New Models for Strength and Deformability ParameterCalculation in Rock Masses Using Data-Mining TechniquesTiago Miranda1; António Gomes Correia2; Manuel Santos3; Luís Ribeiro e Sousa4; and Paulo Cortez5

Abstract: Due to the inherent geological complexity and characterization difficulties in rock formations, the evaluation of geomechanicalparameters is very complex, mostly in the initial project stages and in small-scale geotechnical works, where information is scarce for thedefinition of an accurate geotechnical model. However, in large geotechnical projects, a great amount of data are produced and used toestablish near-homogeneous geotechnical zones. If properly analyzed, these data can provide valuable information that can be used insituations where knowledge of the rock mass is limited. Yet, this implies the organization of geotechnical data in formats for properanalysis using advanced tools which is not normally done. Data-mining techniques have been successfully used in many fields butscarcely in geotechnics. They seem to be adequate as an advanced technique for analyzing large and complex databases that can be builtwith geotechnical information within the framework of an overall process of knowledge discovery in databases �KDD�. In this work, afirst approach of a KDD process applied in the context of rock mechanics is presented. The main goal was to find new models to evaluatestrength and deformability parameters. In this process, a large database of geotechnical data was assembled concerning an importantunderground structure built in a predominantly granite rock formation. These innovative methodologies and tools were used to analyzeand extract new and useful knowledge. The procedure allowed developing new, simple, and reliable models to predict geomechanicalparameters, namely friction angle, cohesion, and deformability modulus using different sets of input data that can be used in differentsituations of information availability.

DOI: 10.1061/�ASCE�GM.1943-5622.0000071

CE Database subject headings: Rock masses; Deformation; Databases; Data analysis; Artificial intelligence; Geotechnical models;Underground structures.

Author keywords: Databases; Data analysis; Artificial intelligence; Geotechnical models; Underground structures.

Introduction

The prediction of rock formation behavior due to changes in thestress/strain field caused by the excavation of an undergroundstructure is complex. The main reason for this complexity is re-lated to uncertainties concerning rock mass characterization and,in particular, definition of geomechanical parameters which isnormally performed using laboratory and in situ tests, comple-mented, by the use of empirical rock mass classification systems

�Barton et al. 1974; Bieniawski 1989; Hoek et al. 2002�. Thesedifferent methods are used in several stages of design to reduceuncertainties related to the rock mass behavior.

Fig. 1 presents a generic methodology for rock mass charac-terization normally used in large geotechnical projects. The meth-odology starts with preliminary research based on geological dataand a limited number of tests to define an initial geotechnicalmodel to be used to support decisions concerning location, orien-tation, and other generic issues. Afterwards, a more thoroughcharacterization is performed and previous results can be updatedwith new data to form a more accurate geotechnical model. Theseupdated parameters are used in numerical modeling and geotech-nical design. During construction, stresses and displacements canbe monitored. Observational data can be used to reevaluate theestablished geotechnical model using back analysis. In this over-all methodology, geomechanical parameters have to be assessedin three levels considering completely different conditions ofavailable geotechnical data, i.e., knowledge about the rock mass.

The evaluation of geomechanical parameters in undergroundworks corresponding to the preliminary stages of design �Level 1as defined in Fig. 1� is normally performed based on scarce anduncertain data. When small amounts of data are available, geome-chanical information concerning other works, developed in simi-lar rock masses, can help in defining values for parameters.

This idea can also be applied to small geotechnical works. Thenumber and type of tests performed in geotechnical site investi-gation is related to the importance of the work, the inherent riskand budget issues. Normally, in geotechnical works with smallerdimensions, the available geological-geotechnical data are limited

1Assistant Professor, Dept. of Civil Engineering, School of Engineer-ing, Univ. of Minho, DEC Campus de Azurém, 4800-058 Guimarães,Portugal �corresponding author�. E-mail: tmiranda@civil.uminho.pt

2Full Professor, Dept. of Civil Engineering, School of Engineering,Univ. of Minho, DEC Campus de Azurém, 4800-058 Guimarães, Portu-gal. E-mail: agc@civil.uminho.pt

3Assistant Professor, Dept. of Information Systems, School of Engi-neering, Univ. of Minho, DSI Campus de Azurém, 4800-058 Guimarães,Portugal. E-mail: mfs@dsi.uminho.pt

4Full Professor, Faculty of Engineering, Dept. of Civil Engineering,Univ. of Porto, Rua Dr. Roberto Frias, s/n 4200-465 Porto, Portugal.E-mail: ribeiro.e.sousa@gmail.com

5Assistant Professor, Dept. of Information Systems, School of Engi-neering, Univ. of Minho, DSI Campus de Azurém, 4800-058 Guimarães,Portugal. E-mail: pcortez@dsi.uminho.pt

Note. This manuscript was submitted on February 4, 2009; approvedon June 8, 2010; published online on June 24, 2010. Discussion periodopen until July 1, 2011; separate discussions must be submitted for indi-vidual papers. This paper is part of the International Journal of Geome-chanics, Vol. 11, No. 1, February 1, 2011. ©ASCE, ISSN 1532-3641/2011/1-44–58/$25.00.

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to only a few or even no in situ and/or laboratory tests. In thesecases, the geomechanical parameters are set based on the avail-able data and conservative engineering judgment. Also in thesecases, great amounts of geotechnical data produced in largeprojects could help in reducing uncertainties related to the estab-lishment of design values for the parameters.

Therefore, the advantages of using geotechnical data gatheredfrom several different projects are indubitable. However, this isnot a straightforward process. The central question to be an-swered, arguably, is how vast quantities of data with differenttypes and origins can be managed and explored to develop mod-els that can provide background for future projects. One first stepfor solving this problem is defining standard ways of collection,organization, and representation of data. In terms of the tech-niques to analyze these databases and repositories, currently, thereare automatic tools from the fields of artificial intelligence andpattern recognition, for instance, which allow for a deeper under-standing of large and complex databases enabling to explore anddiscover potential embedded knowledge �Hand et al. 2001�. It isbelieved that the automated tools of data analysis like data mining�DM� can help in developing complex “data-driven” models.

The formal analysis process, normally called knowledge dis-covery in databases �KDD�, defines the main procedures fortransforming raw data into useful knowledge. DM is just one stepin the KDD process concerned with the application of algorithmsto the data to obtain models. These tools allow a deep analysis ofcomplex data, �i.e., data with a large number of variables, inde-pendent determinations, and complex and unclear relations withanother variables in the database� which would be otherwise verydifficult using classical statistics tools or using only one or even apanel of human experts, who could overlook important details.However, the computational process cannot completely substitutehuman experts. Computational tools are only a complementwhich allows the automatic finding of patterns and models em-bedded in the data. The knowledge discovered in the process mustbe explainable in the light of science and experience and must

always be validated before being used in other applications.DM is just one step in the KDD process, aiming at the extrac-

tion of useful patterns from observed data. The knowledge de-rived through DM is often described as models or patterns and itis very important that this knowledge is both novel and under-standable.

The KDD process consists of the following steps �Fayyad etal. 1996�:• Data selection: the application domain is studied and relevant

data are collected;• Preprocessing or data preparation: noise or irrelevant data are

removed �data cleaning� and multiple data sources may becombined �data integration�;

• Transformation: data are transformed in appropriate forms forthe DM process;

• DM: intelligent methods are applied to extract models or pat-terns; and

• Interpretation: results from the previous step are studied andevaluated.DM is a relatively new area of computer science that is posi-

tioned at the intersection of statistics, machine learning, data man-agement and databases, pattern recognition, artificial intelligence,and other areas. A practical and applied definition of DM is theanalysis and nontrivial extraction of data from databases for thepurpose of discovering new and valuable information, in the formof patterns and rules, from relationships between data elements.

