© Author(s) 2018. CC Atribution 4.0 LicenseGEOLOGIJA 61/1, 25-32, Ljubljana 2018 https://doi.org/10.5474/geologija.2018.002 Quantified joint surface description and joint shear strength of small rock samples Geometrijske lastnosti površine razpok in strižna trdnost po razpoki za manjše vzorce kamnin Karmen FIFER BIZJAK & Andraž GERŠAK Slovenian national building and civil engineering institute, Dimičeva ul. 12, SI-1000 Ljubljana, Slovenia; e-mails: karmen.fifer@zag.si, andraz.gersak@zag.si Prejeto / Received 31. 1. 2018; Sprejeto / Accepted 23. 4. 2018; Objavljeno na spletu / Published online 20. 7. 2018 Key words: camera-type 3D scanner, rock mechanics rock joint, roughness of the joints, rock joint shear strength Ključne besede: 3D skener s kamero, mehanika hribin, hrapavost razpok, strižna trdnost kamnine po razpoki Abstract Geotechnical structures in rock masses such as tunnels, underground caverns, dam foundations and rock slopes often have problems with a jointed rock mass. The shear behaviour of a jointed rock mass depends on the mechanical behaviour of the discontinuities in that particular rock mass. If we want to understand the mechanical behaviour of a jointed rock mass, it is necessary to study the deformation and strength of a single joint. One of the primary objectives of this work is to improve the understanding of the frictional behaviour of rough rock joints under shear loads with regard to the roughness of the joint surface. The main problem is how to measure and quantify the roughness of the surface joint and connect the morphological parameters into a shear strength criterion. Until now, several criteria have been developed; however, all of them used large rock samples (20×10×10 cm). It is often not possible to get large samples, especially when the rock is under a few meters thick layer of soil. In this case, samples of rock can only be acquired with investigation borehole drilling, which means that the samples of rock are small and of different shapes. The paper presents the modified criterion that is suitable for calculating the peak shear stress of small samples. Izvleček Geotehnični objekti v hribini, kot so predori, podzemni prostori, pregrade in strme brežine, pogosto povzročajo težave zaradi različne razpokanosti hribinskega masiva. Strižno obnašanje celotnega hribinskega masiva je odvisno od razpok in njihovih strižnih lastnosti. Če želimo razumeti mehansko obnašanje hribinskega masiva, je potrebno preiskati strižne trdnostne karakteristike vsakega sistema razpok. Namen predstavljene raziskave je, da se preuči obnašanje razpok pod strižnimi obremenitvami v odvisnosti od hrapavosti površine razpok. Največji problem se pokaže pri meritvah hrapavosti razpok in povezave morfoloških parametrov površine razpoke s strižnimi karakteristikami same razpoke. Do sedaj je bilo predstavljenih že več kriterijev, vendar so bili vsi razviti na osnovi testiranja velikih vzorcev kamnine (20×10×10 cm). V večini primerov pa je velikih vzorcev kamnine nemogoče dobiti, predvsem takrat, ko je kamnina globoko pod več metrov debelo plastjo zemljine. V tem primeru se vzorce hribine lahko pridobi samo z raziskovalnim vrtanjem. Tako dobljeni vzorci pa so malih dimenzij in različnih oblik. V članku je predstavljen modificiran kriterij, ki je uporaben za izračun vrhunske strižne trdnosti v primeru, da imamo za raziskave dostopne samo vzorce manjših dimenzij. Introduction Geotechnical structures in rock material such as tunnels, underground caverns, dam founda- tions and rock slopes often have problems with a jointed rock mass. The shear behaviour of a joint- ed rock masses depends on the mechanical be- haviour of the discontinuities in that particular rock mass. If we want to