Peak Friction Research Articles

The Influence of the Fractal Dimension on the Mechanical Behaviors of the Soil–Rock Mixture: A Case Study from Southwest China

As the typical multi-phase geotechnical material, the particle size distribution of the natural soil–rock mixture (S–RM) has a significant impact on the structural and mechanical properties. The coarse grain content used in the laboratory and simulation tests falls short of accurately describing the particle size distribution feature of the entire material. The main subject of this article is the influence of the fractal dimension on mechanical behaviors based on the fractal theory. The double fractal characteristics were principally discussed along with the typical particle size distribution characteristics of the S–RM in the Three Gorges Reservoir and southwest China. The influence of the various fractal dimensions on the mechanical behaviors of S–RM was then investigated using three groups of large–scale triaxial tests, and the responses of the linear and nonlinear strength indexes were analyzed. The results show that the stress–strain curves of S–RM in the hyperbolic shape are visible under various confining pressure, and the nonlinear strength characteristics can be observed. The coarse grain content exhibits a negative correlation to the average fraction dimension. The difference between the coarse and fine grain fraction dimensions becomes considerably more obvious as the coarse grain content increases, which also increases the error when using the average fractal dimension. The voids between the coarse grains cannot be filled with the fine grains as the grain coarseness grows, resulting in a loose structure and a contact frictional effect, which lowers cohesion and raises the peak friction angle.

Shear strength characteristics of two-layer geotextile reinforced with flowable fill

Geosynthetics have been applied in various engineering fields. This study investigates the shear strength of a two-layer geotextile reinforced with a flowable fill. Three types of geotextiles and a flowable fill are used to compare the shear strength characteristics. Direct shear tests on both unreinforced and reinforced geotextiles are performed on three geotextiles under three normal stresses for five curing periods. The experimental results show that the peak and residual shear strengths of the reinforced geotextiles are larger than those of the unreinforced geotextiles. A reinforced geotextile with a higher warp/weft density and crossing-over firmness factor shows significantly higher peak shear strength than the other two geotextiles. The peak and residual strength gains of the reinforced geotextiles depend on the geotextile type and curing period. The peak friction angles of the unreinforced and reinforced geotextiles cured for 28 days are influenced by the weave structure parameters. The two-layer geotextiles reinforced with flowable fill proposed in this study can be adequately used with a better understanding of their shear strength characteristics and influencing factors.

A Discrete Elements Study of the Frictional Behavior of Fault Gouges.

A series of discrete elements simulations is presented for the study of fault gouges' frictional response. The gouge is considered to have previously undergone ultra-cataclastic flow and long-time consolidation loading. We explore the effect of different particle characteristics such as size, polydispersity, and also shearing velocities on gouge's response under the conditions met in the seismogenic zone. Monte-Carlo analyses suggest that the local stick-slip events disappear when averaging over a large number of numerical samples. Moreover, the apparent material frictional response remains almost unaffected by the spatial randomness of particles' position and by the particle's size distribution. On the contrary, the mean particle size controls the formation and thickness of the observed shear bands, which appear after the peak friction is met. Furthermore, the apparent friction evolution fits well to an exponential decay law with slip, which involves a particle size dependent critical slip distance. For the studied conditions and depth, the shearing velocity is found to play a secondary role on the apparent frictional response of the gouge, which highlights the importance of analyses involving multiphysics for studying the rheology of fault gouges. Besides improving the understanding of the underlying physics of the problem, the above findings are also useful for deriving pertinent constitutive models in the case of modeling with continuum theories.

Shear-induced distortion of clay minerals aids in dynamic weakening of shallow faults during earthquakes

