CalculationMethodsofSeepageCoefficientforClayBasedonthe...

Research ArticleCalculation Methods of Seepage Coefficient for Clay Based on thePermeation Mechanism

Yu Zhang 1 Tielin Chen 1 Yujun Zhang2 and Weizhong Ren2

1Key Laboratory of Urban Underground Engineering of Ministry of Education Beijing Jiaotong UniversityBeijing 100044 China2Wuhan Institute of Rock and Soil Mechanics Chinese Academy of Sciences Wuhan 430071 China

Correspondence should be addressed to Yu Zhang zhangyu871030163com

Received 28 September 2018 Accepted 1 January 2019 Published 3 March 2019

Academic Editor Cumaraswamy Vipulanandan

Copyright copy 2019 Yu Zhang et al is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

e existing empirical methods of the seepage coefficient for clay have difficulty in parameter acquisition and are poor incalculation accuracy and it is possible to find reasonable ones based on the mature empirical methods of coarse-grained soilFirstly the permeation mechanism of clay was analysed including influencing factors spatial process and parameter calculationand the ineffective and effective voids were defined then the empirical methods of clay and coarse-grained soil were summarisedand listed Secondly clay was put equivalent to coarse-grained soil according to bound-water consolidation and the parameterldquoequivalent void ratiordquo was introduced to establish the equivalent calculation methods Finally the liquid-plastic limit methoddetermining the volume of ineffective voids was explained and the feasibility of equivalent calculation methods was evaluated bythree examples e results show that seepage permeation and effective permeation are three different concepts groundwaterpermeates in clay via the effective void For certain soil the increasing sequence of permeability coefficients is the seepagecoefficient permeation coefficient and effective permeation coefficient Introduction of the ldquoequivalent void ratiordquo unifies thecalculation of the seepage coefficient for clay and coarse-grained soil e maximum of the bound-water content is about 09 timethe size of liquid limit e Mesri equation and the equivalent calculation method of Terzaghi or CursonndashKarman are suitable forcalculating the seepage coefficient of clay for the closest results to experimental values

1 Introduction

Seepage and permeation are two different concepts the strictdefinitions in this study are as follows Seepage process hasthe characteristics of actual current such as flow directionflow amount water pressure and friction resistance waterfills all soil space continually so it is called ldquovirtual currentrdquoHowever spatial coordinate functions are continuous and aseepage field can be formed Permeation is a motion processthat occurs only via soil voids and the spatial coordinatefunctions are noncontinuous As a result the correspondingacademic terms are called the seepage coefficient seepagevelocity permeation coefficient and permeation velocity

Seepage coefficient is often used for indicating the soilpermeability and evaluating stability in geotechnical engi-neering such as slope engineering subgrade engineering

and tunnel and underground engineering the correlativesubjects are groundwater dynamics fluid mechanicsseepage mechanics etc [1ndash9] Currently seepage coefficientis often obtained by experiment or consolidation inversion[10] while it is hard to be determined correctly for clay andthe difference between different methods is obvious [11]Especially disturbance to undisturbed soil is inevitableSeepage coefficient is related to basic physical parameterssuch as particle size and porosity [3 4 7 10 11] so theempirical calculation methods including the above two mainparameters for clay and coarse-grained soil have alreadybeen obtained based on massive experiment data Howevermethods for clay such as obtaining seepage coefficients byCM and Taylor are limited to parameter acquisition andcalculation accuracy [10 11] Inversely empirical methodsfor coarse-grained soil are relatively correct such as

HindawiAdvances in Civil EngineeringVolume 2019 Article ID 6034526 9 pageshttpsdoiorg10115520196034526

Terzaghi China Institute of Water Resources and Hydro-power Research (abbreviated as ldquoIWHRrdquo) CursonndashKarmanand KC [11] erefore it is possible to nd simple andcorrect approaches to calculate the seepage coecient of claybased on coarse-grained soil

Reddi and angavadivelu suggested one method tocalculate the seepage coecient of clay based on randomnetwork and percolation theory [2] Liang and Fang analysedthe inuencing factors on seepage property for tiny clay andexplained them in terms of ldquomicroelectric eldrdquo andldquomicrosizerdquo eects [4] Deng found the linear positive cor-relation between natural logarithm of the seepage coecientand void ratio for clay and the gradient is about 05e0 (e0 isthe initial void ratio) [10] Dang et al established the eectivecalculation methods of the seepage coecient for clay basedon the eective void ratio [11] He et al obtained the modiedcalculation method of the saturated seepage coecient forbentonite based on the Poiseuille law which includes voidratio and solution concentration [3 12 13] However theabove methods are feasible under certain conditions and theyhave limits in specic applications erefore it is still nec-essary to nd simple and correct calculation methods eacademic thought research idea andmethod in this study arederived from Dangrsquos study [11]

2 Permeation Mechanism of Clay

In order to study the calculation method of the seepagecoecient for clay it is very important to cognise thepermeation mechanism rst en inuencing factorsspatial process and parameter calculation have to be ana-lysed theoretically thus providing fundamental works forthe following study

21 Inuencing Factors A soil void is interconnectedsemiconnected or sealed and the seepage coecient re-duces with the decreasing porosity for certain soil Generallythe seepage coecient of clay is low for low porosity but it isnot because porosity is negatively correlated to the com-pactness and it is inuenced by particle gradation com-paction power and so on but not by the absolute particlesize

Here presuming clay silt sand and roundstone asround balls their equivalent sizes are 0002mm 002mm02mm and 20mm Subsequently they are put uniformlyinto four cubic boxes (50lowast 50lowast 50mm3) respectively andthen the spatial porosities are calculated which are shown inFigure 1

Figure 1 shows that porosities are equal for dierent soilparticles which are about 4767 so they are not correlatedto the absolute particle size erefore the seepage co-ecient of clay may be inuenced by the absolute particlesize under certain porosity

