To explore the effects of freeze‒thaw cycles on the mechanical properties and crack evolution of fissured sandstone,biaxial compression experiments were carried out on sandstone subjected to freeze‒thaw cycles to char...To explore the effects of freeze‒thaw cycles on the mechanical properties and crack evolution of fissured sandstone,biaxial compression experiments were carried out on sandstone subjected to freeze‒thaw cycles to characterize the changes in the physical and mechanical properties of fissured sandstone caused by freeze‒thaw cycles.The crack evolution and crack change process on the surface of the fissured sandstone were recorded and analysed in detail via digital image technology(DIC).Numerical simulation was used to reveal the expansion process and damage mode of fine-scale cracks under the action of freeze‒thaw cycles,and the simulation results were compared and analysed with the experimental data to verify the reliability of the numerical model.The results show that the mass loss,porosity,peak stress and elastic modulus all increase with increasing number of freeze‒thaw cycles.With an increase in the number of freeze‒thaw cycles,a substantial change in displacement occurs around the prefabricated cracks,and a stress concentration appears at the crack tip.As new cracks continue to sprout at the tips of the prefabricated cracks until the microcracks gradually penetrate into the main cracks,the displacement cloud becomes obviously discontinuous,and the contours of the displacement field in the crack fracture damage area simply intersect with the prefabricated cracks to form an obvious fracture.The damage patterns of the fractured sandstone after freeze‒thaw cycles clearly differ,forming a symmetrical"L"-shaped damage pattern at zero freeze‒thaw cycles,a symmetrical"V"-shaped damage pattern at 10 freeze‒thaw cycles,and a"V"-shaped damage pattern at 20 freeze‒thaw cycles.After 20 freeze‒thaw cycles,a"V"-shaped destruction pattern and"L"-shaped destruction pattern are formed;after 30 freeze‒thaw cycles,an"N"-shaped destruction pattern is formed.This shows that the failure mode of fractured sandstone gradually becomes more complicated with an increasing number of freeze‒thaw cycles.The effects展开更多
The construction of sections of bundles with prescribed jet values plays a fundamental role in problems of algebraic and complex geometry.When the jet values are prescribed on a positive dimensional subvariety,it is h...The construction of sections of bundles with prescribed jet values plays a fundamental role in problems of algebraic and complex geometry.When the jet values are prescribed on a positive dimensional subvariety,it is handled by theorems of Ohsawa-Takegoshi type which give extension of line bundle valued square-integrable top-degree holomorphic forms from the fiber at the origin of a family of complex manifolds over the open unit 1-disk when the curvature of the metric of line bundle is semipositive.We prove here an extension result when the curvature of the line bundle is only semipositive on each fiber with negativity on the total space assumed bounded from below and the connection of the metric locally bounded,if a square-integrable extension is known to be possible over a double point at the origin.It is a Hensel-lemma-type result analogous to Artin's application of the generalized implicit function theorem to the theory of obstruction in deformation theory.The motivation is the need in the abundance conjecture to construct pluricanonical sections from flatly twisted pluricanonical sections.We also give here a new approach to the original theorem of Ohsawa-Takegoshi by using the hyperbolic geometry of the punctured open unit 1-disk to reduce the original theorem of OhsawaTakegoshi to a simple application of the standard method of constructing holomorphic functions by solving the equation with cut-off functions and additional blowup weight functions.展开更多
基金supported by the National Natural Science Foundation of China(Project No.52074123).
文摘To explore the effects of freeze‒thaw cycles on the mechanical properties and crack evolution of fissured sandstone,biaxial compression experiments were carried out on sandstone subjected to freeze‒thaw cycles to characterize the changes in the physical and mechanical properties of fissured sandstone caused by freeze‒thaw cycles.The crack evolution and crack change process on the surface of the fissured sandstone were recorded and analysed in detail via digital image technology(DIC).Numerical simulation was used to reveal the expansion process and damage mode of fine-scale cracks under the action of freeze‒thaw cycles,and the simulation results were compared and analysed with the experimental data to verify the reliability of the numerical model.The results show that the mass loss,porosity,peak stress and elastic modulus all increase with increasing number of freeze‒thaw cycles.With an increase in the number of freeze‒thaw cycles,a substantial change in displacement occurs around the prefabricated cracks,and a stress concentration appears at the crack tip.As new cracks continue to sprout at the tips of the prefabricated cracks until the microcracks gradually penetrate into the main cracks,the displacement cloud becomes obviously discontinuous,and the contours of the displacement field in the crack fracture damage area simply intersect with the prefabricated cracks to form an obvious fracture.The damage patterns of the fractured sandstone after freeze‒thaw cycles clearly differ,forming a symmetrical"L"-shaped damage pattern at zero freeze‒thaw cycles,a symmetrical"V"-shaped damage pattern at 10 freeze‒thaw cycles,and a"V"-shaped damage pattern at 20 freeze‒thaw cycles.After 20 freeze‒thaw cycles,a"V"-shaped destruction pattern and"L"-shaped destruction pattern are formed;after 30 freeze‒thaw cycles,an"N"-shaped destruction pattern is formed.This shows that the failure mode of fractured sandstone gradually becomes more complicated with an increasing number of freeze‒thaw cycles.The effects
基金supported by Grant 1001416 of the National Science Foundation
文摘The construction of sections of bundles with prescribed jet values plays a fundamental role in problems of algebraic and complex geometry.When the jet values are prescribed on a positive dimensional subvariety,it is handled by theorems of Ohsawa-Takegoshi type which give extension of line bundle valued square-integrable top-degree holomorphic forms from the fiber at the origin of a family of complex manifolds over the open unit 1-disk when the curvature of the metric of line bundle is semipositive.We prove here an extension result when the curvature of the line bundle is only semipositive on each fiber with negativity on the total space assumed bounded from below and the connection of the metric locally bounded,if a square-integrable extension is known to be possible over a double point at the origin.It is a Hensel-lemma-type result analogous to Artin's application of the generalized implicit function theorem to the theory of obstruction in deformation theory.The motivation is the need in the abundance conjecture to construct pluricanonical sections from flatly twisted pluricanonical sections.We also give here a new approach to the original theorem of Ohsawa-Takegoshi by using the hyperbolic geometry of the punctured open unit 1-disk to reduce the original theorem of OhsawaTakegoshi to a simple application of the standard method of constructing holomorphic functions by solving the equation with cut-off functions and additional blowup weight functions.
