Behavior Of Rocks Research Articles

A study of effects of different impact loads on the dynamic and elastoplastic behavior in reservoir rocks at the beginning of hydraulic fracturing

Successful hydraulic fracturing is very important in the development of hydrocarbon-bearing formations. The loading introduced by hydraulic fracturing causes deformation and failure, which are related to the damage accumulation and hydraulic fracture initiation process. This study employs a numerical model that considers the dynamic and elastoplastic behaviors in rocks under the influence of impact loads. The acceleration and wave propagation behaviors are quantified using the model. A time integration algorithm is used to ensure numerical accuracy and stability. The effects of loading rate, loading location, and heterogeneity are quantified. Results show that the elastoplastic and dynamic can effectively capture the wavy mechanical responses in the domain. Strain rate, acceleration, and plasticity can all exhibit oscillatory distribution patterns. Increasing the loading rate can magnify acceleration, strain rate, and the maximum plastic strain, while it reduces the range experiencing these induced changes. Changing the loading types and introducing the heterogeneity consideration both largely alter the mechanical response in the domain, and the waveforms of the mechanical parameters are significantly changed. Failure can occur earlier in layers with more elastic mechanical properties. Exerting 50 MPa loading in 0.01 ms can effectively introduce deformation and failures in the reservoir rock. Doubling the loading rate can effectively improve the ability of creating rock failures, which facilitates the following fracture initiation and propagation processes. This study can be a reference for the understanding of near-well and instantaneous rock mechanical behaviors at the beginning of fracturing.

Deep learning interprets failure process of coal reservoir during CO2-desorption by 3D reconstruction techniques

This work aims to investigate the failure and mechanical behaviors of coal rocks during CO2-desorption. The unconfined and confined compression experiments with certain depletion pressure-stress path and desorption of CO2 are conducted, in which the cracking process is captured by X-ray CT imaging. A deep learning-based coal fine-crack segmentation (CFCS) network with 3D reconstruction technique is proposed to study the cracking behaviors. In addition, the CO2 evolution effects on the failure process and mechanical responses are also analyzed. Results show that the proposed CFCS can effectively segment the crack-CO2-soid structure in coal with the errors all less than 10% at the range of 3.5620%–9.9967%. The failure process of coal samples can be divided into the extremely fast CO2-desorption + microcracks formation stage, fast CO2-desorption + stable microcracks propagation stage and slow stable CO2-desorption + microcracks coalescence to form macrocracks stage. The shear failures of coal samples are caused by the reduction of lateral effective stress due to CO2-desorption and drainage, which increases the anisotropy of coal samples with microcracking behaviors. The proposed method provides better understanding of failure mechanism and mechanical responses of coal reservoirs, which are helpful for the CO2 storage-based resource explorations.

Micro-scale wettability of carbonate rocks via high-resolution ESEM imaging

The wettability of several materials has been traditionally quantified using macro-scale contact angles. However, precise identification of the three-phase contact (TPC) line is often difficult due to the resolution limit of macro-scale setups. Moreover, micro-level surface chemical heterogeneities can have a notable impact on the predicted wetting behavior which limits macro-scale contact angles. Thus, here, we investigate the micro-scale water wettability of condensed micro-droplets on carbonate rock surfaces via a high-resolution Environmental Scanning Electron Microscopy (ESEM). Macro- and micro-scale contact angles were evaluated under three conditions: 1) natural carbonate surfaces, 2) surfaces aged in crude oil, and 3) surfaces aged in cationic surfactant to allow for a broader insight of the impact of rock composition and surface morphology on wettability.At the macro-scale, carbonate rocks were preferentially oil-wet to intermediate-wet. However, a profound variability was observed in wetting behavior at the micro-scale where a weakly water-wet state (50° ≥ θ ≥ 80°) was prevalent with evidence of minor oil-wet patches too. At the micro-scale, for the 100% dolomite sample, the contact angle (θ) varied from ∼66° to 76° under natural conditions, while the same sample aged in crude oil depicted a remarkable variability, i.e., θ ranged from 58° to 132° with the majority of micro-droplets having θ of ∼85° – thus suggesting a mixed-wet behavior. For the same sample aged in surfactant, θ was <5° at micro and macro-scales, with few micro-droplets having θ of ∼89°. However, the macro-scale θ values were 105° (natural) and 90° (oil-aged) – suggesting notable variability at macro- and micro-scales.These findings reflect: a) significant differences among macro- and micro-scale contact angles, and b) surface wetting at the micro-scale captures physical and chemical properties of the rock, i.e., surface roughness, pore size and distribution, and chemical composition. The study herein presents qualitative and semi-quantitative analyses of the non-uniform wetting behavior of carbonate rocks and the associated rock/fluid interactions through a multi-scale perspective and thus have broader implications for flow in porous medium.

