The Theory of Strata Mechanics

282 Pages·1991·7.138 MB·1-278\282

by  HENRYK GIL (Eds.)

Further Titles in The Series:
1. G. SANGLERAT — THE PENETROMETER AND SOIL EXPLORATION
2. Q. ZARUBA AND V. MENCL—LANDSLIDES AND THEIR CONTROL
3. Ε. E. WAHLSTROM —TUNNELING IN ROCK
4. R. SILVESTER —COASTAL ENGINEERING, 1 and 2
5. R. N. YOUNG AND B. P. WARKENTIN — SOIL PROPERTIES AND BEHAVIOUR
6. Ε. E. WAHLSTROM — DAMS, DAM FOUNDATIONS, AND RESERVOIR SITES
7. W. F. CHEN — LIMIT ANALYSIS AND SOIL PLASTICITY
8. L. N. PERSEN — ROCK DYNAMICS AND GEOPHYSICAL EXPLORATION
Introduction to Stress Waves in Rocks
9. M. D. GIDIGASU — LATERITE SOIL ENGINEERING
10. Q. ZARUBA AND V. MENCL —ENGINEERING GEOLOGY
11. Η. K. GUPTA AND Β. K. RASTOGI —DAMS AND EARTHQUAKES
12. F. H. CHEN — FOUNDATIONS ON EXPANSIVE SOILS
13. L. HOBST AND J. ZAjiC — ANCHORING IN ROCK
14. B. VOIGHT (Editor) — ROCKSLIDES AND AVALANCHES, 1 and 2
15. C. LOMNITZ AND E. ROSENBLUETH (Editors) — SEISMIC RISK AND ENGINEERING
DECISIONS
16. C. A. BAAR —APPLIED SALT-ROCK MECHANICS, 1
The tn-Situ Behaviour of Salt Rocks
17. A. P. S. SELVADURAI — ELASTIC ANALYSIS OF SOIL-FOUNDATION INTERACTION
18. J. FEDA —STRESS IN SUBSOIL AND METHODS OF FINAL SETTLEMENT
CALCULATION
19.A . K&ZDI — STABILIZED EARTH ROADS
20. E. W. BRAND AND R. P. BRENNER (Editors) — SOFT-CLAY ENGINEERING
21. A. MYSLIVEC AND Z. KYSELA —THE BEARING CAPACITY OF BUILDING
FOUNDATIONS
22. R. N. CHOWDHURY — SLOPE ANALYSIS
23. P. BRUUN — STABILITY OF TIDAL INLETS
Theory and Engineering
24. Ζ. ΒΑΖΑΜΕ —METHODS OF FOUNDATION ENGINEERING
25.A . KiZDI — SOIL PHYSICS
Selected Topics
26. H. L. JESSBERGER (Editor) — GROUND FREEZING
27. D. STEPHENSON — ROCKFILL IN HYDRAULIC ENGINEERING
28. P. E. FRIVIK, N. JANBU, R. SAETERSDAL AND L. I. FINBORUD (Editors) — GROUND
FREEZING 1980
29. P. PETER —CANALS AND RIVER LEVIES
30. J. FEDA—MECHANICS OF PARTICULATE MATERIALS
THE PRINCIPLES
31. Q. ZARUBA AND V. MENCL—LANDSLIDES AND THEIR CONTROL
Second, completely revised edition
32. I. W. FARMER (Editors) — STRATA MECHANICS
33. L. HOBST AND J. ZAJIC — ANACHORING IN ROCK AND SOIL
Second, completely revised edition
34. G. SANGLERAT, G. OLIVARI AND B. CAMBOU — PRACTICAL PROBLEMS IN SOIL
MECHANICS AND FOUNDATION ENGINEERING, 1 and 2
35. L. R£mAT I — GROUNDWATER IN CIVIL ENGINEERING
36. S. S. VYALOV — RHEOLOGICAL FUNDAMENTALS OF SOIL MECHANICS
37. P. BRUUN (Editor) — DESIGN AND CONSTRUCTION OF MOUNDS FOR
BREAKWATERS AND COASTAL PROTECTION
38. W. K. CHEN AND G. Y. BALADI — SOIL PLASTICITY
Theory and Implementation
(continued on p. 279)
39. Ε. Τ. HAN RAH ΑΝ — THE GEOTECHNICS OF REAL MATERIALS
The e e Method
gt k
40. J. ALDORF AND K. EXNER —MINE OPENINGS
Stability and Support
41. J. E. GILLOT — CLAY IN ENGINEERING GEOLOGY
42. A. S. CAKMAK (Editor) — SOIL DYNAMICS AND LIQUEFACTION
43. A. S. CAKMAK (Editor) — SOIL-STRUCTURE INTERACTION
44. A. S. CAKMAK (Editor) — GROUND MOTION AND ENGINEERING SEISMOLOGY
45. A. S. CAKMAK (Editor) — STRUCTURES, UNDERGROUND STRUCTURES, DAMS
AND STOCHASTIC METHODS
46. L. RliTHATI — PROBABILISTIC SOLUTIONS IN GEOTECHNICS
47. Β. M. DAS —THEORETICAL FOUNDATION ENGINEERING
48. W. DERSKI, R. IZBICKI, I. KISIEL AND Z. MROZ — ROCK AND SOIL MECHANICS
49. T. ARIMAN, H. HAMADA, A. C. SINGHAL, M. A. HAROUN AND A. S. CAKMAK
(Editors) — RECENT ADVANCES IN LIFELINE EARTHQUAKE ENGINEERING
