Rock has mechanical characteristics and a fracture damage mechanism that are closely related to its loading history and loading path. The mechanical properties, fracture damage features, acoustic emission(AE) characte...Rock has mechanical characteristics and a fracture damage mechanism that are closely related to its loading history and loading path. The mechanical properties, fracture damage features, acoustic emission(AE) characteristics, and strain energy evolution of the Beishan shallow-layer granite used in triaxial unloading tests were investigated in this study. Three groups of triaxial tests, namely, conventional triaxial compression test(Group Ⅰ), maintaining deviatoric stress synchronously unloading confining pressure test(Group Ⅱ), and loading axial pressure synchronously unloading confining pressure test(Group Ⅲ), were carried out for the cylindrical granite specimens. AE monitoring device was utilized in these tests to determine the degree to which the AE waves and AE events reflected the degree of rock damage. In addition, the crack stress thresholds of the specimens were determined by volumetric strain method and AE parameter method, and strain energy evolution of the rock was explored in different damage stages. The results show that the shallow-layer granite experiences brittle failure during the triaxial loading test and unloading test, and the rock has a greater damage degree during the unloading test. The crack stress thresholds of these samples vary greatly between tests, but the threshold ratios of all samples are similar in the same crack damage stage. The Mogi-Coulomb strength criterion can better describe the unloading failure strength of the rock. The evolution of the AE parameter characteristics and strain energy differs between the specimens used in different stress path tests. The dissipative strain energy is the largest in Group Ⅱ and the smallest in Group Ⅰ.展开更多
The far-field microdynamic disturbance caused by the excavation of deep mineral resources and underground engineering can induce surrounding rock damage in high-stress conditions and even lead to disasters.However,the...The far-field microdynamic disturbance caused by the excavation of deep mineral resources and underground engineering can induce surrounding rock damage in high-stress conditions and even lead to disasters.However,the mechanical properties and damage/fracture evolution mechanisms of deep rock induced by microdynamic disturbance under three-dimensional stress states are unclear.Therefore,a true triaxial multilevel disturbance test method is proposed,which can completely simulate natural geostress,excavation stress redistribution(such as stress unloading,concentration and rotation),and subsequently the microdynamic disturbance triggering damaged rock failure.Based on a dynamic true triaxial test platform,true triaxial microdynamic disturbance tests under different frequency and amplitudes were carried out on monzogabbro.The results show that increasing amplitude or decreasing frequency diminishes the failure strength of monzogabbro.Deformation modulus gradually decreases during disturbance failure.As frequency and amplitude increase,the degradation rate of deformation modulus decreases slightly,disturbance dissipated energy increases significantly,and disturbance deformation anisotropy strengthens obviously.A damage model has been proposed to quantitatively characterize the disturbance-induced damage evolution at different frequency and amplitude under true triaxial stress.Before disturbance failure,the micro-tensile crack mechanism is dominant,and the micro-shear crack mechanism increases significantly at failure.With the increase of amplitude and frequency,the micro-shear crack mechanism increases.When approaching disturbance failure,the acoustic emission fractal dimension changes from a stable value to local large oscillation,and finally increases sharply to a high value at failure.Finally,the disturbance-induced failure mechanism of surrounding rock in deep engineering is clearly elucidated.展开更多
The polyurethane foam(PU)compressible layer is a viable solution to the problem of damage to the secondary lining in squeezing tunnels.Nevertheless,the mechanical behaviour of the multi-layer yielding supports has not...The polyurethane foam(PU)compressible layer is a viable solution to the problem of damage to the secondary lining in squeezing tunnels.Nevertheless,the mechanical behaviour of the multi-layer yielding supports has not been thoroughly investigated.To fill this gap,large-scale model tests were conducted in this study.The synergistic load-bearing mechanics were analyzed using the convergenceconfinement method.Two types of multi-layer yielding supports with different thicknesses(2.5 cm,3.75 cm and 5 cm)of PU compressible layers were investigated respectively.Digital image correlation(DIC)analysis and acoustic emission(AE)techniques were used for detecting the deformation fields and damage evolution of the multi-layer yielding supports in real-time.Results indicated that the loaddisplacement relationship of the multi-layer yielding supports could be divided into the crack initiation,crack propagation,strain-hardening,and failure stages.Compared with those of the stiff support,the toughness,deformability and ultimate load of the yielding supports were increased by an average of 225%,61%and 32%,respectively.Additionally,the PU compressible layer is positioned between two primary linings to allow the yielding support to have greater mechanical properties.The analysis of the synergistic bearing effect suggested that the thickness of PU compressible layer and its location significantly affect the mechanical properties of the yielding supports.The use of yielding supports with a compressible layer positioned between the primary and secondary linings is recommended to mitigate the effects of high geo-stress in squeezing tunnels.展开更多
The application of self-compacting recycled concrete can solve the problem of environmental pollution caused by construction waste but its mechanical properties have not been unified and need further study.The strengt...The application of self-compacting recycled concrete can solve the problem of environmental pollution caused by construction waste but its mechanical properties have not been unified and need further study.The strength of recycled concrete is unstable,and its performance still needs further study.The combination of fixed sand and stone volume method and free water cement ratio method is used to determine the mix ratio of self-compacting recycled concrete.24 sets of slump expansion tests and 24 sets of cube axial compression tests were carried out to study the effect of recycled aggregate replacement rate on the flow performance and axial compressive strength of self-compacting recycled concrete,and the performance conversion formula of self-compacting recycled concrete was given.The results show that with the increase of the regenerated coarse aggregate substitution rate,the fluidity and filling property of the self-compacting regenerated concrete mix decreased.The failure of self-compacting recycled concrete is mainly due to the failure of strength between old mortar and new mixture.As the substitution rate increases from 0 to 100%,the axial compressive strength decreases by 15.2%.展开更多
A multi-purpose prototype test system is developed to study the mechanical behavior of tunnel sup-porting structure,including a modular counterforce device,a powerful loading equipment,an advanced intelligent manageme...A multi-purpose prototype test system is developed to study the mechanical behavior of tunnel sup-porting structure,including a modular counterforce device,a powerful loading equipment,an advanced intelligent management system and an efficient noncontact deformation measurement system.The functions of the prototype test system are adjustable size and shape of the modular counterforce structure,sufficient load reserve and accurate loading,multi-connection linkage intelligent management,and high-precision and continuously positioned noncontact deformation measurement.The modular counterforce structure is currently the largest in the world,with an outer diameter of 20.5 m,an inner diameter of 16.5 m and a height of 6 m.The case application proves that the prototype test system can reproduce the mechanical behavior of the tunnel lining during load-bearing,deformation and failure processes in detail.展开更多
