Normal Stress Effects Research Articles

Shearing Performance of Natural Joints with Different Roughnesses under Direct Shearing Tests

Roughness is one of the major characteristics of natural fracture in hydrocarbon and geothermal reservoirs, which has a significant influence on the activation of fractures during hydraulic stimulation. The main purpose of this study is to investigate the effect of different roughnesses and high normal stresses on shear behaviors of rock joints. To do this, replicas of natural rock joint surfaces were constructed using the 3D optical scanning and 3D rigid engraving technique. Direct shear tests were performed on rock joint replicas with three joint roughness coefficient (JRC) indices (i.e., 1.42, 4.98, and 7.96) at two high normal load conditions (i.e., 15 and 30 MPa). The results show that the shear strength dependence on surface roughness is similar at normal stresses of 15 and 30 MPa. In addition, JRC-JCS shear strength criterion can reasonably describe the peak shear strengths that obtained from experimental curves, and the peak shear stresses have a positive correlation with JRC values at both normal stresses. Moreover, at normal stresses of 15 and 30 MPa, the shearing mechanism of joints with different JRC values is asperity shearing off. Results also show that the friction coefficient of joint surface increases as joint roughness increases, and higher normal loads may lead to a decrease of apparent cohesion, which weakens the residual strength during the slip. The results of this study improve insight into the natural fracture activation behavior during hydraulic fracturing.

Efficient fabrication of flame-retarding silicone rubber/hydroxylated boron nitride nanocomposites based on volumetric extensional rheology

Silicone rubber (SR) is one of the most widely used synthetic rubbers owing to its excellent high-temperature resistance and outstanding high-voltage insulation. However, the flammability of SR severely restricts its further promotion and application in fields with high flame-retardancy requirements. In this study, an effective mixing process strategy was proposed for preparing flame-retarding SR/hydroxylated boron nitride (HOBN) nanocomposites using a novel eccentric rotor internal mixer, which could strengthen the hydrogen bond between SR and HOBN through transient normal stress based on volumetric extensional rheology. The strengthening effect of transient normal stress on hydrogen bonds can effectively promote the uniform dispersion, efficient exfoliation, and horizontal orientation of HOBN in the SR matrix. The layer thickness of HOBN was reduced from 200 to 6 nm, and its orientation degree I002/I100 increased from 25 to 112. As expected, the SR/HOBN nanocomposite exhibited excellent flame retardancy with a drastic decrease of 76.4%, 36.0%, 81.7%, and 55.3% in the values of the peak heat release rate, total heat release, smoke production rate, and total smoke production, respectively, compared to neat SR. The flame-retardant mechanism revealed that the physical barrier action of HOBN and the cross-linking reaction between SR and HOBN during combustion showed prominent synergism in the ceramization of the condensed phase to form a compact and adamant protective char layer, thus significantly improving the flame retardancy and smoke suppression of SR. This study provides an efficient and innovative mixing method for the preparation of flame-retardant polymers and will facilitate the development of high-performance rubber processing technology and equipment.

Interfacial plasticity mediated by lath boundaries in reduced-activation ferritic/martensitic steels

• The onset lath boundary sliding sensitively depends on the microscopic structure of the interfacial planes. • The lath boundary sliding is mediated by the motion of dislocation arrays lying on the interfacial plane. • For predominant lath boundary sliding: - The Burgers vector of the interfacial dislocations must lie on the interfacial plane. - The interfacial plane must be parallel to the common slip planes in the BCC structure, i.e., {110}. In the hierarchically-arranged crystallographic structure of reduced-activation ferritic/martensitic (RAFM) steel, the smallest but the most abundant microstructural unit, i.e., the lath, plays an important role in dislocation plasticity. Due to the multi-scale complexity in the lath-martensitic microstructure, miniaturized mechanical characterization at very fine scale is required to understand the deformation mechanism associated with laths. In this study, uniaxial micro-compression tests combined with rigorous crystallographic analysis were performed to figure out the plastic deformation mechanism of lath boundary sliding in RAFM steels. These experimental results were further interpreted via molecular dynamics simulations to discover the underlying dislocation mechanisms. We found that the amount of lath boundary sliding is controlled by the crystallographic orientation of the lath boundary plane, the direction of Burgers vectors of the interfacial dislocations, and the magnitude of resolved shear stress on the lath boundary plane. Also, the effect of normal stress on the lath boundary plane was investigated.

