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The study of the changes in stress and deformation of frozen walls during excavation has always been a hot topic in underground freezing engineering, and the size of the plastic zone is an important basis for evaluating the stability of frozen walls. In response to the shortcomings in the current design of horizontal frozen walls, based on the internal excavation unloading conditions of the frozen wall in artificial ground freezing, an elastoplastic mechanical model for the interaction between a circular horizontal freezing wall and unfrozen soil mass is established under nonuniform loads to obtain the corresponding solutions for stress and displacement in the system. In this study, considering the shear stress of the plastic zone, the method for solving the traditional plastic zone contour equation is modified; consequently, the modified solution of the contour equation of the plastic zone for the frozen wall is obtained. Using this theoretical solution, the influence of the external load p 0 and the lateral pressure coefficient λ on the contour line of plastic zone and tensile stress zone are analyzed by combining the project case, the calculation results show that: the λ = 0. 485 is the critical point where the inner edge of the frozen wall just happens to have tensile stress. When λ < 0. 485 , the tensile stress zone is inevitable in the inner edge of the frozen wall vertical direction, and its range is only related to λ and increases with the decrease of λ. The p 0 only affects the magnitude of tensile stress in the region, but does not affect its range. At this time, the frozen wall compression plastic zone contour evolves from crescent shaped to ear shaped with the increase of p 0 . When 0. 485 < λ < 0.61 , there will be no tensile stress zone, the frozen wall compression plastic zone contour also evolves from crescent shaped to ear shaped with the increase of p 0 . When λ > 0.61 , there will be also no tensile stress zone, with the increase of p 0 , the compression plastic zone contour evolves from the crescent shaped in the horizontal direction to the elliptical shaped, and there is no ear-shaped plastic zone in the whole evolution process. Based on our results, we show that our method can be used to provide a theoretical basis for the stability evaluation and parameter (thickness) design calculation of horizontal frozen walls under nonuniform loads. [ABSTRACT FROM AUTHOR]

The study of the changes in stress and deformation of frozen walls during excavation has always been a hot topic in underground freezing engineering, and the size of the plastic zone is an important basis for evaluating the stability of frozen walls. In response to the shortcomings in the current design of horizontal frozen walls, based on the internal excavation unloading conditions of the frozen wall in artificial ground freezing, an elastoplastic mechanical model for the interaction between a circular horizontal freezing wall and unfrozen soil mass is established under nonuniform loads to obtain the corresponding solutions for stress and displacement in the system. In this study, considering the shear stress of the plastic zone, the method for solving the traditional plastic zone contour equation is modified; consequently, the modified solution of the contour equation of the plastic zone for the frozen wall is obtained. Using this theoretical solution, the influence of the external load p0 and the lateral pressure coefficient λ on the contour line of plastic zone and tensile stress zone are analyzed by combining the project case, the calculation results show that: the λ=0.485 is the critical point where the inner edge of the frozen wall just happens to have tensile stress. When λ<0.485, the tensile stress zone is inevitable in the inner edge of the frozen wall vertical direction, and its range is only related to λ and increases with the decrease of λ. The p0 only affects the magnitude of tensile stress in the region, but does not affect its range. At this time, the frozen wall compression plastic zone contour evolves from crescent shaped to ear shaped with the increase of p0. When 0.485<λ<0.61, there will be no tensile stress zone, the frozen wall compression plastic zone contour also evolves from crescent shaped to ear shaped with the increase of p0. When λ>0.61, there will be also no tensile stress zone, with the increase of p0, the compression plastic zone contour evolves from the crescent shaped in the horizontal direction to the elliptical shaped, and there is no ear-shaped plastic zone in the whole evolution process. Based on our results, we show that our method can be used to provide a theoretical basis for the stability evaluation and parameter (thickness) design calculation of horizontal frozen walls under nonuniform loads.

Abstract The calculation of abutment stress has always been the most important topic in safe underground mining and design. In this paper, based on the formation mechanism of abutment stress, combined with the mechanical properties of actual strata and the theory of elastic foundation beams, a structure model of overlying strata with an elastic foundation is established, and a new theoretical calculation method of abutment stress is proposed. The new calculation method takes into account the interaction of the overlying key strata and the effect on the transmission of the front abutment stress and then analyzes the stress patterns of multilayered key strata under the combined action of the bending moment, shear force, and nonuniform load and its transmission to the underlying strata. In addition, based on field observations of panel 10 305 in the Xinglongzhuang coalmine, the influence range, peak position, and variation trend of the front abutment stress before and after breaking of the overlying key strata are studied and verified. The results show that the influence range of the abutment stress remains unchanged after KS1 breaks (eg, from 0 to 180 m), and its peak position shifts forward from 8 to 19 m, while the influence range (0‐180 m) and its peak position (6‐8 m in front of coal wall) remain unchanged after KS2 breaks; the abutment stress decreases, and the maximum decrease is 3.9 MPa in the range of 0‐22 m ahead of the coal wall after KS1 breaks, while the maximum decrease in the abutment stress is 2.1 MPa in the range of 0‐71 m ahead of the coal wall after KS2 breaks. The results of the new calculation method are basically consistent with the field observations and the existing theoretical results, showing that the method has good adaptability and reliability and can provide a new theoretical basis for on‐site design and construction practices.

