1. Foundation SettlementBy
Kamal Tawfiq, Ph.D., P.E.
Fall 2001

2. Bearing Capacity of Layered Clay SoilsDf
Caly
ϕ1 = 0
c1 = ✓ B qu Z
Caly
ϕ2 = 0
c2 = ✓
Cylindrical
Failure
Surface
By: Kamal Tawfiq, Ph.D., P.E.

3. Bearing capacity on layered clay soils (ϕ = 0)Nc 10
Z/B = 0
0.1
0.2 8
0.3
0.4 6
0.5
1.5
0.75
1.0 4
0.25
0.5
Z/B = 0 2
0.4
0.8
1.2
1.6
2.0
C2 / C1
Bearing capacity on layered clay soils (ϕ = 0)
By: Kamal Tawfiq, Ph.D., P.E.

4. Bearing Capacity of Layered SoilsQu
Bearing Capacity of Layered Soils Df B
Sand
ϕ = ✓
c = 0 H
Sand
ϕ = ✓
c = 0
Caly
ϕ = 0
c = ✓
Caly
ϕ = 0
c = ✓
Foundation on sand layer overlying soft caly
By: Kamal Tawfiq, Ph.D., P.E.

5. Values of Ks ___________________________ Friction Angle of
Sand, ϕ (deg) Ks
By: Kamal Tawfiq, Ph.D., P.E.

6. { { Foundation Settlement: Stotal = Se + Sc
Total Foundation Settlement = Elastic Settlement + Consolidation Settlement
Stotal = Se + Sc {
Foundation 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.

7. 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
Water Table (W.T.)
Voids
Solids
Expulsion of the water
By: Kamal Tawfiq, Ph.D., P.E.

8. Elastic Settlement Se = Bqo (1 - μs) α Se = Bqo (1 - μs) α 2 Es Es
(corner of the flexible foundation) 2 Es
Se = Bqo (1 - μs) α 2
(center of the flexible foundation) Es
Where α = 1/π [ 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.

9. α, αav, αr 3.0 2.5 α αav αr 2.0 1.5 For circular foundation α = 1
Se = Bqo (1 - μs) α E
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.

10. Elastic Settlement of Foundations on Saturated Clay
Janbu, Bjerrum, and Kjaernsli (1956) proposed an equation for evaluation of the average elastic settlement of flixable 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 nd A2 for elastic settlement calculation (after Christian and Carrier, 1978)
By: Kamal Tawfiq, Ph.D., P.E.

11. 1.0 A2
0.9
0.8 5 10 15 20
Df/B
Values of A1 nd A2 for elastic settlement calculation (after Christian and Carrier, 1978)
By: Kamal Tawfiq, Ph.D., P.E.

12. 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
Es3
Average Is
Average Es
ΔZ4
Depth, z
By: Kamal Tawfiq, Ph.D., P.E.

13. By: Kamal Tawfiq, Ph.D., P.E.

14. By: Kamal Tawfiq, Ph.D., P.E.

15. By: Kamal Tawfiq, Ph.D., P.E.

16. By: Kamal Tawfiq, Ph.D., P.E.

18. By: Kamal Tawfiq, Ph.D., P.E.

19. By: Kamal Tawfiq, Ph.D., P.E.

20. By: Kamal Tawfiq, Ph.D., P.E.

21. By: Kamal Tawfiq, Ph.D., P.E.

22. By: Kamal Tawfiq, Ph.D., P.E.