Triaxial Loading Research Articles

Experimental investigation on mechanical behavior, energy evolution and gas permeability of anisotropic phyllite subjected to triaxial compression and cyclic loading

The bedding plane direction significantly affects the mechanical properties, deformation and gas permeability evolution of rock mass in gas storage engineering. In this paper, for phyllite, a series of triaxial compression with cyclic loading and gas permeability apparatus are conducted to investigate such directional effect. The peak stress, Young’s modulus, energy evolution, failure mode and gas permeability coefficient are analyzed. For triaxial compression test, with increasing inclination angles, the deformation parameters (E, E50, μ) and characteristic stress parameters (σcc, σci, σcd) both show a U-shape pattern. For triaxial cyclic loading test, the peak stress of specimen first decreases and then increases, i.e., the peak stresses at the inclination angles of 0°, 30°, 45°, 60° and 90° are 118.18, 84.35, 64.18, 42.54 and 84.57 MPa, respectively. The energy evolutions of specimens at different inclination angles are similar, but increase with increasing cyclic number. i.e., when β=60°, with the cycle number increasing from 1 to 3, the elastic strain energy, the dissipated strain energy and the total strain energy increase by 343.55%, 175.08%, and 259.87%, respectively. In addition, the failure mode of phyllite specimens is analyzed and summarized as three distinct types, i.e., tensile-shear failure, shear-sliding failure and split-shear failure. The relationships between the initial gas permeability and confining pressure, deviatoric stress show positive correlations. The failure of layered phyllite is most likely to occur at a bedding plane inclination angle of 45° to 60°.

Mechanical and Energy Evolution Characteristics of Sandstone under True Triaxial Cyclic Loading

To study the mechanical and energy evolution characteristics of sandstone under true triaxial cyclic loading, a sandstone mechanical test with different intermediate principal stress under true triaxial loading was conducted using the rock true triaxial disturbance unloading test system. The influence of axial load on the deformation, energy evolution, and macroscopic failure characteristics of sandstone under different intermediate principal stress in a true triaxial test was systematically analyzed, and the damage evolution law of sandstone under true triaxial cyclic load was revealed. Results showed that the failure mode of sandstone under true triaxial compression changed from tension–shear composite failure to tension failure. Grading cyclic load σ1 greatly influenced maximum principal strain ε1 and minimum principal strain ε3 but had little influence on intermediate principal strain ε2. Under the same σ2 condition, the input energy and elastic energy in σ1, σ2, and σ3 directions increased nonlinearly. Under different σ2 conditions, the dissipated energy in σ1, σ2, and σ3 directions decreased with the increase in σ2. With the increase in σ2, graded cycles σ1, ε2, and ε3 decreased considerably, and the failure mode changed from tensile failure to shear failure. When the cyclic loading rate increased, the σ1, ε1, ε2, ε3, and volume strain εv of sandstone failure decreased, but the expansion point increased. Under true triaxial grading cyclic loading and unloading, the total dissipated energy of sandstone increased exponentially. The larger σ2 was, the smaller the damage variable was.

A Study of the Effect of Freeze–Thawing by Liquid Nitrogen on the Mechanical and Seepage Characteristics of Coal with Different Moisture Content Values

In order to study the effect of freezing and thawing of liquid nitrogen on the mechanical and seepage characteristics of coal rock with different water content values, conventional triaxial loading tests on freeze–thawed coal samples with different water content values were carried out using non-contact digital image processing technology. The research results showed that with the same water content, the peak strength of a liquid nitrogen freeze–thawed coal sample was smaller than that of a non-freeze–thawed coal sample, and the Poisson’s ratio was larger than that of the non-freeze–thawed coal sample; compared with the non-freeze–thawed coal sample, the strain fluctuation and concentration in the stages of compression density, elasticity, yield, and damage were weakened after freeze–thawing by liquid nitrogen, but the local stress concentration was more obvious; the non-freeze–thawed coal sample mainly showed single shear damage, and the damage fissures were inclined fissures with small openings. The higher the water content, the more obvious the tensile damage; with the increase in water content, the permeability of non-freeze–thawed coal samples showed a linear decreasing trend, and the permeability of coal samples was 0.03 × 10–3 μm2 when the water content reached 9%. The permeability of freeze–thawed coal samples showed a non-linear increasing trend, and the higher the water content under the effect of expansion, the faster the permeability growth rate; the permeability of coal samples could reach 6.30 × 10–3 μm2 when the water content was 9%. The results of the study can provide a theoretical guidance for gas permeation enhancement in deep low-permeability coal seams.