Mechanical excavation,blasting,adjacent rockburst and fracture slip that occur during mining excavation impose dynamic loads on the rock mass,leading to further fracture of damaged surrounding rock in three-dimensiona...Mechanical excavation,blasting,adjacent rockburst and fracture slip that occur during mining excavation impose dynamic loads on the rock mass,leading to further fracture of damaged surrounding rock in three-dimensional high-stress and even causing disasters.Therefore,a novel complex true triaxial static-dynamic combined loading method reflecting underground excavation damage and then frequent intermittent disturbance failure is proposed.True triaxial static compression and intermittent disturbance tests are carried out on monzogabbro.The effects of intermediate principal stress and amplitude on the strength characteristics,deformation characteristics,failure characteristics,and precursors of monzogabbro are analyzed,intermediate principal stress and amplitude increase monzogabbro strength and tensile fracture mechanism.Rapid increases in microseismic parameters during rock loading can be precursors for intermittent rock disturbance.Based on the experimental result,the new damage fractional elements and method with considering crack initiation stress and crack unstable stress as initiation and acceleration condition of intermittent disturbance irreversible deformation are proposed.A novel three-dimensional disturbance fractional deterioration model considering the intermediate principal stress effect and intermittent disturbance damage effect is established,and the model predicted results align well with the experimental results.The sensitivity of stress states and model parameters is further explored,and the intermittent disturbance behaviors at different f are predicted.This study provides valuable theoretical bases for the stability analysis of deep mining engineering under dynamic loads.展开更多
Grouted rock bolts subject to axial loading in the field exhibit various failure modes,among which the most predominant one is the bolt-grout interface failure.Thus,mechanical characterization of the grout is essentia...Grouted rock bolts subject to axial loading in the field exhibit various failure modes,among which the most predominant one is the bolt-grout interface failure.Thus,mechanical characterization of the grout is essential for understanding its performance in ground support.To date,few studies have been conducted to characterize the mechanical behaviour of fiber-reinforced grout(FRG)in rock bolt reinforcement.Here we experimentally studied the mechanical behaviour of FRG under uniaxial compression,indirect tension,and direct shear loading conditions.We also conducted a series of pullout tests of rebar bolt encapsulated with different grouts including conventional cementitious grout and FRG.FRG was developed using 15%silica fume(SF)replacement of cement(by weight)and steel fiber to achieve highstrength and crack-resistance to overcome drawbacks of the conventional grout.Two types of steel fibers including straight and wavy steel fibers were further added to enhance the grout quality.The effect of fiber shape and fiber volume proportion on the grout mechanical properties were examined.Our experimental results showed that the addition of SF and steel fiber by 1.5%fiber volume proportion could lead to the highest compressive,tensile,and shear strengths of the grout.The minimum volume of fiber that could improve the mechanical properties of grout was found at 0.5%.The scanning electron microscopy(SEM)analysis demonstrated that steel fibers act as an excellent bridge to prevent the cracks from propagating at the interfacial region and hence to aid in maintaining the integrity of the cementitious grout.Our laboratory pullout tests further confirmed that FRG could prevent the cylindrical grout annulus from radial crack and hence improve the rebar’s load carrying capacity.Therefore,FRG has a potential to be utilized in civil and mining applications where high-strength and crack-resistance support is required.展开更多
A device for supporting soft rock masses combined with a constant resistance structure characterized by constant resistance and large deformation at the end of a steel bar, known as the constant resistance and large d...A device for supporting soft rock masses combined with a constant resistance structure characterized by constant resistance and large deformation at the end of a steel bar, known as the constant resistance and large deformation(CRLD) bolt, has recently been developed to counteract soft rock swelling that often occurs during deep mining. In order to further study the mechanical properties of the CRLD bolt, we investigated its mechanical properties by comparison with the conventional strength bolt(rebar) using static pull tests on many aspects, including supporting capacity, elongation, radial deformation, and energy absorption. The tests verified that the mechanical defects of the rebar, which include the decrease of bolt diameter, reduction of supporting capacity, and emergence and evolution of fracture until failure during the whole pull process, were caused by the Poisson's ratio effect. Due to the special structure set on the CRLD bolt, the bolt presents a seemingly unusual phenomenon of the negative Poisson's ratio effect, i.e., the diameter of the constant resistance structure increases while under-pulling. It is the very effect that ensures the extraordinary mechanical properties, including high resistance, large elongation, and strong energy absorption. According to the comparison and analysis of numerical simulation and field test, we can conclude that the CRLD bolt works better than the rebar bolt.展开更多
Two-dimensional(2D)materials are potential candidates for electronic devices due to their unique structures and exceptional physical properties,making them a focal point in nanotechnology research.Accurate assessment ...Two-dimensional(2D)materials are potential candidates for electronic devices due to their unique structures and exceptional physical properties,making them a focal point in nanotechnology research.Accurate assessment of the mechanical and tribological properties of 2D materials is imperative to fully exploit their potential across diverse applications.However,their nanoscale thickness and planar nature pose significant challenges in testing and characterizing their mechanical properties.Among the in situ characterization techniques,atomic force microscopy(AFM)has gained widespread applications in exploring the mechanical behaviour of nanomaterials,because of the easy measurement capability of nano force and displacement from the AFM tips.Specifically,AFM-based force spectroscopy is a common approach for studying the mechanical and tribological properties of 2D materials.This review comprehensively details the methods based on normal force spectroscopy,which are utilized to test and characterize the elastic and fracture properties,adhesion,and fatigue of 2D materials.Additionally,the methods using lateral force spectroscopy can characterize the interfacial properties of 2D materials,including surface friction of 2D materials,shear behaviour of interlayers as well as nanoflake-substrate interfaces.The influence of various factors,such as testing methods,external environments,and the properties of test samples,on the measured mechanical properties is also addressed.In the end,the current challenges and issues in AFM-based measurements of mechanical and tribological properties of 2D materials are discussed,which identifies the trend in the combination of multiple methods concerning the future development of the in situ testing techniques.展开更多
In order to study the effect of PVA fiber on the dynamic and static mechanical properties of low-temperature freeze-thaw concrete under the saturated surface dry state,different contents of PVA fiber were added to pre...In order to study the effect of PVA fiber on the dynamic and static mechanical properties of low-temperature freeze-thaw concrete under the saturated surface dry state,different contents of PVA fiber were added to prepare concrete in this experiment.The concrete was subjected to compression,flexural and SHPB impact tests combined with scanning electron microscopy for microstructure analysis,after different times of freeze-thaw cycles in the temperature range of 20-70℃.The experimental results show that the compressive strength of the PVA fiber reinforced concrete first increases and then decreases after freeze and thaw cycles,and the compressive strength is positively correlated with the fiber content.The flexural strength gradually decreases with freeze-thaw cycles.The flexural strength of the concrete with 1.2 kg/m^(3) of PVA fiber presents the lowest strength loss after 45 freeze and thaw cycles,which is about 14%.The dynamic failure strength gradually decreases with the increase of freeze-thaw times,and the reduction amplitude decreases with the increase of PVA fiber content.The best impact resistance is achieved when the PVA fiber dosage is 1.2 kg/m^(3).展开更多
