Axially moving beams are often discussed with several classic boundary conditions, such as simply-supported ends, fixed ends, and free ends. Here, axially moving beams with generalized boundary conditions are discusse...Axially moving beams are often discussed with several classic boundary conditions, such as simply-supported ends, fixed ends, and free ends. Here, axially moving beams with generalized boundary conditions are discussed for the first time. The beam is supported by torsional springs and vertical springs at both ends. By modifying the stiffness of the springs, generalized boundaries can replace those classical boundaries. Dynamic stiffness matrices are, respectively, established for axially moving Timoshenko beams and Euler-Bernoulli (EB) beams with generalized boundaries. In order to verify the applicability of the EB model, the natural frequencies of the axially moving Timoshenko beam and EB beam are compared. Furthermore, the effects of constrained spring stiffness on the vibration frequencies of the axially moving beam are studied. Interestingly, it can be found that the critical speed of the axially moving beam does not change with the vertical spring stiffness. In addition, both the moving speed and elastic boundaries make the Timoshenko beam theory more needed. The validity of the dynamic stiffness method is demonstrated by using numerical simulation.展开更多
Rock bolts have been widely used for stabilizing rock mass in geotechnical engineering.It is acknowledged that the bolt profiles have a sound influence on the support effect of the rock bolting system.Previous studies...Rock bolts have been widely used for stabilizing rock mass in geotechnical engineering.It is acknowledged that the bolt profiles have a sound influence on the support effect of the rock bolting system.Previous studies have proposed some optimal rib parameters(e.g.rib spacing);unfortunately,the interface shear behaviors are generally ignored.Therefore,determination of radial stress and radial displacement on the bolt-grout interface using traditional pull-out tests is not possible.The load-bearing capacity and deformation capacity vary as bolt profiles differ,suggesting that the support effect of the bolting system can be enhanced by optimizing bolt profiles.The aim of this study is to investigate the effects of bolt profiles(with/without ribs,rib spacing,and rib height)on the shear behaviors between the rock bolt and grout material using direct shear tests.Thereby,systematic interfacial shear tests with different bolt profiles were performed under both constant normal load(CNL)and constant normal stiffness(CNS)boundary conditions.The results suggested that rib spacing has a more marked influence on the interface shear behavior than rib height does,in particular at the post-yield stage.The results could facilitate our understanding of bolt-grout interface shear behavior under CNS conditions,and optimize selection of rock bolts under in situ rock conditions.展开更多
To reveal the mechanism of shear failure of en-echelon joints under cyclic loading,such as during earthquakes,we conducted a series of cyclic shear tests of en-echelon joints under constant normal stiffness(CNS)condit...To reveal the mechanism of shear failure of en-echelon joints under cyclic loading,such as during earthquakes,we conducted a series of cyclic shear tests of en-echelon joints under constant normal stiffness(CNS)conditions.We analyzed the evolution of shear stress,normal stress,stress path,dilatancy characteristics,and friction coefficient and revealed the failure mechanisms of en-echelon joints at different angles.The results show that the cyclic shear behavior of the en-echelon joints is closely related to the joint angle,with the shear strength at a positive angle exceeding that at a negative angle during shear cycles.As the number of cycles increases,the shear strength decreases rapidly,and the difference between the varying angles gradually decreases.Dilation occurs in the early shear cycles(1 and 2),while contraction is the main feature in later cycles(310).The friction coefficient decreases with the number of cycles and exhibits a more significant sensitivity to joint angles than shear cycles.The joint angle determines the asperities on the rupture surfaces and the block size,and thus determines the subsequent shear failure mode(block crushing and asperity degradation).At positive angles,block size is more greater and asperities on the rupture surface are smaller than at nonpositive angles.Therefore,the cyclic shear behavior is controlled by block crushing at positive angles and asperity degradation at negative angles.展开更多
