Subcritical Crack Growth Index Research Articles

Effects of fluid salinity and composition on subcritical crack growth in marble

Subcritical fracture growth of rocks in fluid-chemical environments played a crucial role in the weathering process of rocks and the preservation of stone building heritage. Fracture mechanics properties of marble under different fluid compositions and salinity conditions were investigated by carrying out double torsion tests. The subcritical crack growth index (SCI) exhibited different salinity dependencies in two salt solutions. In NaCl solution, the SCI decreased by 1.97 % – 40.50 % with increasing salinity due to the increase in solubility of calcite. The SCI decreased by 4.60 % and 14.01 % respectively as the Na2SO4 salinity increases from 0.01 mol/L to 1 mol/L, and then increased with the increase in salinity, which was related to the relationship between calcite solubility and salinity. Compared to Na2SO4 solution, the weakening effect of NaCl solution on Ka was smaller. In contrast, the fracture toughness (KIC) was insensitive to fluid composition and salinity in the short term, with KIC ranging from 0.65 to 0.79 MPa m1/2 in all salt solutions. The three-dimensional morphology results of the fracture surfaces indicated that the effect of salinity on the roughness of both fracture types was negligible. However, the microstructure of the marble was significantly affected by salinity, and apparent dissolution was observed. The results highlighted the dependence of the subcritical fracture behavior of marble on fluid chemistry, which had implications for the weathering assessment of stone masonry buildings and the permanent protection of stone heritage monuments. In these applications, fluid chemistry could either strengthen or weaken the rock, depending on variations in fluid composition and salinity.

Effects of fluid composition and salinity on subcritical crack growth in granite

Using the double-torsion technique, the fracture mechanical response of granite specimens was investigated under the influence of fluid with different electrolyte types and salinities. The fracture toughness (KIC) and critical mechanical energy release rate (G0) of the granite in electrolyte solution are weakened compared to those in distilled water. The KIC in all electrolyte solutions is 2.08–2.28 MPa·m1/2, which is 8.4 % − 16.5 % lower than that in distilled water, and it is insensitive to ion type and salinity. In contrast, the subcritical crack growth index (n) shows different salinity dependence in three salt (AlCl3, CaCl2, and NaCl) solutions. The slight increase in n with rising salinity of the AlCl3 solution is attributed to crack tip blunting caused by over-dissolution of minerals. The n and G0 decrease and then increase with rising salinity of CaCl2 solution, which may be related to the salinity-dependent dissolution rate of quartz and the weakening of repulsive force between crack surfaces. The n and G0 shows a negative correlation with salinity and decrease by 26.4 % and 15.4 %, respectively as the NaCl salinity increases from 0.1 M to 1.0 M. Limitations in the dissolution reactions of the main minerals (albite, biotite and diopside) is accountable for enhancement of n in silica solutions. Experimental results emphasize the critical and subcritical fracture behavior of the granite in response to chemically reactive fluids with implications for both hydraulic fracture stimulations in geothermal fields and caprock integrity for CO2 sequestration. In these applications, the fracture properties of the reservoir rock can be enhanced or weakened by changing the electrolyte type and salinity of the fluid, depending on the actual requirements.

Water effect on subcritical crack growth and fracture behavior of marble

Understanding the fracture properties and subcritical crack growth of rocks in aqueous environments is significant for the effective assessment of the long-term stability of the masonry buildings, cultural heritage structures, and art sculptures. We use double torsion techniques to systematically investigate the subcritical crack growth behavior of marble under air, fluid, saturated and saturated + fluid test conditions. In the fluid condition and the saturated + fluid condition, the load reductions during the relaxation test are larger than other conditions, reaching 12.81% and 12.26%, respectively. There is a water-weakening effect on both the subcritical crack growth index (SCI) and KIC, but the water weakening sensitivity in KIC is lower than that of SCI. Compared to the air condition, the SCI values of the marble decreased by 43.69% under the fluid condition, 17.64% under the saturated condition, and 38.09 % under the saturated + fluid condition, respectively. The introduction of water during the relaxation test results in an immediate increase in the crack velocity and the major principal strain of the specimen, as evidenced by the appearance of the Ⅳ region on the KI-V curve. Scanning electron microscope images show that the most triangular pits and dissolution pits are present in the marble under fluid and saturated + fluid conditions, leading to a more pronounced deterioration of the mechanical properties. The test results highlight the significant impact of water on subcritical crack growth in marble. In particular, during rainfall, both dry and saturated marble masonry buildings are more prone to cracking due to the introduction of water.