Mechanical characteristics of failure and rockburst proneness of fractured granite from Shuangjiangkou hydropower station under triaxial loading and unloading

Mechanical characteristics of failure and rockburst proneness of fractured granite from Shuangjiangkou hydropower station under triaxial loading and unloading

Tri-axial loading response to anti-gravity running highlights movement strategy compensations during knee injury rehabilitation of a professional soccer player

ABSTRACT Anti-gravity treadmills have been used in rehabilitation to manipulate exposure to loading and to prescribe return to outside running. Analysis is typically restricted to the vertical plane, but tri-axial accelerometry facilitates multi-planar analysis with relevance to injury mechanism. In this case a professional male soccer player, 4 weeks post-operative surgery to repair a medial meniscectomy, 8 months after Anterior Cruciate Ligament reconstruction to the same knee, completed anti-gravity treadmill running at 70–95% bodyweight (BW) at 5% increments. Tri-axial accelerometers were placed proximal to the Achilles tendon of the injured and healthy leg, and at C7. The planar acceleration at touchdown highlighted an increase at 85% BW, identifying 70% and 85% BW as discrete loading progressions. C7 (3.21 ± 0.68 m·s−2) elicited lower (P < 0.001) vertical acceleration than the lower limb (9.31 ± 1.82 m·s−2), with no difference between limbs suggesting bilateral symmetry. However, in the medio-lateral plane the affected limb (−0.15 ± 1.82 m·s−2) was exposed to lower (P = 0.001) medio-lateral acceleration than the non-affected limb (2.92 ± 1.35 m·s−2) at touchdown, indicative of bilateral asymmetry. PlayerLoad during foot contact was sensitive to accelerometer location, with the affected limb exposed to greater loading in all planes (P ≤ 0.082), exacerbated at 90–95% BW. Tri-axial accelerometry provides a means of assessing multi-planar loading during rehabilitation, enhancing objective progression.

Binary-medium constitutive model for freeze-thaw tailings subjected to cyclic triaxial loading

The dynamic response of freeze-thaw tailings dam has attracted worldwide attention because of the increasing mining scale and frequent earthquake activity in cold regions. According to the experimental observations, the dynamic mechanical behaviors and failure mechanisms of the freeze-thaw tailings are reinterpreted, and a dynamic constitutive model for the material is established by utilizing homogenization theory. In this model's framework, tailings are regarded as quasi-continuous materials. Their representative volume element is conceptualized as a binary-medium structure composed of bonded elements with elastic-brittle properties and frictional elements with elastoplastic features. The former can gradually break into the latter upon cyclic loading, and both of the two components contribute to the overall capacity. Subsequently, a strain concentration tensor is adopted to describe the relationship between the local mechanical behaviors and average macro features. The model parameters are determined based on the experimental results. Comparisons between the computed and tested results are discussed specifically in aspects of the evolution of stress, strain and pore pressure. The results show that the model can capture the main features on predicting the dynamic response of tailings. In addition, it reflects the effects of freeze-thaw cycles, confining pressures and cyclical shear stress ratios on the dynamic features.

