Experimental study on the slip evolution of planar fractures subjected to cyclic normal stress

The frictional rupture mechanisms of rock discontinuities considering the dynamic load disturbance still remain unclear.This paper investigates the transitional behaviors of slip events happened on a planar granite fracture under cyclic normal stress with diferent oscillation amplitudes.The experimental results show that the activations of fast slips always correlate with unloading of normal stress.Besides,the intensive normal stress oscillation can weaken the shear strength which is recoverable when the normal stress return to constant.The rupture patterns are quantifed by stress drop,slip length and slip velocity.With the efect of small oscillation amplitudes,the slip events show chaotic shapes,compared to the regular and predictable style under constant normal stress.When the amplitude is large enough,the big and small slip events emerge alternately,showing a compound slip style.Large amplitude of the cyclic normal stress also widens the interval diferences of the slip events.This work provides experimental supports for a convincible link between the dynamic stress disturbance and the slip behavior of rock fractures.

Shear sliding of rough-walled fracture surfaces under unloading normal stress

Through high-precision engraving,self-affine sandstone joint surfaces with various joint roughness coefficients(JRC=3.21e12.16)were replicated and the shear sliding tests under unloading normal stress were conducted regarding various initial normal stresses(1e7 MPa)and numbers of shearing cycles(1 e5).The peak shear stress of fractures decreased with shear cycles due to progressively smooth surface morphologies,while increased with both JRC and initial normal stress and could be verified using the nonlinear Barton-Bandis failure criterion.The joint friction angle of fractures exponentially increased by 62.22%e64.87%with JRC while decreased by 22.1%e24.85%with shearing cycles.After unloading normal stress,the sliding initiation time of fractures increased with both JRC and initial normal stress due to more tortuous fracture morphologies and enhanced shearing resistance capacity.The surface resistance index(SRI)of fractures decreased by 4.35%e32.02%with increasing shearing cycles due to a more significant reduction of sliding initiation shear stress than that for sliding initiation normal stress,but increased by a factor of 0.41e1.64 with JRC.After sliding initiation,the shear displacement of fractures showed an increase in power function.By defining a sliding rate threshold of 5105 m/s,transition from“quasi-static”to“dynamic”sliding of fractures was identified,and the increase of sliding acceleration steepened with JRC while slowed down with shearing cycles.The normal displacement experienced a slight increase before shear sliding due to deformation recovery as the unloading stress was unloaded,and then enhanced shear dilation after sliding initiation due to climbing effects of surface asperities.Dilation was positively related to the shear sliding velocity of fractures.Wear characteristics of the fracture surfaces after shearing failure were evaluated using binary calculation,indicating an increasing shear area ratio by 45.24%e91.02%with normal stress.

Behavior of interfacial stresses between RC beams and GFRP sheets

Seven reinforced concrete （RC） beams with epoxy-bonded glass fiber reinforced plastic （GFRP） sheets and two control RC beams were experimentally tested to investigate the bond behavior of the interfaces between RC beams and GFRP sheets. The variable parameters considered in test beams are the layers of GFRP sheets, the bond lengths and the reinforcement ratios. The results indicate that the flexural strength of the repaired beams is increased, but the ultimate load of beams with GFRP sheets debonding failure is reduced relatively. The bond length is the main factor that results in bonding failure of the strengthened beams. An experimental method of interfacial shear stress is proposed to analyze the distribution of shear stress according to experimental results. The analytical method of shear and normal stresses and a simple equation are proposed to predict the peeling loads. The proposed model is applied to experimental beams. The analytical results show a good agreement with the experimental results.

Nonlinear constitutive models of rock structural plane and their applications

Structural planes play an important role in controlling the stability of rock engineering,and the influence of structural planes should be considered in the design and construction process of rock engineering.In this paper,mechanical properties,constitutive theory,and numerical application of structural plane are studied by a combination method of laboratory tests,theoretical derivation,and program development.The test results reveal the change laws of various mechanical parameters under different roughness and normal stress.At the pre-peak stage,a non-stationary model of shear stiffness is established,and threedimensional empirical prediction models for initial shear stiffness and residual stage roughness are proposed.The nonlinear constitutive models are established based on elasto-plastic mechanics,and the algorithms of the models are developed based on the return mapping algorithm.According to a large number of statistical analysis results,empirical prediction models are proposed for model parameters expressed by structural plane characteristic parameters.Finally,the discrete element method(DEM)is chosen to embed the constitutive models for practical application.The running programs of the constitutive models have been compiled into the discrete element model library.The comparison results between the proposed model and the Mohr-Coulomb slip model show that the proposed model can better describe nonlinear changes at different stages,and the predicted shear strength,peak strain and shear stiffness are closer to the test results.The research results of the paper are conducive to the accurate evaluation of structural plane in rock engineering.