The calculation of abutment stress has always been the most important topic in safe underground mining and design. In this paper, based on the formation mechanism of abutment stress, combined with the mechanical properties of actual strata and the theory of elastic foundation beams, a structure model of overlying strata with an elastic foundation is established, and a new theoretical calculation method of abutment stress is proposed. The new calculation method takes into account the interaction of the overlying key strata and the effect on the transmission of the front abutment stress and then analyzes the stress patterns of multilayered key strata under the combined action of the bending moment, shear force, and nonuniform load and its transmission to the underlying strata. In addition, based on field observations of panel 10 305 in the Xinglongzhuang coalmine, the influence range, peak position, and variation trend of the front abutment stress before and after breaking of the overlying key strata are studied and verified. The results show that the influence range of the abutment stress remains unchanged after KS1 breaks (eg, from 0 to 180 m), and its peak position shifts forward from 8 to 19 m, while the influence range (0‐180 m) and its peak position (6‐8 m in front of coal wall) remain unchanged after KS2 breaks; the abutment stress decreases, and the maximum decrease is 3.9 MPa in the range of 0‐22 m ahead of the coal wall after KS1 breaks, while the maximum decrease in the abutment stress is 2.1 MPa in the range of 0‐71 m ahead of the coal wall after KS2 breaks. The results of the new calculation method are basically consistent with the field observations and the existing theoretical results, showing that the method has good adaptability and reliability and can provide a new theoretical basis for on‐site design and construction practices. [ABSTRACT FROM AUTHOR]

In this paper, the dynamic stress and radial/lateral vibration of circular/annular discs made of fractional-order viscoelastic materials under nonuniform mechanical loads are investigated for the first time, utilizing the exact 3D theory of elasticity, rather than the plate theories. The governing equations of motion of the disc are derived based on the Kelvin–Voigt fractional viscoelastic model. To solve these equations, the spatial partial and the time ordinary derivatives are replaced by adequate central, backward or forward finite difference expressions. Then the resulting Caputo-type time-dependent system of the coupled integro-differential governing equations of the fractional-order is solved by a novel numerical procedure. Namely, a time-marching procedure is employed to extract the time histories of the responses, in the space-time domain for various time and spatial distributions. Finally, comprehensive sensitivity analyses and various 3D plots are presented and discussed. In this regard, effects of the fractional-order of the constitutive law, viscoelastic parameters, material rigidity, distribution and time variation patterns of the nonuniform distributed transverse loads, and boundary conditions on the distributions of the displacement and stress components are investigated. [ABSTRACT FROM AUTHOR]

