1. Kamal Tawfiq, Ph.D., P.E., F.ASCE
Soil Settlement By
Kamal Tawfiq, Ph.D., P.E., F.ASCE
Fall 2010

2. { { Soil Settlement: Stotal = Se + Sc
Total Soil Settlement = Elastic Settlement + Consolidation Settlement
Stotal = Se + Sc {
Load Type (Rigid; Flexible)
Elastic Settlement or Immediate Settlement depends on
Settlement Location (Center or Corner) {
Theory of Elasticity
Elastic Settlement
Time Depended Elastic Settlement (Schmertman & Hartman Method (1978)
Elastic settlement occurs in sandy, silty, and clayey soils.
By: Kamal Tawfiq, Ph.D., P.E.

3. Consolidation Settlement (Time Dependent Settlement)
By: Kamal Tawfiq, Ph.D., P.E.
Consolidation Settlement (Time Dependent Settlement)
* Consolidation settlement occurs in cohesive soils due to the expulsion of the water from the voids.
* Because of the soil permeability the rate of settlement may varied from soil to another.
* Also the variation in the rate of consolidation settlement depends on the boundary conditions.
SConsolidation = Sprimary + Ssecondary
Primary Consolidation Volume change is due to reduction in pore water pressure
Secondary Consolidation Volume change is due to the rearrangement of the soil particles
(No pore water pressure change, Δu = 0, occurs after the primary consolidation)
Water Table (W.T.)
Expulsion of the water
When the water in the voids starts to flow out of the soil matrix due to consolidation of the clay layer. Consequently, the excess pore water pressure (Du) will reduce, and the void ratio (e) of the soil matrix will reduce too.
Water
Voids
Solids

4. Elastic Settlement Se = (1 - μs) α Se = (1 - μs) α Es 2 Es Bqo
(corner of the flexible foundation) 2 Es
Bqo
Se = (1 - μs) α 2
(center of the flexible foundation) 1 p
Where α = [ ln ( √1 + m2 + m / √1 + m2 - m ) + m. ln ( √1 + m2 + 1 / √1 + m )
m = B/L
B = width of foundation
L = length of foundation
By: Kamal Tawfiq, Ph.D., P.E.

5. Se = α, αav, αr 3.0 2.5 α αav αr 2.0 1.5 For circular foundation α = 1
Bqo (1 - μs) α Es
Se =
3.0
2.5 α
αav αr
2.0
α, αav, αr
1.5
For circular foundation
α = 1
αav = 0.85
αr = 0.88
1.0
3.0 1 2 3 4 5 6 7 8 9 10
L / B
Values of α, αav, and αr
By: Kamal Tawfiq, Ph.D., P.E.

6. Elastic Settlement of Foundation on Saturated Clay
Janbu, Bjerrum, and Kjaernsli (1956) proposed an equation for evaluation of the average elastic settlement of flexible foundations on saturated clay soils (Poisson’s ratio, μs = 0.5). Referring to Figure 1 for notations, this equation can be written as
Se = A1 A2 qoB/Es
where A1 is a function H/B and L/B, and is a function of Df/B.
Christian and Carrier (1978) have modified the values of A1 and A2 to some extent, and these are presented in Figure 2.
2.0
L/B = ∞
1.0
L/B = 10
1.5 5 A2
0.9 A1
1.0 2
Square
Circle
0.5
0.8 5 10 15 20
Df/B
0.1 1 10
100
1000
H /B
Values of A1 and A2 for elastic settlement calculation (after Christian and Carrier, 1978)
By: Kamal Tawfiq, Ph.D., P.E.

7. Elastic Settlement Using the Strain Influence Factor: [Schmertman & Hartman Method (1978)]
Se = C1 C2 ( q - q) ∑ (Iz / Es ) Δz
where
Is = strain influence factor
C1 = a correction factor for the depth of foundation embedment
= [q / (q - q)]
C2 = a correction factor to account for creep in soil
= log (time in years /0.1)
q = stress at the level of the foundation
q = overburden pressure = γ Df
The variation of the strain influence factor with depth
below the foundation is shown in Figure 1.
Note that, for square or circular foundations,
Iz = 0.1 at z = 0
Iz = 0.5 at z = 0.5B
Iz = 0 at z = 2B
Similarly, for foundations with L/B ≥ 10
Iz = 0.2 at z = 0
Iz = 0.5 at z = B
Iz = 0 at z = 4B
Example:
B x L q Df
q = γ Df Iz Es
ΔZ1
ΔZ2
Is3
ΔZ3 s3
Average Is
Average Es
ΔZ4
Depth, z

11. Dp Dp Dp Dp Dp Dp
DH =
CS H
1 + eO P0
Po + DP
log ( )

12. DH = log ( ) + CS H 1 + eO PC Po C C H Po + DP log ( ) Dp2 Dp2 Dp2 Dp

13. Dp2
Dp2
Dp2 Dp
Dp2
CS H
Po + DP
DH = log
( ) 2
1 + eO Po