An Investigation into the Rock Properties Influencing the Strength in Some Granitoid Rocks of KwaZulu-Natal,South Africa

The uniaxial compressive strength (UCS) of rocks is a critical parameter required for most geotechnical projects. However, it is not always possible for direct determination of the parameter. Since determination of such a parameter in the lab is not always cost and time effective, the aim of this study is to assess and estimate the general correlation trend between the UCS and indirect tests or indexes used to estimate the value of UCS for some granitoid rocks in KwaZulu-Natal. These tests include the point load index test, Schmidt hammer rebound, P-wave velocity (V_p) and Brazilian tensile strength (σ_t). Furthermore, it aims to assess the reliability of empirical equations developed towards estimating the value of UCS and propose useful empirical equations to estimate the value of UCS for granitoid rocks. According to the current study, the variations in mineralogy, as well as the textural characteristics of granitoid rocks play an important role in influencing the strength of the rock. Simple regression analyses exhibit good results, with all regression coefficients R² being greater than 0.80, the highest R² of 0.92 being obtained from UCS versus σ_t. Comparison of equations produced in the current study as well as empirical equations derived by several researchers serves as a validation. Also illustrate that the reliability of such empirical equations are dependent on the rock type as well as the type of index tests employed, where variation in rock type and index tests produces different values of UCS. These equations provide a practical tool for estimating the value of UCS, and also gives further insight into the controlling factors of the strength of the granitoid rocks, where the strength of a rock is a multidimensional parameter.     

An Empirical Correlation of Index Geomechanical Parameters with the Compressional Wave Velocity

The geomechanical strength of rockmass plays a key role in planning and design of mining and civil construction projects. Determination of geomechanical properties in the field as well as laboratory is time consuming, tedious and a costly affair. In this study, density, slake durability index, uniaxial compressive strength (UCS) and P-wave velocity tests were conducted on four igneous, six sedimentary and three metamorphic rock varieties. These properties are crucial and used extensively in geotechnical engineering to understand the stability of the structures. The main aim of this study is to determine the various mechanical properties of 13 different rock types in the laboratory and establish a possible and acceptable correlation with P-wave velocity which can be determined in the field as well as laboratory with ease and accuracy. Empirical equations were developed to calculate the density, slake durability index and UCS from P-wave velocities. Strong correlations among P-wave velocity with the physical properties of different rock were established. The relations mainly follow a linear trend. Student’s ‘t’ test and ‘F’ test were performed to ensure proper analysis and validation of the proposed correlations. These correlations can save time and reduce cost during design and planning process as they represent a reliable engineering tool.     

基于P波模量的岩石单轴抗压强度预测

传统获取岩石单轴抗压强度参数需要钻进取样、加工制作等严格的试验步骤,需要建立一种参数易于获取且准确的岩石单轴抗压强度预测公式。基于岩石物理力学参数的内在联系,建立了岩石单轴抗压强度与岩石P波模量的关系式。根据英安斑岩和页岩两种岩石的干密度、P波速度及单轴抗压强度的测试数据,采用线性拟合的方法建立了岩石基于P波模量的单轴抗压强度预测公式,并采用统计检验的方法对上述预测公式与传统基于P波速度的预测公式进行了对比分析。结果表明,所建立的强度预测通式简单、精度高,模量容易获取,具有很强的实用性。     

Application of statistical methods for predicting uniaxial compressive strength of limestone rocks using nondestructive tests

Uniaxial compressive strength (UCS) of an intact rock is an important geotechnical parameter for engineering applications. Using standard laboratory tests to determine UCS is a difficult, expensive and time-consuming task. The main purpose of this study is to develop a general model for predicting UCS of limestone samples and to investigate the relationships among UCS, Schmidt hammer rebound and P-wave velocity (V _P). For this reason, some samples of limestone rocks were collected from the southwestern Iran. In order to evaluate a correlation, the measured and predicted values were examined utilizing simple and multivariate regression techniques. In order to check the performance of the proposed equation, coefficient of determination (R ²), root-mean-square error, mean absolute percentage error, variance accounts for (VAF %), Akaike Information Criterion and performance index were determined. The results showed that the proposed equation by multivariate regression could be applied effectively to predict UCS from its combinations, i.e., ultrasonic pulse velocity and Schmidt hammer hardness. The results also showed that considering high prediction performance of the models developed, they can be used to perform preliminary stages of rock engineering assessments. It was evident that such prediction studies not only provide some practical tools but also contribute to better understanding of the main controlling index parameters of UCS of rocks.     

