Principles of Modelling

Question 1

Design Process

Answer 1

Diagram relating ULS and SLS

Question 2

Ultimate Limit State (ULS)

Answer 2

State associated with collapse or with other similar forms of structural behaviour (e.g. exceeding the bearing resistance of the foundation) STRENGTH

Question 3

ULS - Geotechnical design

Answer 3

ULS include failure by excessive deformation, leading to loss of stability of the structures or any part of it.

Question 4

Serviceability Limit State (SLS)

Answer 4

Conditions beyond which specified service requirements for a structure or structural member are no longer met (e.g. excessive settlement leading to cracking in the structure) STIFFNESS

Question 5

Numerical modelling - simple, theoretical or empirical

Answer 5

COST: low-medium risk, quick and cheap
ACCURACY: very low

Question 6

Numerical modelling - complex, iterative/ computational (relatively low cost)

Answer 6

COST: medium-high risk, more time
ACCURACY: relatively low

Question 7

Physical modelling - full scale (high cost)

Answer 7

COST: medium-high risk, more time
ACCURACY: highest

Question 8

Physical modelling - small scale, 1 gravity

Answer 8

COST: low-medium risk, quick and cheap
ACCURACY: low

Question 9

Physical modelling - small scale, enhanced gravity (medium cost)

Answer 9

COST: medium-high risk, more time
ACCURACY: relatively high

Question 10

Numerical modelling - finite element (Abaqus): Assumptions

Answer 10

Soil continua
partial differential equations to describe physical phenomena
Extensive integration method with solution of f = KU

Question 11

Finite Element: Advantages

Answer 11

• general analytical tool
• divide geometry into elements
• adaptive methods can refine mesh & reduce errors
• spatial variation of material properties
• more representative constitutive models
• computing power up
• ideal for service - ability analysis

Question 12

Finite Element: Disadvantages

Answer 12

• approx. solution + engineering judgement vs complex analysis
• displacements and strains must vary according to type of element selected
• element concentration required for areas of high strain/ pore pressure variation
• numerical instability at large strain variations

Question 13

Numerical modelling - finite difference (FLAC): Assumptions

Answer 13

Soil continua + iterative finite-difference formulation i.e. similar to finite element method

Question 14

Finite Difference: Advantages

Answer 14

• competitive with FEM when highly non-linear
• range of constitutive models/ applications inc. user-specified

Question 15

Finite Difference: Disadvantages

Answer 15

• not ideal for certain problems
• strict limitations on mesh pattern unless at the expense of calculation efficiency
• large relative stiffness differences can cause instability?

Question 16

Physical modelling - 1g full scale testing

Answer 16

100 kPa - 140 kPa

Question 17

Physical modelling - 1g full scale testing: Advantages

Answer 17

• stress correct
• can control soil conditions

Question 18

Physical modelling - 1g full scale testing: Disadvantages

Answer 18

• time to construct & diffusion processes (consolidation)
• boundary effects
• cost

Question 19

Physical modelling - field monitoring

Answer 19

100 kPa - 140 kPa

Question 20

Physical modelling - field monitoring: Advantages

Answer 20

• “the real thing”
• stress correct
• soil, geometry, boundaries realistic

Question 21

Physical modelling - field monitoring: Disadvantages

Answer 21

• time (for diffusion)
• cost
• FAILURE not OK
• Boundary/ soil conditions often not clear

Question 22

Physical modelling - 1g small scale testing

Answer 22

1: m (scale) ~ 1

Question 23

Physical modelling - 1g small scale testing: Advantages

Answer 23

• time (very quick)
• cost (very cheap)
  therefore good preliminary test to check equipment & testing principles

Question 24

Physical modelling - 1g small scale testing: Disadvantages

Answer 24

• stress incorrect
• potential for suctions & dilatancy to affect results
• boundary effects

Question 25

Physical modelling - 100g (ng), 1/100 th scale in centrifuge

Answer 25

100 kPa - 140 kPa

Question 26

Physical modelling - 100g (ng), 1/100 th scale in centrifuge: Advantages

Answer 26

• stress correct
• idealise to reveal key mechanisms of behaviour
• select soil & hence soil parameters
• design stress history
• control loading systems
• time
• cost
• allowed to fail: observer witnesses deformation and failure mechanisms

Question 27

Physical modelling - 100g (ng), 1/100 th scale in centrifuge: Disadvantages

Answer 27

• Radial ‘g’ field (in a beam centrifuge)
• ng varies with depth
• Coriolis effect
• size of particles, instrumentation, site investigation devices
• stress path may be different
• the construction method different?
• Boundary effects?
• so take over idealisation

Question 28

Idealise any combination of:

Answer 28

• geometry (dimensions)
• soil (properties)
• structure (properties)
• loading (type - static/ dynamic, magnitude)
• construction effects (construction, excavation)

Question 29

Centrifuges - Beam

Answer 29

A beam is mounted on a central spindle and can rotate about this to allow models made in packages located at each end of the beam to be subjected to increased gravity. Usually, these packages are fixed to a swinging platform so that they are hanging in the vertical plane initially and can swing up to lie in the horizontal plane as the centrifuge acceleration is increased.
Can scale time

Question 30

Centrifuges - Durm

Answer 30

A different style of centrifuge, in which a drum of diameter between 800 mm and > 2m may be rotated respectively, between ~550 & 90 rpm, to present a seabed of 0.1 - 0.5 km wide by 1 - 3 km long in a gravity field of 500g. This allows examination of soil behaviour for specific problems which relate to shallow constructions (shallow foundations onshore and offshore, transport processes for environmental geotechnics, tunnelling, ice forces on structures, slope stability etc.).