23/03/15

1

Numerical modelling from laboratory to in situ scale: some examples

Marco Barla Dipartimento di Ingegneria Strutturale Edile e Geotecnica Politecnico di Torino www.rockmech.polito.it

•! 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

Outline

23/03/15

2

Multi-scale approach

•! SOILS •! SOFT ROCKS •! MASSIVE ROCK MASSES

•! JOINTED ROCK MASSES

•! HEAVILY JOINTED ROCK MASSES

CONTINUUM

DISCONTINUUM

EQUIVALENT CONTINUUM EQUIVALENT CONTINUUM

FEM, FDM

BEM

DEM

FDEM

Numerical modelling in rock engineering

23/03/15

3

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.

Numerical modelling in rock engineering

23/03/15

4

Example 1: Modelling randomly cemented alluvial deposit (DEM)

•! Gravel, cobbles and sand in sandy-silty matrix (surface horizon, 25÷50 m).

•! Random distribution of cementation due to calcareous deposition.

•! Horizontal layers from few centimeters to meters.

Cementation

Torino subsoil

Randomly cemented alluvial deposits

How to model heterogeneity? How to model spatial variability?

23/03/15

5

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 0.015 m < ! <0.03 m 0.015 m < ! <0.03 m <0.03 m

2 m

1 m

Cemented ground

Loose soil

Heterogeneity (DEM)

23/03/15

6

0 20 40 60 80 100

Cementation degree - C% [%]

100

200

300

400

500

600

Def

orm

atio

n m

odul

us [M

Pa]

In situ testFLACPFCEmpirical equationDesign empirical equationRange of laboratory values

0 20 40 60 80 100

Cementation degree - C% [%]

0

1

2

3

4

Unc

onfin

ed c

ompr

essi

ve s

tren

gth

[MPa

]

FLACPFCEmpirical equation

Deformability and strength parameters as a function of C%

!"

#$%

& '

(= 53100%C

i emm#& 100%C

(Barla & Barla 2013)

Heterogeneity (DEM)

Equivalent continuum modelling

-5 m

-12.75 m

•! 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)

Ground level

-10 m

10 m

1.25

1.25

1.50

2.00

1.00 Pipe

Spatial variability (DEM)

23/03/15

7

Cemented areas are reproduced randomly in the cross section to simulate the appropriate degree of cementation.

25%

75%

Loose soil

Cemented ground ground

Spatial variability (DEM)

25%

75%

Normal stress built up as a function of C%

! "! #! $! %! &!!'()*' +

!

"!

#!

$!

,-./01)23.4

22)*5

60+

67()89/4.:;01)0801<242

6=>

>?@A>)&$&

?4.B0CD:

6-1:?-

C* !!!"#

$%&

'(

?4.B0C

%C0278.0n e6.25 !"!=#

(Barla & Camusso 2013)

Spatial variability (DEM)

23/03/15

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

23/03/15

9

N S

(Barla et al. 2005; Bonini et al. 2009)

Chaotic Complex Tectonised Clay Shales Marl and clay with inclusions

Sedimentation and erosion caused high over consolidation of the clay materials. Tectonic deformations modified the original regular layers.

Two level of complexity At decimetric scale (lab) = fissures and texture iso-oriented scales. At metric scale (in situ) = the structure is chaotic with inclusions.

1 km Raticosa tunnel

Triaxial testing results on clay shales

(Bonini 2003)

Isotropic elasto plastic constitutive law with Mohr-Coulomb failure envelope with Mohr-Coulomb failure envelope

Laboratory scale

Axial strain rate versus time obtained for different stress levels (SL)

Time dependent behaviour

23/03/15

10

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.

CALOTTA

PASSO FRA DUE RINFORZI DEL FRONTE SUCCESSIVI

D = 14 m

BARRE IN VETRORESINA

ARCO ROVESCIO+ PIEDRITTI

(a)(b)

H =

12

m

BARRE INCLINATE (n. 45 ~ 60)

BARRE CENTRALI (n. 35 ~ 80)

2 CENTINE ACCOPPIATE I 220 mm/m

crown invert

10 m dowels 45-60 inclined dowels 35-80 horizontal

dowels

14 m

12 m

2 IPN 180-300/m

Full face excavation, ADECO-RS method

!"

