When You Get Down to the Foundations

1
When You Get Down to the Foundations Its
All Based on Soils
Bearing Capacity and All That Wyoming
Engineering Society/ ASCE Cheyenne, WY February
4, 2006

• Thomas V. Edgar, P.E., Ph.D.
• Department of Civil and Architectural Engineering
• University of Wyoming
• Laramie, WY

2
Continuing Education

• Soil Mechanics Lecture Series
• 1995 (Cheyenne) Soil Formation, Index Tests and
  Classification
• 1996 (Casper) Normal Stresses, Induced Stresses
  and Water Pressure in Soils
• 1997 (Rock Springs) Shear Strength and Design in
  Soils
• 1998 (Sheridan) Slope Stability In Soils
• 1999 (Gillette) Alternatives in Retaining
  Structures
• 2000 (Cheyenne) Flow in Porous Media (!!!)
• 2002 (Sheridan) Foundations on Expansive Soils
• 2003 (Cheyenne) How to Read a Soils Report
• 2004 (Casper) Cold and Frozen Soils, CE 2100
• 2006 (Cheyenne) Foundations and Bearing Capacity

3
Standard Introduction

• Soil is the Most Common and the Most Complex
  Building Material Used
• Its Properties are Highly Variable
• With Area
• With Depth
• Soils can Compress, Shear, Take on or Release
  Water (Especially Clays) .
• A different amount for each type of soil
• A different amount for an individual soil
• When placed under different (Stress)
  conditions.
• By Nature (Uncontrolled)
• By People (Controlled)

4
Outline

• Bearing Capacity
• Factors
• Stress Distribution
• Deformation
• Consolidation
• Bearing Capacity
• Soil Properties

5
What is a Foundation?

• To Transmit the weight of a
• Building, Structure, Support, etc.
• So the stress developed may be dissipated into
  the ground below.

6
What is a Foundation?

• It Must
• Minimize Settlement (Usually Long-term)
• Stress Distribution
• Minimize Elastic Deformation
• Minimize Consolidation
• Prevent Shear Failure (Usually Short-Term)
• Rotational Bearing Capacity Failure
• Constrained (Vertical) Bearing Failure

7
Leaning Tower of Pisa

• The Classic Example
• Leaning Tower of Pisa
• Started Construction in 1173
• Worked Ten Years to 3rd ring.
• Foundation is a ring 8 feet wide and 9 feet deep.
  
• Showed tilt in 1178
• Four more floors built in 1272
• These floors tilt back
• Finished in 1372

8
Leaning Tower

• Construction
• 60 m Total Height
• 15.5 m Diameter
• Ring Masonry Foundation 19.6 m Dia
• 5.5 degree tilt
• In 1838, Excavation around the base and concrete
  sidewalk placed, but not tied-in. Increased tilt
  by 0.5o.
• Soils
• 10 m of soft, lagoon silty mud deposits over 40 m
  sensitive clay, then deep dense sand.

9
Leaning Tower of Pisa

• Three Remediation Techniques
• Lead Weights
• 1834 Concrete ring tied into building and
  supported.
• 800 tons of Lead Blocks Placed
• Cable Supports
• Second level wrapped with cable
• Tied by cables to deadman
• Excavation

http//news.bbc.co.uk/1/hi/world/europe/793432.stm
10
Leaning Tower of Pisa

• Cables from secondStory to Deadmen
  Holes drilled
  under
  tower and small
• 
  amount of soil
  removed

11
Leaning Tower of Pisa
Rotation Back to 300 years
Base Rotation
http//www.pubs.asce.org/ceonline/ceonline02/0302f
eat.html
Foundation Settlement
12
Transcona Grain Elevator

• Constructed in 1913
• Largest Grain Elevator in Canada
• Design/Construct before era of Soil Mechanics
• In October, 1913 over a million bushels of wheat
• It started to fail and tilted 27 degrees in 12
  hours

13
Transcona Grain Elevator

• Only damage was to the distribution building on
  top
• Installed piles to stiff bedrock
• Excavated in the foundation area
• Tilted the whole segment up
• Still in operation today.

