The determination of deformation parameters of rock material is an essential part of any design in rock mechanics. The goal of this paper is to show, that there is a relationship between static and dynamic modulus of elasticity (E), modulus of rigidity (G) and bulk modulus (K). For this purpose, different data on igneous, sedimentary and metamorphic rocks, all of which are widely used as construction materials, were collected and analyzed from literature. New linear and nonlinear relationships have been proposed and results confirmed a strong correlation between static and dynamic moduli of rock species. According to rock types, for igneous rocks, the best correlation between static and dynamic modulus of elasticity (E) were nonlinear logarithmic and power ones; for sedimentary rocks were linear and for metamorphic rocks were nonlinear logarithmic and power correlation. Moreover, with respect to different published linear correlations between static modulus of elasticity (E stat ) and dynamic modulus of elasticity (E dyn ), an interesting correlation for rock material constants was established. It was found that the static modulus of elasticity depends on the dynamic modulus only with one parameter formula.

Determination of the mechanical behaviour of intact rock is one of the most important parts of any engineering projects in the field of rock mechanics. The most important mechanical parameters required to understand the quality of intact rock are Young's modulus (E), Poisson's ratio (m), the strength of rock (r c) and the ratio of Young's modulus to the strength of rock known as modulus ratio (M R), which can be used for calculations. The particular interest of this paper is to investigate the relationship between these parameters for Hungarian granitic rock samples. To fulfil this aim, Modulus of elasticity (E), Modulus of rigidity (G), Bulk modulus (K) and the modulus ratio (M R = E/r c) of 50 granitic rock samples collected from Bátaapáti radioactive waste repository were examined. Fifty high-precision uniaxial compressive tests were conducted on strong (r c-[ 100 MPa) rock samples, exhibiting the wide range of elastic modulus (E = 57.425-88.937 GPa), uniaxial compressive strength (r c-= 133.34-213.04 MPa) and Poisson's ratio (m = 0.18-0.32). The observed value (M R = 326-597) and mean value of M R = 439.4 are compared with the results of similar previous researches. Moreover, the statistical analysis for all studied rocks was performed and the relationship between M R and other mechanical parameters such as maximum axial strain (e a, max) for studied rock samples was discussed. Finally, the validity of the proposed mathematical model by Palchik (Geomech Geophys Geo-energy Geo-resour 6:1-12, 2019) for stress-strain behaviour of granitic rock samples was investigated. Keywords Uniaxial compressive test Á Modulus of elasticity (E) Á Modulus of rigidity (G) Á Bulk modulus (K) Á Modulus ratio (M R) Á Maximum axial strain (e a, max) Á Mórágy granite formation Á Mathematical model 1 Introduction Rock engineering properties are considered to be the most important parameters in the design of ground works. Two important mechanical parameters, uniaxial compressive strength (r c) and elastic modulus of rock (E) should be estimated correctly. There are different empirical relations between r c and

The goal of this paper is to present the influence of the water saturation of the intact rock on different mechanical parameters, such as internal friction angle, cohesion, Hoek-Brown constant (mi ). Analyzing the previously published results, it was found that due to water saturation both the uniaxial compressive strength and tensile strength decrease similarly, i.e. the ratio of these two values is constant, thus the internal friction angle does not change but only the cohesion. Likewise, Hoek-Brown constant (mi ) remains constant; it is independent on the moisture content.The ratio of the elastic modulus and the uniaxial compressive strength of the intact rock is also calculated. According to the laboratory results, this ratio (namely modulus ratio) is also independent on the water content.It is shown that the mechanical parameters of the rock mass (such as compressive strength, tensile strength, deformation modulus) similarly depend on the water content than the intact rock.

Understanding the quality of intact rock is one of the most important parts of any engineering projects in the field of rock mechanics. The expression of correlations between the engineering properties of intact rock has always been the scope of experimental research, driven by the need to depict the actual behaviour of rock and to calculate most accurately the design parameters. To determine the behaviour of intact rock, the value of important mechanical parameters such as Young’s modulus (E), Poisson’s ratio (ν) and the strength of rock (σcd) was calculated. Recently, for modelling the behaviour of intact rock, the crack initiation stress (σci) is another important parameter, together with the strain (σ). The ratio of Young’s modulus and the strength of rock is the modulus ratio (MR), which can be used for calculations. These parameters are extensively used in rock engineering when the deformation of different structural elements of underground storage, caverns, tunnels or mining opening must be computed. The objective of this paper is to investigate the relationship between these parameters for Hungarian granitic rock samples. To achieve this goal, the modulus ratio (MR = E/σc) of 50 granitic rocks collected from Bátaapáti radioactive waste repository was examined. Fifty high-precision uniaxial compressive tests were conducted on strong (σc >100 MPa) rock samples, exhibiting the wide range of elastic modulus (E = 57.425–88.937 GPa), uniaxial compressive strength (σc = 133.34–213.04 MPa) and Poisson’s ratio (ν = 0.18–0.32). The observed value (MR = 326–597) and mean value of MR = 439.4 are compared with the results of similar previous researches. Moreover, the statistical analysis for all studied rocks was performed and the relationshipbetween MR and other mechanical parameters such as maximum axial strain $\left( {{\varepsilon }_{\text{a,}\,\text{max}}} \right)$for studied rocks was discussed.