Although particle size does not inuence the porosity itdecides the specic surface area (shape coecient) whichare shown in Figure 2

Figure 2 shows that the dierence in specic surface areais large for dierent soil particles For example it is thousand

times the value of particle size that is 20mm for 0002mmIt is negatively correlated with specic surface area andparticle size and the variation rate is larger when the particlesize is small

Large specic surface areas will cause a variety ofproblems such as long permeation route more pressureloss high surface energy strong adsorptivity and largebound-water volume (shown in Table 1) However boundwater has no solvent ability owability transmission ofwater pressure and permeability so it occupies partialpermeation space thus reducing the void opening per-pendicular to the permeation direction erefore particlesize is one of the main inuencing factors

Similarly under certain particle size and gradation thespecic surface area is a constant Porosity can be reduced byvibration or compaction so the permeation space will alsobe compressed thus decreasing the permeability ereforeporosity is also one of the main inuencing factors

In summary particle size and porosity are the maininuencing factors for clay permeability Under certainporosity the specic surface area and bound-water volumebecome large when the particle size is small so the per-meation route is lengthened and void opening is reducedOn the contrary under certain particle size the void openingis still reduced when the porosity becomes low ereforepermeability of clay is inuenced by the coupling of particlesize and porosity

22 Spatial Process Soil consists of the solid phase liquidphase and gas phase in terms of permeation space soilparticles and permeation voids contained It is mentionedthat specic surface area and bound-water volume are lowfor coarse-grained soil but large for clay In order to presentthe bound-water volume directly presuming colloid claysilt and silty sand as round balls their equivalent sizes are0002mm 0005mm 005mm and 01mm en puttingthem uniformly into four cubic boxes (50lowast 50lowast 50mm3)respectively bound-water porosity and residual porosity arecalculated which are shown in Figure 3

Figure 3 shows that bound-water porosity increases withthe decreasing particle size and the variation rate becomeslarge when the particle size is small It is 754 for theparticle size 0005mm while it is only 038 for the particlesize 01mm erefore bound water in clay cannot beneglected Based on the characteristics of bound water andeective stress principle bound-water voids can be regarded

0

10

20

30

40

50

00 02 04 06 08 10 12 14 16 18 20Particle size (mm)

Poro

sity

()

Figure 1 Spatial porosities for dierent soil particles

2 Advances in Civil Engineering

as ineective voids and the residual is the eective void [11]which is shown in Figure 4

Figure 4 shows that groundwater ows in clay via theeective void mainly according to the concepts of seepageand permeation and it can be called the ldquoeective perme-ationrdquo and the spatial coordinate function is also non-continuous Besides the corresponding academic terms arethe eective permeation coecient and eective permeationvelocity For clay eective permeation is the actual current

and it is not mandatory to regard permeation as the actualcurrent without considering bound water

23 Parameter Calculation Based on the above contextseepage permeation and eective permeation are threedierent concepts Under the same preconditions of crosssection ow direction ow amount water pressure particlevolume and friction for soil they have dierent explana-tions and applications of permeability Although seepage isthe virtual current the value is actual For coarse-grainedsoil eective permeation is equivalent to the permeatione calculation formulas of the permeability coecient forthe above three concepts are shown in Table 2

Table 2 shows that k nkp neke for certain soil that iskle kp le ke Hence dierent calculation methods of thepermeability coecient can be selected for dierent needsand the seepage coecient is widely used for continuousvariables in the seepage eld

3 Empirical Calculation Methods

Particle size and porosity are the main inuencing factors forclay permeability accordingly the existing empirical cal-culation methods [1 10] including these two variables areshown in Table 3

It can be found that the parameter particle size is notincluded in the CM or Taylor equation because it iscertain when established so the limit is inevitableFurthermore parameters in the formulas are dicult tobe acquired Although there is no particle size parameterin the Mesri equation CF and Ac are included so it stillindicates the signicant inuence caused by clay andcolloid particles

For coarse-grained soil the empirical formulas [11] areoften used to calculate the seepage coecient in engineeringpractice which are shown in Table 4

0500

10001500200025003000

0002 0020Particle size (mm)

Spec

ific s

urfa

cear

ea (m

mndash1

)

(a)

05

1015202530

02 04 06 08 10 12 14 16 18 20Particle size (mm)

Spec

ific s

urfa

cear

ea (m

mndash1

)

(b)

Figure 2 Specic surface areas for dierent soil particles with particle sizes of (a) 0002mm and 002mm and (b) 02mm and 20mm

Table 1 Bound-water volumes for dierent soil particles

Particle size (mm) General surface area (mm2) Water-lm thickness [14] (μm) Bound-water volume (mm3)0002 19625000000 012 2355000002 1962500000 012 235500020 196250000 012 23550200 19625000 012 2355

0

10

20

30

40

50

000 002 004 006 008 010Particle size (mm)

Bound-water porosityResidual porositySoil porosity

Poro

sity

()

Figure 3 Curves of bound-water and residual porosities

Soil particle

Bound-water film Effective void

Figure 4 Bound-water lm and eective void for clay

Advances in Civil Engineering 3

Table 2 Calculation formulas of the permeability coefficient for different concepts

Concept Calculation formula Symbol specification

Seepage coefficient k (Qi middot A middot t) (Qprimei middot A)

i (ΔhL)

v ki

⎧⎪⎨

⎪⎩

k is the seepage coefficient (cms)Q is the general flow amount within t (cm3)

i is the hydraulic gradientA is the area of the soil section (cm2)

t is the permeation time (s)Qprime is the general flow amount per second (cm3s)Δh is the water-height difference between infall and

outfall (cm)L is the soil length along the permeation direction

(cm)v is the seepage velocity (cms)

kp is the permeation coefficient (cms)n is the porosity

Av is the equivalent void area (cm2)Vv is the void volume (cm3)

