Stability Determination of Ceilings of Some Caves

International Journal of Geoheritage. 2015, 3(2): 24-32 DOI: 10.17149/ijg.j.issn.2210.3382.2015.02.004

Stability determination of ceilings of some caves

Ivaylo Ivanov Civil Engineering and Geodesy, Department of Geotechnics, University of Architecture, Sofia, Bulgaria

Abstract: The karst areas in Bulgaria hide a number of potential hazards in case of insufficient engineering-geological investigations prior to construction. Some of those hazardous phenomena have been identified in almost all countries with karst locations. One of the biggest hazards is related to the sudden subsidence and collapse of ceilings in the karst caves which may bring about unforeseeable consequences and demolitions in the built areas. One of the well-known and interesting similar phenomena in Bulgaria is the Pro- hodna cave, over which the Karlukovo-Lukovit road passes by. The vibrations from the traffic as well as the additional impact of the blasts at the nearby rubble quarry could bring about problems leading to destruction of the cave’s arch. This paper describes the methods used by the author for determination of a coefficient of stability of karst caves’ ceilings based on the theory of cracks and the critical width of caves. The methodology has been applied for assessment of stability of ceilings of two caves in the Karlukovo karst area – Prohodna and Svirchovitsa.

Keywords: Bulgaria, Karlukovo karst area, cave ceilings, Griffit's cracks theory, stability, calculation

1 Introduction The karst areas in Bulgaria hide a number of potential hazards in case of insufficient engineering-geological investigations prior to construction. Some of those hazardous phenomena have been identified in almost all countries with karst locations. One of the biggest hazards is related to the sudden subsidence and collapse of ceilings in the karst caves which may bring about unforeseeable consequences and demolitions in the built areas (Sowers, G., 1996). One of the well-known and interesting similar phenomena in Bulgaria is the Pro- hodna cave, over which the Karlukovo-Lukovit road passes by. The vibrations from the traffic as well as the additional impact of the blasts at the nearby rubble quarry could bring about problems leading to destruction of the cave’s arch. This paper describes the methods used by the author for determination of a coefficient of stability of karst caves’ ceilings based on the theory of cracks and the critical width of caves. The methodology has been applied for assessment of stability of ceilings of two caves in the Karlukovo karst area – Prohodna and Svirchovitsa.

Author: Ivaylo Ivanov, Civil Engineering and Geodesy, Department of Geotechnics University of Architecture E-mail: [email protected] Ivaylo Ivanov: Stability determination of ceilings of some caves 25

2 Short geological characteristics of studied karst area The Kameno Pole-Karlukovo karst area (Popov, 1970) is situated in the Pre-Balkan region, comprising the outfalls of the Upper Cretaceous period in the river valley of the Iskar, between the towns of Roman and Cherven Bryag (Figure 1).

Figure 1 Situation of Kameno pole – Karlukovo karst area

The development of the karst in the region is related to the thick Campanian layers – Maestrichtian limestones, forming several suits (Dzhuranov S., M. Ivanov, & N. Yolkichev, 1993), distinguished by carbonaceous, clayey content, age and availability of specific fossils. The limestones in the area reach a thickness of over 200 m, the most strongly karsted is Kailaka formation. Downward to Mezdrs and Kunins formations, in parallel with the reduction of the carbonaceous content and the increase of the clayey component in the rocks, karsting sharply decreases and almost abates. The Ap- tian depositions - marls and sandstones of the Roman formation – serve as a common underlying formation for all of them. At the eastern side of the area the limestones are covered by Paleogene and Neogene deposits presented by clays and sands (Figure 2). In terms of tectonic, the area is situated in the Pre-Balkan tectonic region, at the border between the northern and southern Pre-Balkan and between its western and central part. These borders are fixed along large fault structures many of which cross each other in the vicinity (Ivanov, 1999). The Cretaceous depositions form nearly parallel and comparatively shallow syncline and not high anticline folds with approximate direction west-east (Minchev, Pironkov, 1959/60). The syncline lowerings form the individual sub-areas of Kameno pole-Karlukovo karst area, namely Kar- lukovo sub-area, Kameno pole sub-area, and Gabarevo sub-area.

