Evaluation of empirical estimation of uniaxial compressive strength of rock using measurements from index and physical tests

The uniaxial compressive strength(UCS) of rock is an important parameter required for design and analysis of rock structures,and rock mass classification.Uniaxial compression test is the direct method to obtain the UCS values.However,these tests are generally tedious,time-consuming,expensive,and sometimes impossible to perform due to difficult rock conditions.Therefore,several empirical equations have been developed to estimate the UCS from results of index and physical tests of rock.Nevertheless,numerous empirical models available in the literature often make it difficult for mining engineers to decide which empirical equation provides the most reliable estimate of UCS.This study evaluates estimation of UCS of rocks from several empirical equations.The study uses data of point load strength(Is(50)),Schmidt rebound hardness(SRH),block punch index(BPI),effective porosity(n) and density(ρ)as inputs to empirically estimate the UCS.The estimated UCS values from empirical equations are compared with experimentally obtained or measured UCS values,using statistical analyses.It shows that the reliability of UCS estimated from empirical equations depends on the quality of data used to develop the equations,type of input data used in the equations,and the quality of input data from index or physical tests.The results show that the point load strength(Is(50)) is the most reliable index for estimating UCS among the five types of tests evaluated.Because of type-specific nature of rock,restricting the use of empirical equations to the similar rock types for which they are developed is one of the measures to ensure satisfactory prediction performance of empirical equations.     

ISRM Suggested Method for determining the Shore Hardness value for rock

Shore hardness (SH) has been accepted as a convenient and nondestructive method in measuring the hardness of rocks and widely used in rock mechanics since it can be correlated with other mechanical properties of weak rocks, such as uniaxial compressive strength (UCS). However, a need has arisen to propose a standard method as a measure of SH to minimize the errors when it is utilized as a predictor of the UCS as well as other mechanical properties of rocks. Over the last few decades, several studies have been conducted to predict consistent SH values using different procedures. However, the results of the tests can not be compared and analyzed in an overall way. Therefore, this experimental study was implemented to meet and discuss the demand for a new method to determine standardized SH values. In result, a new empirical equation was proposed to estimate size-corrected values of SH based on a critical specimen volume of 80 cm³.     

Predicting the unconfined compressive strength of the Breathitt shale using slake durability, Shore hardness and rock structural properties

Compressive strength is the most widely used design parameter in the construction industry and in rock engineering. For example, Bieniawski [Bieniawski, Z. T., Estimating the strength of rock materials, Is. J. S. Afr. Inst. Min. Metall., 1974, 74, 312–320.] reported that mining engineers request the uniaxial compressive strength (UCS) more often than any other rock property. However, standards set for specimen preparation are very demanding. Therefore it is quite difficult and sometimes impossible to fulfill these requirements using weak rocks and especially shales. This paper evaluates the use of the slake durability and Shore hardness tests to estimate UCS, based on laboratory correlations performed for this study and others and based on analysis of structural and physical material properties affecting both strength and durability.     

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.     

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.

     

Application of neural networks for the prediction of the unconfined compressive strength (UCS) from Equotip hardness

This paper presents the application of a neural network for the prediction of the UCS from hardness tests on rock samples. To investigate the suitability of this approach, the results of the network are compared to predictions obtained by conventional statistical relations.The network was trained to predict the UCS based on the hardness, porosity, density, grain size and rock type information of a rock sample. A dataset containing 194 rock sample records, ranging from weak sandstones to very strong granodiorites, was used to train the network with the Levenberg–Marquardt training algorithm. Two sets, each containing 17 rock samples, were used to validate the generalization and prediction capabilities of the network.     

Indentation hardness test to estimate the sawability of carbonate rocks

The performance of large-diameter circular saws on eight carbonate rocks was recorded and indentation hardness, density and porosity tests were undertaken on the five travertines, two limestone and one dolomitic limestone samples returned to the laboratory. A strong linear correlation between indentation hardness index values and the hourly production of the circular saws was found. The slab production was slowest for the dolomitic limestone rocks with the highest indentation hardness, lowest porosity and highest density values.      

Estimation of strength and deformation properties of Quaternary caliche deposits

The aim of this study was to develop and evaluate statistical models for predicting the uniaxial compressive strength (UCS) and average Young’s modulus (E _av) for caliches, using some index and physical properties. The caliche samples, from Adana, southern Turkey, were of low strength and difficult to sample. X-ray diffraction and microscopy were undertaken and the following physical parameters established: unit weight, apparent porosity, Schmidt rebound number, Shore hardness, P-wave velocity, slake durability, point load, uniaxial compressive strength and average Young’s modulus. Simple and linear regression variable selection analyses were performed. The best relationships were obtained for UCS with P-wave velocity and unit weight and for average Young’s modulus with P-wave velocity, porosity and slake durability. Empirical equations are proposed, although it is emphasised that these may only be applicable for caliche of a similar geological character.      