V is the general volume (cm3)vp is the permeation velocity (cms)

ke is the effective permeation coefficient (cms)ne is the effective porosity 0le ne le n

Ae is the equivalent effective void area (cm2)Ve is the effective void volume (cm3)

Ve is the effective permeation velocity (cms)

Permeation coefficient

kp (Qi middot (n middot A) middot t) (Qprimei middot (n middot A))

i (ΔhL)

n (AvA) (Av middot LA middot L) (VvV)

vp kpi

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

Effective permeation coefficient

ke (Qi middot (ne middot A) middot t) (Qprimei middot (ne middot A))

i (ΔhL)

ne (AeA) (Ae middot LA middot L) (VeV)

ve kei

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

Table 3 Existing empirical calculation methods of the seepage coefficient for clay

Soil sample Empirical calculation method Symbol specification

Sand clay and soft clay k cey (CM equation) c and Cprime are the dimensionless coefficientse is the void ratio

y and m are the empirical exponents and m is 50CF is the content of clay particles

Ac is the activity coefficiente others are the same as given above

k Cprime(em1 + e) (Taylor equation)

Soft clay k 654 times 10minus11((eCF)Ac + 1)4 (Mesri equation)

Table 4 Existing empirical calculation methods of the seepage coefficient for coarse-grained soil

Name of the seepage coefficient Empirical calculation method Symbol specificationTerzaghi k 2e2d2

10 d10 is the effective particle size (mm)k10 is the seepage coefficient when the water

temperature is 10degC (cms)d20 is the particle size in which sieving accumulated

mass is twenty percent of the whole (mm)c2 is the influencing coefficient decided by particle

shape and flow direction (0125)ρWZ is the density of water (10 gcm3)s is the specific surface area (mmminus1)η is the viscosity of water (10minus3 Pamiddots)

Cv is the consolidation coefficient (cm2a)mv is the compressive factor of volume (MPaminus1)

cWZ is the density of water (10 kNm3)av is the compressive coefficient (MPaminus1)

R is the radius of the capillary (mm)β is the globular coefficient of the soil particle it is π6

when the particle is a balld50 is the mean particle size (mm)

λprime is the influencing coefficient caused by theneighboring soil particle it is 3π for the ball particle

in infinite watere others are the same as given above

IWHR k10 234n3d220

CursonndashKarmank (c2ρwze2ns2η)

KC k (e35(1 + e))(d106)2

Expressed by consolidation degree k Cvmvcwz Cvcwzav(1minus n)

Stokes void flow k (cwzR28η)n

Darcy k (βcwzed250nλprimeη)


Table 4 shows that the empirical calculation methods forcoarse-grained soil include particle size and porosity si-multaneously and also the other influencing factors Hencesome parameters are still difficult to be obtained so thewidely used five methods are Terzaghi IWHR CursonndashKarman KC and Stokes void flow [11] According to theactual situation the former four methods and Mesriequation of the seepage coefficient for clay are selected foruse

In summary empirical calculation methods of theseepage coefficient for clay are limited for problems oninfluencing factors and parameter acquisition while thosefor the coarse-grained soil are considerable and relativelyeasy erefore it is significant to find calculation methodsfor clay based on the methods for coarse-grained soil Danget al explored the effective calculation methods for claybased on ldquoeffective void ratiordquo and they found the calcu-lation value and experimental result had the same order ofmagnitude is is one new approach [11] In this studyequivalent calculation methods of the seepage coefficient forclay will be studied based on bound-water ldquoconsolidationrdquoand ldquoequivalent void ratiordquo

4 Equivalent Calculation Methods of SeepageCoefficient for Clay

In order to regard clay as coarse-grained soil it is importantto make it have the same or similar soil structure andpermeation mechanism Groundwater permeates in clay viathe effective void mainly while it permeates through thewhole in coarse-grained soilerefore if the bound water inineffective voids can be regarded as ldquosolid soilrdquo particle sizeof clay will increase and the permeation mechanism will alsobe consistent with coarse-grained soil Hence the equivalentprinciple consolidates the bound water in clay regarding itas ldquosolid soilrdquo

41 Equivalent Calculation Methods e equivalent cal-culation method has to be established under bound-waterldquoconsolidationrdquo so the main parameter values will varyChange of specific surface area after ldquoconsolidationrdquois neglected for the small thickness of the water filmsimultaneously semiconnected and sealed voids are alsoneglected In Dangrsquos study [11] void ratio in empiricalcalculation methods for coarse-grained soil is replaced

by effective void ratio and the calculation accuracy isimproved but it does not consider the equivalent prin-ciple variation of void ratio is also neglected so thedifference is still inevitable erefore when void ratio isreplaced by ldquoequivalent void ratiordquo the equivalent cal-culation methods of the seepage coefficient for clay areobtained

∵ e ee + e0 Ve + V0

Vs

eprime Ve

Vs + V0

Ve

Ve + V0( 1113857e( 1113857 + V0

e

(1 + e) V0Ve( 1113857 + 1

if λ V0

Ve

e0

ee

e0

eminus e0 then eprime

e

λ(1 + e) + 1

(1)

where e is the initial void ratio ee is the effective void ratio e0is the ineffective void ratio Ve is the volume of effectivevoids (mm3) V0 is the volume of ineffective voids (mm3) Vsis the volume of the soil particle (mm3) eprime is the ldquoequivalentvoid ratiordquo and λ is the ratio between ineffective and ef-fective void ratios or volumes and is a constant for certainsoil

Substituting equation (1) into the former four formulasin Table 4 the equivalent calculation methods of the seepagecoefficient for clay can be obtained preliminarily which areshown in Table 5

Table 5 shows that the parameter λ is included in theequivalent calculation methods erefore it is veryimportant to determine λ When parameter λ is lowit indicates the ineffective void is low and the calcula-tion method is also suitable for coarse-grained soil Es-pecially equivalent calculation methods of the seepagecoefficient for clay are the same as those for coarse-grained soil when λ 0 so it unifies different calcula-tion methods

