187 0.307 2.097 0.169 0.105 189.33 0.930 0.0167

Test B -2

1 9.61 0.197 0.285 2.132 0.020 0.013 23.78 1.710 0.0044 2 9.61 0.197 0.285 2.132 0.026 0.018 31.53 2.300 0.0067 3 9.61 0.197 0.285 2.132 0.034 0.023 41.27 3.830 0.0049 4 9.61 0.197 0.285 2.132 0.046 0.031 55.44 5.560 0.0065 5 9.61 0.197 0.285 2.132 0.056 0.038 67.73 7.100 0.0114 6 9.61 0.197 0.285 2.132 0.068 0.045 81.37 7.590 0.0128

Test B -3

1 24.93 0.196 0.310 2.092 0.103 0.063 113.40 3.770 0.0097 2 24.67 0.196 0.310 2.092 0.166 0.102 183.28 5.908 0.0146 3 25.76 0.196 0.310 2.092 0.182 0.112 200.73 6.929 0.0115 4 25.75 0.196 0.310 2.092 0.197 0.121 217.39 8.031 0.0131

Test B -4

1 59.79 0.193 0.280 2.139 0.134 0.091 163.62 5.151 0.0127 2 59.79 0.193 0.280 2.139 0.149 0.101 181.81 6.052 0.0138 3 59.79 0.193 0.280 2.139 0.163 0.111 198.95 7.073 0.0158 4 59.79 0.193 0.280 2.139 0.176 0.120 215.47 8.259 0.0160

Table 4: Summarizes the set-up and the results from suffusion tests type (B).

τ σ

(σx ,τxy)

(σ1 - σ3)/2

2θ

σ1 σ3

(σ1 + σ3)/2

τ

σ σ3

y σ1 x

σ3

σ1

θ

a) b)

Figure 3: Mohr’s circle and stress components across a plane. (a) Construction of Mohr’s circle. (b) The stress components acting on a plane correspond to a point on Mohr’s circle.



The model was created using a 3D rectangular mesh with varying spatial resolution of 1.3-31 mm. The limited journal space does not allow presenting the details of the model. Here, a short summary of the principal steps and procedures follows with focus on the formulation of the model. The model physics was described by the COMSOL Poro-elasticity module. The Plexiglas sidewalls were considered to be elastic which were modelled using a linear isotropic elastic model. The behaviour of the packed soil mixture was modelled using the extended COMSOL Drucker-Prager plasticity model. The soil parameters needed for modelling the soil mixture were taken from Carter and Bentley (2016) for a similar material type used in the present study. The selected properties were soil mixture’s friction angle = 32°, cohesion = 0 (kNm-2) and wall-soil friction angle = 15°.

The Comsol model simulations were done for constant vertical loads of 0, 5, 10, 25 and 50 kPa that were applied to the soil sample. The simulations yielded the soil tensors i.e., σx, σy, σz. These stress distributions were then depth averaged to obtain vertical and horizontal stress coefficients for the soil mixture, (i.e, 0.57 and 0.40 respectively). The required components of the average stresses were calculated through the multiplication of the applied normal force by the stress coefficients; Eqs. 3 and 4 then were then used to calculate the three principle stresses from the depth averaged in-situ stresses.

ResultsAuthors used all data and results from the laboratory experiments together with the soil in-situ stresses to analyse suffusion erosion processes. The combined influences of soil stresses, hydraulic gradient and flow velocity on the initiation of seepage failure are examined and the MHE model is evaluated. By adopting this new envelope, the constitutive law

for suffusion is suggested where the coefficients of the law are extracted empirically from the conducted experiments.

Experimental results

Totally sixteen sets of experiments were done; 8 tests for initiation of erosion (Test 1.1-Test 4.2), 4 tests with constant hydraulic head (Test A-1-Test A-4), and 4 with stepwise incremental hydraulic loading (Test B-1-Test B-4)

Tables 3 summarize the main results for initiation, test types (A) and test type (B) with the corresponding test numbers. It should also be noted that Test 1.1 and Test 2.1 are replications of [14] test on their Soil-A. The former tests are not reported in the table to limit the length of the paper.

Initiation of erosion: The initiation of erosion was determined using two different concepts of local soil particle motion within a small region of the specimen and global sediment motion across the entire soil specimen. The former was determined by monitoring sudden changes in local hydraulic gradients in analogy to the works done by [45,3,15,16] The latter was done by monitoring the continuous slope changes in the measurements of the flux curve versus time under constant hydromechanical loading. In the following text, we refer to the two concepts as local slope and global slope change criteria (abbreviated by LSC and GSC).

Eight tests were done for detecting the initiation of erosion. Four tests were done with normal vertical stress of 0, 10, 25 and 50 kPa (Tests 1.1 to 4.1) and the other four as repetition of the foregoing tests. This repetition was done to ensure the reliability of the measurements, checking the repeatability as well as extending the amount of measured data (referred as Tests 1.2 to 4.2). All tests were started from a hydrostatic and saturated condition where the upstream water head is increased

2

2

Figure 4: Illustration of the change of in-situ principles stresses in porous media under hydraulic loading and seepage of fluid; the undisturbed Mohr-Coulomb circle (black line) shifts i) to the left due to the hydraulic loading (blue line) and ii) upward due to seepage flow (double blue line).



stepwise at increments of 20 mm until reaching the initiation detection point. Each loading step was preserved for at least 10 minutes to monitor the processes and to record adequate data.

