Asperity Angle Research Articles

Experimental Study on the Shear Strength of Sandy Clay Infilled Regular Rough Rock Joints

Infill materials in rock joints usually cause a reduction in the joint shear strength. The shear behavior of rock discontinuities depends upon whether they are clean and unfilled or filled, so this concern invites accurate understanding of the shear behavior and strength of infilled joints. A series of constant normal load direct shear tests was performed to investigate the shear strength of artificial samples with infilled rough joint surfaces having different asperity and infill characteristics. The current study focuses on the effects of factors that influence the shear strength of infilled rock joints samples, with emphasis on forward and reverse shearing. In the forward cycle, the front joint wall is compressed and possibly sheared, and the back side fill is unbonded from the joint surface and slightly disturbed. In the reverse cycle, the disturbed and weakened back side fill is under shearing. The effect of the normal stress on the joint is studied, as this factor plays an important role on the shear behavior of infilled rock joint samples. The results show that joints with low asperity angle exhibit higher shear strength during the forward shearing cycle than the reverse cycle, but in joints with steeper asperity angle, the reverse cycle exhibits greater shear strength. In the reverse cycle, the joint infill has less influence compared to the effect of the rougher surface and higher asperity inclination, even in higher normal stress.

Influence of surface asperities on interfacial extension during solid state pressure welding

The interfacial contact and extension of two joining surfaces are numerically studied using a finite element method. The joining surface is assumed to have two-dimensional triangular asperities. Surface-asperity-induced voids are formed at the initial contact. The interfacial extension of the initial contact area is very different from that of void surface area. The initial void surface area shrank once before full contact was attained. The large asperity angle facilitates interfacial extension and void-surface shrinkage, resulting in the formation of numerous metallic bonds. The pressure-welding-induced interfacial extension and metallic bond formation are largely influenced by the asperity angle, whose effects are experimentally confirmed.

A model for predicting wear rates in tooth enamel

It is hypothesized that wear of enamel is sensitive to the presence of sharp particulates in oral fluids and masticated foods. To this end, a generic model for predicting wear rates in brittle materials is developed, with specific application to tooth enamel. Wear is assumed to result from an accumulation of elastic–plastic micro-asperity events. Integration over all such events leads to a wear rate relation analogous to Archard׳s law, but with allowance for variation in asperity angle and compliance. The coefficient K in this relation quantifies the wear severity, with an arbitrary distinction between ‘mild’ wear (low K) and ‘severe’ wear (high K). Data from the literature and in-house wear-test experiments on enamel specimens in lubricant media (water, oil) with and without sharp third-body particulates (silica, diamond) are used to validate the model. Measured wear rates can vary over several orders of magnitude, depending on contact asperity conditions, accounting for the occurrence of severe enamel removal in some human patients (bruxing). Expressions for the depth removal rate and number of cycles to wear down occlusal enamel in the low-crowned tooth forms of some mammals are derived, with tooth size and enamel thickness as key variables. The role of ‘hard’ versus ‘soft’ food diets in determining evolutionary paths in different hominin species is briefly considered. A feature of the model is that it does not require recourse to specific material removal mechanisms, although processes involving microplastic extrusion and microcrack coalescence are indicated.

절리면의 거칠기 변화가 전단강도에 미치는 영향

Multi-stage shear test has been performed using joint specimens of gneiss, granite and shale to investigate the influence of micro-scale asperity change on the shear strength of joint plane. For each shear test asperity degradation characteristics of joint specimens of different joint surface strength have been analyzed by utilizing the optimum asperity parameter which can reflect the sequential asperity degradation. Elevation of joint surface profile has been measured and both the changes of asperity parameters and micro-scale asperity distribution have been investigated. Two distinctive variation modes of cohesion and friction angle have been delineated and major cause of shear strength parameter change has been analyzed by considering the micro-scale asperity angle change resulting from the abrasion, fracturing and regeneration of micro-scale asperities. Effects of micro-scale asperity variation on the joint shear strength have been also investigated.

