Development of Rock Bolt Elements in Two-Dimensional Discontinuous Deformation Analysis

Computer modeling can be used to explore and gain new insights into the impacts of rock bolt intersecting joints in rock masses, and to estimate the effectiveness of the rock reinforcement system. In order to achieve this goal, we couple a rock bolt element into the two-dimensional discontinuous deformation analysis (DDA^2D) program. The coupling algorithm is based on the analytically-derived interface behavior between a rock bolt and the rock material for grouted rock bolts. The shear force generated by slippage along the interface is assumed to have a linear relationship with respect to the relative slipping distance between the rock bolt and the rock. The linear elastic criterion is applied to determine the material behavior of rock bolts before the axial stress reaches the yield value. The pullout tests are simulated to verify the coupling algorithm and the effects of the proposed rock bolt elements. Parametrical studies are also carried out to analyze the effectiveness of the rock bolts under various end conditions, joint locations and bond stiffness. In addition, the performance of the rock bolt during the interface debonding is analyzed using two types of constitutive laws, i.e., the friction law and the reduction law. The simulation results show that the proposed rock bolt models can predict the shear forces and axial loading along the rock bolts.     

A Discontinuous Approach to the Numerical Modelling of Rock Avalanches

Summary. The runout of dry rock avalanches produced by planar rockslides affecting a limestone formation with clayey interbeds is analysed by means of distinct element modelling. Potential and past rock avalanche events are described with reference to the geotechnical and structural conditions of the slope, typical of several Alpine valleys. Runout prediction analyses of potential rock avalanches performed with the PFC^2D code are based on independent measurement of strength, energy dissipation and stiffness parameters of the rock mass and are validated by means of the back analysis of a historical rockslide occurred in the investigated area. Physical aspects of the avalanching process evidenced by modelling are also discussed. Author’s address: Paolo Tommasi, CNR – Institute for Geo-Engineering and Environmental Geology, c/o Facoltá di Ingegneria, Via Eudossiana 18, 00184 Rome, Italy     

Boundary Element based Discontinuous Deformation Analysis

A Boundary Element based Discontinuous Deformation Analysis (BE‐DDA) method is developed by implementing the improved dual reciprocity boundary element method into the open close iterations based DDA. This newly developed BE‐DDA is capable of simulating both the deformation and movement of blocks in a blocky system. Based on geometry updating, it adopts an incremental dynamic formulation taking into consideration initial stresses and dealing with external concentrated and contact forces conveniently. The boundaries of each block in the discrete blocky system are discretized with boundary elements while the domain of each block is divided into internal cells only for the integration of the domain integral of the initial stress term. The contact forces among blocks are treated as concentrated forces and the open–close iterations are applied to ensure the computational accuracy of block interactions. In the current method, an implicit time integration scheme is adopted for numerical stability. Three examples are used to show the effectiveness of the algorithm in simulating block movement, sliding, deformation and interaction of blocks. At last, block toppling and tunnel stability examples are conducted to demonstrate that the BE‐DDA is applicable for simulation of blocky systems. Copyright © 2016 John Wiley & Sons, Ltd.     

冰-结构动力相互作用过程的DDA模拟

应用非连续变形分析(DDA)方法, 模拟了海冰与直立结构的动力相互作用过程的模拟.该方法的优点是能将冰对结构的碰撞及冰的破碎过程可视化, 同时发生碰撞后结构在每一时间步的响应都可计算出来.数值算例表明, DDA方法进行海冰破碎过程的模拟, 比有限元或边界元等方法更为合理和接近实际.     

滑坡运动过程仿真分析

滑坡是一个动态过程，滑坡体的运动是一个集滑动，转动，拉张等运动方式的复杂运动过程，传统的极限平衡和计算和有限元分析均无法描述滑坡的运动学特点和运动过程。非连续变形分析（DDA）是最近发展起来的一种新的离散数值分析方法。该方法基于块体的运动学理论及数值分析，可以开展块体的静力和动力学计算。应用非连续变形分析方法对长江三峡区新滩滑坡的运动全过程进行了数值模拟研究，模拟方案充分依据该滑坡的地质，地形特征，按不同岩土体和地质结构面类型进行块体单元的划分，共划分成504个块体单元。模拟结果表明，新滩滑坡是以斜坡中部姜家坡一带的局部破坏为其运动的开始阶段，并进一步牵引上部滑体和推动下部滑体。代表性块体单元的位移变化曲线和滑动速度变化曲线反映了滑动过程中滑坡体块体系统的变形是非连续的，各处块体的动态形态各异，从而很好地再现了新滩滑坡的整个动态过程，揭示了滑坡的运动机制。     