Shear behaviors of natural rock fractures infilled with cemented calcite

Shear behaviors of naturally infilled granite fractures were investigated using experimental and numerical approaches in this study. The tested granite fracture samples were collected from two boreholes BS48 and BS49 at the Xinchang site in the Beishan area of Gansu Province, China. Particle-based DEM models for the naturally infilled granite fractures were built up and calibrated with the experimental results. Effects of normal stress and infilling ratio (t/a) on shear behaviors and properties of infilled fractures were investigated. The results show that the shear stress-shear displacement curves of the naturally infilled fractures include three shear phases, i.e., quasi-elastic phase, failure phase, and residual shear phase. The relationships between normal stresses and peak shear strength, residual shear strength, shear stiffness and peak dilation are fitted using an approximately linear function. Infilling ratio (t/a) has a significant influence on the shear properties of the naturally infilled fractures. Shear strength and stiffness of the naturally infilled fractures decrease with increasing (t/a). The different shear behaviors of the various infilled and clean fractures are also briefly compared. Practical implications and outstanding issues in the present study are discussed finally.

Hydraulic and Mechanical Coupling Analysis of Rough Fracture Network under Normal Stress and Shear Stress

The hydraulic and mechanical coupling characteristics of fracture networks under normal stress and shear stress were studied in this paper. The hydraulic and mechanical coupling model of the fracture network comprehensively considers the normal stress, shear stress, seepage pressure and roughness characteristics. Based on the boundary conditions and reasonable assumptions, COMSOL Multiphysics software was used to develop the hydraulic and mechanical coupling finite element model of the fracture network with different intersection points under normal stress and shear stress, focusing on the study of the effect of normal stress and shear stress on the fracture permeability. The degree of permeability change caused by the normal stress and shear stress is different. The shear stress has a significant influence on the fracture permeability, and when the normal stress is low, the relationship between the fracture permeability and shear stress can be described by a linear relationship. Then, the influence of the number of intersection points in the fracture network on the average fracture width, average water pressure, average seepage velocity and seepage passage of the fractured rock mass was analyzed. The number of intersections in the fracture network has little influence on the average fracture gap width and average water pressure but has a great influence on the flow velocity. The analysis in this paper is very helpful to understand the seepage characteristics in rough fractures under normal stress and shear stress.

A new higher order shear and normal deformation theory for FGM sandwich shells

Static and free vibration analysis of simply supported FGM sandwich shells is presented in this paper using a new higher order shear and normal deformation theory. The higher order theory developed herein considers the effects of transverse normal stresses. The theory uses higher order variations of in-plane as well as transverse displacements. Hamilton’s principle is used to formulate the equations of motion. Solutions of simply supported cylindrical and spherical shells are obtained using Navier’s solution technique. Different types of sandwich shells with FGM face sheets and isotropic core are considered for the numerical problems. The present results are compared with previously published results wherever possible to prove the validity of the present theory.

A deviatoric tensile-based critical plane model to predict peak/mean normal stress effects in multiaxial fatigue

This work aims to improve the modeling of peak/mean normal stress effects on multiaxial fatigue lives, applying a deviatoric strain-life model based on the critical plane approach to predict the initiation of tensile-driven cracks. Based on Kujawski’s deviatoric multiaxial fatigue damage parameter, this model assumes the peak deviatoric stress normal to the crack plane controls these effects. Tensile damage models based on deviatoric parameters can solve the main issue with Smith-Watson-Topper’s pioneer model, which is the prediction of no damage in cyclic compression-compression load histories. A calibration procedure based on Coffin-Manson parameters is presented, without the need for additional data-fitting constants to predict peak/mean stress effects. The calibrated multiaxial model is then compared with other tensile-based models for five structural metallic alloys, involving an extensive dataset with 312 uniaxial, torsion, and tension–torsion tests. It is found that the deviatoric formulation is able to explain the fatigue crack initiation behavior under highly compressive mean stresses, including the challenging case of compression-compression loadings. Under zero or positive mean stresses, this formulation provides similar predictions as the Smith-Watson-Topper model, reproducing the observed peak stress effects. Uniaxial versions of this deviatoric model are also presented and calibrated, showing that the minimum instead of the peak stress controls the damage parameter in uniaxial fatigue tests under highly compressive mean loads.

