Deviatoric Stress Levels Research Articles

Experimental study on characterization of resilient modulus and prediction model of saline aeolian sand

The dynamic resilience characteristics of aeolian sand subgrade are influenced by salt content and water content, exhibiting significant stress dependence and anisotropy. The resilient modulus(MR) of aeolian sand represents the stress-strain nonlinearity under cyclic loading, serving as an important parameter for the design of aeolian sand subgrade in desert areas. In order to investigate the variation of MR of aeolian sand subgrade with salt content and water content under traffic loading, as well as the MR characteristics under these conditions, three types of aeolian sand samples with varying water content and four sulphate contents were prepared. The variation of MR of aeolian sand under different confining pressures and deviator stress levels, as well as the influences of water content and salt content, was studied through indoor dynamic triaxial testing. Based on the pattern of the fitting parameters of the benchmark model, a prediction model suitable for the MR of aeolian sand was constructed. The results indicate a rise in aeolian sand's MR with increasing deviator stress and confining pressure, with confining pressure having a more significant impact than deviator stress. With the increase in water content, the MR of aeolian sand decreases nonlinearly, and with the increase in salt content, it exhibits a wave-shaped trend of "increasing-decreasing-increasing," which is related to the dissolution state of sodium sulfate in the soil. Based on the experimental results, a prediction model of the MR of aeolian sand was established, derived from the benchmark model, which can reflect the influence of salt content and water content on the MR, introducing them as variables within the model.

Fouling conditions and associated deformation characteristics of railway ballast

ABSTRACT Ballast is an essential component of the railway track substructure to facilitate load distribution and drainage. However, during service life, ballast loses its strength by reducing friction properties and gets fouled, which fails to perform as desired. Therefore, highly fouled ballast needs to be either cleaned or replaced to restore the expected load-bearing capacity, resiliency, track geometry, and drainage properties. Therefore, it is important to identify the intensity of ballast fouling and the characteristics of fouling materials along with their effect on the strength and deformation of the railway ballast. In this study, field investigation includes a collection of ballast samples from the live railway track of Bangladesh, and related tests are conducted. Based on the findings of the field identification, ballast samples on a scale of 1/5th are prepared in the laboratory with desired gradation and material properties to replicate the field samples. Compaction tests and a series of consolidated drained cyclic triaxial tests are conducted to identify the strength and deformation characteristics of the fouled ballast, considering the effect of water content. Based on the fouling index, four out of six samples are highly fouled, and the fouling materials contain both plastic and non-plastic properties. Triaxial test results indicate that consistency of the fouling material, degree of saturation, and deviator stress level significantly affect the strength and deformation characteristics of the fouled railway ballast. Fouling materials containing plastic properties increases the risk to the stability of the railway track in the presence of moisture.

An improved creep model for unsaturated reticulated red clay

Establishment of a creep model is an important method to analyze the relationship between soil creep deformation and time, and the element model is widely used for studying soil creep. However, the element creep model is employed for fitting saturated soil, and the mechanical element model is generally linear, which cannot well fit the nonlinear deformation of the soil with time in practice. The creep process of the soil is not only time-dependent, but also related to the deviatoric stress level. Therefore, the fractional calculus theory and a parameter n reflecting the effect of deviatoric stress level on the creep properties of the soil were introduced into the element model, and the fractional qBurgers creep model was established by using the fractional Koeller dashpot and Caputo fractional calculus. The proposed model was used to fit the triaxial test data of reticulated red clay under different net confining pressures and matric suctions by unsaturated triaxial apparatus. The proposed model can well describe the nonlinearity of unsaturated reticulated red clay, has memory and global correlation to the creep development process of unsaturated reticulated red clay, and has clear physical meaning. The functional relationships of the model parameters with the matric suction, net confining pressure and deviatoric stress level were deduced, so that the creep curves of unsaturated reticulated red clay can be obtained for any conditions, which is of great value for the study of unsaturated soils.