For each test and each upstream water head, the global changes of flux as well as the local values of water pressure (i.e. PTs at Port A, B and C, see Figure 1) were monitored at constant upstream water head conditions. Figure 6 presents the results obtained from Test 1.1 as an example. These results were then used to detect the initiation of internal erosion by monitoring sudden and local instabilities in local hydraulic gradients (see Figures. 7 and 8 for the Test1.1). In these figureures AB, AC, and BC refer to the vertical sections marked by letters A, B, and C in Figure 1.

Furthermore, the initiation for suffusion was evaluated by monitoring the GSC in the measurements of the flux plots

versus time under constant hydromechanical loading as presented in Figure 9 for Test 1.1.

As presented in Table 2, which summarizes the results for both cases of local and global initiations of erosion and from the comparison of the gradients in Figures, 8 and 9, the local initiation of erosion (i.e. LSC criterion) occurs at lower applied gradients as compared to GSC criterion defined in this study. The soil specimen used in Test 1.1 shows local instabilities in region BC at local gradients as low as 0.075 when only 42 mm of water head difference between upstream and downstream tanks were applied. However, global initiation was observed when 81 mm of water head difference was applied which gave an average gradient of 0.262 over the soil specimen (see Table 2). This value of critical continuous gradient is in good agreement with the results presented by [14-16] (i.e. 0.2, 0.4 and 0.28, respectively) for this specific soil mixture.

´

Effect of flow-induced shear Effect of hydraulic gradient

Figure 5: Illustration of modified hydromechanical concept based on Mohr-Coulomb shear failure envelope concept.

0

0.01

0.02

0.03

0.04

0.05

0

0.2

0.4

0.6

0.8

1

0 2000 4000 6000 8000 10000 12000 14000 16000

Wat

er h

ead

(m)

Time (s)

Pressure_Inlet Pressure PT_A Pressure PT_B Pressure PT_C Flux

Q (l

s-1)

Figure 6: Illustration of pressure and flux readings of Test1.1 until reaching the initiation. Vertical axis to the right in blue is for the flux which is plotted in secondary axis.



The results presented in Table 2, indicate that the local initiation of erosion occurs at lower hydraulic gradients than the observed for global initiation of erosion. In the former case, the initiation zone is close to the soil surface in zone BC for all of the tests with exception of Tests 2.1 and 3.1 where local erosion was observed deeper inside the specimen. Irrespective of the choice of local or global methods, the hydraulic gradients to initiate internal instability increased by application of mechanical loading on the specimens. This behaviour clearly demonstrates the significant impact of soil stresses on initiation of internal erosion. For instance 14 times higher critical gradients were obtained using the LSC and 16 times higher when GSC criterion was used (i.e., Test-1.1 versus Test4.2).

Mass rate of erosion: Results for tests type (A) using constant hydraulic head are presented in Figure 10 where the black dots are the data obtained from continues weight monitoring of the sedimentation tank and the red line is the fitted curves. The first segment of the curve of each test is a logical function, which converts to a natural logarithmic curve at the green point marked on the curves. As it can be seen from the results, the logarithmic behaviour dominates the logistic behaviour when mechanical loading is applied. Greater the mechanical loading becomes the earlier is the shift to a logarithmic behaviour (marked by a dotted line on Figure 10). For Test-A1this shift happens after 3.11×104 seconds from the initiation, which reduces to 2.07×104, 9.08 ×103 and 4.75×103 for tests A-2

-4-3-2-1012

0.0E+05.0E-41.0E-31.5E-32.0E-32.5E-33.0E-33.5E-3

0 2000 4000 6000 8000 10000 12000 14000 16000

k(m

s-1)

Time (seconds)

k_AB k_AC k_BC

k (m

s-1)

Figure 7: Local and global hydraulic conductivity monitoring of specimen during Test1.1. The vertical axis to the right in red is for the k_BC which is plotted in secondary axis.

-4-3-2-1012

00.05

0.10.15

0.20.25

0.3

0 2000 4000 6000 8000 10000 12000 14000 16000

i

Time (seconds)

i_BC k_BC

k (m

s-1)

Figure 8: Local hydraulic conductivity and gradient monitoring of the specimen in during Test1.1. The vertical axis to the right in red is for the k_BC which is plotted in secondary.

-0.0100.010.020.030.040.05

00.025

0.050.075

0.10.1250.15

0 2000 4000 6000 8000 10000 12000 14000 16000

Wat

er h

ead

(m)

Time (seconds)

Δ Head (US-DS) Flux (l/s)

Q (l

s-1)

Figure 9: Total head loss and flux monitoring of specimen in duringTest1.1 to detect initiation of erosion. The vertical axis to the right in black is for the flux which is plotted in secondary axis. Dashed lines indicate the slope changes for each hydraulic loading step.



to A-4, respectively. The values of coefficients of the fitted logical-natural logarithmic curves are given in Table 3 that were used to extract mass removal rates for the tests from the fitted curves.

Mass removal rates were extracted from the cumulative eroded mass curves by differentiating the fitted logical-natural logarithmic curves in time and also by direct calculation using the collected data by considering the eroded mass change in time. For direct calculation, a data smoothing scheme was applied to damp data white noise. For this purpose, a low-pass filter, moving-average algorithm with filter coefficients equal to the reciprocal of the span of 60 and 600 seconds, were applied. Figure 11 illustrates the time variation of mass removal rates for Test-A-3 extracted with both techniques.

The erosion rate evaluated from differentiating the logical-natural logarithmic curve for TestA-3 gives a maximum erosion rate of 2.17 × 10-5 (kgs-1) which is presented in Figure 11b. The maximum mass removal rates for all the four tests of type (A) are presented in Table 3.

