Riedel – Hiermaier – Thoma Research Articles

Dynamic Responses and Crack Propagation of Rock with Crossed Viscoelastic Joints Under Blasting Loads

To investigate the propagation of stress waves in viscoelastic joints under blasting loads, and their impact on crack propagation and dynamic response in rock masses, a numerical model incorporating intersecting viscoelastic joints was developed using LS-DYNA. This study focuses on the influence of various joint geometric parameters, including thickness and angle, on stress wave propagation and damage patterns in rock. The Riedel–Hiermaier–Thoma (RHT) model was employed to simulate the dynamic behavior of rock, while the Poynting–Thomson model was used to describe the viscoelastic properties of the joint fillings. The simulation results provide detailed insights into the principal stress, displacement, and particle vibration velocity around the joints. Based on the stress wave propagation theory, the velocity transmission coefficients were calculated to quantify the attenuation of stress waves across the joints. The findings demonstrate that viscoelastic joint properties significantly affect the damage patterns in the rock mass. Specifically, the area of the crushed zone and the width of cracks on the blasting side are proportional to joint thickness, while crack propagation at the joint tips is governed by differences in principal stress. Moreover, the propagation of vibration velocity is notably weakened at the second joint, highlighting the critical role played by joint characteristics in stress wave dynamics. These results underscore the complex interaction between joint properties and stress wave behavior in rock masses, providing valuable insights for optimizing blasting designs and improving the safety of underground engineering projects.

Research on Damage Evolution Mechanism of Layered Rock Mass under Blasting Load

Rock mass consists of many discontinuities, such as faults, joints, etc., and layered joints are a common kind of rock mass structure. The joints affect the stress wave propagation, and blasting is an economical and efficient rock fragmentation method for rock mass engineering. So, the rock mass fragmentation effect and construction progress are affected by these layered joints. Numerical studies were carried out to analyze the damage evolution process of intact rock and rock mass with layered joints subjected to blasting loads based on the Riedel–Hiermaier–Thoma (RHT) model in LS-DYNA software (smp s R11.0.), and the effects of the location of initiation points and the fracture distribution on dynamic damage evolution of the rock mass were discussed. Bottom initiation tends to direct the blasting energy toward the blasthole mouth, resulting in effective rock fragmentation and ejection. Gradually adjusting the initiation point upward can improve the stress and damage distribution, allowing some of the blasting stress waves to propagate toward the bottom and enhance the fragmentation of the rock at the bottom. The distribution of layered joints exacerbates the damage to the rock mass on the upstream surface, but also acts as a certain shield to the propagation of stress waves, increasing the asymmetry of the damage distribution. It is useful to know the damage mechanism of the rock mass with layered joints to improve the effect of rock mass fragmentation by blasting. These results have very important theoretical significance and application value for the optimization of blasting construction technology.

Failure analysis of Nehbandan granite under various stress states and strain rates using a calibrated Riedel–Hiermaier–Thoma constitutive model

This study presents a comprehensive procedure for determining, calibrating, and validating the Riedel–Hiermaier–Thoma (RHT) material model parameters for granite. The process involves collecting a comprehensive dataset of conventional mechanical tests conducted on various types of granite worldwide. Based on this dataset, one set of RHT material model parameters is determined. Additionally, a specific granite sample from Iran, known as Nehbandan granite, is characterized through physical and mechanical testing to obtain another set of parameters. The challenging task of determining the third set of parameters, which are difficult to obtain analytically and experimentally, is accomplished through a calibration process that iteratively adjusts the parameters based on comparisons between numerical simulation results and experimental data. To validate the determined parameters, a series of tests, including uniaxial compressive strength (UCS), triaxial compressive strength (TCS), Brazilian tensile strength, and dynamic Brazilian using split Hopkinson pressure bar (SHPB) tests, are conducted on the Nehbandan granite. These tests are also simulated using LS-Dyna software, and the numerical simulation results are compared with the corresponding experimental test results. The comparison between the numerical and experimental data serves as a means of validating and verifying the accuracy and reliability of the determined RHT material model parameters for granite. The results demonstrate the successful determination and calibration of the RHT material model parameters for granite. The model exhibits effectiveness in predicting the behavior of granite under various loading conditions. The validation process confirms the accuracy and reliability of the determined parameters through a close agreement between numerical simulations and experimental data. The findings contribute to a better understanding of granite's mechanical response and provide a reliable tool for simulating and predicting its behavior in engineering applications. The validated RHT material model parameters offer a robust framework for accurate numerical simulations, enabling engineers to make informed decisions in rock engineering projects.