Degradation of Fracture Characteristics on Coconino Sandstone Due to Water Content

The water content of a rock affects its fracture characteristics, such as strength and fracture toughness. In this study, the effect of water content on the fracture characteristics, such as strength, fracture toughness and subcritical crack growth index under shear loading for Coconino sandstone was investigated. Here, experiments were conducted in two cases: completely dry and fully saturated. In particular, a short-beam compression specimen was employed to examine the fracture characteristics due to shear; in addition, the shear strength, mode II fracture toughness, and subcritical crack growth index under shear stress were obtained. Consequently, the shear strength and mode II fracture toughness decreased as the water content increased; however, the subcritical crack growth index remained almost the same without significant alterations. The effect of water on the strength reduction of rocks is related to chemical and physical corrosion, pore pressure increase, and frictional reduction. Previous investigations on the deterioration of strength by water have yielded similar results in this research. Under saturated conditions, the shear strength decreased by 15.5%, and the fracture toughness decreased by 11.8%, compared with dry conditions. Regardless of the dry or saturated condition, the subcritical crack growth index n exhibited similar values.

Effect of thermal treatment on the fracture toughness and subcritical crack growth of granite in double-torsion test

An understanding of the fracture behavior and subcritical crack propagation of hard rock under different temperatures is necessary for the design and stability of nuclear waste disposal projects. The aim of this study was to understand the thermal effect on the fracture behavior of granite, which had been heated at 25 (untreated), 100, 200, 400, and 600 °C, respectively. A series of uniaxial compressive tests and double-torsion tests were performed on granite specimens. The three-dimensional digital image correlation technique was used to investigate the strain evolution and fracture pattern in granite specimens during subcritical crack propagation. According to the results, the uniaxial compression strength, Young’s modulus and fracture toughness of the granite specimens increased and then decreased with an increase in treatment temperature. These parameters dropped sharply as the treatment temperature exceeded 400 °C, mainly because of the thermally-induced destruction of the quartz crystal structure and a generation of wider intergranular fractures. A comparison of the subcritical crack length by theoretical calculations and experimental observations from digital image correlation showed that the two values were consistent. At a treatment temperature of 400 °C and 600 °C, the velocity of the subcritical crack propagation was accelerated, so the length of the subcritical crack during the relaxation test was 4.14 times and 5.25 times that at 25 °C, respectively. The subcritical crack growth and fracture process of the double-torsion tests were visible by the three-dimensional digital image correlation system. A subcritical crack growth index (n) can be used to characterize the susceptibility of the subcritical crack propagation in rock relaxation tests, which helps to evaluate the long-term stability of nuclear waste disposal projects.

