Empirical Assessment of the Mean Block Volume of Rock Masses Intersected by Four Joint Sets

Excavations in jointed rock may liberate rock blocks that may fall by gravity or slide along the discontinuity. The orientation of discontinuities is one of the major input parameters in the conventional deterministic stability analysis of rock blocks. As the mean orientation of a discontinuity is often derived from a large number of joint-set data obtained from site investigation, Fisher's constant is commonly employed to represent the degree of dispersion of individual discontinuity orientation. However, such dispersion factors are rarely used in the conventional analysis. A probabilistic-based approach is proposed in this paper to incorporate Fisher's constant in the stability analysis of rock blocks. To account for the uncertainty reflected by the sample dispersion, data are generated systematically around each mean discontinuity normal, based on its Fisher's constant. The probability of rock block failure at a certain location and the largest possible block volume are determined in a logical manner. A microcomputer program has been developed to automate the analysis, and illustrative examples are shown to demonstrate the importance of incorporating the Fisher's constant of individual discontinuity in the stability analysis. In addition, risk mapping plots are presented to enable visual selection of an optimal route for excavation from one location to another. Key words : discontinuity, factor of safety, probability of failure, rock block, rock excavation, stability analysis.

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Block Volume Estimation from the Discontinuity Spacing Measurements of Mesozoic Limestone Quarries, Karaburun Peninsula, Turkey

The Scientific World JOURNAL ◽

10.1155/2014/363572 ◽

2014 ◽

Vol 2014 ◽

pp. 1-10 ◽

Cited By ~ 5

Author(s):

Hakan Elci ◽

Necdet Turk

Keyword(s):

Rock Mass ◽

Shape Factor ◽

Volume Estimation ◽

Ratio Method ◽

Discontinuity Spacing ◽

The Mean ◽

Limestone Quarries ◽

Average Block ◽

Block Volume

Block volumes are generally estimated by analyzing the discontinuity spacing measurements obtained either from the scan lines placed over the rock exposures or the borehole cores. Discontinuity spacing measurements made at the Mesozoic limestone quarries in Karaburun Peninsula were used to estimate the average block volumes that could be produced from them using the suggested methods in the literature. The Block Quality Designation (BQD) ratio method proposed by the authors has been found to have given in the same order of the rock block volume to the volumetric joint count (Jv) method. Moreover, dimensions of the 2378 blocks produced between the years of 2009 and 2011 in the working quarries have been recorded. Assuming, that each block surfaces is a discontinuity, the mean block volume (Vb), the mean volumetric joint count (Jvb) and the mean block shape factor of the blocks are determined and compared with the estimated mean in situ block volumes (Vin) and volumetric joint count (Jvi) values estimated from the in situ discontinuity measurements. The established relations are presented as a chart to be used in practice for estimating the mean volume of blocks that can be obtained from a quarry site by analyzing the rock mass discontinuity spacing measurements.

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Fracture Frequency and Block Volume Distribution in Rock Masses

Rock Mechanics and Rock Engineering ◽

10.1007/s00603-020-02172-6 ◽

2020 ◽

Vol 53 (10) ◽

pp. 4673-4689

Author(s):

Maria Stavropoulou ◽

George Xiroudakis

Keyword(s):

Volume Distribution ◽

Rock Masses ◽

Fracture Frequency ◽

Block Volume

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Photo-electric Hβ and uvby photometry

Symposium - International Astronomical Union ◽

10.1017/s0074180900053407 ◽

1966 ◽

Vol 24 ◽

pp. 170-180

Author(s):

D. L. Crawford

Keyword(s):

Narrow Band ◽

Line Strength ◽

Interference Filter ◽

B Stars ◽

Relative Line ◽

The Mean ◽

F Stars ◽

Two Parameters ◽

Filter Photometry ◽

The Continuum

Early in the 1950's Strömgren (1, 2, 3, 4, 5) introduced medium to narrow-band interference filter photometry at the McDonald Observatory. He used six interference filters to obtain two parameters of astrophysical interest. These parameters he calledlandc, for line and continuum hydrogen absorption. The first measured empirically the absorption line strength of Hβby means of a filter of half width 35Å centered on Hβand compared to the mean of two filters situated in the continuum near Hβ. The second index measured empirically the Balmer discontinuity by means of a filter situated below the Balmer discontinuity and two above it. He showed that these two indices could accurately predict the spectral type and luminosity of both B stars and A and F stars. He later derived (6) an indexmfrom the same filters. This index was a measure of the relative line blanketing near 4100Å compared to two filters above 4500Å. These three indices confirmed earlier work by many people, including Lindblad and Becker. References to this earlier work and to the systems discussed today can be found in Strömgren's article inBasic Astronomical Data(7).

