Saturated Cracks Research Articles

Detection of a cracked and fluid-filled main Himalayan thrust (MHT) and its implications toward the genesis of earthquakes in the Uttarakhand Himalaya

The present study looks into the significant role of metamorphic and aqueous fluids in the mid-crustal Main Himalayan Thrust (MHT) in triggering strong to moderate earthquakes in the Kumaon-Garhwal Himalayas. Using seismic velocity tomograms, crack density (ε) and saturation rates (ξ) have been modelled using the crack theory. All three earthquakes in Uttarakhand with Mw ≥ 6.5 (viz., 1803 Mw7.8 Garhwal, 1991 Mw6.8 Uttrakashi and 1999 Mw6.5 Chamoli earthquakes) occurred within the MHT, which is depicted as a shallow north-dipping layer with low velocity. Our models show that these earthquakes occurred between 10 and 20 km depths where ε (∼0.011–0.012), ξ (∼0.386–0.392), and Vp/Vs (∼1.74–1.90) are all relatively high, indicating a greater possibility of aqueous/metamorphic fluids within the MHT than in the surrounding area. These fluids are suspected to be the trigger for earthquakes in the Uttarakhand Himalaya. As we drill deeper into the crust, we find that ‘ε’ decreases as a result of crack closure (≤0.011), while ‘ξ’ is predicted to increase (∼0.3–0.6) as a result of the presence of more wet and saturated cracks caused by the presence of partial melts (higher Vp/Vs: 1.74–1.92). Our modelling further verifies that the earthquakes in the Uttarakhand Himalaya are primarily driven by the existence of a highly conductive and weakened MHT with a greater concentration of metamorphic/aqueous fluid-filled cracks at depths ranging from 10 to 20 km. The ramifications of our research could significantly impact the earthquake hazard and risk in the Uttarakhand Himalayas.

The Effect of Recycled Sand on the Tensile Properties of Engineered Cementitious Composites

This research aims to investigate the feasibility of replacing natural sand (NS) with recycled sand (RS) to enhance the mechanical property of engineered cementitious composites (ECC). For a comparative study, ECCs incorporating natural sands (NS) and recycled sands with different sieve sizes were taken as experimental subjects. The results demonstrated that RS-ECC possessed better tensile properties featuring saturated cracks and superior strain-hardening behavior than that of NS-ECC. The highest tensile strain capacity of RS-ECC was up to 7%. Meanwhile, the compressive and flexural strengths of RS-ECC were over 50 and 20 MPa. The pseudo-strain-hardening (PSH) index of the RS-ECC-20 grid and RS-ECC-12 grid were 141 and 201, which increased by 46% and 70% than that of NS-ECC. Furthermore, the thicker weak ITZ and comparatively aggregate/ITZ ratio were found in the RE-ECC by a microstructure test, which revealed and explained the mechanism for the lower matrix fracture toughness of RS-ECC.

Frequency-dependent elastic wave propagation through anisotropic media induced by saturated cracks

Frequency-dependent elastic wave propagation through anisotropic media induced by saturated cracks

Thermoelastic Dispersion and Attenuation of P and SV Wave Scattering by Aligned Fluid‐Saturated Cracks of Finite Thickness in an Isothermal Elastic Medium

AbstractP and SV wave scattering by thermally constrained saturated cracks couples elastic deformation with temperature. We estimate the scattering attenuation and velocity dispersion by aligned fluid‐saturated cracks with finite thickness, which are sparsely and randomly embedded in an isothermal and isotropic elastic medium. By incorporating thermoelastic effects into the representation theorem with the non‐interaction Foldy approximation, we formulate the dispersion and attenuation of P and SV waves induced by displacement discontinuities across aligned cracks constrained by a thermoelastic boundary condition. The frequency‐dependent response as a function of temperature is calculated for various P and SV wave incidence angles. The resulting scattering attenuation and dispersion are compared with those of the conventional aligned‐crack model. The examples show that the dissipation increases with increasing temperature, but the scattering is inhibited at a given temperature. The P wave shows a strong sensitivity to temperature along the direction normal to the cracks, whereas the SV wave has an opposite behavior. This theory has the potential to assess the distribution of temperature from seismic attributes.

