With the rapid developments of the high-speed railway in China, a great number of long-span bridges have been constructed in order to cross rivers and gorges. At present, the longest main span of a constructed high-sp...With the rapid developments of the high-speed railway in China, a great number of long-span bridges have been constructed in order to cross rivers and gorges. At present, the longest main span of a constructed high-speed railway bridge is only 630 m. The main span of Hutong Yangtze River Bridge and of Wufengshan Yangtze River Bridge, which are under construction, will be much longer, at 1092 m each. In order to overcome the technical issues that originate from the extremely large dead loading and the relatively small structural stiffness of long-span high-speed railway bridges, many new technologies in bridge construction, design, materials, and so forth have been developed. This paper carefully reviews progress in the construction technologies of multi-function combined bridges in China, including com- bined highway and railway bridges and multi-track railway bridges. Innovations and practices regarding new types of bridge and composite bridge structures, such as bridges with three cable planes and three main trusses, inclined main trusses, slab-truss composite sections, and steel-concrete composite sections, are introduced. In addition, investigations into high-performance materials and integral fabrication and erection techniques for long-span railway bridges are summarized. At the end of the paper, prospects for the future development of long-span high-speed railwav bridges are provided.展开更多
Natural geological structures in rock(e.g.,joints,weakness planes,defects)play a vital role in the stability of tunnels and underground operations during construction.We investigated the failure characteristics of a d...Natural geological structures in rock(e.g.,joints,weakness planes,defects)play a vital role in the stability of tunnels and underground operations during construction.We investigated the failure characteristics of a deep circular tunnel in a rock mass with multiple weakness planes using a 2D combined finite element method/discrete element method(FEM/DEM).Conventional triaxial compression tests were performed on typical hard rock(marble)specimens under a range of confinement stress conditions to validate the rationale and accuracy of the proposed numerical approach.Parametric analysis was subsequently conducted to investigate the influence of inclination angle,and length on the crack propagation behavior,failure mode,energy evolution,and displacement distribution of the surrounding rock.The results show that the inclination angle strongly affects tunnel stability,and the failure intensity and damage range increase with increasing inclination angle and then decrease.The dynamic disasters are more likely with increasing weak plane length.Shearing and sliding along multiple weak planes are also consistently accompanied by kinetic energy fluctuations and surges after unloading,which implies a potentially violent dynamic response around a deeply-buried tunnel.Interactions between slabbing and shearing near the excavation boundaries are also discussed.The results presented here provide important insight into deep tunnel failure in hard rock influenced by both unloading disturbance and tectonic activation.展开更多
To investigate the height growth of multi-cluster fractures during variable fluid-viscosity fracturing in a layered shale oil reservoir,a two-dimensional finite element method(FEM)-discrete fracture network(DFN)model ...To investigate the height growth of multi-cluster fractures during variable fluid-viscosity fracturing in a layered shale oil reservoir,a two-dimensional finite element method(FEM)-discrete fracture network(DFN)model coupled with flow,stress and damage is proposed.A traction-separation law is used to describe the mixed-mode response of the damaged adhesive fractures,and the cubic law is used to describe the fluid flow within the fractures.The rock deformation is controlled by the in-situ stress,fracture cohesion and fluid pressure on the hydraulic fracture surface.The coupled finite element equations are solved by the explicit time difference method.The effects of the fracturing treatment parameters including fluid viscosity,pumping rate and cluster spacing on the geometries of multifractures are investigated.The results show that variable fluid-viscosity injection can improve the complexity of the fracture network and height of the main fractures simultaneously.The pumping rate of15 m^(3)/min,variable fluid-viscosity of 3-9-21-36-45 mPa s with a cluster spacing of 7.5 m is the ideal treatment strategy.The field application shows that the peak daily production of the application well with the optimized injection procedu re of variable fluid-viscosity fracturing is 171 tons(about 2.85 times that of the adjacent well),which is the highest daily production record of a single shale oil well in China,marking a strategic breakthrough of commercial shale oil production in the Jiyang Depression,Shengli Oilfield.The variable fluid-viscosity fracturing technique is proved to be very effective for improving shale oil production.展开更多
We classify all positive solutions for the following integral system：{ui（x）=∫Rn1/│x-y│^n-α fi（u（y））dy,x∈R^n,i=1,…,m,0〈α〈n,and u（x）=（u1（x）,u2（x）…,um（x））.Here fi（u）, 1 ≤ i ≤m, monotone non...We classify all positive solutions for the following integral system：{ui（x）=∫Rn1/│x-y│^n-α fi（u（y））dy,x∈R^n,i=1,…,m,0〈α〈n,and u（x）=（u1（x）,u2（x）…,um（x））.Here fi（u）, 1 ≤ i ≤m, monotone nondecreasing are real-valued functions of homogeneous degree n＋α/n-α and are monotone nondecreasing with respect to all the independent variables U1, u2, ..., urn.In the special case n ≥ 3 and α = 2. we show that the above system is equivalent to thefollowing elliptic PDE system：This system is closely related to the stationary SchrSdinger system with critical exponents for Bose-Einstein condensate展开更多
