© Author(s) 2022. CC Atribution 4.0 LicenseGEOLOGIJA 65/2, 149-158, Ljubljana 2022 https://doi.org/10.5474/geologija.2022.009 Prediction of the peak shear strength of the rock joints with artificial neural networks Napoved vrhunske strižne trdnosti po razpoki v kamnini z nevronskimi mrežami Karmen FIFER BIZJAK & Rok VEZOČNIK Slovenian National Building and Civil Engineering Institute, Dimičeva ul. 12, SI-1000 Ljubljana, Slovenia; e-mail: karmen.fifer@zag.si, rok.vezocnik@zag.si Prejeto / Received 4. 5. 2022; Sprejeto / Accepted 7. 10. 2022; Objavljeno na spletu / Published online 18. 11. 2022 Key words: artificial neural network, camera-type 3D scanner, rock mechanics, rock joint, joint roughness Ključne besede: nevronska mreža, 3D skener s kamero, mehanika kamnin, razpoke, hrapavost razpok Abstract With the development of computer technology, artificial neural networks are becoming increasingly useful in the field of engineering geology and geotechnics. With artificial neural networks, the geomechanical properties of rocks or their behaviour could be predicted under different stress conditions. Slope failures or underground excavations in rocks mostly occurred through joints, which are essential for the stability of geotechnical structures. This is why the peak shear strength of a rock joint is the most important parameter for a rock mass stability. Testing of the shear characteristics of joints is often time consuming and suitable specimens for testing are difficult to obtain during the research phase. The roughness of the joint surface, tensile strength and vertical load have a great influence on the peak shear strength of the rock joint. In the presented paper, the surface roughness of joints was measured with a photogrammetric scanner, and the peak shear strength was determined by the Robertson direct shear test. Based on six input characteristics of the rock joints, the artificial neural network, using a backpropagation learning algorithm, successfully learned to predict the peak shear strength of the rock joint. The trained artificial neural network predicted the peak shear strength for similar lithological and geological conditions with average estimation error of 6 %. The results of the calculation with artificial neural networks were compared with the Grasselli experimental model, which showed a higher error in comparison with the artificial neural network model. Izvleček Nevronske mreže postajajo z razvojem računalniške tehnologije vedno bolj uporabne tudi na področju inženirske geologije in geotehnike. Z nevronskimi mrežami lahko na osnovi večjega števila podatkov napovemo geomehanske lastnosti kamnine ali njihovo obnašanje v različnih napetostnih pogojih. Porušitve brežin ali podzemnih prostorov v kamninskem masivu se večinoma pojavijo po razpokah, zato so strižne lastnosti v razpokah ali prelomih bistvene za stabilnost geotehničnih objektov. Preiskave strižnih lastnosti so večinoma dolgotrajne, prav tako pa je pri vrtanju v fazi raziskav težko pridobiti primerne vzorce. Velik vpliv na velikost vrhunske strižne trdnosti ima hrapavost površine razpoke, natezna trdnost in vertikalna obremenitev. V predstavljenem članku je hrapavost površine razpok izmerjena s fotogravimetričnim skenerjem, vrhunska strižna trdnost pa je določena z Robertsonovo direktno strižno preiskavo. Na osnovi šestih vhodni karakteristik razpok in kamnine ter izmerjene strižne trdnosti z Robertsonovo preiskavo, lahko z naučeno nevronsko mrežo uspešno napovemo vrhunsko strižno trdnost po razpoki. Tako naučena nevronska mreža lahko dovolj natančno napove vrhunsko strižno trdnost za podobne litološke razmere in geološke pogoje, z upoštevanjem dokaj nizke napake, to je 6 %. Rezultate izračuna z nevronskimi mrežami smo primerjali z eksperimentalnim modelom, ki je v primerjavi z nevronskimi mrežami pokazal višjo napako napovedi vrhunske strižne trdnosti. 