Composite Element Model of the Fully Grouted Rock Bolt

Summary The three dimensional elasto-viscoplastic composite element method is formulated in this paper for rock masses reinforced by a fully-grouted bolt. If a bolt segment penetrates a finite element representing the rock mass, then a composite element is formed including five sub-elements corresponding to the rock material, the grout material, the bolt material, the rock-grout interface and the bolt-grout interface. The displacements in each sub-element are interpolated from the corresponding nodal displacements of the composite element. By the virtual work principle the governing equation for the solution of the nodal displacements can be formulated. The elasto-viscoplastic characteristics of the materials are considered in the formulation. The new model can be incorporated into the conventional finite element analysis grid, in which several composite elements have fully grouted bolts embedded. In this way the mesh generation of large scale bolted rock structures becomes convenient and feasible. The model has been implemented in a FEM program, and a comparative study between the numerical analysis and a pull out field test has been carried out, from which the validity and the robustness of the new model are justified.     

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。     

Enriched finite element procedures for analyzing decoupled bolts installed in rock mass

Numerical procedures are developed to analyze interaction between fully grouted bolts and rock mass using ‘enriched finite element method (EFEM)’. A solid element intersected by a rock bolt along any arbitrary direction is termed as ‘enriched’ element. The nodes of an enriched element have additional degrees of freedom for determining displacements, stresses developed in the bolt rod. The stiffness of the enriched element is formulated based on properties of rock mass, bolt rod and grout, orientation of the bolt and borehole diameter. Decoupling at grout–bolt interface and elasto‐plastic behavior of rock mass have also been incorporated into the EFEM procedures. The results of this method are compared with analytical pull‐out test results presented by Li and Stillborg (Int. J. Rock Mech. Min. Sci. 1999; 36 :1013–1029). In addition, a numerical example of a bolted tunnel is provided to demonstrate the efficacy of the proposed method for practical applications. Copyright © 2010 John Wiley & Sons, Ltd.     

压力分散型锚索作用效果的数值模拟分析

通过FLAC3D程序,用实体单元模拟了岩体和砂浆体,用结构单元来模拟锚索,在砂浆体和岩体间设置接触面,对锚索施加预应力时采用新的建模方法,即通过结构单元来模拟压力分散型锚索的承压板,代替在承压板的位置施加均布力的方法,建立预应力锚固数值仿真模型.通过模拟试验,分析了接触面单元、岩体单元以及砂浆体单元的应力云图等,更加清晰地显示了压力分散型预应力锚索作用下岩体沿锚索轴向的应力、砂浆体与孔壁之间的粘结应力分布等情况.     

Numerical estimation of REV and permeability tensor for fractured rock masses by composite element method

The Monte Carlo method is used to generate parent stochastic discrete fracture network, from which a series of fractured rock samples of different sizes and orientations are extracted. The fracture network combined with a regular grid forms composite element mesh of the fractured rock sample, in which each composite element is composed of sub‐elements incised by fracture segments. The composite element method (CEM) for the seepage is implemented to obtain the nodal hydraulic potential as well as the seepage flow rates through the fractured rock samples. The application of CEM enables a large quantity of stochastic tests for the fractured rock samples because the pre‐process is facilitated greatly. By changing the sizes and orientations of the samples, the analysis of the seepage characteristics is realized to evaluate the variation of the permeability components, the existence of the permeability tensor and the representative element volume. The feasibility and effectiveness are illustrated in a numerical example. Copyright © 2008 John Wiley & Sons, Ltd.     

Computing of the Anchor by the Method of Three-Dimension Point-Radiate Infinite Elements

On the basis of the one-dimension infinite element theory, the coordinate translation and shape function of 3D point-radiate 8-node and 4-node infinite elements are derived. They are coupled with 20-node and 8-node finite elements to compute the compression distortion of the prestressed an- chorage segment. The results indicate that when the prestressed force acts on the anchorage head and segment, the stresses and the displacements in the rock around the anchorage head and segment con- centrate on the zone center with the anchor axis, and they decrease with exponential forms. Therefore, the stresses and the displacement spindles are formed. The calculating results of the infinite element are close to the theoretical results. This indicates the method is right. This article introduces a new way to study the mechanism of prestressed anchors. The obtained results have an important role in the re- search of the anchor mechanism and engineering application.     