Analytical solution for two equal collinear modified strip saturated cracks in 2‐D semipermeable piezoelectric media

AbstractAn analytical solution and study is presented for two equal collinear cracks in 2‐D semipermeable piezoelectric media based on modified strip saturation models. The constant saturated condition defined in strip saturation model is modified here by considering the symmetric and polynomial varying saturation conditions. These proposed saturated conditions are multiplicative of saturated electric displacement value and polynomial (constant to cubic order) of a variable defined as ratio of distance of a point on saturated zone length to the extended half‐crack length. Moreover, these are interpolated on the basis of possible saturated values near the crack‐tips and zone tips. To present the analytical study, a problem of two cracks of equal length situated in series is considered in 2‐D arbitrary polarized infinite piezoelectric domain subjected to semipermeable crack‐face and electromechanical loading conditions. Applying the extended Stroh formalism and complex variable approach, these problems are mathematically modeled into non‐homogeneous Riemann Hilbert problems in terms of unknown complex functions representing stress and electric displacement components at any point within the domain. Using Muskhelishvili [1] and Collin's [2] mathematical techniques, these complex functions are obtained from the developed non‐homogeneous Riemann Hilbert problems. Hence, the explicit expressions for saturated zone lengths (inner and outer), crack opening potentials (COPs), crack opening displacements (CODs) and local stress intensity factors (LSIFs) are obtained. Further, the impact of polynomial varying saturated conditions is highlighted on these fracture parameters with respect to inter crack space distance, crack‐face conditions, polarization angle by presenting the numerical applications in infinite 2‐D PZT‐4 media.

Crack fluid identification of shale reservoir based on stress-dependent anisotropy

Shale reservoirs are typically very tight, and crack are only a small part of the reservoir. The directional arrangement of cracks leads to the anisotropic characteristics of shale, and the type of fluid filled in cracks affects the shale reservoir evaluation and late development. Many rock physics theories and methods typically use second- and fourth-order crack density tensors to characterize the elastic anisotropy induced by cracks as well as the normal-to-tangential crack compliance ratio to distinguish between dry and saturated cracks. This study defines an anisotropic crack fluid indicator for vertical transversely isotropy (VTI) media with vertical symmetry axis which is the integration of the normal-to-tangential crack compliance ratio in three directions. A new dimensionless fourth-order tensor, including crack fluid type, azimuth distribution, and geometric shape, is constructed by substituting the normal and tangential compliance into the fourth-order crack density tensor, which can also be used to identify the type of crack fluid in the VTI media. Using the Callovo-Oxfordian shale experimental data, the variation of the elastic properties of dry and saturated shale samples with axial stress is analyzed. The results demonstrate that the anisotropic crack fluid indicator of water-bearing shale samples is less than that of the dry shale samples and that the dimensionless fourth-order tensor of water-bearing shale samples is nearly one order of magnitude greater than that of the dry shale samples. Therefore, the anisotropic crack fluid indicator and dimensionless fourth-order tensor can reflect the crack fluid type in shale samples and can be used for shale reservoir prediction and fluid identification.

In-situ SEM study of crack initiation, propagation and interfacial debonding of Ni-P coating during tensile tests: Heat treatment effect

This study focuses on the effect of annealing temperature onto the mechanisms of crack initiation, propagation and interfacial debonding of the electroless nickel/phosphorus (Ni-P) coatings deposited on steel. An in-situ tensile test has been carried out in a SEM chamber for coated samples annealed at 400 and 600 °C, and at a strain rate of 0.1μm/s. It is observed that when an as deposited Ni-P on steel system is subjected to a uniaxial tensile test, a bended crack is formed on the surface of coating and leads to a debonding of coating at a small strain level. Incontrast, in case of an annealed sample, the N-iP coating shows a severe multiple parallel crackings due to the localized plastic deformation of the substrate. The crack density firstly increases with the rising tensile strain, and then reaches saturation. The spacing between the resulting saturated parallel cracks in the coating surface is defined in the shear lag model to quantify the interfacial shear strength. Despite the large plastic deformation of the substrate, there is no spallation observed at the interface between the two materials. The hardness and the young's modulus of the coating before and after heat treatment are determined by nano-indentation tests. The stiffness of the coatings increases owing to the Ni3P phase precipitation during heat teatment.

