Constant Axial Strain Rate Research Articles

Experimental Insights Into Fault Reactivation and Stability of Carrara Marble Across the Brittle–Ductile Transition

AbstractLittle is known about the impact of pressure (P) and temperature (T) on faulting behavior and the transition to fault locking under high P–T conditions. Using a Paterson gas‐medium apparatus, triaxial compression experiments were conducted on Carrara marble (CM) samples containing a saw‐cut interface at ∼40° to the vertical axis at a constant axial strain rate of ∼1 × 10−5 s−1, P = 30–150 MPa and T = 20–600°C. Depending on the P–T conditions, we observed the complete spectrum of deformation behavior, including macroscopic (shear) failure, stable sliding, unstable stick‐slip, and bulk deformation with locked faults. Macroscopic failure and stable sliding were limited to P < 100 MPa and T = 20°C. In contrast, at P ≥ 100 MPa or T ≥ 500°C, faults were locked, and samples with bulk deformation experienced strain hardening at strains ≤8.8%. At T = 100–400°C and P ≤ 100 MPa, we observed unstable stick‐slip behavior, where both fault reactivation stress and subsequent stress drop increased with increasing pressure and temperature, associated with increasing matrix deformation and less fault slip. Microstructures indicate a mixture of microcracking, twinning and dislocation activity (e.g., kinking and undulatory extinction) that depends on P–T conditions and peak stress. The transition from slip to lock‐up with increasing pressure and temperature is induced by an enhanced contribution of crystal plastic deformation. Our results show that fault reactivation and stability in CM are significantly influenced by P–T conditions, probably limiting the nucleation of earthquakes to a depth of a few kilometers in calcite‐dominated faults.

Constitutive modelling of non-cohesive soils under high-strain rates: a consistency approach

Rapid loading of sands is a common issue in geotechnical engineering problems such as projectile or free-fall impact. At high strain rates (HSR), soils show more strength and enhanced dilation (viscoplastic behaviour) compared to the response at low rates (inviscid behaviour). However, few constitutive models account for the viscoplasticity of sands. Hence, the development of viscoplastic models is highly desired. Usually, viscoplasticity is modelled using overstress methods. However, overstress methods impose an overall modification of the constitutive equations, which prevents control of the evolution of internal state variables and the enforcement of the consistency condition. In this study, a generalised consistency–viscoplasticity method is proposed and applied to a non-associative modified Mohr–Coulomb model with coupled stress–dilation relation. The influence of strain rate is incorporated using a work–energy approach by way of an inertial coefficient. Two explicit integration strategies are proposed and compared, and guidelines for their implementation are shared. The numerical response of the model is tested by using drained triaxial simulations under constant axial strain rate, relaxation and impact loading. The results indicate that the consistency–viscoplasticity is a feasible alternative to simulate soil behaviour under HSR, capturing reasonably well the observed experimental responses.

EXPERIMENTAL RESEARCH ON DEVELOPMENT/DIMINISHING OF ANISOTROPY AND ITS EFFECT ON MECHANICAL BEHAVIOR OF CLAY

Anisotropy refers to the directional dependence of material properties. The knowledge of development/diminishing of anisotropy are very important, to understand the true behavior of naturally deposited soil. The anisotropy of clays and silty clay intimately connected with their structure, which depends on the environmental conditions during which the soil is deposited as well as the stress changes subsequent to deposition. In this paper, triaxial tests were carried out using the vertical and the horizontal extraction specimen of the reconstituted clay and silty clay, for accumulating experimental facts of development of anisotropy during the preliminary consolidation process and the influence of the anisotropy on the shear behavior. Preconsolidation pressure of 200kPa applied to induced initial anisotropy. Undrained shear triaxial test was performed with different isotropic stresses on clay (50 to 1800kPa) and silty clay (50,300 and 600kPa), and undrained shearing was carried out under constant axial strain rate of 0.0056(mm/min). Vertical sample shows larger peak strength as compared to horizontal, because of the development of anisotropy on the compression side. As the confining pressure increases, the difference between peak strength of vertical and horizontal becomes smaller and smaller which indicate that the anisotropy diminished and intensity ratio decreases. By comparing clay and silty clay, silty clay materials lose their anisotropy at lower confining pressure (600kPa) as compared to clay materials (1800kPa). Therefore, the grain sizes have significant effect on the developing and diminishing of anisotropy. Another important fact observed was, critical state index is decreasing and becomes constant as confining pressure increases.

