Compressive Strength Of Intact Rock Research Articles

Reliability of Monte Carlo simulation approach for estimating uniaxial compressive strength of intact rock

The strength of rock has significant influence on its performance, and is, therefore, a key input during modelling and analysis of mining and geotechnical engineering structures. The uniaxial compressive strength (UCS), which is a popular parameter to quantifying rock strength can be determined in the laboratory using suggested method by International Society of Rock Mechanics (ISRM). However, the laboratory determination of UCS consumes time, it is costly, and sometimes may not be feasible to perform because of different conditions of rock. Hence, this study attempts to employ Monte Carlo simulation (MCS) approach to estimate UCS, and to overcome various uncertainties associated with UCS estimation. To use MCS approach for UCS estimation, block punch index (BPI), Brazilian tensile strength (BTS), point load index (IS(50)), and P-wave velocity (Vp) were selected as the model inputs. A multiple linear regression (MLR) equation was developed and used to predict UCS by the MCS approach. The methodology was applied to estimate UCS using real BPI, BTS, Is(50), and Vp data as inputs. The proposed approach simulated UCS values that are consistent with UCS values measured in the laboratory. The mean of the UCS values simulated through the MCS approach is 119.10 MPa, while the mean of the UCS values measured in the laboratory is 118.42 MPa. In addition, hypothesis testing revealed that the Brazilian tensile strength (BTS) is the parameter with the most influence on UCS of rock for the site investigated.

Evaluation on the Squeezing and Design of Support system in Headrace Tunnel of Middle Modi Hydroelectic Project

Tunneling through a weak rock possess a great challenge. These challenges depends upon type of rock, excavation method, stress and deformation behavior of the rock etc. Squeezing is one of the major problem which is likely to occur during excavation of tunnel through weak rock. A reliable prediction of the extent of squeezing is essential so that a strategy can be established regarding stabilizing measures and for optimizing the support well in advance. In this paper, Middle Modi Hydroelectric Project located in the Kaski District has been taken as the case study. In this project, huge squeezing problem occurred at about chainage 1+140m At this section deformation has been recorded well over 65cm Hence, this paper basically deals with squeezing analysis using different approaches. Rock types along the headrace tunnel alignment are sheared phyllite and fractured quartzite. Mostly, intercalation of phyllite and quartzite has been found in the squeezed section Rockmass quality found in the squeezed section is extremely poor to exceptionally poor. Four main methods have been used to evaluate the squeezing phenomenon viz empirical methods such as Singh (1992) and Goel (2000), semi-empirical such as Hoek and Marinos (2000), analytical method such as (Convergence Confinement Method, 2000) and mumerical program Phase2. The main factors that control the squeezing phenomenon are the rock mass parameters and rock stresses. The uniaxial unconfined compressive strength of intact rock has been back calculated from measured deformations using phase2 program and found to be in the range of 10 to 15Mpa in the squeezed section Deformation was calculated using CCM and Compared with phase2 result. Due to excessive deformation temporary supports were provided at several locations, steel ribs are buckled and shotcrete lining is also cracked. All these have to be removed before application of final lining Finally two different approaches have been studied using phase program to address the existing problems in squeezed section of headrace tunnel ie. design of support system considering either circular shape with final lining (shotcrete and steel rib) or reshaping existing D-shaped tunnel into horseshoe shaped and providing final concrete lining.

Study on the evolution and prediction of fracture depth of surrounding rock in deep mining roadway based on numerical analysis and borehole detection

The failure of surrounding rock in deep hard rock roadway is closely related to mining disturbance. In this study, the 13# stope ramp of −767 m level (at a buried depth of 1,197 m) at Hongtoushan copper mine was taken as the engineering background, a comprehensive analysis method of numerical analysis and borehole detection was put forward, and the evolution law of fracture depth of the ramp surrounding rock under the mining influence was obtained. The results show that the maximum tangential stress and fracture depth of the ramp surrounding rock on both sidewalls increase slowly at the initial mining stage. When the ore body above the ramp is mined, the maximum tangential stress and fracture depth of the ramp surrounding rock on both sidewalls increase rapidly, and the two parameters are positively correlated. Based on this, the ratio of the maximum tangential stress of the surrounding rock to the uniaxial compressive strength of intact rock (σθmax/σc) and the equivalent radius (a) of the roadway were used as parameters, and an equation for the fracture depth of the roadway surrounding rock was proposed. Through the case analysis, the results show that the proposed equation of fracture depth of the roadway surrounding rock has good prediction accuracy. This study enriches the research on the stability and failure mechanism of the roadway surrounding rock under the mining disturbance, and provides new basis for the support design of mining roadways.