预应力锚索锚固力损失与岩土体蠕变耦合效应研究

因预应力锚索锚固力损失而导致锚固失效的工程事故屡屡发生,锚索锚固力损失与岩土体蠕变之间存在复杂的耦合效应关系,建立二者之间的耦合效应模型,确立二者之间的计算关系式,为预应力锚固工程的设计、施工、安全运行管理以及锚固力损失的控制与补偿技术提供理论基础和技术手段。通过理论分析和模型研究,在岩土体常用流变模型基础上建立了基于应变相等的耦合效应计算模型,并进行了模型验证。研究结论：（1）建立了与工程实际相符合的锚索锚固力变化和岩土体蠕变的耦合效应计算模型,正确反映了预应力锚索锚固力损失和岩土体蠕变之间的关系,推导出了其本构方程、松弛方程和蠕变方程,从理论上解决了锚固力变化与岩土体蠕变之间的计算关系。（2）通过耦合效应计算模型的蠕变方程,在材料参数已知的情况下,可以计算出边坡蠕变影响引起的锚索锚固力损失量,并结合实际工程中监测到的锚索应力数据进行对比分析,就能够准确地了解、评价锚索锚固力的异常变化情况,指导实际工程中的设计和施工,保证工程建设过程中的安全性。（3）通过耦合效应计算模型的松弛方程,可以对预应力锚索受力状态的监测数据进行分析整理,通过对锚索锚固力损失量的数据进行反分析,分析岩土体的蠕变参数,根据蠕变介质的材料特性,计算岩土体蠕变量,根据蠕变量判断预应力锚索锚固工程的安全性和可靠性,指导锚固工程的安全运行管理。     

预应力锚索受力特性与初始张拉吨位优化分析

基于预应力锚索作用和锚固界面力学传递机制,建立了锚固界面应力计算模型,并提出了一种可以考虑锚固界面剪切滑移的锚索应力计算方法;基于锚索预应力损失机制,对造成预应力损失的各种因素进行了分析,并给出了各种因素影响下的预应力损失计算方法;基于锚索应力求解的基本理论,同时考虑整个施工过程中的预应力损失量,将洞室群开挖过程中锚索应力的变化量作为锚索初始张拉的安全余量,提出了一种预应力锚索初始张拉吨位计算方法。并据此编制有限元计算程序,以某水电站地下厂房洞室群为工程实例,验证了该方法的合理性。     

西江特大桥岩锚锚碇的承载特性研究

针对西江特大桥广州岸岩锚锚碇系统的承载稳定性问题,采用工程地质勘察、室内及现场原位岩石力学特性试验、钻孔摄像及声波测试等手段,获取承载边坡的岩体地质力学特性,并建立边坡地质力学模型,同时进行现场拉锚试验验证预应力锚索设计的可靠性。采用三维数值模拟方法研究锚碇系统在施加预应力和承担外荷载两种情况下,边坡岩体的稳定性和锚碇群锚中不同位置的预应力锚索锚固力的分布特征。研究表明,在桥梁施工荷载的拉拔作用下,广州岸锚碇边坡整体稳定,坡表变形为毫米级;锚索锚固力呈不均匀分布形态,主要集中在锚固段前2 m范围内,最大值出现在锚固段端头;锚碇群锚的锚固力应力集中程度由大到小依次是角锚、边锚、中间锚。超载试验表明,整个锚碇系统的极限抗拔力不小于8倍设计荷载。锚索现场监测数值显示,锚碇承载期间锚索索力基本稳定,中间锚的索力小于角锚。研究方法及成果可供类似的桥梁及抗倾拔工程中的岩锚锚碇设计及安全评价借鉴。     

风化岩体中压力型锚索锚固段的剪应力分析

岩体在风化过程中,其物理力学性质会随着风化程度的不同有所差异。结合均质岩体中压力型锚索受力特点,以及内部对称荷载作用下横观各向同性弹性体内的剪应力分布特点,推导出了压力型锚索在横观各向同性弹性岩体内的剪应力分布方程。假定风化岩体为横观各向同性弹性体,其弹性模量及剪切模量均按指数函数变化,分析结果表明：①由于风化岩体的弹性模量随着深度的变化,锚索锚固段的剪应力也随着岩体的弹性模量的增加（减小）而增加（减小）;②在承压板附近,锚索锚固段的剪应力随锚索孔半径的增加而减小,由于风化岩体剪切模量的变化,因而导致剪应力的变化量很大;③在承压板附近,锚索锚固段接触面上的剪应力随着垂直于岩体横向等向面的剪切模量的改变而相应的改变。研究成果可为实际工程中压力型锚索设计提供参考。     