To ascertain the influence of the boundary friction on mechanical properties of disc-spring vibration isolators a load-displacement hysteresis curve formula of disc-spring vibration isolators is derived on the basis o...To ascertain the influence of the boundary friction on mechanical properties of disc-spring vibration isolators a load-displacement hysteresis curve formula of disc-spring vibration isolators is derived on the basis of the energy conservation law as well as considering the effect of the boundary friction.The formula is validated through the finite element analysis and static load tests.On this basis the effect of the boundary friction on the bearing capacity is researched. Then the dynamic performance of disc-spring vibration isolators is studied by dynamic tests.The experimental results indicate that the boundary friction can promise a larger damping with a ratio of 0.23 for disc-spring vibration isolators.Compared with the loading frequency the loading amplitude has a greater impact on the energy consumption dynamic stiffness and damping of vibration isolators.This research can provide valuable information for the design of disc-spring vibration isolators.展开更多
Rock bolts are widely used in rock engineering projects to improve the shear capacity of the jointed rock mass.The bolt inclination angle with respect to the shear plane has a remarkable influence on the bolting perfo...Rock bolts are widely used in rock engineering projects to improve the shear capacity of the jointed rock mass.The bolt inclination angle with respect to the shear plane has a remarkable influence on the bolting performance.In this study,a new artificial molding method based on 3D scanning and printing technology was first proposed to prepare bolted joints with an inclined bolt.Then,the effects of the bolt inclination angle and boundary conditions on the shear behavior and failure characteristic of bolted joints were addressed by conducting direct shear tests under both CNL and CNS conditions.Results indicated that rock bolt could significantly improve the shear behavior of rock joints,especially in the post-yield deformation region.With the increase of bolt inclination angle,both the maximum shear stress and the maximum friction coefficient increased first and then decreased,while the maximum normal displacement decreased monotonously.Compared with CNL conditions,the maximum shear stress was larger,whereas the maximum normal displacement and friction coefficient were smaller under the CNS conditions.Furthermore,more asperity damage was observed under the CNS conditions due to the increased normal stress on the shear plane.展开更多
The typical shear behaviour of rough joints has been studied under constant normal load/stress （CNL） boundary conditions, but recent studies have shown that this boundary condition may not replicate true practical s...The typical shear behaviour of rough joints has been studied under constant normal load/stress （CNL） boundary conditions, but recent studies have shown that this boundary condition may not replicate true practical situations. Constant normal stiffness （CNS） is more appropriate to describe the stress-strain response of field joints since the CNS boundary condition is more realistic than CNL. The practical implications of CNS are movements of unstable blocks in the roof or walls of an underground excavation, reinforced rock wedges sliding in a rock slope or foundation, and the vertical movement of rock-socketed concrete piles. In this paper, the highlights and limitations of the existing models used to predict the shear strength/behaviour of joints under CNS conditions are discussed in depth.展开更多
