Nature of Soil and Functional Relationships

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Module 1: Nature of Soil and functional relationships, Soil Water,

Permeability and Stress Distribution

INTRD!"TIN

“Soil mechanics” is the study of engineering behavior of soil when it is used either as a

construction material or as a foundation material. This is relatively young discipline of civil

engineering, systemized in its modern form by Karl Terzaghi (1!"#, who is regarded as the

“$ather of %odern &oil %echanics”. 'ccording to him “&oil %echanics is the application of the

laws of mechanics and hydraulics to engineering problems dealing with sediments and other

unconsolidated accumulations of soil particles produced by the mechanical and chemical

disintegration of rocs regardless of whether or not they contain an admi)ture of organic

constituents”.

&oils are aggregates of mineral particles, and together with air and*or water in the void spaces

they form three+phase systems. ' large portion of the earths surface is covered by soils, and they

are widely used as construction and foundation materials. &oil mechanics is the branch of

engineering that deals with the engineering properties of soil and its behavior under stresses and

strains.

SI# $S $ T%R&& P%$S& S'ST&M

(i)ure 1*1+a shows a soil mass that has a total volume -and a total weight, . to develop the

weight+volume relationships, the three phases of the soil mass, i.e., soil solids, air, and water,

have been separated in (i)ure 1*1+b.

(i)ure 1*1: Wei)ht - .olume Relationship for Soil $))re)ate



Terminolo)ies

(1# %oisture /ontent (/#0 t is defined as the ratio of weight of water to the weight of solids

in a given mass of soil.

/ 0 +W/Ws 2 133

(!# 2ensity0(a# 3ul 2ensity (4#0 The bul density or moist density is the total mass of the soil per

unit of its total volume.

4 0 M.

ts unit is )cm5or 6)m5.

(b# 2ry 2ensity (4d#0The dry density is the mass of soil solids per unit volume of soil

mass

4d 0 Md.

ts unit is )cm5or 6)m5.

(c# &aturated 2ensity (4sat#0 hen the soil is saturated its bul density is called saturated

density.

4sat 0 Msat.

(d# &ubmerged 2ensity (47#0 The submerged density is the submerged mass of soil solids

per unit of total volume of the soil mass.

47 0 +Mdsub.

t can also be e)pressed as

4

7

04sat - 4/

where 4/ is the density of water which is e4ual to 1 g*cm5

(5# 6nit eight

(a# 3ul 6nit eight (8#0 The bul unit weight or moist unit weight is the total weight of

the soil mass per unit of its total volume.

8 0 W.

(b# 2ry 6nit eight (8d#0 The dry unit weight is the weight of soil solids per unit volume

of soil mass

8d 0 Wd.

(c# &aturated 6nit eight (8sat#0 hen the soil is saturated its bul unit weight is called

saturated unit weight.

8sat 0 Wsat.

(d# &ubmerged 6nit eight (87#0 The submerged unit weight is the submerged weight of

soil solids per unit of total volume of the soil mass.

87 0 +Wdsub .



t can also be e)pressed as

87 0 8sat - 8/

where 8/ is the unit weight of water which is e4ual to .718*m5

(9# &pecific :ravity (9#0

The specific )raity is the ratio between the density of an ob;ect, and a referencesubstance. The specific gravity can tell us, based on its value, if the ob;ect will sin or

float in our reference substance. 6sually our reference substance is /ater which always

has a density of 1 gram per milliliter or 1 gram per cubic centimeter.

9 0 4s 4/

("# <orosity (n#0 <orosity is defined as the ratio of the volume of voids to the total volume.

n 0 . .

(=# -oid >atio (e#0 -oid ratio is defined as the ratio of the volume of voids to the volume of

solids.

e 0 . .s

(?# 2egree of &aturation (S#0 2egree of saturation is the ratio of the volume of water to the

volume of voids. t is denoted by @&.

S 0 ./.