Viscous normal stresses and fingertip tripling in radial Hele-Shaw flows.

Viscous fingering in radial Hele-Shaw cells is markedly characterized by the occurrence of fingertip splitting, where growing fingered structures bifurcate at their tips, via a tip-doubling process. A much less studied pattern-forming phenomenon, which is also detected in experiments, is the development of fingertip tripling, where a finger divides into three. We investigate the problem theoretically, and employ a third-order perturbative mode-coupling scheme seeking to detect the onset of tip-tripling instabilities. Contrary to most existing theoretical studies of the viscous fingering instability, our theoretical description accounts for the effects of viscous normal stresses at the fluid-fluid interface. We show that accounting for such stresses allows one to capture the emergence of tip-tripling events at weakly nonlinear stages of the flow. Sensitivity of fingertip-tripling events to changes in the capillary number and in the viscosity contrast is also examined.

The Effect of Joint Roughness on Shear Behavior of 3D-Printed Samples Containing a Non-Persistent Joint

The goal of this paper is to study the applicability of 3D printing technology to assess the effect of joint roughness on the shear strength of weakness planes with non-persistent discontinuities. Three disc-shaped profiles were generated to make joints with low, intermediate, and high levels of roughness. Powder-based 3D printing technology was applied to provide two types of samples: Type-A samples (joint samples) and Type-B samples (samples with a non-persistent joint). Type-A samples were printed to assess the shear behavior of 3D-printed joints, and Type-B samples were printed to investigate the joint roughness and rock bridge cohesion contributions to the shear strength of partially discontinuous planes. For comparison purposes, several plaster samples containing a non-persistent joint were cast as well. Three series of direct shear experiments were performed on Type-A, Type-B, and plaster samples under constant normal load conditions. The effects of two parameters, namely normal stress and joint roughness, on the shear behavior of the 3D-printed specimens were separately investigated, and the interaction between them was analyzed. The evaluation of the experimental results indicates the existence of two-way interaction between the joint roughness and the applied normal stress of Type-B samples. The experimental results obtained from plaster samples were compared with those obtained from Type-B samples. The comparison reveals that 3D-printed samples properly reflect the effects of joint roughness and normal stress on the shear strength of partially discontinuous planes, although their prepeak and post-peak behaviors are different from those of plaster specimens.

On a vertical chain of small bubbles ascending in a viscoelastic fluid

Recently, our direct numerical simulations [Yuan et al., “Hydrodynamic interaction and coalescence of two inline bubbles rising in a viscoelastic liquid,” Phys. Fluids 33, 083102 (2021)] indicated that a stable chain can be formed for a pair of bubbles rising in a viscoelastic liquid, consistent with experimental observations. Motivated by the fact that the flow in bubble chains is still poorly understood, this Letter extends the investigations to multiple small bubbles ascending in a vertical file in a viscoelastic medium with different configurations. With an increasing bubble number, it is found that the rising velocity of the bubble group increases and the vertical chain of bubbles becomes unstable due to the distinct oscillation of the uppermost bubble. The terminal separation distance between two adjacent bubbles decreases in the upward direction, diminished by the neighborhood rising bubbles due to increasing loading. By probing the polymeric stresses and deformation, our results demonstrated that the accumulation of viscoelastic normal stresses promotes the aggregation of rising bubbles, while the successive chain of bubbles is stable because of the near-field repulsion induced by the non-monotonic polymer stretching among the bubble chain. In addition, the large bubble deformation appears to enhance the accumulative polymeric normal stress effect, and the bubbles can form more stable vertical chains at increasing initial spacing. Our findings provide insights into the mechanism of bubbles clustering in viscoelastic fluids, as chaining of bubbles is believed to be more prevailing in highly elastic flows.

