Natural Rock Mass Research Articles

Обоснование структуры и анализ функционирования устройства для натяжения арматурных канатов

The paper considers the challenge of creating a compact device for tensioning the cable bolts. Commercially available deep-set cable bolt of the AK01, AKS type have threaded couplings that allow the base plates to be pressed to the reinforced surface or the process equipment to be suspended. Expanding the scope of the cable bolt application, in particular, to reinforce the open-pit walls and natural rock masses, determined the need to use the cable bolts of a great length and without threaded couplings. In this case, the interaction of the end of the cable bolt with the base plate is made using collet clips. The mounting kit includes a base plate, a collet housing, and a collet. Installation of a cable bolt is carried out using a device that provides the following operations: capturing and tensioning the part of the cable bolt extending from the borehole, pressing the base plate, and fixing the collet in the holder. These actions are performed using special devices are designed to include a pneumatic-hydraulic pump and a special hydraulic cylinder. However, in some cases it is necessary to have a simpler design that is small in size and does not require any external energy sources. The article presents a compact device for performing the actions necessary for installing a base plate and securing it to the cable bolt using a collet. A specific feature of the lever mechanism used in the device is the variability of the structural arrangement. The possibility of implementing the movements of two output links from one leading link and sequentially performing operations is justified: tensioning the cable bolt, pressing the body of the collet clamp to the base plate, securing the collet to the cable bolt.

Investigations on the fracture mechanisms of Z-shaped fissured rock-like specimens

Complex shapes of cracks exist in natural rock masses, however, present research has simplified it into straight line-shaped fissures. In view of this, three-dimensional (3D) printing is employed to make Z-shaped fissured specimens with different main fissure angle α and secondary fissure angle β. The compress fracture experiments are conducted, and full-field strain distributions during crack propagations are obtained using Digital Image Correlation (DIC) technology. Traditional Smoothed Particle Hydrodynamics (SPH) method is improved to examine damage process as well as fracture mechanisms in Z-shaped fissured specimens. It can be concluded that: Wing Crack (WC), Main Crack (MC), Outer Crack (OC) and Inner Crack (IC) are observed in the experiment. The secondary fissure angle β guides the initiation of MC, while the main fissure angle α guides the initiation of WC. Stress–strain curve of 3D printing samples with Z-shaped fissures shows similar trends to that of real rock, experiencing four typical parts. Numerical results show high similarities with experimental results. We have also discussed the crack initiation mechanisms in various main fissure angle α and secondary fissure angle β in the end, and concluded the stress distribution characters. The findings of this research will offer some references for correct understanding of the crack evolution processes and fracture mechanics of Z-shaped fissured rock masses.

Visualization test and numerical simulations of 2D blasting crack propagation

Drilling and blasting, characterized by their efficiency, ubiquity, and cost-effectiveness, have emerged as predominant techniques in rock excavation; however, they are accompanied by enormous destructive power. Accurately controlling the blasting energy and achieving the directional fracture of a rock mass have become common problems in the field. A two-dimensional blasting (2D blasting) technique was proposed that utilizes the characteristic that the tensile strength of a rock mass is significantly lower than its compressive strength. After blasting, only a 2D crack surface is generated along the predetermined direction, eliminating the damage to the reserved rock mass caused by conventional blasting. However, the interior of a natural rock mass is a "black box”, and the process of crack propagation is difficult to capture, resulting in an unclear 2D blasting mechanism. To this end, a single-hole polymethyl methacrylate (PMMA) test piece was used to conduct a 2D blasting experiment with the help of a high-speed camera to capture the dynamic crack propagation process and the digital image correlation (DIC) method to analyze the evolution law of surface strain on the test piece. On this basis, a three-dimensional (3D) finite element model was established based on the progressive failure theory to simulate the stress, strain, damage, and displacement evolution process of the model under 2D blasting. The simulation results were consistent with the experimental results. The research results reveal the 2D blasting mechanism and provide theoretical support for the application of 2D blasting technology in the field of rock excavation.