Heterogeneous rock mass classification by means of the geological strength index: the <Emphasis Type="Italic">San Mauro</Emphasis> formation (Cilento,Italy)

This paper describes an application of the geological strength index (GSI) method to the San Mauro formation, which is characterized by sandstones alternating with argillaceous marls. The Sandstone/Pelite (S/P) ratio and structural complexity were determined. Geo-structural and geo-mechanical surveys were undertaken in situ and rock samples were tested in the laboratory. A map of the S/P ratio was produced showing the bedrock divided in four classes. Three ranges of GSI values were identified. The values of the intact UCS and of the constant m _i were appropriately reduced to reflect the variable presence of sandstone compared with the pelitic fraction. A “weighted average” of the intact strength properties of the hard and weak layers was adopted. The values for the intact materials were reduced from 20 to 60% depending on the GSI categories of the heterogeneous rock mass. In this way, seven classes of rock masses characterized by different values of GSI, reduced UCS and m _i values were identified.     

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.     

Classification and assessment of rock mass parameters in Choghart iron mine using P-wave velocity

Engineering rock mass classification,based on empirical relations between rock mass parameters and engineering applications,is commonly used in rock engineering and forms the basis for designing rock structures.The basic data required may be obtained from visual observation and laboratory or field tests.However,owing to the discontinuous and variable nature of rock masses,it is difficult for rock engineers to directly obtain the specific design parameters needed.As an alternative,the use of geophysical methods in geomechanics such as seismography may largely address this problem.In this study,25 seismic profiles with the total length of 543 m have been scanned to determine the geomechanical properties of the rock mass in blocks Ⅰ,Ⅲ and Ⅳ-2 of the Choghart iron mine.Moreover,rock joint measurements and sampling for laboratory tests were conducted.The results show that the rock mass rating(RMR) and Q values have a close relation with P-wave velocity parameters,including P-wave velocity in field(V_(PF)).P-wave velocity in the laboratory(V_(PL)) and the ratio of V_(PF) V_(PL)(i.e.K_p = V_(PF)/V_(PL).However,Q value,totally,has greater correlation coefficient and less error than the RMR,In addition,rock mass parameters including rock quality designation(RQD),uniaxial compressive strength(UCS),joint roughness coefficient(JRC) and Schmidt number(RN) show close relationship with P-wave velocity.An equation based on these parameters was obtained to estimate the P-wave velocity in the rock mass with a correlation coefficient of 91%.The velocities in two orthogonal directions and the results of joint study show that the wave velocity anisotropy in rock mass may be used as an efficient tool to assess the strong and weak directions in rock mass.     

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 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.      

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.     

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.      

Models to predict the uniaxial compressive strength and the modulus of elasticity for Ankara Agglomerate

Determination of the uniaxial compressive strength (UCS) and modulus of elasticity of block-in-matrix rocks (bimrocks) is often impossible in the laboratory since the preparation of the standard core samples from bimrocks is extraordinarily difficult. For this reason, some predictive models were developed to estimate the UCS and modulus of elasticity based on the volumetric portion of blocks in Ankara Agglomerate, which is composed of black and pink andesite blocks in a tuff matrix. The ratio of E_imin of blocks (5.99 GPa) to E_imax of the tuff matrix (2.83 GPa) is 2.2 for Ankara Agglomerate. In addition to this contrast, the minimum ratio of UCS values of andesite blocks (34.99 MPa) to matrix tuff (14.4 MPa) is 2.4. In the first stage of the study, fuzzy logic was used as a tool for the prediction of the UCS of Ankara Agglomerate based on its block and matrix constituents. UCS values for 164 agglomerate cores were evaluated in the prediction model based on fuzzy logic. A triangular chart expressed by “if-then” rules considers different constituent composition of the agglomerate. Considering the membership functions depending on the portion of constituents, a Mamdani fuzzy algorithm was constructed and a fuzzy triangular chart was obtained for the estimation of the UCS of the agglomerate. The ‘variance accounts for’ (VAF) and the root mean square error (RMSE) indices were calculated as 56.9% and 7.3, respectively, to characterize the prediction performance of the triangular chart. In the second stage of the study, the goal was to construct a prediction model for the estimation of the modulus of the elasticity. Regression analyses were performed using 103 UCSs and the unit weight data obtained from core samples prepared from tuff matrix, black and pink andesite blocks and agglomerate. An equation having a correlation coefficient of 0.951 was obtained from the regression analyses. The VAF and RMSE indices for the multiple regression equation were obtained as 88.8% and 0.84, respectively. Both correlation coefficient and the performance indices indicated that the prediction capacity of the equation is high.     

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.     

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.     

Critical embedment length and bond strength of fully encapsulated rebar rockbolts

A series of rock bolt pull tests were carried out in the laboratory to determine the critical embedment length of a specific type of fully cement-grouted rebar bolt. The rebar bolt is 20 mm in diameter, and it is widely used in underground excavations in Norway. Three water-cement (w/c) ratios were used in the tests. It was discovered that the critical embedment length of the rock bolts was approximately 25 cm for the water-cement ratio 0.40 (the corresponding uniaxial compressive strength (UCS) of the grout is 37 MPa), 32 cm for the ratio 0.46 (UCS 32 MPa), and 36 cm for the ratio 0.50 (UCS 28 MPa), for the specific type of cement, Rescon zinc rock bolt cement. It was found that the bond strength of the rock bolt is not a constant but is related to the embedment length. The bond strength was linearly proportional to the UCS of the grout.     

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.