Coseismic faulting may activate complicated physicochemical processes in the fault zone through both mechanical deformation and frictional heating. While plenty of work emphasizes the great importance of thermal effects on dynamic fault weakening, less attention has been paid to the mechanochemical effects. We study the effects of mechanochemical changes of chlorite on its dynamic weakening process via low- and high-velocity friction experiments, simultaneous thermal analysis, X-ray diffraction, microstructural observation, and numerical modeling in this work. With higher degrees of deformation, the experimentally sheared chlorite samples generally show more pronounced reductions in the onset temperature of thermal decomposition (Td0; from 561°C to 189°C in the extreme case) and more striking increases in the reaction rate. The exponential-decay formula can well describe the relation between Td0 and the mechanical work (integral of shear stress with respect to displacement) in the shear deformation. Moreover, the presence of pore water and the variation in chlorite content could significantly affect the mechanochemical changes of the sheared chlorite-bearing samples. Taking the markedly lowered Td0 as the characteristic temperature leading to thermal softening of asperity contacts, numerical modeling shows that flash weakening of chlorite-rich samples can be significantly promoted, dwarfing the thermochemical pressurization that is also enhanced by mechanochemical effects though. This is largely supported by high-velocity experiments (∼m/s) performed on the pre-deformed chlorite samples, which show both lower peak friction and fracture energy, and earlier activation of dynamic weakening. Clearly, shear deformation plays a key role in aiding thermally-activated mechanisms in weakening faults and facilitating rupture propagation during earthquakes.

Effect of Swept Shockwave Boundary-Layer Interaction Strength on Surface Skin Friction

This investigation examines the flowfield topology beneath the single fin-generated shockwave boundary-layer interaction as a function of shock interaction strength and incoming boundary-layer thickness. A systematic application of oil film interferometry produced an experimental reconstruction of global skin friction maps for various Mach number and fin angle combinations. To determine the effect of boundary-layer thickness, data from the current study were compared against existing experimental data sets with thinner incoming boundary layers. Results for identically matching flow/geometric conditions show a good agreement between trends seen across the conical region of the interaction and exhibit skin friction coefficient peaks in the same position. Cases corresponding to a relatively thicker boundary layer showed higher skin friction coefficient values along the interaction periphery and upstream regions. An angular scaling was applied to align the inviscid shocks of data sets that matched interaction strength, and the results show similar behavior. The peak skin friction coefficient shows a monotonic increase with increasing shock strength. Conversely, the upstream normalized peak skin friction coefficient depends on boundary-layer thickness and shock strength. These findings indicate that boundary-layer effects are limited to the interaction periphery, whereas viscous effects driven by shockwave–boundary-layer interactions dominate the interior region.

Frictional properties of Opalinus Clay: influence of humidity, normal stress and grain size on frictional stability

SUMMARYThe Opalinus Clay (OPA) is a clay-rich formation considered as a potential host rock for radioactive waste repositories and as a caprock for carbon storage in Switzerland. Its very low permeability (10−19 to 10−21 m2) makes it a potential sealing horizon, however the presence of faults that may be activated during the lifetime of a repository project can compromise the long-term hydrological confinement, and lead to mechanical instability. Here, we have performed laboratory experiments to test the effect of relative humidity (RH), grain size (g.s.) and normal stress on rate-and-state frictional properties and stability of fault laboratory analogues corresponding to powders of OPA shaly facies. The sifted host rock powders at different grain size fractions (<63 μm and 63 < g.s. < 125 μm), at room (∼25 per cent) and 100 per cent humidity, were slid in double-direct shear configuration, under different normal stresses (5–70 MPa). We observe that peak friction, μpeak and steady-state friction, μss, depend on water vapour content and applied normal stress. Increasing relative humidity from ∼25 per cent RH (room humidity) to 100 per cent RH causes a decrease of frictional coefficient from 0.41 to 0.35. The analysis of velocity-steps in the light of rate-and-state friction framework shows that the stability parameter (a–b) is always positive (velocity-strengthening), and it increases with increasing sliding velocity and humidity. The dependence of (a–b) on slip rate is lost as normal stress increases, for each humidity condition. By monitoring the variations of the layer thickness during the velocity steps, we observe that dilation (Δh) is directly proportional to the sliding velocity, decreases with normal stress and is unaffected by humidity. Microstructural analysis shows that most of the deformation is accommodated within B-shear zones, and the increase of normal stress (σn) promotes the transition from strain localization and grain size reduction to distributed deformation on a well-developed phyllosilicate network. These results suggest that: (1) the progressive loss of velocity dependence of frictional stability parameter (a–b) at σn > 35 MPa is dictated by a transition from localized to distributed deformation and (2) water vapour content does not affect the deformation mechanisms and dilation, whereas it decreases steady-state friction (μss), and enhances fault stability.

