upc group - barcelona a. ledesma & a. gens
TRANSCRIPT
UNDERGROUND M3
UPC GROUP - Barcelona
A. Ledesma & A. Gens
Prague meeting, 24th October 2006
UPC GROUP
• Profs. Antonio Gens & Alberto Ledesma
• Experience on Geotechnical analysis, including systematic backanalysis and parameter identification
• Extensive collaboration with Barcelona Metro and Madrid Metro (associated partners of the project)
UPC GROUP
Program schedule Task 4:
UPC + AP + CTUP + Collaboration from Cambridge (Database)
Funding still pending from Spanish Research Agency
UPC Contribution
3 levels considered when developing data analysis
-1st level: Compilation of data. Rough analysis & identification of critical zones
-2nd level: Mechanical analysis of the potential critical areas. FE analysis + Optimization module to identify material parameters
-3rd level: Suggestion of actions by a decision support system
UPC Contribution
3 levels considered when developing data analysis
-1st level: Compilation of data. Rough analysis & identification of critical zonesSensor data: ID number + Date & Time + Measurement
(i.e. Strain)
Then identify critical zones (i.e., check if a limit value has been reached). That can be performed at a database scale
UPC Contribution
3 levels considered when developing data analysis
-1st level: Compilation of data. Rough analysis & identification of critical zones
-2nd level: Mechanical analysis of the potential critical areas. FE analysis + Optimization module to identify material parameters
Define a 2D section for further analysis
Finite Element code (….PLAXIS)
Optimization module to be developed
UPC Contribution
Define a 2D section for further analysis
Geometry, Soil / Rock properties (elastic, plastic, strength), Water table variations, Lining properties
Initial stresses (construction process, geology)
(It should be defined “ad hoc” … difficult for managing purposes)
Basis of “Inverse analysis”
• Usually a model including geometry and constitutive laws is assumed fixed.
• Some measurements are available.
• Find the best set of parameters (i.e. material properties) that reproduce the measurements
Minimization of the Objective Function
( ) ( )T* 1 *xJ −= − −x x C x x
M( )p M( )p
J( )p
Numerical procedures to minimize that function may require to evaluate the sensitivity matrix:
∂=∂xAp
Computation of A may be performed in the framework of a FE formulation
− ⎡ ⎤∂ ∂ ∂= = −⎢ ⎥∂ ∂ ∂⎣ ⎦
1x f KA K xp p p
Information on the “quality” of the parameters identified is also obtained
11 −−⎡ ⎤= ⎣ ⎦T
p xC A C A
Example 1
Barcelona
Metro (L2)
Example 1
Barcelona Metro
Example 1
Barcelona Metro
Layer 2
Mínimum
UPC GROUP
Contributing to the project by the end of 2006 (expected !!!)
- U Cambridge will contribute on the database definition (a basic compilating program is needed)
- An analysis (Finite Elements) of some sections of Metro Prague could be performed by UPC (beginning 2007)
(It is convenient to know the mechanics of crack development … Reason for crack opening?
A previous FE analysis before installing MEMS?)
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UPC GROUP
Program schedule Task 4:
UPC + AP + CTUP
Example 2
Tunnel in a centrifuge
(Mair, 1979)
Displacements+Pore water pressures
Kaolín
Modified Cam-clay
Example 2
• Two sources of information: Displacements & Pore water press.
• The relative weight of each source can be introduced in the objective function as an additional parameter to be identified
µ=σ2x/σ2
u
Example 2
Dist. Axis/Diamet.
Des
pl./D
iam
eter
Stress in the tunnel (KPa)
Por
e w
ater
pre
ss./1
56 K
Pa
Comparison between observed and computed variables
Measured:
Computed:
Key aspects
Inverse analyses can be performed in a systematic manner, using FE framework.
Level 1 includes data compilation with a basic tool to decide where are the critical sections
Level 2 includes the optimization module itself (inverse problem analysis, i.e. identifying the damaged zones of the concrete lining)
Level 3 should incorporate a decision support tool (i.e. using expert system procedures)
Underground works are usually instrumented
Backanalysis has been used in Geotechnics in an “ad hoc” manner
A systematic backanalysis may be performed in underground works using numerical procedures
i.e. from measured displacements, estimate rock or soil parameters
(Inverse problem)
Basis of “Inverse problem”
Assuming a model, the best parameters are those that minimize the difference between measured and computed variables
• Least squares:
• Maximum likelihood:
( )2m
*i i
i 1J x x
=
= −∑
( ) ( )T* 1 *xJ −= − −x x C x x