Settlements and Elastic Stress Distribution (SEP 2011 Color)

CE5101 Consolidation and SeepageLecture 5

Prof Harry TanSEP 2011

1

CE 5101 Lecture 5 SETTLEMENTS and Stress

Distribution

Sep 2011Prof Harry Tan

1

Outline Foundation Requirements

Elastic Stress DistributionElastic Stress Distribution

Concept of Effective Stress

Settlements of Soils - Immediate, Delayed, and Creep Compression

Hand Calculations

SPREADSHEET Calculations (UNISETTLE)

Finite Element Analysis (PLAXIS)2



2

Requirements for Foundation Design

Adequate Safety (degree of utilisation of soil strength)

Acceptable Deformations Acceptable Deformations(Movements and Settlements limits)

3

What is Adequate Safety(Lambe and Whitman Pg 196)

-2.000 -1.000 0.000 1.000 2.000 3.000 4.000 5.000 6.000 7.000 8.000 9.000 10.000 11.000 12.000

9 000 Failure Load = 866 kPaAA

4.000

5.000

6.000

7.000

8.000

9.000

E

Stress

Strain

2c

Failure Load 866 kPa

Yielded

0.000

1.000

2.000

3.000

Plastic Points

Plastic Mohr-Coulomb point Tension cut-off point

E = 34.48 MN/m2

c=167.6 kN/m2

= 0.3

Yielded Zone

4



3

0.00

Footing CL Settlement [m]

Chart 1

Load vs Settlement Behaviour of Flexible Footing

Settlement (m)

-0.20

-0.15

-0.10

-0.05

Point A

First Yield Local Shear

Failure

0 200 400 600 800 1.00E+03-0.35

-0.30

-0.25

Footing Load (kPa)

General Shear Failure

Load (kPa)5

4 5

Factor of Strength Reduction

Chart 2

Factor of Safety as Measure of Degree of Utilisation of Soil Strength

2.5

3.0

3.5

4.0

4.5

Point AFS = 4.338; q = 200 kPa; qult = 868 kPa

FS = 2 164; q = 400 kPa; qult = 866 kPa

0 0.05 0.10 0.15 0.20 0.25 0.30 0.351.0

1.5

2.0

Settlement (m)

FS = 2.164; q = 400 kPa; qult = 866 kPa

FS = 1.291; q = 670 kPa; qult = 865 kPa

6



4

What is Allowable Settlements

Effects on:

Appearance of Structure

Utility of Structure

Damage to Structure

7

Types of Settlements

Uniform settlement

Non-uniform settlement

Angular distortion = /L

L

L

Angular distortion = /(L/2)

8



5

Allowable Settlements

Controlled by type of settlements (Sowers 1962)y yp ( )

Total settlements

Tilting

Differential settlements

9

Limiting Angular Distortions (Bjerrum, 1963)1/150 - Considerable cracking in panel and brick walls, safe limit for flexible brick wall h/l



6

Limiting Angular Distortions (Bjerrum ,1963)

Max Distortion (/L) vs Max Differential Settlement :

1/500 vs 25 mm For Stiff Footing,1/500 vs 25 mm

1/300 vs 45 mm

1/200 vs 70 mm

1/100 vs 150 mm

g,

Max Diff Sett = 1/4 Max Sett

For Flexible Footing,

Max Diff Sett = 1/2 Max Sett

Typical Foundation Design,

Max Diff Sett < 25 mm

11

Limiting Angular Distortions (Bjerrum ,1963)

350 mm

200 mm

Stiff Footing max diff sett =1/4 max sett Flexible Footing max diff sett=1/2 max sett

12

100 mm



7

ER2010 Review Paper by Ed Cording et al Assessment of excavation-induced building damage Damage is due to combined effects of:effects of: Angular distortion; Lateral strain Bending strain

13

Basic Soil Phase RelationshipsMASSVOLUME Densities (kg/m3)

Air

Water

Solids

0

Mw Mt

Ms

Mw

Va

Vw

Vs

Vv

Vt

Total, t = Mt/VtDry, d = Ms/VtSolids, s = Ms/VsWater, t = Mw/VwSaturated, sat Ratios= (Ms+Mw+ w Va)/VtWater content, w = Mw/Ms

Void ratio, e = Vv/Vs

Porosity, n = Vv/Vt

Degree of saturation = Vw/Vv 14



8

Basic Soil Phase RelationshipsDefine Vs=1, Vv=e

MASSVOLUME Densities (kg/m3)

eS w = w s

Air

Water

Solids

0 t

s

Mw

(1-e)S

eS

1

e

1+e

Total, t = s (1+w)/(1+e)= d (1+w)

Dry, d = s /(1+e)Saturated, sat = (Ms+Mw+ w Va)/VtRatios

Water content, w = t/ d - 1 Void ratio, e = s/d - 1Porosity, n = e/(1+e)