understand the mechan- ical behaviour of a jointed rock mass, it is neces- sary to study the deformation and strength of a single joint. Until now, many experimental and numerical investigations have been carried out on the mechanical behaviour of rock joints (Bar- ton, 1973; 1976; Barton & Choubey, 1977; Gras- 26 Karmen FIFER BIZJAK & Andraž GERŠAK selli & Egger, 2003; Hoek & Brown, 1980; Hoek & Bray, 1981; Hoek, 2000; Huang et al., 1992; Pat- ton, 1966; Pellet et al., 2013). The joint surface is one of the parameters that have the highest influence on the shear strength of the rock joint. Many parameters have been proposed over the past 40 years to describe the joint surface. Barton (1973) proposed a joint roughness coefficient (JRC) to quantify the roughness of a rock joint. The roughness pro- file of the nature rock joint is visually compared with 10 standard profiles suggested by Barton and Choubey (1977). However, the visual com- parison method can be subjective without suffi- cient experience. The JRC has been widely used in rock engineering and is suggested by the In- ternational Society for Rock Mechanics (ISRM) as a useful parameter for describing the joint surface. In the last decade, several researchers published that the roughness of the rock joint could be somewhat underestimated (Hong et al., 2008; Lee et al., 2001). Other methods using the fractal analysis (Ku- latilake, et al., 2006; Odling, 1994) or the statistical approach (Reeves, 1985) have been used for iden- tifying the rock joints. For all those methods, the two-dimensional (2D) description of the surface is used, although the joints have a three-dimen- sional morphology. Nowadays, with the advanced techniques, it is possible to measure and charac- terise the joint surface in three dimensions. The roughness metric based on the three-dimension- al morphology was proposed by Grasselli (2001, 2002). The ATOS scanner was used for the accu- rate measurement of the joint roughness (Grassel- li & Egger, 2003). The procedure of the roughness measurements is quite clear, yet the relationship between the joint mechanical properties and the geometric parameters is still the object of re- search nowadays. An empirical relation with the shear strength of the rock joints was studied and three-dimensional roughness parameters such as the contact area, the roughness parameter C and maximum dip angle Ɵ*max were proposed for the calculation (Grasselli & Egger, 2003; Grasel- li, 2006). All the parameters were determined by morphology functions. However, the anisotropy of rock joint was not considered in this criterion. Further research developed the modified peak shear strength criteria which could reflect the effect of dilatancy (Tang et al., 2014, 2015). The relationship between peak dilatancy angle and three-dimensional morphology characteristics was taken into consideration in these criteria. In the criterion proposed by Xia (2013), the variation law of the dilatancy angle under various normal stresses was not inconsistent with the actual sit- uation. Samples on which the shear tests were performed in all mentioned papers were of large dimensions, at least 200 cm2. It is often not possi- ble to get large samples, especially when the rock is under a few meters thick layer of soil. In this case, samples of rock can only be acquired with investigation borehole drilling, which means that samples of rock are small and of different shapes. In the presented paper, the smaller samples from bore hole drilling were used for direct shear testing. For testing, the Robertson shear apparatus was used. That apparatus is limited by the size of the samples and by the height of normal and shear loads. Based on the experi- ment, a modified peak