On the application of RHT model and SPG algorithm for the analysis of rock cutting process

On the application of RHT model and SPG algorithm for the analysis of rock cutting process

Numerical simulation of blasting behavior of rock mass with cavity under high in-situ stress

With the shift of coal seam mining to the deep, the in-situ stress of coal and rock mass increases gradually. High ground stress can limit the generation of rock cracks caused by blasting, and blasting usually shows different crushing states than low stress conditions. In order to study the blasting expansion rule of rock mass with cavity under high ground stress and the rock mass fracture state under different side stress coefficients. In this paper, the effective range of blasting and the stress distribution under blasting load are analyzed theoretically. The RHT (Riedel-Hiermaier-Thoma) model is used to numerically simulate the blasting process of rock mass with cavity under different ground stress, and the influence of ground stress and lateral pressure coefficient on the crack growth of rock mass is studied. The results show that when there is no ground stress, the damage cracks in rock mass are more concentrated in the horizontal direction and the fracture development tends to the direction where the holes are located, which confirms the guiding effect and stress concentration effect of the holes in rock mass, which helps to promote the crack penetration between the hole and the hole. The length difference of horizontal and vertical damage cracks in rock mass increases with the increase of horizontal and vertical stress difference. Under the same lateral stress coefficient, the larger the horizontal and vertical stress difference is, the stronger the inhibition effect on crack formation is. For blasting of rock mass with high ground stress, the crack formation length between gun holes decreases with the increase of stress level, and the crack extends preferentially in the direction of higher stress. Therefore, the placement of gun holes along the direction of greater stress and the shortening of hole spacing are conducive to the penetration of cracks between gun holes and empty holes. The research can provide reference for rock breaking behavior of deep rock mass blasting.

Damage evolution law of multi-hole blasting igneous rock and quantitative evaluation model of damage degree based on fractal theory and clustering algorithm

The geological phenomenon of igneous rock invading coal seam is widely distributed, which induces mining risk and affects efficient mining. The pre-splitting blasting method of igneous rock is feasible but difficult to implement accurately, resulting in unnecessary safety and environmental pollution risks. In this paper, the blasting model with penetrating structural plane and the multi-hole blasting model with different hole spacing were established based on the Riedel–Hiermaier–Thoma (RHT) damage constitutive to explore the stress wave propagation law under detonation. The damage cloud diagram and damage degree algorithm were used to quantitatively describe the spatio-temporal evolution of blasting damage. The results show that the explosion stress wave presents a significant reflection stretching effect under the action of the structural plane, which can effectively aggravate the presplitting blasting degree of the rock mass inside the structural plane. The damage range of rock mass is synchronously evolved with the change of blasting hole spacing. The blasting in the igneous rock intrusion area of the 21,914 working face is taken as an application example, and the damage degree of rock mass is reasonably evaluated by the box-counting dimension and K-means clustering method, which proves the effectiveness of the blasting scheme and provides reference value for the implementation of related blasting projects.

