Numerical simulation of Brazilian disk rock failure under static and dynamic loading

A numerical simulator based on RFPA (Rock Failure Process Analysis) is used to study the deformation and failure process of a Brazilian disk of heterogeneous rock when subjected to static and dynamic loading conditions. In this simulator, the heterogeneity of rock is considered by assuming that the material properties of elements conform to a Weibull distribution; an elastic damage-based law that considers the strain-rate dependency is used to describe the constitutive law at mesoscopic scale; and a finite element program is employed as a basic stress analysis tool. The simulator is firstly validated by simulating the dynamic spalling of a homogeneous rock bar and by comparing with the theoretical and experimental results. Then, the failure process of a Brazilian disk of rock subjected to static and dynamic loading is numerically simulated, and the numerical results are compared with the available experimental results. Particular attention is given to the typical failure patterns of the rock disk when the incident compressive stress waves with different amplitudes are applied. The numerical simulation also identifies the failure mechanisms of rock during dynamic failure processes that are closely related to the propagation of the stress wave.     

考虑围岩性质劣化的深埋软弱隧道破坏机理数值模拟研究

介绍劣化损伤本构模型在FLAC3D中的二次开发流程以及本构模型中软弱围岩力学参数的选取原则。然后利用FLAC3D劣化损伤本构模型对高速铁路客运专线双线深埋隧道(Ⅳ、Ⅴ级别围岩)损伤破坏机理进行数值模拟研究,分析围岩应力场特征从而确定压力拱边界,在此基础上说明深埋隧道围岩受力分区特点;接着对埋深、侧压力系数、围岩级别对受力分区的影响进行数值模拟研究。研究结果表明:FLAC3D劣化损伤模型可以描述深埋隧道开挖损伤区域的损伤程度,揭示深埋隧道破坏机理即深埋洞室围岩稳定性丧失的区域集中在沿最小主应力方向的"楔形"区内;深埋隧道开挖后受力分区:由隧道洞壁往外依次为劣化损伤严重区-压力拱拱体-原岩应力区;埋深、侧压力系数、围岩级别对隧道围岩受力分区范围有很大的影响。     

Two-scale modeling of jointed rock masses

Numerical modeling of the mechanical behavior of jointed rock masses is a difficult task as the discontinuities not only require special modeling consideration, but also require different treatments depending upon the scale of problem involved. A framework is proposed here that is based upon a meshed based partition of unity method, also known as the numerical manifold method. Specifically, the discontinuities posed by joints or faults are divided into two groups. The primary discontinuity set is the one with a wider spacing and dominates the kinematics of the system. It is modeled explicitly as physical discontinuities. The secondary discontinuity set, characterized by high density and small spacing, is modeled as an equivalent continuum by incorporating joint compliance and strength characteristics. Following the presentation of the formulation, two examples are also provided at the end to highlight the ease with which the proposed approach may be used in mechanical analysis of a complex jointed rock system.     

Influences of the valley morphology and rock mass strength on tunnel convergence: With a case study of Khimti 1 headrace tunnel in Nepal

Underground structures are constructed at the bottom of the valley sides for various purposes and for different reasons. Hydropower projects and transport tunnels are some of the examples of such structures. In this paper, literatures on topographical effects on the in situ stresses in valley and fjord sides are reviewed. An attempt is made to correlate stress anisotropy problems with the valley side topography by using Phase² numerical modelling. Based on an underground construction case study, fifteen in situ stress measurements and the Phase² analysis, stress induced problems have been found to be influenced by the valley morphology. This influence can be monitored by the convergence measurement and by the stress measurement. In addition to the overburden height, the total valley height and the slope need to be considered in the assessment of the stress induced problem. The second aspect dealt with is the influence of the rock strength on the tunnel convergence. In the Khimti 1 headrace tunnel and 66 cases from 15 countries, it has been observed that the tunnel convergence is larger in the weaker rocks than in the stronger rocks though they may have similar Q-values. Rock type such as gneiss or phyllite (corresponding to the rock mass strength) is not considered in the Q-system but it has influence on the convergence that takes place in underground works. Thus, it also needs to be considered in the assessment of potential convergence of an underground structure.     

