Predicting the physico-mechanical properties of rocks from electrical impedance spectroscopy measurements

Electrical resistivity values of eight different samples cored from a fault breccia were measured using an impedance analyser. The uniaxial compressive strength, elastic modulus, point load strength, Schmidt hammer value, P-wave velocity, density and porosity values of the samples were determined in the laboratory. Electrical resistivity values were correlated with the corresponding physico-mechanical properties using the method of least-squares regression and the derived equations were checked by the t and F-test. A strong logarithmic relation between uniaxial compressive strength and resistivity was found. The relation between elastic modulus and resistivity is significant and follows a logarithmic function. Density was linearly, and porosity was exponentially correlated with resistivity.It may be concluded that electrical resistivity can be used as a representative measure of rock properties, particularly for characterizing rocks for which regularly shaped specimen are difficult to obtain. However, the effect of different rock types on the correlations must be further investigated. Additionally, the effect of certain minerals on the rock's resistivity must be taken into account, especially when testing dry or partially saturated rocks.     

A comparative study of stress influence on fracture apertures in fragmented rocks

This study compares the calculated fracture apertures in a fragmented rock layer under different stress scenarios using two different approaches. Approach 1 is a simplified method using a two-dimensional (2D) mapping of the fracture network and projects the far-field stresses to individual fractures, and calculates the dilation, normal and shear displacements using experimental stiffnesses available in the literature. Approach 2 employs a three-dimensional (3D) finite element method (FEM) for the mechanical analysis of the fragmented rock layer considering the interaction with the neighbouring rock layers, frictional interfaces between the rock blocks, stress variations within the fragmented rock layer, and displacements, rotations and deformations of rock blocks. After calculating the fracture apertures using either of the approaches, the permeability of the fragmented rock layer is calculated by running flow simulations using the updated fracture apertures. The comparison between the results demonstrates an example of the inaccuracies that may exist in methods that use simplified assumptions such as 2D modelling, ignoring the block rotations and displacements, projected far-field stresses on fractures, and the stress variations within the rock layer. It is found that for the cases considered here, the permeability results based on apertures obtained from the simplified approach could be 40 times different from the results from apertures calculated using a full mechanical approach. Hence, 3D mechanical modelling implementing realistic boundary conditions, while considering the displacements and rotations of rock blocks, is suggested for the calculation of apertures in fragmented rocks.     

An approach to predicting the shear strength of soil-rock mixture based on rock block proportion

Soil-rock mixture (SRM) shows complicated mechanical behaviors due to their complex compositions and structures, leading to challenging instability problems during the construction process. Typical SRM are composed of rocks with high strength and fine grained soils, and the mechanical characteristic is largely controlled by the rock block proportion (RBP) and component properties. It is noted that the rock sizes of natural SRM make it difficult for laboratory or in situ tests. There are few studies on empirical formulas to predict the mechanical characteristics of SRM. In this study, the nonlinear relationship between SRM shear strength and RBP was investigated, and an empirical formula predicting the shear strength of mixtures consisted of strong rocks and a weak soil matrix was proposed. For this purpose, a database of shear strength and uniaxial compressive strength (UCS) of SRM with different RBPs was built firstly on the basis of the laboratory test results from previous literatures. In order to focus on the interactions of rock blocks and soil matrix in SRM, a RBP range of 30–90% was set as the applicable range of the empirical formula and both of the compositions are held to provide shear resistance in the applicable range. Subsequently, a nonlinear equation to calculate the shear strength of SRM with RBP range of 30–90% was proposed using regression analysis considering the strengths of components and soil-rock contact faces. Several representative properties of rocks and soil matrix, such as RBP, UCS of the matrix (UCS_m), and the friction angle of the blocks (φ_block), were chosen as the input parameters based on the mechanical properties of SRM. An additional parameter “A” was used to describe the connect strengths of the soil-rock contact faces. In addition, uniaxial compression tests and large-scale direct shear tests were performed on the Taoyuan SRM samples. The test results and other measured data from the database were used to compare with the corresponding estimated values. The results demonstrated that the empirical approach could predict the shear strength with R² = 0.75 and can be considered a practical tool in engineering designs when mechanical tests are not available.

