Numerical modelling from laboratory to in situ scale: some examples

Transcription

1 Numerical modelling from laboratory to in situ scale: some examples Marco Barla Dipartimento di Ingegneria Strutturale Edile e Geotecnica Politecnico di Torino Outline! Multi scale approach! Example 1: Modelling randomly cemented alluvial deposit (DEM)! Example 2: Tunnelling in squeezing conditions (FDM)! Example 3: Rock slope stability problem (FDEM)! Final remarks 1

2 Multi-scale approach Numerical modelling in rock engineering FEM, FDM CONTINUUM! SOILS! SOFT ROCKS! MASSIVE ROCK MASSES BEM EQUIVALENT CONTINUUM UM! HEAVILY JOINTED ROCK MASSES DEM DISCONTINUUM! JOINTED ROCK MASSES FDEM 2

3 Numerical modelling in rock engineering Numerical analyses can be conducted in 2D or 3D conditions and can be adopted to solve diverse rock engineering problems. The choice on the method to be adopted is crucial and depends on the problem itself, on its complexity and on the available knowledge on rock mass conditions and properties, e.g. the:! in situ stress state,! degree of fracturing of the rock mass,! geometric ratio between REV and the characteristic dimensions of the engineering problem. Numerical modelling in rock engineering For problems in which large-scale phenomena are strongly influenced by processes occurring at much smaller scales (e.g. fracture propagation), executing exhaustive simulations including the processes at the smallest scales for a domain of engineering significance, is currently impractical, and likely to remain so for a very long time. Numerical methods may be used with a multi-scale approach combining multiple models defined at fundamentally different length scales within the same overall spatial domain. For example, a small-scale model with high resolution can be used in a fraction of the overall domain and linked to a large-scale model with coarse resolution over the remainder of the overall domain, providing necessary efficiency of characterization and computation that will render solution of these problems practical. 3

4 Example 1: Modelling randomly cemented alluvial deposit (DEM) Randomly cemented alluvial deposits Torino subsoil! Gravel, cobbles and sand in sandy-silty matrix (surface horizon, m).! Random distribution of cementation due to calcareous deposition.! Horizontal layers from few centimeters to meters. Cementation How to model heterogeneity? How to model spatial variability? 4

5 Heterogeneity (DEM) Particle element modelling. Calibration of micro parameters by simulating compression loading tests on fully cemented specimen (C%=100%) and loose (C%=0). (Camusso & Barla 2009, Barla & Barla 2013) Heterogeneity (DEM) 3259 Particles m <! <0.03 m Cemented ground 2m Loose soil 1m 5

6 Heterogeneity (DEM) Deformability and strength parameters as a function of C% Deformation modulus [MPa] In situ test FLAC PFC Empirical equation Design empirical equation Range of laboratory values Unconfined compressive strength [MPa] FLAC PFC Empirical equation & C% ' 100 # $! = ( % 53 m m " i e Cementation degree - C% [%] Cementation degree - C% [%] Equivalent continuum modelling (Barla & Barla 2013) Spatial variability (DEM) Ground level -5 m -10 m Pipe ! The model reproduce a cross section, perpendicular to microtunnelling axis (soil response radial to microtunnel contour)! The excavation of 1 m diameter microtunnel is simulated at a depth of 10 m below the ground surface! Size: 10 x 7.75 m! n of particles: ~ 60,000! Concentric upscaling of particles radius to optimise memory and time requirements (Konietzky et al., 2001) m 10 m 6

7 23/03/15 Spatial variability (DEM) Cemented areas are reproduced randomly in the cross section to simulate the appropriate degree of cementation. Cemented ground 25% Loose soil 75% Spatial variability (DEM) Normal stress built up as a function of C% $! 67()89/4.:;01)0801<242 25%,-./01)23.422)*560+ >?@A>)& $ & 6=> #! "0.0278!C ' $! %! ( * #%n = "25.6! e! & # C?4.B 0C 0CD: "! 6-1:?-! 75%! "! #! ' ()*' + $! %! &!! (Barla & Camusso 2013) 7

8 !Ground heterogeneity was studied by a small scale model for geotechnical characterisation purposes.!results can be used for continuum equivalent large scale models.!spatial variability at the large scale was included with DEM modelling (+ upscaling) to obtain more realistic ground behaviour. Example 2: Tunnelling in squeezing conditions 8

9 Raticosa tunnel 1 km N S Sedimentation and erosion caused high over consolidation of the clay materials. Tectonic deformations modified the original regular layers. Chaotic Complex Tectonised Clay Shales Marl and clay with inclusions (Barla et al. 2005; Bonini et al. 2009) Two level of complexity At decimetric scale (lab) = fissures and texture isooriented scales. At metric scale (in situ) = the structure is chaotic with inclusions. Laboratory scale Triaxial testing results on clay shales Time dependent behaviour Isotropic elasto plastic constitutive law with Mohr-Coulomb failure envelope Axial strain rate versus time obtained for different stress levels (SL) (Bonini 2003) 9

