Intact Rock Strength Research Articles

Predicting blast-induced outcomes using random forest models of multi-year blasting data from an open pit mine

Rock fragmentation and movement are two important outcomes of the blasting process in open pit mines. They are influenced by blasting design parameters, as well as by the physical and geomechanical characteristics of the rock mass. This paper presents the analysis results of multi-year blasting data from an open pit mine in Canada and proposes a predictive model for the blast-induced outcomes that incorporates both rock mass properties and blasting parameters. The analysis employed the decision tree (DT) and random forest (RF) models to determine influential parameters, confirming that the blast-induced fragmentation and movement are influenced by rock mass characteristics (i.e. intact rock strength and rock quality designation, RQD), as well as by blasting design parameters. The decision tree model facilitates the visualization of geomechanical and blasting design parameters influencing the blast-induced outcomes. The robust random forest model provides prediction of blast-induced outcomes. The decision tree and random forest models make it possible to determine blasting design parameters that could be modified to achieve better blast-induced outcomes based on the rock mass conditions at the mine site.

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.

A Preliminary Investigation on the Role of Brittle Fracture in the Kinematics of the 2014 San Leo Landslide

The stability of high rock slopes is largely controlled by the location and orientation of geological features, such as faults, folds, joints, and bedding planes, which can induce structurally controlled slope instability. Under certain conditions, slope kinematics may vary with time, as propagation of existing fractures due to brittle failure may allow development of fully persistent release surfaces. In this paper, the progressive accumulation of brittle damage that occurred prior to and during the 2014 San Leo landslide (northern Italy) is investigated using a synthetic rock mass (SRM) approach. Mapping of brittle fractures, rock bridge failures, and major structures is undertaken using terrestrial laser scanning, photogrammetry, and high-resolution photography. Numerical analyses are conducted to investigate the role of intact rock fracturing on the evolution of kinematic freedom using the two-dimensional Finite-discrete element method (FDEM) code Elfen, and the three-dimensional lattice-spring scheme code Slope Model. Numerical analyses show that the gradual erosion of clay-rich material below the base of the plateau drives the brittle propagation of fractures within the rock mass, until a fully persistent, subvertical rupture surface form, causing toppling of fault-bounded rock columns. This study clearly highlights the potential role of intact rock fracturing on the slope kinematics, and the interaction between intact rock strength, structural geology, and slope morphology.

Controls on the geotechnical response of sedimentary rocks to weathering

AbstractWeathering reduces the strength of rocks and so is a key control on the stability of rock slopes. Recent research suggests that the geotechnical response of rocks to weathering varies with ambient stress conditions resulting from overburden loading and/or stress concentrations driven by near‐surface topography. In addition, the stress history experienced by the rock can influence the degree to which current weathering processes cause rock breakdown. To address the combined effect of these potential controls, we conducted a set of weathering experiments on two sedimentary lithologies in laboratory and field conditions. We firstly defined the baseline geotechnical behaviour of each lithology, characterising surface hardness and stress–strain behaviour in unconfined compression. Weathering significantly reduced intact rock strength, but this was not evident in measurements of surface hardness. The ambient compressive stress applied to samples throughout the experiments did not cause any observable differences in the geotechnical behaviour of the samples. We created a stress history effect in sub‐sets of samples by generating a population of microcracks that could be exploited by weathering processes. We also geometrically modified groups of samples to cause near‐surface stress concentrations that may allow greater weathering efficacy. However, even these pronounced sample modifications resulted in insignificant changes in geotechnical behaviour when compared to unmodified samples. The observed reduction in rock strength changed the nature of failure of the samples, which developed post‐peak strength and underwent multiple stages of brittle failure. Although weakened, these samples could sustain greater stress and strain following exceedance of peak strength. On this basis, the multi‐stage failure style exhibited by weaker weathered rock may permit smaller‐magnitude, higher‐frequency events to trigger fracture through intact rock bridges as well as influencing the characteristics of pre‐failure deformation. These findings are consistent with patterns of behaviour observed in field monitoring results. © 2019 John Wiley & Sons, Ltd.

A cohesion loss model for determining residual strength of intact rocks

Residual strength of rock is required in stability evaluation of underground excavations such as tunnels and caverns. Accurate determination of residual strength of rock can facilitate cost-effective design of these underground structures. This study investigates the methods for determining residual strength of intact rocks. Firstly, previous methods for determining residual strength of intact rocks are examined from a literature review, and a new method, which uses the concept of cohesion loss, is proposed. The proposed cohesion loss model is based on the framework of the widely-used Hoek–Brown (H–B) strength model. It is simple and contains only one parameter that controls the nonlinearity of the residual strength envelope. The cohesion loss model is validated using two sets of test data and the results show that the model can represent residual strength envelopes of intact rocks satisfactorily. Finally, the model parameter is studied by examining a large amount of test data collected from previous publications. It is found that the model parameter varies for different rock types and shows a decreasing trend as the rock strength increases. Overall, the results in this study show that the proposed model can capture the residual strength of intact rocks.