Analytical model of the shear behaviors of bolted rough joints based on the dilation effect and surface abrasion

Rock bolts have been widely employed on slopes as a reinforcement measure. Modeling the shear mechanical behaviors of bolted rock joints is very complicated due to the complex factors that affect the axial and shear forces on the bolts. The rough surface of the joint surface undergoes a dilation effect and morphological abrasion under shearing. However, existing analysis models do not fully consider these effects. This study proposes an analytical model for predicting the shear behaviors of bolted rough joints. The model considers the relationship between the dilation effect and the bolt deformation and the influence of joint surface abrasion on the attenuation of the internal friction angle. Moreover, the axial force development is corrected at a bolt installation angle of 90 degrees, and the effect of the initial normal stress of the joint surface on the deformation and fracture of the bolt is also considered. The analysis model successfully predicts the shear load-shear displacement curve of the anchoring joint and the change curve of the anchor shaft force. The analysis model is verified by an indoor direct shear test. The validation shows that the proposed model can effectively describe the deformation characteristics of the bolts in shear tests.

Morphologic characterization and fractal analysis of lapped and polished surfaces of quartz single crystals.

Lapping and polishing are industrial processes sometimes used alternatively for surface finishing of hard and brittle materials. This article presents advanced image analysis of surfaces of quartz crystal blanks finished by lapping and polishing. Scanning electron micrographs were obtained from workpiece surfaces parallel to Y-, AT-, and Z-cut crystal planes treated with different normal stress and abrasive grit size, and stereometric and fractal/multifractal approaches were used to analyze the respective surfaces. Fractal dimensions and segmentation parameters were able to decode the effect of normal stress increasing on the surface roughness of lapped and polished samples. Moreover, the texture isotropy and the bifractal-hence agglomerated-nature of the surface patterns, suggest that both treatments dismiss the anisotropic signature of hardness and fracture toughness inherent to each crystal plane. This study provides promising results regarding the applicability of fractal analysis in the assessment of surfaces severely worn by the combined effect of brittle microcracking and plastic deformation mechanisms.

Water Film Drainage between a Very Viscous Oil Drop and a Mica Surface.

We investigate thin film drainage between a viscous oil drop and a mica surface, clearly illustrating the competing effects of Laplace pressure and viscous normal stress (τ_{v}) in the drop. τ_{v} dominates the initial stage of drainage, leading to dimple formation (h_{d}) at a smaller critical thickness with an increase in the drop viscosity (the dimple is the inversion of curvature of the drop in the film region). Surface forces and interfacial tension control the last stage of film drainage. A scaling analysis shows that h_{d} is a function of the drop size R and the capillary numbers of the film (Ca_{f}) and drop (Ca_{d}), which we estimate by h_{d}=0.5Rsqrt[Ca_{f}/(1+2Ca_{d})]. This equation clearly indicates that the drop viscosity needs to be considered when Ca_{d}>0.1. These results have implications for industrial systems where very viscous liquids are involved, for example, in 3D printing and heavy oil extraction process.

Experimental investigation of the effects of loading rate, contact roughness, and normal stress on the stick-slip behavior of faults

The tectonic movement rate, in situ stresses (e.g., normal stress) and fault roughness may change during the long evolutionary histories of seismogenic faults. To investigate the effects of these three factors on fault slip behaviors, we conducted direct shear tests by sequentially changing the shear loading rate and normal stress on small-scale granite specimens under three roughness conditions. We found that for a given fault system, the shear loading rate is a primary controlling parameter of the recurrence intervals of stick-slip events, and the correlation between them can be empirically expressed by a power law. Stick-slip recurrence intervals can influence the stress drops of stick-slip events via two different tendencies. The shear stress drops increase quasilinearly with the recurrence intervals at a given shear loading rate, while the combined data from all shear rate tests show that the shear stress drops increase with the logarithm of the recurrence time. In the investigated range of fault roughness, we observed that surface roughness conditions strikingly affect the sliding mode and recurrence frequency of stick-slip events. In detail, the two smooth fault systems slide with regular stick-slip events, and the roughest fault system exhibits bimodal behavior. Namely, at lower normal stresses, stick-slip events cannot be stably generated, a few were occasionally generated, and regular stick-slip events were interrupted by local stick-slip. When the applied normal stress is sufficiently high, the fault slides with continuous regular stick-slip events in the same way as those in the smoother fault systems. We further noticed that the recurrence frequency of stick-slip and friction drop are correlated at a fixed sliding distance, and this relationship can be described by an inverse proportional function. Our results suggest that all three factors, namely, shear loading rate, fault surface roughness and normal stress, can influence the behaviors of fault slip and hence are important for evaluating earthquake hazards.