42 Determination of Parameter λ Parameter λ depends onthe method to determine the volume of ineffective voidswhich is equal to that of bound watere liquid-plastic limitmethod of macroscopic soil mechanics is often adopted todetermine the content of bound water [11 14] which isshown in Figure 5 and in the following

w0

ws w 0ltwle 0885wP

ws + ww 0885wP + wminus 0885wP( 1113857 w 0885wP ltwlewP

w wP ltwle αwL 0lt αlt 1

αwL wgt αwL 0lt αlt 1

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

w 0ltwle αwL 0lt αlt 1


(2)


where w0 is the content of bound water ws is the content ofstrong bound water w is the moisture content wP is theplastic limit ww is the content of weak bound water α is aconstant (0lt αlt 1) and wL is the liquid limit

Under permeation condition the moisture content is notthe initial one but the saturated moisture content In Dangrsquosstudy [11] the relation between saturated moisture contentand αwL is not considered and it is not strict to some extent

∵ e0 V0

Vs

mw0ρw( )msρs( )

w0 middot msρw( )( )

msρs( )

wsat middot msρw( )( )msρs( )

wsat middot ρsρw

wsat middot ds e 0ltwsat le αwL

αwL middot msρw( )( )msρs

αwL middot ρs

ρw αwL middot ds wsat gt αwL

0lt α lt 1

(3)

where mw0 is the mass of ineective void water (g) ρw is thedensity of water (10 gcm3)ms is the mass of the soil particle(g) ρs is the density of the soil particle (gcm3) wsat is thesaturated moisture content dsis the relative density of thesoil particle and the others are the same as given above

It can be found that e0 e when 0ltwsat le αwL namelybound water lls the soil void the eective void is inexistentand the seepage coecient is 0 InDangrsquos study [11] α is 09 Inorder to verify its suitability comparison calculations aremadein the next section and the selected values are 080 085 095and 10 the results show they are appropriate when α is 09

5 Evaluation of EquivalentCalculation Methods

In order to verify the feasibility and accuracy of equivalentcalculation methods three types of clay soils are selec-tedmdashcompacted reconstruction loess (No 1) soft clay fromSouth China Sea (No 2) and coastal saline soil from Kuwait(No 3) [5 6 11 15 16] the correlative parameters areshown in Tables 6 and 7 Based on the calculation formulasin Table 5 (formula 1 Terzaghi formula 2 IWHR formula 3CursonndashKarman formula 4 KC) the calculation results

Table 5 Calculation methods of the seepage coecient for coarse-grained soil and clay

Name

Calculation methods

Coarse-grained soil ClayEmpirical calculation

methodsEective calculation

methods [11]Equivalent calculation

methodsSeepage coecient of Terzaghi k 2e2d210 k 2(eminus e0)

2d210 k 2eprime2d210Seepage coecient of IWHR k10 234d220(e1 + e)

3 k10 234d220(eminus e01 + eminus e0)3 k10 234d220(eprime(1 + eprime))

3

Seepage coecient of CursonndashKarman k (c2ρwze3s2η(1 + e)) k (c2ρwz(eminus e0)3s2η(1 + eminus e0)) k (c2ρwzeprime

3s2η(1 + eprime))Seepage coecient of KC k (e35(1 + e))(d106)

2 k ((eminus e0)35(1 + eminus e0))(d106)

2 k (eprime35(1 + eprime))(d106)2

Solid condition

Semisolid condition

Plastic condition

Flow condition Strong bound water

Strong bound water andlittle weak bound water

Bound water andlittle free water

Bound water andfree water

0 Shrinkage limit

Plastic limit

Liquid limit W

Soil conditionWater condition

Figure 5 Liquid-plastic limit condition of soil


under dierent methods can be obtained which are shownin Figures 6ndash8 and Table 8

Table 8 shows that seepage coecients under dierentcalculation methods have the coherence for every soil thedierence between calculation method for coarse-grained

soil and experimental value is the largest the eective cal-culation method for clay takes the second place and theequivalent calculation method for clay is the closest hencethe superiority of the equivalent calculation method is ap-parent In order to evaluate them quantitatively the

00E + 0020E ndash 0440E ndash 0460E ndash 0480E ndash 0410E ndash 0312E ndash 03

1 2 3Calculation formula

Seep

age c

oeffi

cien

t (cm

s)

Empirical calculation method forcoarse-grained soilEffective calculation method for clayEquivalent calculation method for clayTest value of seepage coefficient

(a)


1 3Calculation formula

Seep

age c

oeffi

cien

t (cm

s)


(b)

Figure 6 Seepage coecients of compacted reconstruction loess under (a) formulas (1)ndash(3) and (b) formulas (1) and (3)

Table 6 e parameter λ and equivalent void ratio

Soil no e ds ρw (gcm3) wsat () α wL () e0 λ eprime

1 108 272 10 397 09 220 0539 0813 040132 1933 265 10 729 09 515 1228 1743 031633 1074 249 10 431 09 330 0740 2211 01923

Table 7 e correlative calculation parameters

Soil no d10 (mm) d20 (mm) d50 (mm) c2 ρWZ (gcm3) s (cmminus1) η (Pamiddots) CF () Ac

1 0001 0005783 00345 0125 10 17391304 10ndash3 14113 0102 0001 0002473 001 0125 10 60000 10ndash3 16988 0423 0001 0003086 0008 0125 10 75000 10ndash3 14798 035

00E + 0050E ndash 0510E ndash 0415E ndash 0420E ndash 0425E ndash 0430E ndash 0435E ndash 0440E ndash 0445E ndash 04


Empirical calculation method forcoarse-grained soil Effective calculation method for clay Equivalent calculation method for clay Test value of seepage coefficient

