Mohr Circle Research Articles

A novel hyperboloid cone model for predicting tensile performance of studs in concrete of various properties

Concrete breakout (CB) failure is the most common failure mode for studs in tension. Based on the Griffith's strength theory, Mohr's circle method, and mechanics of materials, the breakout cone failure model and failure mechanism of the CB mode are analyzed; the shape of the breakout cone is hyperboloid cone, and the failure of CB mode is due to the concrete tensile failure. The classic concrete capacity design (CCD) method only applies to normal concrete (NC) substrate. To predict ultimate tensile strength (Nb) of the CB mode for a wider range of concrete properties, including high-strength concrete (HSC), ultra-high performance concrete (UHPC), engineered cementitious composite (ECC), etc., a new "Hyperboloid Cone Model" is proposed, which is based on the original form of CCD method and the Griffith's strength theory. The comparison between the experimental and predicted Nb for the studs in various substrates (NC, HSC, UHPC, and ECC) from past studies shows that the prediction of the proposed model on Nb is more accurate with significantly smaller variances compared to CCD method; the average ratio of the experimental to calculated value of the proposed model and the CCD model is 0.974 and 1.138, respectively, while the coefficient of variance of them is 11.27% and 40.44%, respectively.

Evidencia de una deformación rotacional varisca a partir de braquiópodos distorsionados (Meseta, Marruecos)

En 2021-2022, las obras de construcción de la carretera costera R322, que conecta la Kasbah de Oudayas (Rabat) con la localidad costera de Bouznika, han hecho posible estudiar esquistos con braquiópodos (Spirifer sp.) del Viseense sup. en la playa de Val d’Or, 12 km al suroeste de Rabat. El análisis estructural de las muestras recogidas indica una deformación de los fósiles en el plano XY del clivaje pizarroso (S1), afectados por pliegues recumbentes de vergencia oeste y por una foliación de crenulación (S2) asociada a los pliegues. Los fósiles de Spirifer sp. son triangulares, con forma de mariposa, y tienen el interés de mostrar simetría bilateral en el estado no deformado, con dos direcciones perpendiculares en T (seno o línea de simetría y charnela). Después de la deformación, estos ejes se cruzan con un ángulo agudo / obtuso que indica una deformación angular. Las medidas de los ángulos de cizalla nos llevan a reconstruir el círculo de Mohr para ángulos en el estado deformado, con objeto de obtener la forma de la elipse de deformación finita y determinar los mecanismos responsables de la distorsión utilizando el diagrama de forma de las elipses. Este método permite determinar la relación axial de la elipse de ladeformación finita mediante los círculos de Mohr. Los resultados se comparan con los obtenidos por el método de Wellman y el ábaco de Breddin. Finalmente, se propone un modelo estructural que explica las deformaciones dúctiles observadas como desarrolladas dentro zonas de cizalla dextras de dirección N-S.

ПОСТРОЕНИЕ УПРУГОЙ ЛИНИИ БАЛКИ И ОПРЕДЕЛЕНИЕ ВЕЛИЧИНЫ И НАПРАВЛЕНИЯ ГЛАВНЫХ НАПРЯЖЕНИЙ В СЕЧЕНИИ БАЛКИ

The paper uses the data from diagrams of I-beam transverse forces and bending moments to calculate the values and directions of primary stresses at three points of the beam cross-section – on the neutral axis, above and below it. To calculate the values of primary stresses, the graphic analytical method with the construction of Mohr's circles is used. Further, the article presents an algorithm for constructing a beam deflection line and calculating cross-section deflections. To determine deflections, the universal beam deflection line equation is used. After determining the largest deflection value, conclusion is made that the hardness condition of a steel I-beam is met.

