Vol50,1,2007 1 ANNALS OF GEOPHYSICS, VOL. 50, N. 1, February 2007 Key words Pressure Stimulated Current (PSC) – damage parameter – fracture 1. Introduction Phenomena associated with fracture, particu- larly those concerning materials of inhomoge- neous structure, such as geomaterials, in combi- nation with occurring transient electric phenom- ena, have always attracted the interest of the sci- entific community (Hayakawa and Fujinawa, 1994; Hayakawa, 1999). Although there exist important similarities between the fracture of a pristine rock and an earthquake rupture, there are also important differences (Turcotte et al., 2003). Therefore, such phenomena are promising can- didates of earthquake precursors (Molchanov and Hayakawa, 1995; Tzanis and Vallianatos, 2002). While deformed, geomaterial generates electrical signals that are assumed to be caused by crack generation and propagation in the Earth’s crust (Molchanov and Hayakawa, 1998; Vallia-natos and Tzanis, 1998). In order to understand the mechanisms that produce these electric signals, a number of labo- ratory experiments of mechanical distress to frac- ture have been conducted on minerals and rocks (dry and saturated) (Nitsan, 1997; Ogawa and Miura, 1985; Enomoto and Hashimoto, 1990; Hadjicontis and Mavromatou, 1994; O’Keefe and Thiel, 1995; Takeuchi and Nagahama, 2001). These experiments have been combined with nu- merous studies and recordings of acoustic emis- sions (Tonolini et al., 1987) due to mechanical stress cause microcracking in rocks as well as the Kaiser effect which takes place in rocks and ma- terials subjected to cyclic loading/unloading (Kaiser, 1953; Beattie, 1983; Lavrov, 2003). It is known that when mechanical stress is ap- plied upon a rock sample it reacts by emitting electric current (Hadjicontis and Mavromatou, 1994; O’Keefe and Thiel, 1995; Vallianatos et al., 2004). Recent laboratory experiments conducted on Penteli marble samples have confirmed that the application of a uniaxial stress on geomater- ial samples is accompanied by the production of weak electric currents to which the term Pressure Stimulated Currents (PSC) has been attributed (Stavrakas et al., 2003, 2004; Anastasiadis et al., Correlation of pressure stimulated currents in rocks with the damage parameter Cimon Anastasiadis (1), Ilias Stavrakas (1), Dimos Triantis (1) and Filippos Vallianatos (2) (1) Department of Electronic Engineering, Technological Educational Institution (TEI) of Athens, Greece (2) Department of Natural Resources & Environment, Technological Educational Institute of Crete, Chania, Greece Abstract Pressure Stimulated Current (PSC) experiments were conducted on marble samples to correlate PSC with the damage parameter, D. The phenomena and procedures taking place in the vicinity of the fracture limit were ob- served and analytically described. PSC recordings were conducted by application of uniaxial compressional stress, both at a constant stress rate and at a constant deformation rate. A linear relationship was shown to exist between the emitted PSC and the damage parameter which quantifies the deviation from linear elasticity and the concentration of microcracks. Mailing address: Dr. Cimon Anastasiadis, Department of Electronic Engineering, Technological Educational Insti- tution (TEI) of Athens, Ag. Spiridons Street, GR12210 Ega- leo-Athens, Greece; e-mail: cimon@ee.teiath.gr 2 Cimon Anastasiadis, Ilias Stavrakas, Dimos Triantis and Filippos Vallianatos 2004; Vallianatos et al., 2004). The above exper- imental procedure is described by the term «PSC technique» and consists of recording the currents emitted by geomaterial samples when subjected to either an abrupt stress variation or an extend- ed constant increase in stress rate up to failure. As the magnitude of stress increase reaches the plastic deformation range of the material, micro- cracks occur randomly starting at the hetero- geneities and spreading within the bulk of the sample (Jaeger and Cook, 1979). In the begin- ning, the structural imperfections produced are uncorrelated but as the density of microcracks increases they interact and a correlated microc- rack net structure starts to appear. The microc- racks eventually coalesce leading to the irre- versible fracture process. In the present paper PSC emission is studied in two cases: first, PSC emission when the ap- plied stress S is a linearly increasing function of time (dS/dt = constant), and second PSC emis- sion at a constant strain, ε, rate (dε/dt = con- stant) up