consolidation analysis

Contents  Introduction  Soil permeability  1D theory of Terzaghi  FE implementation of consolidation  Influence of constitutive model and parameters • Influence of compressibility of water • Influence of void ratio dependent permeability • Influence of constitutive model  Example Embankment construction

Dr Minna Karstunen

University of Strathclyde

With help from Dennis Waterman, Marcelo Sanchez,

Antonio Gens & Helmut Schweiger

 Influence of constitutive model and parameters

• Influence of compressibility of water p y

• Influence of void ratio dependent permeability

• Influence of constitutive model

 Example - Embankment construction

Types of Analyses for Geotechnical Problems

soil permeability)

 Intermediate cases: consolidation analysis

 Intermediate cases: consolidation analysis

Excess pore Excess pore water pressure

Consolidation

Initial state Undrained loading Consolidation

Ekofisk tank

Other Examples

 Transient flow occurs in all saturated soils subjected to a change in external load

 Transient flow occurs in all saturated soils subjected to a change in external load

or a change in boundary pore water pressures , but it is important to distinguish to main groups of soils:

• Sands and gravels (with k > 10 -4 m/s): the process is usually very rapid

Consolidation is not relevant in these soils (generally)

• Clays (and possibility silts and peats): due to its low permeability and high

• Clays (and possibility silts and peats): due to its low permeability and high

compressibility, consolidation is very relevant

Basic theory of groundwater flow

h k

h k

Permeability of Soils

Permeability of Soils

 0

materials in the same problem

value lower by a factor 1000 is sufficient

The

 Terzaghi’s theory of one Terzaghi’s theory of one dimensional consolidation dimensional consolidation

compressibility remain constant through the process

and

displacements and pore pressures

FE formulation of consolidation (2)

Stiffness matrix Coupling matrix

Incremental load vector

FE formulation of consolidation (3)

Flow matrix Coupling matrix Water compressibility matrix

FE formulation of consolidation (4)

Boundary Conditions

 Cl d fl b d

Boundary Conditions

Groundwater head = y

Potts & Zdravkovic (1999)

1D Consolidation – Numerical Simulation

applied load = 100 kPa soil layer 2D = 10 m drainage at top and bottom

Investigate influence of:

 compressibility of pore water

(by means of B-value)

 permeability depending on void ratio

 elastic-plastic soil behaviour

(by means of changing constitutive model)

1D Consolidation – Numerical Simulation

perm eability e-dependent

H ardening S oil m odel

1D Consolidation – Numerical Simulation

perm eability e-dependent

0

perm eability e dependent

H ardening Soil m odel

tim e [days]

1D Consolidation – Numerical Simulation

model distribution of excess pore pressures at 50% consolidation along centre line

model distribution of excess pore pressures at 50% consolidation along centre line

l b k C i Example – Embankment Construction

influence of consolidation on stability

influence of construction speed is investigated

•"fast" construction: 2 days of consolidation per placement of 1 m embankment

•"slow" construction: 3 days of consolidation per placement of 1 m layer

embankment

Example – Embankment Construction

influence of consolidation on stability

"slow": max excess pore pressure: 86 kPa

"fast": max excess pore pressure: 100 kPa fast : max excess pore pressure: 100 kPa

Example – Embankment Construction

influence of consolidation on stability

"slow": stable

"fast": failure fast : failure

Example – Embankment Construction

influence of consolidation on stability

excess pore pressure [kPa]

Example – Embankment Construction p

influence of consolidation on stability

0 0.01

0

Time [day]

time [days]