Stability Analysis of Slopes with Spatially Variable Strength Properties

Natural variability of rock properties can significantly affect the strength of rock masses and factor of safety of slopes. The results of a comprehensive point load testing program showed that coefficient of variation of intact rock strength can reach unity in highly heterogeneous formations. Probabilistic numerical analysis was carried out to explore the effect of strength variability on uniaxial compressive strength of large heterogeneous samples. It was shown that mean large-scale strength decreases with increasing small-scale variability. The effect of spatial variability of strength properties on slope stability was examined using limit equilibrium and shear strength reduction methods. Both approaches gave similar results indicating that for stable slopes, increasing strength variability leads to a reduction in mean factor of safety and increase in the probability of failure. In addition, ignoring spatial variability in probabilistic slope analysis can lead to erroneous estimates of the probability of failure. Based on the results of probabilistic analyses on large heterogeneous samples and slopes, an equivalent uniaxial compressive strength can be obtained by reducing the mean strength by one-third of its standard deviation. This relationship was validated using a dataset of back-analyzed strength values in heterogeneous open pit slopes.

Development of a new physical modeling method to investigate the effect of porosity on the parameters of intact rock failure criteria

Porosity is a critical textural parameter in the complex nature of rock and while it has the highest impact on the strength of intact rock, in the case of oil and gas reservoir rocks, it defines the capacity and permeability of the reservoir. A constant value for triaxial strength factor (mi) of rock failure criterion has been given for each type of sedimentary rocks such as sandstone and the effect of porosity on the mi has not been well defined. Rock is not a homogenous material as with varying the porosity, the other inherent variables also control the strength and the mechanical behavior. Rock porosity varies in a wide range in sedimentary rocks such as sandstone. In this study, the effect of porosity on the parameters of failure criteria (mi) for rock-like materials made from cemented grains is investigated. For sample preparation, a mixture of cement-sand-water was compacted with variable water content to obtain specimens having a wide range of porosities using the same grain size of filler material. Two types of grains including sand and silica filler material were used for the experimental program. Sixteen sets of artificial specimens having porosities from 9.00% to 34.09% have been prepared for two filler materials of sand and silica, while other factors affecting the strength have been kept constant. The triaxial strength test results of these specimens show that the triaxial strength factor (mi) of Hoek et al. failure criterion, internal friction angle (ϕ), and cohesive strength (C) significantly decrease with increasing the porosity. The best-fit curves follow power function with high coefficients of regression.

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.

Universal confined tensile strength of intact rock

Strength criteria for intact rock are essential for the safe design of many engineering structures. These criteria have been derived mainly from tests in the compressive stress region. Very few results have been published for confined, direct tensile tests on intact rock. No appropriate criteria are available for addressing the issue on tensile strength of intact rock at current stage. We present the results of direct triaxial tensile tests on Longmaxi Shales under varying confining stresses. These and the results from previous tests in marble and sandstone prove that the phenomenon of “tension cut-off” at low confining stress and the positive correlations between confining stress and tensile strength above the confining stress threshold for brittle rocks occur also in more ductile rocks like shales. Such findings are consistent with the concept that tensile failure processes for intact rock are universal. Our results demonstrate that friction processes still have a significant role on intact rock strength in the tensile region which is leading to confined tensile failure and transitioning to a purely tensile mode. Further, strength criteria are presented which consider the frictional processes leading to failure under confined, direct tension tests and validated against published tensile strength data.

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.

Estimation of the drop modulus using the brittleness index of intact rock and geological strength index of rock mass, case studies: Nosoud and Zagros tunnels in Iran

The drop modulus is defined as the slope for the softening stage of the stress—strain curve of rock mass. Estimation of the mentioned parameter is very difficult because it is related to many parameters such as intact rock properties, quality of rock mass, confinement stress and etc. In this study, based on the actual collected data from Nosoud and Zagros tunnels in Iran, new empirical equations to predict the drop modulus of rock mass using the brittleness indexes is proposed. The results show that there is a direct relation between both parameters and the best correlation between them is achieved using the Altindag’s brittleness index, BI3, to estimate the drop modulus. Finally, the relation between the drop modulus with the brittleness index of intact rock and geological strength Index of rock mass is estimated and a new equation to estimate the drop modulus using both mentioned parameters is proposed.

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.

Effect of tunnel overburden stress on the rock brittle failure depth

Tunneling under high overburden stresses results in many tunnel instability problems due to the rock overstressing. Understanding and simulating the rock failure process is the major issue of a deep excavation to achieve an appropriate rock support system that provides possible cost-effective and stable construction. The excavation of the Pahang Selangor Raw Water Transfer Tunnel is considered in this paper. Three critical cases of the project are analyzed. A possible rock brittle failure was predictable at the tunnel sidewalls under a depth of more than 500 m. The rock overstressing is analyzed based on the in situ stress conditions, intact rock strength, and actual failure depth observed at the site. Failure zones are simulated using the cohesion softening–friction hardening model and compared with the site observed failures. A review of underground openings excavated in different rock mass conditions showed that the ratio of the maximum boundary stress to the uniaxial compressive strength (σθmax/σci) is suggested as the key parameter to determine the tunnel instability problems. In this study, an attempt is made to investigate the influence of the maximum tangential boundary stress to the uniaxial compressive strength ratio(σθmax/σci) on the rock brittle failure depth, stress distribution, and displacement of the rock mass around the tunnel. A parametric study is implemented using different tunnel depths including the actual tunnel depths. The results show that with increasing tunnel depth or (σθmax/σci) ratio, the risk of spalling, rock burst, and other tunnel instabilities are increasing.

