On the use of the RMR system for estimation of rock mass deformation modulus

Estimation of rock mass deformation modulus is the subject of many studies in rock engineering research work. Although numerous predictive models have been developed for the estimation of the deformation modulus, they cannot be generalized for other sites because of inadequate accuracy. Furthermore, it is very valuable that the predictive models involve some accessible input parameters. The rock mass rating (RMR) is a well-known geomechanical parameter, which is usually determined to describe the quality of rock mass in rock engineering projects. In this study, five parameter ratings of the RMR classification system are used to predict the deformation modulus of rock mass in the abutment of the Gotvand earth dam. Statistical analysis and an artificial neural network are employed to present two new predictive models. Finally, probabilistic analysis is used to predict the rock mass deformation modulus, which overcomes the low accuracy caused by the inherent uncertainty in prediction. The results indicated that the parameter ratings used in the RMR classification system can predict the rock mass deformation modulus with a satisfactory correlation. However, the parameters don’t have the same influence on the rock mass deformability with the joint condition and the groundwater as the major and minor influencing parameters, respectively.     

Determination of rock mass modulus of deformation by hammer seismograph

Bulletin of Engineering Geology and the Environment - Rock mass modulus of deformation is one of the most important input parameters in element calculations for rock mass stability. It can be...     

Estimation of limestone rock mass deformation modulus using empirical equations

Determining the geomechanical parameters of rock masses at dam sites is a very important task. Different methods of determining these parameters have been proposed, depending on various factors such as the study phase, facilities, budget, and the time available. The deformation modulus is an important input parameter in any analysis of rock mass behavior. In the present study, the deformation modulus of the rock mass at the site of the Khersan II double-arch concrete dam was investigated using different field and experimental methods. The Khersan II Dam is located in the southwest of Lordegan, Chaharmahal Bakhtiary Province, Iran. The predominant formation at the site of the dam is the Upper Asmari limestone. The results of in situ tests such as plate load tests (PLTs) were analyzed to determine the deformation modulus, using the ASTM standard, Unal, and ISRM methods. These results were then compared to one another and interpreted. After that, engineering classification parameters such as RMR, GSI, and Q were evaluated at the same site that the PLTs were performed. Finally, the correlations between these classification ratings and the in situ deformation modulus of the rock mass were assessed, and some formulae for determining the deformation modulus of the rock mass at the Khersan II Dam site were derived. The accuracy and credibility of every formula was evaluated. These formulae for estimating the deformation modulus of the rock mass at the Khersan II Dam site were found to be highly accurate compared to other similar formulae.     

Estimation of rock mass deformation modulus using variations in transmissivity and RQD with depth

Discontinuity normal stiffness and deformation modulus of large scale rock masses are very difficult to determine. A method for estimation of discontinuity normal stiffness based on the decrease in transmissivity with depth has been proposed by the authors in a former paper. In the current study, the method is further developed by accounting for the changes in both discontinuity aperture and frequency with depth, which are key factors that cause the transmissivity to decrease with depth. The discontinuity frequency can be estimated from RQD measurements, which are readily available in most geotechnical investigations. The transmissivity data from packer tests are usually available in geotechnical investigations for hydropower plants. For a rock mass in a dam site mainly controlled by lithostatic stress, based on transmissivity and RQD data at different depths, the change in discontinuity aperture with depth can be linked to the change in aperture with stress, which defines the normal stiffness of discontinuities. In the case study, the discontinuity normal stiffness is successfully estimated by using transmissivity and RQD data, and the result shows that the normal stiffness increases with stress (depth) and the rate of normal stiffness versus stress (depth) decreases with stress (depth), which is consistent with experimental studies. The estimated normal stiffness has been utilized to calculate the rock mass deformation modulus using an equivalent model. The result of deformation modulus by the proposed method is close to that obtained by using in situ measurements, as well as by using empirical models relating RQD to deformation modulus.     

A new approach for estimation of the rock mass deformation modulus: a rock engineering systems-based model

Bulletin of Engineering Geology and the Environment - The deformation modulus of a rock mass is one of the crucial parameters used in the design of surface and underground rock engineering...     

