Rock Mass Deformation Modulus Research Articles

Evaluating the deformation modulus at representative elementary volume using electrical resistivity tomography

The deformation modulus of rock mass is an essential parameter for evaluating the bearing capacity and deformations. A deformation modulus obtained through conventional approaches, including empirical equations and in situ tests, cannot present the deformation modulus at representative elementary volume (DREV) due to limited test coverage and technical difficulties in harsh geological or topographic conditions. This study utilized electrical resistivity (ER) tomography and numerical back-analysis to investigate DREV at the Asmari-Jahrum formation. We employed geoelectrical contrasts to detect proper locations for installing extensometers at excavated galleries. The deformations recorded by extensometer were used to back-calculate the DREV values by finite difference numerical modeling. We established a correlation between ER and DREV to predict DREV, which were 30–80 % more accurate than those obtained through conventional approaches at the study site. The tested area, anisotropy, creep, ER inaccuracies, and plastic deformations are evaluated as statistically significant factors that can influence DREV. Our methodology provides a systematical approach to assess DREV, which applies to geoengineering projects within the Asmari-Jahrum formation or similar sedimentary units (ER below 200 Ω⸱m). This methodology is also replicable for other geological formations with harsh geology or limited access without exposing an extreme financial burden or environmental issues.

New Method to Estimate Rock Mass Deformation Modulus Based on BQ System

The rock mass deformation modulus is one of the most important design parameters in a range of rock engineering applications. Its value is usually obtained directly through in situ testing or estimated indirectly on the basis of a rock mass quality classification system. Because in situ testing is generally costly, time-consuming, and presents operational difficulties, it cannot be carried out extensively, and many researchers have concentrated on developing indirect procedures to obtain information on the modulus of deformation, such as the RMR method, Q method, and GSI method. The purpose of this paper is to present a new system for estimating the rock mass deformation modulus called the BQ method, which is based on the BQ (basic quality) system. In this paper, the BQ system is first briefly reviewed, and then more than 60 in situ measurements from three large hydropower stations in China are used to develop a new relationship between BQ and the deformation modulus, based on a power function relationship. The paper also derives correlations based on the existing estimation formula and the relationship between BQ and other classification schemes, resulting in several recommended formulas for estimating the deformation modulus of a rock mass using the BQ method.

Probabilistic characterisation of rock mass deformation modulus from P-wave velocity based on information criteria

ABSTRACT Determination of rock mass deformation modulus (Erm ) is an important but very challenging task in rock mechanics and rock engineering. Direct measurements of Erm by in-situ tests are expensive, time-consuming, and sometimes even impossible. Since the nondestructive and easy geophysical method is commonly used to measure the P-wave velocity (Vp ) in the field, the study has developed an empirical correlation between Erm and Vp based on 834 collected datasets by considering both inherent and transformation uncertainties. The information criteria are employed to select the best model for deriving a general empirical correlation. The maximum likelihood estimation (MLE) method and computational intelligence techniques like particle swarm optimisation (PSO), artificial bee colony (ABC), and differential evolution (DE) algorithms are used to specify the incorporated parameters of each candidate model. Based on the derived general empirical equation, a Bayesian equivalent sample approach using Markov Chain Monte Carlo (MCMC) simulation is applied to conduct probabilistic characterisation of Erm by combining prior knowledge and project-specific observed Vp data. Comparative studies of the results from theory and in-situ measured Erm values suggest that the proposed method is effective and validate the applicability of the derived general empirical correlation.