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A one-dimensional self-gravitating stellar gas

Symposium - International Astronomical Union ◽

10.1017/s0074180900105261 ◽

1966 ◽

Vol 25 ◽

pp. 46-48 ◽

Cited By ~ 2

Author(s):

M. Lecar

Keyword(s):

Gravitational Field ◽

Phase Space ◽

Motion Picture ◽

Space Distribution ◽

Two Dimensional ◽

One Dimensional ◽

Phase Space Distribution ◽

Dimensional Phase Space ◽

The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

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The motion of a lunar orbiter

Symposium - International Astronomical Union ◽

10.1017/s0074180900105686 ◽

1966 ◽

Vol 25 ◽

pp. 373

Author(s):

Y. Kozai

Keyword(s):

Degrees Of Freedom ◽

Dimensional Space ◽

Artificial Satellite ◽

Equations Of Motion ◽

Triaxial Ellipsoid ◽

The Moon ◽

Secular Motion ◽

The Earth ◽

Close Satellite ◽

The Mean

The motion of an artificial satellite around the Moon is much more complicated than that around the Earth, since the shape of the Moon is a triaxial ellipsoid and the effect of the Earth on the motion is very important even for a very close satellite.The differential equations of motion of the satellite are written in canonical form of three degrees of freedom with time depending Hamiltonian. By eliminating short-periodic terms depending on the mean longitude of the satellite and by assuming that the Earth is moving on the lunar equator, however, the equations are reduced to those of two degrees of freedom with an energy integral.Since the mean motion of the Earth around the Moon is more rapid than the secular motion of the argument of pericentre of the satellite by a factor of one order, the terms depending on the longitude of the Earth can be eliminated, and the degree of freedom is reduced to one.Then the motion can be discussed by drawing equi-energy curves in two-dimensional space. According to these figures satellites with high inclination have large possibilities of falling down to the lunar surface even if the initial eccentricities are very small.The principal properties of the motion are not changed even if plausible values ofJ3andJ4of the Moon are included.This paper has been published in Publ. astr. Soc.Japan15, 301, 1963.

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On nearly-commensurable periods in the restricted problem of three bodies, with calculations of the long-period variations in the interior 2:1 case

Symposium - International Astronomical Union ◽

10.1017/s0074180900105480 ◽

1966 ◽

Vol 25 ◽

pp. 197-222 ◽

Cited By ~ 4

Author(s):

P. J. Message

Keyword(s):

Periodic Solution ◽

Periodic Solutions ◽

Large Amplitude ◽

Restricted Problem ◽

Small Amplitude ◽

Minor Planets ◽

Long Period ◽

Numerical Integrations ◽

Period Variations ◽

The Mean

An analytical discussion of that case of motion in the restricted problem, in which the mean motions of the infinitesimal, and smaller-massed, bodies about the larger one are nearly in the ratio of two small integers displays the existence of a series of periodic solutions which, for commensurabilities of the typep+ 1:p, includes solutions of Poincaré'sdeuxième sortewhen the commensurability is very close, and of thepremière sortewhen it is less close. A linear treatment of the long-period variations of the elements, valid for motions in which the elements remain close to a particular periodic solution of this type, shows the continuity of near-commensurable motion with other motion, and some of the properties of long-period librations of small amplitude.To extend the investigation to other types of motion near commensurability, numerical integrations of the equations for the long-period variations of the elements were carried out for the 2:1 interior case (of which the planet 108 “Hecuba” is an example) to survey those motions in which the eccentricity takes values less than 0·1. An investigation of the effect of the large amplitude perturbations near commensurability on a distribution of minor planets, which is originally uniform over mean motion, shows a “draining off” effect from the vicinity of exact commensurability of a magnitude large enough to account for the observed gap in the distribution at the 2:1 commensurability.

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