Rock Stiffness Research Articles

Numerical Assessment of the Structural Damage of a Composite Lining Water Conveyance Tunnel Subjected to Reverse Fault Conditions

In this paper, the structural responses and failure characteristics of a new type of water conveyance tunnel lining structure subjected to reverse fault conditions were numerically investigated by considering multiple loads and interaction separation modes between different structural layers. This study proposes a new evaluation standard for the safety level of the damage state of the composite lining water conveyance tunnel. It also discusses the influences of fault dislocation displacement (Δf), dip angle (β), and the mechanical properties of the surrounding rock in the fault fracture zone on the water conveyance tunnel response and damage. The results indicate that the buckling failure of the steel tube under axial compression is the dominant failure mode of the composite lining structure. With increasing fault dislocation displacement, the axial compressive strain and circumferential shear strain of the composite lining are most severely damaged on the sliding plane. With decreasing fault dip angle, the axial compressive strain of the composite lining weakens, while the bending and shear strains increase. The increase in rock stiffness in the fault fracture zone reduces the damage scope but increases the composite lining structural damage severity. Overall, the numerical results of this study provide a better understanding of the failure mode and damage process of composite lining water conveyance tunnels under reverse fault conditions; therefore, this study can serve as a reference for composite lining structure disaster assessments.

Investigating the destressing mechanism of roof deep-hole blasting for mitigating rock bursts in underground coal mines

Rock burst is one of the challenging problems restricting the safe and high-efficiency mining of deep-buried coal seams, and roof deep-hole blasting (RDHB) is commonly practiced in highly burst-prone zones in coal mines to control rock bursts. This research focuses on the interpretation of the destressing mechanisms of RDHB and its application for mitigating rock bursts. The theoretical analysis results show that RDHB reduces the local stress and stiffness of roof rock, thereby reducing the potential of coal failure and changing the energy release mode of the roof-coal-floor system. Then, a strain-softening numerical model based on the Hoek-Brown failure criterion was developed to evaluate the destressing efficiency of RDHB in selected underground coal mines. Further, RDHB was applied to an isolated coal pillar in a coal mine for mitigating rock bursts, and the stress variation of the isolated coal pillar before and after RDHB was detected using active seismic velocity tomography. The results illustrate that RDHB can effectively reduce stress concentration in the target area and drive stress to the surrounding areas. Moreover, due to the high correlation between in situ measurement results and numerical results, the numerical evaluation of RDHB efficiency may be successfully applied to regular use. Finally, a method for evaluating the destressing effect of RDHB based on blasting seismic energy was discussed and applied.

3D numerical prediction of thermal weakening effects on granite

AbstractThis paper presents a numerical method to predict the temperature weakening effects on tensile and compressive strength and stiffness of granitic rock. Thermally induced cracking, leading to degradation of the material stiffness and strength, is modelled in the continuum sense by using a damage‐viscoplasticity model based on the Drucker‐Prager criterion with a rounded tensile cut‐off surface. The governing thermo‐mechanical initial/boundary value problem is solved with an explicit (in time) staggered method while using extreme mass scaling to increase the critical time step. Rock heterogeneity is described as random clusters of finite elements assigned with the constituent mineral, here Quartz, Feldspar, and Biotite, material properties further randomized by Weibull distribution. In the present approach, only Quartz thermal expansion coefficient is assumed temperature dependent due to its strong and anomalous temperature dependence upon approaching the α‐β transition. In the numerical testing, the sample is first volumetrically heated to a target temperature. Then, the uniaxial tension and compression tests are performed on the cooled down numerical samples. The simulations demonstrate the validity of the proposed approach as the experimental weakening effects on the rock strength and stiffness as well as the macroscopic failure modes, both in tension and compression, are realistically predicted in a non‐circular way, that is, not using the temperature dependence of any material parameter, save Quartz thermal expansion, as an input data.