압열인장시험을 이용한 화강암의 지연파괴특성 및 장기안정성 평가

본 연구에서는 임계하균열성장 변수를 구하기 위해 제안된 Wilkins의 시험법을 압열인장시험과 결합하여 화강암의 인장강도, Mode I 파괴인성과 임계하균열성장지수를 동시에 구하였으며 이를 사용하여 암석의 장기거동을 평가하였다. 또한 내부압력을 받는 압축공기저장(CAES) 공동에 대한 장기안정성을 수치해석코드인 FRACOD를 사용하여 해석하였다. 시험 결과 화강암의 임계하균열성장지수(n)는 29.39로 결정되었으며 5 ~ 6 MPa의 내압은 저장공동의 장기안정성에 큰 영향을 미치지 않는 것으로 나타났다. 또한 시험 과정에서 측정한 미소파괴음을 분석한 결과 암석내의 미소균열 생성 및 전파에 따른 암석의 손상을 정량적으로 기술할 수 있었다. 만약, 실내와 동일한 조건으로 현장에서 AE 모니터링을 수행할 경우 AE 모니터링을 통해서 하중을 받는 암석의 현재 상태를 정량적으로 평가하는 것이 가능할 것으로 판단된다. Long-term stability and delayed failure of granite were evaluated through the laboratory test based on Wilkins method and Brazilian disc test (BDT) which yields tensile strength, mode I fracture toughness and subcritical crack growth parameters. Then, the long-term strength of granite was estimated by using analytical models and long-term stability of compressed air-energy storage (CAES) pilot cavern pressurized up to 5 ~ 6 MPa was evaluated using numerical code, FRACOD with the determined subcritical crack growth parameters. The results of test and analyses showed that the subcritical crack growth index, n was determined as 29.39 and the inner pressure of 5 ~ 6 MPa had an insignificant effect on the long-term stability of pilot cavern. It was also found that the measurement and analysis of acoustic emission events can describe the accumulation of damage due to subcritical crack growth quantitatively. That is, AE monitoring can provide the current status of rock under loading if we make an identical installation condition in the field with that of the laboratory test.

Effect of Surrounding Environment on Subcritical Crack Growth Index and Long-Term Strength for Rock

Study of subcritical crack growth is important in estimating the long-term strength of rock and in ensuring the long-term stability of structures in a rock mass. The long-term strength is affected by the value of subcritical crack growth index (SCGI). However, the effect of environmental conditions on SCGI has not been clarified. In this study, we have estimated SCGI under various environmental conditions on a sample of Kumamoto andesite, using the Double-Torsion method. We show that the SCGI decreased when the temperature is higher in both air and water; the SCGI in water is smaller than that in air. When the relative humidity of the air increased, SCGI tended to be smaller and at 90 % relative humidity was close to the value in water. Under alkali conditions, the SCGI decreased slightly. Using the values of SCGI, the long-term strength was estimated and it is shown that the long-term strength decreased when SCGI was smaller. It is concluded that SCGI and the long-term strength is affected by the surrounding environment, specifically by the temperature and water. To ensure the long-term stability of rock, the control of the temperature and water migration is important.

緩亀裂進展による圧縮破壊―岩盤内の均質化亀裂進展（第５報）―

Compressive fracture process of rock under the uni-axial compression is discussed, as a result of the sub-critical crack growth in it. A numerical procedure for the failure prediction is presented and discussed, basing upon the critical pressure-crack elongation curve (pc - a curve) for the pure mode I crack propagation (KII = 0, KI = KIC) in the homogenized joint model, which is analyzed by means of the Stress Compensation-Displacement Discontinuity Method (SC-DDM). The crack elongation rate (da/dt) is formulated by the empirical equation of the form of da/dt ∝ KIn, where n: the sub-critical crack growth index. The applied stress-crack elongation curve (p - a curve) in the uni-axial compression test is analyzed to clarify the strain rate dependency of the macroscopic compressive strength (Sc), and the time-crack elongation curve (t - a curve) in the creep test of the uni-axial compression is analyzed to evaluate the effect of applied stress upon the lifetime (tF). It is concretely shown that the non-linearity of stress-strain curves and time-strain curves is deeply associated with the sub-critical crack growth in rock. Moreover the significant influence of heterogeneity and in-homogeneity of rock is discussed by presenting a parallel plate model to assess the damage effect and so on.

亀裂の緩進展による引張破壊―岩盤内の均質化亀裂進展（第４報）―

A macroscopic tension fracture of rock is analyzed as a result of the sub-critical crack growth in it, and a numerical procedure for the failure prediction is presented and discussed, basing upon the critical pressure-crack elongation curve (pc—a curve) for the pure mode I crack propagation (KII = 0, KI = KIC) in the homogenized joint model, which is accurately evaluated by means of the Stress Compensation-Displacement Discontinuity Method (SC-DDM). The crack elongation rate (da/dt) is formulated by the empirical equation of the form of da/dt ∝ KIn, where n: the sub-critical crack growth index. Computing the applied stress-crack elongation curves (p—a curves), the rate-dependent failure of rock in the tension test is concretely analyzed along with the time-dependent failure of rock in the creep test. The significant correlation between these experiments is discussed by comparing the non-linear stress-strain curves of the tension test to the non-linear time-strain curves of the creep test. It is clarified that the non-linearity is deeply associated with the sub-critical crack growth.