The mechanical properties of the SiC fiber-reinforced Mg-Al metal matrix composite materials have been studied on internal microstructure by (scanning electron microscopy) SEM in-situ tensile test. The emergence and p...The mechanical properties of the SiC fiber-reinforced Mg-Al metal matrix composite materials have been studied on internal microstructure by (scanning electron microscopy) SEM in-situ tensile test. The emergence and propagation of the crack, and the fracture behavior in materials have been observed and studied. It is found that in the case of the tensile test, the crack emerged in SiC fiber initially. In the case of the strong cohesion of the fiber-metal interface, the crack propagated in the fiber, meanwhile the fibers in the neighborhood of the cracked fiber began to crack and the Mg-Al metal deformed plastically, and at last the material fractured. Otherwise the toughness of the materials grows in the case of the lower cohesion of the fiber-metal matrix interface.展开更多
A composite rubber concrete(CRC)was designed by combining waste tire rubber particles with particle sizes of 3~5 mm,1~3 mm and 20 mesh.Taking the rubber content of different particle sizes as the influencing factors,t...A composite rubber concrete(CRC)was designed by combining waste tire rubber particles with particle sizes of 3~5 mm,1~3 mm and 20 mesh.Taking the rubber content of different particle sizes as the influencing factors,the range and variance analysis of the mechanical and impermeability properties of CRC was carried out by orthogonal test.Through analysis,it is concluded that the optimal proportion of 3~5 mm,1~3 mm,and 20 mesh particle size composite rubber is 1:2.5:5.5 kinds of CRC and 3 kinds of ordinary single-mixed rubber concrete(RC)with a total content of 10%~20%were designed under this ratio,and the salt-freezing cycle test was carried out with a concentration of 5%Na 2 SO4 solution.The physical and mechanical damage laws during 120 salt-freezing cycles are obtained,and the corresponding damage prediction model is established according to the experimental data.The results show that:on the one hand,the composite rubber in CRC produces a more uniform“graded”structure,forms a retractable particle group,and reduces the loss of mechanical properties of CRC.On the other hand,colloidal particles with different particle sizes are used as air entraining agent to improve the pore structure of concrete and introduce evenly dispersed bubbles,which fundamentally improves the durability of concrete.Under the experimental conditions,the CRC performance is the best when the overall content of composite rubber is 15%.展开更多
The effect of a variety of geometrics, initial conditions and material properties on the deformation behavior of thin films in the plane-strain bulge test was systematically scrutinized by performing the finite elemen...The effect of a variety of geometrics, initial conditions and material properties on the deformation behavior of thin films in the plane-strain bulge test was systematically scrutinized by performing the finite element analysis, and then the accuracy of the plane-strain bulge test in determining the mechanical properties of thin films in terms of our finite element results was analyzed. The results indicate that although the determination of the plane-strain modulus in the light of the plane-strain bulge equation is fairly accurate, the calculation of the residual stress is not satisfied as expected, especially for low residual stress. Finally, an approach is proposed for analyzing bulge test data, which will improve the accuracy and reliability of this bulge test technique.展开更多
The elastoplastic mechanical properties of the weld and heat affected zone metals have comparatively major impact on the forming process of tailor-welded blanks. A few scholars investigated the elastoplastic mechanica...The elastoplastic mechanical properties of the weld and heat affected zone metals have comparatively major impact on the forming process of tailor-welded blanks. A few scholars investigated the elastoplastic mechanical properties of the weld and heat affected zone, but they only simply assumed that it was a uniform distribution elastoplastic material different from the base materials. Four types of tailor-welded blanks which consist of ST12 and 304 stainless steel plates are selected as the research objects, the elastoplastic mechanical properties of the tailor-welded blanks weld and heat affected zone metals are obtained based on the nanoindentation tests, and the Erichsen cupping tests are conducted by combining numerical simulation with physical experiment. The nanoindentation tests results demonstrate that the elastoplastic mechanical properties of the weld and heat affected zone metals are not only different from the base materials, but also varying between the weld metals and the heat affected zone metals. Comparing the Erichsen cupping test resulted from numerical with that from experimental method, it is found that the numerical value of Erichsen cupping test which consider the elastoplastic mechanical properties of the weld and heat affected zone metals have a good agreement with the experimental result, and the relative error is only 4.8%. The proposed research provides good solutions for the inhomogeneous elastoplastic mechanical properties of the tailor-welded blanks weld and heat affected zone metals, and improves the control performance of tailor-welded blanks forming accuracy.展开更多
It is important to quantify the effect of the root diameter, the embedment length of the root and load speed on the soil-root interface mechanical properties for studying the root anchorage. The soilroot interface mec...It is important to quantify the effect of the root diameter, the embedment length of the root and load speed on the soil-root interface mechanical properties for studying the root anchorage. The soilroot interface mechanical properties can be obtained through the pullout force and root slippage curve(F-S curve). About 120 Pinus tabulaeformis single roots whose diameters ranged from 1 mm to 10 mm divided into 6 groups based on different root embedment length(50 mm, 100 mm and 150 mm) and different load velocity(10 mm·min^(-1), 50 mm·min^(-1), 100 mm·min^(-1) and 300 mm·min^(-1)) were investigated using the pullout method. This study aims to explore the mechanical properties of the soil-root interface in the real conditions using the pullout test method. The results showed two kinds of pullout test failure modes during the experimental process: breakage failure and pullout failure. The results showed that the roots were easier to be broken when the root diameter was smaller or the loading speed was larger. The relationship between the maximum anchorage force and root diameter was linear and the linearly dependent coefficient(R^2) was larger than 0.85. The anchorage force increased with the root embedment length. An increase of 10%^(-1)5% for the maximumanchorage force was found when load speed increased from 10 to 300 mm.min^(-1). The mean peak slippage of the root was from 13.81 to 35.79 mm when the load velocity varied from 10 to 300 mm.min^(-1). The study will be helpful for the design of slopes reinforced by vegetation and in predicting risk of uprooting of trees, and will have practical benefits for understanding the mechanism of landslide.展开更多