Results from the type-B tests with stepwise increasing water

0 2 4 6 8 10

0.5

0.4

0.3

0.2

0.1

0.0

0 2 4 6 8 10 12 14

0.5

0.4

0.3

0.2

0.1

0.0

0 10 20 30

0.3

0.2

0.1

0.0

0 5 10 15 20 25 30 35 40

0.4

0.3

0.2

0.1

0.0

)gk( ssam dedore evitalu

muC

)gk( ssa

m dedore evitalumu

C

)gk( ssam dedore evitalu

muC

)gk( ssa

m dedore evitalumu

C

Time (104 seconds)

Time (104 seconds)

Time (104 seconds)

Time (104 seconds)

Figure 10: The dry mass of commutative eroded soil in kilograms and in time for TestA-1 to TestA-4. The black points are in the data from the experiments and the red curves are the fitted logistic-logarithmic functions.

head loading are presented in Table 4. For each test, the eroded mass was collected at the end of each loading step before changing the hydraulic loading. For calculating the erosion rates, the collected mass was averaged for the length of the loading step. For Tests B-1 and B-2, more loadings steps were applied in comparison to tests B-3 and B-4. This is because the upstream head were increased as multipliers of the initial gradient needed to initiate the erosion process. Furthermore, the highest applicable gradient was limited for the device set-up. The intrinsic velocity and the pore Reynolds number (Re) were calculated based on the mean porosity of each specimen, the average temperature and the characteristic soil mixture diameter (d10). Results from tests type (B) were used to define the constitutive law of erosion for suffusion mechanism which is presented in the discussion section.

Numerical simulations

The results of these simulations indicated that the normal and horizontal stress distributions in depth, are non-linear, predominantly close to the walls and arching effect increases by wall displacement, as illustrated in Figure12. The effect of friction between the soil and wall was found to be



less substantial on the stress distributions than the lateral displacement of the walls. We used the stress distribution results from the numerical models to estimate the mean vertical and horizontal stresses (i.e. minimum and maximum principal stresses) within the erosion chamber in depth.

The latter result was used to plot the hydromechanical paths (e.g. Figure13) and to plot the MHE (e.g. Figure14), which was used to extract the coefficient of the constitutive law for the erosion from the envelope plots as illustrated in Figure15 for the suffusion type (B) tests.

DiscussionThe mechanism of the suffusion erosion

Based on the study findings, authors deduce that the shape of the cumulative eroded mass and its rate are driven by the granulometric and hydromechanical criteria simultaneously.

When the suffusion process is initiated, the soil matrix starts to change due to the transport of the fine particles that increases the porosity. This physical change in the soil matrix results in an increase in the mean fluid velocity and consequently in flow-induced shear stress. On the other hand, the transport of fine particles results in effective stress redistribution in the solid compartment of the soil matrix. This process also results in a change in stress reduction factor α due to the change in the GSD of the soil mixture (i.e. shifting the MHE upwards if α is increased). Simultaneously, reducing the fine fraction in GSD of the soil mixture results in a decrease in the contact surface area of the solid fraction with the fluid, where the flow induced shear forces are applied. This continuous shift reduces the induced excess shear stress in the soil. Consequently, the cumulative mass erosion curves for type (A) tests are “S” shaped and their rates are bell-shaped (e.g. Figures. 10 and 11).

0.0E+0

2.0E-5

4.0E-5

6.0E-5

8.0E-5

0.0E+0 1.0E+5 2.0E+5 3.0E+5 4.0E+5

ṁ(k

gs-1

)

Time (seconds)

ṁ-600ṁ-60

0.0 2.0E+4 4.0E+4 6.0E+4 8.0E+4 1.0E+5

2.5E-5

2.0E-5

1.5E-5

1.0E-5

5.0E-4

0.0

Time (seconds)

ṁ (k

gs-1

)

a)

b)

Figure 11: Mass removal rate evaluated with two methods for Test-A-3 with. The curves on top are from direct calculation and the lower curve is from differentiating the fitted curve.

0

5

10

15

20

0 0.2 0.4 0.6 0.8 1

Dep

th (c

m)

Normalized vertical stress

0

5

10

15

20

0 0.1 0.2 0.3 0.4 0.5

Dep

th (c

m)

Normalized horizontal stress

ɛH = 0.0

ɛH = 1.0×10-4

ɛH = 2.0×10-4

ɛH = 3.0×10-4

ɛH = 4.0×10-4

Coulomb

Figure 12: Vertical and horizontal stress distribution behind the sidewalls of the erosion chamber for different wall displacements normalized by the pressure of the soil’s self-weight at the bottom of the erosion chamber for the suffusion tests with 0 kPa mechanical loading. The soil friction angle was assigned as 32° and the soil/wall interface friction to be 15°.



0.20

0.22

0.24

0.26

0.28

0.30

0.32

0.34

0.50 0.55 0.60 0.65 0.70 0.75 0.80

Shea

r st

ress

τ(k

Nm

-2)

Effective stress σ' (kNm-2)

(σ'1-σ'3)/2Test1.1

Figure 13: Hydromechanical path of Soil-A from suffusion Tests1.1. The half circles show the insitu stress status at the 1st, 3rd, 8th and 13th (last) of the hydraulic loading steps. The principal stresses are marked with dotted circles and the total induced shear stresses, including the flow induced shear with solid circles.

0

2

4

6

8

10

12

-1 4 9 14 19 24

Shea

r st

ress

τ(k

Nm

-2)

Effective stress σ' (kNm-2)

Hydromechanical path tippoints

Soil-A shear strength

Figure 14: Hydromechanical envelope and the triaxial shear strength curve for Soil-A from Skempton and the Brogan (1994). α=0.7588 makes the two lines coincide.