shear strength criterion was proposed, and a comprehensive criterion was developed for samples with smaller size and lower loads. Methods Use of a 3D Scanner For measuring rock joint roughness, a cam- era-type digital three-dimensional scanner was used (fig. 1), which is a combined system with photogrammetry and fringe projection. It uses two cameras to capture the same position or as- perity and can thus produce three-dimensional images showing the height of the asperity. Pho- togrammetry can be used for the measurement of sensor coordinates as well as for the global matching of partial views. In fringe projection, the projector illuminates the stripe of the pat- terned light on an object and two cameras cap- ture the deformed shape of fringe by the object. An accurate roughness profile may be obtained by specific fringe characteristics. Therefore, the roughness underestimation of unevenness can be improved. Although this method requires a merging process because of image overlapping with “multi-viewing”, it produces a high resolu- tion image quickly and conveniently (Reich et al. 2000; Lee & Ahn 2004). While this method can quickly provide the high density cloud point, it is very sensitive to environmental conditions (Fifer, 2010). The selected system for this study was Ad- vanced Topometric Sensor (ATOS I) which combines photogrammetry and fringe projec- tion. Because this system can yield high densi- ty three-dimensional point clouds for each im- age, it also requires a high computing system. ATOS has been used in the field of engineering 27Quantified joint surface description and joint shear strength of small rock samples for product digitization in industries such as the automotive industry. Details of the selected sys- tem are summarized in Table 1. The quality of surface measurements is very important to the estimation of roughness. The accuracy of the morphological model is dependent on the density of measurement points, measurement resolution and the precision with which these points can be located in space. The camera-type 3D scanner has several ad- vantages: • the scanning process is fast and the image is accurate, • the large scale of the specimen can be digitized, • the scanning process can be performed in the field, • the rock surface is not damaged during digi- tizing. Calculation methods The morphological parameters which we ac- quired with the scanning of samples were used for further calculation. The peak shear strength of samples was calculated according to several criteria which have been developed until now. Grasselli (2001) proposed the apparent dip an- gle to calculate the three-dimensional morphol- ogy parameters (Fig. 2). The average inclination angle is used according to the results of his re- search Fig. 1. The ATOS I 3D scanner and the sample. Table 1. The properties of the optical scanning system 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 indivi- dual scan 1032×776 pixels Fig. 2. Calculation of the 3D average angle of the rock joint surface (Grasselli, 2001). Grasselli (2001) proposed the crite- rion (G01) for calculating the peak shear stress according to the eq. 6. 28 Karmen FIFER BIZJAK & Andraž GERŠAK (1) (2) (3) (4) where m is the number of triangles, θ*si is the apparent dip angle of the surface unit, α is the azimuth, is the tilt angle, t is the shear direc- tion vector, n is the outward normal vector of the triangle, n0 is the outward normal vector of the plane (see Fig. 2) and n1 is the projection vector of n. The maximum contact area is calculated as follows: (5) where Al is the sum of the area facing to the shear direction (θ*si is greater than zero) and Am is the actual area of the whole joint surface. (6) where sn is the normal