A semi-empirical solution for estimating the elastic stresses around inclined mine stopes for the Mathews-Potvin stability analysis

The Mathews-Potvin stability method is widely used in the Canadian mining industry as a starting point to determine the maximum dimensions of mine stopes. However, it cannot be applied to inclined (more frequently encountered) mine stopes without conducting numerical modelling to obtain the stress factor A, defined as a function of the ratio of unconfined compressive strength of intact rock to the induced principal stress on the exposed stope walls. The need to conduct numerical modelling significantly limits the application of the Mathews-Potvin method. In addition, given its empirical nature and main application for preliminary design, it is deemed undesirable to conduct numerical modelling, especially elaborate modelling. Alternatively, theoretical methods can provide a much simpler and quicker way to estimate stresses around stopes and the corresponding stress factors. Over the years, a large number of studies have been conducted to estimate stresses around openings excavated with various cross-sections. However, theoretical or graphical solutions remain unavailable for mine stopes that typically consist of horizontal floor and roof, and two parallel inclined walls (hangingwall and footwall). To remedy this situation, a series of numerical simulations is first performed for openings with vertical and inclined walls, including typical stopes commonly encountered in underground mines. A group of empirical solutions is then formulated to estimate the induced principal stresses at the roof centre and mid-height of the stope walls. The validity and predictability of the proposed solution have been verified using additional numerical simulations. The proposed solution can thus be used to calculate stresses and the resultant stress factors A around typical mine stopes with any inclination angle and height to width ratio, under any in-situ stress state, without conducting numerical modelling.

Determination of a New Failure Criterion for Rock Mass and Concrete

The present investigation is based on a new quadratic equation that links the principal stresses σ1 and σ3 at the moment of failure, which allows to obtain the strength in rocks and brittle materials such as concrete. Through this new empirical two-dimensional failure criterion, the normal stress acting on the fracture plane is determined in the first calculation phase by solving the first order linear differential equation, and subsequently the shear streng‘th envelope. To facilitate the calculations, the expression that relates the major and minor principal stresses σ1 and σ3 at failure are defined for a parabolic equation and presented in normalized form. Thus, the algebraic curve is expressed as a function of (σ3/σc) and the parameter ξ. Where, σcrepresents the uniaxial compressive strength of intact rock (rock matrix) or concrete at 28 days, $$f_{c}^{{^{\prime}}}$$ , and on the other hand, ξ = (σt/σc) is a dimensionless parameter whose quotient is obtained by dividing the tensile strength σt by σc. Through the procedure described on this research (Focus Procedure) the parameters k1 and k2 that relate the principal stresses are determined with a good approximation grade through the relation ξ = (σt/σc), both in the intact rock condition as a function of rock mass quality index. All of this, with the additional advantage, that it is not required to know the interval of the principal failure stress (σ3, σ1) through the experimental tests.

Scale Effect and Correlation between Uniaxial Compressive Strength and Point Load Index for Limestone and Travertine

Determining the uniaxial compressive strength of intact rock is the primary objective of a geomechanical project, and a reliable estimate in the early phases saves time and costs for more sophisticated laboratory tests. The problem is knowing which of the correlations between the resistance to uniaxial compression and point load index are reliable, those that cover one or several types of rock (depending on the type of statistical adjustment). In this work, they were evaluated with respect to limestone and travertine from experimental results, and the statistical models of the scale effect of the point load index were determined, and the uniaxial compressive strength being estimated from correlations reported in literature. The limestone model was ascending (strength increases as diameter increases), while the travertine model was descending (strength decreases as diameter increases), obtaining similar exponents for the scale effect equations modeled from the uniaxial compressive strength and point load index in both cases.

Pseudostatic Stability Analysis of Rock Slopes Using Variational Method

In this paper, a rectilinear slope of homogenous rock is analyzed by using the variational method. The strength of the rock medium is assumed to be governed by the Hoek–Brown failure criterion. Although the variational method is developed within the framework of limit equilibrium method, however, neither the shape of the critical slip surface (kinematical assumption) nor the distribution of normal stresses along the slip surface (statical assumption) is required to assume. The aim of this paper is to obtain critical slip surface and the corresponding critical factor of safety (Fs) for different combinations of (i) slope geometries (slope angle, β and height of slope, h), (ii) rock properties (Geological Strength Index, GSI, non-dimensional strength parameter for intact rock, mi, disturbance factor, Df, and uniaxial compressive strength of intact rock, σci) and (iii) seismic loading conditions (coefficient of horizontal seismic acceleration, kh). The magnitude of Fs is evaluated uniquely by implementing certain necessary constraints on the slip and the slope surfaces and optimizing the functionals generated from resisting and driving moments. The failure surfaces drawn for several cases provide an insightful observation of the influence of different (a) material properties, (b) slope geometries and (c) seismic conditions.