There are several DM techniques, each with their own pur-poses and capabilities. Examples of these techniques include de-cision trees and rule induction, neural and Bayesian networks,learning classifier systems, and instance-based algorithms �Leeand Siau 2001; Berthold and Hand 2003�. The description of eachtechnique is outside the scope of this work.

In this paper, a KDD process was developed using geotechni-cal data gathered in an important underground work recently builtin the North of Portugal in a predominantly granite rock mass.New alternative regression models were developed using multipleregression and artificial neural networks �ANNs� for the analyti-cal calculation of strength and deformability parameters. Thesemodels were built up considering different sets of input data,allowing their application in different scenarios of data availabil-ity. Most of the models use less information than the originalformulations but maintain a high predictive accuracy, which canbe useful in the preliminary design stages in any case wheregeological/geotechnical information is limited. The present studyalso provided insight to the most influential parameters for thebehavior of the rock mass of interest. Despite the limitations ofthis study due to its innovative character, the main goal is toprovide, in a practical manner, an overview of potential benefitsof good organization of geotechnical data, the development ofKDD procedures, and application of DM techniques in the geo-technics field, consequently providing a contribution to bridgingthe gap between data analysis and geotechnics.

DM and Geotechnical Engineering

Normally, for scheduling reasons, it is difficult for practitioners toproperly analyze the data produced in great geotechnical works toobtain deeper knowledge concerning the formations. The analysesare normally performed using statistical tools which do not giveadequate response when dealing with large and complex data-bases. Much of these data have significant value to the broadergeotechnical engineering and construction community, as well as

Fig. 1. Scheme of a generic methodology for rock mass character-ization

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for research. Nevertheless, these data are not normally properlystored and explored to take full advantage of any embeddedknowledge. Defining standard ways of creating organized reposi-tories of data �data warehouses� to simplify its exchange andanalysis is necessary. With this kind of structure, it would beeasier to develop more complex and useful data-driven models tohelp in the decision-making process.

The field of geotechnics has observed many advances in dif-ferent fields like constitutive models, testing equipment and in-struments, probabilistic methodologies to deal uncertainty, andnumerical tools, among many others. However, these advanceswere not observed concerning the tools and techniques used toanalyze geotechnical data which did not undergo significant de-velopment during the past decades. The subject is believed todeserve more attention from the broader geotechnical scientificcommunity because both practitioners and researchers could ex-tract much more profit from the data they normally produce orhandle.

The establishment of standard organization and representationmethods of geotechnical data in electronic format is a subjectwhose importance is already recognized by the geotechnical sci-entific community as it is stated by the creation of the JTC2—Joint Committee on Representation of Geo-Engineering Data inElectronic Format �http://www.dur.ac.uk/geo-engineering/jtc2�.The Joint Committee organized a special session under the scopeof the International Society of Rock Mechanics �ISRM� 11thCongress held in Lisbon, Portugal in July 2007 where some de-velopments in the subject of data organization formats were pre-sented. Also, the relevance of DM application was emphasized.However, no study concerning the application of a formal KDDprocess in rock mechanics was presented since the discussion isstill centered on how data must be organized and stored. In thissense, and despite its limitations, the present work is a step for-ward in this subject because it is a first approach to the use of anorganized database to produce new knowledge under the scope ofa KDD process.

In the geotechnics field, there are some successful applicationsof DM to different kinds of problems. Basheer and Najjar �1995�developed a model for soil compaction control based on an ANN.Romo et al. �2001� used recurrent neural networks and construc-tive algorithms to model the behavior of a coarse granular mate-rial on a series of undrained compression triaxial tests with verygood results. Klose et al. �2002� applied DM on geological andseismic data to predict small-scale hazardous geotechnical struc-tures. Guo et al. �2003� developed a model to identify probablefailure on rock mass bases on ANNs.

Lehman �2004� identified cause-effect relationships betweendrilling and construction practices with resulting production lev-els using ANN to mine huge volumes of historical field data. Alsobased in this technique Hanna et al. �2004� developed a model forefficiency prediction of pile groups installed in cohesionless soiland subjected to axial loading. Motta �2004� implemented a clas-sification algorithm for geotechnical risk evaluation and accidentprediction in roads.

Bhattacharya and Solomatine �2005� applied decision trees,ANN, and support vector machines to classify subsurface soilcharacteristics using measured data from the cone penetrationtest. Some applications have been developed for soil slope stabil-ity prediction based on field data �Mayoraz and Vulliet 2002;Zhou et al. 2002; Souza 2004; Sakellariou and Ferentinou 2005�.

Rangel et al. �2005� presented an alternative strategy to evalu-ate the stability of tunnels during the design and constructionstages. They developed a hybrid system, composed of ANN, neu-

rofuzzy networks and analytical solutions. Suwansawat and Ein-stein �2006� successfully applied ANN to predict maximumsurface settlement due to tunneling in soft ground. The writersused data from the Bangkok Subway Project excavated usingearth pressure balance shield machines.

More recently, Akin and Karpuz �2008� applied ANN to esti-mate major drilling parameters for diamond bit drilling operationswith information of about 45,000 m with results comparable withthe mathematically based conventional formulations. At the Uni-versity of Minho, several works are undergoing concerning rockmechanics, compaction control of embankments, slope stability,and soil improvement.

In spite of the described applications of DM techniques, ingeotechnical engineering, the use of these methodologies is notyet generalized and the geotechnical community is not aware oftheir potential. Fig. 2 presents a summary of the number of ref-erence journal publications in DM and areas related to engineer-ing and geotechnics. DM is still a recent field of researchtherefore the plots only start from 1996. Although there is increas-ing interest in this area, the graphs clearly show that, in geotech-nical engineering, the research is still incipient and the fieldalmost unknown.

Materials and Methods

In this section, the geotechnical available data are described aswell as the way they were organized and modeled. Finally theevaluation metrics for the obtained models are presented.

Geotechnical Data

The geotechnical data used to build the database were related toan important underground facility recently built in the north ofPortugal called Venda Nova II, which involves mostly a graniterock mass with good overall geomechanical characteristics. Themain goal was to develop alternative ways for the prediction ofcoefficients �RMR and Q� and geomechanical parameters �de-formability modulus—E; friction angle—��; cohesion—c��. Inthis paper, only the results concerning the models developed forthe strength and deformability parameters are presented.

All the steps of a formal KDD process were followed. In termsof applied DM techniques, multiple regression and ANNs wereused. The multiple regression model is a very well known tech-nique to find relations between variables.

ANNs are formed by groups of connected artificial neurons ina simplified but very similar structure to the brain neurons. Likethe biological structures, ANN can be trained and learn from a set

Fig. 2. Number of journal publications in the DM and in this arearelated to engineering and geotechnics �data source: ISI Web ofKnowledge, http://www.isiknowledge.com�

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of examples to find solutions to complex problems, recognizepatterns and predict future events. The acquired knowledge canthen be generalized to solve new problems. ANNs are complexparallel computational structures based on connected processingunits �neurons� organized in layers. Neurons communicate usingsignals through input/output connections and each connection hasan associated weight. The neuron multiplies each input with theweight of the associated connection. The total input is the sum ofall weighted inputs. Finally, an activation function is applied inorder to relate the input �stimulation� to the output �response�.Multilayer networks are the most common type of network andare composed by different parallel layers of neurons. Fig. 3 showsa generic scheme of a multilayer network. The first is the inputand the last the output layer. Intermediate ones are called hiddenlayers. There are several architectures or topologies for the net-work, each one with its own potentialities, but the most used isthe multilayer feed forward. In this type of network connectionsare unidirectional �from input to output� and there are no connec-tions between neurons in the same layer forming an acyclic net-work.

The main goal of this work was to develop analytical modelsthat could use different sets of parameters in the prediction ofvariables of interest so that they could adapt to the level of knowl-edge concerning the rock mass and to the project developmentstage. Some of the models consider less information than theoriginal formulations, thus keeping a good predictive accuracy.The set of models can be useful in the preliminary design stagesin any case where geological/geotechnical information is limited.

