节理岩体中隧道开挖与支护的数值模拟

由于节理、断层等不连续面的存在造成岩体变形的不连续性,并且这些不连续面对岩体变形、应力等力学行为造成重要影响。对已有的非连续变形分析程序进行了两点改进,应用改进的程序模拟了节理岩体中隧洞开挖与支护的过程,研究了不同节理倾角岩体的应力分布特性、开挖后隧洞围岩的变形和应力分布规律以及支护后衬砌的变形与应力特点。研究结果表明,节理倾角对节理岩体系统的应力和变形有着直接的影响,并且影响着隧洞开挖后的内空收敛效应;隧洞开挖顺序对围岩的变形和稳定也有重要影响。改进后的非连续变形分析方法和程序可以用来分析复杂节理岩体系统中隧洞的开挖与支护。     

A discontinuous numerical model to simulate rock failure process

Due to the difficulty of the classical fracture mechanics in dealing with multicrack coalescence, the simulation of jointed rock failure has remained a worldwide problem since the middle of the last century. Through a nearly 10-year effort, we have developed a novel but simple discontinuum-based approach, namely DDARF (discontinuous deformation analysis for rock failure), to simulate the progressive failure process of jointed rock mass. In the proposed method, by adopting the FE adaptive mesh generation technique—the advanced front method, the computational model of triangular DDA block system is automatically established. Also, the randomly distributed mechanical parameters statistically satisfying Weibull’s law are assigned to the blocks to simulate the heterogeneity of rock mass. In the generating process of the block system, numerous artificial joints come into being. These artificial joints provide the potential paths along which the cracks generate and propagate. The two blocks beside an artificial joint are glued together through adhesive algorithm, and if the glue is invalid, the artificial joint will break and turn into a real crack. In this way, the rock fragmentation process can be simulated. The results of several verification examples indicate that the DDARF method can simulate the whole process of rock fragmentation, and is suitable for cases of intact rock, rock mass with non-penetrative joints, and even blocky rock.     

Implementation of displacement-dependent Barton-Bandis rock joint model into discontinuous deformation analysis

Discontinuous deformation analysis (DDA) has been widely applied in analyzing various rock engineering problems. As the joint strength play a vital role in the stability of jointed rock mass, this paper makes an attempt to implement the Barton-Bandis rock joint model into the DDA code to replace the original Mohr-Coulomb joint model. The developed Barton-Bandis joint model which is characterized by displacement-dependent shear strength is verified by experimental direct shear tests. An example of a block sliding on an inclined plane is used to demonstrate the capacity of the DDA-BB model in predicting the dynamic motion behavior of sliding blocks.     

Implementation of the finite element method in the three‐dimensional discontinuous deformation analysis (3D‐DDA)

A modified three‐dimensional discontinuous deformation analysis (3D‐DDA) method is derived using four‐noded tetrahedral elements to improve the accuracy of current 3D‐DDA algorithm in practical applications. The analysis program for the modified 3D‐DDA method is developed in a C++ environment and its accuracy is illustrated through comparisons with several analytical solutions that are available for selected problems. The predicted solutions for these problems using the modified 3D‐DDA approach all show satisfactory agreement with the corresponding analytical results. Results presented in this paper demonstrate that the modified 3D‐DDA method with discontinuous modeling capabilities offers a useful computational tool to determine stresses and deformations in practical problems involving fissured elastic media with reasonable accuracy. Copyright © 2008 John Wiley & Sons, Ltd.     

Kinetic Energy Dissipation and Convergence Criterion of Discontinuous Deformations Analysis (DDA) for Geotechnical Engineering

The discontinuous deformation analysis (DDA) is a numerical method for modeling discontinuous deformation behaviour of jointed rocks. In this paper, two basic problems are discussed related to kinetic energy dissipation and the convergence criterion for the DDA method when it is applied to geotechnical engineering. In view of the fact that the deformation and progressive failure can be treated as a quasi-static process with low kinetic energy dissipation rates, this paper introduces a viscous damping component to absorb discrete blocks’ kinetic energy, establishes the global equations of motion of the discrete block system that take damping effects into account, investigates the energy dissipation mechanism when solving a static or quasi-static problem, and defines the convergence criteria of displacement, kinetic energy and unbalanced force for DDA solutions when the system arrives at a stable state.     

