喷锚支护节理岩体的复合单元法研究
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摘要
在岩土工程中,大量的锚杆和喷射混凝上被用于加固节理岩体,因此,展开对喷锚支护节理岩体的研究有着重要的实际意义。一般来说,研究喷锚支护节理岩体有两种模型：离散模型和等效模型。二者各有优缺点,离散模型能够较为详尽的来描述喷锚支护节理岩体中各个部件的力学行为,但是其前处理工作比较复杂,需要花费大量的时间在模型的离散上面；而等效模型的前处理工作相对而言比较简单,但其缺点是不能得到喷锚支护节理岩体中每个组成部分的详细力学行为。研究人员一般是有选择地使用这两种模型,对于大量的微裂隙、节理、喷层和系统锚杆,采用等效模型,而对于较大断层和重点关注部位的喷层和锚杆则采用离散模型。但是,随着岩土工程规模的逐步扩大,工程人员会遇到越来越复杂的结构,大量的断层和喷层、锚杆纵横交错,使使用详细划分网格的方法来进行离散模拟几乎成了不可能完成的任务。同时,工程方案的频繁改动也会引起网格的频繁变动,这样既费时又费力的工作也是工程研究人员所不愿意面对的。复合单元法便结合了离散模型和等效模型的优点,它的本质是用复杂的计算来代替复杂的前处理工作,从而来降低前处理工作的难度,进而提高工作效率,同时,其又能够细致地模拟结构的内部构造,因此很适用于对复杂结构的研究。
本文就是基于复合单元法开展对喷锚支护节理岩体的研究。
第一,本文总结了岩土锚固和喷锚支护的发展历程并介绍了喷锚支护的工作特性及作用原理。其主要工作特性有及时性、粘结性、深入性、柔性、易应变性和密封性。这些特性构成最大限度利用围岩强度和自承能力的基本要素。在锚固技术的长期应用中,人们先后提出了几种已普遍接受的理论：悬吊理论、组合梁理论、压缩拱理论。在前人研究的基础上,目前又提出了几种新的理论,如：最大水平应力理论、围岩强度强化理论、围岩松动圈理论、全长锚固中性点理论等。
第二,本文总结了目前节理岩体与锚固的研究方法和现状。目前研究岩土工程节理岩体锚固的方法主要有：物理试验法、工程类比法和数值分析法。锚固理论按照体系可分为两大类：不连续介质力学离散方法和连续介质力学等效方法。前者包括极限平衡理论(LET)、关键块理论(BT)、离散单元法(DEM)、不连续变形分析法(DDA)、块体单元法、界面元法等,后者包括有限单元法(FEM)、边界单元法(BEM)、快速拉格朗日分析法(FLAC)等。近年来还出现了具有综合这两类方法的特性的数值流形方法(NMM),无网格方法(MFM)和复合单元法(CEM)等。本文分别介绍了以上几种数值方法在锚固理论中的应用情况并重点介绍了复合单元法,总结了其的发展历程,介绍了复合单元法的基本原理。
第三,基于复合单元法的基本原理,本文建立了喷锚支护节理岩体的弹性复合单元模型。在喷锚支护节理岩体的弹性复合单元模型中,先划分均质网格,将含有喷层、砂浆、锚杆和节理的岩体单元定义为复合单元,引入8个子单元分别用于描述岩体、砂浆、锚杆、喷层和各种接触面,定义多套位移自由度分别插值岩体、砂浆、锚杆和喷层子单元内的位移,而接触面子单元没有单独自由度,它们的位移是由相邻两种介质子单元的结点位移差插值而得的。对各个结构采用弹性本构关系模型,并根据虚功原理得到控制方程,从而求解。本模型能和常规有限单元法无缝结合,联合计算,常规有限单元可以认为是复合单元的一种退化。算例研究中,对一由砂浆锚杆和喷层加固的节理岩体进行试验,分别采用复合单元法和离散模型有限单元法进行弹性计算。计算结果的比较证明了喷锚支护节理岩体弹性复合单元模型的可靠性,同时也说明了复合单元法在喷锚支护节理岩体研究中的前处理简单的优势。
第四,在喷锚支护节理岩体的弹性复合单元模型的基础上,基于弹粘塑性势理论,建立喷锚支护节理岩体的弹粘塑性复合单元模型,对各个构件采用弹粘塑性本构关系,用来模拟其应力应变随时问变化的过程,能较好地解决实际工程中岩体的应力应变是随时间变化的,简单的弹性模型并不能反映时间对应力应变的影响,也就无法模拟喷锚节理岩体真实的应力应变过程的难题。算例研究中,对与弹性计算相同的模型,分别采川复合单元法和离散模型有限单元法进行弹粘塑性计算。计算结果的比较证明了喷锚支护节理岩体弹粘塑性复合单元模型的可靠性。
第五,本文开展了喷锚支护节理岩体的P型自适应复合单元法研究。复合单元法简化了前处理,在研究复杂结构时拥有强大的优势,但是,常规复合单元法采用的是和常规有限单元法一样的线性形函数,在网格密度较小的情况下难以描述复杂结构的非线性性质,可以通过加密网格解决这一问题,但是有难度,而且也与复合单元法的简化前处理的思想不符。喷锚支护节理岩体结构复杂,在粗糙网格下,其内部构件的非线性性质是常规的线性形函数无法精确模拟的。于是引入P型自适应的思想,定义喷锚节理岩体的P型复合单元,通过不断升阶的阶谱基函数,从物理意义上拟合喷锚支护节理岩体内各个构件的复杂位移模式,从而达到模拟非线性力学行为的目的。通过公式的推导和计算程序的编制,这一研究得以实现。算例研究中,稀疏网格的P型复合单元法计算结果,随着升阶不断趋向一致,通过与常规有限单元法和常规复合单元法计算结果比较,证实该研究的成效。
最后,本文将研究成果应用于瀑布沟水电站地下厂房工程的研究。分别建立了三维复合单元法计算网格和三维有限单元法计算网格,进行比较计算,其中复合单元法计算网格包括12311个单元和12429个结点,为均质网格；而有限单元法计算网格包含70128单元和93516个结点,采用了离散模型。在研究中,模拟了地下洞室的开挖加固到运行的全过程,开挖分为9步进行,喷锚支护伴滞后开挖一步进行。通过丰富的计算结果的比较,进一步证实了复合单元法在喷锚支护节理岩体研究的成效,表现出强大的前处理的优势和离散模拟的准确。
复合单元法在岩土工程有着广阔的应用前景,目前在喷锚支护节理岩体的应力-应变分析中已经取得了一定成果,但是,复合单元法的在这一方面研究仍有待深入,同时,其多元化的应用研究还有待继续开展,可以在开裂问题、局部化问题、热传导问题、耦合问题等方面继续展开研究。