150 Karmen FIFER BIZJAK & Rok VEZOČNIK Introduction The idea for artificial neural networks (ANN) is in the functioning of the human brain. The human brain is the central system of the human nervous system, composed from almost 10 billion biological neurons that are interconnected by synapses. The cellular body of a neuron receives input signals from many synapses with different electrical activity (Flood & Kartam, 1994, Bish- op, 1995, Lopez et. al., 2022). Scientists were therefore drawn to the idea of making a device that mimics the brain. These are made up of a huge number of cells intercon- nected by thin “threads”. These cells are called neurons, and their connections or “threads” are called synapses. Neurons send electrical stimu- li to each other through synapses. Synapses are characterized by differences in electrical con- ductivity, which changes during learning. Thus, the knowledge acquired during learning is accu- mulated in synapses or in their conductivity. If the sum of the signals arriving at an individual neuron via synapses is large enough, the ignition of an individual neuron occurs. This means that this neuron sends a signal to its output, which is transmitted through the synapses to other neu- rons (Jain et al., 1996, Maio & Santillo, 2020). The ANN tries to simulate the human brain activity and until now several applications are already known in rock mechanics field (Lawal & Kwon, 2021; Abdalla et al., 2015; Armaghani, 2015; Hussain et al., 2019; Sarkar et al., 2010). The shear behaviour of a jointed rock mass- es depends on the shear characteristics of the discontinuities in the rock mass. To determine the shear strength in rock mass discontinuities many researchers developed experimental rela- tionships between the roughness of the discon- tinuities and the peak shear strength (Barton, 1973; 1976; Barton and Choubey, 1977; Hoek and Brown, 1980; Hoek and Bray, 1981; Hoek, 2000; Huang et al., 1992; Patton, 1966; Pellet et al., 2013). Recently, scanners have been used as a non-de- structive method to measure and characterise the joint surface in three dimensions. The roughness metric based on the three-dimensional morphol- ogy was proposed by Grasselli (2001, 2002). An ATOS scanner was used for the accurate measure- ment of the joint roughness. Details of the scanner characteristics are summarized in Table 1. Sev- eral empirical relations were developed for deter- mining the geometry of the joint surface, such as contact area A0, roughness parameter C and max- imum dip angle Ɵ*max (Grasselli & Egger, 2003). ANNs have already been used for prediction of the shear characteristics of rock samples in published papers. The shear strength of shale rock samples was predicted based on the mini- mum and intermediate strength using a triaxi- al test (Moshrefi et al., 2018). Back propagation multi-layer perceptron was used for learning. In- fluence of heterogeneity on rock strength at dif- ferent strain rates was predicted with an ANN, as well as parameters of crack inclination, dis- tance, filling and strain rate (Jiang et al., 2021). Shear behaviour of clean rock discontinuities was studied including normal stress, dilation, horizontal displacement, asperity angle, ampli- tude, joint rock compressive strength and friction angle of an intact sample. The ANN model fitted the measuring results better than some analyti- cal models. Shear strength parameters were ob- tained using shale samples, sheared in a triaxial cell. The input parameters were point load index, Brazilian tensile strength, ultrasonic velocity, Schmidt hammer test and friction angle as an output parameter (Armaghani et al., 2014). Drilling data and well logs were used for the uniaxial compressive strength prediction with ANN (Asadi, 2017). Porosity, density, penetration rate and P wave velocity were used to predict the uniaxial strength of rock between wells that are close to each other. For limestone the uniaxial strength was compared with the results of the ANN and regression analysis (Khanlari & Ab- dilor, 2011). Table 1. Characteristics of the scanner with camera (ATOS I). Tabela 1. 3D skener s kamero (ATOS I). Item Value Measured Points 800.000 Measurement Time (seconds) 0.8 Measuring Area (mm²) 125 ×100 - 1000 × 800 Point Spacing (mm) 0.13-1.00 Measuring volume (mm3) 125 × 100 × 90 to 1000 × 800 × 800 Measuring points per individual scan 1032 × 776 pixels 151Prediction of the peak shear strength of the rock joints with artificial neural networks In the presented paper, the ANN was used for the peak shear strength prediction of the rock joints. The input parameters were tensile strength, basic shear angle and the morphologic parameters of the rock joints obtained from the 3D scanner measurements. Results were com- pared with the Robertson direct