外文翻译-锚杆的分析模型

Analytical models for rock bolts.C.L*,StillborgAbstractThree analytical models have been developed for rock bolts: one for bolts subjected to concentrated pull load in pullout tests, one for bolts installed in uniformly deformed rock masses, and one for bolts subjected to the opening of individual rock joints. The development of the models has been based on the description of the mechanical coupling at the interface between the bolt and the grout medium for grouted bolts, or between the bolt and the rock for frictionally coupled bolts. For rock bolts in the pullout tests, the shear stress of the interfaces exponentially with increasing distance from the point of loading when the deformation is compatible across the interface. Decoupling may start first at the loading point when the applied load is large enough and then propagate towards the far end of the bolt with a further increase in the applied load. The magnitude of the shear stress on the decoupled bolt section depends on the coupling mechanism at the interface. For fully grouted bolts, the shear stress on the decoupled section is lower than the peak shear strength of the interface while for fully frictionally coupled bolts if is approximately the same as the peak shear strength. For rock bolts installed in uniformly deformed rock, the loading process of the bolts due to rock deformation has been taken into account in developing the model. Model simulations confirm the previous findings that a bolt in situ has a pick-up length, an anchor length and neutral point. It is also revealed that the face plate plays a significant role in enhancing the reinforcement effect. In jointed rock masses, several axial stress peaks may occur along the bolt because of the opening of rock joints intersecting the bolt.1. IntroductionRock bolts have been widely used for rock reinforcement in civil and mining engineering for a long time. Bolts reinforce rock masses through restraining the deformation within the rock masses. In order to improve bolting design, it is necessary: to have a good understanding of the behaviour of rock bolts in deformed rock masses. This can be acquired through field monitoring, laboratory tests, numerical modeling and analytical studies.Since the 1970s, numerous researchers have carried out field monitoring work on rock bolts installed in various rock formations. Freeman performed pioneering work in studying the performance of fully grouted rock bolts in the Kielder experimental runnel. He monitored both the loading process of the bolts and the distribution of his monitoring data, he proposed the concepts of “neutral point” “pick-up length” and “anchor length”. At the neutral point, the shear stress at the interface between the bolt and the grout medium is zero, while the tensile axial load of the bolt has a peak value. The pick-up length refers to the section of the bolt from the near end of the bolt (on the tunnel wall) to the neutral point. The shear stresses on this section of the bolt pick up the load from the rock and drag the bolt towards the tunnel. The anchor length refers to the section of the bolt from the neutral point to the far end of the bolt (its seating deep in the rock). The shear stresses on this section of the bolt anchor the bolt to the rock. These concepts clearly outline the behaviour of fully grouted rock bolts in a deformed rock formation. Bjonfot and Stephanssons work demonstrated that in jointed rock masses there may exist not only one but several neutral points along the bolt because of the opening displacement of individual joints.Pullout tests are usually used to examine the anchoring capacity of rock bolts. A great number of pullout tests have been conducted so far in various types of rocks. Farmer carried out fundamental work in studying the behaviour of bolts under tensile loading. His solution predicts that the axial stress of the bolt (also the shear stress at the bolt interface) will decrease exponentially from