Bearing Capacity shallow foundation systems

1
Bearing Capacity - shallow foundation systems

• D. A. Cameron
• Rock and Soil Mechanics 2006

2
TERMS

• The foundation of a structure is the earth upon
  which the structure is supported
• structural loads are transferred to the soil
  via the footing
• Reinforced (?) concrete strip footings pads
• take column (point) loads distributed loading
  (line loads)

3
Foundation requirements
1. Safe bearing capacity or strength 2.
Allowable bearing pressure
4
Presumptive qsafe values?No WT within depth, D
B, footing breadth
5
Modes of Failure of Shallow Foundations

6
Bearing Capacity Analysis

• Solution is usually based on
•   a) General bearing capacity failure
• b) Strip footing - width, B, length L ?,
  founded at depth, D
• c) Soil - homogeneous isotropic,
  unit weight, ?
• d) Soil Strength - parameters c? and ??

7
SURFACE FOOTING, B x L ?
qaverage Q/B per m length
SOIL
Stress
Rigid-plastic soil behaviour
Strain
8
Choice of Strengths

• SAND
• Clean sand
• c 0 c?
• ??, ?, ??
• ? not affected by inundation
• BUT lower qu!

• CLAY
• Saturated, NC
• undrained loading?
• ?u 0
• usually more critical
• drained loading?
• c?, ??

9
Q
MECHANISM
L
B

The captured, driven soil wedge
10
Simple upper bound for ?u 0 soils
qu
B

11
Solution

• Take moments about the centre
• Disturbing moment restoring moment
• quB(0.5B) (cu?B)B
• qu (2?)cu

qu 6.3 cu
12
Simple lower bound for ?u 0 soils
45?
45?
B
?Ha
?Hp
Active wedge
Passive wedge
Ka Kp 1
13
Solution
qu 4cu
Shear stress
cu
?Ha
?Hp
qu
0
Active state
Passive state
Principal stress
14
The Correct Answer

• Lower bound estimate (safe) qu 4cu
  
• The correct answer
  qu 5.14cu
• Upper bound estimate (unsafe) qu
  6.3cu

15
The Accepted Failure Mechanism

• Active wedge under footing
• wedge at (45? ??/2)
• Rotational zone of plasticity
  (radial shear zone)
• log spiral
• shear stresses on either side of the radial shear
  zone fn(spiral)
• Passive wedges to either side of footing
• wedges at (45? - ??/2)
• resist soil rotation

16
Mechanism the same both sides
17
(No Transcript)
18
Log Spiral dictates change of shear in the
radial shear zone
?1
?
?2
Normal forces offset by friction, no moments
about centre
19
Comment

• Details of the geometry of the failure mechanism
  are really only of any practical purpose for
  consideration of the influence of adjacent or
  underground works, or the influence of soil
  profile changes
• N.B. ? 0 soils have smallest mechanism

20
The General Bearing Capacity Equation

• Ultimate bearing capacity for a strip footing,
  subjected to vertical load
• other situations handled by empirical expressions

21
FORMULATIONLimit Equilibrium Analysis

• Considers 3 cases
• Surface footing, ?soil, with cohesion, but no
  friction
• Surface footing, soil friction and ?soil
• Burial (surcharge extra shear resistance)
• Contributions are simply summed
• ? an approximation,
• backed up by experience and experimentation

22
Bearing Capacity Factors

• Nc, Nq N? are the bearing capacity factors
  corresponding to
• 1. Cohesion case
• 2. Surcharge or burial case
• 3. Self weight of soil case

Nc, Nq and N? are all functions of ??
23
The Bearing Capacity Factors, Nc, Nq
24
(No Transcript)
25
The Bearing Capacity Factor, N?
26
0.0
27
The Bearing Capacity Equation- for a long
strip footing
28
Variations in the Bearing Capacity Factors
between methods

• Hansen or Brinch-Hansen analyses generally
  accepted as most accurate
• Terzaghi, the pioneer, misconstrued Nc
• Meyerhof the 2nd best of these 3

