Rock Engineering and Rock Mechanics: Structures in and onRock Masses – Alejano, Perucho, Olalla & Jiménez (Eds)

© 2014 Taylor & Francis Group, London, 978-1-138-00149-7

Artificial Neural Network (ANN) based model for predictingof overall strength of Volcanic Bimrock

H. Sonmez, A. Coskun, M. Ercanoglu, D. Turer & K.E. KasapogluDepartment of Geological Engineering, Applied Geology Division, Hacettepe University, Beytepe, Ankara, Turkey

C. TunusluogluDepartment of Geological Engineering, Applied Geology Division, Canakkale Onsekizmart Universitesi,Çanakkale, Turkey

ABSTRACT: The uniaxial compressive strength of rock material (UCS) is one of the fundamental inputparameters for engineering applications to be constructed on/in rock masses such as deep slopes, tunnels anddams. However, preparation of the high quality cores for laboratory studies is generally difficult for some types ofrock such as laminated and/or fragmented rock material. To overcome this difficulty empirical prediction modelswere developed by considering some input parameters. Geological mixtures composed of rock blocks surroundedby weak matrix material are known as Block-In-Matrix-Rock (Bimrock) in literature. Agglomerate is a specialtype of Bimrock, which is composed of andesite fragments surrounded by tuff matrix and it is an example ofVolcanic Bimrock. Preparation of core samples for experimental studies from agglomerate is problematic dueto the strength contrast between andesite rock fragments and tuff matrix. To overcome these difficulties, someprediction tools have been studied by regression analyses in the literature. In this study,Artificial Neural Network(ANN) as a prediction tool was used to construct a model for prediction of overall UCS of Volcanic Bimrock.While Volumetric Block Proportion (VBP), Volumetric Block Count (VBC) and fractal dimensions (1 and 2dimensional) were selected as input parameters, normalized overall uniaxal strength of agglomerate to uniaxalcompressive strength of tuff matrix is output parameter. Fractal geometry has been used as popular methodto define irregular shapes as a quantity in literature. The boundary strength between an-desite fragments andtuff matrix is also sensitive to fragment shape and surface roughness of andesite fragments. Therefore fractaldimensions were selected as input parameters to incorporate this effect on boundary strength. While previouslydeveloped computer code FRACRUN was used to determine average fractal dimension of andesite fragments inagglomerate cores, previously developed computer code ANNES was used for ANN based model construction.In addition, similar to Volumetric Joint Count (Jv) which is widely used in rock mass characterization, VolumetricBlock Count (VBC) was defined as another input parameter for determination of Bimrock UCS consideringsome of studies about performed in literature. The highest prediction performance was obtained from the modelwhich considers Volumetric Block Proportion (VBP), Volumetric Block Count (VBC) and 1D fractal dimensionas inputs.

1 INSTRUCTION

Uniaxial compressive strength of rock material is acrucial input parameter for engineering designs tobe constructed in/on rock masses. The uniaxial com-pressive strength of rock material is determined byconventional laboratory tests employed on high qual-ity core samples. However, for some rocks such aslaminated and fragmented rock materials, prepara-tion of high quality cores is almost impossible. Toovercome this difficulty some empirical predictionmodels for Ankara agglomerate studied in literature(Gokceoglu 2002, Sonmez et al. 2004, Sonmez et al2006a) Mixtures of rocks composed of geotechnicallysignificant strong blocks, within a bonded weak matrixof finer texture defined as Bimrock by Medley (1994).