3 Short information about the studied caves The caves Bankovitsa and Svirchovitsa are situated in the Karlukovo karst sub-area, at the right bank of the Iskar River. They are formed in the limestones of Kaylashka suit (Figure 3). Prohodna cave is a karst bridge, 80 m long. It is part of a cave corridor of

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Gabare subarea

Kameno pole subarea

Karlukovo subarea

Figure 2 Geological map of Kameno pole - Karlukovo karst area 1 - 9. Lithological and stratigraphic units. 1. Kailaka formation (kK2m); 2. Mezdra formation (mzK2cp-m); 3. Dermantsi, Novachene and и Rumyantsevo formations (III,VIK2cp-m); 4. Kalentsi formation (kaK2st); 5. Roman formation (rmK1ap-a); 6. Malo Pestene formation (mpK1a); 7. Paleogene deposits; 8. Neogene deposits; 9. Quaternary deposits.

Figure 3 Situation of the studied caves Ivaylo Ivanov: Stability determination of ceilings of some caves 27 impressive size, with approximate direction “east-west”. The total length of the bridge is about 80-100 m, the height at the east entrance is over 20 m, while the western entrance is the highest one in Bulgaria – over 42 m (Vasilev H., & D. Sinyovsky, 2003). The cave forming possibly begins at the end of Pliocene and continues till the beginning of Pleistocene, which is connected with the change of the level of the Iskar River (Popov, 1985). Its age has been determined on the basis of geomorphological indica- tions and availability of old fluvial terraces.

4 Studies on the mechanism of destruction of the karst caves’ ceilings The issue of the stability and destruction of the karst caves’ ceilings has been poorly studied because of the comparatively rare manifestation of this karst deformation. The main mechanisms are nearly the same that can be seen in the destruction of the ceilings of the mine galleries which are comparatively better studied. The destruction of the karst caves’ and mine galleries’ ceilings may happen basically in two ways (Bak- lashov, 1988; Sowers, 1996). The first one is through exceeding the tensile strength in case of bending of the rocky layers of the ceiling which brings about appearance of a central crack and layer-by-layer detachment of rocky blocks, and also in case of exceeding the shear strength of the layers. The second way is through falling of some fragments from the ceiling and forming arches but it is typical mainly for strongly cracked rock mass (Figure 4).

Figure 4 Principle mechanisms of destruction of the karst caverns ceilings in various conditions (Sowers, 1996).

The author has studied mainly the first way, which is the most widespread way of ceiling destruction, and for that purpose he has used the theory of cracks (Griffith, 1921). According to this theory, the tensile stresses appearing in the middle of the ceiling lead to appearance and development of micro- and macro-cracks (Figure 5). The most hazardous of them are those developed at the middle of the arch and are approximately normally oriented towards it. According to Griffith’s criterion when 1/2 reaching the critical stress 3  2/ET c  , the crack with a length of 2с begins to grow downward. Reaching the lower end of the ceiling, its development continues upward until reaching a horizontal abated surface (inter-layer crack, clayey band or the rock surface). According to the condition of Gordon-Cook, if the tensile strength

28 INTERNATIONAL JOURNAL OF GEOHERITAGE of the respective band does not exceed 1/5 of the tensile strength of the rock, then, in it, before the vertical crack, emerges a horizontal one, and the merger of them stops the vertical development of the crack. The merger of the two cracks proceeds with a detachment of a layer from the roof part of the cave under the impact of the dead weight. As a result, the horizontal crack grows and two overhanging ends of the ceiling are coming out. When the growing horizontal crack reaches the critical length lк, its uncontrolled and unstable development begins (Jaeger, I., & W. Cook, 1969) and respectively, destruction of the ceiling or detachment of part of it.

