A statistical damage-based constitutive model for shearing of rock joints in brittle drop mode

Some rock joints exhibit significant brittleness,characterized by a sharp decrease in shear stress upon reaching the peak strength.However,existing models often fail to accurately represent this behavior and are encumbered by numerous parameters lacking clear mechanical significance.This study presents a new statistical damage constitutive model rooted in both damage mechanics and statistics,containing only three model parameters.The proposed model encompasses all stages of joint shearing,including the compaction stage,linear stage,plastic yielding stage,drop stage,strain softening stage,and residual strength stage.To derive the analytical expression of the constitutive model,three boundary conditions are introduced.Experimental data from both natural and artificial rock joints is utilized to validate the model,resulting in average absolute relative errors ranging from 3%to 8%.Moreover,a comparative analysis with established models illustrates that the proposed model captures stress drop and post-peak strain softening more effectively,with model parameters possessing clearer mechanical interpretations.Furthermore,parameter analysis is conducted to investigate the impacts of model parameters on the curves and unveil the relationship between these parameters and the mechanical properties of rock joints.Importantly,the proposed model is straightforward in form,and all model parameters can be obtained from direct shear tests,thus facilitating the utilization in numerical simulations.

An Anisotropic Geomechanical Model for Jointed Rock Masses at Taishan Nuclear Power Station, Southern China

An anisotropic geomechanical model for jointed rock mass is presented. Simultaneously with deriving the orthotropic anisotropy elastic parameters along the positive axis, the equivalent compliance matrix for the deflection axis orthotropic anisotropy was derived through a three- dimensional coordinate transformation. In addition, Singh＇s analysis of the stress concentration effects of intermittent joints was adopted, based on two groups of intermittent joints and a set of cross- cutting joints in the jointed rock mass. The stress concentration effects caused by intermittent joints and the coupling effect of cross-cutting joints along the deflection-axis are also considered. The proposed anisotropic mechanics parameters method is applied to determine the deformation parameters of jointed granite at the Taishan Nuclear Power Station. Combined with the deterministic mechanical parameters of rock blocks and joints, the deformation parameters and their variability in jointed rock masses are estimated quantitatively. The computed results show that jointed granite at the Taishan Nuclear Power Station exhibits typical anisotropic mechanical characteristics; the elastic moduli in the two horizontal directions were similar, but the elastic modulus in the vertical direction was much greater. Jointed rock elastic moduli in the two horizontal and vertical directions were respectively about 24% and 37% of the core of rock, showing weakly orthotropic anisotropy; the ratio of elastic moduli in the vertical and horizontal directions was 1.53, clearly indicating the transversely isotropic rock mass mechanical characteristics. The method can be popularized to solve other rock mechanics problems in nuclear power engineering.

Determination of mechanical parameters for jointed rock masses

Combining with empirical method, laboratory test and numerical simulation, a comprehensive system was presented to determine the mechanical parameters of jointed rock masses. The system has the following four functions: (1) Based on the field investigation of joints, the system can consider rock mass structures, by using network simulation technology. (2) Rock samples are conducted by numerical simulation with the input engineering mechanical parameters of rocks and joints obtained from laboratory tests. (3) The whole stress-strain curve of jointed rock masses under certain normal stress can be plotted from numerical simulation, and then the shear strength parameters of jointed rock masses can be obtained from the whole stress-strain curves under different normal stresses. (4) The statistical values of mechanical parameters of jointed rock masses can be determined according to numerical simulation. Based on the statistical values, combining with engineering experiences and geological investigations, the comprehensive mechanical parameters of jointed rock masses can be achieved finally. Several cases are presented to prove the engineering feasibility and suitability of this system.

Distinct element modelling of fracture plan control in continuum and jointed rock mass in presplitting method of surface mining

Controlled blasting techniques are used to control overbreak and to aid in the stability of the remaining rock formation. Presplitting is one of the most common methods which is used in many open pit mining and surface blast design. The purpose of presplitting is to form a fracture plane across which the radial cracks from the production blast cannot travel. The purpose of this study is to investigate of effect of presplitting on the generation of a smooth wall in continuum and jointed rock mass. The 2D distinct element code was used to simulate the presplitting in a rock slope. The blast load history as a function of time was applied to the inner wall of each blasthole. Important parameters that were considered in the analysis were stress tensor and fracturing pattern. The blast loading magnitude and blasthole spacing and jointing pattern were found to be very significant in the final results.