Time-dependent crack propagation in a poroelastic medium using a fully coupled hydromechanical displacement discontinuity method

Many problems in subsurface rocks which are naturally filled with saturated cracks and pores (with one or more fluid phases) are better understood in a poroelastic framework. Displacement discontinuity method (DDM) is particularly ideal for problems involving fractures and discontinuities. However, the DDM in its original form is limited to elastic problems. The paper derives fundamental solutions of a poroelastic DDM. Then introduces a numerical formulation and implementation for the poroelastic DDM in a code named constant element poroelastic DDM (CEP-DDM). The accuracy and validity of the proposed solution and the newly developed code is verified by an analytical solution at short-time and long-time. Numerical results showed good agreement with analytical results at short time (undrained response) and long time ( $$t=8000$$ s) (drained response). A crack propagation scheme for crack propagation problems is introduced and demonstrated in an example which enables the code to follow crack propagation in time and space.

Evaluating ion diffusivity of cracked cement paste using electrical impedance spectroscopy

Cracking can significantly accelerate mass transport in concrete and as such, impact its durability. This paper is aimed at quantifying the effect of saturated cracks on ion diffusion. Electrical conductivity, measured by electrical impedance spectroscopy (EIS), was used to characterize the diffusion coefficient of fiber-reinforced cement paste disks that contained one or two through-thickness cracks. Crack widths in the range 20–100 μm were generated by controlled indirect tension test. Crack profiles were digitized and quantified by image analysis to determine crack volume fraction and average crack width. Crack connectivity (e.g., inverse of tortuosity) was calculated from the conductivity results measured by EIS. The results suggest that the diffusion coefficient of cracked samples is strongly and linearly related to the crack volume fraction; but is not directly dependent on crack width. Crack tortuosity does reduce the ion diffusion through cracks, but its impact is not very significant. Overall, the most important parameter governing ion diffusion in saturated cracked concrete is the volume fraction of cracks. Theoretical justifications of these observations are also provided.

Giant strain-sensitivity of acoustic energy dissipation in solids containing dry and saturated cracks with wavy interfaces

Mechanisms of acoustic energy dissipation in heterogeneous solids attract much attention in view of their importance for material characterization, nondestructive testing, and geophysics. Due to the progress in measurement techniques in recent years, it has been revealed that rocks can demonstrate extremely high strain sensitivity of seismoacoustic loss. In particular, it has been found that strains of order 10-8 produced by lunar and solar tides are capable of causing variations in the seismoacoustic decrement on the order of several percent. Some laboratory data (although obtained for higher frequencies) also indicate the presence of very high dissipative nonlinearity. Conventionally discussed dissipation mechanisms (thermoelastic loss in dry solids, Biot and squirt-type loss in fluid-saturated ones) do not suffice to interpret such data. Here the dissipation at individual cracks is revised taking into account the influence of wavy asperities of their surfaces quite typical of real cracks, which can drastically change the values of the relaxation frequencies and can result in giant strain sensitivity of the dissipation without the necessity of assuming the presence of unrealistically thin (and, therefore, unrealistically soft) cracks. In particular, these mechanisms suggest interpretation for observations of pronounced amplitude modulation of seismo-acoustic waves by tidal strains.

Effectiveness of UHTCC to Retard Cover Expansive Cracking Due to Corrosion of Rebar in RC Structure

Ultra high toughness cementitious composite (UHTCC) shows a unique characteristic of limit the crack width with multiple fine cracks whether it is subjected to tensile load or bending load. The failure pattern of UHTCC exhibits saturated multiple fine cracks, so the durability of structures will be improved markedly by utilizing UHTCC partly or entirely instead of concrete. In this study, considering the tensile strain capacity of UHTCC, a formula for calculating the critical rebar corrosion ratio when the UHTCC cover cracking due to rebar corrosion through the theory of plasticity and cylindrical cavity expansion theory. The effectiveness of UHTCC for restraining the cover cracking due to rebar corrosion has been proved by a calculated example. The influences on critical rebar corrosion when the UHTCC cover cracking due to rebar corrosion have been analyzed. The analytical results showed that UHTCC could effectively retard the cover expansive cracking due to corrosion of reinforcing bars, and prolong the service life of concrete structures subjected to the environment being at risk of corrosion.