Microseismic monitoring and experimental study on rockburst in water-rich area of tunnel

During the excavation of tunnels in the Hanjiang-to-Weihe River Diversion Project, many rockbursts occurred in water-rich (WR) areas. To study the mechanism of rockburst under such conditions, the features of microseismic events and rockbursts in WR tunnel sections excavated by both a tunnel boring machine (TBM) and “drilling and blasting” methods were statistically analysed and compared with those of adjacent water-poor (WP) areas. The results show that in both WR and WP areas, rockbursts are related to the classification of surrounding rock and are also affected by the excavation method. The rockbursts in most WP areas are more active than those in the nearby WR areas in sections excavated by TBM. However, the opposite is true under high in situ stress conditions. To explain the microseismic monitoring results, the mechanical behaviour of rock, including short- and long-term mechanical behaviour under different water and loading conditions, was also investigated, and the results show that under high stress conditions, water will accelerate the occurrence of rockburst. Therefore, the appropriate method to control rockburst is stress release, which can be achieved by advanced pilot tunnel excavation, hydraulic fracturing, and presplitting blasting, rather than high-pressure water spraying in the surrounding rock.

Effects of hole shape on mechanical behavior and fracturing mechanism of rock: Implications for instability of underground openings

Rock failure commonly initiates near the wall of openings with various geometries in underground excavation. In this study, to elucidate the hole-shape influences on the mechanical response and fracturing behavior on rock sample subjected to uniaxial compression, a thorough experimental–numerical-theoretical investigation is conducted on the intact and pre-holed rock samples with different hole shapes, including circular, elliptical, rectangular, and inverted-U shapes. Digital image correlation technology is employed to monitor the crack initiation and development around the hole during the loading process. The results show that the presence of different hole shapes leads to varying degrees of mechanical property deterioration in rock samples. The load capacity and stiffness of the tested samples follow the same order: intact sample > circular-holed sample > elliptical-holed sample > inverted-U holed sample > square-holed sample. Irrespective of the hole shape, the primary tensile crack initiates at the top and bottom of the hole, but its development is trapped. The growth and coalescence of shear cracks near the sidewalls eventually give rise to the sample failure. Stress analysis around the holes reveals a positive dependence of the reduction in load capacity on the maximum compressive stress concentration which is controlled by the shape of the hole. This indicates that the amplification of compressive stress induced by the hole governs the rock collapse. These findings offer valuable insights for the design and construction of underground engineering projects.

Qβ, Qc, Qi, Qs of the Gargano Promontory (Southern Italy)

