Principles of Modelling Flashcards
Design Process
Diagram relating ULS and SLS
Ultimate Limit State (ULS)
State associated with collapse or with other similar forms of structural behaviour (e.g. exceeding the bearing resistance of the foundation) STRENGTH
ULS - Geotechnical design
ULS include failure by excessive deformation, leading to loss of stability of the structures or any part of it.
Serviceability Limit State (SLS)
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
Numerical modelling - simple, theoretical or empirical
COST: low-medium risk, quick and cheap
ACCURACY: very low
Numerical modelling - complex, iterative/ computational (relatively low cost)
COST: medium-high risk, more time
ACCURACY: relatively low
Physical modelling - full scale (high cost)
COST: medium-high risk, more time
ACCURACY: highest
Physical modelling - small scale, 1 gravity
COST: low-medium risk, quick and cheap
ACCURACY: low
Physical modelling - small scale, enhanced gravity (medium cost)
COST: medium-high risk, more time
ACCURACY: relatively high
Numerical modelling - finite element (Abaqus): Assumptions
Soil continua
partial differential equations to describe physical phenomena
Extensive integration method with solution of f = KU
Finite Element: Advantages
- 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
Finite Element: Disadvantages
- 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
Numerical modelling - finite difference (FLAC): Assumptions
Soil continua + iterative finite-difference formulation i.e. similar to finite element method
Finite Difference: Advantages
- competitive with FEM when highly non-linear
- range of constitutive models/ applications inc. user-specified
Finite Difference: Disadvantages
- not ideal for certain problems
- strict limitations on mesh pattern unless at the expense of calculation efficiency
- large relative stiffness differences can cause instability?
Physical modelling - 1g full scale testing
100 kPa - 140 kPa
Physical modelling - 1g full scale testing: Advantages
- stress correct
- can control soil conditions
Physical modelling - 1g full scale testing: Disadvantages
- time to construct & diffusion processes (consolidation)
- boundary effects
- cost
Physical modelling - field monitoring
100 kPa - 140 kPa
Physical modelling - field monitoring: Advantages
- “the real thing”
- stress correct
- soil, geometry, boundaries realistic
Physical modelling - field monitoring: Disadvantages
- time (for diffusion)
- cost
- FAILURE not OK
- Boundary/ soil conditions often not clear
Physical modelling - 1g small scale testing
1: m (scale) ~ 1
Physical modelling - 1g small scale testing: Advantages
- time (very quick)
- cost (very cheap)
therefore good preliminary test to check equipment & testing principles
Physical modelling - 1g small scale testing: Disadvantages
- stress incorrect
- potential for suctions & dilatancy to affect results
- boundary effects
Physical modelling - 100g (ng), 1/100 th scale in centrifuge
100 kPa - 140 kPa
Physical modelling - 100g (ng), 1/100 th scale in centrifuge: Advantages
- 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
Physical modelling - 100g (ng), 1/100 th scale in centrifuge: Disadvantages
- 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
Idealise any combination of:
- geometry (dimensions)
- soil (properties)
- structure (properties)
- loading (type - static/ dynamic, magnitude)
- construction effects (construction, excavation)
Centrifuges - Beam
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
Centrifuges - Durm
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.).
