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2.
Estimating the Mean Trace Length of Rock Discontinuities 总被引：24，自引：1，他引：23
Summary Rock discontinuities appear as traces on exposures such as natural outcrops or tunnel walls. Discontinuity size which has
important effects on rock mass behavior is related to trace length.
This paper presents a technique for estimating mean trace length from the observations made on finite, circular sampling
windows. The method takes sampling errors into account and it requires, like existing methods using rectangular sampling windows,
that the numbers of discontinuities with both ends censored, with one end observed and one end censored, and with both ends
observed be known. Knowledge of the lengths of the observed traces and the distribution of trace lengths is not required.
A major advantage of the proposed method over the existing methods is that it does not need sampling data about the orientation
of discontinuities, i.e. the proposed method is applicable to traces with arbitrary orientation distributions.
To check the validity of the proposed method, theoretical relations between the mean trace length and the mean diameter of
circular discontinuities, respectively for lognormal and negative exponential distributions of the diameter of discontinuities,
are derived. The proposed method is then applied to analyze data simulated with the FracMan code, and the predicted results
are compared to the corresponding theoretical solutions. The results show that the proposed method is satisfactory. Comparisons
of the predicted mean trace length with the mean of observed trace lengths show that it is important to consider sampling
biases when estimating mean trace length. 相似文献
3.
The strength and deformability of rock mass primarily depend on the condition of joints and their spacing and partially on
the engineering properties of rock matrix. Till today, numerical analysis of discontinuities e.g. joint, fault, shear plane
and others is conducted placing an interface element in between two adjacent rock matrix elements. However, the applicability
of interface elements is limited in rock mechanics problems having multiple discontinuities due to its inherent numerical
difficulties often leading to non-convergent solution. Recent developments in extended finite element method (XFEM) having
strong discontinuity imbedded within a regular element provide an opportunity to analyze discrete discontinuities in rock
masses without any numerical difficulties. This concept is based on partition of unity principle and can be used for cohesive
rock joints. This paper summarizes the mathematical frameworks for the implementation of strong discontinuities in 3 and 6
nodded triangular elements and also provides numerical examples of the application of XFEM in one and two dimensional problems
with single and multiple discontinuities. 相似文献
4.
三峡水库某库段岩体裂隙网络模拟研究 总被引：9，自引：3，他引：6
为合理评价三峡水库某库岸岩体结构特征及工程整治提供依据,对区内岩体进行了裂隙调查及网络模拟研究。研究基于Monte-Carlo模拟方法,在技术上进行了探讨和一定改进。如采用了聚类分析法确定裂隙优势产状、用直接法产生随机数、广义RQD t及裂隙线连通率的计算等。根据野外调查及计算机模拟研究,研究区发育有3组优势裂隙、平均迹长1.45 m左右。间距一般服从对数正态或负指数分布,而走向和迹长基本上不服从常规分布。裂隙线密度在3－6条/m、t = 0.1 m时RQD t值在90 %左右、t = 0.7 m时RQD t值为10 %－20 %、RQD t值变化可能影响库岸岩体在不同方向的稳定性。 相似文献
5.
Observed frequencies of joint orientations are subject to error due to sampling bias. This error should be corrected before statistical inference is made on the distribution of orientation. Corrections (weighting functions) are developed for sampling bias in orientation for finite joints of different sizes and shapes intersecting rectangular exposures. Chi-square goodness-of-fit procedures available for hemispherical normal and bivariate normal distributions are modified to make them applicable for both raw data and data corrected for sampling bias. The aforementioned corrections and procedures were applied to a joint orientation cluster to study the effect of (a) joint orientation, (b) joint size and (c) joint shape, on the statistical distribution of the orientation. The influences of all these aforementioned factors were found to be significant. However, at present, joint sizes and shapes are not measured in field joint surveys. Therefore, it is suggested to make attempts to obtain joint sizes and shapes in field joint mapping surveys. Since the currently available probability distributions are not adequate to represent all joint orientation distributions, it is suggested either to look for new probability distributions or to develop procedures to use empirical distributions in modelling orientation distributions. 相似文献
6.