the point of loading to the far end of the bolt before decoupling occurs. Fig.1(a) illustrates the results of a typical pullout test. Curve a represents the distribution of the axial stress along the bolt under a relatively low applied load, at which the deformation is compatible on both sides of the bolt interface. Curve b represents the axial stress along the bolt at a relatively high applied load, at which decoupling has occurred at part of the bolt interface. Fig.1(b) shows the axial stress along a rock bolt installed in an underground mine drift. It is seen from this figure that the distribution of the axial stress along the section close to the borehole collar is completely different from that in pullout tests. However, along the section to the far end of the bolt, the stress varies similarly to that in pullout tests. The reason Fig.1 Distribution if the axial stress (a) along a grouted steel bar during pullout test, after Hawkes and Evan, and (b) along a grouted rock bolt in situ after sunfor these results is that bolts in situ have a pick-up length and an anchor length, while bolts in pullout tests only have an anchor length.It is thought that the relative movement between the rock and the bolt is zero at the neutral point. In the solution by Tao and Chen, the position of the neutral point depends only on the radius of the tunnel and the length of the bolt. That solution was implemented in the analytical models created by Indraratna and Kaiser and Hyett et.al. It seems that Tao and Chens solution is valid only when the deformation is compatible across the bolt interface. When decoupling occurs, the position of the neutral point is obviously also related to the shear strength of the interface. Field monitoring and pullout tests have indicated two facts concerning the loading of a rock bolt in situ: (1) rock deformation applied a load on the pick-up section of the bolt; (2) the load on the pick-up section drags the anchor section of the bolt towards the underground opening. These two facts must be taken into account in developing analytical models for rock bolts.The aim of this paper is to develop analytical models for fully coupled rock bolts. A model for rock bolts in pullout tests is introduced first, together with a description of the theoretical background, the development of the model and an illustrative example. Two models for rock bolts in situ are then presented, one in rock masses. The details of the development of the models are summarized in the appendices.2.Coupling between the bolt and the rockWindsor proposed the concept that a reinforcement system comprises four principal components: the rock, the reinforcing element, the internal fixture and the external fixture. For reinforcement with a bolt, the reinforcing element refers to the bolt and the external fixture refers to the face plate and nut. The internal fixture is either a medium, such as cement mortar or resin for grouted bolts, or a mechanical action like “friction” at the bolt interface for frictionally coupled bolts. The internal fixture provides a coupling condition at the interface. With reference to the component of internal fixture, Windsor classified the current reinforcement devices into three groups: “continuously mechanically coupled (CMC)”, “continuously frictionally coupled (CFC)”, “discretely mechanically or frictionally coupled (DMFC)” systems. According to this classification system, cement and resin-grouted bolts belong to the CMC system, while Split set and Swellex bolts belong to the CFC system.When fully grouted bolts are subjected to a pull load, failure may occur at the bolt grout interface, in the grout medium or at the grout rock interface depending on which one is the weakest. For fully frictionally coupled bolts, however, there is only one possibility if failure decoupling at the bolt rock interface. In this study we concentrate on the failure at the interface between the bolt and the coupling medium (either the grout