Shear band evolution and acoustic emission characteristics of sandstone containing non-persistent flaws

Direct shear tests were conducted on sandstone specimens under different constant normal stresses to study the coalescence of cracks between non-persistent flaws and the shear sliding characteristics of the shear-formed fault.Digital image correlation and acoustic emission(AE)techniques were used to monitor the evolution of shear bands at the rock bridge area and microcracking behaviors.The experimental results revealed that the shear stresses corresponding to the peak and sub-peak in the stressdisplacement curve are significantly affected by the normal stress.Strain localization bands emerged at both the tip of joints and the rock bridge,and their extension and interaction near the peak stress caused a surge in the AE hit rate and a significant decrease in the AE b value.Short and curvilinear strain bands were detected at low normal stress,while high normal stress generally led to more microcracking events and longer coplanar cracks at the rock bridge area.Furthermore,an increase in normal stress resulted in a higher AE count rate and more energetic AE events during friction sliding along the shearformed fault.It was observed that the elastic energy released during the crack coalescence at the prepeak stage was much greater than that released during friction sliding at the post-peak stage.More than 75%of AE events were located in the low-frequency band(0e100 kHz),and this proportion continued to rise with increasing normal stress.Moreover,more AE events of low AF value and high RA value were observed in specimens subjected to high normal stress,indicating that greater normal stress led to more microcracks of shear nature.

Experimental investigation on shear strength deterioration at the interface between different rock types under cyclic loading

The shear strength deterioration of bedding planes between different rock types induced by cyclic loading is vital to reasonably evaluate the stability of soft and hard interbedded bedding rock slopes under earthquake;however,rare work has been devoted to this subject due to lack of attention.In this study,experimental investigations on shear strength weakening of discontinuities with different joint wall material(DDJM)under cyclic loading were conducted by taking the interface between siltstone and mudstone in the Shaba slope of Yunnan Province,China as research objects.A total of 99 pairs of similar material samples of DDJM(81 pairs)and discontinuities with identical joint wall material(DIJM)(18 pairs)were fabricated by inserting plates,engraved with typical surface morphology obtained by performing three-dimensional laser scanning on natural DDJMs sampled from field,into mold boxes.Cyclic shear tests were conducted on these samples to study their shear strength changes with the cyclic number considering the effects of normal stress,joint surface morphology,shear displacement amplitude and shear rate.The results indicate that the shear stress vs.shear displacement curves under each shear cycle and the peak shear strength vs.cyclic number curves of the studied DDJMs are between those of DIJMs with siltstone and mudstone,while closer to those of DIJMs with mudstone.The peak shear strengths of DDJMs exhibit an initial rapid decline followed by a gradual decrease with the cyclic number and the decrease rate varies from 6%to 55.9%for samples with varied surface morphology under different testing conditions.The normal stress,joint surface morphology,shear displacement amplitude and shear rate collectively influence the shear strength deterioration of DDJM under cyclic shear loading,with the degree of influence being greater for larger normal stress,rougher surface morphology,larger shear displacement amplitude and faster shear rate.

Rheological Characterization of Systems with Plastic Flow Behavior

Model suspensions with plastic flow behavior were investigated rheologically.Shear stress and first normal stress difference were measured simultaneously with shear flow start-up experiments.After the shear deformation is stopped,the stress relaxation begins,residual shear stress can appear.The relative residual shear stressτRR is the ratio of the residual shear stress to the steady state shear stress.The relative residual shear stress is considered as a measure of the structure of the system.In the case ofτRR=0.98,we assume that an elastic to plastic deformation is occurred,which is the yield point.The system with 7.5%Aerosil 380 has achieved withτRR=0.95 in the first approximation the transition to plastic flow,this is the yield point for the system,with a yield stress of 23 Pa.This is the only one known system with yield point.The systems withτRR>0.30 andτRR<0.95 at the first point,have no transition from elastic to plastic flow,but the structure is strongly destroyed.Analogous to the above,the shear stress at this point will be called yield stress.One requirement is that the start-up experiment is determined with a very low shear rate¾0.00071/s or 0.000961/s.The associated normal stress to the yield stress is called normal yield stress.The dependence of the normal stress of the systems with Aerosil 380 on the shear stress reached,after a short increase/decrease in the values,the straight line of the normal stress/shear stress of the liquid phase M20000.A linear relationship between normal stress and shear stress was found in the systems with Bentone 27 in Araldite GY260.With a certain measured normal stress/shear stress point,you can draw a straight line with 45°in the double logarithmic plot¾a way to receive the normal stress/shear stress points.