We have provided the first estimate of scattering and intrinsic attenuation for the Gargano Promontory (Southern Italy) analyzing 190 local earthquakes with ML ranging from 1.0 to 2.8. To separate the intrinsic {Q}_{i} and scattering {Q}_{s} quality factors with the Wennerberg approach (1993), we have measured the direct S waves and coda quality factors ({Q}_{beta }, {Q}_{c}) in the same volume of crust. {Q}_{beta } parameter is derived with the coda normalization method (Aki 1980) and {Q}_{c} factor is derived with the coda envelope decay method (Sato 1977). We selected the coda envelope by performing an automatic picking procedure from {T}_{mathrm{start}}=1.5{T}_{S} up to 30 s after origin time (lapse time {T}_{L}). All the obtained quality factors clearly increase with frequency. The {Q}_{c} values correspond to those recently obtained for the area. The estimated {Q}_{i} are comparable to the {Q}_{c} at all frequencies and range between 100 and 1000. The {Q}_{s} parameter shows higher values than {Q}_{i}, except for 8 Hz, where the two estimates are closer. This implies a predominance of intrinsic attenuation over the scattering attenuation. Furthermore, the similarity between {Q}_{i} and {Q}_{c} allows us to interpret the high {Q}_{c} anomaly previously found in the northern Gargano Promontory up to a depth of 24 km, as a volume of crust characterized by very low seismic dumping produced by conversion of seismic energy into heat. Moreover, most of the earthquake foci fall in high {Q}_{i} areas, indicating lower level of anelastic dumping and a brittle behavior of rocks.

Dynamic mode II fracture mechanism of rocks using a novel double-edge notched flattened Brazilian disc specimen in the split Hopkinson pressure bar tests

The dynamic mode I fracture behaviors of rocks have been extensively investigated during recent decades, while the dynamic mode II fracture mechanism of rocks and its comparison with dynamic mode I fracture are poorly understood. In this study, a novel double-edge notched flattened Brazilian disc (DNFBD) specimen is introduced for dynamic mode II fracture toughness tests of rocks in the split Hopkinson pressure bar (SHPB) tests. First, using the finite element method (FEM), the stress distribution of the DNFBD specimen is analyzed and the stress intensity factors (SIFs) and the T-stress at the crack tips are determined. Then, dynamic mode II fracture tests are conducted on sandstone using the DNFBD specimen with proper specimen geometry configuration. High-speed photography and digital image correlation (DIC) results show that the shear crack initiates from the notch tips and propagates along the shear ligament of the DNFBD specimen, which demonstrates the reliability of the DNFBD-SHPB method for dynamic mode II fracture tests of rocks. Experimental results show that the dynamic mode II fracture toughness KIIC of rocks generally increases with increasing loading rate, exhibiting significant loading-rate dependence. For comparative investigation, dynamic mode I fracture tests using the notched semi-circular bend (NSCB) specimen are conducted on the same rocks. The results indicate that the mode II fracture toughness KIIC values are always higher than the mode I fracture toughness KIC values of rocks over a wide range of loading rates. The microscopic fracture mechanism of sandstone is interpreted based on the thin section observations. Under quasi-static loading, trans-granular (TG) fractures are more popular in the mode II fracture tests, while inter-granular (IG) fractures dominate the failure of mode I fracture. However, with the increase of loading rate, TG fracture becomes increasingly prevalent in both the dynamic mode II fracture and the dynamic mode I fracture of rocks. The results of this study are of great significance for understanding the dynamic mode II fracture mechanism of rocks.

Characterization and experimental study of volcanic rocks in fluidized beds with a beam-down solar reflector for CSP applications

This work experimentally studied the thermal behavior of volcanic rocks in a lab-scale bubbling fluidized bed with concentrated irradiation from the top. Following an exhaustive review of natural particles that can be radiated and fluidized, volcanic particles are considered a suitable material thanks to their origin (from crystallization upon solidification from temperatures close to 1200 °C), and their ease of volatilization. In the search for natural materials, this work tested two volcanic sands (red and black pozzolana volcanic sand), comparing their results with other solid particles tested previously under similar experimental conditions. This comparison yielded ratios of thermal energy stored versus pumping power of the fluidizing air between 34% and 58% higher than other typical solid particles used for this purpose, such as sand or Silicon carbide (SiC). These two volcanic rocks were also experimentally tested over 10 cycles of charging/discharging without apparent deterioration of their thermal properties, as the thermal response in each cycle was practically the same with a maximum variation of 7% in the mean temperature.