Fractal approach applied to calculate hour‐glass eigenvalue of elastic square 4‐node quad

It is shown that the property of the scale invariance of the eigenvalues and eigenmodes of a finite element can be used as a basis to calculate good approximations to the analytical magnitudes of eigenvalues. This requires the subdivision of the element into a mesh of small elements with the same shape as the large element, the enforcement of the modal boundary displacements of the large element to the mesh of small elements and finally the application of the conditions of both the nodal equilibrium and the equality of the nodal work at both scales. Due to the self‐similarity of the elements at all scales the authors propose to call this method the fractal approach. The method is applied to calculate the hour‐glass eigenvalue of a plane square 4‐node quad for isotropic linear elastic material. The resulting hour‐glass eigenvalue is shown to be a good approximation of the analytical magnitude as derived in a companion paper. Copyright © 2000 John Wiley & Sons, Ltd.     

一种新的节理裂隙岩体弹塑性模型

提出一种节理裂隙岩体弹塑性模型,将结构划分为块体单元和缝单元,其中缝单元可以是实际节理裂隙,也可以是人为缝单元。以块体单元形心的刚体位移和块体的平均应变作为基本未知量。该模型能充分考虑节理裂隙材料和块体材料的本构关系,计算量不大,是一种位移不协调单元。该模型特别适合节理裂隙岩体的数值分析。     

基于Mindlin解的压力型锚杆锚固段的受力分析

假设锚杆为与周围介质相同的材料,视锚杆作用的岩土体为弹性半空间位移体;基于Mindlin位移解,求出集中力作用下周围岩土体沿锚固体的轴向位移;根据压力型锚杆锚固段的受力状态,计算锚固体在轴向荷载作用下压缩变形,利用锚固体与周围岩土体变形协调假定,推导出锚固段轴向应力和剪应力分布的理论解。经过与已有现场试验实测数据对比分析,验证了理论解的可行性,并在此基础上讨论了相关岩土参数对锚固段轴向应力和剪应力的影响。锚杆现场试验和理论分析结果表明:压力型锚杆的锚固段所受轴向应力和剪应力与锚固力成正比;压力型锚杆的锚固段所受剪应力的分布形式受周围岩土体弹模、泊松比以及锚固体与周围岩土体界面的内摩擦角等因素的影响。其中周围岩土体的弹模影响最大。     

深埋巷道围岩稳定性分析与控制技术研究

针对岩石具有应变软化和剪胀的特点,推导了巷道围岩松动圈理论计算公式,理论分析了巷道埋深、围岩强度、应变软化程度以及支护阻力对围岩稳定性的影响,提出了锚喷、锚注和锚索“三锚”支护的新概念,并成功地应用于工程实践,取得了良好的技术和经济效益。     

LOAD DISTRIBUTION ALONG FULLY GROUTED BOLTS,WITH EMPHASIS ON CABLE BOLT REINFORCEMENT

Explanation for the widely reported observation that fully grouted reinforcement is more effective in hard rock that behaves as a discontinuum than in soft rock is presented. Analytical solutions are presented for the distribution of displacement and load along an untensioned fully grouted elastic bolt, of specified bond stiffness, which is activated during excavation by either a continuous or discontinuous distribution of rock displacement. The results indicate that significantly higher axial loads are developed for the discontinuous case. Since the mechanics of bond failure depend on the type of bolt and grout used, in the second part of the paper a finite difference formulation is introduced and combined with a non-linear model for the bond behaviour of a cement grouted seven-wire strand cable bolt. The results of a parametric study indicate that, because the bond is frictional and depends on confinement at the borehole wall, for the same profile of rock mass displacement lower loads are developed in soft rock. Furthermore, in soft rock, excavation induced stress changes can cause a dramatic reduction in bond strength, so that, even after significant rock mass displacement, the axial load developed is significantly less than the tensile strength of the cable. A combination of these effects can explain why failures of cable bolted ground involve debonding at the cable–grout interface in soft rock, and why instances of cable rupture are confined to hard, blocky rock masses.     

