Numerical Modelling

Question 1

What methods are there to solve geotechnical problems?

Answer 1

“Exact” or closed form
Numerical
Limit equilibrium
Empirical, based on experience

Question 2

Types of numerical modelling and an example

Answer 2

Finite Element-Plaxis, Abyses
Finite difference-Flac
Discrete element-flac
Boundary element-Beasy

Question 3

What is a discrete system?

Answer 3

Solution can only be found using a FINITE number of defined components. E.g building frame of slabs columns and beams

Question 4

What is a continuous system?

Answer 4

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

Question 5

Three fundamental steps of the FEM

Answer 5

1. Divide the whole (domain) into parts (subdomains), both to represent the geometry as well as the solution of the problem.
2. Over each part seek an approximation to the solution as a linear combination of nodal values and approximation functions.
3. 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.

Question 6

What is SSI

Answer 6

Soil-structure-interface

Question 7

Basic parts of FEM

Answer 7

Domain-area to be modelled
Elements - smaller areas
Nodes-corner points +extra points
Load
Boundary conditions (pinned at base, roller on edge)
=mesh

Question 8

Inputs for modelling?

Answer 8

Geometry
Soil
Structure
Loading
Construction

Question 9

Outputs from modelling

Answer 9

Displacement (u)
Strain (e)
Stress (sigma)
Pore pressures (sigma pp)
Bending moment (M)

Question 10

What equations are used?

Answer 10

Equilibrium
Continuity
Compatibility
Constitutive

Question 11

Equilibrium Equations

Answer 11

Forces and stress must be in equilibrium

Question 12

Continuity equations

Answer 12

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

Question 13

Compatability

Answer 13

Geometry and displacements must be compatible

(u to e)

Question 14

Constitutive law

Answer 14

Material-dependent stress-strain relationship

Question 15

What is B D L and N

Answer 15

B=differential matrix
D=constitutive matrix
L=Differential operator
N=interpolation function (shape function)

Question 16

What is plane strain

Answer 16

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

Question 17

Examples of plane strain problems

Answer 17

Geotechnical problems:
Embankments
Retaining walls
Tunnels

Question 18

What is axisymmetric problem

Answer 18

Both structure and loading exhibit radial symmetry about the central vertical axis

Circumferential strains can be ignored

Problem is now 2D

Question 19

Example of axisymmetric problems

Answer 19

Pile foundations subject to vertical concentric loads

Excavation of vertical circular cross-section

Consolidation around a vertical drain

Question 20

What is plane stress

Answer 20

One very thin dimension-stress in direction becomes =0

Mainly in structures

Question 21

2D 2nd order expressions

Answer 21

0-constant
1-Linear
2-Quadratic
3-Cubic
4-Quartic

Question 22

What do more points mean

Answer 22

more nodes-more accurate-higher order