Investigation of blast-induced rock fragmentation and fracture characteristics with different decoupled charge structures

Investigation of blast-induced rock fragmentation and fracture characteristics with different decoupled charge structures

Dynamic behaviour of multi-layer composite against single and multiple projectile impact loading

Dynamic behaviour of multi-layer composite against single and multiple projectile impact loading

Damage Zone of the Reinforced Concrete Beam under Rectangular Explosive Contact Explosions

This paper investigates the damaged area of a reinforced concrete beam under rectangular explosive contact explosion, through full-scale beam tests and numerical simulation. The calculation equation of beam surface load distribution based on equivalent impulse is established, with a consideration of the effect of the length and height of rectangular explosive on the load distribution, and the calculation equation of beam damage area is further proposed. Through changing the mass of the rectangular TNT explosive (1~6 kg) and the shape of the 1 kg rectangular explosive, 5 cases of the test were carried out on a full-scale reinforced concrete beam. The damaged area of the beam is divided into three parts: blasting crater, damage span of the front face, and damage span of the bottom face. The RHT (Riedel–Hiermaier–Thoma) material model is used to simulate concrete for numerical simulation. Curve fitting was performed based on the numerical simulation results. With the prediction of the load distribution on the beam surface, the size of the surface crushing area and the span of the damaged area are calculated; the section resistance function of the beam is introduced to calculate the depth of the blasting crater; and the correlation curve between the damaged span of the front face, the depth of the blasting crater, and the mass of the block TNT is established. The local damage to the beam under the contact explosion load can be evaluated more accurately when the mass of the rectangular TNT is 1~6 kg.

Study on cyclic blasting failure characteristics and cumulative damage evolution law of tunnel rock mass under initial in-situ stress

Although in-situ stress significantly affects tunnel rock mass excavation blasting, the crack propagation law of the rock mass under both in-situ stress and cyclic blasting load has not been adequately evaluated. The blasting failure mechanism of rock mass and the cumulative damage evolution effect of cyclic blasting load under different ground stress conditions are systematically studied herein through theoretical analyses, laboratory tests, and numerical analyses. First, the Riedel–Hiermaier–Thoma (RHT) constitutive model is modified and calibrated, and its reliability is improved via an indoor split Hopkinson pressure bar splitting test. Second, the blasting failure analysis model of the dynamic and static load coupling field is established and verified via numerical simulation. Finally, a numerical simulation of the smooth blasting excavation of a rock tunnel is conducted, and the blasting failure mode of a rock tunnel subjected to ground stress is discussed. Notably, the modified and calibrated RHT model can adequately simulate dynamic crack propagation in limestone specimens. Due to the effect of ground stress, the maximum principal stress side is the most favourable direction for blasting crack propagation. The direction of blasting crack propagation is mainly determined by the loading conditions of ground stress, and the number of blasting cycles does not significantly affect the law of rock crack propagation. Smooth blasting during rock tunnel excavation can effectively reduce the dynamic response of surrounding rock in the unexcavated area. Optimizing the cutting-hole and delayed-blasting parameters can improve the blasting quality of tunnel rock mass under in-situ stress.

Dynamic characteristics and crack evolution laws of coal and rock under split Hopkinson pressure bar impact loading

The dynamic mechanical properties and crack evolution characteristics of coal and rock during split Hopkinson pressure bar (SHPB) impact failure are important contents for analysis. In previous studies, the coal and rock specimens used have usually been independent and not closely correlated. In addition, quantitative characterization and analysis methods for coal and rock cracks are immature, and more information has not been fully revealed. The aims of this paper are to comprehensively explore both the dynamic mechanical properties and crack evolution characteristics of coal and rock during impact failure. First, experimental specimens are prepared from coal seam, direct roof rock strata and direct floor rock strata in the same area to highlight the correlations between test pieces. Second, a dynamic strain gauge and high-speed (HS) camera are adopted to reflect the stress wave signal and crack evolution. Then, based on digital image correlation (DIC) technology and the mass screening method, the evolution laws of surface cracks during crushing and the distribution characteristics of sample fragments after crushing are studied from the perspective of fractal, and finally compared with those of the simulation analysis. The results are as follows. (1) The coal and rock samples from the same area have both consistency and differences. The dynamic mechanical properties of coal and rock are affected by the impact velocity and the physical properties of the specimen. Higher impact speeds and densities lead to the more obvious brittleness of the specimen when destroyed. Conversely, the sample shows more plasticity and ductile yield. (2) The self-similarity is significantly manifested in the evolution of surface cracks during impact and the distribution characteristics of fragments after impact. The box dimension and quality screening dimension are applicable to quantitatively characterize the evolution process and results of coal and rock fractures. (3) The simulation results based on the Holmquist–Johnson–Cook (HJC) and Riedel–Hiermaier–Thoma (RHT) constitutive models agree well with the experimental results, and the RHT constitutive model is more consistent. This study may contribute to a more comprehensive understanding of the dynamic characteristics and crack evolution laws of coal and rock under impact loading and provide references for further research and discussion.