Nowadays, some common field tests consist of SPT test and pressuremeter test are performed in investigating the geotechnical parameters of projects such as tunneling. Due to the high cost of pressuremter test performance and its time-consuming procedure, using some empirical relations between SPT and Pressuremeter tests are recommended for primarily study of the project. The purpose of this study is to perform regression analyses between the NSPT and the uniaxial compression strength test and the pressuremeter test parameters obtained from a geotechnical investigation performed in route of 2nd line of Tabriz metro. Correlations were carried out for sandy and clayey soils separately. A series of simple and nonlinear multiple regression analyses are performed and as a result of analyses, several empirical equations are developed. It is shown that the empirical equations developed in this study are statistically acceptable.

Some of the most frequent damages of concrete segments in shield tunnels are chipping and cracking, which are followed by degradation of lining system. In this paper, these types of damages are studied in four subway and two water conveyance tunnels. More than 2100 concrete rings are examined for chipping inspection and another 3000 for determination of the cracking. Statistical analysis of the research data showed that corners of the key and counter-key segments carry the highest number of chipping, while most of the cracking occur in the middle zones and shape of the segments and number of trust jacks affect the cracking pattern. Two kinds of numerical models are used to examine the underlying damages, which are based on geometrical characteristics of tunnel lining and boring machine besides operational mistakes. Findings of the numerical simulation revealed that installation of segmental lining with the least amount of erection tolerances results in low amount of chipping, this is while using key-segments with 12–17 degrees of insertion angle reduces total magnitude of damage due to tensile and compressive stresses. Furthermore, the deviation angle of TBM’s jack and segment’s axis should never be more than 5 degrees; otherwise even high-quality concrete segments wouldn’t remain undamaged. Employment of boring machines with articulated system is proposed in this case.

An accurate determination of Hoek–Brown constant mi is of great significance in the estimation of the failure criteria of brittle rock materials. So far, different approaches such as rigidity index method (R-index), uniaxial compressive strength-based method, and tensile strength-based method, and the combination of these two methods (combination based method) have been proposed to calculate the value of mi. This paper aims to thoroughly review the previously existing methods to calculate the value of mi and make comparison between the obtain results to propose the new material constants that provide the best fit with the experimental data. In order to fulfill this goal, a large number of data for different quasi-isotropic intact rock types from the literature were collected and statistically analyzed. Additionally, based on rock types, new material constants are introduced for igneous, sedimentary, and metamorphic rocks. The obtained results proves that for different rock groups (igneous, sedimentary, and metamorphic rocks), R-index method provides the best fit with the experimental data among the others, and it is also independent of rock type. Interestingly enough, there is significant differences in the predicted mi values using different methods, which is more probably due to the quantity and quality of data used in the statistical analysis.

The Q-system and Q-slope are empirical methods developed for classifying and assessing rock masses for tunneling, underground mining, and rock slope engineering. Both methods have been used extensively to guide appropriate ground support design for underground excavations and stable angles for rock slopes. Using datasets obtained from igneous, sedimentary, and metamorphic rock slopes from various regions worldwide, this research investigates different relationships between the geological strength index (GSI) and the Q-system and Q-slope. It also presents relationships between chart-derived GSI with GSI estimations from RMR89 and Q’ during drill core logging or traverse mapping. Statistical analysis was used to assess the reliability of the suggested correlations to determine the validity of the produced equations. The research demonstrated that the proposed equations provide appropriate values for the root mean squared error value (RMSE), the mean absolute percentage error (MAPE), the mean absolute error (MAE), and the coefficient of determination (R-squared). These relationships provide appropriate regression coefficients, and it was identified that correlations were stronger when considering metamorphic rocks rather than other rocks. Moreover, considering all rock types together, achieved correlations are remarkable.