Effect of Fluid Type and Multiphase Flow on Sand Production in Oil and Gas Wells

Summary Controlled laboratory experiments and some field studies have shown that the onset of sand production in gas wells differs from that in oil wells. Results from a general 3D sand-production numerical model are presented to explain the differences in the onset of sanding and sand-production volume for different fluids and under different flow and in-situ stress conditions. The sand-production model accounts for multiphase-fluid flow and is fully coupled with an elasto-plastic geomechanical model. The sanding criterion considers both mechanical failure and sand erosion by fluid flow. Non-Darcy flow is implemented to account for the high flow rates. The drag forces on the sand grains are computed on the basis of the in-situ Reynolds number. Both the intact rock strength and the residual rock strength depend on water saturation. Water evaporation (drying) resulting from gas flow is modeled using phase equilibrium calculations. The onset of sand production is compared for different fluid types (oil and gas). Model results are shown to be consistent with experimental observations reported in the literature. For example, the onset of sanding is observed at higher compressive stresses for gas wells as compared with oil wells. The primary mechanism for this is for the first time shown to be sand strengthening induced by evaporation of water. This effect is not observed in oil wells. The sand-production rate when non-Darcy effects are considered is lower than for Darcy flow. The reason for this is the lower fluid velocity (for the same drawdown) and, consequently, smaller drag forces on the failed sand grains. The effect of water breakthrough and water cut on sand production is studied from both mechanical and erosion perspectives. The model is shown to be capable of accurately predicting the onset of sanding and sand production induced by multiphase- and compressible-fluid flows, helping us to predict sanding issues in both oil and gas wells.

Analysis and design of axially loaded piles in rock

Despite significant advancements in in situ test techniques, construction practices, understanding of rock joint and rock mass behaviours, and numerical analysis methods, the design of bored concrete cast-in-situ piles in rock is still largely based on the assessment of bearing capacity. However, for many of the rock conditions encountered, the bearing capacity of piles is a nebulous concept and a figment of the designer's imagination. Even if it can be reasonably quantified, it has little, if any, significance to the performance of a pile in rock. The load carrying capacity of even low strength rock (in most situations) is far in excess of the strength of the structure (for example, a building column) transmitting the load. Unsatisfactory performance of a pile in rock is usually a displacement issue and is a function of rock mass stiffness rather than rock mass strength. In addition, poor pile performance is much more likely to result from poor construction practices than excessive displacement of the rock mass. Exceptions occur for footings that are undermined, or where unfavourable structure in the rock allows movement towards a free surface to occur. Standards, codes of practices, reference books and other sources of design information should focus foundation design in rock on displacement rather than strength performance. Ground investigations should measure rock mass stiffness and defect properties, as well as intact rock strength. This paper summarises the fundamental concepts relating to performance of piles in rock and provides a basis for displacement focused design of piles in rock. It also presents comments relating to how piles are modelled in widely used commercial finite element software for soil-structure interaction analysis, within the context of the back-analysis of a pile load test, and proposes recommendations for pile analysis and design.

Extension of tunneling quality index and rock mass rating systems for tunnel support design through back calculations in highly stressed jointed rock mass: An empirical approach based on tunneling data from Himalaya

A preliminary support design is the basic output of an empirical rock mass classification system. Tunneling quality index (Q) and rock mass rating (RMR) systems are used specifically for tunnel support in moderately jointed and massive rocks; however, they do not provide any information/guidance for jointed rock masses in a highly stressed environment. Hence, this study focuses on the already supported drill and blast tunnel sections mapping data of four tunneling projects in Pakistan. The study extends the application of these systems to the tunnel support design for highly stressed jointed rock mass through an empirical approach. In each empirical approach, the parameters for the stress condition are suggested. Rock mass quality (Q or Qc) is determined from back calculations using an installed support and tunnel span. Empirical equations and charts are proposed for the stress reduction factor (SRF) characterization. In the proposed equations and charts, the SRF is a function of intact rock strength, relative block size, and strength–stress ratio. In the case of the RMR system, approximately 90% of the sections show that the actual supports are heavier than the suggested supports by RMR89. The RMR was determined from the installed support for each tunnel section through the back calculations. To select the adjustment rating factor for stress, three hypotheses are considered based on the intact rock strength to the major principal stress ratio. The RMR14 suggested support revealed that all sections are heavily supported. A strong correlation exists between RMR89 and RMR14. Three hypotheses are considered for the stress adjustment factor rating selection for RMR14 based on the correlation equation between RMR89 and RMR14. For the evaluation, the application of modified Q and RMR systems are used in the tunnel support in a case study. The exploration reports show that the tunnel will pass through a jointed rock mass under high in-situ stress environments. The comparison shows that heavy support is recommended from the modified systems for tunnel stability.

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.