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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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M a r t i n ( 2
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H a n s e n
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M i c h a l o w s k i ( 1
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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