Preparation of cores from Bimrocks is extraordinarilydifficult due the strength contrast between blocks andweak matrix. Bimrocks are divided mainly into twosubgroups namely welded and unwelded Bimrocks(Altinsoy 2006, Sonmez & Tunusluoglu 2010). Whilethe strength between matrix and blocks is almostequal to the strength of matrix for welded Bimrocks,the strength between matrix and blocks is less thanstrength of matrix for unwelded Bimrocks. In thisstudy, Ankara agglomerate which is a kind of weldedVolcanic Bimrock was considered as the study rockmaterial (Fig. 1). While Volumetric Block Propor-tion (VBP), Volumetric Block Count (VBC), fractaldimensions (1 and 2 dimensional) were selected asinput parameters, normalized overall uniaxal strengthof agglomerate to uniaxal compressive strength of tuff

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Figure 1. View from Ankara Agglomerate (Sonmez &Tunuslugolu 2010).

matrix is obtained as the output parameter. The arti-ficial neural network (ANN) was used as a predictiontool for construction of the models. Prediction per-formances of the generated models were compared interms of fractal dimensions (1 and 2 dimensional).

2 PROPERTIES OF THE DATABASE ANDDETERMINATION OF FRACTALDIMENSIONS

In this study, the database established by Sonmez &Tunusluoglu (2010) was considered. Establishment ofdatabase was performed on total of 70 core specimenhaving 6 cm diameter and height between 2 to 2.5. Thetop and the bottom circular surfaces and rectangularcylindrical side of the samples were scanned for imageanalysis. Then unit weight (γ) and uniaxial compres-sive strength (UCS) of each core were determined bylaboratory tests as suggested by ISRM (2007).

As it can be followed from the literature, fractaldimension (D) is a statistical quantity that gives anindication of how completely a fractal appears to fillspace, as one zooms down to finer and finer scales (Das2011). In literature, fractal geometry has been used aspopular tool to define particularly irregular shapes bythe theory of fractal developed by Mandelbrot (1967)(Hyslip & Vallejo 1997, Kruhl & Nega 1996, Bagdeet al. 2002, Gulbin & Evangulova 2003, Pardini 2003,Kolay & Kayabali 2006, Hamdi 2008, Zorlu 2009,Sezer 2009). In this study, square gridcell (box) countmethod for 2D and segment (line) count method for1D were followed in the algorithm of FRACRUN.FRACRUN has the capability of determining frac-tal dimensions of many closed polygons on a singleimage, with a click on the start button.The calculationsin 1D and 2D procedure for a single shape followedby FRACRUN are summarized in Figure 2.

While, the relation between overall strength ofBimrock and volumetric block proportion (VBP) hasbeen widely investigated in the literature, some studieswere focused on the characterization of Bimrocks suchas determination of volumetric block proportion, blocksize distribution and their quantification (Lindquist

Figure 2. Schematically illustration for determination of 2D(box-count) and 1D (segment-line count) fractal dimensionsof a single block (Sonmez & Tunusoglu 2010).

1994, Lindquist & Goodman 1994, Medley 2002). Inthis study, by considering the studies performed onthe quantification of blocks in Bimrocks, volumetricblock count (VBC) was defined as additional inputparameter together with VBP. Because the amount ofthe weakest component may depends not only on VBPbut also on VBC. In counting of the number of block ina volume, the engineering volume should be defined.For this study, engineering volume was considered asthe volume of cores. Therefore the number of blockcounted for each core was used as VBC in number ofblock/cubic unit. The VBC values may include someerrors due to counting of blocks on 2D scanned images.

3 ARTIFICIAL NEURAL NETWORK (ANN)BASED MODELS

Considering the simple regression relations betweenUCS and input parameters, two multi inputs ANNmodels were investigated. While VBP, VBC and 1Dwere used as multi input parameters for the first model,

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Figure 3. A criteria for termination of training and selectionof optimum network architecture (Basheer & Hajmeer, 2000).

2D were considered as input parameters instead of 1Dfor the second model.

ANN has been one of the attractive predictiontool used in geo-engineering applications due to thehigh performance on the modeling of nonlinear mul-tivariate problems (Sonmez et al. 2006b). The back-propagation artificial neural network among the othermethods has been widely considered for empiricalpredication models in geo-engineering applications(Goh et al. 1995, Shi et al. 1998, Neaupane & Achet2004, Lee et al. 2003, Gomez & Kavzoglu 2005,Ermini et al. 2005, Yesilnacar & Topal 2005, Sonmezet al. 2006b).

