Shear Strength Of Discontinuities Research Articles

Mathematical Modelling of Peak and Residual Shear Strength of Rough Rock Discontinuities Using Continued Fractions

AbstractEstimating the shear strength of large in situ rock discontinuities is often required to assess the stability of rock masses. This estimation is, however, complicated by the well-known scale effect and the fact that the discontinuity surfaces are only partially accessible through traces. A new approach, referred to as the stochastic approach for discontinuity shear strength (StADSS), was recently presented to address these two points. This approach relies on a random field model and a semi-analytical shear strength model, the latter of which is referred to as the NDSS (Newcastle discontinuity shear strength) model. The NDSS model has to be implemented as a numerical code, and because the StADSS model is a Monte Carlo approach with hundreds if not thousands of simulations, the computational time to obtain a shear strength distribution is not negligible. The objective of this study is to find an efficient alternative to the NDSS model in the form of a continued fraction model that can predict the sheared area within a rough discontinuity subjected to direct shearing under constant normal stress as a function of the material strength, effective normal stress applied to the discontinuity and the standard deviation of asperity gradients (defined as the difference in elevation of two points of the surface over the horizontal distance between these points) of the surface. Using a 10/90 training/testing split of the dataset, a memetic algorithm-based truncated continued fraction regression (CFR) model was formulated. The distribution of CFR predictions was found to be very close to that of the dataset used for training. Then, the CFR model was tested against experimental data of the sheared area and shear strength (peak and residual) obtained from small (90 mm per 90 mm) and large (2 m per 2 m) specimens. It was found that 75% of the predictions fall within 20% of the experimental values. The continued fraction regression model can be used as an efficient alternative to the semi-analytical NDSS model, provided that it is used within the bounds of variables used to establish it.

Effect of Anisotropy on Basic and Residual Friction Angles in Schist Rocks

The basic friction angle (φb) tests are a common and practical method used to determine the shear strength of discontinuities. Tilt device is generally used in basic friction angle experiments. In this study, the effects of the anisotropy properties of green and mica schist rocks taken from the copper mine site in Kastamonu Hanönü district on the basic and residual friction angles were investigated. For this purpose, experiments with a specially designed tilt device were conducted on dried and saturated green schist and mica schist samples with orientation angles of 0°, 15°, 30°, 45°, 60°, 75° and 90° relative to the loading axis. According to the results in dried and saturated conditions, maximum basic and residual friction angle values were obtained for green schist samples at 60°. The results were close to each other in the experiments carried out in both saturated and dried conditions. Green schist samples were less affected by the saturated media. Mica schist samples were not affected by anisotropy for both media, and close values were obtained in all orientation angles. It was determined that the basic and residual friction angles were lower in saturated conditions compared to dried ones.

A Shear Device with Controlled Boundary Conditions for Very Large Nonplanar Rock Discontinuities

Abstract The shear strength of rock discontinuities is an important design parameter that is noted to be scale dependent. Historically, discontinuity shear strength and scale dependency studies have used small to medium size laboratory shear devices that accommodate specimens with a relatively small area (0.01 to 1 m2) compared to real discontinuities. In the literature, there is a limited amount of shear strength studies available on discontinuity surfaces with areas of several square meters. This is inherently linked to the challenging nature of performing large shear tests. As shear strength scale dependency is still a timely topic, there is still a need for conducting large scale direct shear tests to support research. To facilitate investigations into the shear response of large discontinuities, a very large shear device was designed and built at the University of Newcastle, Australia. The device is designed to accommodate 2 m by 2 m specimens and restrict rotation and translations of the top surface during shearing. This article presents the design and characteristics of the shear device, the process undertaken to create 2 m by 2 m mortar discontinuity replicas and the experimental results of the first series of direct shear tests conducted. The experimental results confirm the systems design for restricting undesired translations and rotations of the tested specimen surfaces and test repeatability.

