Stability analysis and optimization of the support system of an underground powerhouse cavern considering rock mass variability

Input parameters, such as rock mass strength parameters and deformation modulus, considered in the design of underground openings involve some uncertainty. The current uncertainty in these parameters is due to the inherent variability of these parameters. To quantify these parameters and design underground openings, the statistical methods must be utilized. In this research, a statistical method was used to define the GSI of rock mass (Geological Strength Index), block volume (V_b), and joint conditions (J_c). Using the GSI distribution function obtained from field data and intact rock strength characteristics, the statistical distribution functions of rock mass parameters were defined using the Monte Carlo method. The statistical analysis of the stability in Azad-pumped storage powerhouse cavern was carried out through the point estimate method. The appropriate support system was suggested according to the support pressure and the plastic zone around the cavern. This study showed the application of the statistical method, by combining the uncertainties of the intact rock strength and discontinuity parameters, in the assessment of the strength and deformability of rock masses and the support selection process in comparison with the deterministic methods.     

Rock mass characterization for the underground cavern design of Khiritharn pumped storage scheme

A general approach to rock engineering designing aspects adopted at the Khiritharn Pumped Storage Scheme is described. The scheme involves excavation of three large caverns and tunnels in jointed sandstone within a suture zone in Southeast Thailand. Geological condition and engineering properties of the sandstone were investigated. Strength and modulus properties of the intact rock were determined from laboratory tests and properties of rock mass were empirically estimated for the design analysis in the de.nite study stage on the basis of three rock mass classi.cation systems namely the Rock Mass Rating (RMR), Geological Strength Index (GSI) and a Japanese system (EPDC). While the GSI gives strength and modulus of deformation values slightly higher than the RMR classi.cation, the EPDC gives a lower value of modulus of deformation but comparable rock mass strength value for the level of con.ning pressures at the depth of the cavern excavation. The results of stress analysis and loosening wedge analysis for the cavern excavations suggest favorable excavation condition.     

Application of Rock Mass Characterization for Determining the Mechanical Properties of Rock Mass: a Comparative Study

The results of geotechnical explorations, engineering geological investigation (including laboratory and in situ tests) and field observations have been used, along with borehole logging charts, to obtain the rock mass geotechnical data. Based on the data, the rock mass along the Sabzkuh water conveyance tunnel route was classified by rock mass rating (RMR), Q-system (Q), rock mass index (RMi) and geological strength index (GSI) (3 methods). A new series of correlations were established between the systems based on the data collected from the study area. These relationships were then compared with those reported in the literature, and two new relations were recommended. The classifications were utilized to calculate mechanical properties (rock mass strength and deformation modulus) of the rock mass along the tunnel according to available empirical relations, and to distinguish the upper-bound and lower-bound relations.     

Updating the models and uncertainty of mechanical parameters for rock tunnels using Bayesian inference

Rock mechanical parameters and their uncertainties are critical to rock stability analysis, engineering design, and safe construction in rock mechanics and engineering. The back analysis is widely adopted in rock engineering to determine the mechanical parameters of the surrounding rock mass, but this does not consider the uncertainty. This problem is addressed here by the proposed approach by developing a system of Bayesian inferences for updating mechanical parameters and their statistical properties using monitored field data, then integrating the monitored data, prior knowledge of geotechnical parameters,and a mechanical model of a rock tunnel using Markov chain Monte Carlo(MCMC) simulation. The proposed approach is illustrated by a circular tunnel with an analytical solution, which was then applied to an experimental tunnel in Goupitan Hydropower Station, China. The mechanical properties and strength parameters of the surrounding rock mass were modeled as random variables. The displacement was predicted with the aid of the parameters updated by Bayesian inferences and agreed closely with monitored displacements. It indicates that Bayesian inferences combined the monitored data into the tunnel model to update its parameters dynamically. Further study indicated that the performance of Bayesian inferences is improved greatly by regularly supplementing field monitoring data. Bayesian inference is a significant and new approach for determining the mechanical parameters of the surrounding rock mass in a tunnel model and contributes to safe construction in rock engineering.     

Probabilistic analysis of tunnel displacements based on correlative recognition of rock mass parameters

Displacement is vital in the evaluations of tunnel excavation processes,as well as in determining the postexcavation stability of surrounding rock masses.The prediction of tunnel displacement is a complex problem because of the uncertainties of rock mass properties.Meanwhile,the variation and the correlation relationship of geotechnical material properties have been gradually recognized by researchers in recent years.In this paper,a novel probabilistic method is proposed to estimate the uncertainties of rock mass properties and tunnel displacement,which integrated multivariate distribution function and a relevance vector machine(RVM).The multivariate distribution function is used to establish the probability model of related random variables.RVM is coupled with the numerical simulation methods to construct the nonlinear relationship between tunnel displacements and rock mass parameters,which avoided a large number of numerical simulations.Also,the residual rock mass parameters are taken into account to reflect the brittleness of deeply buried rock mass.Then,based on the proposed method,the uncertainty of displacement in a deep tunnel of CJPL-II laboratory are analyzed and compared with the in-situ measurements.It is found that the predicted tunnel displacements by the RVM model closely match with the measured ones.The correlations of parameters have significant impacts on the uncertainty results.The uncertainty of tunnel displacement decreases while the reliability of the tunnel increases with the increases of the negative correlations among rock mass parameters.When compared to the deterministic method,the proposed approach is more rational and scientific,and also conformed to rock engineering practices.     

