COMPUTER MODELLING OF CIRCULAR CAVE PASSAGE DEFORMATIONS DEPENDENT OF THE DEPTH RAČUNALNIŠKO MODELIRANJE DEFORMACIJ OKROGLEGA JAMSKEGA ROVA V ODVISNOSTI OD GLOBINE v v KARMEN FIFER-BIZJAK & FRANCE SUSTERSIC Izvleček UDK 624.121:681.3.01 Karmen Fifer-Bizjak & France Šušteršič: Računalniško modeliranje deformacij okroglega jamskega rova v odvisnosti od globine S pomočjo računalniškega modela, ki temelji na metodi končnih razlik smo proučevali globino, na kateri se okrogel jamski kanal poruši zaradi geostatičnega tlaka. To se zgodi pri šibkih apnencih v globinah pod 750m, pri zelo trdnih pa pod 2500m. Ključne besede: speleogeneza, mehanika hribin, računalniško modeliranje Abstract UDC 624.121:681.3.01 Karmen Fifer-Bizjak & France Šušteršič: Computer modelling of circular cave passage deformations dependent of the depth Using a computer model, based on the finite difference methoid we simulated the fail of circular cave channel, due to geostatic pressure. Poor limstone failed at the depth less than 750m, while very good limestone not until 2500m. Key words: spelogenesis, rock mechanics, computer modelling Addresses - Naslova Mag. Karmen Fifer-Bizjak Institute of Geology, Geophysics and Geotechnology Dimičeva 14 SI-1000 Ljubljana Slovenia Prof. dr. France Šušteršič University of Ljubljana, NTF Department of Geology Aškerčeva 12 SI-1000 Ljubljana Slovenia E-mail: france.sustersic@uni-lj.si introduction Present research of the early stages of the cave channel formation revealed the importance of a number controlling factors. Among them, the geomechanical properties of the rock play the key role, during the time between the inception, and the proper channel formation. In the further lines, we will discuss the control of the geomechanical properties of the rock. The simplest and the most fundamental question is: At which depth the formation of the cave channels is impeded due to the large primary stress. For this calculation we used program FLAC var. 3.03. It is installed at the PC computer at the Institute for Geology, Geotechnology and Geophysics in Ljubljana. As a modelhng technique the program uses the finite difference method. According to this method, first, a finite different mesh is designed and in the second step the differential equation is transformed into a difference equation. The program uses Mohr-Coulomb criteria of failure. It is very effective to solve geomechanical problems because it considers the shear properties of the material, for example, angle of friction and cohesion. Till now we have used this program for backanalyses of tunnels deformation on the motorways (for example Debeli hrib and Karavanke), for the research in Velenje coal mine and for feasibility study of underground garage in Piran. the model As the first step we acquired the grid of 20 elements in X direction and 20 elements in Y direction. The assumed diameter of the circular channel was set 1 mm. The calculation was simplified by considering only the upper right quarter of the channel. In the next step we set the geomechanical properties of the limestone. The crucial problem in numerical modelling are the INPUT parameters, as the result of computations depends on the proper values of geomechanical data. At this stage we didn't use any measured field data. Rather than we made use of four general types of limestone, having taken the needed parameters from the literature, according to our previous experience with the numerical modelling. We processed the limestone of four basic groups, presented in the Table 1. Table 1: label E [MPa] fi [0] c[MPa] T[MPa] very good limestone Al 20 42 3.0 1.5 good limestone A2 15 35 1.0 1.0 fair limestone A3 10 28 0.7 1.0 poor limestone A4 7 28 0.7 0.2 In the next step we determined the primary stress field. We equalled the vertical primary stress with the geostatic pressure: a^ = Y X H, where a^ ... vertical stress Y ... specific weight It was assumed that the horizontal and the vertical stresses are equal. In reality the relation between horizontal and vertical stress varies with depth. We computed 18 models in total with various types of limestone at various depths. The results are summarised in Table 2: DISPLACEMENT VECTORS (mm) Label (type of limestone) DEPTH Al A2 A3 A4 500 5.60E-03 5.30E-03 l.OOE-03 2.60E-04 600 9.60.E-03 - - - 750 ßVIL 8.60E-03 2.40E-03 4.90E-04 1000 FAIL 4.50E-03 8.10E-04 1250 7.60E-03 l.lOE-03 1500 FAIL 1.60E-03 2500 4.10E-03 3000 FAIL As a result of our calculations we