Slip behavior of rough rock discontinuity under high velocity impact: Experiments and models

The slip shear failure along rock discontinuities is one of the predominant failure modes of landslides. To simulate impact shear loads during landslide and rockburst, an experimental method is presented to achieve the dynamic shear load in a direct shear testing configuration. The dynamic loading system is derived from the SHPB methodology and can provide high shear velocities around 1–10 m/s. Dynamic direct shear experiments on rough rock discontinuities are conducted by using a dynamic shear apparatus combined with a high-speed digital camera. The effects of shear velocity and normal stress on the slip displacement, slip velocity and slip acceleration of rough rock discontinuities are analyzed using a two-dimensional digital image correlation (DIC) technique. It is observed that the rate of the slip is linearly proportional to the shear velocity and decreases with the increasing normal stress. Using the DIC method, the strain at failing asperities is calculated as a function of the shear velocity and the normal stress. The micro-structural characteristics of the shear zone formed in the slip failure is examined to understand the slip failure mode. Moreover, the dynamic viscous is added to the static Barton's shear strength criterion and the damage evolution occurred at the asperities due to the dynamic loading is introduced by means of a damage control parameter D. Thereafter, a dynamic failure criterion is developed by considering both surface roughness and dynamic loading. The failure model can provide a good prediction of the experimental data, indicating that the proposed models can describe well the dynamic shear process of rock discontinuities under high velocity impact.

Fiber-Matrix Interaction and Fiber Orientation in Simple Shearing of Fibrous Soft Tissues

Fiber-reinforcement is a common feature of many soft biological tissues. The response of fibrous biotissues to applied shear is thus of considerable current interest. We consider here the fundamental deformation of simple shear within the framework of transversely isotropic incompressible hyperelastic materials for fiber-reinforced specimens with a single family of parallel fibers oriented at a general angle to the direction of shear. It is well known that the normal stress effect characteristic of nonlinear elasticity plays a crucial role in maintaining an homogeneous deformation state in the bulk of the specimen. Here we investigate the effects of fiber-matrix interaction on the shear and lateral normal stresses. The inclusion of fiber-matrix interaction stiffens the shear stress response. As regards the normal stress, it is shown that the confining normal traction that needs to be applied to the top and bottom faces of a block in order to maintain simple shear can be compressive or tensile depending on the degree of anisotropy, fiber-matrix interaction and on the angle of orientation of the fibers. In the absence of such an applied traction, an unconfined sample tends to bulge outwards or contract inwards perpendicular to the direction of shear so that one has the possibility of both a positive or negative Poynting effect. It is shown that the fiber-matrix interaction enhances both the positive and negative Poynting effects. The results are illustrated using experimental data obtained by other authors for porcine brain white matter. In particular, it is shown that, for sufficiently small angles of orientation, a transition amount of shear exists at which the normal stress changes character from tensile to compressive with increasing amount of shear. An increase in the degree of fiber-matrix interaction enlarges the range of orientation angles for which this transition can occur and decreases the transition amount of shear. These transition amounts of shear are well within the physiological strain regime. The results obtained here are relevant to the development of accurate shear test protocols for the determination of constitutive properties of fibrous biological soft tissues.

Behavior of discrete fiber-reinforced sandy soil in large-scale simple shear tests

This study presents results from a series of large-scale simple shear tests performed on sandy soil reinforced with randomly distributed fibers. The soil was mixed with polypropylene, glass and basalt fiber, respectively, with fiber content varying from 0% to 2% and sheared under a normal stress ranging from 100 kPa to 300 kPa. The effects of fiber type, content and normal stress on shear strength and the dilatancy behavior were examined. The friction state theory was employed to interpret the influence of fiber reinforcement on the dilatancy behavior. The results indicate that the additions of polypropylene and basalt fibers are beneficial to enhancing ultimate shear strength, whereas the glass fiber makes little contribution. It is shown that the fiber inclusion hinders the close packing and interlocking of soil particles and hence produces relatively looser soil fabric in the as-compacted state, leading to increased volume contraction accompanied by a negligible improvement or even reduction in shearing stiffness over a small to moderate strain range. The most obvious increase in shear strength generally occurs at a shear strain exceeding 10%, where the fibers and particles are in tight contact with each other, allowing full interface interaction and the mobilization of fiber tensile strength.