stress, st is tension strength of the rock and fr a residual angle of friction, θ*max is the maximum apparent dip angle of the surface with respect to the shear direction, C is the roughness parameter, calculated using a best-fit regression function, which characterises the distribution of the apparent dip angles over the surface. The next version of the same criterion (G06) includes parameter β which is the angle between the plane of schistosity and normal to the sample surface and where fb is the basic angle of friction got from the direct shear test in laboratory. (7) A peak shear strength criterion (X13) with the use of a form of the Mohr-Coulomb equation was developed by Xia (Xia, 2013). The criterion is presented with eq. 8. (8) With the further use of the laser scanner tech- nology, new criteria were developed (Tang 2014). The proposed shear strength criterion (T14) is ca- pable of predicting the shear strength of rough joints. (9) All criteria are the common parameters A0, Ɵ*max and C, proposed by Grasselli. All of these criteria are very similar to each other, as they are written according to the equa- tion (7), except for the criterion G01 (equation 6). Common to all of them is , which is multiplied by the tangent of base friction angle to which an additional angle is added, which represents the crushing of the rock teeth of the surface sample and also influence of dilation. The differences be- tween the criteria are actually at this additional angle. It is described with the parameters of the surface, A0,C, θ*max . Test procedure Samples for direct shear test were taken from different rock formations from the northern part of Slovenia. The types of rock vary from clayey limestone, siltstone to the permo-carboniferous shale rock with very low geomechanical charac- teristics. Among many samples, 19 of them were select- ed for testing. All samples have a natural frac- ture. The joint surface was scanned by 3D scan- ner system before the shear test to measure the morphology of the surface (fig. 3). A data process- ing programme was used to calculate the 3D sta- tistical characterisation parameters. tan𝜃𝜃𝜃𝜃𝑠𝑠𝑠𝑠∗ = tan𝜃𝜃𝜃𝜃 (− cos α ) (1) cos𝜃𝜃𝜃𝜃 = 𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑜𝑜𝑜𝑜|𝑛𝑛𝑛𝑛||𝑛𝑛𝑛𝑛𝑜𝑜𝑜𝑜| (2) cosα = 𝑡𝑡𝑡𝑡𝑛𝑛𝑛𝑛1|𝑡𝑡𝑡𝑡||𝑛𝑛𝑛𝑛1| (3) 𝜃𝜃𝜃𝜃∗��� = 𝑡𝑡𝑡𝑡𝑛𝑛𝑛𝑛1|𝑡𝑡𝑡𝑡||𝑛𝑛𝑛𝑛1| 1 𝑚𝑚𝑚𝑚 ∑ 𝜃𝜃𝜃𝜃𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠∗𝑚𝑚𝑚𝑚𝑠𝑠𝑠𝑠=1 (4) 𝐴𝐴𝐴𝐴0 = 𝐴𝐴𝐴𝐴𝑙𝑙𝑙𝑙 𝐴𝐴𝐴𝐴𝑚𝑚𝑚𝑚 �� � �� ∗ ������, � ∗ �1 � ��� �� 1��� ∗ ����∗ � ∗ �� ���� 𝜏𝜏𝜏𝜏𝑝𝑝𝑝𝑝 = 𝜎𝜎𝜎𝜎𝑛𝑛𝑛𝑛 �1 + exp (− 1 9𝐴𝐴𝐴𝐴0 ∗ 𝜃𝜃𝜃𝜃𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚∗ 𝐶𝐶𝐶𝐶 ∗ 𝜎𝜎𝜎𝜎𝑛𝑛𝑛𝑛 𝜎𝜎𝜎𝜎𝑡𝑡𝑡𝑡 � ∗ 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 �𝜑𝜑𝜑𝜑𝑏𝑏𝑏𝑏 + � 𝜃𝜃𝜃𝜃𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚∗ 𝐶𝐶𝐶𝐶 � 1,18𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 � 𝜏𝜏𝜏𝜏𝑝𝑝𝑝𝑝 = 𝜎𝜎𝜎𝜎𝑛𝑛𝑛𝑛 ∗ 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 �𝜑𝜑𝜑𝜑𝑏𝑏𝑏𝑏 + 4 ∗ 𝐴𝐴𝐴𝐴0 ∗ 𝜃𝜃𝜃𝜃𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚∗ 𝐶𝐶𝐶𝐶 + 1 �1 + 𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 �− 1 9𝐴𝐴𝐴𝐴0 ∗ 𝜃𝜃𝜃𝜃𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚∗ 𝐶𝐶𝐶𝐶 + 1 ∗ 𝜎𝜎𝜎𝜎𝑛𝑛𝑛𝑛 𝜎𝜎𝜎𝜎𝑡𝑡𝑡𝑡 ��� 𝜏𝜏𝜏𝜏𝑝𝑝𝑝𝑝 = 𝜎𝜎𝜎𝜎𝑛𝑛𝑛𝑛 ∗ 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 �𝜑𝜑𝜑𝜑𝑏𝑏𝑏𝑏 + 10 ∗ 𝐴𝐴𝐴𝐴0 ∗ 𝜃𝜃𝜃𝜃𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚∗ (𝐶𝐶𝐶𝐶 + 1) ∗ (𝜎𝜎𝜎𝜎𝑡𝑡𝑡𝑡 𝜎𝜎𝜎𝜎𝑛𝑛𝑛𝑛⁄ ) 1 + (𝜎𝜎𝜎𝜎𝑡𝑡𝑡𝑡 𝜎𝜎𝜎𝜎𝑛𝑛𝑛𝑛⁄ ) � Fig. 3. An example of the scanned sample. 