Foundation Engineering CE 483 5. Settlement of shallow foundations Copy right reserved to Dr O. Hamza

Foundation EngineeringCE 483

5. Settlement of shallow foundations

Copy right reserved to Dr O. Hamza

CONTENTS

– Introduction– Vertical stress increase in a soil mass ..caused by foundation load

– Elastic settlement calculation– Consolidation settlement calculation– Field test (Bearing capacity with .Settlement consideration)

– References

CE 483 - Foundation Engineering - 5. Settlement of shallow foundations 2

Introduction


Principal criteria for foundation design Types of settlements Things required to calculate settlements

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When designing foundations, two principal criteria must be satisfied:

1. Maintaining Stability 2. Limiting Settlement

Stability against Bearing failure

Introduction

Principal criteria for foundation design

5

When designing foundations, two principal criteria must be satisfied:

1. Maintaining Stability 2. Limiting Settlement

Embankment and building constructed on soft ground (highly comprisable soil)

Soft ground

Crack

Introduction


Introduction



Therefore, the allowable bearing capacity qall should be the smaller of the following two:

The safe pressure that does not cause bearing failure

The safe pressure that does not cause unacceptable settlement

You learned how to calculate this (see previous chapter)

You will learn (in this chapter) how to estimate settlement

Introduction

Types of settlements


From structural consideration there are two types of settlements:

• Uniform settlement • Differential settlement

should be within the acceptable limit - given in the building code

Introduction


8

From geotechnical consideration, there are two types of settlements:

Time, t

Settlement, S

End of Construction

Immediate (or elastic) settlement, (mostly during construction time)

Consolidation settlement (occurs over long period of time)

• Primary consolidation,• Secondary consolidation,

Introduction


9

So, the total soil settlement ST may be contain one or more of these types:

Immediate settlement

elastic deformation with no change in water content

occurs rapidly during the application of load

occurs in sandy, silty and clayey soils

Introduction


10

The total settlement of a foundation can then be given as:

ST = Se + Sc + Ss

What information do we need to know to calculate these settlements?

Introduction

Things required to calculate settlements

11

Methods used for settlement calculations usually require to know the followings:

q [kPa]

Pressure bulb

Vertical stress increase Ds in soil caused by foundation load

Soil profile & parameters: e.g. E, n, Cc, CR, …

Net foundation load

Ds

Foundation (net load q, type, dimensions (B,L), Rigidity, …)

Vertical stress increase in a soil mass caused by foundation load


Pressure bulb Stress due to a concentrated load Stress due to a circularly loaded area Stress due to vertical line load Stress below rectangular area Average vertical stress increases in a layer Approximate method

13

Pressure bulbVertical stress increase in a soil mass caused by foundation load

• Structure built on ground causes increase in vertical stress (pressure) in the soil below. q [kPa]

Pressure bulb

Net foundation load

Ds

• This pressure increase is distributed to the soil in the form of a pressure bulb (or pressure isobars).

• The stresses Ds of the pressure bulb is determined by elastic theory.

14


2B

2bB

q= 100 kPa q= 100 kPa

0.1 q

0.2 q

Ds=

• The size and shape of the pressure bulbs depend on the size and shape of the loaded area e.g. point load, circular or rectangular loaded area, …et.

Pressure bulbs under largeand small round foundations

15


Comparison between Pressure Bulb for square

and strip footings

16

Stress due to a concentrated load

CE 483 - Foundation Engineering - 5. Settlement of shallow foundations


z

Boussinesq solution (1885)

17

Stress due to a circularly loaded area



z

18

Stress due to vertical line load



z

19

Stress below rectangular area



I

The vertical stress at a depth, z, below the corner of a rectangular subject to uniform pressure is:

Dsv

decreases with depth z

b

l

b

l

q

where:

q is the bearing pressure (net applied loading).

I is influence factor related to the shape of the loaded area. It is given by the following equation (Newmark, 1935):

Dsv = q. I

20

Stress below rectangular areaVertical stress increase in a soil mass caused by foundation load

m

n =

0.1

I

21


To work out the vertical stress increase below the center of foundation, use:

l = ½ L b = ½ B

Dsv = 4 q. I

where: L: foundation lengthB: foundation width

DsvDsv

b

l

b

l

L

B

22


The figure shows 2.5m-square footing constructed in sand layer underlain by clay. Calculate the increase of effective pressure in the clay layer (at the top, middle and bottom) using Newmark method.

