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The Islamic university - Gaza Faculty of Engineering Civil Engineering Department CHAPTER (3) Instructor : Dr. Jehad Hamad BEARING CAPACITY OF SHALLOW STRIP FOUNDATIONS
The Islamic university - Gaza
Faculty of Engineering
Civil Engineering Department
CHAPTER (3)
Instructor : Dr. Jehad Hamad
BEARING CAPACITY OF SHALLOW STRIP FOUNDATIONS
DEFINITION OF SOILDEFINITION OF SOIL
Soil is a mixture of irregularly shaped mineral particles of various
sizes containing voids between particles. The particles are a by-
product of mechanical and chemical weathering of rock and
described as gravels, sands, silts, and clays.
Any manmade structure should, one way or another, rest
and/or transmit its load to the underlying soil
BEARING CAPACITY OF SOILSBEARING CAPACITY OF SOILS
oBearing capacity: is the ability of soil to safely carry the pressure
placed on the soil from any engineered structure without undergoing
a shear failure with accompanying large settlements.
oTherefore, settlement analysis should generally be performed
since most structures are sensitive to excessive settlement.
Types of FoundationsTypes of Foundations
ShallowFoundations
DeepFoundations
Spread Mat or Raft
Friction PilesBelled Pier
Bearing Capacity of Shallow Foundations
Bearing Capacity of Shallow Foundations
Soil Bearing Capacity is Controlled by:
ØBearing Capacity Analysis:
§ Terzaghi’s Theory (1943), based on Prandtl theory (1920).
§ General B.C. Equation.
ØSettlement Analysis:
§ Immediate Settlement.
§ Consolidation Settlement.
Failure Modes for Shallow Foundations
Failure Modes for Shallow Foundations
oGeneral Shear Failure
oLocal Shear Failure
oPunching Shear Failure
This failure alerted engineers to the mechanism of how surface loads may exceeded the shear strength of the soils beneath the foundation.
Terzaghi B/C AssumptionsTerzaghi B/C Assumptions
BD f ≤Ø The foundation is considered to be shallow if
However ,in recent studies ,the foundation is considered to
be shallow if . Other wise it is considered to be
deep foundation.
Ø Foundation is considered to be strip if
Ø The soil from the ground surface to the bottom of the
foundation is replaced by a surcharge .
4/ ≤BDf
00.0/ →LB
fDq γ=
oModes of foundation
failure in sand
General ConceptGeneral Concept
Z o n e I, A c tiv e
Z o n e s II, T ra n s it io n
Z o n e s III , P a s s iv e
General ConceptGeneral Concept
o Active zone, just below thefoundation.
o Transition zone, between the activeand passive zones.
o Passive zone, near the groundsurface, just beside the foundation.
passive active
Transition
Three zones do exist:
Terzaghi Bearing EquationTerzaghi Bearing Equation
qult = qult = c Nc
qult = c Nc + γ1 D Nq + 0.5B γ2 Nγ
qult = c Nc + γ1 D Nq
Cohesion Term
Above F.L.
Below F.L.
Terzaghi Bearing EquationTerzaghi Bearing Equation
are Terzaghi B/C Coefficients ,f(φ)(See table 3.1- P139)
are the soil shear strength parameters
Nc, Nq, Nγ
Φ c
oVariation of
&
for circular and rectangular
plates on the surface of a
sand.
oRange of settlement
of circular & rectangular
plates at ultimate Load
in sand.
Terzaghi’s Equation for Different Foundation Shapes
Terzaghi’s Equation for Different Foundation Shapes
qu = c Nc + γ1 D Nq + 0.5 B γ2 Nγ
qu net = c Nc + γ1 D (Nq - 1) + 0.5 B γ2 Nγ
qu = 1.3c Nc + γ1 D Nq + 0.4B γ2 Nγ
qu= c Nc + γ1 D Nq + 0.3 B γ2 Nγ
Continuous Footing:
Square Footing:
Circular Footing:
• Strip Footing
• Square footing
• Circular footing
'''
21
32
γγBNqNcNq qcu ++=
''' 4.0867.0 γγBNqNcNq qcu ++=
''' 3.0867.0 γγBNqNcNq qcu ++=
Φ=Φ − tan
32tan 1'
''' ,, γNNN qcFactors for bearing capacity given fromtable 3.2 P.140
Bearing Capacity of Clay, φ = 0Bearing Capacity of Clay, φ = 0
qult = c Nc + γ1 D Nq + 0.50 B γ2 N γ
For Clay:
Nc = 5.70, Nq = 1.0, Nγ = 0.0
qult = 5.70 cu + γ1 D
qult net = 5.70 cu
cu = qu/2 qu Unconfined compressive strength
qall net = 1.90 cu
Bearing Capacity of Sand, cu = 0Bearing Capacity of Sand, cu = 0
qult = c Nc + γ1 D Nq + 0.50 B γ2 N γ
For Sand:
Nc, Nq, Nγ are determined from curve, and cu = 0, then:
qult = γ1 D Nq + 0.50 B γ2 N γ
Gross and Net Bearing Capacity“Factor of Safety”
Gross and Net Bearing Capacity“Factor of Safety”
qult (net)= qult - γ1 D
Gross allowable bearing capacity
Net ultimate B/C
Net allowable B/C
γ1 D is the overburden pressure
..