К ВОПРОСУ ОПРЕДЕЛЕНИЯ ЗНАЧЕНИЙ СЦЕПЛЕНИЯ И УГЛА ВНУТРЕННЕГО ТРЕНИЯ ГОРНЫХ ПОРОД

The paper analyses the strength parameters of rocks tested under uniaxial and volumetric stress states. Based on their results, the Mohr stress limit circles and their envelope line were plotted in the field of tangential and normal stresses. According to its slope and intersection with the tangent stress axis, the cohesion (C) and the angle of internal friction (φ) were determined. Calculated, using the values (C and φ), strength in uniaxial compression was higher than the actual strength by 20 and more per cent. It is suggested to change the methodology of determination of adhesion and angle of internal friction. It is proposed to determine them not by the envelope of the limiting circles of Mohr stresses line, but by the change of limiting values of tangential stresses of Mohr's circles from normal stresses.

Experimental study on mechanical properties of recycled aggregate concrete with polypropylene fiber under combined compression‐shear loading

AbstractTo investigate the mechanical properties of polypropylene fiber recycled aggregate concrete (PPFRAC) under compression‐shear, 69 recycled aggregate concrete (RAC) specimens were tested with the parameters of polypropylene (PP) fiber volume content (0, 0.6, 0.9, and 1.2 kg/m3), recycled coarse aggregate (RCA) replacement rate (0%, 30%, 50%, 70%, and 100%), and normal stress (0, 3, and 6 MPa). In the tests, the failure pattern of the specimens was observed, and the effects of the polypropylene fiber content on the direct shear stress, compression‐shear stress, initial shear stiffness, and shear ductility coefficient of the PPFRAC were thoroughly investigated. The results show that as the polypropylene fiber content increases, the direct shear stress of concrete (Natural aggregate concrete and 100% recycled coarse aggregate concrete [100%RCA]) first increases and then decreases gradually. Meanwhile, the best PP fiber content is 0.9 kg/m3 in this study. Furthermore, the compression‐shear stress‐displacement curves of specimens were obtained. The compression‐shear strength under normal stress at 6 MPa is approximately 230% greater than at 0 MPa. However, the peak shear stress of concrete is almost not affected by the replacement rate of RCA. Finally, based on the Mohr circle theory, the compression‐shear calculation model of PPFRAC is verified, and the optimal calculation formula is given.

Elastoplastic solution of a circular tunnel in surrounding rock with any nonlinear yield criteria and plastic flow envelopes

Besides the (semi-)linear Mohr-Coulomb and Hoek-Brown criteria, other nonlinear functions are also used to describe the plastic response of rock mass. For a nonlinear yield and plastic flow function in the form of τ=fσn and/or σ1=fσ3, the equivalent cohesive strength and frictional angle corresponding to the Mohr-Coulomb yield criterion were derived. The normal stress was further related to the minimum principal stress using the geometrical relationship of a Mohr circle. The equivalent dilatancy angle was also derived using the same method. According to the solution of a circular tunnel in Mohr-Coulomb rock mass, this paper derived a semi-analytical solution of a circular tunnel in any nonlinear yield and plastic flow rock masses with a form of τ=fσn and/or σ1=fσ3. A numerical procedure was developed for the stresses and displacement using a reserve method. The proposed solution was verified by the results of a circular tunnel in elasto-perfectly(brittle-)-plastic and/or strain-softening rock mass. The strain-softening analysis of a circular tunnel in the assumed two nonlinear yield criteria and/or plastic flow rock masses was studied. For a linear deteriorated material parameters leads to a nonlinear evolution of equivalent cohesive strength, frictional angle and dilatancy angle in the plastic region.