29
Effects of Soil Properties

• Bearing capacity fn(??, ??, B, c? and qo)
• ?? has the greatest influence
• Both the 2nd and 3rd terms in the equation depend
  on ??
• if water is above the bottom of the footing,
  the surcharge weight is also affected

30
THE SURCHARGE TERM- most footings are buried
?1
D
?
qo ?1D
31
Effect of Footing Size

• Last term with N? has B or footing breadth
• Wider footing, greater bearing capacity
• BUT for ?? 0 soil, B has little effect

N? 0! for ?? 0
32
Factor of Safety, qu to qsafe?

• A Factor of Safety of 3?

nett ultimate bearing capacity ? (FoS)
surcharge qu nett ? (FoS) qo
33
The General Bearing Capacity Eqn.

• Considers
• soil rigidity, (r)
• footing shape, (s)
• depth of embedment, (d)
• Inclined load, (i)
• base inclination, (b)
• Ground inclination, (g)

Note shape factors not used with inclination
factors?
34
Effect of depth, D (?u 0)
35
Effect of depth, D (?u 0)
qu surface
D 0
36
The Influence of a WT
zw
?1
?
??
If zw within 1.5D, assume at underside of footing
and use ?? in self weight term Buoyancy if too
high?
37
Footing Shape shape factors BL
38
Eccentricity of Loading
Plan
39
EXAMPLE 8.7From Barnes, (changed slightly)

• A long, reinforced concrete, retaining wall is to
  be founded at 1.5 m depth below ground level in a
  clay with the water table at 1.5 m below ground
  level. The width of the footing is 2.5 m and the
  base is 1.5 m below ground level. The thickness
  of the footing is 0.5 m. The top 1 m of
  excavation is to be backfilled.
• A vertical line load of 90 kN/m is located 0.45 m
  off the centreline of the footing.
• If c? 4 kPa, ?? 23? and ? 22 kN/m3 cu
  40 kPa and ?u 0
• ?concrete 25 kN/m3 and ?backfill 21 kN/m3,
  then find the factor of safety against bearing
  capacity failure for both short term and long
  term conditions
• DO NOT ignore depth factors

40
Problem from Notes

• A column carries 900 kN.
• The foundation soil is dry sand, 18 kN/m3, ??
  40º.
• A minimum factor of safety of 2.5 is required.
•  FIND the size of
• A square footing if it is placed at the ground
  surface
• A rectangular surface footing L/B 2
• c) A square footing if it is placed 1 m below
  the surface.
• d) A square footing, 1 m below the surface - the
  water table is expected to rise to the underside
  of the footing. Below the water table, the unit
  weight is 21 kN/m3

41
ANSWER (a)

• e 0, so, q 900/B2 kPa
• qu req 2.5 x 900/B2 2250/B2
• BUT for dry sand, AND a surface footing
• qu 0.5(s?)?BN?
• 2250/B2 0.5(s?)18BN?
• 250 (s?)B3N? 0.6 x 85.8 B3
• SOLVE B 1.69 m

42
ANSWER (c)
q 900/B2 kPa qu req 2.5 x 900/B2 - sqdqqo
2250/B2 - 18sqdq BUT for dry sand, AND a
square footing at 1 m, qu sqdqqoNq
0.5(s?)(d?)?BN? 2250/B2 18(1.84)1.16 1.84
(1.16)(18)64.2 0.5(0.6)(1)18B(85.8)
2250/B2 38.4 2466 463.3B
0 0.206B3 1.11B2 - 1
SOLVE B 0.88 m assumed B 1 m for depth
factors
43
ANSWER (b)
q 900/B2 kPa qu req 2.5 x 900/B2
2250/B2 - surface footing BUT for dry sand, and
L/B 2, qu 0.5(s?)?BN? 2250/B2
0.5(0.8)18B(85.8) 3.642 B3 SOLVE B
1.54 m
44
ANSWER (d)
q 900/B2 kPa qu req 2.5 x 900/B2 - sqdqqo
2250/B2 - 18sqdq BUT for wet sand, AND a
square footing at 1 m, qu sqdqqoNq
0.5(s?)(d?)??BN? 2250/B2 18(1.84)1.16 1.84
(1.16)(18)64.2 0.5(0.6)(1)(11.2)B(8
5.8) 2250/B2 38.4 2466 288.2B
0 0.128B3 1.11B2 - 1
SOLVE B 0.90 m assumed B 1 m for depth
factors
45
Inclined Loading
Changed shear mechanism Shallower, longer?
46
Inclined Load correction factors (Meyerhof
guide only use Hansen)
47
Inclination of Load correction factors, ic, iq,
i?