The degree of saturation generally e)pressed as a percentage. t is e4ual to zero when the

soil is absolutely dry and 1AAB when the soil is fully saturated.

(7# <ercentage 'ir -oids (na#0 t is the ratio of volume of air to the total volume.

na 0 .a.

t is also e)pressed as a percentage.

(# 'ir /ontent (ac#0 t is defined as the ratio of the volume of air to the volume of voids.

ac 0 .a.

'lso, na 0 n ac

(1A# >elative 2ensity (ID#0 >elative density or density inde) is the ratio of the

difference between the void ratios of a cohesionless soil in its loosest state and e)isting

natural state to the difference between its void ratio in the loosest and densest states.

ID 0 +ema2 - e +ema2 - emin

(unctional Relationships

+a Relation bet/een e and n

'ir e e 0 ..s



ater e/ f .s 0 1, then e 0 . and .01;e

+1;e <orosity, n0 .. 0 e +1;e CCCCC. (i#

&oil &olids 1 Taing reciprocals on both sides

1n0 +1;ee 0 +1e ; 1

1e 0 1n - 1 0 +1<nn

e 0 n +1<n CCCCCCCCCCCC. (ii#

+b Relation bet/een e, S, / and 9

S 0 ./. 0 e/e e/ 0 e * S

/0 W/Ws 0 +./ 8/ +.s 8s 0 +e/ 2 8/ +1 2 8s

Substitutin) e/0 e 2 S and 8s 0 9 8/, /e )et

/ 0 +e S 8/ +9 8/

e S 0 / 9 CCCCCCCCCCCCC.C. (iii#

+c Relation bet/een 8, 8d and /

/ 0 W/Ws

$dd 1 to both sides

1 ; / 0 +W/ Ws ; 1 0 +W/ ; Ws Ws 0 W Ws

Ws 0 W 1;/

Diidin) both sides by ., /e )et

+Ws. 0 +W. 1;/

8d 0 8 1 ; / ........................................................................................... (iv#

+d Relation bet/een e, 9, 8d and 8/

e have, 8 0 W. 0 +Ws ; W/ . 0 +.s 8s ; ./ 8/ .

0 +1 2 8s ; e/ 2 8/ +1;e

8 0 +98/ ; e S8/ +1;e CCCCCCCCCCCCCCCCCC (v#

$or dry soil mass, 8 0 8d and S 0 3

&ubstituting in D4. (v#, we get

8d 0 +9 8/ +1;e CCCCCCCCCCCCCCCCCC. (vi#

Particle Si=e Distribution

$or measuring the distribution of particle sizes in a soil sample, it is necessary to conduct

different particle<si=e tests. Wet siein) is carried out for separating fine grains from coarse

grains by washing the soil specimen on a ?" micron sieve mesh. Dry siee analysis is carried out

on particles coarser than ?" micron. &amples (with fines removed# are dried and shaen through



a set of sieves of descending size. The weight retained in each sieve is measured. The cumulative

percentage 4uantities finer than the sieve sizes (passing each given sieve size# are then

determined. The resulting data is presented as a distribution curve with )rain si=e along )+a)is

(log scale# and percenta)e passin) along y+a)is (arithmetic scale#.

Sedimentation analysis is used only for the soil fraction finer than ?" microns. &oil particles are

allowed to settle from a suspension. The decreasing density of the suspension is measured at

various time intervals. The procedure is based on the principle that in a suspension, the terminal

velocity of a spherical particle is governed by the diameter of the particle and the properties of

the suspension. n this method, the soil is placed as a suspension in a ;ar filled with distilled

water to which a deflocculating agent is added. The soil particles are then allowed to settle down.

The concentration of particles remaining in the suspension at a particular level can be determined

by using a hydrometer. &pecific gravity readings of the solution at that same level at different

time intervals provide information about the size of particles that have settled down and the mass

of soil remaining in solution.