Empirical and numerical analyses of support requirements for a diversion tunnel at the Boztepe dam site, eastern Turkey

This paper presents the engineering geological properties and support design of a planned diversion tunnel at the Boztepe dam site that contains units of basalt and tuffites. Empirical, theoretical and numerical approaches were used and compared in this study focusing on tunnel design safety. Rock masses at the site were characterized using three empirical methods, namely rock mass rating (RMR), rock mass quality (Q) and geological strength index (GSI). The RMR, Q and GSI ratings were determined by using field data and the mechanical properties of intact rock samples were evaluated in the laboratory. Support requirements were proposed accordingly in terms of different rock mass classification systems. The convergence–confinement method was used as the theoretical approach. Support systems were also analyzed using a commercial software based on the finite element method (FEM). The parameters calculated by empirical methods were used as input parameters for the FEM analysis. The results from the two methods were compared with each other. This comparison suggests that a more reliable and safe design could be achieved by using a combination of empirical, analytical and numerical approaches.     

Rock Cavern Stability Analysis Under Different Hydro-Geological Conditions Using the Coupled Hydro-Mechanical Model

Rock cavern stability has a close relationship with the uncertain geological parameters, such as the in situ stress, the joint configurations, and the joint mechanical properties. Therefore, the stability of the rock cavern should be studied with variable geological conditions. In this paper, the coupled hydro-mechanical model, which is under the framework of the discontinuous deformation analysis, is developed to study the underground cavern stability when considering the hydraulic pressure after excavation. Variable geological conditions are taken into account to study their impacts on the seepage rate and the cavern stability, including the in situ stress ratio, joint spacing, and joint dip angle. In addition, the two cases with static hydraulic pressure and without hydraulic pressure are also considered for the comparison. The numerical simulations demonstrate that the coupled approach can capture the cavern behavior better than the other two approaches without the coupling effects.     

Incorporating Parameter Variability in Rock Mechanics Analyses: Fuzzy Mathematics Applied to Underground Rock Spalling

Although fuzzy analysis has been widely developed, its use in rock mechanics and rock engineering is limited. Here, it has been used to evaluate the potential for underground rock spalling at the boundary of a circular excavation in terms of rock strength and in situ rock stress, given the uncertainty in both of these input parameters. Using standard techniques from fuzzy mathematics, we develop an expression for the fuzzy factor of safety, and extend this to form the crisp parameters Safety Certainty Value and its complement, the Failure Certainty Value. Plots of the Failure Certainty Value in terms of the in situ stress ratio and rock strength/stress ratio show the effect of uncertainty on the assessment of stability. From these plots, we illustrate how the relative importance of uncertainty in the input parameters can be assessed, with the associated ramifications for site investigation and subsequent engineering design.     

Rock mass classification and assessment of stability of critical slopes on national highway-22 in Himachal Pradesh

Rock slopes require geo-engineering evaluation to assess the instability of critical slopes leading to landslides particularly in Himalayan terrain where rocks are highly jointed, fractured and weathering prone. Interplay of discontinuities in the rocks coupled with other parameters is one of the prime causes of failure of slopes. Engineering rock mass classification, such as, rock mass rating (RMR) and slope mass rating (SMR) along with geological strength index (GSI) have widely been used for stability assessment of rock slopes above tunnel portals, and these classifications are employed here for assessment of stability of slopes of critical nature along Rampur-Powari highway in Himachal Pradesh. In the present study, out of 154 numbers of slopes, a total of 29 have been selected for assessment of their criticality by employing RMR, SMR and GSI.     

Risk analysis of fractured rock mass underground structures

Recent accidents in underground structures have raised the risk awareness of the geotechnical engineering community. Geotechnical design is subject to significant uncertainties in load and strength parameters as well as in engineering models. However, engineering models which objectively address such uncertainties in design are still scarce. This paper presents an objective framework for the quantification of the risks involved in underground structures excavated in fractured rock masses, where structural failures may occur due to block falls. The framework considers the structure as a distributed system, where falling block probabilities are integrated over the main structural dimension. Random block size and geometry, arising from random joint orientation, are taken into account, as well as uncertainties in joint strength and geometrical parameters. A cost function is used to quantify failure consequences in terms of the block size. The framework is demonstrated in an application to a case study involving a real structure: the Paulo Afonso IV power station cavern. Results of the case study show that the studied cavern presents high reliability and very low risk. The framework proposed herein is shown to be a practical tool for the risk evaluation of underground structures constructed in rock masses, such as caverns and tunnels.     

