A correlation between P-wave velocity,impact strength index,slake durability index and uniaxial compressive strength

Impact strength index, slake durability index and uniaxial compressive strength (UCS) are important properties of a rock mass which are used widely in geological and geotechnical engineering. In this study, the mechanical properties of one igneous, three sedimentary and three metamorphic rock types were determined in the laboratory and correlated with P-wave velocity. Empirical equations have been developed to predict the impact strength index, slake durability index and UCS from P-wave velocity, which may avoid the necessity for time-consuming and tedious laboratory testing. To check the sensitivity of the empirical relations, a t test was performed which confirmed the validity of the proposed correlations.      

A new testing method for indirect determination of the unconfined compressive strength of rocks

A new testing method for the indirect determination of unconfined compressive strength (UCS) of rock core samples is presented. As known, there exist several methods for indirect estimation of UCS, such as point load index (I_s), Schmidt hammer, sonic velocity, block punch strength test, etc. Although the point load index testing method is widely used to estimate UCS, there are many problems and limitations related to this method as reported in the recent literature. The “core strangle test” (CST) proposed in this paper overcomes some of these deficiencies and limitations. The principle of this test depends on the “strangle” type of loading a core along a circle perpendicular to the core axis. In the first stage of this study, blocks of different types of rocks having the strength in a range from weak to strong were collected and cored for UCS, point load index and CST tests. These tests were then conducted and relationships between UCS with I_s(50) and CST were empirically explained and discussed.     

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.     

Evaluation of simple methods for assessing the uniaxial compressive strength of rock

Published data on 48 different rocks are used to evaluate the correlations between the uniaxial compressive strength (UCS) values and the corresponding results of point load, Schmidt hammer, sound velocity and impact strength tests. The variability of test results for each test and each rock type was evaluated by calculating the coefficient of variation. Using the method of least squares regression, the UCS values were correlated with the other test values. Also, the test methods were evaluated by plotting the estimated values of compressive strength vs. the measured values of compressive strength for each test. The results indicate that the least variability is shown in the impact strength test. So, among the test methods included in this study, the impact strength test is the most reproducible test; but the variability of test results for the other test methods is within acceptable limits for most engineering purposes. Strong linear relations between the point load strength index values and the UCS values were found for the coal measure rocks and the other rocks included in this study. The Schmidt hammer and the sound velocity tests exhibit significant non-linear correlations with the compressive strength of rock. In the sound velocity test, the data points are scattered at higher strength values. There is no clear relation between the impact strength values and the compressive strength values for the coal measure rocks. A weak non-linear correlation was found between the impact strength values and the compressive strength values for the other rocks. All test methods evaluated in this study, except the impact strength, provide reliable estimate of the compressive strength of rock. However, the prediction equations derived by different researchers are dependent on rock types and test conditions, as they are in this study.     

The use of point load test for Dubai weak calcareous sandstones

Intact rock is typically described according to its uniaxial compressive strength(UCS). The UCS is needed in the design of geotechnical engineering problems including stability of rock slopes and design of shallow and deep foundations resting on and/or in rocks. Accordingly, a correct measurement/evaluation of the UCS is essential to a safe and economic design. Typically, the UCS is measured using the unconfined compression tests performed on cylindrical intact specimens with a minimum length to width ratio of 2. In several cases, especially for weak and very weak rocks, it is not possible to extract intact specimens with the needed minimum dimensions. Thus, alternative tests(e.g. point load test, Schmidt hammer) are used to measure rock strength. The UCS is computed based on the results of these tests through empirical correlations. The literature includes a plethora of these correlations that vary widely in estimating rock strength. Thus, it is paramount to validate these correlations to check their suitability for estimating rock strength for a specific location and geology. A review of the available correlations used to estimate the UCS from the point load test results is performed and summarized herein. Results of UCS, point load strength index and Young's modulus are gathered for calcareous sandstone specimens extracted from the Dubai area. A correlation for estimating the UCS from the point load strength index is proposed. Furthermore, the Young's modulus is correlated to the UCS.     

Predicting uniaxial compressive strength,modulus of elasticity and index properties of rocks using the Schmidt hammer

The Schmidt hammer test is a non-destructive method which can be used in both laboratory and field to provide a quick and relatively inexpensive measure of rock hardness. The study investigated the relationship between the Schmidt hardness and modulus of elasticity, uniaxial compressive strength and index properties of nine types of rock including travertine, limestone, dolomitic limestone and schist. The empirical equations developed indicated the Schmidt hardness rebound values have a reliable relationship with the uniaxial compressive strength of rock (r = 0.92). Comparing the results with those reported by other researchers, it is concluded that no single relationship can be considered reliable for all rock types. Whilst the equations developed in this study may be useful at a preliminary stage of design, they should be used with caution and only for the specified rock types.      

