Rock Mass Deformation Modulus Research Articles

Regression analysis between rock moduli: case studies from the Deriner/Artvin and Ermenek/Karaman dams

Rock mass elasticity modulus, rock mass deformation modulus, static elasticity modulus, and dynamic elasticity modulus are the geotechnical properties of a rock mass and intact rock. However, these moduli are confused with each other in the literature. These moduli are determined using different test techniques. These values are different values and should not be used interchangeably. The main purpose of this paper is to illustrate the differences and build a statistical relationship between these rock moduli. The moduli determined in Deriner/Artvin and Ermenek/Karaman dam investigation studies were used and compared in this study. The rock mass elasticity modulus (ED) from the dilatometer test, rock mass deformation modulus (DD) from the dilatometer test, rock mass elasticity modulus (EH) from the plate-loading test, rock mass deformation modulus (DH) from the plate-loading test, intact rock static elasticity modulus (ELS) from laboratory tests, and intact rock dynamic elasticity modulus (ELD) from laboratory tests were correlated with regression analysis. Empirical equations obtained by the regression analysis performed between rock moduli revealed high correlation coefficients. The ratio of the modulus of deformation and modulus of elasticity determined from in situ test at the Deriner dam site was close to 1 at smaller modulus values but the ratio value was scattered at higher modulus values. The ratio of the laboratory determined dynamic elasticity modulus and static elasticity modulus approached 1 by decreasing weathering. Differences between moduli are demonstrated in this paper. The empirical equations proposed in this study were developed with a limited amount of data and every rock mass and intact rock sample have specific modulus values. The equations determined in this study should not be used for other projects or a cross check should be performed.

An Investigation of the Mechanisms Involved in Plate Load Testing in Rock

Accurate determination of rock mass deformation modulus is very important in rock engineering projects. The plate loading test (PLT) is a method that is generally used in dam construction projects to determine rock mass modulus. Numerical simulation was used to investigate the mechanisms involved in this test. The first objective of the paper was to employ 3D modeling in the interpretation of plate load tests conducted at the Bazoft dam site in Iran. Additionally, a parametric study of the effects of key parameters such as displacement measuring depth and loading plate diameter on the test results was another objective of the study. The moduli values determined numerically were compared against actual filed testing data determined from in-situ test data conducted at the Bazoft dam site, and the values determined from the ISRM suggested formula. The analysis showed that the optimum measurement depth for rock mass modulus calculation is approximately equal to the loading plate diameter and the data determined from measurement depths beyond one plate diameter can be unrealistic. Moreover, the plate diameter can have a significant effect on test results. As the measurement depth increases, the determined modulus values increase at a much more rapid pace when employing smaller size loading plates.

Influence of time-dependency on elastic rock properties under constant load and its effect on tunnel stability

In structures excavated in rock mass, load progressively increases to a level and remains constant during the construction. Rocks display different elastic properties such as Ei and v under different loading conditions and this requires to use the true values of elastic properties for the design of safe structures in rock. Also, rocks will undergo horizontal and vertical deformations depending on the amount of load applied. However, under constant loads, values of Ei and v will vary in time and induce variations in the behavior of the rock mass. In some empirical equations in which deformation modulus of the rock mass is taken into consideration, elastic parameters of intact rock become functions in the equation. Hence, the use of time dependent elastic properties determined under constant loading will yield more reliable results than when only constant elastic properties are used. As well known, rock material will play an important role in the deformation mechanism since the discontinuities will be closed due to the load. In this study, Ei and v values of intact rocks were investigated under different constant loads for certain rocks with high deformation capabilities. The results indicated significant time dependent variations in elastic properties under constant loading conditions. Ei value obtained from deformability test was found to be higher than the Ei value obtained from the constant loading test. This implies that when static values of elastic properties are used, the material is defined as more elastic than the rock material itself. In fact, Ei and v values embedded in empirical equations are not static. Hence, this workattempts to emerge a new understanding in designing of safer structures in rock mass by numerical methods. The use of time-dependent values of Ei and v under different constant loads will yield more accurate results in numerical modeling analysis.

