Module 1: Nature of Soil and functional relationships, Soil Water, Permeability and Stress Distribution INTRD!"TIN
“Soil mechanics 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 uncons unconsoli olidat dated ed accumu accumulat lation ionss of soil soil partic particles les produce produced d by the mechani mechanical cal and chemical chemical disint disintegr egrati ation on of rocs rocs regard regardles lesss of whethe whetherr or not they contain contain an admi)t admi)ture ure of organi organicc constituents”. &oils are aggregates of mineral particles, and together with air and*or water in the void spaces they form three+phase systems. ' large large portion of the earths surface is covered b y 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
weight, . to develop develop the (i)ure 1*1+a shows a soil mass that has a total volume -and a total weight, 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# %oistu %oisture re /onten /ontentt (/#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 (!# (!# 2ens 2ensit ity0 y0 (a# (a# 3ul 3ul 2ens 2ensit ity y (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# (b# 2ry 2ry 2ensi 2ensity ty (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# &aturat &aturated ed 2ensit 2ensity y (4sat#0 hen the soil is saturated its bul density is called saturated density. 4sat 0 Msat. (d# &ubmerg &ubmerged ed 2ensity 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 47 04sat - 4/
where 4/ is the density of water which is e4ual to 1 g*cm5 (5# 6nit 6nit eigh eightt (a# 3ul 6nit eight 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 6nit eig eight ht (8d#0 The dry unit weight is the weight of soil solids per unit volume of soil mass 8d 0 Wd. (c# &aturat &aturated ed 6nit e eight (8sat#0 hen the soil is saturated its bul unit weight is called saturated unit weight. 8sat 0 Wsat. (d# &ubmerged &ubmerged 6nit ei eight ght (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 reference substance. 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/ ("# 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# 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 +e ma2 - emin (unctional Relationships +a Relation bet/een e and n
'ir
e
e 0 ..s
ater
f .s 0 1, then e 0 . and .01;e
e/
+1;e
&oil &olids
Taing reciprocals on both sides
1
1n0 +1;ee 0 +1e ; 1 1e 0 1n - 1 0 +1
/ 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, 8 d 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
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
$rom the complete grain+size distribution curve, useful information can be ob tained 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 co nsistency 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
(ine soils
Coarse
?3 < E3 mm
9rael si=e +9
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
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.
"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 > "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$H line in this chart is e)pressed as IP 0 3*G5 +W# < ?3.
2epending on the point in the chart, fine soils are divided into clays +", silts +M, or or)anic soils + . The organic content is e)pressed as a percentage of the mass of organic matter in a given mass of soil to the mass of the dry soil solids. Three divisions of plasticity are also defined as follows.
#o/ plasticity
W#B 5A>
Intermediate plasticity 5A> B W#B A3> %i)h plasticity
W#@ A3>
The H$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 :>'-DG
9P
'-DG
9M
&ilty :>'-DG
9"
/layey :>'-DG
SW
ell+graded &'82
SP
SM
&ilty &'82
S"
/layey &'82
Fine soils
M#
> of low plasticity
MI
> of intermediate plasticity
M%
> of high plasticity
"#
/G'I of low plasticity
"I
/G'I of intermediate plasticity
"%
/G'I of high plasticity
#
Hrganic soil of low plasticity
I
Hrganic soil of intermediate plasticity
%
Hrganic soil of high plasticity
Pt
$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 the degree of plasticity related to the clay content. $ctiity 0 +Plasticity inde2 +> clay particles by /ei)ht
/lassification as per activity is0
$ctiity
"lassification
A.?" nactive A.?" + 1.!"
8ormal
L 1.!"
'ctive
#iCuidity Inde2: n fine soils, especially with clay size content, the e)isting state is dependent on the current water content (/# with respect to the consistency limits (or 'tterbergs limits#. The liCuidity inde2 +#I provides a 4uantitative measure of the present state.
/lassification as per li4uidity inde) is0 "lassification #iCuidity inde2
L1
Gi4uid
A.?" + 1.AA
-ery soft
A."A + A.?"
&oft
A.!" + A. "A
%edium stiff
A + A.!"
&tiff
A
&emi+solid
.isual "lassification &oils possess a number of physical characteristics which can be used as aids to identification in the field. ' handful of soil rubbed through the fingers can yield the following0 S$ND (and coarser# particles are visible to the naed e ye. 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 d ivided 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 to electro 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 vertical stress 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 7 0 - u 0 h18 ; h? 8sat < h? 8/ or, 7 0 h18 ; h?87 CCCCCCCCCC. (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 7 0 - 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
7 0 3 0 h? 87< 2 8/ icr 0 2h? 0 878/ CCCCCCC (7#
where icr is the critical hydraulic gradient
P&RM&$I#IT'
$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
A* De)ree of saturation n partly saturated soils the entrapped air greatly reduces the permeability.
'bove figure shows several layers of soil with horizontal stratification. 2ue to fabric anisotropy, the coefficient of permeability of each soil layer may vary depending on the direction of flow. &o, let us assume that 6 h1, 6 h?,*, 6 hn are the coefficients of permeability of layers 1, !, C., respectively, for flow in the horizontal direction. /onsidering unit width of the soil layers as shown in the above figure, the rate of seepage in the horizontal direction can be given by C 0 C1 ; C? ; C5 ; ; Cn CCCCCCCCCCC (1=#
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?# C 0 6 e+h i % CCCCCCCCCCCCCCCCCCCC. (17# and 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 e4ua tion (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 plane Get 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