Ｉｎ ａｎ ｅｎｇｉｎｅｅｒｉｎｇ ｓｔｒｕｃｔｕｒｅ， ｔｈｅ ｒｏｃｋ ｉｓ ｏｆｔｅｎ ｓｕｂｊｅｃｔｅｄ ｔｏ ｎｏｎｕｎｉｆｏｒｍ ｌｏａｄ； ｉｎ ａｄｄｉ⁃ ｔｉｏｎ， ｔｈｅｒｅ ｉｓ ａ ｓｍａｌｌ ｄｉｓｔｒｉｂｕｔｉｏｎ ａｎｇｌｅ ｕｎｄｅｒ ａ ｃｏｎｃｅｎｔｒａｔｅｄ ｆｏｒｃｅ ｉｎ ａｃｔｕａｌ ｅｘｐｅｒｉｍｅｎｔａｌ ｓｔｕｄｙ， ａｎｄ ｔｈｅ ｌｏａｄ ｄｉｓｔｒｉｂｕｔｉｏｎ ａｌｓｏ ｓｈｏｕｌｄ ｂｅ ｎｏｎｕｎｉｆｏｒｍ． Ｂａｓｅｄ ｏｎ ｔｈｉｓ ｃａｓｅ， ａ ｃｌａｓｓ ｏｆ ｎｏｎｕｎｉｆｏｒｍ ｌｏａｄｓ ｗｅｒｅ ｐｒｏｐｏｓｅｄ ｉｎ ｔｈｅ ｔｒｉｇｏｎｏｍｅｔｒｉｃ ｆｕｎｃｔｉｏｎ ｆｏｒｍ． Ｔｈｅｎ ｔｈｅ ｍａｘｉｍｕｍ ｌｏａｄｉｎｇ ｐｒｅｓｓｕｒｅ ａｐｐｅａｒｅｄ ｉｎ ｔｈｅ ｍｉｄｄｌｅ ｏｆ ｔｈｅ ｄｉｓｔｒｉｂｕｔｉｏｎ ａｎｇｌｅ ａｎｄ ｇｒａｄｕａｌｌｙ ｂｅｃａｍｅ ｓｍａｌｌ ｔｏ ｂｏｔｈ ｓｉｄｅｓ ｕｎｔｉｌ ０． Ｂｙ ｍｅａｎｓ ｏｆ ｔｈｅ ｃｅｎｔｒａｌｌｙ ｃｒａｃｋｅｄ Ｂｒａｚｉｌｉａｎ ｄｉｓｋ （ＣＣＢＤ） Ｔ⁃ ｓｔｒｅｓｓ ｆｏｒｍｕｌａ ｕｎｄｅｒ ａ ｒａｄｉａｌ ｃｏｎｃｅｎｔｒａｔｅｄ ｌｏａｄ， ｔｈｅ ａｎａｌｙｔｉｃａｌ Ｔ⁃ ｓｔｒｅｓｓ ｓｏｌｕｔｉｏｎ ｕｎｄｅｒ ｔｈｉｓ ｋｉｎｄ ｏｆ ｎｏｎｕｎｉｆｏｒｍ ｌｏａｄ ｗａｓ ａｃ⁃ ｑｕｉｒｅｄ ｖｉａ ｔｈｅ ｉｎｔｅｇｒａｌ ｉｎ ｔｈｅ ｒａｎｇｅ ｏｆ ｔｈｅ ｄｉｓｔｒｉｂｕｔｉｏｎ ａｎｇｌｅ， ｍｅａｎｗｈｉｌｅ ｔｈｅ ｆｉｎｉｔｅ ｅｌｅｍｅｎｔ ｓｉｍｕ⁃ ｌａｔｉｏｎ ｗａｓ ｃｏｎｄｕｃｔｅｄ ｔｏ ｏｂｔａｉｎ ｔｈｅ ｎｕｍｅｒｉｃａｌ ｓｏｌｕｔｉｏｎ． Ｔｈｅｒｅ ｉｓ ａ ｖｅｒｙ ｇｏｏｄ ｃｏｎｓｉｓｔｅｎｃｙ ｂｅ⁃ ｔｗｅｅｎ ｔｈｅ ｎｕｍｅｒｉｃａｌ ｒｅｓｕｌｔｓ ａｎｄ ｔｈｅ ａｎａｌｙｔｉｃａｌ ｒｅｓｕｌｔｓ， ｗｈｉｃｈ ｖｅｒｉｆｉｅｓ ｔｈｅ ａｃｃｕｒａｃｙ ｏｆ ｅａｃｈ ｏｔｈ⁃ ｅｒ． Ｃｏｍｐａｒｅｄ ｗｉｔｈ ｔｈｏｓｅ ｕｎｄｅｒ ｔｈｅ ｕｎｉｆｏｒｍ ｌｏａｄ， ｔｈｅ ｄｉｍｅｎｓｉｏｎｌｅｓｓ Ｔ⁃ ｓｔｒｅｓｓ ｖａｌｕｅｓ ｕｎｄｅｒ ｔｈｉｓ ｎｏｎｕｎｉｆｏｒｍ ｌｏａｄ ａｒｅ ｃｌｏｓｅｒ ｔｏ ｔｈｅ ｖａｌｕｅｓ ｕｎｄｅｒ ｔｈｅ ｃｏｎｃｅｎｔｒａｔｅｄ ｌｏａｄ ｗｈｅｎ ｔｈｅ ｏｔｈｅｒ ｃｏｎｄｉｔｉｏｎ ｉｓ ｔｈｅ ｓａｍｅ， ａｎｄ ｔｈｅ ｄｉｓｃｒｅｐａｎｃｙ ｂｅｔｗｅｅｎ ｔｈｅ ｓｔｒｅｓｓｅｓ ｕｎｄｅｒ ｔｈｅ ｎｏｎｕｎｉｆｏｒｍ ｌｏａｄ ａｎｄ ｔｈｅ ｃｏｎ⁃ ｃｅｎｔｒａｔｅｄ ｌｏａｄ ｉｓ ｖｅｒｙ ｓｍａｌｌ． Ｔｈｅ ｆｕｒｔｈｅｒ ｃａｌｃｕｌａｔｅｄ ｒｅｓｕｌｔｓ ｓｈｏｗ ｔｈａｔ ｉｔ ｉｓ ａｃｃｕｒａｔｅ ａｎｄ ｒｅａｓｏｎａ⁃ ｂｌｅ ｔｏ ｕｓｅ ｔｈｅ Ｔ⁃ ｓｔｒｅｓｓ ｆｏｒｍｕｌａ ｆｏｒ ｔｈｅ ＣＣＢＤ ｓｕｂｊｅｃｔｅｄ ｔｏ ｔｈｅ ｃｏｎｃｅｎｔｒａｔｅｄ ｆｏｒｃｅｓ ｉｎ ａｃｔｕａｌ ｔｅｓ⁃ ｔｉｎｇ． [ABSTRACT FROM AUTHOR]