Investigation on permanent deformation of unbound granular material base for permeable pavement: Laboratory and field study

• Deformation of Unbound Granular Materials was investigated in laboratory and field synchronously. • The confining pressures and Shear Stress-strength Ratios affect the deformation greatly. • The deformation prediction model was consistent with the trends of laboratory test results. • A deformation model based on laboratory triaxial load tests, dynamic triaxial repeated load tests and filed LWD tests was developed. Unbound Granular Materials (UGM) base is widely used in permeable pavement structure for infiltration, water storage, and load bearing. However, because of large void content, UGM base easily deforms under repeated loads, resulting in surface rutting and even reducing durability of permeable pavement. Thus, research on practical deformation prediction model of UGM base is necessary to improve the pavement structure design and evaluate the base layer construction quality. This study conducted laboratory and field tests to develop a deformation prediction model of UGM base under varied stress states. The deformation of UGM specimen was tested and analyzed through triaxial shear test and dynamic triaxial repeated load test, with varied confining pressures and Shear Stress-strength Ratios (SSR). A laboratory deformation model based on SSR was developed, and the linear relationship between total deformation and permanent deformation was obtained. The deformation of UGM base in situ was tested with Light Weight Deflectometer (LWD). The trends of laboratory deformation model and field test results were similar, and deformation prediction model for field was fitted. The values of parameters in permanent deformation model were recommended in varied stress ranges, based on mathematical analysis. Accordingly, the deformation of UGM base can be estimated. This study developed a model to estimate the permanent deformation of UGM based on deformation data from field and laboratory tests.

Temporal and spatial distribution characteristics of hydraulic crack propagation under true triaxial loading using the direct current method

Hydraulic fracturing (HF) has been widely used in coal and rock dynamic disasters prevention and control and coalbed methane production in underground coal mines. However, how to effectively and accurately monitor and evaluate the hydraulic crack propagation process and impact range has not been resolved. We developed a novel experimental system for HF-direct current (DC) monitoring under true triaxial loading conditions. With the use of this system, we conducted HF-DC monitoring experiments under true triaxial loading conditions. The response characteristics of the emission current, apparent resistivity, and apparent resistivity difference contour map throughout the entire experimental process were studied. The results showed that the DC monitoring data contain a wealth of effective information on hydraulic cracks propagation. The emission current and apparent resistivity reflected the overall electrical conductivity of the rock. The contour map of the apparent resistivity difference between two measuring lines could accurately characterize the propagation process and spatial distribution of hydraulic cracks. The evolution process of the difference contour map showed that hydraulic cracks were more likely to spread into areas with low homogeneity. The change range and degree of the apparent resistivity were mainly affected by the spatial distribution, water-bearing state of the hydraulic cracks and wet area surrounding the hydraulic cracks. As the hydraulic crack network expanded, a highly conductive channels were formed inside the rock, which could affect the rock conductive properties and patterns. By comprehensively considering the temporal and spatial evolution characteristics of the apparent resistivity difference contour map and the regional apparent resistivity change curve, the dynamic expansion and spatial shape of hydraulic cracks in the rock could be accurately characterized via the DC monitoring method.

Size-Dependent Behaviour of Hard Rock Under Triaxial Loading

Understanding size effects is important to rigorously analyse the behaviour of rocks and rock masses at different scales and for different applications. A number of empirical and numerical studies have included size effects on the uniaxial compressive strength of different rocks, but only few have focussed on the triaxial compressive strength. In this study, several triaxial tests were conducted on granite samples at different confinements (from 0.2 to 15 MPa) and sizes (from 30 to 84 mm in diameter). The most relevant strength parameters were recovered including peak and residual strengths, orientation and frictional response of shear bands. Size effects were observed to be less dominant at high confining pressures for both peak and residual strengths. The resulting data were analysed in the context of size-dependent rock strength theories. For peak strength analyses, the unified size effect law (USEL) and the improved unified size law (IUSEL) were used, in which the double trends, ascending descending behaviours were observed. Size-dependent Hoek–Brown modified failure criteria based on USEL and IUSEL were fit to peak strengths exhibiting a good agreement between the models and the laboratory data. The brittle-ductile transition and the frictional behaviour of shear band under triaxial loading were also analysed. A clear brittle behaviour was particularly observed in samples with large-diameters tested at low confinements. Finally, in regards to frictional behaviour, the shear band angle found to be affected by both confinement and sample size.