Study on Blasting Characteristics of Soft-Hard Rock Strata Based on Energy Fields and Particle Expansion Loading Algorithm

Complex geological conditions often make the blasting effect difficult to control. In order to explore the influence of soft-hard rock strata on rock blasting characteristics, based on PFC2D software, combined with particle expansion loading algorithm, the numerical simulation blasting experiments are carried out. Firstly, the rationality of blasting method is verified by single-hole sandstone blasting experiment. Then, the soft-hard composite strata are established, and the single-hole blasting experiments of composite strata, with different distribution thickness of soft rock stratum and hard rock stratum, are carried out. The experimental results are analyzed from three perspectives: crack network state, internal stress of rock mass, and energy field. Results show that (i) the distance between the interface of soft-hard rock and the blasthole seriously affects the blasting effect. The law of crack number varying with the distance is obtained through further analysis. (ii) When detonated in the hard rock, if the structural plane is about 2 times the radius of crushing area from blasthole, the rock mass will be in a relatively high stress state due to the reflection and superposition of stress waves. (iii) When detonated in the hard rock, if the structural plane is about 2 times the radius of crushing area from blasthole, compared with pure hard rock case, the peak kinetic energy and peak friction energy are increased by about 15 times and 2.6 times, respectively, and the peak strain energy is attenuated by 18%.

Pull-out test and numerical simulation of beam-to-wall connection: Masonry in earthen mortar and hardwood timber

The paper investigates frictional behaviour between hardwood timber and masonry in earthen mortar, Masonry in earthen mortar and hardwood timber are typical construction materials in part of Asian countries. An experiment and numerical analysis were carried out. As the experiment, a pull-out test was performed on specimens composed of a masonry wallet and timber beam. The test was conducted under three levels of a pre-compression load. The numerical analysis was carried out to simulate the test. It focused on the discretisation of frictional behaviour in term of peak and residual friction angles and cohesion. The study helps to understand the contribution of flexible diaphragms in traditional structures.

Direct numerical simulation of shock wave/turbulent boundary layer interaction in a swept compression ramp at Mach 6

Swept compression ramps widely exist in supersonic/hypersonic vehicles and have become a typical standard model for studying three-dimensional (3D) shock wave/turbulent boundary layer interactions (STBLIs). In this paper, we conduct a direct numerical simulation of swept compression ramp STBLI with a 34° compression angle and a 45° sweep angle at Mach 6 using a heterogeneous parallel finite difference solver. Benefitting from the powerful computing performance of the graphics processing unit, the computational grid number exceeds 5 × 106 with the spatiotemporal evolution data of hypersonic 3D STBLI obtained. The results show that the flow of the hypersonic swept compression ramp follows the quasi-conical symmetry. A supersonic crossflow with helical motion appears in the interaction region, and its velocity increases along the spanwise direction. Fluids from the high-energy-density region pass through the bow shock at the head of the main shock and crash into the wall downstream of the reattachment, resulting in the peaks in skin friction and heat flux. The peak friction and heating increase along the spanwise direction because of the spanwise variation in the shock wave inclination. In the interaction region, the unsteadiness is dominated by the mid-frequency motion, whereas the low-frequency large-scale motion is nearly absent. Two reasons for the lack of low-frequency unsteadiness are given: (1) The separation shock is significantly weaker than the reattachment shock and main shock; and (2) because of the supersonic crossflow, the perturbations propagating at the sound speed are not self-sustaining but flow along the r-direction and toward the spanwise boundary.

Some mechanical characterization of the Sandakan formation’s sandstone, Sabah, Malaysia

This work defines the mechanical characteristics of slightly weathered sandstone belonging to sedimentary Sandakan formation in Sandakan, Sabah. The mechanical properties of uniaxial compressive strength, shear strength (includes basic and peak friction angle and cohesion) was determined by the uniaxial compressive strength test, direct shear test, tilt test and triaxial compressive strength test. The slightly weathered very fine sandstone gave higher strength but lower in basic friction angle than slightly weathered fine sandstone. The basic friction angle for very fine and fine sandstone are 28° and 33°, respectively. The value of peak friction angle and cohesion of intact rock by the triaxial compressive strength test (52-58° and 2-4 MPa) is higher than direct shear test (16-20° and 0.25-4.00 MPa) of fine sandstone rock mass (for planar surface).