The high-temperature mechanical properties of 95W-3.5Ni-1.5Fe and 95W-4.5Ni-0.5Co alloys were investigated in the temperature range of room temperature to1100℃. The yield strength and tensile strengths declined gradu...The high-temperature mechanical properties of 95W-3.5Ni-1.5Fe and 95W-4.5Ni-0.5Co alloys were investigated in the temperature range of room temperature to1100℃. The yield strength and tensile strengths declined gradually, and the ductility of both alloys increased as the testing temperature was increased to 300℃. All the three properties reached a plateau at temperatures between 300 and 500℃ in the case of 95W-3.5Ni-l.5Fe and at temperatures between 350 and 700℃ in the case of 95W-4.5Ni-0.5Co. Thereafter, the ductility as well as yield and tensile strengths decreased considerably.展开更多
Mechanical properties of silicon nanobeams are of prime importance in nanoelectromechanical system applications. A numerical experimental method of determining resonant frequencies and Young's modulus of nanobeams by...Mechanical properties of silicon nanobeams are of prime importance in nanoelectromechanical system applications. A numerical experimental method of determining resonant frequencies and Young's modulus of nanobeams by combining finite element analysis and frequency response tests based on an electrostatic excitation and visual detection by using a laser Doppler vibrometer is presented in this paper. Silicon nanobeam test structures are fabricated from silicon-oninsulator wafers by using a standard lithography and anisotropic wet etching release process, which inevitably generates the undercut of the nanobeam clamping. In conjunction with three-dimensional finite element numerical simulations incorporating the geometric undercut, dynamic resonance tests reveal that the undercut significantly reduces resonant frequencies of nanobeams due to the fact that it effectively increases the nanobeam length by a correct value △L, which is a key parameter that is correlated with deviations in the resonant frequencies predicted from the ideal Euler-Bernoulli beam theory and experimentally measured data. By using a least-square fit expression including △L, we finally extract Young's modulus from the measured resonance frequency versus effective length dependency and find that Young's modulus of a silicon nanobeam with 200-nm thickness is close to that of bulk silicon. This result supports that the finite size effect due to the surface effect does not play a role in the mechanical elastic behaviour of silicon nanobeams with thickness larger than 200 nm.展开更多
The mechanical properties are essentially different when rock material is subjected to loading or unloading conditions. In this study, loading and unloading tests with various confining pressures are conducted to inve...The mechanical properties are essentially different when rock material is subjected to loading or unloading conditions. In this study, loading and unloading tests with various confining pressures are conducted to investigate the mechanical properties of marble material samples taken from the deep diversion tunnels of Jinping II Hydropower Station. The stress-strain relationship, failure characteristics and strength criterion are compared and analyzed based on the experiment results. The results show: in the loading and unloading test, peak strength, lateral strain, axial strain and plastic deformation increase significantly as the confining pressure increases. Lateral strain increased significantly and obvious lateral dilatancy can be observed to the change of confining pressure; The fracture mode is mainly the single shear fracture for the triaxial compression test and post-peak test, angle between the failure surface and the ends of the rock material becomes smaller as the confining pressure increases. Hock-Brown strength criterion reflects the strength characteristics of marble material under two different unloading conditions, and has some supplementary effects to the rock material of mechanical field.展开更多
The macro mechanical properties of materials with characteristics of large scale and complicated structural composition can be analyzed through its reconstructed meso-structures.In this work,the meso-structures of tal...The macro mechanical properties of materials with characteristics of large scale and complicated structural composition can be analyzed through its reconstructed meso-structures.In this work,the meso-structures of talus deposits that widely exist in the hydro-power engineering in the southwest of China were first reconstructed by small particles according to the in-situ photographs based on the self-adaptive PCNN digital image processing,and then numerical direct shear tests were carried out for studying the mechanical properties of talus deposits.Results indicate that the reconstructed meso-structures of talus deposits are more consistent with the actual situation because the self-adaptive PCNN digital image processing has a higher discrimination in the details of soil-rock segmentation.The existence and random distribution of rock blocks make the initial shear stiffness,the peak strength and the residual strength higher than those of the "pure soil" with particle size less than 1.25 cm apparently,but reduce the displacements required for the talus deposits reaching its peak shear strength.The increase of rock proportion causes a significant improvement in the internal friction angle of talus deposit,which to a certain degree leads to the characteristics of shear stress-displacement curves having a changing trend from the plastic strain softening deformation to the nonlinear strain hardening deformation,while an unconspicuous increase in cohesion.The uncertainty and heterogeneity of rock distributions cause the differences of rock proportion within shear zone,leading to a relatively strong fluctuation in peak strengths during the shear process,while movement features of rock blocks,such as translation,rotation and crossing,expand the scope of shear zone,increase the required shear force,and also directly lead to the misjudgment that the lower shear strength is obtained from the samples with high rock proportion.That,however,just explains the reason why the shear strength gained from a small amount of indoor test data is not consistent with engineering practice.展开更多
A micro shear testing method which can suit to measure the mechanical properties of heterogeneous materials is introduced, and the properties in each zone of welded joint for CO2 arc welding can be evaluated by using ...A micro shear testing method which can suit to measure the mechanical properties of heterogeneous materials is introduced, and the properties in each zone of welded joint for CO2 arc welding can be evaluated by using this method in this paper. Moreover, these results are compared with those results of Charpy V-notch impact test and their correlation is discussed.展开更多
基金supported by the National Natural Science Foundation of China (Grant No. 52278420)the China Atomic Energy Authority (CAEA) for China’s URL Development Program and the Geological Disposal Program。
文摘Rock has mechanical characteristics and a fracture damage mechanism that are closely related to its loading history and loading path. The mechanical properties, fracture damage features, acoustic emission(AE) characteristics, and strain energy evolution of the Beishan shallow-layer granite used in triaxial unloading tests were investigated in this study. Three groups of triaxial tests, namely, conventional triaxial compression test(Group Ⅰ), maintaining deviatoric stress synchronously unloading confining pressure test(Group Ⅱ), and loading axial pressure synchronously unloading confining pressure test(Group Ⅲ), were carried out for the cylindrical granite specimens. AE monitoring device was utilized in these tests to determine the degree to which the AE waves and AE events reflected the degree of rock damage. In addition, the crack stress thresholds of the specimens were determined by volumetric strain method and AE parameter method, and strain energy evolution of the rock was explored in different damage stages. The results show that the shallow-layer granite experiences brittle failure during the triaxial loading test and unloading test, and the rock has a greater damage degree during the unloading test. The crack stress thresholds of these samples vary greatly between tests, but the threshold ratios of all samples are similar in the same crack damage stage. The Mogi-Coulomb strength criterion can better describe the unloading failure strength of the rock. The evolution of the AE parameter characteristics and strain energy differs between the specimens used in different stress path tests. The dissipative strain energy is the largest in Group Ⅱ and the smallest in Group Ⅰ.