Effect of Confining Pressure on Mechanical and Energy Conversion Properties of Gas-Containing Coal under Loads

Confining pressure is closely related to the deformation and failure characteristics of gas-containing coal and is one of the key factors for gas outburst-rockburst coupled dynamic disaster. Firstly, this paper briefly summarized the triaxial compression test results of gas-containing coal under different confining pressures, including deformation and stiffness and failure and strength. Then, based on the second developed MatDEM gas-solid coupling program, the macro- and microdeformation and failure process of coal samples under different confining pressures and constant gas pressure were simulated, and the distribution of particle stress, pore stress, and crack, as well as energy conversion characteristics, was obtained. Finally, the influence mechanism of confining pressure on deformation and failure of gas-containing coal was discussed, and the occurrence conditions of coal and gas outburst, rockburst, and their coupled dynamic disasters were distinguished. The results show that the peak strength and residual strength after failure of gas-containing coal both increase approximately linearly with the increase of confining pressure, while the elastic modulus does not change much or increases continuously, which is closely related to the number of microdefects in the coal sample. The strengthening effect of confining pressure on rock stiffness and strength mainly comes from external support and compaction. The total number of cracks decreases with the increase of confining pressure, while the number of shear cracks increases, and the inclination angle between the formed macroscopic main crack and the horizontal plane gradually decreases. The maximum cumulative elastic energy and residual elastic energy both increase with the increase of confining pressure, which leads to the increase of the impact tendency index of coal samples.

Effects of fracture-surface geometries on the third-order acoustoelastic constants for aligned fluid-saturated fractures

SUMMARYThe pressure sensitivity of stiffness in fractured rocks is closely related to fracture-surface geometries. The resulting stress-dependence of stiffness can be represented by the third-order elastic constants (3oECs). Fracture surfaces are generally rough at various scales, and can significantly affect the 3oECs of pre-stressed fractures as well as the wave-induced fluid flow (WIFF) induced by the Biot slow P-wave between fractures and the background medium. The WIFF usually depends on the fracture width relative to the slow P-wavelength and the fracture-surface roughness. We generate various fracture-surface geometries at different scales of random roughnesses parametrized by the surface standard deviation (SSD) of fracture-surface heights. With theoretical analyses and numerical simulations, we investigate the effect of fracture-surface geometries on the stress- and frequency-dependent stiffness through the 3oECs for pre-stressed rocks with aligned fractures. For the elastic wave in the low-frequency regime of Biot theory with the fracture scale much less than the wavelength, the induced WIFF significantly enhances the effect of fracture-surface geometries on the 3oECs and P- and S-wave moduli. The stiffness of fractured rocks increases with increasing SSDs, yielding a high sensitivity to pre-stresses. Toward the high-frequency limit, however, the fluid diffusion between fractures and the porous background decreases, which reduces the influence of fracture-surface roughnesses with the 3oECs much less than that in the low-frequency regime. The resulting P-wave modulus of aligned fluid-saturated fractures approximates to the background value.

Anisotropic Mechanical Behavior of Stratified Sandstone Subjected to Cyclic Loading

Abstract To explore the influence of bedding structure on mechanical properties and failure mechanism of anisotropic rocks, six stratified sandstone specimens with different bedding orientations were tested by uniaxial static and cyclic loading. Acoustic emission (AE) and digital image correlation (DIC) were exploited to analyze the mechanism of crack initiation and propagation. The results show that with the increase of the bedding orientation, the peak strength of the stratified sandstone decreases first and then increases, behaving an obvious anisotropic characteristic. The AE characteristic-stress-strain curve can be divided into four stages: crack closure stage, linear elastic deformation stage, stable crack growth stage, and unstable crack growth stage. Moreover, as the bedding orientation increases from 30° to 90°, the crack closure stage gradually lengthens, while the linear elastic deformation stage first shortens and then lengthens. Under uniaxial static compression, due to the presence of bedding surface, the rock surface has a relative slip trend as a result of the uneven distribution of strain on the left and right parts, and the strain field boundary is almost consistent with the bedding orientation. Furthermore, cyclic loading can increase the rock stiffness, and the stain field boundary of 60° stratified sandstone sample in each cycle is slightly different in the cyclic loading.