Degree of saturation = S = ws / ew 15

Common soil mineral densitiesMineral Type Solid Density, kg/m3

Calcite 2800

Quartz 2670

Mica 2800

Pyrite 5000

Kaolinite 2650

Montmorillonite 2750

Illite 270016



9

Typical range of saturated densitiesSoil Type Saturated Density, kg/m3

Sands;gravels 1900-2300

Silts 1500-1900

Soft Clays 1300-1800

Firm Clays 1600-2100

Peat 1000-1200

Organic Silt 1200-1900

Granular Fill 1800-220017

The Textbooks on Foundations They come no better

This is one of the few showingmore than one soil layer

18



10

The Reality With a bit of needed W add-on

19

The Reality Getting closer, at least

20



11

So, with this food for thought, , g ,on to the Fundamental

Principles

21

Determining the effective stress is the key to geotechnical analysis

The not-so-good method:method:

h '' )'(' hz

= buoyant unit weight

)1(' iwt 22



12

It is much better to determine, separately, the total stress and the pore pressure. The effective stress is then the total stress minus the pore pressureminus the pore pressure.

)( hz uz '

23

Determining pore pressure

u = w hu w hThe height of the column of water (h; the head representing the water pressure)is usually not the distance to the ground surface nor, even, the distance to thegroundwater table. For this reason, the height is usually referred to as thephreatic height or the piezometric height to separate it from the depth belowthe groundwater table or depth below the ground surface.

The pore pressure distribution is determined by applying the facts that

(1) in stationary conditions, the pore pressure distribution can be assumed to be linear in each individual soil layer

SAND Hydrostatic distribution

GW

PRESSURE

(2) in pervious soil layers that are sandwiched between less pervious layers, the pore pressure is hydrostatic (that is, the vertical gradient is unity)

CLAY Non-hydrostatic distribution, but linear

SAND Hydrostatic distribution Artesian phreatic head

DEPTH

24



13

Distribution of stress below a a small load area

The 2:1 method

)()(0 zLzBLBqqz

The 2:1-method can only be used for distributions directly under the centerof the footprint of the loaded area. It cannot be used to combine (add)stresses from adjacent load areas unless they all have the same center. it isthen only applicable under the area with the smallest footprint. 25

Boussinesq Method for stress from a point load

2/522

3

)(23

zrzQqz

26



14

Newmarks method for stress from a loaded area

Newmark (1935) integrated the Boussinesq equation over a finite area and obtained a relation for the stress under the corner of aarea and obtained a relation for the stress under the corner of a uniformly loaded rectangular area, for example, a footing

40CBAIqqz

2222

22

112nmnm

nmmnA

(1)

12

22

22

nmnmB

2222

22

112arctannmnm

nmmnC

m = x/zn = y/zx = length of the loaded areay = width of the loaded areaz = depth to the point under the corner

where the stress is calculated

27

Eq. 1 does not result in correct stress values near the ground surface. To represent the stress near the ground surface, Newmarks integration applies an additional equation:

40CBAIqqz

F h 2 + 2 + 1 2 2

(2)

For where: m2 + n2 + 1 m2 n2

28



15

Stress distribution below the center of a square 3 m wide footing

0 0.25Eq. (2) Eq. (2)

-4

-2

DE

PTH

(m)

0.10

0.15

0.20

INFL

UE

NC

E F

AC

TOR

, IEq. (1)

Eq. (1)

0 20 40 60 80 100-6

STRESS (KPa)0.01 0.10 1.00 10.00

0.00

0.05

m and n (m = n)

29

00 25 50 75 100

STRESS (%)

Boussinesq

Westergaard

00 25 50 75 100

SETTLEMENT (%)

Boussinesq

Westergaard

1

2

3

EPTH

(di

amet

ers)

2:1

1

2

3

EPTH

(di

amet

ers)

q

2:1

Comparison between Boussinesq, Westergaard, and 2:1 distributions

4

5

DE

4

5

DE

30



16

00 25 50 75 100

STRESS (%)

Westergaard

00 25 50 75 100

SETTLEMENT (%)

Westergaard

1

2

3

PTH

(di

amet

ers)

Boussinesq

1

2

3

PTH

(di

amet

ers)

Boussinesq

4

5

DEP 2:1

4

5

DEP

2:1

31

0

1

0 25 50 75 100

STRESS (%)

Westergaard

0

1

0 25 50 75 100

SETTLEMENT (%)

Westergaard

1

2

3

EPTH

(di

amet

ers)

2:1

Boussinesq

Characteristic Point; 0.37b from center

1

2

3

EPTH

(di

amet

ers)

Boussinesq

2:1 Characteristic Point; 0.37b from center

4

5

D

4

5

D

Below the characteristic point, stresses for flexible and stiff footings are equal 32



17

Now, if the settlement distributions are so similar, why do we persist in using

Boussinesq stress distribution instead of the much simpler 2:1 distribution?

Because a footing is not alone in this world; near by, there are other footings, and fills,near by, there are other footings, and fills,

and excavation, etc., for example:

33

The settlement imposed

00 25 50 75 100

SETTLEMENT (%)

BoussinesqOutside Point Boussinesq

Center PointThe settlement imposed outside the loaded

foundation is often critical

1

2

3

PTH

(di

amet

ers)

Center Point

4

5

DE

Loaded area

34



18

Calculations using Boussinesq distribution can be used to determine how stressapplied to the soil from one building may affect an adjacent existing building.

