UNDERGROUND M 3. UPC GROUP - Barcelona A. Ledesma & A. Gens. Prague meeting, 24 th October 2006

Transcription

1 UNDERGROUND M 3 UPC GROUP - Barcelona A. Ledesma & A. Gens Prague meeting, 24 th October 2006

2 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)

3 UPC GROUP Program schedule Task 4: UPC + AP + CTUP + Collaboration from Cambridge (Database) Funding still pending from Spanish Research Agency

4 UPC Contribution 3 levels considered when developing data analysis -1 st level: Compilation of data. Rough analysis & identification of critical zones -2 nd level: Mechanical analysis of the potential critical areas. FE analysis + Optimization module to identify material parameters -3 rd level: Suggestion of actions by a decision support system

5 UPC Contribution 3 levels considered when developing data analysis -1 st level: Compilation of data. Rough analysis & identification of critical zones Sensor 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

6 UPC Contribution 3 levels considered when developing data analysis -1 st level: Compilation of data. Rough analysis & identification of critical zones -2 nd 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

7 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)

8

9 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

10 Minimization of the Objective Function J T ( x * x) C 1 ( x * x) x = M( p) M( p) J( p) Numerical procedures to minimize that function may require to evaluate the sensitivity matrix: x A = p

11 Computation of A may be performed in the framework of a FE formulation x 1 f K A= = K x p p p Information on the quality of the parameters identified is also obtained C p T 1 1 = A C x A

12 Example 1 Barcelona Metro (L2)

13 Barcelona Metro Example 1

14 Example 1 Barcelona Metro Mínimum Layer 2

15 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?)

16 UPC GROUP Program schedule Task 4: UPC + AP + CTUP

17 Example 2 Tunnel in a centrifuge (Mair, 1979) Kaolín Displacements+Pore water pressures Modified Cam-clay

18 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=σ 2 x/σ 2 u

19 Example 2 Comparison between observed and computed variables Measured: Computed: Despl./Diameter Dist. Axis/Diamet. Pore water press./156 KPa Stress in the tunnel (KPa)

20 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)

21 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)

22 Basis of Inverse problem Assuming a model, the best parameters are those that minimize the difference between measured and computed variables Least squares: m i= 1 2 ( * ) i i J = x x Maximum likelihood: J T ( x * x) C 1 ( x * x) x =