medium or the rock).In general, the shear strength of an interface comprises three components: adhesion, mechanical interlock and friction. They are lost in sequence as the compatibility of deformation is lost across the interface. The result is a decoupling front that attenuates at an increasing distance from the point of the applied load. The decoupling front first mobilizes the adhesive component of strength, then the mechanical interlock component and finally the frictional component. The shear strength of the interface decreases during this process. The shear strength after the loss of some of the strength components is called the residual shear strength in this paper. For grouted rock bolts like rebar, all the three components of strength exist at the bolt interface. However, for the fully frictionally coupled bolt, the “Split set” bolt, only a friction component exists at the bolt interface. For Swelles bolts, mechanical interlock and friction comprise the strength of the interface.3. The theoretical background of rock bolts in pullout tests4.Concluding remarksAn analytical model has been established for rock bolts subjected to a pull load in pullout tests. Decoupling starts at the loading point and propagates along the bolt with an increasing applied load. The shear stress at the decoupled interface is lower than the ultimate shear stress strength of the interface and even drops to zero for fully grouted bolts, while it is approximately at the same magnitude as the ultimate shear stress strength for fully frictionally coupled interface decreases exponentially with increasing distance from the decoupling bolt.Two analytical models have been developed for rock bolts in situ, one for uniform rock deformation and another for discrete joint opening. For rock bolts in situ, the models confirm the previous findings: (i) in uniformly deformed rock masses, the bolt has a pick-up length, an anchor length and a neutral point;(ii) the face plate enhances the reinforcement effect through inducing a direct tensile load in the bolt and reducing the shear stress carried on the bolt surface;(iii) in jointed rock masses, the opening displacement of rock joint will induce axial stress peaks in the bolt.中文译文锚杆的分析模型C.Li*,B.Stillborg摘要：有三种锚杆的分析模型发展了起来：一种是在拉断试验中，易受到集中拉力载荷影响作用的锚杆，一种是安装在均匀变形岩体中的锚杆，另一种是易受到单个岩石节理影响作用的锚杆。这种分析模型是在注浆锚杆的锚杆与注浆之间或者是磨擦式锚杆的锚杆与岩石之间接触面上的机械耦合作用描述的基础上建立起来的。对于拉断试验中的锚杆，当接触面上的变形较小时，锚杆表面上的剪切应力随着距加载点距离的增加而成指数减小。如果施加的载荷足够大时，耦合首先发生加载点处，然后随着载荷的增加而逐渐向锚杆的深处传播。锚杆耦合部分的剪切应力的大小取决于接触面上的机械耦合作用。对于全长锚固锚杆来说，耦合阶段的剪切应力比接触面上的剪切强度的峰值要小，然而对于磨擦式锚杆，剪切应力大致和剪切强度的峰值相同。安装在均匀变形岩体中的锚杆，在建立锚杆分析模型时，锚杆的加载过程要考虑到岩体的变形情况。模型的模拟实验证实了先前的研究结果，在软岩中的锚杆有传感长度，锚固段长度，和一个中性点。这个实验也说明了锚杆托盘在围岩加固的效果中起着一个非常重要的作用。在有节理的岩体中，由于岩石节理的自由变形作用，锚杆轴向可能会有几个应力峰值发生在锚杆的延伸方向。1、 前言在很长一段时间来，锚杆广泛的应用于民用建筑和矿业工程的岩石加固。锚杆通过在岩体中抑制岩体的变形来加固围岩。为了提高锚杆支护的结构，必须对在变形岩体中的锚杆的作用变化过程有一个良好的认识。这些认识可以通过现场监测、实验室的试验、数字模拟和研究分析来获得。自从20世纪70年代来，在不同的岩石地层中进行了大量的锚杆现场监测的研究工作。一个自由人士在Kielder的试验巷道中，进行了大量关于注浆锚杆特性的研究工作。他监测了锚杆的加载过程和应力沿锚杆的分布情况。在他所监测数据的基础上，他提出了关于“传感长度”、“锚固长度”、“中性点”的概念。在中性点上，锚杆和注浆之间的接触面上的剪切应力为零，然而在该点其轴向载荷的张力是一个峰值。传感长度指的是从接近锚杆末端的地方（在巷道壁上）到中性点的一段距离。在锚杆这部分是其剪切应力来自于岩石的载荷，并把锚杆向巷道方向进行拖拉。锚固长度指的是从锚杆的中性点到锚杆深处（固定在岩石深度）的一部分锚杆。在这部分上的剪切应力将锚杆锚固在岩石上。以上这些概念清楚的指出了安装在已变形岩层中的锚杆的作用变化过程。Bjornfot和Stephansson的研究工作证明，在已有节理的岩体中，由于单个节理的由自变形，在沿锚杆的方向上可能不仅存在一个中性点而且有可能存在多个中性点。锚杆的拉断试验通常用来监测锚杆的锚固能力，在不同种类的岩石中已经进行了大量的这种拉断试验工作测试。一著名人士进行了大量的基础工作来研究在拉力负荷的张力作用下锚杆的作用变化过程。他的解析方法指出：在锚杆发生耦合以前，锚杆的轴向应力（也可能是锚杆接触表面上的剪切应力）从加载点到锚杆的深处呈指数减小的趋势。图1（a）说明了这种典型拉断试验的结果，曲线a表示的是在相对较低的载荷情况下，沿锚杆方向轴向应力的分布情况，在这个图中可以看出，在锚杆锚固界面的两则，其变形是相等的。曲线b表示的是在相对较高的载荷下，沿锚杆方向轴向应力的分布，在此图上，锚杆接触面上已经发生了耦合作用。图1（b）表示的是安装在地下煤矿的主水平巷中的锚杆上的轴向应力分布情况。我们可以从这个图上看出，在接近钻孔口附近的轴向应力分布情况与在拉断试验中的分布情况完全不同。然而，锚杆深处阶段部分的的应力变化与拉断试验中的结果相似。出现这种情况的原因是，在软岩中的锚杆有传感长度和锚固长度，然而在拉断试验中的锚杆仅有锚固长度。图1在拉断试验中，（a）轴向应力沿在Hawkes和Evans之后的全锚固锚杆和(b)Sun之后的加固锚杆的分布我们认为在锚杆中性点上，岩石和锚杆之间的相对移动为零。在陶和陈的分析方法中，中性点的位置仅仅取决于巷道的半径和锚杆的长度。这种解决方法完善了由Kaiser和Hyett发明的分析模型。这看起来好在像陶和陈的解决方法只有当通过锚杆的界面点时，其变形量相互兼容时，才是有效的；当发生耦合后，中性点的位置与接触面的剪切应力强度有明显的关系。现场监测和拉断实验都表明在软岩中锚