In the 1940s, KIRKENDALL showed that diffusion in binary solid solutions cannot be described by only one diffusion coefficient. Rather, one has to consider the diffusivity of both species. His findings changed the tre...In the 1940s, KIRKENDALL showed that diffusion in binary solid solutions cannot be described by only one diffusion coefficient. Rather, one has to consider the diffusivity of both species. His findings changed the treatment of diffusion data and the theory of diffusion itself. A diffusion-based framework was successfully employed to explain the behaviour of the Kirkendall plane. Nonetheless, the complexity of a multiphase diffusion zone and the morphological evolution during interdiffusion requires a physico-chemical approach. The interactions in binary and more complex systems are key issues from both the fundamental and technological points of view. This paper reviews the Kirkendall effect from the circumstances of its discovery to recent developments in its understanding, with broad applicability in materials science and engineering.展开更多
In this note we study subplanes of order q of the projective plane Π=PG( 2, q 3 ) and the ruled varieties V 2 5 of Σ=PG( 6,q ) using the spatial representation of Π in Σ, by fixing a hyperplane Σ ′ with a regula...In this note we study subplanes of order q of the projective plane Π=PG( 2, q 3 ) and the ruled varieties V 2 5 of Σ=PG( 6,q ) using the spatial representation of Π in Σ, by fixing a hyperplane Σ ′ with a regular spread of planes. First are shown some configurations of the affine q-subplanes. Then to prove that a variety V 2 5 of Σ represents a non-affine subplane of order q of Π, after having shown basic incidence properties of it, such a variety V 2 5 is constructed by choosing appropriately the two directrix curves in two complementary subspaces of Σ. The result can be translated into further incidence properties of the affine points of V 2 5 . Then a maximal bundle of varieties V 2 5 having in common one directrix cubic curve is constructed.展开更多
Unconventional resources like shale gas has been the focus of intense research and development for two decades. Apart from intrinsic geologic factors that control the gas shale productivity (e.g. organic matter conten...Unconventional resources like shale gas has been the focus of intense research and development for two decades. Apart from intrinsic geologic factors that control the gas shale productivity (e.g. organic matter content, bedding planes, natural fractures, porosity and stress regime among others), external factors like wellbore orientation and stimulation design play a role. In this study, we present a series of true triaxial hydraulic fracturing experiments conducted on Lushan shale to investigate the interplay of internal factors (bedding, natural fractures and in situ stress) and external factors (wellbore orientation) on the growth process of fracture networks in cubic specimens of 200 mm in length. We observe relatively low breakdown pressure and fracture propagation pressure as the wellbore orientation and/or the maximum in situ stress is subparallel to the shale bedding plane. The wellbore orientation has a more prominent effect on the breakdown pressure, but its effect is tapered with increasing angle of bedding inclination. The shale breakdown is followed by an abrupt response in sample displacement, which reflects the stimulated fracture volume. Based on fluid tracer analysis, the morphology of hydraulic fractures (HF) is divided into four categories. Among the categories, activation of bedding planes (bedding failure, BF) and natural fractures (NF) significantly increase bifurcation and fractured areas. Under the same stress regime, a horizontal wellbore is more favorable to enhance the complexity of hydraulic fracture networks. This is attributed to the relatively large surface area in contact with the bedding plane for the horizontal borehole compared to the case with a vertical wellbore. These findings provide important references for hydraulic fracturing design in shale reservoirs.展开更多
The paper generalizes the direct method of moving planes to the Logarithmic Laplacian system.Firstly,some key ingredients of the method are discussed,for example,Narrow region principle and Decay at infinity.Then,the ...The paper generalizes the direct method of moving planes to the Logarithmic Laplacian system.Firstly,some key ingredients of the method are discussed,for example,Narrow region principle and Decay at infinity.Then,the radial symmetry of the solution of the Logarithmic Laplacian system is obtained.展开更多
This paper deals with the radial symmetry of positive solutions to the nonlocal problem(-Δ)_(γ)~su=b(x)f(u)in B_(1){0},u=h in R~N B_(1),where b:B_1→R is locally Holder continuous,radially symmetric and decreasing i...This paper deals with the radial symmetry of positive solutions to the nonlocal problem(-Δ)_(γ)~su=b(x)f(u)in B_(1){0},u=h in R~N B_(1),where b:B_1→R is locally Holder continuous,radially symmetric and decreasing in the|x|direction,F:R→R is a Lipschitz function,h:B_1→R is radially symmetric,decreasing with respect to|x|in R^(N)/B_(1),B_(1) is the unit ball centered at the origin,and(-Δ)_γ~s is the weighted fractional Laplacian with s∈(0,1),γ∈[0,2s)defined by(-△)^(s)_(γ)u(x)=CN,slimδ→0+∫R^(N)/B_(δ)(x)u(x)-u(y)/|x-y|N+2s|y|^(r)dy.We consider the radial symmetry of isolated singular positive solutions to the nonlocal problem in whole space(-Δ)_(γ)^(s)u(x)=b(x)f(u)in R^(N)\{0},under suitable additional assumptions on b and f.Our symmetry results are derived by the method of moving planes,where the main difficulty comes from the weighted fractional Laplacian.Our results could be applied to get a sharp asymptotic for semilinear problems with the fractional Hardy operators(-Δ)^(s)u+μ/(|x|^(2s))u=b(x)f(u)in B_(1)\{0},u=h in R^(N)\B_(1),under suitable additional assumptions on b,f and h.展开更多
