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SOIL MECHANICSBC – Geology & Geophysics

October 26, 2009

Alfredo Urzúaurzua@bc.edu

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