Simplified micro-model for brick masonry walls under out-of-plane quasi-static and blast loadings

Simplified micro-model for brick masonry walls under out-of-plane quasi-static and blast loadings

Dynamic responses and damage mechanism of rock with discontinuity subjected to confining stresses and blasting loads

• Dynamic finite element models were proposed to investigate the dynamic responses and damage mechanism of rock under blasting. • The propagation of blasting stress waves was analyzed together with the interaction of discontinuity orientation and confining stress magnitude. • The extension mechanism of the discontinuity was explored from the perspective of stress distribution and dynamic stress intensity factor (DSIF). • Rock discontinuity can weaken the crack-guiding effect of high confining stress, and high confining stress can suppress the development of radial cracks around borehole. The propagation of seismic waves induced by blasting changes significantly at rock discontinuities such as joints and faults, many studies have focused on the mechanism of wave propagation at joints. However, in deep rock masses, high in-situ stress is non-negligible, and the interaction between confining stress and discontinuity under blasting disturbance remains poorly understood. To explore the role of confining stress and discontinuity on the dynamic responses and damage mechanism of rock masses, this paper employed the dynamic finite element method and a series of numerical models were subsequently developed. The Riedel-Hiermaier-Thoma (RHT) model was used to simulate the blast-induced damage of rock. Under blasting disturbance, the propagation of stress waves and damage patterns within the rock at different discontinuity orientations and different confining stress magnitudes were presented. Around the discontinuity, the principal stress distribution and displacements were presented and the dynamic stress intensity factor (DSIF) of the discontinuity tip was obtained to analyze the extension mechanism of the discontinuity. Numerical results show that the discontinuity, the magnitude and direction of confining stress significantly contribute to the damage patterns of rock masses, and the guiding effect of high confining stress on cracking will be weakened due to the existence of discontinuity.

Influence of blasting load directions on tunnel stability in fractured rock mass

Tunnels in fractured rock masses are typically damaged by dynamic disturbances from various directions. To investigate the influence of blasting load directions on the stability of a tunnel with a pre-crack nearby, blasting tests were conducted on the physical models of an external crack around a tunnel (ECT) in this study. Failure modes of the tunnels were analysed based on stress wave theory. The Riedel–Hiermaier–Thoma (RHT) material model was employed to perform the numerical simulations on ECT models. Stress distribution around the tunnels and final failure patterns of the tunnels were characterised. The results show that, under blasting loads, the pre-crack propagates and then new cracks initiates on the incident side of the tunnel. These cracks extend towards each other and eventually coalesce. Blasting load directions significantly influence the ultimate failure mode of the tunnel in the fractured rock masses. The new cracks on the shadow side of the tunnel appear at different positions when the blasting stress waves come from various directions. The results are meaningful to the analysis of tunnel stability and optimisation of the tunnel support scheme.