Estimating the rock mass deformation modulus: A comparative study of empirical methods based on 48 rock mass scenarios

Abstract The rock mass deformation modulus, Erm, is an input parameter for most numerical modeling to verify the deformation behavior of rocks due to rock engineering activities within/on it. Among the most common methodologies used for estimating this parameter, empirical correlations based on rock mass classification schemes (e.g., RQD, RMR, GSI, and Q) stand out the most, principally because of their low cost when compared to the other methods. Herein, the main correlations used in practice are evaluated and comparted for 48 different rock quality scenarios, previously characterized and classified according to rock mass classification systems. The results obtained by each of the empirical correlations demonstrated that normalized correlations, that is, based on the ratio of the rock mass and intact rock modulus, Erm/Ei, underestimate the Erm values when compared to those results obtained from not-normalized correlations in the scenarios of better quality rock masses. For poor quality rock mass scenarios, both non-normalized and normalized correlation presented similar results. The correlations proposed by Hoek and Diederichs (2006) and Galera et al. (2007) estimated more central Erm values when compared to the other correlations, for all quality scenarios, while the Mitri et al. (1994) and Sonmez et al. (2006) methods estimated most high and low values of Erm, respectively.

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.

Determination of initial stress state and rock mass deformation modulus at Lavarak HEPP by back analysis using ant colony optimization and multivariable regression analysis

During the design and construction of a project, determination of geomechanical parameters is a key factor for its success. Back analysis is an appropriate method to reduce in situ and field measurements during site investigation and design phase of the projects. Over the past decades, displacement measurements were used as input data for back analysis of geomechanical parameters. In back analysis, an important factor is to choose an appropriate algorithm to minimize the magnitude of the error function in order to reduce the difference between measured and calculated displacements. In this paper, two methods, i.e. continuous ant colony algorithm (CACA) and multivariable regression (MR), were applied to calculate optimized values for four geomechanical parameters in “Lavarak” underground hydroelectric power plant cavern in Iran. These four parameters are maximum principal stress, minimum principal stress, the angle between maximum principal stress and the horizontal axis, and the deformation modulus of the rock mass. Initially, back analysis was conducted with CACA. For this purpose, CACA was programmed in Phase2 software used for numerical modelling to calculate the displacement of the measuring points. Then, back analysis of four parameters was done with both linear and nonlinear MR using Phase2, and the optimized values were calculated. According to the Lar Consulting Engineers’ data for Lavarak HEPP, the results show lower general error function values of CACA than MR. In other words, CACA algorithm shows better performance for obtaining optimal values and for having more accurate calculations. CACA shows better performance for back-calculation of the maximum principal stress, the angel of maximum principal stress, and the deformation modulus of the rock mass.

Estimation of REV for fractured rock masses based on Geological Strength Index

The representative elementary volume (REV) of fractured rock masses is a significant index to investigate the rock mass behaviors in the continuum mechanics. In this research, a new indicator to estimate the REV size of fractured rock masses based on the Geological Strength Index (GSI) is proposed. For this purpose, a new method that combines the PFC-based synthetic rock mass (SRM) model with the Hoek-Brown (HB) failure criterion is proposed to investigate the strength and deformation properties of fractured rock masses under biaxial stress conditions. Extensive numerical analyses are carried out to estimate variation of the uniaxial compression strength (UCS), deformation modulus (E) and GSI of the Brunswick mine rock mass with increasing the size of the SRM models up to a REV size. Results show that the GSI-based indicator gives relatively larger REV size compared with the traditional UCS or deformation modulus (E) based indicators. Compared with the traditional indicators, the proposed GSI-based indicator has merits of not only reflecting the geometrical characteristics of rock structures but also containing both geometrical and mechanical properties of discontinuities.

Parametric study of integrity on the mechanical properties of transversely isotropic rock mass using DEM

The evaluation of the mechanical properties of a transversely isotropic rock mass is a challenging task in practical engineering. This paper aims to study the relationships between the integrity parameters and mechanical properties of a transversely isotropic rock mass. The rock mass quality designation (RQD) is an important index and reference for rock mass quality evaluation that was introduced to establish the numerical models of a jointed rock mass with different integrities. The numerical models of a transversely isotropic rock mass were established using the bonded particle model (BPM) and smooth joint model (SJM) embedded into the Particle Flow Code software (PFC2D). After calibrating the microscopic parameters of the intact rock and structural planes, a series of compression tests of a transversely isotropic rock mass was carried out to determine compressive strength and deformation modulus, and main factors were considered including the RQD, inclined angle of structural planes, structural plane thickness, structural plane properties, intact rock properties, and confining pressure. The experimental results showed that the mechanical parameters and failure modes of a transversely isotropic rock mass were controlled by the integrity parameters. By comparing the value of σcm/σc (ratio of the compressive strength of rock mass to rock mass) and Em/Er (ratio of the deformation modulus of rock mass to rock mass) with field test results, the results obtained from the discrete element method were demonstrated to be reasonable.