《Journal of Structural Geology》2004,26(6-7):1317-1339
Classifying and assessing geotechnical aspects of rock masses involves combining parameters in various ways, guided by empirical considerations, to derive quantitative geotechnical parameters. Geological structures and the deformation history of rocks underpin the nature of rock masses. The kinematics of a deforming rock mass may occur as sliding along throughgoing discontinuities or as distributed sliding on block faces. Distributed sliding will tend to disrupt the continuity of planar structures such that data on the size and shape of blocks is needed, rather than relying on discontinuity orientation data alone. Orientation and spacing data can be combined to provide a geometric analysis of block systems from linear samples, such as drill core. Dihedral angles and spacing of sequential pairs of discontinuities provides a sample of the size and shape of blocks that can be interpreted stereologically. Further detail can be derived by combining neighbouring intersections that enclose or partially enclose individual blocks. The shape and size of a block can be represented on a stereograph with the enclosing faces shown as poles and their perpendicular distance from an arbitrary point inside the block shown as a number. Identifying the size and shape of specific blocks rather than relying on statistical methods is beneficial to critical aspects of design such as analysing keyblocks that would be exposed during excavations. The detailed characterization of block size and shape is also a step toward interpreting the kinematics of rock mass deformation and the analysis of rock masses as ultra-close packed dilatant granular systems. 相似文献
7.
A methodology is developed in SPH framework to analyze the behavior of preexisting multiple intersecting discontinuities or joints in rock material. The procedure does not require any additional unknowns to represent discontinuities and to capture velocity jump across them. Instead, a discontinuity is represented by a set of joint particles placed along the discontinuity plane, in which relative velocity and traction vector is evaluated, obeying the Mohr–Coulomb friction law with zero tension constrain. For failure of continuous rock material, the Drucker–Prager yield criterion with tensile cracking is employed in the elastic‐plastic constitutive model. Free‐sip, no‐slip, and symmetric boundary conditions are also implemented in SPH framework for proper representation of physical system. The paper analyzes behavior of a rock sample having a discontinuity plane under uniaxial loading and compares velocity and stress with a theoretical solution derived considering effective vertical stiffness of the joint planes. The efficacy of the proposed method is successfully demonstrated by solving another two problems of jointed rock mass under uniaxial and gravitational loading conditions.Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
8.
Elastic moduli for fractured rock mass 总被引：8，自引：1，他引：8
Summary The presence of joint discontinuities has long been recognized as an important factor influencing the mechanical behavior of rock masses. This paper proposes a stress-strain model for an assemblage of intact rock blocks separated by joint planes. The stress-strain relationship accounts for spacings and orientations of the joint sets. Closed-form expressions of elastic moduli for a rock mass with three intersecting sets of joints are derived explicitly in terms of properties of joints and intact rock. Applicability of the derived expressions are evaluated by comparing the predicted results with experimental results from physical model tests. 相似文献
9.
The equations that exist in the literature to estimate corrected mean trace length and corrected two-dimensional density of a rock discontinuity set using area sampling technique are critically reviewed. The discontinuity traces appearing in an outcrop in Yingxiu area in China are used along with rectangular windows to calculate the corrected mean trace length and two-dimensional density using Kulatilake and Wu’s equations. Similarly, circular windows are used along with Mauldon’s and Zhang and Einstein’s equation to calculate the mean trace length and Mauldon’s equation to calculate the two-dimensional density for the same discontinuity sets using the same outcrop discontinuity trace data. For both parameters, the predictions based on the rectangular window methods were found to be more accurate than that based on the circular window methods. 相似文献
10.
