George Exadaktylos & George Xiroudakis TUC, Laboratory of Mining Engineering Design, Greece

1. Spatial estimation of geotechnical parameters for numerical tunneling simulations and TBM performance models George Exadaktylos & George Xiroudakis TUC, Laboratory of Mining Engineering Design, Greece Maria Stavropoulou UOA,Greece We aim at the fasttransformation of the conceptual qualitative geological model (left) to the spatial model of each parameter needed either by the numerical model or the tunnel excavation machine (right).

2. Introduction (motivations + proposed approach) • No clear procedures on how geological-geomechanical data needed for the determination of ground behavior is transferred into input data for 3D numerical tools. Dispersed exploration, lab testing, monitoring and other data of a given project. Also, not optimized exploration & sampling designs. • Note: In the majority of models, soil or rock parameters data are averaged over very large volumes (geological units or sections) and assigned uniformly to each building ‘‘brick’’ (element) of the model. • Experience (geological & geotechnical) from previous projects is not usually exploited. • Spatial uncertainty and risk that seriously affecting project development decisions, are frequently not considered properly.

3. Introduction (motivations + proposed approach) cont’d • Concerns of excavation machines developers (i.e. rock & soil TBM’s, Roadheaders) regarding the spatial distribution of geomaterial’s strength and wear parameters inside the geological domain (e.g. for optimization of machine head, cutting tools, operational parameters etc). Also, inverse problem of characterization of geomaterials from logged machine data (see fig. below).

4. Proposed tunnel design procedure • INPUT: DISCRETIZED SOLID GEOLOGICAL MODEL (CAD – MIDAS solid modeling from geological sections, boreholes, geophysics, topographical map etc) do # i=1,n LAB web-driven DATABASE WITH CONSTITUTIVE MODELS LIBRARY REALIZATION OF RANDOM FIELD OF MATERIAL PARAMETERS VIA KRIGSTAT CODE • 3D GEOSTATISTICAL-GROUND MODEL IN SITU STRESSES, BC’s, GROUNDWATER INPUT TO FE/BE/FD MODEL INPUT TO TBM/RH PERFORMANCE MODEL (analytical, fast) TUNNEL ALIGNMENT, SUPPORT MEASURES- SPECS FOR BORING MACHINES- OPERATIONAL PARAMETERS- DESIRED SCHEDULES # continue RUN TBM/RH EXCAVATION MODEL CUTTING-CALC CODE RUN DETERMINISTIC FE/BE/FD TUNNEL MODEL FEEDBACK (Back-analysis of TBM/RH logs, convergence, subsidence etc) POST-PROCESSING (Statistics, Residual Risks, Cost, Advance rate etc) Fig. 1. Non-intrusive modeling scheme

5. KRIGSTAT Input Data:1-3D A. Pre - Processor: Statistical processing Data Check/Correction Compositing/reduction/smoothing/grouping Histogram Main Statistics Normality test (K-S test etc) Gaussian Non Gaussian Data Standardization Power Transform BOX-COX Descriptive statistics module of KRIGSTAT code

6. for all Geostatistical approach:Local estimation accounting for secondary information Stochastic Processes = loosely speaking systems that evolve probabilistically with time. The concept of Random Function (RF): For each xi there is assigned a RV. The theory of stochastic processes and RF’s has been in use for a relatively long time to solve problems of interpolation or filtering. • Intrinsic hypothesis: the variance of the increment of two random variables corresponding to two locations inside a given geological body depends only on the vector h separating these two points The function γ(h) is called semivariogram function and may be anisotropic and periodical.

7. The semivariogram is the simplest way to relate uncertainty with distance from an observation. No spatial dependence From: Chiles JP, Delfiner P (1999) Geostatistics – Modeling Spatial Uncertainty. John Wiley & Sons, New York.