Experimental and Numerical Investigations on the Effect of In Situ Stress and Discontinuities Orientation on the Deformation Modulus of Rock Masses

Experimental and Numerical Investigations on the Effect of In Situ Stress and Discontinuities Orientation on the Deformation Modulus of Rock Masses

Numerical analysis method of equivalent deformation parameters for grouted arch dam abutment fractured rock masses considering scale effects and anisotropy

Research on the equivalent deformation parameters of grouted arch dam abutment rock masses has recently emerged as a key in the design, construction and stability assessment of arch dams. With the aim of synthetically considering scale effects and anisotropy of the rock mass equivalent deformation parameters after grouting, in this paper, a practical numerical calculation method is developed. First, the Latin hypercube sampling method is introduced to generate a network of fractures of the arch dam abutment rock mass. Subsequently, the finite element models of the rock masses with different sizes in various directions are constructed. On this basis, equivalent continuum theory and cohesive element model are applied for numerical calculation of grouting fractured rock masses. Then, the scale effect and anisotropy of the deformation modulus of rock mass under different grouting conditions are investigated. Finally, the Jinping super-high arch dam is taken as an example to validate the theoretical significance and application effect of the proposed method. The analysis results indicate that the process of fracture and fragmentation of grouted rock masses is characterized precisely, and the deformation of material units can be described as fully as possible to calculate more realistic equivalent deformation parameters of the fractured rock masses.

Combination of Artificial Neural Networks and Numerical Modeling for Predicting Deformation Modulus of Rock Masses

Combination of Artificial Neural Networks and Numerical Modeling for Predicting Deformation Modulus of Rock Masses

Back-Analysis of Rock Mass Strength at a Radioactive Waste Disposal Site Using Acoustic Emission Monitoring Data and 3D Numerical Modelling

In this study, a new method was examined that used acoustic emission (AE) monitoring data, in combination with a primary Boundary Element stress analysis, to back-calculate rock mass strength. The presented AE data came from the National Radioactive Waste Repository (NRWR) for low- and intermediate-level waste (LLW/ILW). AE monitoring is able to detect the pre-peak, peak, and post-peak stress changes in rock mass. The presented method used AE monitoring data to back-calculate parameters, such as uniaxial compressive strength and the rock mass deformation modulus. The AE initiation threshold was used to develop an objective function that considered the stress in the rock mass and the rock mass strength. The findings of this research propose that most AE events can be related to the crack initiation threshold, and in space, most of them are located at points away from the excavated walls. In the vicinity of the excavation damage zones around the cavities, the stress conditions beyond the crack damage boundary of the rock mass occur in many areas, leading to significant irreversible deformations. This novel method was demonstrated to aid in the prediction of rock mass strength and is a valuable, non-invasive method for improving the spatial prediction of rock mass parameters, which will lead to safer underground storage facilities.

Machine learning models to predict the tunnel wall convergence

Deformation and damage of the rock mass induced by excavation operations can result in the tunnel wall convergence. Accurate prediction of the convergence is crucial for ensuring safe, economical, and efficient construction of tunnel projects. In this study, six popular and reliable machine learning (ML) models, including back-propagation neural network (BPNN), general regression neural network (GRNN), extreme learning machine (ELM), kernel extreme learning machine (KELM), least squares support vector machine (LSSVR) and random forest (RF) were selected to predict the tunnel wall convergence. The jellyfish search optimizer (JSO) was utilized to find the optimal hyperparameters of these models. A total of 142 sets of highway tunnel convergence data were collected for model training and testing, six parameters including overburden thickness (H), rock mass rating index (RMR), rock mass quality index (Q), rock mass cohesion (Crm), deformation modulus of rock mass (Erm), and internal friction angle of rock mass (φrm) were used as input variables and the mean convergence of tunnel wall (Y) was considered as the output variable. Mean absolute error (MAE), root mean squared error (RMSE), coefficient of determination (R2), and variance accounted for (VAF) as evaluation indicators were used to compare the predictive performance of the proposed models. The results from various evaluation methods demonstrate that the overall performance of the JSO-RF model is superior, with MAE, RMSE, R2, and VAF values of 4.288, 6.219, 0.917, and 89.480 during the training phase, and 3.141, 3.958, 0.939, and 93.164 during the testing phase. When compared with RF, multivariate regression (MVR), and empirical equations, the JSO-RF model also exhibits better predictive performance. The importance results of all input variables showed that φrm, Erm, and H were more important input variables than other variables.