The results are then plotted between > finer +passin) and lo) si=e.

9rain<Si=e Distribution "ure

The size distribution curves, as obtained from coarse and fine grained portions, can be combined

to form one complete )rain<si=e distribution cure (also nown as )radin) cure#. ' typical

grading curve is shown.



$rom the complete grain+size distribution curve, useful information can be obtained such as0

1* 9radin) characteristics, which indicate the uniformity and range in grain+size distributionE

?* Percenta)es (or fractions of gravel, sand, silt and clay+size.

9radin) "haracteristics

' grading curve is a useful aid to soil description. The geometric properties of a grading curve

are called )radin) characteristics.

To obtain the grading characteristics, three points are located first on the grading curve.

2=A F size at =AB finer by weight

25A F size at 5AB finer by weight

21A F size at 1AB finer by weight

The grading characteristics are then determined as follows0

1* &ffectie si=e F 21A

?* !niformity coefficient,

5* "urature coefficient,



3oth /u and /c will be 1 for a single+sized soil.

/u @ A indicates a /ell<)raded soil, i.e. a soil which has a distribution of particles over a wide

size range.

/c bet/een 1 and 5 also indicate a well+graded soil.

/u B 5 indicates a uniform soil, i.e. a soil which has a very narrow particle size range.

"onsistency of Soils

The consistency of a fine+grained soil refers to its firmness, and it varies with the water content

of the soil. ' gradual increase in water content causes the soil to change from solid to semi-solid

to plastic to liquid states. The water contents at which the consistency changes from one state to

the other are called consistency limits (or $tterber)7s limits#. The three limits are nown as the

shrinage limit (WS#, plastic limit (WP#, and li4uid limit (W## as shown. The values of these

limits can be obtained from laboratory tests.

Two of these are utilized in the classification of fine soils0

#iCuid limit (W## + change of consistency from plastic to li4uid state

Plastic limit (WP# + change of consistency from brittle*crumbly to plastic state



The difference between the li4uid limit and the plastic limit is nown as the plasticity inde2 (IP#,

and it is in this range of water content that the soil has a plastic consistency. The consistency of most soils in the field will be plastic or semi+solid.

Indian Standard Soil "lassification System

"lassification ased on 9rain Si=e

The range of particle sizes encountered in soils is very large0 from boulders with dimension of

over 5AA mm down to clay particles that are less than A.AA! mm. &ome clay contains particles

less than A.AA1 mm in size which behave as colloids, i.e. do not settle in water. n the Indian

Standard Soil "lassification System +ISS"S, soils are classified into groups according to size,

and the groups are further divided into coarse, medium and fine sub+groups. The grain+size range

is used as the basis for grouping soil particles into boulder, cobble, gravel, sand, silt or clay.

.ery coarse soils oulder si=e @ 533 mm

"obble si=e E3 < 533 mm

"oarse soils

9rael si=e +9Coarse ?3 < E3 mm

Fine F*GA < ?3 mm

Sand si=e +S Coarse ? < F*GA mm Medium 3*F?A < ? mm

Fine 3*3GA < 3*F?A mm

(ine soils Silt si=e +M 3*33? < 3*3GA mm

"lay si=e +" B 3*33? mm

:ravel, sand, silt, and clay are represented by )roup symbols 9, S, M, and " respectively.



<hysical weathering produces very coarse and coarse soils. /hemical weathering produces

generally fine soils. "oarse<)rained soils are those for which more than "AB of the soil material

by weight has particle sizes greater than A.A?" mm. They are basically divided into either gravels

(:# or sands (&#. 'ccording to )radation, they are further grouped as well+graded (W# or poorly

graded (P#. f fine soils are present, they are grouped as containing silt fines (M# or as containing

clay fines ("#. $or e)ample, the combined symbol SW refers to well+graded sand with no fines.

3oth the position and the shape of the grading curve for a soil can aid in establishing its identity

and description. &ome typical grading curves are shown.