Empirical estimation of rock mass modulus

The deformation modulus of a rock mass is an important input parameter in any analysis of rock mass behaviour that includes deformations. Field tests to determine this parameter directly are time consuming, expensive and the reliability of the results of these tests is sometimes questionable. Consequently, several authors have proposed empirical relationships for estimating the value of rock mass deformation modulus on the basis of classification schemes. These relationships are reviewed and their limitations are discussed. Based on data from a large number of in situ measurements from China and Taiwan a new relationship, based upon a sigmoid function, is proposed. The properties of the intact rock as well as the effects of disturbance due to blast damage and/or stress relaxation are also included in this new relationship.     

Genetic programming approach for estimating the deformation modulus of rock mass using sensitivity analysis by neural network

We use genetic programming (GP) to determine the deformation modulus of rock masses. A database of 150 data sets, including modulus of elasticity of intact rock (Ei), uniaxial compressive strength (UCS), rock mass quality designation (RQD), the number of joint per meter (J/m), porosity, and dry density for possible input parameters, and the modulus deformation of the rock mass determined by a plate loading test for output, was established. The values of geological strength index (GSI) system were also determined for all sites and considered as another input parameter. Sensitivity analyses are considered to find out the important parameters for predicting of the deformation modulus of rock mass. Two approaches of sensitivity analyses, based on “statistical analysis of RSE values” and “sensitivity analysis about the mean”, are performed. Evolution of the sensitivity analyses results establish the fact that variable of UCS, GSI, and RQD play more prominent roles for predicting modulus of the rock mass, and so those are considered as the predictors to design the GP model. Finally, two equations were achieved by GP. The statistical measures of root mean square error (RMSE) and variance account for (VAF) have been used to compare GP models with the well-known existing empirical equations proposed for predicting the deformation modulus. These performance criteria proved that the GP models give higher predictions over existing empirical models.     

Performance analysis of empirical models for predicting rock mass deformation modulus using regression and Bayesian methods

Deformation modulus of rock mass is one of the input parameters to most rock engineering designs and constructions. The field tests for determination of deformation modulus are cumbersome, expensive and time-consuming. This has prompted the development of various regression equations to estimate deformation modulus from results of rock mass classifications, with rock mass rating (RMR) being one of the frequently used classifications. The regression equations are of different types ranging from linear to nonlinear functions like power and exponential. Bayesian method has recently been developed to incorporate regression equations into a Bayesian framework to provide better estimates of geotechnical properties. The question of whether Bayesian method improves the estimation of geotechnical properties in all circumstances remains open. Therefore, a comparative study was conducted to assess the performances of regression and Bayesian methods when they are used to characterize deformation modulus from the same set of RMR data obtained from two project sites. The study also investigated the performance of different types of regression equations in estimation of the deformation modulus. Statistics, probability distributions and prediction indicators were used to assess the performances of regression and Bayesian methods and different types of regression equations. It was found that power and exponential types of regression equations provide a better estimate than linear regression equations. In addition, it was discovered that the ability of the Bayesian method to provide better estimates of deformation modulus than regression method depends on the quality and quantity of input data as well as the type of the regression equation.     

Estimation of deformation modulus of rock masses by using fuzzy clustering-based modeling

The paper describes a method which incorporates Takagi–Sugeno (TS) fuzzy modeling with two data clustering approaches including fuzzy-c-means (FCM) clustering and subtractive clustering to estimate the rock mass modulus of deformation. For this aim, a database including 120 cases collected from several galleries of dam sites locations was established. The information returned by fuzzy clustering was initially used to define the number of rules and antecedent membership functions and afterwards linear least squares estimation implemented to obtain fuzzy consequent parameters. An adaptive neuro-fuzzy inference system (ANFIS) was applied to modify the pre-determined TS clustering-based model structures to improve the generalization performance of those. For evaluation of the performance, root mean square error (RMSE) and variance account for (VAF) values have been utilized as performance criteria. It can be said, that ANFIS approach enhances the performances of fuzzy clustering-based models in predicting modulus of deformation of rock masses successfully.     