Q=1000 kN

Example problem2.5x2.5m

Bed rock

Dry sand

Sand

3m

3m

3m

1.5m

ClayKey solution:

zLet’s assume ’t , ’m and ’b represent the increase in the effective pressure at the top, middle, and bottom of the clay, respectively, under the center of the footing.

23


Q=1000 kN

2.5 x 2.5m

Bed rock

Dry sand

Sand

3m

3m

3m

1.5m

Clay

Key solution (cont..):

z

l = ½ L = b = ½ B = 2.5/ 2 = 1.25 m

Ds’ = 4 q. I = 4 (1000/2.52) I = 640 I

Z m = l/z n = b/z I Ds’ [kPa]

4.5

6

7.5

’t

’m

’b

From the chart

24

Average vertical stress increases in a layerVertical stress increase in a soil mass caused by foundation load

• The increase in the vertical stress ’z in soil caused by a load q, applied over a limited area decreases with depth z

z

Compressible Layer

’z under the center of foundation varies

parabolically

q

25

Average vertical stress increases in a layerVertical stress increase in a soil mass caused by foundation load

• For settlement calculation, we can use the average pressure increase ’av , using weighted average method (Simpson’s rule):

z

where:

’t , ’m and ’b represent the increase in the effective pressure at the top, middle, and bottom of the layer, respectively.

Compressible Layer

’z under the center of foundation

q

26

Approximate methodsVertical stress increase in a soil mass caused by foundation load

GL

soil

q kPa

For wide uniformly distributed load, such as for vey wide embankment fill, the stress increase at any depth, z, can be given as:

z = q z

zdoes not decreases with depth z

27


For other cases, the vertical stress at any depth, z, can be calculated using 2:1 linear distribution method.

Z

2:1 method of finding stress increase under a foundation

q

2 vertical to 1 horizontal

2 vertical to 1 horizontal

B + Z

B

decr

ease

with

dep

th z

28


Z

ZZ

29


• For settlement calculation of a soil layer we usually use the average pressure increase ’av

• Based on the “Approximate Method”, ’av can be considered at the middle of the layer:

where ’m is the increase in the effective pressure at the middle of the layer.

Average pressure increase

z

Compressible Layer

H Li

near

dist

ributi

on

q

30


The following figure presents a rectangular foundation with length L= 3m and width B =2m. The net applied pressure is 100kPa.The ground profile consists of a clay layer of H=4m high. Sand is presented below and above this clay.

What is the increase of the effective pressure ’ at the middle of the layer

caused by the foundation loading q ?(use the approximate method)

Example problem q=100 kPa

z

Clay

Sand

Sand

2:1

1m

H

31


Using 2:1 linear distribution of approximate method, ’

at the middle of the layer can be calculated from:

Example problem- key solution

For Rectangular Foundation

where Z = ? = ……

Elastic settlement calculation


Contact Pressure and Settlement Profile Settlement based on general theory of Elasticity Elastic Settlement of saturated clayElastic Settlement of sandy soil: use of

strain .influence factor

33

Contact Pressure and Settlement ProfileElastic settlement calculation

CE 481 - Geotechnical Engineering II - 2. Compressibility of Soil 33

The contact pressure distribution and settlement profile under the foundation are not uniform and will depend on:

• flexibility of the foundation (flexible or rigid).• type of soil (clay, silt, sand, or gravel).

flexible flexible

rigid rigid

SAND

CLAY

CLAY

SAND

Contact pressure distribution Contact pressure distribution

Settlement profile

Settlement profile

34

Settlement based on theory of ElasticityElastic settlement calculation

Settlement Se =integration of vertical strain ez


35


For flexible shallow foundation subjected to a net force per unit area equal to Ds :

rigid

(based on elastic theory)

q (flexible)

More details about the calculation are given in Section 5.10 (Das, 2011).

q

36


Thick foundation Thin foundation

q


37


Due to the nonhomogeneous nature of soil deposits, the magnitude of Es may vary with depth. For that reason, Bowles (1987) recommended using a weighted average value of Es.

where:Es(i) soil modulus of elasticity within a depth Dz. whichever is smaller

Es(1)

Es(2)

Es(3)

H

B


38

Elastic Settlement of saturated clayElastic settlement calculation

Section 5.9 (Das, 2011)

39

Elastic Settlement of saturated clayElastic settlement calculation

40

Elastic Settlement of sandy soil: use of strain influence factor


(applied by the foundation)

(changes with depth)

(changes with depth)

41



42



is obtained from CPT test

qc

qcE

by interpolation we can find:

1 ≤ L/B ≤10

How about if there is no CPT date available?