Effect of freeze–thaw and wetting–drying cycles on the CBR, shear strength, stiffness and permanent deformation of crushed waste rocks

Waste rocks produced from mining operations are widely reused for the construction of mine haul roads. However, seasonal changes expose mining facilities to repeated freeze–thaw and wetting–drying cycles which can significantly affect the geotechnical characteristics of the materials in situ. In this study, cyclic and monotonic triaxial and California bearing ratio (CBR) tests were conducted to measure the geotechnical properties of crushed waste rocks subjected to freeze–thaw and wetting–drying cycles. Results showed that freeze–thaw cycles caused a reduction of the resilient modulus and shear strength, and an increase of the permanent deformation. A greater water content during freeze–thaw cycles resulted in a significant increase of the permanent deformation. Wetting–drying cycles could contribute to increase the stiffness, CBR and permanent deformation of crushed waste rocks. Predictive models were also developed to estimate the effect of freeze–thaw cycles on resilient modulus and permanent deformation.

Impact of HCl Acidizing Treatment on Mechanical Integrity of Carbonaceous Shale.

Hydrocarbon production from unconventional resources especially shale reservoirs has tremendously increased during the past decade. Eagle Ford shale formation is one of the major sources of oil and gas in United States. However, due to extremely low permeability of this formation, stimulation treatments are implemented for hydrocarbon production. Eagle Ford shale requires a very high breakdown pressure during fracturing treatment due to high mechanical strength and low permeability. This study aims to address these challenges through applying the acidizing treatment on the shale and studying its impact. A detailed experimental investigation was carried out in this work to evaluate mechanical integrity and mineralogical and morphological changes of the shale formation when exposed to HCl acidizing treatment. Two crucial aspects of acidizing treatment, that is, impact of acid concentrations and treatment time, were given additional focus in this study. Different parameters such as porosity, nanopermeability, uniaxial compressive strength (UCS), acoustic velocities, dynamic elastic parameters, rock surface hardness (RSH) and brittleness index (BI) were analyzed before and after the acidizing treatment for different HCl concentrations. Microimaging was done through scanning electron microscopy (SEM) and whole cores were scanned using medical computed tomography (MCT) to understand the small-scale features. X-ray diffraction was used for the minerals’ identification. A continuous profile of UCS was measured through the scratch test system. Post-treatment results revealed that HCl treatment has a profound impact on rock mechanical properties of Eagle Ford shale. Considerable mass loss in core plugs was recorded after treatment at each concentration. Mineralogical composition and microimaging revealed compositional changes and porosity enhancement after the treatment. Reaction rate is higher in the first 10 min for higher acid concentrations resulting in significant changes in properties in that time interval. UCS and RSH exhibited a progressive decrease with increasing concentrations. The rate of RSH reduction increased with the increase in acid concentration nonlinearly. Acoustic velocities exhibited a considerable decrease even at low acid concentrations due to the enhancement of pore spaces. Noticeable reduction was observed in dynamic rock stiffness and BI with the increase in acid concentrations. On the contrary, Poisson’s ratio showed a significant increment. Experimental findings of this research can be used to optimize the acidizing treatment for Eagle Ford shale and other similar formations. Formation breakdown pressure can be reduced significantly by applying the acid treatment to improve the production of hydrocarbons. Furthermore, a better understanding of matrix acidizing can lead to savings in time and resources during production operations.

Induced-seismicity geomechanics for controlled CO2 storage in the North Sea (IGCCS)

The aim of the current study, IGCCS (2017–2020), is to evaluate the feasibility of micro-seismic (MS) monitoring of CO2 injection into representative storage candidates in the North Sea, based on broad and quantitative characterization of relevant subsurface behavior with respect to geology, geomechanics and seismicity. For this purpose, we first group potential CO2 storage sites in the North Sea into three different depths. Then, advanced triaxial rock mechanical tests are performed together with acoustic emission (AE) acquisition under representative loading for CO2 storage sites in the North Sea and for formations of each depth group, covering shale, mudstone and sandstone cores. Our work focuses particularly on quantifying the effects of injected fluid type and temperature on mechanical behavior and associated MS response of subsurface sediments. The experiment results show that each depth group may behave differently in responses to CO2 injection. Particularly, the occurrence of detectable MS events is expected to increase with depth, as the combined effects of rock stiffness and temperature contrast between the host rock and injected CO2 are increasing. In addition, lithology plays an important role in terms of the MS response, i.e. high AE event rate is observed in sandstones, while aseismicity in shale and mudstone. The test results are then scaled up and applied to advanced coupled flow-geomechanics simulations and a synthetic field-scale MS data study to understand micro-seismicity at fracture, reservoir and regional scales. The numerical simulation of scCO2 injection scenario shows quite different stress-strain changes compared to brine injection, resulting mainly from the thermally-induced behavior. Furthermore, the numerical simulation study via so-called Cohesion Zone Modeling (CZM) approach shows strong potential to improve our understanding of the multiphase-flow-driven fracture propagation. Our synthetic MS data study, focused on slow-earthquake scenario, also suggests that sensors with high sensitivity at low frequency might be necessary for better signal detection and characterization during CO2 injection. This manuscript covers the main findings and insights obtained during the whole study of IGCCS, and refers to relevant publications for more details.