Effect of particle regularity on the shear response of geogrid-granular material interface under cyclic normal loading

The investigation of shear behaviour on geogrid-granular material interface under cyclic normal loading (CNL) is significant in seismic design of reinforcement structure. The cyclic shear mechanism about the effect of particle overall regularity on reinforced soil interface was analysed using dynamic direct shear apparatus. Five mixtures of round spherical media and crushed limestone with different percentages were selected to obtain various particle overall regularity. By comparing the shear behaviour under various overall regularity, the interface shear stress and vertical displacement under the CNL condition were smaller than those under the static loading condition. The decrement in interface shear stress of lower overall regularity was smaller than that of higher overall regularity. The interface peak shear stress, final vertical displacement decreased with the increase of cyclic normal loading amplitude and overall regularity. The effect of initial normal loading on ratio of strength reduction and energy consumption was reverse to that of the overall regularity. Based on the constant relative phase shift of the peak normal stress and friction coefficient for various overall regularity, the prediction formula was proposed. The test results improve the understanding on how normal loading perturbations and particle overall regularity affect the shear behaviour of reinforced soil interface.

Frictional behavior and micro-damage characteristics of rough granite fractures

Natural faults or discontinuities in general are usually rough at different scales, and the roughness of fault surfaces plays a dominant role in determining the mode of sliding (stable or unstable). Understanding the frictional behavior of rough fractures is important for investigating the mechanics and nucleation of earthquakes, and other dynamic geo-hazards such as induced seismicity and fault slip rockburst. We perform direct shear tests on rough granite fractures to investigate the shear behavior, microscopic asperity damage and surface wear characteristics under different normal stresses (10 to 40 MPa). We then compare our test results with those obtained using ground saw-cut fault surfaces. Results indicate that stick-slip occurs on all the rough fractures during the sliding stage, and the amount of stress drops and fault gouges tends to increase with normal stress. The peak friction coefficient is much higher than that of ground fault surfaces, while the steady-state friction coefficient is comparable with that of the ground surfaces. We identify three different scales of brittle fractures, which are considered to be closely related to the stick-slip sliding, namely shear-off of asperities, fracturing of the survived asperities and off-fault tensile fractures propagating into the host rock. The micro-damage of the post-shear surface occurs in the form of powder-sized gouge, micro-cracks and grain edge wear; and the micro-crack number, maximum length and aperture tend to increase with increasing normal stress. Influence of different fault types (rough fractures, ground saw-cut surfaces and gouges) on the stress drop is not very discernable, which is partly because that stick-slip is highly susceptible to different loading conditions. Friction drops for different fault types are found to be clustered around 0.1 but lower than 0.3 below 50 MPa normal stress, which also depend on the loading conditons (e.g., stiffness). Our study contributes to a better understanding of the mechanics underlying the dynamic geohazards (earthquakes, induced seismicity, fault slip rockburst) which are associated with the unstable shear failure on rough faults or fracture surfaces.

Prediction of the peak and steady-state ply–ply friction response for UD C/PAEK tapes

Excessive ply–ply friction can lead to process-induced defects during the hot press forming of thermoplastic composite laminates. Process simulations can be used to enable first-time-right defect-free manufacturing. However, a good understanding of the ply–ply friction is required to improve the constitutive models to allow simulation of more complex parts. We performed friction experiments on UD C/PAEK tapes, showing a typical response with a peak followed by a steady-state friction. Micrographs of tested specimens were analyzed to evaluate the matrix interlayer thickness distribution in the ply–ply interface, which we combined with the matrix viscosity to predict the peak friction. Generated fiber distributions, mimicking the ply–ply interface, were successfully used to obtain the matrix interlayer as well. The steady-state friction was accurately described by including a critical shear stress to represent wall slip, substantiating the concept of wall slip as the dominant underlying mechanism for the start-up friction response.