基金the financial support from the National Natural Science Foundation of China(No.52109119)the Guangxi Natural Science Foundation(No.2021GXNSFBA075030)+2 种基金the Guangxi Science and Technology Project(No.Guike AD20325002)the Chinese Postdoctoral Science Fund Project(No.2022M723408)the Open Research Fund of State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin(China Institute of Water Resources and Hydropower Research)(No.IWHR-SKL-202202)。
文摘The far-field microdynamic disturbance caused by the excavation of deep mineral resources and underground engineering can induce surrounding rock damage in high-stress conditions and even lead to disasters.However,the mechanical properties and damage/fracture evolution mechanisms of deep rock induced by microdynamic disturbance under three-dimensional stress states are unclear.Therefore,a true triaxial multilevel disturbance test method is proposed,which can completely simulate natural geostress,excavation stress redistribution(such as stress unloading,concentration and rotation),and subsequently the microdynamic disturbance triggering damaged rock failure.Based on a dynamic true triaxial test platform,true triaxial microdynamic disturbance tests under different frequency and amplitudes were carried out on monzogabbro.The results show that increasing amplitude or decreasing frequency diminishes the failure strength of monzogabbro.Deformation modulus gradually decreases during disturbance failure.As frequency and amplitude increase,the degradation rate of deformation modulus decreases slightly,disturbance dissipated energy increases significantly,and disturbance deformation anisotropy strengthens obviously.A damage model has been proposed to quantitatively characterize the disturbance-induced damage evolution at different frequency and amplitude under true triaxial stress.Before disturbance failure,the micro-tensile crack mechanism is dominant,and the micro-shear crack mechanism increases significantly at failure.With the increase of amplitude and frequency,the micro-shear crack mechanism increases.When approaching disturbance failure,the acoustic emission fractal dimension changes from a stable value to local large oscillation,and finally increases sharply to a high value at failure.Finally,the disturbance-induced failure mechanism of surrounding rock in deep engineering is clearly elucidated.
基金supported by the National Key Research and Development Program of China (Grant No.2021YFB2600800)the National Key Research and Development 451 Program of China (Grant No.2021YFC3100803)the Guangdong Innovative and Entrepreneurial Research Team Program (Grant No.2016ZT06N340).
文摘The polyurethane foam(PU)compressible layer is a viable solution to the problem of damage to the secondary lining in squeezing tunnels.Nevertheless,the mechanical behaviour of the multi-layer yielding supports has not been thoroughly investigated.To fill this gap,large-scale model tests were conducted in this study.The synergistic load-bearing mechanics were analyzed using the convergenceconfinement method.Two types of multi-layer yielding supports with different thicknesses(2.5 cm,3.75 cm and 5 cm)of PU compressible layers were investigated respectively.Digital image correlation(DIC)analysis and acoustic emission(AE)techniques were used for detecting the deformation fields and damage evolution of the multi-layer yielding supports in real-time.Results indicated that the loaddisplacement relationship of the multi-layer yielding supports could be divided into the crack initiation,crack propagation,strain-hardening,and failure stages.Compared with those of the stiff support,the toughness,deformability and ultimate load of the yielding supports were increased by an average of 225%,61%and 32%,respectively.Additionally,the PU compressible layer is positioned between two primary linings to allow the yielding support to have greater mechanical properties.The analysis of the synergistic bearing effect suggested that the thickness of PU compressible layer and its location significantly affect the mechanical properties of the yielding supports.The use of yielding supports with a compressible layer positioned between the primary and secondary linings is recommended to mitigate the effects of high geo-stress in squeezing tunnels.
文摘The application of self-compacting recycled concrete can solve the problem of environmental pollution caused by construction waste but its mechanical properties have not been unified and need further study.The strength of recycled concrete is unstable,and its performance still needs further study.The combination of fixed sand and stone volume method and free water cement ratio method is used to determine the mix ratio of self-compacting recycled concrete.24 sets of slump expansion tests and 24 sets of cube axial compression tests were carried out to study the effect of recycled aggregate replacement rate on the flow performance and axial compressive strength of self-compacting recycled concrete,and the performance conversion formula of self-compacting recycled concrete was given.The results show that with the increase of the regenerated coarse aggregate substitution rate,the fluidity and filling property of the self-compacting regenerated concrete mix decreased.The failure of self-compacting recycled concrete is mainly due to the failure of strength between old mortar and new mixture.As the substitution rate increases from 0 to 100%,the axial compressive strength decreases by 15.2%.
文摘A multi-purpose prototype test system is developed to study the mechanical behavior of tunnel sup-porting structure,including a modular counterforce device,a powerful loading equipment,an advanced intelligent management system and an efficient noncontact deformation measurement system.The functions of the prototype test system are adjustable size and shape of the modular counterforce structure,sufficient load reserve and accurate loading,multi-connection linkage intelligent management,and high-precision and continuously positioned noncontact deformation measurement.The modular counterforce structure is currently the largest in the world,with an outer diameter of 20.5 m,an inner diameter of 16.5 m and a height of 6 m.The case application proves that the prototype test system can reproduce the mechanical behavior of the tunnel lining during load-bearing,deformation and failure processes in detail.