Effects of multiple reflected P waves on crack-tip stress and crack propagation in directional fracturing blasting

Directional fracturing blasting is effective for rock engineering, but it is inevitably disturbed by multiple reflected waves from different directions in natural rock mass due to discontinuous boundaries. Reflected waves affect both crack-tip stress and crack propagation, hence affect the results of directional fracturing blasting. In this paper, with the aid of high-speed photography, an optical caustics method is used to study effects of multiple reflected P waves on a directional blast-induced crack in a polymethyl methacrylate (PMMA) plate, specifically on crack path, crack fracturing mode, crack-tip stress and crack velocity. Crack-tip stress field is indicated by the shape of caustics pattern. Before the loading of reflected P waves, the mode I directional crack driven by blast-induced gases propagates in a straight path; crack-tip stress field is K-dominated, and crack-tip caustics pattern is consistent with classical caustics theory. On the contrary, under the loading of reflected P waves, the directional crack changes to be mixed-mode I + II and propagates in a curved path; Crack-tip stress field is non-K-dominated due to transient stress superposition of reflected P waves, and crack-tip caustics pattern is consistent with modified caustics theory. Transient stress superposition is not obvious for reflected P waves with a longer reflection distance. The tension loading of reflected P waves plays a more important role than the compression loading, which increases crack-tip stress intensity factors and crack velocity. This study provides a comprehensive understanding of effects of multiple reflected P waves from different directions on directional fracturing blasting.

Investigation of local mechanical behavior during the shear process of rough rock joints using DEM

Rough joints are prevalent in natural rock masses, and their shear mechanical properties are crucial for ensuring the safety and stability of these masses. Existing studies often neglect the contribution of various joint asperities to shear stress resistance. This study addresses this gap by eluci-dating the local shear mechanisms of different asperities in rough joints throughout the shear process. This was achieved through a combination of quantitative and qualitative analyses using the Discrete Element Method (DEM). Initially, Barton's ten standard roughness joint profiles were dig-itized, and rough joints were modeled using the Modified Smooth Joint Model (MSJM). Direct shear tests on joint specimens under constant nor-mal stress were performed using servo-controlled methods. Subsequently, the shear stress behavior was analyzed in relation to the test results. The failure modes of the joint specimens were examined in detail using crack tracking and force chain analysis. The study also explored the relation-ship between the number of cracks and shear stress. Additionally, variations in average stress across ten different segments of joints during shear were monitored using the measuring circle function. The shear resistance contributions of local joint segments were quantitatively assessed using three stress indices: maximum stress, upper limit of maximum stress, and the distribution range of maximum stress. The Joint Roughness Coeffi-cient (JRC) of joints was found to correlate well with these indices. Overall, the progressive failure of local joint segments was analyzed both qual-itatively and quantitatively. The study confirmed that the local shear mechanisms of different joint segments during the shear process are distinct.

Examining theoretical applicability of displacement discontinuity model to wave propagation across rock discontinuities

Rock discontinuities such as joints widely exist in natural rock masses, and wave attenuation through rock masses is mainly caused by discontinuities. The displacement discontinuity model (DDM) has been widely used in theoretical and numerical analysis of wave propagation across rock discontinuity. However, the circumstance under which the DDM is applicable to predict wave propagation across rock discontinuity remains poorly understood. In this study, theoretical analysis and ultrasonic laboratory tests were carried out to examine the theoretical applicability of the DDM for wave propagation, where specimens with rough joints comprising regular rectangular asperities of different spacings and heights were prepared by 3D printing technology. It is found that the theoretical applicability of the DDM to predict wave propagation across rock discontinuity is determined by three joint parameters, i.e. the dimensionless asperity spacing (L), the dimensionless asperity height (H) and the groove density (D). Through theoretical analysis and laboratory tests, the conditions under which the DDM is applicable are derived as follows: and , . With increase in the groove density, the thresholds of the dimensionless asperity spacing and the dimensionless asperity height show a decreasing trend. In addition, the transmission coefficient in the frequency domain decreases with increasing groove density, dimensionless asperity spacing or dimensionless asperity height. The findings can facilitate our understanding of DDM for predicting wave propagation across rock discontinuity.