岩石爆破能量分析的数值方法

本文通过球形装药与岩石爆炸作用的力学分析,给出确定爆炸能量利用率的数值方法。通过算例,对于以破碎为主要目的的岩石工程爆破,爆炸能量利用率约为50%,爆炸作用初期的爆炸能量传递率约为40%。对于算例涉及到的炸药和岩石,两者的波阻抗越接近,爆炸能量利用率就越高。     

A Model of Point-to-Face Contact for Three-Dimensional Discontinuous Deformation Analysis

Summary The key to three-dimensional discontinuous deformation analysis (3D DDA) is a rigorous contact theory that governs the interaction of many three-dimensional blocks. This theory must provide algorithms to judge contact types and locations and the appropriate state of each contact, which can be open, sliding or locked. This paper presents a point-to-face contact model, which forms a part of the contact theory, to be used in 3D DDA. Normal spring, shear spring and frictional force submatrices are derived by vector analysis and the penalty method. Also given are the open-close iteration criteria and operations performed for different changes in contact state. Sliding at a contact can occur in any direction parallel to the contact face, as opposed to one of two directions in two-dimensional DDA. This point-to-face contact model has been implemented into a 3D DDA computer program, and numerical results from several test cases demonstrate the validity of the model and the capability of the program.     

岩石爆破不同掏槽形式的对比分析

在对不同掏槽形式进行对比分析的基础上,结合工程实例,试验分析了不同掏槽形式下的爆破效果,认为斜眼掏槽和直眼掏槽都存在各自的缺陷,提出采用和推广准直眼掏槽方式的建议。     

基于DDA方法的膨胀土边坡稳定性研究

非连续变形分析方法（DDA）是近年来发展起来的数值计算方法,其以新颖的思想、先进的数值技术,得到了学术界的认可和广泛关注。针对宁明高速公路膨胀土路堑边坡破坏的特点,建立地质模型和计算模型,编制了二维DDA程序,对DDA理论模型进行了推广和发展,将非饱和土的本构模型引入程序。对非连续变形分析方法中的控制参数设置进行了探讨,应用DDA程序模拟了膨胀土边坡破坏特征。程序计算结果与工程实际情况比较吻合,验证了程序的合理性和有效性,分析成果可为设计、施工提供参考依据。     

Modelling Two-Phase Incompressible Flow in Porous Media Using Mixed Hybrid and Discontinuous Finite Elements

In this paper, we present a numerical model for simulating two-phase (oil–water and air–water) incompressible and immiscible flow in porous media. The mathematical model which is based on a fractional flow formulation is formed of two nonlinear partial differential equations: a mean pressure equation and a water saturation equation. These two equations can be solved in a sequential manner. Two numerical methods are used to discretize the equations of the two-phase flow model: mixed hybrid finite elements are used to treat the pressure equation, h-based Richards' equation and the diffusion term in the saturation equation, the advection term in the saturation equation is treated with the discontinuous finite elements. We propose a better way to calculate the nonlinear coefficients contained in our equations on each element of the discretized domain. In heterogeneous porous media, the saturation becomes discontinuous at the interface between two porous media. We show in this paper how to use the capillary pressure–saturation relationship in order to handle the saturation jump in the mixed hybrid finite element method. The two-phase flow simulator is verified against analytical solutions for some flow problems treated by other authors.     

Correlations of SMR-Qslope Data in Stability Classification of Discontinuous Rock Slope: A Modified Relationship Considering the Iranian Data

Geotechnical and Geological Engineering - The preliminary responses on stability assessment are very effective in discontinuous rock slope stabilisations, which geo-mechanical empirical...     

Numerical Modelling of the Heterogeneous Rock Fracture Process Using Various Test Techniques

Summary A series of numerical tests including both rock mechanics and fracture mechanics tests are conducted by the rock and tool (R–T^2D) interaction code coupled with a heterogeneous masterial model to obtain the physical–mechanical properties and fracture toughness, as well as to simulate the crack initiation and propagation, and the fracture progressive process. The simulated results not only predict relatively accurate physical–mechanical parameters and fracture toughness, but also visually reproduce the fracture progressive process compared with the experimental and theoretical results. The detailed stress distribution and redistribution, crack nucleation and initiation, stable and unstable crack propagation, interaction and coalescence, and corresponding load–displacement curves can be proposed as benchmarks for experimental study and theoretical research on crack propagation. It is concluded that the heterogeneous material model is reasonable and the R–T^2D code is stable, repeatable and a valuable numerical tool for research on the rock fracture process.     