Using the shakedown theory to study the cyclic behaviour of an unreinforced and fibre-reinforced stabilized soft soil

ABSTRACT When a material is subjected to cyclic loading, there are changes in the material’s geomechanical behaviour that need to be characterized for a safe design. For unbounded granular materials, the shakedown theory is used to explain the soil’s behaviour under cyclic loading. However, it is not clear yet if such theory is extendable to unreinforced and fibre-reinforced stabilized soils. To this end, a series of unconfined compression cycling loading tests were performed, to study the effect of the number of cycles and initial deviatoric stress level on the behaviour of an unreinforced and reinforced stabilized soil. The results were analysed in terms of shakedown theory, elastic and plastic deformation energy and damping ratio. It was observed that shakedown theory seems to represent the behaviour of the stabilized unreinforced and fibre-reinforced soils under cyclic loading, with threshold between the plastic shakedown and the plastic creep shakedown behaviour at around an absolute axial strain 1 × 10–3. The effect of increasing binder content (from 12 to 39%), comparable to reducing the initial deviatoric stress level (from 85 to 15%), promoted a reduction in plastic deformation (from 2.09 to 0.19% without fibres, and 2.21 to 0.24% with fibres) and damping ratio (from 25.17 to 10.01% without fibres, and 29.18 to 15.95% with fibres) due to the lower degradation of the solid matrix. It also promoted an increase in the difference between elastic and plastic energy (from − 1.04 to 13.92 kJ/m3 without fibres, and − 1.68 to 10.19 kJ/m3 for the first cycle).

Creep behavior of sandstone under the coupling action of stress and pore water pressure using three-dimensional digital image correlation

Understanding the damage evolution and time-dependent property of rock creep is of great significance for predicting geohazards and evaluating the long-term stability of geotechnical structures. In this study, a three-dimensional digital image correlation system was adopted to investigate the creep behavior of sandstone under the coupling action of stress and pore water pressure. The apparent strain fields, deformation characteristics of the localization zone, and micromorphology of the fracture surface were analyzed. The results demonstrated that when the applied deviatoric stress level was above σci (crack initial stress) or σcd (crack damage stress), the increase in pore water pressure promoted creep deformation evidently, improved the creep rate significantly and shortened the time-to-failure of the rock obviously. In the radial strain field, the localized development of substantial microcracks on the rock surface was concentrated in the steady-state creep, while the microcracks interconnected to form macroscopic shear cracks that dominated the accelerating creep, and this damage evolution characteristic can be used as a precursor and early warning of rock creep failure. Besides, increasing the pore water pressure also would cause the divergence point of strain curves inside and outside the localization zone to appear earlier at the secondary creep, and produce a wider localization zone at the tertiary creep. The creep fracture surface of the rock was dominated by intergranular microcracks. Increasing the pore water pressure would result in the deterioration of the cemented structure and breakage of the cemented matrix more seriously, thus stimulating the generation of more microcracks.

Experimental study on strain accumulation characteristics of saturated remolded loess under pure rotation of the principal stress axis

The study conducted a pure rotation test of 720° for saturated remolded Q2 loess under principal stress axis (PSA) rotation when deviatoric stress and the intermediate principal stress ratio are different, also paying attention to examining the changes of strain accumulation and pore pressure of such loess. According to the test, as the PSA rotates continuously, the pore water pressure exhibited by saturated remolded loess presents a normal cyclic accumulation elevation, and under the same deviatoric stress conditions, the pore water pressure accumulation trend of different principal stress ratios is the same; however, the magnitude is different. The increment of pore water pressure becomes smaller as the number of cycles increases. When the deviatoric stress level is low, the material hardening is in a cyclic stable state, the strain component remains stable with the continuous rotation of the PSA, and the strain path area is reduced, together with a stable final size. In case of higher deviatoric stress, the material strength cycle becomes weaker and the strain component accumulates slowly as the PSA (the spiral line of the strain path) continuously rotates in the γzθ−(ϵz−ϵθ) plane, and gradually expands until failure. The increased intermediate principal stress is accompanied by accelerated strain development speed and advanced failure.