EXISTING NEW 0 20 40 60 80 100STRESS (%)

ADJACENT BUILDING

BUILDING WITH LARGE LOAD OVER FOOTPRINT

AREA

2 m2 m 4 m

0

5

10

15

DEP

TH (

m) STRESSES

UNDER THE FOOTPRINT OT THE LOADED BUILDING

STRESSES UNDER AREA

BETWEEN THE TWO BUILDINGS

20

25

30

STRESSES ADDED TO THOSE UNDER THE FOOTPRINT OF THE ADJACENT BUILDING

35

Calculation of Stress DistributionDepth 0 u0 0 1 u1 1(m) (KPa) (KPa) (KPa (KPa) (KPa) (KPa)

Layer 1 Sandy silt = 2,000 kg/m30.00 0.0 0.0 0.0 30.0 0.0 30.0STRESS (KPa)0.00 0.0 0.0 0.0 30.0 0.0 30.0

GWT 1.00 20.0 0.0 20.0 48.4 0.0 48.42.00 40.0 10.0 30.0 66.9 10.0 56.93.00 60.0 20.0 40.0 85.6 20.0 65.64.00 80.0 30.0 50.0 104.3 30.0 74.3

Layer 2 Soft Clay = 1,700 kg/m34.00 80.0 30.0 50.0 104.3 30.0 74.35.00 97.0 40.0 57.0 120.1 43.5 76.66.00 114.0 50.0 64.0 136.0 57.1 79.07.00 131.0 60.0 71.0 152.0 70.6 81.48.00 148.0 70.0 78.0 168.1 84.1 84.09.00 165.0 80.0 85.0 184.2 97.6 86.6

10.00 182.0 90.0 92.0 200.4 111.2 89.211.00 199.0 100.0 99.0 216.6 124.7 91.912.00 216.0 110.0 106.0 232.9 138.2 94.613.00 233.0 120.0 113.0 249.2 151.8 97.414.00 250.0 130.0 120.0 265.6 165.3 100.315.00 267.0 140.0 127.0 281.9 178.8 103.116.00 284.0 150.0 134.0 298.4 192.4 106.0

0

5

10

15

0 100 200 300 400 500

( )

DEP

TH (m

)

SAND

CLAY

17.00 301.0 160.0 141.0 314.8 205.9 109.018.00 318.0 170.0 148.0 331.3 219.4 111.919.00 335.0 180.0 155.0 347.9 232.9 114.920.00 352.0 190.0 162.0 364.4 246.5 117.921.00 369.0 200.0 169.0 381.0 260.0 121.0

Layer 3 Silty Sand = 2,100 kg/m321.00 369.0 200.0 169.0 381.0 260.0 121.022.00 390.0 210.0 180.0 401.6 270.0 131.623.00 411.0 220.0 191.0 422.2 280.0 142.224.00 432.0 230.0 202.0 442.8 290.0 152.825.00 453.0 240.0 213.0 463.4 300.0 163.4

20

25

SAND

HYDROSTATIC PORE PRESSURE DISTRIBUTION

36



19

Calculation of Stress DistributionSTRESS DISTRIBUTION (2:1 METHOD) BELOW CENTER OF EARTH FILL (Calculations by means of UniSettle)

ORIGINAL CONDITION (no earth fill) FINAL CONDITION (with earth fill and artesian pore pressure in sand)

Depth 0 u0 0 1 u1 1(m) (KPa) (KPa) (KPa (KPa) (KPa) (KPa)

Layer 1 Sandy silt = 2,000 kg/m30.00 0.0 0.0 0.0 30.0 0.0 30.0

GWT 1 00 20 0 0 0 20 0 48 4 0 0 48 4GWT 1.00 20.0 0.0 20.0 48.4 0.0 48.42.00 40.0 10.0 30.0 66.9 10.0 56.93.00 60.0 20.0 40.0 85.6 20.0 65.64.00 80.0 30.0 50.0 104.3 30.0 74.3

Layer 2 Soft Clay = 1,700 kg/m34.00 80.0 30.0 50.0 104.3 30.0 74.35.00 97.0 40.0 57.0 120.1 43.5 76.66.00 114.0 50.0 64.0 136.0 57.1 79.07.00 131.0 60.0 71.0 152.0 70.6 81.48.00 148.0 70.0 78.0 168.1 84.1 84.09.00 165.0 80.0 85.0 184.2 97.6 86.6

10.00 182.0 90.0 92.0 200.4 111.2 89.211.00 199.0 100.0 99.0 216.6 124.7 91.912.00 216.0 110.0 106.0 232.9 138.2 94.613.00 233.0 120.0 113.0 249.2 151.8 97.414.00 250.0 130.0 120.0 265.6 165.3 100.315 00 267 0 140 0 127 0 281 9 178 8 103 115.00 267.0 140.0 127.0 281.9 178.8 103.116.00 284.0 150.0 134.0 298.4 192.4 106.017.00 301.0 160.0 141.0 314.8 205.9 109.018.00 318.0 170.0 148.0 331.3 219.4 111.919.00 335.0 180.0 155.0 347.9 232.9 114.920.00 352.0 190.0 162.0 364.4 246.5 117.921.00 369.0 200.0 169.0 381.0 260.0 121.0