ṁ = 1.9×10-3 ×[τb-τenv]

00.00020.00040.00060.0008

0.0010.00120.00140.00160.0018

0.002

0.00 0.20 0.40 0.60 0.80 1.00

ṁ(k

gm-3

s-1)

[τb-τenv] (kNm-2)

ṁ Constitutive law of suffusion mechanism

Figure 15: Linear regression of mass removal versus induced excessive shear stresses to extract the coefficient of mass erosion rate for suffusion (Cs). For Soil-A from Skempton and Brogan (1994) and suffusion test type (B), Cs = 1.9×10-3 (m-2 s) was extracted.



In the early stages of suffusion, the rate of the flow-induced shear stress is higher than the rate of the change of α factor. This behaviour, changes after the amount of fine particles transported out of the matrix reaches a critical limit. At this critical limiting point, the combined effects of the increase in the effective stresses in the solid compartment, the change in α and reduction of the contact area, overcomes the effects of the increased fluid velocity and its induced shear forces. After reaching this prescribed critical point, the erosion rate decreases until it reaches a balance point where the hydromechanical path falls beneath the MHE and mass removal stops for that specific hydromechanical loading and physical property of that soil matrix. However, by any change in hydromechanical loading (e.g. applying a new hydraulic load) the balance is disturbed and the erosion process starts again and continues until a new balance is established or the erodible fraction of the soil mixture diminishes.

To control the amount of the changes in the soil matrix in each test of type (B), the duration of each experimental step was kept limited. The cumulative eroded mass of each step was kept at a low level less than 0.5% of the specimen weight so that the effect of the eroded mass on the soil matrix could be neglected and the structure of the soil matrix could be assumed to remain unchanged. The implication is that the erosion process can be solely considered prevailing under constant granulometric condition for test type B.

Verification of MHE

To verify the hypothesis of applicability of the MHE model, all the three stress components were calculated from the experimental results (i.e. normal, lateral effective soil stresses and flow-induced shear stress). The core of the present work is the foregoing task, which amounted to the modification of Mohr-Coulomb critical shear stress for initiation of instability in the soil matrix. As presented in the theoretical model in Figure 5, internal erosion initiation could be triggered even with application of small values of the hydraulic gradients (i.e. higher in-situ stress state) when the effect of flow-induced shear stress is considered. Authors suggest that the contribution of flow-induced shear stress is the main cause for inaccuracy of the previously suggested stress reduction factors.

To verify the hypothesis, the MHE model for Soil-A was constructed as shown in Figures. 13 and 14. It is produced by the analysis of complete set of data. The hydromechanical path was plotted from a single tests results and the envelope from a set of tests of the same material undergoing suffusion. The steps taken to accomplish the foregoing task are essential parts that need to be listed. The principal stress distributions were evaluated from the numerical simulations conducted for this purpose where the lateral deformation of the erosion chamber (εH) and the wall-soil friction were taken into account. The vertical stress coefficient for the erosion rig filled with Soil-A (i.e. soil friction angle = 32° and wall-soil friction = 15°) was evaluated to be equal to 0.651.

1. The horizontal stress, which is proportional to the

vertical stress, was calculated. The stress coefficient for the current study was also extracted from the numerical simulation results and was implemented as 0.36 for both lateral directions. However, similar to vertical stress, the coefficients can be assigned based on lateral boundary conditions using the available plots for horizontal stress coefficients in literature [46]. This is done by assuming active or passive behaviour with outwards and inwards movements and the friction between the soil and the wall.

2. For each step of hydraulic loading, the principal effective stresses were calculated (i.e.𝜎 𝑖 = 𝜎𝑖 − 𝑝𝑓, where 𝜎𝑖 is the applied stress and pf is the pore water pressure at the centre of the specimen). It is worth mentioning that the magnitude of the pore water pressure is equal in all directions and therefore needs to be subtracted from the lateral soil stresses without applying the horizontal stress coefficients.

3. The flow-induced shear stress on porous matrix were calculated using Carman’s equation [47] which reads:

223

1 12 4x y xy x y (4)

In Eq.5, τf is the flow-induced shear stress on the soil particle, U is the superficial flow velocity in the media, ρ is the fluid density and Re1 is the modified Reynolds number for the media which is defined in Eq.6.

(5)

In which 𝜇 is the fluid dynamic viscosity and Sv is the specific surface area per unit grain volume and for a porous medium. Sv can be calculated from Sv=Ksp/d10, where Ksp is the three-dimensional effective grain shape-factor of the porous matrix and d10 is the effective diameter. In the current study, Ksp=35 was adopted for the soil mixture taken from [48] and their Petrographic-Image studies on porous media by considering an oval shape for the pore openings. For effective diameter, the fine fraction of the Soil-A was considered and d10= 0.182 mm was assigned when calculating the flow-induced shear stress.

4. Based on the upstream water head and the flux under constant mechanical loading, three hydromechanical parameters of 𝜎1, 𝜎3 and 𝜏𝑓 were used to evaluate the combined induced shear stress on the soil for each upstream water head loading-step.

5. The hydromechanical path for the material is produced if the maximum points of the total induced shear stress circles are connected. The path would indicate the maximum induced shear stress on the soil starting from the hydrostatic condition and ending by the observation of initiation of internal erosion instability. Figureure 13 shows the path for the suffusion Test1.1.

To construct the MHE for each soil, first the tip points (i.e. where erosion started were extracted from) marking the hydromechanical paths were extracted from the multiple tests.

