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MoU on Soft Soil Engineering1996 - 2001
Regional Teaching Program 2001 Stability theory
and exercises Republic of Indonesia Kingdom of
the Netherlands RT-10 July 9th - 2001
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Stability theory and exercisesContents

• Failure mechanism
• Determination of stability of slopes
• Wedge method
• Bishop method
• Spencer method
• c- tan f reduction by Finite Element Method
• Three dimensional effects
• uplift
• squeezing

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Failure mechanism

• settlements
• local failure (slip surface)
• overall stability failure
• sliding failure
• bearing capacity failure
• squeezing
• uplift

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Failure mechanism

• circular slip surface
• local failure
• overall stability failure

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Failure mechanism

• Sliding failure
• Bearing capacity failure
• squeezing failure
• uplift

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Slope stability

• When, where and why
• occurs mainly edge of fill or excavation
• loss of equilibrium (no Sfx0, Sfy0, SM0)
• hypothesis form of planes of failure
• maximum shear resistance mobilised
• How
• Manual calculations (trial and error, tables and
  graphs)
• using computer (Bishop method, Plaxis FEM
• What
• determine Factor of Safety (SF)

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Stability, Wedge method

• horizontal slip surface
• use of vertical slices
• ignore shear forces vert. Slices
• determine needed hor. Slice force
• from hor. and vert Equilibrium
• iteratively reduction c and tan f
• by SF
• at boundary E00 and En0 kN
• DISADVANTAGES
• NO SM0
• only straight slip surfaces
• trial and error solution

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Stability, Wedge method (2)
Wedge formulation
i index number for the slice concerned from
1-n (-) Ei horizontal force on slice i (kN) Pwi
force due to pore water pressure z surface of
the slice i (kN) N' angle of internal friction
surface of slice i (') SF stability factor (-)
ci cohesion slip surface of slice i (kPa) bi
Width of slice i (m) (i unit weight of the
soil in slice i (kN /m3), hi height of slice I
(m) "i angle of slip surface of slice i
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Stability, Bishop

• circular slip surface
• vertical slices

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Stability, Bishop (2)
Definition of SF
SF
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Stability, Bishop (3)
From vertical equilibrium
From Mohr Coulomb
Gives
Solved iteratively
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Stability, Bishop (4)
Lowest SF centre point and R changed

• Limitations
• only circular slip surfaces
• no external nor internal horizontal equilibrium
• Sfy0 (in- and external), SM0 (external)

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Stability, Spencer

• Extension Bishop method
• Inter-slice force not horizontal, angle 2 with
  horizontal

For 20, Spencer Bishop
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Stability, Spencer (2)

• Iterative solution as in Bishop

Pros

• Meets all equilibrium conditions
• non circular slip surfaces possible

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Stability, Plaxis

• Finite Element Method
• SF by reducing tan(f) and c
• meets all equilibrium criteria
• slip surface any shape
• failure mechanism

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Stability, Plaxis
Bishop analysis SF 1.542 Plaxis analysis
SF 1.57
? 16 kN/m3 ? 20 c 5
kPa Slope 24.5
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Three dimensional effects

• Effect of surface load
• increase failure probability (Mdrivinggtgt)
• decrease failure probability (?res and Mresgtgt)
• concentrated load spreads 3-D
• gt increase ?e point load lt increase ?e strip
  loading
• gt increase ? point load lt increase ? strip load
• gt SF 3D analysis gtSF 2D
• THUS in 2D point load regards as strip footing
• SF underestimated (hidden
  reserve)

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Vertical equilibrium and uplift

• Bottom heave ltgt loss of equilibrium
• Example
• ?e 0 at interface aquifer-soil
• max piezometric head Hg

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Vertical equilibrium and uplift
Calculate Hg

• With
• HG piezometric head in aquifer m
• ?v vertical effective stress at
  interface m
• gw unit weight of water kN/m3
• i layer number -
• n number of layers above aquifer -
• Hp piezometric head m
• hi thickness of layer I m
• dz thickness of layers m

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Vertical equilibrium and uplift
Example
dz -11 m Hp - 2 m
gt Hg -29.6 m
Piezometric head in sand layer lt -29.6 m
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Squeezing
with
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IJsselijk method
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Stability during construction
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Stability during construction

• Design
• SF end condition (100 consolidation)
• SF during construction
  ltlt !!

• Why?
• Load increase total stressgt ?wgt
• Speed of construction

• How?
• Determine ?w dissipation ltgt U -
• SF for 30, 60 and 90 consolidation

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