The rock mass consists of rock blocks and structural planes,which can reduce its integrity and strength.Therefore,accurately obtaining the characteristics of the rock mass structural plane is a prerequisite for evalua...The rock mass consists of rock blocks and structural planes,which can reduce its integrity and strength.Therefore,accurately obtaining the characteristics of the rock mass structural plane is a prerequisite for evaluating stability and designing supports in underground engineering.Currently,there are no effective testing methods for the characteristic parameters of the rock mass structural plane in underground engineering.The paper presents the digital drilling technology as a new testing method of rock mass structural planes.Flawed rock specimens with cracks of varying widths and angles were used to simulate the rock mass structural planes,and the multifunctional rock mass digital drilling test system was employed to carry out the digital drilling tests.The analysis focuses on the variation laws of drilling parameters,such as drilling pressure and drilling torque,affected by the characteristics of prefabricated cracks,and clarifies the degradation mechanism of rock equivalent compressive strength.Additionally,an identification model for the characteristic parameters of rock mass structural planes during drilling is established.The test results indicate that the average difference of the characteristics of prefabricated cracks identified by the equivalent compressive strength is 2.45°and 0.82 mm,respectively.The identification model while drilling is verified to be correct due to the high identification accuracy.Based on this,a method for testing the characteristic parameters of the surrounding rock structural plane while drilling is proposed.The research offers a theoretical and methodological foundation for precise in situ identification of structural planes of the surrounding rock in underground engineering.展开更多
The existence of high-density bedding planes is a typical characteristic of shale oil reservoirs.Understanding the behavior of hydraulic fracturing in high-density laminated rocks is significant for promoting shale oi...The existence of high-density bedding planes is a typical characteristic of shale oil reservoirs.Understanding the behavior of hydraulic fracturing in high-density laminated rocks is significant for promoting shale oil production.In this study,a hydraulic fracturing model considering tensile failure and frictional slip of the bedding planes is established within the framework of the unified pipe-interface element method(UP-IEM).The model developed for simulating the interaction between the hydraulic fracture and the bedding plane is validated by comparison with experimental results.The hydraulic fracturing patterns in sealed and unsealed bedding planes are compared.Additionally,the effects of differential stress,bedding plane permeability,spacing,and the friction coefficient of the bedding plane are investigated.The results showed that a single main fracture crossing the bedding planes is more likely to form in sealed bedding planes under high differential stress.The decrease in bedding plane permeability and the increase in the friction coefficient also promote the fracture propagating perpendicular to the bedding planes.Shale with high-density bedding planes has a poorer fracturing effect than that with low-density bedding planes,as the hydraulic fracture is prone to initiate and propagate along the bedding planes.Moreover,higher injection pressure is needed to maintain fracture propagation along the bedding.An increase in bedding density will lead to a smaller fracturing area.Fracturing fluid seepage into the bedding planes slows shale fracturing.It is recommended that increasing the injection flow rate,selecting alternative fracturing fluids,and employing multi-well/multi-cluster fracturing may be efficient methods to improve energy production in shale oil reservoirs.展开更多
The mechanism of dimethyl carbonate（DMC） formation from CO2 and methanol is investigated using three well-shaped CeO2 catalysts, nanorod, nanocube and octahedron, which are packed with different crystal planes. In s...The mechanism of dimethyl carbonate（DMC） formation from CO2 and methanol is investigated using three well-shaped CeO2 catalysts, nanorod, nanocube and octahedron, which are packed with different crystal planes. In situ Fourier Transform Infrared Spectroscopy（FTIR） is employed to probe each reaction step in the DMC synthesis. The number of –OH groups and the species of CO2 adsorptions on ceria surface have significant influence on the activity of ceria with different morphologies. Rod-ceria has favorable catalytic activity because of the large amount of –OH groups and the formation of bidentate carbonate species.展开更多
Steel mesh is used as a passive skin confinement medium to supplement the active support provided by rock bolts for roof and rib control in underground coal mines. Thin spray-on liners(TSL) are believed to have the po...Steel mesh is used as a passive skin confinement medium to supplement the active support provided by rock bolts for roof and rib control in underground coal mines. Thin spray-on liners(TSL) are believed to have the potential to take the place of steel mesh as the skin confinement medium in underground mines.To confirm this belief, large scale laboratory experiments were conducted to compare the behaviour of welded steel mesh and a TSL, when used in conjunction with rock bolts, in reinforcing strata with weak bedding planes and strata prone to guttering, two common rock conditions which exist in coal mines. It was found that while the peak load taken by the simulated rock mass with weak bedding planes acting as the control sample(no skin confinement) was 2494 kN, the corresponding value of the sample with 5 mm thick TSL reinforcement reached 2856 kN. The peak load of the steel mesh reinforced sample was only2321 kN, but this was attributed to the fact that one of the rock bolts broke during the test. The TSL reinforced sample had a similar post-yield behaviour as the steel mesh reinforced one. The results of the large scale guttering test indicated that a TSL is better than steel mesh in restricting rock movement and thus inhibiting the formation of gutters in the roof.展开更多