A unified educational mobile application to aid in teaching solid mechanics using interactive Mohr's circle

The interpretation and visualization of engineering problems are complex. Therefore, engineers have always developed graphic procedures to solve these problems, one technique being Mohr's circle. The study of geometric properties of the cross-sections, plane stress, and plane strain are some applications of such techniques in Solid Mechanics. In practically all literature adopted in undergraduate courses on these topics, the efforts of authors to teach with the greatest clarity are remarkable, using all possible resources in books, with very well-designed graphics. However, concerning Mohr's circle, the mental visualization of some movement is needed, be it the rotation of points on the circle, the rotation of the cross-section, the axes, or the differential element. This need makes such topics ideal to be taught through interactive animations, impossible in books. Computer programs about these subjects do exist, however, with reduced user interactivity. Thus, this work presents a new unified mobile application with several useful interactivity features for teaching plane stress, plane strain, and moment of inertia in engineering courses, using Mohr's circle. The application is developed in Java programming language, using Android Studio software. The graphical environment was developed with the aim of being a didactic and intuitive way to study and learn about cross-section properties, plane stress, and plane strain. The results provided by the application are compared with examples from the literature, presenting accurate responses, with easy visualization and interpretation. The usage of the program makes studying the initial concepts of solid mechanics and Mohr's circle enjoyable for engineering students.

Fault detection methods for 2D and 3D geomechanical numerical models

AbstractWe develop automated methods for fault detection utilizing static stress and deformation fields at the onset of failure derived from numerical analysis. We calculate combinations and normalization of the distance from the Mohr circle to the Coulomb envelope, and of the second deviatoric strain invariant. A variation of the Cauchy distribution of these fields allows us to focus on the low values indicating rupture, with the help of the scale parameter δ. A threshold is then applied to decide at each spatial node of the mesh whether the material has reached failure or not. We then determine fault lines and planes from these isolated failure zones using image processing techniques, such as the Hough and the Radon transforms, or through a combined approach involving automated sorting of the nodes reaching failure through the k‐means clustering technique followed by polynomial fitting to retrieve analytic expressions of the fault curves (in 2D) or fault surfaces (in 3D). The methods are efficient except when the stress field results in diffuse rupture zones that do not localize onto fault surfaces despite tuning δ. We also highlight the advantages of using the combined clustering/poly‐fitting approach for 3D models compared to the image processing techniques. These automated fault detection methods should be useful in the interpretation of diverse failure mechanisms obtained through parametric sensitivity analyses requiring hundreds of simulations. The stress and strain fields used were derived from a numerical implementation of limit analysis, but classical finite‐difference or finite‐element techniques could have been used.

Early Paleozoic ductile deformation of the South China Block: the polyphase shear zones in the eastern Jiangnan belt

Three parallel east–west-trending shear zones are components of the polyphase shear zones in the eastern Jiangnan belt. The meso- and microstructural characteristics and the estimates of deformation temperatures, vorticities and geochronology of these shear zones provide significant information regarding the tectonic evolution of the South China Block (SCB) during the early Paleozoic. Most shear sense indicators (e.g. asymmetric folds, S-C fabrics and rotating porphyroclasts) reveal that the kinematics were characterized by east–west dextral shear. Finite strain measurements indicate an oblate strain ellipsoid shape with S-type and SL-type tectonites. The rotated rigid porphyroclasts and Mohr circle methods yield vorticity ( Wk ) values of 0.58–0.80 and 0.66–0.89, respectively, indicating that the flow was generally shear-dominated with almost equal proportions of simple and pure shear. Both mineral deformation thermometers and quartz c -axis fabrics indicate that the deformation occurred at medium temperature conditions of 400–550°C. Combined with our new age and regional geological data, the east–west-trending shear zones might represent an increment of deformation during the last period of the early Paleozoic orogeny in the SCB.

In situ stress field detection of stress-induced strong anisotropy media based on Mohr circle theory

