Ring foundation on elastic subgrade: an analytical solution for computer modelling using the Lagrangian multiplier method

In the practice of geotechnical engineering, the case of a ring footing carrying a set of concentrated point loads is a common problem. At times, the induced vertical and angular displacements for the ring footing need to be evaluated at a relatively precise level. By making use of the governing set of equations derived for the case of a general curved beam, expressions that can be easily implemented in modern computing software are derived for the vertical and angular displacements of a ring footing of rectangular cross section as functions of the radial position. The loading case considered is a vertical point load, and the soil is modelled as elastic. Estimates of the displacements have been shown for a common range of practical applications. The behaviour for a set of concentrated loads may be evaluated using the derived equations through direct superposition. Nonlinear finite element analysis is used to evaluate the vertical deflection and angular twist of the ring foundation. Numerical analysis performed for three ring foundations with different radii and cross sections is reported to validate the accuracy of the derived analytical solution. Copyright © 2016 John Wiley & Sons, Ltd.     

Elastic fields in two joined transversely isotropic media of infinite extent as a result of rectangular loading

This paper presents the closed‐form solutions for the elastic fields in two bonded rocks induced by rectangular loadings. Each of the two bonded rocks behaves as a transversely isotropic linear elastic solid of semi‐infinite extent. They are completely bonded together at a horizontal surface. The rectangular loadings are body forces along either vertical or horizontal directions and are uniformly applied on a rectangular area. The rectangular area is embedded in the two bonded rocks and is parallel to the horizontal interface. The classical integral transforms are used in the solution formulation, and the elastic solutions are expressed in the forms of elementary harmonic functions for the rectangular loadings. The stresses and displacements in the rocks induced by both the horizontal and vertical body forces are also presented. The numerical results illustrate the important effect of the anisotropic bimaterial properties on the stress and displacement fields. The solutions can be easily implemented for numerical calculations and applied to problems encountered in rock mechanics and engineering. Copyright © 2011 John Wiley & Sons, Ltd.     

Particle manifold method (PMM): A new continuum‐discontinuum numerical model for geomechanics

Particle manifold method (PMM) is a new extension of the numerical manifold method (NMM). PMM uses a mathematical cover system to describe the motion and deformation of a particle‐based physical domain. By introducing the concept of particle into NMM, PMM takes the advantages of easy topological and contact operations with particles. In this article, the methodology, formulations and implementation of the method are presented, together with modelling examples for validation. It is found that good solutions for both continuous and discontinuous problems are obtained by the new developed PMM. Due to the underlying coupled continuum‐discontinuum property of PMM, it has great potential for modelling of geomechanical problems. Copyright © 2012 John Wiley & Sons, Ltd.     

Soft rock pillars

Summary Soft rock pillars can be designed by several methods available in the mining literature. All of these methods include the effect of shape, or geometry, on the average strength of specimens and pillars. All of the pillar design methods include some measurement of the strength of specimens of the pillar rock. The most common rock specimen strength property measured is the unconfined compressive strength. However, the average strength of triaxially confined rock specimens is much greater than the unconfined specimen strength, which can be more important to pillar strength. The estimation of the strength of a pillar is complicated by the decrease in rock specimen strength with increase in specimen size.Editor's note: In common with North American engineering practise, the paper uses English units throughout, where feasible conversions are included in the text. Where not, the following factors may be used: 1 inch=25.4 mm; 1 ft=0.3048 m; 1 lbf/in.^–2=6.895 kn/m^–2; 1Tonf.=8.896 kN.     

Influence of longwall support on the occurrence of roof cavities

Summary The forming of roof cavities in longwall faces is a complicated process. A likely explanation for this process is the presence of relaxed zones in the first beds of the roof above and ahead of the support. If existing or potential fissures are allowed to open through insufficient constraint, the block of roof delimited by these fissures will collapse. An increasing unsupported distance, an increasing distance between the face and the first row of legs, a lower vertical bearing force and a lower support pressure on the roof will increase the extent of the relaxed zones. These effects are investigated through underground observations and numerical modelling.Supplementary to this local influence, there is also a spatial relation between the support characteristics of one element in one coal step and the occurrence of fall outs in the roof uncovered by the next coal steps (3 on average) and above the neighbourhood elements (2 to 4 on average). It is probable that, once a cavity is formed, it is extended easily (in the two directions), until appropriate measures are taken.     

The fractal geometry of flow paths in natural fractures in rock and the approach to percolation

The distributions of contact areas in single, natural fractures in quartz monzonite (Stripa granite) are found to have fractal dimensions which decrease fromD=2.00 to values nearD=1.96 as stress normal to the fractures is increased from 3 MPa up to 85 MPa. The effect of stress on fluid flow is studied in the same samples. Fluid transport through a fracture depends on two properties of the fracture void space geometry. the void aperture; and the tortuosity of the flow paths, determined through the distribution of contact area. Each of these quantities change under stress and contribute to changes observed in the flow rate. A general flow law is presented which separates these different effects. The effects of tortuosity on flow are largely governed by the proximity of the flow path distribution to a percolation threshold. A fractal model of correlated continuum percolation is presented which quantitatively reproduces the flow path geometries. The fractal dimension in this model is fit to the measured fractal dimensions of the flow systems to determine how far the flow systems are above the percolation threshold.     

非线性弹性模型的改进

本文在邓肯-张模型进行深入探讨的基础上,提出了切线模量实质物理意义是剪切模量的观点,并分别采用应力法和应变法推导了剪切模量和体积模量(或变形模量)公式,还进行了考虑Biot固结非线性弹性油罐地基有限元实例分析。对不同的变形模量计算方法进行了比较,提出了改进的非线性弹性模型。     

The frictional behavior of lizardite and antigorite serpentinites: Experiments,constitutive models,and implications for natural faults

Laboratory studies of the frictional behavior of rocks can provide important information about the strength and sliding stability of natural faults. We have conducted friction experiments on antigorite and lizardite serpentinites, rocks common to both continental and oceanic crustal faults. We conducted both velocity-step tests and timed-hold tests on bare surfaces and gouge layers of serpentinite at room temperature. We find that the coefficient of friction of lizardite serpentinite is quite low (0.15–0.35) and could explain the apparent low stresses observed on crustal transform faults, while that of antigorite serpentinite is comparable to other crustal rocks (0.50–0.85). The frictional behavior of both types of serpentinite is well described by a two-mechanism model combining state-variable-dominated behavior at high slip velocities and flow-dominated behavior at low velocities. The two-mechanism model is supported by data from velocity-step tests and timed-hold tests. The low velocity behavior of serpentinite is strongly rate strengthening and should result in stable fault creep on natural faults containing either antigorite or lizardite serpentinite.     

冻土切削力学特性的试验和理论分析

利用笔者所研制的冻土切削试验台，在室内对不同冻土在不同温度、含水量、切削速度、切削深度和切刀前角下进行了一系列切削试验。结果表明，切削时，冻土主要呈脆性断裂破坏，其切削过程被认为是刀刃切入和撕裂冻土的结果，切削阻力随冻土温度降低而非线性增加，随切削速度提高而略有增加，随切削深度增加而近似线性增加，最佳切刀前角随切削深度增大有增大趋势。但平均切削阻力与最大切削阻力之比值对不同试验条件基本在０．４－０．６５间变化。同时，根据切削过程机理，从理论上建立了最大切削力模型，此模型考虑了切入和撕裂冻土阻力。