AN ANALYSIS MODEL OF THE MECHANICS OF JOINTED ROCK MASS

The creep fracture damage model of jointed rock mass is proposed, the basic methods and properties of engineering structure forecast analysis in split surrounding rock mass is discussed, numericalized way is analyzed, and the computing program of RCFD rock mechanics problems known is modified.Moreover, this program is used to make practical forecast analysis for the stability of surrounding rock mass of one large section (vertical)shaft which is buried in the earth 300 m deep.

Advances in statistical mechanics of rock masses and its engineering applications

To efficiently link the continuum mechanics for rocks with the structural statistics of rock masses,a theoretical and methodological system called the statistical mechanics of rock masses(SMRM)was developed in the past three decades.In SMRM,equivalent continuum models of stressestrain relationship,strength and failure probability for jointed rock masses were established,which were based on the geometric probability models characterising the rock mass structure.This follows the statistical physics,the continuum mechanics,the fracture mechanics and the weakest link hypothesis.A general constitutive model and complete stressestrain models under compressive and shear conditions were also developed as the derivatives of the SMRM theory.An SMRM calculation system was then developed to provide fast and precise solutions for parameter estimations of rock masses,such as full-direction rock quality designation(RQD),elastic modulus,Coulomb compressive strength,rock mass quality rating,and Poisson’s ratio and shear strength.The constitutive equations involved in SMRM were integrated into a FLAC3D based numerical module to apply for engineering rock masses.It is also capable of analysing the complete deformation of rock masses and active reinforcement of engineering rock masses.Examples of engineering applications of SMRM were presented,including a rock mass at QBT hydropower station in northwestern China,a dam slope of Zongo II hydropower station in D.R.Congo,an open-pit mine in Dexing,China,an underground powerhouse of Jinping I hydropower station in southwestern China,and a typical circular tunnel in Lanzhou-Chongqing railway,China.These applications verified the reliability of the SMRM and demonstrated its applicability to broad engineering issues associated with jointed rock masses.

Strength and deformation characteristics of irregular columnar jointed rock mass: A combined experimental and theoretical study

The irregularity of jointed network poses a challenge to the determination of field mechanical param-eters of columnar jointed rock mass(CJRM),and a reasonable prediction of deformation and strength characteristics of CJRM is important for engineering construction.The Voronoi diagram and three-dimensional printing technology were used to make an irregular columnar jointed mold,and the irregular CJRM(ICJRM)specimens with different dip directions and dip angles were prepared.Uniaxial compression tests were performed,and the anisotropic strength and deformation characteristics of ICJRM were described.The failure modes and mechanisms were revealed in accordance with the final appearances of the ICJRM specimens.Based on the model test results,the empirical correlations for determining the field deformation and strength parameters of CJRM were derived using the dip angle and modified joint factor.The proposed empirical equations were used in the Baihetan Project,and the calculated mechanical parameters were compared with the field test results and those obtained from the tunneling quality index method.Results showed that the deformation parameters determined by the two proposed methods are all consistent with the field test results,and these two methods can also estimate the strength parameters effectively.

Shear strength criteria for rock,rock joints,rockfill and rock masses:Problems and some solutions

Although many intact rock types can be very strong,a critical confining pressure can eventually be reached in triaxial testing,such that the Mohr shear strength envelope becomes horizontal.This critical state has recently been better defined,and correct curvature or correct deviation from linear Mohr-Coulomb（MC） has finally been found.Standard shear testing procedures for rock joints,using multiple testing of the same sample,in case of insufficient samples,can be shown to exaggerate apparent cohesion.Even rough joints do not have any cohesion,but instead have very high friction angles at low stress,due to strong dilation.Rock masses,implying problems of large-scale interaction with engineering structures,may have both cohesive and frictional strength components.However,it is not correct to add these,following linear M-C or nonlinear Hoek-Brown（H-B） standard routines.Cohesion is broken at small strain,while friction is mobilized at larger strain and remains to the end of the shear deformation.The criterion ＇c then σn tan φ＇ should replace ＇c plus σn tan φ＇ for improved fit to reality.Transformation of principal stresses to a shear plane seems to ignore mobilized dilation,and caused great experimental difficulties until understood.There seems to be plenty of room for continued research,so that errors of judgement of the last 50 years can be corrected.

