054_krigstat-midas seminar v0.3

“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 XiroudakisTUC, Laboratory of Mining Engineering Design, Greece

Maria StavropoulouUOA, 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).


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)


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


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 MODELCUTTING-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


Descriptive statistics module of KRIGSTAT code

Gaussian

Non Gaussian

A. Pre - Processor:Statistical

processing

Main StatisticsHistogram

KRIGSTAT

Input Data:1-3D

Data Check/Correction

Compositing/reduction/smoothing/grouping

Power TransformBOX-COX

Normality test (K-S test etc)

Data Standardization


• 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

Vxfor all hxZhxZExZhxZVar 2

2

1

2

1

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 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.

Geostatistical approach:Local estimation accounting for secondary information


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 dependenceNo spatial dependence


The expected value of variable z – i.e. z may stand for RMR - at location x0 can be interpolated as follows

)(ˆ 0xz

m

i

ii xzxz

1

0ˆ

Ordinary Kriging (OK) determines the weights (i=1,…,m) by solving the following system of equations (m=number of hard data):

i

)(ˆ)( 0

1

xxxx iji

m

j

i

1

1

m

i

i mi ,,2,1

System of (m+1) eqns with (m+1) unknowns(β=Lagrange multiplier)

Minimization of thevariance of estimation error(BLUES)

Estimation error oruncertainty

Kriging estimation: Equations in Kriging module of KRIGSTAT

)(ˆ 0

1

2000

2j

m

j

iOK xxxzxzEx

OKOK xzxz 00 ˆ,ˆ16% risk estimation:16% risk estimation:


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

hh

hhOF

2

2

(<1) = rate of temperature decrease(<1) = rate of temperature decrease


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)* Based on geological criteria and hard data (boreholes, geophysics etc)


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. (1989-2006), http://www.midas-diana.com


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


1st 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


Kriging RMR model

RMR semivariogram


RMR simulated and theoretical histograms

Kriging estimation of RMR in GR1 formation SA estimation of RMR in GR1 formation

Anisotropic semivariogram of GR1


Special upscaling procedure for rocks (Linking RMR with rock mass properties)

A

AD D

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).

3,2,1,1

~

iDi

i

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 scaleElasticity &Strength(RMDB)

Physicaldegradation

Rock massElasticity &Strength

Sizeeffect

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.


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.

2ˆ

ˆtan

ˆˆ1)( 1

d

cRMRbaRMRDD

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 effectSize effect


)1(,1

,tantan)1(tan,1,1

,),1(

DUTSUTSDUCSUCS

DDDppDcc

DEE

dmdm

jmTdTmdm

mm

3.0/,3.0/ 1010 UTSUTSUCSUCS dd

Upscaling relations for the 7-parameter linear-elastic, perfectly-plastic HMCM

Size effect

Size effect of UCS (left) & UTS (right) of rocks


3D Ground+Tunnel Models (KRIGSTAT/MIDAS)

The rest of ground parameters derived from RMR & lab data in a The rest of ground parameters derived from RMR & lab data in a similar fashion based on the “special upscaling theory”.similar fashion based on the “special upscaling theory”.


TBM & Roadheader performance modelsThe 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


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.

MPabMPaa

MPaSEbSE

aRMR

10,1253

][,100max

Upgraded RMR data (boreholes & TBM)

Boreholes only

Boreholes and TBM logging: Reduction of kriging errorExadaktylos 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.


2nd 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.


Geological Model

Discretized solid geological model

Tube geology

Mas-Blau models: KRIGSTAT-MIDASMas-Blau models: KRIGSTAT-MIDAS


NSPT variogram (KRIGSTAT)

NSPT kriging Model on nodes created by MIDAS


V

PtSE

1

SE2 (MPa) Kriging model

Traces of knives,with S=10 cm

pS

F

pS

F

V

FSE s

T

TsTs

2

EPB (S-461)

Knives design

Specific Energy of soil cutting

EPB boring performance at Mas-Blau


Plasticity slip-line analytical model for soil cuttingPlasticity slip-line analytical model for soil cutting

S

pe

cSE

24tantantan

2tan

1

tan

1

24tan

sin1

cos22tan

tansn FF


Back-analysis of SE logged data for estimation of cohesionBack-analysis of SE logged data for estimation of cohesion

y = 0.1812x + 113.65

y = 0.515x + 102.67

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30

Fs [kN], SE2: Fs [kN]

Fn

[kN

], F

/N=

Fn

[kN

]

100 m - 300 m

300 - 500 m

Linear (100 m - 300 m)

Linear (300 - 500 m)tansn FF


3rd 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-221S-221


Finite Element Model


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

tancn FF

12tan

24tantantan

2tan1

tan1

24tan

S

pe

SEUCS


3rd 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 ofinterest encircled

Geological model of the tunnel Paierdorf


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.

3

1~~

3

1~~

1)(1)(0

,)()(

i

ii

i

ii

xnxn

PxnxP

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


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.


Initial discretized geological model (MIDAS)

MIDAS-KRIGSTAT ground & tube models


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)BEFE++ (Beer et al., 2009)


Concluding remarksConcluding 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.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”.


Thank you for your kind attention!!..Thank you for your kind attention!!..If you need further information or you would like to make comments orIf you need further information or you would like to make comments orseek cooperation for research and applications do not seek cooperation for research and applications do not hesitate to contact us:hesitate to contact us:

[email protected]

[email protected]

Technology Innovation in Underground Construction

Acknowledgements

MIDAS-GTSMIDAS-GTSTNO DIANA BVTNO DIANA BV

054_krigstat-midas seminar v0.3

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