shear test for different rock samples. Methods Artificial Neural network model The model of the ANN tries to simulate the behaviour of the human brain and nervous sys- tem by its architecture. A detailed description of the ANNs is beyond the scope of this paper and can be found in many publications (Masters, 1993; Jain et al., 1996; Almeida, 2002; Shahin et al., 2002). ANNs learn from the presented data and use these data to adjust their weights in an attempt minimise the model input variables and the cor- responding outputs. The advantage of ANNs is that they do not need any prior knowledge about the relationship between the input-output varia- bles. This is a benefit in comparison with most of the empirical and statistical methods. The basic unit of ANN is a neuron or node (Fig. 1). It receives input signals (x1 .. xn) and a bias value, which is always 1. In the neuron input, signals are multiplied with their weight values (w1 .. wn). The bias assures that even if all input signals are zero, there is activation in the neuron. The activation function (G(I)) is used for introduc- ing the non-linearity to the ANN. (1) A typical ANN is composed of three different layers of neurons; one input layer, one or multiple hidden layers and one output layer. The simpli- fied model is presented in Figure 2. The input layer consists of neurons which re- ceive information from input data. The number of neurons in the input layer depends on input data sources. For presented application the input neurons were; st (tensile strength), fb (basic fric- tion angle) and scanning parameters A0 (maxi- mum contact area), C (roughness parameter) and θmax* (maximum apparent dip angle). The hidden layer contains a different number of neurons and is connected with the input and output layer with a linear or non-linear transfer function (Rashidian et al., 2013). The hidden lay- er processes the information received from the input neurons, and passes it to the output layer. The output layer produces an appropriate re- sponse to the given input. For presented ANN there is a single output neuron; measured shear peak shear stress (tp). The propagation of information in ANNs starts at the input layer where the network is pre- sented with a historical set of input data and the corresponding (desired) outputs. The back-prop- agation algorithm, used in this paper, is the most widespread because it has a simple structure and clear mathematical meaning (Cybenko, 1989). It consists of two phases: forward and backward. In the forward phase, the training data set was introduced to the network and fed forward until a prediction was calculated. The final output is then compared to the target value and the error signal is calculated. In the backward phase, the error signal is back propagated in the network from the output layer to the input layer and the Fig. 1. Typical neuron in ANN. Sl. 1. Značilen nevron v ANN. Fig. 2. Structure of the BP artificial neural network. Sl. 2. Struktura povratne nevronske mreže. 𝐼𝐼𝐼𝐼 = 𝑤𝑤𝑤𝑤0 + 𝑤𝑤𝑤𝑤1𝑦𝑦𝑦𝑦1 + 𝑤𝑤𝑤𝑤2𝑦𝑦𝑦𝑦2 … . +𝑤𝑤𝑤𝑤𝑛𝑛𝑛𝑛𝑦𝑦𝑦𝑦𝑛𝑛𝑛𝑛 152 Karmen FIFER BIZJAK & Rok VEZOČNIK appropriate weight changes are calculated using a mathematical criterion that minimizes the er- rors (Jain et al., 1996; Khandelwal et al., 2004). Using these errors and a learning rule, the net- work adjusts its weights until it can find a set of weights that calculate an input/output pair with the smallest error. This phase is called “learn- ing” or “training”. Once the training phase of the model has been successfully finished, the per- formance of the trained model has to be validat- ed using an independent validation set of data. For the presented application 70 % of the data were used for a training set and the rest for the testing. The test set measured how well the mod- el learned based on the data from the learning phase. For validation, data are usually taken from the whole set when there are not enough ad- ditional data for this procedure. Use of a 3D Scanner For measuring rock joint surface roughness, an Advanced Topometric Sensor (ATOS I) was used (Fig. 3) which operates by combining mea- suring principles of optical triangulation, pho- togrammetry and fringe projection (Keller & Mendricky, 2015). With the help of a projector, different light-dark fringe patterns are produced by the measuring part. The