10) Foundation Settlements

10) Foundation Settlements

Immediate (Elastic) settlement
Both clays and sands

Time dependent settlement (clays)

(Primary) consolidation settlement Secondary compression settlements (significant in highly plastic and organic soils)

- An example of time-displacement curve from consolidation tests of clays.

Primary

consolidation Secondary compression

time (log scale) t100

displacement

Settlements due to elastic deformations of soil mass.

Based on the theory of elasticity, the elastic settlement of a shallow foundation Se can be defined as,

∫

∫

= ^H _{z s x s y}

s H

z

e dz

dz E

S 0ε 1 0( σ µ σ µ σ )

where, E_s : modulus of elasticity of soil µs : Poisson’s ratio of soil

Theoretically, for Df ⁼⁰, H =∞ and perfectly flexible foundations, '

) 1

( ²

0 µ_s α

s

e E

S = Bq − (Harr, 1966)

where, α' is a is a function of shape and flexibility of foundation and location of concerning points.

flexible foundation : at center, α'=α at corner, α'=α/2

average, α'=α_ave rigid foundation : α'=α_r

Comments

Harr’s equation generally results in too conservative value (i.e. overestimating settlement).

a) H (depth to the relatively incompressible layer) < 2B ~ 3B S _e b) The deeper the embedment D_f , the lesser is S . _e

Es may vary with depth.

Bowles (1987) recommended to use a weighted average of E^s,

z z E

Σ E

∆

=

∆Z1

∆Z2

∆Z3

∆Z4 Es(4)

Es(3)

Es(2)

Es(1)

H

Es

Estimation of elastic settlements by Mayne and Poulous (1999), - It takes into account

1) the rigidity of the foundation

2) the depth of embedment of the foundation

3) the increase in the modulus of elasticity of the soil with depth 4) the location of rigid layers at a limited depth

) 1

( ²

0 0

s E

F G e

e E

I I I B

S = q −

µ

where, B_e : the equivalent diameter =

π BL

4 for rectangular foundation = B for circular foundation

IG : influence factor for the variation of E_s(=E₀ +kz) with depth

= _







 =

e

e B

H kB

f β( E⁰ ),
Fig. 5.17

IF : foundation rigidity correction factor =

3

0

2

2 10

6 . 4

1 4

























+ +

+

e e f

B t B k

E E

π
Fig. 5.18

IE : foundation embedment correction factor =

) 6 . 1 )(

4 . 0 22 . 1 exp(

5 . 3 1 1

+

−

−

f e

s D

µ B
Fig. 5.19

<Figure 5.17 Variation of I_G with β >

<Figure 5.18 Variation of rigidity correction factor I_F with flexibility factor K_F>

<Figure 5.19 embedment correction factor I_E with D /_F B_e>

IE

Immediate settlement of sandy soil : use of strain influence factor (Schmertmann and Hartman (1978))

∑ ^∆

−

=

s z

e

z

E q I

q C C S

0 2

1

( )

where :

C = A correction factor for the depth of foundation embedment 1

(=1−0.5[q/(q−q)])

C = A correction factor for creep 2

=

1 . log0 2 . 0

1 t

+  t in years

I = Strain influence factor (chiefly related to shear stress increase z

in soil mass due to foundation load)

For square, circular ft. For strip footing (L/B >10)

=0

z I_z =0.1 z=0 I_z =0.2

B

z₁ =0.5 I_z =0.5 z =₁ B I_z =0.5 B

z₂ =2 I_z =0 z₂=4B I_z =0

For rectangular ft, interpolate two cases.

- This method is effective for layered soils (E is varying with depth.)

Determination of Young’s modulus

-E and _s µ_s can be determined from the laboratory tests.

- Correlation between E and SPT and CPT results. _s

Schmertmann(1970) ; for sands

8N60

p E

a

s =

where N₆₀ : standard penetration resistance pa : atmosphere pressure ≈ 100kPa

c

s q

E =2

where q_c : static cone resistance

Schmertmann and Hartman(1978) ; for strain influence factors,

c

s q

E =2.5 for square and circular foundation

c

s q

E =3.5 for strip foundation

Es for clays

c to c

E =250 500 for normally consolidation clays

Primary consolidation  Secondary compression 

Consolidation settlement

∫

= dz

S_c ε_v (ε_v : vertical strain)

∫

= dz

e e 1 0

'