Water-Weakening and Time-Dependent Deformation of Organic-Rich Chalks

The Ghareb Formation is a shallowly buried porous chalk in southern Israel that is being considered as a host rock for a geologic nuclear waste repository. Setup and operation of a repository will induce significant mechanical, hydrological and chemical perturbations in the Ghareb. Developing a secure repository requires careful characterization of the rock behavior to different loads. To characterize hydromechanical behavior of the Ghareb, several short- and long-term deformation experiments were conducted. Hydrostatic loading tests were conducted both dry and water-saturated, using different setups to measure elastic properties, time-dependent behavior, and permeability. A set of triaxial tests were conducted to measure the elastic properties and rock strength under differential loading at dry and water-saturated conditions. The hydrostatic tests showed the Ghareb began to deform inelastically around 12–15 MPa, a relatively low effective pressure. Long-term permeability measurements demonstrated that permeability declined with increasing effective pressure and was permanently reduced by ~ 1 order of magnitude after unloading pressure. Triaxial tests showed that water saturation significantly degrades the rock properties of the Ghareb, indicating water-weakening is a significant risk during repository operation. Time-dependent deformation is observed during hold periods of both the hydrostatic and triaxial tests, with deformation being primarily visco-plastic. The rate of deformation and permeability loss is strongly controlled by the effective pressure as well. Additionally, during holds of both hydrostatic and triaxial tests, it is observed that when water-saturated, radial strain surpassed axial strain when above effective pressures of 13–20 MPa. Thus, deformation anisotropy may occur in situ during operations even if the stress conditions are hydrostatic when above this pressure range.

Modelling the creep behaviour and induced failure of clay rock from microscale viscosity to large-scale time-dependant gallery convergences using a multiscale numerical approach

The large-scale creep behaviour of Callovo-Oxfordian (COx) clay rock is modelled from small-scale viscous mechanisms of the rock using a multiscale numerical approach in the context of radioactive waste repositories. At the mesoscale, the saturated non-homogeneous rock is represented in digital 2D Representative Elementary Areas (REAs) as a cracked composite material consisting of rigid elastic mineral inclusions (quartz, calcite, and pyrite) embedded in a clay matrix. The modelling of these materials is considered within double-scale finite element framework, in which the homogenised responses of the REA to the enforced global kinematics serve as a numerical constitutive relation at the macroscale. To reproduce the rock creeping, two viscous mechanisms have been introduced to consider the creep of the clay matrix: either the viscoplasticity of the clay aggregates or the viscoelasticity of their contacts, or both. Firstly, laboratory biaxial creep tests of clay rock samples are simulated. A three-stage creep stage is reproduced and the creep failure process is discussed. Then, large-scale underground engineering structures are modelled to reproduce its time-dependent behaviour. It is found that the developed multiscale model is able to provide some valuable insights into the large-scale creep behaviour of clay rocks through the morphological and material small-scale characterization of REA.

Thermo-Hydro-Chemo-Mechanical (THCM) Continuum Modeling of Subsurface Rocks: A Focus on Thermodynamics-Based Constitutive Models

Abstract Accurate multiphysics modeling is necessary to simulate and predict the long-term behavior of subsurface porous rocks. Despite decades of modeling subsurface multiphysics processes in porous rocks, there are still considerable uncertainties and challenges remaining partly because of the way the constitutive equations describing such processes are derived (thermodynamically or phenomenologically) and treated (continuum or discrete) regardless of the way they are solved (e.g., finite element or finite volume methods). We review here continuum multiphysics models covering aspects of poromechanics, chemo-poromechanics, thermo-poromechanics, and thermo-chemo-poromechanics. We focus on models that are derived based on thermodynamics to signify the importance of such a basis and discuss the limitations of the phenomenological models and how thermodynamics-based modeling can overcome such limitations. The review highlights that the experimental determination of thermodynamics response coefficients (coupling or constitutive coefficients) and field applicability of the developed thermodynamics models are significant research gaps to be addressed. Verification and validation of the constitutive models, preferably through physical experiments, is yet to be comprehensively realized which is further discussed in this review. The review also shows the versatility of the multiphysics models to address issues from shale gas production to CO2 sequestration and energy storage and highlights the need for inclusion of thermodynamically consistent damage mechanics, coupling of chemical and mechanical damage, and two-phase fluid flow in multiphysics models.

