Settlement Analysis

1
Settlement Analysis

• D. A. Cameron
• Rock and Soil Mechanics, 2006

2
COMPONENTS

• Elastic or immediate settlement
• Consolidation
• slow draining, saturated soils
• Creep or secondary consolidation

3
Elastic or Immediate Settlement

• The elastic settlement due to a surface load is
•  

where ?z vertical strain
4
Strains from -

• Stress distribution due to surface load
• Soil profile
• Youngs modulus, E, Poissons ratio, ?, for the
  soils

Apply Hookes Law to evaluate strains
5
q
??z/q
??r /q
DEPTH
6
Elastic Soil Parameters

• Saturated NC clays, short term loading?
• Eu and ?u
• - ?u 0.5
• By definition, cant be any volume change

7
Typical values of the elastic constants
8
Solutions for a homogeneous soil of semi-infinite
depth

• where q udl (kPa)
• B width of loaded area (m)
• Is Settlement Influence Factor
• and s settlement in (mm)

9
Settlement influence factors
10
Consider.

• Settlement of rigid footings?
• Settlement of corners of rectangles?
• as for stress distribution, an extremely useful
  solution
• geometric superposition!
• Influence of limited soil depth? Finite layer
• superposition allows treatment of soil profile

11
Real Footings?

• Flexible footings - uniform contact stress
• ideal for theoretical treatment
• Rigid small but thick footings
• no differential settlement
• settlement ? 0.8(scentre-flexible) ? smean
• In-between stiffnesses (real footings)
• corrections for rigidity, relative to soil
  stiffness

12
Solutions for a homogeneous soil of finite depth,
h

• Ueshita and Meyerhofs charts (1968) corner of
  a uniformly loaded, flexible rectangle,
  semi-infinite soil ? L/B gt 1

13
Ueshita and Meyerhof
Irc tabulated in notes as follows
14
Ueshita and Meyerhof, ? 0.5
15
Ueshita and Meyerhof, ? 0.3
16
Corners of Rectangles
GEOMETRIC SUPERPOSITION to get settlements below
any point e.g. point A 3 rectangles
A
Rectangles must meet at a common corner
17
FINITE LAYER SUPERPOSITION
Irc1
Rigid Base
Irc2
18
General Solution, for ? constant
19
Example

• Check the differential settlement of a 10 x 20 m
  floor, carrying a udl of just 80 kPa, assuming
  the floor to be flexible
• The soil profile consists of clays, the first
  layer being 4 m thick while the second layer is 8
  m thick. Rock thereafter. The clay near the
  surface has an undrained shear strength of 30
  kPa, while the lower layer is much stiffer - 100
  kPa.
• The stiffness of either soil may be approximated
  by 300cU.

20
Solution Centre

• 4 rectangles 5 x 10 m
• ? B 5 LB 2
• Layer 1 depth 4 m
• hB 0.8 ?Irc 0.066 Eu 9 MPa
• Layer 2 depth 12 m
• hB 2.4 ?Irc 0.252 Eu 30 MPa
• sct 4x80x5 (0.066/9 (0.252 - 0.066)/30)
• sct 1600 (0.0073 0.0062) 11.7 9.9 mm

21
Solution Corner

• 1 rectangles 10 x 20 m
• ? B 10 LB 2
• Layer 1 depth 4 m
• hB 0.4 ?Irc 0.022 Eu 9 MPa
• Layer 2 depth 12 m
• hB 1.2 ?Irc 0.118 Eu 30 MPa
• scnr 80x10 (0.022/9 (0.118 - 0.022)/30)
• scnr 800 (0.0024 0.0032) 1.9 2.6 mm

22
ANSWER

• Centre 21.6 mm
• Corner 4.5 mm
• Differential 17.1 mm
• Should check mid-sides too
• B 10 m and LB 1
• B 5 m and LB 4

23
Validity of Elastic Solutions

• Limited by Boussinesq theory
• Chiefly
• ??z underestimated when soil is underlain by a
  rigid boundary
• ??z overestimated when a stiff soil layer
  overlies a less stiff soil

24
1. Vertical stress distribution boundary
?z / ?z Boussinesq
Soil, E
z / H
H
ROCK
25
2. Vertical stress distribution layered soil
?z
Soil 1, E1
Soil 2, E2
26
Part II. Settlements on Sands a special case

• Theoretical settlements of sands inadequate
• E increases rapidly with z in a uniform deposit,
• due to increasing confinement

• ? settlement estimates usually based on
• stiffness data from field tests
• empirical or semi-empirical settlement equations

27
FIELD TESTS

• SPT, Standard Penetration Test
• Dynamic, disturbed soil sample, blowcount
• N no. of blows per 300 mm of penetration
• Corrections to N
• Unreliability worn equipment, operators
• BUT robust
• Density of sands
• Average settlement of footings

28
SPT Device http//www.archway-engineering.com/prod
ucts/spt_sampler.html
Automatic trip hammer
Split spoon sampler
29
Field Tests, continued

• CPT, Cone Penetration Test
• Less robust, much faster
• No soil sample
• Much information
• penetration resistance, qc and fs
• FR fs/qc used to distinguish soil types
• Piling applications
• E fn (qc)