σp : Maximum past pressure C : Compression indexc

C : Swelling indexs '

σ0 : Average present effective stress

'

σave

∆ : Average increase of pressure on the clay layer by loading e0

Cs

∆e

e

p

'

σ

Cc p'

σ

0' σ

'

0' σave

σ +∆

- When thickness of clay layer is H and initial void ratio is e_c 0,

' ) ' log( '

1 log '

1

0 0

'

0 p

ave p

c p c

s c

c e

C H e

C S H

σ σ

∆ + σ + +

σ σ

= +

For normally consolidated clay (σ'₀=σ'_p),

' ) ' log( '

1 ₀

0

0 σ

σ

σ _ave

c c

c e

C

S H +∆

= +

For overconsolidated clay (σ'₀<σ'_p),

a) )

' ' log( '

' 1 '

'

0 0 0

0 σ

σ σ σ

σ

σ _{ave p c} ^{c s ave}

e C

S H +∆

= +

≤

∆ +

b) ' ' )

1 log(

' ) 1 log(

' '

' '

0 0

0 '

0 0

p ave c

p c s

c c p

ave e

C H e

C S H

σ σ σ σ

σ σ σ

σ ^+∆

+ +

= +

>

∆ +

i) ∆σ_av=1/6(∆σ_t +4∆σ_m+∆σ_b)

σ0 = effective stress at the middle of clay layer.

⇒ Calculate S _c

ii) Divide the clay layer into several thin layers

⇒ ∆σ and σ₀' are obtained from the middle of each thin layers.

⇒ Calculate settlements of each thin layers, S . _ci

⇒ Total consolidation settlement, ^Sc=

∑

Estimation of stress increase on the clay layer due to external loads (Uniform load and flexible foundation)

- ∆σ determined from Bousinesq approach

(Assuming soil as a semi-infinite, elasitc, isotopic, and homogeneous medium.)

m = B/z, n=L/z

a) The stress increase ∆σ below the corner of rectangular loaded area.

I q₀

=

∆σ

where values of I are given in Table 5.2.

(or ∆σ can be directly calculated with Eq (5.5) and (5.6) in textbook.)

b) Stress increase below any point below rectangular loaded area.

) (I₁ I₂ I₃ I₄

q_o + + +

=

∆σ

- Approximate method for ∆p (2:1 method)

) ( )

0 BL/{B z L z

q + +

=

∆σ

Case study (p.235)

Secondary compression settlement

) / log(

log

log _{2 1} t₂ t₁ e t

t

C e = ∆

−

= ∆

α

p c p s

c t

H t e

S C log

) 1

( = +^α

where t_p= time at the end of primary consolidation C_α =(1+e_p)C_α'

Cα changes with consolidation stress, so it should be selected based on present stress level. (C for OC soil is quite lower than that for NC soil.) _α

-

α(%) C

Skempton-Bjerrum modification for consolidation settlement

(Two or three dimensional effect on primary consolidation settlement.)

Conventionally, σ1

∆

=

∆u

But practically,

)

( _{1 3}

3 σ σ

σ + ∆ −∆

∆

=

∆u A

where A=Pore pressure parameter

= f(stress history, soil type, ****)

∫

= )/ )

(1 (

1 ₀ , u

e m e

e dz S e

o v

al

convention

⁼

∫

dz m_v∆σ₁

=

∫

where mv= volume coefficient of compressibity

∫

− = m udz

S_{S B v}

Hc ∆σ₃

σ1

∆

q

∫

∫

∆

∆

−

∆ +

= ∆

= ⁻

dz

dz A

S K S

conv B S

1 3 1

3 ( )]

[

σ σ σ σ

(1 ) ( )

1

3 settlement ratio dz

dz A

A =

∆

− ∆ +

=

∫

∫

σ σ

For H =thickness of clay layer, _c

∫

∫

∆

− ∆ +

= Hc

c

dz dz A

A K

H

0 1

0 3

) 1 (

σ σ

Generally, A < 0.5 for overconsolidated clays.

= 0.5 ~ 1.0 for normally consolidated clays.

> 1.0 for sensitive clays.

K is a function of A, shape of foundation and thickness of clay layer,

- Procedure for S_{c(Skempton−Bjerrum)}. 1. Determine S_{c(conventional)}. 2. Determine A, H_c/B. 3. Obtain K from the figure.

4. Calculate S_{c(Skempton−Bjerrum)}.

- Note K