基金the financial support from the National Natural Science Foundation of China(No.52109119)the Guangxi Natural Science Foundation(No.2021GXNSFBA075030)+2 种基金the Guangxi Science and Technology Project(No.Guike AD20325002)the Chinese Postdoctoral Science Fund Project(No.2022 M723408)the Open Research Fund of State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin(China Institute of Water Resources and Hydropower Research)(No.IWHR-SKL-202202).
文摘Mechanical excavation,blasting,adjacent rockburst and fracture slip that occur during mining excavation impose dynamic loads on the rock mass,leading to further fracture of damaged surrounding rock in three-dimensional high-stress and even causing disasters.Therefore,a novel complex true triaxial static-dynamic combined loading method reflecting underground excavation damage and then frequent intermittent disturbance failure is proposed.True triaxial static compression and intermittent disturbance tests are carried out on monzogabbro.The effects of intermediate principal stress and amplitude on the strength characteristics,deformation characteristics,failure characteristics,and precursors of monzogabbro are analyzed,intermediate principal stress and amplitude increase monzogabbro strength and tensile fracture mechanism.Rapid increases in microseismic parameters during rock loading can be precursors for intermittent rock disturbance.Based on the experimental result,the new damage fractional elements and method with considering crack initiation stress and crack unstable stress as initiation and acceleration condition of intermittent disturbance irreversible deformation are proposed.A novel three-dimensional disturbance fractional deterioration model considering the intermediate principal stress effect and intermittent disturbance damage effect is established,and the model predicted results align well with the experimental results.The sensitivity of stress states and model parameters is further explored,and the intermittent disturbance behaviors at different f are predicted.This study provides valuable theoretical bases for the stability analysis of deep mining engineering under dynamic loads.
文摘Grouted rock bolts subject to axial loading in the field exhibit various failure modes,among which the most predominant one is the bolt-grout interface failure.Thus,mechanical characterization of the grout is essential for understanding its performance in ground support.To date,few studies have been conducted to characterize the mechanical behaviour of fiber-reinforced grout(FRG)in rock bolt reinforcement.Here we experimentally studied the mechanical behaviour of FRG under uniaxial compression,indirect tension,and direct shear loading conditions.We also conducted a series of pullout tests of rebar bolt encapsulated with different grouts including conventional cementitious grout and FRG.FRG was developed using 15%silica fume(SF)replacement of cement(by weight)and steel fiber to achieve highstrength and crack-resistance to overcome drawbacks of the conventional grout.Two types of steel fibers including straight and wavy steel fibers were further added to enhance the grout quality.The effect of fiber shape and fiber volume proportion on the grout mechanical properties were examined.Our experimental results showed that the addition of SF and steel fiber by 1.5%fiber volume proportion could lead to the highest compressive,tensile,and shear strengths of the grout.The minimum volume of fiber that could improve the mechanical properties of grout was found at 0.5%.The scanning electron microscopy(SEM)analysis demonstrated that steel fibers act as an excellent bridge to prevent the cracks from propagating at the interfacial region and hence to aid in maintaining the integrity of the cementitious grout.Our laboratory pullout tests further confirmed that FRG could prevent the cylindrical grout annulus from radial crack and hence improve the rebar’s load carrying capacity.Therefore,FRG has a potential to be utilized in civil and mining applications where high-strength and crack-resistance support is required.
基金supported by National Key Research and Development Program(2016YFC0600901)the National Natural Science Foundation of China(Grant Nos.51374214,51134005 and 51574248)+1 种基金the Special Fund of Basic Research and Operating of China University of Mining&Technology,Beijing(Grant Nos.2009QL03)the State Scholarship Fund of China
文摘A device for supporting soft rock masses combined with a constant resistance structure characterized by constant resistance and large deformation at the end of a steel bar, known as the constant resistance and large deformation(CRLD) bolt, has recently been developed to counteract soft rock swelling that often occurs during deep mining. In order to further study the mechanical properties of the CRLD bolt, we investigated its mechanical properties by comparison with the conventional strength bolt(rebar) using static pull tests on many aspects, including supporting capacity, elongation, radial deformation, and energy absorption. The tests verified that the mechanical defects of the rebar, which include the decrease of bolt diameter, reduction of supporting capacity, and emergence and evolution of fracture until failure during the whole pull process, were caused by the Poisson's ratio effect. Due to the special structure set on the CRLD bolt, the bolt presents a seemingly unusual phenomenon of the negative Poisson's ratio effect, i.e., the diameter of the constant resistance structure increases while under-pulling. It is the very effect that ensures the extraordinary mechanical properties, including high resistance, large elongation, and strong energy absorption. According to the comparison and analysis of numerical simulation and field test, we can conclude that the CRLD bolt works better than the rebar bolt.
基金support from the National Natural Science Foundation of China(Nos.52005151,12172118,52205591,12227801,and 12072005)the Local Science and Technology Development Fund Projects Guided by the Central Government of China(No.236Z1810G)+4 种基金the Natural Science Foundation of Hebei Province(Nos.E2021202008 and E2021202100)the Fund for Innovative Research Groups of Natural Science Foundation of Hebei Province(No.A2020202002)the Key Program of Research and Development of Hebei Province(No.202030507040009)the Project of High-Level Talents Introduction of Hebei Province(No.2021HBQZYCSB009)the Key Project of National Natural Science Foundation of Tianjin(No.S20ZDF077).
文摘Two-dimensional(2D)materials are potential candidates for electronic devices due to their unique structures and exceptional physical properties,making them a focal point in nanotechnology research.Accurate assessment of the mechanical and tribological properties of 2D materials is imperative to fully exploit their potential across diverse applications.However,their nanoscale thickness and planar nature pose significant challenges in testing and characterizing their mechanical properties.Among the in situ characterization techniques,atomic force microscopy(AFM)has gained widespread applications in exploring the mechanical behaviour of nanomaterials,because of the easy measurement capability of nano force and displacement from the AFM tips.Specifically,AFM-based force spectroscopy is a common approach for studying the mechanical and tribological properties of 2D materials.This review comprehensively details the methods based on normal force spectroscopy,which are utilized to test and characterize the elastic and fracture properties,adhesion,and fatigue of 2D materials.Additionally,the methods using lateral force spectroscopy can characterize the interfacial properties of 2D materials,including surface friction of 2D materials,shear behaviour of interlayers as well as nanoflake-substrate interfaces.The influence of various factors,such as testing methods,external environments,and the properties of test samples,on the measured mechanical properties is also addressed.In the end,the current challenges and issues in AFM-based measurements of mechanical and tribological properties of 2D materials are discussed,which identifies the trend in the combination of multiple methods concerning the future development of the in situ testing techniques.