Numerical investigations on rock breaking mechanism and parameter influence of torsional percussive drilling with a single PDC cutter

Torsional percussive drilling tool was designed to reduce the risk of stick-slip and improve drilling efficiency, but there are few studies on the influence of torsional impact parameters, including amplitude, frequency, waveform, on the rate of penetration (ROP) while drilling the hard rock. The design of the torsional percussive drilling tool was proposed, and the mathematical model of torsion hammer movement was developed, the Riedel-Hiermaier-Thoma (RHT) rock dynamic material model was applied to analyze the rock-breaking process of the tool. A numerical model of hard rock cutting with a single polycrystalline diamond composite (PDC) bit cutter was established, the influences of amplitude, frequency, time parameters, and waveforms on the penetration depth of the PDC bit cutter were analyzed in the process of torsional percussive drilling. The results showed that the numerical simulation results were in good agreement with the indoor test results, which verified the correctness of the numerical simulation. Compared with conventional drilling, the penetration depth of torsional percussive drilling was increased by 20.0%, and the cutting debris particles were smaller, which was conducive to improving ROP and reducing stick-slip vibration of the bit. With the increase of the peak value of torsional percussive amplitude, the penetration depth of the cutter first increased and then decreased. When the ratio of torsional impact load to axial static load was 1.0, the penetration depth of the drilling cutter reached a maximum. When the torsional impact frequency was 40 Hz–100 Hz, the penetration depth decreased with the increase of the frequency, but the diameter of cuttings became smaller and smaller, which was conducive to cleaning the wellbore with drilling fluid. The latter has the highest rock-breaking efficiency compared with triangular, sine, and rectangular waves. Finally, suggestions are given on how to adjust these parameters by adjusting engineering parameters and tool structure parameters to optimize the efficiency of the torsional percussive drilling tool.

Experimental and numerical investigations on rock-breaking mechanism of rotary percussion drilling with a single PDC cutter

To achieve high-efficiency drilling in hard formations, the rotary percussive drilling tool was designed to improve rock-breaking efficiency. Currently, few studies are conducted to analyze the relationship between the percussion parameters and rock breaking efficiency, considering the dynamic characteristics of rock during rock breaking. According to this situation, to quantify the influence of different percussion parameters on the rock-breaking efficiency, a series of dynamic experiments on hard rock and numerical simulations were carried out. Orthogonal experiments of split Hopkinson pressure bar (SHPB) device were conducted to analyze 13 parameters of the Riedel Hiermaier Thoma (RHT) material model. A polycrystalline diamond compact (PDC) cutter was selected as the research object, and a corresponding numerical model was established, considering the actual size of the drilling teeth and the load transmitted to the formation. Subsequently, the numerical simulation results of the SHPB test and cutting experiment were verified using the physical model. A sensitivity analysis was carried out to analyze the effect of different factors, including dynamic amplitude, frequency, and waveform, on the penetration depth and eroded volume fraction of formation. The results proved that rotary percussion drilling increased the penetration depth and eroded volume fraction of hard rock. The rock-breaking efficiency of the square wave was more obvious than that of the triangular and sine waves. Increasing the dynamic to static load ratio was beneficial for increasing the penetration depth and eroded volume fraction of formation. When the frequency increased, the cutting section became smoother, and the cuttings were finer, which was beneficial in cleaning the borehole. • Orthogonal experiments were used to obtain RHT material model parameters. • The physical model verified the rock failure of numerical simulation. • The rock-breaking efficiency of the square wave was most apparent.

An RHT-Model-Based Equivalent Parameter Scheme for Blast Response Simulation of RC Frames

In this paper, a novel equivalent parameter scheme based on the Riedel–Hiermaier–Thoma (RHT) model is proposed for blast response simulations of reinforced concrete (RC) frames. Considering the strengthening effect of longitudinal and stirrup reinforcements on concretes, constitutive parameters in the RHT model are modified to homogenize RC components based on reasonable simplifications and numerical tests. Numerical results of RC beams illustrate that this scheme significantly improves the computational efficiency and effectively predicts real explosion response behaviors with high accuracy. The scheme is then employed for the blast simulation of an RC frame with multiple components with results compared with those of real frame experiments to further demonstrate its reliability. Owing to its efficiency and accuracy, the present RHT-model-based equivalent parameter scheme can serve as a feasible tool to conduct blast response analysis of the RC frame and guide the corresponding anti-explosion designs.

