Influence of vibration and ground deformation on historic structures: Case study

Acta Montanistica Slovaca, Volume 27 (2022), 3; DOI: 10.46544/AMS.v27i3.17 Influence of Vibration and Ground Deformation on Historic Structures: Case Study Zdeněk KALÁB 1,2 *, Roman ŚCIGAŁA 3 and Piotr STRZAŁKOWSKI 4 Authors' affiliations and addresses: 1 Institute of Geonics, Czech Academy of Sciences, Studentská 1768, 70800 OstravaPoruba, Czech Republic, e-mail: [email protected] 2 VŠB – Technical University of Ostrava, Faculty of Civil Engineering, 17. listopadu 15, 70800 Ostrava-Poruba, Czech Republic, e-mail: [email protected] 3 Silesian University of Technology, 44-100 Gliwice, Akademicka 2, Poland, e-mail: [email protected] 4 Silesian University of Technology, 44-100 Gliwice, Akademicka 2, Poland, e-mail: [email protected] *Correspondence: Zdeněk Kaláb, Institute of Geonics, Czech Academy of Sciences, Studentská 1768, 70800 Ostrava-Poruba, Czech Republic, tel: +420-604245362 e-mail: [email protected] Funding information: Research program of the Academy of Sciences of the Czech Republic, RVO: 68145535 Acknowledgement: The paper was prepared with the financial support of the Research program of the Academy of Sciences of the Czech Republic, RVO: 68145535 How to cite this article: Kaláb, Z., Ścigała, R. and Strzałkowski, P. Influence of Vibration and Ground Deformation on Historic Structures: Case Study. Acta Montanistica Slovaca, Volume 27 (3), 783-799. DOI: https://doi.org/10.46544/AMS.v27i3.17 Abstract When discussing historic structures, a significant problem is how to preserve and protect these structures. The presented paper deals with some issues of the unfavourable impact of industrial activity on some historic structures. Long-term influences from the industrial activity are one of the common sources of damage observed in these structures. Due to the size and volume of such structures, they are characterized by very low resistance to vibration and ground deformations. At the same time, the high cultural and material value of historic structures necessitates their costly protection and repair. Knowing the origin of problems, one may take proper actions to protect them. This paper discusses two important types of impact typical for industrial areas, especially affected by mining, seismically induced vibrations and continuous ground deformations from underground extraction. The presented discussion is based on the case study examples of historical sites located in some industrial areas in the Czech Republic and Poland. They point to different sources of damage to those structures that may arise as well as a combined effect of mining-induced seismic events and land subsidence. The medieval Jeroným Mine represents an underground structure loaded with natural and technical seismicity. The paper also includes a short overview of the process of seismic loading evaluation and basic information about historic structures with respect to seismic standards and land surface subsidence caused by underground mining. Keywords historic structures, vibration, seismic loading, ground deformation, underground extraction, mining damages © 2022 by the authors. Submitted for possible open access publication under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). Zdeněk KALÁB et al. / Acta Montanistica Slovaca, Volume 27 (2022), Number 3, 783-799 784 Introduction One of the basic activities of humankind from the very beginning is construction. It began with the purely functional need for a controlled environment to moderate the effects of climate. Constructed shelters were one way human beings could adapt themselves to a wide variety of climates and become global species. Construction today is an important part of industrial culture, a manifestation of its diversity and complexity and a measure of its mastery of natural forces, which can produce a widely varied built environment to serve the diverse needs of society (Swenson, 2021). If we walk through a built-up area, we are attracted by various structures or even just parts of them. Historical structures are often the subject of our interest. Generally, historical sites/structures are official locations where pieces of political, military, cultural, or social history have been preserved due to their cultural heritage value. Historic sites are usually protected by law, and many have been recognized with the official national historic site status (according to Historic site, 2020). When considering historic structures, a significant problem is how to preserve and protect these structures (Boyer, 2018). Historic preservation is the practice of protecting and preserving sites, structures or districts which reflect elements of local or national cultural, social, and historic preservation of structures, but it is a broader effort that began mainly in museums. The actual job is much more complex. Historic preservationists not only need to know how to preserve and protect historic structures, they need to be able to research, determine what is worthy of historic designation and navigate