Flexural and Crack Behaviors of RC Beams Applied with UHTCC Cover Subjected to Rebar Corrosion

Ultra high toughness cementitious composite (UHTCC) is a newly developed, high performance, fiber-reinforced cementitious composite with substantial benefit in both high ductility and improved durability due to its tight crack width. The failure pattern of UHTCC exhibits saturated multiple fine cracks, so the durability of structures will be improved markedly by utilizing UHTCC partly or entirely instead of concrete. In this study, a total of 20 beams, including reinforced concrete beams that the cover zone was replaced by UHTCC (the thickness is 15mm, not containing reinforcement, and 50mm, containing reinforcement, respectively), reinforced concrete beams and reinforced UHTCC beams, had been manufactured. A power supply was used to accelerate the corrosion process of reinforcing bars, inducing different degrees of corrosion (the corrosion ratio was 1%, 2%, 4% and 5%) into reinforcing bars. The time of the cracks occurred and the crack width were recorded and the beams having different corrosion ratios of reinforcing bars were then tested under four-point bending for their load-deflection relations. The results showed that UHTCC could restrict the corrosion expansive crack of cover effectively, convert the crack pattern, and delay the appearance of first corrosion expansive crack, thereby to raise the service life of reinforcement concrete structures or components. Meanwhile, the bending test of beams after accelerated corrosion showed that the beams with a cover replaced by 50mm UHTCC and reinforced UHTCC having smaller amount of strength reduction and a reasonable ductile failure after corrosion. The experimental results showed that UHTCC could effectively delay the cover expansive cracking due to corrosion of reinforcing bars retain the ductile properties of reinforced concrete beams after reinforcing bar corroded.

Elements of poro-micromechanics applied to concrete

Linear elastic behavior of fluid saturated cement-based materials is first considered within a micromechanical framework. The damaging effect of saturated cracks is then examined for parallel cracks and for an isotropic distribution of the crack orientations. The principle of a theory of crack growth in saturated condition is also presented. The unsaturated conditions are briefly discussed. At last, these results are applied to the chemomechanical couplings induced by alkali-silica reaction in concrete.

A differential scheme for elastic properties of rocks with dry or saturated cracks

Differential effective medium (DEM) theory is applied to the problem of estimating physical properties of elastic media with penny-shaped cracks, filled either with air or liquid. These cracks are assumed to be randomly oriented. It is known that such a model captures many of the essential physical features of fluid-saturated or partially saturated rocks. By making the assumption that the changes in certain factors depending only on Poisson’s ratio do not strongly affect the results, it is possible to decouple the equations for bulk (K ) and shear (G) modulus, and then integrate them analytically. The validity of this assumption is then tested by integrating the full DEM equations numerically. The analytical and numerical curves for both K and G are in very good agreement over the whole porosity range of interest. Justification of the Poisson’s ratio approximation is also provided directly by the theory, which shows that, as porosity tends to 100%, Poisson’s ratio tends towards small positive values for dry, cracked porous media and tends to one-half for liquid saturated samples. A rigorous stable fixed point is obtained for Poisson’s ratio, c, of dry porous media, where the location of this fixed point depends only on the shape of the voids being added. Fixed points occur at c = 1/5 for spheres, and c ’ / 18 for cracks, being the aspect ratio of penny-shaped cracks. Results for the elastic constants are then compared and contrasted with results predicted by Gassmann’s equations and with results of Mavko and Jizba, for both granite-like and sandstone-like examples. Gassmann’s equations do not predict the observed liquid dependence of the shear modulus G at all. Mavko and Jizba predict the observed dependence of shear modulus on liquid bulk modulus for small crack porosity, but fail to predict the observed behavior at higher porosities. In contrast, the analytical approximations derived here give very satisfactory agreement in all cases for both K and G.