Rate- and Normal Stress-Dependent Mechanical Behavior of Rock Under Direct Shear Loading Based on a Bonded-Particle Model (BPM)

Rate- and Normal Stress-Dependent Mechanical Behavior of Rock Under Direct Shear Loading Based on a Bonded-Particle Model (BPM)

Scaling Mechanism and Permeability Evolution of Sandstone Reservoir

Knowledge of scaling mechanisms and the permeable behavior of rocks is highly important for geothermal energy development. In this study, the sandstone was soaked in a solution with the same chemical composition as geothermal water in Linyi City, Shandong Province. Permeability tests, scanning electron microscope tests, and nuclear magnetic resonance tests were performed on sandstone samples after different soak times (0, 30, 60, and 90 days) and temperatures (25 and 85 °C) to characterize the changes in microstructure and permeability properties. In addition, the changes in ion concentration in chemical solutions were compared. The results show that the wet mass and porosity of sandstone increase with the increase of soak time (0-70 d), and then entered the stable periods (70-90 d). As the soaking time, the medium and large pores inside the sandstone are transformed into small pores. The permeability of sandstone shows an overall decreasing trend, with the maximum decline when the soaking time is 30 d. At 25 °C, the scaling behavior is mainly involved by Ca2+, but at 85 °C Mg2+ is also involved in the scaling behavior. The scaling mechanism becomes the joint participation of Ca2+ and Mg2+. The results of the PHREEQC simulations are almost the same as the laboratory test results, indicating that sodium feldspar, potassium feldspar, and chlorite are generated slowly during the fouling process.

HORIZONTAL ACCELERATION OF FLOOR-MOUNTED NONSTRUCTURAL COMPONENTS UNDER ROCKING MOTION

Floor-mounted nonstructural components (NSCs) that are attached through various types of angles are susceptible to seismic damage as they experience severe rocking motion resulting from their slender geometric configuration. However, current design codes do not reflect such complex dynamic behavior and prescribe design factors based on simplified single-degree-of-freedom (SDOF) models, which might cause an under-estimation of seismic design forces. Therefore, to properly control their seismic damage, the complex rocking dynamic behavior needs to be thoroughly investigated. This paper analyzed the rocking behavior of the floor-mounted NSCs and their effects on the horizontal acceleration response. Floor-mounted NSCs and their mounting attachments were idealized as rigid blocks restrained by linear vertical springs at the corner of the block. The nonlinear equations for the rocking behavior of rigid block were developed, and the analysis was conducted based on the fourth-order Runge-Kutta integration method. First, it is shown that the resonance period of rocking NSCs is mainly affected by the NSC slenderness and the location of the center of gravity of the component. The horizontal acceleration tends to increase as the slenderness and the height of the center of gravity of NSCs increase. Based on the observations, some useful design recommendations were suggested for designing attachments of floor-mounted NSCs.

Experimental and Numerical Investigation on the Behavior of a New Replaceable Steel Device Used in Self-Centering Prefabricated Shear Wall

An experimental and numerical investigation on the behavior of a new replaceable steel device (RSD), is presented in this paper. The RSD consists of a steel pipe with two circular steel plates that close the ends of the tube, four stiffeners, and an added damping and stiffness (ADAS)-type steel plate that functions as a fuse element. This RSD is characterized by its compressive strength, which is much higher than its tensile strength and is compatible with the rocking behavior of a self-centering prefabricated shear wall (SCPSW), and also by its ability to dissipate energy. Three-dimensional finite element analyses were carried out to investigate the behavior and performance of the RSD, both individually and in the case where they were installed at the bottom of the toe and heel of a SCPSW. The results show that the RSD has stable behavior and is compatible with the gap opening in the corner of the SCPSW. The combined specimen of SCPSW and RSD (SCPSWR) remains stable under cyclic loading, with a maximum drift ratio of 3.98%, demonstrating that the RSD could be a viable candidate for practical use in seismic-prone areas. The behavior of the RSD was assessed by conducting two sets of cyclic tests, which provided good agreement with the numerical results. The results indicate that the RSD’s performance is influenced by the plastic behavior of the fuse element, plastic buckling of the disks, and pipe deformation. If the RSD is damaged, it can be easily replaced, because fabrication and installation of the proposed RSD is easy and cost-effective.