Design of large cuttings in jointed rock

The article presents a stability study on a very high cutting in a granitic gneiss, as part of the construction of a bypass in the French Pyrenees. The preliminary study highlighted questions as to the most appropriate method of designing the rock cuts, as such methods are not standardized in France. A temporary stop in the roadworks allowed a second study to be carried out based on a statistical analysis of the discontinuities of the site and better-developed modeling tools, including Resoblok. A comparative analysis of these methods and their results in terms of bolt sizing is presented, taking into account the difficulty of use of each method.      

节理岩体各向异性力学研究综述

对节理岩体各向异性力学研究的现状与进展进行了系统分析和阐述,分别探讨了节理本身的各项异性力学性质,岩石介质和节理综合(即整个节理岩体)的各向异性力学性质,并对节理岩体本构模型、各向异性力学参数和屈服准则研究进行了较为详细的描述和比较,以指导实践。     

直剪条件下节理岩体的变形和强度特征研究

通过建立单一闭合水平节理岩体的数值模型，运用数值模拟软件对节理岩体模型在直剪试验条件下节理的剪切变形和强度特征进行模拟，并对模拟结果做了分析。     

节理岩体变形分析与计算模型探讨

主要分析了岩体模型的简化,提出了均质节理岩体的本构模型,并在简单讨论了非连续变形数值分析方法的同时,讨论和分析了非连续变形计算力学模型的基本原理,它可以很精确地预测岩土工程中的变形和接触力分布及其整体稳定安全系数,并论证了它的合理性。     

Responses of jointed rock masses subjected to impact loading

Impact-induced damage to jointed rock masses has important consequences in various mining and civil engineering applications. This paper reports a numerical investigation to address the responses of jointed rock masses subjected to impact loading. It also focuses on the static and dynamic properties of an intact rock derived from a series of laboratory tests on meta-sandstone samples from a quarry in Nova Scotia, Canada. A distinct element code (PFC2D) was used to generate a bonded particle model (BPM) to simulate both the static and dynamic properties of the intact rock. The calibrated BPM was then used to construct large-scale jointed rock mass samples by incorporating discrete joint networks of multiple joint intensities into the intact rock matrix represented by the BPM. Finally, the impact-induced damage inflicted by a rigid projectile particle on the jointed rock mass samples was determined through the use of the numerical model. The simulation results show that joints play an important role in the impact-induced rock mass damage where higher joint intensity results in more damage to the rock mass. This is mainly attributed to variations of stress wave propagation in jointed rock masses as compared to intact rock devoid of joints.     

Squeezing rock conditions at an igneous contact zone in the Taloun tunnels, Tehran-Shomal freeway, Iran: a case study

Squeezing rock conditions at the contact zone of an andesitic-basaltic body and tuff country rocks in the Taloun tunnels were investigated and analyzed. Evaluation of the rock mass properties illustrates the fact that they were significantly reduced at the contact zone, especially when wet. Detailed monitoring and measurements of tunnel-wall convergence at the contact zone in the Taloun service tunnel, during the 10 months following excavation and installation of initial support, prior to installation of heavy support, showed greater than 3% of the normalized tunnel closure. This confirms moderate squeezing conditions at the contact zone. The measured displacement was even higher than that of the fault zone in which deformation was decreased during the first month and eventually stabilized. Similarly, numerical modeling of the deformation at the contact zone not only confirmed a higher value of the tunnel convergence but also demonstrated the reduction of in situ stress and development of plastic zones across the contact zone. These data are also believed to account for the squeezing condition at the contact zone. It is expected that this condition will be significantly increased in the main road tunnels due to the fact that these tunnels are twice as wide as the service tunnel. Therefore, proper and timely support must be applied. Numerical analysis of the support at the contact zone showed that the stress due to bending moment is greater than that of the axial forces on the lining. This calls for certain support measures in the form of permanent lining and two layers of steel bars to compensate for the tensile stress exertion on the lining.     

Numerical simulation of blasting-induced rock fractures

In the present study, the Johnson–Holmquist (J–H) material model is implemented into the commercial software LS-DYNA through user-subroutines to simulate the blasting-induced rock fractures. The J–H model consists of strength models for both intact and fully fractured materials, a polynomial equation of state, and a damage model that represents the material from an intact state to a fully fractured state. Influences of the key parameters in smooth blasting, viz., loading rate, distance from a free face, earth stress, and pre-existing joint planes, etc., on fracture patterns are explored. According to the simulation results, the rock fracture pattern is significantly influenced by the loading rate. Fracture control techniques, namely, notched borehole and charge holder with slits are also simulated. Effectiveness of the fracture control techniques is demonstrated. The numerical simulation in the present study reproduces some of the well-known phenomena observed by other researchers. It has the potential to be applied in practical blast control and gas and hydraulic fracturing engineering.     