An Appropriate Model for the Prediction of Rock Mass Deformation Modulus among Various Artificial Intelligence Models

The rock mass deformation modulus (Em) is an essential input parameter in numerical modeling for assessing the rock mass behavior required for the sustainable design of engineering structures. The in situ methods for determining this parameter are costly and time consuming. Their results may not be reliable due to the presence of various natures of joints and following difficult field testing procedures. Therefore, it is imperative to predict the rock mass deformation modulus using alternate methods. In this research, four different predictive models were developed, i.e., one statistical model (Muti Linear Regression (MLR)) and three Artificial Intelligence models (Artificial Neural Network (ANN), Random Forest Regression (RFR), and K-Neighbor Network (KNN)) by employing Rock Mass Rating (RMR89) and Point load index (I50) as appropriate input variables selected through correlation matrix analysis among eight different variables to propose an appropriate model for the prediction of Em. The efficacy of each predictive model was evaluated by using four different performance indicators: performance coefficient R2, Mean Absolute Error (MAE), Mean Squared Error (MSE), and Median Absolute Error (MEAE). The results show that the R2, MAE, MSE, and MEAE for the ANN model are 0.999, 0.2343, 0.2873, and 0.0814, respectively, which are better than MLR, KNN, and RFR. Therefore, the ANN model is proposed as the most appropriate model for the prediction of Em. The findings of this research will provide a better understanding and foundation for the professionals working in fields during the prediction of various engineering parameters, especially Em for sustainable engineering design in the rock engineering field.

Estimation of rock mass deformability based on empirical relations for Ghezel Ozan dam site in the north of Iran

Rock mass deformability modulus is one of the most important parameters for underground structures and dam site design. The current methods for determining this parameter are in situ tests and empirical equations. In situ tests are the best and most accurate methods and include plate bearing, flat jack and dilatometer tests. However, these in situ tests are difficult, time-consuming, expensive and sometimes even impossible. Therefore, many empirical equations have been developed to determine the rock mass deformability indirectly based on various parameters. In this study, the correlation between the deformation modulus values, rock mass rating (RMR) and tunnelling quality index ( Q ) classification has been studied for the Ghezel Ozan dam site in NW Iran. Then, empirical equations are used to calculate the rock mass deformation modulus ( E m ) based on dilatometer in situ tests and rock mass classifications as mentioned above are defined. Finally, the correlation between the equations given in this study and the empirical equations presented by other researchers based on RMR and TQI ( Q ) are also investigated using statistical indicators. According to this analysis, the equation estimated based on RMR has a good compliance with the equations presented by earlier researchers. Supplementary material: Supplementary datasets and figures are available at https://doi.org/10.6084/m9.figshare.c.6139108

Assessment of rock mass quality and deformation modulus by empirical methods in Nepal Himalaya

Assessment of rock mass quality and deformation modulus by empirical methods in Nepal Himalaya

Empirical estimation of rock mass deformation modulus of rocks: comparison of intact rock properties and rock mass classifications as inputs

Deformation modulus of rock mass (Em) is an important parameter for the analysis and design of mining engineering projects. However, field tests for measuring deformation modulus of rock mass are difficult, time-consuming, and capital intensive. This has led to the development of numerous empirical models for estimating rock mass deformation modulus, which are in different forms and scattered in the literature. The numerous models available in the literature use different types of inputs. Therefore, this study provides a comprehensive compilation of different empirical models for estimating the deformation modulus of rock masses. The compiled models are grouped based on their type of input parameter(s) into three categories such as those using intact rock properties, rock mass classification indices, and combination of intact rock properties and rock mass classification indices. Then, a comparative analysis was performed using absolute average relative error percentage (AAREP) and variance accounted for (VAF) to assess the reliability of using different types of inputs for estimation of deformation modulus of rock masses using data from two sites. The results of the analyses show that rock mass classification indices are the most reliable indices for estimating the deformation modulus of rock masses among the categories considered for analyses. For AAREP analyses in the two illustrative examples considered in this study, models (7 out of 10) using rock mass classification indices in the estimation of Em have the best performances with AAREP values ranging from 24.07 to 55.15%. For VAF analyses in the two examples, models (8 out of 10) using rock mass classification indices in the estimation of Em have the best performances with values ranging from 59.81 to 88.11%. The lowest errors and highest deviation similarities from models using rock mass classification indices indicate that they produce the most reliable estimations of Em. It is important to note that the reliability of deformation modulus estimated from empirical models depends on the quality of input data as the models performed differently across the sites used in this study. This study therefore provides a compilation of available models for estimating deformation modulus, performance evaluation of available models for estimating deformation modulus, and guidelines for selecting appropriate model for estimating deformation modulus of rock mass.

