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).
Exadaktylos Slide 1 of total 38
“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010
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.
Exadaktylos Slide 2 of total 38
“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010
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).
Exadaktylos Slide 3 of total 38
“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010
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 GEOSTATISTICALGROUND MODEL
INPUT TO TBM/RH
PERFORMANCE MODEL
(analytical, fast)
INPUT TO
FE/BE/FD
MODEL
# continue
RUN TBM/RH
EXCAVATION MODEL
CUTTING-CALC CODE
FEEDBACK
(Back-analysis of
TBM/RH logs,
convergence,
subsidence etc)
RUN DETERMINISTIC
FE/BE/FD TUNNEL MODEL
IN SITU STRESSES, BC’s,
GROUNDWATER
TUNNEL ALIGNMENT,
SUPPORT MEASURESSPECS FOR BORING MACHINESOPERATIONAL PARAMETERSDESIRED SCHEDULES
POST-PROCESSING
(Statistics, Residual
Risks, Cost, Advance
rate etc)
Fig. 1. Non-intrusive modeling scheme
Exadaktylos Slide 4 of total 38
“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010
Descriptive statistics module of KRIGSTAT code
KRIGSTAT
Input Data:1-3D
A. Pre Processor:
Statistical
Compositing/reduction/smoothing/group processing
Data Check/Correction
ing
Histogra
m
Main Statistics
Gaussian
Normality test
(K-S test etc)
Non Gaussian
Data
Standardization
Exadaktylos Slide 5 of total 38
Power Transform
BOX-COX
“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010
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
for all
x V


1
1
Var Z x  h   Z x   E Z x  h   Z x 2   h 
2
2
The function γ(h) is called semivariogram function and may be anisotropic
and periodical.
Exadaktylos Slide 6 of total 38
“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010
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.
Exadaktylos Slide 7 of total 38
“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010
Kriging estimation: Equations in Kriging module of KRIGSTAT
The expected value zˆ( x0 ) of variable z – i.e. z may stand for RMR - at
location x0 can be interpolated as follows
m
zˆx0  

i zxi 
i 1
Ordinary Kriging (OK) determines the weights
(i=1,…,m) by solving the following system
of equations (m=number of hard data):
i
m

Minimization of the
variance of
estimation error
(BLUES)

i ( xi  x j )    ˆ ( xi  x0 )
j 1
m

i  1 i  1,2,, m
System of (m+1)
eqns with (m+1)
unknowns
(β=Lagrange multiplier)
i 1
Estimation error or
uncertainty


2
x0   E z x0   zˆx0 2 
 OK
m

i ( x0  x j )  
j 1
16% risk estimation: zˆx0    OK , zˆx0    OK 
Exadaktylos Slide 8 of total 38
“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010
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) function OF (average squared
difference between the experimental and the model
semivariogram) has been decreased.
OF 

h

 h   h

2
 h 2
(<1) = rate of temperature decrease
Exadaktylos Slide 9 of total 38
“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010
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)
Exadaktylos Slide 10 of total 38
“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010
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)
L9, La Salut-Liefa (EPB tunnel in soil)
Exadaktylos Slide 11 of total 38
References:
MIDAS GTSII: Geotechnical and Tunnel analysis System,
MIDASoft Inc. (1989-2006), http://www.midas-diana.com
“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010
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.
Exadaktylos Slide 12 of total 38
“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010
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)
Exadaktylos Slide 13 of total 38
Finite Element model (MIDAS-GTS)
“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010
RMR semivariogram
Kriging RMR model
Exadaktylos Slide 14 of total 38
“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010
RMR simulated and theoretical histograms
Kriging estimation of RMR in GR1 formation
Exadaktylos Slide 15 of total 38
Anisotropic semivariogram of GR1
SA estimation of RMR in GR1 formation
“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010
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.
Lab scale
Elasticity &
Strength
(RMDB)
Size
effect
Physical
degradation
Rock mass
Elasticity &
Strength
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).
D
AD
A
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”.
~i 
Exadaktylos Slide 16 of total 38
i
1 D
, i  1,2,3
“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010
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.

