The influence of a boundary fracture on the elastic stiffness of a deeply embedded anchor plate

The problem of the axial loading of a rigid disk-shaped anchor plate embedded in an isotropic elastic medium of infinite extent is examined. At the boundary of the disk anchor plate the elastic medium contains a cracked region of finite extent. The presence of the cracked region decreases the elastic stiffness of the anchor plate. The mathematical formulation of the problem is developed, and a numerical scheme is presented which can be used to solve the resulting coupled integral equations. The numerical technique is used to evaluate the results, which illustrate the manner in which the elastic stiffness of the anchor plate is influenced by the extent of cracking. Similar results are developed for the flaw shearing mode stress intensity factor at the external boundary of the cracked region.     

拉力型锚杆锚固界面剪应力分布偶应力理论分析

锚杆锚固段界面剪应力分布规律是锚杆设计研究的重点,直接影响锚固效果。锚固段界面上的剪应力会引起界面附近的岩土体较大的应变梯度,而用经典弹性理论分析锚固段剪应力时没有考虑应变梯度。偶应力理论引进弯曲曲率,考虑弯曲效应对介质变形特性的影响,基于该理论建立平面应变问题的有限元计算模型,研究拉力型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,拉力型锚杆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少明显;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,出现一个过渡区域。特征长度减小,过渡区域变小,应变梯度增大,第二剪切模量对剪应力分布的影响不明显。     

The response of a deep rigid anchor due to undrained elastic deformations of the surrounding soil medium

The equations governing the undrained linear elastic behaviour of a saturated soil are formally similar to the equations governing slow of an incompressible Newtonian viscous fluid. This principle of equivalence can then be effectively employed to obtain the load-deflection reiationship for a deep rigid anchor with the shape of a solid of revolution which is embedded in bonded contact with an unbounded incompressible elastic medium. It is found that the load-deflection relationship for the deep rigid anchor can be directly recovered from the expression for the drag induced on an impermeable object with the same size and shape as the anchor, which is appropriately placed in a slow viscous flow region of uniform velocity.     

预应力锚索损伤软化精细有限元模型

预应力锚索作为岩土工程的一种主要加固技术已得到日益广泛的应用,但现有的计算方法难以反映岩体、砂浆、钢绞线相互之间的滑移变形等实际情况,计算结果难以体现实际的加固效果。通过研究接触面的特性引入损伤软化概念,建立了包含钢绞线、砂浆、接触面的损伤软化精细有限元模型,并与现场试验进行了对比分析。该模型优点是精细地描述了钢绞线、砂浆和接触面等结构的力学行为,可以反映接触面力学材料损伤软化的过程,更加精确地反映了锚固段的力学变化过程。试验结果对比显示,两者随着荷载不断加大,锚固段接触面上的剪应力峰值由端口往里转移。当端口处于弹性阶段,峰值在端口,呈指数衰减模式;当端口处出现损伤软化,峰值往里转移。计算分析反映的锚固段应力变化规律与试验基本一致。     

Elastic properties of polycrystalline minerals: Comparison of theory and experiment

Literature compressional and shear wave velocities measured versus pressure and temperature on dense, isotropic polycrystals of periclase, corundum, forsterite, fayalite, alpha-quartz, rutile, germania, and cassiterite are compared with the Voigt, Reuss, and Hashin-Shtrikman bounds calculated from single-crystal elastic stiffnesses and their first pressure and temperature derivatives. The Hashin-Shtrikman bounds reduce the separation between the Voigt and Reuss bounds by factors of from 3 to 15. There is very good agreement between the Hashin-Shtrikman bounds and the experimental data when errors in the polycrystal data and in the single-crystal elastic stiffnesses are taken into account. This comparison demonstrates that the Hashin-Shtrikman bounds can be used with considerable confidence in modeling velocities in mineral assemblages, particularly mantle assemblages, and are especially useful in problems where sensitivity of the results to the uncertainties in all the input parameters is of interest.     

