Soil Mechanics. Calculations, Principles, and Methods

447 Pages·2017·17.46 MB·English

by  Victor Kaliakin (Auth.)

In Memory of Professors
Kandiah (“Arul”) Arulanandan
and
Edward A. Nowatzki
Soil Mechanics
Calculations,Principles,andMethods
Victor N. Kaliakin
University of Delaware, Newark, DE
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Preface
The first course in soil mechanics typically proves to be challenging for
undergraduatestudents.Thisisduetothefactthatsoilsarethree-phasepartic-
ulate materials, and thus must be treated differently than other engineering
materialsthatundergraduatesareintroducedtoaspartoftheircurriculum.The
situationisfurthercomplicatedbytheneedtoaccountforthepresenceofpore
fluid,both underhydrostatic andtransientconditions,aswellasthe subjectof
shearstrength.
Oneofthebiggestdifficultiesinteachingsoilmechanicsisthelackoflecture
timeinwhichtopresentasufficientnumberofexampleproblems,withvarying
degreesofdifficulty,thatillustratetheconceptsassociatedwiththesubject.This
book has been written to address the aforementioned shortcoming. It presents
workedexampleproblemsthatwillfacilitateastudent’sunderstandingoftopics
presentedinlecture.Thisbookisnotmeanttoreplaceexistingsoilmechanics
textbooksbuttoserveasasupplementaryresource.
VictorN.Kaliakin
xi
Acknowledgments
ProfessorNamunu(Jay)MeegodafromtheNewJerseyInstituteofTechnology
firstsuggestedtheideaforthepresentbookandencouragedmetoundertakethe
task of writing it. The example problems presented in the book have been
developed over several years of teaching soil mechanics. Some of the more
challengingproblemsarepatternedaftersimilaronesthatwereprovidedbymy
formerUniversityofDelawarecolleague,Dr.DovLeshchinsky.Finally,special
thanks goes to my current colleague, Dr. Kalehiwot Nega Manahiloh for
criticallyreviewingselectchaptersofthebookandforprovidingsomeideasfor
example problems.
Cheers,
Victor N. Kaliakin
xiii
Chapter 1
Example Problems Involving
Phase Relations for Soils
1.0 GENERAL COMMENTS
Soils are prime examples of complex engineering materials, whereas in
elementary physics, solid, liquid, and gaseous states are distinguished. Soils
are not simple bodies that can be placed in one of these three groups. Soils
are generally composed of solid, liquid, and gas, with the solid part being a
porous medium made up of numerous particles. Soils are thus particulate
materials.
The behavior of soils is largely determined by the relative amounts of the
aforementioned constituents. To quantify these relative amounts requires
knowledge of the “massevolume” or “weightevolume” relations. These re-
lations quantify a soil’s aggregate properties.
1.1 GENERAL DEFINITIONS
The volume of the various constituents of a soil is quantified by following
quantities:
V¼total volume of a soil. In some books V denotes the total volume.
t
V ¼volume of the voids (pores).
v
V ¼volume of the solid phase.
s
V ¼volume of the gas in the voids.
a
V ¼volume of the liquid in the voids.
w
Thus, for all soils
V ¼V þV ¼ðV þV ÞþV (1.1)
v s a w s
The mass of the various constituents of a soil is quantified by following
quantities:
M¼total mass of a soil. In some books M denotes the total mass.
t
M ¼mass of the gas in the voids (pores)¼0.
a
M ¼mass of the liquid in the voids.
w
M ¼mass of the solid phase.
s
SoilMechanics.http://dx.doi.org/10.1016/B978-0-12-804491-9.00001-X
Copyright©2017ElsevierInc.Allrightsreserved. 1
2 SoilMechanics
Theweight of the various constituents of a soil is quantified by following
quantities:
W¼total weight of a soil. In some books W denotes the total weight.
t
W ¼weight of the gas in the voids (pores)¼0.
a
W ¼weight of the liquid in the voids.
w