Friction Prediction and Application to Lateral or Longitudinal Slip Force Prediction

The empirical or semi-empirical model is widely used for vehicle simulation because of its high accuracy but relies on massive experimental data of tire force and moment. Therefore, tire mechanical prediction is of great significance to improve tire modeling efficiency and to reduce costs. Typical prediction methods or models based on normalization presented by Pacejka and Radt assume that different loads could be close to one normalized curve, but it is not always accurate enough to predict tire force under pure slip conditions and there is no mention of friction prediction methods. In the paper, a theoretical model considering the deformation of belt/carcass is established, which lays the foundation for a normalization model. A method for separation of friction from test data and the proportional assumption of longitudinal and lateral peak friction coefficient between target tire and reference tire are proposed, and the experimental results show that this assumption is acceptable. Finally, according to the separation of friction method and assumption, a new prediction method for tire force under pure slip conditions is presented and validated by comparison with the experimental data. It shows that the proposed method has good prediction capability with satisfactory accuracy.

Studying effects of interface surface roughness, mean particle size, and particle shape on the shear behavior of sand-coated CFRP interface

Carbon fiber-reinforced polymer (CFRP) composites can be considered an ideal alternative for conventional structural elements due to their superior benefits, such as high durability, satisfactory strength, and cost-effectiveness. This study is focused on interface shear behavior between sand-coated CFRP [spark plasma sintering CFRP (SPSCFRP)] and different types of sand with varying mean particle sizes (D50), and particle shapes [well-rounded (glass beads or GB), well-angular (glass powder or GP), and sub-rounded to sub-angular (natural sand)] under two levels of initial relative density. Four types of SPSCFRP surfaces with different levels of surface roughness, ranging from very smooth (VS) to highly rough (HR) were selected to perform interface shear tests. Analysis of sand-SPSCFRP data highlights an increase in surface roughness, mean particle size, angularity, and initial relative density resulting in mobilization of higher peak and critical-state friction angles. Rough SPSCFRP shows the most effective performance of the tested configurations in interface shear response. A critical value for normalized roughness (Rn) is observed (0.2≤Rcr≤0.5), within which the highest value of peak and critical-state friction angles is obtained. A well-pronounced post-peak reduction in shear stress of interfaces with Rn≥ 0.3 is observed. The peak and critical-state friction angles of sand-rough SPSCFRP interfaces are 15–32% and 11–32% higher than those of sand-CFRP interfaces, respectively. Given the same surface roughness and mean particle size, smaller peak and critical-state interface friction angles are mobilized for well-rounded sand than for well-angular sand. For the sand-SPSCFRP and sand-CFRP interfaces, the sand-structure design ratio (D.R.) ranges between 1.04 and 1.16 and 0.79–0.96, respectively. The average efficiency factor (E.F.) of the sand-SPSCFRP surfaces are 1.02 and 1.06, respectively, for medium-dense and dense specimens, while this value is much lower for sand-uncoated CFRP (∼0.8).

An Experimental Investigation of the Mechanical Behavior and Particle Crushing Characteristic of Volcanic Soil.

Volcanic soil is a special soil that is well-known for its distinctive texture, vesicular nature, and particle fragility. The fragility characteristic of volcanic soil is the main factor affecting the foundation stability in road engineering. This study focuses on the mechanical properties and particle crushing characteristics of volcanic soil retrieved from Northeast China. A series of triaxial consolidation and drainage shear tests are performed on volcanic coarse-grained soil (5 mm > d > 0.075 mm) under different initial relative densities and effective confining pressures. Results show the peak friction angle of volcanic soil significantly decreases with the increase of confining pressure. The particle crushing degree of volcanic soil increases with the increase of confining pressure, particle size, and relative density. The relative breakage rate of the same particle size group has a good linear relationship with a fractal dimension. Moreover, for the same particle size, the relationship between plastic work and relative breakage rate can be fitted by a power function, which is not significantly affected by relative density or effective confining pressure. From an engineering view, in addition to increasing the compaction degree of volcanic soil, volcanic soil with fine particles used as a roadbed filler can significantly reduce the deformation of the roadbed and improve the bearing capacity of the foundation.