"ure $ + a poorly+graded medium &'82

"ure + a well+graded :>'-DG+&'82 (i.e. having e4ual amounts of gravel and sand#

"ure " + a gap+graded /H33GD&+&'82

"ure D + a sandy &GT

"ure & + a silty /G'I (i.e. having little amount of sand#

(ine<)rained soils are those for which more than "AB of the material has particle sizes less than

A.A?" mm. /lay particles have a fla6y shape to which water adheres, thus imparting the property

of plasticity. ' plasticity chart, based on the values of li4uid limit (W## and plasticity inde)

(IP#, is provided in ISS"S to aid classification. The H$H line in this chart is e)pressed as IP 0 3*G5

+W# < ?3.



2epending on the point in the chart, fine soils are divided into clays +", silts +M, or or)anic

soils +. The organic content is e)pressed as a percentage of the mass of organic matter in agiven mass of soil to the mass of the dry soil solids. Three divisions of plasticity are also defined

as follows.

#o/ plasticity W#B 5A>

Intermediate plasticity 5A> B W#B A3>

%i)h plasticity W#@ A3>

The H$H line and vertical lines at W# e4ual to 5A> and A3> separate the soils into various

classes. $or e)ample, the combined symbol "% refers to clay of high plasticity.

&oil classification using group symbols is as follows0

9roup Symbol "lassification

Coarse soils

9W ell+graded :>'-DG9P <oorly+graded :>'-DG

9M &ilty :>'-DG

9" /layey :>'-DG

SW ell+graded &'82



SP <oorly+graded &'82

SM &ilty &'82

S" /layey &'82

Fine soilsM# &GT of low plasticity

MI &GT of intermediate plasticity

M% &GT of high plasticity

"# /G'I of low plasticity

"I /G'I of intermediate plasticity

"% /G'I of high plasticity

# Hrganic soil of low plasticityI Hrganic soil of intermediate plasticity

% Hrganic soil of high plasticity

Pt <eat

$ctiity

J/layey soilsJ necessarily do not consist of 1AAB clay size particles. The proportion of clay

mineral flaes ( A.AA! mm size# in a fine soil increases its tendency to swell and shrin with

changes in water content. This is called the actiity of the clayey soil, and it represents thedegree of plasticity related to the clay content.

$ctiity 0 +Plasticity inde2 +> clay particles by /ei)ht

/lassification as per activity is0

$ctiity "lassification

A.?"nactive

A.?" + 1.!" 8ormal

L 1.!" 'ctive



#iCuidity Inde2:

n fine soils, especially with clay size content, the e)isting state is dependent on the current water

content (/# with respect to the consistency limits (or 'tterbergs limits#. The liCuidity inde2

+#I provides a 4uantitative measure of the present state.

/lassification as per li4uidity inde) is0

#iCuidity inde2

"lassification

L 1 Gi4uid

A.?" + 1.AA -ery soft

A."A + A.?" &oft

A.!" + A. "A %edium stiff

A + A.!" &tiff

A &emi+solid

.isual "lassification&oils possess a number of physical characteristics which can be used as aids to identification in

the field. ' handful of soil rubbed through the fingers can yield the following0

S$ND (and coarser# particles are visible to the naed eye.

SI#T particles become dusty when dry and are easily brushed off hands.

"#$' particles are sticy when wet and hard when dry, and have to be scraped or washed off

hands.

SI# W$T&R

ater present in a soil mass is called soil water. t is broadly divided into two types.

(1# $ree ater of :ravitational ater0 ater that is free to move through a soil mass under

the influence of gravity is nown as free water.



(!# Meld ater0 Meld water is the water that is held within a soil mass by soil particles. t is

not free to move under the influence of gravitational forces. 2epending on tenacity with

which it is held by soil particles, held water is further classified into following categories.('#&tructural ater0 t is the water chemically combined in the crystal structure of the

soil particle. t cannot be removed without breaing the structure of the soil particle.

