1. GLE/CEE 330: Soil Mechanics Settlement of Shallow Footings
Geological Engineering
University of Wisconsin-Madison

2. Learning Objectives Discuss service limit state
Learn approach for estimating consolidation settlement
Learn approach for estimating elastic settlement
Learn approaches for estimating settlement from results of field tests (SPT & CPT)

3. Foundation Design Philosophy
Limit State = “condition beyond which a component/member of a foundation or other structure ceases to satisfy the provisions for which the component/member was designed”
Strength Limit State (bearing capacity analysis)
Service Limit State (settlement analysis)
Extreme Event Limit State
Fatigue Limit State

4. Settlement of Shallow Footings
Total Settlement (d) d
Differential Settlement (dD) dD S
Angular Distortion(q) dD
q=dD/S

5. Serviceability Requirements
Total Settlement (d)
Typical Values
Type of Structure
dmax (in)
dmax (mm)
Office Building
0.5 – 2.0
12-50
Heavy Industrial
1.0 – 3.0
Bridges
2.0 50
Need to consider:
Connections (other structures)
Utilities (gas, electric, hydraulic)
Surface Drainage
Access
Aesthetics

6. Serviceability Requirements
Differential Settlement (dD)
q = angular distortion
S = span (e.g., column spacing, footing width)
Typical Values
Type of Structure q
Steel Tanks
1/25
Bridges (simple supp.)
1/125
Commercial Buildings
1/500
Machinery Foundations
1/1500

7. Types of Settlement Analysis
Primary Consolidation Settlement (Time Dependent)
Elastic Settlement (Immediate)

8. Primary Consolidation Settlement
Similar to 1D consolidation analysis (Cr, Cc, s’p)
Must consider how induced load varies with depth and rigidity of footing
s’zf = final vertical effective stress beneath center of footing
s’z0= initial vertical effective stress beneath center of footing
(sz)induced= induced vertical total stress beneath center of footing
Initial effective stress and induced stress vary with depth
break into sublayers and calculate settlement of each
do analysis at middle of each layer
the more layers, the more accurate

9. Generally 3 layers is sufficient for manual calculations…
(e.g., square footing) Df B
B/2 B 2B

10. B
B/2 2B zf P
q = P/A Df
Circular Footings:
Square Footings:

11. B
B/2 2B zf P
q = P/A Df
Strip Footings:
Rectangular Footings:

12. P
Calculate d for each layer…
q = P/A
Normally Consolidated Clay (s’z0 = s’p)
r = “rigidity factor” (r = 0.85 for reinforced concrete, r = 1.0 for flexible footing)
Log s’ e Cc Df B
B/2 zf B
Overconsolidated Clay – Case I (s’zf < s’p)
Log s’ e Cr 2B
Overconsolidated Clay – Case II (s’z0 < s’p < s’zf )
Log s’ e Cr Cc

13. Elastic Settlement (Clay)
Arbitrarily shaped footing
Settlement:
Undrained Elastic Parameters (UU Triaxial Tests):
Eu = Undrained elastic modulus
vu = Undrained Poisson’s ratio
Shape, Embedment, and Side-Wall Factors:

14. Settlement Based on Field Tests
Most applicable for coarse-grained soils (difficult to obtain high quality lab samples)
Standard Penetration Test (SPT)
Cone Penetration Test (CPT)
Plate Load Test (PLT)

15. Elastic Settlement Based on SPT
Normally Consolidated Sand: (Burland and Burbridge, 1985)
r = mm
sa = vert. stress applied by footing
N = uncorrected blow count
See Budhu, Section

16. What N value do we use????
Boring 1
Boring 2 15 16 18 20 17 23 B
N = ?
Use some average in the heavily loaded zone (z = Df + B)
Pick a conservative value (lowest N)
Use engineering judgment!

17. Elastic Settlement Based on CPT
Sands: (Schmertmann, 1970)
See Budhu, Section