Nonlinear Elastic Constitutive Model of Soil-Structure Interfaces Under Relatively High Normal Stress

The shear characteristics of soil-structure interfaces with different roughness are studied systematically by us-ing the DRS-1 high normal stress and residual shear apparatus. The experimental results indicate that,under a relatively high normal stress,normal stress and the coefficient of structural roughness are the most important factors affecting the mechanical interface characteristics. The relationship between shear stress and shear displacement of the soil-structure interface is a hyperbolic curve with high regression accuracy. Based on our experimental results,a nonlinear elastic con-stitutive model of the soil-structure interface under relatively high normal stress is established with a definite physical meaning for its parameters. The model can predict the strain hardening behavior of the soil during the shearing process. The results show an encouraging agreement with experimental data from direct shear tests.

Impact of normal stress-induced closure on laboratory-scale solute transport in a natural rock fracture

The impact of normal stress-induced closure on fluid flow and solute transport in a single rock fracture is demonstrated in this study.The fracture is created from a measured surface of a granite rock sample.The Bandis model is used to calculate the fracture closure due to normal stress,and the fluid flow is simulated by solving the Reynold equation.The Lagrangian particle tracking method is applied to modeling the advective transport in the fracture.The results show that the normal stress significantly affects fluid flow and solute transport in rock fractures.It causes fracture closure and creates asperity contact areas,which significantly reduces the effective hydraulic aperture and enhances flow channeling.Consequently,the reduced aperture and enhanced channeling affect travel time distributions.In particular,the enhanced channeling results in enhanced first arriving and tailing behaviors for solute transport.The fracture normal stiffness correlates linearly with the 5th and 95th percentiles of the normalized travel time.The finding from this study may help to better understand the stress-dependent solute transport processes in natural rock fractures.

Reflection and transmission of quasi-plane waves at the interface of piezoelectric semiconductors with initial stresses

We examine the reflection and transmission phenomena of quasi-longitudinal plane(QP)waves in an AlN-ZnO laminated composite structure.The structure is designed under the influence of the initial stresses in which one carrier piezoelectric semiconductor(PSC)half-space is in welded contact with another PSC half-space.The secular equations in the transversely isotropic PSC material are derived from the general dynamic equation,taking the initial stresses into consideration.It is shown that the incident quasi-longitudinal wave(QP-mode)at the interface generates four types of reflected and transmitted waves,namely,QP wave,quasi-transverse(QSV)wave,electric-acoustic(EA)wave,and carrier plane(CP)wave.The algebraic equations are obtained by imposing the boundary conditions on the common interface of the laminated structure.Reflection and transmission coefficients of waves are obtained by implementing Cramer’s rule.Profound impacts of the initial stresses and exterior electric biasing field on the reflection and transmission coefficients of waves are investigated and presented graphically.

Identification and evaluation of reference genes for normalization in quantitative real-time PCR analysis in the premodel tree Betula luminifera

Betula luminifera is a commercial tree species that is emerging as a new model system for tree genomics research. A draft genomic sequence is expected to be publicly available in the near future, which means that an explosion of gene expression studies awaits. Thus, the work of selecting appropriate reference genes for q PCR normalization in different tissues or under various experimental conditions is extremely valuable. In this study, ten candidate genes were analyzed in B. luminifera subjected to different abiotic stresses and at various flowering stages.The expression stability of these genes was evaluated using three distinct algorithms implemented using ge Norm,Norm Finder and Best Keeper. The best-ranked reference genes varied across different sample sets, though RPL39,MDH and EF1 a were determined as the most stable by the three programs among all tested samples. RPL39 and EF1 a should be appropriate for normalization in N-starved roots,while the combination of RPL39 and MDH should be appropriate for N-starved stems and EF1 a and MDH should be appropriate in N-starved leaves. In PEG-treated（osmotic） roots, MDH was the most suitable, whereas EF1 a was suitable for PEG-treated stems and leaves. TUA was also stably expressed levels in PEG-treated plants. The combination of RPL39 and TUB should be appropriate for heat-stressed leaves and flowering stage. For reference gene validation, the expression levels of SOD and NFYA-3were investigated. This work will be beneficial to future studies on gene expression under different abiotic stress conditions and flowering status in B. luminifera.