The available data were mainly applications of the empiricalsystems and results from laboratory �uniaxial compressivestrength and sliding of discontinuities� and in situ tests �small flatjacks, large flat jacks �LFJ�, and dilatometers� �LNEC 1983, 2003,2005�. Only the empirical systems application formed a set largeenough to be mined. Data were dispersed into 110 spreadsheetfiles. There was a necessity to perform data cleaning tasks toremove duplicated records. The reduced number of some testshindered the possibility to include them on the process because itis important that, for each type of input variable, a great amountof data exists. Finally, data were then organized and structured ina database composed of 1,230 examples and 22 attributes whichare described in Table 1. As it can be observed in the referredtable the attributes within the original database were the param-eters of the empirical classification systems RMR and Q, theRMR class and the uniaxial compressive strength of the intactrock ��c�.

From the original attributes others were calculated includingthe geomechanical parameters by means of analytical solutions.Later in this work, the adopted methodologies used to computethese parameters will be presented. After their calculation, thegeomechanical parameters were added to the database with otherattributes to check their possible influence on the models. Glo-bally, eleven new attributes were added and are presented in Table2. From now forth the geomechanical parameters obtained usingthis methodology will be called “computed values” while the onesobtained with the DM models will be called “predicted values.” Itis important to mention that the “computed values” for the de-formability modulus were calibrated with the results of reliableand large-scale in situ tests as it will be described latter in thiswork.

In spite of the high number of records within the database,there were some limitations. Considering the histograms of eachvariable of interest, the main limitations were: high uniaxial com-pressive strength ��c�100 MPa�, RQD values over 65%, andslightly wet to dry rock mass. The models developed in this workshould only be applied to rock masses with similar characteristics.In Table 3 some statistical measures of the input variables arepresented.

Modeling and Evaluation

The SAS Enterprise Miner software �www.sas.com� was used asthe modeling tool. The evaluation of the models was performed

Table 1. Name and Description of the Attributes in the Original Database

Name Description

RQD Rock quality designation

Jw, Jn, Jr, Ja,SRF

Q system factor related to: undergroundwater, numberof disc. sets, disc. rugosity, weathering degree ofdisc., and stress state in the rock mass, respectively.

Q Rock mass quality index proposed by Barton et al.�1974�

Q� Altered form of the Q index �Q�=RQD /Jn�Jr /Ja�

�c Uniaxial compressive strength

P1, P2, P3, P4,P5, P6

RMR weights related to: uniaxial compressivestrength of the intact rock, RQD, disc. spacing, disc.conditions, undergroundwater conditions, and disc.orientation, respectively.

P41, P42, P43,P44, P45

Disc. conditions—persistence, aperture, rugosity,filling, and weathering, respectively.

RMR, class Rock mass rating proposed by Bieniawski �1989� andclassification based on this value

Table 2. List of Attributes Added to the Original Database

Name Description

RQD /Jn, Jr /Ja,Jw /SRF

Ratios of the Q system representing:compartmentalization of the rock mass, shear strengthof disc., and an empirical factor named “activestress,” respectively.

log Q, log Q� Base 10 logarithm of the Q and Q� values

GSI Geological strength index proposed by Hoek et al.�2002�

N Altered form of the Q index �Q�=RQD /Jn�Jr /Ja

�Jw�RCR Altered form of the RMR index �RCR= P2+ P3+ P4

+ P5+ P6���, c�, E Friction angle, cohesion, and deformability modulus

Fig. 3. Scheme of a multilayer network

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using the results provided by this software and complementarycalculations on spreadsheets. In Fig. 4, the workflow used in thiswork is presented.

The algorithms used for the regression models were multipleregression and ANN. The applied ANN was a multilayer feed-forward network with one hidden layer of six neurons whichshown in trial calculations to have a good performance. Nonethe-less, focus was drawn to the multiple regression models becauseobtaining the explanatory physical knowledge behind the models,which is possible using this technique, was considered to be veryimportant. Moreover, these models are easier to use and imple-ment. The ANN models were mainly used for comparison pur-poses and are an open issue for further research becauseoptimizing their behavior was not attempted.

In regression problems, the goal is to estimate the modelwhich minimizes an error measurement between real and pre-dicted values considering N examples. The error measures usedwere the following:

Mean absolute deviation �MAD� =

�i=1

N

�ei�

N�1�

Root-mean-squared error �RMSE� =��

i=1

N

ei2

N�2�

To validate and assess the models accuracy, the holdoutmethod was used. In this method, data are randomly partitionedinto two independent sets, a training and a test set. Two-thirds ofdata were used for training and one-third was used for testing.The training set is used to estimate the model and its accuracy isevaluated using the test set. For each model, ten runs were per-formed, randomizing the data within the training and testing sets.The mean and confidence intervals for the error measures werethen computed considering the results of the ten runs and a 95%confidence interval of a T-student distribution. These statisticalmeasures define the range of expected errors for future predic-tions of the final model, which is estimated using all the data fortraining.

In addition to the error measures, there is also the coefficientof determination �R2�, which is very common in many statisticalapplications. R2 is a measure of variability explained by themodel but should not be used alone because it can lead to inac-curate conclusions. It varies between zero and one and a valuenear one may mean that the model explains most of the data. Forthe ANN, only the RMSE measure was used due to computationallimitations.

Results

This section describes the studies conducted to compute thestrength and deformability parameters for the rock mass. Then,the new developed models for each parameter are presented andanalyzed.

Strength Parameters

Calculation of the Parameter ValuesBoth strength and deformability parameters were not originallypresent in the database. They were indirectly derived from avail-able information using established analytical methodologies. Con-cerning the strength parameters, the main goal was to developmodels to predict the Mohr-Coulomb parameters using different

Table 3. Statistical Measures of the Input Variables

Statistical measures

Attribute Minimum Maximum Mean MedianStd.dev.

RQD 20.0 100.0 81.0 85.0 12.9

Jw 0.66 1.00 0.99 1.00 0.06

Jn 2.00 36.00 6.59 6.00 4.38

Jr 1.00 3.00 1.69 1.50 0.65

Ja 0.75 12.00 4.06 3.00 2.72

SRF 1.00 10.00 1.46 1.00 1.40

Q 0.014 133.300 13.605 8.800 18.341

P1 1.0 12.0 11.0 12.0 2.0

P2 3.0 20.0 16.2 17.0 2.6

P3 6.0 20.0 14.6 15.0 2.8

P4 0.0 30.0 15.0 16.0 6.6

P5 4.0 15.0 14.1 15.0 1.7

P6 �12.0 0.0 �7.0 �5.0 3.2

RMR 16.0 89.0 63.8 68.0 14.8

P41 0.0 4.0 1.9 2.0 0.8

P42 0.0 6.0 2.6 4.0 2.1

P43 0.0 6.0 3.5 3.0 1.6

P44 0.0 6.0 2.6 2.0 2.0

P45 0.0 6.0 4.3 5.0 1.6

Q� 0.069 133.333 13.972 8.889 18.176

RQD /Jn 0.556 47.500 16.249 15.000 7.967

Jr /Ja 0.083 4.000 0.757 0.500 0.809

Jw /SRF 0.100 1.000 0.873 1.000 0.259

log Q �1.854 2.125 0.741 0.945 0.709

log Q� �1.158 2.125 0.836 0.949 0.567

GSI 19.0 84.0 59.1 63.0 14.1

N 0.069 133.333 13.935 8.889 18.192

RCR 0.0 81.0 59.6 62.0 12.3

�c �MPa� 3.0 193.8 173.8 193.8 39.7

�� �degrees� 23.8 62.5 57.4 59.6 5.7

c� �MPa� 0.501 9.000 3.694 3.623 1.548

Fig. 4. Workflow used for the DM tasks

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types of data. To obtain the values of these parameters to includein the database, the Hoek and Brown �H-B� strength parameterswere first computed. Then c� and �� were derived by fitting anaverage linear relationship to the generated failure envelope for-mulated in effective stresses �Hoek et al. 2002�.