29Quantified joint surface description and joint shear strength of small rock samples For the direct shear testing, the Robertson apparatus was used. This equipment is very useful for small sam- ples which were acquired with borehole drilling. Shear tests of several rock joint samples under different nor- mal loads have been tested (0.1, 0.2, 0.4 MPa) in order to relate the peak shear strength of a rock joint with the three-dimensional (3D) surface. The test was performed according to the standard ASTM D5607 -08. When the shear displacement reached the post-peak stage and stabi- lised for a while, the test was stopped. During shearing, normal deformation, horizontal deformation, normal load and shear force of the joint samples were monitored and recorded. Results The peak shear strength was calculated for every sam- ple according to the criterion described in the previous chapter. The input data for the calculation are presented in Table 2 and include the input data for the shear peak strength criteria; G01, G06, X13 and T14. The results of the direct shear test and the results of the calculated peak shear strength according to the different criteria are pre- sented in Table 3. No. τp measured (MPa) τp G01 (MPa) τp G06 (MPa) τp X13 (MPa) τp T14 (MPa) τp X13 mod (MPa) 1 0.401 0.444 0.595 0.459 0.492 0.012 2 0.106 0.087 0.118 0.106 0.126 0.006 3 0.070 0.081 0.119 0.063 0.069 0.169 4 0.064 0.086 0.104 0.061 0.066 0.046 5 0.245 0.327 0.388 0.257 0.269 0.021 6 0.232 0.323 0.410 0.302 0.322 0.165 7 0.115 0.129 0.200 0.138 0.162 0.064 8 0.168 0.130 0.181 0.175 0.177 0.070 9 0.087 0.075 0.098 0.077 0.081 0.225 10 0.276 0.222 0.286 0.267 0.251 0.055 11 0.217 0.280 0.429 0.271 0.307 0.181 12 0.087 0.078 0.102 0.081 0.085 0.056 13 0.278 0.191 0.326 0.357 0.353 0.366 14 0.065 0.085 0.101 0.064 0.068 0.052 15 0.077 0.077 0.092 0.064 0.066 0.239 16 0.219 0.235 0.277 0.232 0.221 0.035 17 0.106 0.067 0.119 0.124 0.156 0.045 18 0.170 0.215 0.309 0.279 0.340 0.411 19 0.328 0.480 0.688 0.465 0.519 0.306 No. Lithology σt (MPa) σn (MPa) ϕb (°) A0 (-) C (-) Ɵ*max (°) 1 marly limestone 1.99 0.60 24 0.415 17.03 86.86 2 marly limestone 1.99 0.10 24 0.579 16.99 89.69 3 marly limestone 1.99 0.10 24 0.177 12.87 86.20 4 marly limestone 1.99 0.10 24 0.300 22.04 75.11 5 marly limestone 1.99 0.40 24 0.395 27.92 86.95 6 marly limestone 1.99 0.40 24 0.454 12.20 51.89 7 dolomite 2.17 0.15 25 0.341 11.90 90.00 8 perm. slate 0.30 0.20 24 0.542 15.04 86.21 9 perm. slate 0.30 0.10 24 0.472 9.22 42.93 10 perm. slate 0.30 0.40 24 0.471 9.30 41.42 11 siltstone 2.00 0.40 26 0.200 11.61 87.28 12 claystone 0.30 0.20 20 0.120 19.98 84.74 13 claystone 0.30 0.40 24 0.502 9.40 84.24 14 claystone 1.00 0.10 24 0.366 28.62 89.90 15 claystone 0.30 0.10 24 0.395 24.40 79.72 16 claystone 0.30 0.40 24 0.395 25.60 77.60 17 claystone 0.30 0.10 24 0.511 9.25 89.05 18 siltstone 2.00 0.20 30 0.515 12.46 84.87 19 dolomite 2.49 0.60 28 0.260 12.72 84.31 Table 3. Results of peak shear strength calculation under different criteria. Table 2. Input data for the peak shear strength calculation. 30 Karmen FIFER BIZJAK & Andraž GERŠAK For all results, the average estimation er- ror was calculated Eave (Kulatilake et al., 1995), which is presented in Table 4. (10) According to the results, a small correction was used to get a better correlation between the measured and calculated peak shear strength for the criterion X13. For the testing with the Rob- erston apparatus, the samples have to be smaller and with the small change of the equation, better correlation was achieved and modified criterion (X13mod) is presented in eq 11. (11) Discussion This paper presented a detailed methodolo- gy to evaluate the three-dimensional roughness of joint surfaces in rock material. The present- ed methodology uses 3D surface measurements, which are becoming more widely available with the increasing availability of commercial opti- cal measuring devices. The advantage of using 3D scanner is in determining the morphological parameters for the whole surface, not only