A lot of bolts and shotcrete lining are applied to reinforce jointed rock masses in geotechnical engineering. The analysis of jointed rock masses reinforced by bolts and shotcrete lining is very important to the engineering. Generally speaking, the equivalent model and the explicit model have been proposed to study jointed rock masses reinforced by bolts and shotcrete lining. They have their own merit and shortcoming:using the former, the behaviors of all of the components can be well simulated, however, much preprocess work is needed; the latter has the little limit in preprocess, but it cannot have very detailed simulation of the components. So, equivalent model are applied to simulate great quantities of joints or fissures, shotcrete lining and system bolts. As to the larger faults and important shotcrete lining and bolts, explicit simulation is usually proposed. As the scale of geotechnical engineering is greater and greater, more and more complicated geology condition including many faults, shotcrete lining and bolts is to be treated. It is very difficult to simulate all important faults, bolts, and shotcrete lining explicitly. Even worse, when the configuration of a structure is modified, it will cost much time and manpower to remesh. Combining the merits of the two models, the composite element method (CEM) is proposed to explicitly simulate jointed rock masses reinforced by bolts and shotcrete lining, which transfers the difficulties in preprocess into computation and heightens the efficiency.
Comprehensive researches of jointed rock masses reinforced by bolts and shotcrete lining are conducted in this dissertation on the basis of CEM.
Firstly, a review of ground anchorage and bolts and shotcrete lining support is made, and the working characteristic and action principle of bolts and shotcrete lining support is present in this dissertation. For bolts and shotcrete lining support, it has the characteristic of betimes, cohesiveness, deeply, flexible, adaptability to change and sealing which composite the basic elements of using the strength and self-support of surrounding rocks completely. During the long-term application of anchorage technology, several theories such as suspension theory, combined beam theory and combined arch theory have been proposed and generally accepted. Based on them, new theories including maximum horizontal stress, surrounding rock strength intensify theory, surrounding rock loosening circle and the full-length anchoring neutral point theory etc. have been present recently.