Artificial neural network model for prediction of rock properties from sound level produced during drilling

In many rock engineering applications such as foundations, slopes and tunnels, the intact rock properties are not actually determined by laboratory tests, due to the requirements of high quality core samples and sophisticated test equipments. Thus, predicting the rock properties by using empirical equations has been an attractive research topic relating to rock engineering practice for many years. Soft computing techniques are now being used as alternative statistical tools. In this study, artificial neural network models were developed to predict the rock properties of the intact rock, by using sound level produced during rock drilling. A database of 832 datasets, including drill bit diameter, drill bit speed, penetration rate of the drill bit and equivalent sound level (L_eq) produced during drilling for input parameters, and uniaxial compressive strength (UCS), Schmidt rebound number (SRN), dry density (ρ), P-wave velocity (V_p), tensile strength (TS), modulus of elasticity (E) and percentage porosity (n) of intact rock for output, was established. The constructed models were checked using various prediction performance indices. Goodness of the fit measures revealed that recommended ANN model fitted the data as accurately as experimental results, indicating the usefulness of artificial neural networks in predicting rock properties.     

The effect of cubic specimen size on uniaxial compressive strength of carbonate rocks from Western Turkey

One of the most important quality and design parameters of natural rock materials is uniaxial compressive strength (UCS). UCS value of a building stone determines its application area such as cladding, roofing, facing, and coverings. In rock mechanics and engineering practice determination of UCS values of rock materials is suggested on core specimens whereas in construction and building stone sector, cubic specimens are suggested. In this experimental study, the effect of cubic specimen size on UCS values of some carbonate rocks which are being used as dimension stones are investigated. A total of 299 cubic specimens at five different edge sizes (3, 5, 7, 9, and 11 cm) from limestone, marble, and travertine are prepared. Chemical, petrographic analyses and physical properties of specimens are determined and after that UCS tests are carried out. It is observed that as the specimen sizes increase from 3 to 11 cm, average UCS values decrease about 7% for the tested carbonate rocks. In the light of this finding, results of UCS tests could be interpreted considering cubic specimen sizes for the same rock types in various fields.     

Use of the Boussinesq Equation for Determining the Distribution of Stress Within a Diametrical Point Load Test

Summary The maximum tensile stress at failure for a dry specimen, as determined by the Boussinesq equation for the diametrical point load test, was found to be in very good agreement with the diametrical point load tensile strength (Is) as defined by ISRM (1985). The force at failure for specimens of different geometry was used to determine the stress distribution along the line of loading. Distinctive tensile stress gradients dominate almost 84 percent of the specimen radius regardless of the size of the specimen. The maximum tensile stress is located away from the centre of the specimen at a distance approximately 76 percent along the specimen radius, measured from the centre. The stress magnitude at the centre of the specimen is small and represents about 13 percent of the maximum tensile stress calculated, which suggests that the initiation of the fracture is not from the specimen centre. At the zone of contact between the specimen and the loading cones there exists great compressive stress in areas where much material destruction occurs under the loading platen cones. The value of this compressive stress varies from specimen to specimen and, for the material used in these experiments (Oolitic limestone), ranges from 5.3 to 7.2 times the dry unconfined compressive strength of the material. According to the ISRM Suggested Method for Point Load Test, Is ₍₅₀₎ is approximately 0.8 times the uniaxial tensile strength. The maximum tensile stress revealed by the Boussinesq equation (Bs) was correlated with Is ₍₅₀₎ and found to be in the order of 0.9 times the uniaxial tensile strength.     

