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Joints and fissures with similar orientation or characteristics are common in natural rocks; the inclination and density of the fissures affect the mechanical properties and failure mechanism of the rock mass. However, the strength, crack coalescence pattern, and failure mode of rock specimens containing multi-fissures have not been studied comprehensively. In this paper, combining similar material testing and discrete element numerical method (PFC2D), the peak strength and failure characteristics of rock-like materials with multi-fissures are explored. Rock-like specimens were made of cement and sand and pre-existing fissures created by inserting steel shims into cement mortar paste and removing them during curing. The peak strength of multi-fissure specimens depends on the fissure angle α (which is measured counterclockwise from horizontal) and fissure number ( N f ). Under uniaxial compressional loading, the peak strength increased with increasing α . The material strength was lowest for α  = 25°, and highest for α  = 90°. The influence of N f on the peak strength depended on α . For α  = 25° and 45°, N f had a strong effect on the peak strength, while for higher α values, especially for the 90° sample, there were no obvious changes in peak strength with different N f . Under uniaxial compression, the coalescence modes between the fissures can be classified into three categories: S-mode, T-mode, and M-mode. Moreover, the failure mode can be classified into four categories: mixed failure, shear failure, stepped path failure, and intact failure. The failure mode of the specimen depends on α and N f . The peak strength and failure modes in the numerically simulated and experimental results are in good agreement.

The mechanical properties of rock material with length/diameter ratios varying from 1.0 to 3.0 were determined using a newly developed servo-hydraulic machine at a wide range of strain rates. The uniaxial compressive strength, initiation and dilatancy stresses, peak axial strain, and strain energy gradually decreased with increasing length/diameter ratios at the same loading condition; for the same length/diameter ratio, these properties increased with increasing strain rate. The elastic modulus increased with increasing specimen shape and strain rate, whereas the Poisson’s ratio was independent on these two factors. The fracture modes were significantly dependent on both strain rate and specimen shape. When the strain rate was below 10 −3  s −1 , splitting was the main fracture mode for the short specimens while the shearing fracture mode dominates the longer specimens; when the strain rate was above 10 −3  s −1 , the fracture mode changed directly from cone-shaped fractures to shearing fractures. The recommended length/diameter ratio was 2.5 at strain rates of 10 −5 –10 −2  s −1 .

Rock engineers often encounter materials with a large number of discontinuities that significantly influence rock stability. However, the strength and failure patterns of ubiquitous-joint rock specimens have not been examined comprehensively. In this study, the peak uniaxial compressive strength (UCS J ) and failure patterns of ubiquitous-joint rock-like specimens are investigated by combining similar material testing and numerical simulation using the two-dimensional particle flow code. The rock-like specimens are made of white cement, water, and sand. Flaws are created by inserting mica sheets into the fresh cement mortar paste. Under uniaxial compressional loading, the failure patterns of ubiquitous-joint specimens can be classified into four categories: stepped path failure, planar failure, shear-I failure, and shear-II failure. The failure pattern of the specimen depends on the joint-1 inclination angle α and the intersection angle γ between joint-1 and joint-2, while α strongly affects UCS J . The UCS J of specimens with γ  = 15° or 30° shows similar tendencies for 0° ≤  α  ≤ 75°. For specimens with γ  = 45° or 60°, UCS J increases for 0° ≤  α  ≤ 30° and decreases for α  > 30°. For specimens with γ  = 75°, the UCS J peaks when α  = 0° and increases for 60° ≤  α  ≤ 75°. The numerical and experimental results show good agreement for both the peak strength and failure patterns. These results can improve our understanding of the mechanical behavior of ubiquitous-joint rock mass and can be used to analyze the stability of rock slopes or other rock engineering cases such as tunneling construction in heavily jointed rock mass.

To investigate the energy evolution characteristics of rock materials under uniaxial compression, the single-cyclic loading–unloading uniaxial compression tests of four rock materials (Qingshan granite, Yellow sandstone, Longdong limestone and Black sandstone) were conducted under five unloading stress levels. The stress–strain curves and failure characteristics of rock specimens under the single-cyclic loading–unloading uniaxial compression tests basically corresponded with those of under uniaxial compression, which indicates that single-cyclic loading–unloading has minimal effects on the variations in the loading–deformation response of rocks. The input energy density, elastic energy density and dissipated energy density of four rocks under five unloading stress levels were calculated using the graphical integration method, and variation characteristics of those three energy density parameters with different unloading stress levels were explored. The results show that all three energy density parameters above increased nonlinearly with increasing unloading stress level as quadratic polynomial functions. Meanwhile, both the elastic and dissipated energy density increased linearly when the input energy density increased, and the linear energy storage and dissipation laws for rock materials were observed. Furthermore, a linear relationship between the dissipated and elastic energy density was also proposed. Using the linear energy storage or dissipation law, the elastic and dissipated energy density at any stress levels can be calculated, and the internal elastic (or dissipated) energy density at peak compressive strength (the peak elastic and dissipated energy density for short) can be obtained. The ratio of the elastic energy density to dissipated energy density with increasing input energy density was investigated using a new method, and the results show that this ratio tends to be constant at the peak compressive strength of rock specimens.

