节理岩体中应力波传播规律研究的进展

讨论了位移不连续模型与特征值法结合的方法,对垂直于单一线性变形节理、多个平行线性变形节理、单一非线性变形节理,分别采用线性变形不连续模型、双曲线变形不连续模型(BB模型)进行的理论与相应的实验研究。用离散元程序UDEC,对上述问题进行数值模拟;用三维离散元程序3DEC,对节理岩体中三维波的传播进行的数值模拟。并用UDEC与有限差分程序AUTODYN-2D耦合,模拟爆炸过程及爆炸波在节理岩体中的传播。同时提出了几个有待研究的问题。     

A finite element slideline approach for calculating tunnel response in jointed rock

The general purpose finite element code DYNA2D is used to calculate the response of an unlined tunnel in jointed rock, with sliding interfaces used to represent the joints. The model problem selected for analysis closely follows a calculation using the discrete element code UDEC. Results for two cases [(1) jointed rock with lubricated joints (no joint friction) and (2) jointed rock with frictional resistance to joint motion] are presented and compared with each other and the UDEC results.     

A 2D coupled finite element and boundary element scheme to simulate the elastic behaviour of jointed rocks

In this paper a coupled finite and boundary element formulation is developed for the analysis of excavation in jointed rock. The presence of joints in the rock mass has been included implicitly by treating it as an appropriate anisotropic elastic continuum. The boundary element formulation for an anisotropic medium is briefly discussed. Good agreement has been found between numerical and analytical solutions for several example problems, demonstrating the accuracy of the present formulation. Numerical solutions are also presented for the problems of a deep circular tunnel and a basement excavated in a variety of jointed rock masses.     

Stability of openings in jointed rock

The slide line approach is combined with the finite element method to represent the action of a removable block on a lined tunnel. The present paper examines the strength and ductility required of the tunnel liner to resist the forces imposed by a block when the surrounding rock mass is subjected to explosive loading. Key block theory developed by Goodman and Shi provides the conceptual framework for simplifying a general jointed domain to a manageable size for analysis with finite element models.     

Elastoplastic analysis of jointed rocks using a coupled finite element and boundary element method

This paper presents a coupled, elastoplastic, finite element and boundary element method for the two-dimensional, non-linear analysis of anisotropic jointed rock. The non-linear and anisotropic behaviour of a jointed rock mass is simulated by representing the mass as an equivalent anisotropic, elastoplastic continuum, so that the influence of the jointing system is ‘smeared’ across the continuum, i.e. the individual joints are not modelled as discrete entities. Numerical examples have been solved to verify the capability, accuracy and efficiency of the present technique. The proposed technique has also been applied to the analysis of tunnel excavation problems in plane strain. The effects of anisotropy and non-linearity of the jointed rock mass during excavation have been investigated in some detail.     

Verification for numerical modelling of jointed rock mass using thin layer elements

Thin layer finite elements are employed to model the response of rock joints in finite element analyses of rock mechanics problems. The case of a circular opening embedded in a rock mass is investigated. Results are obtained for both solid and jointed rock masses, and the effects of the presence of joints on the stress and strain field are investigated. Results from the finite element analysis are verified with respect to measurements from physical modelling. It is shown that the comparison between measured and computed results is satisfactory and that the presence of joints has a pronounced effect on the stress and strain field as compared to that realized in the absence of any rock joints. This study provides valuable data which contribute to the verification of thin layer finite elements for modelling the response of rock joints.     