基金Funded by the National Natural Science Foundation of China (No.51972214)the Innovation Team of Higher Education Institutions in Liaoning Province (No.LT2019012)。
文摘In order to study the effect of PVA fiber on the dynamic and static mechanical properties of low-temperature freeze-thaw concrete under the saturated surface dry state,different contents of PVA fiber were added to prepare concrete in this experiment.The concrete was subjected to compression,flexural and SHPB impact tests combined with scanning electron microscopy for microstructure analysis,after different times of freeze-thaw cycles in the temperature range of 20-70℃.The experimental results show that the compressive strength of the PVA fiber reinforced concrete first increases and then decreases after freeze and thaw cycles,and the compressive strength is positively correlated with the fiber content.The flexural strength gradually decreases with freeze-thaw cycles.The flexural strength of the concrete with 1.2 kg/m^(3) of PVA fiber presents the lowest strength loss after 45 freeze and thaw cycles,which is about 14%.The dynamic failure strength gradually decreases with the increase of freeze-thaw times,and the reduction amplitude decreases with the increase of PVA fiber content.The best impact resistance is achieved when the PVA fiber dosage is 1.2 kg/m^(3).
文摘The mechanical properties of the SiC fiber-reinforced Mg-Al metal matrix composite materials have been studied on internal microstructure by (scanning electron microscopy) SEM in-situ tensile test. The emergence and propagation of the crack, and the fracture behavior in materials have been observed and studied. It is found that in the case of the tensile test, the crack emerged in SiC fiber initially. In the case of the strong cohesion of the fiber-metal interface, the crack propagated in the fiber, meanwhile the fibers in the neighborhood of the cracked fiber began to crack and the Mg-Al metal deformed plastically, and at last the material fractured. Otherwise the toughness of the materials grows in the case of the lower cohesion of the fiber-metal matrix interface.
基金supported by the National Key Research and Development Program of China under the Grant No.2018YFC0809400.
文摘A composite rubber concrete(CRC)was designed by combining waste tire rubber particles with particle sizes of 3~5 mm,1~3 mm and 20 mesh.Taking the rubber content of different particle sizes as the influencing factors,the range and variance analysis of the mechanical and impermeability properties of CRC was carried out by orthogonal test.Through analysis,it is concluded that the optimal proportion of 3~5 mm,1~3 mm,and 20 mesh particle size composite rubber is 1:2.5:5.5 kinds of CRC and 3 kinds of ordinary single-mixed rubber concrete(RC)with a total content of 10%~20%were designed under this ratio,and the salt-freezing cycle test was carried out with a concentration of 5%Na 2 SO4 solution.The physical and mechanical damage laws during 120 salt-freezing cycles are obtained,and the corresponding damage prediction model is established according to the experimental data.The results show that:on the one hand,the composite rubber in CRC produces a more uniform“graded”structure,forms a retractable particle group,and reduces the loss of mechanical properties of CRC.On the other hand,colloidal particles with different particle sizes are used as air entraining agent to improve the pore structure of concrete and introduce evenly dispersed bubbles,which fundamentally improves the durability of concrete.Under the experimental conditions,the CRC performance is the best when the overall content of composite rubber is 15%.
基金Project(11172258)supported by the National Natural Science Foundation of China
文摘The effect of a variety of geometrics, initial conditions and material properties on the deformation behavior of thin films in the plane-strain bulge test was systematically scrutinized by performing the finite element analysis, and then the accuracy of the plane-strain bulge test in determining the mechanical properties of thin films in terms of our finite element results was analyzed. The results indicate that although the determination of the plane-strain modulus in the light of the plane-strain bulge equation is fairly accurate, the calculation of the residual stress is not satisfied as expected, especially for low residual stress. Finally, an approach is proposed for analyzing bulge test data, which will improve the accuracy and reliability of this bulge test technique.
基金Supported by National Natural Science Foundation of China(Grant No.51275444)Specialized Research Fund for the Doctoral Program of Higher Education(Grant No.20121333110003)Natural Science Foundation-Steel and Iron Foundation of Hebei Province,China(Grant No.E2014203271)
文摘The elastoplastic mechanical properties of the weld and heat affected zone metals have comparatively major impact on the forming process of tailor-welded blanks. A few scholars investigated the elastoplastic mechanical properties of the weld and heat affected zone, but they only simply assumed that it was a uniform distribution elastoplastic material different from the base materials. Four types of tailor-welded blanks which consist of ST12 and 304 stainless steel plates are selected as the research objects, the elastoplastic mechanical properties of the tailor-welded blanks weld and heat affected zone metals are obtained based on the nanoindentation tests, and the Erichsen cupping tests are conducted by combining numerical simulation with physical experiment. The nanoindentation tests results demonstrate that the elastoplastic mechanical properties of the weld and heat affected zone metals are not only different from the base materials, but also varying between the weld metals and the heat affected zone metals. Comparing the Erichsen cupping test resulted from numerical with that from experimental method, it is found that the numerical value of Erichsen cupping test which consider the elastoplastic mechanical properties of the weld and heat affected zone metals have a good agreement with the experimental result, and the relative error is only 4.8%. The proposed research provides good solutions for the inhomogeneous elastoplastic mechanical properties of the tailor-welded blanks weld and heat affected zone metals, and improves the control performance of tailor-welded blanks forming accuracy.