The purpose of this review is to discuss the development and the state of the art in dynamic testing techniques and dynamic mechanical behaviour of rock materials. The review begins by briefly introducing the history of rock dynamics and explaining the significance of studying these issues. Loading techniques commonly used for both intermediate and high strain rate tests and measurement techniques for dynamic stress and deformation are critically assessed in Sects.  2 and 3 . In Sect.  4 , methods of dynamic testing and estimation to obtain stress–strain curves at high strain rate are summarized, followed by an in-depth description of various dynamic mechanical properties (e.g. uniaxial and triaxial compressive strength, tensile strength, shear strength and fracture toughness) and corresponding fracture behaviour. Some influencing rock structural features (i.e. microstructure, size and shape) and testing conditions (i.e. confining pressure, temperature and water saturation) are considered, ending with some popular semi-empirical rate-dependent equations for the enhancement of dynamic mechanical properties. Section  5 discusses physical mechanisms of strain rate effects. Section  6 describes phenomenological and mechanically based rate-dependent constitutive models established from the knowledge of the stress–strain behaviour and physical mechanisms. Section  7 presents dynamic fracture criteria for quasi-brittle materials. Finally, a brief summary and some aspects of prospective research are presented.

An experimental investigation is conducted to study the quasi-static and dynamic fracture behaviour of sedimentary, igneous and metamorphic rocks. The notched semi-circular bending method has been employed to determine fracture parameters over a wide range of loading rates using both a servo-hydraulic machine and a split Hopkinson pressure bar. The time to fracture, crack speed and velocity of the flying fragment are measured by strain gauges, crack propagation gauge and high-speed photography on the macroscopic level. Dynamic crack initiation toughness is determined from the dynamic stress intensity factor at the time to fracture, and dynamic crack growth toughness is derived by the dynamic fracture energy at a specific crack speed. Systematic fractographic studies on fracture surface are carried out to examine the micromechanisms of fracture. This study reveals clearly that: (1) the crack initiation and growth toughness increase with increasing loading rate and crack speed; (2) the kinetic energy of the flying fragments increases with increasing striking speed; (3) the dynamic fracture energy increases rapidly with the increase of crack speed, and a semi-empirical rate-dependent model is proposed; and (4) the characteristics of fracture surface imply that the failure mechanisms depend on loading rate and rock microstructure.

Inner stress exists in rocks, affecting rock engineering, yet has received very little attention and quantitative investigation because of uncertainty about its characteristics. Previous studies have suggested that the inner stresses of rock materials are closely related to their physical state variation. In this work, a novel mold was designed to simulate the storage process of inner stress in specimens composed of quartz sands and epoxy. Then, thermal tests were carried out to change the physical state of the specimens, and expansion of the specimens was monitored. The results indicated that inner stress could be partly locked by the mold and it could also be released by heating. It can be inferred from the analysis that one necessary condition of storage and release of inner stress is physical state variation. Additionally, by using an XRD method, the variations in the interplanar spacing of the quartz sands were detected, and the results reflect that inner stress could be locked-in aggregates (quartz sands) by a cement constraint (solid epoxy). The inner stress stored in quartz sands was calculated using height and interplanar spacing variations.

The International Society for Rock Mechanics has so far developed two standard methods for the determination of static fracture toughness of rock. They used three different core-based specimens and tests were to be performed on a typical laboratory compression or tension load frame. Another method to determine the mode I fracture toughness of rock using semi-circular bend specimen is herein presented. The specimen is semi-circular in shape and made from typical cores taken from the rock with any relative material directions noted. The specimens are tested in three-point bending using a laboratory compression test instrument. The failure load along with its dimensions is used to determine the fracture toughness. Most sedimentary rocks which are layered in structure may exhibit fracture properties that depend on the orientation and therefore measurements in more than one material direction may be necessary. The fracture toughness measurements are expected to yield a size-independent material property if certain minimum specimen size requirements are satisfied.

The relationship between the static and dynamic elastic modulus in rock materials has been frequently addressed in scientific literature. Overall, when it comes to the study of materials with a wide range of elastic moduli, the functions that best represent this relationship are non-linear and do not depend on a single parameter. In this study, the relationships between the static and dynamic elastic modulus of eight different igneous, sedimentary and metamorphic rock types, all of which are widely used as construction material, were studied. To this end, the elastic modulus values of 33 samples were obtained which, together with the values obtained for 24 other samples in a previous study, allowed a new relationship between these parameters to be proposed. Firstly, linear and nonlinear classical models were used to correlate static and dynamic moduli, giving R 2 of 0.97 and 0.99, respectively. A classical power correlation between static modulus and P-wave velocity has also been proposed, giving an R 2 of 0.99 and a sum of the squared differences (SSE) of 553.93. Finally, new equations relating static and dynamic modulus values have been proposed using new nonlinear expressions. These consider: (a) bulk density ( R 2  = 0.993 and SSE = 362.66); (b) bulk density and total porosity of rock ( R 2  = 0.994 and SSE = 332.16); and (c) bulk density, total porosity of rock and uniaxial compressive strength ( R 2  = 0.996 and SSE = 190.27). The expressions obtained can be used to calculate the static elastic modulus using non-destructive techniques, in a broad range of rock materials.

Damage and fracture are the most extensive failure modes of rock materials, which may easily induce disaster and instability of engineering structures. This study developed a nonlocal damage fracture phase field model for rocks considering the heterogeneity of rocks. The modified phase field model introduced the heterogeneity of fracture parameters and modified the governing equations. Meanwhile, the free energy was constructed by the elastic strain energy sphere‐bias decomposition and the plastic strain energy. As for the numerical implementation, the three layers finite elements method structure was used in the frame of the finite element method. The ability of the modified phase field model has been illustrated by reproducing the experiment results of rock samples with pre‐existing cracks under compression. This paper developed a nonlocal damage fracture phase field model for rocks considering the heterogeneity of rocks. The modified phase field model introduces the heterogeneity of fracture parameters and modifies the governing equations. The numerical implementation uses the three layers finite elements method structure.