Secondly, method and status of recent research about jointed rock masses and anchorage has been summarized. Physics experiment method, engineering analogy and numerical analysis are the mainly used methods on jointed rock masses anchorage. The theory system about anchorage is divided into discontinuous medium mechanics discrete method and continuous medium mechanics equivalent method. The former includes limited equilibrium theory (LET), key block theory(BT), discrete element method (DEM), discontinuous deformation analysis(DDA), block element method and interface element method. Finite element method (FEM), boundary element method and fast Lagrange analysis of code (FLAC) are attributed to the latter. Recently, methods combined of their characteristics are proposed taking the numerical manifold method (NMM), mesh free method (MFM) and composite element method (CEM) for example. All of their applications in anchorage theory are presented in the dissertation while emphasis on the CEM where its development course and basic theory are introduced.
Thirdly, on the basis of CEM, the elastic composite element model for jointed rock masses supported by bolt and shotcrete lining is present in the dissertation. In this model, mesh can be generated without considering joint, grout, bolt and shotcrete lining firstly, and the elements containing them are defined as composite elements.8sub-elements are established to cover rock, grout, bolt, shotcrete lining and all interfaces. The displacements of the rock, grout, bolt and shotcrete lining can separately be interpolated from the sub-elements'nodal displacements. The interfaces have no independent nodes, and their displacements can be interpolated from the difference between the nodal displacements of rock, grout, bolt and shotcrete lining. According to the elastic constitutive relation and the virtual work principle, the equilibrium equation can be established. With the solved nodal displacements, the detailed behaviors of sub-elements can be described. This model can be incorporated into the conventional finite element analysis without any difficult. The conventional finite element can be treated as a degradation of the composite element. In the numerical example, elastic calculation for a jointed rock mass supported by grout-bolt and shotcrete lining is carried out by CEM and distinct element FEM. The comparison of the calculation results shows the validity of this model and the advantage of CEM in the pre-process of jointed rock mass supported by bolt and shotcrete.
Fourthly, on the basis of elastic composite element model for jointed rock masses supported by bolt and shotcrete lining, an elastic-viscoplastic composite element is established. For every component, we use the elastic-viscoplastic constitutive relation to simulate the course of stress and strain changing with the time. In practical engineering, for the simple elastic model, it cannot show that the stress and strain of rock is changing with the time, so it cannot simulate the actual process of stress-strain of jointed rock mass. The elastic-viscoplastic model can solve the problem. In the numerical example, with the same model as elastic calculation, elastic-viscoplastic calculation is carried out by CEM and distinct element FEM. The comparison of the calculation results shows the validity of this elastic-viscoplastic model.
Fifthly, the P-version adaptive CEM for jointed rock masses supported by bolt and shotcrete lining is proposed in this dissertation. With the simple preprocess, CEM has many advantages to simulate the complex structures. Using linear shape function as conventional FEM, CEM will have some difficulties in describing detailed nonlinear mechanical characteristics of complex structures under a low density of mesh. Generally speaking, increasing the density of the mesh is usually proposed to solve the problem. But it will increase the difficulties of preprocess. Furthermore, this approach disobeys to the CEM principle of simple preprocesses. To more complex mechanical characteristics of jointed rock masses supported by bolt and shotcrete lining, the linear shape function of conventional CEM has more difficulties to make a detailed simulation under a coarse mesh. Thereupon, P-version composite elements are defined to describe the jointed rock masses supported by bolt and shotcrete lining in this study. With the hierarchical basic function upgrading, the displacement mode of jointed rock masses supported by bolt and shotcrete lining and mechanical characteristics of all of the sub-structures can be well simulated by P-version CEM in physical hypostasis. Equation formulated, the method proposed can be realized in the program. The actual effect is shown through a comparison of calculation results among P-version CEM, conventional CEM and conventional FEM for an example.