Numerical evaluation of Failure Assessment Diagram (FAD) for hydraulic fracture propagation in sandstone

This paper evaluates the degree of inelasticity in hydraulic fracture propagation in weak sandstone by using models obtained by the Discrete Element Method as a basis for quantifying Failure Assessment Diagram (FAD) and J-integral. Although current engineering models use Linear Elastic Fracture Mechanics (LEFM), including improvements like fracture tip damage zone where fracture tip plasticity is small enough to fit into the near-field stress zone, this paper hypothesizes that hydraulic fracture propagates in an inelastic regime in certain conditions typically for underground rock reservoirs. Discrepancies within field or laboratory data, including microcrack clouds identified as acoustic emissions that induce plastic deformations, motivate the investigation of inelasticity and implementation of elastoplastic fracture propagation theories. Discrete Element Method (DEM) has been widely used to approach rock failure problems from the micromechanical level, where explicit modeling of local particle-bond breakage enables insights into propagating fracture branching, damage, microcrack coalescence, stress–strain re-distribution, irreversible deformation, and fracture arrest. Results show that inelastic J-integral increases dramatically with rock confinement, especially its non-elastic portion, and the elastic portion of the total J-integral remains a relatively small part. Higher confinement stresses and higher confinement stress contrast enhance the inelastic fracture propagation. Additionally, shorter fracture lengths and smaller dry tip zones characterize inelasticity. Rock stiffness increase leads to total J-integral increase and decrease of J-elastic, leading to pronounced inelasticity. Therefore, results indicate that LEFM is rarely applicable for describing fracture propagation through rock at higher confinement stresses and stiffness.

Cyclic triaxial test investigation on tuffs with different water content at Badantoru Hydropower Station in Indonesia

The weakening effect of water in rocks has been extensively investigated over the past few decades. The degradation of the strength and stiffness of rocks can vary greatly with rock type. To investigate the water-weakening effect on the mechanical properties and failure modes of a Hydropower station's bedrock, static and cyclic triaxial compressive tests were carried out on dry, natural, and saturated tuffs (from the Badantoru Hydropower Station in Indonesia) under different confining pressures. Analysis of the failure modes, stress-strain curves, and brittleness index revealed that all of the samples exhibited typical brittle fracture behavior, i.e., a stress drop, volumetric dilation, and no compaction bands. The decreases in the peak stress, residual stress, and elastic modulus with increasing water content verify the water-weakening effect. The correlations between the water content and the confining pressure and other characteristic parameters calculated using the Pearson correlation coefficient indicate that the peak stress and elastic modulus are negatively correlated with the water content, and the peak stress, peak strain, and elastic modulus are positively correlated with the confining pressure. Compared with the Mohr-Coulomb criterion, the Hoek-Brown criterion can better describe the failure behavior of tuffs. Two damage variables, DE and Dε, were defined based on the hysteretic energy and residual strain. Both can characterize the damage evolution and failure mechanism, and DE can describe the stages of the damage evolution in more detail.

