• Example: Finite-strain consolidation of a two-dimensional solid
• This example involves the large-scale consolidation of a two-dimensional solid (Benchmark Problem 1.14.3).
• The modeled strip of soil is fully saturated and the analysis is transient.
Model of soil strip
Mesh:
– 35, quadratic, reduced integration, plane strain elements with pore pressure (CPE8RP) Boundary conditions:
– Free drainage across top surface – Other surfaces impermeable and smooth Loading:
– Pressure = 3.4457 MPa
– The loaded portion of the strip is 1/5 of the width
H
B
H
Analysis of Geotechnical Problems with Abaqus
© Dassault Systèmes, 2008
• Nonlinearities caused by the large geometry changes are considered, as well as the effects of the change in the void ratio on the permeability of the material.
• The load is applied in two equal time increments during the first transient soils consolidation step, and it is kept constant thereafter.
• Practical consolidation analyses require solutions across several orders of magnitude of time, and the automatic time incrementation scheme is designed to generate cost-effective solutions for such cases.
• The algorithm is based on the user-supplied tolerance on the pore pressure change permitted in any increment, UTOL.
• Abaqus uses this value in the following manner:
• If the maximum change in pore pressure at any node is greater than UTOL, the increment is repeated with a proportionally reduced time increment.
• If the maximum change in pore pressure at any node is consistently less than UTOL, the time increment size is proportionally increased.
Analysis of Geotechnical Problems with Abaqus
© Dassault Systèmes, 2008
• In this analysis the maximum pore pressure change per increment (UTOL) is set to 15 psi.
• This is about 3% of the maximum pore pressure in the model following application of the load.
• With this value the first time increment is 7.2 seconds and the final time increment is 5,437 seconds.
• This is quite typical of diffusion processes: at early times the time rates of pore pressure are significant and at later times these time rates are very low.
• The analysis is performed both with and without finite-strain effects.
• The soil permeability varies with void ratio in the model that includes finite-strain effects.
• Permeability is constant in the small-strain analysis.
L5.54
Saturated Example Problems
• Results of the finite-strain analysis:
Final deformed shape Pore pressure histories
A B
Point A
Point B
Analysis of Geotechnical Problems with Abaqus
© Dassault Systèmes, 2008
• The finite-strain and small-strain analyses predict large differences in the final consolidation:
• The small-strain result shows about 40% more deformation than the finite-strain case.
• This is consistent with results from the one-dimensional Terzaghi consolidation solutions.
• Clearly, in cases where settlement magnitudes are significant, finite-strain effects are important.
• Example: Steady-state analysis of a dam
• This problem involves the analysis of a concrete dam on a rock foundation.
• The problem description provided by Dr. G. Pande of Swansea University formed the basis of the analysis.
Concrete dam on rock foundation
Mesh:
– 110, quadratic, reduced integration, plane strain elements with pore pressure (CPE8RP)
Boundary conditions:
– Exterior edges initially impervious – Symmetry at the foundation sides
and bottom
Analysis of Geotechnical Problems with Abaqus
© Dassault Systèmes, 2008
• We assume the rock behaves as a Drucker-Prager material with nonassociated flow and orthotropic permeability.
*MATERIAL, NAME=ROCK
Vertical permeability, kv= 0.00001m/sec
L5.58
• The dam is composed of concrete. The concrete model cracks in tension at a stress of 0.15 MPa. This is a very low tensile strength, perhaps less than one-tenth of the real tensile strength of the material.
Saturated Example Problems
Analysis of Geotechnical Problems with Abaqus
© Dassault Systèmes, 2008
• The analysis is done in three stages.
• The first step establishes geostatic equilibrium where the geostatic stresses balance the gravity loads in the rock.
• This state of stress corresponds to the undeformed configuration of the rock mass.
• This type of analysis step is discussed in Lecture 6.
• The vertical stress in the rock foundation is zero at the surface and increases linearly to approximately
−0.7 MPa at the impervious bottom boundary.
• The horizontal stresses are 0.6 times the vertical stress.
• The excess pore pressure in the rock is zero.
Vertical stress
g
L5.60
• The second step of the analysis includes the following additional loads:
• Gravity loads due to the concrete dam construction
• Pressure loads on the upstream side of the dam and foundation representing the filling of the reservoir.
• In this step we assume that no pore pressures develop, because we are concerned with short-term behavior and the modeled materials have very low permeabilities.
Analysis of Geotechnical Problems with Abaqus
© Dassault Systèmes, 2008
• In the final stage of analysis we perform a steady-state pore fluid diffusion/stress analysis to calculate the state of the structure 25 years after filling the reservoir.
• Applied pore pressure boundary conditions represent the upstream and downstream conditions for the seepage part of the problem.
• We also include a phreatic surface in the concrete dam wall.
• The position of this zero pore pressure surface is assumed, the analysis is performed, and the validity of the assumption is checked.
• An iterative procedure can then be used to correct the location of the phreatic surface at steady state.
• Although not done in this case, Abaqus is capable of calculating the phreatic surface automatically.
L5.62
Saturated Example Problems
• Results
Pore pressure boundary conditions and long-term pore pressure contours
Zero excess pore pressure
Nonzero excess pore pressures corresponding to the hydrostatic pressure caused by the head of water in the full reservoir
Zero flux boundary
phreatic surface
Analysis of Geotechnical Problems with Abaqus
© Dassault Systèmes, 2008
• Results (cont'd)
• It is observed from the pore fluid effective velocity (FLVEL) plot that the pore water flows from the upstream to the downstream of the dam.
• The magnitude of FLVEL is greatest just under the concrete dam because the pressure gradient is greatest in this region of the bedrock.
Pore fluid effective velocity vector plot