[FOUNDATION ENGINEERING] CHAPTER FOUR FOUNDATION SETTLEMENT · [FOUNDATION ENGINEERING] Assist....
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[FOUNDATION ENGINEERING] Assist. lecturer : Haidar Hassan Haidar
CHAPTER FOUR
FOUNDATION SETTLEMENT
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CH.4 FOUNDATION SETTLEMENT
4.1 Introduction
In general, settlement caused in soil due to loading may be divided into the
following categories:
A. Immediate settlement (Si), which is due to the elastic deformation of dry
soils and of moist and saturated soils without any change in the water
contant.
B. Consolidation settlement(Sc), which is the result of volume change in
saturated fine grained soils due to the expulsion of water occupying the
void spaces.
C. Secondary compression (Ss), which is due to the plastic adjustment of soil
fabrics. It is measured after complete dissipation of excess pore water
pressure.
The total settlement (St) is the sum of the above three components.
i.e., (St = Si + Sc + Ss).
[FOUNDATION ENGINEERING] Assist. lecturer : Haidar Hassan Haidar
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4.2 Contact pressure
The pressure transformed to the soil at foundation level and distribution
beneath the loaded area depend on rigidity of foundation structure and nature
of the soil. The actual contact pressure distribution is as following:
Note: in practice it is generally assumed that the pressure distribution
beneath the loaded area uniform for concentric loading and linearly
increasing for eccentric loading.
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4.3Stresses in soil mass
The soil is assumed as: semi-infinte in extent, isotropic, homogeneous,
elastic and obeys hooke's law. The stresses at a point due to more than one
surface load are obtained by superposionition.
1) Point load
2) Vertical line load
See Table (4-1)
3) Uniform vertical loading on a strip
See Table (4.2)
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4) Liner increasing vertical loading on a strip
See Table (4-3)
5) Vertical triangular load on strip
See Fig. (4-1)
6) Circularly load ( vertical)
See Fig. (4-2)
7) Rectangular loaded area
See Fig. (4-3)
8) Embankment loading
See Fig. (4-4)
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Table 4-1 Table 4-2
Values of σz/q , σx/q and τxz/q
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Table 4-3
Figure 4-1
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Figure 4-2
Figure 4-3
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Figure 4-4
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Example 1
Calculate the σz at 10m below the edge of circular footing (diameter =25m)
which have qo = 122 kPa.
Ans. Use figure( 4-2)
Z/r = 10/12.5= 0.8
X/r= 12.5/12.5 = 1
I = 35
σz = I x qo /100 =35x122/100= 42.7 kpa
Example 2
Find the stress beneath the
the corner (Z=2 m)
and center (Z=0,1,2,3AND 4)
for the square footing shown.
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Example 3
Find the stress @ point O @ depth Z=2m
Knowing that qo =400 kpa
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4.4 Immediate (elastic) settlement
4.4.1
Si=
(1-v2).Iw.F3
Where:
Iw : influence factor, [see table (4.4)].
B: lesser dimension of footing
Es: young's modulus of soil,[ see table (4-5)]
v : poisons ratio of soil [see table (4-6)].
F3: depth correction factor.
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4.4.2 (v = 0.5 , i.e, saturated clay, ∅=0)
Si. = μ1 μo
Where
μ1 : correct factor for thickness of elastic soil layer.
Μo : correct factor for depth of embedment of footing.
See figure (4-7)
Figure (4-7)
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Example 4
Estimate the immediate settlement beneath the center and the corner of the
adjacent flexible square footing.
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4.4.3 CPT
Schmertman proposed a method based on CPT to give prediction of
settlement.
Si= C1 C2 q ∑
Where
Iz : strain influence factor.
C1: correction factor for depth of embedment.
C1 = 1-0.5 log (q'/q)
C2 : correction factor to account for the creep in soil
C2=1+0.2 log (t/0.1)
q' : effective overburden pressure @ foundation level.
q : net foundation pressure increase.
t : time in years.
E = 2qc
qc : cone point resistance.
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Example 5
Predict the immediate settlement after (10) year for cohesionless soil as
shown. If it is subjected to a concentric load of (700) kN.
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4.5 Consolidation settlement
4.5.1 Compressibility characteristics
The compressibility of the clay can be represented by one of the following
coefficients:
A- The coefficient of volume change (mv), defined as the volume change
per unit volume per unit increase in effective stress. It is a function of
the stress range for a particular soil and has the units of (L2/F).
mv =
(
)
Where:
eo :initial void ratio
Ho :initial thickness
σo' : intial effective overburden stress.
B- The compression index (Cc), which is the slope of the liner portion of
the (e-log σ') plot (figure 4-8).
Cc =
For normally consolidation clay, it can be estimated using the following
approximate formulae: Cc = 0.009(L.L – 10)
The expansion portion of the (e-log σ') plot can be approximate to a straight
line, the slop of which is referred to as the expansion index or recompression
index (Cr), [Cr (0.1-0.2) Cc]
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4.5.2 pre-consolidation pressure(σc')
It is the maximum effective vertical stress that has acted on the clay in the past.
It can be estimated from (e-log σ') curve using the empirical method shown in
figure (4-9) which is proposed by Gasagrande.
A term (over consolidation ratio) can be calculated from dividing this pressure
by the current effective overburden pressure.
According, there are two types of clay soils:
A. Normally consolidation clay (O.C.R = 1), present effective overburden
pressure is the maximum pressure that the soil has been subjected in the
past.
B. Over consolidation clay (O.C.R > 1) present effective overburden
pressure is less than that the soil has been subjected in the past.
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4.5.3 calculation of consolidation settlement
A. for N.C. clay
Sc = c
eo Ho log
B. For O.C.clay and (σ'o σ) σ
Sc = r
eo Ho log
C. For O.C.clay and (σ'o σ) σ
Sc = r
eo Ho log
σ
+ = c
eo Ho log
σ
ffect of ( σ) decrease with depth
For more realistic settlement prediction,
1. Use ( σ av.) =
( σ top + 4 σ middle σ bottom)
2. Divide the clay layer in to n sub-layer
Sc =∑ c ini=
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Example 6
Estimate the consolidation settlement of the square footing shown
below.
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Example 7
Check the suitability of the circular raft foundation for the tower shown in
below if the maximum permissible consolidation settlement is (50 mm).
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4.6 Secondary Compression Settlement ( Ss)
Sc =
ep Hp log
Where:
: coefficient of secondary compression.
tp : time required for 100% primary consolidation.
ep: void ratio at the end of primary consolidation.
Hp : thickness of layer at the end of primary consolidation.