A calculation methodology of fault relative displacement used to study the mechanical characteristic of fault slip

Fault slip caused by mining disturbance is a crucial issue that can pose considerable threats to the mine safety. This paper proposes a point-by-point integration calculated methodology of fault relative slip and studies fault instability behavior induced by coal seam mining. A physical model with the existence of a fault and an extra-thick rock stratum is constructed to simulate the fault movement and calculate relative slip using the methodology. The results indicate that the fault relative slip can be regarded as a dynamic evolution process from local slip to global slip on the fault surface. The movement of surrounding rock masses near the fault experiences three stages, including along vertical downward, parallel to the fault and then approximately perpendicular to the fault. There will be an undamaged zone in the extra-thick rock strata when the mining face is near the fault structure. The collapse and instability of this undamaged zone could induce a violent fault relative slip. In addition, the influence of dip angles on the fault relative slip is also discussed. A formula for risk of fault relative slip is further proposed by fitting the relative displacement curves with different fault dip angles.

Effective Slip Lengths for Stokes Flow over Rough, Mixed-Slip Surfaces

<p>In this thesis, homogenization and perturbation methods are used to derive analytic expressions for effective slip lengths for Stokes flow over rough, mixed-slip surfaces, where the roughness is periodic, and the variation in slip length has the same period. If the classical no-slip boundary condition of fluid mechanics is relaxed, the slip velocity of the fluid at the surface is non-zero. For simple shear flow, the slip velocity is proportional to the shear rate. The constant of proportionality has dimensions of length and is known as the slip length. Any variation in the slip length over the surface will cause a perturbation to the flow adjacent to the surface. Due to the diffusion of momentum, at sufficient height above the surface, the flow perturbations have diminished, and flow is smooth and uniform. The velocity and shear rate at this height imply an effective slip length of the surface. The purpose of this thesis is to predict that effective slip length. Homogenization is a technique for finding approximate solutions to partial differential equations. The essence of homogenization is to construct a mathematical model of a physical problem featuring some periodic heterogeneity, then generate a sequence of models such that the period in question reduces with each increment in the sequence. If the sequence is appropriately defined, it has a limit model in the limit of vanishing period, for which a solution can be found. The solution to the limit system is an approximation to the solutions of systems with a finite period. We use homogenization to find the effective slip length of a system of Stokes flow over a periodically rough surface, described by periodic function h(x; y), with a local slip length b(x; y) varying with the same period. For systems where the period L is smaller than both the domain height P and typical slip lengths, the effective slip length bₑff is well-approximated by the harmonic mean of local slip lengths, weighted by area of contact between liquid and surface: [See 'Thesis' document below for equation.] We further use a perturbation technique to verify the above expression in the special case of a flat surface, and to derive another effective slip length expression: For a flat surface with local slip lengths much smaller than the period and domain height, the effective slip length bₑff is well-approximated by the area-weighted average of local slip lengths: [See 'Thesis' document below for equation.]</p>

Effective Slip Lengths for Stokes Flow over Rough, Mixed-Slip Surfaces

<p>In this thesis, homogenization and perturbation methods are used to derive analytic expressions for effective slip lengths for Stokes flow over rough, mixed-slip surfaces, where the roughness is periodic, and the variation in slip length has the same period. If the classical no-slip boundary condition of fluid mechanics is relaxed, the slip velocity of the fluid at the surface is non-zero. For simple shear flow, the slip velocity is proportional to the shear rate. The constant of proportionality has dimensions of length and is known as the slip length. Any variation in the slip length over the surface will cause a perturbation to the flow adjacent to the surface. Due to the diffusion of momentum, at sufficient height above the surface, the flow perturbations have diminished, and flow is smooth and uniform. The velocity and shear rate at this height imply an effective slip length of the surface. The purpose of this thesis is to predict that effective slip length. Homogenization is a technique for finding approximate solutions to partial differential equations. The essence of homogenization is to construct a mathematical model of a physical problem featuring some periodic heterogeneity, then generate a sequence of models such that the period in question reduces with each increment in the sequence. If the sequence is appropriately defined, it has a limit model in the limit of vanishing period, for which a solution can be found. The solution to the limit system is an approximation to the solutions of systems with a finite period. We use homogenization to find the effective slip length of a system of Stokes flow over a periodically rough surface, described by periodic function h(x; y), with a local slip length b(x; y) varying with the same period. For systems where the period L is smaller than both the domain height P and typical slip lengths, the effective slip length bₑff is well-approximated by the harmonic mean of local slip lengths, weighted by area of contact between liquid and surface: [See 'Thesis' document below for equation.] We further use a perturbation technique to verify the above expression in the special case of a flat surface, and to derive another effective slip length expression: For a flat surface with local slip lengths much smaller than the period and domain height, the effective slip length bₑff is well-approximated by the area-weighted average of local slip lengths: [See 'Thesis' document below for equation.]</p>