Experimental determination of subcritical crack growth parameters in sedimentary rock

Mounting evidence suggests that subcritical crack growth is an important mechanism for the development of natural fractures. Numerical simulations of fracture patterns are sensitive to the subcritical crack growth index, the exponent used to describe the power law dependence of crack velocity on stress intensity. Few measured values of subcritical indices in sedimentary rocks have been published, however, and no systematic studies of diagenetic controls of subcritical crack index behavior are available. Subcritical crack index measurements are especially difficult in weak, porous rock, primarily because non‐elastic material response can obscure fracture‐related behavior. We have carried out numerous subcritical crack index measurements with the widely used dual torsion beam test configuration and developed a modified test methodology for subcritical crack index measurements on porous rocks. The principal element of the methodology is a specimen pre‐loading procedure to minimize transient material response. Measurement reliability is documented in the study by documentation of reproducibility in three sets of sandstone and carbonate specimens.

Scaling of fracture length and distributed damage

The linear theory of elasticity formulated in terms of dimensionless strain components does not allow the introduction of any space scaling except linear relations between fracture length and displacements and thus the determination theoretically of the strength of a body or structure directly. Self-similarity of a fracture process means the existence of a universal faulting mechanism. However, the general applicability of universal scaling to field observations and rock mechanics measurements remains the subject of some debate. Complete self-similarity of a fracture process is hardly ever found experimentally, except in some aluminium alloys. At early stages of the loading, material degrades due to increasing microcrack concentrations. Later, these microcracks where distributed in the process zone localize into a subcritically growing macrocrack, and finally the fracture process accelerates and rupture runs away, producing dynamic fracture. The macroscopic effects of distributed cracking and other types of damage require treatment by constitutive models that include non-linear stress–strain relations together with material degradation and recovery. The present model treats two physical aspects of the brittle rock behaviour: (1) a mechanical aspect, that is, the sensitivity of the macroscopic elastic moduli to distributed cracks and to the type of loading, and (2) a kinetic aspect, that is, damage evolution (degradation/recovery of elasticity) in response to ongoing deformation. To analyse the scaling of a fracture process and the onset of the dynamic events, we present here the results of numerical modelling of mode I crack growth. It is shown that the distributed damage and the process zone created eliminate the stress–strain crack-tip singularities, providing a finite rate of quasi-static crack growth. The growth rate of these cracks fits well the experimentally observed power law, with the subcritical crack index depending on the ratio between the driving force and the confining pressure. The geometry of the process zone around a quasi-static crack has a self-similar shape identical to that predicted by universal scaling of the linear fracture mechanics. At a certain stage, controlled by dynamic weakening and approximated by the reduction of the critical damage level proportional to the rate of a damage increase, the self-similarity breaks down and crack velocity significantly deviates from that predicted by the quasi-static regime. The subcritical crack growth index increases steeply, crack growth accelerates, the size of the process zone decreases, and the rate of crack growth ceases to be controlled by the rate of damage increase. Furthermore, the crack speed approaches that predicted by the elastodynamic equation. The model presented describes transition from quasi-static crack propagation to the dynamic regime and gives proper time and length scales for the onset of the catastrophic dynamic process.

