Updated flowcharts for rock mechanics modelling and rock engineering design

In an earlier paper, the ways ahead for rock engineering design methodologies were discussed. In this paper, following an overview of earlier approaches, we present two updated flowcharts: one for rock mechanics modelling in which the modelling options are outlined; and one for rock engineering design in which the three phases of overall assessment, initial design and final design are incorporated. We outline the steps necessary and the principles involved in utilising the flowcharts, especially the appropriateness of the modelling methods for different circumstances together with the integration of methods. Particular emphasis is placed on the cycling through feedback and final design. We demonstrate the procedure with three illustrative case study examples representing the range of complexity: a conventional tunnel, the design and construction of the underground powerhouse for the Shuibuya hydro-electric project in Hubei Province, China, and designing a radioactive waste repository. The first and third case examples are presented briefly: the first because of its relative simplicity; the third because of its relative complexity. The second case of the powerhouse design and construction is presented at greater length because it clearly illustrates the application of the flowcharts.     

A review of techniques, advances and outstanding issues in numerical modelling for rock mechanics and rock engineering

The purpose of this review paper is to present the techniques, advances, problems and likely future developments in numerical modelling for rock mechanics. Such modelling is essential for studying the fundamental processes occurring in rocks and for rock engineering design. The review begins by explaining the special nature of rock masses and the consequential difficulties when attempting to model their inherent characteristics of discontinuousness, anisotropy, inhomogeneity and inelasticity. The rock engineering design backdrop to the review is also presented. The different types of numerical models are outlined in Section 2, together with a discussion on how to obtain the necessary parameters for the models. There is also discussion on the value that is obtained from the modelling, especially the enhanced understanding of those mechanisms initiated by engineering perturbations. In Section 3, the largest section, states-of-the-art and advances associated with the main methods are presented in detail. In many cases, for the model to adequately represent the rock reality, it is necessary to incorporate couplings between the thermal, hydraulic and mechanical processes. The physical processes and the equations characterizing the coupled behaviour are included in Section 4, with an illustrative example and discussion on the likely future development of coupled models. Finally, in Section 5, the advances and outstanding issues in the subject are listed and in Section 6 there are specific recommendations concerning quality control, enhancing confidence in the models, and the potential future developments.     

Numerical methods in rock mechanics

The purpose of this CivilZone review paper is to present the techniques, advances, problems and likely future development directions in numerical modelling for rock mechanics and rock engineering. Such modelling is essential for studying the fundamental processes occurring in rock, for assessing the anticipated and actual performance of structures built on and in rock masses, and hence for supporting rock engineering design. We begin by providing the rock engineering design backdrop to the review in Section 1. The states-of-the-art of different types of numerical methods are outlined in Section 2, with focus on representations of fractures in the rock mass. In Section 3, the numerical methods for incorporating couplings between the thermal, hydraulic and mechanical processes are described. In Section 4, inverse solution techniques are summarized. Finally, in Section 5, we list the issues of special difficulty and importance in the subject. In the reference list, ‘significant’ references are asterisked and ‘very significant’ references are doubly asterisked.     

Numerical back analysis for estimation of soil parameters in the Resalat Tunnel project

Determination of in situ soil or rock geotechnical properties is a difficult task for a design engineer. Back analysis is a helpful technique for evaluation of soil properties by considering and measuring the convergence of an underground opening. In this article, the results of numerical back analysis, performed for Resalat tunnel in Tehran, Iran, are reported. The main purpose of this study was to estimate the soil cohesion and the in situ horizontal stress. Back analysis was performed by matching numerical modeling results with the measured tunnel convergence. In addition, the results of in situ direct shear, plate load and pressure meter tests are reported and compared with those from back analysis. It is shown that the back analysis presented is capable of determining the horizontal in situ stress and soil cohesion with good accuracy.     