The prediction and evaluation of in situ stress field plays an important role in many engineering fields. How to accurately obtain in situ stress field information of a large area becomes a focus in geophysics. Wide-azimuth seismic data establish a bridge between in situ stress and rock anisotropy, making it possible to predict the large-scale in situ stress field. Ellipse fitting (EF) is a common method to predict in situ stress according to the characteristics of seismic attribute change with azimuth, but there are some problems such as 90° ambiguity in orientation prediction and the unclear stress-related physical meaning of the fitting parameters. Moreover, the variation of azimuthal seismic attribute in strongly anisotropic media does not meet ellipse hypothesis, which also limits the application of EF method. Through mathematical simulation experiment, the mechanism of seismic response characteristics under orthotropic stress situation is explored. Focusing on the property of strong anisotropy induced by in situ stress in subsurface media, a new stress circle fitting (SCF) method for in situ stress prediction is established by combining the azimuthal variation characteristics of reflection coefficient with the Mohr circle theory. The fitting results have clear physical significance related to in situ stress. In addition, through analysis of fitting parameters, the influence of 90° ambiguity problem can be eliminated. EF and SCF methods are applied to actual wide-azimuth seismic data. Comparison indicates that the SCF result is more suitable for azimuth seismic data in strongly anisotropic media. Compared to EF, in situ stress field distribution predicted by SCF method is more reasonable. The actual imaging logging results also prove the accuracy of SCF method.

Roof stability analysis of cylindrical tunnels in hard soil/soft rock with reduced tension strength

Three-dimensional roof stability analyses of cylindrical tunnel segments limited along the tunnel direction were performed based on the modified Mohr–Coulomb failure criterion with reduced tensile strength. A wedge-shaped region of the classical Mohr–Coulomb envelope, where unrealistic tensile and shear strengths are predicted, is truncated by a Mohr circle associated with the true tensile strength. This revised failure criterion with partial nonlinearity allows geomaterials deep into the roof to deform with large velocity gradients under the normality plastic flow rule, observed in field investigations. Using the kinematic approach of limit analysis, rigorous bounds for three quantitative stability measures–stability number, factor of safety, and supporting pressure–were calculated. The roof failure mechanism adopted is relatively elaborate, involving three-dimensional geometry intersecting with a cylindrical tunnel segment; thus, an efficient approach was presented for tunnels with long length constraints. With respect to extremely short tunnel lengths, a modified roof failure mechanism with distinct ridges was proposed. The factor of safety with accommodation of the nonlinear pressure dependency was estimated by a consistent procedure associated with a reduced elliptic failure criterion. The results show that roof stability distinctly depends on the magnitude of the true tensile strength, internal friction angle, and length constraint.

Probabilistic Evaluation of Geomechanical Risks in CO2 Storage: An Exploration of Caprock Integrity Metrics Using a Multilaminate Model

The probabilistic uncertainty assessment of geomechanical risk—specifically, caprock failure—attributable to CO2 injection, as presented in a simplified hypothetical geological model, was the focus of this study. Our approach amalgamates the implementation of a multilaminate model, the creation of a response surface model in conjunction with the Box–Behnken sampling design, the execution of associated numerical modeling experiments, and the utilization of Monte Carlo simulations. Probability distributions to encapsulate the inherent variability (elastic and mechanical properties of the caprock and reservoir) and uncertainty in prediction estimates (vertical displacement, total strain, and F value) were employed. Our findings reveal that the Young modulus of the caprock is a key factor controlling equivalent total strain but is insufficient as a stand-alone indicator of caprock integrity. It is confirmed that the caprock can accommodate significant deformation without failure, if it possesses a low Young’s modulus and high mechanical strength properties, such as the friction angle and uniaxial compressive strength. Similarly, vertical displacement was found to be an unreliable indicator for caprock integrity, as caprock failure can occur across a broad spectrum of vertical displacements, particularly when both the Young modulus and mechanical strength properties have wide ranges. This study introduces the F value as the most dependable indicator for caprock failure, although it is a theoretical attribute (the shortest distance between the Mohr circle and the nearest failure envelope used to measure the sensitivity to failure) and not physically measurable in the field. Deviatoric stress levels were found to vary based on stress regimes, with the maximum levels observed under extensive and compressive stress regimes. In conjunction with the use of the response surface method, this study demonstrates the efficacy of the multilaminate framework and the Mohr–Coulomb constitutive model in providing a simplified, yet effective, probabilistic model of the mechanical behavior of caprock failure, reducing mathematical and computational complexities.