Joints in unsaturated rocks:Thermo-hydro-mechanical formulation and constitutive behaviour

A formulation for the coupled analysis of thermo-hydro-mechanical （THM） problems in joints is first presented. The work involves the establishment of equilibrium and mass and energy balance equations. Balance equations were formulated taking into account two phases： water and air. The joint element developed was implemented in a general purpose finite element computer code for THM analysis of porous media （Code_Bright）. The program was then used to study a number of cases ranging from laboratory tests to large scale in situ tests. A numerical simulation of coupled hydraulic shear tests of rough granite joints is first presented. The tests as well as the model show the coupling between permeability and the deformation of thejoints. The experimental investigation was focused on the effects of suction on the mechanical behaviour of rock joints. Laboratory tests were performed in a direct shear cell equipped with suction control. Suction was imposed using a vapour forced convection circuit connected to the cell and controlled by an air pump. Artificial joints of Lilla claystone were prepared.Joint roughness of varying intensity was created by carving the surfaces in contact in such a manner that rock ridges of different tip angles were formed. These angles ranged from 0° （smooth joint） to 45° （very rough joint profile）. The geometric profiles of the two surfaces in contact were initially positioned in a ＂matching＂ situation. Several tests were performed for different values of suctions （200, 100, and 20 MPa） and for different values of vertical stresses （30, 60, and 150 kPa）. A constitutive model including the effects of suction and joint roughness is proposed to simulate the unsaturated behaviour of rock joints. The new constitutive law was incorporated in the code and experimental results were numerically simulated.

Development of an improved three-dimensional rough discrete fracture network model:Method and application

Structure plane is one of the important factors affecting the stability and failure mode of rock mass engineering.Rock mass structure characterization is the basic work of rock mechanics research and the important content of numerical simulation.A new 3-dimensional rough discrete fracture network(RDFN3D)model and its modeling method based on the Weierstrass-Mandelbrot(W-M)function were presented in this paper.The RDFN3D model,which improves and unifies the modelling methods for the complex structural planes,has been realized.The influence of fractal dimension,amplitude,and surface precision on the modeling parameters of RDFN3D was discussed.The reasonable W-M parameters suitable for the roughness coefficient of JRC were proposed,and the relationship between the mathematical model and the joint characterization was established.The RDFN3D together with the smooth 3-dimensional discrete fracture network(DFN3D)models were successfully exported to the drawing exchange format,which will provide a wide application in numerous numerical simulation codes including both the continuous and discontinuous methods.The numerical models were discussed using the COMSOL Multiphysics code and the 3-dimensional particle flow code,respectively.The reliability of the RDFN3D model was preliminarily discussed and analyzed.The roughness and spatial connectivity of the fracture networks have a dominant effect on the fluid flow patterns.The research results can provide a new geological model and analysis model for numerical simulation and engineering analysis of jointed rock mass.

CONSTITUTIVE MODEL AND STRENGTH THEORY FOR JOINTED ROCK MASSES

Widely distributed macrocracks (joints)make rock masses discontinuous media with notable anisotropy. To develop constitutive models and strength theories for rock masses is an interesting and difficult task in theoretical researches on rock masses. Though some researchers have introduced damage theory, it is not suitable for real rock mass with

A continuum model of jointed rock masses based on micromechanics and its integration algorithm

The paper is devoted to proposing a constitutive model based on micromechanics. The joints in rock masses are treated as penny-shaped inclusion in solid but not through structural planes by considering joint density, closure effect, joint geometry. The mechanical behavior of the joints is represented by an elasto-plastic constitutive law. Mori-Tanaka method is used to derive the relationship between the joint deformations and macroscopic strains. The incremental stress-strain relationship of rock masses is formulated by taking the volume average of the representative volume element. Meanwhile, the behavior of joints is obtained. By using implicit integration algorithms, the consistent tangent moduli are proposed and the method of updating stresses and joint displacements is presented. Some examples are calculated by ABAQUS user defined material subroutine based on this model.