Influence of water content on the basic friction angle of porous limestones—experimental study using an automated tilting table

An accurate evaluation of the shear strength of discontinuities is frequently a key aspect for determining the safety of mining and civil engineering works and for solving instability issues at rock mass scale. This is usually done by using empirical shear strength criteria in which the basic friction angle (φb) is a relevant input parameter. Tilt testing is probably the most widespread method to obtain the φb due to its simplicity and low cost, but previous research has demonstrated that the results are strongly affected by several factors (e.g. surface finishing, cutting speed, specimen geometry, wear, time and rock type). In this connection, despite it is well known that water significantly reduces the mechanical properties of sedimentary rocks, very scarce research has focused on assessing the impact of the variations in water content on tilt test results. With the aim to fill this gap, saw-cut slabs of three limestone lithotypes were tilt tested in dry state, wet condition (fully water saturated, non-submerged samples) and under exposure to an environmental relative humidity (RH) of 90%. The results revealed that full water saturation caused moderate φb reductions in two lithotypes and a φb increase in one lithotype. This can be explained by their different microstructure and mineralogy, which makes that lubrication effect prevails over suction effect or vice versa. However, the exposure to a high RH environment did not cause significant φb variations. In addition, some important considerations related to tilt testing are provided and discussed, such as the intrinsic variability of the sliding angle (β) and the impact of multiple sliding on the same rock surfaces on β.

A Study of Instantaneous Shear Mechanical Properties on the Discontinuity of Rock Mass Based on 3D Morphological Properties

In order to study the instantaneous mechanical properties of rock mass discontinuities with different 3D morphologies during the shear process, the Brazilian splitting method is used to prepare natural rock mass discontinuities, and the high-precision 3D scanning test of discontinuities is carried out. The Z 2 is selected as the evaluation parameter of the discontinuities. Based on the graded cyclic shear test results of discontinuities, the influence of the morphology characteristics on the strength and deformation characteristics is analyzed. With the increase of shear times, the 3D morphology characteristic parameters of the structural plane decrease steadily after the graded cyclic shear. Based on the test curve, the graded cyclic shear characteristics of rock mass discontinuities are analyzed from the shear deformation, and the shear process of the discontinuities is finely divided by combining with the variation characteristics of shear stiffness. Combined with the 3D morphology parameters, an empirical formula for the shear strength of discontinuities is proposed. Through verification, the effect of the new model is better than that of the classical JRC-JCS model.

Quantification of joint roughness using various empirical relations between JRC and roughness parameters

The mechanical and hydraulic properties of rock joints are significantly controlled by the joint surface roughness at low normal stresses. For this reason, it is necessary to accurately quantify joint roughness. The Joint Roughness Coefficient (JRC) has been widely used in engineering practice to quantify joint roughness and to estimate discontinuity shear strength over the years. However, several researchers have pointed out drawbacks of the JRC. This study presents a review of various attempts that have been made over the years to improve JRC and reduce its subjectivity. In addition, various empirical equations that are available in the literature between JRC and roughness parameters at 0.5 mm sampling interval have been assessed and compared using some widely accepted roughness parameters including the root mean square of the slope of the profile, Z 2 , structure function, SF, the maximum apparent dip angle in the shear direction/an empirical roughness parameter + 1, θ*Max/[C+1] 2D , and the standard deviation of the inclination angle of the profile, SD θ P . Using a one-meter square joint surface digitized at 0.5 mm sampling interval, over 1715 joint profiles in the X direction and 1,515 joint profiles in the Y direction have been used to calculate JRC values through the aforementioned roughness parameters and empirical equations at joint lengths of 1000 mm, 500 mm, 250 mm and 125 mm, and the roughness anisotropy has been studied. New empirical relations have also been suggested in this study between JRC and four roughness parameters based on Barton’s ten standard profiles digitized at 0.5 mm. The suggested empirical relations were successfully used to quantify the roughness of the studied rock joint surface.