Delayed failure at the Messochora tunnel, Greece

Geodetic and extensometer data are used to shed light on the poorly known effect of delayed tunnel deformation. Four weeks after full section excavation and without any evidence of gradual strain accumulation, significant convergence of the tunnel walls and cracking of the lining occurred along a 36 m long, weak rock zone in the Messochora tunnel (Greece). Deformation extended also to nearby, previously stabilized sections. This event is in variance with predictions of an exponential-type pattern of decrease of strain accumulation based on theoretical and field evidence; it can only be explained if we accept that at the weak zone the tunnel was at a critical stability level, and that some small-scale interventions, which would otherwise have no effects, triggered a new phase of deformation transferred to nearby sections. Evidence from this tunnel indicates that, especially in weak rock zones, post-excavation stabilization may only be transient, depending on the balance between stresses and the combined strength of the rocks/lining.     

Numerical simulations of rock mass damage induced by underground explosion

The damage prediction of rock mass under blast loads induced by accidental explosions, rock bursts or weapon attacks is crucial in rock engineering. In this paper, parametric studies are conducted to evaluate the effect of loading density, rock mass rating (RMR) and weight of charge on the rock mass damage induced by underground explosions. The numerical simulations are carried out based on the transient dynamic finite element program ANSYS-LSDYNA. The numerical model was calibrated against the data obtained from a field blast test. A fully coupled numerical analysis, incorporating the explosion process, has been performed, where the large deformation zone near the charge is solved by the Arbitrary Lagrange–Euler (ALE) method. The deformable modulus and compressive strength of rock mass of granite are estimated by the RMR system. The peak particle velocity (PPV) damage criterion and the plastic strain criterion were adopted to study the damage zone around the charge hole, and an empirical formula considering the effects of loading density, RMR and weight of charge was obtained to estimate the damage zone in granite based on the numerical results.     

Volumetric analysis of rock mass instability around haulage drifts in underground mines

Haulage networks are vital to underground mining operations as they constitute the arteries through which blasted ore is transported to surface. In the sublevel stoping method and its variations, haulage drifts are excavated in advance near the ore block that will be mined out. Numerical modeling is a technique that is frequently employed to assess the redistribution of mining-induced stresses, and to compare the impact of different stope sequence scenarios on haulage network stability. In this study, typical geological settings in the Canadian Shield were replicated in a numerical model with a steeply-dipping tabular orebody striking EW. All other formations trended in the same direction except for two dykes on either side of the orebody with a WNW–ESE strike. Rock mass properties and in situ stress measurements from a case study mine were used to calibrate the model. Drifts and crosscuts were excavated in the footwall and two stope sequence scenarios – a diminishing pillar and a center-out one – were implemented in 24 mining stages. A combined volumetric-numerical analysis was conducted for two active levels by comparing the extent of unstable rock mass at each stage using shear, compressive, and tensile instability criteria. Comparisons were made between the orebody and the host rock, between the footwall and hanging wall, and between the two stope sequence scenarios. It was determined that in general, the center-out option provided a larger volume of instability with the shear criterion when compared to the diminishing pillar one (625,477 m³ compared to 586,774 m³ in the orebody; 588 m³ compared to 403 m³ in the host rock). However, the reverse was true for tensile (134,298 m³ compared to 128,834 m³ in the orebody; 91,347 m³ compared to 67,655 m³ in the host rock) instability where the diminishing pillar option had the more voluminous share.     