In this context,we experimentally studied the anisotropic mechanical behaviors of rough-walled plaster joints using a servo-controlled direct shear apparatus under both constant normal load(CNL)and constant normal sti...In this context,we experimentally studied the anisotropic mechanical behaviors of rough-walled plaster joints using a servo-controlled direct shear apparatus under both constant normal load(CNL)and constant normal stiffness(CNS)conditions.The shear-induced variations in the normal displacement,shear stress,normal stress and sheared-off asperity mass are analyzed and correlated with the inclination angle of the critical waviness of joint surfaces.The results show that CNS condition gives rise to a smaller normal displacement due to the larger normal stress during shearing,compared with CNL condition.Under CNL conditions,there is one peak shear stress during shearing,whereas there are no peak shear stress for some cases and two peaks for other cases under CNS conditions depending on the geometry of joint surfaces.The inclination angle of the critical waviness has been verified to be capable of describing the joint surface roughness and anisotropy.The joint surface is more significantly damaged under CNS conditions than that under CNL conditions.With increment of the inclination angle of the critical waviness,both the normal displaceme nt and shea red-off asperity mass increase,following power law functions;yet the coefficient of deternination under CNL conditions is larger than that under CNS conditions.This is because the CNS condition significantly decreases the inclination angle of the critical waviness during shearing due to the larger degree of asperity degradation.展开更多
Fault activation has been the focus of research community for years.However,the studies of fault activation remain immature,such as the fault activation mode and its major factors under constant normal stiffness(CNS)c...Fault activation has been the focus of research community for years.However,the studies of fault activation remain immature,such as the fault activation mode and its major factors under constant normal stiffness(CNS)conditions associated with large thickness of fault surrounding rock mass.In this study,the rock friction experiments were conducted to understand the fault activation modes under the CNS conditions.Two major parameters,i.e.the initial normal stress and loading rate,were considered and calibrated in the tests.To reveal the response mechanism of fault activation,the local strains near the fault plane were recorded,and the macroscopic stresses and displacements were analyzed.The testing results show that the effect of displacement-controlled loading rate is more pronounced under the CNS conditions than that under constant normal load(CNL)conditions.Both the normal and shear stresses drop suddenly when the stick-slip occurs.The decrease and increase of the normal stress are synchronous with the shear stress in the regular stick-slip scenario,but mismatch with the shear stress during the chaotic stick-slip process.The results are helpful for understanding the fault sliding mode and the prediction and prevention of fault slip.展开更多
为从宏、细观角度揭示常法向刚度(Constant Normal Stiffness,CNS)条件下锯齿状砂岩-混凝土结构面剪切机制,首先采用湖南大学自主改造的CNS岩石直剪仪开展3组砂岩-混凝土结构面室内剪切试验.在此基础上,采用刚性墙替代法建立与室内试验...为从宏、细观角度揭示常法向刚度(Constant Normal Stiffness,CNS)条件下锯齿状砂岩-混凝土结构面剪切机制,首先采用湖南大学自主改造的CNS岩石直剪仪开展3组砂岩-混凝土结构面室内剪切试验.在此基础上,采用刚性墙替代法建立与室内试验相应的离散元数值模型,并引入3个显式运动学方程控制砂岩试样运动轨迹从而实现CNS条件加载,将数值模拟与试验结果对比验证了模型的合理性.随后,开展16个工况的数值剪切试验,通过观察剪切裂纹扩展和力链演化形态,从细观角度揭示结构面破坏模式和荷载传递机制,并从宏观角度分析锯齿几何尺寸(半波长λ、起伏角θ)和加载边界条件(初始法向应力σn0、法向刚度K)对剪切强度和法向膨胀的影响.结果表明:剪切裂纹按照“平稳增加—急剧增加—增幅减小”的发展趋势由结构面区域逐渐向岩石内部扩展,结构面破坏模式随起伏角的增大由滑移磨损向剪断破坏过渡,剪切强度随λ、θ、σn0和K的增加呈指数函数型增加.展开更多
深部岩体节理往往存在不同程度的软弱充填物质,导致岩体力学性质更为复杂。开展恒定法向刚度CNS边界条件下,考虑高初始法向应力及不同节理粗糙系数JRC−充填度△组合模式的加锚充填节理岩体剪切试验,结合微观电镜扫描(scanning electron ...深部岩体节理往往存在不同程度的软弱充填物质,导致岩体力学性质更为复杂。开展恒定法向刚度CNS边界条件下,考虑高初始法向应力及不同节理粗糙系数JRC−充填度△组合模式的加锚充填节理岩体剪切试验,结合微观电镜扫描(scanning electron microscope,简称SEM)分析充填节理部分宏微观结构演变特征,推导CNS边界条件下峰值剪胀角相关计算方法。研究结果表明:当△<0.5,试件剪应力强度呈现应力硬化;当1.0<△≤1.5,剪应力强度由基本恒定演化为应力软化。当△小于临界充填度△_(cr),JRC成为峰值抗剪强度主要影响因素。△在节理法向变形中起到控制作用,随着△的增加,出现剪胀、先剪胀后剪缩、剪缩3种演化规律,JRC则影响着试件剪胀−剪缩变化程度。充填节理部分破坏模式随着△的增加主要经历3个阶段:粗糙点磨平、充填物质摩擦、充填物质磨碎。微观角度下由疏松多孔结构形式演化为散体碎屑状结构形式。受挤压破碎区与挤压应力集中区二者的相互演化机制影响,锚杆剪切变形模式逐渐由△=0的“近似”拉剪变形向△=1.5的拉弯变形模式演变。在此基础上,提出了一种CNS边界条件下加锚充填节理岩体峰值剪胀角的计算公式,并进行了试验验证及边界条件影响参数敏感性分析。展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.11772181 and11422214)the “Dawn” Program of Shanghai Education Commission(Nos.17SG38 and 2019-01-07-00-09-E00018)the Key Research Project of Shanghai Science and Technology Commission(No.18010500100)
