Numerical Modelling Flashcards
What methods are there to solve geotechnical problems?
“Exact” or closed form
Numerical
Limit equilibrium
Empirical, based on experience
Types of numerical modelling and an example
Finite Element-Plaxis, Abyses
Finite difference-Flac
Discrete element-flac
Boundary element-Beasy
What is a discrete system?
Solution can only be found using a FINITE number of defined components. E.g building frame of slabs columns and beams
What is a continuous system?
Sub-division of problem is continued infinitely
Simple linear problems solved mathematically
Complex non-linear involves discretstion into components and then use mathematical method such as FEM
Three fundamental steps of the FEM
- Divide the whole (domain) into parts (subdomains), both to represent the geometry as well as the solution of the problem.
- Over each part seek an approximation to the solution as a linear combination of nodal values and approximation functions.
- Derive the algebraic relations amping the nodal values of the solution over each part and assemble the pets to obtain the solution of the whole.
What is SSI
Soil-structure-interface
Basic parts of FEM
Domain-area to be modelled
Elements - smaller areas
Nodes-corner points +extra points
Load
Boundary conditions (pinned at base, roller on edge)
=mesh
Inputs for modelling?
Geometry
Soil
Structure
Loading
Construction
Outputs from modelling
Displacement (u)
Strain (e)
Stress (sigma)
Pore pressures (sigma pp)
Bending moment (M)
What equations are used?
Equilibrium
Continuity
Compatibility
Constitutive
Equilibrium Equations
Forces and stress must be in equilibrium
Continuity equations
Rate of volumetric change equal to the rate of flow of water out of soil with the aid of the following:
Compatibility eqns
Constitutive law
Compatability
Geometry and displacements must be compatible
(u to e)
Constitutive law
Material-dependent stress-strain relationship
What is B D L and N
B=differential matrix
D=constitutive matrix
L=Differential operator
N=interpolation function (shape function)
What is plane strain
One dimension is considerably greater than the other two
Strains in the long dimension can be assumed to be 0
Numerical integration is for 1unit length
Examples of plane strain problems
Geotechnical problems:
Embankments
Retaining walls
Tunnels
What is axisymmetric problem
Both structure and loading exhibit radial symmetry about the central vertical axis
Circumferential strains can be ignored
Problem is now 2D
Example of axisymmetric problems
Pile foundations subject to vertical concentric loads
Excavation of vertical circular cross-section
Consolidation around a vertical drain
What is plane stress
One very thin dimension-stress in direction becomes =0
Mainly in structures
2D 2nd order expressions
0-constant
1-Linear
2-Quadratic
3-Cubic
4-Quartic
What do more points mean
more nodes-more accurate-higher order
