1. Shallow Foundations Website

8/9/2019 1. Shallow Foundations Website

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Operational strength parameters:

importance of stress-path

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Deep Foundation

Shallow Foundation


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Vertical load-displacement curve

from centrifuge and FE modelling


Failure Mechanisms


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Drained Loading


Undrained Loading


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Bearing Capacity: Rankine

Limit equilibrium of active (RST) and passive (SZT) wedges.

Limit pressure qlim can be obtained from the following relationship:

qlim = cNc + qNq + ½ γBNγ .


In caso of soil characterized by parameters c’ and φ’ but without any weight

(γ’= 0) and surface footing (q’=0), qlim is

qlim = c’Nc,

With Nc = [tan2 (45 + φ’/2)eπtanφ -1]cotφ

In case of strip footing with γ’= 0, φ’‡ 0, q’ ‡ 0,

qlim = q’Nq,

Bearing Capacity: Prandtl


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Terzaghi obtained a complete solution by superimposing the effects and usingthe limit global equilibrium method.

Assumptions are: strip footing, fully frictional soil-footing contact, applied loadcentral and vertical, footing bedding plane and ground level horizontal, line BC

of slip surface is a log spyral.

The solution can still be formulated as:

qlim = cNc + qNq + ½ γBNγ .

Bearing Capacity: Terzaghi


Bearing Capacity: Terzaghi (1943)


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0

5

10

15

20

25

T e r z a

g h i ( 1 9 4 3 )

M e y e r h o f ( 1

9 5 1 )

K u m b h o j k a r ( 1

9 9 3 )

Z h u e t a l . ( 2

0 0 1 )

S i l v e s t r i ( 2

0 0 3 )

C a q u o t & K

e r i s e l ( 1

9 5 3 )

B o o k e r ( 1

9 7 0 )

G r a h a m

& S t u

a r t ( 1 9 7 1 )

S a l e n

c o n &

M a t a r ( 1

9 8 2 )

B o l t o n &

L a u ( 1 9 9 3 )

K u m a r ( 2

0 0 3 )

M a r t i n ( 2

0 0 4 )

L u n d g r e

n & M o r t e n s e n ( 1

9 5 3 )

H a n s e n

& C h r i s t e n

s e n ( 1 9 6 9 )

M a r t i n ( 2

0 0 5 )

C h e n ( 1

9 7 5 )

M i c h a l o w s k i ( 1

9 9 7 )

S o u b r a ( 1

9 9 9 )

Z h u ( 2 0 0 0 )

W a n g

e t a l . ( 2

0 0 1 )

G r i f f i t h s ( 1

9 8 2 )

M a n o h a

r a n & D a

s g u p t a ( 1

9 9 5 )

F r y d m

a n & B u

r d ( 1 9 9 7 )

Y i n e t a l . ( 2

0 0 1 )

S l o a n

& Y u ( 1

9 9 6 )

U k r i t c h o

n e t a l . ( 2

0 0 3 )

H j i a j e t a l . ( 2

0 0 5 )

M a k r o

d i m o p o u l o s

& M a

r t i n ( 2 0 0 5 )

M e y e r h o f ( 1

9 6 3 )

B r i n c h H

a n s e n ( 1

9 7 0 )

V e s i c ( 1

9 7 5 )

E u r o c

o d e 7 ( 1

9 9 6 )

P o u l o s e t a l . ( 2

0 0 1 )

N γ

computed by different metods, with = 30°, =

Eq. limite Caratteristiche ODEs Upper Bd FE/FD

Analisi

limite

FE Formule


Bearing Capacity: Brinch-Hansen (1970)

The general relationship for the computation of qlim refers to Brinch-Hansen’sformula, obtained by the linear superposition of solutions of specific cases:

qlim = c • Nc • sc • ic • bc • gc• dc

+ q • Nq • sq • iq • bq • gq• dq

+ ½ γ • B • Nγ

• sγ

• iγ

• bγ

• gγ

• eγ

sc , sq , sγ are foundation shape factors;

dc , dq , are depth factors;

ic , iq , iγ are load inclination factors;

eγ is load eccentricity factor;

bc , bq , bγ are foundation inclination factors;

gc , gq , gγ are ground inclination factors.


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Brinch-Hansen (1970)

Shape Factors

Brinch-Hansen and Vesic (1975)

sc = 1 + (B • Nq)/(L • Nc),

sq = 1 + (B / L) tanφ,

sγ = 1− 0.4 • (B / L) ,DeBeer (1970)

sγ = 1 + [0.2 • (B / L)]/[1+(B/L)] ,

Meyerhof (1963)

sc = 1 + [0.2 • (B / L)] tan2[45° + φ /2],

sq = sγ = 1 + [0.1 • (B / L)] tan2[45° + φ /2].


Bearing capacity: cohesive stratified soils

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