Anisotropic stress mechanisms for different dielectric multi-layer films deposited by ion-beam assisted deposition on flexible substrates

This study simulates and tests various prototype multi-layer films on polyethylene terephthalate (PET) and polycarbonate (PC) substrates. The optical and stress response properties of three commonly used optoelectronic anti-reflector (AR) coatings (TiO2/SiO2)2, (Ta2O5/SiO2)2 and (Nb2O5/SiO2)2 were determined. A lab-designed phase-shifting shadow moiré interferometer and Mohr circle approach were used to collect and interpret data. Results showed that the refractive indices of the four different dielectric films were 2.24(TiO2) > 2.23(Nb2O5) > 2.1(Ta2O5) > 1.44(SiO2). The transmittances of the three different AR coatings, in decreasing order, were 95.28%(Ta2O5/SiO2)2 > 94.86%(TiO2/SiO2)2 > 94.03%(Nb2O5/SiO2)2. The maximum shear stress of three different AR coatings, in decreasing size, were (Nb2O5/SiO2)2 > (Ta2O5/SiO2)2 > (TiO2/SiO2)2, for both the PET and PC substrate; however, the maximum principal stresses of three different AR coatings were tensors for the PET substrate, and compressive for the PC substrate. The principal stresses recorded were -916 MPa (Nb2O5/SiO2)2 > 438 MPa (Ta2O5/SiO2)2 > 346 MPa (TiO2/SiO2)2 for PET, and -951 MPa (Nb2O5/SiO2)2 > -838 MPa (Ta2O5/SiO2)2 > -766 MPa (TiO2/SiO2)2 for PC. The different elasticity moduli (ΔE) and relative elasticity between the different film layers may potentially be used to mitigate stress relief in multilayer coatings.

SHPB experiments and FDM-DEM coupled simulations on calcareous sand under uniaxial to triaxial deformation

The impact behavior of sand is paramount to geotechnical and protective engineering. Although the one-dimensional impact responses of sand are extensively studied, the behavior of shear under impact loading remains poorly understood as the shear stresses in uniaxially compressed sand cannot attain the failure state. This paper reports the macroscopic responses of crushable calcareous sand under uniaxial to triaxial deformation by split Hopkinson pressure bar (SHPB) experiments. In addition, the mesoscopic mechanism is analyzed by coupled finite difference method (FDM) and discrete element method (DEM) numerical simulations. With an increasing lateral confined stiffness, the p-q curves exhibit a clockwise rotation, signifying a deviation of the stress path from the critical state line (CSL) during the transition from triaxial to uniaxial deformation, meanwhile the Mohr circle experiences a shift from intersecting to tangential contact with the failure line, indicating that shear failure occurs under triaxial deformation. The stress-strain relationships for both compression and shear exhibit four distinct regimes, the initial elastic stage mainly overcomes intergranular friction through particle rotation; the yield stage mainly compresses the skeleton by contribution of displacement; the hardening stage experiences critical particle breakage and then promotes particle displacement and rotation; and the unloading stage with strain softening caused by the asynchrony between impact loading and deformation. Both compressed and shear yield stress increases with an increasing confined stiffness, but the shear friction angle decreases. This indicates that the governing factor in triaxial compression under impact loading is the stress state rather than kinetic friction. Particle breakage in triaxial compression state tends to approach the splitting mode, while in uniaxial squeezing state it tends to approach the Mixed mode.

Collaborative formation pattern of surface topography and residual stress in hard turning of steels