Probabilistic Evaluation of Geomechanical Risks in CO2 Storage: An Exploration of Caprock Integrity Metrics Using a Multilaminate Model

The probabilistic uncertainty assessment of geomechanical risk—specifically, caprock failure—attributable to CO2 injection, as presented in a simplified hypothetical geological model, was the focus of this study. Our approach amalgamates the implementation of a multilaminate model, the creation of a response surface model in conjunction with the Box–Behnken sampling design, the execution of associated numerical modeling experiments, and the utilization of Monte Carlo simulations. Probability distributions to encapsulate the inherent variability (elastic and mechanical properties of the caprock and reservoir) and uncertainty in prediction estimates (vertical displacement, total strain, and F value) were employed. Our findings reveal that the Young modulus of the caprock is a key factor controlling equivalent total strain but is insufficient as a stand-alone indicator of caprock integrity. It is confirmed that the caprock can accommodate significant deformation without failure, if it possesses a low Young’s modulus and high mechanical strength properties, such as the friction angle and uniaxial compressive strength. Similarly, vertical displacement was found to be an unreliable indicator for caprock integrity, as caprock failure can occur across a broad spectrum of vertical displacements, particularly when both the Young modulus and mechanical strength properties have wide ranges. This study introduces the F value as the most dependable indicator for caprock failure, although it is a theoretical attribute (the shortest distance between the Mohr circle and the nearest failure envelope used to measure the sensitivity to failure) and not physically measurable in the field. Deviatoric stress levels were found to vary based on stress regimes, with the maximum levels observed under extensive and compressive stress regimes. In conjunction with the use of the response surface method, this study demonstrates the efficacy of the multilaminate framework and the Mohr–Coulomb constitutive model in providing a simplified, yet effective, probabilistic model of the mechanical behavior of caprock failure, reducing mathematical and computational complexities.

Study on the Strength and Failure Characteristics of Silty Mudstone Using Different Unloading Paths.

To investigate the strength and failure characteristics of silty mudstone using different stress paths, silt-like mudstone specimens were subjected to triaxial unloading tests. The results indicate the following. (1) When subjected to equivalent initial deviator stress levels and differing confining pressures, the peak stress, residual stress, and elastic modulus, exhibited during unloading, increased concordantly with greater initial confining pressure. Both the peak strain and residual strain increased with rising initial confining pressure. The increase in peak strain and residual strain initially decelerated, then noticeably increased, before ultimately decreasing again. Additionally, the unloading failure time and strain rate demonstrated a negative correlation as the confining pressure increased. (2) Under different initial deviatoric stress conditions, the peak stress, residual stress, and residual strain, under unloading confining pressure conditions, decreased as the initial deviatoric stress levels elevated. Conversely, the peak strain and elastic modulus initially increased, then decreased under increasing initial deviatoric stress conditions. The unloading failure time and strain rate were both observed to decrease as the initial deviatoric stress levels increased. (3) Utilizing the Mohr stress circle enabled the characterization of the shear strength variation in the specimens during the unloading process. The cohesion and internal friction angle remained relatively consistent across the different unloading stress paths appraised, with cohesion being greater in path I versus path II, whereas the internal friction angle exhibited an inverse relationship. (4) The specimen failed during unloading due to lateral expansion caused by unloading confining pressure and collapse failure. The failure fracture surfaces predominantly manifested shear failure morphologies.

Sediment buoyancy controls the effective slab pull force and deviatoric stress along trenches: Insights from 3D free-subduction model