加锚节理岩体的复合单元法研究

加锚节理岩体有着复杂的细部结构和力学行为,常规的数值模型很难满足模拟这种力学行为的要求。进一步发展了笔者建立的加锚岩体的复合单元法,提出加锚节理岩体的复合单元法研究。在不考虑锚杆、节理等细部结构的情况下划分网格,分别定义了加锚岩体复合单元、不连续岩体复合单元和加锚节理岩体复合单元,并建立了其数值模型。同时,在复合单元中还定义了不同材料介质的子单元用来模拟加锚节理岩体内复杂的细部构造。对加锚节理复合单元法进行了理论推导和算例研究,通过与常规有限单元法计算结果的比较,表明了加锚节理岩体复合单元法的合理性,同时也突出体现了其前处理简便的优势。     

Analysis on Bearing Capacity of Tunnel-Type Anchorage of a Long-Span Suspension Bridge

INTRODUCTION Tunnel typeanchoragehasobviousadvantages inbearingcapacityversusinvestment(LiuandHu,1996).However,itisrarelyusedinapracticalpro jectbecauseofitsrequirementofgoodrockcondi tions.Siduhebridge(Fig.1),whichliesintheBa dongmountainsinthewestplatea…     

基于卸荷和抗震分析理论的大岗山坝肩边坡锚固优化研究

基于卸荷岩体的理论和方法,对大岗山水电站坝肩边坡进行研究。以大型通用有限元程序ADINA为计算平台,对比分析坝肩边坡卸荷后,不同地震加速度及不同锚固长度和锚固吨位在卸荷条件下关键点的位移和应力以及塑性区的变化规律,认为边坡开挖变形由两部分组成,一部分为卸荷回弹,另一部分是由于大吨位锚索施加后产生的朝向坡内的压缩变形。研究表明,由于锚索穿过V岩体底部界线,在可能的滑坡剪出口形成强大的阻滑键,增加锚索长度或吨位均可有效地减小坝肩塑性区,地震加速度为0.1g和0.15g时,在各加固吨位下均可能形成塑性区的贯通;在不同的地震加速度下,受不同锚固长度和锚固力影响,不同关键点处水平向位移呈现线性变化和非线性变化,非线性关系中的拐点应重点关注;若要减少岩体塑性区,相同比例下增大锚固长度效果更好。为了有效减少在高地震烈度时边坡塑性区的发育,建议采用增加120%的锚固长度。     

Cyclic macro‐element for soil–structure interaction: material and geometrical non‐linearities

This paper presents a non‐linear soil–structure interaction (SSI) macro‐element for shallow foundation on cohesive soil. The element describes the behaviour in the near field of the foundation under cyclic loading, reproducing the material non‐linearities of the soil under the foundation (yielding) as well as the geometrical non‐linearities (uplift) at the soil–structure interface. The overall behaviour in the soil and at the interface is reduced to its action on the foundation. The macro‐element consists of a non‐linear joint element, expressed in generalised variables, i.e. in forces applied to the foundation and in the corresponding displacements. Failure is described by the interaction diagram of the ultimate bearing capacity of the foundation under combined loads. Mechanisms of yielding and uplift are modelled through a global, coupled plasticity–uplift model. The cyclic model is dedicated to modelling the dynamic response of structures subjected to seismic action. Thus, it is especially suited to combined loading developed during this kind of motion. Comparisons of cyclic results obtained from the macro‐element and from a FE modelization are shown in order to demonstrate the relevance of the proposed model and its predictive ability. Copyright © 2001 John Wiley & Sons, Ltd.     

拉力型锚索锚固段周边岩体的应力分布

采用弹性空间体内部一点受集中力的Kelvin解,推导了拉力型锚索锚固段的附加应力和位移分布的理论公式,并依此推出了锚固段周边的剪应力分布公式。在此基础上,讨论了锚固体、岩土体的力学参数对附加应力、位移和剪应力的影响。结果表明,锚固段周边岩体中的正应力场和位移为锥形,在锚固段的起始点上部形成了压应力场,下部为拉应力场,并以力的作用点为中心快速衰减。锚固段周边剪应力形成了一个锥面,并随远离作用点快速衰减。