Mechanical Properties of Soft Rocks Subjected to Water‐Rock Reaction and Cyclic Pressure

Studying the mechanical properties of soft rocks subjected to water and cyclic loading would contribute to a better understanding of the stability analysis of soft rock engineering under the conditions of storm and carrier dynamics. In this paper, two soft rocks from Southwest China (i.e., muddy siltstone and silty mudstone) were selected as test samples. Uniaxial compressive tests were applied to investigate the strength and deformation characteristics under water‐rock reactions. Meanwhile, triaxial tests were carried out to analyse the fatigue damage and failure characteristics by applying cyclic axial loading under different confining pressures. The results indicated a reduction in the uniaxial compressive strength (UCS) under saturated conditions, which is correlated with the disintegration resistance of soft rocks. Moreover, the samples exhibited a softening phenomenon due to water absorption and rock expansion, decreasing the elastic modulus. The triaxial tests demonstrated that axial strain accumulated with the number of loading cycles due to fatigue and even failed when applying increased cyclic loading with certain cycles. The cohesion decreased during cyclic loading, but the friction angle was relatively independent of the number of cycles. In addition, reductions in the dynamic elastic modulus and shear modulus decreased with increasing loading time. This study indicated that water and cyclic loadings could cause significant degradation of the strength and stiffness of soft rocks, which need to be considered carefully during the engineering utilization of such materials.

Research on Control Method of the Power System of Stepping-Type Anchoring Equipment.

To improve the roadway adaptability and control accuracy of anchoring equipment, a stepping anchoring device was designed. A permanent-magnet synchronous motor control and a harmonic suppression algorithm were integrated to optimize the dynamic control system of stepping-type anchoring equipment. The results of an experimental simulation and analysis showed that when the coefficient of coal rock hardness f = 5, 6, and 7, the pulsation coefficient of the hydraulic pump outlet pressure, hydraulic motor output speed, and pump-controlled hydraulic cylinder advance speed in the hydraulic circuit of a pump-controlled motor did not exceed 3% after the equipment based on sliding mode control (SMC) entered the steady state, while the maximum pulsation coefficient was only 32.5% of the PI control. Based on the SMC, the harmonic components of the permanent magnet synchronous motor in the power system were suppressed and compensated for. This enhanced the stiffness of the hydraulic system under motor drive. When the rock stiffness factor gradually changed from f = 5 to f = 8 and increased suddenly from f = 5 to f = 6, the pressure overshoot at the outlet of the hydraulic pump of the pump-controlled motor system was reduced from 11.19% to 7.97% and from 61.19% to 52.88%, respectively, compared with that before the optimization. It was thereby proven that SMC based on harmonic suppression can effectively reduce the system pulsation caused by the multi-factor coupling of anchoring equipment and provide technical support for the optimal control of the power system of stepping-type anchoring equipment.

The Role of Tuffs in Sealing Volcanic Conduits

AbstractAcid‐sulphate alteration commonly changes the physicochemical properties of volcanic conduits. Although several conduit pressurization models suggest hydrothermal sealing, little experimental evidence exists from conduit‐filling rocks on the development of such a seal. Here we show that acid‐sulphate alteration affects conduit‐filling lavas and tuffs differently, with implications for their role in sealing the conduit. In lavas, alteration creates fluid pathways and decreases rock stiffness by dissolving primary minerals. In contrast, in the inherently porous tuffs, alteration reduces fluid pathways and increases rock stiffness by precipitating secondary minerals. Compaction of tuffs under subsurface pressures together with such alteration‐related sealing can form low porosity and low permeability zones within the conduit. Such zones could promote fluid‐pressure build‐up and predispose the volcano to explosive eruptions. We discuss our results in the context of observed seismicity and ground deformation and suggest using our elastic properties data to constrain geophysical inversions of acid‐sulphate altered volcanic conduits.

The influence of the rigidity of mining security structures on the stability of side rocks in the coal-rock massif