Development of a Large-Scale Direct Shear Testing Machine for Unfilled and Infilled Rock Joints Under Constant Normal Stiffness Conditions

In the past, numerous studies have been undertaken to understand the shear behavior of unfilled and infilled rock joints by conducting tests on conventional direct shear apparatus, where normal load is kept constant during the shearing process. This is suitable for planar joints, but rock joints are seldom planar, and, in reality, normal stress on the shearing plane is not constant and testing such rock joints by conventional direct shear apparatus will give inappropriate results. The estimation of correct shear strength is important for safe and economical design of underground openings in jointed rocks, stability analysis of anchored rock slopes, risk assessment of underground waste disposal repositories, design of foundations on rock, and socketed piles in rock. Hence, in the present study, a servo-controlled large-scale direct shear testing machine is designed and fabricated to test the rock samples under varying normal load, i.e., constant normal stiffness (CNS) conditions. Direct shear tests have been performed on physically modeled unfilled and infilled rock joints with asperity angle 30°–30°, at different initial normal stress (Pi). The test results indicate that the CNS conditions greatly influence the shear behavior of rock joints.

Effects of Cyclic Loading on the Shear Behaviour of Infilled Rock Joints Under Constant Normal Stiffness Conditions

The variation of the shear strength of infilled rock joints under cyclic loading and constant normal stiffness conditions is studied. To simulate the joints, triangular asperities inclined at angles of 9.5° and 18.5° to the shear movement were cast using high-strength gypsum plaster and infilled with clayey sand. These joints were sheared cyclically under constant normal stiffness conditions. It was found that, for a particular normal stiffness, the shear strength is a function of the initial normal stress, initial asperity angle, joint surface friction angle, infill thickness, infill friction angle, loading direction and number of loading cycles. Based on the experimental results, a mathematical model is proposed to evaluate the shear strength of infilled rock joints in cyclic loading conditions. The proposed model takes into consideration different initial asperity angles, initial normal stresses and ratios of infill thickness to asperity height.

A Fractal-Based Model for Fracture Deformation Under Shearing and Compression

This study presents an improved model for calculating mechanical deformation of individual fractures subject to shearing and compression processes. Considering that the fracture-surface roughness can be characterized by fractals, a relationship between asperity angle and size of a fracture with fractal surfaces is derived. In addition, plastic work is employed to account for the effects of fracture-asperity degradation during the shearing process. Based on these developments, a scale-dependent relationship between shear stress and displacement is proposed, and also a formulation to calculate fracture aperture during shearing and compression processes is developed, by relating normal displacement to shear displacement for fractal surfaces. The usefulness of this model is demonstrated by agreements between calculated results and observations from laboratory experiments under different test conditions.

A macrostructural model for simulating the combined effects of roughness and plasticity induced fatigue crack closure

We adapt a weight function based modified strip-yield model to geometrically include the mode I effects of roughness induced crack closure. A rough crack geometry is simulated as a sine wave fitted to a sawtooth defined by an asperity angle and period. Additional crack closure due to the sliding of crack faces is incorporated into the strip-yield model by lengthening and shortening the crack face elements, creating a sawtooth-like crack wake. We study combined roughness and plasticity induced crack closure by varying the crack face asperity angle and period. The addition of rough crack face geometry effects causes the amount of crack closure to oscillate above and below an average value influenced primarily by the asperity angle. The periodicity of the rough crack has little or no effect on closure.

A study of combined roughness and plasticity induced fatigue crack closure for long cracks using a modified strip-yield model

Combined roughness- and plasticity-induced crack closure for long cracks is studied using a Design and Analysis of Computer Experiments approach. A newly developed modified strip-yield model which has been adapted to incorporate the mode I effects of roughness induced crack closure is used for the study. The effects of maximum stress, load ratio, roughness asperity angle, and roughness periodicity are quantified. In addition, conditions affecting the benefit of roughness-induced crack closure are investigated.

Effects of Surface Roughening on Asperity Flattening

A series of experiments have been conducted using aluminum strips, which manifest a strong tendency toward roughening in forming processes, to investigate the evolvement of surface roughness and its resistance to flattening. The strips are stretched to specific bulk strains and are then compressed by a smooth glass at various pressures. It is found that except for very high bulk strain, the free surface on the transverse specimen roughens more seriously and irregularly than the longitudinal one due to the fierce rotations of grains, which make the grains parallel to the straining direction and eventually mutate the topography into an isotropic one. As the roughened surface is compressed, the transverse specimen may roughen further in the case of large bulk strain. According to the finite element method (FEM) analysis using serrated surfaces, the sharper asperity undergoes more serious straining on its peak and basically such a strain increment is not affected by the degree of flattening. The ability to resist flattening, defined as the “asperity hardness,” varies with asperity angle as well as the enhanced shear strength on the asperity tip, rather than the substrate. A new quantitative description of the asperity hardness is suggested, and the new calculated contact area ratios are in good agreement with the experiments except for very high pressure where additional mechanics such as adiabatic recrystallization might happen. The concept of the additional hardening on asperity peaks can be employed to refine the prediction of asperity contact in the analysis of metal forming.