Experimental study on I/II/III mixed mode fracture characteristics of a combined rock mass under creep loading

I/II/III mixed mode fractures of intersecting joint fissures often occur in natural rock masses, and jointed rock masses are prone to rockbursts in deep underground engineering when subjected to long-term crustal stresses. However, most studies of the mechanical mechanisms of these intersected joints have been conducted by simplifying two-dimensional joint model tests. Furthermore, the fracture mechanisms of two-dimensional intersected joints under tension and compression are completely different from those of three-dimensional joints. This paper presents a novel prefabricated specimen with combinations of intersecting joints capable of detecting the failure behaviours of rock I/II/III mixed mode fractures under creep loading. Uniaxial compression and multistage creep tests are performed on prefabricated sandstone specimens with intersecting joints of 0°/0°, 0°/30°, 0°/60°, and 0°/90°. The experimental results show that with the increase in the number of prefabricated intersecting joints, the uniaxial compressive strength and elastic modulus values of the sandstone specimens gradually decrease. In addition, the sandstone specimens experience relatively few AE events and minor axial strain variations in the first creep stage and the second creep stage of the multistage creep test. The axial strain increases sharply due to the sharp increase in the number of AE events in the third creep stage. The 0°/60° sandstone specimen undergoes accelerated creep failure, resulting in mixed X-shaped tensile‒shear rupture. The RA value is high based on the quantification of the creeping cracks using the acoustic emission parameters of the rise angle (RA) and average frequency (AF). The AF values of the 0°/0°, 0°/30°, and 0°/90° sandstone specimens are high. The experimental results show that a larger joint intersection angle leads to greater mutual restraints and greater effects of prefabricated crack propagation in the rock specimens, thus increasing the final failure strength. Finally, based on the acoustic emission count, a characteristic variable D suitable for characterizing the creep damage evolution of a joint rock mass is established. The findings of this paper can facilitate an effective understanding of the creep effect of I/II/III mixed mode fracture and its micromechanism. The research results will have a certain reference value for the detection and risk mitigation of instantaneous and time-delayed rockbursts.

Combined acoustic methods in monitoring the crack development in granite

Detecting cracks of various sizes is crucial for monitoring and predicting rock failure. This study combines two acoustic methods—the passive acoustic emission (AE) and the active ultrasonic P-wave velocity to investigate the cracking process from initiation to propagation and coalescence of rocks containing pre-existing flaws, which simulate the intrinsic defects in natural rocks or rock masses, across different scales in three-dimensional space. The resultant AE activity is found sensitive to microcracks even in the early loading stage and can be divided into three stages: quiet, stable, and high growth periods. The positions of the microcracks can be obtained with the assistance of several AE sensors. It is also found that the P-wave velocity attenuation is more sensitive to macrocracks but less sensitive to microcracks. The results indicate that combining the AE and active ultrasonic-wave methods can provide comprehensive information to evaluate the damage levels and localize the internal cracks with multiple scales in the entire cracking process of rocks. The study also indicates the potential for predicting crack coalescence and failure based on the combination of these two nondestructive methods. In addition, the findings can also be applicable in the monitoring and prediction of failure in other brittle materials.

Three-dimensional damage and rupture patterns of different thicknesses of rock mass with open joints under blast loading