Time-dependent behavior of tunnel lining in weak rock mass based on displacement back analysis method

Weak rock mass behavior is an important and challenging consideration during construction and utilization of a tunnel. Tunnel surrounding ground deformation in weak rocks causes to gradual development of loading on the support system and threats the opening stability. In this research, time-dependent behavior of Shibli twin tunnels was investigated using laboratory testing, monitoring data, and finite difference numerical simulation approaches. The host rock of Shibli tunnels are mainly composed of gray to black Shale, Marl and calcareous Shale. Geological maps and reports demonstrate a heavily jointed condition in the host rock through two orogenic phases. The experiment was organized in following order to understand the behavior of the rock mass around the tunnels. At first, triaxial creep test were conducted on intact rock specimens. Then, the time-dependent behavior of the tunnel host rock was numerically simulated considering Burger-creep visco-plastic model (CVISC). Finally, displacement based direct back analysis using univariate optimization algorithm was applied. Also, the properties of the CVISC model and initial stress ratio were estimated. Numerical modeling was verified by its comparison with tunnel displacement monitoring results. The creep behavior of the rock mass was predicted during tunnel service life based on back analysis results. Results show that thrust force, bending moment, and the resulting axial stresses will gradually increase at the spring line of the final lining. After 55 years of tunnel utilization the compressive strengths of lining concrete will not be stable against the induced-stresses by thrust force and bending moment, thus the tunnel inspection and rehabilitation are recommended.     

The excavation of a circular tunnel in a bedded argillaceous rock (Opalinus Clay): Short-term rock mass response and FDEM numerical analysis

The Opalinus Clay formation is currently being investigated as a potential host rock for the deep geological disposal of radioactive waste in Switzerland. Recently, a test tunnel was excavated at the Mont Terri underground rock laboratory (URL) as part of a long-term research project (“Full-scale Emplacement (FE) experiment”) aimed at studying the thermo-hydro-mechanical (THM) effects induced by the presence of an underground repository. The objective of this paper is twofold. Firstly, the results of the rock mass monitoring programme carried out during the construction of the 3 m diameter, 50 m long FE tunnel are presented, with particular focus on the short-term deformation response. The deformation measurements, including geodetic monitoring of tunnel wall displacements, radial extensometers and longitudinal inclinometers, indicate a strong directionality in the excavation response. Secondly, the deformational behaviour observed in the field is analyzed using a hybrid finite-discrete element (FDEM) analysis to obtain further insights into the formation of the excavation damaged zone (EDZ). The FDEM simulation using the Y-Geo code is calibrated based on the average short-term response observed in the field. Deformation and strength anisotropy are captured using a transversely isotropic, linear elastic constitutive law and cohesive elements with orientation-dependent strength parameters. Overall, a good agreement is obtained between convergences measured in the field and numerical results. The simulated EDZ formation process highlights the importance of bedding planes in controlling the failure mechanisms around the underground opening. Specifically, failure initiates due to shearing of bedding planes critically oriented with respect to the compressive circumferential stress induced around the tunnel. Slippage-induced rock mass deconfinement then promotes extensional fracturing in the direction perpendicular to the bedding orientation. The simulated fracture pattern is consistent with previous experimental evidence from the Mont Terri URL.     

New approaches to quantify progressive damage and associated dynamic rock mass blockiness

In the past decade, numerical modelling has been increasingly used for simulating the mechanical behaviour of naturally fractured rock masses. In this paper, we introduce new algorithms for spatial and temporal analyses of newly generated fractures and blocks using an integrated discrete fracture network (DFN)-finite-discrete element method (FDEM) (DFN-FDEM) modelling approach. A fracture line calculator and analysis technique (i.e. discrete element method (DEM) fracture analysis, DEMFA) calculates the geometrical aspects of induced fractures using a dilation criterion. The resultant two-dimensional (2D) blocks are then identified and characterised using a graph structure. Block tracking trees allow track of newly generated blocks across timesteps and to analyse progressive breakage of these blocks into smaller blocks. Fracture statistics (number and total length of initial and induced fractures) are then related to the block forming processes to investigate damage evolution. The combination of various proposed methodologies together across various stages of modelling processes provides new insights to investigate the dependency of structure's resistance on the initial fracture configuration.     