公路隧道局部塌方洞段的围岩稳定性评价

结合某公路隧道工程,以现场地质调查和监测资料为基础,在结构面发育且可能发生大规模塌方的围岩洞段,根据现场实际统计的优势结构面产状,采用关键块体理论、非连续变形方法（DDA）首先确定围岩主要的失稳破坏模式,然后运用连续介质分析程序FLAC,在DDA方法确定的围岩实际变形破坏塌方形态的基础上进行计算分析,评价围岩的整体稳定性及加固措施的有效性。分析表明,围岩破坏的主要模式为受结构面控制的局部块体的失稳,工程开挖后围岩不会发生大变形,这与实际情况基本一致,为安全施工提供了保证。采用非连续变形方法和连续介质计算相结合的分析方法对隧道工程塌方稳定性进行研究,取得了较好的效果,研究方法和经验可为类似工程参考并借鉴。     

节理岩质边坡变形的DDA模拟

对原非连续变形分析方法（DDA方法）中边界约束方法进行了推广，将其应用于节理岩质边坡变形规律的数值模拟，并利用模型实验结果验证了推广方法的正确性。     

节理对爆炸波传播影响的数值研究

采用加入无反射边界条件的DDA程序,研究了节理面对应力波传播的影响。结果表明,节理面能阻碍波的传播,有利于波的衰减,节理面越多,波的反射越强,而波的透射越弱。模拟了一个现场爆炸试验,研究爆炸产生的应力波在节理岩体中传播、衰减的规律,模拟结果与现场试验结果比较吻合。研究表明,DDA方法可以模拟节理面对应力波传播的阻碍作用,用它来模拟爆炸波在节理岩体中的传播是适用的。     

连拱隧道围岩变形和破坏形态的DDA分析

连拱隧道围岩一般为由节理结构面相互切割的非连续岩体,利用非连续性分析方法研究这类围岩的变形和破坏形态可以更好地反映工程实际情况。采用非连续变形分析方法 DDA,对金鸡山连拱隧道围岩的变形和破坏过程进行了模拟,将整个变形破坏过程划分为了3个阶段：中墙上方岩体变形、地表下沉、滑移面产生阶段、隧道左右洞两侧滑移带（或滑移面）的形成阶段以及中墙顶部块体失稳、隧道上方岩体快速塌落阶段。研究了金鸡山隧道浅埋围岩和深埋围岩的变形破坏特征,其中边墙部位、靠近中墙的内侧拱顶或拱肩部位、外侧拱肩部位会首先受到变形破坏。     

Modelling the effects of discontinuity orientation, continuity, and dip on the process of burden breakage in bench blasting

The objective of this paper is to introduce the development of a dynamic blasthole expansion model, which is coupled to the discontinuous deformation analysis (DDA) code of Shi (1988). The developed model considers the effects of blast geometry (blasthole shape, angle, and location), the physical properties of the intact rock and existing discontinuities, the distribution and orientation of pre-existing discontinuities, and the blasthole pressure on the processes of burden breakage, fragment throw and muckpile formation. The newly modified DDA code (DDA_BLAST) describes the expansion of the blasthole as a function of blast chamber volume and time. It is assumed in the code that the rock is already fragmented in-situ due to the intersection of pre-existing discontinuities and the passage of stress wave. Hence, the model only considers the gas pressurization phase of the blasting process. Moreover, the proposed model for the blasthole expansion assumes an adiabatic expansion of explosion products and variations in the explosion pressure upon expansion of the blast chamber are calculated from an equation of state. Accordingly, the newly modified DDA_BLAST code was used to simulate typical blasting problems in jointed media and delve into the mechanisms involved (in a macro scale) in the gas pressurization phase of the blasting process, burden breakage, and the effects of the discontinuity properties on the process of rock breakage by blasting.     

