Upload
others
View
12
Download
0
Embed Size (px)
Citation preview
1
Shallow Foundations
- Bearing Capacity
Reference:
Foundation Design, Principles and Practices,
Donald P. Coduto, Part B, Chapter 6
2
Shallow Foundations
Bearing Capacity
• The problems of soil mechanics can be
divided into two principal groups
- stability problems
and
- elasticity problems
- Karl Terzaghi, 1943
3
Karl Terzaghi (1883-1963)
• Father of modern soil mechanics
• Born in Prague, Czechoslovakia
• Wrote “Erdbaumechanick” in 1925
• Taught at MIT (1925-1929)
• Taught at Harvard (1938 and after)
4
Karl Terzaghi at Harvard, 1940
5
Bearing Capacity Failure
6
Transcosna Grain Elevator Canada (Oct. 18, 1913)
West side of foundation sank 24-ft
7
Stability Problem
Bearing Capacity Failure
• How do we estimate the maximum bearing
pressure that the soil can withstand before
failure occurs?
8
Bearing Capacity Failures
Types/Modes of Failure
general shear failure
local shear failure
punching shear failure
9
General Shear Failure
10
Punching Shear Failure
11
Local Shear Failure
12
Model Tests by Vesic (1973)
13
General Guidelines
Footings in clays - general shear
Footings in Dense sands ( > 67%)
- General Shear
Footings in Loose to Medium dense (30%< < 67%)
- Local Shear
Footings in Very Loose Sand ( < 30%)
- Punching Shear
rD
rD
rD
14
Bearing Capacity Formulas- Consider a continuous footing and assume;
- Footing experiences a bearing capacity failure,
- Failure occurs along a circular shear surface,
- Soil is an undrained clay with a shear strength su-Neglect the shear strength between ground surface and a Depth D
15
Bearing Capacity Formulas
Considering a slice of the foundation of length b and taking
moments about Point A
)2/())(()2/()( BbBBbBsBbBqM zDuultA
zDuult sq 2
16
Bearing Capacity Formulas
zDucult sNq
17
Terzaghi Bearing Capacity Formulas
D B
no sliding between footing and soil
soil is a homogeneous semi-infinite mass
shear strength of soil s = c' + σ' tan φ'
general shear failure occurs
no consolidation of soil occurs
settlement is due to the shearing and lateral movement of soil
footing is very rigid compared to soil
soil to depth D has no shear strength, and serves as surcharge
applied load is compressive applied vertically to the centroid of foundation
18
Terzaghi Bearing Capacity FormulasTerzaghi considered three zones in the soil :
* Immediately beneath the foundation, a wedge zone that
remains intact and moves downward with the foundation
19
Terzaghi Bearing Capacity Formulas* A radial shear zone extends from each side of the wedge, where
the shape of the shear planes is considered to be logarithmic
spirals
20
Terzaghi Bearing Capacity Formulas* Outer portion, the linear shear zone in which the soil shears
along planar surfaces.
21
Terzaghi Bearing Capacity Formulas
BNNNcq qzDcult 5.0
For Square foundations:
For Continuous foundations:
BNNNcq qzDcult 4.03.1
For Circular foundations:
BNNNcq qzDcult 3.03.1
22
Terzaghi Bearing Capacity Factors
07.5 whenNc
0tan
1
when
NN
q
c
)2/45(cos2 2
2
aNq
tan)360/75.0(expa
1
cos2
tan2
pKN
)4sin(4.01
tan)1(2
qNN
23
Bearing Capacity Factors
24
Example 6.1
25
Example 6.2
26
Further Developments
Skempton (1951)
Meyerhof (1953)
Brinch Hanson (1961)
De Beer and Ladanyi (1961)
Meyerhof (1963)
Brinch Hanson (1970)
Vesic (1973, 1975)
27
Vesic (1973, 1975) Formulas
Shape factors….… Eq. 6.14, 6.15 and 6.16
Depth Factors ……. Eq. 6.17, 6.18 and 6.19
Load Inclination Factors …. Eq. 6.20, 6.21 and 6.22
Base Inclinations factors .. Eq. 6.25 and 6.26
Ground Inclination Factors….Eq. 6.27 and 6.28
Bearing Capacity Factors …. Eq. 6.29, 6.30 and 6.31
gbidsBNgbidsNgbidsNcq qqqqqqzDccccccult 5.0
28
Vesic Formula Shape Factors
c
q
cN
N
L
Bs 1
tan1
L
Bsq
L
Bs 4.01
29
Vesic Formula Load Inclination Factors
0'
1
c
cNcA
Vmi
0
'tan
1'
m
qcA
P
Vi
0
'tan
1
1
'
m
cAP
Vi
LB
LBm
/1
/2
For loads inclined in B direction
30
Vesic Formula Depth Factors
B
Dk 1tan
2)sin1(tan21 kdq
1d
kdc 4.01
31
Groundwater Table Effect
32
Groundwater Table Effect;
Case I
1. Modify ′zD
2. Calculate ′ as follows:
wb
33
Groundwater Table Effect;
Case II
1. No change in ′zD
2. Calculate ′ as follows:
B
DDww 1
34
Groundwater Table Effect;
Case III
1. No change in ′zD
2. No change in ′
35
Example 6.3
36
Allowable Bearing Capacity
F
qq ulta
….. Allowable Bearing Capacity
F …. Factor of safety
aq
37
Factor of Safety
Depends on:
Type of soil
Level of Uncertainty in Soil Strength
Importance of structure and consequences
of failure
Likelihood of design load occurrence
38
Factor of Safety
39
Factor of Safety
• Shear strength data are normally interpreted
conservatively, so the design values of c and ø implicitly
contain another factor of safety.
• Service loads are probably less than the design loads.
• Settlement, not bearing capacity, often controls the
final design, so the footing will likely be larger than that
required to satisfy bearing capacity criteria.
• Spread footings are commonly built somewhat larger
than the plan dimensions.
40
Minimum Factor of Safety
41
BEARING CAPACITY ON LAYERED SOILS
Three primary ways
1. Evaluate the bearing capacity using the lowest
values of c‘ and ø’ in the zone between the bottom
of the foundation and a depth B below the bottom.
2. Use weighted average values of of c‘ and ø’
based on the relative thicknesses of each stratum.
3. Consider a series of trial failure surfaces beneath
the footing and evaluate the stresses on each
surface using methods similar to those employed in
slope stability analyses.
42
Example 6-5
43
Accuracy of Bearing Capacity
Analysis
In Clays …..Within 10% of true value (Bishop and
Bjerrum, 1960)
Smaller footings in Sands…. Bearing capacity
calculated were too conservative – but
conservatism did not affect construction cost much
Large footings in Sands … Bearing capacity
estimates were reasonable but design was
controlled by settlement
44
Accuracy; Bearing Capacity Analysis