Seep

age c

oeffi

cien

t (cm

s)

(a)



Seep

age c

oeffi

cien

t (cm

s)


(b)

Figure 7 Seepage coecients of clay from South China Sea under (a) formulas (1)ndash(3) and (b) formulas (1) and (3)


multiples between them are calculated the results showthat for every soil (1) the dierence between calculationmethod for coarse-grained soil and experimental value is alittle larger and the minimal and maximal dierence inorders of magnitude is one and three (2) the dierencebetween seepage coecient of IWHR in every method andexperimental value is also a little larger and the minimaland maximal dierence in orders of magnitude is two andthree and (3) seepage coecients of Terzaghi andCursonndashKarman in every method are closer to experi-mental values and the coecients of the equivalent cal-culation method are the closest that is they are equalapproximately erefore the equivalent calculationmethod of the seepage coecient for clay is feasible and itis accurate to some extent

From Table 8 it can be found that seepage coecientsof KC are all low under dierent methods for every soiland the dierence between results calculated by theequivalent method and experimental value is three ordersof magnitude so it is not suitable for calculating theseepage coecient for clay In addition results (shown inTable 9) calculated by the Mesri equation in Table 3 arealso close to experimental values they have the sameorder of magnitude as well and they are also equal ap-proximately erefore the recommended methods tocalculate the seepage coecient for clay are the Mesriequation and equivalent calculation method of Terzaghior CursonndashKarman

6 Conclusions

e following conclusions can be obtained

(1) Particle size and porosity are the main inuencingfactors for clay permeability Under certain porosityspecic surface area and bound-water volume arelarge when the particle size is small thus lengtheningthe permeation route along the permeation directionand reducing the void opening perpendicular to thepermeation direction Similarly under certain par-ticle size void opening is also small when the po-rosity is low ese eects consume the permeationenergy and compress the permeation space thusreducing the clay permeability

(2) Seepage permeation and eective permeation arethree dierent concepts groundwater permeates in

00E + 0050E ndash 0510E ndash 0415E ndash 0420E ndash 0425E ndash 0430E ndash 0435E ndash 04


Seep

age c

oeffi

cien

t (cm

s)


(a)

00E + 00

50E ndash 07

10E ndash 06

15E ndash 06

20E ndash 06

25E ndash 06


Seep

age c

oeffi

cien

t (cm

s)


(b)

Figure 8 Seepage coecients of coastal saline soil from Kuwait under (a) formulas (1)ndash(3) and (b) formulas (1) and (3)

Table 8 Seepage coecients of KC under dierent methods

Calculation methodsSoil

Seepage coecient (cms)No 1 No 2 No 3

Empirical calculation methods for coarse-grained soil 3365lowast10minus9 1368lowast10minus8 3318lowast10minus9Eective calculation methods for clay 5708lowast10minus10 1142lowast10minus9 1552lowast10minus10Equivalent calculation methods for clay 2562lowast10minus10 1336lowast10minus10 3313lowast10minus11Experimental value 42lowast10minus7 27lowast10minus7 648lowast10minus8

Table 9 Seepage coecients of clay based on the Mesri equation

Soil

Calculation methodSeepage coecient (cms)Mesri

equationExperimental

valueCompacted reconstructionloess 1532lowast10minus7 42lowast10minus7

Soft clay from South China Sea 2696lowast10minus7 27lowast10minus7Coastal saline soil from Kuwait 5463lowast10minus8 648lowast10minus8


clay via the effective void mainly and the effectivepermeation is the actual current while it permeatesvia voids in coarse-grained soil For certain soil theincreasing sequence of permeability coefficients isthe seepage coefficient permeation coefficient andeffective permeation coefficient

(3) Based on bound-water ldquoconsolidationrdquo clay can beequivalent to coarse-grained soil in terms of soilstructure and permeation mechanisme void ratioafter ldquoconsolidationrdquo is not the simple subtraction ofinitial and ineffective void ratios and introduction ofldquoequivalent void ratiordquo unifies the calculationmethods of the seepage coefficient for clay andcoarse-grained soil

(4) Bound-water content can be calculated by the liquid-plastic limit method the maximal value is about 09time the size of liquid limit and the saturatedmoisture content needs to be considered certainly

(5) e feasible methods to calculate the seepage co-efficient of clay are the Mesri equation and theequivalent Terzaghi or CursonndashKarman methodbecause their calculation results are the closest toexperimental values

Data Availability

e data used to support the findings of this study are in-cluded within the article

Disclosure

An earlier version of this article was presented as an abstractin ldquoProceedings of the International Conference on Geo-Mechanics Geo-Energy and Geo-Resources (IC3G 2018)rdquo

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

anks are due for all relevant material providers and au-thors cited especially the academic thought research ideaand methods shared in Dangrsquos study is study was sup-ported by the National Key RampD Plan Special Project ofChina (Grant No 2017YFC0805406) and Beijing MunicipalNatural Science Foundation (Grant No 8161001)

References

[1] G Mesri L Kwan O Dominic et al ldquoSettlement of em-bankments on soft claysrdquo Geotechnical Special Publicationvol 1 no 40 pp 8ndash56 1994

[2] L N Reddi and S angavadivelu ldquoRepresentation ofcompacted clay minifabric using random networksrdquo Journalof Geotechnical Engineering vol 122 no 11 pp 906ndash9131996

[3] J He and J Y Shi ldquoCalculation of saturated permeabilitycoefficient of bentoniterdquo Chinese Journal of Rock Mechanicsand Engineering vol 26 no 2 pp 3920ndash3925 2007

[4] J W Liang and Y G Fang ldquoExperimental study of seepagecharacteristics of tiny-particle clayrdquo Chinese Journal of RockMechanics and Engineering vol 29 no 6 pp 1222ndash12302010