There are an immense number of discontinuous structural surfaces represented by tensile joints in natural rock mass, in which the thickness of tensile joints determines the form how stress wave interacts with joint surface, which has a significant influence on the fracture behavior of jointed rock mass under blast loading. Open joint specimens were prepared using 3D printing technology, an indoor 3D blasting experiment was carried out with respect to different open joint thicknesses. Through CT scanning and three-dimensional reconstruction, the rupture and the distribution patterns of three-dimensional cracks of the post-blasting specimens were compared, and the rupture characteristics of the rock masses with different open joint thicknesses under blast loading were analyzed. The blasting process of the rock masses with open joints was inverted by AUTODYN numerical simulation software, the effects of open joint thickness on the propagation of stress wave and the three-dimensional damage characteristics of rock mass were revealed. Results showed that under the blast load, the wing cracks derived from the end of the open joints are greatly affected by the thickness of the joints and as the joint thickness increases, the annular derived cracks formed on the right outer surface of the specimen gradually decrease. In case of a change in the open joint thickness, the intensity at which the stress wave diffracts and transmits through the end of the joint will be directly affected. This makes it hard for the wing cracks at the end to initiate, the distribution density of the radial tension cracks traversing through the open joint surface attenuates obviously, resulting in the decrease of the fractal dimension and the damage extent of the specimen. As the thickness of open joints increases, the blast stress wave running through the joint surface will endure a time delay and reduced intensity, the closure of the joint surface gradually reduces, and the degree of stress concentration at the end gets weak. In the course of stress wave propagation, the rock mass on the back-blast side of the joint endures the combined actions of compressive stress field, tensile and tangential stress field and compressive and tangential stress field. As the thickness of open joint increases, the time point for the back-blast side to reach the peak stress is delayed, the intensity of the composite stress field subjected to compressive and tangential stress field decreases, and the normal displacements on the near-blast side and the back-blast side of the joint follow the opposite trend.

Study on multi-scale damage and failure mechanism of rock fracture penetration: experimental and numerical analysis

In natural rock masses, joints or fractures usually occur at different penetrations. To study the deformation and failure behavior of rock mass with different fracture penetrations, a series of triaxial compression experiments were conducted on rock specimens containing prefabricated fracture at penetrations of 0%, 25%, 50%, 75% and 100%. The results show that the greater the fracture penetration and the smaller the strength of the rock sample, the more obvious the plastic deformation section of the stress–strain curve. Confining pressure can greatly improve the compressive strength of rock samples. For intact rock samples, confining pressure will change the failure mode from tensile failure to shear failure. For fractured rock samples, the confining pressure will aggravate the degree of damage to the rock sample. PFC 3D simulation shows that the failure process of rock samples is accompanied by the transformation of strain energy to damping energy and particle sliding energy, which can quantitatively characterise the damage process of rock. The increasing trend of crack number is slow-steep-slow, which is the ‘S’ type. It began to grow rapidly after reaching peak strength and gradually stabilised after reaching residual strength. It is consistent with the trend of energy change.

Uniaxial Compressive Damage Characteristics of Rock-like Materials with Prefabricated Conjugate Cracks

Joined fractures are an important factor affecting natural rock masses’ mechanical and deformation properties. In this paper, indoor uniaxial compression experiments reproduce prefabricated cracks’ generation, extension, and coalescence in rock-like specimens. For the fractured specimens, a single crack with an inclination of α = 45° was placed on the left and right sides, and a third crack with an angle of β = 30°, 45°, 60°, and 90° to the single crack on the right side was placed in groups III–VI, respectively. All cracks extended in the thickness direction. Vertical pressure was applied at a constant loading rate of v = 0.1 mm/min until the stress dropped dramatically. In addition, numerical calculations were performed on the rock specimens using PFC2D, a sub-module of the Discrete Element Method (DEM). The experimental results agree with the numerical simulations in that the strength of the specimens containing a conjugate crack is significantly reduced, and the mechanical and deformation properties of the specimens are related to the internal angle of the conjugate crack, with the lowest peak strength and lowest percentage energy dissipation at β = 45°.