Acoustic Emission Associated with Self-Sustaining Failure in Low-Porosity Sandstone Under Uniaxial Compression

Two sets of uniaxial compression tests were conducted on a brittle sandstone under a constant circumferential strain rate (2 × 10−6 s−1) and a constant axial strain rate (2.5 × 10−6 s−1), respectively. A combination of active and passive ultrasonic techniques was implemented to study the effect of the control method on mechanical deformation, ultrasonic P-wave velocity, acoustic emission (AE) characteristics, and the ultrasonic amplitude spectrum. During each test, active surveys were performed at regular time intervals. P-wave velocity was found to be strongly anisotropic and was used for the construction of a time-dependent transversely isotropic velocity model for each specimen. AE data were continuously acquired and digitized at 10 MHz and 16-bits for the duration of each test where four channels were amplified 30 dB and the rest 50 dB. Discrete AE events were harvested from the continuous waveforms and were then used for source location analysis based on the constructed velocity model and the collapsing grid search routine. An analysis of the ultrasonic amplitude spectrum was also performed to relate attenuation to the formation of macroscopic fracture. In addition, the post-peak energy balance was quantitatively estimated by calculating the rupture energy, surplus energy, and residual elastic energy, suggesting a typical self-sustaining failure. Differences in the post-peak energy balance between the two sets of tests are also reflected in the AE magnitude distribution in addition to the failure modes. Finally, the reason for the large amount of missing AE data associated with eventual rupture was investigated, with the conclusion that multiple gain levels should be adopted during brittle failure of rocks.

Strength Behavior, Creep Failure and Permeability Change of a Tight Marble Under Triaxial Compression

The coupled hydro-mechanical behaviors of a tight marble are investigated by a series of laboratory tests with continuous gas injection during the hydrostatic compression, triaxial compression and compressive creep tests. Hydrostatic compression tests are firstly carried out in three steps to identify the viscous effect of hydrostatic stress on deformation and permeability of the marble. Coupled triaxial tests are then conducted at a constant axial strain rate under five different confining pressures (P c) with continuous gas injection. Coupled creep behaviors of the marble are also characterized by a constant deviatoric stress test under P c = 30 MPa with gas flowing at a constant injection pressure. The high-stress unloading failure behavior of the marble is finally investigated by an unloading test with a previous multi-step creep phase to realize a high-stress state as well as to investigate the time-dependent deformation of marble under different deviatoric stresses. Experimental results reveal that gas permeability of the marble shows an evident rate-dependent effect in hydrostatic compression. Mechanical behaviors of the tight marble are closely depended on the applied P c in triaxial tests, and its permeability exhibits a decrease phase at initial deviatoric loading and turns to increase at a critical stress corresponding to the initial yield stress. Marble can withstand more important plastic deformation under high P c than under lower ones. Gas flow seems to be more sensitive than the strains to characterize the creep behaviors of the marble. No time-dependent strains are observed when deviatoric creep stress is lower than 50% of its peak strength under P c = 30 MPa.

Mode-I stress intensity factor in single layer graphene sheets

We use the freely available software, LAMMPS, and the Tersoff potential to find the mode-I stress intensity factor during crack propagation in an edge-cracked single layer graphene sheet deformed at a constant axial strain rate. The axial stress and the stress intensity factor (SIF) at atoms’ locations are computed by using, respectively, the Virial theorem and either the stress at the atom located at the crack-tip or the average axial stress in the sheet. It is found that the two values of the SIF differ from each other by about 8%, and agree with those reported in the literature derived either analytically or from test data. The method proposed and used herein can be applied to find the SIF in any nanostructure.

