“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010 Exadaktylos Slide 1 of total 38 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 fast transformation 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).

“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010 Exadaktylos Slide 2 of total 38 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. Introduction (motivations + proposed approach)

“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010 Exadaktylos Slide 3 of total 38 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). Introduction (motivations + proposed approach) cont’d

“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010 Exadaktylos Slide 4 of total 38 Fig. 1. Non-intrusive modeling scheme INPUT: DISCRETIZED SOLID GEOLOGICAL MODEL (CAD – MIDAS solid modeling from geological sections, boreholes, geophysics, topographical map etc) 3D GEOSTATISTICAL- GROUND MODEL REALIZATION OF RANDOM FIELD OF MATERIAL PARAMETERS VIA KRIGSTAT CODE RUN DETERMINISTIC FE/BE/FD TUNNEL MODEL IN SITU STRESSES, BC’s, GROUNDWATER # continue POST-PROCESSING (Statistics, Residual Risks, Cost, Advance rate etc) FEEDBACK (Back-analysis of TBM/RH logs, convergence, subsidence etc) do # i=1,n INPUT TO FE/BE/FD MODEL INPUT TO TBM/RH PERFORMANCE MODEL (analytical, fast) RUN TBM/RH EXCAVATION MODEL CUTTING-CALC CODE LAB web-driven DATABASE WITH CONSTITUTIVE MODELS LIBRARY TUNNEL ALIGNMENT, SUPPORT MEASURES- SPECS FOR BORING MACHINES- OPERATIONAL PARAMETERS- DESIRED SCHEDULES Proposed tunnel design procedure

“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010 Exadaktylos Slide 5 of total 38 Descriptive statistics module of KRIGSTAT code Gaussian Non Gaussian A. Pre - Processor: Statistical processing Main Statistics Histogra m KRIGSTAT Input Data:1-3D Data Check/Correction Compositing/reduction/smoothing/group ing Power Transform BOX-COX Normality test (K-S test etc) Data Standardization

“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010 Exadaktylos Slide 6 of total 38 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 for all The function γ(h) is called semivariogram function and may be anisotropic and periodical. Stochastic Processes = loosely speaking systems that evolve probabilistically with time. The concept of Random Function (RF): For each x i 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. Geostatistical approach:Local estimation accounting for secondary information

“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010 Exadaktylos Slide 7 of total 38 The semivariogram is the simplest way to relate uncertainty with distance from an observation. From: Chiles JP, Delfiner P (1999) Geostatistics – Modeling Spatial Uncertainty. John Wiley & Sons, New York. No spatial dependence

“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010 Exadaktylos Slide 8 of total 38 The expected value of variable z – i.e. z may stand for RMR - at location x 0 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 Kriging estimation: Equations in Kriging module of KRIGSTAT 16% risk estimation:

“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010 Exadaktylos Slide 9 of total 38 : Geostatistical estimation: Simulation Annealing (SA) module of KRIGSTAT 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) function OF (average squared difference between the experimental and the model semivariogram) has been decreased. SA = Spatially consistent Monte Carlo simulation method (<1) = rate of temperature decrease

“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010 Exadaktylos Slide 10 of total 38 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). Modeling methodology * Based on geological criteria and hard data (boreholes, geophysics etc)

“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010 Exadaktylos Slide 11 of total 38 Discretized Solid Geological Models (DSGM) with KRIGSTAT-MIDAS L9, La Salut-Liefa (EPB tunnel in soil) 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. ( ),

“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010 Exadaktylos Slide 12 of total 38 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. Modeling methodology cont’d

“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010 Exadaktylos Slide 13 of total 38 1 st case study: Singuerlin-Esglesias L9 TBM tunnel in weathered granite Conceptual geological model RMR sampling Finite Element model (MIDAS-GTS) RMR sampling locations in boreholes Solid geological model (MIDAS-GTS) KRIGSTAT: Stratigraphy of layers

“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010 Exadaktylos Slide 14 of total 38 Kriging RMR model RMR semivariogram

“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010 Exadaktylos Slide 15 of total 38 RMR simulated and theoretical histograms Kriging estimation of RMR in GR1 formation SA estimation of RMR in GR1 formation Anisotropic semivariogram of GR1

“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010 Exadaktylos Slide 16 of total 38 Special upscaling procedure for rocks (Linking RMR with rock mass properties) 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”. Lab scale Elasticity & Strength (RMDB) Physical degradation Rock mass Elasticity & Strength Size effect 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.