High-performance manufacturing (HPM) is essential for high-quality equipment and parts manufacturing, which requires not only geometric accuracy but also control of surface integrity to satisfy functional performance. Surface topography and residual stress are important elements of surface integrity. However, they are always investigated individually, and their collaborative formation pattern has been ignored for a long time. In this study, surface topography will be measured by a 3D laser scanning microscope and analyzed from the perspective of spectral wavelength (λ) along with its corresponding amplitude. Whereas the residual stress (RS) is going to be analyzed by X-Ray diffraction and finite element (FE) model. Thereafter we introduce the formation pattern of both surface topography and RS. Hereby, simulated points clouds of machined surface topography are generated by superimposing the normally distributed random numbers that take into account the springback of the workpiece material response on tool kinematics and geometry. Furthermore, the RS is divided into mechanical loads induced (RSM) and thermal loads induce (RST) according to the mechanism of formation, which were obtained in cutting speed (Y-direction) and feed direction (Z-direction) by the Mohr circle. Our experimental and numerical results showed that an increase in the feed rate (from 0.05 mm/r to 0.15 mm/r) significantly increases the surface roughness and cutting temperature. The increase in temperature increased the RST by up to 286.1%, resulting in a reduction of compressive RS in Z-direction and an increase of tensile RS in Y-direction. Moreover, the increase in cutting speed (from 40 m/min to 80 m/min) results in a more regular surface and a reduction in surface roughness because of the smaller springback. At the same time, it also leads to a decrease of RSM in Z-direction and an increase of RSM in Y-direction. In addition, the increment in cutting speed leads to a minor increase in temperature and RST (maximum increase of 47.0%). Combining the effects of RSM and RST, RS in both directions increases slightly.

Modelling of subsurface geological structure related to anomalous magnetotelluric phase data exceeding 90° in Central India

SUMMARY We note anomalous phase (>90°) in magnetotelluric (MT) measurements at several stations along the Narmada river course normal to the Tan Shear Zone (TSZ) in central India. We made efforts to derive a possible cause of the anomalous phase by comparing the results of numerical modelling based on the tectonics of the TSZ with the measured impedance tensor data. A zone of multiple reactivations of the TSZ leads to the formation of a damage zone and conjugate Riedel shear faults parallel and normal to the TSZ, respectively. The conjugate Riedel shear faults act as a pathway for the Narmada River course. The multiple tectonic activities associated with the TSZ induce surficial heterogeneity that results in distortion in the MT data. The Mohr circle and phase tensor analysis establish the effect of distortion in the data. To understand the cause of distortion as well as anomalous phase in the present data, we carried out synthetic 3-D modelling. We modelled the damage zone and conjugate Riedel shear faults by a cross shape. From the results, we noted that the near-surface 3-D heterogeneity across the TSZ critically distorted the YX component of the MT impedance tensor due to the strong current channelling. When the current flows across the conjugate Riedel shear zone (Narmada river course) charges are accumulated along the boundaries of near-surface heterogeneity. The charges associated with the current channelling brought out the reversion of the electric field direction that is reflected in the form of an anomalous phase in the YX component of the impedance tensor in measured data.

Development of methodology for assessing flowability of milk protein powders using shear failure testing device

Protein-rich milk powders can be susceptible to caking and clumping during manufacture and storage. A method was developed for objective and reliable assessment of their flowability, i.e., tendency of powders not to stick to the equipment surfaces. Milk protein powder (MPC 80) was subjected to three-point shear failure testing on a powder shear cell attached to a MCR302e rheometer. Flow function coefficients (ffc) were obtained after the Mohr circle analysis of pre-shear and shear-to-failure points. Due to their globular shape and significantly larger particle size (50–70 μm), milk protein powders exhibited more stick-slip phenomenon and lack of shear to failure point particularly at higher pre-shear (>6 kPa) and shearing normal stresses than the flat-shaped, smaller size (<20 μm) cohesive calcium carbonate powder (ffc value 2.1 at 3.0 kPa). Absence of shear-to-failure points in milk protein powders was attributed to instant failure of the powder at higher normal stresses due to larger particle size and globular shape, which was avoided by lowering pre-shear (3, 6, and 9 kPa to 1, 3 and 6 kPa) and shearing normal stresses, increasing data capturing interval and optimizing shear speed. Reliable ffc values at 3.0 kPa pre-shear normal stress, characterizing MPC 80 powder (4.6 ± 0.4) as easy flowing and MPI 85 as cohesive (3.7 ± 0.5) were obtained successfully using developed protocol.