W ¼weight of the solid phase.
s
Thus, for all soils
W ¼W þW (1.2)
w s
Remark: If Vv¼Vw(0Va¼0) and Wws0, the soil is said to be saturated;
otherwiseitisunsaturated.
Averyconvenient,althoughsomewhatidealized,wayinwhichtovisualize
the massevolume and weightevolume relations is through the use of phase
diagrams. A phase diagram depicts the three phases of a soil as being segre-
gated.Forexample,Figure1.1showsaphasediagramthatrelatesthevolume
and mass of the three phases.
Figure 1.2 shows a similar phase diagram that relates the volume and
weight of the three phases.
FIGURE1.1 Phasediagramshowingtherelationshipbetweenvolumeandmassofgas,fluid,and
solidphasesinasoil.
ExampleProblemsInvolvingPhaseRelationsforSoils Chapter j1 3
FIGURE1.2 Phasediagramshowingtherelationshipbetweenvolumeandweightofgas,fluid,
andsolidphasesinasoil.
1.2 MASS DENSITIES
The following mass densities are used to quantify the relative amounts of a
soil’s constituents:
l Soil (moist) mass density:
M
r¼ (1.3)
V
l Solid mass density:
M
r ¼ s (1.4)
s V
s
l Dry mass density:
M
r ¼ s (1.5)
d V
l Mass density of water:
M
r ¼ w (1.6)
w V
w
At 4(cid:2)C, r ¼r ¼1000kg/m3¼1g/cm3¼1Mg/m3¼1.941slug/ft3. For
w 0
ordinary engineering applications at other temperatures, r yr .
w 0
4 SoilMechanics
1.3 UNIT WEIGHTS
Thefollowingunitweightsareusedtoquantifytherelativeamountsofasoil’s
constituents:
l Soil (moist) unit weight:
W Mg
g¼ ¼ ¼rg (1.7)
V V
l Solid unit weight:
W M g
g ¼ s ¼ s ¼r g (1.8)
s V V s
s s
l Dry unit weight:
W M g
g ¼ s ¼ s ¼r g (1.9)
d V V d
l Unit weight of water:
W
g ¼ w (1.10)
w V
w
At 4(cid:2)C, g ¼g ¼9810N/m3¼9.81kN/m3¼62.4lb/ft3. For ordinary en-
w 0
gineering applications at other temperatures, g zg . In the equations,
w 0
g¼9.81m/s2¼32.2ft/s2 is the gravitational acceleration.
1.4 DEFINITION OF FUNDAMENTAL QUANTITIES
The specific gravity of solids is defined as follows:
g g W
G ¼ sz s ¼ s (1.11)
s g g V g
0 w s w
Remark:Gsnormalizesthesolidunitweightofamaterial.
The volume of voids is defined by two quantities, namely the porosity n,
and the void ratio e, where,
(cid:1) (cid:3)
V
n¼ v (cid:3)100% (1.12)
V
and
V
e¼ v (1.13)
V
s
ExampleProblemsInvolvingPhaseRelationsforSoils Chapter j1 5
The relative weight and volume of the pore fluid is quantified by the
moisture content (w) and the degree of saturation (S), where,
(cid:1) (cid:3)
W
w¼ w (cid:3)100% (1.14)
W
s
and
(cid:1) (cid:3)
V
S¼ w (cid:3)100% (1.15)
V
v
For a saturated soil, V ¼V and S¼100%.
w v
1.5 RELATIONS DERIVED FROM FUNDAMENTAL
QUANTITIES
The basic quantities G, n, e, w, and S can be suitably combined to form re-
s
lations that are particularly useful for particular types of problems. These
relations do not, however, constitute anynew definitions of quantities used to
describethephaserelationsforsoils.Somespecificexamplesofsuchrelations
are given in the following section.
1.5.1 Case 1.1: Relation Between Void Ratio and Porosity
Rewriting the void ratio definition in terms of the volume of voids (V )
v
and then dividing through by the total volume (V) gives the following
relation:
V V V =V n
e¼ v ¼ v ¼ v ¼ (1.16)
V V (cid:4)V 1(cid:4)ðV =VÞ 1(cid:4)n
s v v
where n is understood to be a decimal number.
1.5.2 Case 1.2: Relation Between Porosity and Void Ratio
Rewriting the porosity definition by expanding the total volume (V) and
then dividing through by the volume of solids (V ) gives the following
s
relation:
(cid:1) (cid:3) (cid:1) (cid:3) (cid:1) (cid:3)
V V V =V
n¼ v (cid:3)100%¼ v (cid:3)100%¼ v s (cid:3)100%
V V þV 1þV =V
(cid:1) (cid:3) s v v s (1.17)
e
¼ (cid:3)100%
1þe
This result could likewise have been obtained by solving the equation
derived in Case 1.1 for porosity in terms of void ratio.