Static Pre-stress Research Articles

Dynamic fracture mechanism and fragment characteristics of sandstone specimens with asymmetrical conjugate fissures under static pre-compression

This paper systematically investigates the dynamic mechanical response and fragment characteristics of sandstone with asymmetrical conjugate fissures subjected to preexisting static stress based on the split Hopkinson pressure bar apparatus. The cross-fissured sandstone exhibits significant variations in mechanical behavior when exposed to higher dynamic strain rates under identical static pre-stress. The cross-fissured sandstone with a higher dynamic strain rate is characterized by a greater coupled strength under the same static pre-stress; for a given dynamic load, the highest coupled strength occurs under the static pre-stress of 60% UCS. The failure mode of the cross-fissured sandstone is predominantly governed by the dynamic strain rate, independent of static pre-stress variations considered in this investigation. At lower dynamic strain rates, the specimens typically exhibit a mixed tensile-shear failure mode, characterized by the dominance of larger fragments in the broken specimens. In contrast, under high dynamic impacts, the sandstone tends to fail in a shear-dominated manner, resulting in smaller fragments with a more uniform size distribution. Furthermore, the study explores how varying dynamic strain rates and static pre-stress influence the fragment characteristics of the cross-fissured sandstone. Higher dynamic strain rates and increased static pre-stress generally lead to smaller mean fragment sizes. This phenomenon is quantitatively described by fitting fragment size distributions using the Generalized Extreme Value (GEV) distribution, revealing a decrease in the location parameter (μ) and an increase in fractal dimension. These metrics indicate that higher dynamic strain rates and static pre-stress result in sandstone specimens breaking into smaller fragments with a more homogeneous size distribution. These findings contribute to a deeper understanding of rock dynamics, with potential implications for engineering applications involving similar geological configuration under dynamic loading conditions.

Experimental investigation on rockburst characteristics of highly stressed D-shape tunnel subjected to impact load

Rockburst has always been a challenge for the safe construction of deep underground engineering. This study investigated the rockburst characteristics in highly-stressed D-shape tunnels under impact loads from rock blasting and other mining-related dynamics disturbances. The biaxial Hopkinson pressure bar was utilized to apply varying biaxial prestress and the same impact loads to cube specimens with D-shape hole. High-speed camera and digital image correlation (DIC) were used to capture the failure process and strain field of specimen. The test results demonstrate that the D-shape hole specimen experience rockburst under coupled static stress and impact load. Under this circumstance, the rockburst mechanism of the D-shaped hole specimens involves spalling in sidewall induced by impact load, indicating dynamic tensile failure. The high static prestress provides the initial stress field, while the impact load disrupts the stress equilibrium, result in the stress or strain concentration in the sidewall of the D-shape hole, inducing rockburst. Moreover, the rockburst process can be divided into (1) calm stage, (2) crack initiation, propagation, and coalesce stage, (3) spalling stage and (4) rock fragments ejection stage. Impact load triggers rockburst occurrence, while vertical stress further determines the rockburst characteristics. The influence range and magnitude of strain concentration zone and displacement deformation of the tunnel surrounding rock increases with increasing vertical stress, thus inducing more severe rockburst.

Experimental and numerical studies on mechanical behavior of pre-stressed infilled rock joints subjected to horizontal vibration loading

Underground jointed rock masses are usually subjected to a coupled effect of static pre-stress and vibration disturbance from rock-cutting in Tunnel Boring Machines (TBMs) tunneling. To investigate the mechanical behavior of pre-stressed infilled rock joints disturbed by horizontal vibration loading, a series of laboratory and numerical experiments were conducted, based on the in-situ vibration characteristics during TBM rock-cutting. The P-wave velocity and direct shear test techniques are combined to quantitatively characterize the damage of infilled rock joints. The experimental results reveal that the damage degree of rock joints exhibits a nonlinear increase with the increase of vibration frequency and amplitude, and the decrease of static pre-stress. Low static pre-stress (below 0.5 MPa), high vibration frequency (above 70 Hz) and high vibration amplitude (above 0.3 mm/s) are adverse factors to the stability of rock joints. From the PFC2D simulation, the contact force chain and contact force field were analyzed to elucidate the failure mechanism of infilled rock joints. The failure mode of infilled rock joints is closely related to the level of parameters, consisting with the results in laboratory experiments. In addition, the comparison of vibration results for weakly and strongly filling material demonstrates that grouting reinforcement enhanced the vibration resistance of in-situ jointed rock masses.