Sandstone Slope Stability Analysis Under Wetting-Drying Cycles Based on Generalized Hoek-Brown Failure Criterion

The deterioration of rock strength due to cyclic fluctuations in the groundwater level in drawdown regions influences bank slope stability. Based on wetting–drying cycling and uniaxial compression tests of sandstone specimens, the intact rock strength deterioration characteristics were analyzed. Considering different types of rock mass discontinuities, the rock mass strength deterioration features were shown. The results of rock mass strength deterioration characteristics were then applied in sandstone slope stability analysis. Using the finite element method, the safety factors of the slope under different wetting–drying cycles were computed based on the generalized Hoek–Brown failure criterion. Meanwhile, statistical distribution features of strength parameters were considered, and safety factor distribution of studied slopes was obtained with Monte Carlo simulation. The results show that rock mass deformation modulus decreased during wetting–drying cycling. The mean safety factors of the slope with any type of discontinuities were reduced by wetting–drying cycling in probabilistic analyses. Wetting–drying cycling plays an important role in damaging slope stability at initial stages since the degree of rock mass strength deterioration is remarkable during initial wetting–drying cycles. However, the rock mass strength and safety factor of the slope are reduced gently after 10 wetting–drying cycles. This research presents the phases of the effect of wetting–drying cycles on sandstone slope stability in drawdown regions.

A new estimation method and an anisotropy index for the deformation modulus of jointed rock masses

The deformation modulus of a rock mass is an important parameter to describe its mechanical behavior. In this study, an analytical method is developed to determine the deformation modulus of jointed rock masses, which considers the mechanical properties of intact rocks and joints based on the superposition principle. Due to incorporating the variations in the orientations and sizes of joint sets, the proposed method is applicable to the rock mass with persistent and parallel joints as well as that with non-persistent and nonparallel joints. In addition, an anisotropy index AIdm for the deformation modulus is defined to quantitatively describe the anisotropy of rock masses. The range of AIdm is from 0 to 1, and the more anisotropic the rock mass is, the larger the value of AIdm will be. To evaluate the proposed method, 20 groups of numerical experiments are conducted with the universal distinct element code (UDEC). For each experimental group, the deformation modulus in 24 directions are obtained by UDEC (numerical value) and the proposed method (predicted value), and then the mean error rates are calculated. Note that the mean error rate is the mean value of the error rates of the deformation modulus in 24 directions, where for each direction, the error rate is equal to the ratio of numerical value minus predicted value to the numerical value. The results show that (i) for different experimental groups, the mean error rates vary between 5.06% and 22.03%; (ii) the error rates for the discrete fracture networks (DFNs) with two sets of joints are at the same level as those with one set of joints; and (iii) therefore, the proposed method for estimating the deformation modulus of jointed rock masses is valid.

Numerical modeling in determining deformation characteristics of fractured rock massifs

The article proposes a method for determining the deformation modulus of fractured-block rock masses, weakened by mutually-orthogonal systems of cracks within the linear section (after the closure of cracks) of the deformation curve σ= f (ε). The values of normal - kn and tangential - ks stiffness are used as elastic characteristics of joints. It is shown that in such rocky structures it is impossible to apply the laws of mechanics of a solid elastic body to calculate their deformation characteristics, since the opening of interblock joints is observed when performing numerical experiments. The discrepancy between the results of numerical and analytical calculations is up to 40%. For these purposes, it is proposed to use the regression equation obtained on the basis of regression analysis based on the results of numerical modeling and the method of experiment planning. The presented equation allows, depending on three independent factors: the modulus of elasticity of the rock block - Eo, the rock quality designation index - RQD and the dip angles of systems of mutually orthogonal ioints – α, to determine the modulus of deformation ofthe rock mass.

