• Tunnel and Underground Space
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• v.14 no.4
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• pp.261-268
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• 2004

The main objectives of this study are to investigate the anisotropic characteristics of rocks and to evaluate the relationships between physical properties. A series of experiments were performed in three mutually perpendicular directions for three rock types, which are granite, granitic gneiss and limestone. The relationships of measured physical properties were evaluated. The results of ultrasonic wave velocity measurement show that granite of three rock types gives the largest directional difference, and that the wave velocity in a plane parallel to a transversely isotropic one is dominantly faster than that in a subvertical or vertical plane. It implies that ultrasonic wave velocity for rock could be used as a useful tool for estimating the degree of anisotropy. The ratio of uniaxial compressive strength to Brazilian tensile strength ranges approximately from 13 to 16 for granite. from 8 to 9 for granite gneiss, and from 9 to 18 for limestone. The directional differences for granite and granitic gneiss are very small, and on the other hand, is relatively large for limestone. It is suggested that strength of rock makes quite difference depending on the rock types and loading directions, especially for the anisotropic rocks such as transversely isotropic or orthotropic rocks. The ratio of uniaxial compressive strength to point load strength index ranges from 18 to 20 for granite, from 17 to 19 for granitic gneiss, and from 21 to 24 for limestone. These results show that point load strength index makes also a difference depending on rock types and directions. Therefore. it should be noted that the ratio of uniaxial compressive strength to point load strength index could be applied to all rock types. Uniaxial compressive strength shows relatively good relationship with point load strength index, Schmidt hammer rebound value, and tensile strength. In particulat, point load strength index is shown to be the best comparative relationship. It is indicated that point load test is the most useful tool to estimate an uniaxial compressive strength indirectly.

• Geomechanics and Engineering
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• v.29 no.1
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• pp.53-63
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• 2022

Simplified analytical solutions are developed for the dynamic analyses of an axially loaded pile foundation embedded in a transverse-isotropic, fluid-filled, poro-visco-elastic soil with rigid substratum. The pile is modeled as a viscoelastic Rayleigh-Love rod, while the surrounding soil is regarded as a transversely isotropic, liquid-saturated, viscoelastic, porous medium of which the mechanical behavior is represented by the Boer's poroelastic media model and the fractional derivative model. Upon the separation of variables, the frequency-domain responses for the impedance function of the pile top, and the vertical displacement and the axial force along the pile shaft are gained. Then by virtue of the convolution theorem and the inverse Fourier transform, the time-domain velocity response of the pile head is derived. The presented solutions are validated, compared to the existing solution, the finite element model (FEM) results, and the field test data. Parametric analyses are made to show the effect of the soil anisotropy and the excitation frequency on the pile-soil dynamic responses.

• Tunnel and Underground Space
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• v.26 no.5
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• pp.363-374
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• 2016

All five independent elastic constants of a transversely isotropic rock sometimes need to be determined from a single specimen. Saint-Venant approximation has been widely used for a long time in the analysis of single specimen test. This paper has proven how this empirical equation can be mathematically transformed into a form of the apparent Young's modulus based on theory of elasticity. The transformed equation is a monotonous function on anisotropic angle and can be useful in the analysis of the in-situ stress measurement in an anisotropic rock mass. The estimations of data in literatures have shown that the measured values of $G^2$ are uniform on anisotropic angles and smaller than that of Saint-Venant's case. This decrement may be caused by sliding of the interface of strata and the decrement rate is inferred to relate well with the combination of bonding condition of strata and strength of rock material. Accumulation of these kinds of studies in the future enables to define the decrement and to determine elastic constants of a transversely isotropic rock from a single specimen from modifying Saint-Venant approximation.

• Tunnel and Underground Space
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• v.20 no.3
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• pp.153-168
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• 2010

A fifth equation is required to determine the five independent elastic constants of a transversely isotropic rock from compression test of a single specimen. As an approximation proposed by Saint-Venant has been used for long time, it may cause an erroneous result in some cases, especially for specimen with low angle of anisotropy. Three equations were suggested replacing this traditional equation and proved to be applicable by the model analysis in the previous studies. As Saint-Venant's approximation is turned out the same as the first one of them, it has the characteristics that the apparent Young's modulus is monotonously increasing according to the anisotropic angle. The methodology to analyze the elastic constants from four independent strain measurements by uniaxial compressive test of a single standard specimen is concisely described, and the necessity and compatibility of new suggested equations are discussed. Saint-Venant's approximation can determine the elastic constants close to true values and other equations may be unnecessary in specimens with medium to large angle. Nevertheless, they may become applicable because they can produce the almost same amount. For the specimens of small angle of anisotropy, Saint-Venant's approximation may result in out of general ranges or thermodynamic constraints, but other suggested equations can produce the almost true value. Thus they can be applied before other alternative equation is known. The guide map constructed by model study may decide the most compatible one of the three equations.

• Tunnel and Underground Space
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• v.22 no.5
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• pp.346-353
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• 2012

Multi-specimen uniaxial compression test has been carried out in order to find the method to determine the five independent elastic constants from a single standard specimen of a transversely isotropic rock. Total 35 specimens of 7 different angles from a large block of rhyolite presenting the flow structure obviously are used in tests. This second report is to focus on the statistical evaluation of measured strains and analyzed elastic constants. And the determination of their true or near-true values is discussed. As the result of RSD analysis, it turns out that the reliability of measured strains is sufficiently obtained and Saint-Venant approximation is well applicable except 15 degree angled specimen in tests. RSD is decreasing on the increase of the angle of anisotropy. This tendency may be caused not only by the decreasing of the deviation of measured strains, but also by the better applicability of Saint-Venant approximation on the increase of angle. It can be concluded that the analyzed values are considered the near-true ones of five independent constants on the high reliability. But the variation of the apparent Young's modulus expected by these values is not proved to match the measured tendency. It is inferred that the factor to decrease the apparent Young's modulus and/or to increase the shear strain, is present in the test or in the nature of the anisotropy in consideration of this inconsistency.