(3# 'dsorbed ater0 t is the water which is held by fine grained soil particles due toelectro chemical forces of adhesion. t can be nearly removed by oven drying (usually

at 1A" N 11Ao /# but on e)posure to atmosphere the adsorbed layer is again formed

due to moisture present in atmosphere.

(/# /apillary ater0 t is the water which is held in soil mass due to capillary action.

/apillary water can e)ist on a macroscopic scale compared to other types of held

water which can e)ist on microscopic scale.

&((&"TI.& STR&SS "N"&PT

Terzaghi was the first to suggest the principle of effective stress. 'ccording to this, the total verticalstress at a point O in a soil mass as shown in above figure can be given by

0 h18 ; h? 8sat CCCCCCCCCCCC (1#

The total vertical stress consists of two parts. Hne part is carried by water and is continuous and acts

with e4ual intensity in all directions. This is the pore water pressure or neutral stress u. from



u 0 h? 8/ CCCCCCCCCCCC (!#

The other part is the stress carried by the soil structure and is called the effective stress. Thus

0 7 ; u CCCCCCCCCCCC. (5#

/ombining e4uations (1# and (5#, we get

70 - u 0 h18 ; h? 8sat < h? 8/

or, 70 h18 ; h?87CCCCCCCCCC. (9#

where, 87 0 8sat - u F submerged unit weight



"ritical %ydraulic 9radient and oilin)

/onsider a condition where there is an upward flow of water through a soil layer, as shown in

above figure. The total stress at point H is

0 h1 8/ ; h? 8sat CCCCCCC ("#

The pore water pressure at H is

u 0 +h1 ; h? ; 2 8/CCCCCCC (=#

'nd the effective stress at H is

70 - u 0 h1 8/ ; h? 8sat < +h1 ; h? ; 2 8/ 0 h? 87< 2 8/CCCCCCC (?#

f the flow rate of water through the soil is continuously increased, the value of x will increase

and will reach a condition where 7 0 3* This condition is generally referred to as boiling . &ince

the effective stress in the soil is zero, the soil will not be stable. Thus



70 3 0 h? 87< 2 8/

icr 0 2h? 0 878/ CCCCCCC (7#

where icr is the critical hydraulic gradient

P&RM&$I#IT'

<ermeability is a property of water by virtue of which the soil mass allows water to flow through

it. t is an engineering property, which is re4uired to be determined for study of soil engineering

problems involving flow of water through soils, such as seepage through body of earth dams and

settlement of foundations.

Darcy7s #a/

'ccording to 2arcys law, for laminar flow conditions the velocity of flow, v is directly

proportional to the hydraulic gradient, i.

v O i 0 6 i CCCCCCCCCC (#

6 is called as 2arcys coefficient of proportionality. hen i F 1we have F v. Therefore,

coefficient of permeability can also be defined as the velocity of flow through soil under unit

hydraulic gradient.

$urther, C 0 $ 0 6i$ CCCCCCCCCC (1A#

8ote that ' is the cross section of the soil perpendicular to the direction of flow.

The coefficient of permeability has the units of velocity, such as cm* s or mm*s, and is a

measure of the resistance of the soil to flow of water. hen the properties of water affecting the

flow are included, we can e)press by the relation

6 0 J4)K CCCCCCCCCC (11#

where, F intrinsic permeability, PFdensity of fluid, g F acceleration due to

gravity and QF viscosity of fluid

t must be pointed out that the velocity v given by &Cuation +L is the discharge velocity

calculated on the basis of the gross cross+sectional area. &ince water can flow only through the

interconnected pore spaces, the actual velocity of seepage through soil, s, can be given by

s 0 n CCCCCCCCCCCC.. (1!#

where n is the porosity of the soil.