Numerical evaluation of new Austrian tunneling method excavation sequences: A case study

The main aspects that require attention in tunnel design in terms of safety and economy are the precise estimation of probable ground conditions and ground behavior during construction. The variation in rock mass behavior due to tunnel excavation sequence plays an important role during the construction stage.The purpose of this research is to numerically evaluate the effect of excavation sequence on the ground behavior for the Lowari tunnel project, Pakistan. For the tunnel stability, the ground behavior observed during the actual partial face excavation sequence is compared with the top heading and bench excavation sequence. For this purpose, the intact rock parameters are used along with the characterization of rock mass joints related parameters to provide input for numerical modelling via FLAC 2D. The in-situ stresses for the numerical modelling are obtained using empirical equations. From the comparison of the two excavation sequences, it was observed that the actual excavation sequence used for Lowari tunnel construction utilized more support than the top heading and bench method. However, the actual excavation sequence provided good results in terms of stability.

A non-Archimedean number system to characterize the structurally inhomogeneous rock behavior nearby a tunnel

The development of mathematical models of structurally inhomogeneous media leads to the necessity to consider structure of space itself where deformation occurs, i.e. change of mathematical apparatus itself. The space, whose coordinate axes are non-Archimedean straight lines, has been considered. Refusing the fulfillment of Archimedes’s law allows to describe multi-scaling of the space, and so to consider deformation processes on different scale levels. The construction of two-scale mathematical model of rock masses has been considered as an example. The constitutive equations have been formulated on micro-and macro-levels and interaction condition between different levels as well. On micro-level, the elastic behavior of grains and plastic sliding between grains with possible softening are taken into account. On macro-level, the model represents a nonlinear system of equations describing the anisotropic rock mass behavior. On the basis of model, the numerical algorithm and code have been carried out to solve the plane boundary value problems. Examples of numerical simulations of stress-strain state of structural rock masses nearby a tunnel opening are presented. The deformation contours and isolines of stresses are plotted.

考虑截面规则性的柱状节理岩体变形及强度特性研究

柱状节理岩体的复杂结构使其现场力学参数的确定存在困难,可靠地估计柱状节理岩体强度及变形特性对工程安全至关重要。结合Voronoi图形及3D打印技术制作不规则柱状节理岩体光敏树脂模具,并制备了具有不同倾角的规则及不规则柱状节理岩体试样。基于开展的单轴压缩试验结果,分析不同截面柱状节理岩体的变形及强度特性差异。根据试样最终破坏形态,揭示柱状节理岩体破坏模式及机制。结合已有研究结果,描述节理面材料对柱状节理岩体破坏形态及强度的影响。基于传统节理系数方法,提出了更能反映柱状节理岩体柱体结构特征的修正节理系数方法。采用修正节理系数法建立规则及不规则柱状节理岩体试验结果与现场变形及强度参数间的经验关系,将所提出计算公式应用于白鹤滩水电站工程,预测结果与现场实测值及RMR法(RMR为岩石质量评分指标)、Q法(Q为岩体质量指标)的预测值进行比较。结果表明,对于现场变形和强度参数,所提出的修正节理系数法的预测结果与现场实测结果较为吻合。

Statistical Principles in Mechanics of Rock Masses

For many years, the authors systematically summed up the previous studies, ex-plored the statistical characters of rock mass structure, and the mechanical characters,and developed the principle system of'Statistic Mechanics of Rock Mass'. This notewill briefly introduce the primary principles of the theory.

