Acta Polytechnica https://doi.org/10.14311/AP.2023.63.0011 Acta Polytechnica 63(1):11–18, 2023 © 2023 The Author(s). Licensed under a CC-BY 4.0 licence Published by the Czech Technical University in Prague ESTIMATION OF STRESSES IN A MASSIVE GRANITE USING LASER ULTRA-SONIC TESTING AND STRESS MEMORY EFFECT Ondřej Kašpara, Alexander Kravcovb,∗, Jiří Štollerc, Petr Kubečekb, Radovan Vnukb, Zbyněk Zušťákb a Charles University in Prague, Faculty of Science, Engineering Geology and Applied Geophysics, Albertov 6, 128 43 Prague 2, Czech Republic b Czech Technical University in Prague, Faculty of Civil Engineering, Department of Construction Technology, Thákurova 7, 160 00 Prague, Czech Republic c University of Defence in Brno, Faculty of Military Technologies, Kounicova 65, 662 10 Brno, Czech Republic ∗ corresponding author: kravtale@fsv.cvut.cz Abstract. This paper addresses in-situ stress-estimation methods based on the Kaiser effect. The physical and mechanical properties of granite, diorite, and granodiorite samples selected at different depth intervals of the core obtained from a wellbore were examined. The ultimate uniaxial compressive strength, modulus of elasticity, and Poisson’s ratio of the rock samples were determined using presses and strain gauges. Also, local longitudinal and shear wave velocities were measured using a high-accuracy laser-ultrasonic system with a view to assessing the structure of the samples. Based on the resulting elastic wave velocity maps, samples with no obvious discontinuities were chosen. These undisturbed samples were subjected to uniaxial compression and their acoustic emission was simultaneously measured. In-situ stresses were estimated from the results of the interpretation of acoustic emission measurements. The experimental in-situ stresses were compared with the results of a numerical simulation. The ratio of the estimated in-situ stresses to the calculated ones is within the range from 0.81 to 1.11. This means that the laser ultrasonic and acoustic emission methods make it possible to effectively estimate in-situ stresses in a rock mass and assess the degree of rock mass damage. Keywords: Rock cores, acoustic emission, laser ultrasonic method, structure, stress state, rocks, Kaiser effect. 1. Introduction Rocks are heterogeneous media that contain defects at different scales; this may cause crack initiation even at light loads [1]. That is why mining operations should be preceded by a detailed study of the geological and geotechnical conditions and analysis of the stress state of the rock mass [2, 3]. Note that one of the main methods for studying the stress state is numerical simulation [4–6]. This is due to the fact that there are no direct methods for measuring in-situ stresses in a rock mass. However, the results of a numeri- cal simulation need to be verified, which is usually done with indirect methods. These are borehole meth- ods, such as hydrofracturing, borehole stress relief, analysis of the erosion of the walls of boreholes, as well as methods for estimating in-situ stresses using core samples (strain recovery analyses, core disking, and acoustic emission testing based on the Kaiser ef- fect). Also, there are methods for stress control in rock outcrops (rock stress relief through the use of hydraulic pads and slots) and analyses of large-scale geological structures (analyses of focal mechanisms of earthquakes and shear displacements) [7–9]. Each of these methods works at a certain scale, which de- pends on the volume of the rock mass examined. For example, the acoustic methods require the volume of the rock sample to be in the order of 10-3 m3. On the recommendation of the International Society for Rock Mechanics (ISRM) [10], two downhole methods have been widely adopted: hydraulic fracturing (HF) and complete stress relief. However, these methods are quite complicated