Numerical Modelling Strategies for Column Rocking Behavior in Traditional Timber Structures

ABSTRACT As a typical feature of traditional Chinese timber structures, columns with floating foot joints are prone to rocking under horizontal force. The column rocking behavior plays an important role in resisting lateral loads. This paper proposes modelling strategies for the rocking behavior of traditional timber columns. The proposed model can capture the contact state of the column foot via a series of distributed axial springs and the possible sliding via a horizontal spring. It has a lower computational cost than refined finite element (FE) models and is independent of numerical calibration compared to rotational spring models. The modelling strategies were validated against refined FE models and experimental data available in the literature. The principle behavior of the approach was carefully investigated including contact stiffness, distribution modes, spring numbers, column bending effects, and computational efficiency. Results show that the effective compression height of the column foot can take the value of the column radius to determine spring stiffness. Column bending needs to be considered in the mechanical analysis of column foot joints for slender columns. The case study on the lateral stiffness of traditional timber frames confirms the applicability of the proposed model in the structural analysis of ancient timber buildings.

Research on crack evolution law and mechanical analysis of three cracked rock masses subjected to compression load

Rocks containing various types of cracks may undergo microcrack expansion and connection under compressive load, which leads to rock fracture under different loading conditions, posing a significant threat to the stability of underground tunneling. Therefore, studying the mechanical response of rocks with different types of cracks is of great importance for controlling the stability of underground mining projects. In this study, we conducted compression tests on three cracked rock samples with different crack types, using an electro-hydraulic servo universal testing machine. We investigated the effect of crack dip angle on the compressive strength, stress–strain curve, and failure pattern of the three cracked rocks, and examined the fracture morphology of the specimens using an industrial camera and the digital image correlation (DIC) technique. To verify the test results, we constructed a parallel bond model in the discrete element method PFC2D to describe the compression process, and compared the peak strength, damage results, and crack number curves. We also investigated the effect of in-situ stress on the mechanical characteristics of the rock by applying in-situ stress values based on the successful PFC2D model. Our research findings revealed that the weakening effect of cracks parallel to the loading direction on the strength of rock is smaller than that of cracks perpendicular to the loading direction. During the compression process, stress concentration phenomena appear first at the crack tip, and the specimen eventually undergoes tensile splitting-type damage. Furthermore, the compressive strength of the three cracked rock samples tends to increase first and then decrease with the application of in-situ stress. These results provide valuable insights into the behavior of cracked rocks and can be utilized to improve the stability of underground mining projects.

Experimental study of real-time temperature-dependent nonlinear deformation of sandstone

In contrast to thermal heating, the real-time heated rock exhibits significant nonlinearity during the elastic deformation stage. Hence, an experiment assembled by a high and low-temperature test chamber and a microcomputer-controlled rock direct shear instrument is built to evaluate the effect of real-time temperature on the nonlinear deformation behavior of rock. A set of nonlinear stress–strain relationships of forty sandstone samples under moderate real-time temperature conditions are obtained from experiments and agree well with the theoretical predictions from the two-part Hooke’s model (TPHM). The soft and hard parts respond to the real-time temperature are quite different. The ratio of the soft part (γt) increases and the elastic modulus of the hard part (Ee) decreases with the temperature below 125℃. On the contrary, γt decreases and Ee increases with the temperature above 125℃ up to 200℃. Thermally-induced and expandable microcracks (thermal weakening) incur structural damage of the hard part below 125℃, while thermal expansion (thermal strengthening) can lead to tighter compaction between grains above 125℃. Therefore, there is a threshold temperature 125℃ under real-time heating condition due to the thermal cracks and expansion. The elastic modulus of the soft part (Et) decreases continuously with increasing temperature, indicating inconsistent thermal expansion effects on the soft part with mixture of impurity particles and the hard part whose mineral particles are closely contacted at higher temperature. Based on the experimental data and TPHM, empirical relationships between the real-time temperature and nonlinear deformation are proposed. This study will provide support for the safe production and disaster prevention of geological engineering under thermo-mechanical coupling working condition.