束状孔与当量大孔爆破应力波在节理岩体中的衰减规律

束状孔当量球形药包爆破技术是基于大直径深孔采矿法的新型爆破技术,与单孔爆破技术相比,其炸药能量利用率更高。为了探究节理岩体中束状孔与当量大孔爆破应力波衰减规律的不同,开展束状孔与当量大孔爆破模型试验研究。试验采用混凝土制作相似模型并用无缝钢管将炮孔包围以忽略爆生气体的作用,同时考虑不同节理厚度的影响,得到了爆炸应力波峰值速度与节理厚度的关系,并将两种布孔方式在相同节理条件下进行对比分析。结果表明:两种布孔方式的爆炸应力波峰值速度均随着节理厚度的增加而逐渐降低,在相同节理厚度条件下,束状孔爆破的应力波衰减相对更小。

A new constitutive law for the nonlinear normal deformation of rock joints under normal load

In view of the deviation of the fitting results of the classical exponential model and the hyperbolic model （the BB model） from several experiment data during intermediate stress period, a new constitutive model for the nonlinear normal deformation of rock joints under normal monotonous load is established with flexibility-deformation method. First of all, basic laws of the deformation of joints under normal monotonous load are discussed, based on which three basic conditions which the complete constitutive equation for rock joints under normal load should meet are put forward. The analysis of the modified normal con- stitutive model on stress-deformation curve shows that the general exponential model and the improved hyperbolic model are not complete in math theory. Flexibility-deformation monotone decreasing curve lying between flexibility-deformation curve of the classical exponential model and the BB model is chosen, which meets basic conditions of normal deformation mentioned before, then a new normal deformation constitutive model of rock joints containing three parameters is established. Two main forms of flexibility-deformation curve are analyzed and specific math formulas of the two forms are deduced. Then the range of the parameters in the g-δ model and the g-2 model and the correlative influence factor in geology are preliminarily discussed. Referring to different experiment data, the validating analysis of the g-δ model and the g-γ model shows that the g-2 model can be applied to both the mated joints and unmated joints. Besides, experiment data can be better fit with the g-2 model with respect to the BB model, the classical exponential model and the logarithm model.

陡倾岩层隧道破坏机理及其稳定性研究

倾斜层状岩体具有明显的各向异性,隧道修建过程中易产生大变形、塌方、初期支护破坏、二衬开裂等一系列问题。为深入研究隧道在层状岩层中的力学特性和破坏机理,以大岗山隧道为项目依托,借助数值模拟研究有、无支护状态下不同节理倾角对隧道稳定性的影响,并针对现有支护方案提出优化。结果表明:节理的存在使得隧道开挖后变形具有非对称性,无支护状态下,当节理倾角在30°~60°变化时,隧道洞周最大变形发生在右拱肩处,塑性区破坏前期以拉伸破坏为主,集中于右拱肩及左拱脚,随着节理角度增大,后期以剪切破坏为主;支护状态下,洞周变形得到有效改善,其中拱底隆起最为明显,但最大隆起量降至30 mm以内,围岩塑性区域减小,当节理角度为45°时,拱顶、拱底产生最大变形,随着节理角度的增大,左右两侧变形非对称性降低;布设局部加长锚杆,增加隧道仰拱厚度的优化方案能增强围岩稳定性,抑制围岩进入塑性状态,减小拱底隆起,增强隧道稳定性,减小节理岩层引起的潜在风险,为现场施工提供理论指导。

基于双目立体视觉的岩体结构三维建模及其参数优化

为研究岩体结构面的快速、高效建模方法,基于便携型LenaCV双目立体视觉成像系统,对左、右双目图像进行校正、对齐、纠偏和三维建模算法研究,提出确定相机内外参数的最优标定工况,分析适于点云建模的目标对象特征,确定三维点云建模的最佳拍摄距离与基线距离关系,获取双目视觉建模的最优参数。研究结果表明:以0.5像素为误差上限,LenaCV相机标定的最佳棋盘格尺寸为10 mm、最优标定距离为25倍基线距离;对比三维点云模型建模效果,表面粗糙对象建模效果优于光滑对象,目标在视野中图幅占比高的对象建模效果优于图幅占比低的对象;12 cm基线距离相较于6 cm基线距离的LenaCV双目系统,建立并输出的目标对象的三维点云数据结果更优。基于几种现场测试讨论了最优标定工况、摄影工况和建模对象特点,为岩体三维结构重建提供了可参考的实践经验,验证了基于LenaCV双目摄像机的三维岩体结构面建模的可行性。