Application of Fuzzy Set Theory to Rock Engineering Classification Systems: An Illustration of the Rock Mass Excavability Index

The characterization of rock masses is one of the integral aspects of rock engineering. Over the years, many classification systems have been developed for characterization and design purposes in mining and civil engineering practices. However, the strength and weak points of such rating-based classifications have always been questionable. Such classification systems assign quantifiable values to predefined classified geotechnical parameters of rock mass. This results in subjective uncertainties, leading to the misuse of such classifications in practical applications. Fuzzy set theory is an effective tool to overcome such uncertainties by using membership functions and an inference system. This study illustrates the potential application of fuzzy set theory in assisting engineers in the rock engineering decision processes for which subjectivity plays an important role. So, the basic principles of fuzzy set theory are described and then it was applied to rock mass excavability (RME) classification to verify the applicability of fuzzy rock engineering classifications. It was concluded that fuzzy set theory has an acceptable reliability to be employed for all rock engineering classification systems.     

基于GSI值量化和修正方法的岩体力学参数确定

为了准确确定岩体力学参数,通过综合分析多种地质强度指标(GSI)量化方法,提出了一种改进的GSI值量化和修正方法。首先,利用测线法估算结构面平均间距(d)和岩体块度指数(RBI)的改进型岩体块度率(RBR),根据岩体三维结构面网络,获得岩体体积节理数(Jv)和岩体结构等级(SR),然后采用上述参数和结构表面条件(SCR)及结构表面特性参数(Jc)进行了GSI值的定量化处理。为了克服GSI体系的缺点,考虑结构面产状和地下水对岩体力学性质的影响,提出了GSI值的修正方法和公式。以某铅锌矿体的矿岩体为例,根据改进的GSI值量化和修正方法及Hoek-Brown强度准则来确定矿岩体力学参数,通过与原位变形试验的对比分析,验证了该方法的精确性和可行性。该方法为从室内岩石力学试验合理地获取节理岩体力学参数提供了理论及实现的依据。     

Estimation of Block Sizes for Rock Masses with Non-persistent Joints

Summary  Discontinuities or joints in the rock mass have various shapes and sizes. Along with the joint orientation and spacing, the joint persistence, or the relative size of the joint, is one of the most important factors in determining the block sizes of jointed rock masses. Although the importance of joint persistence on the overall rock mass strength has long been identified, the impact of persistence on rock strength is in most current rock mass classification systems underrepresented. If joints are assumed to be persistent, as is the case in most designs, the sizes of the rock blocks tend to be underestimated. This can lead to more removable blocks than actually exist in-situ. In addition, a poor understanding of the rock bridge strength may lead to lower rock mass strengths, and consequently, to excessive expenditure on rock support. In this study, we suggest and verify a method for the determination of the block sizes considering joint persistence. The idea emerges from a quantitative approach to apply the GSI system for rock mass classification, in which the accurate block size is required. There is a need to statistically analyze how the distribution of rock bridges according to the combination of joint orientation, spacing, and persistence will affect the actual size of each individual block. For this purpose, we generate various combinations of joints with different geometric conditions by the orthogonal arrays using the distinct element analysis tools of UDEC and 3DEC. Equivalent block sizes (areas in 2D and volumes in 3D) and their distributions are obtained from the numerical simulation. Correlation analysis is then performed to relate the block sizes predicted by the empirical equation to those obtained from the numerical model simulation. The results support the concept of equivalent block size proposed by Cai et al. (2004, Int. J. Rock Mech. Min. Sci., 41(1), 3–19).     

An empirical method for design of grouted bolts in rock tunnels based on the Geological Strength Index (GSI)

The procedure presented in this paper has been developed for the design of grouted rock bolts in rock tunnels during preliminary design stage. The proposed approach provides a step-by-step procedure to set up a series of practical guidelines for optimum pattern of rock bolting in a variety of rock mass qualities. For this purpose, a new formula for the estimation of the rock load (support pressure) is recommended. Due to its wide-spread acceptance in the field of rock engineering, the Geological Strength Index (GSI) is adopted in support pressure equation. For poor and very poor rock mass where the GSI < 27, the use of Modified-GSI is, instead, recommended. The supporting action is assumed to be provided by rock bolts carrying a total load defined by the rock load height. The mechanism of bolting is assumed to rely on roof arch forming and suspension principle. Integrated with support pressure function, the bolt density parameter is modified in order to provide an optimized bolt pattern for any shape of tunnel. The modified bolt density can also be used in analysis of a reinforced tunnel in terms of Ground Reaction Curve (GRC) in such a way as to evaluate the reinforced rock mass and the tunnel convergence. By doing so, the effectiveness of the bolting pattern is well evaluated. The proposed approach based on GSI is believed to overcome constrains and limitations of existing empirical bolt design methods based on RMR or Q-system, which are doubtful in poor rock mass usage. The applicability of the proposed method is illustrated by the stability analysis and bolt design of a rail-road tunnel in Turkey.     