Predicting Unconfined Compressive Strength of Intact Rock Using New Hybrid Intelligent Models

Bedrock unconfined compressive strength (UCS) is a key parameter in designing thegeosciences and building related projects comprising both the underground and surface rock structures. Determination of rock UCS using standard laboratory tests is a complicated, expensive, and time-consuming process, which requires fresh core specimens. However, preparing fresh cores is not always possible, especially during the drilling operation in cracked, fractured, and weak rocks. Therefore, some attempts have recently been made to develop the indirect methods, i.e. intelligent predictive models for rock UCS estimation, which require no core preparation and laboratory equipment. This work focuses on the application of new combinations of intelligent techniques including adoptive neuro-fuzzy inference system (ANFIS), genetic algorithm (GA), and particle swarm optimization (PSO) in order to predict rock UCS. These models were constructed based on the collected laboratory datasets upon 93 core specimens ranging from weak to very strong rock types. The proposed hybrid model results were compared with each other, and the real data and multiple regression (MR) results. These comparisons were made using coefficient of correlation, mean of square error, mean of absolute error, and variance account for indices. The comparison results proved that the ANFIS-GA combination had a relatively higher accuracy than the ANFIS-PSO combination, and both had a higher capability than the MR model. Furthermore, the ANFIS-GA and ANFIS-PSO model results were completely in accordance with the UCS laboratory test, and they were more accurate than the previous single/hybrid intelligent models. Lastly, a parametric study of the suggested models showed that the density and Schmidt hammer rebound had the highest influence, and porosity had the lowest influence on the output (UCS).

A Comparison Between Schmidt Rebound Hammer Test and Point Load Index Test (IS50) for the Effectiveness in Estimating the Unconfined Compressive Strength of Intact Rock- A Case Study with respect to Limestone of Early Eocene Nammal Formation, Central Salt

In a bid to find some possible relation of Unconfined Compressive Strength (UCS) with relatively simplelaboratory tests like Point Load Test (PLT) and Schmidt Rebound Hammer Test (SRHT), some 50 core samples ofMiddle Eocene Nammal formation from Central Salt Range in Pakistan were collected and subjected to these testmethods as per respective test standards of International Society of Rock Mechanics (ISRM). The values of SRHT andPLT were separately compared to the respective values of UCS so as to find the linear relations. On the basis of the R2value of Regression Analysis, it has been found that a strong correlation with a high degree of accuracy exists betweenPLT and UCS while the degree of accuracy between SRHT and UCS was found to be low.

A Comparison Between Schmidt Rebound Hammer Test and Point Load Index Test (IS50) for the Effectiveness in Estimating the Unconfined Compressive Strength of Intact Rock- A Case Study with respect to Limestone of Early Eocene Nammal Formation, Central Salt

In a bid to find some possible relation of Unconfined Compressive Strength (UCS) with relatively simplelaboratory tests like Point Load Test (PLT) and Schmidt Rebound Hammer Test (SRHT), some 50 core samples ofMiddle Eocene Nammal formation from Central Salt Range in Pakistan were collected and subjected to these testmethods as per respective test standards of International Society of Rock Mechanics (ISRM). The values of SRHT andPLT were separately compared to the respective values of UCS so as to find the linear relations. On the basis of the R2value of Regression Analysis, it has been found that a strong correlation with a high degree of accuracy exists betweenPLT and UCS while the degree of accuracy between SRHT and UCS was found to be low.

Probabilistic prediction of intact rock strength using point load tests using a Bayesian formulation

ABSTRACT This paper develops probabilistic predictive models for the unconfined compressive strength of intact rock based on the point load strength tests. A database of point load strength and unconfined compressive strength measurements for sedimentary, igneous and metamorphic rocks is first developed. The measurements are corrected to their standard equivalent values, namely unconfined compressive strength and point load strength for specimens with 50 mm diameter. A Bayesian framework is used to assess different candidate model forms and to estimate the corresponding model parameters. This Bayesian approach uses the prior information for the values of the unconfined compressive strength and point load strength measurements to develop an unbiased method for prediction of unconfined compressive strength based on point load strength tests. The Bayesian estimation of the model parameters accounts for the relevant sources of uncertainty including aleatory and epistemic uncertainties and for possible measurement errors in the point load strength test data. Probabilistic models are developed for sedimentary, igneous and metamorphic rocks. It is found that (i) a model of form provides the best fit to the laboratory data, and (ii) accounting for measurement errors and separating the database into subgroups based on different rock types decrease the model uncertainty.