     

Strength and failure modes of rock mass models with non-persistent joints

Most problems faced by the practicing rock engineer involve the evaluation of rock mass strength and deformability. The theoretical evaluation of the mechanical properties of fractured rock masses has no satisfactory answer because of the great number of variables involved. One of these variables, the influence of which over rock mass behavior is poorly documented, is the degree of fracture persistence. This paper presents the results of biaxial tests performed on physical models of rock with non-persistent joints. The failure modes and maximum strengths developed were found to depend on, among other variables, the geometry of the joint systems, the orientation of the principal stresses, and the ratio between intermediate stress and intact material compressive strength (σ₂/σ_c). Tests showed three basic failure modes: failure through a planar surface, stepped failure, and failure by rotation of new blocks. Planar failure and stepped failure are associated with high strength behavior, and small failure strains, whereas rotational failure is associated with a very low strength, ductile behavior, and large deformation.     

The effect of rock classes on the relation between uniaxial compressive strength and point load index

Uniaxial compressive strength and point load tests were carried out on 17 igneous, 16 metamorphic and 19 sedimentary rocks and the values correlated with their I _s values. The influence of the different rock type was investigated using regression analysis and the derived equations were statistically tested. Although the derived equation for all data is significant, the data points are scattered and the coefficient of correlation is not strong. However, when the regression analysis was repeated for igneous, metamorphic and sedimentary rocks respectively, the data were less scattered and stronger correlation coefficients were obtained.      

Multifractal characterization of rock fracture surfaces

The multifractal behavior of rock fracture surfaces is studied taking into account fractal heterogeneity and anisotropy of surface structures. A projective covering method (PCM) is proposed and used to estimate directly the fractal dimension D_s[2, 3) of a fracture surface. The study indicates that the multifractal spectrum of the fracture surfaces provide much additional information on the fracture mechanism and the distribution of asperity concentration on the surface. The fracture surfaces induced in rocks under different failure mechanisms display distinct multifractal behavior.     

Nail penetration test for determining the uniaxial compressive strength of rock

We offer a new and practical index test method, the nail penetration test (NPT), to estimate the UCS of intact rocks, to be used as alternative to the point load test (PLT) or Schmidt rebound hammer test (SRH). The major tools used in the investigation include a gasnailer with 130 J power and its nails ranging from 25 to 60 mm in length. The study material covers 65 rock blocks of gypsum, tuff, ignimbrite, andesite, sandstone, limestone, and marble. For the NPT, five nail shots were performed on each block sample and the average value was obtained. Two to three uniaxial compression tests were carried out on each specimen. Ten impacts were applied on rock blocks by using both the L- and N-types of SRH. Regarding the PLT, either 10 axial or 10 block tests was applied on each rock type.The average nail penetration depths were correlated with the UCS, I_S(50) and rebound number for both types of the SRH. Also, the measured UCS values were compared with those obtained from the empirical relationships using the data from the NPT, PLT, and SRH. It was found that the NPT provides better estimates for UCS than the PLT or SRH. Particularly applicable to weak to very weak rocks, the NPT is capable of indirectly estimating the UCS of intact rocks up to 100 MPa. The test is proposed for use in mainly in situ applications.     

Simulation of excavations in jointed rock masses using a practical equivalent continuum approach

A simple practical equivalent continuum numerical model previously presented by Sitharam et al. (Int. J. Rock Mech. Min. Sci. 38 (2001) 437) for simulating the behaviour of jointed rock mass has been incorporated in the commercial finite difference programme fast Lagrangian analysis of continua (FLAC). This model estimates the properties of jointed rock mass from the properties of intact rock and a joint factor (J_f), which is the integration of the properties of joints to take care of the effects of frequency, orientation and strength of joint. A FISH function has been written in FLAC specially for modelling jointed rocks. This paper verifies the validity of this model for three different field case studies, namely two large power station caverns, one in Japan and the other in Himalayas and Kiirunavara mine in Sweden. Sequential excavation was simulated in the analysis by assigning null model available in FLAC to the excavated rock mass in each stage. The settlement and failure observations reported from field studies for these different cases were compared with the predicted observations from the numerical analysis in this study. The results of numerical modelling applied to these different cases are systematically analysed to investigate the efficiency of the numerical model in estimating the deformations and stress distribution around the excavations. Results indicated that the model is capable of predicting the settlements and failure observations made in field fairly well. Results from this study confirmed the effectiveness of the practical equivalent continuum approach and the joint factor model used together for solving various problems involving excavations in jointed rocks.     