In the complicated force equilibrium of subduction dynamics, the slab pull resulting from the negative buoyancy of the lithosphere is considered the primary driving force of plate tectonics. In contrast, the isostatic restoring force due to lighter materials covering the oceanic crust (e.g., sediment) has been recognized as a relatively minor contributor. However, as the restoring force counteracts the gravitational pull, the resultant interaction has the potential to control the force balance governing the subduction system. Here, we conducted a series of three-dimensional viscoelastic-free subduction simulations with varying sediment distributions, thicknesses, and densities. We found that a higher restoring force suppressed the trench retreat and decreased the trench velocity. The trench curvatures increased with a high differential restoring force along the trench strike over time. Our results consistently showed a negative correlation between the effective slab pull and the isostatic restoring forces. Moreover, the magnitude and distribution of the isostatic restoring force along the trench strike determined the deviatoric stress level and location of the stress concentration within the subducting slab. We also found that locally abundant sediment margins may lead to a high deviatoric stress in the trench, which is associated with the occurrence of large earthquakes. We argue that sediment buoyancy can significantly affect the subduction kinematics and dynamics to a greater degree than previously suggested. Our findings provide fresh insights into the development of a global predicted velocity model, that reflects the effect of the isostatic restoring force, and provides a better understanding of subduction earthquakes.

Experimental study on the static and dynamic elastic stiffness of rock samples from a shale oil reservoir

Shale reservoirs play essential roles in numerous geoengineering applications, including storing CO2 and radioactive waste and producing hydrocarbons. To fulfill these applications, the mechanical properties of shale are of great interest so that people can locate shales with preferred sealing or frackable characteristics. One can estimate the static stiffness related to the rock deformation from the dynamic stiffness derived from the wave velocity through some empirical correlations. However, a gap exists between dynamic and static stiffness in sedimentary rocks. Anisotropy further complicates the prediction of the static stiffness from the dynamic stiffness of shale. This paper investigates the link and contrast between the dynamic and static stiffness and the effects of anisotropy by performing triaxial tests on two shale samples cored in the vertical and horizontal directions from a shale oil reservoir in China. We analyze the effects of stress (strain) rate, stress (strain) amplitude, and the base level of deviatoric stress. The secant Young’s modulus is found to decrease with the increasing stress rate or stress amplitude. By introducing the nonlinear elastic theory, Young’s modulus can be expressed as a linear function of axial strain, where the slope is related to the stress sensitivity of the static stiffness, and the intercept is associated with the elastic property at the infinitesimal strain. The slopes and intercepts of linear functions are negatively correlated. Furthermore, six linear fittings from the two samples in the three tests are found to link with the strain amplitude, the base stress level, and anisotropy. This study provides insights into the prediction of static stiffness from dynamic one. With proper models of dynamic-static transition, seismic or wireline logging measurements can assist in solving engineering issues. People can better ensure the quality of the geomechanical model and reduce the cost of various engineering applications.

Experimental study on the deformation behaviour, energy evolution law and failure mechanism of tectonic coal subjected to cyclic loads

Compared to intact coal, tectonic coal exhibits unique characteristics. The deformation behaviours under cyclic loading with different confining pressures and loading rates are monitored by MTS815 test system, and the mechanical and energy properties are analysed using experimental data. The results show that the stress–strain curve could be divided into four stages in a single cycle. The elastic strain and elastic energy density increase linearly with deviatoric stress and are proportional to the confining pressure and loading rate; irreversible strain and dissipated energy density increase exponentially with deviatoric stress, inversely proportional to the confining pressure and loading rate. The internal structure of tectonic coal is divided into three types, all of which are damaged under different deviatoric stress levels, thereby explaining the segmentation phenomenon of stress–strain curve of tectonic coal in the cyclic loading process. Tectonic coal exhibits nonlinear energy storage characteristics, which verifies why the tectonic coal is prone to coal and gas outburst from the principle of energy dissipation. In addition, the damage mechanism of tectonic coal is described from the point of energy distribution by introducing the concepts of crushing energy and friction energy.