Sidewall rockburst of highly stressed D-shape hole tunnel triggered by impact load: An experimental investigation

This study aims to clarity the failure mechanism of sidewall rockburst of highly stressed D-shape tunnel triggered by impact load. Using the biaxial Hopkinson pressure bar (BHPB) system, we have developed experimental capabilities to study the sidewall rockburst of D-shape tunnel by applying various prestresses, including horizontal and vertical static stresses, to sand prefabricated D-shape hole specimen, followed by impact loads. High-speed (HS) camera and digital image correlation (DIC) were used to tracked the process and strain field of the sidewall rockburst. The test results reveal that the process of sidewall rockburst can be summarized as: calm stage, crack initiation, propagation, and coalesce stage, spalling stage and rock fragments ejection stage. During the rockburst process, the surrounding rock experienced spalling and violent ejection, involving both tensile and tensile-shear failure. The mechanism of sidewall rockburst under the coupled of static stress and impact loads has been elucidated, i.e., the static prestress determines the initial stress and strain distribution, and the horizontal prestress influences the affected range and strain values of strain concentration zone; the impact load disrupts the original static stress equilibrium, inducing alterations in the stress and strain of the surrounding rock and triggering sidewall rockburst.

Influence of the static pre-stress on the thermal quality factor of a micro-resonator under the dual-phase-lag heat conduction model

Influence of the static pre-stress on the thermal quality factor of a micro-resonator under the dual-phase-lag heat conduction model

Dynamic Mechanical Characteristics of Horseshoe Tunnel Subjected to Blasting and Confining Pressure

The blast loading direction and in-situ stress field have an effect on the destruction process in the surrounding rock around the tunnel. Five blasting directions are considered in the experiment and simulation. The static stress distribution by confining pressure and the superposition stress waves process are discussed by simulation in LS-DYNA. Results indicated that the hoop stress accelerates the radial cracks growing, and the damage around the hole is not influenced by the blasting direction. The stress wave superposition and failure process along the tunnel are affected by the blasting direction. The distribution of static prestress is symmetrical under the uniform confining pressure (k = 1) and decelerates the crack extension by confining pressure. Under the non-uniform confining pressure loading (k ≠ 1), the tensile prestress is formed with a k increase and accelerates the horizontal crack propagation after blast loading. The concentrated stress is serious in the partial region along the tunnel, especially in the vault position under the static-dynamic coupling loading. Notably, the horizontal destruction area between the hole and the tunnel further expands when k increases.

Effect of the three-dimensional static pre-stress on the dynamic behaviours of conglomerate: True triaxial Hopkinson pressure bar tests

As the main component of gravel layer, the dynamic mechanical properties of conglomerate are closely related to the efficient rock-breaking methods while drilling in the formation rich in gravels. The characteristics of high strength and strong heterogeneity of conglomerate lead to severe vibration of drill string, causing the bottom hole rock of gravel layer is in a complex stress state of impact loads and three-dimensional confining pressure. Due to the lack of relevant study previously, this kind of dynamic mechanical behaviour is still unclear. Using the three-dimensional split Hopkinson pressure bar (3D SHPB) system, the dynamic mechanical behaviours of conglomerate under the condition of various impact loads and different levels of static pre-stress state were studied. The CT scanning results indicate that the conglomerate is characterized by strong randomness in gravel size, shape, content, and distribution, which plays an important role in the heterogeneity. The dynamic mechanical behaviours of conglomerate show a significant strain rate correlation, and that is influenced by the impact loads and static pre-stress state. There will be the highest dynamic strength and the lowest failure strain in the impact direction when the specimen is in a hydrostatic pre-stress state. With the increase of hydrostatic pre-stress, the dynamic strength of conglomerate increase linearly, while the failure strain changes the opposite. The research makes a beneficial exploration of the dynamic behaviors of conglomerate, which is expected to provide a reference for the design of high-efficiency rock-breaking methods while drilling in the stratum rich in gravels.