Specimen shape and cross-section effects on the mechanical properties of rocks under uniaxial compressive stress

Uniaxial compressive properties of rocks are very important for designing and constructing engineering projects. Based on the available standards for determining these properties, high quality core specimens with proper geometry are needed. In many cases, the standard specimens, especially in clay-bearing, fractured, and weathered rocks, are always not able to be prepared. On the other hand, in some natural conditions, rocks with different size, shape, and cross-section are undergoing uniaxial compressive loading. Therefore, in order to evaluate the uniaxial compressive strength dependency behaviors of rocks on the shape and cross-section of tested specimens, some marble specimens with three different cross-sections, including circular, square, and rectangular, as well as four different shape ratios (height to diameter/width ratio) of 0.5, 1, 2, and 3 were prepared and tested. Axial and lateral strains, acoustic emission (AE), and camera photographs were recorded during the tests. Rock strength behavior was evaluated based on several stress thresholds, including crack closure stress (σ_cc), crack initiation stress (σ_ci), damage stress (σ_cd), and peak stress (σ_ucs). The results indicated that σ_cc was not dependent on the cross-sectional shape of specimens. With increasing shape ratio, σ_cc gradually increased, while σ_cd and σ_ucs greatly decreased, and σ_ci remained at a constant value. The cross-sectional shape effect became operative when r was less than or equal to 1. Moreover, the values of σ_cd and σ_ucs of rectangular prism specimens and square prism specimens are lower than those of cylindrical specimens, indicating that the unstable crack propagation of prism specimens occurs earlier. The difference gap of σ_cd and σ_ucs between specimens with different cross-sectional shapes was dramatically decreased with increasing shape ratio. The AE and camera recorded data indicated that the fracture modes of rectangular and square prism specimens are more likely to change from shearing to slabbing fracture when the shape ratio decreased from 3 to 0.5. The main crack developed surface turned from wide surface to narrow surface with the shape ratio of rectangular prism specimens changing from 3 to 1 and 0.5. The research results are of referential meaning to the design of pillars in underground hard rock mines.

     

Utilizing the strength conversion factor in the estimation of uniaxial compressive strength from the point load index

The strength conversion factor (k) is the ratio between the uniaxial compressive strength (UCS) and the point load index (PLI). It has been used to estimate the UCS from the PLI since the 1960s. Many researchers have investigated the relationship between UCS and PLI for various rock types of different geological origins, such as igneous, sedimentary, and metamorphic rocks. In this study, the k values for subclasses of igneous (pyroclastic, volcanic, and plutonic), sedimentary (chemical and clastic), and metamorphic (foliated and nonfoliated) rocks were evaluated. For this purpose, UCS and PLI data for a total of 410 rock samples extracted from literature published around the world as well as UCS and PLI data obtained in this work for 80 rock samples taken from the Eastern Black Sea Region in Turkey were evaluated together to determine the k values of different rock classes. Strength conversion factors were obtained using zero-intercept regression analysis, formulation, and a graphical approach. This study confirmed that there is no single k value that is applicable to all rock classes. According to statistical analyses, k varied between 12.98 and 18.55 for the rocks studied. These findings demonstrate that the k values derived in this work can be reliably used to estimate the strengths of rock samples with specific lithologies.     

Effects of confinement on rock mass modulus: A synthetic rock mass modelling (SRM) study

The main objective of this paper is to examine the influence of the applied confining stress on the rock mass modulus of moderately jointed rocks (well interlocked undisturbed rock mass with blocks formed by three or less intersecting joints). A synthetic rock mass modelling (SRM) approach is employed to determine the mechanical properties of the rock mass. In this approach, the intact body of rock is represented by the discrete element method (DEM)-Voronoi grains with the ability of simulating the initiation and propagation of microcracks within the intact part of the model. The geometry of the pre-existing joints is generated by employing discrete fracture network (DFN) modelling based on field joint data collected from the Brockville Tunnel using LiDAR scanning. The geometrical characteristics of the simulated joints at a representative sample size are first validated against the field data, and then used to measure the rock quality designation (RQD), joint spacing, areal fracture intensity (P₂₁), and block volumes. These geometrical quantities are used to quantitatively determine a representative range of the geological strength index (GSI). The results show that estimating the GSI using the RQD tends to make a closer estimate of the degree of blockiness that leads to GSI values corresponding to those obtained from direct visual observations of the rock mass conditions in the field. The use of joint spacing and block volume in order to quantify the GSI value range for the studied rock mass suggests a lower range compared to that evaluated in situ. Based on numerical modelling results and laboratory data of rock testing reported in the literature, a semi-empirical equation is proposed that relates the rock mass modulus to confinement as a function of the areal fracture intensity and joint stiffness.     