and very costly; therefore, al- ternative methods for determining in-situ stresses are required. One of the optimal methods for studying in-situ stresses in a rock mass is the method of acoustic emission (AE) [11–14] based on the Kaiser effect [15, 16]. Importantly, this method does not require high- accuracy deformation measurements. The Kaiser effect describes the phenomenon that repeated loading cycles cause the level of AE signals decrease up to their complete absence until the level of the previously applied load is exceeded [17, 18]. A sharp increase is observed when approaching the pre- viously achieved maximum value of load [12]. There- fore, the repeated loading of samples recovered from different depths makes it possible to estimate the re- spective in-situ stresses from a sharp increase in the acoustic emission [17, 18]. For this purpose, the Fe- licity ratio is introduced in [17] and [18], which is the ratio of the load at which acoustic emission (AE) pulses reappear to the maximum load of the previous 11 https://doi.org/10.14311/AP.2023.63.0011 https://creativecommons.org/licenses/by/4.0/ https://www.cvut.cz/en O. Kašpar, A. Kravcov, J. Štoller et al. Acta Polytechnica load cycle. This ratio can be either greater than 1 or less, depending on the structural and textural fea- tures of rock samples, the directions of the principal stresses in the rock mass and other parameters [19–21]. In work [22], data on the seismic wave velocities are used to estimate Young’s modulus and Poisson’s ratio, in [23], the damage characterisations of granites were studied by a combination of AE and ultrasonic trans- mission methods under a quasi-static uniaxial com- pression test. Mechanical characteristics and failure prediction of cement mortar with a sandwich structure was investigated in [24]. In studies [25–29], acoustic emission is used for understanding the mechanical properties of materials. The value of the Felicity ratio changes in response to an increase in the time interval between loading cycles, which may make the effect less distinct. The duration of stress memory also depends on the rock type, the loading regime in successive cycles, and the effect of other factors (heating and moistening). Moreover, some rocks retain information on the experienced mechanical stresses for many months, or even years. That is why it is important to study and identify patterns of AE activity inside one type of rocks. In this study, we investigate if it is possible to esti- mate in-situ stresses in a granite mass using acoustic emission observed during uniaxial compression of core samples preliminarily examined in structural terms using laser ultrasonic methods. 2. Materials and methods 2.1. Materials To assess the possibility of using the method of acous- tic emission when studying the stress-strain state of a rock mass, granite samples taken from a core sam- ple while drilling a well in the crystalline massif from depths from 70 m to 400 m were studied. Sample PB1-11 (depth 95.5 m) is grey, heteroge- neous, fine-to-medium-grained, dense, massive gra- nodiorite containing inclusions of light-coloured min- erals and thin long healed cracks running through the sample; Sample PB1-32 (depth 95.5 m) is dark pink with a greyish tinge, medium-to-coarse-grained, dense, massive granite interspersed with dark-coloured minerals and thin cracks no more than 1.5 cm long in places; Sample PB1-56 (depth 230.2 m) is dark pink, het- erogeneous, fine-to-medium-grained, dense, massive granite with a large number of inclusions of dark- coloured minerals (> 20 %) and occasional inclu- sions of mica; no visible cracks are present; Sample PB1-80 (depth 302.0 m) is light pink with a greyish tinge, fine-to-medium-grained, dense, mas- sive granite interspersed with inclusions of biotite (no more than 5 %); solitary thin cracks no more than 1 cm long