A rational and realistic rock mass modelling strategy for the stability analysis of blocky rock mass
Due to the importance of a realistic rock mass model for the achievement of accurate and reliable results from numerical analysis of blocky rock mass, a probability based rock mass geometrical model is proposed in the present study. The rock mass geometry is built based on site investigation data and stochastic analysis of the discontinuity mapping results. The discontinuities and/or sets of them, either finite or infinite in size, planar or non-planar, convex or concave in shape, can be implemented in the three-dimensional rock mass model. Key block analysis and support design are then suggested to the stochastic rock mass models. To achieve a realistic stability analysis of the rock mass with the proposed probabilistic rock mass model, a few suggestions have also been made. These include the adoption of realistic constitutive models to intact rock and rock discontinuities, use of numerical model to technically handle numerical difficulties and development of a realistic modelling strategy to achieve realistic and affordable computational cost, etc. 相似文献
11.
天然岩体中广泛发育两侧岩性不同的异性结构面,开展异性结构面变形和强度特性研究旨在为岩体稳定性评价和利用提供依据。选取三峡库区侏罗系典型的砂岩-泥岩异性岩层,首先运用分形几何理论,定量计算了平直和4种不同不规则起伏形态结构面的粗糙度系数JRC值,然后基于PFC2D颗粒流程序,分别开展了以上5种形态异性结构面的数值剪切试验,获得了各形态结构面在不同正应力下的剪切应力-位移曲线。根据数值试验结果,采用巴顿的JRC-JCS模型分析了异性结构面强度特性,并与同性结构面强度性质进行对比研究。最后,在考虑异性结构面剪切破坏机制的基础上,引入强度因子的概念,提出了新的适用于异性结构面强度评价的两类改进巴顿准则。研究结果表明：异性岩体结构面抗剪强度介于相同粗糙度的两种同性结构面强度之间,在较低正应力下接近软岩同性结构面强度,符合Ⅰ型改进巴顿准则;在较高正应力下偏向硬岩同性结构面强度,符合Ⅱ型改进巴顿准则。实际工程中可利用改进准则并根据异性结构面应力状态对岩体稳定性进行评价,弥补了以往研究的不足。 相似文献
12.
Discontinuity controlled probabilistic slope failure risk maps of the Altindag (settlement) region in Turkey 总被引：7，自引：0，他引：7
The evaluation of potential rock slope problems using stereographic projection techniques known as kinematic analysis is one of the most important parts of a slope stability investigation to be carried out in jointed rock media. In conventional stereoprojection techniques for the assessment of possible rock slope failures, the peak orientations of joints together with the slope geometry and the friction angle of the weakness planes are used. Other possible joint orientations which may be encountered in the rock media are ignored, although they belong to the group of joint peak orientations. In this study, nearly vertical jointed andesites cropped out at the Altindag settlement region in Ankara were studied in order to evaluate the relevance of this ignored discontinuity orientation data on slope stability. As a result, probabilistic risk maps for planar, toppling and wedge failures were produced using the kinematic rules and digital elevation model of the study area. The comparison of the distribution of the actual failures in the area and the probabilistic risk maps prepared for the study area revealed that all of the identified failures are found to be located in the higher risk zones on the probabilistic risk maps. 相似文献
13.
Influence of discontinuities and clay minerals in their filling materials on the instability of rock slopes 总被引：1，自引：0，他引：1
Davood Fereidooni 《Geomechanics and Geoengineering》2018,13(1):11-21
To assess the influence of discontinuities and clay minerals in their filling materials on the instability of rock slopes, seven rock slopes along the margin of Ganjnameh–Shahrestaneh Road, Hamedan Province, Western Iran were selected, and the physical and mechanical properties of their rocks and discontinuities were determined. By statistical studies of the discontinuities, rock slope stability analysis has been performed using kinematic and limit equilibrium methods so that safety factors for the rock slopes can be calculated. Also, sampling of filling materials and X-ray diffraction tests have been done to identify the clay minerals in the filling materials. The lithologies of the studied rock slopes are granite, diorite and hornfels. The presence of discontinuities and weakness planes with different orientations and clay minerals in filling materials of discontinuities are effective factors that cause plane, wedge and toppling failures in the rock slopes. Clay minerals as filling materials of discontinuities in the studied rock slope facilitate their instability by two different methods. First, absorption of water by infilling clay minerals causes the friction angle of discontinuity surfaces that leads to plane and wedge failures to be reduced. Second, water absorption causes the swelling of clay infilling minerals that leads to toppling failure. 相似文献
14.