local, state and national regulations when working with historic places. They also must abide by national guidelines for treating historic properties. In many instances, they have to be able to diagnose what needs to be done to preserve a structure. This work includes examination, documentation, treatment and preventive care, i.e. to protect from harm or destruction (according to Boyer, 2018). Generally, structures are affected by a number of occasional and/or permanent loadings (Chudley and Greeno, 2014). The effect of vibration on the structures is one of the negative effects (Villaverde, 2009; Kaláb, 2018). The sources of vibration are different; especially earthquakes are a purely natural source. The properties (parameters) of earthquakes are studied in detail by seismologists (for instance, Bolt, 1999; Lee et al., 2002; Shearer, 2019); special attention is given to the influence of earthquakes on structures which are the subject of seismic engineering (Towhaka, 2008; Elnashai and Di Sarno, 2015). However, so-called technical seismicity can significantly affect the "acceleration of ageing" of older structures or their damage. Blasting in quarries is a typical and the most intensive source of this seismicity. The duration of this vibration effect is usually short but with a very strong peak and higher frequencies than vibration generated by earthquakes (Dauetas, 1993; Pijush, 2005). Other types of technical seismicity (such as the effect of traffic or industrial seismicity) usually cause smaller vibration load and, therefore, smaller damage to structures (Thompson, 2009; Kondela and Pandula, 2012; Kaláb and Hrubešová; 2015). A number of surface manifestations can be observed in the mined areas (for instance, Kwiatek et al., 1997, Doležalová et al., 2008; Kwiatek, 2010). For the purposes of this article, vibration induced by mine-induced seismicity is also necessary to mention (for instance, Gibowicz, Kijko, 1994; Lednická and Kaláb, 2016), and manifestations after the end of mining can be observed for a longer period (Martinec et al., 2006). The second selected negative influence is ground deformation caused by underground mining. Such deformations are often an important factor favouring the creation of structure damage. The scale of damage depends on the type of deformations and their intensity. Two main types of deformations may occur: continuous and discontinuous (Kratzsch, 1983; Whittaker et al., 1989; Peng, 1992; Strzałkowski, 2010). Discontinuous deformations manifested as ground steps, cracks or fissures, although very dangerous for urban constructions, do not always accompany underground extraction. It may even be said that they occur rarely. On the other hand, continuous deformations manifested in the form of subsidence troughs always occur as an effect of underground mining. Hence, the ability of their precise prediction is of great importance due to the development planning and the protection of existing infrastructure against mining damage. More detailed information about occasional and permanent loads of structures was presented in, for instance, Chudley and Greeno (2014) or Kaláb (2018). The paper presents case studies of the influence of vibrations and post-mining deformations on historic structures in the Czech Republic and Poland. The article also deals with a short overview of the process of seismic loading evaluation and basic information about historic structures with respect to seismic standards and land surface subsidence caused by underground mining. Seismic loading evaluation The Eurocodes are the ten European standards specifying how structural design should be conducted within the European Union (Eurocodes, 2021). For this topic, "Eurocode 8: Design of buildings for earthquake resistance" (abbreviated EN 1998 or, informally, EC 8) describes how to design structures in the seismic zone using the limit state design philosophy. It was approved by the European Committee for Standardization (CEN) on 23 April 2004. Its purpose is to ensure that in the event of earthquakes, human lives are protected, the damage is limited, and structures important for civil protection remain operational. Zdeněk KALÁB et al. / Acta Montanistica Slovaca, Volume 27 (2022), Number 3, 783-799 785 In seismic regions, the aspect of seismic hazard shall be taken into account in the early stages of the conceptual design of a building, thus enabling the achievement of a structural system which, within acceptable costs, satisfies the fundamental requirements (see EC 8): • structural simplicity; • uniformity, symmetry and redundancy; • bi-directional resistance and stiffness; • torsional resistance and stiffness; • diaphragmatic behaviour at storey level; • adequate foundation. A certain number of structural members (for instance, beams and/or columns) may be designated as "secondary" seismic members (or elements), not forming part of the seismic action-resisting system of the building. The strength and stiffness of these elements against seismic actions shall be neglected. Nonetheless, these members and