are present; Figure 1. Samples of granite from crystalline massif. Sample PB1-96 (depth 350.4 m) is dark grey, medium-to-fine-grained, dense, massive diorite inter- spersed with dark-coloured minerals and inclusions of mica (about 5 %); no visible cracks are present; and Sample PB1-113 (depth 400.6 m) is dark grey, fine-grained, dense, massive diorite interspersed with dark-coloured minerals and inclusions of mica (about 5-7 %); no visible cracks are present. Figure 1 shows six granite samples recovered from different depths. Cylindrical specimens about 10 cm long and about 6 cm in diameter were prepared from these samples. The volume V and density ρ of the specimens were determined. According to the research, it was found that gran- odiorites of fine-grained structure, dense and massive, with healed cracks noted (according to sample PB1- 11), belong to the migmatite-plagiogranite formation. They are composed of plagioclase, quartz, and biotite in variable amounts – hornblende, epidote, microcline. The structure of the rock shows elements of gneiss and taxite appearance and without metallogenic prospects. One typical photograph of granite is presented in Figure 2 (No. 2). The samples are presented slightly different in composition, structure (PB1-32 – coarse-medium-grained, PB1-56 and 80 – fine-medium- grained) and patterns of relationship with the rocks of the enclosing frame by species and varieties. Unlike granodiorites, they are two-feldspar rocks with higher silicic acidity and potassium alkalinity. There are two pictures of diorites (No. 3 – medium- grained and No. 4 – fine-grained) – these samples include plagioclase, hornblende, biotite, as well as apatite, garnet, epidote, chlorite, ore (magnetite, sul- phides) in the smallest proportions. Texturally dense, massive, structurally intact. 2.2. Ultrasonic measurements First, it was necessary to select specimens without long internal cracks which could relieve the stress the spec- imens experienced in situ; in that case, information 12 vol. 63 no. 1/2023 Estimation of stresses in a massive granite using laser ultra-sonic . . . Figure 2. Results of microscopic study of characteristic polished sections of each sample of rocks – grano-diorite (No. 1 – PB1-11), granite (No. 2 – PB1-32 / 56/80) and diorites (No. 3 and 4 – PB1-113 and PB1-96) using a Phenom ProX scanning electron microscope. about these stresses may get lost. To check the “ho- mogeneity” of the specimens, they were scanned using a laser-ultrasonic flaw detector operating in an auto- matic pulse-echo mode. Figure 3 shows a schematic diagram of scanning. A laser optoacoustic transducer excites a short powerful longitudinal wave pulse. At the transducer-specimen interface, the longitudinal wave is partially converted into shear wave. Both waves are reflected from the diametrically opposite generatrix of the specimen and recorded by a broad- band piezoelectric transducer (Figure 3). Their veloc- ities are calculated from the time delay of the waves for a given sample diameter. The measurement error of elastic wave velocities was 0.2 % [21]. Scanning was carried out along the generatrix with a step of 1 cm. Longitudinal wave velocity maps produced using the MatLab software were used for a visual inspection of the specimens to find out if there are large-scale defects such as cracks/pores larger than 5 mm in size. Also, the dynamic Young’s modulus Ed and shear modulus G, and Poisson’s ratio ν were calculated from the velocities using the formula [21]: Ed = ρ · V 2 p · [ 3 − 1 χ−1 ] , (1) G = ρ · V 2 s , (2) ν = χ−2 2 · (χ−1) , (3) where G is the shear modulus, ρ is the density, and χ = (νp νs )2 is the square of the ratio of longitudinal wave velocity to shear wave velocity. 