Prediction of TBM jamming risk in squeezing grounds using Bayesian and artificial neural networks

This study presents an application of artificial neural network (ANN) and Bayesian network (BN) for evaluation of jamming risk of the shielded tunnel boring machines (TBMs) in adverse ground conditions such as squeezing grounds. The analysis is based on database of tunneling cases by numerical modeling to evaluate the ground convergence and possibility of machine entrapment. The results of initial numerical analysis were verified in comparison with some case studies. A dataset was established by performing additional numerical modeling of various scenarios based on variation of the most critical parameters affecting shield jamming. This includes compressive strength and deformation modulus of rock mass, tunnel radius, shield length, shield thickness, in situ stresses, depth of over-excavation, and skin friction between shield and rock. Using the dataset, an ANN was trained to predict the contact pressures from a series of ground properties and machine parameters. Furthermore, the continuous and discretized BNs were used to analyze the risk of shield jamming. The results of these two different BN methods are compared to the field observations and summarized in this paper. The developed risk models can estimate the required thrust force in both cases. The BN models can also be used in the cases with incomplete geological and geomechanical properties.

Load-displacement response of drilled shaft tip in soft rocks of sedimentary origin

A database of in situ drilled shaft and plate load tests in soft rock mass is developed. Analyses of the in situ load tests suggest that (i) the development of tip contact pressures is related to the rock mass shear strength, rock mass deformation modulus, and the vertical displacement of the drilled shaft tip, (ii) embedding the drilled shaft tip contributes to the development of punching shear failure mechanism in the underlying rock mass, however, the mobilized tip contact pressures do not significantly increase as the embedment depth increases unless the rock mass shear strength and deformational properties drastically increase with embedment depth, and (iii) the drilled shaft diameter does not significantly influence the development of the contact pressures, especially in large diameter drilled shafts. A framework for the analysis of the load-displacement response of the drilled shaft tip in soft rock mass is proposed using the in situ load tests. The proposed framework accounts for the observed nonlinear load-displacement response of soft rock mass and is a function of the initial normal stiffness and the initial yield pressure of the rock mass under the drilled shaft tip. Simple equations are developed for the initial normal stiffness and the initial yield pressure of soft sedimentary rocks. Additionally, in situ and laboratory test results are used to provide recommendations for the prediction of the parameters that are required in the proposed models for the initial normal stiffness and the initial yield pressure, namely the unconfined compressive strength and deformation modulus for the rock mass.

Development of an Intelligent and Statistical Model for Prediction of Rock Mass Deformation Modulus

The rock mass deformation modulus (Em) takes into account the plastic and the elastic deformation of the rock mass. It has been widely used for designing structures such as dams, tunnels, caverns, and mines, etc. Since the tests available for ascertaining Em are expensive and time consuming, several equations were suggested in the past. However, it has been found that the existing models are limited to specific type of rock mass rendering constraints for its application to general use. Therefore, to cater to this need a comprehensive data set of 147 series, comprising of elastic modulus of intact rock (Ei), rock mass rating (RMR) and Em have been collected from the literature covering various types of rocks from across the globe. This data set has been used in constructing a non- linear regression (NLR) based equation to render ease to the design engineers for calculating Em. In addition to it, an intelligent model is proposed having a basis on artificial neural network (ANN). The credibility of the empirical and intelligent model has been ascertained using the R2 and RMSE. Based on these performance evaluation indices, both models have been found to predict the Em with considerable accuracy vis-a-vis the existing models. Subsequently, a chart has been designed to ascertain Em using Ei and RMR for several classes of rock mass.