基于Hoek-Brown强度准则的应变软化模型在隧道工程中的应用

基于Hoek-Brown强度准则及量化GSI围岩评级系统,分析岩体强度弱化行为,总结出确定岩体峰值及峰后强度参数的方法,提出应变软化模型的简化计算方法,并以FLAC3D数值模拟软件为工具,采用收敛-约束法对深埋大断面隧道支护结构及围岩稳定性进行分析,计算出支护结构安全系数。通过分析得出：随着围岩应力释放,岩体软化参数随之减小,岩体强度弱化行为突出;高地质强度GSI指标（GSI=75）的岩体虽然强度弱化程度较大,但围岩的变形量仍然较小,而低GSI指标（GSI=25）的岩体表现出了理想弹塑性行为;提出的简化Hoek-Brown应变软化模型适合应用于隧道中岩质相近区段围岩的研究;采用收敛-约束法对隧道支护结构的稳定性进行分析,可为隧道工程的初期支护优化设计及安全性评价提供参考。     

Mechanical Tests on Pervasively Jointed Rock Material: Insight into Rock Mass Behaviour

Summary In the exploration phase for the design of an underground cavern in a limestone formation a large number of triaxial compression tests were carried out on laboratory specimens which were characterized by a variable degree of fracturing. The data were analyzed to investigate the influence of fracture intensity and of confining stress on the mechanical parameters. In particular, investigations focused on the relationships between the parameters of the strength criteria, respectively in residual and peak conditions, on the decay of the Young modulus with stress level in the prepeak phase of the test, and on the brittleness of the rock in the postpeak phase. The tested rock can be considered as a small-scale model of a jointed rock mass, and the laboratory data therefore provide useful insight into the mechanical behaviour of rock masses, especially the relationships between residual and peak strength parameters, which are required in many analytical models and in numerical codes for the analysis of underground excavations.     

Preliminary support design for Ankara subway extension tunnel

This paper presents the results of preliminary support design of the subway tunnel for Ankara subway project in accordance with some empirical and numerical methods, using the phase 2D finite element method (FEM). The 5 m diameter subway tunnel will advance through slightly to moderately weathered dacite and weak zones. Rock masses were characterized in terms of rock mass rating (RMR), geological strength index (GSI) and Q System. Core samples were tested in the rock mechanics laboratory to determine uniaxial compressive strength, deformability parameters, unit weight, tensile strength and triaxial compressive strength properties. Finally, rock mass strengths were determined by empirical and numerical methods. Required support system was suggested.     

A Methodology for Reliability-Based Design of Rock Slopes

Summary A reliability-based methodology for the design of rock slopes, that can easily be implemented by the practicing engineers is proposed. The advanced first-order second-moment (AFOSM) method is adopted as the reliability assessment model and its application is illustrated for the case of plane failure. A model is developed within the framework of first-order second-moment approach to analyze the uncertainties underlying the in situ shear strength properties of rock discontinuities. Here, particular emphasis is given on the assessment of uncertainties related to the shear characteristics of clean, unfilled rock discontinuities under low normal stress levels. An extensive literature survey on the shear characteristics of discontinuities is carried out in order to collect data for the quantification of uncertainties. The data extracted from this literature survey are classified and reprocessed so that they can be utilized in the uncertainty analysis model. A user friendly software called ROCKREL is developed to carry out the numerical computations and to make the proposed design format more practical. Received April 16, 2001; accepted June 10, 2002; Published online November 19, 2002 Authors' address: Prof. Celal Karpuz, Middle East Technical University, Faculty of Engineering, Department of Mining Engineering, 06531 Ankara, Turkey; e-mail: karpuz @metu.edu.tr     

围岩质量分级的模糊综合评判研究

岩体本身具有许多不确定性和随机性,围岩质量分级取决于许多因素。选择岩石单轴饱和抗压强度Re、岩体完整程度（RQD）、平均节理裂隙间距d、不连续面状态系数f、结构面方位φ以及地下水状态w六个指标,采用模糊数学方法,引入模糊数学隶属函数的概念,建立边坡岩体质量综合评判模型,并将其应用于黄河上游某电站引水隧洞围岩岩体质量评价。评判结果显示,该模型使用模糊综合评价的评价结果与现场定性判断及报告中RMR分类结果基本一致。