their connections shall be designed and detailed to maintain the support of gravity loading when subjected to the displacements caused by the most unfavourable seismic design condition. All structural members not designated as being secondary seismic members are taken as being primary seismic members. They are taken as being part of the lateral force-resisting system and should be modelled in the structural analysis in accordance with the rules of EC8. For the purpose of seismic design, structures are categorized into being regular or non-regular, which has an impact on the design model, calculation method and ductility coefficient. Criteria of regularity in a planar or a spatial model are defined (for detail, see EC8). If we study the above requirements, it is quite clear that monuments usually do not meet most of them. Nor is it possible to make additional repairs/adjustments to meet the requirement. It, therefore, follows that monuments are very vulnerable to seismic loading. However, not only do vibrations contribute to the deterioration of the technical condition of monuments, respectively, their gradual destruction. One of the examples is the information presented on the website of the Auroville Earth Institute (Earthquakes and structures, 2021). The diagram of the masonry building shows various damages with more detailed information about the cause of the damage (Fig. 1). Structural elements, such as walls, columns and beams, are only bearing the weight of the building and the live load under normal conditions: mostly compression forces for the walls and columns, and vertical bending for the beams. Under dynamic load, they also have to withstand horizontal bending and shear forces and extra vertical compression forces. Depending on their current conditions, any damage can cause a serious threat to historic buildings, especially if the load-bearing elements are damaged. Fig. 1 Typical damages in a masonry building (Earthquakes and structures, 2021). Legend: 1: Diagonal shear crack of piers;2: Horizontal shear crack of the long pier; 3: Bending cracks at feet and lintels; 4: Bending crack of the wall (bad corner bond); 5: Bending crack of spandrel; 6: Bending crack of gable; 7: Plaster peeling off; 8: Crushing of weak masonry under vertical ground motion; 9: Damage of corner eaves under vertical ground motion; 10: Badly anchored roof, pulled out by vertical ground motion; 11: Falling of tiles from the roof eave; 12: Damage of tiles roof with shear (roof not braced) It is also possible to state another characteristic of cracks on the structure due to seismic loading. An essential feature for determining the origin of cracks is that cracks caused by dynamic effects in most cases do not have a Zdeněk KALÁB et al. / Acta Montanistica Slovaca, Volume 27 (2022), Number 3, 783-799 786 clear course. They are scattered completely unevenly and do not form a continuous pattern. Thus, differently than, for example, in the case of cracks caused by static stress (tensile, compressive or shear cracks), from which the direction of the influence of their force effect is evident (according to Solar, 2017). Technical seismicity can also sometimes be a serious problem; some cracks or damages may occur. "Czech Technical Standard 73 0040 Loads on buildings by technical seismicity and their response" (valid up to 2019) is used in the Czech Republic to evaluate buildings' responses to technical seismicity. This standard defines acceptable limit values of maximum velocity for different types of seismic loading and acceptable degree of damage. This evaluation is established according to the class of resistance (A – F) and the class of economic and social significance of buildings and structures (U, I – III). Structures of A type are usually historical monuments and buildings, the oldest and poorly structures and buildings with large plastic decorations; structures of B type are common masonry buildings, usually up to three levels and surface up to 200 m 2 . The determination of the resistance class depends on the constructional technology and the material used. From the constructional point of view, there are monolithic structures with resistance class E, framed structures with class D, half-timbered structures with class D, buildings up to three storeys with class B and prefabricated panel structures with class C. Resistance class is based on the material used: stone - resistance class A, masonry - resistance class A, B, C, concrete - resistance class C, D, steel - resistance class D, E and steel concrete – E. Class of significance U represents structures of an extraordinary economic and/or social significance (for instance, dams, significant bridges …), the following class I is represented by structures of great significance (for instance, schools, churches …), classes II and III include structures of medium and small importance, respectively. Of course, local geology is necessary to take into account because it significantly influences the values of vibrations and their characteristics. According to the Czech Standard, historical