A load-transfer function for the side resistance of drilled shafts in soft rock

The shear stress and shear displacement relationship for the rock socket sidewalls is required for the calculation of the drilled shaft butt settlement under the service loads. This paper first introduces a comprehensive database of in situ axial load tests on drilled shafts, anchors and plugs that are embedded in different soft rock formations. The database includes measurements of (i) the initial shear stiffness, (ii) the peak shear stress and (iii) the post-peak reduction in shear stresses for the socket sidewalls. In addition to the load test results, information on soft rock mass mechanical properties and rock socket geometry is also included. It is found that (i) the initial shear stiffness is directly related to the deformation modulus of the soft rock mass and inversely proportional to the rock socket diameter and length, (ii) the mobilized peak shear stress is related to the drained friction angle of the rock mass and normal stress on the socket sidewalls at failure. The rock mass friction angle is related to the rock type and the geological strength index, and the normal stress at failure is directly related to deformation modulus of rock mass and inversely to the product of rock socket length and diameter, and (iii) the post-peak brittleness is related to the soft rock type and the post-peak shear displacement. An empirical framework for the prediction of the load-transfer function for side resistance of sockets in soft sedimentary and fine-grained rock is developed using the load test database introduced herein. The proposed framework accounts for the socket geometrical characteristics, and the rock mass engineering properties. The pre-peak range in the load-transfer function is modeled using a hyperbolic function, and the post-peak range is modeled using a brittleness index to account for the reduction in shear stresses with post-peak displacement.

Feasibility of Monte Carlo simulation for predicting deformation modulus of rock mass

Deformability of rock mass significantly influences its behavior and is, therefore, an important consideration for the design of underground structures. The deformation modulus of rock mass (Em) is directly measured from the time-consuming and expensive uniaxial jacking tests, whose results often have a large scatter. Hence, in this study, an attempt has been made to evaluate Em in different conditions using the Monte Carlo simulation (MCS). To achieve this aim, the most important parameters influencing Em were investigated. The parameters of rock mass rating (RMR), depth, uniaxial compressive strength of intact rock (UCS), and elastic modulus of intact rock (Ei) were selected as the model inputs. First, an equation was developed by the multiple non-linear regression (MNLR), and it was then used for evaluation and prediction of Em by the MCS technique. The results indicated that this approach is capable of simulating Em ranges with a good level of accuracy. The mean of the MCS-simulated values of Em was obtained as 15.13 GPa, while the measured values of Em had a mean equal to 14.54 GPa. Moreover, the results of a sensitivity analysis demonstrated that the deformation modulus of the intact rock (Ei), among the other parameters, is of the most influence on Em.

An empirical method for determining the mechanical properties of jointed rock mass using drilling energy

Characterization of jointed rock masses and evaluation of their mechanical properties are challenging tasks in rock engineering. This paper presents an experimental investigation of the response characteristics of drilling energy to the discontinuity of rock mass using a drilling method. The linear relationship between the drilling energy and discontinuity frequency is revealed, which only depends on the rock type, and is independent of calculation units. A new empirical method for determining the rock quality designation (RQD) versus the variation of drilling energy is proposed based on the discontinuity frequency. Comparison between the prediction and in situ investigation results demonstrates that the RQD can be estimated from this empirical method. The Em/Er (modulus ratio) and σcm/σc (strength ratio) versus RQD relations are modified for the determination of rock mass strength and deformation modulus in order to consider the continuous variation of Em/Er and σcm/σc with the model parameter η, which is related to the drilling energy and modulus of elasticity of intact rock and the variation of drilling energy for rock mass. The results show that the modified Em/Er (σcm/σc) versus RQD relations can give proper values compared with the field test results as well as compared with the various proposed relations from RMR, Q and GSI. The modified relations can provide a practical, fast and easy-to-use method for the estimated rock mass strength and deformation modulus, but they are only a first approximation.

Efficiency evaluation of empirical models on the basis of rock mass rating for prediction of deformation modulus in rock mass and developing a new models according to the fuzzy system

Summary Prediction of deformation modulus for rock mass in analysis and design of rock structures is very important. Because deformation modulus represents behavior of rock mass subjected to stresses. Up to now, various empirical models for prediction of deformation modulus have been developed. In this research, efficiency of different models for prediction of deformation modulus is evaluated. Then, according to the fuzzy model a sufficient model is developed and results are compared with the empirical models. Results indicated the efficiency of the new proposed model in comparison with the available models. Introduction Determining geo-mechanical parameters for analysis and design of rock structure is inevitable. Deformation modulus of rock mass is one of the most important geo-mechanical parameters. Estimation of deformation modulus for rock mass utilizing empirical models is widely used in civil and mining engineering projects. This is due to its less time requirement , cost and acceptable estimation. But there are differences between results of empirical model and real values of modulus which leads to uncertain decisions for designers in choosing appropriate model. Thus, it is important to investigate and evaluate the experimental models. Fuzzy model is one of the best models that is proposed for determining the deformation modulus in the present study. Methodology and Approaches For efficiency evaluation of 19 available models and also the proposed model, 33 data sets of different dam’s constructions in Iran is collected. Root Mean Squared Error , Mean Absolute Percentage Error and index of higher squared correlation coefficient are applied for evaluation of models’ performance. Results and Conclusions According to the performance indices, two models are selected from different empirical models that indicated the best predictions. In addition, results showed the efficiency of the proposed fuzzy model for prediction of deformation modulus.