Numerical simulation of strength and failure analysis of heterogeneous sandstone under different loading rates

Natural rock masses often contain heterogeneous structures with varying sizes, non-uniform distributions, and strengths, which influence the mechanical response characteristics and crack propagation modes under loading. Furthermore, heterogeneous structures can affect the stability of the rock mass, in serious cases, leading to geotechnical and mining engineering disasters. In the present work, a parallel-bond model (PBM)-based numerical simulation using Particle Flow Code (PFC) was carried out to study the strength and failure characteristics of sandstone specimens with heterogeneous structures under different loading rates. The results show that the peak strength increases with the increasing loading rate. In addition, all of the initial cracks occurred at the edges of the heterogeneous structures of specimens under different loading rates. The greater the loading rate, the greater the stress concentration degree at the edge of the heterogeneous structures, the greater the dissipated energy as the sandstone specimens with heterogeneous structures suffer damage, the more intense the acoustic emission activity, and the greater the damage degree of the specimens. The number of cracks generated in sandstone specimens with heterogeneous structures increases gradually with the increasing loading rate during the initial loading stage, and gradually decreases after the specimens are damaged. Cracks propagate and develop from the upper right region to the lower right region of the specimens, forming crack groups that rapidly penetrate the specimens, leading to failure. Under different loading rates, the final failure behavior of the sandstone specimens with heterogeneous structures changes from an inverted V-type to θ-type, then gradually evolves to O-type failure.

Quantitative investigation of crack propagation and fracture mechanism of fissured granite from the mesoscopic perspective

Natural rock masses comprise numerous fissures, which affect the stability of rock mass engineering. It is crucial for rock engineering to comprehend the crack propagation and fracture mechanisms of fissured rock. In this study, uniaxial compression tests were conducted on fissured granite specimens with various flaw inclinations (0°, 30°, 45°, 60°, and 90°). After specimen failure, the cracks originating from pre-existing fissures were classified (tensile, shear, and tensile-shear cracks). To link the macroscopic failure behavior and mesoscopic fracture mechanism in fissured granite specimens, a quantitative method combining deep learning and scanning electron microscope (QMDL-SEM) was employed for the identification of the mesoscopic fracture mechanism of macroscopic cracks. Identified results suggested that the failure of fissured specimens was attributed to secondary cracks characterized by tensile stress (failure area caused by tensile stress accounting for more than 87%) and far-field cracks dominated by shear stress (failure area caused by shear stress accounting for more than 60%). Additionally, for secondary cracks, as the transition went from tensile crack to tensile-shear crack and then to shear crack in a macroscopic scale, the proportion of failure area caused by shear stress on the failure surface gradually increased. However, tensile stress still dominated the failure area.

Dynamic mechanical response and fracture mechanism of granite with structural plane containing planar and circular filling simultaneously: The influence of extension length

Weakly filled structural planes are an important influence on the stability control of engineering rock mass. Weak fillings with different geometrical characteristics are randomly distributed in the natural rock mass. To investigate the dynamic mechanical response and fracture mechanism of granite containing both planar and circular weak filling, the Split Hopkinson Pressure Bar (SHPB) experimental system was used to conduct the dynamic impact test. In this paper, the dynamic mechanical properties, the fracture process, the energy evolution and the micro-morphological characteristics of the fragments are mainly analyzed. The results show that: (1) the dynamic uniaxial compressive strength (DUCS), peak strain, and deformation modulus are synergistically affected by the extension length (L) of planar filling and strain rate. The presence of planar weak filling leads to a decrease in strain rate dependence while weakening the specimens' DUCS, and improves the overall synergistic deformation capacity of the specimen. (2) Strain rate and L jointly affect the energy distribution and evolution characteristics of the specimen; L has an enhancement effect on the distribution of reflected energy and a weakening effect on the distribution of transmitted energy. The effect of L on the dissipation of energy is transformed by the strain rate. The strain rate and L are the dominant factors in the variability of stress waveform conversion. (3) At a low strain rate, L has a positive effect on the intensification of the degree of fragmentation, however, at a high strain rate, the effect is characterised by a shift between positive and negative. The degree of fragmentation has a strain rate effect. As L increases, L has a “negative effect” on the “strain rate effect” that affects the degree of fragmentation. (4) The degree of fragmentation of macroscopic fragments is closely related to the energy dissipation density, the relationship between the two appears as a logarithmic function change. The presence of weak filling does not significantly change the microscopic morphology of granite fragments. The loose and porous microstructure of gypsum is the main reason for the altered propagation characteristics of the stress waves.