Experimental study of the dynamic mechanical responses and failure characteristics of coal under true triaxial confinements

Investigations on the dynamic mechanical properties and failure mechanisms of coal under in-situ stress is essential for the prevention of dynamic disasters in deep coal mines. Thus, a modified true triaxial Hopkinson bar was employed to explore the dynamic mechanical behaviors of coal at different confining pressures (0–20 MPa) and strain rates (40–220 s−1). The results show that the dynamic peak stress is positively correlated with lateral static pre-stress σy and σz, but negatively correlated with axial static pre-stress σx. At approximate strain rates, increasing the lateral static pre-stress facilitates increasing the dynamic peak stress, but the minimum lateral static pre-stress is the primary factor limiting a significant increase in dynamic peak stress of coal. Furthermore, the dynamic differential stress is linearly related to the logarithm of strain rate, and the peak strain varies linearly with strain rate. However, there is no significant correlation between confining pressure and peak strain. Moreover, X-ray CT images and photographic fracture observations of coal samples show the failure patterns under uniaxial and triaxial conditions are splitting failure and shear failure, respectively. The device provides a viable approach for fully comprehending the dynamic mechanical behaviors of rock-like material in complex stress conditions.

Numerical Investigation into the Mechanical Behaviours and Energy Characteristics of Hard Coal Subjected to Coupled Static-Dynamic Loads

In practical engineering, coal burst is usually caused by the combination of high geo-stress and dynamic loading. To study the dynamic response of coal in geo-stress conditions, numerical models of a coupled static–dynamic split Hopkinson pressure bar (SHPB) test system were established, based on which impact tests for coal specimens at different impact speeds and static pre-stress levels were conducted. The mechanical properties, energy characteristics and failure patterns of coal specimens under coupled static and dynamic loads were analyzed. The results show that when the pre-stress is constant, peak stress, the maximum strain energy and the maximum kinetic energy increase significantly with impact speed. Nevertheless, they are less affected by the static pre-stress, increasing linearly with a pre-stress level under lower impact speeds but becoming stable under higher impact speeds. In addition, weak dynamic loads may trigger the instability of the coal specimen in a high pre-stress condition. Overall, both the impact speed and static pre-stress have influence on the mechanical behavior and energy characteristics of coal specimens under coupled static and dynamic loads, but the influence of the impact speed outweighs that of the static pre-stress.

Frequency domain analysis of pre-stressed elastomeric vibration isolators

Two types of elastomeric vibration isolators used for equipment vibration isolation in aerospace vehicles are considered for the present study. These isolators are constructed using elastomers mounted in steel encasings. These isolators are initially deformed statically and dynamic loads are applied on the deformed configuration. To capture the static deformation, equivalent static load corresponding to its load rating and specified displacements are created. Static deformation is computed using Finite Element methods with four node axi-symmetric element which include the geometric non-linear effect for steel and with standard Yeoh hyper-elastic material model for elastomers (Muhammed and Zu, 2012) [1]. Yeoh material constants are derived from uni-axial tension test data of the elastomer specimen. These isolators are subjected to harmonic and random excitations in the pre-deformed state. For numerical analysis, elastomeric constants at dynamic conditions are obtained as complex function of frequency using Dynamic Mechanical Analyzer (DMA) for a range of frequencies. The standard material model of Yeoh is modified incorporating frequency dependant material characteristics and damping in the range of frequencies of interest. A multiplicative non-separable variables law is derived for Yeoh material model to include the effect of static pre-stress, based on the methodology given in literature (Nashif et al., 1985; Beda et al., 2014) [2,3]. The modifications of Yeoh model suitable for frequency domain analysis is the novelty in the present study. In the analysis, while dynamic loads are applied, the configuration is updated considering initial static loading. The frequency response of the isolators is computed using material properties evaluated at progressive dynamic strains until a match in natural frequency is observed. Appropriate damping corrections are then incorporated to match the test observed transmissibility. Then updated material properties are used to compute the random response which showed good agreement with results of experiments, validating the approach taken for the development of this model.