The object of research is the processes of controlling the state of side rocks to prevent the collapse of the stratified rock strata in the coal-rock massif containing the workings. The studies carried out made it possible to establish the influence of the rigidity of the guard structures of mine workings on the stability of side rocks in the coal-rock massif. It is proved that as a result of the action of an external compressive load on the supporting lateral rocks, the structure, in the form of a model of bunches made of wooden posts, increases its rigidity until the destruction of the security structure. After that, there is an increase in the convergence of side rocks and their destruction. The change in the stiffness of the crushed rock in the filling massif model, which is used to support the lateral rocks, occurs as a result of the compaction of the original material. This is due to repackaging of crushed rock fractions of different sizes and its additional grinding. As a result of this interaction of the side rocks with the filling massif, the integrity of the roof and soil is ensured and convergence is limited. To assess the stability of side rocks, it is proposed to use a dimensionless stress concentration factor k. This coefficient takes into account the rigidity of the guard structures of the mine workings and the flexural rigidity of the side rocks. It was found that when the values of the coefficient k are close to zero (k→0), there is a loss of stability of the guard structures of mine workings and the destruction of side rocks in the coal-rock massif. The preservation of the integrity of the side rocks and the stability of security structures is ensured at values of k>0.1, which corresponds to the parameters of the pliable supporting structures. Most favorably on the condition of side rocks in the coal-rock massif is influenced by the method of backing up the mined-out space of crushed rock. The use of this method excludes the collapse of side rocks. When solving the problem of stability of mine workings at the stage of making technical decisions, it is necessary to predetermine the issues of rigidity of security structures with deformation characteristics of side rocks.

Stress rotation – impact and interaction of rock stiffness and faults

Abstract. It has been assumed that the orientation of the maximum horizontal compressive stress (SHmax) in the upper crust is governed on a regional scale by the same forces that drive plate motion. However, several regions are identified where stress orientation deviates from the expected orientation due to plate boundary forces (first-order stress sources), or the plate wide pattern. In some of these regions, a gradual rotation of the SHmax orientation has been observed. Several second- and third-order stress sources have been identified in the past, which may explain stress rotation in the upper crust. For example, lateral heterogeneities in the crust, such as density and petrophysical properties, and discontinuities, such as faults, are identified as potential candidates to cause lateral stress rotations. To investigate several of these candidates, generic geomechanical numerical models are set up with up to five different units, oriented by an angle of 60∘ to the direction of shortening. These units have variable (elastic) material properties, such as Young's modulus, Poisson's ratio and density. In addition, the units can be separated by contact surfaces that allow them to slide along these vertical faults, depending on a chosen coefficient of friction. The model results indicate that a density contrast or the variation of Poisson's ratio alone hardly rotates the horizontal stress (≦17∘). Conversely, a contrast of Young's modulus allows significant stress rotations of up to 78∘, even beyond the vicinity of the material transition (>10 km). Stress rotation clearly decreases for the same stiffness contrast, when the units are separated by low-friction discontinuities (only 19∘ in contrast to 78∘). Low-friction discontinuities in homogeneous models do not change the stress pattern at all away from the fault (>10 km); the stress pattern is nearly identical to a model without any active faults. This indicates that material contrasts are capable of producing significant stress rotation for larger areas in the crust. Active faults that separate such material contrasts have the opposite effect – they tend to compensate for stress rotations.

Stress rotation – impact and interaction of rock stiffness and faults

Abstract. It has been assumed that the orientation of the maximum horizontal compressive stress ( SHmax ) in the upper crust is governed on a regional scale by the same forces that drive plate motion. However, several regions are identified where stress orientation deviates from the expected orientation due to plate boundary forces (first-order stress sources), or the plate wide pattern. In some of these regions, a gradual rotation of the SHmax orientation has been observed. Several second- and third-order stress sources have been identified in the past, which may explain stress rotation in the upper crust. For example, lateral heterogeneities in the crust, such as density and petrophysical properties, and discontinuities, such as faults, are identified as potential candidates to cause lateral stress rotations. To investigate several of these candidates, generic geomechanical numerical models are set up with up to five different units, oriented by an angle of 60 ∘ to the direction of shortening. These units have variable (elastic) material properties, such as Young's modulus, Poisson's ratio and density. In addition, the units can be separated by contact surfaces that allow them to slide along these vertical faults, depending on a chosen coefficient of friction. The model results indicate that a density contrast or the variation of Poisson's ratio alone hardly rotates the horizontal stress ( ≦17 ∘ ). Conversely, a contrast of Young's modulus allows significant stress rotations of up to 78 ∘ , even beyond the vicinity of the material transition ( >10 km ). Stress rotation clearly decreases for the same stiffness contrast, when the units are separated by low-friction discontinuities (only 19 ∘ in contrast to 78 ∘ ). Low-friction discontinuities in homogeneous models do not change the stress pattern at all away from the fault ( >10 km ); the stress pattern is nearly identical to a model without any active faults. This indicates that material contrasts are capable of producing significant stress rotation for larger areas in the crust. Active faults that separate such material contrasts have the opposite effect – they tend to compensate for stress rotations.

