Anisotropic time-dependent behaviors of shale under direct shearing and associated empirical creep models

Understanding the anisotropic creep behaviors of shale under direct shearing is a challenging issue.In this context,we conducted shear-creep and steady-creep tests on shale with five bedding orientations (i.e.0°,30°,45°,60°,and 90°),under multiple levels of direct shearing for the first time.The results show that the anisotropic creep of shale exhibits a significant stress-dependent behavior.Under a low shear stress,the creep compliance of shale increases linearly with the logarithm of time at all bedding orientations,and the increase depends on the bedding orientation and creep time.Under high shear stress conditions,the creep compliance of shale is minimal when the bedding orientation is 0°,and the steady-creep rate of shale increases significantly with increasing bedding orientations of 30°,45°,60°,and 90°.The stress-strain values corresponding to the inception of the accelerated creep stage show an increasing and then decreasing trend with the bedding orientation.A semilogarithmic model that could reflect the stress dependence of the steady-creep rate while considering the hardening and damage process is proposed.The model minimizes the deviation of the calculated steady-state creep rate from the observed value and reveals the behavior of the bedding orientation's influence on the steady-creep rate.The applicability of the five classical empirical creep models is quantitatively evaluated.It shows that the logarithmic model can well explain the experimental creep strain and creep rate,and it can accurately predict long-term shear creep deformation.Based on an improved logarithmic model,the variations in creep parameters with shear stress and bedding orientations are discussed.With abovementioned findings,a mathematical method for constructing an anisotropic shear creep model of shale is proposed,which can characterize the nonlinear dependence of the anisotropic shear creep behavior of shale on the bedding orientation.

Reservoir heterogeneity analysis using multi-directional textural attributes from deep learning-based enhanced acoustic impedance inversion:A study from Poseidon,NW shelf Australia

Reservoir heterogeneities play a crucial role in governing reservoir performance and management.Traditionally,detailed and inter-well heterogeneity analyses are commonly performed by mapping seismic facies change in the seismic data,which is a time-intensive task.Many researchers have utilized a robust Grey-level co-occurrence matrix(GLCM)-based texture attributes to map reservoir heterogeneity.However,these attributes take seismic data as input and might not be sensitive to lateral lithology variation.To incorporate the lithology information,we have developed an innovative impedance-based texture approach using GLCM workflow by integrating 3D acoustic impedance volume(a rock propertybased attribute)obtained from a deep convolution network-based impedance inversion.Our proposed workflow is anticipated to be more sensitive toward mapping lateral changes than the conventional amplitude-based texture approach,wherein seismic data is used as input.To evaluate the improvement,we applied the proposed workflow to the full-stack 3D seismic data from the Poseidon field,NW-shelf,Australia.This study demonstrates that a better demarcation of reservoir gas sands with improved lateral continuity is achievable with the presented approach compared to the conventional approach.In addition,we assess the implication of multi-stage faulting on facies distribution for effective reservoir characterization.This study also suggests a well-bounded potential reservoir facies distribution along the parallel fault lines.Thus,the proposed approach provides an efficient strategy by integrating the impedance information with texture attributes to improve the inference on reservoir heterogeneity,which can serve as a promising tool for identifying potential reservoir zones for both production benefits and fluid storage.

Anisotropic shearing mechanism of Kangding slate:Experimental investigation and numerical analysis

The shear mechanical behavior is regarded as an essential factor affecting the stability of the surrounding rocks in underground engineering.The shear strength and failure mechanisms of layered rock are significantly affected by the foliation angles.Direct shear tests were conducted on cubic slate samples with foliation angles of 0°,30°,45°,60°,and 90°.The effect of foliation angles on failure patterns,acoustic emission(AE)characteristics,and shear strength parameters was analyzed.Based on AE characteristics,the slate failure process could be divided into four stages:quiet period,step-like increasing period,dramatic increasing period,and remission period.A new empirical expression of cohesion for layered rock was proposed,which was compared with linear and sinusoidal cohesion expressions based on the results made by this paper and previous experiments.The comparative analysis demonstrated that the new expression has better prediction ability than other expressions.The proposed empirical equation was used for direct shear simulations with the combined finite-discrete element method(FDEM),and it was found to align well with the experimental results.Considering both computational efficiency and accuracy,it was recommended to use a shear rate of 0.01 m/s for FDEM to carry out direct shear simulations.To balance the relationship between the number of elements and the simulation results in the direct shear simulations,the recommended element size is 1 mm.