The Mohr-Coulomb parameters derived from the H-B criterionare peak values. For poorer rock mass conditions, the peak andresidual parameters can be considered similar because a perfectlyplastic postpeak behavior can be assumed. However, average andgood rock masses exhibit a strain softening and a brittle postpeakbehavior, respectively, with associated dilatancy �more pro-nounced for the last case�. For good quality rock masses, a re-sidual c� and �� 25% lower than the peak value can be considered�Hoek 2001�. Alternatively, it is possible to obtain H-B param-eters for extreme ends of the rock competency scale using theformulation proposed by Carvalho et al. �2007�. For average rockmass conditions, assuming that residual strength parameters canbe obtained using H-B failure criterion and using a reduced GSIvalue, which characterizes the broken rock mass, can be consid-ered reasonable.

For the calculation of the H-B strength parameters, a compara-tive study between the methods proposed by Hoek et al. �2002�and Douglas �2002� was performed. The mean �� derived usingDouglas formulas �57.2°� is approximately 6% higher than thevalue corresponding to the Hoek et al. methodology �53.9°�which means that the difference in this particular case is not sig-nificant. The main difference is found in the c� values. In fact, theones obtained using the Douglas method �mean value of 11.6MPa� are much higher than those by Hoek et al. the mean valueof which is only about 33% �3.8 MPa� of the mean c� obtainedwith Douglas method. Based on experience and empirical knowl-edge, the computed values by the methodology developed byHoek et al. are more reasonable. The reasons for such differenceare outside the scope of this work but they can be related to thefact that Douglas method was developed mostly to enhance H-Bcriterion for poor rock mass conditions. The studied database pre-sents a small number of records concerning this type of rockmass, therefore, probably Douglas method needs to be fine tunedfor better quality rock masses. Thus, in this work, the adoptedmethodology for the calculation of strength parameters was theone defined by Hoek et al. �2002�.

The prediction models for �� and c� were developed consid-ering a reference depth �H� of 350 m �the depth of the maincaverns of the powerhouse complex� and a disturbance factor �D�of zero. To allow for a simple and direct transformation of thevalues predicted by the models for other conditions �different Hand D�, a parametric study was performed. Based on this study, ageneric methodology for transforming the geomechanical param-eters for a given H and D to a different pair of values was devel-oped and then particularized for the DM models. The genericmethodology is based on the application of two correction factors,one for each parameter, and is described in Miranda �2007�.

Developed Models for Friction Angle „��…

Fig. 5 shows a plot of the most important parameters in the pre-diction of ��. There is a great amount of variables related to theprediction of this geomechanical parameter. Several variables aresimilarly important. However, the most important variables are:�1� �c �unconfined compressive strength �UCS in the picture�,which was expected because this value is also a strength measureand �2� the Q index �with logarithmic transformation� and othervariables related to the Q system. This is unexpected because theQ system is normally used only for classification purposes and

not for the calculation of strength parameters considering the rockmass as a continuum medium. Nevertheless, the Q index is verycomplete and should be used in models for the prediction of geo-mechanical parameters.

In this context, several sets of parameters were tested to obtainthe best prediction models that could simplify the way �� is cal-culated. The input variable sets �IVS� which presented the bestresults were• IVS 1: all variables;• IVS 2: Q; log Q; Q�; log Q�; RMR;• IVS 3: all RMR parameters �P1 , P2 , . . . , P6�; and• IVS 4: RMR parameters P1, P4, and P6.

The results for different IVS are presented in Table 4. Theexpressions for the regression models of IVS 2, 3, and 4 are thefollowing:

�� = 40.566 − 0.398 � Q + 0.342 � Q� + 6.726 � log Q − 4.853

� log Q� + 0.260 � RMR �3�

�� = 27.143 + 1.867 � P1 + 0.184 � P2 + 0.145 � P3 + 0.165

� P4 + 0.246 � P5 + 0.181 � P6 �4�

�� = 32.146 + 2.123 � P1 + 0.229 � P4 + 0.211 � P6 �5�

As expected, the models using IVS 1 were the most accurate.Nevertheless, the remaining models also had very good predictiveperformances. IVS 3, which uses all the RMR parameters, is onlyslightly outperformed by IVS 1. The error measures and R2 arevery close. The good behavior of this model is also observed inFig. 6, the plot of computed versus predicted values. For a widerange of values, approximately from 35° to 63°, the predictioncapacity is very uniform and reliable because the plotted valueslie near the 45° line, even though a small accuracy reduction canbe observed for the lower values of ��. This range of values

Table 4. Results for the Models Using the Different IVS for �� Predic-tion

IVS

Regression ANN

R2 MAD RMSE RMSE

1 0.968�0.004 0.521�0.020 1.002�0.106 0.672�0.195

2 0.869�0.012 1.162�0.043 2.019�0.154 1.970�0.502

3 0.965�0.001 0.600�0.021 1.051�0.068 0.807�0.092

4 0.952�0.002 0.776�0.019 1.226�0.071 2.290�0.303

Fig. 5. Relative importance of the attributes for the �� prediction

INTERNATIONAL JOURNAL OF GEOMECHANICS © ASCE / JANUARY/FEBRUARY 2011 / 49

covers a great variety of possible weathering states of the graniterock mass from fresh rock to transition from rock to soil, i.e., itexcludes only the soil state.

IVS 2 presented the worst performance. In spite of using in-formation from the RMR and Q coefficients, it was outperformedby the simpler models. For the case of ��, the use of specificinformation about rock mass characteristics presented better re-sults than using overall quality indexes like the RMR and Q. Theplot in Fig. 7 shows that this model had the worst performancewithin the approximate range of 35° to 45°, in which absolute

errors up to 10° can be found and thus, estimates in this rangeshould be used with caution. Nevertheless, the MAD and RMSEvalues point to a mean expected overall prediction error between1° and 2°, which is small.

The most important RMR parameter was by far the one relatedto �c as it can be stated by the observation of Fig. 8 meaning thatin granite rock masses, �� is closely related to this strength mea-sure. The variables related to discontinuity conditions and orien-tation �P4 and P6, respectively� also appear to be good predictors.Even though a high importance of the discontinuities conditionsshould be expected in the prediction of this strength parameter,the considerable weight of the parameter related to the disconti-nuities orientation is not as acceptable. It can be due to limitationsof the database or even of the RMR system itself which canoverrate the importance of this parameter.

IVS 4 uses these three parameters for the prediction of �� withvery good results has it is stated in the plot of Fig. 9. Comparingwith IVS 1 and 3, error measures are higher but the model has theadvantage of being very simple because it uses only three param-eters. Considering the MAD and RMSE values from Table 4, themean expected error for this model and the cited models is onlyabout 1°, which can be considered negligible for engineering pur-poses.

The ANN outperformed the regression models for IVS 1 to 3in terms of the RMSE and this is especially true for IVS 1, wherethe error was reduced in more than 30%. For IVS 4, the RMSE ofthe ANN is 87% higher than the RMSE for the regression model.The ANN performs worst when using fewer parameters. Never-theless, the RMSE of all the trained ANN were acceptable forevery considered model, which means that they are highly accu-rate in the prediction of ��.