structures of resistance class A and the significance class of type U require dynamic calculation for the response of the structure at an effective velocity value of 0.6 mm.s -1 (not valid for blasts, see Czech tešchnila standard 73 0040, tab. 10). Summarizing all these remarks, vibrations can cause minor damage (damage to paintings, flaking of plaster ornaments, small cracks in plaster, etc.), as well as extensive damage to the complete destruction of monuments. Therefore, it is necessary to conduct expert research on damaged monuments to gain additional knowledge enabling the right mitigation of damage and minimizing the effects of vibration. Obviously, this must be done in close cooperation with a number of different professions, in particular fields including architecture, architectural history, conservation, engineering, landscape architecture, historical archaeology, construction, museums, city/state agencies, advocacy, and heritage tourism. Seismic measurements in the church in Světí The church dedicated to St. Andrew in the village of Světí (near Hradec Králové, Czech Republic) is first mentioned in archival sources as early as 1365 (Fig. 2A). The church has preserved its late Gothic layout to this day, although it was remodelled in the Renaissance style at the end of the 16th century and later in the slightly Baroque. The last significant building modifications took place in the second half of the 19 th century (more Kostel svatého Ondřeje ve Světí, 2021/). The area of the church is about 20 * 10 m, and the tower's height is about 23 m (personal communication). The church is registered in the List of Immovable Cultural Monuments of the Czech Republic. However, the walls and the ceiling have considerably fractured. The typical examples of failures generated by traffic are presented in Fig. 2B. From a geological point of view, the area is characterized by very thick Quaternary sediments. The main cause of failures is probably the instability of soils under the basement, partly in a slow slope. Vibrations generated by traffic, especially by agricultural vehicles and trucks, increase the loading of this historic church. The minimum distance between the sensor and the road was 14 m. (see Fig. 3). To evaluate seismic loading, seismic measurements were performed in 2010. The measuring points were located not only in the church (ground floor and higher places under the roof) but also on the profiles leading from the church to the road. Seismic apparatuses GAIA and seismometers Le3D type were used (frequency range of seismic channels is 0.5 – 100 Hz, dynamic range is more than 130 dB). The example of a wave pattern was obtained from the seismometer that was located inside the church near the wall with the most significant failures (Fig. 4 and Fig. 5). This vibration was caused by a passing truck. Generally, the maximum component value of velocity (horizontal component towards the road) during an experimental measurement was 0.44 mm.s -1 , important harmonic vibration about 8 – 12 Hz, and the duration of seismic effects was approximately 7 s (Kaláb et al., 2012). Experimental measurements have shown that the primary cause of damage to the church in Světí is the foundation of the building in a sloping area. The vibrations generated by traffic on nearby roads do not reach values that would directly cause damage to the building. Thanks to the historical value of the building, we can reduce the values of maximum permissible vibrations. It can be reasonably assumed that the vibrations significantly worsen the technical condition of the building. Zdeněk KALÁB et al. / Acta Montanistica Slovaca, Volume 27 (2022), Number 3, 783-799 787 Fig. 2A Church dedicated to St. Andrew in the village of Světí (near Hradec Králové, Czech Republic); photo: Kaláb Fig. 2B Fractures of the walls and on the ceiling in the St. Andrew church; photo: Lednická Zdeněk KALÁB et al. / Acta Montanistica Slovaca, Volume 27 (2022), Number 3, 783-799 788 Fig. 3 Sketch of location of sensors during experimental measurements; base: www.mapy.cz Fig. 4 Wave pattern of vibration induced by road traffic (the sensor signed as SVE was located inside the church) Fig. 5 Frequency spectrum of vibration induced by road traffic (the sensor was located inside the church) Zdeněk KALÁB et al. / Acta Montanistica Slovaca, Volume 27 (2022), Number 3, 783-799 789 Seismic measurements in the medieval Jeroným Mine The second example of seismic loading of a building monument is a medieval mine. Industrial Heritage Site, the Jeroným Mine, is located in West Bohemia, the Czech Republic. The Jeroným Mine is a valuable example of preserved historical mining operations dating back to the 16 th century (for instance, Žůrek, Kořínek, 2001/2002). The Jeroným Mine consists of an underground system of workings, galleries, shafts and chambers on at least three horizontal levels (10 – 55 m below the surface). The lowest level is permanently flooded. In an underground complex, we can find mine workings made by different medieval mining methods such as the extraction