The Donalda gold deposit in the southern part of the Archean Abitibi greenstone belt consists mainly of a subhonzontal gold-quartz vein perpendicular to subvertical shear zones.The 0.3—0.5 m thick vein is characteriz...The Donalda gold deposit in the southern part of the Archean Abitibi greenstone belt consists mainly of a subhonzontal gold-quartz vein perpendicular to subvertical shear zones.The 0.3—0.5 m thick vein is characterized by vein-parallel banding structures indicating multiple episodes of fracture opening and mineral precipitation.Measurement of the c-axis of primary growth quartz indicates that quartz preferentially grew perpendicular to the fracture,suggesting open space filling and/or extensional nature of the fracture.Measurement of the orientations of microfractures,veinlets and fluid—inclusion planes（FIPs） crosscutting primary growth quartz indicates that the vein minerals were subject to a vertical maximum principal stress（σ_1）,which is inconsistent with the subhorizontalσ_1 inferred from the regional stress field with N—S shortening.This apparent discrepancy is explained by invoking episodic fluid pressure fluctuation between supralithostatic and hydrostatic regimes accompanied by episodic opening and closing of the sub-horizontal fracture.When fluid pressure was higher than the lithostatic value,the fracture was opened and primary growth minerals were precipitated,whereas when fluid pressure decreased toward the hydrostatic value,the hanging wall of the fracture collapsed,causing collision of protruding primary growth minerals from both sides of the fracture and resulting in formation of vein-parallel deformation bands.The columns where the two facing sides of the fracture collided were subject to higher-than-lithostatic stress due to the bridging effect and reduced support surface area,explaining the development of verticalσ_1.This hypothesis is consistent the fault-valve model,and explains the flipping ofσ_1 without having to change the regional stress field.展开更多
The performance of underground excavations is inevitably influenced by rock mass characteristics, presence of joints and their geometrical properties, depth below surface and state of in-situ stress field. The objecti...The performance of underground excavations is inevitably influenced by rock mass characteristics, presence of joints and their geometrical properties, depth below surface and state of in-situ stress field. The objective of this paper is to investigate the behaviour of deep underground tunnel opening existed between two bedding planes, Such planes weaken the strength of rock mass and may cause rock slippage/rotation along them. Therefore, the state of stress-displacement, after tunnel opening has been introduced, is examined using two-dimensional elasto-plastic finite-elements code, RS^(2D). The results indicate that, there is significant drop in the normal stress along joints over tunnel opening; slip occurs due to reversal in the direction of shear stress(e.g., inward shear displacement is produced) and there is discontinuity in the strength contours of rock surrounding tunnel after they have been intersected by bedding planes.展开更多
Jinsha River Bridge is located along the Lijiang-Xamgyi＇nyilha railway on the southeastern Tibet plateau; it is an area with a high prevalence of earthquakes. The bridge abutments were designed to be constructed in r...Jinsha River Bridge is located along the Lijiang-Xamgyi＇nyilha railway on the southeastern Tibet plateau; it is an area with a high prevalence of earthquakes. The bridge abutments were designed to be constructed in river bank slopes, where rocks are controlled by two sets of joint planes that significantly influence the stability of the left bank slope. According to the engineering-geological conditions and the characteristics of discontinuities, strength properties of the rock mass were obtained based on Barton model and direct shear test. Numerical analyses were performed using FLAC3D software to examine the slope＇s response to seismic loading. Then in order to evaluate the damage trends of the rock mass under the different loading conditions, a calculation model based on the geological parameters and slope stability was simulated and analyzed using the discrete element numerical simulation program UDEC （Universal Dis- tinct Element Code）, and the effect of degradation of discontinuities on the slope stability was investigated. The results show that the destruction of rock mass under the gravity, bridge foundation, and seismic load are mainly concentrated within 30 m depth of slope, and the slope under loading may slide along joint planes. In addition, the dynamic analysis by amplification of the input loading indicates that instability occurs to the bank slope at a height of about 200 m, and rock blocks will fail under seismic load. Therefore, to prevent the slope from deformation under the engineering loading and strong earthquakes, the bridge foundation should be strengthened.展开更多