A shear strength model for idealised infilled joints under constant normal stiffness

Infill materials found in natural rock joints may cause a reduction in joint shear strength, influencing rock mass stability. This paper reports a study aimed at developing a semi-empirical methodology for predicting the shear strength of infilled joints, taking into account joint surface characteristics and the properties of the joint and infill materials. A new model for predicting the shear strength of infilled joints is presented, on the basis of a series of tests carried out on two types of model joint surface having asperity angles of 9·5° and 18·5°, with graphite and bentonite used as infill materials. All tests were carried out in a large-scale shear apparatus under constant normal stiffness (CNS) conditions. The results indicate that at low infill thickness to asperity height ratio (t/a), the combined effect of the basic friction angle (ϕb) and the joint asperity angle (i) is pronounced, but it diminishes with increasing t/a ratio so that the shear strength converges towards that of the infill alone. Summation of two algebraic functions (A and B) that represent the joint and infill characteristics correctly models the decay of normalised shear strength with increasing t/a ratio. The new model successfully describes the observed shear strengths of the graphite and clay (bentonite) filled model joints.

A shear strength model for idealised infilled joints under constant normal stiffness

Infill materials found in natural rock joints may cause a reduction in joint shear strength, influencing rock mass stability. This paper reports a study aimed at developing a semi-empirical methodology for predicting the shear strength of infilled joints, taking into account joint surface characteristics and the properties of the joint and infill materials. A new model for predicting the shear strength of infilled joints is presented, on the basis of a series of tests carried out on two types of model joint surface having asperity angles of 9·5° and 18·5°, with graphite and bentonite used as infill materials. All tests were carried out in a large-scale shear apparatus under constant normal stiffness (CNS) conditions. The results indicate that at low infill thickness to asperity height ratio (t/a), the combined effect of the basic friction angle (ϕb) and the joint asperity angle (i) is pronounced, but it diminishes with increasing t/a ratio so that the shear strength converges towards that of the infill alone. Summation of two algebraic functions (A and B) that represent the joint and infill characteristics correctly models the decay of normalised shear strength with increasing t/a ratio. The new model successfully describes the observed shear strengths of the graphite and clay (bentonite) filled model joints.

Abrasiveness Variation in a Thin Boron Carbide Coating

Boron carbide (B4C) is well known for its high hardness and wear resistance. It has been found to polish its mating surface, thereby providing fatigue resistance to the coated part. Employing such run-in coatings demands a thorough understanding of the abrasiveness changes that the coatings undergo during the polishing process. Both the coating asperity height and angle of attack were investigated as a function of sliding distance and were correlated with changes in the coating abrasiveness. Furthermore, a semi-empirical equation relating the coating abrasiveness, the asperity height and the asperity angle of attack was presented.

Behavior of Dilative Sand Interfaces in a Geotribology Framework

Frictional resistance along the exterior of an embedded structure or structural element develops through relative displacement at the interface. An understanding of how surface topography influences interface strength and deformation behavior is required to develop comprehensive interface models for soil-structure analyses, to develop interface design methods and for producing enhanced construction materials. This paper presents the results of an investigation to quantify the influence of surface topography on shear stress and volume change behavior of dilative granular material interface systems. The root spacing, asperity spacing, asperity height, and asperity angle of machined, idealized surfaces are systematically varied. Direct interface shear test results using Ottawa 20/30 sand and glass microbeads show that maximum interface efficiency for these materials is achieved for a asperity spacing to median grain diameter ratio between 1.0 and 3.0, and an asperity height to median grain diameter ratio greater than 0.9. An asperity angle of 50 degrees or greater yields maximum efficiency for any given asperity spacing or height. The results suggest that interface behavior is governed by predictable geometric and mechanical relationships that are applicable to more complex manufactured surfaces.