DEM Simulation of Direct Shear: 2. Grain Boundary and Mineral Grain Strength Component Influence on Shear Rupture

The influence of mineral grain and grain boundary strength is investigated using a calibrated intact (non-jointed) brittle rock specimen subjected to direct shear with a particle-based distinct element method and its embedded grain-based method. The adopted numerical approach allows one to independently control the grain boundary and mineral grain strength. The investigation reveals that, in direct shear, the normal stress (σ _n) applied to a rock specimen relative to its uniaxial compressive strength (UCS) determines the resulting rupture mechanism, the ultimate rupture zone geometry, and thus its shear stress versus horizontal displacement response. This allows one to develop a rupture matrix based on this controlling parameter (i.e., σ _n/UCS). Mineral grain strength reductions result in the lowering of the apparent cohesion intercept of the peak linear Coulomb strength envelope, while grain boundary strength reductions change the peak linear Coulomb strength envelope to a bi-linear or curved shape. The impact of grain boundary strength is only relevant at σ _n/UCS ratios <0.17 where tensile and dilatant rupture mechanisms dominate. Once shear rupture begins to be the dominant rupture mechanism in a brittle rock (i.e., at σ _n/UCS ratios >0.17), the influence of weakened grain boundaries is minimized and strength is controlled by that of the mineral grains.     

Lower crustal fluid distribution in the northeastern Japan arc revealed by high-resolution 3D seismic tomography

The Ou Backbone Range strikes northwards through the central northeastern Japan arc and is bounded on both sides by the active reverse Uwandaira and Sen'ya faults. We have applied a traveltime inversion method (seismic tomography) with spatial velocity correlation to active and passive seismic data in order to investigate a three-dimensional (3-D) velocity structure. The data set contains 33,993 P- and 18,483 S-wave arrivals from 706 natural sources and 40 blasts, as well as 2803 P-wave traveltime data from 10 explosions detonated during the 1997 controlled source experiment. The traveltime inversion reveals a zone beneath the Ou Backbone Range in which P-wave velocities (V_P) are approximately 6–8% lower than the average velocity at equivalent depths. The low V_P and a low V_P to S-wave velocity (V_S) ratio (V_P/V_S) of about 1.65 suggest the presence of aqueous fluids in the middle crust.     

Analysis of size effects on the geomechanical parameters of intact granite samples under unconfined conditions

A total of 28 uniaxial compressive strength tests were performed on cylindrical Blanco Mera granite samples with diameters ranging between 14 and 100 mm, with results indicating that this granite undergoes a significant reverse size effect: the UCS increases as sample diameter increases up to 54 mm, but thereafter decreases. It was also found that the results tend to be more scattered for smaller sample diameters. We also found an apparent correlation between Young’s modulus and sample diameter. It was not possible to draw any clear conclusions regarding the variability in Poisson’s ratio with sample size. With respect to crack initiation and crack damage stresses, the behaviour of the tested samples also indicates a reverse effect. This research would suggest that the traditionally assumed decrease in strength as sample size increases does not hold for granite samples with diameters below 54 mm.     

In-situ Rock Spalling Strength near Excavation Boundaries

It is widely accepted that the in-situ strength of massive rocks is approximately 0.4 ± 0.1 UCS, where UCS is the uniaxial compressive strength obtained from unconfined tests using diamond drilling core samples with a diameter around 50 mm. In addition, it has been suggested that the in-situ rock spalling strength, i.e., the strength of the wall of an excavation when spalling initiates, can be set to the crack initiation stress determined from laboratory tests or field microseismic monitoring. These findings were supported by back-analysis of case histories where failure had been carefully documented, using either Kirsch’s solution (with approximated circular tunnel geometry and hence σ _max = 3σ ₁ ?σ ₃) or simplified numerical stress modeling (with a smooth tunnel wall boundary) to approximate the maximum tangential stress σ _max at the excavation boundary. The ratio of σ _max /UCS is related to the observed depth of failure and failure initiation occurs when σ _max is roughly equal to 0.4 ± 0.1 UCS. In this article, it is suggested that these approaches ignore one of the most important factors, the irregularity of the excavation boundary, when interpreting the in-situ rock strength. It is demonstrated that the “actual” in-situ spalling strength of massive rocks is not equal to 0.4 ± 0.1 UCS, but can be as high as 0.8 ± 0.05 UCS when surface irregularities are considered. It is demonstrated using the Mine-by tunnel notch breakout example that when the realistic “as-built” excavation boundary condition is honored, the “actual” in-situ rock strength, given by 0.8 UCS, can be applied to simulate progressive brittle rock failure process satisfactorily. The interpreted, reduced in-situ rock strength of 0.4 ± 0.1 UCS without considering geometry irregularity is therefore only an “apparent” rock strength.     