Microseismic properties of a homogeneous sandstone during fault nucleation and frictional sliding

SUMMARY The formation and evolution of faulting in three initially intact, oil-saturated specimens of Clashach sandstone is examined under conditions of constant strain rate loading at three different confining pressures, simulating the effect of tectonic loading at different depths in the Earth’s upper crust. After a fault is formed the specimens are slid for a time, and then the initial confining pressure is increased to simulate the long-term recovery of strength expected in the Earth. The differential stress u and natural acoustic emissions (AE) are measured during the three separate phases of fault nucleation, sliding and strengthening. At the end of each individual phase the fluid permeability is measured by a pulse-decay technique at constant stress. The AE are interpreted using a mean field theory for damage evolution which calculates a mean crack length (c) from the seismic event rate N and the b-value, and a mean energy release rate (G) from u and (c). (c) and (G) both increase non-linearly in the nucleation stage, and are associated with large fluctuations in the scaling exponent b. In contrast, the b value remains almost constant at a value near unity in the sliding phase, even when the fault is mechanically strengthened. Small fluctuations in ( G ) observed during sliding may be associated with the breaking of individual asperities. The relative stability of b, combined with a relatively constant sliding stress, implies that frictional sliding has all the hallmarks of a self-organized critical (SOC) phenomenon. In contrast, the fresh fracture of intact rock shows a continuum of states with power-law scaling at a variety of b values, where b is negatively correlated to (G). During the fault nucleation stage the implied subcritical crack growth index n’ obtained from the AE data shows a distinct break of slope during the failure of the intact specimens, from n’ 2, consistent with a theoretical transition from stable damage to dynamic instability. A possible mechanism is the transition from local mechanisms dominated by dilatant hardening (negative feedback) to microcrack coalescence (positive feedback). Interpreted in this way, the results imply that the organized coalescence of microcracks to form a fault occurs before the ultimate strength (peak stress) is reached. This emphasizes the fact that local mechanisms of softening or hardening do not always scale simply to the macroscopic rheology in a heterogeneous medium. The fluid permeability reduces steadily throughout all phases of deformation, testament to the self-sealing nature of deformation in porous sedimentary rocks.

Application of a modified Griffith criterion to the evolution of fractal damage during compressional rock failure

A modified Griffith criterion for a fractal ensemble of cracks is applied to the interpretation of Acoustic Emission (AE) statistics during the compressional deformation of intact and artificially pre-cut rock specimens in the laboratory. A mean energy release rate per unit crack surface area [G] is recovered from the observed AE event rate N and the seismic b value, by calculating an inferred mean crack length [c] and measuring the differential stress sigma for a range of experimental conditions. Temporal variations in [G] under compressive deformation show very similar trends to those predicted by a synoptic model determined by direct extrapolation from observations of subcritical crack growth under tension. (In the tensile case, deformation is centred on a dominant macrocrack and the stress intensity K, which scales as the square root of G, is the relevant measured variable.)The three independent variables measured during the tests (sigma, N, b) are reduced to points that map out a path through a 3-D phase space ([G], N, b), which depends on the material type and the experimental conditions. 2-D slices through this phase space [([G], N), ([G], b)] are compared with results from the tensile tests [(K, N), (K, b)]. The event rate N is found to scale with square-root [G] according to a power law, with an exponent n' which is smaller than that for tensile fracture, reflecting the greater stability of compressional rock fracture in its early stages. The effective subcritical crack growth index n' is correlated with the material type and degree of apparent 'ductility' on a macroscopic scale, with more brittle behaviour corresponding to higher n'. The value of n' is similar on unloading of the stress after dynamic faulting as on the loading portion, though the curve is systematically offset, most probably due to the material weakening associated with faulting. The model does not apply near the period of dynamic failure, where strong local interactions are dominant. The seismic b value is also found to scale negatively with square root [G], in a manner similar to experiments where K can be measured independently. The acceleration of the mean seismogenic crack length [c] = f(t) has a similar power-law form to that predicted from Charles' law for a single tensile macrocrack, with an implied subcritical crack growth index n smaller than that for fracture in compression. The extra dimension introduced by the time dependence of [c] allows an independent check on the validity of the theory used to calculate [G]. In particular n' from the diagram ([c], t) is found to be similar in magnitude to the exponent obtained from the event rate dependence ([G], N), a phenomenon first discovered by empirical observation of tensile subcritical crack growth.