Fracture mechanism of rock around a tunnel-shaped cavity with interconnected cracks under blasting stress waves

The existence of cracks in the surrounding rock significantly affects tunnel stability under dynamic disturbances. To study the fracture mechanism of tunnels in fractured rock masses under blasting stress waves, a new specimen, i.e., the specimen with a tunnel-shaped cavity and interconnected cracks (TCIC), was proposed in this paper. Using these specimens, blasting tests were conducted. The crack propagation data were monitored by crack propagation gauges (CPGs) and strain gauges (SGs). The Riedel-Hiermaier-Thoma (RHT) model was used to perform equal-scale numerical simulations on TCIC specimens. The stress distribution and fracture modes around the tunnel in a fractured rock mass under blasting stress waves were characterised. The results show that the interconnected cracks have an important influence on the dynamic response of the tunnel under blasting stress waves. The stress distribution around the tunnel remarkably changes due to the existence of the interconnected cracks, resulting in the initiation and propagation of these cracks, but there is no fracture on the tunnel boundary. The dynamic crack propagation behaviours are influenced by the incident direction of the blasting stress wave. The crack propagation velocity in the front blasting side of the tunnel is higher than that in the back blasting side. The research results are significant to the analysis of tunnel stability and the support design.

Simulation of the Effects of Angle of Attack and Projectile Contour in Damage Development in Reinforced Concrete

The impact of projectiles in reinforced or unreinforced concrete is of prime importance in applied mechanics and engineering. Parameters such as penetration depth, velocity or energy of the projectile, and the geometry and the angle of attack of the projectile are the most critical factors, among several others, that determine whether the concrete body will tolerate damage due to the impact or not. For numerical simulations of damage, the Riedel-Hiermaier-Thoma (RHT) concrete failure is an established approach, which is also used in this research. In this work, numerical simulations have been performed on shooting a rigid large-scale projectile with different tip contours at a concrete target that is reinforced with steel. For each tip contour, the angle of attack varied. The penetration depth of the projectile tip and the damage of the target were reported for the different tip contours as a function of the angle of attack. The results show that the maximal damage occurred at ~45° of the angle of attack, while penetration of the projectile into the target increased with increasing the angle of attack.

Effect of confining pressure on damage accumulation of rock under repeated blast loading

• The hoop stress distribution under static loading was analyzed using elasticity solution. • The parameters of the RHT model were determined and validated against the results of repeated blast tests. • The tensile failure behavior and dynamic crack propagation of rock material under the coupling action of in-situ stress and repeated blast loading were studied. • The application of pre-split blasting technique to a rock slope was numerically explored and an optimized blasting design under in-situ stress conditions was proposed. In-situ stress has complex impacts on the blasting excavation of rock mass, but the effect of confining pressure on the crack propagation under repeated blast loading is still unclear. This study investigated the effect of confining pressure on blasting damage through theoretical, experimental and numerical analyses. First, the stress distribution around blasthole under static loading was theoretically analyzed. Then, the parameters of Riedel-Hiermaier-Thoma (RHT) model were determined and validated by repeated blast tests. The effect of confining pressure on the failure mode of granite sample was included. Finally, pre-split blasting of rock slope was numerically simulated to explore the failure behaviors of rock mass under in-situ stress conditions. The numerical results indicate that the RHT model can well reproduce the tensile failure behavior and dynamic crack propagation of granite sample. Confining pressure significantly changes the failure mode of granite sample and the blast-induced cracks mainly propagate along the direction of maximum principal stress. Repeated blast loading has little contribution to rock breakage in the direction of minimum principal stress. The pre-split blasting technology can considerably improve the stability of remaining rock mass in the blasting excavation of rock slope. A plum-blossom-shape arrangement of blastholes and delayed initiation of production holes can promote the quality of blasting operations under pre-stress conditions.