Anchorage behaviour of reinforced specimens containing a single fissure under uniaxial loading: a particle mechanics approach

Particle flow code (PFC^2D) software was adopted to investigate the anchorage behaviour and the characteristics of crack initiation, propagation and coalescence of reinforced specimens containing a single fissure (RSCSF). The microscopic parameters of the specimens in the numerical simulation were first validated by experimental outcomes of intact specimens, while the microscopic parameters of the rock bolts were validated based on the results of the RSCSF tests. Then, the mechanical parameters as well as the failure modes in the physical experiments were compared with those derived by the numerical simulation; the results showed good agreement between the simulated macroscopic mechanical properties and failure modes and those obtained in the laboratory experiments. The peak strength, number of cracks and the failure mode varied considerably as the anchorage angle α and fissure angle β increased. Three types of stress–strain curves, types I to III, were obtained from the RSCSF. Shear cracks were observed for all three categories of curves, but the tensile cracks were dominant. The number of cracks and the rate of bond failures decreased as the curve changed from type II to type I to type III. RSCSF failure can be classified into three failure modes: (1) tip crack propagation mode, (2) midpoint crack propagation mode and (3) rock bolt crack propagation mode. These failure modes are primarily differentiated by relations between α and β, and the ratio UCS_S/UCS_I between the uniaxial compressive strength (UCS, σ _max) of the RSCSF (UCS_S) and the uniaxial compressive strength of the intact specimen (UCS_I).     

Size and shape effects in point load tests of irregular rock fragments

Summary Point-load tests were performed on three hard rocks of the Lake Superior district, ironformation, metadiabase, and ophitic basalt. More than 500 irregular, mine-run fragments ranging in diameter up to about 250 mm were tested in the field, using a specially designed, semi-portable test rig. Results were analyzed by multiple regression techniques, seeking a best expression for the point-load strength in terms of a size effect and shape effects. Standard unconfined compression tests and Brazilian tests were also performed on the metadiabase and the basalt, three core sizes of each, in order to determine their respective size effects. The size-effect exponents for compression were found to be a variable characteristic of rock type, as previously reported for other rocks by the senior author, whereas the size-effect exponent in the point-load test was constant over all three rocks.Notation A Load-bearing area of prismatic compression specimen, mm² - Probability level of a statistical significance test - b, w Long and short prism dimensions, mm, in plane perpendicular to load - c _i ,c _L Exponent in equation for strength (coefficient, in the log-linear form) - d Diameter, mm - D, H Initial and final (at rupture) distance between the load points, mm - E Young's modulus, MPa - F Axis of the fracture surface normal toD, mm, point-load test - G, J Semiminor, semimajor, specimen axis, mm, perpendicular to direction of point load - h Height of prismatic compression specimen, mm - K Constant in linear regression model, basic rock strength parameter - L, M, S Long, intermediate, and short axes, of point-load-test specimen - log Natural (Napierian) logarithm - n Number of tests - v Poisson's ratio - P Resistance of test specimen at rupture, Newtons - Q Compressive strength, MPa, determined from unconfined compression test - R Multiple correlation ratio for a multilinear regression analysis - SE Standard error of estimate for a multilinear regression analysis - T Tensile strength, MPa, determined from diametral compressive test of core - t Thickness, mm - U Geometric mean diameter, mm, of the minimum cross section through the load points=(DG)^1/2 - V Geometric mean diameter, mm, of point-load specimen=(LMS)^1/3 - W Geometric mean diameter, mm, of the specimen midsection perpendicular to the point-load direction=(GJ)^1/2 - X, Y Geometric mean diameter, mm, of the fracture surface, estimated by (DF)^1/2, by (HF)^1/2 - Z _LM ,Z _RA , ... Differences between values of logK, used to express category effects, those attributed to specimen orientation and/or rock type     