14
Niigata, Japan Apartments

• 7.4 M Earthquake, June 16, 1964
• 26 people killed, almost 10,000 buildings
  damaged
• Bearing Capacity lost because of soil
  Liquefaction
• In these apartments, people climbed out of
  windows and walked down side of buildings.

15
Niigata, Japan Apartments

• The foundations for these apartments were a layer
  of cobbles supporting the concrete floor slab
  about at grade.
• Like Transcona, these apartments were not
  severely damaged.
• Tilted back up and in use today!

16
From National Information Service for Earthquake
Engineering, University of California at Berkeley
17
Shallow Foundations

• Shallow Foundations are usually easy to see and
  evaluate
• They are commonly of two types
• Long Continuous Strip Footings (Shown Here)
• Fixed Shape Footings
• Round
• Square
• Rectangular

18
Shallow Foundations

• Round Square Rectangular

19
Stress Distribution

• When a Load is placed on a Footing, a Stress is
  developed at the base (including the weight of
  the footing).
• The stress is distributed radially away from the
  base, the greatest at the centerline and reducing
  with distance away.
• As the stress spreads with depth, its intensity
  decreases until it adds little increase to the
  geostatic stresses.

20
Stress Distribution

• Boussinesq developeda relationship for Stress
  Distribution Beneath a point load.
• The solution assumes a
• Linearly Elastic
• Homogeneous, Isotropic
• Semi-Infinite Half Space
• i.e., A Perfect Representation of Real Soil

21
Stress Distribution

• Boussinesq Point Load Solution

22
Stress Distribution

• If we strike a horizontal plane at any depth, the
  resulting stress diagram would be bell shaped,
  with the greatest stress under the point of
  application and decreasing as it spreads out in a
  radial direction.
• The volume under the stress-area curve equals
  the applied force.

?? r
23
Stress Distribution
Solution of more Complex Areas is completed using
summation of individual areas.
24
Stress Distribution

• We can see the variation of Stress under the long
  strip footing.
• Highest Stress along the centerline
• Decreasing with distance away from the
  centerline.
• Still, Areas under the curve are equal.

25
Example

• A 15 foot wide strip footing has a vertical
  stress of q 500 psf. Find the stress
  distribution perpendicular to the centerline at a
  depth of 10 feet.
• Z/B 10/15 0.67

X/B 0.00 .125 .250 .375 .500 .625 .75 1.00 1.25 1.50
?? (psf) 358 349 322 282 230 177 129 64 32 17
26
Consolidation
Sand
Clay
27
Consolidation

• Soil is an Engineering Material that Strains when
  it is Stressed.
• The Settlement at a point is defined
  aswhere Settlement Full
  thickness of Clay body Initial Void
  Ratio Change in Void Ratio

28
Consolidation

• The Change in Void Ratio can be defined as
• where Initial Effective Stress, and
  Compression Index, i.e., the
  slope of the Virgin Curve.

29
Consolidation
30
Consolidation
We see 1.13 Settlement in the Center of the slab
versus 0.75 At the Edge, a bow of 0.38 in 7.5
feet.
X/B 0.00 .125 .250 .375 .500 .625 .75 1.00 1.25 1.50
?? (psf) 358 349 322 282 230 177 129 64 32 17
S 1.13 1.10 1.02 0.91 0.75 0.59 0.43 0.22 0.11 0.06
31
Consolidation

• Therefore, using simple tests, we can determine
  if deformation is going to be a problem in the
  long term.
• If it is, then the logical alternative is to use
  Deep Foundations rather than shallow ones.

32
Bearing Capacity
33
Bearing Capacity

• Three Potential Modes of Failure
• General Shear Dense Soil, Shear Plane fully
  developed, Relative Density, Dr gt 0.7
• Local Shear Medium Dense Soil, Shear Plane
  Partially Developed, 0.35ltDrlt0.7
• Punching Shear Loose Soil, No Developed Shear
  Plane, Dr lt 0.35

34
ASTM- D1194 Plate Load Test
35
Plate Load Tests

• General Shear
• Local Shear
• Punching Shear

36
General Shear Failure

• Terzaghi developed the first basic relationship
  for bearing capacity.
• qult is a stress
• Qult is the Force per length of wall
• is the unit weight beneath the bottom of
  the footing

• N?, Nq and Nc are the Bearing Capacity Factors
  which are functions of ? only.
• One of Terzaghis Greatest Achievements.

