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SM1_1 October 20, 2010 1
Soil Mechanics I
1 Basic characteristics for soils
Introduction
Description
State
Classification
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GEOTECHNICAL STRUCTURES
[1]
Introduction
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Input data for design (geotechnical, structural)
Engineering Geology - maps, cross sections,rocks, soils, mineralogy, origin....
Mechanical propertiesStrengthCompressibilityPermeabilityTechnology – compaction...
Ground Water
Geotechnical (Engineering Geology) Site Investigation
Introduction
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GEOMECHANICS
Mechanics of Rocks
Mechanics of Soils
Mechanics of Snow and Ice
+ Mechanics of Powders
= MECHANICS OF PARTICULATE MATERIALS
Introduction
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Influence of water on mechanical behaviour
Introduction
PARTICULATE MATERIALS
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Role of pore volume, pore liquid
The pore liquid – water – exhibits the primary role in the soil (particulate materials) mechanical behaviour
„principle of effective pressure“ σ' = σ - uσ' controls the mechanical behaviour of soils (strength, deformation)
Introduction
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Rock bolts
[3]
Introduction
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[3]
Rock bolts
Introduction
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[3]
Introduction
Rock bolts
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DILATANCY
A further energy necessary for shearing dense particulate materials (below a limiting porosity)
(Casagrande, 1936)
Introduction
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STRUCTURE, SENSITIVITY
Leda Clay (Can)
[2]
Introduction
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SUBSIDENCE
Mexico Basin – lowering of GWL
(Legget and Karrow, 1982, Geology in civil engineering, McGraw Hill)
Introduction
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Influence of water – pore pressures
[1]
Introduction
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HISTORY of SM
1775 Coulomb (France) – friction in soils - fortifications
ca 1911 Atterberg (Sweden) – clay plasticity
1925 Terzaghi – (Austria, USA) - his book „Erdbaumechanik...“ „Theoretical soil mechanics (1943) = foundation of the new discipline; principle of effective stress (±1936); one-dimensional consolidation...
Casagrande, Hvorslev (USA) – strength, dilatancy, „critical void ratio“, plasticity, soil classification...
Roscoe, Schofield, Wroth (UK – Cambridge) – the first theory combining deformations and strength based „critical state soil mechanics“
Skempton (UK) colloid activity of clays, residual strength
Fellenius, Petterson, Bishop, Janbu - ...slope stability...1930's to 1960's
from 1970 FEM, BEM ... DEM... in geomechanics
Introduction
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GRAIN SIZE DISTRIBUTION (= description, not state)
sieving and/or sedimentation → grading curve
Soil Description
[2]
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Sieving
POPIS ZEMIN
[4]
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Sedimentationusing hydrometer
Stokes' law
v=f(D2;density, viscosity)
[4]
Soil Description
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Combination of sieving and sedimentation
POPIS ZEMIN
[4]
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Quantification of the grading curves:
Effective diameter: Def = D
10 to D
20
Uniformity coefficient: CU = D
60 / D
10
CU< ca 5 uniform soil = poorly graded
CU>15 non-uniform soil (well graded)
Coefficient of curvature: CC = (D
30)2 / (D
60 × D
10)
CC = 1 to 3 (and C
U> 4 to 6) well graded
CC = <1 or >3 gap-graded
Soil Description
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Particle size Fractions EN 14688-1
Soil Description
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Composite soil:
Principal fractions
Secondary fractions
saGr = sandy gravelgrCl = gravelly clay
Interlayered soil
e.g.: gravelly clay interbedded with sand: grClsa
Soil Description - Classification
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WATER CONTENT – STATE
w = Mw / M
d = M
w / M
s
Volumetric water content θ = Vw / V
t ( = S × n)
Soil Description × State
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CONSISTENCY LIMITS(„Atterberg limits“)
Liquid limit wL (the water content at which the soil changes from liquid to solid
material with plastic behaviour)
Plastic limit wP (with further decrease of the water content the soil stops being
plastic)
Shrinkage limit wS
Determination on a paste, D < 0.4 mm
Plasticity index IP= w
L-w
P
DESCRIPTION (= constants for a given soil!)
Soil Description
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Liquid limit wL
Looking for water content at which an arbitrary penetration is reached (10mm with 60º/60g cone (20mm with 30º/80g))
'foundation' failure – undrained strength of about 2-3 kPa
[4]
Soil Description
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[2]
Liquid limit wL
Casagrande method
Looking for the water content at which the groove closes at 10 mm (slope failure – undrained strength of about 2-3 kPa)
Soil Description
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Casagrande apparatus
[2]
Soil Description
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Plastic limit wP
[2]
Looking for the water content at which the soil crumbles as shown – undrained strength of about 200 - 300 kPa
Soil Description
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PLASTICITY
Casagrande plasticity chart
PLASTICITY (L, I, H...) determined by wL only
Soil Description - Classification
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[2]
Soil Description
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ACTIVITY A (of clay minerals)
A (= IA) = I
P / (% of clay fraction by mass)
(Skempton, 1953)
Soil Description
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CONSISTENCY (STATE) - fine-grained soils
Consistency Index IC
= (wL-w) / (w
L-w
P)
Liquidity Index IL=(w-w
P) / (w
L-w
P)
Consistency:liquid I
C<0
soft, firm (plastic) IC = 0 to 1
stiff IC >1
EN 14688-2very soft I
C<0,25
soft IC = 0,25 to 0,50
firm IC = 0,50 až 0,75
stiff IC = 0,75 až 1,0
very stiff IC > 1,0
State properties
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Amount of pores / voids
POROSITY n = Vp / V
t
VOID RATIO e = Vp / V
s
...„phase diagram“
State properties
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DENSITY (UNIT MASS)
Density of solid particles - Specific density (description not state)
ρs= M
s / V
s = M
d / V
s
Density at natural water content (bulk density)ρ
= M
t / V
t = (M
w +M
d) / V
t
Saturated densityρ
sat= M
t / V
t = (M
w +M
d) / V
t
Dried densityρ
d= M
d / V
t
State properties
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UNIT WEIGHT
γ = ρg
...unit weight under water table: Archimédes law
→ γ' = γsat
– γw
State properties
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Determination of densities - determination of volume
density of solid particles – density bottle
State properties
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Determination of densities - determination of volume
Other densities – ρ, ρsat
, ρd
- undisturbed sample – cylinder/cube – measuring the dimensions
- undisturbed sample – irregular shape weighing under water / expelled water
State properties
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....Determination of densities - determination of volume
- if impossible to take undisturbed sample (sands...) measuring of the volume of „excavation“ (and weighing the excavated soil)
State properties
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Using the phase diagram for useful expressions
for example e = n / (1 - n)
→ ρd = ρ
s / (1 + e) → determination of e from the dry density:
e = (ρs – ρ
d) / ρ
d
→ ρd = ρ / (1 + w); ...etc...