using a picker and miner's hammer, fire setting, underhand or overhand stopping, chamber mining, etc. (Fig. 6). For many years, uncovered underground rocks in this complex had been exposed to devastation and weathering. The territory where the Jeroným Mine deposit is found consists of metamorphized rocks of the Slavkov mantle crystalline complex (primarily the biotite paragneisses that are migmatitized in various intensities and granitized upon the intrusion of granites) and of Variscian granites of the Ore Mountain pluton. The Jeroným deposit came into existence by the action of mineralizing solutions in the already solidified rock of the Krudum massif. The Sn-W mineralization is bound to two types of formation, either the quartz vein with cassiterite and wolframite or the impregnation of cassiterite and wolframite in altered granites. The closest focal area of natural earthquakes to the monitored area of the Jeroným Mine in Čistá is located approximately 25 km to the west (for instance, Fischer et al., 2010, 2014). Young tectonic movements accompanied by volcanic activity influenced the geological pattern of this region as early as during the Tertiary. Even today, weaker earthquakes are detected in West Bohemia and Vogtland (Germany), the strongest of which are felt by people who live here, or they can damage buildings. This area is characterized by seismic swarms lasting several days up to a few months. Critical places from the viewpoint of vibration effect are fissured and weathered supporting pillars, hanging layers on the roof in chambers, and caving falls of rock leading into the chambers due to collapsed overburden. Fig. 6 Photos taken in the historical parts of the mine (fire setting, extraction using a picker and miner's hammer, underhand stopping or overhand stopping); photo: Lednická The mine is exploited, among other things, as a natural laboratory for geomechanical and geophysical experiments, for which a distributed monitoring system is used (for instance, Kaláb et al., 2010, 2011; Lednická and Kaláb, 2013; Lyubushin et al., 2014; Kaláb and Lednická, 2016; Lednická and Kaláb, 2016a). Permanent seismic monitoring has been carried out since 2004 using a seismic station JER1, installed in the mine about 35 m below the surface in one of the largest chambers. Three seismometers SM3 in geographical orientation are anchored on the concrete pillar; seismic recording apparatus PCM3-EPC3 has a special modification for the environment with high air humidity and drip water. From 2004 to 2006, the seismic station JER 1 monitored especially the effects of blasting operations during the reconstruction of drainage adit. The aim was to determine the critical value of vibrations in order to avoid damage to the mining spaces. The main aim of long-term seismic monitoring is to obtain information about the seismic loading of historical mine workings. The most significant sources of loading of the Jeroným Mine are (for instance, Kaláb et al., 2015): • earthquakes from the area in West Bohemia/Vogtland (maximum measured component vibration velocity is 0.8 mm.s -1 in the frequency range 2 – 10 Hz for local magnitude 3.6, maximum expected component vibration velocity is 8 mm.s -1 in the frequency range 1 – 10 Hz for local magnitude 5.0), • blasting operations from adjacent quarries (body wave: maximum measured component vibration velocity is 0.01 mm.s -1 in the frequency range 1 – 6 Hz, • traffic from the road above the mine (maximum measured component vibration velocity is 0.05 mm.s -1 in frequency range Hz 9 – 15 Hz, Zdeněk KALÁB et al. / Acta Montanistica Slovaca, Volume 27 (2022), Number 3, 783-799 790 • blasting operations as a part of technology for driving underground spaces(maximum measured component vibration velocity is 0.2 mm.s -1 in the frequency range 40 – 80 Hz. Since 2010, five natural swarms have happened: in 2011, 2014, 2017, 2018, and 2020 (not finished until the end of the year). The strongest earthquake occurred during the swarm in 2014, with a local magnitude of 4.4 (doi:10.7914/SN/WB). To document the seismic loading of the mine due to natural seismicity, the following number of earthquakes were recorded from the mentioned area: in 2017 – 202 earthquakes; in 2018 – 124; and in 2019 – only 27 earthquakes. The example of the wave pattern recorded by the seismic station JER1 placed in the mine and the spectra are presented in Fig. 7. Fig. 7 Wave pattern and spectra of the earthquake from the West Bohemia focal zone recorded at the seismic station JER1; left – wave pattern of ML 3.6 earthquake occurred on 4 August 2014; right – spectra of ML 3.6 earthquake (solid line) and spectra of ML 2.1 earthquake (dashed line) Although earthquakes cause the maximum vibration effect, technical seismicity also causes not negligible vibration effect in underground spaces (as mentioned above). Detailed analysis of the vibration effect caused by individual seismic sources is performed in the time and frequency domain. The example of the wave pattern and spectra of a quarry blast recorded at the seismic station