2.3. Mechanical testing The physical and mechanical properties of the spec- imens (ultimate uniaxial compressive strength Rc, static modulus of elasticity E, and Poisson’s ratio ν) were determined with the use of TP-1-1500 press with Figure 3. Schematic diagram of measurement of elas- tic wave velocities using laser ultrasonic flaw detector: optical cable (1), laser (2), computer (3), detector (4), laser radiation (5), optoacoustic generator (6), pulses (7), granite specimen (8). a maximum load of 1500 kN and a tensometric com- plex consisting of an LTR crate system and ACTEST- OEM software (modules LTR 212M-2 and LTR-EU- 2-5). The press and the tensometric complex were synchronised to stress recording. Then, longitudinal and lateral compressive strains were measured as the specimens were subjected to load changing from 5 % to 50 % of the ultimate compressive strength. 2.4. Acoustic emission measurements The memory effect was studied with a SDS 1008 acous- tic emission monitoring system and Maestro 1.2.2 soft- ware for data processing. The cumulative AE count Nand acoustic emission activity CΣ were analysed [1]. 13 O. Kašpar, A. Kravcov, J. Štoller et al. Acta Polytechnica № habb h d m V ρ Vp VS ν E Rc [m] [cm] [cm] [g] [cm3] [g cm−3] [m s−1] [m s−1] [GPa] [MPa] 1 74,6 9,83 6,26 864,19 308,2 2,78 6018 3774 0,21 102 51 2 95,5 9,99 6,3 881,03 315,2 2,76 5490 2998 0,22 72 94 3 150 10,31 6,3 847,48 325,3 2,61 5253 3096 0,23 72 158 4 158,2 10,19 6,3 833,13 321,5 2,59 5673 3067 0,22 84 150 5 201,2 10,24 6,29 839,46 322,1 2,61 5523 3106 0,27 80 191 6 212,2 9,94 6,29 823,75 313,6 2,63 5696 3443 0,21 85 195 7 230,2 11,74 6,3 908,62 370,4 2,57 6485 3781 0,24 103 195 8 260 10,43 6,26 853,73 326 2,62 6052 3507 0,25 96 146 9 302 10,31 6,3 850,54 326,3 2,61 5627 3124 0,28 83 175 10 350,4 10,16 6,28 925,96 319,6 2,85 5971 3467 0,25 103 116 11 400,6 10,31 6,28 925,8 326,3 2,78 5764 3044 0,31 94 149 Table 1. Physical and mechanical properties of specimens. 3. Results The physical and mechanical properties of the speci- mens are shown in Table 1. According to Table 1, the specimens are hard; the highest values of rock skeletal density are typical of granodiorite and diorite (ρ = 2.81–2.90 g cm−3) unit, the density of granite specimens (ρ) varies from 2.57 to 2.63 g cm−3; the dynamic modulus of elasticity varies from 72 to 103 GPa. The hardest granite is found in the middle of the analysed depth interval (from 200 to 230 m). The specimens were subjected to uniaxial compres- sion and their acoustic emission was simultaneously recorded. The rocks in the massif were in stress state, so the goal of acoustic emission testing was to estimate in-situ stresses and compare them with the results of a numerical simulation. However, since available archive materials do not have the level of detail that is required for a numerical simulation, the vertical stresses in the rock mass were calculated under the assumption that rock stress changes with depth as a result of geostatic load, according to which the expression for vertical stresses is as follows σ = ρ g h, (4) where habb is the depth. Accordingly, horizontal stresses can be estimated in terms of the parameters presented in Table 1: σ = ξ ρ g h, (5) where ξ is the lateral earth pressure coefficient: ξ = ν (1 − ν) , (6) where ν is Poisson’s ratio. In this approximation, vertical and horizontal stresses were calculated with respect to the borehole axis. Figure 4 shows longitudinal velocity maps for Spec- imens No. 4 and No. 5 (given in Table 1). Specimens C and D (sample depths of 157.1 and 200.3 m, re- spectively) were discarded due to the considerable variation of the P-wave velocity. Specimen C has a variation coefficient of 3.5 %, and specimen D of 2.1 %. A total of 54 velocity values were determined for each specimen (the grid of scanning was 9 by 6 points). Specimens A and B were homogeneous and structurally undisturbed; so they were investigated using the acoustic emission method. Stress calculations were performed