Relation between crustal stress and thickness of earth's crust

Available models for estimation of crustal stress consider the vertical stress component as weight of above laying rocks, while horizontal stress components are estimated as function of vertical component. Herein, it is assumed that horizontal stress is effect of strain formed at seismogenic depth and transferred to shallower depth of rock mass. Strain rate is different depending on thickness of the crust and is different in different locations. Using available data regarding the measured maximum horizontal stress and depth of Moho discontinuity trend between these is obtained. Trend shows that maximum horizontal stress is decreasing with the thickness of the Earth’s crust and vice versa. Finally, expression that defines maximum horizontal stress from Moho depth and deformation modulus of rock mass is provided.

Applying evolutionary optimization algorithms for improving fuzzy C-mean clustering performance to predict the deformation modulus of rock mass

This paper focuses on the capability of the evolutionary computation methods namely, genetic algorithm (GA) and particle swarm optimization (PSO) in design and optimizing the fuzzy c-means clustering (FCM) structure and their applications to predict the deformation modulus of rock masses. Accordingly, evolutionary algorithms are used to tune the pre-determined FCM clustering-based model to make better the accuracy of modulus estimation. A new empirical equation with the aid of multiple regression analysis is also suggested and on the basis of it a prediction chart is presented for determination of the rock mass deformation modulus. Finally, a comprehensive credibility assessment of the prediction performances of some existing empirical equations is done and the results are compared with that obtained by the evolutionary algorithms based FCM clustering models. It is concluded that the new proposed approaches provide more accurate results compared with the existing empirical equations.

Estimation of rock mass deformation modulus using indirect information from multiple sources

Deformation modulus (Em) of rock masses is an important design parameter in many rock engineering projects such as tunnels excavation, slopes, and foundations. As direct (field) measurements of Em are time consuming and sometimes impossible to perform, data of Em is often limited or not available in many rock engineering projects. When there is limited or non-availability of Em data from rock engineering projects, various indirect information from multiple sources (e.g., different rock mass classifications) often available during preliminary stages of rock engineering projects can be combined to estimate Em. How to combine various information from multiple sources to estimate values of Em remains a difficult task. This study aims to address this challenge by developing a Bayesian sequential updating approach, which uses information from multiple sources to estimate Em. The proposed approach is formulated to combine information from tunneling quality index (Q) and rock mass rating (RMR) obtained during rock mass classifications to estimate Em, in terms of its statistics and probability distribution. The proposed approach is illustrated using real Q and RMR data as inputs, and it is shown to satisfactorily estimate Em values. The approach can also be used in big data analytics, by using multiple sources of information to uncover patterns and trends of rock properties and other useful information, especially during investigation into rock engineering projects such as underground excavations.

Estimating the Rock Mass Properties of Ultramafic Rocks in Central Greece Using the Triaxial Tests of Intact Rock and the Geological Strength Index

Due to the fact that the estimation of the rock mass properties is very important in any geotechnical project, many studies have become with the aim of their determination. But, the immediate determination is very difficult because the in situ tests are time-consuming, expensive and sometimes unreliable. For this reason, many researches have attempted to calculate the rock mass characteristic through empirical equations, but only few have focused on the ultramafic rocks. The main purpose of this study is to estimate the engineering properties of the ultramafic rock masses through the uniaxial compressive strength of the intact rock, the influence of blast damage, the material constant and the Geological Strength Index with the use of Hoek and Brown criterion (Roclab Software). Thus, sixteen samples, taken from central Greece (the western part of Othrys mt and the Kallidromo mt), were tested (uniaxial compressive strength and triaxial tests) and the results were statistically described and analysed. The manuscript reveals strong positive linear correlation between the estimated (through the Hoek and Brown failure criterion) uniaxial compressive strength and the measured (determined by strength tests) uniaxial compressive strength. The values of the uniaxial rock mass compressive strength, the global rock mass compressive strength, the rock mass tensile strength, and the rock mass modulus of deformation are finally calculated and presented. Furthermore, an attempt to correlate the rock mass deformation modulus (Erm) with the tangent young modulus (Ei) results that there is high correlation between them both for peridotites and serpentinites.

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 (Vb), and joint conditions (Jc). 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.