岩土工程数值分析中反分析方法探讨

通过查阅大量关于岩土工程方面的反分析文献资料,简要叙述了岩土工程反分析的概念,主要方法,并且介绍了目前具有代表性的反分析模型及各自的特点和适用性,同时阐述了在岩土工程非确定性反分析研究的发展方向,以期解决复杂岩土问题。     

Determination of the natural stress state in a Brazilian rock mass by back analysing excavation measurements: a case study

The Serra da Mesa Hydroelectric Power Plant, located in the Tocantins river, 210 km north of Brasilia, Brazil, has been completed and power (1200 MW) has been generated since 1998. This project includes one of the largest underground structures in Brazil, totalling 550,000 m³ of underground excavations in rock for the hydraulic circuit which was excavated in very high quality granite. Geotechnical investigations, laboratory tests and geological mapping showed that the rock mass could be considered as a continuous, homogeneous, isotropic and linearly elastic (CHILE) material.

In situ tests, for obtaining the natural stress tensor, namely hydraulic fracturing and small flat jack tests (SFJ), were executed. The hydraulic fracturing tests were performed in two boreholes, at the planned position of the future underground structures. SFJ were executed in a test gallery especially constructed for the purpose. These latter tests confirmed the in situ rock stress data obtained from the hydraulic fracturing tests.

This paper presents a new technique for interpretation of the SFJ results. This is achieved by inputting the SFJ measurements into a 3D program that compiles the influence matrix of the excavated rock mass domain and then, via the least square technique, the determination of the stress tensor. All the equations are fully developed and the methodology is presented in its entirety. The successful application of the methodology is also presented, with comparisons between the results obtained and the in situ stress tensor determined by other methods.     

Applications of numerical limit analysis (NLA) to stability problems of rock and soil masses

This work presents formulations and results obtained with computer implementations of an alternative to the more standard techniques for the determination of the state of collapse of geotechnical structures in rock or soil masses. Examples of normally available and used techniques for those purposes are limit equilibrium based procedures and elasto-plastic finite elements. As an alternative to these techniques, the present paper describes Numerical Limit Analysis (NLA). The fundamentals for limit analysis, summarized in the so-called bound theorems, have been known for decades. Analytical solutions obtained with limit analysis are however limited in scope and are seldom used in the engineering practice. NLA on the other hand, by solving the limit analysis equations through numerical methods are general and applicable to a wide range of problems. The paper presents a discussion on available alternatives for the formulation of NLA specialized for the determination of collapse load factors of geotechnical structures in/on rock (fractured or not) and soil masses. Rock masses in particular are modelled as standard continua, Cosserat equivalent continua and true discontinua formed by discrete blocks. Finite elements are used for the solution of NLA equations of standard continua and Cosserat continua. The paper presents derivation of the pertinent equations, the numerical formulations used and details of their numerical implementation in computer programs. Attempt was made to validate all the implementations through existing analytical solutions. The obtained results permit to state that NLA is a promising and very often advantageous numerical technique to establish collapse states of geotechnical structures in rock and soil masses.     

工程力学中的数值分析方法评述

对工程中常用的数值分析方法进行了论述,简单阐述了它们的基本原理及优缺点,提出了新的数值方法——半弥散单元法,指出该方法的研究刚起步但在理论分析和实际应用中都有重要意义和广阔前景。     

Influence of geometry and material properties on the axial vibration of a rock bolt