基于强度折减法的顺层路堑边坡土钉墙支护结构稳定性分析

将非线性有限元分析和极限分析相结合形成强度参数折减有限元法,可以灵活地分析强度不均匀顺层路堑边坡支护结构稳定性问题。将岩体力学理论、非线性有限元分析技术和强度折减系数法相结合,对顺层岩体路堑边坡稳定性进行分析。在对密集假设节理有限元模拟中,假设节理在岩体内连续分布,采用连续介质力学方法建立密集分布节理岩体材料模型。采用强度折减系数法计算岩体结构安全系数,建议采用给定的岩体强度参数计算节理岩质边坡开挖、支护完毕后的内力,再逐渐降低岩体强度参数进行岩体边坡非线性有限元分析,直至岩体边坡达到极限状态,从而求出岩质边坡安全系数。采用该方法对渝怀铁路梅江河右岸DK409+989.4～DK410+020段顺层路堑边坡土钉墙支护结构稳定性进行分析,分析结果表明：采用土钉墙支护后的节理边坡塑安全系数为2.3,支护后的岩质边坡处于稳定状态;土钉墙潜在破裂面为岩体弹性区和塑性区的交界面,与测试得到的各排土钉拉力最大值位置一致。     

节理岩体冲击破坏的数值流形方法模拟

节理的存在是岩体明显区别于岩石的一个重要特征,也是导致岩体具有非均质性及各向异性的一个重要因素。节理岩体在爆炸冲击荷载作用下的破坏特征不仅是岩体力学研究的一个热点问题,也是岩石爆破领域经常遇到的一个工程问题。目前,常用的有限元和离散元等数值方法都不能很客观地反映岩体中节理分布的实际规律,而最新出现的数值流形方法则完全能够按照岩体中节理的实际分布规律进行建模,并能够很好地模拟岩体在外力作用下新裂纹的产生及已有节理的开裂。对3种不同节理岩体,即无节理岩体、均布水平节理岩体、均布垂直节理岩体等在均布垂直于圆周方向上的冲击荷载作用下的破坏过程进行了模拟。由模拟结果可以明显看出,节理的存在对岩体的破坏型式起到了关键性的控制作用。对于完整岩体,其破坏型式呈现出了很好的对称性;而对于水平及垂直节理岩体,其破坏型式在很大程度上受到节理分布的控制。研究结果对岩石爆破工程设计具有一定的指导意义。     

Development and validation of computer models for structures in jointed rock

An extensive program was conducted to develop and validate computer models for the deformation of structures in jointed rock. Both discrete element and finite element models were investigated. The program comprised a sequence of seven calculational and experimental studies. In the final step, model predictions were compared with experimental data from a well-instrumented jointed-rock precision test. The results show that the sophisticated models developed were able to predict some elements of structural deformation in jointed rock, but that it is difficult to make high-confidence predictions of all aspects of structural deformation with these models. Copyright © 1999 John Wiley & Sons, Ltd.     

Analysis of support requirements for a shallow diversion tunnel at Guledar dam site, Turkey

Engineering geological properties and support design of a planned diversion tunnel at Guledar dam site, which was located at the North of Ankara, Turkey were studied in this article. The main purpose of the construction of the planned tunnel is to regulate, drainage and to provide water for irrigation purposes. The diversion tunnel runs mainly through formations of limestone, sandstone and diabase. Rock masses at the site were characterized using Rock Mass Rating (RMR), Rock Mass Quality (Q), Rock Mass Index (RMi) and Geological Strength Index (GSI). RMR, Q, RMi and GSI were determined by using field data and mechanical properties of intact rock samples, measured in the laboratory. Support requirements for the planned diversion tunnel were determined accordingly in terms of the rock mass classification systems. Recommended support systems by empirical methods were also analyzed using 2D Finite Element method. Calculated parameters based on empirical methods were used as input parameters in the finite element models. The results from both methods were compared with each other. This comparison suggests that more reliable support design could be achieved by using the finite element method together with the empirical methods.     

Probabilistic prediction of the spatial distribution of potential key blocks during tunnel surrounding rock excavation

Jointed network simulations tend to be more random in nature due to the uncertainty of rock mass structures. In this paper, a series of jointed network models can be established in batches using Monte Carlo simulation (MSC) and loop iteration. Taking the joints, tunnel profile and their intersections as the edges E and vertices V of graph G, the jointed network model can serve as an unweighted undigraph. Then, the breadth-first search is introduced to search the closed paths around the tunnel profile, such as the potential key blocks. With batch simulation of network models, the spatial distribution characteristics and probability distribution rules of blocks can be automatically analysed during the search process. For comparison, the Laohushan tunnel of the Jinan Belt Expressway in China has been analysed using the breadth-first search, discontinuous deformation analysis method and procedure of “Finding the Key Blocks-Unrolled Tunnel Joint Trace Maps”. Each simulation starts from the same probabilistic model of geometrical parameters of joints but develops differently with different outcomes. The spatial distribution rule of potential key blocks simulated by the aforementioned batch jointed network models is essentially identical to the actual rockfall during tunnel excavation.