DEFINITION of ?n for inclined loading

48
Inclined Loading

• Has a tremendous influence
• Cannot use shape factors (strip solution)
• The solution is always for the VERTICAL component
  only of the force, Q
• Q ?N2 T2 and qu N/A
• MUST design against sliding arising from the
  HORIZONTAL component of force
• i.e. T N(tan?)

49
CLASS EXAMPLE

• A footing 2 m wide by 4 m long is to be placed on
  a dense layer of sand, overlain by poorly
  compacted fill (?fill 16 kN/m3) to a depth of 2
  m. The sand has the properties c? 0 kPa, ??
  38? and ? 20 kN/m3. There is no water table
  near the footing.
• Check the ultimate bearing capacity of the
  footing for
• a vertical central load
• a central load inclined at 10? to the vertical
  (in plan, the load is parallel to the short side
  or breadth, B, of the footing)

50
Non-Homogeneous Soil - soil profiles

• Approximations can apply, SO LONG AS the general
  mechanism of instability remains

• NOT THE CASE for very soft clay, in thin layer,
  over hard soil
• Toothpaste tube?
• NOR strong thin layer over weak layer
• Punching shear

51
Non-Homogeneous Soil?
Load spreading technique
Stronger layer
Weaker Layer

52
Load, Q Footing, B x L Depth to layer, DL
Ignore lower layer and check surface qa
New footing area (BDL)(LDL) Pressure, qL
Q/area Check qa2
Ensure lower layer not overstressed by qL -
reduce qa as required
53
Example

• Returning to the previous question, had the
  footing been a surface footing and the poorly
  compacted fill had the properties c? 5 kPa, ??
  25?, compute the ultimate bearing capacity
  under vertical loading .

54
Alternative treatment if ?u 0 soils
Layer 1, cu1
B
Radius, B?
Layer 2 , cu2

55
Other Factors

• a) Adjacent footings ? suitably spaced to reduce
  interaction (refer to failure mechanisms)
• b) Rate of loading ? appropriate strength
  parameters?
• c) Inclined slopes adjacent to footings ?
  influence on slope stability?

56
SUMMARY

• Bearing capacity is determined by limit
  equilibrium methods
• Complexity requires semi-empirical solutions
• Endnote some new developments will improve
  these methods

57
GROUND COVERED

• types of failure
• general bearing capacity analysis
• correction factors for depth, shape, inclination
• influence of eccentric load
• dealing with soil profiles

58
BEARING CAPACITY ON ROCKS

• Rock can be stronger than a concrete footing
• BUT consideration of rock mass strength may be
  necessary
• closed joints frequently spaced, can treat as
  Bell-Terzaghi bearing problem
• ALSO defects and their orientation may impact
  upon performance

59
Rock Mass??
Close, but open vertical joints
Unconfined compressive strength of rock rules!
60
Rock Mass??
B
S
Widely spaced joints
Tension splitting of rock slab? Bishnois
theoretical solution Refer Sowers G F,
Introductory Soil Mechanics and Foundations
61
Other Considerations
H
Rigid
Weak
Flexural failure
Punching failure
62
KEY POINT

• Mechanisms of bearing capacity failure of rock
  masses are usually quite different from soil