[5] H Liao L Su Z Li Y Pan andH Fukuoka ldquoTesting study onthe strength and deformation characteristics of soil in loesslandslidesrdquo in Proceedings of 10th International Symposiumon Landslides and Engineered Slopes pp 443ndash447 CRC Press-TaylorampFrancis Group Xirsquoan China June 2008

[6] H J Liao T Li and J B Peng ldquoStudy of strength charac-teristics of high and steep slope landslide mass loessrdquo Rockand Soil Mechanics vol 32 no 7 pp 1939ndash1944 2011

[7] X Y Wang and C L Liu ldquoDiscussion on permeability law ofdeep clayey soilrdquo Chinese Journal of Geotechnical Engineeringvol 25 no 3 pp 308ndash312 2003

[8] X D Zhang Y Zhang B Zhang et al ldquoOptimization andimprovement of Sweden Slice Method considering the porewater pressurerdquo Chinese Quarterly of Mechanics vol 34 no 4pp 643ndash649 2013

[9] Y Zhang T L Chen Z FWang et al ldquoAn equivalent methodfor calculating the seepage coefficient of clay based on so-lidified micro-bound waterrdquo Chinese Journal of Rock Me-chanics and Engineering vol 37 no 4 pp 1004ndash1010 2018

[10] Y F Deng S Y Liu D W Zhang et al ldquoComparison amongsome relationships between permeability and void ratiordquoNorthwestern Seismological Journal vol 33 pp 64ndash66 2011

[11] F N Dang H W Liu X WWang et al ldquoEmpirical formulasof permeability of clay based on effective pore ratiordquo ChineseJournal of Rock Mechanics and Engineering vol 34 no 9pp 1909ndash1917 2015

[12] H Komine ldquoPredicting hydraulic conductivity of sand-bentonite mixture backfill before and after swelling de-formation for underground disposal of radioactive wastesrdquoEngineering Geology vol 114 no 3-4 pp 123ndash134 2010

[13] H Tanaka D R Shiwakoti N Omukai F Rito J Locat andM Tanaka ldquoPore size distribution of clayey soils measured bymercury intrusion porosimetry and its relation to hydraulicconductivityrdquo Soils and Foundations vol 43 no 6 pp 63ndash732003

[14] D S Cui W Xiang L J Cao et al ldquoExperimental study onreducing thickness of absorbed water layer for red clay par-ticles treated by Ionic Soil Stabilizerrdquo Chinese Journal ofGeotechnical Engineering vol 32 no 6 pp 944ndash949 2010

[15] R Ananth Geotechnical Investigation-Factual Report of TrialEmbankment of Bubiyan Seaport Phase-1 Stage-1 Road Bridgeand Soil Improvement (No 200702 109-TM) Gulf InspectionInternational Company Kuwait City Kuwait 2008

[16] H M Yang ldquoTest investigations of the permeability behavior ofthe soft clay in the South China Seardquo MS thesis WuhanUniversity of Technology Wuhan China 2012


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Terzaghi China Institute of Water Resources and Hydro-power Research (abbreviated as ldquoIWHRrdquo) CursonndashKarmanand KC [11] erefore it is possible to nd simple andcorrect approaches to calculate the seepage coecient of claybased on coarse-grained soil

Reddi and angavadivelu suggested one method tocalculate the seepage coecient of clay based on randomnetwork and percolation theory [2] Liang and Fang analysedthe inuencing factors on seepage property for tiny clay andexplained them in terms of ldquomicroelectric eldrdquo andldquomicrosizerdquo eects [4] Deng found the linear positive cor-relation between natural logarithm of the seepage coecientand void ratio for clay and the gradient is about 05e0 (e0 isthe initial void ratio) [10] Dang et al established the eectivecalculation methods of the seepage coecient for clay basedon the eective void ratio [11] He et al obtained the modiedcalculation method of the saturated seepage coecient forbentonite based on the Poiseuille law which includes voidratio and solution concentration [3 12 13] However theabove methods are feasible under certain conditions and theyhave limits in specic applications erefore it is still nec-essary to nd simple and correct calculation methods eacademic thought research idea andmethod in this study arederived from Dangrsquos study [11]

2 Permeation Mechanism of Clay

In order to study the calculation method of the seepagecoecient for clay it is very important to cognise thepermeation mechanism rst en inuencing factorsspatial process and parameter calculation have to be ana-lysed theoretically thus providing fundamental works forthe following study

21 Inuencing Factors A soil void is interconnectedsemiconnected or sealed and the seepage coecient re-duces with the decreasing porosity for certain soil Generallythe seepage coecient of clay is low for low porosity but it isnot because porosity is negatively correlated to the com-pactness and it is inuenced by particle gradation com-paction power and so on but not by the absolute particlesize

Here presuming clay silt sand and roundstone asround balls their equivalent sizes are 0002mm 002mm02mm and 20mm Subsequently they are put uniformlyinto four cubic boxes (50lowast 50lowast 50mm3) respectively andthen the spatial porosities are calculated which are shown inFigure 1

Figure 1 shows that porosities are equal for dierent soilparticles which are about 4767 so they are not correlatedto the absolute particle size erefore the seepage co-ecient of clay may be inuenced by the absolute particlesize under certain porosity

Although particle size does not inuence the porosity itdecides the specic surface area (shape coecient) whichare shown in Figure 2

Figure 2 shows that the dierence in specic surface areais large for dierent soil particles For example it is thousand

times the value of particle size that is 20mm for 0002mmIt is negatively correlated with specic surface area andparticle size and the variation rate is larger when the particlesize is small

Large specic surface areas will cause a variety ofproblems such as long permeation route more pressureloss high surface energy strong adsorptivity and largebound-water volume (shown in Table 1) However boundwater has no solvent ability owability transmission ofwater pressure and permeability so it occupies partialpermeation space thus reducing the void opening per-pendicular to the permeation direction erefore particlesize is one of the main inuencing factors