     

充水节理岩体中大断面隧洞开挖的数值模型研究

采用非饱和的渗流应力耦合模型分析了糯扎渡水电站2#导流洞的开挖过程,导流洞部分洞身穿过节理带,洞顶水头较高。详细地讨论了高水头和节理带对施工过程的影响。节理带采用描述高密度平行节理组的各向异性节理本构来逼近;考虑开挖引起的介质变形对渗透系数的影响;考虑排水引起的饱和度变化对渗透系数的影响。所用的非饱和瞬态耦合模型可以模拟出开挖引起的EDZ区域孔隙水压力急剧升高、有效应力减小、渗透系数动态的变化以及排水对洞室稳定性的提高。数值模拟的计算结果与国外类似试验的一般性观测结论相吻合,因此,可以用来评价水位以下隧洞施工方法和施工速度的合理性和经济性。     

Finite element algorithm for jointed concrete pavements subjected to moving aircraft

An algorithm based on the finite element method is developed to analyze the dynamic response of multiple, jointed concrete pavements to moving aircraft loads. In the finite element idealization, the pavement-subgrade system is idealized by thin plate finite elements resting on Winkler-type viscoelastic foundation represented by a series of distributed springs and dashpots. The dowel bars at the transverse joints are represented by beam elements. It i assumed that the dowel bar is fully embedded into the pavement thus neglecting dowel-pavement interaction effects. The longitudinal keyed or aggregate interlock joints are modeled by vertical spring elements. The dynamic aircraft-pavement interaction effects are considered in the analysis by modeling the aircraft by masses supported by spring-dashpot systems representing the landing gear of the aircraft. It is assumed that the aircraft travels along a straight line with a specific initial velocity and acceleration. The aircraft-pavement interaction takes the form of two sets of coupled equations which result ina non-symmetric stiffness matrix. An approximate mixed iteration-direct elimination scheme is used to solve for the dynamic equations. The accuracy of the computer code is verified by the available experimental and analytical solutions. A parametric study is conducted to investigate the effects of various parameters on the dynamic response of pavements.     

节理岩体蠕变特性研究

在已知岩石和节理蠕变规律的前提下,推导了节理岩体蠕变模型的一般表达式。假定岩石体积变形和节理法向压缩变形为弹性变形,忽略节理的剪胀现象,认为只有岩石畸变和节理剪切滑移与时间有关,从而推导了含三组相交节理的岩体蠕变模型及其参数。根据反演出的岩石和节理蠕变模型,计算了含三组相交节理的岩体在单轴应力作用下一些节理参数对岩体单轴蠕变的影响。分析表明,节理间距、剪胀系数以及节理夹角都对岩体的单轴蠕变变形有明显影响。节理间距越大,剪胀系数越大,节理夹角越小,节理岩体的单轴蠕变柔量也就越小,岩体的蠕变变形也越小。     

Elastic stress and strain in jointed rock masses by means of crack tensor analysis

Summary An elastic stress-strain relation is formulated in terms of crack tensors which makes it possible to take into account explicitly the effect of joints on elastic behavior of rock masses. The present study is to discuss some related topics which may be encountered in its practical application. Two problems are solved by incorporating the elastic stress-strain relation into a program for three-dimensional finite element analyses; i. e., stress concentration by surface loading and displacement by excavation of an intersecting tunnel. Validity of the results is checked by comparing them with a laboratory model test and a field test, with the following conclusions: The overall distribution of stress definitely depends on a joint stiffness ratio (i. e., normal stiffness to shear stiffness). If the ratio is chosen as unity, the stress concentration occurs mainly in the direction parallel to major joints. If the ratio is high, say 10, then the stress concentrates along the perpendicular as well as the parallel directions to major joints. It can be said, on the basis of the fairly good agreement of the calculations using the high stiffness ratio with the field and laboratory measurements, that the elastic solution by crack tensors provides a practical tool for estimating the stress and strain in strongly jointed rock masses.     

