Intact Rock Strength Research Articles

Effects of orientation, frequency, and number of sets of discontinuities on rock strength under triaxial stresses

Effects of orientation, number of sets, and frequency of discontinuities on the rock strength under triaxial stresses have been investigated by the empirical method in this research. Twenty groups of rock specimens including intact rock, rock specimens having one, two, or three sets of discontinuities with various frequencies and orientations of 0°, 30°, 45°, 60°, and 90° have been prepared and tested under triaxial compressive stresses. The axial strength of each group has been tested under confining pressure of 0, 5, 7, 10, 14, and 20 MPa. Axial specimen strength, having one set of discontinuity, decreases a little with increase of the orientation angle from 0° to 30° under the most confining pressures; the relationship between axial strength and orientation angle between 30° and 90° has a shoulder shape under low values of confining pressures. The shoulder shape relationship also changes with increase of the confining pressure as it disappears at high values of confining pressures. The shoulder shape range of reduction axial strength under confining pressures due to the orientation of discontinuities changes similar to a twin symmetrical shoulder shape for specimens having two or more perpendicular sets of discontinuities as another minimum axial strength occurs at orientation angle of 30° on the opposite direction as well as orientation of 60°. The uniaxial compressive strength approaches approximate zero value at orientation angle of 60° for specimens having different sets and frequencies of discontinuities and it also approaches to zero at orientation angle of 30° for specimens having two or more sets of discontinuities; axial strength has considerable value under triaxial stresses. Effects of three parameters of orientation, frequency, and number of sets of discontinuities on the axial strength decreases with increase of confining pressure as minimum and maximum values of the axial strengths of specimens are between 74 and 100 % of the axial strength of intact rock under confining pressure greater than or equal to 10 MPa in this research.

Coastline retreat via progressive failure of rocky coastal cliffs

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A Simplified Failure Criterion for Intact Rocks Based on Rock Type and Uniaxial Compressive Strength

The uniaxial compressive strength (UCS) of intact rock, which can be estimated using relatively straightforward and cost-effective techniques, is one of the most practical rock properties used in rock engineering. Thus, constitutive laws to represent the strength and behavior of (intact) rock frequently use it, along with additional intrinsic rock properties. Although triaxial tests can be employed to obtain best-fit failure criterion parameters that provide best strength predictions, they are more expensive and require time-consuming procedures; as a consequence, they are often not readily available at early stages of a project. Based on the analysis of an extensive triaxial test database for intact rocks, we propose a simplified empirical failure criterion in which rock strength at failure is expressed in terms of confining stress and UCS, with a new parameter which can be directly estimated from the UCS for a specified rock type in the absence of triaxial test data. Performance of the proposed failure criterion is then tested for validation against experimental data for eight rock types. The results show that strengths of intact rock estimated by the proposed failure criterion are in good agreement with experimental test data, with small discrepancies between estimated and measurements strengths. Therefore, the proposed criterion can be useful for preliminary (triaxial) strength estimation of intact rocks when triaxial tests data are not available.

Instrumented Static Load Test on Rock-Socketed Micropile

AbstractRock-socketed piles are often used to transfer heavy loads from a superstructure to competent underlying rock layers. The loads are transferred by the pile to the surrounding rock mass through shaft and base resistance. Several researchers have investigated the behavior of rock-socketed drilled shafts and related the uniaxial compressive strength of intact rock to pile-shaft resistance. However, the load-transfer behavior and load-settlement response of micropiles are different from those of drilled shafts because of the large slenderness ratio (pile length/pile diameter) of micropiles. This study presents results from a fully instrumented field-scale load test on a 0.2-m-diameter micropile socketed 4.2 m into limestone layers (2.7 m into weathered limestone and 1.5 m into hard limestone). The results show that practically no base resistance is mobilized until the pile-head settlement reaches approximately 7% of the diameter of the test micropile. The measured limit shaft resistance values are com...