ATOS system consists of three separate components: the fringe digital projector and two CCD cameras. The two cameras, separated by a fixed distance, operate on the basis of known rel- ative orientation thus forming the basis for tri- angulation. The fringe digital projector, located midway between both cameras, projects a struc- tured light pattern onto the object to be scanned. During the scanning process, the coded fringe pattern undergoes a phase shift which means the pattern rapidly changes and is therefore nearly invisible to the human visual perception abilities. This pattern alteration process is recorded by the two CCD sensors with 3D coordinates calculated for each camera pixel by applying optical trans- formation equations. The resulting highly-de- tailed image consists of millions of measuring 3D points which are acquired within a very short time (few seconds) without physically contacting the scanned surface. In the final step, the accom- panying sensor software automatically generates a high-resolution point cloud which represents a precise 3D image of the scanned surface. Option- ally, this point cloud can be further transformed into a surface model (using typical triangular or square grid templates (Fig. 4). In the figure the roughness of the rock joint surface measured from the share plane is presented. The quality of surface measurements is obvi- ously very important for the estimation of sur- face roughness. The quality of the morphological model depends on the density of the measuring points, the measuring resolution and the preci- sion with which these points can be located in space. The measuring area of the ATOS I system ranges from 125 × 100 mm2 to 1000 × 800 mm2 and the number of measuring points per individual scan reaching up to 1032 × 776 pixels. Calculation methods of Grasselli model for the peak shear stress calculation Morphological parameters were calculated from scanning samples according to the Grassel- li (2001) procedure (G01). The apparent dip an- gle was used to calculate the three-dimensional morphology parameters (Fig. 5). The procedure is presented in equations 2 to 6. Fig. 3. The ATOS I 3D scanner and the sample. Sl. 3. Skener ATOS I 3D in skenirani vzorec. Fig. 4. Surface model of the rock joint. Sl. 4. Skenirana površina razpoke. 153Prediction of the peak shear strength of the rock joints with artificial neural networks (2) (3) (4) (5) where m is the number of triangles, θ* is the apparent dip angle of the surface unit, α is the azi- muth, θ is the dip angle between the shear plane and the joint surface, t is the shear direction vec- tor, n is the outward normal vector of the trian- gle, n0 is the outward normal vector of the plane and n1 is the projection vector of n. The maxi- mum contact area (A0) is calculated as follows: (6) Where Am is the area of the rock joint and Al the contact area after the shear test. The results from the ANN and from the Gras- selli procedure were used for comparison. The peak shear strength of the samples was calculat- ed according to the proposed criteria (Grasselli, 2001) according to the eq. 7. (7) where sn is the normal stress, st is tensile strength of the rock, fr basic angle of friction, θ*max is the maximum apparent dip angle of the surface unit, C is the roughness parameter, calcu- lated using a best-fit regression function, which characterises the distribution of the apparent dip angles over the surface. Brazilian tests were done for tensile strength of the rock samples. An average estimation error (Eave) was cal- culated (Kulatilake et al., 1995) for both results (ANN and Grasselli model). (8) Test procedure Samples of different lithology were taken from the north part of Slovenia for a direct shear Rob- ertson test. Samples had a diameter of less than 10 cm and had a natural rock joint. They were tested under different vertical stress between 0.1 and 0.4 MPa. Robertson direct shear tests were performed according to the ASTM D5607 -16 standards and the final result of these tests was peak shear strength for every sample (tp). A shear test of basic friction angle was performed in a shear apparatus for every lithological type of rock (fr). Before the capsulation of the samples, the joints of the samples were scanned with the ATOS I scanner to obtain the morphological pa- rameters. A data processing