obtained for each model the maximal displacements around the channel. Our model failed for poor limestone at the depth 600 m, for the fair limestone after 750 m, for the good limestone after 1250 m and for the very good limestone after 2500 m. That means that at the listed depths formation of stable channels is not possible any more. some discussion Extremes are of our main interest because they display the limits of the results in various conditions. In the figure of displacements showed that larger displacements appeared with the poor limestone. Displacementsare of the size order 10 ^ m and for the good limestone 10' m. In both cases displacements have the same direction. The largest vertical displacements occur in both cases at the top of the channel. Again, in different size orders. Displacements for the poor limestone presents Figure 1, and for very good limestone Figure 2. In the pattern of maximum principal stresses the zone of weakness appears around the channel. After the zone of weakness, zone of higher stress occurs, which influences on the stabilisation of channel. The difference in both cases is in the dimension of the weakness zone. For the poor limestone (Fig. 3) zone of weakness is larger than for the good limestone (Fig. 4). The zone of plasticity is larger for the poor limestone than for the very good limestone. Dimension of the plasticity zone has an influence on stabilisation of the channel. As expected, the channel in very good limestone is more stable that in poor limestone. Though the model is rudimentary, the listed figures show the importance of the geomechanics properties of limestone for the final result of modelling. conclusions According to the results of numerical modelling we can conclude that the limits of stability of circular voids in limestone are between depths of 600 to 2500 m. In the other words, in the limestones which have suffered complete diagenesis, karstification may reach approximatively four times deeper than in the nonconsohdated ones. The depth of the failure depends on geomechanical properties of the limestone. It must be pointed out that at this stage of research we didn't use any concrete field data of the geomechanical properties of the limestone, and we intended first to set the approximate limits of failure. In the future we intend to investigate samples from selected location. With known properties of limestone and known stress field on the selected location we can make better model. Another issue that is intended to be investigated is the geometry of the primary chatmel, which will be approximated by ellipses of various a/b ratios. references E. Hoek, E.T. Brown, 1980. Underground excavations in rock. The institution of mining and metallurgy, England. C.S. Desai, J.T. Christian, 1982. Numerical methods in geotechnical engineering. McGraw- Hill Company, New York, ITASCA Consulting group, 1991. FLAC user's guide. računalniško modeliranje deformacij okroglega jamskega rova v odvisnosti od globine Povzetek Eno pomebnih vprašnj speleogeneze je, do katere globine lahko sploh nastanejo jamski kanali, ne da bi jih sproti porušil geostatični tlak. Kot prvi korak k odgovoru smo s pomočjo računalniškega programa FLAC var. 3.03, ki temelji na metodi končnih diferenc, simulirali porušitev okroglega kanale pri štirih vrstah apnenecev. Njihovo mehansko trdnost smo definirali na osnovi podatkov z literature: Tabela 1: E [MPa] fi [0] C [MPa] T [MPa] zelo trden apnenec Al 20 42 3.0 1.5 trden apnenec A2 15 35 1.0 1.0 primeren apnenec A3 10 28 0.7 1.0 šibak apnenec A4 7 28 0.7 0.2 Rezultate simulacije kaže Tabela 2: VEKTORJI PREMIKA (mm) Tip apnenca glede na Tabelo 1 GLOBINA Al A2 A3 A4 500 5.60E-03 5.30E-03 l.OOE-03 2.60E-04 600 9.60.E-03 - - - 750 PORUŠITEV 8.60E-03 2.40E-03 4.90E-04 1000 PORUŠITEV 4.50E-03 8.10E-04 1250 7.60E-03 l.lOE-03 1500 PORUŠITEV 1.60E-03 2500 4.10E-03 3000 PORUŠITEV Skupaj smo torej izračunali 18 modelov, pri čemer je za vsakega potrebnih več tisoč iteracij. Na osnovi povedanega nastopi porušitev v globinah med 600 in 2500 metri. To pomeni, da lahko seže v trdnih apnencih, ki so prestali popolno diagenezo, zakrasevanje, štirikrat globlje, kot v tistih, kjer konsolidacija še ni končana. m THE LIMESTONE A4._Älj«PTO_500jin Fy«:(Versiott3.03j 7/il>7/lBS5 07M ^ 1120 -4.167E-04 FLftC(Versbtta,03) S^S®. 7/Ö7/19B5 07;42 slip lOOS -4.ie7E-04 iDt lB-3 CBMflga ZiWD UttoANA ifsmwaa; ■ sao .isa (»ID— Fig. 3 FIK; (Version 3.03) 7/07/1995 07:47 attp 1180 -ijers-o*