Applying Bayesian Models to Forecast Rock Mass Modulus

The deformation modulus of a rock mass (Em) is one of the most significant properties used by designers for estimating deformation behavior of rock masses encountered in rock engineering projects (slopes, foundations and tunnels). The Em can only be determined by employing large-scale in situ tests on the rock mass, itself, for example, plate jacking, plate loading, pressuremeter, flat dilatometer, and Goodman jacking. It is sometimes difficult to apply the large scale in situ tests because of time consuming processes and installation required. To overcome this difficulty, the current study aims at predicting the Em on the basis of the rock parameters including the uniaxial compressive strength of intact rock, rock mass rating, Depth and elastic modulus of intact rock (Ei). The Bayesian inference approach is implemented to identify the most appropriate models for estimating the Em among six candidate models that have been proposed. The models were applied to available data given in open source literature. The unknown parameters of the models are considered as random variables. The WinBUGS software which uses Bayesian analysis of complex statistical models and Markov chain Monte Carlo (MCMC) techniques is employed to compute the posterior predictive distributions. The mean values of the model parameters obtained via MCMC simulations are considered for the model prediction performance evaluation. Various statistical performance indexes indexes [mean squared error, root mean squared error, squared correlation coefficient (R2) and mean absolute percentage error] were utilized to compare the performance of estimation models. Overall, the results indicate that the proposed Em model possesses satisfactory predictive performance.

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.

توسعه روشی کاربردی برای تعیین پارامترهای ژئومکانیکی توده ‏سنگ با در نظر گرفتن عدم قطعیت

In analysis and design of rock structures, determination of geomechanical parameters is very important. Discontinuity characteristics severely affect these parameters. But uncertainty in discontinuities and inherent inhomogeneity of rock mass decreases the reliability toward the determined parameters. In this situation, considering a range of parameters leads to more reliable results. In this paper, fuzzy logic and Monte Carlo simulation are developed for considering the uncertainty in rock mass. Hoek and Brown criterion is used as the performance function. For evaluating the efficiency of this method, available data sets in the literature are used. First, by considering the uncertainty in input parameters consist of geological strength index, constant of intact rock (mi) and uniaxial compressive strength of intact rock, sets of fuzzy numbers for S, a, mb are determined. Latter, utilizing the obtained results, geomechanical parameters of rock mass are obtained as sets of fuzzy numbers. Finally by the Monte Carlo simulation, random data are generated and for each parameter, confidence interval is determined by the 95% of confidence. Results indicate that the proposed method is reliable in problems with uncertainty in parameters and reduces the risk of design and analysis.

Determining relative block structure rating for rock erodibility evaluation in the case of non-orthogonal joint sets

The most commonly used method for assessing the hydraulic erodibility of rock is Annandale's method. This method is based on a correlation between the erosive force of flowing water and the capacity of rock resistance. This capacity is evaluated using Kirsten's index, which was initially developed to evaluate the excavatability of earth materials. For rocky material, this index is determined according to certain geomechanical factors related to intact rock and rock mass, such as compressive strength of intact rock, rock block size, discontinuity shear strength and relative block structure. To quantify the relative block structure, Kirsten (1982) developed a mathematical expression that accounts for the shape and orientation of the blocks relative to the direction of flow. Kirsten's initial concept for assessing the relative block structure considers that the geological formation is mainly fractured by two joint sets forming an orthogonally fractured system. An adjusted concept is proposed to determine the relative block structure when the fractured system is non-orthogonal where the angle between the planes of the two joint sets is greater or less than 90°. An analysis of the proposed relative block structure rating shows that considering a non-orthogonally fractured system has a significant effect on Kirsten's index and, as a consequence, on the assessment of the hydraulic erodibility of rock.

Quantitative hazard assessment system (Has-Q) for open pit mine slopes

Rock slope hazard assessment is an important part of risk analysis for open pit mines. The main parameters that can lead to rock slope failures are the parameters traditionally used in geomechanical classifications, the slope geometrical parameters and external factors like rainfall and blasting. This paper presents a methodology for a hazard assessment system for open pit mine slopes based on 88 cases collated around the world using principal components analysis, discriminant analysis and confidence ellipses. The historical cases used in this study included copper, gold, iron, diamond, lead and zinc, platinum and claystone mines. The variables used in the assessment methodology are uniaxial compressive strength of intact rock; spacing, persistence, opening, roughness, infilling and orientation of the main discontinuity set; weathering of the rock mass; groundwater; blasting method; and height and inclination of the pit. While principal component analysis was used to quantify the data, the discriminant analysis was used to establish a rule to classify new slopes about its stability condition. To provide a practical hazard assessment system, confidence ellipses were used to propose a hazard graph and generate the HAS-Q. The discriminant rule developed in this research has a high discrimination capacity with an error rate of 11.36%.