Layer 3 Silty Sand = 2,100 kg/m321.00 369.0 200.0 169.0 381.0 260.0 121.022.00 390.0 210.0 180.0 401.6 270.0 131.623.00 411.0 220.0 191.0 422.2 280.0 142.224.00 432.0 230.0 202.0 442.8 290.0 152.825.00 453.0 240.0 213.0 463.4 300.0 163.4

Aquifer with artesian head

37

Stress Distribution

00 100 200 300 400 500

STRESS (KPa)

00 100 200 300 400 500

STRESS (KPa)Stress from Fill

5

10

15DEP

TH (m

)

5

10

15DEP

TH (m

)

SAND

CLAY

20

25

20

25

SAND

Artesian Pore Pressure HeadThe distribution for the hydrostatic case

38



20

Effective Stress Concept

Effective stress = Total stress - Pore pressure

= - uUnit weight = g (kN/m3)g assumed to be 10 m2/s

T t l ti l t b dTotal vertical stress or overburden stress, z = t.z

39

Pore Water Pressure (PWP)

Pore water pressure u = uw = uss + uexcuss = Steady state condition, hydrostatic or steady seepage

uexc = Excess pwp due to soil loading

Buoyant unit weight

= t - w for hydrostatic condition = t - w + i wi = hydraulic gradient (head diff/ distance)

i is negative for upward artesian flow 40



21

Elastic Stress Distribution with DepthQ

QqL

B

1(H):2(V)zL+z

B+z

qo

qz

BLQqo

))(( zLzBBLqq oz

Only can be used for stress at centre ofOnly can be used for stress at centre of loaded area

Cannot use for combined effects of two or more loaded areas, unless they have same centres

41

Boussinesq Distribution (1885)Assumes: isotropic linear elastic halfspace, Poisson ratio = 0.5

Q

z

For Point load Q kN

2/522

3

)(2)3(zrzQqz

Integrate for Line Load, P kN/m

32Pr

qz 222

3

)(2

rzzPqz

Integrate for Rectangular Area, get Fadums Influence Chart Fig.1; for Circular Area, get Foster and Alvin Chart Fig.2

42



22

Weastergaard Distribution (1938)Assumes: isotropic linear elastic halfspace, Poisson ratio = 0, rigid horizontal layers

Q

z

, g y

For Point load Q kN

2/322 ))/(21( zrzQqz

Differences with Boussinesq is

rqz

qsmall

For wide flexible loaded areas Westergaard method is preferred

43

UniSettle 2.4 21 Jan 2000EX02.STL page 1

Effective Stress Comparison, ( 4.11 , 8.11 )-----------------------------------------------------------------

BOUSSINESQ WESTERGAARD 2:1Depth Ini. Fin. Ini. Fin. Ini. Fin.

Stress Stress Stress Stress Stress Stress(m) (kPa) (kPa) (kPa) (kPa) (kPa) (kPa)

-----------------------------------------------------------------

Comparison of stresses under a 3m square footing below its

Layer 1 Any Soil 0. kg/m^30.00 100.0 0.0 100.0 0.0 100.0 0.00.10 97.9 0.0 89.3 0.0 93.7 0.00.20 94.3 0.0 79.4 0.0 87.9 0.00.30 89.4 0.0 71.4 0.0 82.6 0.00.40 83.2 0.0 64.4 0.0 77.9 0.00.50 76.8 0.0 58.4 0.0 73.5 0.00.60 70.9 0.0 53.2 0.0 69.4 0.00.70 65.6 0.0 48.9 0.0 65.7 0.00.80 61.1 0.0 45.1 0.0 62.3 0.00.90 57.2 0.0 41.9 0.0 59.2 0.01.00 53.7 0.0 39.1 0.0 56.3 0.01 10 50 8 0 0 36 7 0 0 53 5 0 0

q gcharacteristic point

Characteristic point is point where vertical stress is equal for both rigid and flexible footing, this point is located at 0.37B and 0.37L from centre of rectangular footing, or 0.37R of 1.10 50.8 0.0 36.7 0.0 53.5 0.0

1.20 48.1 0.0 34.5 0.0 51.0 0.01.30 45.8 0.0 32.5 0.0 48.7 0.01.40 43.7 0.0 30.8 0.0 46.5 0.01.50 41.7 0.0 29.2 0.0 44.4 0.01.60 40.0 0.0 27.8 0.0 42.5 0.01.70 38.3 0.0 26.4 0.0 40.7 0.01.80 36.8 0.0 25.2 0.0 39.1 0.01.90 35.4 0.0 24.1 0.0 37.5 0.02.00 34.0 0.0 23.0 0.0 36.0 0.0

g g,circular footing

Results show that under characteristic point 2:1 method is similar to Boussinesq result

