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.

Mechanical Properties of New Type Negative Offset Structure During Shearing Process of Heavy Steel Plate

According to the revised Cailikefu＇s rolling shear force formula, motion path equation of spatial seven-bar path was built, and a mechanical model, with the new structural feature of negative offset, was thus successfully established for 2 800 mm heavy shear of some iron and steel company. Shear and bar forces of steel plate, before and after the adoption of negative offset structure, were analyzed, as well as horizontal force component of mechanism that influences pure rolling shear and back-wall push force that keeps blade clearance. It was found that the back-wall push force keeps large even at the time that the maximum rolling shear was obtained; meanwhile, back-wall push force is the most approximate to side forces when 60--100 mm of offset was adopted. Both theoretical results and onsite shear quality show that the negative offset plays an important role in ensuring the stability of pure rolling shear and keeping blade clearance constant.

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.

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.

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.

Shear behavior and off-fault damage of saw-cut smooth and tension-induced rough joints in granite

The damage of rock joints or fractures upon shear includes the surface damage occurring at the contact asperities and the damage beneath the shear surface within the host rock.The latter is commonly known as off-fault damage and has been much less investigated than the surface damage.The main contribution of this study is to compare the results of direct shear tests conducted on saw-cut planar joints and tension-induced rough granite joints under normal stresses ranging from 1 MPa to 50 MPa.The shear-induced off-fault damages are quantified and compared with the optical microscope observation.Our results clearly show that the planar joints slip stably under all the normal stresses except under 50 MPa,where some local fractures and regular stick-slip occur towards the end of the test.Both post-peak stress drop and stick-slip occur for all the rough joints.The residual shear strength envelopes for the rough joints and the peak shear strength envelope for the planar joints almost overlap.The root mean square(RMS)of asperity height for the rough joints decreases while it increases for the planar joint after shear,and a larger normal stress usually leads to a more significant decrease or increase in RMS.Besides,the extent of off-fault damage(or damage zone)increases with normal stress for both planar and rough joints,and it is restricted to a very thin layer with limited micro-cracks beneath the planar joint surface.In comparison,the thickness of the damage zone for the rough joints is about an order of magnitude larger than that of the planar joints,and the coalesced micro-cracks are generally inclined to the shear direction with acute angles.The findings obtained in this study contribute to a better understanding on the frictional behavior and damage characteristics of rock joints or fractures with different roughness.

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.

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。

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.

Fabrication of fine-grained,high strength and toughness Mg alloy by extrusion−shearing process

A novel extrusion-shearing(ES) composite process was designed to fabricate fine-grained, high strength and tough magnesium alloy. The structural parameters of an ES die were optimized by conducting an orthogonal simulation experiment using finite element software Deform-3D, and Mg-3 Zn-0.6 Ca-0.6 Zr(ZXK310) alloy was processed using the ES die. The results show that the optimized structural parameters of ES die are extrusion angle(α) of 90°, extrusion section height(h) of 15 mm and inner fillet radius(r) of 10 mm. After ES at an extrusion temperature and a die temperature of 350 °C, ZXK310 alloy exhibited good ES forming ability, and obvious dynamic recrystallization occurred in the forming area. The grain size decreased from 1.42 μm of extrusion area to 0.85 μm of the forming area. Owing to the pinning of second phase and formation of ultrafine grains, the tensile strength, yield strength and elongation of alloy reached 362 MPa, 289 MPa and 21.7%, respectively.

Hybrid finite-discrete element modelling of asperity degradation and gouge grinding during direct shearing of rough rock joints

A hybrid finite-discrete element method was implemented to study the fracture process of rough rock joints under direct shearing. The hybrid method reproduced the joint shear resistance evolution process from asperity sliding to degradation and from gouge formation to grinding. It is found that, in the direct shear test of rough rock joints under constant normal displacement loading conditions, higher shearing rate promotes the asperity degradation but constraints the volume dilation, which then results in higher peak shear resistance, more gouge formation and grinding, and smoother new joint surfaces. Moreover, it is found that the joint roughness affects the joint shear resistance evolution through influencing the joint fracture micro mechanism. The asperity degradation and gouge grinding are the main failure micro-mechanism in shearing rougher rock joints with deeper asperities while the asperity sliding is the main failure micro-mechanism in shearing smoother rock joints with shallower asperities. It is concluded that the hybrid finite-discrete element method is a valuable numerical tool better than traditional finite element method and discrete element method for modelling the joint sliding, asperity degradation, gouge formation, and gouge grinding occurred in the direct shear tests of rough rock joints.

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.

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.

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.

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℃.

Grain refinement of AZ91D alloy by intensive melt shearing and its persistence after remelting and isothermal holding

Intensive melt shearing has a significant grain refining effect on some light alloys.However,the persistence of the grain refining effect during isothermal holding and remelting is still unclear,although it is very important for the practical application.In this study,intensive melt shearing was achieved in a twin-screw mechanism to investigate its grain refining effect on AZ91D magnesium alloy.The refinement mechanism was discussed and the persistence of grain refinement after remelting and isothermal holding was also studied.A Zeiss imaging system with polarized light was used for quantitative measurement of grain size.The results show that the intensive melt shearing has a significant grain refining effect on AZ91D magnesium alloy.With the application of intensive melt shearing,the grain size of AZ91D magnesium alloy can be reduced from 530 μm(for a typical as-cast microstructure) to 170 μm,which is about 70% size reduction.The grain refinement achieved by the intensive melt shearing can be partially kept after isothermal holding and remelting.It is believed that the refinement effect was mainly due to the finer and well dispersed oxide particles formed by high intensive shearing.The smaller size of oxide particles and their slow motion velocity in the sheared melt could make important contributions to the remained grain refinement.