This paper is devoted to the study of a translation plane π(C) associated with a t-spread set C and its transposed t-spread set C t. In this paper, an explicit matrix form of the inverse of an isomorphism from a tran...This paper is devoted to the study of a translation plane π(C) associated with a t-spread set C and its transposed t-spread set C t. In this paper, an explicit matrix form of the inverse of an isomorphism from a translation plane into another translation plane associated with t-spread sets is derived and proved that two translation planes associated with t-spread sets are isomorphic if and only if their corresponding transposed translation planes are isomorphic. Further, it is shown that the transpose of a flag-transitive plane is flag-transitive and derived a necessary and sufficient condition for a translation plane π(C) to be isomorphic to its transposed translation plane.展开更多
文摘With the rapid developments of the high-speed railway in China, a great number of long-span bridges have been constructed in order to cross rivers and gorges. At present, the longest main span of a constructed high-speed railway bridge is only 630 m. The main span of Hutong Yangtze River Bridge and of Wufengshan Yangtze River Bridge, which are under construction, will be much longer, at 1092 m each. In order to overcome the technical issues that originate from the extremely large dead loading and the relatively small structural stiffness of long-span high-speed railway bridges, many new technologies in bridge construction, design, materials, and so forth have been developed. This paper carefully reviews progress in the construction technologies of multi-function combined bridges in China, including com- bined highway and railway bridges and multi-track railway bridges. Innovations and practices regarding new types of bridge and composite bridge structures, such as bridges with three cable planes and three main trusses, inclined main trusses, slab-truss composite sections, and steel-concrete composite sections, are introduced. In addition, investigations into high-performance materials and integral fabrication and erection techniques for long-span railway bridges are summarized. At the end of the paper, prospects for the future development of long-span high-speed railwav bridges are provided.
基金Projects(52004143,51774194)supported by the National Natural Science Foundation of ChinaProject(2020M670781)supported by the China Postdoctoral Science Foundation+2 种基金Project(SKLGDUEK2021)supported by the State Key Laboratory for GeoMechanics and Deep Underground Engineering,ChinaProject(U1806208)supported by the NSFC-Shandong Joint Fund,ChinaProject(2018GSF117023)supported by the Key Research and Development Program of Shandong Province,China。
文摘Natural geological structures in rock(e.g.,joints,weakness planes,defects)play a vital role in the stability of tunnels and underground operations during construction.We investigated the failure characteristics of a deep circular tunnel in a rock mass with multiple weakness planes using a 2D combined finite element method/discrete element method(FEM/DEM).Conventional triaxial compression tests were performed on typical hard rock(marble)specimens under a range of confinement stress conditions to validate the rationale and accuracy of the proposed numerical approach.Parametric analysis was subsequently conducted to investigate the influence of inclination angle,and length on the crack propagation behavior,failure mode,energy evolution,and displacement distribution of the surrounding rock.The results show that the inclination angle strongly affects tunnel stability,and the failure intensity and damage range increase with increasing inclination angle and then decrease.The dynamic disasters are more likely with increasing weak plane length.Shearing and sliding along multiple weak planes are also consistently accompanied by kinetic energy fluctuations and surges after unloading,which implies a potentially violent dynamic response around a deeply-buried tunnel.Interactions between slabbing and shearing near the excavation boundaries are also discussed.The results presented here provide important insight into deep tunnel failure in hard rock influenced by both unloading disturbance and tectonic activation.
基金funded by the National Natural Science Foundation of China(Nos.52192622,51874253,U20A202)
文摘To investigate the height growth of multi-cluster fractures during variable fluid-viscosity fracturing in a layered shale oil reservoir,a two-dimensional finite element method(FEM)-discrete fracture network(DFN)model coupled with flow,stress and damage is proposed.A traction-separation law is used to describe the mixed-mode response of the damaged adhesive fractures,and the cubic law is used to describe the fluid flow within the fractures.The rock deformation is controlled by the in-situ stress,fracture cohesion and fluid pressure on the hydraulic fracture surface.The coupled finite element equations are solved by the explicit time difference method.The effects of the fracturing treatment parameters including fluid viscosity,pumping rate and cluster spacing on the geometries of multifractures are investigated.The results show that variable fluid-viscosity injection can improve the complexity of the fracture network and height of the main fractures simultaneously.The pumping rate of15 m^(3)/min,variable fluid-viscosity of 3-9-21-36-45 mPa s with a cluster spacing of 7.5 m is the ideal treatment strategy.The field application shows that the peak daily production of the application well with the optimized injection procedu re of variable fluid-viscosity fracturing is 171 tons(about 2.85 times that of the adjacent well),which is the highest daily production record of a single shale oil well in China,marking a strategic breakthrough of commercial shale oil production in the Jiyang Depression,Shengli Oilfield.The variable fluid-viscosity fracturing technique is proved to be very effective for improving shale oil production.