program, written in MatLab, was developed for the calculation of the rock joint morphological parameters according to Grasselli (2001). Results The morphological parameters of the rock joints (A0, C, θ*max) were calculated as a result of scanning. The rest of the input parameters; sn, st, and fb, were obtained from the Robertson direct shear test. The morphological parameters and shear strength parameters are presented in Table 2. Fig. 5. Geometrical identifica- tion of apparent dip angle - θ*. Sl. 5. Geometrična predstavi- tev navideznega kota - θ*. tan𝜃𝜃𝜃𝜃𝑠𝑠𝑠𝑠∗ = tan𝜃𝜃𝜃𝜃 (− cos α ) (2) cos 𝜃𝜃𝜃𝜃 = 𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑜𝑜𝑜𝑜|𝑛𝑛𝑛𝑛||𝑛𝑛𝑛𝑛𝑜𝑜𝑜𝑜| (3) cosα = 𝑡𝑡𝑡𝑡𝑛𝑛𝑛𝑛1|𝑡𝑡𝑡𝑡||𝑛𝑛𝑛𝑛1| (4) 𝜃𝜃𝜃𝜃∗��� = 𝑡𝑡𝑡𝑡𝑛𝑛𝑛𝑛1|𝑡𝑡𝑡𝑡||𝑛𝑛𝑛𝑛1| 1 𝑚𝑚𝑚𝑚 ∑ 𝜃𝜃𝜃𝜃𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠∗𝑚𝑚𝑚𝑚𝑠𝑠𝑠𝑠=1 (5) 𝐴𝐴𝐴𝐴0 = 𝐴𝐴𝐴𝐴𝑙𝑙𝑙𝑙 𝐴𝐴𝐴𝐴𝑚𝑚𝑚𝑚 (6) 𝜏𝜏𝜏𝜏𝑝𝑝𝑝𝑝 = 𝜎𝜎𝜎𝜎𝑛𝑛𝑛𝑛 ∗ 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡(𝜑𝜑𝜑𝜑𝑟𝑟𝑟𝑟 , ) ∗ �1 + 𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 �− 1 9𝐴𝐴𝐴𝐴0 ∗ 𝜃𝜃𝜃𝜃𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 ∗ 𝐶𝐶𝐶𝐶 ∗ 𝜎𝜎𝜎𝜎𝑛𝑛𝑛𝑛 𝜎𝜎𝜎𝜎𝑡𝑡𝑡𝑡 �� (7) 𝐸𝐸𝐸𝐸𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 = 1 𝑚𝑚𝑚𝑚 ∑ �𝜏𝜏𝜏𝜏𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡−𝜏𝜏𝜏𝜏𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐. 𝜏𝜏𝜏𝜏𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 �𝑚𝑚𝑚𝑚𝑖𝑖𝑖𝑖=1 ∗ 100% (8) 154 Karmen FIFER BIZJAK & Rok VEZOČNIK Table 2. Input data for the peak shear strength calculation Tabela 2. Vhodni podatki za izračun vrhunske strižne trdnosti No Lithology σt (MPa) σn (MPa) A0 (-) C (-) Ɵ*max (°) ϕb (°) 1 limestone 1.99 0.1 0.4147 17.03 86.86 24 2 limestone 1.99 0.3 0.5791 16.99 89.69 24 3 limestone 1.99 0.4 0.5499 28.75 75.55 24 4 limestone 1.99 0.4 0.1773 12.87 86.2 24 5 limestone 1.99 0.4 0.4859 20.87 82.807 24 6 limestone 1.99 0.3 0.4015 11.82 89.86 24 7 limestone 1.99 0.2 0.3953 27.92 86.95 24 8 limestone 1.99 0.4 0.4535 12.2 51.89 24 9 dolomite 2.17 0.15 0.3410 11.9 90 25 0 shale 0.3 0.4 0.5420 15.04 86.21 24 11 shale 0.3 0.2 0.4720 9.22 42.93 24 12 siltstone 2 0.1 0.4606 6.26 73.33 26 13 siltstone 2 0.4 0.2000 11.61 87.28 26 14 siltstone 2 0.4 0.3037 13.88 89.12 26 15 claystone 0.3 0.2 0.1200 19.98 84.74 20 16 claystone 0.3 0.2 0.4707 24.69 87.1 20 17 claystone 0.3 0.1 0.3459 13.27 89.9 20 18 sandstone 1 0.4 0.4613 11 79.25 30 19 claystone 0.3 0.1 0.4999 6.69 89.7 20 20 claystone 0.3 0.4 0.5020 9.4 84.24 24 21 siltstone /claystone 1 0.4 0.3655 28.62 89.9 24 22 claystone 0.3 0.4 0.3953 24.4 79.72 24 23 siltstone/ claystone 0.3 0.2 0.5105 9.25 89.05 24 24 siltstone 7.37 0.4 0.4238 15.05 89.71 30 25 dolomite 3.02 0.1 0.5829 6.46 79.12 30 26 dolomite 3.02 0.3 0.4821 7.21 82.08 30 27 siltstone 2 0.3 0.5153 12.46 84.87 30 28 dolomite 3.02 0.3 0.4821 7.21 82.09 30 29 dolomite 2.49 0.25 0.4126 6.06 90 28 30 claystone 0.3 0.4 0.4824 15.59 85.47 20 The prediction of peak shear stress (tp) with ANN and G01 model was performed in the next step. For both calculations the same input pa- rameters were used (sn, st, A0, C, θ*max, fb). Results of the ANN model Several ANN structures were used for the tp prediction, with a different number of neurons in the input layer, but the best results were achieved with the next structure: Input layer; 6 neurons (sn, st, A0, C, θ*max, fb) Hidden layer, 29 neurons Output layer, one neuron (tp) For example, if we added residual shear angle (fr) and type of lithology to the presented 6 input neurons, the calculation made by the ANN did not converge to the minimum error. A hyperbolic tangent transfer function was used as the activation function. We also used an sigmoidal function, but the average estima- tion error (Eav) was almost the same. The trained ANN predicted the peak shear strength with quite a small average estimation error; Eav = 6 % (Table 2). A comparison between the predicted peak shear strength with the ANN and with the results from the laboratory Robertson test is pre- sented in Figure 6. 