Multi-component wavefield simulation in viscous extensively dilatancy anisotropic media

A finite difference method for the simulation of multi-component wavefield in viscous extensively dilatancy anisotropic (EDA) media is presented. Transformation of the stress and strain relation from frequency domain to time domain reveals that the viscous effect in EDA media is embedded into the terms of the third derivatives of the strain with respect to time. Numerical examples for viscous EDA media with dry and saturated cracks are calculated, respectively. In the calculation of the wavefields, the absorbing boundary conditions are used to suppress the artificial boundary reflection, the grid dispersion is suppressed by flux corrective transformation (FCT) technique. Snapshots and seismic records show that the existence of cracks and the material contents in the cracks exhibits significant influences on the wave propagation, especially on the radiation pattern and attenuated factor.

An asperity-deformation model for effective pressure

Variations of the mechanical and transport properties of cracked and/or porous rocks under isotropic stress depend on both the confining pressure (Pc) and the pore-fluid pressure (Pp). To a first approximation, these rock properties are functions of the differential pressure, Pd = Pc − Pp; at least for low differential pressures. However, at higher differential pressures, the properties depend in a more complicated way upon the two pressures. The concept of effective pressure, Pe, is used to denote this variation and it is defined as Pe(Pc,Pp) = Pc − n(Pc,Pp)Pp. If n = 1 (and therefore, is independent of Pc and Pp), the effective pressure is just the differential pressure.We have used an asperity-deformation model and a force-balance equation to derive expressions for the effective pressure. We equate the total external force (in one direction), Fc, to the total force on the asperities, Fa, and the force of the fluid, Fp, acting in that same direction. The fluid force, Fp, acts only on the parts of the crack (or pore-volume) faces which are not in contact. Then, the asperity pressure, Pa, is the average force per unit area acting on the crack (or grain) contacts Pa = Fa/A=Fc/A−Fp/A= Pc − (1 −Ac/A)Pp, where A is the total area over which Fc acts and Ac is the area of contact of the crack asperities or the grains. Thus, the asperity pressure, Pa, is greater than the differential pressure, Pd, because Pp acts on a smaller area, A−Ac, than the total area, A. For elastic asperities, the area of contact Ac and the strain (e.g., crack and pore openings) remain the same, to a high degree of approximation, at constant asperity pressure. Therefore, transport properties such as permeability, resistivity, thermal conductivity, etc. are constant, to the same degree of approximation, at constant asperity pressure. For these properties, the asperity pressure is, very accurately, the effective pressure, Pc.Using this model, we find that the dynamic (undrained) elastic modulus (Mcr) of saturated cracks (rocks) at low effective pressure is given by Mcr = (1 − PpA′f)Ma + (1 − Af)Mf = −wdPc/dw, where Ma is the (dry-matrix or crack-) asperity modulus, Mf is the fluid's modulus, Af is the fractional area of contact (Af = Ac/A), A′f =dAf/dPa and w is a measure of the crack or pore openings. This simple model accounts for the dependence of the rock modulus (and elastic velocity) on: (1) the elastic properties of the fluid, (2) the elastic properties of the dry rock, and (3) the pore-fluid and confining pressures. Explicit expressions depend upon the choice of the asperity- (or grain-) deformation models and their contact distribution functions. The effective pressures for transport properties are different than the ‘effective pressure’ for the mechanical properties. Calculated results based on the ‘bed-of-nails’ model having power-law (or fractal) asperity-height distribution functions can be fitted quite well to experimental data with a minimum of fitting parameters.