“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010 Exadaktylos Slide 17 of total 38 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. 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) Size effect

“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010 Exadaktylos Slide 18 of total 38 Upscaling relations for the 7-parameter linear-elastic, perfectly-plastic HMCM Size effect Size effect of UCS (left) & UTS (right) of rocks

“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010 Exadaktylos Slide 19 of total 38 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”.

“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010 Exadaktylos Slide 20 of total 38 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

“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010 Exadaktylos Slide 21 of total 38 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. Upgraded RMR data (boreholes & TBM) Boreholes only 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.

“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010 Exadaktylos Slide 22 of total 38 2 nd case study: Mas-Blau L9 EPB tunnel in soft alluvial deposits 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. Mas-Blau tunnel will run in the alluvial Quaternary deposits of Llobregat river, composed by intercalated strata of sands, gravel, silts and clay.

“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010 Exadaktylos Slide 23 of total 38 Geological Model Discretized solid geological model Tube geology Mas-Blau models: KRIGSTAT-MIDAS

“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010 Exadaktylos Slide 24 of total 38 N SPT variogram (KRIGSTAT) N SPT kriging Model on nodes created by MIDAS

“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010 Exadaktylos Slide 25 of total 38 SE 2 (MPa) Kriging model Traces of knives, with S=10 cm EPB (S-461) Knives design Specific Energy of soil cutting EPB boring performance at Mas-Blau

“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010 Exadaktylos Slide 26 of total 38

“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010 Exadaktylos Slide 27 of total 38 Plasticity slip-line analytical model for soil cutting

“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010 Exadaktylos Slide 28 of total 38 Back-analysis of SE logged data for estimation of cohesion

“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010 Exadaktylos Slide 29 of total 38 3 rd case study: La Salut-Liefa L9 EPB tunnel in hard tertiary alluvial formation 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. S-221

“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010 Exadaktylos Slide 30 of total 38 Finite Element Model

“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010 Exadaktylos Slide 31 of total 38 UCS along chainage from back-analysis of SE data based on the slip-line model

“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010 Exadaktylos Slide 32 of total 38 3 rd case study: Koralm alpine tunnel in soft rock (molassic) formations Solid geological model of the particular domain of interest (MIDAS) 3D view of the Koralm alpine tunnel with the region of interest encircled Geological model of the tunnel Paierdorf

“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010 Exadaktylos Slide 33 of total 38 Example of the geology mapped at the face that is conceived as a mixture Homogenization method: Derive the spatial distribution of volume fraction n of silt, sand and sandstone along tunnel using 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. 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

“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010 Exadaktylos Slide 34 of total 38 Example: Validation of siltstone’s Kriging model Spatial distribution of cohesion (c) and elastic modulus (E) along tunnel 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.

“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010 Exadaktylos Slide 35 of total 38 Initial discretized geological model (MIDAS) MIDAS-KRIGSTAT ground & tube models

“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010 Exadaktylos Slide 36 of total 38 Deformed shape and contour of displacement results Rock parameters along the tunnel Vertical displacements on the tunnel roof (comparison with the measurements) position 213m behind the exploration shaft Paierdorf BEFE++ (Beer et al., 2009)

“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010 Exadaktylos Slide 37 of total 38 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. Also the best sampling strategy should be found. 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”.

“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010 Exadaktylos Slide 38 of total 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: Technology Innovation in Underground Construction Acknowledgements MIDAS-GTS TNO DIANA BV