偶应力理论下全长粘结式锚杆拉拔特性数值分析
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摘要
锚杆锚固技术广泛应用于边坡、隧道和矿井等领域中。由于锚杆锚固工程本身的复杂性以及受地理环境、岩土种类和分布区域等因素的影响,目前的锚杆锚固机理、设计理论都不够完善。锚杆锚固段界面剪应力分布规律是锚杆设计研究的重点,它直接影响锚固效果。锚固段界面上的剪应力在界面附近的岩土体中会引起较大的应变梯度。传统的连续介质理论没有考虑应变梯度的影响,不能很好地解释锚固段附近岩土体中出现的弯曲变形及破坏现象。偶应力理论引进弯曲曲率,考虑了弯曲效应对介质变形特性的影响。
根据理论分析,得出偶应力理论的基本方程,与有限元方法结合,基于Matlab软件编写基于偶应力理论的有限元分析程序；并通过简单悬臂梁的算例来验证程序的正确性。
基于偶应力理论,建立了平面应变问题的有限元计算模型,研究全长粘结式锚杆锚固段界面上的剪应力分布、界面附近的边界层效应和偶应力的尺度效应,并将偶应力理论的计算结果和经典弹性理论的计算结果进行比较。结果表明：在偶应力理论下,锚固段界面的剪应力和剪应变有所减小,特别是峰值处的剪应力减小明显；界面处的剪应力不再连续；界面附近的剪应变突变有所改善,出现了一个过渡区域。
分析了特征长度、第二剪切模量、岩土体弹性模量和围压对锚固界面的受力特性的影响。
结果表明：特征长度对锚固界面剪应力、剪应变有一定的影响,特征长度减小,过渡区域变小,而应变梯度增大；第二剪切模量对剪应力、剪应变分布的影响不明显。岩土越松软弹性,模量越小,受到的最大剪应力就越小；反之,岩土越坚硬,弹性模量越大,受到的剪应力则越大。围压越大,锚杆的剪应力得到明显的减少,在峰值的地方偶应力尺度效应尤为明显。
The technology of bolt anchoring is widely used in slope, tunnels and mines and other fields. The bolt anchoring itself is very diversity and is impacted by geographical environment, rock and soil types and distribution area and other factors. So, the bolt anchoring mechanism and design theory are not perfect. Shear stress distribution in anchorage interface of anchor is the attention points of anchor design. It directly affects anchoring effect. Shear stress in anchorage interface will cause larger strain gradient in rock and soil near anchorage interface. The strain gradient is not considered in classical elastic theory which can't explain the phenomena of bending deformation and failure in the anchoring section. Bending curvature is introduced into couple stress theory which considers the effect on the deformation characteristics of the bending.
Finite element analysis program of couple stress theory was wrote base on MATLAB, which was combined with the basic equations of couple stress theory and finite element method. The correctness of the program was verified through the simple cantilever operator.
The finite element model of plane strain was established base on couple stress theory. The fully bonded was used to research interface shear stress distribution, boundary layer effect and scale effect. The results of couple stress theory were compared with the results of classical elasticity theory. The results show that the shear stress and shear strain near anchorage interface in couple stress theory are smaller than that in classical theory, especially at the peak of shear stress. The shear stress on interface is not continuous. But shear strain abrupt change on interface has been improved and a transition region appears near the interface.
The Mechanical Characteristics of anchoring interface was researched on characteristic length, shear modulus, modulus of elasticity of rock and soil and confining pressure.
The results show that the impact of characteristic length to anchor interface shear stress was obvious, as the characteristic length decreases, the transition region becomes smaller, while the strain gradient increases. The impact of second shear modulus to shear stress distribution was not obvious. As the rock more softly elastic modulus is smaller, the maximum shear stress and axial force are smaller; conversely, the harder Rock, the greater the elastic modulus, The shear stress and axial force are greater. As the greater the confining pressure, the anchor shear stress and axial force are significantly reduced, especially at the peak of scale effect.