155Prediction of the peak shear strength of the rock joints with artificial neural networks Result of G01 model Next calculation was done based on the G01 model (eq. 8) and compared with the results ob- tained from laboratory Robertson tests. The av- erage estimation error between the Robertson tests and calculation with G01 model was much higher, Eav = 28 % (Table 3). The comparison between the calculated peak shear strength with the G01 model and with the results from the laboratory Robertson test is pre- sented in Figure 7. Fig. 6. Measured peak shear stress vs ANN predicted. Sl. 6. Primerjava izmerjene vrhunske strižne trdnosti in izračunane z ANN. Fig. 7. Measured peak shear stress vs G01 model. Sl. 7. Primerjava izmerjene vrhunske strižne trdnosti in izračunane z G01 modelom. Table 3. Results of peak shear strength calculation for ANN and G01 model. Tabela 3. Rezultati izračuna vrhunske strižne trdnosti izra- čunani z ABB in G01 modelom. No τp meas. (MPa) τp ANN (MPa) τp G01 (MPa) No τp meas. (MPa) τp ANN (MPa) τp G01 (MPa) 1 0.06 0.06 0.35 16 0.07 0.07 0.68 2 0.25 0.18 0.01 17 0.05 0.06 0.13 3 0.17 0.17 1.05 18 0.31 0.31 0.11 4 0.21 0.21 0.54 19 0.06 0.06 0.21 5 0.20 0.22 0.63 20 0.28 0.30 0.31 6 0.18 0.18 0.31 21 0.27 0.27 0.10 7 0.12 0.12 0.47 22 0.22 0.22 0.05 8 0.23 0.22 0.36 23 0.14 0.09 0.19 9 0.12 0.12 0.12 24 0.25 0.25 0.80 0 0.30 0.30 0.28 25 0.09 0.09 0.18 11 0.13 0.09 0.06 26 0.29 0.29 0.06 12 0.08 0.08 0.14 27 0.23 0.23 0.39 13 0.22 0.22 0.29 28 0.29 0.29 0.06 14 0.21 0.22 0.48 29 0.24 0.12 0.07 15 0.09 0.09 0.10 30 0.16 0.16 0.07 Eave 6% 28% Discussion The presented calculation was demonstrated by analysing 30 samples of jointed rock. The in- put parameters for the Grasselli calculation (G01) and the ANN were the same. The peak shear stress depends on the normal stress under which the shear test is performed and because of this, the normal stress (sn) is one of the most impor- tant parameters. Grasseli (2001) showed that A0, C and θ*max, are the most important morphologi- cal parameters and tensile strength (st) and basic friction angle ϕb are the most important strength characteristics of the rock. The peak shear stress of the rock joints was measured in laboratory and then predicted with the ANN and with the G01 model. The results of both calculations are presented in Figure 8. Pre- diction of peak shear stress with the ANN is very close to the measured results, while the calcula- tions with the Grasselli model were much higher in comparison to the measured results for at least for 30 % of samples. Samples used in a comparable study (Gras- selli, 2001) have larger dimensions, at least 200 mm × 100 mm × 100 mm and were consolidat- ed under a normal load higher than 1 MPa. In our case, samples were tested under the normal loads between 0.1 and 0.4 MPa. The use of smaller sam- ples and lower vertical load are probably a reason for the higher average estimation error obtained with the G01 model. Such large samples are often difficult to obtain for testing. Samples are usual- ly taken from boreholes and they have a maximal diameter of 10 cm and in this case the Robertson shear test is much more convenient. The result of the Robertson test was peak shear stress which was then calculated with the ANN and Grasselli model. 156 Karmen FIFER BIZJAK & Rok VEZOČNIK The calculation with the ANN reaches very good results; Eave was 6 %. The calculated Pear- son coefficient was 0.93, which confirms a very high correlation between the measured peak shear stress and the predicted peak shear stress with ANN. The comparison between the calcu- lated and measured peak shear strength is pre- sented in Figure 8. Results of more tests with different rock li- thology have to be included in to the ANN in the future. Given the diverse lithological composition in Slovenia, it is necessary to include samples of metamorphic and igneous rocks. Also, the num- ber of samples of soft rock has to be increased, because the main geotechnical problems usually occurred in soft rocks like shale or claystone. Higher number of samples could assure that the trained ANN would be a useful tool in engi- neering practice. Conclusions Shear geomechanical characteristic are the most important factor in the stability of the joint- ed rock mass. Usually the failure occurs along a fissure or a joint. Peak shear stress is the main parameter for a slope design, foundations or tunnel excavations. If it is exceeded, the failure could cause large damage to geotechnical struc- tures. In the paper the technology of rock joint scanning was used for determining the morpho- logical parameters of the joint roughness. 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