A Morphological Visualization Method for Removability Analysis of Blocks in Discontinuous Rock Masses

Block theory has been successfully applied to solve practical problems in rock engineering associated with the stability of discontinuous rock masses. Traditional methods of block theory, which have not proposed detailed schemes for characterizing geometric features of arbitrary blocks with complex geometries, are difficult to simultaneously visualize the locations of blocks. To overcome the shortcomings of these traditional methods, this paper introduces the concept of block morphology to systematically represent the morphological characteristics of blocks. Morphological visualization analysis involves the classification, characterization and visualization of various blocks and the determination of their removability using the stereo-analytical method. The proposed morphological visualization method provides a basis for computer modeling and mechanical calculations of large-scale rock mass systems. Furthermore, examples are presented in this paper to verify the validity and demonstrate the exceptional performance of this method.     

桩基存在对基坑坑底变形性状的作用分析

基坑开挖时的卸荷,使土体应力场发生变化,引起坑底土体向上隆起。根据土体变形与模量的关系,探讨桩基的存在对土体模量以及基坑坑底隆起的影响。通过有限元ANSYS计算模拟了基坑开挖的过程,得出了有桩基和无桩基时基坑坑底隆起的趋势,讨论了桩距、桩长、桩荷的影响。计算结果与室内模拟试验得出的结果相同,与现场实测结果基本相符。     

Prediction of Rock Fragmentation Due to Blasting in Sarcheshmeh Copper Mine Using Artificial Neural Networks

The main objective in production blasting is to achieve a proper fragmentation. In this paper, rock fragmentation the Sarcheshmeh copper mine has been predicted by developing a model using artificial neural network. To construct the model, parameters such as burden to spacing ratio, hole-diameter, stemming, total charge-per-delay and point load index have been considered as input parameters. A model with architecture 9-8-5-1 trained by back propagation method was found to be optimum. To compare performance of the neural network, statistical method was also applied. Determination coefficient (R ²) and root mean square error were calculated for both the models, which show absolute superiority of neural network over traditional statistical method.     

Constitutive Relationships for Elastic Deformation of Clay Rock: Data Analysis

Geological repositories have been considered a feasible option worldwide for storing high-level nuclear waste. Clay rock is one of the rock types under consideration for such purposes, because of its favorable features to prevent radionuclide transport from the repository. Coupled hydromechanical processes have an important impact on the performance of a clay repository, and establishing constitutive relationships for modeling such processes are essential. In this study, we propose several constitutive relationships for elastic deformation in indurated clay rocks based on three recently developed concepts. First, when applying Hooke’s law in clay rocks, true strain (rock volume change divided by the current rock volume), rather than engineering strain (rock volume change divided by unstressed rock volume), should be used, except when the degree of deformation is very small. In the latter case, the two strains will be practically identical. Second, because of its inherent heterogeneity, clay rock can be divided into two parts, a hard part and a soft part, with the hard part subject to a relatively small degree of deformation compared with the soft part. Third, for swelling rock like clay, effective stress needs to be generalized to include an additional term resulting from the swelling process. To evaluate our theoretical development, we analyze uniaxial test data for core samples of Opalinus clay and laboratory measurements of single fractures within macro-cracked Callovo-Oxfordian argillite samples subject to both confinement and water reduced swelling. The results from this evaluation indicate that our constitutive relationships can adequately represent the data and explain the related observations.     

Rock Wedge Stability Analysis Using System Reliability Methods

Summary We present a system reliability approach to rock wedge stability analysis. Different failure modes are considered, and a disjoint cut-set formulation is employed – with each cut-set corresponding to a different failure mode – to explore the system aspects of the problem, so that the reliability of the system is assessed by computing the probability of failure of the slope under each failure mode. An example case is used to demonstrate different approaches to compute the reliability of the slope design. Our results show that an approximation to the “exact” probability of failure – given by Monte Carlo simulation results – may be obtained using a first order approximation to the failure domain, and that linear programming techniques may be used to obtain bounds of the probability of failure. Furthermore, we identify the most likely failure mode, and we explore the sensitivity of the computed probabilities to changes in the random variables considered. The results indicate that the reliability results are quite sensitive to the geometry of the wedge. Changes in water conditions are also found to have a significant impact on the computed probabilities, while changes in unit weight of the rock have a considerably smaller effect on the reliability.     

钻孔内岩石局部爆破破碎若干影响因素分析

钻孔内小自由面条件下对岩矿石局部进行准确地爆破破碎并非易事,这一问题的解决将有助于便捷地通过钻孔获取大量的矿物岩石,提高水溶法采盐、地浸采铀的作业效率,同时使得通过钻孔开采某些具有重大潜在价值的难采矿产成为可能,这无论对钻孔取样还是钻孔采矿都具有重要的意义。论述了钻孔内岩石爆破破碎涉及的技术问题,并对钻孔内岩石爆破破碎若干影响因素进行了分析。在充分考虑各种岩矿赋存条件的基础上,采取合理的加载形式获得钻孔局部岩层较好的爆破破碎效果是可行的。