Exploration of novel faying surface treatment for high-strength frictional bolted joints to enhance its after-slip performance

<p>Welded joints is adopted rather than bolted joints for megastructure’s connections because the former can carry large force. However, the former has several problems, such as quality control of welding in situ, which the latter can solve. By contrast, as the load transfer ratio of each bolt becomes uneven proportionally to the number of bolts, local slip around extreme bolts occurs before the whole slip. Extreme bolts to which a large shear force is applied will break before other bolts. For utilizing the strength of all bolts, the problem is solved by improving shear deformation capacity in faying surface with novel surface treatment. Here, the treatment concepts were explored, and the coating’s effectiveness was evaluated through friction tests. The deformation capacity can be twice or more than that of conventional treatment, and the slip coefficient doesn’t depend on contact pressure. These features have the advantage to give stable slip behaviour.</p>

Steady moving contact line of water over a no-slip substrate

The movement of the triple contact line plays a crucial role in many applications such as ink-jet printing, liquid coating and drainage (imbibition) in porous media. To design accurate computational tools for these applications, predictive models of the moving contact line are needed. However, the basic mechanisms responsible for movement of the triple contact line are not well understood but still debated. We investigate the movement of the contact line between water, vapour and a silica-like solid surface under steady conditions in low capillary number regime. We use molecular dynamics (MD) with an atomistic water model to simulate a nanoscopic drop between two moving plates. We include hydrogen bonding between the water molecules and the solid substrate, which leads to a sub-molecular slip length. We benchmark two continuum methods, the Cahn–Hilliard phase-field (PF) model and a volume-of-fluid (VOF) model, against MD results. We show that both continuum models reproduce the statistical measures obtained from MD reasonably well, with a trade-off in accuracy. We demonstrate the importance of the phase-field mobility parameter and the local slip length in accurately modelling the moving contact line.

Modelling of pulse-like velocity ground motion during the 2018 Mw 6.3 Hualien earthquake, Taiwan

SUMMARY The 2018 February 6 Mw 6.3 Hualien earthquake caused severe localized damage in Hualien City, located 20 km away from the epicentre. The damage was due to strong (&gt;70 cm s−1) and sharp (duration ∼2.5 s) velocity pulses. The observed peak ground-motion velocity in Hualien City symmetrically decays with distance from the nearby Milun fault. Waveforms observed on the opposite sides of the fault show reversed polarity on the vertical and N–S components while the E–W component is almost identical. None of the published finite-fault slip models can explain the spatially highly localized large velocity pulses. In this study, we show that an Mw 5.9 strike-slip subevent on the Milun fault at 2.5 km depth, rupturing from north to south at ∼0.9Vs speed, combined with site effects caused by surficial layers with low S-wave speed, can explain the velocity pulses observed at the dense strong-motion network stations. This subevent contributes only 25 per cent of the total moment of the 2018 Hualien earthquake, suggesting that a small local slip patch near a metropolis can dominate the local hazard. Our result strongly suggests that seismic hazard assessments should consider large ground-motion variabilities caused by directivity and site effects, as observed in the 2018 Hualien earthquake.

Extension of Spencer’s Circular Model to Stability Analysis of Landslides with Multicircular Slip Surfaces

This paper presents a new limit equilibrium method based on analysis of landslides with multicircular slip surfaces in the Three Gorges Reservoir area, China. An important innovation of this method is that the rigid sliding mass is divided into numerous interrelated Spencer’s circles sharing the same factor of stability, so that each of them possesses a real centre of rotation and an independent inclination of interslice forces. The analysis is accomplished by iterations to satisfy both force and moment equilibrium for each circle. Two real cases were then adopted to verify the effectiveness of the method in the analysis of both slope stability and the design forces on piles. Factors influencing the performance of the method were also investigated, which reveal that the concavity of the local slip surface near the slope toe has a major impact. The importance of the proximity between the actual and the fitted sliding surfaces was highlighted for ensuring accuracy of the method when extended to the real cases.