Engineering aspects and time effects of rapid deterioration of sandstone in the tropical environment of Sabah, Malaysia

Cut slopes in rock masses start to deteriorate directly after excavation due to stress relief and weathering. The deterioration is a time dependent process that depends on the local climate and the rock mass including its history, and the environment. The amount of deterioration per time unit (‘the weathering intensity rate’) is not a constant over time, but is for most rock masses larger when the mass is less weathered and becomes smaller with further progressing weathering. A study has been carried out to establish the relationship between weathering intensity rate and exposure time for the intact rock strength (IRS) of sandstone in humid tropical areas. The data set for the study was collected in and near Kota Kinabalu, Sabah, Malaysia, which has a humid tropical climate. The geology in the area consists of thick sequences of sandstone and shale beds of the Crocker Formation. Results show that the best relationship between intact rock strength (IRS) and exposure time (t) is by a logarithmic function; IRS (t)=105−34 log (1+t). This relationship can likely be used for prediction of the intact rock strength development of similar sandstone over the engineering lifetime of man-made slopes in tropical areas.

Development of optimal fuzzy models for predicting the strength of intact rocks

Fuzzy models have been used in a wide variety of applications particularly problems associated with the strength of rocks and rock masses. However, a systematic approach of modeling has not been presented thus far and developing appropriate fuzzy models is usually carried out by trial and error. In this paper a new soft-computing approach is introduced which benefits from searching capabilities of Multi-Objective Genetic Algorithm (MOGA) to develop fuzzy models optimized in terms of complexity and accuracy. The proposed method is then used to find optimal fuzzy models to predict the strength of intact rock specimens under conventional triaxial stresses. In addition, laboratory tests are conducted on specimens of three rock types to evaluate the models. It is shown that a relatively simple model, with few manageable rules, is able to estimate the strength of intact rocks properly and hence may be selected as the best fuzzy model.

Numerical simulation of the failure mechanism of circular tunnels in transversely isotropic rock masses

This paper studies the failure mechanism for a circular tunnel in transversely isotropic rock using the numerical code Realistic Failure Process Analysis (RFPA). In RFPA, an elastic damage model is used to describe the constitutive law of the meso-scale elements, and the maximum tensile strain criterion and the Mohr–Coulomb criterion are adopted as damage thresholds to determine the tensile and shear damage respectively. A series of numerical simulations of the failure process for a plane circular tunnel in rock are conducted. Based on the simulations, two major failure modes around circular tunnels in transversely isotropic rock are numerically reproduced. Whether failure is caused by sliding along the laminated layers depends on the orientation of the laminated layers, the confining pressure, and the strength ratio of the laminated layers to the intact rock. Numerical simulations of the failure modes are given for different ratios of discontinuity strength to intact rock strength, as well as different dimensionless ratios of discontinuity width. Finally, both the failure process of tunnels in up-roll foliated rock masses and down-roll foliated rock masses are investigated by RFPA.

Performance of pillar design in underground stone mines that include discontinuities

This paper describes a pillar design methodology that was developed from a study of pillar performance in operating stone mines. A number of methodologies have been developed to calculate full-scale mine pillar strengths based on laboratory scale strength obtained from specimens. Data were collected on rock mass quality, pillar conditions, mining dimensions and intact rock strength. Results showed that current mining practices have resulted in generally stable pillar layouts, without recent cases of extensive pillar collapses; however, failure of the pillars was found to be related to spalling of hard brittle rock, shearing along pre-existing angular discontinuities or progressive extrusion of soft infill material on bedding planes. A numerical model (FLAC3D) for the entire rock mass has been developed in order to analyze the stability of the entire underground opening. A preliminary monitoring phase has been realized, aimed at controlling abandoned rock structure movement at the most significant discontinuities. Some measurements of the vertical stress in the pillars and in the walls have also been performed and were used for model calibration. Once the model has been calibrated, analysis of the actual stress and deformation conditions can then be evaluated, the stability condition of the entire structure can be computed and a forecast analysis of what intervention could be realized to guarantee underground public access can be performed. The developed strength equation can be used to design stable pillar layouts, keeping in mind that the safety factor is greater than 1.5 and the width:height ratio of the pillars is between 0.6 and 0.8. It is concluded that, by applying the developed equation and selecting appropriate input parameters, it should then be possible to calculate the factor of safety.