Prediction of strength parameters of sedimentary rocks using artificial neural networks and regression analysis

Accurate laboratory measurement of geo-engineering properties of intact rock including uniaxial compressive strength (UCS) and modulus of elasticity (E) involves high costs and a substantial amount of time. For this reason, it is of great necessity to develop some relationships and models for estimating these parameters in rock engineering. The present study was conducted to forecast UCS and E in the sedimentary rocks using artificial neural networks (ANNs) and multivariable regression analysis (MLR). For this purpose, a total of 196 rock samples from four rock types (i.e., sandstone, conglomerate, limestone, and marl) were cored and subjected to comprehensive laboratory tests. To develop the predictive models, physical properties of studied rocks such as P wave velocity (V_p), dry density (γ_d), porosity, and water absorption (A_b) were considered as model inputs, while UCS and E were the output parameters. We evaluated the performance of MLR and ANN models by calculating correlation coefficient (R), mean absolute error (MAE), and root-mean-square error (RMSE) indices. The comparison of the obtained results revealed that ANN outperforms MLR when predicting the UCS and E.     

Estimation of Durability Aspects of Al Masjid Al-Haram Marble,Makkah City,Saudi Arabia

The durability is a measure of the rock’s ability to resist degradation during its working life. Rock durability is greatly related to the mineralogical composition of rocks, rock texture (crystal interlocking, crystal shape and size), and the nature of fluids that are in contact with rock. Marbles have been among the most important building materials since ancient times. The main aim of this study is to evaluate the durability of Al Masjid Al-Haram marble and Ordinary white marble “Carrara” (M₁ and M₂) and develop some correlations among the physical and mechanical properties such as P-wave velocity, slake durability index, dry uniaxial compressive strength (UCS_Dry), abrasion resistance, point load index, impact strength index, Brazilian tensile strength, and Shore hardness. After testing and the evaluation of the test results, strong statistical correlations were found between P-wave velocity and other rock properties. Statistical correlations between the UCS_Dry other tests were also carried out. The coefficients of regressions (R²) range from 0.6177 to 0.997. The study shows that the UCS_Dry values of M1 and M2 have positive relationship with P wave velocities. Concluding remark is that the rocks tested in the study have good durability characteristics and can be reliably used for construction projects. On the other hand, the derived empirical equations can be used for the estimation purposes for similar rock types.     

注浆材料和预制裂纹缺陷角度对类岩石试件单轴抗压强度及破坏模式的影响

选用环氧树脂和纯水泥浆作为注浆材料,对含不同角度和不同注浆材料裂隙试样进行单轴压缩试验。试验结果表明,注浆材料和裂纹缺陷角度对类岩石试件单轴抗压强度及破坏模式具有重要影响;环氧树脂加固效果优于纯水泥浆,环氧树脂可以有效地消除预制裂纹尖端的应力集中;在裂纹缺陷角度很小( <30°)和角度很大( =90°)的情况下无论裂隙是注环氧树脂还是纯水泥浆,注浆效果都不明显,当 =60°时两种注浆材料的加固效果都很好。提出滑动裂纹模型,对注浆裂隙进行力学分析发现,含注浆裂隙试样的抗压强度随着注浆材料和完整材料胶结面摩擦系数和黏聚力的增大而增大,不同注浆材料和完整材料胶结面的摩擦系数和黏聚力不同,解释了为什么不同的注浆材料对注浆试样强度提升作用不同。研究成果为分析工程中注浆材料和裂纹缺陷角度对岩体强度的影响提供了一定的理论基础。     

