settlement of shallow foundation. 2 types of settlement elastic ( immediate ) settlement time...
TRANSCRIPT
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SETTLEMENTOf
SHALLOW FOUNDATION
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2 types of settlementElastic ( Immediate ) settlementTime independentCauses:
Elastic deformation of dry soil particles
Consolidation settlementTime dependantCauses:
Water expulsion
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CONSOLIDATION SETTLEMENT
To calculate the consolidation settlement we have to perform
ONE DIMENSIONAL CONSOLIDATION
TEST
Consolidometer
Audiometer
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time
deformation
P1
P2
P3
P4
P4<< P3 << P2 << P1
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I
II
III
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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
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eo
e1
e2
P1 P2 Log P
e
While P2 is greater than P1
e2 is smaller than e1
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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
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Soil History
We can find Soil History by finding what is called
PRECONSOLIDATION PRESSUREOrMax Past Effective Overburden
Pressure Pc
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e
Log PPc
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Based on values of Pc
Clay soils may be
NCC – Normally Consolidated ClayOCC – Over Consolidated Clay
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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
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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
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Pc
Cc
Cs
NCCOCC
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Total settlement S = Si + Sp + Ss
•INITIAL COMPRESSION ( Si ) •PRIMARY CONSOLIDATION SETTLEMENT ( Sp )•SECONDARY SETTLEMENT ( Ss )
ep
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t2
t1
Cα
=/log( )
ep
Ss = C’α H
log( )
C’α =
Cα
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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)
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TIME RATE OF SETTLEMENT
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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
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Settlement due to surcharge
S = f ( P, soil, Z, X, load application type )
Load application types: point line stripcirclesquarerectangleirregular
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The settlement of a foundation can be divided into two major categories:
A- Elastic or immediate settlement
B- Consolidation settlement
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Time
Sett
lem
en
t Consolidation Settlement
Secondary Settlement
Immediate or Elastic Settlement
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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
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dr. isam jardaneh / foundation engineering 61303 / 2010
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2 : 1 Method
dr. isam jardaneh / foundation engineering 61303 / 2010
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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
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Elastic SettlementElastic settlement Based on The Theory
of Elasticity
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Elastic SettlementBased on The Theory of Elasticity
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dr. isam jardaneh / foundation engineering 61303 / 2010
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dr. isam jardaneh / foundation engineering 61303 / 2010
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Elastic Settlement of Foundation on Saturated Clay
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Settlement of Sandy Soil: Use of Strain Influence Factor
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Continuous
Footing
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Need Interpolation ???
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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
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0.1
0.5
2m
2.5m
0.5m
1m
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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
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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)
‒
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Range of Materials Parameters for Computing Settlement
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Range of Materials Parameters for Computing Settlement
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dr. isam jardaneh / foundation engineering 61303 / 2010
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Example 1
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Example 2
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Problem # 1
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Problem # 2
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Problem # 3
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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