A coupled time integration algorithm for discontinuous deformation analysis using the numerical manifold method

To improve the computational efficiency of the numerical manifold method for discontinuous deformation simulations, a spatial-domain coupled explicit-implicit time integration algorithm is proposed. A subdomain partition algorithm based on a super manifold element is developed for the numerical manifold method to simulate dynamic motions of blocky rock mass. In different subdomains, explicit or implicit time integration method is employed respectively based on its contact and motion status. These subdomains interact through assembling the corresponding explicit or implicit time integration-based matrices of different rock blocks. The computational efficiency of the discontinuity system under dynamic loading is improved by partially diagonalizing the global matrices. Two verification examples of a sliding block along an inclined plane under a horizontal acceleration excitation and a multiblock system acted on by dynamic forces are studied to examine the accuracy of the proposed numerical method, respectively. A highly fractured rock mass situated on an inclined slope subjected to seismic excitations is then studied to show the computational efficiency of the developed algorithm. The simulated results are in good agreement with those from the versions using purely implicit or explicit time integration algorithm for the numerical manifold method. The computational efficiency is shown to be higher using the proposed algorithm, which demonstrates its potential for application in dynamic analysis of highly fractured rock masses.     

用改进的DDA方法模拟公路隧道的稳定性

用改进的非连续变形分析(DDA)方法对某公路隧道进行了稳定性分析。采用有限元网格生成方法--行波法,在计算区域内自动生成三角形的DDA块体。块体的边界分为真实节理和虚拟节理,虚拟节理的强度取岩体的真实强度。另外,计算中还考虑了预应力锚杆对隧道围岩的加固作用。将计算得到的隧道拱顶、边墙的位移与现场监测结果进行了对比,两者基本吻合,说明改进的DDA方法在地下隧道的稳定性分析方面具有应有前景。     

基于DDA方法一种流-固耦合模型的建立及裂隙体渗流场分析和应用

以非连续变形分析方法（DDA）为基础并采用稳态流体计算方法将二者结合进行裂隙岩体流-固耦合分析。利用DDA方法生成裂隙岩体模型,在此基础上采用矩阵搜索等方法形成新的裂隙水通网络模型。采用稳态迭代算法和立方定律求得裂隙水压力,并把裂隙水压力作为线载荷施加到块体边界,在DDA算法中每个迭代步完成后更新裂隙开度和水压值,与DDA算法结合研究裂隙水与块体之间相互作用关系。利用以上裂隙岩体流-固耦合计算方法研究了某水封油库开挖和运行过程洞室围岩流量和密封性,为该工程预测水封效果提供了有益的主要依据,也是国内首次采用DDA方法做大型工程的流-固耦合模型分析。     

Initial stress formulae of high-order NMM and DDA for large deformation analysis

With high-order numerical manifold method (NMM) or high-order discontinuous deformation analysis method (DDA), computational accuracy of structure deformation can be improved greatly. However, poor accuracy is obtained and even computation is not convergent while treating large deformation problems, due to inaccurate or incorrect high-order initial stress formulae. Based on 2D triangular mathematical meshes and polynomial cover functions in high-order NMM, exact formulae for high-order initial stresses are deduced to depict configuration change of structures under large deformations. The formulae are expressed in polynomial forms so as to be used in simplex integrations. The approach is also extended to high-order DDA. Comparing with analytical solutions, accurate results for large deformation of a cantilever beam prove the validity of the proposed formulae.     

混合多位移模式的非连续变形分析法研究

传统的非连续变形分析法（DDA）法采用简单的线性位移模式计算效率高,描述大块体的高阶多项式位移模式在一定程度保留了该特点,并提高了计算精度。近年来流行的耦合有限元、自然单元的DDA法实质上是引入相应的插值形函数构成块体位移函数,计算相对低效,但具有计算更精细、更容易施加边界条件等优点。为结合传统DDA法与DDA耦合法各自的优点,建立了一种同时利用传统DDA法线性位移模式与耦合型DDA法非线性位移模式的混合法。该方法非线性模式主要针对大块体,采用了自然单元插值,缘于其具有一定无网格特征,且效率比有限元高。建立了混合模式下的整体矩阵并推导出接触等因素刚度子矩阵和荷载子向量的具体表达式。该方法建模更加方便合理,计算精度、效率介于线性模式的传统DDA法和非线性位移模式的耦合法之间。通过基本算例验证了混合法的有效性,并给出了节理围岩-隧道衬砌整体分析模型的计算结果,体现了新方法的优越性。     