JER1 are presented in Fig. 8. The fall of a rock block from the ceiling is a long-term process that is the consequence of deformation, weathering, and seismic loading. Currently, these situations were described first of all in the inaccessible part of the mining work but not only (Kaláb, Loskot, 2020). Fig. 8 Wave pattern and spectra of a quarry blast at Vítkov recorded at the seismic station JER1 The Church of the Body of God, Upper Silesia, Poland A separate issue is the phenomenon of seismic activity induced by underground mining. In Poland, these phenomena have been observed during hard coal extraction in the Upper Silesian Coal Basin and, in particular, in Zdeněk KALÁB et al. / Acta Montanistica Slovaca, Volume 27 (2022), Number 3, 783-799 791 the LGOM Copper Basin. Nowadays, these phenomena often occur as an effect accompanying underground extraction and are the cause of damage to objects. The impact of the underground extraction on the church object in the town of Polish Silesia, both in terms of land subsidence and mining-induced seismic impacts, is presented below. The Church of the Body of God was erected in the years 1914-17 according to the design of the architect Theodor Ehl (Fig. 9). The building is 48 m long and 29 m high and has an area of 777 square meters. The object was built of brick on a cross plan; the walls were plastered. The spire of the tower was covered with copper sheets when the building was renovated in 1996. After World War II, the church was damaged several times as a result of mining operations. Therefore, the building was repeatedly renovated in the years 1949-50, 1963-65, 1986-1989, and 1999-2000. The building is the best-preserved example of a neo-baroque structure. Therefore, it was entered in the Register of Monuments of the Silesian Voivodeship. Fig. 9 General view of the church construction; photo: Ścigała Last twenty-two years, underground mining has been carried out in the area of the church in the coal seams: 503 at the height of 2.3 m, 507 in two layers with a thickness of 2.0 m each, 509 in two layers with a thickness of 2.0 m each, and in the seam 510 also in two layers with thicknesses of 2.0 - 2.4 m. The mining was carried out using a longwall system with a roof caving. Levelling measurements were taken on the benchmark stabilized on the wall of the building every six months from May 2010, using technical levelling. Measurements were performed between May 2010 and October 2017. In the period covered by the measurements, the subsidence of the building was 200 mm. The results of the calculations applying the Budryk-Knothe theory (Knothe, 1953) show that the extraction led from the year 2000 resulted in subsidence of approx. 0.70 m, tilt of 6.8 mm/m and horizontal strain of 5.3 mm/m. Thus, according to the Polish classification of mining areas, there were deformations in category III of mining areas. The mining-induced seismic events of the rock mass also affected the church object. In Poland, the intensity of the impact of mining-induced seismic events on the buildings is assessed with the GSIS-2017 scale (Mutke et al., 2018). Primary is the scale based on the PGV values (peak ground velocity), and the auxiliary scale lies in the PGA values (peak ground acceleration). Both scales take into account the duration of the intense vibration phase. The scale intensity is read from specially developed diagrams for the given PGV or PGA value and the duration of the intense vibration phase - Fig.10. The diagrams were developed on the basis of statistical analysis of practical cases of mining-induced seismic events and related to them damages to structures (Mutke, 1991). The scale is numerical, consisting of levels from 0 to VI (Roman numerals). The vibrations of levels 0 and I do not damage objects; vibrations of level II usually intensify existing damages. The first new damage appears when the vibration intensity reaches level III. When assessing the impact of shocks on the building, the first is to determine the PGV and PGA values at the site location. Calculations of PGV & PGA are conducted with empirical formulae worked out by (Mutke, 1991) unless measurements were taken on the site. The obtained values should then be multiplied by the value of the amplification factor to get the results for the object located on the land surface (the formulae relate only to propagation over Carboniferous rocks). With the values of PGV and PGA and with a duration of the intense phase of vibrations, one should use diagrams to determine the degree of vibration intensity according to the GSIS2017 scale. Zdeněk KALÁB et al. / Acta Montanistica Slovaca, Volume 27 (2022), Number 3, 783-799 798 Kaláb, Z., Lednická, M ., Knejzlík, J., Telesca, L. (2010). First results from long-term monitoring of distance using a laser distance meter in shallow medieval mine. Acta Geodyn. Geomater., 7, 4 (160), p. 469-475. https://www.irsm.cas.cz/materialy/acta_content/2010_04/8_Kalab.pdf Kaláb, Z., Lednická. M., Kořínek, R., Hrubešová, E. (2012). 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