Exact solution for thermal vibration of multi-directional functionally graded porous plates submerged in fluid medium

An analytical method for analyzing the thermal vibration of multi-directional functionally graded porous rectangular plates in fluid media with novel porosity patterns is developed in this study.Mechanical properties of MFG porous plates change according to the length,width,and thickness directions for various materials and the porosity distribution which can be widely applied in many fields of engineering and defence technology.Especially,new porous rules that depend on spatial coordinates and grading indexes are proposed in the present work.Applying Hamilton's principle and the refined higher-order shear deformation plate theory,the governing equation of motion of an MFG porous rectangular plate in a fluid medium(the fluid-plate system)is obtained.The fluid velocity potential is derived from the boundary conditions of the fluid-plate system and is used to compute the extra mass.The GalerkinVlasov solution is used to solve and give natural frequencies of MFG porous plates with various boundary conditions in a fluid medium.The validity and reliability of the suggested method are confirmed by comparing numerical results of the present work with those from available works in the literature.The effects of different parameters on the thermal vibration response of MFG porous rectangular plates are studied in detail.These findings demonstrate that the behavior of the structure within a liquid medium differs significantly from that within a vacuum medium.Thereby,they offer appropriate operational approaches for the structure when employed in various mediums.

Roughness characterization and shearing dislocation failure for rock-backfill interface

Shearing dislocation is a common failure type for rock–backfill interfaces because of backfill sedimentation and rock strata movement in backfill mining goaf.This paper designed a test method for rock–backfill shearing dislocation.Using digital image techno-logy and three-dimensional(3D)laser morphology scanning techniques,a set of 3D models with rough joint surfaces was established.Further,the mechanical behavior of rock–backfill shearing dislocation was investigated using a direct shear test.The effects of interface roughness on the shear–displacement curve and failure characteristics of rock–backfill specimens were considered.The 3D fractal dimen-sion,profile line joint roughness coefficient(JRC),profile line two-dimensional fractal dimension,and the surface curvature of the frac-tures were obtained.The correlation characterization of surface roughness was then analyzed,and the shear strength could be measured and calculated using JRC.The results showed the following:there were three failure threshold value points in rock–backfill shearing dis-location:30%–50%displacement before the peak,70%–90%displacement before the peak,and 100%displacement before the peak to post-peak,which could be a sign for rock–backfill shearing dislocation failure.The surface JRC could be used to judge the rock–backfill shearing dislocation failure,including post-peak sliding,uniform variations,and gradient change,corresponding to rock–backfill disloca-tion failure on the field site.The research reveals the damage mechanism for rock–backfill complexes based on the free joint surface,fills the gap of existing shearing theoretical systems for isomerism complexes,and provides a theoretical basis for the prevention and control of possible disasters in backfill mining.

A statistical damage-based constitutive model for shearing of rock joints in brittle drop mode

Some rock joints exhibit significant brittleness,characterized by a sharp decrease in shear stress upon reaching the peak strength.However,existing models often fail to accurately represent this behavior and are encumbered by numerous parameters lacking clear mechanical significance.This study presents a new statistical damage constitutive model rooted in both damage mechanics and statistics,containing only three model parameters.The proposed model encompasses all stages of joint shearing,including the compaction stage,linear stage,plastic yielding stage,drop stage,strain softening stage,and residual strength stage.To derive the analytical expression of the constitutive model,three boundary conditions are introduced.Experimental data from both natural and artificial rock joints is utilized to validate the model,resulting in average absolute relative errors ranging from 3%to 8%.Moreover,a comparative analysis with established models illustrates that the proposed model captures stress drop and post-peak strain softening more effectively,with model parameters possessing clearer mechanical interpretations.Furthermore,parameter analysis is conducted to investigate the impacts of model parameters on the curves and unveil the relationship between these parameters and the mechanical properties of rock joints.Importantly,the proposed model is straightforward in form,and all model parameters can be obtained from direct shear tests,thus facilitating the utilization in numerical simulations.