to sample fracture. The stress, S, on the material is given as a function of strain ε. For the linear elasticity range it can be stated that (1.1) where Y0 is Young’s modulus of the undamaged material which is constant in the elastic range. When the stress takes values that lead into the plastic deformation range, then microcracks oc- cur. For a prescribed stress S, the strain ε is greater than the value given by eq. (1.1). Ac- cordingly (Turcotte et al., 2003) (1.2) where Yeff is the effective Young’s modulus and it is no longer considered as constant. In the plastic range Young’s modulus becomes progressively smaller while stress increases. A more descriptive approach to the results of this process is to intro- duce a damage parameter D so that (Lemaitre and Chaboche, 1990; Krajcinovic, 1996) . (1.3) The damage parameter, D, quantifies the devia- (1 )Y Y Deff 0= − S Yeff $ ε= S Y0 $ ε= tion from linear elasticity and the concentration of microcracks. In general 0 ≤ D ≤ 1. When D = = 0, linear elasticity is obtained with eq. (1.1) valid, but when D = 1, failure occurs. The dam- age parameter, D, is a function of the applied stress, S, only. However in most cases of inter- est the development of damage in a material is a transient process, so that we have D(S). Thus in the range where deviations from linear elas- ticity observed, eq. (1.2) can be written . (1.4) 2. Material and experimental technique The samples used to perform the experi- ments were of marble collected from Mt. Pen- teli located in Attica, Greece (Pentelicon or Dionysos marble). Its chemical composition is 98% calcite and 2% quartz and other minerals such as muscovite, sericite and chlorite. Its porosity is low, of the order 0.371%. The geo- metric characteristics of the samples as well as the loading parameters are summarised below. All samples were cylindrical measuring 106.4 mm in height, with a diameter of 51 mm. Those of the samples that were compressed at a constant stress rate suffered a pressure in- creasing at a rate of 20 kPa/s. Those of the samples that were compressed at a constant strain rate, were contracted in one dimension and suffered shortening at a rate of 0.5 µm/s. The fracture limit in the former case was 101 MPa while it was only 88 MPa in the latter as they were measured on the basis of their stress- strain curves. Stress-strain curves depict the stress re- quired by a material sample to expand or con- tract by a specified percentage with respect to its initial dimensions. They depend on various factors such as stress history, humidity, water content and porosity. In order to prevent signif- icant variations in the stress-strain curves of the sample under test, all samples were extracted together from the same rock mass and they were kept under the same conditions of temper- ature and humidity. Figure 1 shows a typical stress-strain curve of one of the samples used. The values on the ( )S Y D10 ε= − 3 Correlation of pressure stimulated currents in rocks with the damage parameter stress axis correspond to stress, s, normalized by the maximum stress recorded before fracture (Smax). Each stress-strain, (s-ε), curve can be di- vided into three parts: In the first part a non-lin- ear relationship between stress and strain is ob- served. This is a very short initial quasi-plastic range, that does not extend over 0.1 of Smax, which can be attributed to the closing of pores and to probable pre-existing microcracks (Grif- fith, 1920). The long linear part of the curve corresponds to the elastic range of the material. This range extends up to s = 0.7, where the plas- tic behaviour of the sample starts and linearity is no further maintained. This range continues up to fracture. Hereafter, all stress values noted with s, will be normalized with respect to Smax. The stress was applied by a loading ma- chine (model MTS-815) capable of applying a maximum force of ±1600 kN and a maximum deformation of ±50 mm. An integrated elec- tronic micro-console (model MTS-453.20), equipped with a load and displacement con- troller as well as a function generator unit, were used to provide a closed loop control of the ser- vo-hydraulic system. A Keithley electrometer (model 617) was used to measure PSC and all data were stored in a computer hard disk through a GPIB interface. A detailed description of the loading system and measuring system as well as sample mounting and data recording is given elsewhere (Anastasiadis et al., 2004; Stavrakas et al., 2004). 