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.     

Reply to Discussion on “Empirical methods for determining shaft bearing capacity of semi-deep foundations socketed in rocks”

Semi-deep foundations socketed in rocks are considered to be a viable option for the foundations in the presence of heavy loads imposed by high-rise buildings and special structures, due to the low settlement and high bearing capacity. In this study, the unconfined compressive strength (UCS) and rock mass cuttability index (RMCI) have been applied to investigating the shaft bearing capacity. For this purpose, a comprehensive database of 178 full-scale load tests is compiled by adding a data set (n = 72) collected by Arioglu et al. (2007) to the data set (n = 106) presented in Rezazadeh and Eslami (2017). Using the database, the applicability and accuracy of the existing empirical methods are evaluated and new relations are derived between the shaft bearing capacity and UCS/RMCI. Moreover, a general equation in case of unknown rock types is proposed and it is verified by another set of data (series 3 in Rezazadeh and Eslami (2017)). Since rock-socketed shafts are supported by rock mass (not intact rock), a reduction factor for the compressive strength is suggested and verified in which the effect of discontinuities is considered using the modified UCS, based upon RMR and RQD to consider the effect of the rock mass properties.     

Evaluation of the mechanical degradation of carbonate aggregate by rock strength tests

Aggregate degradation (AD) is one of the major reasons accounting for failure of aggregate materials, and the mechanical degradation of aggregate materials can be determined by different test methods. This process basically requires many aggregate samples and special instruments, and thus is time-consuming. The main purpose of this research is to evaluate the possibility of estimating the AD characteristics using rock strength tests and to investigate the relationships between AD properties and rock strength tests. For understanding the relationships, two common rock strength tests are employed, i.e. unconfined compressive strength (UCS) and point load index (PLI) tests. In the tests, the AD properties of 40 kinds of carbonate aggregates sampled from Iran were studied. The AD properties were determined by Los Angeles abrasion value (LAAV), aggregate impact value (AIV) and aggregate crushing value (ACV). Also, the samples are classified according to the strength and rock types, and the effect of this classification is investigated based on the relationship between rock strengths and AD properties. The results indicate that the PLI is better than UCS for evaluation of AD properties. Among rock strength tests, PLI has a closer relationship with AIV (R² = 0.832). Also, UCS has relative larger effects on the ACV (R² = 0.812) under the same loading condition. The weakest correlation occurs between LAAV and UCS (R² = 0.679). In view of the rational AD properties in the predictive procedure, it is possible to predict AD properties based on the strength tests and rock types. The results also show that the prediction of AD properties using rock strength test based on rock types yields better correlations than that using unclassified samples. The classification based on rock types can extrapolate the different relationships of AD prediction from rock strength tests. The results in this context could be used for preliminarily selecting proper rock aggregates with a limit of allowable AD tests for practical applications by PLI.     

Relationship between cleavage orientation,uniaxial compressive strength and Young’s modulus for slates in NW Spain

Slates from North Western Spain have been studied to establish the influence of the cleavage orientation on the uniaxial compressive strength (UCS) and Young’s modulus (E). Slate, sandstone and intercalated slate/sandstone lithologies were tested and the higher strengths were always obtained when the load was applied parallel, or close to parallel, to the slaty cleavage. This study suggests the following empirical relationships for unweathered slates in saturated conditions UCS = 0.037β ² − 7.622(β + 200.6, E × 10⁴ = 0.002β ² − 0.134β + 3.453. E can be estimated from UCS values using E × 10⁴ = 429,56 (UCS)^0.9122. These empirical equations will assist in geotechnical studies in this area of NW Spain where slate quarrying is an important industry.      

Empirical models and numerical analysis for assessing strength anisotropy based on block punch index and uniaxial compression tests

This study aims to investigate the strength anisotropy associated with discontinuity orientation by performing block punch index (BPI) tests and uniaxial compressive strength (UCS) tests, and to develop some empirical relationships for estimating the BPI and UCS in the strongest direction, and the UCS from the BPI determined at any angle between the loading direction and weakness plane. The experimental results obtained from six rock types show that these rocks fall into the moderate-to-low strength anisotropy classes. The comparison between the observed and predicted UCS values indicated that the prediction performances of the equations developed are quite good. Numerical simulations revealed that numerically estimated BPI values are very close to experimentally determined values for each angle between the loading direction and the weakness planes involved by the BPI specimens. As the angle between the weakness planes and loading increases, plastic zones become wider and unsymmetrical. The results of this study are also applicable to anisotropic rocks outside the strength ranges of the rocks studied by the authors, but their degree of anisotropy should be in the range of low-to-moderate.     