Prediction of unconfined compressive strength of carbonate rocks using artificial neural networks

The unconfined compressive strength (UCS) of intact rocks is an important geotechnical parameter for engineering applications. Determining UCS using standard laboratory tests is a difficult, expensive and time consuming task. This is particularly true for thinly bedded, highly fractured, foliated, highly porous and weak rocks. Consequently, prediction models become an attractive alternative for engineering geologists. The objective of study is to select the explanatory variables (predictors) from a subset of mineralogical and index properties of the samples, based on all possible regression technique, and to prepare a prediction model of UCS using artificial neural networks (ANN). As a result of all possible regression, the total porosity and P-wave velocity in the solid part of the sample were determined as the inputs for the Levenberg–Marquardt algorithm based ANN (LM-ANN). The performance of the LM-ANN model was compared with the multiple linear regression (REG) model. When training and testing results of the outputs of the LM-ANN and REG models were examined in terms of the favorite statistical criteria, which are the determination coefficient, adjusted determination coefficient, root mean square error and variance account factor, the results of LM-ANN model were more accurate. In addition to these statistical criteria, the non-parametric Mann–Whitney U test, as an alternative to the Student’s t test, was used for comparing the homogeneities of predicted values. When all the statistics had been investigated, it was seen that the LM-ANN that has been developed, was a successful tool which was capable of UCS prediction.

Testing and evaluation of strength and deformation behaviour of jointed rocks

The objective of the paper is to derive the strength and modulus properties of rockmass as a function of intact rock strength and joint factor. The joint factor reflects the combined effect of joint frequency, joint inclination and joint strength. A study for the strength and deformation characteristics of jointed rock is done by conducting standard laboratory tests on cylindrical specimens of plaster of Paris after introducing artificial joints. The specimens having one to four joints at different inclinations which vary from 0° to 90° were tested at different confining conditions. The test results were examined to understand the effect of joint frequency and joint inclination on the strength and deformation behaviour of rock mass. Empirical correlations were developed for prediction of the uniaxial compressive strength and elastic modulus of jointed rocks. Results are compared with the earlier work on jointed specimens covering a wide variety of rocks. So, knowing the intact rock properties and the joint factor, the jointed rock properties can be estimated. These relations can be used for developing an equivalent continuum model for rock mass for handling boundary value problems. A failure criterion as proposed by Ramamurthy (1993) has been validated from these experimental results.

A new three-dimensional Hoek-Brown strength criterion

The Hoek-Brown (HB) strength criterion has been widely applied to the estimation of strength of intact rock and rock mass, while evolving ever since. However, negligence of the effect of the intermediate principal stress still remains in the criterion’s latest version. At the same time, several three-dimensional (3D) HB strength, which can takes into account the influence of the intermediate principal stress, have already been proposed, among which the 3D HB criterion proposed by Zhang and Zhu seems to be the most reasonable one. However, the Zhang 3D HB criterion may have problems with some stress path close to triaxial extension state because of the non-convexity characteristic of its failure surface. In this paper, a new 3D HB strength criterion is presented based on a generalized form of the HB criterion, which also considers the effect of the intermediate principal stress and inherits all the merits of the original version of the HB criterion. In addition, this new criterion can remedy to some extent the shortcomings observed in the Zhang 3D HB criterion. Polyaxial tests for five different rocks from published literatures are used for evaluating this new criterion and comparing it with the Zhang 3D HB criterion. The results show that this new criterion may over-predict or under-predict the polyaxial strength of rocks but the errors are relatively small, and similar results are also found for the Zhang 3D HB criterion, which one is better depends on the type of the rock under estimation.