Effect of casting speed on floating grains and macrosegregation ofdirect-chill cast 2024 alloy with intensive melt shearing

The ingot was prepared by direct-chill(DC)casting technology with different casting speeds under the influence of intensive melt shearing to explore the effect of casting speed and intensive melt shearing on the floating grains and negative centerline segregation.The results indicate that the application of intensive melt shearing in DC casting process can distribute the floating grains uniformly,reduce the area fraction of the floating grains,alleviate the negative centerline segregation,and improve the uniformity of temperature field in the sump.It is also suggested that under the influence of intensive melt shearing,the casting speed plays a crucial role in the amounts and distribution of floating grains.At low casting speed,the intensive melt shearing can significantly reduce the area fraction of the floating grains and distribute them uniformly throughout the ingot.However,this effect gradually disappears with the increase of casting speed.

Numerical analysis of loess and weak intercalated layer failure behavior under direct shearing and cyclic loading

The mechanical behavior of the joints inside a loess layer is greatly important in weak intercalation studies owing to its involvement in a wide range of landslides in the loess region in China.The shear behavior of the joints in the loess stratum during direct shear and cyclic loadings was investigated using the PFC2D discrete element software.Loess mudstone and mudstone with weak intercalated layer materials were subjected to direct testing,and cyclic shear tests were conducted with consideration to the influence of normal stress and shear velocity.The macroscopic properties and damage patterns were obtained for six numerical configurations;namely,loess-weathered mudstone with 0°,10°,and-10°joints and weathered mudstone with 0°,10°,and-10°weak intercalated layers.The numerical test results revealed that,in the direct shear tests,the shear stress and shear displacement of the samples increased with the normal stress.In the cyclic shear tests with a total cycle number N=20,the shear stress-shear strain curve of the six different configurations exhibited a hysteresis loop.The numerical tests also revealed that,under cyclic shear,the normal stress and shear velocity affected the shear strength.The degree of damage increased as the shear velocity decreased from 0.1 mm/s to 0.005 mm/s for all six numerical configurations.Compared with the damage pattern of the direct shear tests,the damage of the cyclic shear tests mainly comprised shear cracks and fractures,some shaking consolidation settlement and fewer shear strain occurred around the joints.In the direct shear tests,more compression cracks and fractures occurred in the samples.The damage mainly developed along the joints,and shearing-off damage occurred.The results obtained by this study further elucidate the failure mechanism and microscopic damage response of the joints in the loess stratum in Northwest China.

Formation of adiabatic shearing band for high-strength Ti-5553 alloy:A dramatic thermoplastic microstructural evolution

By using split Hopkinson pressure bar, optical microscopy and electronic microscopy, we investigate the influence of initial microstructures on the adiabatic shear behavior of high-strength Ti-5Al-5V-5Mo-3Cr(Ti-5553) alloy with lamellar microstructure and bimodal microstructure. Lamellar alloy tends to form adiabatic shearing band(ASB) at low compression strain, while bimodal alloy is considerably ASBresistant. Comparing with the initial microstructure of Ti-5553 alloy, we find that the microstructure of the ASB changes dramatically. Adiabatic shear of lamellar Ti-5553 alloy not only results in the formation of recrystallized β nano-grains within the ASB, but also leads to the chemical redistribution of the alloying elements such as Al, V, Cr and Mo. As a result, the alloying elements distribute evenly in the ASB.In contrast, the dramatic adiabatic shear of bimodal alloy might give rise to the complete lamination of the globular primary a grain and the equiaxial prior β grain, which is accompanied by the dynamic recrystallization of a lamellae and β lamellae. As a result, ASB of bimodal alloy is composed of a/β nanomultilayers. Chemical redistribution does not occur in ASB of bimodal alloy. Bimodal Ti-5553 alloy should be a promising candidate for high performance armors with high mass efficiency due to the processes high dynamic flow stress and excellent ASB-resistance.

Influence of AZ31 sheet treated by cryogenic on punch shearing

Punch shearing is used to form the part in the material process.Cryogenic treatment(CT)has active effect on local mechanical properties of steel,but it is still uncertain of the influence of CT on the properties of the magnesium alloy during punch shearing.In this work,the influence of AZ31 sheet treated by cryogenic on punch shearing was studied.Microstructures were observed with a ZEISS optical microscope,and mechanical properties,as well as shear properties were tested by tensile testing and punch shearing.The results show that the number of secondary phase increases and a large number of twins appear in the grains after CT.Meanwhile,the ultimate tensile strength(UTS),the ductility,and hardness of AZ31 are improved,while the yield strength(YS)decreases gradually during CT.During punch shearing,the shearing strength decreases,the rollover radius changes insignificantly,and the height of the burr on the edge of the cross section decreases.At the same time,a larger proportion of smooth zone on the cross section has been achieved.