SFq
q ultall =
..
SFq
q netultnetall =
Effect of Water Table on B/C
):1(Case
γ1 D = γ D1 + γsub D2,γ2 = γsub
qult = c Nc + γ1 D Nq + 0.5B γ2 Nγ
Effect of Water Table on B/C
):2(Case
γ1 D = γDf , γ2 = γsub+d/B (γ−γsub)
qult = c Nc + γ1 D Nq + 0.5B γ2 Nγ
Effect of Water Table on B/C
):3(Case
The water has no effect on bearing capacity
qult = c Nc + γ1 D Nq + 0.5B γ2 Nγ
γ = Bulk unit weightγsub = Submerged Unit weight
γsub = γsat - γwater
Meyerhof’s equationMeyerhof’s equation
• Nc, Nq, Nγ are Meyerhof’s B/C Factors, f(φ)
(See table 3.3- P144)
• Shape Factors
• Depth Factors
• Inclination Factors(See table 3.4 in the text book)
idsqiqdqsqcicdcscu FFFBNFFFqNFFFcNq γγγγγ5.0++=
٣١
Fci, Fqi, Fγ i
P
Footings with inclined loadsFootings with inclined loads
Pβ
Inclined Load Factors
L
Eccentrically Loaded FoundationEccentrically Loaded Foundation
B’=B-2e , L’=L , A’=B’*L’To find shape factors: use B’,L’To find depth factors: use B, LTo find the gross ultimate load
idsqiqdqsqcicdcscu FFFNBFFFqNFFFcNq γγγγγ '' 5.0++=
'' AqQ uu ×=
±
×=
×±
×=
×±
×=
××±
×=
=
=
=×=
±=
Be
LBP
LBeP
LBP
LB
ePLB
P
LB
BePLB
Pq
Bc
LBI
PeMLBA
IMc
APq
616
61
121
2/2/
121.
223
3
oFor e<B/6:
−
×=
+
×=
Be
LBPq
Be
LBPq
61
61
min
max
)2(34
max eBLPq−
=
oFor e = B/6:
oFor e > B/6:
0.0
61
min
max
=
+
×=
qBe
LBPq
Failure of eccentrically loaded foundation
Two way eccentricityTwo way eccentricity
How to find A' ?
By
Lx
ePMePM
×=×=
idsqiqdqsqcicdcscu FFFNBFFFqNFFFcNq γγγγγ '' 5.0++=
61&
61
≥≥Be
Le BL
'
''
11'
1
1
11'
),max(
35.1
35.1
21
LAB
LBLLeLL
Be
BB
LBA
L
B
=
=
−=
−=
=
oCase (I)
610&
21
<<<Be
Le BL
oCase (II)
( )
graph. eThrough th :
&LL
:axis- xLe
:axis-y
. figureat look L and L find To
),max(........21
21L
21
'
''
21'
21'
Be
LL
LAB
LLLBLLA
B
=
=+=
210&
61
<<<Be
Le BL
( )
graph. eThrough th :
&BB:axis-x
Be :axis-y
beside figureat look B and B find To
21
21
B
21
''
21'
Le
BB
LAB
LBBA
L
=
+=
oCase (III)
61&
61
<<Be
Le BL
( )( )
graph. eThrough th :
&LL:axis-x
Be :axis-y
beside figureat look B and L find To
21
22
B
22
''
222'
Le
BB
LAB
LLBBBLA
L
=
−++=
oCase (IV)