Roughness Effects of Crack Surfaces on the Elastic Moduli of Cracked Rocks

Crack surfaces are usually rough on various scales, and are sensitive to loading stresses and hence significantly affecting the mechanical properties of cracked rocks. We design a number of dry- and fluid-saturated numerical cracked samples to investigate the roughness influence of crack surfaces on the elastic stiffness. The fracture surface roughness is characterized by non-uniform fracture radii. We calculate the elastic moduli of cracked samples by finite-element simulation. Comparisons with the theoretical predictions by Gassmann and C&S (Ciz and Shapiro) (Ciz and Shapiro, Geophysics, 2007, 72(6), A75–A79) substitution equations demonstrate that the rough crack surfaces for both dry- and fluid-saturated samples can induce a stress concentration around the crack that reduces the elastic moduli and decreases the stiffness of rocks. For the fluid/solid-saturated cracks under the normal (shear) loading stresses, because the stress-concentration can induce shear (normal) strains around fracture, shear (bulk) modulus of the filling material will have contributions to the effective bulk (shear) modulus of rocks. The extra contribution, however, makes the Gassmann equation and C&S equation invalid.

Effect of cyclic wetting\u2013drying on tensile mechanical behavior and microstructure of clay-bearing sandstone

The understanding of the weakening mechanism of tensile strength of rock subjected to cyclic wetting-drying is critical for rock engineering. Tensile strength tests were conducted on a total of 35 sandstone specimens with different wetting-drying cycles. The crack propagation process and acoustic emission characteristics of the tested samples were obtained through a high-speed camera and acoustic emission system. The results indicate that the tensile strength is observably reduced after cyclic wetting-drying, and the extent of the reduction is not only related to the number of wetting-drying cycle, but also closely related to the clay mineral content of the sample. In addition, as the cycles of wetting-drying increase, the effect of each single cycle on tensile strength get reduced until it becomes constant. Moreover, the crack initiation and penetration time is prolonged as the number of wetting-drying cycle increases, which indicates that cyclic wetting-drying weakens the rock stiffness and enhances the ductility of sandstone. Meanwhile, the acoustic emission characteristics of the tested samples further confirmed the ductile behaviour of the sandstone samples with increasing wetting-drying cycle. Furthermore, through the analysis of the microstructure and mineral composition of the samples with different wetting-drying cycles, it is concluded that the main weakening mechanisms of sandstones containing clay minerals are frictional reduction, chemical and corrosive deterioration.

Diagenetic Trends of Synthetic Reservoir Sandstone Properties Assessed by Digital Rock Physics

Quantifying interactions and dependencies among geometric, hydraulic and mechanical properties of reservoir sandstones is of particular importance for the exploration and utilisation of the geological subsurface and can be assessed by synthetic sandstones comprising the microstructural complexity of natural rocks. In the present study, three highly resolved samples of the Fontainebleau, Berea and Bentheim sandstones are generated by means of a process-based approach, which combines the gravity-driven deposition of irregularly shaped grains and their diagenetic cementation by three different schemes. The resulting evolution in porosity, permeability and rock stiffness is examined and compared to the respective micro-computer tomographic (micro-CT) scans. The grain contact-preferential scheme implies a progressive clogging of small throats and consequently produces considerably less connected and stiffer samples than the two other schemes. By contrast, uniform quartz overgrowth continuously alters the pore space and leads to the lowest elastic properties. The proposed stress-dependent cementation scheme combines both approaches of contact-cement and quartz overgrowth, resulting in granulometric, hydraulic and elastic properties equivalent to those of the respective micro-CT scans, where bulk moduli slightly deviate by 0.8%, 4.9% and 2.5% for the Fontainebleau, Berea and Bentheim sandstone, respectively. The synthetic samples can be further altered to examine the impact of mineral dissolution or precipitation as well as fracturing on various petrophysical correlations, which is of particular relevance for numerous aspects of a sustainable subsurface utilisation.