Elastic anisotropy due to aligned cracks in porous rock1

AbstractAll theoretical expressions which relate the characteristics of saturated aligned cracks to the associated elastic anisotropy are restricted in some important way, for example to the case of stiff pore fluids, or of the absence of equant porosity, or of a moderately high frequency band. Because of these restrictions, previous theory is not suitable for application to the upper crust, where the pore fluid is brine (Kf≅ K820), the equant porosity is often substantial (φp > 0.1), and the frequency band is sonic to seismic. This work removes these particular restrictions, recognizing in the process an important mechanism of dispersion. A notable feature of these more general expressions is their insensitivity, at low frequency, to the aspect ratio of the cracks; only the crack density is critical. An important conclusion of this more general model is that many insights previously achieved, concerning the shear‐wave splitting due to vertical aligned saturated cracks, are sustained. However, conclusions on crack orientation or crack aspect ratio, which were derived from P‐wave data or from shear‐wave‘critical angles’, may need to be reconsidered. Further, the non‐linear coupling between pores and cracks, due to pressure equalization effects, means that the (linear) Schoenberg‐Muir calculus may not be applied to such systems. The theory receives strong support from recent data by Rathore et al. on artificial samples with controlled crack geometry.

The influence of dry and water saturated cracks on seismic velocities of crustal rocks — a comparison of experimental data with theoretical model: T. Popp & H. Kern, Surveys in Geophysics, 15(5), 1994, pp 443–465

The influence of dry and water saturated cracks on seismic velocities of crustal rocks — a comparison of experimental data with theoretical model: T. Popp & H. Kern, Surveys in Geophysics, 15(5), 1994, pp 443–465

The influence of dry and water saturated cracks on seismic velocities of crustal rocks - A comparison of experimental data with theoretical model

The pressure dependence of P- and S-wave velocities, velocity anisotropy, shear wave splitting and crack-porosity has been investigated in a number of samples from different crustal rock types for dry and wet (water saturated) conditions. At atmospheric pressure, P-wave velocities of the saturated, low-porosity rocks (< 1%) are significantly higher than in dry rocks, whereas the differences for S-wave velocities are less pronounced. The effect of intercrystalline fluids on seismic properties at increased pressure conditions is particularly reflected by the variation of the Poisson's ratio because P-wave velocities are more sensitive to fluids than S-wave velocities in the low-porosity rocks. Based on the experimental data, the respective crack-density parameter (e), which is a measure of the number of flat cracks per volume unit contained within the background medium (crack-free matrix), has been calculated for dry and saturated conditions. There is a good correlation between the calculated crack-densities and crack-porosities derived from the experimentally determined volumetric strain curves. The shear wave velocity data, along with the shear wave polarisation referred to a orthogonal reference system, have been used to derive the spatial orientation of effective oriented cracks within a foliated biotite gneiss. The experimental data are in reasonable agreement with the self consistent model of O'Connell and Budiansky (1974). Taking the various lithologies into account, it is clear from the present study, that combined seismic measurements ofVp andVs, using theVpVs-ratio, may give evidence for fluids on grain boundaries and, in addition, may provide an estimate on the in-situ crack-densities.

Seismic velocities in fractured rocks: an experimental verification of Hudson's theory1

AbstractFlow of fluids in many hydrocarbon reservoirs and aquifers is enhanced by the presence of cracks and fractures. These cracks could be detected by their effects on propagation of compressional and shear waves through the reservoir: several theories, including Hudson's, claim to predict the seismic effects of cracks. Although Hudson's theory has already been used to calculate crack densities from seismic surveys, the predictions of the theory have not yet been tested experimentally on rocks containing a known crack distribution. This paper describes an experimental verification of the theory. The rock used, Carrara marble, was chosen for its uniformity and low porosity, so that the effect of cracks would not be obscured by other influences. Cracks were induced by loading of laboratory specimens. Velocities of compressional and shear waves were measured by ultrasound at 0.85 MHz in dry and water‐saturated specimens at high and low effective pressures. The cracks were then counted in polished sections of the specimens. In ‘dry’ specimens with both dry and saturated cracks, Hudson's theory overpredicted observed crack densities by a constant amount that is attributed to the observed value being systematically underestimated. The theory made poor predictions for fully saturated specimens. Shear‐wave splitting, caused by anisotropy due to both crystal and crack alignment, was observed. Cracks were seen to follow grain boundaries rather than the direction of maximum compression due to loading. The results demonstrate that Hudson's theory may be used in some cases to determine crack and fracture densities from compressional‐ and shear‐wave velocity data.