Genetic programming approach for estimating the deformation modulus of rock mass using sensitivity analysis by neural network

We use genetic programming (GP) to determine the deformation modulus of rock masses. A database of 150 data sets, including modulus of elasticity of intact rock (Ei), uniaxial compressive strength (UCS), rock mass quality designation (RQD), the number of joint per meter (J/m), porosity, and dry density for possible input parameters, and the modulus deformation of the rock mass determined by a plate loading test for output, was established. The values of geological strength index (GSI) system were also determined for all sites and considered as another input parameter. Sensitivity analyses are considered to find out the important parameters for predicting of the deformation modulus of rock mass. Two approaches of sensitivity analyses, based on “statistical analysis of RSE values” and “sensitivity analysis about the mean”, are performed. Evolution of the sensitivity analyses results establish the fact that variable of UCS, GSI, and RQD play more prominent roles for predicting modulus of the rock mass, and so those are considered as the predictors to design the GP model. Finally, two equations were achieved by GP. The statistical measures of root mean square error (RMSE) and variance account for (VAF) have been used to compare GP models with the well-known existing empirical equations proposed for predicting the deformation modulus. These performance criteria proved that the GP models give higher predictions over existing empirical models.     

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.      

Point-load strength: An index for classification of rock material

Point-load strength (Is) as a measure for the determination of rock strength and for estimating uniaxial (unconfined) compressive strength (UCS) are described and both put together and used for rock strength classification of brittle and hard rocks. The estimated point-load strength values of specimens of varying sizes and also the values corrected to a standard thickness of 50 mm, and the resultant point-load strength values (Is-50) have been used to estimate the uniaxial (unconfined) compressive strength which correlates well with actual recorded uniaxial (unconfined) compression test results. Using graphical and mathematical relationships between the observed and estimated UCS and Is values, a conversion factor of 16 is obtained for estimating uniaxial (unconfined) compressive strength values from point load strength results. A nomogram for computing point-load strength index and a system for the classification of rock material are presented.     

Predicting performance of impact hammers from rock quality designation and compressive strength properties in various rock masses

Predicting the performance of the impact hammers is one of the major subjects in determining the economics of the underground excavation projects in which they are utilized. Therefore, researchers have been attracted to developing performance prediction models for these machines. Physical and mechanical properties of rocks have been used to estimate the performance of impact hammers over the last few decades. In this study, the instantaneous breaking rate (IBR, m³/h) of an impact hammer used in construction of Levent-Hisarüstü metro tunnel (Istanbul) is recorded in detail. Sixty rock samples are obtained from tunnel route during the excavation of which the machine is employed. Physical and mechanical property tests are performed on the obtained samples. A data set including uniaxial compressive strength (UCS), rock quality designation index (RQD), Brazilian tensile strength (BTS), density (ρ), Schmidt hammer hardness (SHH), Shore scleroscope hardness (SSH), Cerchar abrasivity index (CAI), and IBR is formed. Regression analysis techniques are applied to the created data set in order to develop a performance prediction model. The investigation results in a model that can predict IBR based on UCS, RQD, and the output power of the impact hammer. The proposed model passes both F-test and t-test at 0.95 confidence level. The soundness of the model is successfully tested against two formerly developed models. Covering a wide range of application and requiring only two of the most common and versatile rock properties as input parameters are the other advantages of the suggested model.     

Estimation of rock modulus: For intact rocks with an artificial neural network and for rock masses with a new empirical equation

The elastic modulus of intact rock is used for many rock engineering projects, such as tunnels, slopes, and foundations, but due to the requirements of high-quality core samples and associated sophisticated test equipment, instead the use of empirical models to obtain this parameter has been an attractive research topic. In the rock mechanics literature, some empirical relations exist between the elastic modulus of intact rock and other rock properties, such as the uniaxial compressive strength (σ_ci), unit weight (γ), Schmidt hammer rebound number, point load index and petrographic composition. However, the past use of specific rock types is the main limitation of the existing empirical equations. In other words, they are not open to the general purpose use. To eliminate this deficiency, a total of 529 datasets, including uniaxial compressive strength, unit weight and elastic modulus of intact rock (E_i), were collected via an extensive literature review. In addition to these datasets, a further total of 80 datasets was obtained from laboratory tests performed on greywacke and agglomerate core samples for this study. To prepare a chart for the prediction of the elastic modulus of intact rock, an artificial neural network was constructed using the large database. In addition, after a brief overview of existing empirical equations, a new empirical equation, which considers RMR and the elastic modulus of intact rock (E_i) as input parameters, is also proposed using worldwide data.     