A way to determine the positive direction of the shear force on the elemental area

This study is devoted to amendment to some concepts related to the construction of Mohr's circles on the plane of variables “normal and tangential components of the stress vector on the elemental area”. As the tangential component is positive by definition (as a square root), we have to talk only about semicircles instead of Mohr's circles. To introduce negative values, we bring in the concept of the positive direction of the shear force connected with the projection on the first principal direction of the stress tensor. The considered approach allows us to determine the direction of the shear force (positive/negative) relatively to the principal axes of the stress tensor on any elemental area with known values of the principal stresses. The same approach is applied to the vector of deformations on the elemental area. To represent the application of these two vectors on the elemental area, we consider the work done by the forces acting (in the form of the Cauchy vector of stresses) on changes in the vector of strains. It is also shown that this work, even in the case of elasticity, does not always lead to an unambiguous result. It does not depend on the loading path only on octahedral elemental areas. The foregoing does not negate the existence of the elasticity potential as a whole (non-potency on one elemental area is annulled by the same non-potency on the other one). All this is important when, based on a set of slip areas, physical theories of plasticity and destruction (slip theories) are constructed.

Study of Strain-rate Effect in Two-dimensional Biaxial Test on Granular Material using Discrete Element Method

Numerical study to investigate the effect of various strain rates on global friction angle in the sand has been performed. Granular material behavior is influenced by several factors, among others: pack configuration, grain macro and micro roughness, confinement pressure, loading rate, etc. Sand is a granular material composed of discrete particles that the most refined microscopic techniques are needed to study its mechanical properties. In Indonesia, research related to the Discrete Element Method is still very limited. The two-dimensional discrete element method is capable to calculate the motion and interparticle contacts of large number of small particles, and each particle is modeled as a rigid circular element. The study started with the validation of the DEM model using YADE. Particles with a local friction angle of 35° are arranged in a closed rectangular box (frictionless wall). The number of particles used in this model validation simulation is 1000 sphere-type particles with monodisperse particle gradations. The simulation was done by a drained biaxial test with confinement stress of 100 kPa, thereafter varying strain rate are applied. Based on the deviatoric stress–axial strain curve from YADE, the result can be depicted on the Mohr circle to obtain the value of the global friction angle. It is found that the different value of strain rate affects its global friction angle. Increasing the value of the strain rate can increase the material global friction angle, which increases the strain rate from 1% to 5%, 10%, 25%, and 50% will increase its global friction angle by 5%, 5%, 14%, and 18%, respectively.

Rate and State Simulation of Two Experiments With Pore Fluid Injection Under Creep Conditions

AbstractThis study uses a spring‐block model and rate and state friction to simulate experiments conducted in a double direct‐shear apparatus on carbonate fault gouge (Scuderi et al., 2017, https://doi.org/10.1016/j.epsl.2017.08.009) and on shale bearing rock (Scuderi &amp; Collettini, 2018, https://doi.org/10.1029/2018jb016084). Both sets of experiments used the same loading protocol and injected pore fluid under creep conditions. When velocity strengthening rate and state friction is used to simulate the experiments on the carbonate fault gouge the results agree well with the observed onset of tertiary creep in the experiment. Thus, the simulation reinforces the observation that pore fluid injection can induce rapid slip even when the friction relation is velocity strengthening. The rate and state framework provides an interpretation alternative to the standard one of the Mohr's circle moving to the left as pressure increases. In the rate and state framework, the friction coefficient must increase with pore pressure increase. The shale has a low nominal friction coefficient (0.28) and is much more velocity strengthening than the carbonate. The simulation agrees with the observations that increases in pore pressure induce an increase in slip velocity but the magnitudes reach only about 100 microns/s by the end of the experiment. The simulation for the shale also agrees well with the magnitude of the observed displacement at the end of the experiment but observed displacement is increasing much more rapidly the calculated. Although the calculations agree well with features of the observations near failure, the overall curves of displacement and velocity are significantly different.