A continuous dynamic model for the axial vibration of a rock bolt system is presented. The model comprises three sections: the fixed length, bonded into the rock, the free length, which is not coupled to the rock, and the protruding length, which extends beyond the rock. The head assembly is modelled as a discrete mass and a spring, and a further discrete mass is included, representing a testing device that can be attached to the protruding end. Each section is modelled as a continuous elastic rod governed by the wave equation, with suitable compatibility conditions applied between the sections and boundary conditions, which also account for the effect of the discrete components, applied at the ends. Solutions in non-dimensional form are substituted into the boundary conditions to allow the natural frequencies to be calculated, and it is shown that two possible solutions for the mode shapes can be used for the fixed length—an exponential solution or the classical sinusoidal solution—depending on the stiffness of the grout relative to that of the bar. The conditions for which the two solutions are valid are developed, and changes in the frequency ratio with changes in length ratio, and the stiffness ratios of the grout and the anchor head relative to the stiffness of the fixed length of the anchorage are examined. Generally, the state of a bolt after installation is unknown and this does not provide proper assurance of the safety of the structure for which the bolts are used. The model provides a viable tool for helping to assess the condition of the bolt by using the natural frequencies associated with areas of the bolt of particular interest, e.g. the free length. The results show how the changes in the stiffness and/or length ratios affect the dynamics associated with fixed length of the bolt and the quality of the bonding installation. A case study is presented showing how the model can be used effectively to interpret real data.     

Three-dimensional numerical analysis of geocell reinforced shell foundations

The effects of geocell reinforcement on the behavior of shell foundations were studied using PLAXIS 3D finite element software. For this purpose, conical and pyramidal geometries were adopted as shell foundations. The real honeycomb shape of geocell and rigid body behavior of shells were simulated in PLAXIS 3D. The numerical models for shell foundations and geocell reinforced foundations were separately validated using several laboratory studies in the literature. The validated models were extended to the shell foundations resting on geocell reinforced sandy beds. The inclusion of geocell-reinforcement provided more than 70% reduction in the settlement of pyramidal and conical shell foundations. The stress transferred to the sand beds were reduced and distributed a wider area compared to the unreinforced cases. The maximum improvement in the bearing capacity and the settlement were observed in the case of conical shell foundation. The effect of adopted geocell and shell configuration on the foundation behavior was also analyzed for realistic prototype foundation size.     

Slope reliability and back analysis of failure with geotechnical parameters estimated using Bayesian inference

A Bayesian approach is proposed for the inference of the geotechnical parameters used in slope design. The methodology involves the construction of posterior probability distributions that combine prior information on the parameter values with typical data from laboratory tests and site investigations used in design. The posterior distributions are often complex, multidimensional functions whose analysis requires the use of Markov chain Monte Carlo (MCMC) methods. These procedures are used to draw representative samples of the parameters investigated, providing information on their best estimate values, variability and correlations. The paper describes the methodology to define the posterior distributions of the input parameters for slope design and the use of these results for evaluation of the reliability of a slope with the first order reliability method (FORM). The reliability analysis corresponds to a forward stability analysis of the slope where the factor of safety (FS) is calculated with a surrogate model from the more likely values of the input parameters. The Bayesian model is also used to update the estimation of the input parameters based on the back analysis of slope failure. In this case, the condition FS = 1 is treated as a data point that is compared with the model prediction of FS. The analysis requires a sufficient number of observations of failure to outbalance the effect of the initial input parameters. The parameters are updated according to their uncertainty, which is determined by the amount of data supporting them. The methodology is illustrated with an example of a rock slope characterised with a Hoek-Brown rock mass strength. The example is used to highlight the advantages of using Bayesian methods for the slope reliability analysis and to show the effects of data support on the results of the updating process from back analysis of failure.     

西部矿区软岩巷道支护结构监测及数值模拟分析

通过以西部矿区的泊江海子井田内软岩巷道为对象,首先,对原巷道支护结构进行受力和变形监测,结果表明:锚杆拉力在观测后期有减小的趋势,而混凝土应变值变化也较大;然后根据所监测的数据提出了优化方案,并利用有限元软件对优化前后的支护方案进行了对比分析,结果为该矿的开采施工提供了可靠的理论依据,并为后续软岩巷道支护的理论研究提供了有力的实例参考,对西部矿区矿井建设具有很强的指导意义。     

隧道围岩位移智能化反演研究

在分析隧道工程特点及围岩位移反分析研究现状的基础上,着重介绍了三种位移智能反演方法的原理、特点及普遍存在的问题,经研究证实了隧道位移智能化反演结果的正确性,对隧道围岩稳定性评价、信息化施工及岩石力学反问题研究具有重要意义.     