37
Bearing Capacity Factors

• Terzaghis original factors were very
  conservative (which they needed to be at the
  time).
• They were based on both theory by Prandtl (1921)
  and Reissner (1924) and by his own model studies
  and development.

• Terzaghis Brilliance was in evaluating the
  problem and breaking into appropriate pieces.
• Each term dealt with a piece of the puzzle, and
  T. recognized they could be pieced together
  independently.

38
Fitting the Pieces Together

• Terzaghi assumed that ß was equal to ? .
• Later studies shows closer to
• Zone 1 is an arrowhead.
• Zone 2 is a logarithmic spiral
• Zone 3 is a Passive Wedge
• Support by Friction (?) on Failure surface.

39
Fitting the Pieces Together

• The second term accounts for vertical stress
  above the base of the footing.
• q is the surface stress
• Second term deals with overburden soil.
• The failure is shown on both sides of the
  footing.
• Generally not true
• Failure occurs where (q?Df) is a minimum.

40
Fitting the Pieces Together

• The third term accounts for cohesive soil.
• Nc is primarily a measure of the length of the
  failure surface over which the cohesion acts.
• Bearing Capacity failures are almost always rapid
• Use Unconfined Compressive Strength or UU tests
  for c.

41
Bearing Capacity Factors
42
Bearing Capacity Factors
f Kp N? Nq Nc   f Kp N? Nq Nc
0 1.0 0.0 1.0 5.1   31 3.1 26.0 20.6 32.7
1 1.0 0.1 1.1 5.4   32 3.3 30.2 23.2 35.5
2 1.1 0.2 1.2 5.6   33 3.4 35.2 26.1 38.6
3 1.1 0.2 1.3 5.9   34 3.5 41.1 29.4 42.2
4 1.1 0.3 1.4 6.2   35 3.7 48.0 33.3 46.1
5 1.2 0.4 1.6 6.5   36 3.9 56.3 37.8 50.6
6 1.2 0.6 1.7 6.8   37 4.0 66.2 42.9 55.6
7 1.3 0.7 1.9 7.2   38 4.2 78.0 48.9 61.4
8 1.3 0.9 2.1 7.5   39 4.4 92.2 56.0 67.9
9 1.4 1.0 2.3 7.9   40 4.6 109.4 64.2 75.3
10 1.4 1.2 2.5 8.3   41 4.8 130.2 73.9 83.9
11 1.5 1.4 2.7 8.8   42 5.0 155.5 85.4 93.7
12 1.5 1.7 3.0 9.3   43 5.3 186.5 99.0 105.1
13 1.6 2.0 3.3 9.8   44 5.6 224.6 115.3 118.4
14 1.6 2.3 3.6 10.4   45 5.8 271.7 134.9 133.9
15 1.7 2.6 3.9 11.0   46 6.1 330.3 158.5 152.1
16 1.8 3.1 4.3 11.6   47 6.4 403.7 187.2 173.6
17 1.8 3.5 4.8 12.3   48 6.8 496.0 222.3 199.3
18 1.9 4.1 5.3 13.1   49 7.2 613.1 265.5 229.9
19 2.0 4.7 5.8 13.9   50 7.5 762.9 319.1 266.9
20 2.0 5.4 6.4 14.8   51 8.0 955.8 386.0 311.8
21 2.1 6.2 7.1 15.8   52 8.4 1206.5 470.3 366.7
22 2.2 7.1 7.8 16.9   53 8.9 1535.4 577.5 434.4
23 2.3 8.2 8.7 18.0   54 9.5 1971.2 715.1 518.8
24 2.4 9.4 9.6 19.3   55 10.1 2554.9 893.5 624.9
25 2.5 10.9 10.7 20.7   56 10.7 3346.0 1127.4 759.8
26 2.6 12.5 11.9 22.3   57 11.4 4431.6 1438.0 933.2
27 2.7 14.5 13.2 23.9   58 12.2 5942.1 1855.5 1158.8
28 2.8 16.7 14.7 25.8   59 13.0 8075.4 2425.1 1456.5
29 2.9 19.3 16.4 27.9   60 13.9 11137.6 3214.1 1855.1
30 3.0 22.4 18.4 30.1   61 15.0 15612.1 4326.0 2397.4
43
Other Shapes