As the target variable, tan���� was also considered because ofits physical meaning. The preliminary runs pointed to the signifi-cant importance of the GSI, which is normal because �� is indi-rectly dependent on this parameter. Moreover, the RMRparameters, mainly the one related to �c �P1� and some param-eters related to discontinuities �P4 and P6� were significantly im-portant. Regression models were then developed considering allRMR parameters and a simpler solution considering only the pa-rameters P1, P4, and P6. The equations obtained for multiple re-gression models were

ϕ

ϕ

Fig. 6. Computed versus predicted �� values for regression modelwith IVS 3

ϕ

ϕ

Fig. 7. Computed versus predicted �� values for regression modelfor IVS 2

Fig. 8. Relative importance of the RMR classification weights for the�� prediction

50 / INTERNATIONAL JOURNAL OF GEOMECHANICS © ASCE / JANUARY/FEBRUARY 2011

tan �� = 0.245 + 0.070 � P1 + 0.010 � P2 + 0.012 � �P3 + P4�

+ 0.013 � P5 + 0.011 � P6 �6�

tan �� = 0.526 + 0.084 � P1 + 0.017 � P4 + 0.014 � P6 �7�

Table 5 and Fig. 10 present the overall performance of bothmodels. The results are very similar to those obtained for �� withthe same sets of parameters. When using all RMR parameters, thevalue of �� can be estimated with acceptable accuracy eventhough there is a slight loss of accuracy for lower values com-pared to the remaining range. As expected, the consideration ofonly the three most important parameters increases the mean er-rors, but the models have the advantage of being simpler. In bothcases, and considering only the RMSE, the multiple regressionmodels outperformed the ANN in the prediction of the target vari-able.

Also note the correlation between tan���� and E, which istranslated by the following equation:

tan �� = 0.772 + 0.287 ln E �8�

The correlation presents a R2 of 0.953. MAD and RMSE take thevalues 0.0387 and 0.059, respectively. These values translate aperformance which is comparable to the previously presentedmodels which can be corroborated by the plot of computed andpredicted values in Fig. 11. The correlation presents the intrinsicinterest of allowing the evaluation of the strength parameter froman estimation of a deformability parameter and vice versa.

Interesting and simple correlations were found betweentan���� and the value of GSI from which it is derived. Thesecorrelations are translated by the following equations:

tan �� = 0.0181 · GSI + 0.5331; R2 = 0.889 �9�

tan �� = 0.93 · ln�GSI� − 2.1574; R2 = 0.909 �10�

Developed Models for Cohesion „c�…

The preliminary runs for this variable highlighted the necessity ofa variable transformation to enhance the prediction capacity of themodels. After some preliminary tests, the logarithmic transforma-tion �ln�c��� was concluded to be the most suited for this case.Fig. 12 shows the plots of computed versus predicted values for

Table 5. Results for the Models Developed for tan���� Prediction

IVS

Regression ANN

R2 MAD RMSE RMSE

P1 to P6 0.976�0.003 0.025�0.015 0.046�0.013 0.057�0.006

P1, P4,and P6

0.953�0.008 0.045�0.014 0.062�0.015 0.070�0.006

ϕ

ϕ

Fig. 9. Computed versus predicted �� values for regression modelfor IVS 4

(b)

(a) ϕ

ϕϕ

ϕ

Fig. 10. Computed versus predicted tan���� values for regressionmodels with �a� parameters P1 to P6; �b� parameters P1, P4, and P6

INTERNATIONAL JOURNAL OF GEOMECHANICS © ASCE / JANUARY/FEBRUARY 2011 / 51

the regression models which use all attributes with and withoutthe logarithmic transformation. The enhancement of predictioncapacity using the transformation of the variable is clear. Never-theless, a loss of accuracy for higher cohesion values �approxi-mately above 6 MPa� can still be observed.

Fig. 13 shows that for c� a great number of variables havesimilar importance. GSI appears to be the main parameter for itsprediction which can be considered normal because GSI is usedin the original formulation of the c� calculation. GSI was notconsidered for the development of the new models because themain goal was to develop alternative models which use differentparameters. The models which presented the best results usedsimilar IVS to those used for �� meaning that they are the oneswith higher relation to these geomechanical parameters. Thus, themost accurate IVS were:• IVS 1: all variables;• IVS 2: Q; log Q; Q�; log Q�; RMR;• IVS 3: all RMR parameters �P1 , P2 , . . . , P6�; and• IVS 4: RMR parameters P3, P4, and P6.

Table 6 presents the main results. The expressions for the re-gression models of IVS 2, 3, and 4 are

ln c� = − 0.747 + 0.000 99 � Q + 0.0394 � log Q� + 0.0298

� RMR �11�

ln c� = − 0.906 + 0.067 � P1 + 0.022 � P2 + 0.027 � P3 + 0.033

� P4 + 0.021 � P5 + 0.022 � P6 �12�

ln c� = − 0.191 + 0.059 � P3 + 0.046 � P4 + 0.021 � P6

�13�

The results for IVS 2 and 3 are quite similar in terms of theerror measures and R2. However, Fig. 14 shows different behav-iors in the range of c� values. For IVS 3, the predicted valuesshow a relatively stable trend until values of approximately 6MPa. For higher values, a strong accuracy loss is observed andthe model tends to make underestimations. On the other hand,

IVS 2 shows a higher dispersion than the previous set for valuesbelow 6 MPa. For values above this threshold, there is also atendency to underestimate which is not so pronounced. IVS 3 hasthe advantage of being a simpler model because it requires lessinformation.

The c� values ranged from 0.5 to 9 MPa in the database. Theapparently high upper bound value is explained by the consider-ation, in the calculations, of undisturbed conditions �D=0� and350-m depth, which translates a high confining stress. When com-puting the Mohr-Coulomb parameters from the H-B strength cri-terion, by adjusting a line to the curved failure envelope, theconsideration of increasing confining stresses result in higher c�

ϕ

ϕ

Fig. 11. Computed versus predicted tan���� values for the correla-tion with E

(b)

(a)

Fig. 12. Computed versus predicted c� values for regression modelswhich use all attributes: �a� without logarithmic transformation; �b�with logarithmic transformation of the target variable

52 / INTERNATIONAL JOURNAL OF GEOMECHANICS © ASCE / JANUARY/FEBRUARY 2011

and lower �� values. Moreover, c� values around 9 MPa wereobtained for almost fresh rock masses with RMR values higherthan 85.

The expected error for these regression models is approxi-mately 0.21 MPa which is acceptable considering existing rangeof values. When using the models, attention should be paid toconservative estimation for high c� values. Despite the logarith-mic transformation, a slight nonlinear trend is still observedwhich is probably the main reason for the enhanced behavior ofANN, especially for IVS 3 where the RMSE value is almostone-half of the RMSE of the regression model.

From IVS 3, the most important RMR parameters for c� pre-diction, when analyzed separately from the remaining variables,were those related to the discontinuities �P3, P4, and P6� as shownin Fig. 15. This is odd since, as shown in Fig. 15, the parameterP1 presented a high influence on the prediction of c�, which iscorroborated by engineering practice. As observed for ��, theparameter P6 appears with an overstressed importance which canbe, as stated before, due to limitations of the database or of theRMR system itself.

Nevertheless, IVS 4 was created considering only the threeabovementioned parameters. As expected, an accuracy loss is ob-served in Fig. 16. Again, a nonlinear trend is present with anoverestimation tendency for the lowest values ��1.1 MPa� andunderestimation tendency for the highest values ��6.4 MPa�. Inthese ranges, special care should be used when applying themodel. Still, the average expected error is about 0.32 MPa. Con-sidering the range of c� values, this regression model provides areasonable preliminary estimation even though being outper-formed by the ANN, which presents a RMSE value about 10%lower. Deformability Modulus

Calculation of the Parameter ValueThe deformability modulus �E� is an important input parameter inany rock mass behavior analysis. However, this parameter is notan intrinsic material characteristic since it depends on other vari-ables, mainly the associated strain level. Several different deform-ability moduli can be defined. The value to use in design shouldbe associated to the expected level of strains according to theserviceability limit state of the structure.