根据理论分析,得出偶应力理论的基本方程,与有限元方法结合,基于Matlab软件编写基于偶应力理论的有限元分析程序；并通过简单悬臂梁的算例来验证程序的正确性。
基于偶应力理论,建立了平面应变问题的有限元计算模型,研究全长粘结式锚杆锚固段界面上的剪应力分布、界面附近的边界层效应和偶应力的尺度效应,并将偶应力理论的计算结果和经典弹性理论的计算结果进行比较。结果表明：在偶应力理论下,锚固段界面的剪应力和剪应变有所减小,特别是峰值处的剪应力减小明显；界面处的剪应力不再连续；界面附近的剪应变突变有所改善,出现了一个过渡区域。
分析了特征长度、第二剪切模量、岩土体弹性模量和围压对锚固界面的受力特性的影响。
结果表明：特征长度对锚固界面剪应力、剪应变有一定的影响,特征长度减小,过渡区域变小,而应变梯度增大；第二剪切模量对剪应力、剪应变分布的影响不明显。岩土越松软弹性,模量越小,受到的最大剪应力就越小；反之,岩土越坚硬,弹性模量越大,受到的剪应力则越大。围压越大,锚杆的剪应力得到明显的减少,在峰值的地方偶应力尺度效应尤为明显。
The technology of bolt anchoring is widely used in slope, tunnels and mines and other fields. The bolt anchoring itself is very diversity and is impacted by geographical environment, rock and soil types and distribution area and other factors. So, the bolt anchoring mechanism and design theory are not perfect. Shear stress distribution in anchorage interface of anchor is the attention points of anchor design. It directly affects anchoring effect. Shear stress in anchorage interface will cause larger strain gradient in rock and soil near anchorage interface. The strain gradient is not considered in classical elastic theory which can't explain the phenomena of bending deformation and failure in the anchoring section. Bending curvature is introduced into couple stress theory which considers the effect on the deformation characteristics of the bending.
Finite element analysis program of couple stress theory was wrote base on MATLAB, which was combined with the basic equations of couple stress theory and finite element method. The correctness of the program was verified through the simple cantilever operator.
The finite element model of plane strain was established base on couple stress theory. The fully bonded was used to research interface shear stress distribution, boundary layer effect and scale effect. The results of couple stress theory were compared with the results of classical elasticity theory. The results show that the shear stress and shear strain near anchorage interface in couple stress theory are smaller than that in classical theory, especially at the peak of shear stress. The shear stress on interface is not continuous. But shear strain abrupt change on interface has been improved and a transition region appears near the interface.
The Mechanical Characteristics of anchoring interface was researched on characteristic length, shear modulus, modulus of elasticity of rock and soil and confining pressure.
The results show that the impact of characteristic length to anchor interface shear stress was obvious, as the characteristic length decreases, the transition region becomes smaller, while the strain gradient increases. The impact of second shear modulus to shear stress distribution was not obvious. As the rock more softly elastic modulus is smaller, the maximum shear stress and axial force are smaller; conversely, the harder Rock, the greater the elastic modulus, The shear stress and axial force are greater. As the greater the confining pressure, the anchor shear stress and axial force are significantly reduced, especially at the peak of scale effect.
引文
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[3]程良奎.岩土锚固的现状与发展[J].土木工程学报,2001,34(3)：7-12.
[4]陈卫忠,李术才,朱维申等.考虑裂隙闭合和摩擦效应的节理岩体能量损伤理论及应用[J].岩石力学与工程学报,2000,19(2)：131-135.
[5]汪明武,王鹤龄.锚固质量的无损检测技术[J],岩石力学与工程学报,2002,21(1).126-129.
[6]Philips S H E. Factors affecting the design of anchorages in rock[R]. London: cementation Research Ltd,1970.
[7]Gunnar Wijk. A theoretical remark on the stress field around prestressed rock Bolts[J]. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts,1878 (15):289-294.
[8]孔宪宾,余跃欣,李炜等.土-锚杆相互作用机理的研究[J].工程力学2000,17(3)：80-86.
[9]牟瑞芳,王建宁,张武国.按共同变形原理计算地锚锚固段粘结力分布[J].路基工程,1999(2)：31-34.
[10]张季如,唐保付.锚杆荷载传递机理分析的双曲函数模型[J].岩土工程学报,2002,24(2)：32-42
[11]Coates D F, Yu Y S. Three-dimensional stress distributions around a cylindrical hole and anchor [J]. International Society for Rock Mechanics,1970,3 (6-7): 175-182.
[12]A M Ferrero. The shear strength of reinforced rock joints [J]. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 1995(32):595-605.
[13]Pellet F, Egger P. Analytical model for the mechanical behavior of bolted rock joints subjected to shearing [J]. Rock Mechanics and Rock Engineering,1996 (29):73-97.
[14]朱浮声,郑雨天.全长粘结式锚杆的加固作用分析[J].岩石力学与工程学报,1996,15(4)：333-337.
[15]周力军.考虑接触非线性的锚杆-土体非连续问题有限元分析[J].水运工程,2001(10)：28-30.
[16]丁秀丽,盛谦,韩军.预应力锚索锚固机理的数值模拟试验研究[J].岩石力学与工程学报,2002,21(7)：980-988.
[17]付敬,盛谦.高边坡预应力锚索加固的数值模拟分析[J].长江科学院院报,1996,13(3)：52-55.
[18]Lutz L, Gergeley P. Mechanics of band and slip of deformed bars in concrete [J]. Journal of American Concrete Institute,1967,64(11):711-721.
[19]Hanson N W. Influence of surface roughness of prestressing strand on band performance [J]. Journal of Prestressed Concrete Institute,1969,14(1):32-45.
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