A method of analysis for horizontally embedded anchors in an elastic soil

A general method is presented for the analysis of horizontally embedded anchors in an elastic soil. Provision is made in the analysis for the consideration of anchor shape, layer depth, anchor–soil interface condition, breakaway of the anchor from the underlying soil and interaction between groups of anchors. Application of the analytical technique is illustrated for strip and circular anchors, and these solutions are presented in the form of influence charts which may be used directly in hand calculations to predict the elastic load deflection behaviour, of anchor plates for a wide variety of material and geometric conditions.     

The axial loading of a rigid circular anchor plate embedded in an elastic half-space

The present paper examines the axisymmetric problem related to the loading of a rigid circular anchor plate which is embedded in bonded contact with an isotropic elastic half-space. A Hankel transform development of the governing equations is used to reduce the associated mixed boundary value problem to a set of coupled Fredholm integral equations of the second kind. These equatons are solved in a numerical fashion to generate results of engineering interest. In particular, the results indicate the influence of the depth of embedment on the axial stiffness of the rigid anchor plate.     

自由段先注浆对预应力锚索抗拔试验结果影响研究

为了解决无法采用已注浆锚索进行抗拔试验问题,基于界面脱黏剪切模型,利用荷载传递和弹性变形理论,考虑锚索锚固段与自由段长度比Lb /La的影响,建立了采用自由段已注浆锚索抗拔试验结果评价锚索抗拔性能的方法。结果表明：自由段注浆对锚索抗拔力有较大幅度的提高,尤其是当界面剪切阶段由弹性向脱黏过渡时,提高比例快速增加,并在脱黏后逐渐趋于稳定。其次,锚索自由段与锚固段交界面处剪切位移和轴力最大,并向两端逐渐降低。随着拉拔力的提高,界面剪切位移和轴力都不断增大,同时向锚索两端的衰减速度也加快。此外,弹性阶段时剪应力曲线为山峰型,而脱黏阶段为马鞍型,并随抗拔力的提高,马鞍开口逐渐扩大。最后,锚固段与自由段长度比Lb /La对锚索极限抗拔力的影响较小,其极限抗拔力折减系数?Q取值介于0.81～0.83之间,且Lb /La =2.5时,?Q计算值仅比实测结果小6.02%,验证了本文方法的可行性。     

玻璃纤维增强聚合物抗浮锚杆抗拔性能试验研究与机制分析

抗浮锚杆作为一种竖向锚固技术在我国许多地区广泛应用,锚杆作为抗浮结构的核心其性能受到极大关注。但因钢材易腐蚀,传统金属锚杆的耐久性受到质疑,特别是地铁等地下工程存在杂散电流,限制了金属抗浮锚杆的应用。玻璃纤维增强聚合物(GFRP)抗浮锚杆是一种由树脂基体和玻璃纤维复合而成的新材料,与金属锚杆相比,它具有耐腐蚀、抗拉强度高、自重轻等优良特性。通过植入式裸光纤传感测试技术对GFRP抗浮锚杆的界面应力分布、荷载传递规律及破坏机制进行了研究,论证了GFRP抗浮锚杆使用的适宜性。试验表明,GFRP抗浮锚杆破坏以杆体基体材料剪切破坏为主,?28 mm锚杆极限抗拔力为250 kN,能够满足工程需要;杆体轴力沿深度方向逐渐递减,并且超过一定长度后杆体不再受力。结果显示,中风化岩地区,当锚固段长度为3.95⁶.95 m时,轴力影响深度范围约为3.7 m,说明GFRP抗浮锚杆同样存在临界锚固深度问题。锚杆界面剪应力呈不均匀分布,剪应力峰值随荷载的增加逐渐向下转移,同时0值点也向杆体深部转移。研究成果可为GFRP抗浮锚杆应用于工程实际提供依据。     

An analytical solution for stresses induced by a post-tensioned anchor in rocks containing two perpendicular joint sets