30
CPT
31
Typical Results
32
Interpretation
Robertson Campanella 1982
33
Field Tests, continued

• Downhole Screw Plate
• Helical plate (dia. ? 150 mm) attached to rods
• Screwed below borehole pushed to fail soil
• Mini-plate loading test
• Soil strength and stiffness

34
Field Tests, continued

• Marchetti Dilatometer
• Spade like device
• Pushed into soil to required depth
• Pressurized, expanded circular membrane
• Soil stiffness
• Earth pressure coefficient at rest

35
Marchetti Dilatometer http//www.marchetti-dmt.it/
36
Field Tests

• Self-Boring Pressuremeter (SBP)
• cylindrical device
• theoretically superior to dilatometer
• MUCH soil information
• http//www.cambridge-insitu.com/specs/Instruments/
  LCPM_Spec.html

37
http//www.cambridge-insitu.com/specs/Instruments/
LCPM_Spec.html
38
Semi-Empirical Approach to Settlement in Sands

• The field tests provide variations of soil
  stiffness
• Schmertmann proposed using a STRAIN INFLUENCE
  FACTOR, based initially on elastic theory of
  stress distributions beneath a circle
• Then modified for experimental behaviour

39
STRAIN INFLUENCE FACTOR for stress beneath
centre of a flexible circle, with udl
GF geometric factor
40
STRAIN INFLUENCE FACTOR
K ratio of horizontal to vertical stress
41
Strain Influence Factor - circle, radius R
I?
0.2
0.6
0.8
0.4
0
Theory ? 0.4
1
Theory ? 0.5
z / R
2
3
4
42
Schmertmann Approach

• Find strains and therefore settlements in layers
  throughout the soil profile
• Correct for creep
• Restricted to flexible circular footings
• equivalent circles?
• Central settlement only
• Kay and Cavagnaro developed I? for sides

43
END NOTE

• Schmertmann developed his approach further to
  account for footing shape which influenced
• E - qc relationship
• I? distribution

44
Kay and Cavagnaro Approach

• Kay and Cavagnaro (1983) applied the theoretical
  I? distributions for estimation of differential
  settlement on stiff Adelaide clays
• I? for centre and side of circle
• could apply to rectangles up to LB ? 2
• requires radius, a, of equivalent area
• correction of diff. settlement for relative
  rigidity of footing after P T Brown

45
Kay and Cavagnaro - Centre
I?
1
2
3
4
0.5
1.0
0.0
?
46
Kay and Cavagnaro - Corner
I?
1
2
3
4
0.5
1.0
0.0
?
47
100 kPa Diameter 9 m
I?
1
2
3
4
0.5
1.0
0.0
? 30.4 mm
48
Variation with Poissons ratio
49
Part III. Stress Path Testing

• Triaxial testing
• Not to fail the soil, but to apply the stress
  and drainage paths expected in the soil and
  determine precisely the soil response

50
Stress Path Testing

• Potentially most accurate method to evaluate
  consolidation and immediate settlement
• Dependence of E on stress level accommodated
• Numerous tests on different samples to find
  strains in soil profile
• Testing peculiar to the design problem

51
Example

• Oil Tank differential settlement?
• 40 m diameter
• Surface pressure, 263 kPa
• 4 layered soil, soft sediments
• Top layer quite weak
• ?' 5 kPa
• Ko 0.4

52
(No Transcript)
53
Testing Procedure

• Obtain good quality samples
• Estimate effective soil stress at point in soil
• Apply as total stress in triaxial cell with
  drains closed
• anisotropic stress state?
• Open drains, allow consolidation
• at equilibrium, soil at field condition
• Close drains, apply extra stresses
• measure immediate settlement
• Open drains
• measure consolidation settlement

54
50 kPa
20 kPa
u gt 0
After drainage ?' ?
No drainage
Anisotropic consolidation Getting the soil back
to its field condition
55
50 250 kPa
si
20 140 kPa
u gt 0
After drainage ?' ?
No drainage - no volume change
Influence of Tank Loading Immediate and
Consolidation Settlement
56
Stress Path
Black total stress pathBlue effective stress
path
3
undrained
t (?1 - ?3)/2
1
2
25
Field State
s' (?'1 ?'3)/2
57
NOTES on stress path testing

• Unlike shear strength testing, the soil is not
  taken to failure
• Major limitation a relatively minor shift in the
  design of the structure may invalidate the
  settlement predictions

58
Part IV. CREEP

• Sands (Schmertmann)
• Silts and Clays?

59
The Creep Factor
60
THE KEY POINTS

• Three types of settlement
• Elastic stress distribution solutions limited
• Settlement under corner of a rectangle on a
  finite layer
• geometric superposition
• layer superposition
• Sands need field evaluation of E with depth
• strongly dependent on stress state
• may need semi-empirical solution

61
Summary, contd.

• Stress path method
• many samples
• complex testing
• anisotropic consolidation
• pore pressure monitoring
• accurate, IF samples are good
• too dependent on design parameters
• Numerical methods?