Finally, the study present above is applied onto the underground engineering of Pubugou powerstation. With the3dimensions calculation meshes of CEM and FEM, the engineering is analyzed separately by CEM and FEM. The mesh of CEM which contains12311elements and12429nodes is generated without considering the grouts, bolts, shotcrete lining, joints etc. With a mesh containing73788elements and98188nodes, the distinct model is applied into FEM calculation. In the study, excavation is divided into9steps and reinforcement is applied after every excavation step. The comparison of the calculation results shows the advantage of CEM in preprocess and the preciseness of CEM in distinct simulation.
With a good foreground in the engineering, the study of CEM for jointed rock masses supported by bolts and shotcrete lining has been achieved, but many problems need to be solved to improve them, yet. Crack analysis, dynamic analysis, thermal analysis, localization analysis, coupling analysis, etc, are all the fields where CEM can show its advantages.
本文就是基于复合单元法开展对喷锚支护节理岩体的研究。
第一,本文总结了岩土锚固和喷锚支护的发展历程并介绍了喷锚支护的工作特性及作用原理。其主要工作特性有及时性、粘结性、深入性、柔性、易应变性和密封性。这些特性构成最大限度利用围岩强度和自承能力的基本要素。在锚固技术的长期应用中,人们先后提出了几种已普遍接受的理论：悬吊理论、组合梁理论、压缩拱理论。在前人研究的基础上,目前又提出了几种新的理论,如：最大水平应力理论、围岩强度强化理论、围岩松动圈理论、全长锚固中性点理论等。
第二,本文总结了目前节理岩体与锚固的研究方法和现状。目前研究岩土工程节理岩体锚固的方法主要有：物理试验法、工程类比法和数值分析法。锚固理论按照体系可分为两大类：不连续介质力学离散方法和连续介质力学等效方法。前者包括极限平衡理论(LET)、关键块理论(BT)、离散单元法(DEM)、不连续变形分析法(DDA)、块体单元法、界面元法等,后者包括有限单元法(FEM)、边界单元法(BEM)、快速拉格朗日分析法(FLAC)等。近年来还出现了具有综合这两类方法的特性的数值流形方法(NMM),无网格方法(MFM)和复合单元法(CEM)等。本文分别介绍了以上几种数值方法在锚固理论中的应用情况并重点介绍了复合单元法,总结了其的发展历程,介绍了复合单元法的基本原理。
第三,基于复合单元法的基本原理,本文建立了喷锚支护节理岩体的弹性复合单元模型。在喷锚支护节理岩体的弹性复合单元模型中,先划分均质网格,将含有喷层、砂浆、锚杆和节理的岩体单元定义为复合单元,引入8个子单元分别用于描述岩体、砂浆、锚杆、喷层和各种接触面,定义多套位移自由度分别插值岩体、砂浆、锚杆和喷层子单元内的位移,而接触面子单元没有单独自由度,它们的位移是由相邻两种介质子单元的结点位移差插值而得的。对各个结构采用弹性本构关系模型,并根据虚功原理得到控制方程,从而求解。本模型能和常规有限单元法无缝结合,联合计算,常规有限单元可以认为是复合单元的一种退化。算例研究中,对一由砂浆锚杆和喷层加固的节理岩体进行试验,分别采用复合单元法和离散模型有限单元法进行弹性计算。计算结果的比较证明了喷锚支护节理岩体弹性复合单元模型的可靠性,同时也说明了复合单元法在喷锚支护节理岩体研究中的前处理简单的优势。
第四,在喷锚支护节理岩体的弹性复合单元模型的基础上,基于弹粘塑性势理论,建立喷锚支护节理岩体的弹粘塑性复合单元模型,对各个构件采用弹粘塑性本构关系,用来模拟其应力应变随时问变化的过程,能较好地解决实际工程中岩体的应力应变是随时间变化的,简单的弹性模型并不能反映时间对应力应变的影响,也就无法模拟喷锚节理岩体真实的应力应变过程的难题。算例研究中,对与弹性计算相同的模型,分别采川复合单元法和离散模型有限单元法进行弹粘塑性计算。计算结果的比较证明了喷锚支护节理岩体弹粘塑性复合单元模型的可靠性。
第五,本文开展了喷锚支护节理岩体的P型自适应复合单元法研究。复合单元法简化了前处理,在研究复杂结构时拥有强大的优势,但是,常规复合单元法采用的是和常规有限单元法一样的线性形函数,在网格密度较小的情况下难以描述复杂结构的非线性性质,可以通过加密网格解决这一问题,但是有难度,而且也与复合单元法的简化前处理的思想不符。喷锚支护节理岩体结构复杂,在粗糙网格下,其内部构件的非线性性质是常规的线性形函数无法精确模拟的。于是引入P型自适应的思想,定义喷锚节理岩体的P型复合单元,通过不断升阶的阶谱基函数,从物理意义上拟合喷锚支护节理岩体内各个构件的复杂位移模式,从而达到模拟非线性力学行为的目的。通过公式的推导和计算程序的编制,这一研究得以实现。算例研究中,稀疏网格的P型复合单元法计算结果,随着升阶不断趋向一致,通过与常规有限单元法和常规复合单元法计算结果比较,证实该研究的成效。
最后,本文将研究成果应用于瀑布沟水电站地下厂房工程的研究。分别建立了三维复合单元法计算网格和三维有限单元法计算网格,进行比较计算,其中复合单元法计算网格包括12311个单元和12429个结点,为均质网格；而有限单元法计算网格包含70128单元和93516个结点,采用了离散模型。在研究中,模拟了地下洞室的开挖加固到运行的全过程,开挖分为9步进行,喷锚支护伴滞后开挖一步进行。通过丰富的计算结果的比较,进一步证实了复合单元法在喷锚支护节理岩体研究的成效,表现出强大的前处理的优势和离散模拟的准确。
复合单元法在岩土工程有着广阔的应用前景,目前在喷锚支护节理岩体的应力-应变分析中已经取得了一定成果,但是,复合单元法的在这一方面研究仍有待深入,同时,其多元化的应用研究还有待继续开展,可以在开裂问题、局部化问题、热传导问题、耦合问题等方面继续展开研究。
