Computing Displacements in Transversely Isotropic Rocks Using Influence Charts

Summary  This paper presents a simple graphical method for computing the displacement beneath/at the surface of a transversely isotropic half-space subjected to surface loads. The surface load can be distributed on an irregularly-shaped area. The planes of transverse isotropy are assumed to be parallel to the horizontal surface of the half-space. Based on the point load solutions presented by the authors, four influence charts are constructed for calculating the three displacements at any point in the interior of the half-space. Then, by setting z=0 of the derived solutions, another four influence charts for computing the surface displacements can also be proposed. These charts are composed of unit blocks. Each unit block is bounded by two adjacent radii and arcs, and contributes the same level of influence to the displacement. Following, a theoretical study was performed and the results showed that the charts for interior displacements are only suitable for transversely isotropic rocks with real roots of the characteristic equation; however, the charts for surface displacements are suitable for all transversely isotropic rocks. Finally, to demonstrate the use of the new graphical method, an illustrative example of a layered rock subjected to a uniform, normal circular-shaped load is given. The results from the new graphical method agree with those of analytical solutions as well. The new influence charts can be a practical alternative to the existing analytical or numerical solutions, and provide results with reasonable accuracy.     

Mechanical and Elastic Properties of Transversely Isotropic Slate

Planes of weakness like schistosity and foliation affect the strength and deformational behaviors of rocks. In this paper, an attempt has been made to study the elastic and strength behavior of slate rocks obtained from foundation of Sardasht dam site in Iran. Wet and dry specimens with different orientation of foliation were evaluated under uniaxial, triaxial, and Brazilian tests. According to the results obtained, slate mechanically pronounced U-shaped anisotropy in uniaxial and triaxial compression tests. In addition, the degree of anisotropy for the slates tested in current study was relatively high, showing the effect of foliation plane on strength and elastic parameters. It was concluded that stiffness of the samples decrease as the angle of anisotropy reaches 30–40°. This change was more pronounced for wet comparing to dry samples. However, the tensile strength obtained during Brazilian tests indicated that there is no apparent relationship between angle of anisotropy and tensile strength. However, increasing the water saturation decreased the tensile strength of the samples. The calculated elastic moduli referring to different anisotropy angles could be valuable for the design of various engineering structures in planar textured rock masses.     

横观各向同性地基模型的理论分析及其应用

根据横观各向同性体各向同性面水平时本构方程推导出了横观各向同性面倾斜时的本构方程并得出了横观各向同性地基在上述两种情况下的自重应力计算公式。运用本论文的理论 ,从自重应力角度能很好的解释水平应力大于竖直应力和水平应力的各向异性这些重要的实测现象     

Prediction of Land Subsidence Under Cyclic Pumping Based on Laboratory and Numerical Simulations

In this study subsidence due to groundwater withdrawal was investigated. Kerman Province in Iran is struggling with land subsidence problem due to extensive groundwater withdrawal mainly for farming. The rate and type of groundwater withdrawal has very important impact on settlement rate. In this research, effective parameters on land subsidence caused by groundwater withdrawal were determined by laboratory tests. Sampling had done up to depth of 300 m mainly with remolded specimens from Shams-abad, Nouq plain in Kerman province. Similar to the field preconsolidation pressure was applied on specimens in the laboratory. Rate of applied stress on prepared specimens was similar to effect of oscillation of groundwater level. In order to model the actual soil behavior in the laboratory, one-dimensional consolidation device (odometer) was adopted for testing. In these tests, the effect of loading caused by seasonal oscillation of groundwater table is considered by means of cyclic loading in the testing which has great effect on rate of settlements. The results of tests show that when the water table level periodically increases and decreases the amount of settlement decrease, comparing with the case when the groundwater table drop to a constant level. In order to predict the further effects of groundwater level oscillation and actual field condition on land subsidence, a finite element model based on Biots’ three-dimensional consolidation theory was developed. After calibration of finite element model with laboratory tests, this model was used for prediction the effect of groundwater level oscillation on actual field conditions.     

Numerical Simulations of Magnetized Astrophysical Jets and Comparison with Laboratory Laser Experiments

The results of MHD numerical simulations of the formation and development of magnetized jets are presented. Similarity criteria for comparisons of the results of laboratory laser experiments and numerical simulations of astrophysical jets are discussed. The results of laboratory simulations of jets generated in experiments at the Neodim laser installation are presented.     

Numerical and Laboratory Analysis of Relaxation Tests for Determining Time-Dependent Properties of Rock

Roof falls in coal mines may occur within a few months to a few years after excavation. In this paper, we proposed the use of relaxation tests as a substitute for time-dependent tests. The relation between creep behavior and relaxation behavior was numerically investigated and demonstrates that the material assigned with creep model can show relaxation behavior. Then the relaxation model was developed by modifying the Burgers creep model. Numerical simulation of a relaxation test on a simulated rock model in 3DEC yielded results that were similar to theoretical prediction. A relaxation test was performed on two groups of specimens under varying load conditions. Results from the laboratory tests validated the approach of using relaxation test to determine time-dependent properties. Finally, time-dependent properties were investigated by performing relaxation tests at different stages of a complete stress–strain curve. The relaxation test during strain-softening was unsuccessful; however, the relaxation behavior at residual stage in post-failure region was more significant than that in pre-failure region and the sudden drop in stress indicated there was strength deterioration due to the accumulation of viscous strain.     