Engineering behaviour of in situ cored deep cement mixed marine deposits subjected to undrained and drained shearing

The deep cement mixing(DCM)is used to improve the capacity and reduce the settlement of the soft ground by forming cemented clay columns.The investigation on the mechanical behaviour of the DCM samples is limited to either laboratory-prepared samples or in-situ samples under unconfined compression.In this study,a series of drained and undrained triaxial shearing tests was performed on the in-situ cored DCM samples with high cement content to assess their mechanical behaviours.It is found that the drainage condition affects significantly the stiffness,peak and residual strengths of the DCM samples,which is mainly due to the state of excess pore water pressure at different strain levels,i.e.being positive before the peak deviatoric stress and negative after the peak deviatoric stress,in the undrained tests.The slope of the failure envelope changes obviously with the confining pressures,being steeper at lower stress levels and flatter at higher stress levels.The strength parameters,effective cohesion and friction angle obtained from lower stress levels(c′0 andφ′0)are 400 kPa and 58°,respectively,which are deemed to be true for design in most DCM applications where the in-situ stress levels are normally at lower values of 50-200 kPa.Additionally,the computed tomography(CT)scanning system was adopted to visualize the internal structures of DCM samples.It is found that the clay pockets existing inside the DCM samples due to uneven mixing affect markedly their stress-strain behaviour,which is one of the main reasons for the high variability of the DCM samples.

Prediction of Shear Bond Strength of Asphalt Concrete Pavement Using Machine Learning Models and Grid Search Optimization Technique

Determination of Shear Bond strength(SBS)at interlayer of double-layer asphalt concrete is crucial in flexible pavement structures.The study used three Machine Learning(ML)models,including K-Nearest Neighbors(KNN),Extra Trees(ET),and Light Gradient Boosting Machine(LGBM),to predict SBS based on easily determinable input parameters.Also,the Grid Search technique was employed for hyper-parameter tuning of the ML models,and cross-validation and learning curve analysis were used for training the models.The models were built on a database of 240 experimental results and three input variables:temperature,normal pressure,and tack coat rate.Model validation was performed using three statistical criteria:the coefficient of determination(R2),the Root Mean Square Error(RMSE),and the mean absolute error(MAE).Additionally,SHAP analysis was also used to validate the importance of the input variables in the prediction of the SBS.Results show that these models accurately predict SBS,with LGBM providing outstanding performance.SHAP(Shapley Additive explanation)analysis for LGBM indicates that temperature is the most influential factor on SBS.Consequently,the proposed ML models can quickly and accurately predict SBS between two layers of asphalt concrete,serving practical applications in flexible pavement structure design.

Structure uniformity and limits of grain refinement of high purity aluminum during multi-directional forging process at room temperature

The effect of forging passes on the refinement of high purity aluminum during multi-forging was investigated. The attention was focused on the structure uniformity due to deformation uniformity and the grain refinement limitation with very high strains. The results show that the fine grain zone in the center of sample expands gradually with the increase of forging passes. When the forging passes reach 6, an X-shape fine grain zone is initially formed. With a further increase of the passes, this X-shape zone tends to spread the whole sample. Limitation in the structural refinement is observed with increasing strains during multi-forging process at the room temperature. The grains size in the center is refined to a certain size （110 μm as forging passes reach 12, and there is no further grain refinement in the center with increasing the forging passes to 24. However, the size of the coarse grains near the surface is continuously decreased with increasing the forging passes to 24.

四分之一空间内椭圆孔对SH(shearing horizontal,反平面剪切)波的散射

利用保角变换和多极坐标移动技术,求解四分之一空间内含有椭圆孔时椭圆孔对入射平面SH(shearing hori-zontal)波的稳态散射问题。首先利用四分之一空间两垂直边界处的应力自由条件,写出不含椭圆孔时空间介质内的反射波场;其次,通过保角映射技术考虑空间介质内含有任意主轴方向的椭圆孔时,由于椭圆孔对入射和反射波场的散射作用而产生的散射波场,并预先使得该散射波场满足四分之一空间介质两垂直边界处的应力自由条件,利用叠加原理,将入射波场、反射波场和散射波场叠加起来,即可得到问题的总位移波场。最后借助于椭圆孔边界处的应力自由条件和傅里叶级数展开列出求解散射波解中未知系数的无穷代数方程组,在满足计算精度的前提下将方程组进行有限项截断,得到一个有限线性方程组并求解。通过算例具体讨论四分之一空间内椭圆孔边界处的环向动应力集中系数随入射波入射角、无量纲波数、椭圆孔方位参数的变化情况。

Numerical simulation on bolted rock joint shearing performance

A Double Shear Model(DSM) was used in a numerical simulation on bolted rock joint shearing performance.An entire bolt deformed as the letter'U'under a shear load between two joints.Near the bolt-joint intersection,the bolt partly deformed as the letter'Z'.There were two critical points along the bolt:one was at the bolt-joint intersection with zero bending moment and the other at the maximum bending moment(plastic hinge) with zero shear stress.The blocks on two sides slid along the bolt as it deformed. A separation area was found between the two joint contact surfaces of the middle rock block and sided block.This area of separation was related to bolt diameter and external forces.We assume that this area is related to the work of external forces.Further research is needed.