Evaluating Kinematic Controls on Planar Translational Slope Failure Mechanisms Using Three-Dimensional Distinct Element Modelling 总被引：1，自引：0，他引：1
This paper investigates the importance of kinematic release mechanisms on planar translational slope failure using three-dimensional distinct element codes. The importance of the dip and dip direction of the rear, basal and lateral release surfaces and their influence on failure mechanism, dilation, and the development of step-path failures is illustrated. The three-dimensional block shape and volume of the unstable rock masses simulated with the different discontinuity set geometries are characterized. Two assumed three-dimensional slope models are investigated in order to assess the importance of varying kinematic confinement/release mechanisms. These two assumed boundary conditions are shown to be critical in the development of asymmetrical rock mass deformation patterns. Scale effects due to the block size and discontinuity persistence are shown to control the calculated displacement and failure mechanisms. The numerical modelling results are also demonstrated to be sensitive to the assumed normal and shear stiffness of the discontinuities. The influence of the factors investigated on the failure of a single rock block versus a rock mass are compared and discussed. 相似文献
15.
Basanta K. Sahu 《Sedimentary Geology》1976,16(3):177-192
Currently popular line and ribbon methods yield grain counts that are differentially biassed in regard to sizes and orientations of the maximum projection diameter of the grains in the sample. Bias correction factors covering the entire range of counting situations are obtained using probability theory and coordinate geometry. The corrected numbers are true unbiassed Fleet counts that are suitable for estimating true statistical measures and for estimating economic potential of mineral(s). Irregular grains can be counted by classifying them into either elliptical or rectangular shapes by means of nondimensional discriminant equations based on area or length measurements. Wadell roundness (ρ) for elliptical and rectangular outlines shows inconsistency, but the modified Wadell roundness (ρ′) proposed herein is a consistent measure of roundness for all types of shapes, and hence the latter is recommended for use. Theoretically, roundness is linearly correlated with the form factor (B/A) for elliptical outlines and hence, a linear correlation of average roundness and average form factor in sediments is to be expected. The entire spectrum of shape comprising two continuous variables, form factor and modified Wadell roundness, may be classified into two discrete shape states (elliptical and rectangular) or into several discrete shape states having ranges of ρ′ and B/A values. 相似文献
16.
A. H. Ghazvinian M. J. Azinfar R. Geranmayeh Vaneghi 《Rock Mechanics and Rock Engineering》2012,45(3):349-359
In this study, the shear behavior of discontinuities possessing two different rock wall types with distinct separate compressive
strengths was investigated. The designed profiles consisted of regular artificial joints molded by five types of plaster mortars,
each representing a distinct uniaxial compressive strength. The compressive strengths of plaster specimens ranged from 5.9
to 19.5 MPa. These specimens were molded considering a regular triangular asperity profile and were designed so as to achieve
joint walls with different strength material combinations. The results showed that the shear behavior of discontinuities possessing
different joint wall compressive strengths (DDJCS) tested under constant normal load (CNL) conditions is the same as those
possessing identical joint wall strengths, but the shear strength of DDJCS is governed by minor joint wall compressive strength.
In addition, it was measured that the predicted values obtained by Barton’s empirical criterion are greater than the experimental
results. The finding indicates that there is a correlation between the joint roughness coefficient (JRC), normal stress, and
mechanical strength. It was observed that the mode of failure of asperities is either pure tensile, pure shear, or a combination
of both. Therefore, Barton’s strength criterion, which considers the compressive strength of joint walls, was modified by
substituting the compressive strength with the tensile strength. The validity of the modified criterion was examined by the
comparison of the predicted shear values with the laboratory shear test results reported by Grasselli (Ph.D. thesis n.2404,
Civil Engineering Department, EPFL, Lausanne, Switzerland, 2001). These comparisons infer that the modified criterion can predict the shear strength of joints more precisely. 相似文献
17.