ANALYTICAL SOLUTION OF RESTRAINED TORSIONAL STRESSES AND DISPLACEMENT FOR RECTANGULAR- SECTION BOX BAR WITH HONTYCOMB CORE

Differential equation of restrained torsion for rectangular-section box bar with honeycomb core was established and solved by using the method of undetermined function.Non-dimension normal stress, shear stress acting in the faceplate and shear stress acting in the honeycomb-core and warping displacement were deduced. Numerical analysis shows the normal stress attenuates quickly along x-axis. Normal stress acting on the cross section at a distance of 20 h from the fixed end is only one per cent of that acting on the fixed end.

Experimental and Numerical Study on the Shear Strength and Strain Energy of Rock Under Constant Shear Stress and Unloading Normal Stress

Excavation and earth surface processes(e.g.,river incision)always induce the unloading of stress,which can cause the failure of rocks.To study the shear mechanical behavior of a rock sample under unloading normal stress conditions,a new stress path for direct shear tests was proposed to model the unloading of stress caused by excavation and other processes.The effects of the initial stresses(i.e.,the normal stress and shear stress before unloading)on the shear behavior and energy conversion were investigated using laboratory tests and numerical simulations.The shear strength of a rock under constant stress or under unloading normal stress conforms to the Mohr Coulomb criterion.As the initial normal stress increases,the cohesion decreases linearly and the tangent of the internal friction angle increases linearly.Compared with the results of the tests under constant normal stress,the cohesions of the rock samples under unloading normal stress are smaller and their internal friction angles are larger.A strength envelope surface can be used to describe the relationship between the initial stresses and the failure normal stress.Shear dilatancy can decrease the total energy of the direct shear test under constant normal stress or unloading normal stress,particularly when the stress levels(the initial stresses in the test under unloading normal stress or the normal stress in the test under constant normal stress)are high.The ratio of the dissipated energy to the total energy at the moment failure occurs decreases exponentially with increasing initial stresses.The direct shear test under constant normal stress can be considered to be a special case of a direct shear test under unloading normal stress with an unloading amount of zero.

Parameter Estimations of the TFR Model Under Exponential Distribution at a Normal Stress

The TFR（Tampered Failure Rate） model was proposed by Bhattacharyya and Soejoeti（1989） for step-stress accelerated life tests, On step-stress completely accelerated test occasions, the paper gives a method of estimating parameters under a normal stress.

Experimental Study on Shear Mechanical Properties and Section Morphology of Coal Samples

The mechanical properties of rocks under cyclic and dynamic loading are important research topics for solving the structural stability of large engineering rocks. As underground mining in coal mines goes deeper, ground stresses are increasing and instability damage of coal rocks by shear loading is frequent. Therefore, in order to investigate the shear mechanical properties and section morphological characteristics of intact coal samples in the direct shear test, the RDS-200 rock direct shear instrument was used to carry out direct shear tests on intact coal samples under different normal stresses, and the shear section was scanned for three-dimensional morphology. The results show that: 1) from the strength characteristics, the peak shear strength of the coal samples increased linearly with increasing normal stress, and the residual shear strength increased logarithmically. 2) In terms of deformation characteristics, the peak shear displacement of the coal sample increases linearly with increasing normal stress, the pre-peak shear stiffness increases logarithmically, and the residual normal displacement decreases linearly. 3) From the morphological characteristics of the shear surface, with the increase of normal stress, the section transitions from high-order undulating to flattening type. The maximum height of the fracture surface profile and kurtosis coefficient of the shear section decreased linearly, and the profile area ratio and root mean square of slope decreased as a power function, i.e. the higher the normal stress, the smaller the undulation of the section, the sharpness of the roughness shape and the roughness coefficient JRC, and the flatter and smoother the section. The findings of this study can help to provide some reference for the evaluation of shear instability occurring in coal bodies under different normal stresses.

Modified MK model combined with ductile fracture criterion and its application in warm hydroforming

A modified MK model combined with ductile fracture criterion（DFC-MK model） is proposed to compute the forming limit diagrams（FLDs） of 5A06-O aluminum alloy sheet at different temperatures.The material constant（C） of ductile fracture criterion and initial thickness imperfection parameter（f0） at various temperatures are determined by using a new computing method based on wide sheet bending test.The FLDs at 20 and 200 °C are calculated through the DFC-MK model.The DFC-MK model,which includes the influence of through-thickness normal stress,is written into the subroutine VUMAT embedded in Abaqus/ Explicit.The cylindrical cup hydroforming tests are carried out to verify the model.The results show that compared with experimental observations,the predicted FLDs based on DFC-MK model are more accurate than the conventional MK model;the errors between the simulations and experiments in warm hydroforming are 8.23% at 20 °C and 9.24% at 200 °C,which verify the effectiveness of the proposed model.