文摘Axially moving beams are often discussed with several classic boundary conditions, such as simply-supported ends, fixed ends, and free ends. Here, axially moving beams with generalized boundary conditions are discussed for the first time. The beam is supported by torsional springs and vertical springs at both ends. By modifying the stiffness of the springs, generalized boundaries can replace those classical boundaries. Dynamic stiffness matrices are, respectively, established for axially moving Timoshenko beams and Euler-Bernoulli (EB) beams with generalized boundaries. In order to verify the applicability of the EB model, the natural frequencies of the axially moving Timoshenko beam and EB beam are compared. Furthermore, the effects of constrained spring stiffness on the vibration frequencies of the axially moving beam are studied. Interestingly, it can be found that the critical speed of the axially moving beam does not change with the vertical spring stiffness. In addition, both the moving speed and elastic boundaries make the Timoshenko beam theory more needed. The validity of the dynamic stiffness method is demonstrated by using numerical simulation.
基金This study is supported by the key projects of the Yalong River Joint Fund of the National Natural Science Foundation of China(Grant No.U1865203)the National Key Research and Development Program of China(Grant Nos.2019YFC0605103,2019YFC0605100)the National Natural Science Foundation of China(Grant No.51279201).The partial support from the Youth Innovation Promotion Association CAS is gratefully acknowledged。
文摘Rock bolts have been widely used for stabilizing rock mass in geotechnical engineering.It is acknowledged that the bolt profiles have a sound influence on the support effect of the rock bolting system.Previous studies have proposed some optimal rib parameters(e.g.rib spacing);unfortunately,the interface shear behaviors are generally ignored.Therefore,determination of radial stress and radial displacement on the bolt-grout interface using traditional pull-out tests is not possible.The load-bearing capacity and deformation capacity vary as bolt profiles differ,suggesting that the support effect of the bolting system can be enhanced by optimizing bolt profiles.The aim of this study is to investigate the effects of bolt profiles(with/without ribs,rib spacing,and rib height)on the shear behaviors between the rock bolt and grout material using direct shear tests.Thereby,systematic interfacial shear tests with different bolt profiles were performed under both constant normal load(CNL)and constant normal stiffness(CNS)boundary conditions.The results suggested that rib spacing has a more marked influence on the interface shear behavior than rib height does,in particular at the post-yield stage.The results could facilitate our understanding of bolt-grout interface shear behavior under CNS conditions,and optimize selection of rock bolts under in situ rock conditions.
基金financially supported by the National Natural Science Foundation of China(Grant No.42172292)Taishan Scholars Project Special Funding,and Shandong Energy Group(Grant No.SNKJ 2022A01-R26).
文摘To reveal the mechanism of shear failure of en-echelon joints under cyclic loading,such as during earthquakes,we conducted a series of cyclic shear tests of en-echelon joints under constant normal stiffness(CNS)conditions.We analyzed the evolution of shear stress,normal stress,stress path,dilatancy characteristics,and friction coefficient and revealed the failure mechanisms of en-echelon joints at different angles.The results show that the cyclic shear behavior of the en-echelon joints is closely related to the joint angle,with the shear strength at a positive angle exceeding that at a negative angle during shear cycles.As the number of cycles increases,the shear strength decreases rapidly,and the difference between the varying angles gradually decreases.Dilation occurs in the early shear cycles(1 and 2),while contraction is the main feature in later cycles(310).The friction coefficient decreases with the number of cycles and exhibits a more significant sensitivity to joint angles than shear cycles.The joint angle determines the asperities on the rupture surfaces and the block size,and thus determines the subsequent shear failure mode(block crushing and asperity degradation).At positive angles,block size is more greater and asperities on the rupture surface are smaller than at nonpositive angles.Therefore,the cyclic shear behavior is controlled by block crushing at positive angles and asperity degradation at negative angles.