Lubricated compression and X-ray microtomography to analyse the rheology of a fibre-reinforced mortar

In this work, the microstructure and the rheology of a glass-fibre-reinforced fresh mortar were studied. Various fibre contents and aspect ratios and two types of fibrous reinforcement, i.e. slender fibre bundles and fibres, were tested. The microstructure was analysed by using X-ray microtomography. It is shown that the non-deformed mortar is a porous granular suspension, the porous microstructure of which is not influenced by the presence of fibres, which in turn display a 2D planar random fibre orientation. The rheology was investigated by subjecting samples to constant axial strain rate and lubricated compression. The roles of the actual strain, the mortar resting time, the fibre content and aspect ratio on recorded stress levels are emphasised. Besides, for the investigated strain rate and material parameters, the mortar flow is quasi-incompressible and does not affect significantly the porous microstructure nor the fibrous one. Lastly, the stress increase which is induced by the addition of fibre bundles is similar to that predicted by Newtonian models of semi-dilute fibre suspensions.

Strain rate effects on sand and its quantitative analysis

Strain rate effects on the stress—strain behavior of sand were investigated by performing special plane strain and triaxial compression tests on saturated and air-dried sand specimens. In these tests, the loading strain rate was changed many times by a factor of up to 1 000 during otherwise monotonous loading at a constant axial strain rate. Test results show that the stress jump upon a stepwise change in the strain rate decays with an increase in the irreversible strain when monotonous loading continues at the changed strain rate and the amount of stress jump is essentially proportional to the instantaneous stress. Based on the amount of these stress jumps, a parameter β called the rate-sensitivity coefficient is introduced to represent the quantity of the observed viscous properties of sand, which equals 0.021 3 and 0.024 2 respectively for Hostun and Toyoura sands. Further analyses on the results indicate that the effect of the presence of pore water is deemed to be negligible with sand and the β value is rather independent of loading method, wet condition and confining pressure.

Acoustic emission and velocities associated with the formation of compaction bands in sandstone

A series of laboratory experiments has been conducted in which three‐dimensional (3‐D) locations of acoustic emissions (AE) were recorded and used to analyze the development of compaction bands in Bleurswiller sandstone, which has a porosity of 25%. Results were obtained for saturated samples deformed under triaxial compression at three different confining pressures (60, 80, and 100 MPa), a pore pressure of 10 MPa, and room temperature. We recorded acoustic emissions, compressional and shear wave velocities, and porosity reduction under hydrostatic condition and under triaxial loading conditions at a constant axial strain rate. Our results show that seismic velocities and their amplitude increased during hydrostatic pressure build up and during initial axial loading. During shear‐enhanced compaction, axial and radial velocities decreased progressively, indicating an increase of stress‐induced damage in the rock. In experiments performed at confining pressures of 80 and 100 MPa during triaxial loading, acoustic emissions were localized in clusters. During progressive loading, AE clusters grow horizontally, perpendicular to the maximum principal stress direction, indicating formation of compaction bands throughout the specimens. Microstructural analysis of deformed specimens confirmed a spatial correspondence of AE clusters and compaction bands. For the experiment performed at a confining pressure of 60 MPa, AE locations and microstructural observations show symmetric compaction bands inclined to the cylinder axis of the specimen, in agreement with predictions from recent theoretical models.

Sequential growth of deformation bands in the laboratory

We investigate the formation and evolution of localised faulting in high porosity sandstone by laboratory triaxial compression of intact 100-mm-diameter core samples. Experiments were carried out dry, at constant confining pressure (34MPa), constant axial strain rate (5×10−6s−1) and increasing axial strain (1.5–11.2%). Tests generated fault zones consisting of sets of distinct pale granulated strands, separated by lenses of apparently undamaged host rock. The sets of strands were sub-parallel to the shear direction but showed complex anastamosing geometry in perpendicular section. The individual strands had reduced grain size, porosity and sorting compared to undeformed rock. A strong correlation was found between the number of strands occurring in a fault zone and the applied axial strain. Mean grain size, however, reached a steady value irrespective of axial strain. This implies that a limited amount of strain is accommodated on each strand with further strain requiring new strands to form. However, no direct evidence for strain hardening was observed in the post-failure macroscopic stress–strain curves. Our laboratory induced deformation zones strongly resemble the key characteristics of natural deformation bands. We show the first laboratory evidence for the sequential development of increasing numbers of discrete deformation bands with increasing strain.