Similarly under certain particle size and gradation thespecic surface area is a constant Porosity can be reduced byvibration or compaction so the permeation space will alsobe compressed thus decreasing the permeability ereforeporosity is also one of the main inuencing factors

In summary particle size and porosity are the maininuencing factors for clay permeability Under certainporosity the specic surface area and bound-water volumebecome large when the particle size is small so the per-meation route is lengthened and void opening is reducedOn the contrary under certain particle size the void openingis still reduced when the porosity becomes low ereforepermeability of clay is inuenced by the coupling of particlesize and porosity

22 Spatial Process Soil consists of the solid phase liquidphase and gas phase in terms of permeation space soilparticles and permeation voids contained It is mentionedthat specic surface area and bound-water volume are lowfor coarse-grained soil but large for clay In order to presentthe bound-water volume directly presuming colloid claysilt and silty sand as round balls their equivalent sizes are0002mm 0005mm 005mm and 01mm en puttingthem uniformly into four cubic boxes (50lowast 50lowast 50mm3)respectively bound-water porosity and residual porosity arecalculated which are shown in Figure 3

Figure 3 shows that bound-water porosity increases withthe decreasing particle size and the variation rate becomeslarge when the particle size is small It is 754 for theparticle size 0005mm while it is only 038 for the particlesize 01mm erefore bound water in clay cannot beneglected Based on the characteristics of bound water andeective stress principle bound-water voids can be regarded

0

10

20

30

40

50

00 02 04 06 08 10 12 14 16 18 20Particle size (mm)

Poro

sity

()

Figure 1 Spatial porosities for dierent soil particles











0500

10001500200025003000


Spec

ific s

urfa

cear

ea (m

mndash1

)

(a)

05

1015202530

02 04 06 08 10 12 14 16 18 20Particle size (mm)

Spec

ific s

urfa

cear

ea (m

mndash1

)

(b)




0

10

20

30

40

50

000 002 004 006 008 010Particle size (mm)


Poro

sity

()


Soil particle







i (ΔhL)

v ki

⎧⎪⎨

⎪⎩














i (ΔhL)


vp kpi

⎧⎪⎪⎪⎨

⎪⎪⎪⎩



i (ΔhL)


ve kei

⎧⎪⎪⎪⎨

⎪⎪⎪⎩




















IWHR k10 234n3d220


KC k (e35(1 + e))(d106)2











∵ e ee + e0 Ve + V0

Vs

eprime Ve

Vs + V0

Ve

Ve + V0( 1113857e( 1113857 + V0

e

(1 + e) V0Ve( 1113857 + 1

if λ V0

Ve

e0

ee

e0


e

λ(1 + e) + 1

(1)





w0

ws w 0ltwle 0885wP




⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩



(2)




∵ e0 V0

Vs

mw0ρw( )msρs( )


msρs( )


wsat middot ρsρw



αwL middot ρs


0lt α lt 1

(3)






Name

Calculation methods







3





Solid condition

Semisolid condition

Plastic condition





0 Shrinkage limit

Plastic limit

Liquid limit W









Seep

age c

oeffi

cien

t (cm

s)


(a)



Seep

age c

oeffi

cien

t (cm

s)


(b)




1 108 272 10 397 09 220 0539 0813 040132 1933 265 10 729 09 515 1228 1743 031633 1074 249 10 431 09 330 0740 2211 01923







Seep

age c

oeffi

cien

t (cm

s)

(a)



Seep

age c

oeffi

cien

t (cm

s)


(b)





6 Conclusions






Seep

age c

oeffi

cien

t (cm

s)


(a)

00E + 00

50E ndash 07

10E ndash 06

15E ndash 06

20E ndash 06

25E ndash 06


Seep

age c

oeffi

cien

t (cm

s)


(b)







Soil










Data Availability


Disclosure




Acknowledgments


References




















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia











0500

10001500200025003000


Spec

ific s

urfa

cear

ea (m

mndash1

)

(a)

05

1015202530

02 04 06 08 10 12 14 16 18 20Particle size (mm)

Spec

ific s

urfa

cear

ea (m

mndash1

)

(b)




0

10

20

30

40

50

000 002 004 006 008 010Particle size (mm)


Poro

sity

()


Soil particle







i (ΔhL)

v ki

⎧⎪⎨

⎪⎩














i (ΔhL)


vp kpi

⎧⎪⎪⎪⎨

⎪⎪⎪⎩



i (ΔhL)


ve kei

⎧⎪⎪⎪⎨

⎪⎪⎪⎩




















IWHR k10 234n3d220


KC k (e35(1 + e))(d106)2











∵ e ee + e0 Ve + V0

Vs

eprime Ve

Vs + V0

Ve

Ve + V0( 1113857e( 1113857 + V0

e

(1 + e) V0Ve( 1113857 + 1

if λ V0

Ve

e0

ee

e0


e

λ(1 + e) + 1

(1)





w0

ws w 0ltwle 0885wP




⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩



(2)




∵ e0 V0

Vs

mw0ρw( )msρs( )


msρs( )


wsat middot ρsρw



αwL middot ρs


0lt α lt 1

(3)






Name

Calculation methods







3





Solid condition

Semisolid condition

Plastic condition





0 Shrinkage limit

Plastic limit

Liquid limit W









Seep

age c

oeffi

cien

t (cm

s)


(a)



Seep

age c

oeffi

cien

t (cm

s)


(b)




1 108 272 10 397 09 220 0539 0813 040132 1933 265 10 729 09 515 1228 1743 031633 1074 249 10 431 09 330 0740 2211 01923







Seep

age c

oeffi

cien

t (cm

s)

(a)



Seep

age c

oeffi

cien

t (cm

s)


(b)





6 Conclusions






Seep

age c

oeffi

cien

t (cm

s)


(a)