The foregoing procedure is illustrated in the diagram shown



in Figure 14. The blue line in Figure14 shows the MHE for Soil-A which was plotted by fitting the best-fit line to the tip points of these paths. Comparison of this envelope with the results for the soil strength data from the triaxial tests yields an offset in shear stress diagram. This offset is due to the non-uniformity of stress distribution within the soil matrix and the stress reduction in the finer fraction of the soil mixture. Authors quantify it by assigning a stress reduction factor, α , as a multiplier to the soil shear strength curve from triaxial tests. For this study the soil shear strength curve was taken from [49-55] for a similar soil mixture. The reduction factor makes the curve to fall on the MHE. Authors believe that this offset is a unique property of each material type that could be evaluated with the presented methodology.

The constitutive law of erosion

The constitutive law for the suffusion erosion mechanism is defined as the rate of removal of mass due to application of excessive shear stress higher than the material internal erodibility resistance that is specified by the MHE of the material. This constitutive law reads:

(6)

Equation 7 is in analogy with the existing relations for surface erosion [37] and has been also adopted widely for hole erosion test results [1]. For suffusion mechanism, the definition implies a stress-dependency of constitutive law of erosion for both initiation and the mass removal rate.

The initiation of erosion is controlled by implementation of the MHE and evaluating the total in-situ shear stress (τb) compared to the shear resistance of the material from the envelope (τenv). Both τb and τenv are dependent on the applied hydraulic and mechanical loadings and can vary if the loads change. When the in-situ shear stress reaches the envelope value, the constitutive law governs. The mass removal function remains active while an excessive shear stress is applied. The

rate of this mass removal is proportional to the excess shear stress which is higher than the envelope value. The coefficient of proportionality for this law can be assigned by fitting the equation to the data from the experiments that were evaluated for the tests conducted for this study. Results from test type (B) were considered to evaluate the erosion constitutive law, which is presented in Table 5 and Figure 15 as the mass removal in kilograms per volume in time (kgm 3 s -1).

ConclusionsIn this work the suffusion phenomenon, a major mechanism of initiation of internal erosion in earth fill structures was studied by means of laboratory experiments to develop a new theoretical framework. The work was successful in defining the continuum-based constitutive laws of erosion which should find applications in problems related to internal erosion. The suggested procedures and methods could be considered as improvements of the present state of knowledge. The main study findings are:

• A new criterion to determine the initiation of the suffusion erosion is suggested. In this method, a continuous slope change of the seepage velocity curve versus time, under constant hydromechanical loading is suggested as an indicator of erosion initiation. This method successfully detected the initiation of erosion.

• The initiation of internal erosion due to suffusion is found to be dependent on in-situ soil stresses.

• A modified theoretical concept for the hydromechanical envelope (i.e. MHE) is suggested that accounts for soil in-situ stress dependency of internal erosion initiation in soil media. This theoretical concept is developed based on Mohr-Coulomb’s shear failure envelope where all soil principal stresses, as well as flow-induced shear stress are included.

• The distribution of the cumulative eroded soil mass,

Test Step F (K Pa)

K v L (m)

γsat (gcm-3)

Q (ls -1)

Re1 τf (kPa)

σ1 (kPa)

σ'1 (kPa) i K h σ'3

(kPa) σ3

(kPa) τb

(kPa) τenv (kPa)

τb-τenv (kPa)

(kgm-3s-1)

Test B -1

1 0 0.651 0.187 2.1 0.05 0.01 0.15 1.92 0.76 0.3 0.36 0.27 1.44 0.395 0.28 0.11148 3.54×10-4

2 0 0.651 0.187 2.1 0.07 0.03 0.35 1.92 0.67 0.4 0.36 0.24 1.5 0.567 0.25 0.31291 6.68×10-4

3 0 0.651 0.187 2.1 0.09 0.03 0.43 1.92 0.46 0.6 0.36 0.17 1.63 0.579 0.19 0.39308 7.87×10-4

4 0 0.651 0.187 2.1 0.11 0.04 0.52 1.92 0.32 0.8 0.36 0.11 1.72 0.625 0.14 0.48429 1.09×10-3

5 0 0.651 0.187 2.1 0.12 0.05 0.6 1.92 0.25 0.8 0.36 0.09 1.76 0.678 0.12 0.55727 8.23×10-4

6 0 0.651 0.187 2.1 0.14 0.05 0.68 1.92 0.21 0.9 0.36 0.07 1.79 0.743 0.11 0.63773 1.03×10-3

7 0 0.651 0.187 2.1 0.17 0.07 0.84 1.92 0.15 0.9 0.36 0.06 1.83 0.887 0.09 0.79949 1.70×10-3

Test B -2

1 9.6 0.651 0.197 2.13 0.02 0.01 0.12 8.32 5.7 1.7 0.36 2.06 4.68 1.933 1.88 0.05491 4.23×10-4

2 9.6 0.651 0.197 2.13 0.03 0.01 0.15 8.32 5.13 2.3 0.36 1.86 5.05 1.789 1.69 0.09522 6.44×10-4

3 9.6 0.651 0.197 2.13 0.03 0.01 0.2 8.32 3.65 3.8 0.36 1.32 5.99 1.365 1.22 0.14899 4.73×10-4

4 9.6 0.651 0.197 2.13 0.05 0.02 0.27 8.32 1.98 5.6 0.36 0.72 7.06 0.902 0.68 0.22536 6.33×10-4

5 9.6 0.651 0.197 2.13 0.06 0.02 0.33 8.32 0.49 7.1 0.36 0.18 8 0.488 0.2 0.29184 1.10×10-3

6 9.6 0.651 0.197 2.13 0.07 0.03 0.4 8.32 0.01 7.6 0.36 0 8.31 0.404 0.04 0.36083 1.24×10-3