3. Experimental results and discussion During the experiments either the stress rate or the deformation rate were kept constant. As a result, two series of experiments were real- ized, keeping in each of them either the stress or the strain rate constant. Figure 2 represents the temporal behaviour of the pressure stimulated current when a mar- ble sample is compressed uniaxially at a con- stant stress rate of 20 kPa/s up to the fracture while the inset diagram show the variation of the PSC with respect to the normalized stress. The PSC signal was recorded when the nor- malised stress exceeded a value of approxi- mately 0.7. At this stress range irreversible structural changes occur due to plastic behav- iour of the material. This observation was veri- fied repeatedly (Stavrakas et al., 2004) since at Fig. 1. Typical marble stress-strain curve on nor- malised stress axis. Fig. 2. PSC with respect to time, when stress at a constant rate is applied. The inset diagram shows the PSC versus normalized stress. 4 Cimon Anastasiadis, Ilias Stavrakas, Dimos Triantis and Filippos Vallianatos approximately such stress values correspond to the beginning of the plastic range of the materi- al where changes in structure are irreversible due to microcracks taking place (Jaeger and Cook, 1979; Turcotte et al., 2003). In this range Yeff gets gradually lower than Y0. The nor- malised stress curve at values exceeding 0.7 ex- hibits a smooth ascending, and it seems to reach a maximum value slightly before fracture. The peak is not clear because the process develops quickly as the stress increase rate is high and the time elapse corresponding to the range 0.9 < s < 1.0 is relatively short. In order to show the peak in detail during the fracture process, uniaxial compression at constant deformation rate was applied. Figure 3 depicts the temporal recording of PSC when the marble sample is subjected to an increase in the uniaxial compression at a constant deformation rate of 0.5 µm/s. In the same diagram the tem- poral variation of the normalized stress s is rep- resented too. When the material enters the plas- tic deformation range (s>0.7) the stress rate continuously decreases, and diminishes at s=1, when the sample fails. As can be seen in fig. 3 the PSC peak at fracture is clearly distin- guished. The emitted PSC acquires a maximum value and consequently decreases; this corre- sponds to a decrease of the PSC rate which be- comes continuously smaller and slightly before Fig. 4. Variation of the damage parameter, D, with respect to the normalized uniaxial stress, s, applied to a typ- ical marble sample. Fig. 5. PSC with respect to the damage parameter, D, when the sample is under constant stress rate conditions: open circles; PSC with respect to the damage parameter, D, when the sample is under constant deformation rate: solid circles. 4 5 Fig. 3. Detailed representation of the temporal vari- ations of both PSC (curve a) and normalized stress applied on a marble sample (curve b) while the de- formation rate is kept constant. 5 Correlation of pressure stimulated currents in rocks with the damage parameter fracture (s ≈ 0.98) the PSC gets to a maximum and an abrupt decrease follows. Based on the experimental data of the stress-strain curve (fig. 1) the damage parame- ter, D, was determined by the use of eq. (1.4). The diagram of fig. 4 shows the variation of the damage parameter as a function of normalized stress s. It can be seen that the damage parame- ter, for values of normalized stress greater than 0.7 takes values different from zero and contin- uously increases. Figure 5 depicts a correlation between the PSC and the damage parameter, D, when the sample is under constant stress rate and con- stant deformation rate respectively. Both dia- grams exhibit a linear relationship between PSC and D in the range of D < 0.8. 4. Conclusions In this work we correlated the PSC with structural damage introduced in a material by the external application of uniaxial stress. The damage is quantified by the parameter D that can be calculated with good approximation by the use of the stress-strain curve. Correlating the emitted PSC with the damage parameter, D, showed a linear relation. This finding holds for D < 0.8. Since damage mainly occurs at stress levels close to plastic deformation and fractur- ing, experiments of constant deformation were performed for a better analysis of this process. These experiments validated the linearity be- tween PSC and D. 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