A lot of bolts and shotcrete lining are applied to reinforce jointed rock masses in geotechnical engineering. The analysis of jointed rock masses reinforced by bolts and shotcrete lining is very important to the engineering. Generally speaking, the equivalent model and the explicit model have been proposed to study jointed rock masses reinforced by bolts and shotcrete lining. They have their own merit and shortcoming:using the former, the behaviors of all of the components can be well simulated, however, much preprocess work is needed; the latter has the little limit in preprocess, but it cannot have very detailed simulation of the components. So, equivalent model are applied to simulate great quantities of joints or fissures, shotcrete lining and system bolts. As to the larger faults and important shotcrete lining and bolts, explicit simulation is usually proposed. As the scale of geotechnical engineering is greater and greater, more and more complicated geology condition including many faults, shotcrete lining and bolts is to be treated. It is very difficult to simulate all important faults, bolts, and shotcrete lining explicitly. Even worse, when the configuration of a structure is modified, it will cost much time and manpower to remesh. Combining the merits of the two models, the composite element method (CEM) is proposed to explicitly simulate jointed rock masses reinforced by bolts and shotcrete lining, which transfers the difficulties in preprocess into computation and heightens the efficiency.
Comprehensive researches of jointed rock masses reinforced by bolts and shotcrete lining are conducted in this dissertation on the basis of CEM.
Firstly, a review of ground anchorage and bolts and shotcrete lining support is made, and the working characteristic and action principle of bolts and shotcrete lining support is present in this dissertation. For bolts and shotcrete lining support, it has the characteristic of betimes, cohesiveness, deeply, flexible, adaptability to change and sealing which composite the basic elements of using the strength and self-support of surrounding rocks completely. During the long-term application of anchorage technology, several theories such as suspension theory, combined beam theory and combined arch theory have been proposed and generally accepted. Based on them, new theories including maximum horizontal stress, surrounding rock strength intensify theory, surrounding rock loosening circle and the full-length anchoring neutral point theory etc. have been present recently.
Secondly, method and status of recent research about jointed rock masses and anchorage has been summarized. Physics experiment method, engineering analogy and numerical analysis are the mainly used methods on jointed rock masses anchorage. The theory system about anchorage is divided into discontinuous medium mechanics discrete method and continuous medium mechanics equivalent method. The former includes limited equilibrium theory (LET), key block theory(BT), discrete element method (DEM), discontinuous deformation analysis(DDA), block element method and interface element method. Finite element method (FEM), boundary element method and fast Lagrange analysis of code (FLAC) are attributed to the latter. Recently, methods combined of their characteristics are proposed taking the numerical manifold method (NMM), mesh free method (MFM) and composite element method (CEM) for example. All of their applications in anchorage theory are presented in the dissertation while emphasis on the CEM where its development course and basic theory are introduced.