Test B -3

1 25 0.651 0.196 2.09 0.1 0.04 0.49 18.2 13.7 3.8 0.36 4.94 9.53 4.847 4.45 0.39952 9.40×10-4

2 25 0.651 0.196 2.09 0.17 0.07 0.8 18.1 11.4 5.9 0.36 4.14 10.8 4.443 3.73 0.7145 1.42×10-3

3 26 0.651 0.196 2.09 0.18 0.07 0.88 18.8 11.2 6.9 0.36 4.04 11.7 4.435 3.64 0.7922 1.12×10-3

4 26 0.651 0.196 2.09 0.2 0.08 0.95 18.8 10.1 8 0.36 3.65 12.3 4.167 3.3 0.86974 1.28×10-3

Test B -4

1 59 0.651 0.193 2.14 0.13 0.05 0.82 41 35.1 5.2 0.36 12.7 18.5 12.03 11.4 0.64259 1.25×10-3

2 59 0.651 0.193 2.14 0.15 0.06 0.92 41 34.3 6.1 0.36 12.4 19.1 11.85 11.1 0.73814 1.36×10-3

3 59 0.651 0.193 2.14 0.16 0.06 1 41 33.3 7.1 0.36 12.1 19.7 11.62 10.8 0.82887 1.56×10-3

4 1.58×10-3

m

Table 5: Constitutive law for suffusion mechanism and extracting its coefficients for Soil-A from tests type (B).



under constant mechanical load and hydraulic gradient, is found to follows a logistic-natural logarithmic shape.

• The fitted MHE to Soil-A resulted to a stress reduction factor of α = 0.7588.

• The constitutive law of erosion for the suffusion mechanism ṁ = 1.9×10-3 [τb-τenv] is suggested for the specific soil mixture studied (i.e. Soil-A from [14] where τb and τenv are in (kNm-2) and ṁ is in (kgm-3 s -1).

AcknowledgmentsThis study was performed as part of a joint research project between KTH Royal Institute of Technology and the University of Florence (UNIFI) and financed by the Swedish Hydropower Centre (Svenskt Vattenkraft Centrum, SVC, http://www.svc.nu). The authors also acknowledge Vattenfall for their help and support in conducting the experiments at Vattenfall R&D laboratory in Älvkarleby, Sweden and Professor Vladimir Cvetkovic for supporting this work.

References1. Bonelli S (2013) Erosion in Geomechanics Applied to Dams and

Levees. John Wiley and Sons, London, UK. [View Article]

2. Howard AD, McLane CF III (1988) Erosion of cohesionless sediment by groundwater seepage. Water Resource Research 24: 1659–1674. [View Article]

3. Moffat R (2005) Experiments on the internal stability of widely graded cohesionless soils. PhD thesis, the University of British Columbia, Vancouver, Canada. [View Article]

4. Terzaghi K (1939) Soil mechanics: a new chapter in engineering science. Journal of Institution of Civil Engineers 12: 106-142. [View Article]

5. U.S. Army Corps of Engineers (USACE) (1953) Investigation of filter requirements for underdrains. US Army, Waterways Experiment Station,Vicksburg, MS, Technical Memorandum No. 183-1. US Beauru of Recklamation (USBR) (2004). Design Standards-Embankment Dams. No.13, Denver, US. [View Article]

6. Karpoff KP (1955) The use of Laboratory Tests to Develop Design Criteria for Protective Filters. Proc., American Society for Testing Materials 5: 1183-1198. [View Article]

7. Bureau of Reclamation (USBR) (1947) Laboratory Tests on Protective Filters for Hydraulic and Static Structures. Laboratory Report No. EM-132. [View Article]

8. Bureau of Reclamation, (USBR) (1955) The Use of Laboratory Tests to Develop Design Criteria for Protective Filters. Earth Laboratory Report No. EM-425, June 20, 1955. (Also: [with recommendations and modifications] K.P. Karpoff, Proc., the American Society for Testing Materials, 55: 1183). [View Article]

9. Sherard JL, Dunnigan LP, Talbot JR (1984) Basic Properties of Sand and Gravel Filters. Journal of Geotechnical Engineering 110: 684-700. [View Article]

10. Lafleur J (1984) Filter testing of broadly graded cohesionless tills. Canadian. Geotechnical Journal 21: 634-643. [View Article]

11. Tomlinson SS, Vaid YP (2000) Seepage forces and confining pressure effects on piping erosion. Canadian Geotechnical Journal 37: 1-13. [View Article]

12. Kenney TC, Lau D (1985) Internal stability of granular filters. Canadian Geotechnical Journal, 22: 215-225. [View Article]

13. Kenney TC, Lau D (1986) Internal stability of granular filters: Reply. Canadian Geotechnical Journal 23: 420-423. [View Article]

14. Skempton AW, Brogan JM (1994) Experiments on piping in sandy gravels. Geotechnique 44: 449-460. [View Article]

15. Li M (2008) Seepage induced instability in widely graded soils. PhD thesis, the University of British Columbia, Vancouver, Canada. [View Article]

16. Crawford-Flett KA (2014) An improved hydromechanical understanding of seepage-induced instability phenomena in soil. PhD thesis, the University of British Columbia, Vancouver, Canada. [View Article]

17. Vardoulakis I, Stavropoulou M, Papanastasiou P (1996) Hydro-mechanical aspects of the sand production problem. Transport in Porous Media 22: 225-244. [View Article]

18. Vardoulakis I, Papanastasiou P, Stavropoulou M (2001) Sand Erosion in Axial Flow Conditions. Transport in Porous Media 45: 267-280. [View Article]