3D characterization of localized shear failure in loess subject to triaxial loading

The reduction of shear strength of loess slopes is generally driven by localized failure in loess that lowers the trigger thresholds of major landslide geohazards in these materials. Shear failure is initially manifested as discontinuous microscale fractures that progressively develop into macroscale rupture surfaces. In this study, the development of localized shear failure in Malan loess is investigated through an approach combining laboratory triaxial shear test and X-ray micro-computed tomography (μ-CT). The spatial distribution and morphological evolution of fractures associated with the shear failure plane are observed at different loading stages in a non-destructive manner. It is found that, with ongoing strain, the number and persistence of multiple undulating fracture surfaces gradually increase after peak strength condition are reached until a single, dominant shear failure plane is formed. Most fracture surfaces are oblique to the major principal stress direction forming a shear band of finite thickness. Within this band it is possible to observe zones where varying strain magnitude is accommodated by a network of fracture surfaces. The effect of strain accumulation and local shear failure on the sample's macroporosity was determined by performing calculations on the CT images of each loading stage. Whereas the bulk sample underwent a reduction in macroporosity as a result of the triaxial compression, movement along undulating fracture surfaces results in the opening (and closing) of apertures with ongoing shear strain within a shear band of finite thickness. The overall result is an increase in macroporosity in this shear band with an estimated thickness of approximately 5 mm. Image analysis also allows characterization of changes in the 3D macropore network of the original loess fabric. Macropore network can be disconnected, dislocated and even destroyed when affected by shear failure development. These morphological variations of macropores serve as benchmarks that indicate the early initiation and expanding range of local shear failure and also allow the evaluation of the effect of local shear failure on seepage characteristics. The results of this study could provide important insights into multi-scale modelling of mechanical behaviour of loess.

Mechanical behavior of steel fiber reinforced recycled aggregate concrete under dynamic triaxial compression

An experimental study of cylindrical steel fiber reinforced recycled aggregate concrete (SFRAC) specimens subjected to hydrostatic pressure and dynamic axial loading in a triaxial cell was performed. A confining stress range of 0–40 MPa and strain rate from 10−5 s−1 to 10−2 s−1 were employed using a servo-hydraulic testing system. In addition, two other control variables – volume fraction of steel fiber and replacement ratio of recycled coarse aggregate were also considered. A series of complete stress-strain curves were obtained, and the results were discussed in the aspects of the failure modes, peak triaxial strength, toughness, octahedral stress and failure criterion. The results indicated that an increase in the confining pressure resulted in a change in the failure modes, a significant increase in the peak strength and ductility. In particular, with an increase in confining pressure, the enhancement of strain rate on the peak strength decreased, indicating that there was a coupling effect between these two. The steel fibers had little influence on the failure modes of SFRAC, but significantly improved its ductility and toughness. The addition of recycled coarse aggregates markedly reduced the peak strength and the reduction reached nearly 20%, which was larger than other reports in uniaxial and true triaxial loading. Finally, a failure criterion for SFRAC specimens subjected to dynamic loading was used for validating the experimental results.