Estimation of mean trace length of discontinuities 总被引：18，自引：0，他引：18
Summary Trace lengths of discontinuities observed on finite exposures are biased due to sampling errors. These errors should be corrected in estimating mean trace length. A technique, which takes into account the sampling errors, is proposed for estimating the mean trace length on infinite, vertical sections from the observations made on finite, rectangular, vertical exposures. The method is applicable to discontinuities whose orientation is described by a probability distribution function. The method requires that the numbers of discontinuities with both ends observed, one end observed, and both ends censored be known. The lengths of observed traces and the density function of trace length are not required. The derivation assumes that midpoints of traces are uniformly distributed in the vertical plane. Also independence between trace length and orientation is assumed. Data on a Pennsylvania shale in Ohio, U. S. A., were used as an example.Notations
dip direction
-
direction of sampling plane
-
acute angle between dip direction and sampling plane
-
dip angle
-
A
apparent dip angle
-
mean density of trace mid-points per unit area
-
mean trace length
-
D
diameter of discontinuity
-
f (.),g (.)
probability density function
-
h
height of rectangular window
-
estimator of mean trace length
-
m
sample size, number of discontinuities intersecting window
-
m
0
number of discontinuities intersecting window with both ends censored
-
m
2
number of discontinuities intersecting window with both ends observed
-
n, N
expected number of discontinuities intersecting the window
-
n
0,N
0
expected number of discontinuities intersecting the window with both ends censored
-
n
2,N
2
expected number of discontinuities intersecting the window with both ends observed
-
Pr (.)
probability
-
w
width of rectangular window
-
x
trace length 相似文献
18.
长江三峡库区广泛发育着两侧岩性不同的不连续面（称为异性不连续面）,研究其峰值剪切强度可为相关岩体的稳定性分析和评价提供理论依据。采用高强石膏浇注3组不同形貌且上、下壁面强度不同的不连续面试件,并在不同常法向应力下进行剪切试验。引入不连续面壁组合系数λ来综合量化不连续面壁的抗压强度和基本摩擦角对异性不连续面峰值剪切强度的影响,λ越小,上、下不连续面壁强度差异越大。异性不连续面的峰值剪切强度随λ的增加呈非线性增加,且在高法向应力下更为显著。在Barton公式的基础上,通过多元回归分析建立了估算异性不连续面峰值剪切强度的经验公式。采用天然和人工锯齿形异性不连续面的直剪试验结果对新公式做了进一步验证,试验剪切强度与新公式预测值吻合较好。简要分析了新公式在软硬互层岩质边坡稳定性评价中的应用。最后,讨论了Wu公式的适用性以及新公式的优点和不足。 相似文献
19.
20.
The fracturing phenomenon within the reservoir environment is a complex process that is controlled by several factors and may occur either naturally or by artificial drivers. Even when deliberately induced, the fracturing behaviour is greatly influenced by the subsurface architecture and existing features. The presence of discontinuities such as joints, artificial and naturally occurring faults and interfaces between rock layers and microfractures plays an important role in the fracturing process and has been known to significantly alter the course of fracture growth. In this paper, an important property (joint friction) that governs the shear behaviour of discontinuities is considered. The applied numerical procedure entails the implementation of the discrete element method to enable a more dynamic monitoring of the fracturing process, where the joint frictional property is considered in isolation. Whereas fracture propagation is constrained by joints of low frictional resistance, in non-frictional joints, the unrestricted sliding of the joint plane increases the tendency for reinitiation and proliferation of fractures at other locations. The ability of a frictional joint to suppress fracture growth decreases as the frictional resistance increases; however, this phenomenon exacerbates the influence of other factors including in situ stresses and overburden conditions. The effect of the joint frictional property is not limited to the strength of rock formations; it also impacts on fracturing processes, which could be particularly evident in jointed rock masses or formations with prominent faults and/or discontinuities. 相似文献