Effects of time-dependent deformation of shale on the integrity of a geological nuclear waste repository

Safety assessment of geological nuclear waste repositories is essential for the permanent disposal of spent nuclear fuels and high-level radioactive waste. The long-term integrity of the host rock as well as the engineered barrier system (e.g., bentonite buffer) surrounding nuclear waste canisters is of particular importance as decay heat from nuclear waste canisters, which will last over thousands of years, significantly disturbs the thermo-hydromechanical (THM) state of the repository. In this study, THM coupled simulations were carried out to investigate the effect of time-dependent deformation (i.e., creep) of shale on the long-term integrity of a generic subsurface nuclear waste repository. The Norton-Bailey creep model, which is also known as the Lemaitre-Menzel-Schreiner model, was employed to simulate the power-law type creep that is observed in shales. The TOUGH-FLAC simulator was employed for the THM coupled modeling of the repository. The objective of this study is to assess the effect of creep in different shales (i.e., high creep shale vs. low creep shale) on long-term stress and permeability changes in the repository. Results show potential advantages of constructing repositories in the high creep shale, as deviatoric stress levels in the formation decreased to zero in 100 years since the emplacement of nuclear waste canisters and the permeability also decreased to the undamaged, intrinsic levels in 10,000 years. Also, mean effective stress levels in the bentonite buffer increased by 100% in the high creep shale case relative to the low creep shale case at 10,000 years due to creep-induced contraction of the nuclear waste disposal tunnel. However, in earlier periods (e.g., 1000 years), the stress levels in the bentonite buffer were twice smaller in the high creep shale case than in the low creep shale case, which shows a tradeoff between the intermediate- (∼1000 years) and long-term (>10,000 years) compaction levels in the bentonite buffer depending on the creep characteristics of the host shale.

Experimental Investigation of Nonlinear Energy Evolution and Failure Characteristics of Granite under Different Water Content States

To study the energy evolution law and failure characteristics of granite under different water content states, a series of compression failure tests of dry, natural, and saturated granite samples under different confining pressures were carried out based on the RMT-150B rock mechanics test system. The research results show that the compressive strength, cohesion, and internal friction angle of granite samples decrease to different degrees with increased water content. The growth rate of the total input energy and elastic strain energy of granite samples in the energy evolution process decreases with increased water content. The higher the water content of granite samples, the lower the total input energy, the slower the elastic strain energy rises, the lower the energy storage limitation, the earlier the dissipation energy starts to increase rapidly, and the lower the final energy dissipated. Based on the principle of self-repression of energy, a nonlinear model and its mathematical equations for the energy evolution of granite are established. The higher the water content of granite samples, the greater the energy iterative growth factor and its increasing rate, and the lower the deviator stress level of granite sample systems entering the period-doubling bifurcation and chaos areas. The samples show three failure modes: splitting failure, splitting-shear composite failure, and shear failure. The failure modes of granite samples have an excellent matching relationship with the distribution range of its energy storage limitation. When the energy storage limitation of the samples is minor, it is more likely to occur splitting failure. When the energy storage limitation of the samples is significant, it is more likely to occur shear failure.

Effect of wetting stress paths on mechanical behavior and instability of unsaturated soil in stress state space

In current study, a test program is designed to observe the influence of wetting stress paths on behavior and instability of unsaturated soil in stress state space. The mechanical behavior was studied by performing three test series in constant matric suction plane. In first series, water infiltration was performed together with shearing starting from zero (0 kPa) deviatoric stress. In second series, first water was infiltrated at zero (0 kPa) deviatoric stress then samples were sheared in drained pore water pressure conditions. In third series, water was first infiltrated at zero deviatoric stress then specimens were sheared in undrained pore water pressure conditions. Instability was studied in constant shear stress plane by first shearing soil up to predefined level of deviatoric stress then infiltrating water keeping deviatoric stress constant on the specimen. This research also describes how unsaturated soil behavior and instability is varied with variation in net confining stresses when suction is decreased from initial measured value to start water infiltration with different wetting stress paths and their effect on shear state and failure surface in stress state space. The test results revealed that the movement of stress paths was independent of net confining stress, matric suction and shearing conditions employed in the study.