19. Papamichos E, Vardoulakis I, Tronvoll J, Skjærstein A (2001) Volumetric sand production model and experiment. International journal for numerical and analytical methods in geomechanics 25: 789–808. [View Article]

20. Papamichos E, Vardoulakis I (2005) Sand erosion with a porosity diffusion law. Computers and Geotechnics 32: 47–58. [View Article]

21. Steeb H, Diebels S (2003) A thermodynamic-consistent model describing growth and remodeling phenomena. Computational Materials Science 28: 597-607. [View Article]

22. Xu T, Tang CA, Yang TH, Zhu WC, Liu J (2006) Numerical investigation of coal and gas outbursts in underground collieries. International Journal of Rock Mechanics and Mining Sciences 43: 905–919. [View Article]

23. Wan RG, Wang J (2002a) A coupled erosion-stress deformation model for sand production using streamline upwind finite elements. Proc., NUMOG VIII, Numerical models in geomechanics, Swets & Zeitlinger, Lisse, Netherlands. [View Article]

24. Wan RG, Wang J (2002b) Modelling sand production within a continuum mechanics framework. Journal of Canadian Petroleum and Mining Technology 41: 46–52. [View Article]

25. Brivois O, Bonelli S, Borghi R (2007) Soil erosion in the boundary layer flow along a slope: a theoretical study. European Journal of Mechanics - B/Fluids 26: 707-719. [View Article]

26. Bonelli, S, Marot D (2008) On the modelling of internal soil erosion.” The 12th International Conference of International Association for Computer Methods and Advances in Geomechanics (IACMAG). Goa, India. [View Article]

27. Steeb H, Diebels S, Vardoulakis I (2005b) A multiphase continuum-based model capturing erosion and deposition. Trends in Applications of Mathematics to Mechanics, K Hutter, Y Wangeds., Shaker, Aachen pp: 519–528. [View Article]

28. Steeb H, Diebels S, Vardoulakis I (2007) Modelling internal erosion in porous media. Computer Applications in Geotechnical Engineering. [View Article]

29. Golay F, Bonelli S (2011) Numerical modeling of suffusion as an interfacial erosion process. EJECE 15: 1225-1241. [View Article]

30. Einstein HA (1937) Sediment transport in probabilistic approach (in German).Mitt. d. Versuchsanstaltf Wasserbau Eidg TH, Zurich

https://www.wiley.com/en-us/Erosion+in+Geomechanics+Applied+to+Dams+and+Levees-p-9781848214095

http://onlinelibrary.wiley.com/doi/10.1029/WR024i010p01659/abstract

https://open.library.ubc.ca/cIRcle/collections/ubctheses/831/items/1.0063322

https://www.icevirtuallibrary.com/doi/abs/10.1680/ijoti.1939.14534

http://acwc.sdp.sirsi.net/client/es_ES/default/?rm=WATERWAYS+EXPE0%7C%7C%7C1%7C%7C%7C0%7C%7C%7Ctrue

https://books.google.co.in/books/about/The_Use_of_Laboratory_Tests_to_Develop_D.html?id=1RzASgAACAAJ&redir_esc=y

https://ascelibrary.org/doi/abs/10.1061/%28ASCE%290733-9410%281984%29110%3A6%28684%29

http://www.nrcresearchpress.com/doi/abs/10.1139/t84-070#.WnFuCqiWbIU

http://www.nrcresearchpress.com/doi/abs/10.1139/t99-116#.WnFkG6iWbIU

http://www.nrcresearchpress.com/doi/abs/10.1139/t85-029#.WnFvwaiWbIU

http://www.nrcresearchpress.com/doi/abs/10.1139/t86-068#.WnFvaqiWbIU

http://www.nrcresearchpress.com/doi/abs/10.1139/t86-068#.WnFvaqiWbIU

https://www.icevirtuallibrary.com/doi/abs/10.1680/geot.1994.44.3.449



https://link.springer.com/article/10.1007/BF01143517

https://link.springer.com/article/10.1023/A:1012035031463

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https://www.sciencedirect.com/science/article/pii/S0266352X04001351

https://www.sciencedirect.com/science/article/pii/S0927025603001447


https://www.onepetro.org/journal-paper/PETSOC-04-04-04

https://www.onepetro.org/journal-paper/PETSOC-02-04-04

https://doi.org/10.1016/j.euromechflu.2007.03.006

http://hal.univ-nantes.fr/hal-00343941/

https://www.researchgate.net/profile/Lev_Steinberg/publication/256974508_Mesoscale_Mathematical_Modeling_of_Intercalation_Battery_Materials/links/00463524598a31524a000000.pdf

https://doi.org/10.1061/40901(220)16



31. Sakthivadivel R, Irmay S (1966) A review of filtration theories. HEL 15-4, University of California, Berkeley, US. [View Article]

32. Steeb H, Diebels S, Vardoulakis I (2005a) Modelling erosive processes in the framework of the theory of porous media. Tagungsband des Symposiums ’Grenzschicht Wasser und Boden, Phänomene und Ansätze’9. März 2005, TU Hamburg-Harburg, J. Grabe, ed. pp:189–197. [View Article]

33. Kezdi A (1979) Soil physics – selected topics. Elsevier Scientific Publishing Company, Amsterdam p: 160. [View Article]

34. Kovacs G (1981) Seepage hydraulics. Elsevier Scientific Publishing Company, Amsterdam. [View Article]

35. Burenkova VV (1992) Assessment of suffusion in non-cohesive and graded soils, Proc., the First International Conference “Geo-Filters, Karlsruhe, Germany pp. 357-360. [View Article]