Laboratory Experiments and Grain Based Discrete Element Numerical Simulations Investigating the Thermo-Mechanical Behaviour of Sandstone

Geotechnical and Geological Engineering - Thermo-mechanical loading can occur in numerous engineering geological environments, from both natural and anthropogenic sources. Different minerals and...     

稀疏非正交填充裂隙岩体水流—传热—应力模型与离散元模拟

为研究填充裂隙水流速度对岩体温度和应力的影响，选取甘肃北山地区的花岗岩，制作了稀疏非正交裂隙岩体模 型，采用河砂填充裂隙后进行模型试验；并对模型试验进行离散元数值模拟，分析了模型试验所测岩体温度和热应力与数 值模拟结果的差异和原因。结果显示：填砂裂隙强化了裂隙介质的热导能力，无填充时岩体温度和热应力比填砂时低；模 型试验和离散元模拟均表明，岩体温度和岩体应力随裂隙水流速度增大而减小，但是系统达到稳态所需要的时间变短；模 型试验中斜裂隙水流对温度场起主要作用；由于现有3DEC软件不能考虑水的热物性参数随温度的变化，进而产生自然对 流换热，斜裂隙水流和靠近热源侧的竖裂隙水流对温度场起主要作用。     

稀疏非正交填充裂隙岩体水流—传热—应力模型与离散元模拟

为研究填充裂隙水流速度对岩体温度和应力的影响,选取甘肃北山地区的花岗岩,制作了稀疏非正交裂隙岩体模 型,采用河砂填充裂隙后进行模型试验;并对模型试验进行离散元数值模拟,分析了模型试验所测岩体温度和热应力与数 值模拟结果的差异和原因。结果显示：填砂裂隙强化了裂隙介质的热导能力,无填充时岩体温度和热应力比填砂时低;模 型试验和离散元模拟均表明,岩体温度和岩体应力随裂隙水流速度增大而减小,但是系统达到稳态所需要的时间变短;模 型试验中斜裂隙水流对温度场起主要作用;由于现有3DEC软件不能考虑水的热物性参数随温度的变化,进而产生自然对 流换热,斜裂隙水流和靠近热源侧的竖裂隙水流对温度场起主要作用。     

Investigation of a Limestone Pillar Failure Part 1: Geology, Laboratory Testing and Numerical Modeling

Summary A pillar failure at shallow depth of overburden, featuring the recent formation of subvertical open cracks in the rock was observed. An extensive laboratory test program including Brazilian tests, uniaxial and triaxial compression tests for obtaining strength and deformation characteristics of the limestone was executed. Strength from single and multiple failure triaxial compression tests on intact rock and from tests on small scale rock mass specimens were obtained. Classification of the rock mass was conducted for use with the Hoek-Brown strength criterion. Numerical analysis shows that the strength of the rock mass exceeds by far the applied stress, suggesting a stable pillar. This typical rock engineering approach to assess rock mass stability is shown to be inadequate.     

Application of Stochastic Fracture Network with Numerical Fluid Flow Simulations to Groundwater Flow Modeling in Fractured Rocks

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Semi-Analytical Solution for Stresses and Displacements in a Tunnel Excavated in Transversely Isotropic Formation with Non-Linear Behavior

A semi-analytical solution based on the transfer matrix technique is proposed to analyze the stresses and displacements in a two-dimensional circular opening excavated in transversely isotropic formation with non-linear behavior. A non-isotropic far field can be accounted for and the process of excavation is simulated by progressive reduction of the internal radial stress. A hyperbolic stress–strain law is proposed to take into account the non-linear behavior of the rock. The model contains seven independent parameters corresponding to the five elastic constants of an elastic material with transverse isotropy and to the friction coefficient and cohesion along the parallel joints (weakness planes). This approach is based on the discretization of the space into concentric rings. It requires the establishment of elementary solutions corresponding to the stress and displacement fields inside each ring for given conditions at its boundaries. These solutions, based on complex variable theory, are obtained in the form of infinite series. The appropriate number of terms to be kept for acceptable approximation is discussed. This non-linear model is applied to back analyze the convergence measurements of Saint-Martin-la-Porte access gallery. Short-term and long-term ground parameters are evaluated.     

桩土相互作用模型及模型实验

本文介绍了目前在桩基测量及计算中使用的一些桩土相互作用摸型,同时也介绍了在动载情况下研究桩土相互作用的模型实验,并将桩土模型的计算与实验结果进行了比较和分析。     

Correction to: A Size-Dependent Bonded-Particle Model for Transversely Isotropic Rock and its Application in Studying the Size Effect of Shale

Geotechnical and Geological Engineering -     

A Size-Dependent Bonded-Particle Model for Transversely Isotropic Rock and its Application in Studying the Size Effect of Shale

Geotechnical and Geological Engineering - The bonded-particle model (BPM) method has been used to study the size effect and anisotropy of rock strength. This research proposes a new bonded-particle...