Determination of the basic friction angle ϕb of joints using the field tilt test: results of various “fast” tests on outcrops

The basic friction angle of rock joints is usually obtained from tilt tests, being the most common the laboratory tilt tests. This test has been standardized according to the ISRM. However, most of the times when calculating the shear strength of discontinuities, reference tables are used to obtain the basic friction value for the lithology under study. These tables omit some lithologies complicating the search of adequate references. An alternative, straightforward and economical way to obtain ϕb is through the field tilt test, which is carried out by sliding two blocks aside a joint. It is a well-known test, but there are few references to its implementation. In this test, unlike the laboratory tilt test, the samples are not “polished” and it is necessary to evaluate the roughness of the joint and the normal component to the weight of the upper blocks. The idea is to calculate the term of ϕb from the Barton-Bandis’ equation and include the tilt angle α. Various tilt-test measurements were carried out with field blocks on both sides of the same joint, considering different lithologies (granite, limestone, andesite, dacite, coal and slate) and block sizes, evaluating the ideal ranges of applicability of the test.

The Analytical Investigation on the Shear Strength of Discontinuities in Rocks Considering the Effect of Roughness and Dilatancy Angle

The Analytical Investigation on the Shear Strength of Discontinuities in Rocks Considering the Effect of Roughness and Dilatancy Angle

DEVELOPMENT OF A MODEL FOR THE ESTIMATION OF SHEAR STRENGTH OF DISCONTINUITY IN MASSIVE AND KARSTIFIED LIMESTONE

In this paper, the problem of estimating the shear strength of discontinuity is presented, which especially occurs in massive and karstified limestones, where discontinuity walls can be extremely rough and irregular, with or without filling material, and for which the current models have proven to be unsatisfactory. A characteristic example of such limestones is the deposit of dimension stone “Kanfanar”, located on the Istrian peninsula in Croatia. For the purpose of developing a model for estimating the shear strength of discontinuity, field research was conducted in which large samples of blocks with natural discontinuities were prepared, as well as samples of filling material in limited conditions, on which detailed laboratory tests of shear strength were performed. Special attention was paid to determining the joint roughness coefficient JRC, the actual contact area between the discontinuity walls, the basic or residual friction angle and the friction angle of the built-in filling material between the discontinuity surfaces. The development of the model for estimating the shear strength of discontinuity was based on Barton’s JRC-JCS empirical model, given the fact that it is one of the most commonly applied models in engineering practice. Based on the results of the tests, a modification of Barton’s JRC-JCS model was made, in such a way that the friction angle of the built-in filling material in the case of discontinuity with a filling was applied instead of the basic or residual friction angle. In addition, for the correct evaluation of the roughness of the discontinuity walls in massive and karstified limestones, it was found that it is necessary to increase the roughness coefficient to values larger than 20, which has been proposed as the maximum so far. Evaluation of the proposed model showed that it is satisfactorily accurate in estimating the shear strength of discontinuity with clay filling material of different states of consistency.

Rock mass properties and their suitability as a foundation for a rolled compacted concrete gravity dam: case study of Beni Haroun dam (Mila, NE Algeria)

Dams are generally designed and built to resist the most severe destabilizing conditions. Their failures have caused severe damages and loss of lives through history. The investigations carried out on failed dams have, in most cases, unveiled that foundation problems are usually the cause. These problems are very often related to the condition of discontinuities dissecting the rock foundations. Being weak, they are the preferred planes for deformation and rupture causing the collapse of the whole structure. This study deals with the rock mass properties and their suitability as rock foundation for Beni Haroun dam, the largest dam in Algeria. The dam is located in the north-eastern part of Algeria on Wadi El-Kebeir, approximately 40 km from its outfall in the Mediterranean Sea. The dam is a roller-compacted concrete type with a height of 120 m, a crest length of 710 m, and a water storage capacity of approximately 1 billion m3. The dam is founded on Ypresian limestone rock mass. The present study was carried out both in the field and in a laboratory. The field study included geological mapping of the engineering, an intensive discontinuity survey, and sampling. Laboratory tests were conducted to determine shear strength, uniaxial compressive strength, tensile strengths, and Young’s modulus of rock samples. The shear strength of discontinuity was evaluated according to the criterion developed by Barton and Choubey. The joint roughness coefficient was calculated through a statistical approach using the parameter Z2, and an empirical approach based on a visual comparison with standard profiles of the Barton–Choubey roughness. The quality of the rock mass was estimated using Rock Mass Rating (RMR) and Geological Strength Index (GSI) systems. The stability of the dam foundation was assessed using the DMR system and the Hoek and Brown failure criteria. The rock mass of the dam foundation is the Ypresian limestone formation and is of fair quality. This study has shown that this rock mass is adequate as foundation for Beni Haroun RCC dam.