A shear damage model of the interface between soil and sulfate-corroded concrete

In order to investigate the mechanical properties of the interface between sulfate-corroded concrete piles and soil, a corrosion shear damage model and a method to determine the model parameters were proposed based on statistical damage theory. Assuming that the corrosion damage of the interface obeys Weibull random distribution, a damage model is established, which contains only six parameters. By fitting curves, the model parameters are obtained from the interface direct shear test. The shear damage model can not only predict the shear deformation behaviors, but also consider the effects of normal stress and corrosion time on the shear properties of the interface after corrosion. The results show that the shear stress-displacement relationships are significantly affected by normal stress and corrosion time. The peak shear stress increases with normal stress, and the corresponding peak shear displacement also increases. The longer the corrosion time is, the less obvious the shear softening phenomenon of soil-concrete interface is, and as the corrosion time reaches a threshold level, the softening phenomenon of shear stress-displacement relationship changes into weak softening. Finally, the rationality and feasibility of the proposed model are verified by comparing the theoretical curves with the experimental curves.

Deformation and failure behaviours of rock-concrete interfaces with natural morphology under shear testing

The shearing performance and strength of the interface between rock foundations and structural concrete is a key issue for safety estimation in geotechnical engineering containing rock-concrete interface. In this paper, we focused on the effects of concrete wall strength and normal stress on the unbonding performances of sandstone-concrete interface. First, many sandstone-concrete specimens containing a natural dam bedrock interface had been produced by using “3D optical scanning technology + 3D digital engraving technology + pouring concrete” method. Subsequently, after the sandstone-concrete specimens were prepared, a series of shear tests for these sandstone-concrete specimens were carried out under different normal loading conditions. Finally, the shear characteristics of sandstone-concrete interface were discussed, and an improved rock-concrete shear strength formula was proposed based on the exposed experimental tests and theoretical derivation. Three primary outcomes are as follows: (i) shear damage only occurred at some special positions of the concrete wall, and its degree of shear damage gradually increased with increasing normal stress; (ii) the damage degree of the concrete surface performed obvious localization and nonuniformity was affected by the concrete strength; (iii) the global shear strength and residual strength of the rock-concrete interface were affected by the concrete strength and the normal load. Moreover, an improved rock-concrete shear strength formula was proposed based on the experimental cognition. This strength formula considers both the interface roughness and the mechanical strength of rock/concrete materials, and is more reasonable for estimating the shear strength of rock-concrete interfaces in geotechnical engineering.

Seismic reflectivity and transmissivity parametrization with the effect of normal in situ stress

SUMMARY In situ stress has a significant effect on the properties of underground formations, including seismic wave velocity, porosity and permeability, and further affects seismic reflectivity and transmissivity. Research works on the effect of in situ stress are helpful to construct more precise seismic reflection and transmission coefficient equations. However, previous studies on seismic reflectivity equations did not take the effect of normal in situ stress into consideration. The mechanism of stress on seismic reflectivity and transmissivity is still ambiguous. In this study, we propose new explicit equations to help analyse the changes of seismic reflectivity and transmissivity under the effect of normal in situ stress. First, we deduce the Christoffel equation on the basis of solid acoustoelastic theory. Then, we utilize appropriate boundary conditions to formulate analytical equations of the reflectivity at the interface between two stressed formations, which can provide some new insights into the role of in situ stress. The shear wave birefringence will vanish because we assume that the wave propagates in the X–Z plane. Different rock models with different lithology and saturation are used to analyse the variation of seismic reflectivity and transmissivity with normal stress and incident angle at the interface. The main effect of normal stress on reflection and transmission coefficients is to change amplitude and critical incident angle. When the upper and lower layers are sandstones, the critical incident angle decreases with the increase of normal in situ stress, which is consistent with previous studies. In addition, the reflectivity equation can be degenerated to the Zoeppritz equation when the normal in situ stress vanishes, which further validates that the equation proposed is correct. Seismic reflectivity equations that couple the effect of stress can lay a foundation for direct prediction of in situ stress.