Artificial neural networks to predict deformation modulus of rock masses considering overburden stress

ABSTRACT The effect of overburden stress on the rock mass deformation modulus is a known issue. However, the effect of overburden stress has been studied less with empirical methods due to the lack of appropriate data. In this study, it is aimed to investigate the effect of overburden stress on rock mass deformation modulus using artificial neural network (ANN). Four ANN models have been developed in accordance with the purpose of the study. Two of these models do not contain the overburden stress parameter, but the other two models contain the overburden stress parameter. The prediction performance of the models containing the overburden stress parameter was obtained drastically higher than the others. In other words, the value account for (VAF) and root-mean-square error (RMSE) indices of the model having the inputs of rock mass rating (RMR) and elasticity modulus of intact rock (Ei) are 73.3% and 462, respectively, while those of the model having the inputs of RMR, Ei and overburden stress are 90% and 265. The other models developed in the present study yielded similar results. Consequently, with the ANN models developed in this study, the effect of overburden stress on Em is revealed, clearly.

Applying optimized relevance vector regression approach for indirect forecasting rock mass deformation modulus

Applying optimized relevance vector regression approach for indirect forecasting rock mass deformation modulus

Upscaling of fractured rock mass properties – An example comparing Discrete Fracture Network (DFN) modeling and empirical relations based on engineering rock mass classifications

In this study a comparison of Discrete Fracture Network (DFN) modeling and empirical relationships based on conventional engineering rock mass classifications is carried out in order to determine the elastic properties of fractured rock masses. Uncertainties are considered by a stochastic description of the fracture network geometry and a probabilistic approach, utilizing Monte Carlo simulation techniques, for the various other input parameters. The proposed workflow is applied to two sandstone outcrops. Geometric information on the fracture systems is obtained from terrestrial laser scanning providing the input parameters (orientation, size and intensity) for each fracture set including probability density functions required for DFN modeling. After adding the mechanical properties of intact rock and fractures obtained by laboratory tests, the DFN approach allows to calculate values for rock mass deformation modulus and Poisson's ratio assuming either isotropy or vertical-transverse isotropy. These estimates are compared to values derived from empirical relationships based on engineering rock mass classifications. The comparison of the two approaches and, in particular, of the different empirical relationships reveals a significant scatter in the estimated rock mass properties. Only those empirical equations which incorporate intact rock properties in addition to the classification score yield plausible results, i.e., a pronounced weakening due to the fractures, and are in agreement with the estimates of the DFN approach. The additional effort of generating a DFN model shows its benefits if an anisotropic rock mass and/or spatially varying properties have to be considered, thus, providing a comprehensive hydromechanical characterization of anisotropic fractured rock masses.

Rock mass deformation modulus estimation models based on in situ tests

Rock mass deformation modulus estimation models based on in situ tests

A generalized Bayesian approach for prediction of strength and elastic properties of rock

Rock mass elastic and strength properties are needed for calculation of deformation and determination of stability of underground structures. Most available models for prediction of rock mass properties are site-specific, are deterministic, and cannot properly propagate uncertainty in reliability analysis of underground structures. A generalized Bayesian approach is used to develop probabilistic predictive models for the rock mass properties. A set of training and testing databases for rock mass deformation modulus, unconfined compressive strength, and Poisson's ratio based on point load strength index, water content, and geological strength index are also developed. Evaluation of the existing models using our databases show rather large mean absolute percentage errors. Our models, calibrated using training databases, (i) are probabilistic and include model parameter statistics needed for uncertainty propagation in reliability analysis, (ii) are rock-specific, (iii) show smaller prediction errors compared to existing models, and (iv) can be updated as new information become available.