Considerations of the discontinuous deformation analysis on wave propagation problems

In rock engineering, the damage criteria of the rock mass under dynamic loads are generally governed by the threshold values of wave amplitudes, such as the peak particle velocity and the peak particle acceleration. Therefore, the prediction of wave attenuation across fractured rock mass is important on assessing the stability and damage of rock mass under dynamic loads. This paper aims to investigate the applications of the discontinuous deformation analysis (DDA) for modeling wave propagation problems in rock mass. Parametric studies are carried out to obtain an insight into the influencing factors on the accuracy of wave propagations, in terms of the block size, the boundary condition and the incident wave frequency. The reflected and transmitted waves from the interface between two materials are also numerically simulated. To study the tensile failure induced by the reflected wave, the spalling phenomena are modeled under various loading frequencies. The numerical results show that the DDA is capable of modeling the wave propagation in jointed rock mass with a good accuracy. Copyright © 2009 John Wiley & Sons, Ltd.     

节理化块体边坡失稳机理数值分析

针对三峡库区移民新址的工程地质问题，用改进的岩土工程软件系统FINAL，研究了节理化块体岩坡的失稳机理，指出除了节理的C，值控制岩块的滑移、倾覆变形，倾倒等破坏形式外，岩块的模量E也对倾覆变形破坏起重要作用，从而不仅说明了保护坡脚，防止岩块浸水软化的必要性，也说明了应用传统离散元法分析这类问题的局限性。     

不连续岩体扩展有限元法的前处理

扩展有限元法是针对不连续问题提出的一种改进的有限元法,由于其计算网格独立于结构内不连续面,该方法十分适用于处理不连续问题,因此,该方法需能将不连续面和计算网格的几何信息转化为计算分析所需的单元拓扑信息的前处理。针对扩展有限元法在不连续岩体问题中的应用,系统地研究了二维扩展有限元解决不连续问题时单元拓扑信息生成等前处理问题,给出了单元拓扑信息自动生成算法,将不连续面和计算网格几何信息转化为计算所需要的单元拓扑信息,并在此基础上开发了不连续岩体二维扩展有限元法前处理程序。结果表明该算法和程序的适用性和正确性,同时还表明扩展有限元法在不连续岩体问题求解中有较好的应用前景     

Application of DDA to simulate characteristics of the Tsaoling landslide

This study simulates the kinematic behavior of sliding blocks of rock in the earthquake-induced Tsaoling landslide using seismic discontinuous deformation analysis (DDA). We assume sliding rocks are elastic blocks. Detailed joint shear strength parameters are set in DDA in a manner compatible with what is known about the Tsaoling landslide mechanisms. Landslide run-out distance, information from survivors, and the post-failure topography are used to constrain the computational results. Calculations demonstrate that sliding rocks from the ground surface decoupled from those near the basal shear surface during the landslide. Local residents survived because surficial rocks were never deeply buried during the landslide. Additionally, shear strength parameters of material in the deposition area strongly govern final deposit topography. Computational results correlate well with actual post-failure topography.     

Comparative study of Sarma's method and the discontinuous deformation analysis for rock slope stability analysis

This paper presents a comparative study of two methods, Sarma's method and the discontinuous deformation analysis (DDA), for rock slope stability analysis. The comparison concerns the stability analysis of two classic rock slopes. The study shows that the DDA, which accounts for the block kinematics, provides a very different factor of safety as compared with Sarma's method. More realistic reaction forces around each rock block can be obtained by the DDA, including the thrust forces between rock blocks and the forces between the base and the blocks. The DDA's result shows two possible directions for the relative movement between two contiguous blocks at the initiation of slope failure. It also indicates that the limit equilibrium condition may not occur along the interfaces of rock blocks at the initiation of slope failure. The determination of realistic interaction forces around each block will be very important in rock slope stability analysis if nonlinear failure criteria are considered.