Behaviour of joints containing clay infill under constant normal stiffness, with and without bolting

The shear behaviour of bolted and non-bolted joints containing infill material was studied under the constant normal stiffness condition. More than 40 sawtooth-shaped samples having an asperity angle of 18·5° were tested. The shear behaviour of bolted and non-bolted joints containing infill material, up to 7·5 mm in thickness, was studied under various initial normal stress levels between 0·13 and 3·25 MPa, at a constant strain rate of 0·5 mm/min and a constant stiffness of 8·5 kN/mm. Significant reduction in shear strength was observed when the joint contained a layer of clay infill of 1·5 mm. Bolting contributed to increasing the strength and stiffness of the joint composite, except at large normal stress levels and at high infill thickness. The dilation and overall friction angle for bolted and non-bolted joints were also compared along with stress profiles. At high infill thickness, the shear behaviour under both constant normal load (CNL) and constant normal stiffness (CNS) conditions was found to be similar for both bolted and non-bolted joints, while at low infill thickness the CNL strength envelope plotted significantly above the CNS envelope.

Behaviour of joints containing clay infill under constant normal stiffness, with and without bolting

The shear behaviour of bolted and non-bolted joints containing infill material was studied under the constant normal stiffness condition. More than 40 sawtooth-shaped samples having an asperity angle of 18·5° were tested. The shear behaviour of bolted and non-bolted joints containing infill material, up to 7·5 mm in thickness, was studied under various initial normal stress levels between 0·13 and 3·25 MPa, at a constant strain rate of 0·5 mm/min and a constant stiffness of 8·5 kN/mm. Significant reduction in shear strength was observed when the joint contained a layer of clay infill of 1·5 mm. Bolting contributed to increasing the strength and stiffness of the joint composite, except at large normal stress levels and at high infill thickness. The dilation and overall friction angle for bolted and non-bolted joints were also compared along with stress profiles. At high infill thickness, the shear behaviour under both constant normal load (CNL) and constant normal stiffness (CNS) conditions was found to be similar for both bolted and non-bolted joints, while at low infill thickness the CNL strength envelope plotted significantly above the CNS envelope.

Influence of asperity degradation on the mechanical behavior of rough rock joints under cyclic shear loading

A cyclic shear testing system was established to investigate the mechanical behavior of rough rock joints under cyclic loading conditions . Laboratory cyclic shear tests were conducted for two joint types of Hwangdeung granite and Yeosan marble: saw-cut and split tensile joints. Prior to test, the roughness of each specimen was characterized by measuring the surface topography using a laser profilometer . Several important aspects of cyclic joint behavior, such as high peak shear strength and non-linear dilation in the first loading cycle, different frictional resistance for the reversed shear loading direction, and anisotropic shear behavior and its dependence on the normal stress level were identified from the cyclic shear test results. These features and their variations in the subsequent loading cycles are mainly due to the effect of second order asperities and strength of rock material. It was also observed from experimental results that degradation of asperities under cyclic shear loading also followed the exponential degradation laws for asperity angle and the mechanism for asperity degradation would be different depending upon the shearing direction and the type of asperities. Based on the experimental results an elasto-plastic constitutive model, which can consider the degradation of second order asperities, was proposed. Numerical simulations for the monotonic and cyclic shear loading indicated agreement with the laboratory test results.

An experimental study on the progressive shear behavior of rock joints with tooth-shaped asperities