Formation and Evolution of Non-dendritic Microstructures of Semisolid Alloys Prepared by Shearing/Cooling Roll Process

The shearing/cooling roll （SCR） process was adopted to prepare semi-solid A2017 alloy. The formation and evolution of non-dendritic microstructures in semi-solid A2017 alloy were studied. It is shown that the microstructures of semi-solid billets transform from coarse dendrites into fine equiaxed grains as the pouring temperature of molten alloy decreases o.r roll-shoe cavity height is reduced. From the inlet to the exit of roll-shoe cavity, microstructure of semi-solid slurry near the shoe surface is in the order of coarse dendrites, degenerated dendrites or equiaxed grains, but fine equiaxed grains are near the roll surface. Microstructural evolution of semi-solid slurry prepared by SCR process is that the molten alloy nucleates and grows into dendrite firstly on the roll and shoe＇s surface. Under the shearing and stirring given by the rotating roll, the dendrites crush off and disperse into the melt. Under the shearing and stirring on semi-solid slurry with high volume fraction of solid, the dendrite arms fracture and form equiaxed grain microstructures.

Three-dimensional analysis of the modified sloping cooling/shearing process

A self-designed setup of modified sloping cooling/shearing process was made to prepare the semisolid Al-3wt%Mg alloy. A three-dimensional simulation model was established for the analysis of preparing the semisolid Al-3wt%Mg alloy. Through simulation and experiment, it is shown that the sloping angle of the plate greatly affects temperature and velocity distributions, and the temperature and velocity of the alloy at the exit of the sloping plate increase with the increase of the sloping angle. The alloy temperature decreases linearly from the pouring mouth to the exit. The alloy temperature at the exit increases obviously with the increase of pouring temperature. To prepare the semisolid Al-3wt%Mg alloy with good quality, the sloping angle θ=45° is reasonable, and the pouring temperature is suggested to be designed above 650-660℃ but under 700℃.

Electro-elastic Fields of Piezoelectric Materials with An Elliptic Hole under Uniform Internal Shearing Forces

The existing investigations on piezoelectric materials containing an elliptic hole mainly focus on remote uniform tensile loads. In order to have a better understanding of the fracture behavior of piezoelectric materials under different loading conditions, theoretical and numerical solutions are presented for an elliptic hole in transversely isotropic piezoelectric materials subjected to uniform internal shearing forces based on the complex potential approach. By solving ten variable linear equations, the analytical solutions inside and outside the hole satisfying the permeable electric boundary conditions are obtained. Taking PZT-4 ceramic into consideration, numerical results of electro-elastic fields along the edge of the hole and axes, and the electric displacements in the hole are presented. Comparison with stresses in transverse isotropic elastic materials shows that the hoop stress at the ends of major axis in two kinds of material equals zero for the various ratios of major to minor axis lengths; If the ratio is greater than 1, the hoop stress in piezoelectric materials is smaller than that in elastic materials, and if the ratio is smaller than 1, the hoop stress in piezoelectric materials is greater than that in elastic materials; When it is a circle hole, the shearing stress in two materials along axes is the same. The distribution of electric displacement components shows that the vertical electric displacement in the hole and along axes in the material is always zero though under the permeable electric boundary condition; The horizontal and vertical electric displacement components along the edge of the hole are symmetrical and antisymmetrical about horizontal axis, respectively. The stress and electric displacement distribution tends to zero at distances far from the elliptical hole, which conforms to the conclusion usually made on the basis of Saint-Venant’s principle. Unlike the existing work, uniform shearing forces acting on the edge of the hole, and the distribution of electro-elastic fields inside and outside the elliptic hole are considered.

Ductility enhancement of EW75 alloy by multi-directional forging

In this study,the Mg-7Gd-5Y-1Nd-0.5Zr alloy can reach a high ductility by the process of multi-directional forging,and the evolution of the microstructure,texture and the mechanical properties were discussed systematically.The results show that after the solutionized sample was multi-forged at 500℃,its grain size can be refined from 292 um to 58 um.As the forging temperature decreased,fine particles precipitated in the matrix.The volume fraction of the particles increased with the forging temperature decreasing,so the nucleation and growth of crystallization were strongly restricted.There was no recrystallization as the forging temperature fell to 410℃,and the severe deformed grains distributed as streamlines perpendicular to the final compression axis.The texture intensity decreased with increasing forging passes.The sample with best ductility was obtained after compressed at 470℃,with an elongation to failure of 21%at room temperature,which is increased by 200%,in comparison with that of the samples in solutionized condition.EBSD results revealed that the mean grain size was 15 um.Refined grains as well as the weakened texture were the key factors to its high ductility.