A new analytical approach for the analysis of stress around a post-tensioned anchor in rock with two perpendicular joint sets is presented. The solution considers nonlinear shear stresses developed along the anchor bond length as well as debonding at the tendon–grout interface. The bearing plate effects are also considered in the analyses. The following assumptions are made: (1) homogeneous and orthotropic elastic rock; (2) half-space rock mass with plane strain conditions; (3) trilinear bond-slip model for the behavior of the tendon–grout interface; (4) an elastic anchor. The employed methodology is to decompose the anchor problem into two problems of simpler loadings: stresses produced under a rigid bearing plate and stresses induced by interfacial shear stresses mobilized along the bond length. Based on the proposed solution, an illustrative example is given and the results show that a large compressive region is formed around the anchor free length. Tensile stress concentrations are also observed around the bond length and near the rock surface outside the bearing plate. A parametric study is also conducted to investigate the effects of joint properties on the induced stresses. The results show that as the number of joints intersecting the anchor axis increases, the magnitude of compressive stresses in the free zone decreases, while the size of compression zone around the anchor increases. To verify the results of the analytical approach, a comparison is made with numerical results obtained by using the finite element method. The analytical solutions compare very well with the results obtained by numerical method.     

自承载式预应力锚索现场试验研究

自承载式预应力锚索是一种不需要注浆即可进行张拉锁定的拉压复合型预应力锚索,适合于滑坡灾害应急抢险的快速锚固工程施工。本文结合现场试验数据,分析了自承载式预应力锚索的张拉力、锚索应力分布规律,并与普通拉力集中型锚索进行对比,阐明自承载式预应力锚索不仅有不注浆即可张拉发挥快速锚固作用的特点,同时自承载式预应力锚索锚固段的应力分布均匀,能充分发挥锚固段全长的锚固作用。     

不同岩性条件下预应力锚索锚固力损失规律研究

影响预应力锚索锚固效果的因素多而复杂,并且各因素之间又相互影响。锚固力损失与岩土体性质密切相关,通过理论分析、试验研究、数值模拟等方法,研究岩土体的蠕变变形和压缩变形对锚固力损失的影响机理,对坚硬岩体、软弱岩体、破碎岩体以及土体所造成的预应力锚索锚固力损失规律进行研究,研究表明:岩土体性质不同,引起的预应力锚索锚固力损失也不相同; 岩土体质量越好,在相同初始锚固力条件下其锚固力损失就越小。该研究成果可指导锚固工程的设计、施工和运行管理,有利于提高锚固工程的经济效益和社会效益。     

双锚固段新型锚索锚固性能研究及工程应用

为探究高路堤、深路堑边坡锚固系统耐久性以及锚固效果,研制了一种内外双锚固段新型锚索,从其结构设计、结构特点及锚固机理入手,分析其受力模式与计算方法,并通过室内足尺模型试验分析双锚固段新型锚索锚固效果,试验结果表明,（1）外锚固段有效的起到了双重锚固作用;（2）双锚固段锚索系统能有效避免因锚索失效导致的预应力损失;（3）整个锚固系统能实现反向自锁功能,与传统的锚索比,安全可靠性更高,能有效避免因锚索破坏突发灾难性的安全事故,长期性价比高;（4）工程实例验证石炭系岩关组砂岩、泥岩及深灰色灰岩呈互层地层外固段长度不少于8 m,才能有效地避免外锚头失效自由段预应力不损失。试验结果对正确分析双锚固段新型锚索加固作用机制和工程设计应用具有一定的参考价值。     

The eccentric loading of a rigid circular foundation embedded in an isotropic elastic medium

This paper examines the problem of the eccentric loading of a rigid circular disc-shaped foundation embedded in bonded contact with an istropic elastic medium of infinite extent. The solution of this problem is achieved by using a Hankel integral transform technique which reduces the problem to two sets of dual integral equations. These systems of dual integral equations represent the equations which govern the axisymmetric and asymmetric states of deformation induced by the loaded foundation. Explicit results are derived both for the displacement and rotation of the circular foundation and for the contact stress at the interface.     