Note

Use

43



44



The strain influence factor Iz can be graphically presented by this diagram

Iz0

Izp

Z1

Z2

Why does strain influence factor take this shape?

Maximum stain influence factor

Initial value

45



Iz0

Izp

Z1

Z2

= Iz0

Z1

Z2

= Izp or Iz(m)

= 0 Depth of influence

(required for the calculation of Izp)

46



Iz0

Izp

Z1

Z2Variables

Iz diagram varies with L/B

L

47



zZ

Izp Izp Izp

z

z

Z2 =2B

Z2 =

Z2 = 4B

Z1=B

Z1=0.5B

Z1

2

Iz0

10 ≤ L/B

General caseSquareStrip footingL/B = 1 1 ≤ L/B ≤10(Axisymmetric)

(Plane strain)

48



Z

* Calculated by interpolation between Case 1 and Case 3

Z2

Z1

Table summary of Iz profile

Z2

Z1

Z0

49


Z2

Z1

50



SquareL/B = 1

General case1 ≤ L/B ≤10

Strip10 ≤ L/B

Z IzZ Iz

Z Iz

0 0.1 0 0 0.2

0.5B B

2B 0 0 4B 02

Izp=Izp Izp

*

*

*

* Calculated by interpolation between Case 1 and Case 3

1. 2. 3.

Z2

Z1

51



Z2

Z1

52

In preparation for settlement calculation using strain influence method, the

soil is divided to smaller layers. Explain why the soil

is divided to 10 layers?

Class example

53



A 3 m wide strip foundation on a deposit of sand layer is shown along with the variation of modulus of elasticity of the soil (Es). The unit weight of sand is 18 kN/m3.

Calculate the elastic settlement of foundation using the strain influence factor. Assume there is a creep over a period of 10 years.

Class example

Solution

54



Solution

First step is to plot the variation of strain influence factor Iz with depth (to scale).

Strip footing10 ≤ L/B

Z Iz

0 0.2

B=3

4B=12 0

Izp

= 18 x (1.5 + 3) = ….

55



Solution (cont..)

Es profile is given.

We divide the soil into a number of layers depending on the variation of Iz and Es values with depth.

Then prepare the following table:

56



Solution (cont..)

57



More examples are given in Das’s text book – Section 5.12

Consolidation settlement calculation


Basic consolidation process Laboratory Consolidation Test Soil compressibility parameters Normally Consolidated and Overconsolidated Clays Calculation of Primary Consolidation Settlement Secondary Consolidation Settlement

59

Basic consolidation processConsolidation settlement calculation

When a saturated soil is loaded,

saturated soil

GL

• in coarse soils (sand & gravel) the settlement takes place instantaneously. How can this be explained?

• in fine soils (clay & silt): settlement takes far much more time to complete. Why?

Time (months or years)

Sett

lem

ent

coarse soils

Fine soils


http://images.google.co.uk/imgres?imgurl=http://www.tve.org/images/janus/uploaded/MakingHayWithClay4.jpg&imgrefurl=http://www.tve.org/ho/doc.cfm?aid=1401&lang=English&h=252&w=360&sz=34&tbnid=OwokP1OoMKp_NM:&tbnh=81&tbnw=117&hl=en&start=177&prev=/images?q=clay+soil&start=160&svnum=10&hl=en&lr=&sa=N

60

Basic consolidation processConsolidation settlement calculation

In coarse soils (sands & gravels) any volume change resulting from a change in loading occurs immediately; increases in pore pressures are dissipated rapidly due to high permeability. This is called drained loading.

In fine soils (silts & clays) - with low permeabilities - the soil is undrained as the load is applied. Slow seepage occurs and the excess pore pressures dissipate slowly, consolidation settlement occurs.

So, consolidation settlement: is decrease in voids volume as pore-water is squeezed out of the soil. It is mostly significant in fine soil (clay & silt).

http://images.google.co.uk/imgres?imgurl=http://www.tve.org/images/janus/uploaded/MakingHayWithClay4.jpg&imgrefurl=http://www.tve.org/ho/doc.cfm?aid=1401&lang=English&h=252&w=360&sz=34&tbnid=OwokP1OoMKp_NM:&tbnh=81&tbnw=117&hl=en&start=177&prev=/images?q=clay+soil&start=160&svnum=10&hl=en&lr=&sa=N

61


Laboratory Consolidation Test

• Data obtained from laboratory testing can be used to predict consolidation settlement reasonably, but rate is often poorly estimated.