Research on application of annular concrete-filled steel tube support in deep roadway

In this paper, through on-site investigation and monitoring, the characteristics of roadway deformation and the causes of deformation and damage are analyzed. Among them, the unreasonable support system is an external factor, and the nature of rock mass, deterioration degree of surrounding rock, and high ground stress are internal factors. A simulation method of CFST considering initial defects in core concrete is proposed and utilized to analyze the mechanical properties of CFST supports. Building upon numerical simulation results, we introduce an optimized support scheme comprising annular CFST support, segmental fissure surrounding rock grouting, and bolts. Field comparison tests demonstrate that the application of the new repair technology yields remarkable enhancements in the bearing capacity of surrounding rock and supporting structures while ensuring a more uniform stress distribution within the rock mass.

3D spatial fracture behavior of sandstone containing a surface flaw under uniaxial compression

Surface defects are prevalent in natural rock masses, and the newborn cracks that initiate from these defects and significantly affect structural stability usually extend in a three-dimensional (3D) manner. Hence, in this research, a series of uniaxial compression tests were conducted on sandstone specimens containing a surface flaw to examine the effect of nondimensional flaw depth (0, 0.3, 0.5 and 0.75) on the fracture behavior. The crack propagation process was monitored by digital image correlation (DIC) technique, and postmortem microscopic fracture morphology was measured using scanning electron microscope (SEM) method. In addition, the fracture energy evolution and stress intensity factors (SIFs) along the semi-elliptical flaw perimeter were discussed in detail to theoretically interpret the experimental phenomena. The results indicate that the strength decreased by 2.70%, 10.90% and 11.91% for nondimensional surface flaw depths of 0.3, 0.5 and 0.75, respectively, and elastic modulus exhibited a reduction of 3.71%, 10.69% and 3.21%, respectively. Full-field deformation contours demonstrate that crack paths in the front surface of the specimen were totally different from those in the back surface, but the failure pattern tended to be similar to that of specimens containing a penetrated flaw with the increasing flaw depth. The micro appearance of a typical fracture further reveals the complicated stress state (mixed I-II-III mode) under uniaxial compression. For a larger flaw depth, the proportion of releasable elastic strain energy in total input strain energy was improved, while the percentage of dissipated energy was reduced. Based on fracture mechanics, SIFs along the flaw periphery uncover the magnitude of KI, KII and KIII and further the type of initiation crack type. Finally, parametric analysis was carried out to investigate the effects of flaw length and specimen thickness. The difference in crack pattern from surface and penetrated flaw was also discussed in detail.

Study on the Influence of the Joint Angle between Blast Holes on Explosion Crack Propagation and Stress Variation

The joints and fissures in a natural rock mass can affect the mechanical properties of the rock mass, the propagation of a blasting stress wave, and the blasting effect of the smooth surface of roadways. In the process of roadway drilling and blasting, there will inevitably be some joints between the two blast holes. Taking the joint angle as the starting point, this paper studies the rule of rock explosion crack propagation and stress variation when there are joints with different angles between two blast holes and analyzes the influence of joints on rock mechanical properties and blasting effects. The numerical simulation method and the software ANSYS/LS-DYNA are used to establish 7 rock mass models with various joint angles. When there is no joint between two holes and joints of 15°, 30°, 45°, 60°, 75°, and 90°, the propagation of explosive cracks and stress variations in the rock mass are discussed. The results show that the joints at different angles have obvious guiding and blocking effects on the propagation of explosive cracks, and as joint angles increase, the guiding effect becomes more apparent and the blocking effect becomes weaker. The effective stress of the rock mass will vary depending on the angles of the joints between the hole and the joint. As the joint angle increases, the joint’s influence on the reflection and superposition of stress waves gradually weakens, and the peak value of the effective stress of the rock mass gradually decreases. The peak effective stress of the rock mass on the blasting side of the joint is similarly impacted by the superposition of stress waves, and the extreme value may be seen at the critical node of each change curve. The explosive crack will break through at the critical location because the maximal effective stress of the rock mass is distributed in a “W” form on the blasting side of the joint.