44



23

AA

-1.000 0.000 1.000 2.000 3.000 4.000 5.000 6.000

Elastic Stress Bulb for Circular Footing

BCDEFGHIJKLMNOPQRS

2.000

3.000

4.000

5.000

[ kN/m2]

A : -0.900

B : -0.850

C : -0.800

D : -0.750

E : -0.700

F : -0.650

G : -0.600

H : -0.550

I : -0.500

J : -0.450

K : -0.400

L : -0.350

M : -0.300

N : -0.250

O : -0.200

P : -0.150

-0.000

1.000

E ffective mean stressesExtrem e effec tive mean stress -882.98*10

-3 kN/m

2

Q : -0.100

R : -0.050

S : 0.000

T : 0.050

45

Elastic Settlement for Circular Flexible LoadSurface settlements is given by Terzaghi,1943 as:

R

q

R

D =

3.),( FigseerfisI

IEqR

Edge settlement = 0.7 centre settlement

Centre settlement is :

footingFlexibleforERqz )1(2

2

footingRigidforERqz )1(2

2 46



24

Flexible and Rigid Footing

-0.300 -0.200 -0.100 0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900 1.000 1.100

Flexible Footing-0.300 -0.200 -0.100 0.000 0. 100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900 1.000 1.100

Rigid Footing

0.08 0.16 0.24 0. 32 0.40 0.48 0.56 0.64 0.72 0.80 0.88 0.96 1.04

10.40

10.48

A

A

9.300

9.400

9.500

9.600

9.700

9.800

9.900

10.000

10.100

10.200

9.200

9.300

9.400

9.500

9.600

9.700

9.800

9.900

10.000

10.100

10.200

0.08 0. 16 0.24 0.32 0.40 0.48 0.56 0.64 0.72 0.80 0.88 0.96 1.04

10 40

10.48

AA*

9.76

9.84

9.92

10.00

10.08

10.16

10.24

10.32

E=1000 kPa, =0, q=10 kPa, sett= 20 mm

AA*

9.76

9.84

9.92

10.00

10.08

10.16

10.24

10.32

10.40

E=1000 kPa, =0, q=10 kPa, sett= 16 mm47

Approximate Ratio at corner, centre and edge to average settlement

Flexible Load Area RigidgFooting

FoundationDepth

Corner/Ave

Edge/Ave

Centre/Ave

Rigid/Ave

H/L= 0.6 0.9 1.2 0.9H/L=1 0.5 0.7 1.3 0.8

H/L=1/4 0.4 0.7 1.3 0.8

48



25

Elastic Settlement for Other Flexible LoadCorner settlements is given by Terzaghi,1943 as:

B

D =

4.)/(

)1( 2

FigseeLBfisI

IE

qB

Points other than corner for any combination of rectangles can be obtained by superposition

qL

For centre of square loaded area:

)1(12.1 2 EBqz

49

Superpostion Principle for Rectangles

= + + +z

- - +=z

50



26

Elastic Settlement for Other Flexible Load

For Flexible Rectangular Loaded area, Corner settlement , g , ,with finite depth of elastic layer, use Steinbrenner chart

)21()1(

)1(

22

2

FFI

IE

qB B

qL

5.

)21()1(

21

22

12

FigingivenFandFFFI

FiniteD

51

Equivalent Footings for Pile Groups SettlementsGround level

Soft Clay

Ground level

L2/3L

Equivalent FtgL

2/3L

Soft Clay

Equivalent Ftg

2

1Homogeneous Clay

2

1Firm Layer

52



27

The end result of a geotechnical design analysis

is

Settlement

53

Movement, Settlement, and CreepMovement occurs as a result of an increase of stress, but the term should be reservedto deformation due to increase of total stress. Movement is the result of a transfer ofstress to the soil (the movement occurs as necessary to build up the resistance to theload), and when the involved, or influenced, soil volume successively increases as thestress increases. For example, when adding load increments to a pile or to a plate in astatic loading test (where, erroneously, the term "settlement" is often used). As a term,mo ement is sed hen the in ol ed or infl enced soil ol me increases as the loadmovement is used when the involved, or influenced, soil volume increases as the loadincreases.

Settlement is volume reduction of the subsoil as a consequence of an increase ineffective stress. It consists of the sum of "elastic" compression and deformation due toconsolidation. The elastic compression is the compression of the soil grains (soilskeleton) and of any free gas present in the voids, The elastic compression is oftencalled "immediate settlement. It occurs quickly and is normally small (theelastic compression is not associated with expulsion of water). The deformation due toconsolidation on the other hand is volume change due to the compression of the soilconsolidation, on the other hand, is volume change due to the compression of the soilstructure associated with an expulsion of waterconsolidation. In the process, theimposed stress, initially carried by the pore water, is transferred to the soil structure.Consolidation occurs quickly in coarse-grained soils, but slowly in fine-grained soils. Asa term, settlement is used when the involved, or influenced, soil volume stays constantas the effective stress increases.