基金supported by NSF Grant DMS-0604638Li partially supported by NSF Grant DMS-0401174
文摘We classify all positive solutions for the following integral system：{ui（x）=∫Rn1/│x-y│^n-α fi（u（y））dy,x∈R^n,i=1,…,m,0〈α〈n,and u（x）=（u1（x）,u2（x）…,um（x））.Here fi（u）, 1 ≤ i ≤m, monotone nondecreasing are real-valued functions of homogeneous degree n＋α/n-α and are monotone nondecreasing with respect to all the independent variables U1, u2, ..., urn.In the special case n ≥ 3 and α = 2. we show that the above system is equivalent to thefollowing elliptic PDE system：This system is closely related to the stationary SchrSdinger system with critical exponents for Bose-Einstein condensate
文摘In the 1940s, KIRKENDALL showed that diffusion in binary solid solutions cannot be described by only one diffusion coefficient. Rather, one has to consider the diffusivity of both species. His findings changed the treatment of diffusion data and the theory of diffusion itself. A diffusion-based framework was successfully employed to explain the behaviour of the Kirkendall plane. Nonetheless, the complexity of a multiphase diffusion zone and the morphological evolution during interdiffusion requires a physico-chemical approach. The interactions in binary and more complex systems are key issues from both the fundamental and technological points of view. This paper reviews the Kirkendall effect from the circumstances of its discovery to recent developments in its understanding, with broad applicability in materials science and engineering.
文摘In this note we study subplanes of order q of the projective plane Π=PG( 2, q 3 ) and the ruled varieties V 2 5 of Σ=PG( 6,q ) using the spatial representation of Π in Σ, by fixing a hyperplane Σ ′ with a regular spread of planes. First are shown some configurations of the affine q-subplanes. Then to prove that a variety V 2 5 of Σ represents a non-affine subplane of order q of Π, after having shown basic incidence properties of it, such a variety V 2 5 is constructed by choosing appropriately the two directrix curves in two complementary subspaces of Σ. The result can be translated into further incidence properties of the affine points of V 2 5 . Then a maximal bundle of varieties V 2 5 having in common one directrix cubic curve is constructed.
基金supported by the National Natural Science Foundation of China(Grant Nos.52064006 and 52004072)It was.also supported by the program(Grant No.202006050112)of China Scholarship Council(CSC)for the first author's visit at the Helm-holtz Centre Potsdam,GFZ German Research Centre for Geosciences.
文摘Unconventional resources like shale gas has been the focus of intense research and development for two decades. Apart from intrinsic geologic factors that control the gas shale productivity (e.g. organic matter content, bedding planes, natural fractures, porosity and stress regime among others), external factors like wellbore orientation and stimulation design play a role. In this study, we present a series of true triaxial hydraulic fracturing experiments conducted on Lushan shale to investigate the interplay of internal factors (bedding, natural fractures and in situ stress) and external factors (wellbore orientation) on the growth process of fracture networks in cubic specimens of 200 mm in length. We observe relatively low breakdown pressure and fracture propagation pressure as the wellbore orientation and/or the maximum in situ stress is subparallel to the shale bedding plane. The wellbore orientation has a more prominent effect on the breakdown pressure, but its effect is tapered with increasing angle of bedding inclination. The shale breakdown is followed by an abrupt response in sample displacement, which reflects the stimulated fracture volume. Based on fluid tracer analysis, the morphology of hydraulic fractures (HF) is divided into four categories. Among the categories, activation of bedding planes (bedding failure, BF) and natural fractures (NF) significantly increase bifurcation and fractured areas. Under the same stress regime, a horizontal wellbore is more favorable to enhance the complexity of hydraulic fracture networks. This is attributed to the relatively large surface area in contact with the bedding plane for the horizontal borehole compared to the case with a vertical wellbore. These findings provide important references for hydraulic fracturing design in shale reservoirs.
基金Supported by the National Natural Science Foundation of China(11501342,12001344)。
文摘The paper generalizes the direct method of moving planes to the Logarithmic Laplacian system.Firstly,some key ingredients of the method are discussed,for example,Narrow region principle and Decay at infinity.Then,the radial symmetry of the solution of the Logarithmic Laplacian system is obtained.
基金supported by the NSFC(12001252)the Jiangxi Provincial Natural Science Foundation(20232ACB211001)。
文摘This paper deals with the radial symmetry of positive solutions to the nonlocal problem(-Δ)_(γ)~su=b(x)f(u)in B_(1){0},u=h in R~N B_(1),where b:B_1→R is locally Holder continuous,radially symmetric and decreasing in the|x|direction,F:R→R is a Lipschitz function,h:B_1→R is radially symmetric,decreasing with respect to|x|in R^(N)/B_(1),B_(1) is the unit ball centered at the origin,and(-Δ)_γ~s is the weighted fractional Laplacian with s∈(0,1),γ∈[0,2s)defined by(-△)^(s)_(γ)u(x)=CN,slimδ→0+∫R^(N)/B_(δ)(x)u(x)-u(y)/|x-y|N+2s|y|^(r)dy.We consider the radial symmetry of isolated singular positive solutions to the nonlocal problem in whole space(-Δ)_(γ)^(s)u(x)=b(x)f(u)in R^(N)\{0},under suitable additional assumptions on b and f.Our symmetry results are derived by the method of moving planes,where the main difficulty comes from the weighted fractional Laplacian.Our results could be applied to get a sharp asymptotic for semilinear problems with the fractional Hardy operators(-Δ)^(s)u+μ/(|x|^(2s))u=b(x)f(u)in B_(1)\{0},u=h in R^(N)\B_(1),under suitable additional assumptions on b,f and h.