预应力锚索孔内扩孔工艺的研究

预应力锚索技术是进行滑坡治理、边坡锚固等地质灾害治理中的常用技术,传统锚索内锚头自由地搁置在内锚固段孔内,在无预应力状态下进行内锚固段注浆;而自承载式预应力锚索在有预应力的状态下注浆,有利于充分发挥浆体材料及岩体的力学性能。对于中硬以下碎裂岩层,采取在锚固段进行扩孔,在扩孔段安装自承载式锚索承载体,承载体扩体后,利用孔壁的摩擦力和扩孔段端部的承载力进行初张拉锁定。因此,研究了一种适用于中硬以下岩层（抗压强度＜30 MPa）且适合使用空气潜孔锤钻进工艺的扩孔钻具和钻孔工艺,通过进行扩孔钻进室内试验,结果表明,该扩孔钻具和工艺能够实现在锚固段进行分段扩孔。     

基于突变理论的单根锚杆脱黏分析

针对工程中单根预应力锚杆的脱黏失效问题,基于突变理论提出一种研究的新思路。在建立简化力学模型的基础上,推导出锚固界面的非线性剪切滑移模型;视预应力锚杆为弹性体,根据弹性理论得出锚杆的总势能;引入突变理论,将锚杆势函数化简为尖点突变模型的标准形式,构建锚杆失效的临界判据,并进行脱黏分析。结果表明：所建非线性剪切滑移模型可以合理考虑锚固界面的软化特性;拉拔荷载作用下,锚杆杆体与周围注浆体的界面剪应力分布逐渐演化为单峰曲线,直至极限状态下整个锚固界面发生软化破坏;推导出的临界松动位移理论公式简单实用,可为研究单根预应力锚杆的脱黏失效提供参考。通过对工程算例进行验算分析,证明所提方法是合理可行的。     

预应力锚索锚固作用机理的数值模拟研究

在探讨预应力锚索现场足尺试验实施难点的基础上,利用FLAC3D对预应力锚固体的应力、位移特点,不同的锚索刚度、岩土体弹性模量以及预应力大小对锚固体剪应力的分布规律的影响、塑性破坏区的转移趋势进行了数值模拟,拟合了剪应力呈指数函数关系的分布公式。在剪应力峰值不断向锚固端扩展的推断下,提出了注浆体接触面处的锚索极限锚固力的计算公式,具有一定的理论和实践意义。     

扭转导波在锚固锚杆中传播的数值模拟

采用有限元数值模拟的方法研究了扭转导波在锚固锚杆中的传播性质。建立了自由锚杆和锚固锚杆的有限元模型,在锚杆顶端激发20～60 kHz扭转导波信号,计算得到导波在自由锚杆和锚杆锚固段的传播速度值与理论值吻合很好,证明了扭转导波数值模拟方法的有效性。数值模拟结果表明：随着激发波频率的增大,扭转导波在自由锚杆和锚杆锚固段中的衰减值均呈线性递增趋势,导波在锚杆锚固段上界面的反射回波逐渐减弱;扭转导波在锚杆锚固段的衰减值较大,无法在锚杆顶端采集到锚杆底端反射回波信号,所以扭转导波不适用于锚杆长度的检测;随着锚固介质弹性模量的增大,同一频率扭转导波在锚杆锚固段上界面的反射波逐渐增强。通过检测扭转导波在锚杆锚固段上界面的反射回波,可以确定锚固介质弹性模量的大小。     

基于岩体蠕变效应的锚杆应力分布及其变化规律研究

考虑岩体蠕变效应的锚杆应力分布及变化特征对研究工程锚固效应具有非常重要的意义,而目前关于这方面的研究并不多见。首先从锚固微元体受力特点的角度出发,研究微元体在围岩蠕变条件下的受力变化规律,得到如下结论：蠕变岩体下锚杆锚固力的变化趋势和岩体所受应力状态及其变形密切相关。当微元体受拉时,锚杆轴力随时间有不断增长的趋势;而当微元体受压时,锚杆轴力则随时间不断减小。针对锚杆在黏弹塑性围岩体中的受力分布,以解析方法推导了锚杆应力峰值所在位置与围岩体塑性区重合的重要结论,且从工程数值计算角度进一步验证了锚杆应力峰值的位置特点,并分析了地下工程中锚杆应力随围岩体蠕变而逐渐增大的变化特征。     

受断裂面性质控制的构造位移场的数学模拟

地质体有着十分复杂的结构和构造,因此,如何掌握地质体中各点的位移规律和应力分布规律,对工程地质研究,预测矿山边坡稳定性和地下工程稳定性,地震预测和预报以及地质构造形变的规律都是十分重要的。