Effects of confinement pressure on the mechanical behavior of an oil well cement paste

Oil well cement paste is a key structural component in wells that should provide mechanical support to the casing and prevent uncontrolled flow of formation fluids along the wellbore and to the environment. Since the annular cement paste is subjected to both hydrostatic pressure and to loads from formation or through the casing, it is important to understand the mechanical behavior and strength of oil well cement pastes under confining conditions. We study cement specimens cored from test sections that were cemented using a full-scale batch mixer. The specimens were tested mechanically without confinement and under 10, 20 and 40 MPa confining pressures using a state of the art triaxial test system. Unconfined samples are found to exhibit linear elastic behavior up to axial strains of approximately 0.2% with an average Young’s modulus of 14.9 GPa and a Poisson ratio of 0.21. At larger strains, the stress–strain response deviates from the initial slope, terminating with a brittle shear failure at axial strains of approximately 0.5%. The corresponding average uniaxial compressive strength is 58 MPa, in good agreement with previously published results. When subjected to confining pressures of 10 MPa or higher, the cement paste accommodated larger strains at a given level of deviatoric stress, and maintained its load-carrying capacity through the entire test cycle. The Young’s modulus for the initial loading phase was found to decrease with increasing confining pressures, and the ultimate deviatoric stress approached approximately 80 MPa, independent of the magnitude of the confining pressures used in this study. The results suggest that the main effect of increasing confining pressure is to increase the sample ductility and the axial strain corresponding to the ultimate deviatoric stress. It is further found that the confined stress–strain behavior of the oil well cement paste can be described by a simple nonlinear constitutive equation. The more ductile and flexible response of well cement under relevant confining pressures is considered to be a positive characteristic of cement as a barrier material for zonal isolation. This study is based on a commercial well cement slurry that is mixed and placed using field equipment. The results are therefore considered novel and unique, and can contribute toward improved knowledge and evaluation of mechanical well cement behavior under realistic, confined conditions.

Creep Behavior of Saturated Clay in Triaxial Test and a Hyperbolic Model

As one of the basic mechanical properties of soil, the creep property of a given type soil is related to stress path, and stress level. In this paper, triaxial shear creep tests under different deviatoric stress levels were performed on both intact sample and the reconstituted sample of clay taken from Hangzhou, China. Based on the Boltzmann linear superposition principle, the creep curves of the clay sample under different levels of deviatoric stress were obtained, and the creep characteristics of the intact sample and the reconstituted sample were compared in both total stress creep analysis and effective stress creep analysis. Furthermore, the creep curves were fitted using a hyperbolic creep model. The results show that (1) under the same stress level, the creep of intact sample evolves more than that of reconstituted sample; (2) the hyperbolic creep model is suited to describe the creep characteristics of intact and reconstituted clay, and the model parameters A s and B s can be linearly correlated to the stress level D r ; (3) for the application of the hyperbolic model, the total stress analysis works better, and the model parameters A s and B s can be determined by a linear relationship with Dr.

Deformation modulus of reconstituted and naturally sedimented clays

The undrained secant deformation modulus Eu is an important parameter to quantitatively estimate the undrained settlement of soft clays. A series of isotropically consolidated undrained triaxial compression shear tests were carried out on four reconstituted clays and two naturally sedimented clays to evaluate the effects of the initial water content w0, liquid limit wL, and soil structure on Eu. The test results showed that the variation in Eu with deviator stress was significantly affected by w0 and wL for reconstituted clays. The normalized modulus Eu/(p′)0.9 linearly decreased with increasing w0/wL. This linear relation at a lower wL lies above that at a higher wL. These observations suggest that the soil with lower plasticity and lower initial water content possessed higher values of Eu. As the deviator stress increased, the effect of w0 and wL on Eu gradually vanished. It is also evidenced that the value of Eu for naturally sedimented clays depended on the soil structure. The soil structure clearly enhanced the Eu in the preyield regime in comparison with the corresponding reconstituted clay. Once the soil structure was damaged with increasing consolidation stress in the postyield regime, a significant reduction in Eu was observed with a lower value than that of reconstituted clays. The difference in Eu/Su between naturally sedimented and reconstituted clays gradually decreased with increasing deviator stress. This implies that the effect of the soil structure on Eu diminished at higher deviator stress levels.