金安桥水电站岩体变形模量参数的分析研究

中国水能资源的丰富和开发程度较低的国情,决定了加快水电开发的迫切性。国内外一系列大中型水电工程的开发建设,存在的大量工程地质问题使人们逐渐认识到岩体力学参数选取的重要性。据有关资料显示,国际上大坝失事40%是由岩体力学参数选取不合理造成的,如法国的布泽(Bouzey)坝、美国的奥斯汀(Austin)坝等。结合金安桥水电站现场岩体变形模量及相关成果数据,与各种变形模量参数分析的方法,进行了变形模量与声波的关系研究,变形模量的经验估算法研究,变形模量的分形、分类研究。合理的变形模量参数的选取,是工程投资和安全风险博弈的岩体力学参数选取的重点。     

Correlations between rock mass intactness index (Kv) and other rock mass classification indices (RMR89 system and GSI)

Bulletin of Engineering Geology and the Environment - Rock mass integrity is related to rock mass quality and strength. It can be characterized by a single index, or a combination of multiple...     

岩体分级BQ与RMR的关系及其力学参数估计

在国标《工程岩体分级标准》（GB50218—94）岩体质量分级的基础上,提出了岩体基本质量指标BQ的简化计算方法。根据规范中建议的岩体物理力学参数取值范围,编制了各参数与BQ关系曲线图,通过非线性拟合分析,建立了各物理力学参数与BQ之间关系的经验公式。基于内摩擦角等效原则,通过比较已有的分别用RMR和BQ表达的岩体内摩擦角经验公式,推导出1个BQ和RMR之间的关系方程。同样基于变形模量等效原则,通过比较已有的分别用RMR和BQ表达的岩体变形模量经验公式,推导出4个BQ和RMR之间的关系方程。这5个关系方程与实测结果进行了比较分析,得到了上限线和下限线方程;由内摩擦角等效获得的关系方程趋势较好,取上限线和下限线的中间线对其进行修正,得到了本文建议的RMR和BQ之间的关系方程。     

基于UDEC下溶洞控制危岩体变形过程

利用UDEC分别对降雨前及降雨后的危岩体进行模拟,显示指出岩体沿溶洞节理方向发生变形;因陡倾裂隙与溶洞贯通,导致力学性能迅速降低,岩体沿着溶洞节理产生了下滑;在降雨条件下,危岩体将处于不稳定状态,沿软弱面发生剪切破坏。     

Comparison among different criteria of RMR and Q-system for rock mass classification for tunnelling in Korea

Recent increase in the number of tunneling projects in Korea resulted in a large amount of good quality data such as RMR and Q-value for the assessment of rock mass class. In addition, a new bidding system, so-called Turn-Key system, has also made the data quality better than ever before, due to the increase of the budget for site investigation. A conventional guideline for rock mass classification by KHC (Korea Highway Corporation) has been widely used in Korea but other forms of classification using different criteria of RMR or Q-value have been recently used. Since there have been few studies on the relationship among such different criteria on RMR or Q-value, this study mainly focuses on the comparison of the conventional guideline for rock mass classification with several individual classification schemes in Korea. Analysis of the coincidence among the different criteria using both RMR and Q-value showed that there is higher coincidence if rock mass is in relatively good condition. It was also found that there is less consistency between RMR criteria and Q-value criteria in conventional KHC Guideline for rock mass classification than the recently adopted individual criteria.     

Estimating the deformation modulus of rock masses: a comparative study

Although the modulus of deformation of rock masses has crucial importance for geotechnical projects, such as tunnels and dams, the determination of this parameter by in situ tests requires considerable costs and involves difficult operational processes. For this reason, empirical equations for the indirect estimation of the modulus of deformation are an interesting issue for rock engineers and engineering geologists. This study includes assessment of the prediction performances of some existing empirical equations, using in situ plate loading test data and rock mass properties, producing an empirical equation depending on the new data, construction of a fuzzy inference system for the estimation of modulus of deformation, and making a comparison between results obtained from the empirical equations and fuzzy inference system. A series of calculations and statistical analyses were undertaken. It is concluded that the performance of the empirical equations and fuzzy inference system obtained in this study is satisfactory. However, the prediction models developed in this study are limited by the number of the data used and the rock types employed. For these reasons, a cross-check should be performed before using these prediction models for design purposes.     

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.     

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。