基金Transformation Program of Science and Technology Achievements of Jiangsu Province(No.BA2008030)
文摘To ascertain the influence of the boundary friction on mechanical properties of disc-spring vibration isolators a load-displacement hysteresis curve formula of disc-spring vibration isolators is derived on the basis of the energy conservation law as well as considering the effect of the boundary friction.The formula is validated through the finite element analysis and static load tests.On this basis the effect of the boundary friction on the bearing capacity is researched. Then the dynamic performance of disc-spring vibration isolators is studied by dynamic tests.The experimental results indicate that the boundary friction can promise a larger damping with a ratio of 0.23 for disc-spring vibration isolators.Compared with the loading frequency the loading amplitude has a greater impact on the energy consumption dynamic stiffness and damping of vibration isolators.This research can provide valuable information for the design of disc-spring vibration isolators.
基金Project(U1865203)supported by the Key Projects of the Yalong River Joint Fund of the National Natural Science Foundation of ChinaProject(51279201)supported by the National Natural Science Foundation of ChinaProjects(2019YFC0605103,2019YFC0605100)supported by the National Key R&D Program of China。
文摘Rock bolts are widely used in rock engineering projects to improve the shear capacity of the jointed rock mass.The bolt inclination angle with respect to the shear plane has a remarkable influence on the bolting performance.In this study,a new artificial molding method based on 3D scanning and printing technology was first proposed to prepare bolted joints with an inclined bolt.Then,the effects of the bolt inclination angle and boundary conditions on the shear behavior and failure characteristic of bolted joints were addressed by conducting direct shear tests under both CNL and CNS conditions.Results indicated that rock bolt could significantly improve the shear behavior of rock joints,especially in the post-yield deformation region.With the increase of bolt inclination angle,both the maximum shear stress and the maximum friction coefficient increased first and then decreased,while the maximum normal displacement decreased monotonously.Compared with CNL conditions,the maximum shear stress was larger,whereas the maximum normal displacement and friction coefficient were smaller under the CNS conditions.Furthermore,more asperity damage was observed under the CNS conditions due to the increased normal stress on the shear plane.
文摘The typical shear behaviour of rough joints has been studied under constant normal load/stress （CNL） boundary conditions, but recent studies have shown that this boundary condition may not replicate true practical situations. Constant normal stiffness （CNS） is more appropriate to describe the stress-strain response of field joints since the CNS boundary condition is more realistic than CNL. The practical implications of CNS are movements of unstable blocks in the roof or walls of an underground excavation, reinforced rock wedges sliding in a rock slope or foundation, and the vertical movement of rock-socketed concrete piles. In this paper, the highlights and limitations of the existing models used to predict the shear strength/behaviour of joints under CNS conditions are discussed in depth.
基金partially funded by National Natural Science Foundation of China(Grant Nos.51979272 and 51709260)State Key Laboratory for Geomechanics and Deep Underground Engineering,China University of Mining and Technology,China(Grant No.SKLGDUEK1906)。
文摘In this context,we experimentally studied the anisotropic mechanical behaviors of rough-walled plaster joints using a servo-controlled direct shear apparatus under both constant normal load(CNL)and constant normal stiffness(CNS)conditions.The shear-induced variations in the normal displacement,shear stress,normal stress and sheared-off asperity mass are analyzed and correlated with the inclination angle of the critical waviness of joint surfaces.The results show that CNS condition gives rise to a smaller normal displacement due to the larger normal stress during shearing,compared with CNL condition.Under CNL conditions,there is one peak shear stress during shearing,whereas there are no peak shear stress for some cases and two peaks for other cases under CNS conditions depending on the geometry of joint surfaces.The inclination angle of the critical waviness has been verified to be capable of describing the joint surface roughness and anisotropy.The joint surface is more significantly damaged under CNS conditions than that under CNL conditions.With increment of the inclination angle of the critical waviness,both the normal displaceme nt and shea red-off asperity mass increase,following power law functions;yet the coefficient of deternination under CNL conditions is larger than that under CNS conditions.This is because the CNS condition significantly decreases the inclination angle of the critical waviness during shearing due to the larger degree of asperity degradation.