Creep Rupture and Permeability Evolution in High Temperature Heat-Treated Sandstone Containing Pre-Existing Twin Flaws

Utilizing underground coal gasification cavities for carbon capture and sequestration provides a potentially economic and sustainable solution to a vexing environmental and energy problem. The thermal influence on creep properties and long-term permeability evolution around the underground gasification chamber is a key issue in UCG-CCS operation in containing fugitive emissions. We complete multi-step loading and unloading creep tests with permeability measurement at confining stresses of 30 MPa on pre-cracked sandstone specimens thermally heat-treated to 250, 500, 750 and 1000 °C. Observations indicate a critical threshold temperature of 500 °C required to initiate thermally-induced cracks with subsequent strength reduction occurring at 750 °C. Comparison of histories of creep, visco-elastic and visco-plastic strains highlight the existence of a strain jump at a certain deviatoric stress level—where the intervening rock bridge between the twin starter-cracks is eliminated. As the deviatoric stress level increases, the visco-plastic strains make up an important composition of total creep strain, especially for specimens pre-treated at higher temperatures, and the development of the visco-plastic strain leads to the time-dependent failure of the rock. The thermal pre-treatment produces thermal cracks with their closure resulting in increased instantaneous elastic strains and instantaneous plastic strains. With increasing stress ratio, the steady-state creep rates increase slowly before the failure stress ratio but rise suddenly over the final stress ratio to failure. However, the pre-treatment temperature has no clear and apparent influence on steady creep strain rates. Rock specimens subject to higher pre-treatment temperatures exhibit higher permeabilities. The pre-existing cracks close under compression with a coplanar shear crack propagating from the starter-cracks and ultimately linking these formerly separate cracks. In addition, it is clear that the specimens pre-treated at higher temperatures accommodate greater damage.

DEM investigation of the creep behavior of methane hydrate-bearing sand

In this paper, the creep behavior of cemented methane hydrate-bearing sand is studied using discrete element model. Methane hydrate is modeled as contact bonds between particles, and the time-dependent bond strength method is adopted to simulate the creep procedure. The simulation results are in good agreement with laboratory test results, i.e., the creep of methane hydrate-bearing sands exhibits deceleration and acceleration phase, and strain rate is larger with higher deviator stress levels. Furthermore, the micro evolutions including bond breakage and shear band formation are revealed with the DEM model.

Decomposition of elastic potential energy and a rational metric for aftershock generation

SUMMARY The occurrence of earthquakes can be regarded as shear fracture releasing the elastic potential energy stored in the Earth. The potential energy density of linear elastic forces is generally represented in the quadratic form of strain tensor components with the fourth-order coefficient tensor of elastic stiffness. When the material is isotropic, since the stiffness tensor is expressible as a linear combination of two independent symmetric tensors, we can decompose the elastic potential energy density into two independent parts, namely the volumetric part and the shearing part. By definition, the partial derivatives of the elastic potential energy density with respect to volumetric and shearing deformations give the corresponding generalized forces in the sense of Lagrangian mechanics: specifically, one-third of the first invariant of stress tensor (equivalent to the mean stress) to volumetric deformation and the square root of the second invariant of deviatoric stress tensor (equivalent to $\sqrt {3/2} $ times the octahedral shear stress). With these generalized forces instead of the normal and tangential stresses on a specific fault plane, we correctly represented the original concept of Coulomb's failure criterion (shear failure occurs when shearing stress is equal to shearing strength) and defined energetics-based failure stress (EFS). The change in EFS associated with the occurrence of a main fracture (ΔEFS) gives a rational metric for aftershock generation, which can be reduced to previously proposed various metrics in special cases. For example, when the level of background deviatoric stress is much higher than the magnitude of coseismic stress changes, the expression of ΔEFS is reduced to a similar form to the well-known Coulomb failure stress change (ΔCFS). Even in the energetics-based metric, the effects of pore-fluid pressure changes are essential. We theoretically examined the mechanical effects of induced and enforced pore-fluid pressure changes and elucidated that the difference between them is reflected in the focal mechanisms of aftershocks.