10 In situ scale (b) 10 m PASSO FRA DUE RINFORZI DEL FRONTE SUCCESSIVI dowels BARRE IN VETRORESINA inclined dowels BARRE INCLINATE (n. 45 ~ 60) horizontal dowels (a) BARRE CENTRALI (n. 35 ~ 80) Full face excavation, ADECO-RS method crown invert CALOTTA 12 m ARCO ROVESCIO + PIEDRITTI H = 12 m 14 m D = 14 m 2 CENTINE 2 IPN ACCOPPIATE /m I 220 mm/m 3D FDM numerical model Lab data are scaled based on GSI # The numerical model allows to reproduce the tunnel short term behaviour but not that in the long term if the time dependent component is not included. "! In situ scale Comparison between monitoring data and computed results. Application of time dependent constitutive models allow to simulate long term behaviour. Time dependent parameters were not scaled from lab to in situ scales. at the laboratory scale at the tunnel scale RTC3 RTC5 Axial strain [-] RTC Experimental data Fitting with SHELVIP Time [day] 1 0

11 !Numerical models were conducted both at laboratory and tunnel scale with FDM.!The need to scale parameters from small to large scale is not a general rule. In this example, deformability and strength parameters needed to be scaled while time dependent parameters not.!high quality monitoring data are essential to guide the scaling process and link the models at different scales. Example 3: Rock slope stability (FDEM) 11

12 Torgiovannetto di Assisi Pilot site PRIN )%&$34564$!""#$%&'()*%+%(,$ -.)/0$)&)+,'%'1$$ Torgiovannetto di Assisi Pilot site PRIN 2009 Evolution? FDEM 1 m Main unstable area ( m 3 ) Slide december 2005 Sliding surface 15 cm Quarry yard Geosynthetic rock fall barrier S.P. 294/1 di Spello 1 2

13 Geotechnical caracterisation Maiolica: cretaceous flysch constituted by micritic limestone ( m) with interbedded clay layers (up to 0.4 m). Intact rock: # ci = 82.5 MPa # ti = 6 MPa E s = 92.5 GPa $ = 26.4 kn/m 3 m i = 14.2 Interbedded clay layers: " = 19.6 c =21 kpa TXCU tests (from Ribacchi et al., 2005 and 2006; Graziani et al. 2009, Antolini 2014) Laboratory scale Three point bending test on Single End Notched Beam (SENB) Determination of fracture energy (G f ) L d 0 LLPD a 0 a 0 CMOD 1 3

14 Laboratory scale Uniaxial compression tests (UCS) Experimental vs FDEM In situ scale December 2005 collapse back analyses Verification through back analysis Triggering and Scenario analysis Study of triggering and runout of the m 3 unstable wedge (Antolini 2014) 1 4

15 Back analysis December 2005 rock slide BG (stratification): 355 /30 K1: 75 / /80 K2: 180 /80 Back analysis Area where most rock blocks accumulated FDEM cross section Area of detachment Laser scanner digital model made after the 2005 rock slide. Debris limit (10 m from the slope s toe) 1 5

16 Back analysis Equivalent continuum parameters (GSI = 40) Intact rock (GSI = 100) + discontinuities parameters Back analysis! The geometry of the accumulated blocks and the propagation distance on the quarry yard well reproduce observations.! The validated parameters can be adopted for the scenario analysis. Before sliding FDEM result Area where most rock blocks accumulated Area of detachment Sliding surface FDEM cross section Debris limit (10 m from the slope s toe) 1 6

17 In situ scale FDEM model of the collapse of the whole unstable wedge In situ scale Thresholds can be determined for specific locations along the slope. Example of comparison to monitoring data for this Early Warning System. ROI 3 ROI

18 !Numerical models were conducted both at the laboratory and in situ scale with FDEM.!Continuum equivalent as well as discontinuum modelling approach were adressed.!back analysis are essential for calibration and validation. Final remarks 1 8

19 Final remarks Three examples were considered to show that:! Numerical methods may be used with a multi-scale approach combining models defined at fundamentally different length scales within the same overall spatial domain to render possible the solution for practical engineering problems in which large-scale phenomena are strongly influenced by processes occurring at much smaller scales (still time consuming though!).! Multi scale approach may allow to simulate ground heterogeneity and spatial variability.! Links between behaviors at the small and large scale have to be defined (e.g. the need to scale parameters from small to large scale is not a general rule)! Back analysis and high quality monitoring data are essential in this process for calibration and validation. References 1 9

20 References EXAMPLE 1 Marco Camusso, Marco Barla Microparameters Calibration for Loose and Cemented Soil When Using Particle Methods. International Journal of Geomechanics 9, No. 5, Marco Barla, Giovanni Barla Torino subsoil characterisation by combining site investigations and numerical modelling. Geomechanics and tunnelling 5/3. Marco Barla, Marco Camusso A method to design microtunnelling installations in randomly cemented Torino alluvial soil. Tunnelling and Underground Space Technology, Volume 33, EXAMPLE 2 M. Bonini, D. Debernardi, M. Barla, G. Barla The Mechanical Behaviour of Clay Shales and Implications on the Design of Tunnels. Rock Mech. Rock Engng. References EXAMPLE 3 Marco Barla, Giovanna Piovano, Giovanni Grasselli Rock Slide Simulation with the Combined Finite Discrete Element Method. International Journal of Geomechanics 12(6). Atzeni, Barla, Pieraccini, Antolini Early warning monitoring of natural and engineered slopes with Ground-Based Synthetic Aperture Radar. Rock Mechanics & Rock Engineering. Also available open access online at: ADDITIONAL REFERENCE Marco Barla Elementi di meccanica e ingegneria delle rocce, Celid. 2 0