基金supported by the Key Projects of the Yalong River Joint Fund of the National Natural Science Foundation of China(Grant No.U1865203)the National Natural Science Foundation of China(Grant Nos.52109142 and 41941018).
文摘Fault activation has been the focus of research community for years.However,the studies of fault activation remain immature,such as the fault activation mode and its major factors under constant normal stiffness(CNS)conditions associated with large thickness of fault surrounding rock mass.In this study,the rock friction experiments were conducted to understand the fault activation modes under the CNS conditions.Two major parameters,i.e.the initial normal stress and loading rate,were considered and calibrated in the tests.To reveal the response mechanism of fault activation,the local strains near the fault plane were recorded,and the macroscopic stresses and displacements were analyzed.The testing results show that the effect of displacement-controlled loading rate is more pronounced under the CNS conditions than that under constant normal load(CNL)conditions.Both the normal and shear stresses drop suddenly when the stick-slip occurs.The decrease and increase of the normal stress are synchronous with the shear stress in the regular stick-slip scenario,but mismatch with the shear stress during the chaotic stick-slip process.The results are helpful for understanding the fault sliding mode and the prediction and prevention of fault slip.
文摘为从宏、细观角度揭示常法向刚度(Constant Normal Stiffness,CNS)条件下锯齿状砂岩-混凝土结构面剪切机制,首先采用湖南大学自主改造的CNS岩石直剪仪开展3组砂岩-混凝土结构面室内剪切试验.在此基础上,采用刚性墙替代法建立与室内试验相应的离散元数值模型,并引入3个显式运动学方程控制砂岩试样运动轨迹从而实现CNS条件加载,将数值模拟与试验结果对比验证了模型的合理性.随后,开展16个工况的数值剪切试验,通过观察剪切裂纹扩展和力链演化形态,从细观角度揭示结构面破坏模式和荷载传递机制,并从宏观角度分析锯齿几何尺寸(半波长λ、起伏角θ)和加载边界条件(初始法向应力σn0、法向刚度K)对剪切强度和法向膨胀的影响.结果表明:剪切裂纹按照“平稳增加—急剧增加—增幅减小”的发展趋势由结构面区域逐渐向岩石内部扩展,结构面破坏模式随起伏角的增大由滑移磨损向剪断破坏过渡,剪切强度随λ、θ、σn0和K的增加呈指数函数型增加.
文摘深部岩体节理往往存在不同程度的软弱充填物质,导致岩体力学性质更为复杂。开展恒定法向刚度CNS边界条件下,考虑高初始法向应力及不同节理粗糙系数JRC−充填度△组合模式的加锚充填节理岩体剪切试验,结合微观电镜扫描(scanning electron microscope,简称SEM)分析充填节理部分宏微观结构演变特征,推导CNS边界条件下峰值剪胀角相关计算方法。研究结果表明:当△<0.5,试件剪应力强度呈现应力硬化;当1.0<△≤1.5,剪应力强度由基本恒定演化为应力软化。当△小于临界充填度△_(cr),JRC成为峰值抗剪强度主要影响因素。△在节理法向变形中起到控制作用,随着△的增加,出现剪胀、先剪胀后剪缩、剪缩3种演化规律,JRC则影响着试件剪胀−剪缩变化程度。充填节理部分破坏模式随着△的增加主要经历3个阶段:粗糙点磨平、充填物质摩擦、充填物质磨碎。微观角度下由疏松多孔结构形式演化为散体碎屑状结构形式。受挤压破碎区与挤压应力集中区二者的相互演化机制影响,锚杆剪切变形模式逐渐由△=0的“近似”拉剪变形向△=1.5的拉弯变形模式演变。在此基础上,提出了一种CNS边界条件下加锚充填节理岩体峰值剪胀角的计算公式,并进行了试验验证及边界条件影响参数敏感性分析。