Comparison of experimental and empirical methods for estimating the shear strength of rock joints based on the statistical approach

One of the most common geological hazards in mining and civil projects is the occurrence of instability in the rock slopes. Rock slope behavior is mainly influenced by the presence of discontinuities in the rock masses. Therefore, the determination of shear strength parameters for these weak surfaces is of particular importance. There are various shear strength criteria for estimating the shear strength of discontinuities, which among them the Barton–Bandis criterion (B‒B criterion) and Mohr–Coulomb criterion (M‒C criterion) are the most widely used. Accurate estimation of shear strength properties does not only depend on the correct procedure of tests, but it requires an accurate and detailed explanation of test results. The uncertainty in the measured shear strength leads to many problems in the analyzing and designing of rock slopes. Therefore, to reduce the uncertainty and increase the accuracy of rock slopes analyzing, it is better to use probability methods. The probability distribution function can be assigned for each input parameter of the failure criterion. In this research, the results of the direct shear tests related to Azad pumped storage power plant project have been considered to estimate the shear strength properties of rock discontinuities. The results are divided into three groups based on the magnitude of the joint roughness coefficient (JRC). Shear strength for each group is estimated depending on the two most well-known criteria i.e., the B‒B criterion and the M‒C criterion. Further, the probability distribution functions (PDF) for each shear strength parameter are determined by @RISK software. Besides, the results of the empirical B‒B criterion are compared with the results of the direct shear tests for the three groups of rock joints. The confidence intervals associated with both criteria are estimated and compared together. The results showed that the overlapping of the confidence interval of the M‒C criterion with the confidence interval of B‒B criterion increases with increasing JRC of rock joint. The results show the B‒B criterion covers data of the direct shear test almost at low normal stress levels for different JRC groups too.

Influence of Shear Rate on the Shear Strength of Discontinuities with Different Joint Roughness Coefficients

Abstract Loading rate dependency is one of the significant time-dependent behaviors of rock and rock discontinuities. To investigate the shear rate– dependent behavior of the shear strength of discontinuities with different joint roughness coefficients (JRCs), direct shear tests with various shear rates were conducted on samples with artificial joint surfaces based on Barton’s standard profile lines. A new test method, called shear test with alternate shear rates, was introduced to verify the direct shear results, and a JRC weakening model was established to explain the mechanism of shear rate dependency of discontinuities and the influence of the JRC on shear rate dependency. Results revealed that the shear strength increased with an increase in shear rate and the shear rate dependency of discontinuities was significantly influenced by surface morphology. Hence, the greater the JRC is, the stronger the shear rate dependency will be. Results also demonstrated that the direct shear test is the process of the JRC resistance weakening and frictional resistance strengthening, and the shear rate dependency was caused by the time-dependent behavior of the crack growth.

Shear velocity-based uncertainty quantification for rock joint shear strength

The shear strength of rock joints is an important property required in order to analyze the stability of rock slopes and tunnels. However, estimation of the shear strength of rock joints for in situ conditions is a complex task due to various influencing factors present in the field. Among these factors, the shear velocity or the shear displacement rate along the rock joints are important parameters which are relatively less studied since their effect is considered to be of second order compared to other factors. However, some recent studies in the literature suggest that shear velocity has a significant influence on the shear strength of rock joints, and hence the shear strength of joints estimated at low shear velocities in laboratories cannot be used under in situ conditions where the possibility of higher shear velocities exist due to the presence of different factors, such as blasting, excavation, and thermal and seismic loads. In this paper, we have addressed these issues in three steps. In the first step, an experimental study on jointed rock specimens is presented to investigate the influence of the displacement rate on the shear strength of rock joints. In the second step, a probabilistic method is developed based on the experimental results and the compiled data from the literature to estimate the in situ shear strength of joints under higher displacement rate conditions, i.e., blasting, excavation, and seismic loads from laboratory-estimated shear strength at the International Society for Rock Mechanics suggested low displacement rates. In the third step, a case study of a Himalayan rock tunnel was used to demonstrate the described approach. It was observed that the shear strength of discontinuities reduced with ncreasing shear velocity and that the rate dependency was higher for low-density rocks and under high confining stress. Further, a considerable effect was observed on the probability of failure of the rock tunnel when the effect of shear velocity was considered in the stability analysis.