Creep–fatigue mechanical characteristics of salt rocks under triaxial loading: An experimental study

Salt rock is a sedimentary rock that is widely distributed in the crust. Since salt rock has a low permeability, rheological behavior, and self-healing characteristics, it has been extensively exploited for subsurface energy storage and waste disposal. The construction of compressed air energy storage (CAES) facilities using salt caverns for solution mining is a practical solution to achieve carbon peaking and carbon neutrality goals worldwide. The stability of the salt cavern surrounding rock is critical to the function of a CAES plant. Considering the triaxial stress condition of the rock surrounding such underground salt caverns, a number of triaxial creep–fatigue mechanics tests were performed on salt rock using an MTS815 mechanical testing device. The creep–fatigue damage to the salt rock was examined under various confining pressures and stress levels. The main research results and conclusions are as follows. First, the triaxial creep–fatigue stress–strain curves show a similar tendency to classical triaxial fatigue results: the strength and ultimate deformation of salt rocks increase as the confining pressure increases. Second, in contrast to typical fatigue test results, the residual strain before the high-stress plateaus is larger than that after the plateaus during a creep–fatigue test. However, as the confining pressure increases, this disparity decreases. Third, fatigue loading increases creep deformation, and this effect weakens when the confining pressure increases. Fourth, the residual strain differential before and after the high-stress plateau increases together with the stress level, and the contribution of creep strain increases correspondingly. Last, as the confining pressure increases, the salt rock behavior transitions from a brittle response to a fully ductile response. A high confining pressure prevents relative sliding between the salt rock particles. Thus, the effect of confining pressure on the creep–fatigue mechanical behavior of the salt rock reaches a threshold.

On the influence of tool contact stress on tensile instabilities in plane strain stretching and bending of sheet metals

It is well known that the widely used forming limit curve (FLC) based upon in-plane stretching fails to account for the delay in plastic instability in the presence of appreciable bending and tool contact pressure. The recently proposed General Incremental Stability Criterion (GISC) – a generalization of the Modified Maximum Force Criterion (MMFC) to triaxial loading – revealed the dependence of the boundary conditions on the formation of tensile instabilities. Nevertheless, it remains unclear how the combined effect of radial bending stresses and tool contact pressure affects the formation of an acute neck. It is shown in this study that a compressive normal stress causes a shift of the strain state from initial plane strain tension to positive minor strains for material layers within the cross-section. The convex (outer) layer remains in a state of plane strain-plane stress. Accounting for the shift in the strain state is key to capture the dependence of the contact pressure on necking. A simplified modelling approach, which enforces plane strain tension of the cross-section, was able to capture the formability gain due to bending but failed to account for the delay in plastic instability due to the contact pressure. An incremental multi-layer model was required to account for non-monotonic loading due to bending over the punch and the biaxial shift in the strain path caused by the contact pressure. The models were then applied to the experimental forming limits of a 3rd Gen 1180 advanced high strength steel to demonstrate the formability gains under triaxial loading due to the contact pressure.

Analysis of Electrical Resistivity Characteristics and Damage Evolution of Soil-Rock Mixture under Triaxial Shear.

Construction of engineering structures in geomaterials with soil-rock mixture (S-RM) is often a challenging task for engineers. When analyzing the stability of the engineering structures, the mechanical properties of S-RM often receive the most attention. To study the mechanical damage evolution characteristics of S-RM under triaxial loading conditions, a modified triaxial apparatus was used to conduct shear test on S-RM, and the change of electrical resistivity was measured simultaneously. The stress-strain-electrical resistivity curve and stress-strain characteristics under different confining pressures were obtained and analyzed. Based on the electrical resistivity, a mechanical damage model was established and verified to analyze the damage evolution regularities of S-RM during shearing. The results show that the electrical resistivity of S-RM decreases with increasing axial strain and that the differences in decrease rates correspond to the different deformation stages of the samples. With the increase in loading confining pressure, the stress-strain curve characteristics change from a slight strain softening to a strong strain hardening. Additionally, an increase in rock content and confining pressure can enhance the bearing capacity of S-RM. Moreover, the derived damage evolution model based on electrical resistivity can accurately characterize the mechanical behavior of S-RM under triaxial shear. Based on the damage variable D, it is found that the damage evolution process of S-RM can be divided into a non-damage stage, a rapid damage stage and a stable damage stage. Furthermore, the structure enhancement factor, which is a model modification parameter for the effect of rock content difference, can accurately predict the stress-strain curves of S-RMs with different rock contents. This study sets the stage for an electrical-resistivity-based monitoring method for studying the evolution of internal damage in S-RM.