• Economic and Environmental Geology
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• v.27 no.3
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• pp.281-287
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• 1994

The present paper deals with numerical modeling of Love channel waves in transversely isotropic elastic medium. First, an explicit finite-difference scheme of second order approximation is formulated with the wave equation of SH particle displacement in transversely isotropic medium. Since it is a heterogeneous formulation, it should enable efficient modeling of complex model structures without additional treatment of the internal boundary matching. With a model of isotropic coal seam embedded in high velocity host rock, seismograms are synthesized and tutn out to be essentially identical with published ones of Korn and $St{\ddot{o}}ckl$. Next, anisotropic coal seams are investigated. It is found that the horizontal velocity of the seam appears to play a major role of determining the group velocity of Love channel waves. The group velocity increases with the increase of the horizontal velocity or vice versa. However, further study will be needed to exploit fully Love channel waves for the determination of lithology, stratification, fracture in sedimentary rocks, for instance, for hydrocarbon exploration and development.

• Tunnel and Underground Space
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• v.26 no.3
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• pp.235-252
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• 2016

This study presents a methodology to reproduce the mechanical behavior of isotropic or transversely isotropic rock using the polygonal grain-based distinct element model. A numerical technique to monitor the evolution of micro-cracks during the simulation was developed in the present study, which enabled us to examine the contribution of tensile cracking and shear cracking to the progressive process of the failure. The numerical results demonstrated good agreement with general observations from rock specimens in terms of the behavior and the evolution of micro-cracks, suggesting the capability of the model to represent the mechanical behavior of rock. We also carried out a parametric study as a fundamental work to examine the relationships between the microscopic properties of the constituents and the macroscopic behavior of the model. Depending on the micro-properties, the model exhibited a variety of responses to the external load in terms of the strength and deformation characteristics. In addition, a numerical technique to reproduce the transversely isotropic rock was suggested and applied to Asan gneiss from Korea. The behavior of the numerical model was in good agreement with the results obtained in the laboratory-scale experiments of the rock.

• The Journal of Engineering Geology
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• v.33 no.4
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• pp.573-586
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• 2023

Joints or weak planes can induce anisotropy in the strength and deformability of fractured rock masses. Comprehending this anisotropic behavior is crucial to engineering geology. This study used plaster as a friction material to mold specimens with a single joint. The strength and deformability of the specimens were measured in true triaxial compression tests. The measured results were compared with three-dimensional numerical analysis based on the distinct element method, conducted under identical conditions, to assess the reliability of the modeled values. The numerical results highlight that the principal stress conditions in the field, in conjunction with joint orientations, are crucial factors to the study of the strength and deformability of fractured rock masses. The strength of a transversely isotropic rock mass derived numerically considering changes in the dip angle of the joint notably increases as the intermediate principal stress increases. This increment varies depending on the dip of the joint. Moreover, the interplay between the dip direction of the joint and the two horizontal principal stress directions dictates the strength of the transversely isotropic rock mass. For a rock mass with two joint sets, the set with the steeper dip angle governs the overall strength. If a rock bridge effect occurs owing to the limited continuity of one of the joint sets, the orientation of the set with longer continuity dominates the strength of the entire rock mass. Although conventional three-dimensional failure criteria for fractured rock masses have limited applicability in the field, supplementing them with numerical analysis proves highly beneficial.

• Tunnel and Underground Space
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• v.25 no.1
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• pp.56-67
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• 2015

In this study, a source locating technique applicable to transversely isotropic media was developed. Wave velocity anisotropy was considered based on the partition approximation method, which simply enabled AE source locating. Sets of P wave arrival time were decided by the two-step AIC algorithm and they were later used to locate the AE sources when having the least error compared with the partitioned elements. In order to validate the technique, pencil lead break test on artificial transversely isotropic mortar specimen was carried out. Defining the absolute error as the distance between the pencil lead break point and the located point, 1.60 mm ~ 14.46 mm of range and 8.57 mm of average were estimated therefore it was regarded as thought to be 'acceptable' considering the size of the specimen and the AE sensors. Comparing each absolute error under different threshold levels, results showed small discrepancies therefore this technique was hardly affected by background noise. Absolute error could be decomposed into each coordinate axis error and through it, effect of AE sensor position could be understood so if optimum sensor position was able to be decided, one could get more precise outcome.

• Tunnel and Underground Space
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• v.30 no.3
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• pp.242-255
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• 2020

The numerical simulations of Heater Experiment-D (HE-D) at the Mont Terri rock laboratory in Switzerland were performed to investigate an applicability of FLAC3D to reproduce the coupled thermo-hydro-mechanical (THM) behaviour in Opalinus Clay, as part of the DECOVLEX-2015 project Task B. To investigate the reliability of numerical simulations of the coupled behaviour using FLAC3D code, the simulation results were compared with the observations from the in-situ experiment, such as temperature at 16 sensors, pore pressure at 6 sensors, and strain at 22 measurement points. An anisotropic heat conduction model, fluid flow model, and transversely isotropic elastic model in FLAC3D successfully represented the coupled thermo-hydraulic behaviour in terms of evolution for temperature and pore pressure, however, performance of the models for mechanical behavior is not satisfactory compared with the measured strain.