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