Research on Tire/Road Peak Friction Coefficient Estimation Considering Effective Contact Characteristics between Tire and Three-Dimensional Road Surface

In the field of transportation, the accurate estimation of tire–road peak friction coefficient (TRPFC) is very important to improve vehicle safety performance and the efficiency of road maintenance. The existing estimation algorithms rarely consider the influence of road roughness and road texture on the estimation results. This paper proposes an estimation method of TRPFC considering the effective contact characteristics between the tire and the three-dimensional road. In the longitudinal and lateral directions of tire–road contact, the model is optimized by incorporating the effective contact area ratio coefficient into the LuGre tire model. The optimized model characterizes the road texture by road power spectrum and establishes the relationship between road texture and tire force. In the vertical direction of tire–road contact, the force transfer between tire and road is represented by a new multi-point contact method. By combining the above models with the normalization method and the unscented Kalman filter (UKF), the timely and accurate estimation of the peak friction coefficient of the tire and the 3D road is realized. Simulation and real vehicle experiments verify the effectiveness of the estimation algorithm.

Study on blasting characteristics of rock mass with weak interlayer based on energy field

In order to explore the influence of weak interlayer on blasting characteristics in natural rock mass, by using the particle flow code (PFC2D), a single hole blasting numerical model of hard rock with soft interlayer is established. The blasting experiments at different positions and thicknesses of weak interlayer are carried out. Then an in-depth analysis from the perspectives of crack effect, stress field and energy field is made. Results showed that: (i) When the explosion is initiated outside the weak interlayer, if the interlayer is located within about twice the radius of the crushing area, the closer the interlayer is to the blast hole, the higher the damage degree of the rock mass around the blast hole. And the number of cracks will increase by about 1–2% when the distance between the weak interlayer and the blast hole decreases by 0.5 m. (ii) When detonating outside the weak interlayer, if the interlayer is within about 4 times radius of the crushing area, the hard rock on both sides of the weak interlayer will in a high stress state. Under the same case, the peak kinetic energy and peak friction energy will increase by about 23 and 13%, respectively, and the peak strain energy will increase by about 218 kJ for every 0.1 m increase in the thickness of the weak interlayer.

Numerical Investigation on the Spudcan Penetration into Sand Overlying Clay Considering the Strain Effects

A numerical model with a Coupled Eulerian–Lagrangian (CEL) approach is proposed for spudcan penetration into sand overlying clay. Both stress-dependence and strain-softening effects are incorporated into the M–C model to describe the sand, whereas the Tresca model with softening effect is used to describe the clay. Effects of the critical state strain threshold in the strain-softening model of sand and the clay sensitivity in the strain-softening model for clay are investigated. The model is verified against different soil conditions: uniform sand, loose sand overlying clay, and dense sand overlying clay. It is found that the stress-dependence effect dominates shallow penetration, whereas the strain-softening effect dominates deep penetration. The assumption of a constant peak friction angle for the accumulated deviatoric plastic strain less than the threshold of peak friction angle leads to an overestimation of the resistance in loose sand. Furthermore, the fit parameter obtained from triaxial tests tends to underestimate the peak resistance in dense sand. The proposed model should provide a valuable tool for geotechnical engineering analysis in sand.

Effect of one cycle of heating-cooling on the clay-concrete pile interface shear strength parameters

This study investigated the effect of applying a one heating-cooling cycle on the interface strength parameters of saturated clay soil in contact with concrete, and the potential use of heating to improve/increase the pile capacity. A large direct shear test device with inner dimensions of 300 mm, 300 mm, and 200 mm for width, length, and height, respectively, was modified to perform the soil-concrete interface tests. A concrete block was built and placed in the bottom section of the shear device. Heating rods system were used to heat the circulating water that heated the specimens. The experimental tests were conducted on low plasticity soil with PI = 12, medium plasticity soil with PI = 29, and high plasticity soil with PI = 60. The specimens were first consolidated to a target normal stress prior to shearing. Two tests were performed for each normal stress and clay type with one test performed without heating-cooling cycle at ∼20 °C and the other test performed at ∼20 °C after a heating-cooling cycle up to 70 °C. The specimens were tested under different normal stresses ranging from 30 to 150 kPa. The specimens' temperature was increased gradually during the heating process from room temperature (∼20 °C) to ∼70 °C. The specimens were then gradually cooled back to room temperature. The test results showed significant increase in both the peak and residual interface friction angles by a percent ranges from 13.6% to 35.5%. The specimens subjected to a one heating-cooling cycle during shear experienced significant volumetric reduction by a percent ranges from 11.3% to 96%. The thermally induced “contraction” volumetric strain (TIVS) was found to increase with increasing temperature loading and the plasticity index, PI, but independent of the applied normal stress.