Mechanical Responses of Underground Unparallel-Fissured Rocks Subjected to Coupled Static-Dynamic Loading

Abstract Preexisting fissures within a natural rock mass significantly affect the mechanical responses of underground engineering rocks when subjected to coupled static-dynamic loads. Understanding the dynamic mechanical responses of prestressed fissured rocks is beneficial for optimizing the stability of rock engineering structures. Based on the split Hopkinson pressure bar (SHPB) device, a series of coupled static-dynamic compression tests were systematically performed to investigate the mechanical properties, the failure behaviors, the fragment characteristics, and the energy dissipation of unparallel-fissured rocks. Results show that the coupled dynamic strength increases with the applied strain rate for a given static prestress, while the elastic modulus does not exhibit any clear loading rate dependence. Under the given strain rate, the fissured sandstone has the highest strength under the static prestress of 0.6 uniaxial compressive strength (σs), followed by the static prestress of 0.4 σs, 0.2 σs, and 0.8 σs. The failure modes of fissured sandstone highly depend on the dynamic strain rate, and the ultimate failure pattern gradually changes from the mixed tensile-shear failure mode to the shear failure dominant mode with increasing strain rate. With an increasing dynamic strain rate, fissured rocks should absorb more energy in a short time, which results in more crack formation in the failure process. A higher static prestress can induce greater energy dissipation density and energy utilization efficiency when the static prestress is less than 0.8 σs. In addition, the relationships between energy dissipation and mechanical response of fissured sandstones under coupled static-dynamic loads are established and discussed.

The vibration of viscothermoelastic static pre-stress nanobeam based on two-temperature dual-phase-lag heat conduction and subjected to ramp-type heat

In this work, the two-temperature dual-phase-lag theorem has been used to present an analytical mathematical model for calculating the vibration in a viscothermoelastic nano-resonator. The governing equations have been derived when a simply supported nano-resonator is exposed to a ramp-type thermal load and static pre-stress. The governing equations have been solved by using a direct method and obtained the solution in the Laplace transform domain where the inversions of the Laplace transform have been calculated by using the Tzou approximation method. The increments of the dynamic and conductive temperatures, volumetric deformation, and stress regarding the resonator length for various cases of temperature type, static-pre-stress, and viscothermoelastic properties with different values of ramping heat parameter have been presented in figures and studied. The parameter of the two-temperature model, static pre-stress, ramp-type heat parameter, and viscothermoelastic parameter has a significant impact on all functions studied. The ramping time parameter may be utilized to change the thermal and mechanical properties of the nano-resonator.

Strength weakening effect of high static pre-stressed granite subjected to low-frequency dynamic disturbance under uniaxial compression

This study aimed to elucidate the strength weakening effect of high static pre-stressed rocks subjected to low-frequency disturbances under uniaxial compression. Based on the uniaxial compressive strength (UCS) of granite under static loading, 70%, 80%, and 90% of UCS were selected as the initial high static pre-stress (σp), and then the pre-stressed rock specimens were disturbed by sinusoidal stress with amplitudes of 30%, 20%, and 10% of UCS under low-frequency frequencies (f) of 1, 2, 5, and 10 Hz, respectively. The results show that the rockburst failure of pre-stressed granite is caused by low-frequency disturbance, and the failure strength is much lower than UCS. When the σp or f is constant, the specimen strength gradually decreases as the f or σp increases. The experimental study illustrates the influence mechanism of the strength weakening effect of high static pre-stress rocks under low-frequency dynamic disturbance, that is, high static pre-stress is the premise and leading factor of rock strength weakening, while low-frequency dynamic disturbance induces rock failure and affects the strength weakening degree.