Effects of bolt profile and grout mixture on shearing behaviors of bolt-grout interface

Shearing behavior and failure mechanism of bolt-grout interface are of great significance for load transfer capacity and design of rock bolting system.In this paper,direct shear tests on bolt-grout interfaces under constant normal load(CNL) conditions were conducted to investigate the effects of bolt profile(i.e.rib spacing and rib height) and grout mixture on the bolt-grout interface in terms of mechanical behaviors and failure modes.Test results showed that the peak shear strength and the deformation capacity of the bolt-grout interface are highly dependent on the bolt profile and grout mixture,suggesting that bolt performances can be optimized,which were unfortunately ignored in the previous studies.A new interface failure mode,i.e.'sheared-crush' mode,was proposed,which was characterized by progressive crush failure of the grout asperities between steel ribs during shearing.It was shown that the interface failure mode mainly depends on the normal stress level and rib spacing,compared with the rib height and grout mixture for the range of tested parameters in this study.

Study on Measurement Methods of Multi-Directional Waves—Wave Gauge Array Method

Measuring multi-directional waves with the wave gauge array is one of the fundamental and easily realised methods. In this paper, the wave gauge array is described and the effects of the gauge spacing, the array orientations, etc. of the three array arrangements, i. e., linear array, T-type array and pentagon array, on the resolution of the directional spreading of waves, are investigated experimentally. This study can be used as a reference in the experimental study and the field measurement of directional waves.

Numerical simulation of two-dimensional granular shearing flows and the friction force of a moving slab on the granular media

This paper studies some interesting features of two-dimensional granular shearing flow by using molecular dynamic approach for a specific granular system. The obtained results show that the probability distribution function of velocities of particles is Gaussian at the central part, but diverts from Gaussian distribution nearby the wall. The macroscopic stress along the vertical direction has large fluctuation around a constant value, the non-zero average velocity occurs mainly near the moving wall, which forms a shearing zone.. In the shearing movement, the volume of the granular material behaves in a random manner. The equivalent fl＇iction coefficient between moving slab and granular material correlates with the moving speed at low velocity, and approaches constant as the velocity is large enough.

Microstructure,texture evolution and yield strength symmetry improvement of as-extruded ZK60 Mg alloy via multi-directional impact forging

Multi-direction impact forging(MDIF)was applied to the as-extruded ZK60 Mg alloy,and the microstructure,texture evolution and yield strength symmetry were investigated in the current study.The results showed that the average grain size of forged piece was greatly refined to 5.3μm after 120 forging passes,which was ascribed to the segmenting effect of{10–12}twins and the subsequent multiple rounds of dynamic recrystallization(DRX).A great deal of{10–12}twins were activated at the beginning of MDIF process,which played an important role in grain refinement.With forging proceeding,continuous and discontinuous DRX were successively activated,resulting in the fully DRXed microstructure.Meanwhile,the forged piece exhibited a unique four-peak texture,and the initial<10-10>//ED fiber texture component gradually evolved into multiple texture components composed of<0001>//FFD(first forging direction)and<11–20>//FFD texture.The special strain path was the key to the formation of the unique four-peak texture.The{10–12}twinning and basal slip were two dominant factors to the evolution of texture during MDIF process.Grain strengthening and dislocation strengthening were two main strengthening mechanisms of the forged piece.Besides,the symmetry of yield strength was greatly improved by MDIF process.

Three-dimensional free vibration analysis of multi-directional functionally graded piezoelectric annular plates on elastic foundations via state space based differential quadrature method

The three-dimensional free vibration analysis of a multi-directional func- tionally graded piezoelectric （FGP） annular plate resting on two parameter （Pasternak） elastic foundations is investigated under different boundary conditions. The material properties are assumed to vary continuously along the radial and thickness directions and have exponent-law distribution. A semi-analytical approach named the state space based differential quadrature method （SSDQM） is used to provide an analytical solution along the thickness using the state space method （SSM） and an approximate solution along the radial direction using the one-dimensional differential quadrature method （DQM）. The influence of the Winkler and shear stiffness of the foundation~ the material property graded variations, and the circumferential wave number on the nomdimensional natural frequency of multi-directional FGP annular plates is studied.