1. Describe the burland triangle, where does the engineer fit in?
Ground profile --> Appropriate model --> Soil behaviour
The engineer fits in the middle with precedent, empiricism and well-winnowed experience
2. What is limit state? Which two types are identified?
A Limit State is a condition of a structure beyond which it no longer fulfils the relevant design criteria. (Eurocode 2001)
Typically two types are identified
- Ultimate limit state (ULS)
- Serviceability limit state (SLS)
3. What is the difference between probabilistic and deterministic methods?
A deterministic method gives a precisely determined outcome out of say calculations through known relationships between states and events without any random variations
A propabilistic method estimates the likelyhood of something happening on the basis of past the data which makes it reliant on the data which you give it. The method includes randomness and even though the initial conditions might be the same, the result of two identical evaluations might be different.
4. What is a reliability index?
It's a way of describing the reliability of a system, which is basically the cumulative normal distribution which is a function of the probability of failure
5. Which levels of probabilistic design do exist? What are the difference between them?
Which of those are used in Geotech?
Several levels of probabilistic analysies to design for an acceptable level of reliability:
From most complex, requires a lot of statistical data on failure rate
Level IV methods: -risk based- (consequence times probability of failure)
• Level III methods: -numerical- uncertain quantities are modelled by their joint distribution functions
• Level II methods: -approximation- uncertain parameters are modelled by the mean values and the standard deviations, and by the correlation coefficients between the stochastic variables
• Level I methods: -semi-probabilistic design- uncertain parameters are modelled by one characteristic value for load and resistance (Load and Resistance Factor Design )
• Level 0 methods: -deterministic calculations- global safety factor
Simple and perhaps unsafe
Structural mechanics uses Level II – IV methods much more often
Although we have quite a good idea on (structural) loads in geotechnics we are ‘stuck’ with level 0 and level 1 methods due to uncertainties related to the soil
Level 1 methods: Eurocode
Level 0 methods: Total safety factor approach
6. Explain LRFD
Load and Resistance Factor Design (LRFD)
- Factor characteristic load Sk and characteristic resistance Rk (capacity) with a partial safety factor
7. How do we obtain characteristic values in Geo?
– In Geotechnics the ENGINEER decides on the relevant strength-profile, or identifies a weak layer the failure plane should pass through
– EC7 provides some recommendations depending on coefficient of variation
8. How does this differ from structures
In structures these are not calibrated with more advanced probabilistic methods as there is not sufficient data in order to do it
9. Describe ULS for GEO
Failture or excessive deformations in the ground
1. Local stability --> Stability against rotational, vertical and translational failure
2. Overall stability --> Stable against slope failure of a retaining structure supporting a sloping ground
3. Stability against movement --> Of a geotechnical structure and/or adjacent ground – e.g. excavation near an adjacent building or on top of a tunnel
10. How can we assess SLS?
The SLS in geotechnics is mostly a differential settlement in the ground resulting in cracks in the structure (or foundation)
11. Describe some possible approaches for geotechnical modelling
Empirical model:
- Based on experience. For example CPT
Theoretical modelling:
- Analytical model -> Often closed form limit state
- Numerical model -> Idealise material characterisation and boundary condition to obtain limit state solution for all possible loads and mechanisms
12. Which assumptions are made for limit analysis?
1. Soil behaves perfectly plastic. Work hardening or softening does not occur. This is an oversimplification
2. Yield surface is convex in shape and exhibits normality condition. This is reasonable
3. No significant change in geometry of soil mass during failure allowing the equations of virtual work to be applied
13. What is the limiting feature of limit analysis?
Full numerical analysis are perferred when more realism is required.
14. Difference between lower bound and upper bound theorems
The lower one is the safe theorem where we underestimate the capacity of the system, while the upper bound theroem is an unsafe estimation of the failure load.
15. What is a closed form solution in context to limit analysis?
In case Lower bound == Upper bound a closed form solution is obtained