settlement of shallow foundation. 2 types of settlement elastic ( immediate ) settlement time...

SETTLEMENTOf

SHALLOW FOUNDATION

2 types of settlementElastic ( Immediate ) settlementTime independentCauses:

Elastic deformation of dry soil particles

Consolidation settlementTime dependantCauses:

Water expulsion

CONSOLIDATION SETTLEMENT

To calculate the consolidation settlement we have to perform

ONE DIMENSIONAL CONSOLIDATION

TEST

Consolidometer

Audiometer

time

deformation

P1

P2

P3

P4

P4<< P3 << P2 << P1

I

II

III

I – Initial compression II – Primary ConsolidationIII – Secondary Settlement I – Initial compression S1

Causes: imperfect contact surface, loading, particles relocation

II – Primary Consolidation S2

Causes: water expulsion

III – Secondary Settlement S3

Causes: Particles relocation, Particles deformation, Particles destruction

Total settlement S = S1 + S2 + S3

eo

e1

e2

P1 P2 Log P

e

While P2 is greater than P1

e2 is smaller than e1

Cc

Cc Compression Index

We can use any curve because the slope is the same

The slope from the curveCc = 0.009 ( LL – 10 ) for undisturbed samplesCc = 0.007 ( LL – 10 ) for remolded samples

Log P

e

Soil History

We can find Soil History by finding what is called

PRECONSOLIDATION PRESSUREOrMax Past Effective Overburden

Pressure Pc

e

Log PPc

Based on values of Pc

Clay soils may be

NCC – Normally Consolidated ClayOCC – Over Consolidated Clay

NCC – Normally Consolidated Clay. Where Po is greater than Pc

Pc = Max Past Effective Overburden

PressurePo = Max Present Effective

Overburden Pressure

Pc Po

P

Cc

The slope of the curve in this area is Cc

OCC – Over Consolidated Clay. Where Po is smaller than Pc

Pc = Max Past Effective Overburden

PressurePo = Max Present Effective

Overburden Pressure

PcPo

P

The slope of the curve in this area is Cs Cs

Pc

Cc

Cs

NCCOCC

Total settlement S = Si + Sp + Ss

•INITIAL COMPRESSION ( Si ) •PRIMARY CONSOLIDATION SETTLEMENT ( Sp )•SECONDARY SETTLEMENT ( Ss )

ep

t2

t1

Cα

=/log( )

ep

Ss = C’α H

log( )

C’α =

Cα

INITIAL COMPRESSION ( Si )

Si = q B Iρ

Where:q- net applied pressureB- width of footing

-Poisson’s ratio (tab. 6.6 p 167)-E- modulus of elasticity (tab. 6.5 p 167)Iρ- influence factor (tab. 6.4 p 167)

-Poisson’s ratio (tab. 6.6 p 167)-E- modulus of elasticity (tab. 6.5 p 167)Iρ- influence factor (tab. 6.4 p 167)

TIME RATE OF SETTLEMENT

summary

S =

Si = q B IρImmediate settlement

Primary consolidation

Secondary settlement

Ss = C’α H log( )

NCC

OCC

P0 + ΔP Pc

P0 + ΔP Pc <Consolidation settlement

Initial compression

Si = q B Iρ

Settlement due to surcharge

S = f ( P, soil, Z, X, load application type )

Load application types: point line stripcirclesquarerectangleirregular

The settlement of a foundation can be divided into two major categories:

A- Elastic or immediate settlement

B- Consolidation settlement

Time

Sett

lem

en

t Consolidation Settlement

Secondary Settlement

Immediate or Elastic Settlement

For the calculation of foundation settlement, it is required to determine the vertical stress increase in the soil mass due to the load applied on the foundation.

This chapter is divided into the following three parts:1. Procedure for calculation of vertical

stress increase2. Elastic settlement calculation3. Consolidation settlement calculation

dr. isam jardaneh / foundation engineering 61303 / 2010

2 : 1 Method

dr. isam jardaneh / foundation engineering 61303 / 2010

Average Vertical Stress Increase Due to a Rectangularly Loaded

AreaAs suggested by Griffiths 1984, to find average pressure increase between z = H1 and z = H2 below the corner of a uniformly loaded rectangular area

Elastic SettlementElastic settlement Based on The Theory

of Elasticity

Elastic SettlementBased on The Theory of Elasticity

dr. isam jardaneh / foundation engineering 61303 / 2010

dr. isam jardaneh / foundation engineering 61303 / 2010

Elastic Settlement of Foundation on Saturated Clay

Settlement of Sandy Soil: Use of Strain Influence Factor

Continuous

Footing

Need Interpolation ???

Example

3 x 3 m

10000

8000

E KN/m²

16000

1.5m

3.0m

1.0m

q = 160 KN/m²

¯

γ = 17.8 KN/mᶟ

FindElastic Settlement After 5 years

UsingInfluence Factor Method

3x3m

0.1

0.5

2m

2.5m

0.5m

1m

Depth

m

ΔZ

m

Es

KN/m²

AverageIz

----- ΔZ

mᶟ/KN

0.0 – 1.0

1.0 8000 0.233 0.291x10¯⁴

1.0 – 1.5

0.5 10000 0.433 0.217x10¯⁴

1.5 – 4.0

2.5 10000 0.361 0.903x10¯⁴

4.0 – 6.0

2.0 16000 0.111 0.139x10¯⁴

∑ = 1.55x10¯⁴

Es

Iz

C1 = 1-0.5 ( ---- ) = 1-0.5 [-------------] = 0.9

C2 = 1 + 0.2 log (5/0.1) = 1.34

Se = C1 C2 ( q – q ) ∑ (Iz/E)Δz

Se = 24.9 mm

q - q

q_ 17.8x

1.5160 – (17.8x1.5)

‒

Range of Materials Parameters for Computing Settlement

Range of Materials Parameters for Computing Settlement

dr. isam jardaneh / foundation engineering 61303 / 2010

Example 1

Example 2

Problem # 1

Problem # 2

Problem # 3

Estimate the consolidation settlement of the clay layer shown in Figure below using 2:1 method and trapezoidal rule. Note 1 ton = 2000 lb.

Problem # 4