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SOIL MECHANICS
DeformationProblems
SeepageGroundwater
Strength
Mechanical Basis ForGeotechnical Engineering
Typical slope stability failure
Methodology of Solving Geotechnical Engineering Problems.
Various types of solutions:-analytical, graphical, numerical.
Determine MaterialProperties (index, engineering)
-field investigations, laboratory tests,empirical correlations, others.
Develop Mechanical /Physical Model
What you don’t see is the important part !
N. Hourani
Who is a Geo-Engineer (G.E.) ?A G.E. is an engineering/geologist professional who
deals with infrastructure that is on, adjacent to, or below ground (excavations, dams, open pits,
buildings, tunnels, etc.)
The US National Research Council (NRC) defines various fields of Geo-Technology:
Foundations (Buildings, Bridges, …)Tunneling (Transportation, Utilities, …)Slopes Stabilization & LandslidesMining EngineeringEarth Retaining Systems (walls …)Dams (The most critical and challenging!)Waste Control (Landfills, burial systems, …)Subgrades (Roadways, parking lots, …)Ground Improvement systems !
Soils & Rocks: Natural / Man madeMaterials
Geo-Engineering is the Intersection of different Abilities
Field Investigation
Testing
Experience
Theory
GEOTECHNICAL ENGINEERING• The following problems in soil mechanics are being
investigated:- Subsurface Investigations & Geotechnical
Characterization- In-situ Methods- Stress distribution- 1-Dimensional settlement- Settlement versus time- Seepage- Distribution of excess pore pressures- Some basic dynamic considerations
Objectives:
Use of simple soil mechanical models to understand behaviour and performance (i.e 1-D compression and consolidation, stresses)
Stress Distribution on a Wall• This example shows
the increments of horizontal stress imposed on a wall due to placement of additional load such as a building, road construction, etc..
1-Dimensional Settlement• This example explores 1-
dimensional settlement under a widespread uniform vertical load: A five foot high fill is placed over a compressible clay layer.
1-D ConsolidationSettlement and Pore Pressures versus Time
• The silo example shows the effect of periodic loading on settlement. This is a realistic situation seen in tanks, silos, and other storage facilities.
Uplift pressures,exit gradients and quantities of flow
TotalWeight= W
TotalVolume= V
Air
Water
Solid
Wt
Ws
Ww
Va
Vw
Vs
VvVt
w
Phase Relations For SoilsThe following relationships are defined:
Wa
e = void ratio
n = porosity
Water
Solid
γ = total unit weight
Gs = specific gravitys
v
VV
VVv
v
w
VV
s
w
WW
VW
w
sγγ
S = saturation
ω = water content
Stress Distribution in a Linearly Elastic Half-Space
• Essential first step in settlement analysis.
• Solutions are used for loads on the surface of an isotropic, homogeneous linearly elastic half-space.
• Superposition applies.
• Real world does not conform very well to these assumptions, but the results work remarkably well for a great many practical cases.
• This is because the distribution of increments of stress − especially vertical stress − does not differ much from the results of this theory as long as several conditions are met.
• These include loads at or near the surface, stiffness increasing with depth, and loads small enough to preclude extensive plastic or viscous deformation.
• Therefore, these solutions apply to a much wider range of conditions than would seem initially to be the case.
23
25
])(1[2
])(1[23
222
22sin
−−
−−
+=
+=
Kzr
zKP
Zr
zP
dWestergaarV
esqBousV
πσ
πσ
r2= x2 + y2
)1(221
vvK
−−
=
in which:
2/1222
2222
2/122
22
22
2222
2/122
)(tan
2
]1
)1(2tan12
1)1(2[
4
KnmKmnap
nmnmnmmna
nmnm
nmnmnmmnp
vW
VB
++=
−++++
+++++
⋅+++++
=
πσ
πσ
)-2(12-1K
zyn :in which
νν
===zxm
Increment of Vertical Stress at Depth Z Below Corner
The ring foundation of the oil storage tank carries an average loading of 500 psf. The objective is to find the increments of vertical stresses below the bottom of the ring foundation as a function of depth.
STRESSES UNDER A RING FOUNDATION
One-Dimensional Settlement Analysis
• An important part of foundation analysis and design is the estimation of settlement, for, when the total settlement or the differential settlement across the foundation exceeds certain tolerances, the appearance, function, or even safety of the structure may be impaired.
• A full analysis of the deformations and displacements of a soil profile under an arbitrary set of loads involves non-linear material properties and complicated distributions of stress and strain.
