[FOUNDATION ENGINEERING] CHAPTER FOUR FOUNDATION SETTLEMENT · [FOUNDATION ENGINEERING] Assist. lecturer : Haidar Hassan Haidar CHAPTER FOUR FOUNDATION SETTLEMENT 2 4.2 Contact pressure

[FOUNDATION ENGINEERING] Assist. lecturer : Haidar Hassan Haidar

CHAPTER FOUR

FOUNDATION SETTLEMENT

1

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).


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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.

[FOUNDATION ENGINEERING] CHAPTER FOUR FOUNDATION SETTLEMENT · [FOUNDATION ENGINEERING] Assist. lecturer : Haidar Hassan Haidar CHAPTER FOUR FOUNDATION SETTLEMENT 2 4.2 Contact pressure

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