基金supported by the National Key Research and Development Program of China(Grant No.2023YFC2907600)the National Natural Science Foundation of China(Grant Nos.42277174 and 52204260).
文摘The rock mass consists of rock blocks and structural planes,which can reduce its integrity and strength.Therefore,accurately obtaining the characteristics of the rock mass structural plane is a prerequisite for evaluating stability and designing supports in underground engineering.Currently,there are no effective testing methods for the characteristic parameters of the rock mass structural plane in underground engineering.The paper presents the digital drilling technology as a new testing method of rock mass structural planes.Flawed rock specimens with cracks of varying widths and angles were used to simulate the rock mass structural planes,and the multifunctional rock mass digital drilling test system was employed to carry out the digital drilling tests.The analysis focuses on the variation laws of drilling parameters,such as drilling pressure and drilling torque,affected by the characteristics of prefabricated cracks,and clarifies the degradation mechanism of rock equivalent compressive strength.Additionally,an identification model for the characteristic parameters of rock mass structural planes during drilling is established.The test results indicate that the average difference of the characteristics of prefabricated cracks identified by the equivalent compressive strength is 2.45°and 0.82 mm,respectively.The identification model while drilling is verified to be correct due to the high identification accuracy.Based on this,a method for testing the characteristic parameters of the surrounding rock structural plane while drilling is proposed.The research offers a theoretical and methodological foundation for precise in situ identification of structural planes of the surrounding rock in underground engineering.
基金The authors wish to acknowledge the financial support from Key Laboratory of Deep Earth Science and Engineering(Sichuan University),Ministry of Education(DESE202202,H.Y)State Energy Center for Shale Oil Research and Development(33550000-22-ZC0613-0365,H.Y)+2 种基金National Natural Science Foundation of China(42307209,X.Y)China Postdoctoral Science Foundation(2022M712425,X.Y)Shanghai Pujiang Program(2022PJD076,X.Y).
文摘The existence of high-density bedding planes is a typical characteristic of shale oil reservoirs.Understanding the behavior of hydraulic fracturing in high-density laminated rocks is significant for promoting shale oil production.In this study,a hydraulic fracturing model considering tensile failure and frictional slip of the bedding planes is established within the framework of the unified pipe-interface element method(UP-IEM).The model developed for simulating the interaction between the hydraulic fracture and the bedding plane is validated by comparison with experimental results.The hydraulic fracturing patterns in sealed and unsealed bedding planes are compared.Additionally,the effects of differential stress,bedding plane permeability,spacing,and the friction coefficient of the bedding plane are investigated.The results showed that a single main fracture crossing the bedding planes is more likely to form in sealed bedding planes under high differential stress.The decrease in bedding plane permeability and the increase in the friction coefficient also promote the fracture propagating perpendicular to the bedding planes.Shale with high-density bedding planes has a poorer fracturing effect than that with low-density bedding planes,as the hydraulic fracture is prone to initiate and propagate along the bedding planes.Moreover,higher injection pressure is needed to maintain fracture propagation along the bedding.An increase in bedding density will lead to a smaller fracturing area.Fracturing fluid seepage into the bedding planes slows shale fracturing.It is recommended that increasing the injection flow rate,selecting alternative fracturing fluids,and employing multi-well/multi-cluster fracturing may be efficient methods to improve energy production in shale oil reservoirs.
基金Financial support by Natural Science Foundation of China (NSFC) (Nos. 21325626, 21176179, U1510203)the Program for New Century Excellent Talents in University (No. NCET-13-0411)the Program of Introducing Talents of Discipline to Universities (No. B06006)
文摘The mechanism of dimethyl carbonate（DMC） formation from CO2 and methanol is investigated using three well-shaped CeO2 catalysts, nanorod, nanocube and octahedron, which are packed with different crystal planes. In situ Fourier Transform Infrared Spectroscopy（FTIR） is employed to probe each reaction step in the DMC synthesis. The number of –OH groups and the species of CO2 adsorptions on ceria surface have significant influence on the activity of ceria with different morphologies. Rod-ceria has favorable catalytic activity because of the large amount of –OH groups and the formation of bidentate carbonate species.