Discussion on “Empirical methods for determining shaft bearing capacity of semi-deep foundations socketed in rocks”[J Rock Mech Geotech Eng 6(2017)1140-151]

A new comprehensive set of data(n = 178) is compiled by adding a data set(n = 72) collected by Arioglu et al.(2007) to the data set(n = 106) presented in Rezazadeh and Eslami(2017). Then, the compiled data set is evaluated regardless of the variation in lithology/strength. The proposed empirical equation in this study comprises a wider range of uniaxial compressive strength(UCS)(0.15 MPa σ_(rc) 156 MPa) and various rock types. Rock mass cuttability index(RMCI) is correlated with shaft resistance(r_s) to predict the shaft resistance of rock-socketed piles. The prediction capacity of the RMCI versus r_s equation is also found to be in a fair good agreement with the presented data in Rezazadeh and Eslami(2017). Since the RMCI is a promising parameter in the prediction of shaft resistance, the researchers in the rock-socketed pile design area should consider this parameter in the further investigations.     

Estimating uniaxial compressive strength of rocks using genetic expression programming

The aim of this paper is to estimate the uniaxial compressive strength(UCS) of rocks with different characteristics by using genetic expression programming(GEP).For this purpose,five different types of rocks including basalt and ignimbrite(black,yellow,gray,brown) were prepared.Values of unit weight,water absorption by weight,effective porosity and UCS of rocks were determined experimentally.By using these experimental data,five different GEP models were developed for estimating the values of UCS for different rock types.Good agreement between experimental data and predicted results is obtained.     

Empirical methods for determining shaft bearing capacity of semi-deep foundations socketed in rocks

Semi-deep foundations socketed in rocks are considered to be a viable option for the foundations in the presence of heavy load imposed by high-rise structures, due to the low settlement and high bearing capacity. In the optimum design of semi-deep foundations, prediction of the shaft bearing capacity, rs, of foundations socketed in rocks is thus critically important. In this study, the unconfined compressive strength(UCS), qu, has been applied in order to investigate the shaft bearing capacity. For this, a database of 106 full-scale load tests is compiled with UCS values of surrounding rocks, in which 34 tests with rock quality designation(RQD), and 5 tests with rock mass rating(RMR). The bearing rocks for semi-deep foundations include limestone, mudstone, siltstone, shale, granite, tuff, granodiorite, claystone, sandstone, phyllite, schist, and greywacke. Using the database, the applicability and accuracy of the existing empirical methods are evaluated and new relations are derived between the shaft bearing capacity and UCS based on the types of rocks. Moreover, a general equation in case of unknown rock types is proposed and it is verified by another set of data. Since rock-socketed shafts are supported by rock mass(not intact rock), a reduction factor for the compressive strength is suggested and verified in which the effect of discontinuities is considered using the modified UCS, qu(modified), based upon RMR and RQD in order to take into account the effect of the rock mass properties.     

Predicting the deformation moduli of rock masses

Predictive empirical models for the mechanical properties of rock masses have been used in rock engineering because direct measurement of the properties is difficult due to the presence of discontinuities. Such empirical models are open to improvement because they are based on collected data. The purposes of the present study are to assess the existing empirical equations and to develop a new empirical approach. For this reason, in the first stage of the study, the prediction performance of the existing models proposed for predicting the deformation modulus of rock masses were evaluated statistically by using a database including 115 data values obtained from in situ plate loading and dilatometer tests. A new empirical approach with higher prediction capacity than the existing empirical models was developed in the subsequent stage of the study. The new empirical model considers the modulus ratio of intact rock (E_i/UCS), rock quality designation (RQD) and weathering degree (WD). Although, data obtained from very weak and weak rock masses were included in the development of the new empirical equation, the type of rocks employed in the study were limited. Therefore, a crosscheck between the new empirical equation and previous empirical approaches should be performed in the design stage.