00E + 00

50E ndash 07

10E ndash 06

15E ndash 06

20E ndash 06

25E ndash 06


Seep

age c

oeffi

cien

t (cm

s)


(b)







Soil










Data Availability


Disclosure




Acknowledgments


References




















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





i (ΔhL)

v ki

⎧⎪⎨

⎪⎩














i (ΔhL)


vp kpi

⎧⎪⎪⎪⎨

⎪⎪⎪⎩



i (ΔhL)


ve kei

⎧⎪⎪⎪⎨

⎪⎪⎪⎩




















IWHR k10 234n3d220


KC k (e35(1 + e))(d106)2











∵ e ee + e0 Ve + V0

Vs

eprime Ve

Vs + V0

Ve

Ve + V0( 1113857e( 1113857 + V0

e

(1 + e) V0Ve( 1113857 + 1

if λ V0

Ve

e0

ee

e0


e

λ(1 + e) + 1

(1)





w0

ws w 0ltwle 0885wP




⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩



(2)




∵ e0 V0

Vs

mw0ρw( )msρs( )


msρs( )


wsat middot ρsρw



αwL middot ρs


0lt α lt 1

(3)






Name

Calculation methods







3





Solid condition

Semisolid condition

Plastic condition





0 Shrinkage limit

Plastic limit

Liquid limit W









Seep

age c

oeffi

cien

t (cm

s)


(a)



Seep

age c

oeffi

cien

t (cm

s)


(b)




1 108 272 10 397 09 220 0539 0813 040132 1933 265 10 729 09 515 1228 1743 031633 1074 249 10 431 09 330 0740 2211 01923







Seep

age c

oeffi

cien

t (cm

s)

(a)



Seep

age c

oeffi

cien

t (cm

s)


(b)





6 Conclusions






Seep

age c

oeffi

cien

t (cm

s)


(a)

00E + 00

50E ndash 07

10E ndash 06

15E ndash 06

20E ndash 06

25E ndash 06


Seep

age c

oeffi

cien

t (cm

s)


(b)







Soil










Data Availability


Disclosure




Acknowledgments


References




















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia








∵ e ee + e0 Ve + V0

Vs

eprime Ve

Vs + V0

Ve

Ve + V0( 1113857e( 1113857 + V0

e

(1 + e) V0Ve( 1113857 + 1

if λ V0

Ve

e0

ee

e0


e

λ(1 + e) + 1

(1)





w0

ws w 0ltwle 0885wP




⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩



(2)




∵ e0 V0

Vs

mw0ρw( )msρs( )


msρs( )


wsat middot ρsρw



αwL middot ρs


0lt α lt 1

(3)






Name

Calculation methods







3





Solid condition

Semisolid condition

Plastic condition





0 Shrinkage limit

Plastic limit

Liquid limit W









Seep

age c

oeffi

cien

t (cm

s)


(a)



Seep

age c

oeffi

cien

t (cm

s)


(b)




1 108 272 10 397 09 220 0539 0813 040132 1933 265 10 729 09 515 1228 1743 031633 1074 249 10 431 09 330 0740 2211 01923







Seep

age c

oeffi

cien

t (cm

s)

(a)



Seep

age c

oeffi

cien

t (cm

s)


(b)





6 Conclusions






Seep

age c

oeffi

cien

t (cm

s)


(a)

00E + 00

50E ndash 07

10E ndash 06

15E ndash 06

20E ndash 06

25E ndash 06


Seep

age c

oeffi

cien

t (cm

s)


(b)







Soil










Data Availability


Disclosure




Acknowledgments


References




















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




∵ e0 V0

Vs

mw0ρw( )msρs( )


msρs( )


wsat middot ρsρw



αwL middot ρs


0lt α lt 1

(3)






Name

Calculation methods







3





Solid condition

Semisolid condition

Plastic condition





0 Shrinkage limit

Plastic limit

Liquid limit W









Seep

age c

oeffi

cien

t (cm

s)


(a)



Seep

age c

oeffi

cien

t (cm

s)


(b)




1 108 272 10 397 09 220 0539 0813 040132 1933 265 10 729 09 515 1228 1743 031633 1074 249 10 431 09 330 0740 2211 01923







Seep

age c

oeffi

cien

t (cm

s)

(a)



Seep

age c

oeffi

cien

t (cm

s)


(b)





6 Conclusions






Seep

age c

oeffi

cien

t (cm

s)


(a)

00E + 00

50E ndash 07

10E ndash 06

15E ndash 06

20E ndash 06

25E ndash 06


Seep

age c

oeffi

cien

t (cm

s)


(b)







Soil










Data Availability


Disclosure




Acknowledgments


References




















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







Seep

age c

oeffi

cien

t (cm

s)


(a)



Seep

age c

oeffi

cien

t (cm

s)


(b)




1 108 272 10 397 09 220 0539 0813 040132 1933 265 10 729 09 515 1228 1743 031633 1074 249 10 431 09 330 0740 2211 01923







Seep

age c

oeffi

cien

t (cm

s)

(a)



Seep

age c

oeffi

cien

t (cm

s)


(b)





6 Conclusions






Seep

age c

oeffi

cien

t (cm

s)


(a)

00E + 00

50E ndash 07

10E ndash 06

15E ndash 06

20E ndash 06

25E ndash 06


Seep

age c

oeffi

cien

t (cm

s)


(b)







Soil










Data Availability


Disclosure




Acknowledgments


References




















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




6 Conclusions






Seep

age c

oeffi

cien

t (cm

s)


(a)

00E + 00

50E ndash 07

10E ndash 06

15E ndash 06

20E ndash 06

25E ndash 06


Seep

age c

oeffi

cien

t (cm

s)


(b)







Soil










Data Availability


Disclosure




Acknowledgments


References




















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






Data Availability


Disclosure




Acknowledgments


References




















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


CalculationMethodsofSeepageCoefficientforClayBasedonthe...

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