Comparative verification of hydro-mechanical fracture behavior: Task G of international research project DECOVALEX–2023

Numerical simulations become a necessity when experimental approaches cannot cover the required physical and time scale of interest. One of such area is a simulation of long-term host rock behaviors for nuclear waste disposal and simulation tools involved in the assessment must go through rigorous validation tests. The DECOVALEX project (Development of COupled models and their VAlidation against EXperiments) is dedicated to this purpose by international participants.aawww.decovalex.org. This work is part of the ongoing phase DECOVALEX–2023 (D–2023, Task G) particularly aiming to simulate fracture behaviors under various conditions. Here, we cross-verified a variety of numerical methods including continuous and discontinuous approaches against four benchmark exercises with emphasis on numerical accuracy and parameterization of the various numerical approaches. The systematic inter-comparisons of test cases highlight advantages and disadvantages of the different numerical models. Numerical details on discretization effects (e.g. mesh density and orientation) and domain size were investigated in detail for practical applications. It became evident that meticulous attention to mesh resolution and domain size is imperative for achieving accurate numerical simulations, even for static cracks. Moreover, when comparing numerical methods to closed-form solutions for static cracks, all models successfully reproduced the maximum crack opening but encountered challenges near the crack tips. Finally, the paper discusses how to convert between and therefore compare parameters of various numerical approaches. Our benchmark studies reveal that each model necessitates a distinct number of parameters, even in simple scenarios like static crack aperture benchmarks. It is generally more practical to employ fewer parameters to mitigate model over-parameterization and enhance experimental feasibility.

Anisotropic mechanical behavior of ultra-deep shale under high in-situ stress, a case study in the Luzhou block of the southern Sichuan Basin, China

The safe and efficient development of ultra-deep shale gas deeper than 4500 m is closely related to the comprehensive evaluation of the mechanical behavior, brittleness and anisotropy characteristics of reservoir rocks under in-situ stress conditions. However, the above-mentioned information about ultra-deep shale is rarely reported. This study aims to fill this gap by systematically investigating the mechanical and anisotropic characteristics of cores, with 0° and 90° bedding orientations, from different layers in the vertical depth of 4900–4930 m, under confining pressure of 110 MPa. Furthermore, a new brittleness index with three parts related to brittle failure, i.e., the energy storage performance in the pre-peak stage, the performance of elastic energy used to maintain the post-peak failure, and the severity of the energy released during the post-peak stage, all of which are physically meaningful, was proposed. Subsequently, the index was validated and applied to the brittleness evaluation of ultra-deep reservoir rocks. The brittleness was evaluated in the following descending order: black shale of Longmaxi Formation ＞ gray-black shale of Wufeng Formation ＞ limestone of Baota Formation. Overall, the Wufeng- Longmaxi Formation shale still exhibits brittle failure under such high confining pressure, while the Baota Formation limestone exhibits quasi-ductile failure, which is consistent with the phenomenological behavior of cores. Further, various experimental techniques have been employed to study the brittle and quasi-ductile failure mechanisms of reservoir rocks. The anisotropy evaluation results show that the anisotropy degree of the mechanical and brittleness parameters corresponding to the deep formation is significantly lower than that of the shallow formation. The anisotropy degree of strength and deformation parameters (Young's modulus, Poisson's ratio) is closely related to the content of quartz and clay minerals, respectively. The above results are expected to provide data support and theoretical guidance for the development of deep and ultra-deep shale gas in the southern Sichuan region of China.