Retaining walls design Subgrade reaction method

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Retaining walls designSubgrade reaction method
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Summary

• Introduction
• Principles of the calculation method
• Required data
• Definition of the construction stages
• Typical output

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Introduction

• The subgrade reaction method allows for the
  analysis of flexible retaining walls such as
  diaphragm walls, soldier-pile walls, or
  sheet-pile walls.
• It enables to calculate the horizontal
  displacements and bending moments of the
  retaining wall through its various construction
  stages
• The initial stage consists in building the
  retaining wall itself.
• The following stages correspond to various
  actions such as earthworks (excavations, fills,
  ), installation of anchors or struts, change of
  the water level, or load application.

Introduction
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Plane and circular diaphragm walls
Applications
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Sheet-pile walls
Soldier-pile walls
Applications
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The calculation method

• The wall is assumed to extend to infinity in the
  out-of-plane direction, so that the problem is
  plane strain (except in the case of a circular
  retaining wall).
• The wall inertia be defined according to depth.
  The wall can be subjected to
• Earth and water pressures
• Horizontal loads
• Forces applied by struts or anchors
• Imposed external moments
• Rotation springs (embedment of external
  structures).
• The earth and water pressures are modeled by
  horizontal pressures applied on both sides of the
  wall. Earth pressures are related to the wall
  displacements by an elasto-plastic soil behaviour
  law. The parameters for this law are calculated
  at each depth they depend on the soil properties
  of the corresponding layer, and on the vertical
  stress in the soil (depending on the excavation
  level, the water level and the possible loads).

Calculation method
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• The retaining wall is assumed to be a flexible
  beam, laying on elasto-plastic supports.

• Soil layers are modeled as springs reacting
  linearly until they reach a plastification stress
  (either on active or passive pressure side).
• In construction stages, various actions can be
  defined, resulting in forces acting on the beam.
• The calculation consists in finding the
  equilibrium state between the beam displacements
  and the stresses in the soil layers iterative
  calculation.

Calculation method
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Soil behaviour elasto-plastic

• At-rest pressurepi p0 k0 sv0 for the first
  calculation stage with sv0 vertical effective
  stress at rest
• Active pressurepa ka sv ca c
• Passive pressurepp kp sv cp c
• Modulus of subgrade reactiongradient kh dkh
  . z with kh modulus (i.e. coefficient)of
  subgrade reaction

Calculation method
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Soil behaviour changes after soil plastification

Soil behaviour changes when the wall is
 separated  from the soil(no traction allowed)
Calculation method
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Soil behaviour varies depending on loading
conditions soft soils are taken into account
with unloading and reloading coefficients (for
soft clays for example).
Reloading conditions

• ?pi kr ?sv if ?sv gt 0 with kr reloading
  coefficient
• ?pi kd ?sv if ?sv lt 0 avec kd unloading
  coefficient

As the initial state is modified, the
displacement required to reach plastification
changes.
Calculation method
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The project data

• Required data include
• Project general settings
• Soil properties
• Retaining wall properties

Required data
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General settings

• Units
• Water unit weight
• Number of iterations allowed for the calculation
  of each stage
• Calculation step along the wall (maximum value)

Required data
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Soil properties

• Soil properties
• Zl and Zwater top level of the layer and water
  level
• PVh and PVd moist unit weight and buoyant unit
  weight
• c, Dc/m and j.

• Specific calculation properties
• k0, ka, kp coefficients of at-rest, active and
  passive earth pressures
• kd, kr unloading and reloading coefficients
• ca, cp active and passive earth pressure
  coefficients for cohesion
• kh, Dkh/m modulus of subgrade reaction and its
  variation with depth

K-REA includes useful wizards.
Required data
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Calculation of active and passive earth pressure
coefficients
3 methods

• Kérisel and Absi (tables)
• Coulomb method (formulae)

Required data
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• Rankine formulae

Caquot formulae for ca and cp
Required data
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Calculation of the reaction modulus
3 methods

• Balay method
• Schmitt method
• Chadeisson curves

Required data
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Retaining wall properties

• The retaining wall should be defined either by
  its
• Total product of inertia,
• Thickness and Youngs modulus.

• Advanced properties
• Working length out-of-plane,
• Circular retaining wall.

Required data
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Definition of construction stages
All the construction stages are defined via the
user interface. Main features allow for

• The creation of new stages,
• The definition of actions in stages,
• The graphical display of the actions in
  real-time,
• The launch of the calculations,
• The output display.

Construction stages
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Adding a new calculation phase
Staged construction zone
Construction stages
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Selecting the relevant action
Action selection zone
Construction stages
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Defining and validating the selected action
Action parameters zone
Construction stages
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Definition of construction stages
Various action types are used to define the
construction stages. They are divided into 6
categories

• Initial conditions,
• Loading / Forces / Couples,
• Earthworks,
• Anchors / Wall,
• Soil properties,
• Hydraulic conditions.

Construction stages
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Initial conditions
These actions can be applied only once, in the
initial conditions.

•  Caquot  load (uniform and distributed. It is
  removed when earthworks are applied on the same
  side).

Between z1 and z2 Active pressure multiplied by
R Passive pressure multiplied by RC Water pr. of
both sides multiplied by R Kh multiplied by R

• Reduced pressures for soldier-pile walls.
  Pressures are applied again at 100 (i.e.
  without reduction) after sheeting installation.

• Maximum pressure (in the case of precast walls).

Construction stages
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Loads forces - couples

• Boussinesq load(localised, limited extent)

• Graux load(localised, limited extentand
  diffused)

Construction stages
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Loads forces - couples

• External moments (additional moment,due to an
  embedded floor for example)

• Horizontal loads(trapezoidal)

Construction stages
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Earthworks
3 different excavation types

• Simple (possibility to excavate, change water
  level and apply a Caquot load on excavation side
  at the same time),
• With berm,
• With sheeting installation (if the  reduced
  pressures  option was activated in the initial
  stage).

Construction stages
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• Fill (with the option to define a separation at
  formation level, and/or to apply a Caquot load on
  top of the fill).

Construction stages
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Anchors Retaining wall
3 types of anchors can be applied and superposed

• Struts

• Anchors (its prestress can be used as a linear
  load)

• Embedments (allow for definition of a rotation
  stiffness).

These elements can be deactivated in later
stages.
Construction stages
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• Modification of the wall stiffness (the wall
  stiffness can only be decreased)

• Wall upraising (additional wall element on top)

Construction stages
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Soil properties

• Modification of the soil properties (separate
  modification of each soil parameter, either on
  one side only, or for both sides at the same
  time).

Construction stages
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Hydraulic conditions

• Hydaulic gradient.

Example To apply at depth z 50 m the
hydraulic pressure of a 20 m water column,
Construction stages
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Output

• Most important results for each stage are
• horizontal displacements of the retaining wall
• bending moments
• shear forces.

Results output
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• Additional detailed results display of
  tables/graphs
• For both wall sides
• Soil state for each cell
• Earth pressures
• Water pressures
• Vertical pressures
• Limit pressure on active and passive sides
• Annular pressure for a circular retaining wall.

Limiting/mobilised earth resistance ratio
Results output
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• Envelopes
• Displacements
• Shear forces
• Bending moments.

Results output
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Summary of the maximum values reached for each
stage
Summary of the staged construction
Results output
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