Integrating laboratory acoustic measurements, deep neural networks, and micro-CT imaging for characterizing rock brittle deformation

Brittle deformation is prevalent in both geological processes and engineered structures, so probing its actions is an important task as much for Earth materials and engineered ones. To characterize brittle deformation, acoustic waves are especially useful in revealing deformation processes. To promote the use of acoustic techniques, we present an integrated characterization approach that includes both acoustic data collection and analysis. By customizing a rock sample and acoustic sensor assembly, we incorporate acoustic data acquisition into a core holder system that accommodates relatively small samples (2.54 cm diameter) under triaxial loading. Along with fast and high-resolution acoustic waveform recording, the compact design facilitates convenient collection of high-quality acoustic data. To meet the challenge of efficiently and accurately picking P-wave arrivals for hundreds of thousands of acoustic waveforms, we modified and implemented a deep neural network model from the seismology literature called PhaseNet. After training with an augmented dataset of manually-picked arrivals (a total of around 50,000 waveforms), the modified PhaseNet model achieved more than 88% (96%) picking accuracy within ±1 μs (±2 μs) time residual relative to manual picks. This demonstrates the potential of integrating deep learning techniques into the workflow of acoustic data analysis for rapid and accurate extraction of valuable information from a large acoustic dataset. Finally, we conducted high-resolution micro-computed tomography (micro-CT) to inform and complement acoustic characterization at micron- and centimeter-scales. Microscopic observations validate the spatial development of two macroscopic fractures, and suggest that deformation-induced changes in velocity need to be incorporated for accurately locating microcracking events. Thus, integrating acoustic monitoring, a deep neural network, and micro-CT imaging offers an effective means to understand brittle deformation from micro to centimeter scales.

Determination method of rock characteristic stresses based on the energy growth rate

Introduction: Precisely determining the characteristic stress value of a rock progressive failure process has important theoretical and practical significance for reasonably defining the rock deformation and failure stage, mechanical mechanism, and design parameters.Methods: Based on the energy characteristics in the process of rock deformation and failure, this paper proposes a new method of rock characteristic stress (EGR) around the index of elastic energy storage capacity, elastic energy growth rate, and dissipative energy growth rate. First, the rationality of the new method is verified by the indoor uniaxial and triaxial loading test data of coal and marble. Second, five different determination methods, namely, lateral strain method, lateral strain difference method, crack strain method, energy dissipation rate method, and volumetric strain method, are compared to further verify the scientific nature of the new method. Finally, the method is applied to the conventional triaxial unloading confining pressure test and true triaxial loading and unloading test of marble, and the new method is fully extended to verify its universality.Results: The results show that the theoretical basis of the EGR characteristic stress determination method is rigorous and sufficient, and the value process is objective and reasonable. Compared with different methods, the EGR method can accurately define the process of rock asymptotic failure, and its corresponding characteristic stress level is well-consistent and in a reasonable range.Discussion: The EGR method is applicable to the conventional triaxial unloading confining pressure test and true triaxial loading and unloading test and has good universality.

The effects of changing the deviatoric and spherical stresses during cyclic loading on the drained response of a sand

Changing the deviatoric and spherical stresses could affect the accumulative deformation behaviour of soils under cyclic loading. Drained cyclic triaxial loading tests were performed on saturated sand to study the dependence of cyclic loading-induced axial and volumetric strain accumulations on changing the deviatoric and spherical stresses in between loading cycles. The change in the stresses was simulated by changing cell pressure and axial load along different stress paths. The variation of axial and volumetric strain accumulations before and after changing the stresses is compared and discussed. It is found that changing the stresses could have different impacts on the axial and volumetric strain accumulations, as the accumulations are affected by different mechanisms. The axial strain accumulation after changing the stresses is affected by the average stress ratio and precedent stress history. The volumetric strain accumulation is hardly affected by changing the stresses unless an increase in the average stress ratio is caused. Both axial and volumetric strain accumulations show independence on the stress path of the disturbance. For the samples with decreasing average stress ratio, the strain accumulation direction after changing the stresses cannot be fully described using Modified Cam Clay flow rule.