考虑分层特性的尾砂胶结充填体强度折减试验研究

充填体分层现象在分段或阶段嗣后填充采空区过程中较为常见。设置65%、70%、72%和75% 4个浓度,填充次数为1、2、3和4制作不同分层胶结充填体试件,进行单轴压缩试验探究其力学强度及其破坏模式。试验结果表明：（1）相同浓度条件下,随着填充次数增多,胶结充填体的单轴抗压强度弱化效应越明显,而当浓度在65%～75%之间变化时,对应强度折减系数介于0.592～0.967;（2）充填体单轴抗压强度与填充次数之间满足二次多项式函数关系,而与料浆浓度呈对数函数分布;（3）不同分层胶结充填体的破坏模式主要表现为共轭剪切破坏和贯穿分层面的张拉破坏。低强度夹层可能是导致分层胶结充填体强度降低的原因,能够为后期填充采空区的充填体强度设计提供可靠的理论依据。     

Empirical Correlations for Predicting Strength Properties of Rocks from P-Wave Velocity Under Different Degrees of Saturation

Determination of P-wave velocity (V _p), which is closely related to intact rock properties both in laboratory and in situ conditions, is a non-destructive, easy and less complicated procedure. Due to these advantages, there is an increasing trend to predict the physico-mechanical properties of rocks from V _p. By considering that no attempt on the estimation of mechanical properties of rocks from V _p under different degrees of saturation has been made, in this study, it was aimed to correlate strength properties (uniaxial compressive and tensile strengths) with V _p of various rock types under different degrees of saturation. For this purpose, fourteen different rock types were collected from several parts of Turkey and a comprehensive laboratory testing program was conducted. Experimental results indicated that strength and deformability properties of the rocks decreased with increasing degree of saturation, while V _p showed increasing and decreasing trends depending on degree of saturation. Simple regression analysis results indicated that although prediction of the strength properties of rocks directly from V _p at different degrees of saturation was possible, the equations developed would yield some under- or over-predictions. In the second stage of statistical analyses, a series of different prediction relationships were developed by using independent variables such as V _p, degree of saturation and effective clay content (ECC). The statistical tests suggested that the resultant multivariate equations had very high prediction performances and were very useful tools to estimate the strength properties from V _p determined at any degree of saturation. In addition, the comparisons between the theoretical Gassmann–Biot velocities, which were calculated at different degrees of saturation, and the experimental results suggest that the theoretical Gassmann–Biot velocities show inconsistencies with the experimental results obtained from the investigated rock types with high ECC. Therefore, it was concluded that the use of theoretical velocities is not suitable for rock types with high ECC.     

裂隙形式对岩体强度特征及破坏模式影响的试验研究

利用RMT－150C电液伺服机对含不同预制裂隙形式（单、双、T形交叉及X形交叉裂隙）的类岩石试样进行了单轴压缩试验,系统地研究了裂隙形式对试样强度特征及失稳模式的影响。试验发现,（1）不同裂隙形式下裂隙的起裂破坏模式主要表现为初始裂隙起裂破坏,裂隙形式与破坏模式关系不突出;（2）单轴抗压强度受裂隙形式影响明显,随着裂隙形式由单裂隙到X形交叉裂隙变化,裂隙试样抗压强度呈现增高趋势,同时试样起裂和失稳时的声发射总能量也逐渐增大。进一步对裂隙形式影响强度特征的机制进行了初步分析,研究成果可以反映不同裂隙形式组合对工程岩体稳定性的影响规律。     

Prediction of specific energy of carbonate rock in industrial stones cutting process

Specific energy (SE) measurements of circular saws were conducted on 12 different carbonate rocks. Rock samples were collected from the factories for laboratory tests. Bulk density, apparent porosity, uniaxial compressive strength, Brazilian tensile strength, flexural strength, Schmidt rebound hardness, Shore hardness, point load strength index, Los Angeles abrasion values, and P-wave velocity values were determined in the laboratory. SE and rock properties were evaluated using simple regression analysis and empirical equations were developed. The equations were verified by statistical tests. Regression analysis showed that high correlations exist between SE and uniaxial compressive strength, Shore and Schmidt hardness, bulk density, apparent porosity, and flexural strength. It was found that the SE value of rocks in cutting process was highest for those rocks having the high density, compressive strength, flexural strength, Schmidt and Shore hardness, point load strength index, and P-wave velocity values.