基于离散元法的节理岩体边坡稳定性分析

节理岩体边坡的稳定性在很大程度上取决于节理的强度及其分布形式。由于节理岩体边坡的失稳破坏具有大变形和非连续的特点,因此,离散单元法成为研究节理岩体边坡破坏机制的最有效方法之一。通过采用离散元软件PFC2D进行数值模拟,对完整岩石及节理的力学性能进行研究,并建立含密集节理的岩体边坡模型,讨论了节理连通率对边坡破坏形式的影响。结果表明,节理岩体边坡的失稳破坏是一个渐进的过程;在多组节理密集分布的岩体边坡中,连通率越大,其稳定性越差;随着连通率的减小,边坡的破坏形式由大范围的滑坡转变为局部崩塌的形式     

Eulerian finite element analysis of excess pore pressure generated by spudcan installation into soft clay

This paper reports an analytical exploration into excess pore pressures generated during offshore spudcan installations. The analysis was conducted using ABAQUS/Explicit for three effective-stress constitutive models coded using the user-defined material subroutine VUMAT. The results demonstrate the feasibility of conducting effective-stress finite element analysis of undrained spudcan penetration using Eulerian approach. They also show that the computed penetration resistance and pore pressure response depend significantly on the undrained shear strength computed by the different models.     

Implementation of hierarchical single surface δ0 and δ1 models in finite element procedure

Hierarchical single surface (HISS) δ₀ and δ₁ models are briefly discussed. An algorithm for the implementation of δ₀ and δ₁ models in a finite element code and the associated subroutines, written in FORTRAN 77, are presented. The algorithm is general and can be adopted for other computer codes with minor changes. Detailed steps and subroutines are included for easy implementation of the models in specific codes. Two example problems are also presented to enable the user to verify the implementation.     

地震动下考虑各向异性土体-盾构隧道数值模拟

针对层状土体-盾构隧道地震反应分析,引入了横观各向同性弹塑性模型,建立了横观各向同性介质的双渐近-多向透射边界条件。针对盾构隧道抗震设计的特点,基于横观各向同性弹塑性模型,研制了考虑层状土体各向异性和施工开挖效应,适合于地下结构动力计算的弹塑性动力有限元程序。在程序中对不同的材料采用了不同的本构关系和单元形式,并采用了关联流动法则和多种屈服准则,可同时进行横观各向同性土体与地下结构的平面应力、平面应变和轴对称问题的静动力有限元分析。最后,利用所研制的程序对上海地铁二号线石门一路站附近区间隧道在不同超越概率地震波输入下的地震反应进行了计算。结果表明,在层状土体-地铁盾构隧道的抗震分析中考虑土体各向异性的影响是必要的,所提出的计算模型是合理易行的。     

Analysis of strength and moduli of jointed rocks

This paper deals with two aspects of jointed rock mass behavior, first the finite element modeling of a jointed rock mass as an equivalent continuum, second the comparison of empirical strength criteria of a jointed rock mass. In finite element modeling the jointed rock properties are represented by a set of empirical relationships, which express the properties of the jointed medium as a function of joint factor and the properties of the intact rock. These relationships have been derived from a large set of experimental data of tangent elastic modulus. It is concluded that equivalent continuum analysis gives the best results for both single and multiple jointed rock. The reliability of the analysis depends on the estimation of joint factor, which is a function of the joint orientation, joint frequency and joint strength.Empirical strength criteria for jointed rocks, namely Hoek and Brown, Yudhbir et al., Ramamurthy and Arora, Mohr–Coulomb have been incorporated in a nonlinear finite element analysis of jointed rock using the equivalent continuum approach, to determine the failure stress. The major principal stress at failure, obtained using Ramamurthy's criteria, compares very well with experimental results.