The Toughness of Polypropylene Fiber-Reinforced Foam Concrete under Various Uni- and Tri-Axial Compression Loads

Foam concrete has recently become a key construction material in terms of meeting the special needs of modern engineering applications such as thermal insulation, absorption of static and dynamic loads. In this study, the effect of polypropylene fiber content and various uni- and tri-axial compression loads on the toughness response of polypropylene fiber-reinforced foam concrete was investigated. Up to a certain strain level (0.1 mm/mm), the ultimate compression stress of specimens under uni- and tri-axial loading increased from about 1 MPa to 16 MPa with the increased target densities of foam concrete. There was a strain-hardening capability of low-density foam concrete while the specimens failed by strain-softening in the high-density series. The optimum fiber amounts were found to be 3.9%, 4.6%, and 6.4% for low, medium, and high target densities of foam concrete, respectively. At low-density series, the bubbles were observed to be relatively bigger and mostly merged with each other. A reduction in foam content (vice versa, increasing target density of mixture) and the presence of fiber resulted in smaller pore size and a more homogenous distribution of them in the matrix. In conclusion, the desired pore structure and efficient bridging of fibers in the matrix allowed the production of favorable foam concrete with higher toughness.

Molecular Dynamics Simulations Correlating Mechanical Property Changes of Alumina with Atomic Voids under Triaxial Tension Loading

The functionalization of nanoporous ceramics for applications in healthcare and defence necessitates the study of the effects of geometric structures on their fundamental mechanical properties. However, there is a lack of research on their stiffness and fracture strength along diverse directions under multi-axial loading conditions, particularly with the existence of typical voids in the models. In this study, accurate atomic models and corresponding properties were meticulously selected and validated for further investigation. Comparisons were made between typical material geometric and elastic properties with measured results to ensure the reliability of the selected models. The mechanical behavior of nanoporous alumina under multiaxial stretching was explored through molecular dynamics simulations. The results indicated that the stiffness of nanoporous alumina ceramics under uniaxial tension was greater, while the fracture strength was lower compared to that under multiaxial loading. The fracture of nanoporous ceramics under multi-axial stretching, was mainly dominated by void and crack extension, atomic bond fracture, and cracking with different orientations. Furthermore, the effects of increasing strain rates on the void volume fraction were found to be similar across different initial radii. It was also found that the increasing tension loading rates had greater effects on decreasing the fracture strain. These findings provide additional insight into the fracture mechanisms of nanoporous ceramics under complex loading states, which can also contribute to the development of higher-scale models in the future.

Integration and calibration of UBCSAND model for drained monotonic and cyclic triaxial compression of aggregates

We report on results from triaxial drained monotonic and cyclic compression tests for four different aggregates (gabbro, limestone, demolished concrete, steel slag), and discuss the applicability of UBCSAND model for simulating the relevant non-linear stress-strain curves. First, UBCSAND is integrated analytically for the elastic and plastic volumetric and deviatoric strains, leading to a pair of novel closed-form solutions expressed in terms of hypergeometric functions. These solutions are inherently free of numerical errors and can be used for the evaluation of results from numerical integration. Second, three calibration techniques for the model parameters are presented and compared: (1) a graphical “chart” solution based on results from forward numerical simulations; (2) a numerical approach based on minimization of residuals; and (3) an informed trial-and-error approach based on the analytical solution. Errors in numerical integration of the model are explored by comparing the analytical solution against results from an Euler integration. Variations in the calibrated parameters are discussed for drained monotonic and cyclic triaxial loading considering different types of aggregates.