54



28

Movement, Settlement, and Creep

Creep is compression occurring without an increase of effective stress.Creep is usually small, but may in some soils add significantly to thecompression of the soil skeleton and, thus, to the total deformation of thesoil It is then acceptable to talk in terms of creep settlement

The term "settlement" is normally used for the deformation resulting from thecombined effect of load transfer, increase of effective stress, and creep duringlong-term conditions. It is incorrect to use the term settlement to meanmovement due to increase of load such as in a loading test.

soil. It is then acceptable to talk in terms of creep settlement.

55

StrainLinear Elastic Deformation (Hookes Law)

E'

= induced strain in a soil layer= imposed change of effective stress in the soil layer

E = elastic modulus of the soil layer (Youngs Modulus)

Youngs modulus is the modulus for when lateral expansion is allowed, which may be the case for soil loaded by a small footing, but not when the load is applied over a large area. In the latter case, the lateral expansion is constrained (or confined). The constrained modulus, D, is larger than the E-modulus. The constrained modulus is also called the oedometer modulus. For ideally elastic soils, the ratio between D and E is:

'

)21()1()1(

ED

= Poissons ratio56



29

Stress-Strain

57

Stress-strain behavior is non-linear for most soils. The non-linearity cannot be disregarded when analyzing compressible soils, such as silts and clays, that is, the elastic modulus approach is not appropriate for these soils.

Non-linear stress-strain behavior of compressible soils, is conventionally modeled as follows.

where = strain induced by increase of effective stress from 0 to 1

0

1

0

1

0 ''

lg''

lg1

CR

eCc

y 0 1Cc = compression indexe0 = void ratio0 = original (or initial) effective stress1 = final effective stressCR = Compression Ratio = (MIT)

01 eCCR c

58



30

In overconsolidated soils (most soils are)

)''lg

''

lg(1

1 100 p

cp

cr CCe

where p = preconsolidation stressp pCcr = re-compression index

59

The Janbu Method

The Janbu tangent modulus approach, proposed by Janbu (1963; 1965; 1967; 1998), and referenced by the Canadian Foundation Engineering Manual, CFEM (1985; 1992), applies the same basic principles of linear and non-linear stress-strain behavior. The method applies to all soils, clays as well as sand. By this method, the relation between stress and strain is a function of two non-dimensional parameters which are unique for a soil: a stress exponent, j, and a modulus number, m.

Janbus general relation is

])'()'[(1 01 jj ])'

()'

[( 01 jr

j

rmj

where r is a reference stress = 100 KPa

j > 0

60



31

The Janbu Method

Dense Coarse-Grained Soil j = 1

'1)''(1 01 mm

'1)''(1

KPa

ksf

Cohesive Soil j = 00

1

''ln1

m

2)(

2 01

mmksf

)''(51

01 m KPaSandy or Silty Soils j = 0.5

pm''(2 1 ksf

61

There are direct mathematical conversions

between m and the E and Cc-e0

For E given in units of KPa (and ksf), the relation between the modulus number and the E-modulus is

m = E/100 (KPa)m = E/2 (ksf)

For Cc-e0, the relation to the modulus number is

22

00 69.02lg10ln13.21

10ln

cc Ce

Cem

62



32

Typical and Normally Conservative Virgin Modulus Numbers

SOIL TYPE MODULUS NUMBER STRESS EXP.

Till, very dense to dense 1,000 300 (j = 1)

Gravel 400 40 (j = 0.5)

Sand dense 400 250 (j = 0.5)compact 250 150 - " -loose 150 100 - " -

Silt dense 200 80 (j = 0.5)compact 80 60 - " -loose 60 40 - " -

Silty clay hard, stiff 60 20 (j = 0)and stiff, firm 20 10 - -

Clayey silt soft 10 5 - -

Soft marine claysSoft marine claysand organic clays 20 5 (j = 0)

Peat 5 1 ( j= 0)

For clays and silts, the recompression modulus, mr, is often five to tentimes greater than the virgin modulus, m, listed in the table

63

1 00

1.20

p'c 20

25

Evaluation of compressibility from oedometer results

0.40

0.60

0.80

1.00

10 100 1 000 10 000

Voi

d R

atio

(- -

)

m = 12(CR = 0.18)

0

5

10

15

10 100 1,000 10,000

Stra

in (

%)

p 10p

Cc

Cc = 0.37

e0 = 1.01 p'c

p 2.718p

1/m

Slope = m = 12

10 100 1,000 10,000

Stress (KPa) log scale Stress (KPa) log scale

Void-Ratio vs. Stress and Strain vs. Stress Same test data

64



33

Comparison between the Cc/e0 approachand the Janbu method

0 30

0.35

30

35

m

0.05

0.10

0.15

0.20

0.25

0.30

CO

MPR

ESSI

ON

IND

EX, C

c Do these values indicate a

compressible soil, a medium compressible

soil, or a non-compressible soil?5

10

15

20

25

30

VIR

GIN

MO

DU

LUS

NU

MB

ER, m

Data from a 20 m thick sedimentary deposit of medium compressibility.

0.000.40 0.60 0.80 1.00 1.20

VOID RATIO, e0

00.400.600.801.001.20

VOID RATIO, e0

65

75

100

125

150

OR

MA

LIZE

D C

c (%

)

75

100

125

150

OR

MAL

IZED

m (

%)

The Cc-e0 approach implies that the the compressibility varies by 30 %.