8. Kriging estimation: Equations in Kriging module of KRIGSTAT The expected value of variable z – i.e. z may stand for RMR - at location x0 can be interpolated as follows Ordinary Kriging(OK) determines the weights (i=1,…,m) by solving the following system of equations (m=number of hard data): System of (m+1) eqns with (m+1) unknowns (β=Lagrange multiplier) Minimization of the variance of estimation error (BLUES) Estimation error or uncertainty 16% risk estimation:

9. Geostatistical estimation:Simulation Annealing (SA) module of KRIGSTAT SA = Spatially consistent Monte Carlo simulation method The initial picture is modified by swapping the values in pairs of grid nodes (concept from Solid State Physics: annealing process). A swap is accepted if the objective (energy) functionOF (average squared difference between the experimental and the model semivariogram) has been decreased. (<1) = rate of temperature decrease

10. Modeling methodology First, distinct statistical and geotechnical populations should be defined* in order to group data with similar characteristics into subsets, called geotechnical units (i.e statistically homogeneous regions). * Based on geological criteria and hard data (boreholes, geophysics etc)

11. Discretized Solid Geological Models (DSGM) with KRIGSTAT-MIDAS L9, Mas-Blau (EPB tunnel in soft soil) L9, Singuerlin-Esglesias (TBM tunnel in hard rock) Koralm (alpine tunnel in soft rock) References: MIDAS GTSII: Geotechnical and Tunnel analysis System, MIDASoft Inc. (1989-2006), http://www.midas-diana.com L9, La Salut-Liefa (EPB tunnel in soil)

12. Modeling methodology cont’d Second, proceed with geostatistical interpolation of the parameter of interest inside each geological unit and in the tube, using KRIGSTAT at the nodes already created with MIDAS-GTS. One may use either Kriging or SA. Before this, for both approaches the semivariogram model should be fitted on the experimental data.

13. 1st case study: Singuerlin-Esglesias L9 TBM tunnel in weathered granite RMR sampling RMR sampling locations in boreholes Conceptual geological model KRIGSTAT: Stratigraphy of layers Solid geological model (MIDAS-GTS) Finite Element model (MIDAS-GTS)

14. RMR semivariogram Kriging RMR model

15. Anisotropic semivariogram of GR1 RMR simulated and theoretical histograms SA estimation of RMR in GR1 formation Kriging estimation of RMR in GR1 formation

16. Special upscaling procedure for rocks (Linking RMR with rock mass properties) Exadaktylos G. and Stavropoulou M., A Specific Upscaling Theory of Rock Mass Parameters Exhibiting Spatial Variability: Analytical relations and computational scheme, International Journal of Rock Mechanics and Mining Sciences, 45 (2008) 1102–1125. Rock mass Elasticity & Strength Lab scale Elasticity & Strength (RMDB) Physical degradation Size effect Hypothesis A: In a first approximation upscaling due to degradation effect of joints may be based on the constant scalar or vector damage parameter D for the anisotropic case of joint induced anisotropy of the rock mass (n is the unit normal vector of the plane of interest). Hypothesis B: “Strain Equivalence Principle” (Lemaitre, 1992), namely: “Any strain constitutive equation for a damaged geomaterial may be derived in the same way for an intact geomaterial except that the usual stress is replaced by the effective stress”.

17. Hypothesis C:The function linking damage D with rock mass quality described with RMR (or Q or GSI) must have a sigmoidal shape resembling a cumulative probability density function giving D in the range of 0 to 1 for RMR or GSI varying between 100 to 0 or for Q varying from 1000 to 0.001, respectively. Size effect Calibration of the parameters of the Lorentzian curve on in situ test data presented by Hoek and Brown (1997) Verification of the Lorentzian law with additional data on deformability of rock masses presented by Hoek and Diederichs (2006)

18. Upscaling relations for the 7-parameter linear-elastic, perfectly-plastic HMCM Size effect Size effect of UCS (left) & UTS (right) of rocks

19. 3D Ground+Tunnel Models (KRIGSTAT/MIDAS) The rest of ground parameters derived from RMR & lab data in a similar fashion based on the “special upscaling theory”.

20. TBM & Roadheader performance models • The new CUTTING_CALC software for excavation performance analysis & optimization of TBM’s. The concept of transformation of “geological model” into “machine performance model”. CUTTING_CALC code may be add-on of tunneling machines or for work nearly real-time in the office. GUI of the algorithm

21. RMR estimations along the tunnel from the TBM data by virtue of empirical hyperbolic relationship during TBM advance are combined with the borehole data in order to upgrade the initial geotechnical model (RMR model) derived from the Kriging analysis of borehole data. Boreholes only Upgraded RMR data (boreholes & TBM) Boreholes and TBM logging: Reduction of kriging error Exadaktylos G., M. Stavropoulou, G. Xiroudakis, M. de Broissia and H. Schwarz, (2008) A spatial estimation model for continuous rock mass characterization from the specific energy of a TBM, Rock Mechanics & Rock Engineering, 41: 797–834, Springer.