基金supported by the Fundamental Research Funds for the Central Universities(No.YX2010-20)the Open Projects Foundation of Key Laboratory of Soil and Water Conservation & Desertification Combat (Beijing ForestryUniversity), Ministry of Education of P.R. China (No.201002) the National Natural Science Foundation of China (No. 31570708, No.30901162)
文摘It is important to quantify the effect of the root diameter, the embedment length of the root and load speed on the soil-root interface mechanical properties for studying the root anchorage. The soilroot interface mechanical properties can be obtained through the pullout force and root slippage curve(F-S curve). About 120 Pinus tabulaeformis single roots whose diameters ranged from 1 mm to 10 mm divided into 6 groups based on different root embedment length(50 mm, 100 mm and 150 mm) and different load velocity(10 mm·min^(-1), 50 mm·min^(-1), 100 mm·min^(-1) and 300 mm·min^(-1)) were investigated using the pullout method. This study aims to explore the mechanical properties of the soil-root interface in the real conditions using the pullout test method. The results showed two kinds of pullout test failure modes during the experimental process: breakage failure and pullout failure. The results showed that the roots were easier to be broken when the root diameter was smaller or the loading speed was larger. The relationship between the maximum anchorage force and root diameter was linear and the linearly dependent coefficient(R^2) was larger than 0.85. The anchorage force increased with the root embedment length. An increase of 10%^(-1)5% for the maximumanchorage force was found when load speed increased from 10 to 300 mm.min^(-1). The mean peak slippage of the root was from 13.81 to 35.79 mm when the load velocity varied from 10 to 300 mm.min^(-1). The study will be helpful for the design of slopes reinforced by vegetation and in predicting risk of uprooting of trees, and will have practical benefits for understanding the mechanism of landslide.
文摘The high-temperature mechanical properties of 95W-3.5Ni-1.5Fe and 95W-4.5Ni-0.5Co alloys were investigated in the temperature range of room temperature to1100℃. The yield strength and tensile strengths declined gradually, and the ductility of both alloys increased as the testing temperature was increased to 300℃. All the three properties reached a plateau at temperatures between 300 and 500℃ in the case of 95W-3.5Ni-l.5Fe and at temperatures between 350 and 700℃ in the case of 95W-4.5Ni-0.5Co. Thereafter, the ductility as well as yield and tensile strengths decreased considerably.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 41075026 and 61001044)the Open Re-search Fund of Key Laboratory of Microelectromechanical System of Ministry of Education,Southeast University,China (Grant Nos. 2009-03 and 2010-02)+1 种基金the Special Fund for Meteorology Research in the Public Interest,China (Grant No. GYHY200906037)the Priority Academic Program Development of Sensor Networks and Modern Meteorological Equipment of Jiangsu Provincial Higher Education Institutions
文摘Mechanical properties of silicon nanobeams are of prime importance in nanoelectromechanical system applications. A numerical experimental method of determining resonant frequencies and Young's modulus of nanobeams by combining finite element analysis and frequency response tests based on an electrostatic excitation and visual detection by using a laser Doppler vibrometer is presented in this paper. Silicon nanobeam test structures are fabricated from silicon-oninsulator wafers by using a standard lithography and anisotropic wet etching release process, which inevitably generates the undercut of the nanobeam clamping. In conjunction with three-dimensional finite element numerical simulations incorporating the geometric undercut, dynamic resonance tests reveal that the undercut significantly reduces resonant frequencies of nanobeams due to the fact that it effectively increases the nanobeam length by a correct value △L, which is a key parameter that is correlated with deviations in the resonant frequencies predicted from the ideal Euler-Bernoulli beam theory and experimentally measured data. By using a least-square fit expression including △L, we finally extract Young's modulus from the measured resonance frequency versus effective length dependency and find that Young's modulus of a silicon nanobeam with 200-nm thickness is close to that of bulk silicon. This result supports that the finite size effect due to the surface effect does not play a role in the mechanical elastic behaviour of silicon nanobeams with thickness larger than 200 nm.
基金Supported by National Natural Science Foundation of China(No.50974100)WHUT(NO.125106002)
文摘The mechanical properties are essentially different when rock material is subjected to loading or unloading conditions. In this study, loading and unloading tests with various confining pressures are conducted to investigate the mechanical properties of marble material samples taken from the deep diversion tunnels of Jinping II Hydropower Station. The stress-strain relationship, failure characteristics and strength criterion are compared and analyzed based on the experiment results. The results show: in the loading and unloading test, peak strength, lateral strain, axial strain and plastic deformation increase significantly as the confining pressure increases. Lateral strain increased significantly and obvious lateral dilatancy can be observed to the change of confining pressure; The fracture mode is mainly the single shear fracture for the triaxial compression test and post-peak test, angle between the failure surface and the ends of the rock material becomes smaller as the confining pressure increases. Hock-Brown strength criterion reflects the strength characteristics of marble material under two different unloading conditions, and has some supplementary effects to the rock material of mechanical field.
基金Project(2013BAB06B00) supported by the National Key Technology R&D Programof ChinaProject(2011CB013504) supported by the National Basic Research Program of ChinaProject(50911130366) supported by the National Natural Science Foundation of China
文摘The macro mechanical properties of materials with characteristics of large scale and complicated structural composition can be analyzed through its reconstructed meso-structures.In this work,the meso-structures of talus deposits that widely exist in the hydro-power engineering in the southwest of China were first reconstructed by small particles according to the in-situ photographs based on the self-adaptive PCNN digital image processing,and then numerical direct shear tests were carried out for studying the mechanical properties of talus deposits.Results indicate that the reconstructed meso-structures of talus deposits are more consistent with the actual situation because the self-adaptive PCNN digital image processing has a higher discrimination in the details of soil-rock segmentation.The existence and random distribution of rock blocks make the initial shear stiffness,the peak strength and the residual strength higher than those of the "pure soil" with particle size less than 1.25 cm apparently,but reduce the displacements required for the talus deposits reaching its peak shear strength.The increase of rock proportion causes a significant improvement in the internal friction angle of talus deposit,which to a certain degree leads to the characteristics of shear stress-displacement curves having a changing trend from the plastic strain softening deformation to the nonlinear strain hardening deformation,while an unconspicuous increase in cohesion.The uncertainty and heterogeneity of rock distributions cause the differences of rock proportion within shear zone,leading to a relatively strong fluctuation in peak strengths during the shear process,while movement features of rock blocks,such as translation,rotation and crossing,expand the scope of shear zone,increase the required shear force,and also directly lead to the misjudgment that the lower shear strength is obtained from the samples with high rock proportion.That,however,just explains the reason why the shear strength gained from a small amount of indoor test data is not consistent with engineering practice.
文摘A micro shear testing method which can suit to measure the mechanical properties of heterogeneous materials is introduced, and the properties in each zone of welded joint for CO2 arc welding can be evaluated by using this method in this paper. Moreover, these results are compared with those results of Charpy V-notch impact test and their correlation is discussed.