Lower bound stability analysis of plane strain headings in Hoek-Brown rock masses

Tunnel face stability is an important issue for the safety assessment of tunneling constructions. In this paper, the lower bound (LB) finite element limit analysis in conjunction with semidefinite programming (SDP) is developed and employed to investigate the stability of plane strain tunnel headings in Hoek-Brown (HB) rock masses. Lower bound solutions of the load factor of the problem for the practical ranges of dimensionless parameters are extensively examined including the cover-depth ratio of headings, the normalized uniaxial compressive strength of intact rock, the Geological Strength Index (GSI), and the HB material constant (mi). The failure mechanisms associated with those parameters are discussed and compared. The safety assessment of relatively long-wall tunnels or mining in rock masses can be reliably and accurately performed by employing the presented results in practice.

Stability of unlined square tunnels in Hoek-Brown rock masses based on lower bound analysis

In this paper, the lower bound (LB) finite element limit analysis in conjunction with semidefinite programming (SDP) is developed and employed to investigate the stability of unlined square tunnels in Hoek-Brown (HB) material. Extensive parametric studies on the load factor of unlined square tunnels are conducted on practical ranges of the cover-depth ratio of tunnels, normalized uniaxial compressive strength of intact rock, geological strength index (GSI) and HB material constant (mi). The presented results are useful for a reliable and accurate assessment of the stability of unlined square tunnels in rock masses in practice.

ARMR, a new classification system for the rating of anisotropic rock masses

The engineering behavior of rock masses is strongly dependent on anisotropy, which is present at different scales, from the microscale in the intact rock due to the alignment of rock crystals (inherent anisotropy) to the macroscale in rock masses with anisotropic rock structure, characterized by distinct bedding or schistosity planes. This paper presents a new rock mass classification system, Anisotropic Rock Mass Rating (ARMR), specifically developed for the classification of anisotropic rock masses. ARMR considers the following rating parameters: (a) anisotropy strength index, RC; (b) uniaxial compressive strength of intact rock; (c) degree of structure anisotropy; (d) corrected rock quality designation (RQD); (e) condition of anisotropy surfaces; and (f) groundwater conditions. Its use is illustrated and explained by application to specific case studies in anisotropic rock masses, and the advantages and limitations of the classification system are outlined. The strength of anisotropic rock masses is determined using the modified Hoek–Brown criterion (Saroglou and Tsiambaos, Int J Rock Mech Mining Sci 45:223–234, 2008), which is extended to rock masses with the use of ARMR.

Comprehensive statistical analysis of intact rock strength for reliability-based design

Rock engineering design is currently evolving from the traditional use of safety factors and towards the more rational reliability-based design (RBD), as witnessed by the introduction of a number of geotechnical limit states design (LSD) standards worldwide. The probabilistic nature of RBD requires statistical characterization of design parameters, including the strength of intact rock. The triaxial compressive strength of intact rock is commonly characterized as a function of confining pressure, and values of the parameters that define this function are generally obtained by regression analysis of laboratory test data. However, the problem of fitting strength criteria to intact rock strength data has been historically tackled as a problem of obtaining best fit curves only, and has inadvertently omitted characterization of the variability inherent in the strength data. As a result, the uncertainty in parameter estimations resulting from this variability are often not quantified rigorously. Not only does this omission render such regression analyses incomplete, it also limits development of reliability-based design protocols for rock engineering which require statistical characterization of design parameters. To overcome both of these deficiencies, this paper presents frequentist (i.e. classical) and Bayesian regression models that rigorously incorporate variability and uncertainty associated with estimated Hoek-Brown strength parameters. In particular, it discusses the limitations of the frequentist model when dealing with limited data or a combination of tensile and compressive strength data. It discusses the potential of Bayesian data analysis techniques to overcome the issue of limited data in rock engineering design by using informative prior distributions. The paper also demonstrates the main issue in fitting strength criteria to tensile and compressive data simultaneously from a statistical perspective, and presents a Bayesian regression model that rigorously fits the strength criterion to a combination of tensile and compressive data. The paper concludes with suggested statistical approaches – Bayesian or frequentist – for conditions encountered in the analysis of intact rock strength data.