Thirdly, on the basis of CEM, the elastic composite element model for jointed rock masses supported by bolt and shotcrete lining is present in the dissertation. In this model, mesh can be generated without considering joint, grout, bolt and shotcrete lining firstly, and the elements containing them are defined as composite elements.8sub-elements are established to cover rock, grout, bolt, shotcrete lining and all interfaces. The displacements of the rock, grout, bolt and shotcrete lining can separately be interpolated from the sub-elements'nodal displacements. The interfaces have no independent nodes, and their displacements can be interpolated from the difference between the nodal displacements of rock, grout, bolt and shotcrete lining. According to the elastic constitutive relation and the virtual work principle, the equilibrium equation can be established. With the solved nodal displacements, the detailed behaviors of sub-elements can be described. This model can be incorporated into the conventional finite element analysis without any difficult. The conventional finite element can be treated as a degradation of the composite element. In the numerical example, elastic calculation for a jointed rock mass supported by grout-bolt and shotcrete lining is carried out by CEM and distinct element FEM. The comparison of the calculation results shows the validity of this model and the advantage of CEM in the pre-process of jointed rock mass supported by bolt and shotcrete.
Fourthly, on the basis of elastic composite element model for jointed rock masses supported by bolt and shotcrete lining, an elastic-viscoplastic composite element is established. For every component, we use the elastic-viscoplastic constitutive relation to simulate the course of stress and strain changing with the time. In practical engineering, for the simple elastic model, it cannot show that the stress and strain of rock is changing with the time, so it cannot simulate the actual process of stress-strain of jointed rock mass. The elastic-viscoplastic model can solve the problem. In the numerical example, with the same model as elastic calculation, elastic-viscoplastic calculation is carried out by CEM and distinct element FEM. The comparison of the calculation results shows the validity of this elastic-viscoplastic model.
Fifthly, the P-version adaptive CEM for jointed rock masses supported by bolt and shotcrete lining is proposed in this dissertation. With the simple preprocess, CEM has many advantages to simulate the complex structures. Using linear shape function as conventional FEM, CEM will have some difficulties in describing detailed nonlinear mechanical characteristics of complex structures under a low density of mesh. Generally speaking, increasing the density of the mesh is usually proposed to solve the problem. But it will increase the difficulties of preprocess. Furthermore, this approach disobeys to the CEM principle of simple preprocesses. To more complex mechanical characteristics of jointed rock masses supported by bolt and shotcrete lining, the linear shape function of conventional CEM has more difficulties to make a detailed simulation under a coarse mesh. Thereupon, P-version composite elements are defined to describe the jointed rock masses supported by bolt and shotcrete lining in this study. With the hierarchical basic function upgrading, the displacement mode of jointed rock masses supported by bolt and shotcrete lining and mechanical characteristics of all of the sub-structures can be well simulated by P-version CEM in physical hypostasis. Equation formulated, the method proposed can be realized in the program. The actual effect is shown through a comparison of calculation results among P-version CEM, conventional CEM and conventional FEM for an example.
Finally, the study present above is applied onto the underground engineering of Pubugou powerstation. With the3dimensions calculation meshes of CEM and FEM, the engineering is analyzed separately by CEM and FEM. The mesh of CEM which contains12311elements and12429nodes is generated without considering the grouts, bolts, shotcrete lining, joints etc. With a mesh containing73788elements and98188nodes, the distinct model is applied into FEM calculation. In the study, excavation is divided into9steps and reinforcement is applied after every excavation step. The comparison of the calculation results shows the advantage of CEM in preprocess and the preciseness of CEM in distinct simulation.
With a good foreground in the engineering, the study of CEM for jointed rock masses supported by bolts and shotcrete lining has been achieved, but many problems need to be solved to improve them, yet. Crack analysis, dynamic analysis, thermal analysis, localization analysis, coupling analysis, etc, are all the fields where CEM can show its advantages.
引文
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