The influence of grain size and porosity on crack initiation stress and critical flaw length in dolomites

The influence of rock texture on crack initiation stress (σ_i) and critical flaw length (L_i) is studied by a series of triaxial tests performed on monomineralic dolomites. The critical flaw length, as predicted by analytical models, is shown to be larger than the measured mean grain size (d_m) by two–three orders of magnitude. This discrepancy is explained by rock texture variations, which influence the fracture propagation mode and consequently fracture initiation stress. The quantification of rock texture is accomplished using porosity. Fracture initiation stress is shown to be inversely related to both porosity and mean grain size. When porosity is low, the sensitivity of σ_i to mean grain size is high. This effect is reduced with higher porosity values. A model for initial flaw length is developed by a synthesis of Griffith initiation criteria with our empirical model for fracture initiation stress. Initial flaw length is found to be directly proportional to the elastic modulus, mean grain size and porosity of the rock. When porosity and mean grain size decrease simultaneously, the initial flaw length rapidly decreases and approaches the mean grain size value. Therefore, the classical assumption that grain size scales initial flaw size is shown to be valid only in the very restricted case of low porosity-low grain size rocks. In such textures, where void space is minimal, available crystal faces function as truly initial flaws, and variations in mean grain size influence crack initiation stress significantly. In more porous textures, however, the initial flaw length is shown to be up to two orders of magnitude higher than the mean grain size in the rock, depending upon the porosity and mean grain size values. In such textures crack initiation stress is much less sensitive to variations in mean grain size, indicating that the role of individual grains is less significant.     

Predicting the sawability of carbonate rocks using multiple curvilinear regression analysis

Performance measurements of large-diameter circular saws were conducted on 13 different carbonate rocks in marble factories located in Turkey. Rock samples were collected from the factories for laboratory tests. Cohesion, friction angle, uniaxial compressive strength, tensile strength, Schmidt hammer value, point load strength, impact strength, Los Angeles abrasion loss and P-wave velocity values were determined in the laboratory. Slab production and rock properties were evaluated using multiple curvilinear regression analysis and estimation models were developed. Advancing rate of saw, saw diameter, depth of cut, tensile strength and impact strength were included for the best model. Alternative and more universal models were developed, including each rock property in turn together with the rotational speed of the saw. The developed models were verified by statistical tests.It was concluded that the slab production of carbonate rocks using large-diameter circular saws can reliably be estimated using one of the developed models. The models which include Schmidt hammer value, point load strength, impact strength and P-wave velocity have practical and economical advantages for the stone industry.     

TBM performance estimation using rock mass classifications

Three tunnels for hydraulic purposes were excavated by tunnel-boring machines (TBM) in mostly hard metamorphic rocks in Northern Italy. A total of 14 km of tunnel was surveyed almost continually, yielding over 700 sets of data featuring rock mass characteristics and TBM performance. The empirical relations between rock mass rating and penetration rate clearly show that TBM performance reaches a maximum in the rock mass rating (RMR) range 40–70 while slower penetration is experienced in both too bad and too good rock masses. However, as different rocks gives different penetrations for the same RMR, the use of Bieniawski's classification for predictive purpose is only possible provided one uses a normalized RMR index with reference to the basic factors affecting TBM tunneling. Comparison of actual penetrations with those predicted by the Innaurato and Barton models shows poor agreement, thus highlighting the difficulties involved in TBM performance prediction.     

The effect of length to diameter ratio of test specimens on the uniaxial compressive strength of rock

One of the parameters which affect the uniaxial compressive strength (UCS) of rock materials is the length to diameter ratio (L/D) of test cores. ASTM recommends a ratio of between 2 and 2.5, and ISRM suggests 2.5–3:1. Research has shown that high UCS values are obtained for L/D ratios <2, a very slight difference in values between 2 and 2.5, and they remain effectively constant with a L/D ratio >2.5:1. In this study, the shape effect on the UCS of seven rocks was investigated by testing dry cores with L/D ratios from 1 to 2.5:1. Based on the results, a decrease in UCS with increasing L/D ratios up to 2.5:1 was measured for all the rocks except the tuff. By omitting the data from the tuff sample, a correction formula was determined for the rocks tested in this study and results obtained from the literature. However, further work is required on different types of rock to verify or modify this formula.     