Generally, there is an agreement that strains involving the ser-viceability of geotechnical structures range from 0.001 to 0.5%�Gomes Correia et al. 2004�. Consequently, ground behavior fromsmall to medium strains should be accurately characterized. Both

Table 6. Results for the Models Using the Different IVS for c� Predic-tion

IVS

Regression ANN

R2 MAD RMSE RMSE

1 0.986�0.002 0.038�0.002 0.058�0.005 0.055�0.006

2 0.963�0.002 0.054�0.002 0.092�0.004 0.085�0.006

3 0.973�0.002 0.054�0.001 0.078�0.003 0.043�0.006

4 0.913�0.007 0.097�0.003 0.143�0.008 0.128�0.009

Fig. 13. Relative importance of the attributes for the ln�c�� predic-tion

(a)

(b)

Fig. 14. Computed versus predicted c� values for regression modelsfor �a� IVS 2; �b� IVS 3

INTERNATIONAL JOURNAL OF GEOMECHANICS © ASCE / JANUARY/FEBRUARY 2011 / 53

soils and rocks demonstrate an approximate elastic behavior atvery small and small strains and a nonlinear prefailure behavior atmedium strains. Thus, defining and identifying the type of modu-lus that will be adopted for design purposes is extremely impor-tant.

The subject has been an important research issue mostly in thecase of soil formations. Many advances have been reached inrecent years. For instance, the development of high precision de-formation measurement devices for the triaxial test, which permitthe assessment of very small and small strains, is one example.

However, the question is substantially different in rock forma-tions. The intact rock is not representative of the overall rockmass deformability behavior like in a larger scale with soilsamples. For a more correct definition of E, considering all fac-tors which govern deformation behavior of the rock mass, large-scale in situ tests are needed. They can be very time consumingand expensive, and their reliability can be sometimes doubtful�Hoek and Diederichs 2006�. Because of these difficulties, backanalysis procedures can constitute a source of reliable informationabout rock mass characteristics.

In this context, most procedures found in the literature to es-timate this parameter for isotropic rock masses are based onsimple expressions related to empirical systems or other indexvalues like the RQD �Zhang and Einstein 2004� and intact rockmodulus—Ei �Mitri et al. 1994; Sonmez et al. 2004; J. Carvalho,personal communication, 2004�.

Miranda �2003�, in the framework of the development of aknowledge based system for the calculation of geomechanicalparameters, performed a comparative study of these expressions,selecting those which presented the best results based on empiri-cal judgment. In the present work, to calculate E, the expressionsselected in that comparative study were used. The results of otherexpressions found in the meantime were also studied and the firstselection was added to other expressions which proved to providereliable estimations of this parameter, namely the one by Read etal. �1999� and the two proposed by Hoek and Diederichs �2006�.The first was chosen because all exponential equations poorly fitexperimental data for very good quality rock masses which isbecause of the inadequate definition of asymptotes. The equationby Read et al. �1999� uses a third power curve to better definethem. The expressions by Hoek and Diederichs �2006� were also

added because they are based on a very large database of casesand were validated by historical measurements from severalcountries. Some expressions use the elasticity modulus of the in-tact rock Ei in order to compute E. That parameter was not avail-able in a great number of cases and therefore, to estimate Ei, acorrelation with �c, developed by Miranda �2003�, was used. Theexpressions used, their limitations and writers are presented inTable 7.

To obtain one final value of E from the application of theseexpressions, a statistical methodology was established. For eachcase, the results of all expressions were computed, as well as theirmean and standard deviation. The values outside the range of onestandard deviation from the mean were eliminated and the meanof the reminiscent was computed and considered the final value ofE.

However, defining what kind of E to which these equationslead is important. As shown in Fig. 17, there are several types ofE that can be defined. Most writers have based their expressionson field test data reported by Serafim and Pereira �1983� andBieniawski �1978� and, in some cases, by Stephens and Banks�1989�. They mostly refer to the secant modulus, typically fordeformations corresponding to 50% of the peak load which isthought to be higher than the serviceability levels of most of thegeotechnical works built in rock masses. Thus, these expressionsare expected to typically provide conservative estimates of E.

The values of E obtained by the described methodology werecompared with the results of LFJ tests �LNEC 1983, 2003�. Theresults of these tests were compared with the computed values ofthe parameter near the area where the tests took place so thevalues could be comparable. Table 8 presents some statistical re-sults of this evaluation.

A similarity between the mean values obtained by both meth-odologies is observed �around 4% of variability�. The main dif-ference is the higher dispersion in the calculated values translatedby a higher standard deviation which is normal because the LFJtests are much more accurate in measuring E than the empirically

Fig. 15. Relative importance of the RMR classification weights forthe c� prediction

Fig. 16. Computed versus predicted c� values for regression modelwith IVS 4

54 / INTERNATIONAL JOURNAL OF GEOMECHANICS © ASCE / JANUARY/FEBRUARY 2011

based expressions. Thus, despite the higher variability, the calcu-lated values match well to those obtained by reliable in situ testsand can be considered realistic predictions.

To have an insight of the results from the analytical expres-sions, Table 9 presents, for each expression: the number of timeseach was calculated, the number of times the result was within theconsidered reasonable interval �one standard deviation from themean�, and the ratio between the two previous values. In general,the expressions gave similar results and mostly fell within theconsidered interval, with exceptions to the ones proposed byHoek and Diederichs �2006� �a� and Bieniawski �1978�. Nor-mally, the results of these expressions were lower than the re-maining and should be interpreted with caution when analyzinggranite formations.

Obtained Models for EThe study started developing the most accurate models to esti-mate E and then the number of input variables was reduced toobtain simpler models using only the most important ones vari-ables for the prediction of E �Miranda et al. 2008�.

Table 7. Expressions Used for the Calculation of E

Expression Limitations Reference

E=2·RMR−100 RMR�50 and �c�100 Bieniawski �1978�

E=10�RMR−10/40� RMR�80 Serafim and Pereira �1983�

E=0.1· �RMR /10�3 Not limited Read et al. �1999�

E= �Ei /100� · �0.0028·RMR2+0.9·exp�RMR /22.82�� E�Ei Nicholson and Bieniawski �1997�

E=10·Qc1/3; Qc=Q ·�c /100 Q�1 Barton and Quadros �2002�

E=25· log Q Q�1 Barton et al. �1980�

E=1.5·Q0.6 ·Ei0.14 E�Ei and Q�500 Singh et al. �1997�

E= �1−D /2� ·��c /100·10��RMR−10�/40� �c�100 Hoek et al. �2002� �a�

E= �1−D /2� ·10��RMR−10�/40� �c�100 Hoek et al. �2002� �b�

E=100,000· ��1−D /2� / �1+exp��75+15·D−GSI� /11�� Not limited Hoek and Diederichs �2006� �a�

E=Ei · ��1−D /2� / �1+exp��60+15·D−GSI� /11�� Not limited Hoek and Diederichs �2006� �b�

Table 8. Comparison of Calculated and Measured Values of E

E�GPa�—LFJ

E�GPa�—calculated

N Mean95% confidence

interval for meanStd.

deviation N Mean95% confidence

interval for meanStd.

deviation

160 36.9 35.9–37.8 6.1 76 38.5 34.5–42.5 17.6

Table 9. Comparison of the Number of Times the Expression Was Calculated and the Number of Times the Result Was within the Considered Interval

Writer�s�Number of times itwas calculated �1�

Number of timeswithin the considered

interval �2�Ratio �2�/�1�

�%�

Bieniawski �1978� 773 447 57.8

Serafim and Pereira �1983� 1,114 1,094 98.2

Read et al. �1999� 1,222 1,180 96.6

Nicholson and Bieniawski �1997� 1,222 1,221 99.9

Barton et al. �1980� and Barton and Quadros �2002� 1,215 1,055 86.8

Singh et al. �1997� 1,209 1,088 90.0

Hoek et al. �2002� �a� and �b� 1,223 1,223 100

Hoek and Diederichs �2006� �a� 1,229 36 2.9

Hoek and Diederichs �2006� �b� 1,222 1,003 82.1

Fig. 17. Alternative definitions for the deformability of a rock mass

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Preliminary calculations allowed to conclude that a logarith-mic transformation �ln�E�� would improve the accuracy of themodels �even though a minor enhancement was observed�. Themain reason of this transformation was to avoid the prediction ofnegative values for E in poorer rock mass conditions, which wasobserved in some cases with the linear model.