• For many cases this would require fairly elaborate analytical tools, probably involving finite element methods. In the practice of geotechnical engineering simpler procedures have evolved that are adequate for many practical problems.
General Settlement Due to Loading
in
iii
n
i i
i HHee ∑∑
===⋅
+Δ
11 01εSettlement =
1
2
3
4
1
2
3
4
H1
H2
Hi
Hn
TotalWeight= W
TotalVolume= V
Air
Water
Solid
Wt
Ws
Ww
Va
Vw
Vs
VvVt
w
Phase Relations For SoilsThe following relationships are defined:
Wa
e = void ratio
n = porosity
Water
Solid
γ = total unit weight
Gs = specific gravitys
v
VV
VVv
v
w
VV
s
w
WW
VW
w
sγγ
S = saturation
ω = water content
Gsγw
Solid
Water
Air
Background Theory1-D Compression (settlement) in a Typical Soil Sample
e0
1
Va
Vw
Vs
e HWa
Ww
Ws
H
s
vVV
ε=Δ=
+Δ
HH
ee
01
HeeH
01+Δ
=Δ
e =
Settlement:
Have the following relationship:Vv
D⋅=Δ εσ
Dσε Δ=
vm⋅Δ= σε
vmHH
⋅Δ=Δ
= σε
HmH v ⋅⋅Δ=Δ σ
)1(D
mv =
Strain
Stress
Di = tangent modulus
Ds= secant modulus
1-D Compression
in
ivi Hm
i⋅⋅Δ=∑
=1σ
D = constrained modulusMv = coefficient of volume change
Δσ = increment of vertical stress
In general,
(e1, σv1) 00 11 eeHH
ee
HH
+Δ
=Δ⇒+Δ
=Δ
(e2, σv2)
21
21loglog σσ −
− ee
e
log σ C =
2_
1_
logσ
σ⋅=Δ Ce
-
-
1-D Compression: Oedometer Test
σvm
log σ
σv0
σvf = σv0 + Δσv
Δσv
ef
e0Σγihi
--
-
Δ e
e1- e2 =2
_1
_
logσ
σ⋅=Δ Ce
)(log1
)(log1
02
0_
_
01
−
−
⋅+
⋅+
⋅+
⋅=Δ
vme
HC
eHCH
vf
v
mv
σ
σ
σ
σ
HeeH ⋅
+Δ
=Δ01
-
1-D Compression: Oedometer Test
log σ
σvm∆e
Cc
Cr
Oedometer Test: Typical Curve
= preconsolidationpressure or maximum past pressure
= Coefficient of compression
= Coefficient of recompression
e void ratio
Correlations For Cc
Terzaghi, Peck, & Mesri (1996)
Clays, silts, peats and shales
See figure
ASCE (1994)Uniform sand, denseCc = 0.02 to 0.03
ASCE (1994)Uniform sand, looseCc = 0.05 to 0.06
ASCE (1994)Uniform SiltsCc = 0.20
ASCE (1994)Organic Soils, PeatCc = 0.0115wn (3)
Terzaghi & Peck (1967)
Clay of Medium to low sensitivity (S<4)1
Cc = 0.009 (LL-10) (2)
SourceSoilCorrelation
1. S = sensitivity = Undisturbed undrained shear strength/Remolded undrained shear strength2. LL = liquid limit3. Wn = natural water content
Correlations for Compression Index
Empirical Correlation Between Compression Index andIn-Situ Water Content for Clay and Silt deposits, Shalesand for Peats (Terzaghi et al., 1996)
An example of relation between Cα and Cc(Terzaghi et al., 1996)
Bearing Capacity Index C’ Values for Granular Soils
Circular Footing System
Raft Foundation on Sand and Clay
WINSAF-I uses the classic method of estimating 1-D settlements under design loads; i.e., by summing the vertical strains along a vertical profile modeled as a set of horizontal layers. Stress calculations use either Boussinesq’s or Westergaard’s solutions for vertical surface loads on a half-space (Section 4 –Chapter 5 – DM 7.1)
Increments of stress are determined for the same surface loading options than in WINSTRESS.
Settlement can be computed:● by void ratio change computed from the stress changes (compression indices)● by vertical strain computed from the stress changes (compression ratios)● from predetermined changes in void ratio or from compression and rebound
curves● from stress changes multiplied by the coefficient of volume change.
The values of the compression, recompression, and swelling indices can be described by several standard procedures. The user can also specify the prior stress history.
Settlement ExampleHomeworkQA Session