• 1-D field consolidation can be simulated in Laboratory.

field

GL

lab

undisturbed soil specimen

Dia = 50-75 mmHeight = 20-30 mm

porous stone

Wide foundation simulation of 1-D field consolidation in Lab

Saturated clay

Sand or Drainage layer

62


Laboratory Consolidation Test

Typical plot of e against log s’

Effective pressure, s’ (log scale)

Typical results of laboratory consolidation test

The study of the change in the void ratio of the specimen with pressure will allow us to find soil compressibility parameters.

What are soil compressibility parameters?


63


Soil compressibility parameters

log ’

void

rati

o,

e

1

Cc

Cc compression index

Cs : swell index

1

1Cs

For one-dimensional compression and swelling there are simple relationships between the void ratio, e, and the logarithm of the vertical effective stress, s ‘.

Cs

CC and Cs are slopes of the e–log s‘ plot

Note. Swell index (Cs) may be also called re-compression index (Cr)

or Cr

64

• These indexes are required for the calculation of field settlement caused by consolidation.

• These indexes is best determined by the laboratory test results for void ratio, e, and pressure s’ (as shown above).

• Several empirical expressions have been also suggested:

For undisturbed clays, Skempton (1944)

For natural clays, Rendon-Herrero (1983)

(Kulhawy and Mayne, 1990)

PI: Plasticity IndexLL: Liquid Limit

GS: Specific Gravitye0 : in situ void ratio



65

Compression and Swell Indexes of some Natural Soils




66

Void

ratio

, e


The upper part of the e –log s’ plot is somewhat curved with a flat slope, followed by a linear relationship having a steeper slope.

This is can be explained:

• A soil in the field at some depth has been subjected to a certain maximum effective past pressure in its geologic history.

• This maximum effective past pressure may be equal to or less than the existing effective overburden pressure at the time of sampling.

Normal Com

pression

Swelling re-compression

Normally Consolidated and Overconsolidated ClaysConsolidation settlement calculation


67

Void

ratio

, e

s’c


Casagrande (1936) suggested a simple graphic construction to determine the preconsolidation pressure s’c from the laboratory e–log s‘ plot.

In general the overconsolidation ratio (OCR) for a soil can be defined as:

where s ’ is the present effective vertical pressure.

Normally Consolidated and Overconsolidated ClaysConsolidation settlement calculation

If OCR > 1 overconsolidated soilIf OCR = 1 normally consolidated

68

Saturated clay

Ground level (GL) q kPa

Ho

Time = 0+

e = eo

H

Time =

e = eo - e

average vertical strain = oH

H

Let us consider a saturated clay layer of initial thickness Ho (or H), where the average effective pressure increases, from s ’0 to s ’ 0 +Ds ’ causing consolidation settlement Sc= DH.

s ’ 0 + Ds ’

Sand layer

s ’ 0

Calculation of Primary Consolidation Settlement


69

Consider an element of soil where the volume of solid, Vs = 1 initially

e

1

eo

Time = 0+ Time =

average vertical strain =oe

e

1

Vs



70

Equating the two expressions for average vertical strain,

oe

e

1

oH

H

consolidation settlement

initial thickness of clay layer initial void ratio

change in void ratio

as, Sc = DH

How to get the changes in void ratio De ?



Note: is also called 71

For normally consolidated clay ( s ’ 0 > s c’ )

OA or AD on the graph:

Thus,

where:CC is “Compression Index” obtained from the slope of the e–log s‘ plot. CC is soil parameter.

c

s c’ = Preconsolidation pressure.



72

For over-consolidated clay ( s ’ 0 < s c’ )

There are two cases:

• Case (1): when s ’ 0 +Ds ’ ≤ s c’

• Case (2): when s ’ 0 +Ds ’ > s c’

c





73


Case (1): when s ’ 0 +Ds ’ ≤ s c’

i.e. along the line BC on the laboratory rebound curve.

Thus,

• Where CS is slope of rebound curve. • CS or Cr is soil parameter and called “Swell Index”

or re-compression index.

c


Calculation of Primary Consolidation SettlementConsolidation settlement calculation

74


Case (2): when s ’ 0 +Ds ’ > s c’

i.e. along the line BC then CD.

Thus,

• CS = Swell Index or recompression index Cr

• CC = Compression Index

c

s c’ = Pre-consolidation pressure.