36. Scheuermann A, Steeb H, Kiefer J (2010) Internal erosion of granular materials - identification of erodible fine particles as a basis for numerical calculations. 9th HSTAM International Congress on Mechanics Vardoulakis mini-symposia, 12-14 July, Limassol, Cyprus. [View Article]

37. Shields A (1936) Application of the Aehnlichkeitsmechanik and turbulence research on the bed movement (in German). Mitteilung der Preussischen Versuchsanstalt fur Wasserbau und Schiffbau, Heft 26, Belin. [View Article]

38. Lewis J (1996) Turbidity-controlled suspended sediment sampling for runoff-event load estimation. Water Resource research 32: 2299-2310. [View Article]

39. Honjo Y, Haque MA, Tsai KA (1996) Self-filtration behavior of broadly and gap graded cohesionless soils. Geofilters’ 96. BiTech Publishers, Montreal, Canada pp. 227- 236. [View Article]

40. Leeks G (2006) Measuring Sediment Loads, Yields, and Source Tracing. Encyclopedia of Hydrological Sciences. [View Article]

41. Zielina M (2010) Measurement of suspended particles in water filtration. 14th International Water Technology Conference, IWTC 14 2010, Cairo, Egypt 105-112. [View Article]

42. Kenney TC, Chacal R, Chiu E, Ofeogbu GI, Omanga GN, et.al (1985) Controlling constriction sizes of granular filters. Canadian Geotechnical Journal 22: 32-43[View Article]

43. Head KH (1992) Manual of soil laboratory testing. Pentech Press, London. [View Article]

44. Khan AS (2003) Experimental Study for Evaluating the Internal Stability of Gap-Graded Soils, M.Sc. Thesis, University of British Columbia, Vancouver, BC, Canada. [View Article

45. Moffat R (2002) A Laboratory Study of Particle Migration in Cohesionless Soils. M. Sc. Thesis, University of British Columbia, Vancouver, BC, Canada. [View Article]

46. Clayton C, Milititsky J (1986) Earth pressure and earth-retaining structures. University Press, Glasgow. [View Article]

47. Carman PC (1997) “Fluid flow through granular beds.” Chemical Engineering Research And Design 75: S32-S48. [View Article]

48. Clelland W, Fens T (1991) Automated Rock Characterization With SEM/Image Analysis Techniques. SPE Formation Evaluation 6: 437-443. [View Article]

49. Carter M, Bentley S (2016) Soil Properties and their Correlations. John Wiley and Sons, London. [View Article]

50. Bonelli S, Benahmed N, Brivois O (2006) On the modelling of the hole erosion test. 3 Rd Conference on Scour and Erosion, Amsterdam. [View Article]

51. Bonelli S, Brivois O (2008) The scaling law in the hole erosion test with a constant pressure drop. International journal for Numerical. Methods Engineering 32: 1573–1595. [View Article]

52. Kezdi A, Konyary Z (1971) Laboratory permeability tests (In Hungarian). Diploma work, T. U. Budapest, Budapest. [View Article]

53. Lowe J (1988) Seepage analysis, in advanced dam engineering, for design, construction and rehabilitation. Ed. Robert B. Jansen, Van Nostrand Rheinhold pp 270-275. [View Article]

54. U.S. Army Corps of Engineers (1953) Filter experiments and design criteria, Technical Memorandum, No. 3-360, Waterways Experiment Station, Vicksburg, US. [View Article]

55. US Department of the Interior and State of Idaho (DOI-Idaho) (1976) Failure of Teton Dam. Idaho falls, Idaho, US. [View Article]

Citation: Ferdos F, Dargahi B, Solari L (2018) Mechanism of Suffusion Erosion Phenomenon In Porous Media. J Geol Geosci 2: 001-018.

Copyright: © 2018 Ferdos F, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

https://books.google.co.in/books?id=FUKIfyhCsCYC&pg=PA942&lpg=PA942&dq=A+review+of+filtration+theories.+HEL+15-4&source=bl&ots=uYYRvwlDPu&sig=s23Ahrw-J3E9fDdMFKHZcxjCk00&hl=en&sa=X&ved=0ahUKEwiPgfn2y4HZAhUSS48KHYLzCzYQ6AEIKjAB#v=onepage&q=A review of filtration theories. HEL 15-4&f=false

https://www.researchgate.net/publication/273128878_Modelling_erosive_processes_in_the_framework_of_the_Theory_of_Porous_Media

http://www.scirp.org/(S(351jmbntvnsjt1aadkposzje))/reference/ReferencesPapers.aspx?ReferenceID=1289571

http://www.scirp.org/(S(oyulxb452alnt1aej1nfow45))/reference/ReferencesPapers.aspx?ReferenceID=1778716

https://espace.library.uq.edu.au/view/UQ:238442

https://repository.tudelft.nl/islandora/object/uuid:a66ea380-ffa3-449b-b59f-38a35b2c6658

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http://www.nrcresearchpress.com/doi/abs/10.1139/t85-005#.WnFwXKiWbIU




https://www.onepetro.org/journal-paper/SPE-20920-PA

https://books.google.co.in/books?hl=en&lr=&id=QxesDAAAQBAJ&oi=fnd&pg=PA10&dq=Soil+Properties+and+their+Correlations&ots=Rz6mU6IU6K&sig=TNotZCIziN-Ufp7hjcn_VWvUSeQ#v=onepage&q=Soil Properties and their Correlations&f=false

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https://searchworks.stanford.edu/view/1319544

http://www.scirp.org/(S(lz5mqp453edsnp55rrgjct55))/reference/ReferencesPapers.aspx?ReferenceID=1363961

https://archive.org/details/reporttousdepart00inde

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