Range Versus Surface Denoising of Terrestrial Laser Scanning Data for Rock Discontinuity Roughness Estimation

Surface roughness represents a major component of rock discontinuity shear strength. To achieve comprehensive, accurate, and efficient estimates of in situ discontinuity roughness, the traditional contact measuring methods are being replaced by advanced remote-sensing technologies. Terrestrial laser scanner (TLS) is well suited for measuring large inaccessible discontinuities; however, inherent TLS range noise strongly influences the surface details and roughness estimation. The aim of this research is to establish an optimal wavelet-denoising procedure for the TLS data acquired with different scanning configurations (range and incidence angle), and for rock discontinuities having different roughness characteristics and surface reflectivity. The conventional discrete wavelet transform and stationary wavelet transform in combination with four threshold selection methods are applied on TLS data in the direction of range measurements (range denoising) and in the direction perpendicular to the best-fit plane (surface denoising). The performance of the denoising procedures is assessed by comparing the range and surface-denoised TLS surfaces with reference surfaces acquired with the Advanced TOpometric Sensor. Comparative analyses of the roughness calculated according to the angular thresholding method (Grasselli, in Shear strength of rock joints based on quantified surface description, Ph.D. thesis. EPF Lausanne, Lausanne; Grasselli, Shear strength of rock joints based on quantified surface description, Ph.D. thesis, EPF Lausanne, Lausanne, 2001) indicate that all the denoising methods improve the roughness estimated from the TLS data appreciably; however, the level of improvement depends intrinsically on geometrical characteristics of the rock surface and scanning configuration. Range denoising has been found to provide more reliable noise estimations.

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.

Influence of weathering-induced iron precipitation on properties of sandstone in a tropical environment

Weathering-induced iron dissolution and precipitation in rock masses lead to reduction in shear strength of discontinuities, amongst others, while precipitation leads to an increase, and precipitated iron may reduce the susceptibility to future weathering. This effect is investigated in fieldwork campaigns with detailed rock mass characterization and chemical analyses in Kota Kinabalu, Malaysia. Many cut slopes in this area consist of different zones in which iron in various forms is either dissolved or precipitated. Iron-coated and -cemented discontinuities have a marked higher shear friction, while staining has little influence on friction. Discontinuities with iron-coating and -cementing reduce the susceptibility to weathering of a rock mass as weathered material is less easily eroded and underlying material is protected from further weathering. On the other hand, dissolution zones, which are mostly found below the precipitation zones, have considerably lower rock mass quality. In engineering works the latter are invisible before excavation. Just assuming the continuation downward of the surface rock mass with precipitated iron, or, worse than this, assuming a less weathered rock mass with better characteristics, may be very erroneous. This study emphasizes that forecasting the susceptibility to weathering should include the influence of morphology, environment and climate.

Elastoplastic constitutive model for hydraulic aperture analysis of hydro-shearing in geothermal energy development

Geothermal energy is renewable, clean and green energy generated and stored in the Earth’s crust. The most important consideration for geothermal energy development in non-hydrothermal scenarios is the use of hydraulic fracturing technology to establish an effective network pathway to conduct fluid from injectors to producers. Hydraulic fracturing in geothermal wells is referred to as hydro-shearing and the aim is to improve the conductivity of natural fractures. In this paper, linear elastic constitutive relationships and shear strength of discontinuities in the pre-peak region are initially considered. Based on the dynamic frictional weakening, a proved conductive aperture and the post-peak elastoplastic constitutive models are proposed to analyze the deformation and conductivity of the natural fracture. Simulation research has shown that the joint compressive strength (JCS) mainly affects the shear displacement and hardly affects the dilation. The joint roughness coefficient (JRC) is more important for decreasing the shear strength and improves the dilation aperture. To no one’s surprise, reducing the effective normal stress is the best way for increasing the shear displacement, dilation and conductivity of the natural fracture. Almost 90% of the slip displacement and dilation occurs after fracture shear failure. This displacement not only increases the hydraulic conductivity of the fracture, but also reduces the required surface pumping pressure.