Dynamic fracture behaviors and fragment characteristics of pre-compressed flawed sandstones

Because of tectonic stress and dynamic disturbance, underground rock masses containing pre-existing flaws usually undergo complex loading conditions combining static pre-stress (SPS) and external dynamic loads. Comprehending the mechanical behaviors of flawed rocks under coupled static-dynamic loads is helpful to assess the stability of underground engineering. This study presented a series of coupled static-dynamic compression experiments on sandstone containing two non-coplanar flaws. The results indicated that the dynamic strength of the flawed sandstone increased first and then decreased with the increase in the SPS for a given dynamic strain rate (DSR), and the coupled strength of the flawed sandstone was less dependent on the DSR under the SPS of 60% of the uniaxial compressive strength than the other SPS values. Low SPS and DSR generally induced an asymmetrically X-shaped shear failure mode of the specimen, while this failure pattern could be observed in the tests with high SPS and DSR. Moreover, both a greater SPS and a higher DSR could lead to smaller location parameter values in the generalized extreme value fitting and a higher fractal dimension of the rock fragments, resulting in a more severe crushing destruction of the flawed sandstone. In addition, this study demonstrates that both the fracture process zones and the higher-order stress terms in the Williams series expansion, which are often neglected in traditional related studies, cannot be thoughtlessly ignored when analyzing the crack initiation, propagation, and coalescence of flawed rocks.

Acoustoelastic analysis of soft viscoelastic solids with application to pre-stressed phononic crystals

The effective dynamic properties of specific periodic structures involving rubber-like materials can be adjusted by pre-strain, thus facilitating the design of custom acoustic filters. While nonlinear viscoelastic behaviour is one of the main features of soft solids, it has been rarely incorporated in the study of such phononic media. Here, we study the dynamic response of nonlinear viscoelastic solids within a ‘small-on-large’ acoustoelasticity framework, that is we consider the propagation of small amplitude waves superimposed on a large static deformation. Incompressible soft solids whose behaviour is described by the Fung–Simo quasi-linear viscoelasticity theory (QLV) are considered. We derive the incremental equations using stress-like memory variables governed by linear evolution equations. Thus, we show that wave dispersion follows a strain-dependent generalised Maxwell rheology. Illustrations cover the propagation of plane waves under homogeneous tensile strain in a QLV Mooney–Rivlin solid. The acoustoelasticity theory is then applied to phononic crystals involving a lattice of hollow cylinders, by making use of a dedicated perturbation approach. In particular, results highlight the influence of viscoelastic dissipation on the location of the first band gap. We show that dissipation shifts the band gap frequencies, simultaneously increasing the band gap width. These results are relevant to practical applications of soft viscoelastic solids subject to static pre-stress.

Characterization of the Thermal Quality Factor Due to the Static Pre-Stress in Thermoelastic Nano Resonator of Silicon Under Time-Fractional Dual-Phase-Lag Heat Conduction

Characterization of the Thermal Quality Factor Due to the Static Pre-Stress in Thermoelastic Nano Resonator of Silicon Under Time-Fractional Dual-Phase-Lag Heat Conduction

Mechanical Properties of Roof Rocks under Superimposed Static and Dynamic Loads with Medium Strain Rates in Coal Mines

Roof rocks in coal mines are subjected to the combination of in situ stresses and dynamic stresses induced by mining activities. Understanding the mechanical properties of roof rocks under static and dynamic loads at medium strain rates is of great significance to revealing the mechanism of rock bursts. In this study, we employ the digital image correlation (DIC) technique to investigate the energy concentration and dissipation behaviors, failure mode, and deformation characteristics of roof rocks under combined static and dynamic loads. Our results show that both the static pre-stress and dynamic loading rate have significant effects on the uniaxial compressive strength of rock specimens. From the energy principle, when the static pre-stress is the same, both elastic strain energy density and dissipated energy density increase with increasing dynamic loading rate. The hazard of rock bursts increases with decreasing static pre-stress and increasing dynamic loading rate. At higher dynamic loading rates, more cracks are generated, and the failure becomes more violent. The crack initiation, propagation and coalescence processes are identified, and the failure mode is closely related to the evolution of the global principal strain field of the rock specimens.