However, the Janbu methods shows it to vary only by 10 %. The modulus number, m, ranges from 18 through 22; It would be unusual to find a clay with less variation

500.40 0.60 0.80 1.00 1.20

VOID RATIO, e0

N 500.400.600.801.001.20

VOID RATIO, e0

NO

find a clay with less variation.

What about Immediate Settlement and Consolidation? 66



34

CE 5101 - SETTLEMENTS AND 1D Compression TheorySettlements of Soils - Immediate, Delayed, and Creep Compressionp p

Delayed Consolidation Compressionmv methode-logP methodJanbu method

Terzaghis Theory of 1D ConsolidationTerzaghi s Theory of 1D ConsolidationEffects of Drainage and Initial Stress Distribution

SPREADSHEET Calculations (UNISETTLE)Finite Element Analysis (PLAXIS)

67

Foundation Settlement Issues

How Much settlements will occur?

Interested in Ultimate settlements in fully drained state, as well as long-term creep settlements

How Fast and how long will it take for most of settlements to occur?

Involved Consolidation and SecondaryInvolved Consolidation and Secondary Compression theories to estimate rate of settlements, and

Methods to accelerate settlements and minimise long-term settlements

68



35

Types of Ground Movements and Causes of Settlements

Compaction - due to vibrations, pile driving, earthquake

El ti V l t i S ttl t i OC Cl i iElastic Volumetric Settlement in OC Clay in recompression, use E and or recompression index, Cr or Immediate or Undrained Settlement - Distortion without volume change, use Eu and uMoisture changes - Expansive soils, high LL and PI, high swelling and shrinkage

S ll P t ti l (%) 0 1(PI 10) l ( / )Swell Potential (%) = 0.1(PI-10) log (s/p)

Effects of vegetation - related to moisture changes by root system

Effects of GWT lowering - shrinkage ad consolidation

69

Types of Ground Movements and Causes of Settlements

Effects of temperatures - Frost heaving, drying by furnace and boilers

Effects of seepage and scouring - Erosion byEffects of seepage and scouring - Erosion by piping, scouring and wind action, mineral cement dissolved by GW eg limestone, rock salts and chalk areas

Loss of lateral support - Footings beside unsupported excavation, movement of natural slopes and cuttings

Effects of mining subsidence - collapse of ground cavities

Filled ground - settlements of the fill soils, compaction, consolidation, and creep

70



36

Shrink/ swell potential is function of Clay Activity = %clay fraction/ PI

Swell Potential (%) = 0.1(PI-10) log (s/p)

Where s=suction before construction and p=final bearing pressure71

1D Settlements

Soil deformations are of two types: Distortion (change of shape 2D effects)Compression (change of volume)

Components of Settlements:

distortionsettlementimmediateswheressss

i

scit

,

ncompressiosecondarysncompressiosettlementionconsolidats

distortionsettlementimmediateswhere

s

c

i

,

,

72



37

Undrained Immediate Settlements

Distortion of clay layer:Calculate by elastic theory eg JanbuCalculate by elastic theory eg Janbu Chart

by JanbufactorsessdimensionlIandIarealoadedflexibleforsettlementimmediateswhere

EqBIIs

i

i

)1( 210

layerclay of ratio sPoisson' layerclay of modulus Undrained E

B dthfootong wi on loadAverage qby JanbufactorsessdimensionlIandI 10

73

Immediate Settlements in Clays by Janbu

74



38

Example on Janbu Chart: Foundation 4x2m with q=150kPa, located at 1m in Clay layer 5m thick with Eu=40MN/m2. Below is second clay layer of 8m thickness and Eu=75 MN/m2.What is average settlement under foundation? Assume =0.5

D:MN/m40Ewithlayer,clay upperConsider(1)

9.0 0.5, 1/2D/B 2;4/2L/B Now2

u

0

H

DB mm5.35.01

402*150*7.0*9.0s

7.0 2,4/2L/B and 24/2H/By ,ypp( )

21i

1

u

mm3.25.0175

2*150*85.0*9.0s

85.0 2,4/2L/B and 612/2H/B:MN/m75E withcombined, layers two Consider (2)

22i

1

2u

mm9.15.0175

2*150*7.0*9.0s

7.0 2,4/2L/B and 24/2H/B:MN/m75E withlayer, upper Consider (1)

23i

1

2u

mm 3.9 1.9 -2.3 5.3sssss

;inciplePrionSuperposit By

i

3i2i1ii

75

1D Primary Consolidation Settlements

Time delayed Primary Consolidation Compression:

water

solids

0e

1

e0H

H

)()(

00

0

volumeverticalc

0volumevertical

HHHse1e

HH

'vv P where P), vs(e methodm e

Pe -ility compressib of coeffnav

a1e0e

fe

fP0P P

0

v

0v e1

aP1

)e(1e -change volume of coeffnm

00

vc

0v00

c

HPe1

a s

HPm He1e sH

76



39

mv and Constrained Modulus D

For wide loaded area, get 1D compression d K diti l ti d l t lunder Ko condition, elastic modulus to apply

is called the Constrained Modulus D defined by:

hlftC ffi ih211

1Em1D

v

0.35)( ratio Poisson drained Soil elasticity of modulus drained Soil E

changevolume oftCoefficienmwhere v

77

Sc by (e vs logP) MethodNormally Consolidated Clays - non-linear stress strain for soil, but linear in logP Pge