Peak shear strength prediction for discontinuities between two different rock types using a neural network approach

The peak shear strength of discontinuities between two different rock types is essential to evaluate the stability of a rock slope with interlayered rocks. However, current research has paid little attention to shear strength parameters of discontinuities with different joint wall compressive strength (DDJCS). In this paper, a neural network methodology was used to predict the peak shear strength of DDJCS considering the effect of joint wall strength combination, normal stress and joint roughness. The database was developed by laboratory direct shear tests on artificial joint specimens with seven different joint wall strength combinations, four designed joint surface topographies and six types of normal stresses. A part of the experimental data was used to train a back-propagation neural network model with a single-hidden layer. The remaining experimental data was used to validate the trained neural network model. The best geometry of the neural network model was determined by the trial-and-error method. For the same data, multivariate regression analysis was also conducted to predict the peak shear strength of DDJCS. Prediction precision of the neural network model and multivariate regression model was evaluated by comparing the predicted peak shear strength of DDJCS with experimental data. The results showed that the capability of the developed neural network model was strong and better than the multivariate regression model. Finally, the established neural network model was applied in the stability evaluation of a typical rock slope with DDJCS as the critical surface in the Badong formation of China.

Degradation of a discrete infilled joint shear strength subjected to repeated blast-induced vibrations

This paper presents the results of a series of numerical modeling experiments aimed at quantifying blast-induced degradation of shear strength of discontinuities. Near-field vibration history of a single-row production blast in a limestone quarry was used as input to the numerical model. For this purpose, two rock blocks, representing a stiff massive sulfide rock and a weaker limestone rock, were simulated using the 2D Particle Flow Code (PFC2D). Rock mass containing a single inclined joint was modeled as Mohr-Coulomb. The results show that the crack generation rate is increased in both samples after repetitive vibration loading. Joint shear strength degradation rate in the stiffer massive sulfide rock sample is higher than the softer limestone rock, which is attributed to the higher seismic impedance mismatch. The results show that even low-amplitude blasting vibrations (<80 mm/s), when repeated as in multi-hole blasts, can significantly degrade joint shear strength in the nearby pit walls.

Correction to: Rapid field test for shear strength characterization of dacite at Cerro Rico de Potosi (Bolivia): tilt test with a Schmidt hammer and compass-clinometer

In competent rock masses submitted to low shear stress (e.g., close to the surface), stability is controlled by the geometry of blocks and strength of the discontinuity planes that separate the blocks. The basic friction angle is a relevant parameter to estimate shear strength of discontinuities. The most employed technique to determine the basic friction angle is the tilt test, which can be applied in laboratory settings or in situ, utilizing two blocks of rock that are tilted until the top block slides. No studies on the determination of basic friction angle in field settings were found for specific volcanic rocks such as andesites, dacites and rhyolites, which are typical of the acid and intermediate volcanism of Andean mountain range volcanoes. Rhyodacitic rocks of the Potosi mine, in Bolivia, were selected for basic friction angle characterization in situ. Cerro Rico is 4782 m high, and has been declared a humanity heritage site along with the city of Potosi in 1987, being one of the most important silver mines in the world. Cerro Rico is constituted by an intrusion of dacitic volcanic rocks with silver and tin mineralization. The results of the study agree with basic friction values of intrusive rocks with similar texture. It is highlighted that this simple field methodology is useful and effective to obtain preliminary values of shear strength for discontinuities. The obtained values of basic friction for rhyodacite add to the database of geomechanical rock characterization.