bˆ

D  D( RMR)  1  aˆ 

 
 1 RMR  cˆ    

tan





ˆ
2
d





Size effect
Calibration of the parameters of
the Lorentzian curve on in situ
test data presented by Hoek and
Brown (1997)
Exadaktylos Slide 17 of total 38
Verification of the Lorentzian law with additional
data on deformability of rock masses presented
by Hoek and Diederichs (2006)
“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010
Upscaling relations for the 7-parameter linear-elastic, perfectly-plastic HMCM
Em  E (1  D),  m   ,
cm  cd  1  D , pTm  pTd  1  D , tanm  (1  D) tan  D tan j ,
UCSm  UCSd 1  D , UTSm  UTSd (1  D)
Size effect
UCSd / UCS10  0.3, UTSd / UTS10  0.3
Size effect of UCS (left) & UTS (right) of rocks
Exadaktylos Slide 18 of total 38
“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010
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”.
Exadaktylos Slide 19 of total 38
“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010
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
Exadaktylos Slide 20 of total 38
“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010
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.
a
, [ SE]  MPa
SE  b
a  1253MPa, b  10 MPa
RMRmax  100 
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.
Exadaktylos Slide 21 of total 38
“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010
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.
Exadaktylos Slide 22 of total 38
“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010
Mas-Blau models: KRIGSTAT-MIDAS
Geological Model
Tube geology
Discretized solid geological model
Exadaktylos Slide 23 of total 38
“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010
NSPT variogram (KRIGSTAT)
NSPT kriging Model on nodes created by MIDAS
Exadaktylos Slide 24 of total 38
“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010
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
SE1 
Pt
V
F
F
F
SE2  s T  s T  s
V
pS T pS
Knives design
Exadaktylos Slide 25 of total 38
“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
Plasticity slip-line analytical model for soil cutting

  tan
1
1
    

 tan2    

 e




4
2
tan



tan
2





2c cos 

 
 p
SE 
1  sin 
S
  
tan  tan tan  
 4 2
Fn  Fs tan
Exadaktylos Slide 27 of total 38
“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010
140
120
Fn [kN], F/N= Fn [kN]
100
80
60
100 m - 300 m
300 - 500 m
Linear (100 m - 300 m)
Linear (300 - 500 m)
40
20
Fn  Fs tan
y = 0.1812x + 113.65
y = 0.515x + 102.67
0
0
5
10
15
20
25
30
Fs [kN], SE2: Fs [kN]
Back-analysis of SE logged data for estimation of cohesion
Exadaktylos Slide 28 of total 38
“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010
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.
Exadaktylos Slide 29 of total 38
“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010
Finite Element Model
Exadaktylos Slide 30 of total 38
“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010
Fn  Fc tan 
   tan
 
1
1
    
 tan2    

 
 e

 4 2   tan    tan2       p 
UCS  SE

S
  

tan  tan tan  


 4 2


1
UCS along chainage from back-analysis of SE data based on the slip-line model
Exadaktylos Slide 31 of total 38
“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010
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)
Exadaktylos Slide 32 of total 38
“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010
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.
3
P( x) 
~

ni ( x) Pi ,
i 1
~
3
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)
Exadaktylos Slide 33 of total 38
0  ni ( x)  1 
Spatial model of siltstone’s specific
volume (%) at every 5 m along the 500
m tunnel section
~

i 1
ni ( x)  1
~
Example statistics of mechanical
parameters of siltstone
“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010
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
Exadaktylos Slide 34 of total 38
“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010
Initial discretized geological model (MIDAS)
MIDAS-KRIGSTAT ground & tube models
Exadaktylos Slide 35 of total 38
“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010
BEFE++ (Beer et al., 2009)
Rock parameters along the tunnel
Deformed shape and contour
of displacement results
Exadaktylos Slide 36 of total 38
Vertical displacements on the tunnel roof
(comparison with the measurements)
position 213m behind the exploration shaft Paierdorf
“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010
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”.
Exadaktylos Slide 37 of total 38
“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010
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
Exadaktylos Slide 38 of total 38
“Geotechnical Advances in Urban Renewal: Analysis & Design”,London 20/4/2010