State properties
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Degree of saturation S (≡ Sr)
S = Vw / V
p
Determination from e and w
State properties
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RELATIVE DENSITY
ID=(e
max- e) / (e
max- e
min)
loose ID= 0 to 0,33
medium ID = 0,33 to 0,67
dense ID = 0,67 to 1
very loose ID= 0 to 0,15
loose ID= 0,15 to 0,35
medium ID= 0,35 to 0,65
dense ID= 0,65 to 0,85
very dense ID = 0,85 to 1,0
State properties
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Clayey sand (25% C a 75% S) of e = 0,5.What is the role of clay fraction in the mechanical behaviour of the soil?
Consider removing of clay fraction:
→ e = 1,0
The loosest sand with its spherical particles in contact: → e < 1
→ Sand grains (spheres) at e = 1 cannot be in contact
→ At 25% of C and 75% of S spherical grains 'float' in the clay 'matrix'
→ Clay may be expected to control the behaviour of the above soil having just 25% of clay fraction
Role of Fines and of Def
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Change in hydraulic conductivity (permeability) with the amount of fines (in a mixture of ash and sludge)
Role of Fines and of Def
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Change in strength with the amount of fines (in a crushed rock)
(Mašín, 2000)
Role of Fines and of Def
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Estimation of emin
and emax
of a snad from C
u and shape of grains
Examples of Use of Grading Curve (± Description)
(Youd, 1973 in Mitchell and Soga, 2005)
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Dependence of emin
a emax
on amount of silt fraction in a sand
(Polito and Martin, 2001 in Mitchell and Soga, 2005)
Examples of Use of Grading Curve (± Description)
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Estimation of hydraulic conductivity of a sand
Hazen: k [ms-1] = 0,01D10
2 [mm]
...fine and medium sand: k = [A / (Cu+B) + C] D
102, where A, B a C depend on
density
Estimation of hydraulic conductivity of fine-grained soil
k = f (e, wP, I
P)
k = f (e, CF%, IA)
(full correlations in Soos and Boháč (2002), Geotechnical Engineering Handbook, Ernst & Sohn)
Examples of Use of Grading Curve (± Description)
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Use of soil in filters
D15
(of filter) / D85
(of soil) < 4 to 5 < D15
(of filter) / D15
(of soil)
Examples of Use of Grading Curve (± Description)
(Cedergren, 1988)
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Use of soil in fills
Dams – for the impervious core the soil must be from the zone 1 or 2; for the stabilisation part from zone 3 or 4
Examples of Use of Grading Curve (± Description)
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Use in estimating frost heave – frost susceptibility
Examples of Use of Grading Curve (± Description)
(Beskow, 1935 in [2])
[2]
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POJMENOVÁNÍ
[5]
Classification according to EN
→Grading only
Soil Classification
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USCS classification → grading + plasticity chart
The Czech modification:
+
Soil Classification
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http://labmz1.natur.cuni.cz/~bhc/s/sm1/
Atkinson, J.H. (2007) The mechanics of soils and foundations. 2nd ed. Taylor & Francis.
Further reading:
Wood, D.M. (1990) Soil behaviour and critical state soil mechanics. Cambridge Univ.Press.
Mitchell, J.K. and Soga, K (2005) Fundamentals of soil behaviour. J Wiley.
Atkinson, J.H: and Bransby, P.L. (1978) The mechanics of soils. McGraw-Hill, ISBN 0-07-084077-2.
Bolton, M. (1979) A guide to soil mechanics. Macmillan Press, ISBN 0-33318931-0.
Craig, R.F. (2004) Soil mechanics. Spon Press.
Holtz, R.D. and Kovacs, E.D. (1981) An introduction to geotechnical engineering, Prentice-Hall, ISBN 0-13-484394-0
Feda, J. (1982) Mechanics of particulate materials, Academia-Elsevier.)
Literature for the course Soil Mechanics II
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[1] Atkinson, J.H. (2007) The mechanics of soils and foundations. 2nd ed. Taylor & Francis.
[2] Holtz, R.D. and Kovacs, E.D. (1981) An introduction to geotechnical engineering, Prentice-Hall, ISBN 0-13-484394-0
[3] Hoek, E. (2007) Practical rock engineering (2007 edition). http://www.rocscience.com/hoek/PracticalRockEngineering.asp (downloaded 2008/02).
[4] TS/ISO 17892
[5] EN ISO 14688
References (used figures)