The magnitude of lк is determined according to the formula (Kositsin, Figure 5 Central crack development and collapse of 1980): the ceiling of karst cavern, according to the cracks theory (Griffith, 1921)

1/2 Kicr 1/4 lhк  2 , (1)  1/2 where Kiк (MPa.m ) – critical value of the coefficient of intensity of stresses, γ – bulk density of the rock (N/m3); h – thickness of the arch part or layer (m). In order to determine the critical length at which an uncontrolled destruction of the cave’s ceiling may occur, it is necessary an experimental determination of the critical value of the coefficient of intensity of stresses - Kicr to be carried out. The methodology implemented for the test of samples presumes determination of the ultimate load under which rock samples with artificially created beginning of crack are destructed. The sample is loaded in a press and bending stresses leading to destruction are created in its central part (Figure 6, 7). The value of the critical coefficient of intensity of stresses КIcr is determined by the formula: 33 dcc3/2 22 KphIcr 4, 2 1 1 , (2) 2 dh where р – load (N/m); c, d, h – dimensions of sample (m).

Figure 6 Scheme of the experimental determination of Кicr Ivaylo Ivanov: Stability determination of ceilings of some caves 29

Figure 7 Experimental determination of Кicr in a hydraulic press

5 Stability determination of the ceilings of some caves in the area of Karlukovo village The calculations have been made for the caves Prohodna and Svirchovitsa situated in the land of Pladnishteto, near Karlukovo village. The values received for the ultimate loads at which the rock samples from this area are destructed, and the values of Kiк respectively are shown in Table 1.

Table 1 Determination of Kicr for the studied area Input data

Sample Main parameters of the samples Kicr Situation 1/2 No. Distance High of the Thickness of Depth of the Vo lu me Linear (MPa.m ) between the sample - h the sample - initial crack weight - γ stress - Р supports - d (m) (m) b (m) 2c (m) (N/m3) (N/m) 1.1 0,17 0,02 0,01 0,007 25166,950 13734,00 1,61 Karlukovo village 1.2 0,17 0,02 0,01 0,007 24978,922 10987,20 1,29 1.3 0,17 0,02 0,01 0,007 23085,246 11379,60 1,33

The results of the experiments allow the critical width of the karst caves to be determined by formula (1). The ratio between the calculated critical width - Lcr and the actual width of the karst caves’ ceiling found in the studies – L, can be expressed through the introduction of a stability coefficient – Kst..

Lcr K  (3) st L The stability coefficient may be used in the local assessments of the hazard of emergence and show of karst deformations which are negative for the construction.

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In order for the results to be verified, values of ceiling thickness in the caves Pro- hodna and Svirchvitsa were set. At the entrance parts of Svirchovitsa cave they are about 28 m wide in plan view which is higher than the critical width for Pladnishteto land. This has brought about the formation of the entrance opening through the subsidence of the arch. The thickness of the layers in the ceiling of Prohodna cave is about 8-10 m. The calculations show that in this case the critical width is 30.35 m. The average width of the ceiling calculated on the ground of the maps drawn is about 25 m. The difference between the critical width of the arch and the width of Prohodna is about 5 m, i.e. there is no practical hazard of arch subsidence with the exception of an emergency situation (Figure 8).

Figure 8 West entry of the Prohodna cave

Table 2 shows the results for the critical width of the caves Prohodna and Svir- chovitsa at an average thickness of their ceilings. The roof of the Svirtchovirsa cave is destroyed.