22. 2nd case study: Mas-Blau L9 EPB tunnel in soft alluvial deposits Mas-Blau tunnel will run in the alluvial Quaternary deposits of Llobregat river, composed by intercalated strata of sands, gravel, silts and clay. Generation of 3D terrain model Point data from boreholes are interpolated with Kriging and feeded to MIDAS for modeling the surface of each geological formation.

23. Mas-Blau models: KRIGSTAT-MIDAS Geological Model Tube geology Discretized solid geological model

24. NSPT variogram (KRIGSTAT) NSPT kriging Model on nodes created by MIDAS

25. EPB boring performance at Mas-Blau EPB (S-461) Traces of knives, with S=10 cm SE2 (MPa) Kriging model Specific Energy of soil cutting Knives design

27. Plasticity slip-line analytical model for soil cutting

28. Back-analysis of SE logged data for estimation of cohesion

29. 3rd case study: La Salut-Liefa L9 EPB tunnel in hard tertiary alluvial formation S-221 Note: The gravel QB2g was not found in crown of the tunnel. The profile is an interpretation of boreholes and georadar. A re-interpretation of georadar situated the QB2g about 2 m higher, clearly outside the tunnel section.

30. Finite Element Model

31. UCS along chainage from back-analysis of SE data based on the slip-line model

32. 3rd case study: Koralm alpine tunnel in soft rock (molassic) formations 3D view of the Koralm alpine tunnel with the region of interest encircled Geological model of the tunnel Paierdorf Solid geological model of the particular domain of interest (MIDAS)

33. Homogenization method: Derive the spatial distribution of volume fraction n of silt, sand and sandstonealong tunnelusing KRIGSTAT and then derive the effective elastic and strength properties (P) of the homogenized material using Mixtures theory and assuming mean values derived from statistics. Example of the geology mapped at the face that is conceived as a mixture Experimental & model variograms of siltstone concentration (%) exhibiting a “hole effect” (periodicity) Spatial model of siltstone’s specific volume (%) at every 5 m along the 500 m tunnel section Example statistics of mechanical parameters of siltstone

34. Example: Validation of siltstone’s Kriging model Upscaling method: Assuming the hyperbolic Mohr-Coulomb model and a perfectly-plastic behavior the 16 properties of the homogenized geomaterial are derived assuming a size effect of strength properties (50% reduction) but not on elastic properties. Spatial distribution of cohesion (c) and elastic modulus (E) along tunnel

35. Initial discretized geological model (MIDAS) MIDAS-KRIGSTAT ground & tube models

36. BEFE++ (Beer et al., 2009) Rock parameters along the tunnel Vertical displacements on the tunnel roof (comparison with the measurements) Deformed shape and contour of displacement results position 213m behind the exploration shaft Paierdorf

37. Concluding remarks Modeling and visualization of the geology and geotechnical parameters, as well as the performance of tunneling machines (boring TBM’s and excavation RH’s) are the most important tasks in tunneling design and construction. The design process should take into account the risk associated with the rock or soil quality, and the performance of the excavation machine.Also the best sampling strategy should be found. In this perspective there have been developed among others: 1. The new Geostatistics package KRIGSTAT for 1D, 2D & 3D spatial analysis and interpolation through kriging (or co-kriging) or simulation of stratigraphical or geotechnical parameters of each geological formation with evaluation of uncertainty of predictions. This software could be combined with the concept of “DSGM” developed to feed directly numerical simulation tools like MIDAS & Risk Analysis software. 2. The new CUTTING_CALC software for excavation performance analysis & optimization of TBM’s. The concept of transformation of “geological model” into “machine performance model”.

38. Thank you for your kind attention!!.. If you need further information or you would like to make comments or seek cooperation for research and applications do not hesitate to contact us: exadakty@mred.tuc.gr mstavrop@geol.uoa.gr Acknowledgements Technology Innovation in Underground Construction MIDAS-GTS TNO DIANA BV