Measurement of uniaxial compressive strength of rocks using reconstructed cores from rock cuttings

Uniaxial compressive strength of intact rock is an important mechanical parameter required for the design of geotechnical, mining engineering and petroleum reservoir projects. In geotechnical and mining projects, rock cores are usually available to be tested for such purposes. In the petroleum reservoirs, however, the extreme high cost and time-consuming of coring operation is a main issue and thus, rock core for mechanical destructive testing are rarely available. In this study, a new technique is proposed for measuring the uniaxial compressive strength of reconstructed cores from rock cuttings. For this purpose, a total of 23 blocks of limestone having different densities including Asmari and Sarvak Formations from Western part of Iran and also Cretaceous limestone from Northern part of the country were used. After preparing appropriate cores from the blocks, uniaxial compressive strength test was performed on rock cores. Next, rock cuttings were produced from the same blocks and were reconstructed into artificial cylindrical specimens. The size of the rock cuttings varied between 0.075mm and 0.4mm, since it proved promising in preparing specimens with a maximum density of about 80% of the intact rock. Thus, cylindrical specimens with the diameter of 38mm and the length of 76mm were built from the cuttings using standard compaction test. Cores with the same dimensions were taken from the same rock blocks. The two sets of samples were next subjected to the uniaxial compression test.Results showed an acceptable relationship between uniaxial compressive strength (UCS) of rock cores and the unconfined compressive strength of reconstructed cores (qu). A correlation coefficient of about or higher than 0.85 was obtained between UCS and qu for all samples tested. The proposed method can be used for determining the UCS of rocks whenever no cores are available.

Application of artificial neural networks and multivariate statistics to estimate UCS using textural characteristics

Before any rock engineering project, mechanical parameters of rocks such as uniaxial compressive strength and young modulus of intact rock get measured using laboratory or in-situ tests, but in some situations preparing the required specimens is impossible. By this time, several models have been established to evaluate UCS and E from rock substantial properties. Artificial neural networks are powerful tools which are employed to establish predictive models and results have shown the priority of this technique compared to classic statistical techniques. In this paper, ANN and multivariate statistical models considering rock textural characteristics have been established to estimate UCS of rock and to validate the responses of the established models, they were compared with laboratory results. For this purpose a data set for 44 samples of sandstone was prepared and for each sample some textural characteristics such as void, mineral content and grain size as well as UCS were determined. To select the best predictors as inputs of the UCS models, this data set was subjected to statistical analyses comprising basic descriptive statistics, bivariate correlation, curve fitting and principal component analyses. Results of such analyses have shown that void, ferroan calcitic cement, argillaceous cement and mica percentage have the most effect on USC. Two predictive models for UCS were developed using these variables by ANN and linear multivariate regression. Results have shown that by using simple textural characteristics such as mineral content, cement type and void, strength of studied sandstone can be estimated with acceptable accuracy. ANN and multivariate statistical UCS models, revealed responses with 0.87 and 0.76 regressions, respectively which proves higher potential of ANN model for predicting UCS compared to classic statistical models.

Deep structure of lithospheric fault zones

[1] We calculate the cumulative width w of ductile shear zones accommodating plate motion in continental lithosphere, based on the assumptions that (1) the flow stress is controlled by the yield strength of intact rock at any given depth; (2) the yield strength profile through the crust can be constrained from observations in exhumed shear zones; and (3) strain localization is primarily caused by grainsize reduction leading to a switch to grainsize-sensitive creep. We use a mid-crustal stress-temperature profile measured in the Whipple Mountains, California, and calculate stress profiles at depth from published flow laws for feldspar and olivine. We conclude thatwfor a plate boundary shear zone accommodating 50 mm/yr displacement (comparable to the San Andreas Transform) may reach 180 km in the quartz-rich mid-crust, depending on water fugacity and thermal gradient. It narrows to a few meters in feldspathic lower crust and in the uppermost mantle, and then widens rapidly with depth in the lower lithosphere. We explore the effects of differences in crustal thickness and composition, thermal gradient, and water activity.