The parameters that produced the most accurate model weredirectly related to geomechanical indexes, namely the RMR andQ values. The explanation is that they are used in most of theanalytical expressions. Additionally, these indexes assemble im-portant information for the rock mass deformability prediction.These models can be used for the prediction of E when a thor-ough characterization of the rock mass is available. The resultsare presented in Table 10. The obtained regression model is de-scribed through expression �14�

ln E = − 2.622 + 0.2594 � Q0.25 + 0.1185 � RMR − 0.000 58

� RMR2 �14�

The linear regression model is highly accurate, and evenslightly outperforms the ANN model in terms of RMSE. Becauseln�E� ranged from approximately �1.57 to 4.22, the error can beconsidered negligible for engineering practice. The model isstable for all ranges of observed values as shown in Fig. 18.

In terms of geomechanical coefficients, the RMR was the mostimportant for the prediction of E computed by the presented for-mulation. Indeed, several regression models were tested but themost reliable models were based in this index. A simple correla-

tion between E and RMR using all available data led to veryacceptable results. The expression for this correlation is the fol-lowing:

E �GPa� = 3 � 10−5 � RMR3.2388 �15�

When only parameters related to the discontinuities are avail-able �P3, P4, and P6�, which also showed to be important param-eters in the prediction of E, the procedure that leads to betterresults is first to calculate the RMR with a model based on theseparameters �Miranda 2007� and second, using Eq. �15�, calculatethe final value of the parameter. Table 11 presents the results forthese two methods. In these cases, there are no confidence inter-vals because the results were based on a simple correlation pro-cedure using all data. The error measures and the plots ofcomputed versus predicted values �Fig. 19� are also presented inlogarithmic form for comparison with the previous models.

The correlation with the RMR index presents very good resultsbecause there is a very low accuracy loss compared to the previ-ous more complex model which considered information providedby the Q index. Fig. 19 shows the plot of computed versus pre-dicted values and it substantiates this conclusion, showing a gooddistribution of values around the 45° line. The correlation has theadvantage of avoiding the Q index evaluation. However, it doesnot have the statistical validation present in the previous, morecomplex model.

For the last method, the decreasing accuracy is much moresignificant, especially for E values corresponding to poorer rockmasses �ln�E��1 or RMR�34�. This was expected because theexpression to calculate RMR from P3, P4, and P6 presented thesame drawback. The developed method can be used in prelimi-nary studies to obtain a first approach of E or when only infor-mation about discontinuities is available and should be used withcaution for rock masses of lower geomechanical quality.

A final important remark is that the rock mass presented closeddiscontinuities in an important area. In this case, E was expectedto be very much related to the deformability modulus of the intactrock �Ei�. Some values of this parameter were available fromlaboratory tests performed by �LNEC 1983, 2005�. However,their reduced number �compared to the number of records in thedatabase� hindered the inclusion of this information in the pro-cess. In the calculation of E, some expressions used Ei and thisvalue was estimated using a correlation with �c. However, it wasinappropriate to use this approximation in the overall DM processbecause it could lead to erroneous conclusions.

Conclusions

In the context of rock mechanics, the evaluation of strength anddeformability parameters presents a fundamental importance inunderground structures design. This task is performed consideringthe results of in situ and laboratory tests and analytical solutionsbased on application of empirical classification systems.

Table 10. Results for the Models That Use the RMR and Q Coefficients

RMR and Q coefficients

Regression ANN

R2 MAD RMSE RMSE

0.978�0.001 0.088�0.004 0.137�0.009 0.141�0.016

Table 11. Results for the Models That Use the RMR and Only SomeParameters of This Index

Correlationwith RMR

CorrelationP3, P4, P6—RMR—E

R2 MAD RMSE R2 MAD RMSE

Linear 0.962 2.357 3.156 0.930 3.120 4.138

Logarithmic 0.970 0.116 0.164 0.889 0.192 0.319

Fig. 18. Computed versus predicted ln�E� values for regressionmodel with the RMR and Q parameters

56 / INTERNATIONAL JOURNAL OF GEOMECHANICS © ASCE / JANUARY/FEBRUARY 2011

However, in the preliminary stages of design and in smallergeotechnical works, the decision regarding the parameter valuesis based on limited information. Thus, the use of data from pastprojects to help in this task appears as a rational solution to thisproblem. The application of DM techniques to well organizeddata gathered from large geotechnical works like undergroundstructures can provide the basis of the development of models thatcan be very useful in future projects.

In this context, an innovative work was performed consideringthe use of DM tools to uncover new and useful knowledge in adatabase of geotechnical data through a KDD process. In particu-lar, developing new models for the evaluation of geomechanicalparameters that could be used in many conditions of data avail-ability was the goal. The main achievements of this work arepointed out in the next items.

• Identification of a new and important field of study that canenhance the way geotechnical data are analyzed. DM field canprovide a significant contribution in increasing the knowledgeabout formations of interest.

• Development of new and reliable regression models based onmultiple regression and ANN for the calculation of the geome-chanical parameters ��, c�, and E. Several models were devel-oped using different sets of input information, which allowtheir use in different conditions of knowledge about the rockmass and can be helpful in the decision-making process. Mostof the estimated models use less information than the originalformulations while maintaining a high accuracy level.

• Enhancement of the understanding of the main parameters re-lated to the behavior of the granite rock mass. The utmostimportance of discontinuities characteristics in rock mass be-havior was verified. However, some conclusions, for instance,the importance of the orientation of discontinuities, were prob-ably due to limitations of the database or even of the empiricalsystems themselves, in particular, the RMR.

• The relevance of the Q index for determining rock massstrength parameters was already known since the relationarctan�Jr /Ja� is used to approximate the inter block shearstrength. In this work it was found that the Q index can also beused to compute strength parameters of jointed rock massesassumed as a continuum medium corroborating the idea thatthe Q index is a very complete and useful parameter.

• The results of some expressions concerning the calculation ofE were compared. A methodology to define a single final valuefor this parameter was established and validated with the re-sults of reliable in situ tests. Some expressions may not beadequate for application to granite rock masses.

Acknowledgments

The writers wish to express their thanks to EDP Produção EM forauthorization and making available the necessary data. This workwas financed by the Foundation for Science and Technology�FCT� in the framework of the Research Project No. POCI/ECM/57495/2004, entitled Geotechnical Risk in Tunnels for High SpeedTrains.

References

Akin, S., and Karpuz, C. �2008�. “Estimating drilling parameters for dia-mond bit drilling operations using artificial neural networks.” Int. J.Geomech., 8, 68–73.

Barton, N., Lien, R., and Lunde, J. �1974�. “Engineering classification ofrock masses for the design of tunnel support.” Rock Mech., 6, 189–236.

Barton, N., Loset, F., Lien, R. and Lune, J. �1980�. “Application ofQ-system in design decisions concerning dimensions and appropriatesupport for underground installations.” Int. Conf. on Subsurfacespace, Rockstore, Stockholm, Sweden, 2, 553–561.

Barton, N., and Quadros, E. �2002�. “Engineering and hydraulics injointed rock masses.” Proc., EUROCK 2002—Course A, ISRM, ed.,Portuguese Geotechnical Society and LREC, Funchal, Portugal.

Basheer, I., and Najjar, Y. �1995�. “A neural-network for soil compac-tion.” Proc., 5th Int. Symp. on Numerical Models in Geomechanics,Pande and Pietruszczak, eds., Davos, Switzerland, 435–440.

Berthold, M., and Hand, D. �2003�. Intelligent data analysis: An intro-duction, 2nd Ed., Springer, Berlin.