75

Example problem

A soil layer 3 m thick is consolidated under an effective vertical stress of 50 kPa at a void ratio of 0.891. If the compression index Cc of the soil is 0.138, what is the settlement, when the effective vertical stress is increased to 100 kPa.

Key Solution

The consolidation settlement for a layer of thickness H can be represented by the compression index Cc defined by:



76

Example problem

A soil profile is shown in the figure. If a uniformly distributed load is applied at the ground surface, what will be the settlement of the clay layer caused by primary consolidation?

We are given that sc for the clay is 125 kN/m2 and Cs=1/6 Cc , where:



q

77

Solution



NOTE:If the loaded area is limited (e.g. rectangular foundation) we will need to compute the stress increase ‘ within the soil mass using Boussinesq method or other approach assuming elasticity.

For wide uniformly distributed load, such as given in the question, the stress increase at any depth, z, can be given as:

‘ = q = 50 kPa

The important procedure for determining consolidation settlement is to calculate:

• o‘ the initial effective pressure at the middle of compressible soil layer • ‘ the average net effective stress increase in the compressible soil layer.

78



Solution (cont..)

79

Solution (cont..)


80


Time rate of consolidation


• You learned above how to calculate the ultimate settlement of primary consolidation Sc (at the end of consolidation).

• However this settlement usually takes long time, much longer than the time of construction.

• And we may need to know the settlement at a specific time.

Time, t

Settlement, S(time)

End of Construction

End of primary consolidation

81


Time rate of consolidation

H ClayHdr

Hdr

Hdr

Permeable layer

Cv is obtained from laboratory testing

U = the degree of consolidation

CE 481 - Geotechnical Engineering II - 2. Compressibility of Soil 82

• In some soils (especially recent organic soils) the compression continues under constant loading after all of the excess pore pressure has dissipated, i.e. after primary consolidation has ceased.

• This is called secondary compression or creep, and it is due to plastic adjustment of soil fabrics.

• This settlement can be calculated using the secondary compression index, Ca.

• The Log-Time plot (of the consolidation test) can be used to estimate the coefficient of secondary compression Ca.

void

rati

o,

et1 t2

Deep

Secondary Consolidation SettlementConsolidation settlement calculation

83

• The magnitude of the secondary consolidation can be calculated as:

void

rati

o,

et1 t2

Deep

where:

ep void ratio at the end of primary consolidation.H thickness of clay layer.• The general magnitudes of Ca is observed to

correlate with Cc as follows:

Secondary Consolidation SettlementConsolidation settlement calculation

Field test (Bearing capacity with settlement consideration)


Plate load test Standard Penetration Test (SPT) Cone Penetration Test (CPT)

85


Plate load test

Plate Load Test is a field test for determining the ultimate bearing capacity of soil and the likely settlement under a given load (ASTM D-1194-72).

The Plate Load Test basically consists of loading a steel plate placed at the foundation level and recording the settlements corresponding to each load increment.

http://www.theconstructioncivil.org/foundation-or-footings

86

Plate load test

BF = width of the proposed foundation Bp = width of test plateSp= settlement of test plate for a given intensity of load, qSF = settlement of the foundation for a given intensity of load, q


87

Standard Penetration Test (SPT)

• Bearing Capacity for sandy soil can be based on SPT N value and settlement consideration.

• Meyerhof (1956) proposed a correlation for the net allowable bearing pressure for foundations with the standard penetration resistance, N60.


88

Standard Penetration Test (SPT)

• Bearing Capacity for sandy soil can be based on CPT value and tolerable settlement.

• Meyerhof (1956) proposed a correlation for the net allowable bearing pressure for foundations with the cone resistance, qc .



References

89CE 483 - Foundation Engineering - 5. Settlement of shallow foundations

1. Braja M Das, 2011, Principles of Foundation Engineering, 7th ed, Chapter- 5.

2. Previous course materials and presentations at KSU.3. Geotechnical on the web:

http://environment.uwe.ac.uk/geocal/foundations/founbear.htm.4. Andrew Bond and Andrew Harris, 2008, Decoding Eurocode 7, London.5. The Institution of Structural Engineers library:

www.istructe.org/resources-centre/library

http://environment.uwe.ac.uk/geocal/foundations/founbear.htm

http://www.istructe.org/resources-centre/library

Documents

Foundation Engineering CE 483 5. Settlement of shallow foundations Copy right reserved to Dr O. Hamza