Rock mechanics have commonly tended to focus on static stability where the initial peak shear strength is the principal concern. Recently, a need has arisen to assess dynamic stability because of an increased concern for earthquake, rock burst and explosion safety. Many computer models of rock masses [1–3] are usually based on the superposition or extrapolation of static experimental results. As numerical analysis capabilities increase, a means is required for obtaining a complete shear stress–displacement relationship for rock joints from pre-peak to their residual state. Essentially, the shear stress–displacement curves of rock joints generally fall into two classifications. Some shears reach peak strength, drop off rapidly and finally taper off in strength to a residual value. Others behave more or less plastically with little or no distinct peak. Actually, this type of shear stress–displacement curve is greatly influenced by the joint surface roughness. These changes can be related to the selective destruction of the asperities present on both joint faces. Because this information is not usually compiled, the transition from peak to residual values is often assumed to decrease either linearly or exponentially when the joints exhibit strain softening behavior [4–6]. Understanding the progressive failure process after the first peak strength is a meaningful matter. Joint roughness has an essential influence on the development, and as a consequence, the shear strength of joints. To date, joint roughness has only been considered as a dilation parameter that effectively increases the friction angle above the basic friction angle by some angle. Generally, the dilation term is not constant, but gradually decreases due to the asperities being destroyed with the increase in shear displacement. Patton [7] recognized that the asperity of rough joints occurs on many scales. He first categorized asperity into first-order (waviness) and second-order (unevenness) categories. The behavior of rock joints is controlled primarily by the second-order asperity during small displacements and the first-order asperity governs the shearing behavior for large displacements. Barton [8] and Hoek and Bray [9] also stated that at low normal stress levels the second-order asperity (with highestangle) controls the shearing process. As the normal stress increases, the second-order asperity is sheared off and the first-order asperity (with a longer base length and lower-angle) takes over as the controlling factor. In numerical modeling, Cundall et al. [10] intended to simulate the intrinsic mechanism of progressive joint damage under shear illustrated in Fig. 1. This is based on the hypothesis that the asperity roughness is not a constant attribute and account must be taken for the effects of changes in roughness, due to asperities being worn down and destroyed. He assumed that a complete shear stress-displacement curve of a rock joint is made up of many sizes of asperities, such that the resultant curve is more or less a summation of many basic curves. In his report, two basic curves for a given tooth-shaped asperity were proposed. These curves depend upon the normal stress level and asperity angle. At lower normal stress (see Fig. 1), shear stress initially causes elastic deformation of the asperity up to the yield deformation. The sliding of one asperity up over another (dilation of the joint) then follows. At a certain shear displacement, the resistance of the asperity is exceeded and shearing through the asperity occurs. Further shearing leads to residual shearing resistance along the newly created surface. At high normal stress, no dilation occurs and the asperities are immediately sheared off at the base. In order to enhance the applicability of this constitutive *Corresponding author. Tel.: +886-2623-4215; fax: +886-26209747. E-mail addresses: yang@freebsd.ce.tku.edu.tw (Z.Y. Yang).

Surface Roughening and Contact Behavior in Forming of Aluminum Sheet

The evolution of the surface topography and tool-workpiece contact behavior of an aluminum sheet during plastic deformation has been investigated by a series of indentation tests for various loads, strain rates, and bulk strains. A simple formulation for estimating the roughness of the indented surface and a model of asperity flattening have been proposed. Dynamic balance between the flattening and roughening processes, such as changes of asperity angle and spacing, is considered. Theoretical predictions of the variation of real area of contact with strain show good agreement with experiments. It is found that the very different frictional behavior of aluminum compared with steel sheets is due to the serious change of roughness, including asperity angle and spacing. When the angle is small, the increases in asperity angle and spacing have strong effect on increasing the contact area ratio. However, when the asperity angle is large, increased asperity angle has a significant contribution to the resistance to flattening. The asperity flattening velocity and the increasing rate of contact area ratio arise with the prestrain; however, they are not affected by the strain rate significantly. From FFT analysis, low frequency components (below 10 cycle/mm) due to the rotation of single grains or grain groups are observed on free surface during plastic straining. While in the contact area, in all cases, the low frequency components generated by plastic deformation are compressed.

A model for sliding mode crack closure part I: Theory for pure mode II loading

A physical model has been developed to quantify the sliding mode crack closure (SMCC) experienced in cyclic mode II loading conditions. Idealized crystallographic surface geometry and Coulomb friction behaviour were assumed in the model. The results reveal that faceted crack surfaces will generate a local wedging mode I component while frictional attenuation tends to reduce the effective mode II stress intensity factor range. It is found that asperity angle and friction coefficient are two fundamental factors influencing near-threshold fatigue crack growth behaviour during the entire fatigue cycle. The local stress-strain field is significantly altered due to the wedging mode I component and frictional attenuation of the nominal mode II component. It is concluded that ideal mode II loading may never be achieved in practice for polycrystalline materials due to the inevitable existence of local mixed mode loading conditions.