An alternative method for in situ determination of rock strength

The friction-transfer method, which is described in this paper, can be used for in situ determination of intact rock strength. With this method it is possible to estimate the equivalent uniaxial compressive strengths (UCS), using appropriate calibration graphs. In this method a specially devised apparatus fits over the top the partial core and is clamped to it. To measure the rock strength, torque is applied using an ordinary torque meter and the maximum torque at failure is recorded. Comparative studies of UCS values and friction-transfer test results showed that a strong correlation exists between UCS and the friction-transfer readings. The measured values for uniaxial compressive tests ranged from 26 to 207 MPa. The average coefficients of variation of laboratory and site tests were found to be less than 14% for uniaxial compressive tests and less than 12.5% for the friction-transfer method. Fully saturated rock samples showed between about 18%–56% reduction in their torsional and core compressive strengths compared with their respective values obtained under dry laboratory conditions.

Quantifying bedrock-fracture patterns within the shallow subsurface: Implications for rock mass strength, bedrock landslides, and erodibility

[1] The role of bedrock fractures and rock mass strength is often considered a primary influence on the efficiency of surface processes and the morphology of landscapes. Quantifying bedrock characteristics at hillslope scales, however, has proven difficult. Here, we present a new field-based method for quantifying the depth and apparent density of bedrock fractures within the shallow subsurface based on seismic refraction surveys. We examine variations in subsurface fracture patterns in both Fiordland and the Southern Alps of New Zealand to better constrain the influence of bedrock properties in governing rates and patterns of landslides, as well as the morphology of threshold landscapes. We argue that intense tectonic deformation produces uniform bedrock fracturing with depth, whereas geomorphic processes produce strong fracture gradients focused within the shallow subsurface. Additionally, we argue that hillslope strength and stability are functions of both the intact rock strength and the density of bedrock fractures, such that for a given intact rock strength, a threshold fracture-density exists that delineates between stable and unstable rock masses. In the Southern Alps, tectonic forces have pervasively fractured intrinsically weak rock to the verge of instability, such that the entire rock mass is susceptible to failure and landslides can potentially extend to great depths. Conversely, in Fiordland, tectonic fracturing of the strong intact rock has produced fracture densities less than the regional stability threshold. Therefore, bedrock failure in Fiordland generally occurs only after geomorphic fracturing has further reduced the rock mass strength. This dependence on geomorphic fracturing limits the depths of bedrock landslides to within this geomorphically weakened zone.

Artificial neural networks as a basis for new generation of rock failure criteria

Conventional methods for prediction of rock strength are based on using classical failure criteria. In this study, artificial neural networks were regarded as new tools for considering the strength of intact rock in a wide range of loading condition from uniaxial tension to triaxial compression. A comprehensive data set of the values of major and minor principal stresses at failure from 1638 laboratory tests on seven rock types was collected. For each rock type, data were randomly divided into two subsets, training and test sets. Neural networks were trained using training sets to predict the value of major principal stress at failure from uniaxial compressive stress and minor principal stress. Small architecture and regularization method were adopted to avoid over-fitting problems. The same training sets were used in determining the constants of two popular empirical failure criteria, namely Bieniawski–Yudhbir and Hoek–Brown. Then, the test sets were used to examine the accuracy and generalization of the models in predicting the strength in new situations. Comparison of the results of the neural network models with those of the empirical criteria showed that the former approach always lead to less root mean squared error and higher coefficient of determination. On average, for different rock types, using ANN models led to about 30% decrease in prediction error relative to best empirical models. These models also showed better flexibility in the prediction of major principal stress at failure in both brittle and ductile failure regimes.