on a single profile. The use of these parameters allows studying the directional micro-mechanical re- sponse of the entire sheared joint. The proposed roughness evaluation methodol- ogy was demonstrated by digitizing and analys- ing the fracture surfaces of 19 specimens. Sam- ples used in the referred studies (Grasselli, 2001, 2006; Xia, 2013; Tang, 2014) have a dimension at least 200 mm × 100 mm x 100 mm and were con- solidated under high normal stresses (more than 1 MPa). It is often not possible to get large sam- ples for testing material in a large direct shear test. Borehole samples are smaller and have var- ious shapes and sizes. In this case, samples are usually tested in Robertson direct shear test ap- paratus. In our case, the samples were taken from boreholes and were different with regard to their dimension and shape. The samples were tested under low normal load (no more than 0.4 MPa). The peak shear strengths of natural joints ob- tained experimentally in laboratory tests were compared with the values calculated by Eq. 7, 8, 9 and 10 as listed in Table 3. According to the correlation analysis, the calculated values are slightly larger than the measured values (fig. 4), but the predicted shear strength from criteria is close to the experimental shear strength of nat- ural joints. Hence, it can be deduced that the proposed shear strength criterion is capable of predicting the shear strength of rough joints. For all criteria, the average estimation errors were 𝐸𝐸𝐸𝐸𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 = 1 𝑚𝑚𝑚𝑚 �� 𝜏𝜏𝜏𝜏𝑡𝑡𝑡𝑡𝑎𝑎𝑎𝑎𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 − 𝜏𝜏𝜏𝜏𝑐𝑐𝑐𝑐𝑎𝑎𝑎𝑎𝑐𝑐𝑐𝑐. 𝜏𝜏𝜏𝜏𝑡𝑡𝑡𝑡𝑎𝑎𝑎𝑎𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 � 𝑚𝑚𝑚𝑚 𝑖𝑖𝑖𝑖=1 ∗ 100% Table 4. Average estimation error for every criterion. τp G01 (%) τp G06 (%) τp X13 (%) τp T14 (%) τp X13 mod (%) 23 45 16 23 13 𝜏𝜏𝜏𝜏𝑝𝑝𝑝𝑝 = 𝜎𝜎𝜎𝜎𝑛𝑛𝑛𝑛 ∗ 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 �𝜑𝜑𝜑𝜑𝑏𝑏𝑏𝑏 + 4,9 ∗ 𝐴𝐴𝐴𝐴0 ∗ 𝜃𝜃𝜃𝜃𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚∗ 𝐶𝐶𝐶𝐶 + 1 �1 + 𝑒𝑒𝑒𝑒𝑥𝑥𝑥𝑥𝑝𝑝𝑝𝑝 �− 1 𝐴𝐴𝐴𝐴0 ∗ 𝜃𝜃𝜃𝜃𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚∗ 𝐶𝐶𝐶𝐶 + 1 ∗ 𝜎𝜎𝜎𝜎𝑛𝑛𝑛𝑛 𝜎𝜎𝜎𝜎𝑡𝑡𝑡𝑡 ��� Fig. 4. The comparison between calculated. 31Quantified joint surface description and joint shear strength of small rock samples calculated according to the eq. 10. The criterion which fits the best with the measurement data is criterion X-13 with the average estimation error 16 %. To improve the results, we changed the cri- terion X-13 in a part of the equation where the area Ao is included (Eq. 11), because smaller sam- ples in our research were used. With this small correction, the average estimation error decreas- es to 13 %. The comparison between calculated and measured peak shear strength for modified criterion X13mod is presented in fig. 5. For future research, it is necessary to test more samples of the same lithology. The samples tested in our case were very different in the sense of the surface roughness. We could probably get better results if tests were done for every type of rock separately, of course with an adequate num- ber of samples. The size of the samples affected the results and there is probably a reason that the average estimation errors in our research work were not lower for other already known and used criteria. Conclusions Shear behaviour of rock joints is investigated with the Robertson apparatus. The shear strength increases with the increasing of normal stress and roughness. The proposed modified criterion can be used as a predictive tool to assess the peak shear strength under the low normal load and if we could only use small samples from the inves- tigation boreholes. 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