Although the complexity of BMNN architectureincreases by addition of hidden layers, the simpleststructure having sufficient and applicable predictioncapacity is preferred to avoid overlearning. Each layerincluding input(s) and output(s) layers consist of neu-rons (nodes), and the neurons are joined by weightedlinks. The final weights and thresholds of activationfor decreasing the error between observed and com-puted outputs under a sufficient level defined by useris set by training phase of ANN algorithm (Sonmezet al. 2006b). The sigmoid transfer function is consid-ered as an activation function in this study, because itis commonly preferred in application of predicationpurposes. The maximum number of training cycles(epoch) for back and forward stages is limited by10000, together with the minimum threshold for rootmean square error (RMSE) as 0.001.

Another important point of the ANN applicationis avoiding of overlearning, otherwise ANN maylose its generalization capacity (Fig. 3). While thelearning rate was used as 0.1, the momentum coef-ficient was set to 0.95, considering recommendationand application used in literature. For solution ofthe most problems by ANN one hidden layer maybe sufficient (Rumelhart et al. 1986, Hect-Neilsen1987, Lippmann 1987, Basheer 2000). By considering

Figure 4. The ANN architecture considered in this study.

Figure 5. The graph of root mean square error (RMSE)versus number of cycles (epochs) for two models.

the recommendation mentioned in the literature, onehidden layer was preferred in this study.

Overlearning problem may be observed when largenumber of neurons preferred in hidden layers. For thispropose some recommendation is available in litera-ture (Hecht-Nielsen, 1987, Hush 1989, Ripley 1993,Wang 1994, Masters 1994, Kaastra & Boyd 1996,Kannellopoulas & Wilkinson 1997). In this study,three neurons were used by considering number ofinputs and output (Fig. 4).

Whole data in the database were normalizedbetween 0 and 1. Then the database composed of 70data set was divided into 55 data set for training (∼80%of data) and 15 data set for testing (∼20% of data set).After ANNES was run for both first and second mod-els, the graph for number of training cycle versus rootmean square error for both training and testing datasets were drawn as in Figure 5.

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Figure 6. Cross correlation between predicted and mea-sured UCS values of Bimrock cores for two models.

RMSE values of testing data tends to increase after∼2100 cycles (epoch) and ∼1900 for the first (inputs:VBC, VBP, 1D) and the second (inputs: VBC, VBP,2D), respectively. Therefore, above these thresholds,generalization of the models decreases. By using theweights and thresholds of activation at 2100th and1900th epochs for the two models predicted values oftraining and testing data were generated by ANNES.Then comparison of the two models was made by crosscorrelation graph (Figure 6).

As it can be followed from Figure 6, the first modelwhich consider 1D (segment-line) fractal dimensionexhibit slightly better prediction capacity than the sec-ond model which considers 2D (box-counting) fractaldimension. Because 1D fractal dimension have bettercapability for defining roughness of the blocks.

4 RESULTS AND CONCLUSIONS

In this study, Ankara agglomerate as a kind of vol-canic bimrock was selected for the study material.

Preparation of cores for laboratory test from Bimrocksis extraordinarily difficult due the strength contrastbetween blocks and weak matrix. The artificial neuralnetwork (ANN) was used for construction of the UCSprediction models. The main important findings of thestudy can be summarized as follows.

The use of Volumetric Block Count (VBC) togetherwithVolumetric Block Proportion (VBP) exhibits highimportance on the prediction of overall strength ofBimrocks.

1D (line) fractal dimension seems to be more sensi-tive than 2D fractal as input parameter on prediction ofoverall strength of Bimrock. Because 1D (line) fractaldimension may define roughness of andesite blocks(grain) better than 2D fractal dimension. Similar tothe study carried by Kolay & Kayabali (2006), higher1D fractal dimension is obtained for rougher grains.The contact strength between matrix and blocks maybe expected to be higher with the increase of surfaceroughness of the blocks as emphasized in literature.

ACKNOWLEDGEMENT

The database used in this study was established duringTUBITAK Project (The Scientific and TechnologicalResearch Council of Turkey, Project No: 108Y002).

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