Bhattacharya, B., and Solomatine, D. �2005�. “Machine learning in soil

(a)

(b)

Fig. 19. Computed versus predicted values for �a� correlation withRMR; �b� correlation with P3, P4, and P6

INTERNATIONAL JOURNAL OF GEOMECHANICS © ASCE / JANUARY/FEBRUARY 2011 / 57

classification.” Proc., Int. Joint Conf. on Neural Networks, Montreal.Bieniawski, Z. �1978�. “Determining rock mass deformability, experience

from case histories.” Int. J. Rock Mech. Min. Sci., 15, 237–247.Bieniawski, Z. �1989�. Engineering rock mass classifications, Wiley, New

York.Carvalho, J., Carter, T., and Diederichs, M. �2007�. “An approach for

prediction of strength and post-yield behaviour for rock masses of lowintact strength.” 1st Can.-U.S. Rock Symp., Vancouver, Canada.

Douglas, K. �2002�. “The shear strength of rock masses.” Ph.D. thesis,Univ. of New South Wales.

Fayyad, U., Piatesky-Shapiro, G., and Smyth, P. �1996�. “From data min-ing to knowledge discovery: An overview.” Advances in knowledgediscovery and data mining, U. Fayyad, ed., AAAI Press/The MITPress, Cambridge, Mass., 471–493.

Gomes Correia, A., Viana da Fonseca, A., and Gambin, M. �2004�. “Rou-tine and advanced analysis of mechanical in situ tests. Results onsaprolitic soils from granites more or less mixed in Portugal.” 2nd Int.Conf. on Site Characterization ISC ’02, Viana da Fonseca and Mayne,eds., Porto, Portugal, 75–95.

Guo, L., Wu, A., Zhou, K., and Yao, Z. �2003�. “Pattern recognition andits intelligent realization of probable rock mass failure on RES ap-proach.” Chin. J. Nonferrous Met., 13�3�, 749–753.

Hand, D., Mannila, H., and Smyth, P. �2001�. Principles of data mining,MIT Press, Cambridge, Mass.

Hanna, A., Morcous, G., and Helmy, M. �2004�. “Efficiency of pilegroups installed in cohesionless soil using artificial neural networks.”Can. Geotech. J., 41�6�, 1241–1249.

Hoek, E. �2001�. “Underground mining methods: Engineering fundamen-tals and international case studies.” Rock mass properties for under-ground mines, Hustrulid and Bullock, eds., Society for Mining,Metallurgy and Exploration �SME�, Littleton, Colo.

Hoek, E., Carranza-Torres, C., and Corkum, B. �2002�. “Hoek-Brownfailure criterion—2002 edition.” Proc., 5th North American Rock Me-chanics Symp., Toronto, 267–273.

Hoek, E., and Diederichs, M. �2006�. “Empirical estimation of rock massmodulus.” Int. J. Rock Mech. Min. Sci., 43, 203–215.

Klose, C., Giese, R., Low, S., and Borm, G. �2002�. “Geological andseismic data mining for the development of an interpretation systemwithin the Alp transit project.” EGS XXVII General Assembly, abstract2302, Nice, France.

Lee, S., and Siau, K. �2001�. “A review of data mining techniques.”Industrial Management & Data Systems, 101�1�, 41–46.

Lehman, L. �2004�. “Mitigating drilling and completion risks throughexpert planning.” Scandinavian Oil-Gas Mag., 11�12�, 10–12.

LNEC. �1983�. “LNEC collaboration in the geological and geotechnicalstudies concerning the hydraulic circuit of Venda Nova II.” TechnicalRep., LNEC Rep. No. 47/1/7084, Lisbon, Portugal �in Portuguese�.

LNEC. �2003�. “Venda Nova II scheme. Determination of the state ofstress.” Technical Rep., LNEC Rep. No. 371/03, Lisbon, Portugal �inPortuguese�.

LNEC. �2005�. “Venda Nova II scheme. Laboratory tests for the charac-terization of the powerhouse cavern rock mass.” Technical Rep.,LNEC Rep. No. 160/05, Lisbon, Portugal �in Portuguese�.

Mayoraz, F., and Vulliet, L. �2002�. “Neural networks for slope move-ment prediction.” Int. J. Geomech., 2, 153–173.

Miranda, T. �2003�. “Contribution to the calculation of geomechanicalparameters for underground structures modelling in granite forma-tions.” M.S. thesis, Univ. of Minho, Guimarães, Portugal �in Portu-guese�.

Miranda, T. �2007�. “Geomechanical parameters evaluation in under-ground structures. Artificial intelligence, Bayesian probabilities andinverse methods.” Ph.D. thesis, Univ. of Minho, Guimarães, Portugal.

Miranda, T., Gomes Correia, A., and Ribeiro e Sousa, L. �2008�. “Devel-opment of new models for geomechanical characterisation using DataMining techniques.” Geomech. and Tunnelling, 5, 328–334.

Mitri, H., Edrissi, R., and Henning, J. �1994�. “Finite element modellingof cable bolted stopes in hard rock underground mines.” Proc., SMEAnnual Meeting, SME, Albuquerque, N.M., 14–17.

Motta, C. �2004�. “Intelligent system for evaluation of risk in roads ofterrestrial transport.” Ph.D. thesis, Rio de Janeiro Federal Univ., Bra-zil �in Portuguese�.

Nicholson, G. and Bieniawski, Z. �1997�. “A non-linear deformationmodulus based on rock mass classification.” Int. J. Mining & GeologyEng., 8�3�, 181–202.

Rangel, J., Viveros, U., Ayala, A., and Cervantes, F. �2005�. “Tunnelstability analysis during construction using a neuro-fuzzy system.”Int. J. Numer. Analyt. Meth. Geomech., 29, 1433–1456.

Read, S., Richards, L., and Perrin, N. �1999�. “Applicability of the Hoek-Brown failure criterion to New Zealand greywacke rocks.” Proc., 9thInt. Cong. on Rock Mechanics, Paris, 655–660.

Romo, M., Garcia, S., Mendoza, M., and Taboada-Urtuzuastegui, V.�2001�. “Recurrent and constructive-algorithm networks for sand be-havior modeling.” Int. J. Geomech., 1, 371.

Sakellariou, M., and Ferentinou, M. �2005�. “A study of slope stabilityprediction using neural networks.” Geotech. Geologic. Eng., 23, 419–445.

Serafim, J., and Pereira, J. �1983�. “Considerations of the geomechanicsclassification of Bieniawski.” Proc., Int. Symp. of Eng. Geol. Under-ground Construction, LNEC, Lisbon, Portugal, II.33–II.42.

Singh, B., Viladkar, M., Samadhiya, N., and Mehrotra, V. �1997�. “Rockmass strength parameters mobilised in tunnels.” Tunn. Undergr. SpaceTechnol., 12, 47–54.

Sonmez, H., Gokceoglu, C., and Ulusay, R. �2004�. “Indirect determina-tion of the modulus of deformation of rock masses based on the GSIsystem.” Int. J. Rock Mech. Min. Sci., 41, 849–857.

Souza, T. �2004�. “Rio de Janeiro landslides prediction by a Data Miningapproach.” Ph.D. thesis, Rio de Janeiro Federal Univ., Brazil.

Stephens, R., and Banks, D. �1989�. “Moduli for deformation studies ofthe foundation and abutments of the Portugues dam—Puerto Rico.”Proc., 30th U.S. Symp.: Rock Mechanics as a Guide for EfficientUtilization of Natural Resources, Morgantown, W.Va., 31–38.

Suwansawat, S., and Einstein, H. �2006�. “Artificial neural networks forpredicting the maximum surface settlement caused by EPB shieldtunneling.” Tunnelling and Underground Space Technol., 21, 133–150.

Zhang, L., and Einstein, H. �2004�. “Using RQD to estimate the defor-mation modulus of rock masses.” Int. J. Rock Mech. Min. Sci., 41,337–341.

Zhou, K., Luo, Z., and Shi, X. �2002�. “Acquirement and application ofknowledge concerning slope stability based on Data Mining.” MiningRes. Devel., 22�5�, 1–4.

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