Measurements of Elastic Properties of Geomaterials in Laboratory Compression Tests

AbstractTwo types of axial loading devices having high and low capacities of axial load, respectively, for use in displacement-controlled compression tests on geomaterials (i.e., natural soils and rocks, and treated soils) in the laboratory are described. They were designed so that the loading direction can be reversed without any noticeable time lag under a highly constant axial strain rate while using a gear system. Results of representative triaxial and plane strain compression tests on a sand, a sedimentary soft rock, and a clay are presented. These results were obtained from very slow monotonic (or one-way) loading tests with several unload/reload cycles measuring axial strains locally along the lateral surfaces of a specimen continuously for a strain range from the order of 0.0001% (10−6) to that at failure. It is demonstrated that initial stiffness at strains less than about 0.001% (10−5) during primary loading is the same as stiffness during small unload/reload cycles applied immediately after the start of loading. Initial deformation properties are rather linear and elastic.

UNDRAINED BEHAVIOR OF SATURATED SAND SUBJECTED TO SIMULTANEOUS MONOTONIC AND CYCLIC LOADING

Simultaneous monotonic and cyclic loading may be applied to a soil element near, for example, retaining structures during earthquakes. To study into the behavior of saturated sand in such a case as above, a series of undrained triaxial tests were performed by applying cyclic stresses to a specimen which is subjected to continuous monotonic loading at a constant axial strain rate simultaneously. It was found that the behavior of sand in these tests was different from those in other types of cyclic loading tests in which cyclic stresses are fully or partially reversed or not reversed between the triaxial compression and extension conditions.Furthermore, a sort of interaction effect of cyclic and monotonic loading on the liquefaction was observed, of which the tendency depended on the density of specimen.

An Incremental Formulation of Constitutive Equations for Deposited Snow

Abstract The behaviour of a snow mass under natural loadings (gravity forces, boundary conditions) can be computed by the finite-element method, in so far as a convenient formulation of the stress–strain relationship for snow is available. This paper deals with such a formulation given in incremental form. Experiments have been performed, which show that deposited snow can be considered as a non-linear visco-elastic material with memory effect. The proposed theoretical formulation takes into account these properties. The elastic part of the deformation is assumed to be isotropic and non-linear; the viscous part is expressed in terms of a creep-rate, which results from a superposition of elementary creep-rates according to Boltzmann’s principle. The values of parameters can be obtained from isotropic creep experiments. The experimental data and the resulting parameters are reported. Since the parameters were determined, the formulation of the rheological law was then tested by integration on “stress–strain paths" corresponding to other experiments of a different type, performed on the same snow. The experiments are triaxial tests at constant axial strain-rate, with a preliminary stage of isotropic compression. Experimental data are compared to theoretical curves obtained by integration of the rheological law. The calculated behaviour is consistent with the experimental results.

An Incremental Formulation of Constitutive Equations for Deposited Snow

AbstractThe behaviour of a snow mass under natural loadings (gravity forces, boundary conditions) can be computed by the finite-element method, in so far as a convenient formulation of the stress–strain relationship for snow is available. This paper deals with such a formulation given in incremental form.Experiments have been performed, which show that deposited snow can be considered as a non-linear visco-elastic material with memory effect. The proposed theoretical formulation takes into account these properties. The elastic part of the deformation is assumed to be isotropic and non-linear; the viscous part is expressed in terms of a creep-rate, which results from a superposition of elementary creep-rates according to Boltzmann’s principle.The values of parameters can be obtained from isotropic creep experiments. The experimental data and the resulting parameters are reported.Since the parameters were determined, the formulation of the rheological law was then tested by integration on “stress–strain paths" corresponding to other experiments of a different type, performed on the same snow. The experiments are triaxial tests at constant axial strain-rate, with a preliminary stage of isotropic compression. Experimental data are compared to theoretical curves obtained by integration of the rheological law. The calculated behaviour is consistent with the experimental results.