(actor $ffectin) the "oefficient of Permeability

/omparing 2arcys law with <oiseuilles law of low through capillary tube we get

6 0 Ds? +8/ e5 +1;eO " CCCCCCCCCCCCCCC.. (15#

$rom this the various factors affecting permeability are listed below.

1* 9rain si=e

<ermeability varies appro)imately to the s4uare to the grain size. &ince soils consist of

many different+size grains, some specific grain size has to be used for comparison. 'llen

Mazen (17!# proposed following relationship

6 0 c D13?CCCCCCCCCCCCCC (19#

where, F coefficient of permeability (cm*sec#21AFeffective diameter (cm#

/ F constant appro) e4ual to 1AA when 21A is e)pressed in cm

?* Properties of pore fluid

's per e4uation (15#, permeability is directly proportional to unit weight of water and

inversely proportional to viscosity.

5* .oid ratio

<ermeability increases with increase of void ratio. D4. (15# indicates that the effect of

void ratio on permeability can be e)pressed as

6 16 ? 0 e15+1;e1Qe?

5+1;e?Q CCCCCCCCCCCCCC.. (1"#

t has been found that semi+logarithmic plot of void ratio versus permeability is appro). a

straight line for both coarse grained and fine grained soils.F* Structural arran)ement of particles and soil stratification

The structural arrangement of the particle nay vary, at the same void ratio, depending

upon the method of deposition or compacting the soil mass. The structure may be entirely

different for a disturbed sample as compared to an undisturbed sample which may

possess stratification. &tratified soil masses have mared variations in their permeabilities

in direction parallel and perpendicular to the stratification.





here 4 is the flow rate through the stratified soil layers combined, and C1, C?, C5

is the

rate of flow through soil layers 1, !, 5,C. respectively.

8ote that for flow in the horizontal direction (which is the direction of stratification of the

soil layers#.the hydraulic gradient is the same for all layers. &o,

C10 6 h1 i %1

C?0 6 h? i %?

C50 6 h5 i %5 CCCCCCCCCCCCCCCCCCCC. (1?#

and C 0 6 e+h i % CCCCCCCCCCCCCCCCCCCC. (17#

where, i F hydraulic gradient

6 e+h 0 effective coefficient of permeability in horizontal direction

8ow, % 0 %1 ; %? ; %5 ;* ; %n CCCCCCCCCC (1#

&ubstitution of e4uation (1?# and (17# into e4uation (1=# yields

6 e+h i % 0 6 h1 i %1 ; 6 h? i %? ; 6 h5 i %5 CCCCCCCCCC. (!A#

hence, 6 e+h 0 1% +6 h1 %1 ; 6 h? %? ; 6 h5 %5 ; CCCCCCCCCCCC (!1#

(3# 'verage permeability perpendicular to bedding planeGet 6 1, 6 ?,***, 6 n be the coefficients of permeability for flow in the vertical

direction. $or flow in the vertical direction for the soil layers shown in the below figure

v F v1 F v! F v5 CCCC F vn CCCCCCCCCCCCCC.. (!!#

where v1, v!, v5,C. are the discharge velocities in layers 1, !, 5, C., respectively

v F e(v#i F v1 i1 F v! i! F v5 i5 F CCCCCCC.CCCCC.. (!5#

where e(v# F effective coefficient of permeability for flow in vertical direction

$or flow at right angles to the direction of stratification,

Total head F (head loss in layer 1 R (head loss in layer !# RCC..



iM F i1M1 R i!M! R i5M5 F CCCCCCCCCCCCCCCCC (!9#

/ombining e4uations (!5# and (!9#, we get

v* e(v# M F v* v1 M1 R v* v! M! R v* v5 M5 R CCCCCCC

or, e(v# F M*S(M1* v1# R (M!* v!# R (M5* v5# R CCCCC CCCCC. (!"#

STR&SS DISTRI!TIN

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Nature of Soil and Functional Relationships