for granite, dior- ite, and granodiorite, which are igneous rocks; they are characterised by similar structural-textural fea- tures and similar behaviour under load. The resulting values of vertical and horizontal stresses are given in Table 2. The third column of the table contains the names of the specimens subjected to uniaxial com- pression accompanied with simultaneous recording of acoustic emissions. Figure 5 shows the calculated distribution of the stress with depth (based on Table 2). The specimens mentioned in Table 2 were subjected to uniaxial compression and acoustic emission was simultaneously recorded. It was found that the ex- perimental relationship between stress and AE count is similar to that determined from theoretical experi- ments aimed at recovering in-situ stresses in different types of granite. Figure 6 shows the cumulative num- ber of AE events (AE count N) versus the applied load (Specimen PB1-50). Calculated by the above formula, the averaged vertical stress at the sampling depth of PB1-50 is equal to 5.44 MPa. Using inflection of the experimental AE count versus stress curve (Figure 6), the in-situ stress the specimen experienced is esti- mated at 5.56 MPa; so the Felicity ratio is FR = 1.02 . Thus, the error of in-situ stress estimation is 2 %. The AE testing of Specimen PB1-113 produced similar results. Figure 6 shows the AE activity (Σ) versus the applied load for this sample. Clearly, two differently inclined tangents can be drawn to the AE 14 vol. 63 no. 1/2023 Estimation of stresses in a massive granite using laser ultra-sonic . . . Figure 4. Velocity distributions: homogeneous specimens (A and B) and heterogeneous specimens (C and D). Depth h Specimen № ρ ν ξ Rock typefrom to [m] [g cm−3] [MPa] [MPa] 0 20,5 2,01 0,29 0,69 0,40 0,69 quaternary sediments 20,5 44,0 2,63 0,22 0,28 1,01 0,28 granite 44,0 74,8 PB1-4(74.6 m) 2,78 0,21 0,27 1,84 0,49 granite 74,8 95,7 PB1-11(95.5 m) 2,76 0,22 0,28 2,41 0,64 granodiorite 95,7 107,0 2,78 0,21 0,27 2,73 0,72 granodiorite 107,0 119,5 2,63 0,22 0,28 3,05 0,86 granite 119,5 121,8 2,58 0,33 0,49 3,11 1,53 granite 121,8 145,0 2,63 0,22 0,28 3,71 1,05 granite 145,0 150,2 PB1-29(150.0 m) 2,61 0,23 0,49 3,83 1,89 granite 150,2 153,0 2,58 0,33 0,49 3,91 1,93 granite 153,0 158,4 PB1-32(158.2 m) 2,59 0,22 0,28 4,04 1,14 granite 158,4 177,3 2,63 0,22 0,28 4,54 1,28 granite 177,3 193,7 2,64 0,21 0,28 4,96 1,40 granite 193,7 201,4 PB1-46(201.2 m) 2,61 0,29 0,41 5,15 2,10 granite 201,4 208,6 2,61 0,29 0,41 5,34 2,18 granite 208,6 212,4 PB1-50(212.2 m) 2,62 0,28 0,40 5,43 2,22 granite 212,4 228,2 2,61 0,29 0,41 5,84 2,38 granite 228,2 230,4 PB1-56(230.2 m) 2,65 0,20 0,25 5,89 1,47 granite 230,4 260,2 PB1-66(260.0 m) 2,65 0,20 0,25 6,67 1,67 granite 260,2 302,4 PB1-80(302.2 m) 2,65 0,20 0,25 7,76 1,94 granite 302,4 302,7 2,65 0,20 0,25 7,78 1,94 diorite 302,7 305,0 2,61 0,32 0,47 7,83 3,69 diorite 305,0 350,6 PB1-96(350.4 m) 2,65 0,20 0,25 9,01 2,25 diorite 350,6 400,6 PB1-113(400.6 m) 2,65 0,20 0,25 10,32 2,58 diorite Table 2. The most intense UV-Vis spectral lines of SM-I and its investigated derivatives. 15 O. Kašpar, A. Kravcov, J. Štoller et al. Acta Polytechnica Figure 5. Distribution of averaged vertical and hor- izontal stresses with depth (deformation properties ignored) along the borehole axis: Quaternary sedi- ments (1), granite (2), granodiorite (3), and granite (4); zone of higher level of fracturing (5); diorite (6) Quaternary sediments (1); granite (2); granodiorite (3); granite (4); zone of higher level of fracturing (5); diorite (6). activity versus the applied load curve. The coordinate of the intersection of these tangent lines corresponds to the value of the in-situ vertical stress the specimen experienced before its recovery from the borehole. So, based on the results of AE testing of this sample, the vertical in-situ stress is 10.33 MPa, the stress memory factor being equal to 0.97 (based on numerical simu- lations, the vertical in-situ stress is 10.00 MPa). Note that this sample demonstrates a classical example of estimating the stress memory effect using the gener- ally accepted technique of drawing tangents to linear sections of the AE count (N) vs. stress plot (point Z is the intersection of the tangents in Figure 7). 