foundation engineering - الصفحات الشخصية...

25 September 2016Bearing Capacity1

4th Year Civil

FOUNDATION ENGINEERING

Instructor : Dr. Jehad Hamad

BEARING CAPACITY OF SHALLOW STRIP FOUNDATIONS


DEFINITION 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 man made structure should, one way or another, rest and/or transmit its load to the underlying soil


Ultimate BEARING CAPACITY OF SOILS

Bearing 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.

Therefore, settlement analysis should generally be performed since most structures are sensitive to excessive settlement.

Types of Foundations


ShallowFoundations

DeepFoundations

SpreadMat or Raft

Friction Piles

Belled Pier

Bearing Capacity of Shallow Foundations

• Soil Bearing Capacity is Controlled by:–Bearing Capacity Analysis:

• Terzaghi’s Theory (1943), based on Prandtl theory (1920).

• General B.C. Equation.

–Settlement Analysis:• Immediate Settlement• Consolidation Settlement


Failure Modes for Shallow Foundations


General Shear Failure, Zones I, II, III, Dense Sand

Local Shear Failure,Zones I, II, Medium Dense Sand

Failure Modes, Continued

25 September 2016Bearing Capacity7Punching Failure, Zone I Only, Loose Sand and Soft Clay

Terzaghi B/C Assumptions 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.

Foundation is considered to be strip if

The soil from the ground surface to the bottom of the foundation is replaced by a surcharge .


BD f ≤

4/ ≤BD f

00.0/ →LB

fDq γ=

General Concept


Zone I, Active.Zones II, Transition.

Zones III, Passive.


General ConceptThree zones do exist:

1- Active zone, just below the foundation.2- Transition zone, between the active and passive zones.3- Passive zone, near the ground surface, just beside the foundation.

passive active

Transition

Terzaghi Bearing Equation for Strip Footing


B

qu net = c Nc + γ1 D (Nq - 1) + 0.5 B γ2 Nγ

γ1 D

Generalized soil strength : c, φ(drainage as applicable)

Soil unit weight : γ2 (total oreffective as applicable)

Overburden

Failure Zone (depth ≈ 2B)


Terzaghi Bear ing 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 Bear ing Equation

Nc, Nq, Nγ are Terzaghi B/C Coefficients, f(φ)(See table 4.1)

C, φ are the soil shear strength parameters

Terzaghi’s Equation for Different Foundation Shapes

• Continuous (Strip) Footing:qu = c Nc + γ1 D Nq + 0.5 B γ2 Nγ

qu net = c Nc + γ1 D (Nq - 1) + 0.5 B γ2 Nγ

• Square Footing:qu = 1.3c Nc + γ1 D Nq + 0.4B γ2 Nγ

• Circular Footing:qu = 1.3 c Nc + γ1 D Nq + 0.3 B γ2 Nγ


• 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 from table 4.2


Bear ing 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 qall net = 1.90 cu

cu = qu/2 qu Unconfined compressive strength


Bear ing 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 Bear ing Capacity“Factor of Safety”

..

SFqq ult

all =

qult (net)= qult - γ1 D

Gross allowable bear ing capacity

Net ultimate B/C

..

SFqq netult

netall = Net allowable B/C

γ1 D is the overburden pressure

Effect of Water Table on B/C


Meyerhof’s equation

• Nc, Nq, Nγ are Meyerhof’s B/C Factors, f(φ)(See table 4.3-)

• Shape Factors• Depth Factors• Inclination Factors

(See table 4,4 in the text book)25 September 2016Bearing Capacity39

idsqiqdqsqcicdcscu FFFBNFFFqNFFFcNq γγγγγ5.0++=


Terzaghi Bearing Equation

BP


Fci, Fqi, Fγ i

P

Footings with inclined loads

Pβ

Inclined Load Factors

L


Inclined Loads

Correction Factors, Fci , Fqi , and Fγi are empirically determined from experiments

Fci = Fqi = (1.0 - β / 90)2

Fγi = (1.0 - β / φ)2

Eccentrically Loaded Foundation


idsqiqdqsqcicdcscu FFFNBFFFqNFFFcNq γγγγγ '' 5.0++=

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

oFor e<B/6:


oFor e = B/6:


oFor e > B/6:

Failure of eccentrically loaded foundation


Two way eccentricity

25 September 2016Bearing Capacity51 How to find A' ?

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