0e

fe

indexncompressioCc

0

fc0fc P

PlogCPlogPlogCe

0

f

0

c0c P

Plog

e1CHHs

fP0P Plog

0

cc e1

CC CRRatio, nCompressio

78



40

Sc by (e vs logP) MethodOver-Consolidated Clays (Pf < Pc), Preconsolidation Pressure

e

0efe

fP0P Plog

indexncompressioCc

0

fr0fr P

PlogCPlogPlogCe

0

f

0

r0c

ssettlementsmallPP

loge1

CHHs cP

indexswellingCindexionrecompressC

s

r

f0 Plog

cr C than smaller times10 to5 is C asssettlementsmall

0

rr e1

CC RR, Ratio ncompressioRe

c

79

Sc by (e vs logP) MethodOver-Consolidated Clays (Pf > Pc), Preconsolidation Pressure

Pe0ece

fP0P Plog

cC

0

cr0cr1 P

PlogCPlogPlogCe

e1eeHHs 210c

cP

sr CorC

fe

c

fccfc2 P

PlogCPlogPlogCe

f0 Plog

ssettlementlarge mean willThisPP

logCPPlogC

e1H

e1

c

fc

0

cr

0

0

0

c

80



41

Sc by Janbu Tangent Modulus MethodCanadian Foundation Manual 1985

Janbu (1963, 1965,1967,1998); For Cohesionless Soils; j>0

Th i d i P U iS ttl (b UNISOFT C d )Theory is used in Program UniSettle (by UNISOFT, Canada)

P stresseffective vertical initial

stresseffective vertical inchange by induced strain vertical where

mj1 get to Integrate m'M

0,

0

v

j

,

r

,

0

j

,

r

,

fv

j1

'r

''rt

kPa100 stresseffective verticalReference

test field or lab from obtained number, modulus Janbu mexponent stress Janbuj

P stresseffective vertical final

,

r

f,

f

0

81

Cohesionless Sands and Silts; j=0.5Normally Consolidated Cohesionless Soils

,0,fv

,

r

5m1

kPa100 0.5j SOIL TYPE mSAND DENSE 400-250

MEDIUM 250-150

LOOSE 150-100

SILT DENSE 200-80

MEDIUM 80-60

LOOSE 60-40

82



42

Cohesionless Sands and Silts; j=0.5Over-Consolidated Cohesionless Soils

kPa100 'P'f

,

r0.5j; for CASE

,

0

,

fr

v

,

r

'p

'f

5m1

kPa,100 ; for CASE ,0.5j

m than larger times10 to5 usually is m number, modulus OC

kPa inpressure dationpreconsoli

where5m

15m

1

f

r

,

P

,

P

,

f

,

0

,

Pr

v

r

83

Cohesive Soils; j=0

Normally Consolidated Clays

, kPa1000j SOIL TYPE mSILTY HARD, 60-20

c

0

c

0

,

0

,

f

0

c,

0

,

fv

r

Ce13.2

Ce110lnm

loge1

Clnm1

kPa100 0j

SILTY

CLAYSHARD,STIFF

60 20

AND STIFF,FIRM

20-10

CLAYEYSILT

FIRM TOSOFT

10-5

SOFTMARINEC S

20-5

CLAYSORGANICCLAYS

10-3

PEAT 5-1

84



43

Over-consolidated Clays; j=0Over- Consolidated Clays

,

P

,

f

0

c,

0

,

P

0

rv

,

P

,

f,

0

,

P

rv

loge1

Cloge1

C

lnm1ln

m1

r

0

r

0r

c

0

c

0

Ce13.2

Ce110lnmand

Ce13.2

Ce110lnm

85

Linear Elastic Soil; j=1

j,j,

Em100E,therefore

m1001

mj1 ,

0

,

f,

r

,

0,

r

fv

100Em

86



44

Janbu compared to e-logP

87

Oedometer Results in linear scale by Janbu

88



45

Calculation of Settlement

Determine soil profile to get initial effective stresses

Determine soil compressibility parameters, e-logP, Cc, Cr and Pc OR Janbu modulus number, m and mr

Determine final effective stresses due to imposed loads, excavations, fills, GWT changes etc

Divide each soil layer into sublayers, calculate strain caused by change from initial to final effective stresses in each sublayer

Calculate the settlement for each sublayer and the accumulated settlement

89

UNISETTLE Calculation of Settlement

90



46

Hand Calculation

91

UniSettle Input

92



47

InputLoading and Excavation

93

Results

94



48

Settlements Distribution

95

Alternative Conditions

96

Documents

Settlements and Elastic Stress Distribution (SEP 2011 Color)