Reliability-based design for allowable bearing capacity of footings on rock masses by considering angle of distortion

This study addresses the impact of spatial variability on the angle of distortion between two footings in rock masses. A simple elasto-perfectly-plastic model based on the Hoek–Brown criterion is taken to simulate the spatial variation of rock mass properties in the finite element analyses. This model is calibrated by a large rock mass database. With Monte Carlo simulations, stochastic samples of angle of distortion between two footings are obtained, which are further used to derive reliability-based allowable bearing stresses. The analysis results show that the geological strength index (GSI) of rock masses and uniaxial compressive strength of intact rock are the two dominate factors that affect the reliability-based design. Comparisons to the existing codes show that these codes are appropriate for poor to fair rock masses, conservative for good to very good rock masses and un-conservative for very poor rock masses.

Reply to the Discussion by Arıoglu et al. on “Estimating the Strength of Jointed Rock Masses” by Zhang, DOI 10.1007/s00603-009-0065-x

The author would like to express his thanks to the discussers for their interest in the paper and their effort to provide the community with detailed and constructive comments. The discussers’ comments and concerns are addressed below. It is clearly stated in the paper that ‘‘RQD is only one of the many factors that affect the strength of jointed rock masses.’’ The discussers correctly re-emphasized this point and discussed the effect of joint conditions on the rock mass to intact rock strength ratio (rcm/rc). However, as the discussers correctly stated again in the discussion, in many cases, RQD is the only parameter available for describing rock discontinuities. So, it is extremely important to develop a method for estimation of rock mass strength when only RQD is available. The new rcm/rc versus RQD relation developed in the paper provides such a method for a first hand estimation. When RQD and the joint condition information are available, the rcm/rc versus RQD relation can be used together with other empirical methods considering joint condition to evaluate the rock mass strength. The empirical methods including the new rcm/rc versus RQD relation developed in the paper are for estimating the strength of a jointed rock mass which can be treated as an equivalent continuum in analysis. As stated in the paper, the structure being analyzed must be much larger than the rock blocks formed by the discontinuities in order for the rock mass to be treated as an equivalent continuum. The effect of tunnel span on the strength of rock masses, as described by the discussers, is essentially the scale effect as emphasized in the paper. Disturbance caused by excavation will obviously affect the strength of rock masses. The effect of disturbance can be considered using a disturbance factor as done by Hoek et al. (2002) or modifying the parameter for describing the discontinuities. To use the new rcm/rc versus RQD relation to estimate the strength of disturbed rock masses, the modified RQD should be utilized. The discussers also discussed the effect of loading time on the strength of rock masses. It needs to be noted that the loading time also affects the strength of intact rock. So, if an empirical relation uses the strength ratio rcm/rc and the intact rock strength rc at the corresponding loading time is used, the effect of loading time on the rock mass strength rcm will be (partially) considered. Besides the loading time, loading rate will also affect the strength of both intact rock and rock mass (Kobayashi 1970; Cristescu and Hunsche 1998).

A complement to Hoek-Brown failure criterion for strength prediction in anisotropic rock

In this paper, a complement to the Hoek-Brown criterion is proposed in order to derive the strength of anisotropic rock from strength of the corresponding truly intact rock. The complement is a decay function, which unlike other modifications or suggestions made in the past, is multiplied to the function of the original Hoek-Brown failure criterion for intact rock. This results in a combined and extended form of the criterion which describes the strength of anisotropic rock as a varying fraction of the corresponding truly intact rock strength. Statistical procedures and in particular regression analyses were conducted into data obtained in experiments conducted in the current research program and those collected from the literature in order to define the Hoek-Brown's criterion complement. The complement function was best described by a simple polynomial including only three constants to be empirically evaluated. Further investigations also showed that these constants can be related to the other readily available parameters of rock material which further facilitate determining the constants. A great and prime advantage of the proposed complement is that it is mathematically simple including the least possible number of empirical constants which are easily estimated with minimum experimental effort. Moreover, proposed concept does not suggests any change to the original Hoek-Brown criterion itself or its constants and serves whenever anisotropy does exist in the rock. This further implies on the possibility of using any other failure criterion for intact rock in conjunction with the compliment to reach the strength of anisotropic rock.