非连续变形计算力学模型弹塑性数值分析方法及其应用

在笔者所建立的非连续变形计算力学模型弹性分析方法基础上 ,进一步考虑材料的弹塑性 ,基于分区参变量最小势能变分原理 ,建立了非连续变形计算力学模型弹塑性分析的数学列式和求解方法 ,分析了不同材料特性的基础梁和岩基相互作用问题。计算结果表明 :这种非连续变形计算力学模型弹塑性分析方法将材料的非线性与多体相互作用系统的接触非线性或界面非连续性相耦合 ,能够模拟多体间的非线性相互作用特性 ,是一种处理岩土工程中多体非连续变形体系的新颖而有力的数值计算方法     

岩体工程与岩体力学仿真分析——各向异性开挖卸荷岩体力学研究

概述了岩体工程与岩体力学研究现状 ,讨论了现理论研究成果与岩体工程实际监测资料不相吻合的问题。分析其主要原因 ,是现岩体力学研究理论模型与岩体工程实际力学模型不相吻合所致。故应严格根据岩体工程实际力学动态相应进行岩体力学仿真分析 ,方可得到正确的分析成果。笔者曾提出“卸荷岩体力学”的概念 ,以归纳开挖卸荷岩体力学研究内容 ,已经高边坡和地下工程实例所验证 ,开挖卸荷岩体力学研究是岩体工程及其力学仿真分析的重要组成部分。     

Overhanging rock slope by design: An integrated approach using rock mass strength characterisation,large-scale numerical modelling and limit equilibrium methods

Overhanging rock slopes(steeper than 90°) are typically avoided in rock engineering design, particularly where the scale of the slope exceeds the scale of fracturing present in the rock mass. This paper highlights an integrated approach of designing overhanging rock slopes where the relative dimensions of the slope exceed the scale of fracturing and the rock mass failure needs to be considered rather than kinematic release of individual blocks. The key to the method is a simplified limit equilibrium(LE) tool that was used for the support design and analysis of a multi-faceted overhanging rock slope. The overhanging slopes required complex geometries with constantly changing orientations. The overhanging rock varied in height from 30 m to 66 m. Geomechanical modelling combined with discrete fracture network(DFN)representation of the rock mass was used to validate the rock mass strength assumptions and the failure mechanism assumed in the LE model. The advantage of the simplified LE method is that buttress and support design iterations(along with sensitivity analysis of design parameters) can be completed for various cross-sections along the proposed overhanging rock sections in an efficient manner, compared to the more time-intensive, sophisticated methods that were used for the initial validation. The method described presents the development of this design tool and assumptions made for a specific overhanging rock slope design. Other locations will have different geological conditions that can control the potential behaviour of rock slopes, however, the approach presented can be applied as a general guiding design principle for overhanging rock cut slope.     

Interaction of shotcrete with rock and rock bolts—A numerical study

The shotcrete–rock interaction is very complex and is influenced by a number of factors. The influence of the following factors was investigated by a series of numerical analyses: the surface roughness of the opening, the rock strength and Young's modulus, the discontinuities, the extent and properties of the excavated disturbed zone, the mechanical properties of the interface between shotcrete and rock, and the thickness of the shotcrete lining and the rock bolts. The study was carried out as a sensitivity analysis. The results showed that the rock strength and the surface roughness had significant impact on the number of failures at the rock–shotcrete interface and in the shotcrete lining. Furthermore, the behaviour of the lining is sensitive to small amplitudes of the surface roughness. In all the cases investigated, a high interface strength was favourable. The results indicate that if a thick shotcrete lining is dependent on the bond strength. The benefit of using a thicker lining can be doubtful. The analyses showed that for an uneven surface the extent of the EDZ had a minor effect on the behaviour of the shotcrete lining. Furthermore, if rock bolts were installed at the apex of the protrusion instead of at the depression, the number of failures decreased both at the interface and in the lining.