Rock fracture toughness testing in Mode II—punch-through shear test

A new testing method called punch-through shear test for measurement of Mode II fracture toughness, K_IIC, of rock is introduced. Results from a finite element modelling (FEM) and a series of laboratory tests on limestone, marble and granite are presented. Core samples with 50 mm diameter are cut to length equal to diameter. Circular notches are drilled to different depths at both ends leaving an intact portion in the centre of the core. The sample is subjected to different confining pressures up to 70 MPa and an axial load is applied to punch through the central portion of the core. K_IIC is calculated from a displacement gradient approach using FEM, assuming linear elasticity to be valid according to the fracture breakdown zone model by Cowie and Scholz. Results from testing show that K_IIC increases with increasing confining pressure and in the order of limestone, marble and granite. At confining pressures higher than 30 MPa the Mode II fracture toughness approaches a constant value. Fracture initiation and propagation differ among the three rock types where grain size is found to have a strong influence on the mechanism of microfracturing and failure. It is suggested that data of K_IIC should be presented for high confining pressures as large confining pressures enhance the appearance of shear fractures.     

Development of a quantitative relationship between unconfined compressive strength and los angeles abrasion loss for carbonate rocks

Dry density, absorption, and uncofined compressive strength were determined for ten NX-size cores of each of the 15 carbonate rocks sampled from various quarries, strip mines, and road cuts. Three Los Angeles abrasion tests were performed on aggregate prepared from the same rock blocks from which the cores were cut. Regression analyses were performed to determine relationships that L.A. abrasion loss, dry density, and absorption may have with unconfined compressive strength. Results indicate that multiple linear regression, with unconfined compressive strength as a function of Los Angeles abrasion loss, dry density, and absorption, yields a useful predictive equation (adjusted R²=0.729) for the rocks studied. The equation was further validated by using test data from five additional samples.     

Stress-dependent shear wave splitting and permeability in fractured porous rock

It is well known that shear wave propagates slower across than parallel to a fracture, and as a result, a travelling shear wave splits into two directions when it encounters a fracture. Shear wave splitting and permeability of porous rock core samples having single fracture were experimentally investigated using a high-pressure triaxial cell, which can measure seismic shear wave velocities in two directions mutually perpendicular to the sample axis in addition to the longitudinal compressive wave velocity. A single fracture was created in the samples using a modified Brazilian split test device, where the cylindrical sample edges were loaded on two diametrically opposite lines by sharp guillotines along the sample length. Based on tilt tests and fracture surface profilometry, the method of artificially induced tensile fracture in the sample was found to create repeatable fracture surfaces and morphologies. Seismic velocities of the fractured samples were determined under different levels of stress confinement and fracture shear displacement or mismatch. The effective confining stress was varied from 0.5 MPa to 55 MPa, while the fractures were mismatched by 0 mm, 0.45 mm and 1 mm. The degree of matching of the fracture surfaces in the core samples was evaluated using the joint matching coefficient (JMC). Shear wave splitting, as measured by the difference in the magnitudes of shear wave velocities parallel (V_S1) and perpendicular (V_S2) to the fracture, is found to be insensitive to the degree of mismatching of the fracture joint surfaces at 2 MPa, and decreased and approached zero as the effective stress was increased. Simple models for the stress- and JMC-dependent shear wave splitting and fractured rock permeability were developed based on the experimental observations. The effects of the joint wall compressive strength (JCS), JMC and stress on the stress dependency of joint aperture were discussed in terms of hydro-mechanical response. Finally, a useful relationship between fractured rock permeability and shear wave splitting was found after normalization by using JMC.     

Correlations between ultrasonic pulse wave velocities and rock properties of quartz-mica schist

Physico-mechanical properties are critically important parameters for rocks. This study aims to examine some of the rock properties of quartz-mica schist (QMS) rocks in a cost-effective manner by establishing correlations between non-destructive and destructive tests. Using simple regression analysis, good correlations were obtained between the pulse wave velocities and the properties of QMS rocks. The results were further improved by using multiple regression analysis as compared to those obtained by the simple linear regression analysis. The results were also compared to the ones obtained by other empirical equations available. The general equations encompassing all types of rocks did not give reliable results of rock properties and showed large relative errors, ranging from 23% to 1146%. It is suggested that empirical correlations must be investigated separately for different types of rocks. The general empirical equations should not be used for the design and planning purposes before they are verified at least on one rock sample from the project site, as they may contain large unacceptable errors.     

Prediction of mode I fracture toughness of rock using linear multiple regression and gene expression programming

Prediction of mode I fracture toughness(KIC) of rock is of significant importance in rock engineering analyses. In this study, linear multiple regression(LMR) and gene expression programming(GEP)methods were used to provide a reliable relationship to determine mode I fracture toughness of rock. The presented model was developed based on 60 datasets taken from the previous literature. To predict fracture parameters, three mechanical parameters of rock mass including uniaxial compressive strength(...