4. Discussion Thus, in the case of specimen PB1-50 (granite), the stress memory effect is manifested by a significant increase in the AE count after the applied load has exceeded the previously experienced stress, which was observed in theoretical experiments as well. Specimen PB1-113 (diorite) did not show such a pattern; there- fore, it was required that tangents be drawn. This is most likely due to lithological differences between the specimens. Figure 6. Cumulative AE count versus stress (Speci- men PB 1-50): recovered in-situ stress value (purple arrow – approximate value of stresses acting in the ar- ray; blue arrow – the value of the restored voltage). Figure 7. Cumulative AE count versus stress (speci- men PB 1-113). Table 3 shows the values of calculated vertical stress σy and vertical stress σestimated y recovered from AE measurements, and the Felicity ratio FRy. Clearly, except for a depth of 95.5-95.7 m, the values of the Felicity ratio are close to 1, belonging to the interval [0.81; 1.12], which indicates that the principal in-situ stress can be recovered. 5. Conclusions The acoustic emission method based on the Kaiser effect has some advantages over other in-situ stress estimation methods. The method is an efficient and easy-to-use one. No complex high-precision deforma- tion measurements are required. It is quite reasonable to use this AE method for studying the stress state of a rock mass. The method is very informative, de- scribing in detail how the distribution of stress with depth depends on the structure of the rock mass. Acknowledgements This study was financially supported by the research team from the National Ministry of the interior of the Czech Republic VB01000057 and the authors also want to express their gratitude to the Czech Technical University in Prague for the grants No. 211453T11 and No. 211473T11. 16 vol. 63 no. 1/2023 Estimation of stresses in a massive granite using laser ultra-sonic . . . Depth h Specimen № σy σestimated y F Ryfrom to [m] [MPa] [MPa] 74,6 74,8 4 1,85 2,29 0,81 95,5 95,7 11 2,42 1,36 1,55 150,0 150,2 29 3,84 3,82 1,00 158,2 158,4 32 4,05 - - 201,2 201,4 46 5,15 6,18 0,83 212,2 212,4 50 5,44 5,54 0,99 230,2 230,4 56 5,90 5,25 1,12 260,0 260,2 66 6,67 6,78 0,98 302,2 302,4 80 7,77 9,62 0,81 350,4 350,6 96 9,02 - - 400,6 400,8 113 10,32 10,0 0,96 Table 3. Estimation of in-situ stresses using the AE method. References [1] Y. A. Kashnikov, S. G. Ashikhmin, A. E. Kukhtinskii, D. V. Shustov. 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Minerals 8(6):244, 2018. https://doi.org/10.3390/min8060244 18 https://doi.org/10.1007/s00603-017-1178-2 https://doi.org/10.1007/s00603-020-02062-x https://doi.org/10.14489/td.2020.06.pp.032-039 https://doi.org/10.4028/www.scientific.net/KEM.755.147 https://doi.org/10.4028/www.scientific.net/KEM.755.147 https://doi.org/10.1016/j.jrmge.2019.07.014 https://doi.org/10.3390/min9030143 https://doi.org/10.25018/0236-1493-2020-7-0-125-134 https://doi.org/10.25018/0236-1493-2020-7-0-125-134 https://doi.org/10.1016/j.enggeo.2020.105823 https://doi.org/10.3390/ma13040903 https://doi.org/10.4028/www.scientific.net/KEM.755.212 https://doi.org/10.4028/www.scientific.net/KEM.755.212 https://doi.org/10.3390/min8060244 Acta Polytechnica 63(1):11–18, 2023 1 Introduction 2 Materials and methods 2.1 Materials 2.2 Ultrasonic measurements 2.3 Mechanical testing 2.4 Acoustic emission measurements 3 Results 4 Discussion 5 Conclusions Acknowledgements References