Table 2 Widths of the ceilings of the studied caves and stability coefficients Average ceiling Real average width of the Stability coeffi- Cave L (m) thickness (m) cr ceiling – L (m) cient Prohodna cave 10.00 30.35 25 1.21 Svirtchovitsa cave 5.50 26.63 28 0.95

6 Determination of time for ceiling destruction in some karst caves on the basis of the calculated denudation and weathering processes This study is a theoretical one and is based on the results obtained for the value of the karst denudation in the Karlukovo karst area. Due to denudation, a step by step re- moval of carbonate substance layer from the walls of the karst caves is observed, and this process flows not only under the underground water table but also in the zone of aeration and because of the condensation water flowing on the walls of the karst caves. Ivaylo Ivanov: Stability determination of ceilings of some caves 31

Because of that the cavities are gradually widening and at the same time their ceilings become thinner with the value of the calculated-for-the-area karst denudation. For the underground slopes, at constant weather factors, the destruction is exclusively on the account of the chemical denudation, which, for Karlukovo-Kameno Pole area, varies from 2.2 to 5.7 cm/1000 a. To this process in the open slopes (for example in Prohodna cave) we have to add also the impact of the frost weathering which gradually destroys the walls and ceilings of the caves. According to Kosev’s investigations (1993) the average rate of frost and chemical weathering of the limestone in the area in case of open cracked slopes is 1.6 mm/a. With a view of the protection of walls and ceiling at the entry parts of the caves from direct atmospheric impact and on the basis of the experience of the author, it can be assumed that the average rate of weathering at the entry parts of the caves is about 5 mm/10a or 0.5 mm/a. Thinning leads to reduction of the critical width of the cave at which its ceiling is being destroyed, and the time of this destruction can be approximately foreseen (Table 3). The analysis does not take into consideration additional loads from earthquakes, buildings and transport vehicles, as is the case with Prohodna cave, which additionally shortens the “life time” of the karst cave.

Table 3 Approximate destruction speed of the roof of the cave “Prohodna” Average ceiling Critical ceiling Real ceiling Stability coeffi- Cave Years thickness (m) width - Lcr (m) width – L, m cient 0 10.00 30.35 25.00 1.21 1000 7.50 29.90 26.00 1.15 Prohodna cave 3000 6.50 28.85 28.00 1.03 4000 6,00 28.27 29,00 0.97

It could be concluded from the above table that the ceiling of Prohodna will be naturally destroyed after 3500 years approximately.

7 Conclusions The investigations made and the results received allow for some important conclusions to be drawn up: 1) The experimental determination of Kiк , respectively lк allows the hazard rate of possible natural destruction of the karst caves’ ceilings to be specified. 2) Studying the natural speed of the weathering processes in certain karst area allows for the approximate definition of the time in which the width of a karst cave will exceed the critical one, leading to the destruction of the ceiling. 3) The critical width could be used as an indicator in the determination of protec- tive measures during the construction in karst terrains, especially in case of shallow-located karst.

References

Baklashov, I. (1988). Deformation and destruction of rock masses (on Russian). Nedra, Moscow. 272 Griffith, A. A. (1921). The phenomena of rupture and flow in solids. Philosophical Transactions of the

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Royal Society of London, A, 221,163–198. Ivanov, I. (1999). Connection between foult network, karstification and draining of the karst waters in the Kameno pole-Karlukovo karst region (on Bulgarian). Proceedings of National Scientific Conference on Problems of Karst and Speleology. Sofia – 1999, 63 – 70. Jaeger, I., W. Cook. (1969). Fundamentals of Rock Mechanics. London, Methuen, 513. Kositsin, A. (1980). Mechanism of deformation and destruction of rock masses by exploitation (on Rus- sian). Report. Fund of Moscow Geological Institute Popov, V. (1970). Distribution of karst in Bulgaria and some of its features (on Bulgarian). Proceedings of the Geographical Institute of Bulgarian Academy of Sciences. XIII, 5-17. Popov, V. (1985). About the genesis and age of the rock bridge "Prohodna" (on Bulgarian). Problems of Geography, 4, 61-63. Sowers, G. (1996). Building oh Sinkholes. New York, ASCE Press. 202.