Damage evolution and constitutive model of the rock masses with non-penetrating cracks under repeated impact loading.

A large number of cracks exist in natural rock masses, which significantly affects the stability of surrounding rocks in engineering under impact loading. Repeated impact tests by Split Hopkinson Pressure Bar are performed on non-penetrating cracked granite specimens with different prefabricated-crack inclination angles (0, 30, 45, 60, and 90°). The damage evolution law of cracked rock under repeated impact loading is investigated. Macroscopic damage variables considering geometric and mechanical parameters of cracks are proposed. Further, a constitutive model for the impact loading test is developed based on the coupling damage. It has been found that, the impact resistance of fractured rock first decreases and then increases with the increased prefabricated-crack inclination angle. The impact resistance for specimens with an inclination angle of 45° is the minimum. Theoretical results from the developed model agree with the experimental data. The model could well describe the progressive damage characteristics of cracked rock masses.

Experimental investigation on mode I fracture behavior of sandstone after grouting filling under three-point bending

The widespread presence of fissures in natural rock masses poses numerous challenges to the design and construction of rock engineering. As an effective reinforcement method, grouting filling is crucial for maintaining the safety and stability of underground engineering. In this study, a testing and monitoring system was established to perform three-point bending tests on sandstone specimens with a pre-notch after grouting filling utilizing high-definition cameras and the rock mechanics testing machine. Combined with the digital image correlation (DIC) method and 3D scanning technique, the influence of grouting filling type on the mechanical behavior and fracture characteristics of sandstones was investigated. Simultaneously, a novel approach for quantitatively determining crack initiation and propagation was proposed based on the maximum principal strain theory. The results indicated that the peak load of specimens all tends to rise with the increase of filling rate and filling material strength. The fracture toughness and nominal tensile strength initially ascend and then slightly decline when the filling rate goes up, whereas both grow continuously as the filling material strength improves. Increasing the filling rate and filling material strength can decrease the opening degree of the pre-notch and postpone the development of the fracture process zone (FPZ). The crack propagates steadily to a certain length before remarkably increasing as the load rises, while the FPZ length exhibits a growth trend from slow to rapid and subsequently to sluggish. Moreover, the grouting filling effect will also have a pronounced impact on the crack propagation path and fracture surface morphology.

Collapse caldera walls: Mechanical controls on slope failure and morphology

Volcanic calderas are enclosed topographic depressions that are commonly delimited by steep annular cliffs (caldera walls). The walls represent degraded scarps of ring faults that accommodated caldera collapse. Here, we assess the mechanical controls on caldera wall morphology and failure by: (i) analysing slope properties of recently formed calderas; (ii) examining analytical solutions for slope failure; and (iii) simulating progressive slope failure via Distinct Element Method (DEM) numerical modelling. Average slope angles of the caldera walls in nature range from 20° to 65° and slope heights range from 99 m to 1080 m. Smaller slope heights are weakly tied to greater slope inclinations. Almost 60% of sampled caldera wall profiles show a steeper upper section and a gentler lower section, which in numerical models are reproduced as an upper slope comprising intact wall rock and a lower slope comprising failed material inclined at the angle of repose. Moreover, modelled material with a low angle of internal friction and low cohesion exhibits shear failure, whereas material with high friction and high cohesion shows tension cracking, buckling and toppling. The slope height and inclination data from the numerical models agree well with those in nature. The numerical model data correspond more closely to analytically-predicted failure planes than critical (i.e. limit equilibrium) slopes because they are short-lived and therefore unlikely to be sampled in either model or nature. If rock mass cohesions or friction angles constrained analytically from natural slopes are determined by assuming the slope is critical, they are likely to be underestimates. The homogeneous numerical models here give an estimated natural rock mass cohesion of 0.5 MPa or less. This is much lower than typical laboratory-scale cohesion values, and it highlights the importance of strength reduction when upscaling mechanical parameters from laboratory experiments for modelling slope stability and volcano deformation.