Low amplitude fatigue performance of sandstone, marble, and granite under high static stress

Fatigue tests under high static pre-stress loads can provide meaningful results to better understand the time-dependent failure characteristics of rock and rock-like materials. However, fatigue tests under high static pre-stress loads are rarely reported in previous literature. In this study, the rock specimens were loaded with a high static pre-stress representing 70% and 80% of the uniaxial compressive strength (UCS), and cyclic fatigue loads with a low amplitude (i.e., 5%, 7.5% and 10% of the UCS) were applied. The results demonstrate that the fatigue life decreased as the static pre-stress level or amplitude of fatigue loads increased for different rock types. The high static pre-stress affected the fatigue life greatly when the static pre-stress was larger than the damage stress of rocks in uniaxial compression tests. The accumulative fatigue damage exhibited three stages during the fatigue failure process, i.e., crack initiation, uniform velocity, and acceleration, and the fatigue modulus showed an “S-type” change trend. The lateral and volumetric strains had a much higher sensitivity to the cyclic loading and could be used to predict fatigue failure characteristics. It was observed that volumetric strain $$\varepsilon _{{\text{v}}}$$ = 0 is a threshold for microcracks coalescence and is an important value for estimating the fatigue life.

Failure characteristics of brittle rock containing two rectangular holes under uniaxial compression and coupled static-dynamic loads

To deeply understand the failure characteristics of defective rock under actual stress condition, impact tests were conducted on prismatic granite containing two rectangular holes with different axial static pre-stresses by a modified split Hopkinson pressure bar (SHPB), and uniaxial compression tests were also carried out for comparison. Combined with digital image correlation (DIC), the dynamic damage and fracture process of specimens were observed by low-speed and high-speed cameras. Moreover, the energy evolution characteristics of specimens were analyzed to further understand the failure mechanism. The results indicate that the pre-stress has dual effects on the dynamic mechanical behavior of rock specimens, and the transition mechanism of the effect of pre-stress can be revealed by the elastic deformation limit. Observations show that the failure of specimens under different loads is caused by the growth of secondary cracks at hole corners. However, with the increase in pre-stress, the crack mode tends to shear and the strain localization tends to concentrate on sidewalls, resulting in severe rock bursting and extensive fracturing. Four coalescence modes around two rectangular holes were summarized: diagonal shear coalescence under static load, no coalescence under dynamic load, shear coalescence inside the middle rock bridge area under the pre-stress of 25–55% UCS, and indirect coalescence outside the rock bridge area under the pre-stress of 75% UCS. The specimen with the pre-stress of 75% UCS releases the internal strain energy during dynamic failure process, while the specimen with lower pre-stress absorbs the external impact energy. Finally, some insights are provided for deep rock engineering based on the test results.

Effect of Filling on Failure Characteristics of Diorite with Double Rectangular Holes Under Coupled Static–Dynamic Loads

The effect of infilling on mechanical response and crack behavior of pre-stressed rock with double rectangular holes under dynamic load was investigated through a series of coupled static–dynamic loading tests on diorite specimens in three different filling states, i.e., no infilling, single infilling and double infilling, using a modified split Hopkinson pressure bar. The deformation, damage and fracture process of specimens were recorded and analyzed by low-speed and high-speed cameras with digital image correlation method. Test results reveal that under the same dynamic load, the strength of specimens increases first and then decreases with the increase of axial static pre-stress, and reaches the maximum under 25% UCS due to crack closure. The strengthening effect of double infilling on strength is much more significant than that of single infilling and increases with the pre-stress. Observations show that with the increase of pre-stress, the degrees of damage and strain localization of specimens increase, and the superficial damage on the free surface of sidewalls are more severe. The effect of infilling is significant on the crack initiation and propagation, especially on the inhibition of sidewall spalling, rock ejection and the axial displacement failure of rock septum between holes. With the increase of pre-stress, the failure pattern and the crack coalescence mode change from obvious tensile to shear, and the coalescence position changes from the inside to outside of the septum area. However, the change of filling state has little effect on the coalescence mode, only on the coalescence position.