文摘Steel mesh is used as a passive skin confinement medium to supplement the active support provided by rock bolts for roof and rib control in underground coal mines. Thin spray-on liners(TSL) are believed to have the potential to take the place of steel mesh as the skin confinement medium in underground mines.To confirm this belief, large scale laboratory experiments were conducted to compare the behaviour of welded steel mesh and a TSL, when used in conjunction with rock bolts, in reinforcing strata with weak bedding planes and strata prone to guttering, two common rock conditions which exist in coal mines. It was found that while the peak load taken by the simulated rock mass with weak bedding planes acting as the control sample(no skin confinement) was 2494 kN, the corresponding value of the sample with 5 mm thick TSL reinforcement reached 2856 kN. The peak load of the steel mesh reinforced sample was only2321 kN, but this was attributed to the fact that one of the rock bolts broke during the test. The TSL reinforced sample had a similar post-yield behaviour as the steel mesh reinforced one. The results of the large scale guttering test indicated that a TSL is better than steel mesh in restricting rock movement and thus inhibiting the formation of gutters in the roof.
文摘The Donalda gold deposit in the southern part of the Archean Abitibi greenstone belt consists mainly of a subhonzontal gold-quartz vein perpendicular to subvertical shear zones.The 0.3—0.5 m thick vein is characterized by vein-parallel banding structures indicating multiple episodes of fracture opening and mineral precipitation.Measurement of the c-axis of primary growth quartz indicates that quartz preferentially grew perpendicular to the fracture,suggesting open space filling and/or extensional nature of the fracture.Measurement of the orientations of microfractures,veinlets and fluid—inclusion planes（FIPs） crosscutting primary growth quartz indicates that the vein minerals were subject to a vertical maximum principal stress（σ_1）,which is inconsistent with the subhorizontalσ_1 inferred from the regional stress field with N—S shortening.This apparent discrepancy is explained by invoking episodic fluid pressure fluctuation between supralithostatic and hydrostatic regimes accompanied by episodic opening and closing of the sub-horizontal fracture.When fluid pressure was higher than the lithostatic value,the fracture was opened and primary growth minerals were precipitated,whereas when fluid pressure decreased toward the hydrostatic value,the hanging wall of the fracture collapsed,causing collision of protruding primary growth minerals from both sides of the fracture and resulting in formation of vein-parallel deformation bands.The columns where the two facing sides of the fracture collided were subject to higher-than-lithostatic stress due to the bridging effect and reduced support surface area,explaining the development of verticalσ_1.This hypothesis is consistent the fault-valve model,and explains the flipping ofσ_1 without having to change the regional stress field.
文摘The performance of underground excavations is inevitably influenced by rock mass characteristics, presence of joints and their geometrical properties, depth below surface and state of in-situ stress field. The objective of this paper is to investigate the behaviour of deep underground tunnel opening existed between two bedding planes, Such planes weaken the strength of rock mass and may cause rock slippage/rotation along them. Therefore, the state of stress-displacement, after tunnel opening has been introduced, is examined using two-dimensional elasto-plastic finite-elements code, RS^(2D). The results indicate that, there is significant drop in the normal stress along joints over tunnel opening; slip occurs due to reversal in the direction of shear stress(e.g., inward shear displacement is produced) and there is discontinuity in the strength contours of rock surrounding tunnel after they have been intersected by bedding planes.
基金China Railway EryuanEngineering Group CO.LTD (2009-LiXiang Railway-13)the Fundamental Research for the Central Uni-versities (SWJTU09BR033)
文摘Jinsha River Bridge is located along the Lijiang-Xamgyi＇nyilha railway on the southeastern Tibet plateau; it is an area with a high prevalence of earthquakes. The bridge abutments were designed to be constructed in river bank slopes, where rocks are controlled by two sets of joint planes that significantly influence the stability of the left bank slope. According to the engineering-geological conditions and the characteristics of discontinuities, strength properties of the rock mass were obtained based on Barton model and direct shear test. Numerical analyses were performed using FLAC3D software to examine the slope＇s response to seismic loading. Then in order to evaluate the damage trends of the rock mass under the different loading conditions, a calculation model based on the geological parameters and slope stability was simulated and analyzed using the discrete element numerical simulation program UDEC （Universal Dis- tinct Element Code）, and the effect of degradation of discontinuities on the slope stability was investigated. The results show that the destruction of rock mass under the gravity, bridge foundation, and seismic load are mainly concentrated within 30 m depth of slope, and the slope under loading may slide along joint planes. In addition, the dynamic analysis by amplification of the input loading indicates that instability occurs to the bank slope at a height of about 200 m, and rock blocks will fail under seismic load. Therefore, to prevent the slope from deformation under the engineering loading and strong earthquakes, the bridge foundation should be strengthened.
文摘This paper is devoted to the study of a translation plane π(C) associated with a t-spread set C and its transposed t-spread set C t. In this paper, an explicit matrix form of the inverse of an isomorphism from a translation plane into another translation plane associated with t-spread sets is derived and proved that two translation planes associated with t-spread sets are isomorphic if and only if their corresponding transposed translation planes are isomorphic. Further, it is shown that the transpose of a flag-transitive plane is flag-transitive and derived a necessary and sufficient condition for a translation plane π(C) to be isomorphic to its transposed translation plane.