• Continuous Strip
• Square Footing
• Circular Footing

44
Allowable Bearing Capacity

• The Ultimate Bearing Capacities weve looked at
  are at failure conditions.
• We want to work with Allowable conditions
• F.S.sand 2.5-3.0
• F.S.clay 3.0

• Continuous
• Square and Circular

45
WE KNOW

• Water Flows
• Static Water has buoyancy effects
• Water Footing Width B below Footing
• Water at Base of Footing
• Water at Ground Surface

46
Meyerhof Bearing Capacity

• Accounts for some limitations of Terzaghi
  Equations
• Shape other than square
• Depth
• Inclination
• Same Bearing Capacity Factors as Before

47
Meyerhof Bearing Capacity
Factors Shape Depth Inclination Angle From Vertical
F?
Fq
Fc
48
f
f
Bearing Capacity Worksheet Bearing Capacity Worksheet Bearing Capacity Worksheet Bearing Capacity Worksheet

Deep Water


? 120 10 Kp 3.9 Fgs 0.988  
?-sat 128 B or Dia. 3 N? 56.3 Fqs 1.022  
f 36 L 100 Nq 37.8 Fcs 1.022  
c 0 Inclin ß 0 Nc 50.6    
?-2 120 q-surface 0   (Df/B)lt1 (Df/B)gt1
?-2sat 128 ?-eff 120 Fgd 1.000 1.000
FS 2.5 ?-2eff 120 Fqd 1.823 1.316
Dwater 15 Fcd 2.333 1.512
?-water 62.4    
Fgi 1.000  
  ? q c q-ult Q-ult Q-all Fqi 1.000  
Terzaghi 10136 45303 0 55439 166317 66527 Fci 1.000  
T-Square 8109 45303 0 53412 480706 192282
T-Circle 6082 45303 0 51385 363216 145286
   
Meyerhof 10014 60913 0 70927 212781 85112
D
f
49
Bearing Capacity Worksheet Bearing Capacity Worksheet Bearing Capacity Worksheet Bearing Capacity Worksheet

Water At Base


? 120 10 Kp 3.9 Fgs 0.988  
?-sat 128 B or Dia. 3 N? 56.3 Fqs 1.022  
f 36 L 100 Nq 37.8 Fcs 1.022  
c 0 Inclin ß 0 Nc 50.6    
?-2 120 q-surface 0   (Df/B)lt1 (Df/B)gt1
?-2sat 128 ?-eff 65.6 Fgd 1.000 1.000
FS 2.5 ?-2eff 120 Fqd 1.823 1.316
Dwater 10 Fcd 2.333 1.512
?-water 62.4    
Fgi 1.000  
  ? q c q-ult Q-ult Q-all Fqi 1.000  
Terzaghi 5541 45303 0 50844 152532 61013 Fci 1.000  
T-Square 4433 45303 0 49736 447622 179049
T-Circle 3325 45303 0 48628 343728 137491
   
Meyerhof 5474 60913 0 66387 199162 79665
f
D
50
Bearing Capacity Worksheet Bearing Capacity Worksheet Bearing Capacity Worksheet Bearing Capacity Worksheet

Water At surface


? 120 10 Kp 3.9 Fgs 0.988  
?-sat 128 B or Dia. 3 N? 56.3 Fqs 1.022  
f 36 L 100 Nq 37.8 Fcs 1.022  
c 0 Inclin ß 0 Nc 50.6    
?-2 120 q-surface 0   (Df/B)lt1 (Df/B)gt1
?-2sat 128 ?-eff 65.6 Fgd 1.000 1.000
FS 2.5 ?-2eff 65.6 Fqd 1.823 1.316
Dwater 0 Fcd 2.333 1.512
?-water 62.4    
Fgi 1.000  
  ? q c q-ult Q-ult Q-all Fqi 1.000  
Terzaghi 5541 24766 0 30307 90920 36368 Fci 1.000  
T-Square 4433 24766 0 29198 262786 105114
T-Circle 3325 24766 0 28090 198558 79423
   