Investigation on reinforcement-sand-clay layer system using direct-shear test

The property of the contact surface between geosynthetics and soil directly affects the whole structure＇s stability. The interface property is one of the most important indices for the reinforced structure. Systematic direct-shear tests with large direct-shear apparatus are carded out for geobelt reinforced clay under different normal stresses and water content. A reinforcement-sand-clay layer system improving the interface behavior greatly is designed. The stress-strain relationship is investigated on the basis of the experimental results. The results show that with the increase of the normal stress, the shear strength between the clay and the reinforcement increases nonlinearly, and with the increase of the water content, the friction coefficient between the clay and the reinforcement decreases dramatically and the cohesion between the clay and the polypropylene geobelt increases initially, then decreases. There is an optimal value for the water content between the clay and the polypropylene geobelt, which is 2% lower than the optimal water content of clay compaction. This reinforcement-sand-clay layer system improves the shear strength of the interface remarkably. Therefore, the clay-sand-reinforcement layer system is a rather good design for practical use in reinforcement engineering.

Study on fault induced rock bursts

In order to study the rules of rock bursts caused by faults by means of mechanical analysis of a roof rock-mass balanced structure and numerical simulation about fault slip destabilization, the effect of coal mining operation on fault plane stresses and slip displacement were studied. The results indicate that the slip displacement sharply increases due to the decrease of normal stress and the increase of shear stress at the fault plane when the working face advances from the footwall to the fault itself, which may induce a fault rock burst. However, this slip displacement will be very small due to the increase of normal stress and the decrease of shear stress when the working face advances from the hanging wall to the fault itself, which results in a very small risk of a fault rock burst.

Limit equilibrium method for slope stability based on assumed stress on slip surface

In the limit equilibrium framework, two- and three-dimensional slope stabilities can be solved according to the overall force and moment equilibrium conditions of a sliding body. In this work, based on Mohr-Coulomb(M-C) strength criterion and the initial normal stress without considering the inter-slice(or inter-column) forces, the normal and shear stresses on the slip surface are assumed using some dimensionless variables, and these variables have the same numbers with the force and moment equilibrium equations of a sliding body to establish easily the linear equation groups for solving them. After these variables are determined, the normal stresses, shear stresses, and slope safety factor are also obtained using the stresses assumptions and M-C strength criterion. In the case of a three-dimensional slope stability analysis, three calculation methods, namely, a non-strict method, quasi-strict method, and strict method, can be obtained by satisfying different force and moment equilibrium conditions. Results of the comparison in the classic two- and three-dimensional slope examples show that the slope safety factors calculated using the current method and the other limit equilibrium methods are approximately equal to each other, indicating the feasibility of the current method; further, the following conclusions are obtained: 1) The current method better amends the initial normal and shear stresses acting on the slip surface, and has the identical results with using simplified Bishop method, Spencer method, and Morgenstern-Price(M-P) method; however, the stress curve of the current method is smoother than that obtained using the three abovementioned methods. 2) The current method is suitable for analyzing the two- and three-dimensional slope stability. 3) In the three-dimensional asymmetric sliding body, the non-strict method yields safer solutions, and the results of the quasi-strict method are relatively reasonable and close to those of the strict method, indicating that the quasi-strict method can be used to obtain a reliable slope safety factor.

A new apparatus for investigating stress,deformation and seepage coupling properties of rock fractures

A true triaxial apparatus which is composed of three units was presented.The apparatus allows for investigations on deformation and seepage behaviors of a single rock fracture subjected to lateral stress and normal stress.The first unit has three jacks which can apply loads independently in three orthogonal directions.The second unit is used to supply water inflow,control seepage pressure and measure flow velocity in real time.The third unit is for measuring the normal deformation of rock fractures.Some tests for investigating the normal deformation and seepage behaviors of rock fractures subjected to normal and lateral loads on hard granite specimens with an artificial persistent fracture,were introduced.The results show that both the normal deformation and the hydraulic conductivity are influenced not only by the normal stress but also by the lateral stress.It is also shown that the aperture and the hydraulic conductivity decrease with the increasing normal stress but increase with the increasing lateral stress and both the aperture and the hydraulic conductivity obey exponential relationships with the normal stress and the lateral stress.