Effects of confinement on rock mass modulus: A synthetic rock mass modelling (SRM) study

The main objective of this paper is to examine the influence of the applied confining stress on the rock mass modulus of moderately jointed rocks (well interlocked undisturbed rock mass with blocks formed by three or less intersecting joints). A synthetic rock mass modelling (SRM) approach is employed to determine the mechanical properties of the rock mass. In this approach, the intact body of rock is represented by the discrete element method (DEM)-Voronoi grains with the ability of simulating the initiation and propagation of microcracks within the intact part of the model. The geometry of the pre-existing joints is generated by employing discrete fracture network (DFN) modelling based on field joint data collected from the Brockville Tunnel using LiDAR scanning. The geometrical characteristics of the simulated joints at a representative sample size are first validated against the field data, and then used to measure the rock quality designation (RQD), joint spacing, areal fracture intensity (P₂₁), and block volumes. These geometrical quantities are used to quantitatively determine a representative range of the geological strength index (GSI). The results show that estimating the GSI using the RQD tends to make a closer estimate of the degree of blockiness that leads to GSI values corresponding to those obtained from direct visual observations of the rock mass conditions in the field. The use of joint spacing and block volume in order to quantify the GSI value range for the studied rock mass suggests a lower range compared to that evaluated in situ. Based on numerical modelling results and laboratory data of rock testing reported in the literature, a semi-empirical equation is proposed that relates the rock mass modulus to confinement as a function of the areal fracture intensity and joint stiffness.     

Influence of intermediate principal stress on rock fracturing and strength near excavation boundaries—Insight from numerical modeling

The influence of the intermediate principal stress on rock fracturing and strength near excavation boundaries is studied using a FEM/DEM combined numerical tool. A loading condition of σ₃=0 and σ₁≠0, and σ₂≠0 exists at the tunnel boundary, where σ₁, σ₂, and σ₃, are the maximum, intermediate, and minimum principal stress components, respectively. The numerical study is based on sample loading testing that follows this type of boundary stress condition. It is seen from the simulation results that the generation of tunnel surface parallel fractures and microcracks is attributed to material heterogeneity and the existence of relatively high intermediate principal stress (σ₂), as well as zero to low minimum principal stress (σ₃) confinement. A high intermediate principal stress confines the rock in such a way that microcracks and fractures can only be developed in the direction parallel to σ₁ and σ₂. Stress-induced fracturing and microcracking in this fashion can lead to onion-skin fractures, spalling, and slabbing in shallow ground near the opening and surface parallel microcracks further away from the opening, leading to anisotropic behavior of the rock. Hence, consideration of the effect of the intermediate principal stress on rock behavior should focus on the stress-induced anisotropic strength and deformation behavior of the rocks. It is also found that the intermediate principal stress has limited influence on the peak strength of the rock near the excavation boundary.     

Micromechanics-based continuum model for a jointed rock mass and excavation analyses of a large-scale cavern

An analysis method that can grasp the behavior of a rock mass is necessary to establish a rational method for designing and constructing large-scale caverns. In underground excavation, sliding and opening of joints due to stress relaxation are considered to be the governing mechanisms of the behavior of a jointed rock mass. In the present study, a micromechanics-based continuum model of a jointed rock mass is proposed and an analysis method for underground excavation is developed. To examine the performance of the proposed method, the excavation of Shiobara power station cavern constructed by the Tokyo Electric Power Co., Ltd. is analyzed and results are compared to measured data. In numerical results, for instance, displacement of the measurement facilities during excavation are in good agreement with measured data.     

Numerical modeling of thermally-induced fractures in a large rock salt mass

Numerical modeling of thermally-induced fractures is a concern for many geo-structures including deep underground energy storage caverns. In this paper, we present the numerical simulation of a large-scale cooling experiment performed in an underground rock salt mine. The theory of fracture mechanics was embedded in the extended finite element code used. The results provide reliable information on fracture location and fracture geometry. Moreover, the timing of the fracture onset, as well as the stress redistribution due to fracture propagation, is highlighted. The conclusions of this numerical approach can be used to improve the design of rock salt caverns in order to guarantee their integrity in terms of both their tightness and stability.     

Numerical analysis of tunnel thermal plume control using longitudinal ventilation

A CFD model of the 4th Beijing subway line was used to study the effect of longitudinal ventilation on heat and smoke plume movement in the tunnel. The critical ventilation velocity is correlated with the heat release rate for both a simplified heat fire source model and a complete combustion fire source model with methane gas as fuel. The influences of the heat source length and the fuel gas inlet geometry on the critical velocity are investigated for both fire source models. The results show that the influences of the combustion process and fire source area variation are not included in models based on Froude number preservation theory. Thus, Ri is no longer suitable as a dimensionless number for the critical ventilation velocity when the fire geometry or combustion conditions influence the results. The back-layering air temperature above the front of the fire source can be used to explain the different critical velocity variation regimes for all the simulation conditions.