#

In situ scale

0 1 2 3 4 5 6Time [day]

0

0.001

0.002

0.003

0.004

0.005

Axi

al s

trai

n [-

]

Experimental dataFitting with SHELVIP

RTC4

RTC5RTC3

…at the laboratory scale …at the tunnel scale

In situ scale Application of time dependent constitutive models allow to simulate long term behaviour. Time dependent parameters were not scaled from lab to in situ scales.

Comparison between monitoring data and computed results.

23/03/15

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)

23/03/15

12

Torgiovannetto di Assisi

!""#$%&'()*%+%(,$-.)/0$)&)+,'%'1$$

2)%&$34564$

Pilot site PRIN 2009

Pilot site PRIN 2009

Main unstable area (182.000 m3)

Slide december 2005

Geosynthetic rock fall barrier

S.P. 294/1 di Spello

Quarry yard

1 m

15 cm

Sliding surface

Torgiovannetto di Assisi Evolution? FDEM FDEM FDEM

23/03/15

13

Interbedded clay layers: "’ = 19.6° c’ =21 kPa

Intact rock: #ci = 82.5 MPa

#ti = 6 MPa Es = 92.5 GPa

$ = 26.4 kN/m3

mi = 14.2

Maiolica: cretaceous flysch constituted by micritic limestone (0.2 – 2.0 m) with interbedded clay layers (up to 0.4 m).

TXCU tests

Geotechnical caracterisation

(from Ribacchi et al., 2005 and 2006; Graziani et al. 2009, Antolini 2014)

Laboratory scale

a0 a0

d0

L

LLPD

CMOD

Determination of fracture energy (Gf) Three point bending test on Single End Notched Beam (SENB)

23/03/15

14

Laboratory scale Uniaxial compression tests (UCS)

Experimental vs FDEM

Experimental

December 2005 collapse back analyses

Verification through back analysis

Study of triggering and runout of the 182000 m3

unstable wedge

Triggering and Scenario analysis

In situ scale

(Antolini 2014)

23/03/15

15

BG (stratification): 355°/30° K1: 75°/80° - 255°/80° K2: 180°/80°

Back analysis December 2005 rock slide

Laser scanner digital model made after the 2005 rock slide.

Debris limit (10 m from the slope’s toe)

FDEM cross section

Area where most rock

blocks accumulated

Area of detachment

Back analysis

23/03/15

16

Equivalent continuum parameters (GSI = 40)

Intact rock (GSI = 100) + discontinuities parameters

Back analysis

Equivalent continuum Equivalent continuum parameters (GSI = 40) parameters (GSI = 40)

Intact rock (GSI = 100) + discontinuities parameters

Sliding surface

Before sliding

FDEM result

Debris limit (10 m from the slope’s toe)

FDEM cross section

Area where most rock

blocks accumulated

Area of detachment

•! 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.

Back analysis

23/03/15

17

FDEM model of the collapse of the whole unstable wedge

In situ scale

Thresholds can be determined for specific locations along the slope.

ROI 1-2 ROI 1-2

In situ scale

Example of comparison to monitoring data for this Early Warning System.

ROI 3

23/03/15

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

23/03/15

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

23/03/15

20

References

Marco Barla, Marco Camusso 2013. A method to design microtunnelling installations in randomly cemented Torino alluvial soil. Tunnelling and Underground Space Technology, Volume 33, 73-81

Marco Barla, Giovanni Barla 2012. Torino subsoil characterisation by combining site investigations and numerical modelling. Geomechanics and tunnelling 5/3.

EXAMPLE 1

Marco Camusso, Marco Barla 2009. Microparameters Calibration for Loose and Cemented Soil When Using Particle Methods. International Journal of Geomechanics 9, No. 5, 217–230.

EXAMPLE 2

M. Bonini, D. Debernardi, M. Barla, G. Barla 2007. The Mechanical Behaviour of Clay Shales and Implications on the Design of Tunnels. Rock Mech. Rock Engng.

References

Atzeni, Barla, Pieraccini, Antolini 2014. Early warning monitoring of natural and engineered slopes with Ground-Based Synthetic Aperture Radar . Rock Mechanics & Rock Engineering. Also available open access online at: www.rockmech.polito.it/download

EXAMPLE 3

Marco Barla, Giovanna Piovano, Giovanni Grasselli 2012. Rock Slide Simulation with the Combined Finite Discrete Element Method. International Journal of Geomechanics 12(6).

Marco Barla 2010. Elementi di meccanica e ingegneria delle rocce, Celid.

ADDITIONAL REFERENCE