Meyerhof 5474 33299 0 38773 116320 46528
f
D
51
Bearing Capacity Worksheet Bearing Capacity Worksheet Bearing Capacity Worksheet Bearing Capacity Worksheet

  Inclination  


? 120 10 Kp 3.9 Fgs 0.988  
?-sat 128 B or Dia. 3 N? 56.3 Fqs 1.022  
f 36 L 100 Nq 37.8 Fcs 1.022  
c 0 Inclin ß 15 Nc 50.6    
?-2 120 q-surface 0   (Df/B)lt1 (Df/B)gt1
?-2sat 128 ?-eff 120 Fgd 1.000 1.000
FS 2.5 ?-2eff 120 Fqd 1.823 1.316
Dwater 15 Fcd 2.333 1.512
?-water 62.4    
Fgi 0.340  
  ? q c q-ult Q-ult Q-all Fqi 0.694  
Terzaghi 10136 45303 0 55439 166317 66527 Fci 0.694  
T-Square 8109 45303 0 53412 480706 192282
T-Circle 6082 45303 0 51385 363216 145286
   
Meyerhof 3408 42300 0 45708 137124 54850
f
D
52
Bearing Capacity Factors
f Kp N? Nq Nc   f Kp N? Nq Nc
0 1.0 0.0 1.0 5.1   31 3.1 26.0 20.6 32.7
1 1.0 0.1 1.1 5.4   32 3.3 30.2 23.2 35.5
2 1.1 0.2 1.2 5.6   33 3.4 35.2 26.1 38.6
3 1.1 0.2 1.3 5.9   34 3.5 41.1 29.4 42.2
4 1.1 0.3 1.4 6.2   35 3.7 48.0 33.3 46.1
5 1.2 0.4 1.6 6.5   36 3.9 56.3 37.8 50.6
6 1.2 0.6 1.7 6.8   37 4.0 66.2 42.9 55.6
7 1.3 0.7 1.9 7.2   38 4.2 78.0 48.9 61.4
8 1.3 0.9 2.1 7.5   39 4.4 92.2 56.0 67.9
9 1.4 1.0 2.3 7.9   40 4.6 109.4 64.2 75.3
10 1.4 1.2 2.5 8.3   41 4.8 130.2 73.9 83.9
11 1.5 1.4 2.7 8.8   42 5.0 155.5 85.4 93.7
12 1.5 1.7 3.0 9.3   43 5.3 186.5 99.0 105.1
13 1.6 2.0 3.3 9.8   44 5.6 224.6 115.3 118.4
14 1.6 2.3 3.6 10.4   45 5.8 271.7 134.9 133.9
15 1.7 2.6 3.9 11.0   46 6.1 330.3 158.5 152.1
16 1.8 3.1 4.3 11.6   47 6.4 403.7 187.2 173.6
17 1.8 3.5 4.8 12.3   48 6.8 496.0 222.3 199.3
18 1.9 4.1 5.3 13.1   49 7.2 613.1 265.5 229.9
19 2.0 4.7 5.8 13.9   50 7.5 762.9 319.1 266.9
20 2.0 5.4 6.4 14.8   51 8.0 955.8 386.0 311.8
21 2.1 6.2 7.1 15.8   52 8.4 1206.5 470.3 366.7
22 2.2 7.1 7.8 16.9   53 8.9 1535.4 577.5 434.4
23 2.3 8.2 8.7 18.0   54 9.5 1971.2 715.1 518.8
24 2.4 9.4 9.6 19.3   55 10.1 2554.9 893.5 624.9
25 2.5 10.9 10.7 20.7   56 10.7 3346.0 1127.4 759.8
26 2.6 12.5 11.9 22.3   57 11.4 4431.6 1438.0 933.2
27 2.7 14.5 13.2 23.9   58 12.2 5942.1 1855.5 1158.8
28 2.8 16.7 14.7 25.8   59 13.0 8075.4 2425.1 1456.5
29 2.9 19.3 16.4 27.9   60 13.9 11137.6 3214.1 1855.1
30 3.0 22.4 18.4 30.1   61 15.0 15612.1 4326.0 2397.4