50. Β. M. DAS —EARTH ANCHORS
51. K. THIEL—ROCK MECHANICS IN HYDROENGINEERING
52. W. F. CHEN AND X. L. LIU —LIMIT ANALYSIS IN SOIL MECHANICS
Second, completely revised edition
53. W. F. CHEN AND E. MIZUNO — NONLINEAR ANALYSIS IN SOIL MECHANICS
54. F. H. CHEN —FOUNDATIONS ON EXPANSIVE SOILS
Second, completely revised edition
55. J. VERFEL —ROCK GROUTING AND DIAPHRAGM WALL CONSTRUCTION
56. B.N. WHITTAKER AND D.J. REDDISH— SUBSIDENCE
Occurrence, Prediction and Control
57. E. NONVEILLER —GROUTING
Theory and Practice
58. V. KOLAR AND I. Ν EM EC — MODELLING OF SOIL-STRUCTURE INTERACTION
59A. R.S. SINHA —UNDERGROUND STRUCTURES
Design and Instrumentation
59B. R.S. SINHA AND L. OZDEMIR — UNDERGROUND STRUCTURES
Instrumentation and Constructions
60. R. L. HARLAN, Κ. E. KOLM AND E. D. GUTENTAG — WATER-WELL DESIGN
AND CONSTRUCTION
61. I. KAZDA —FINITE ELEMENT TECHNIQUES IN GROUNDWATER FLOW STUDIES
with applications in hydraulic and geotechnical engineering
62. L. FIALOVSZKY —SURVEYING INSTRUMENTS AND THEIR OPERATIONAL
PRINCIPLES
63. H. GIL —THE THEORY OF STRATA MECHANICS
DEVELOPMENTS IN GEOTECHNICAL ENGINEERING VOL. 63
THE THEORY OF
STRATA MECHANICS
by
HENRYK GIL
Silesian Technical University
Gliwice, Poland
ELSEVIER
Amsterdam-Oxford-New York-Tokyo
PWN —POLISH SCIENTIFIC PUBLISHERS
Warsaw
1991
Translated from the Polish by Jolanta Krauze
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Library of Congress Cataloging-in-Publication Data
Gil, Henryk. 1933-
The theory of strata mechanics / by Henryk Gil: [translated by Jolanta Krauze].
p. cm. — (Developments in geotechnical engineering: vol. 63)
Includes bibliographical references.
ISBN 0-444-98761-4 (U.S.)
1. Mining engineering. 2. Rock mechanics. I. Series:
Developments in geotechnical engineering: 63.
TO153.G49 1990
622'.2—dc20
90-31420
CIP
ISBN 0-444-98761-4 (Vol. 63)
ISBN 0-444-41662-5 (Series)
Copyright (g) by PWN—Polish Scientific Publishers—Warszawa, 1991
All rightsr eserved. No part of this publication may be reproduced, stored in retrieval system
or transmitted in any form or by any means, electronic, mechanical, photocopying, recording
or otherwise, without the prior written permission of the copyright owner
Printed in Poland
Introduction
0.1 Development of rock mass mechanics
During the last thirty years, the increasing need for extracting coal from
new mining fields, especially from unmined protective pillars and seams that
are threatened with rock bursts and rock-gas eruptions, has accelerated the
development of research in the fundamental mining discipline known as rock
mass mechanics or geomechanics. The importance of methods developed by
rock mass mechanics is still growing because the depths at which mining is
carried out nowadays increase, and this is associated with increased stresses
and increased mining hazards. Moreover, at greater depths it is more difficult
to maintain the transportation and mining drifts in continuous operation.
Generally, rock mass mechanics is concerned with rock mass movements
and with the phenomena accompanying them. The rock mass surrounding
an excavation moves towards it, causing the rocks to deform and altering the
primary stress state that existed when the rock mass was undisturbed. The
strain and stress state produced by mining also depends essentially on the
physical properties of the rocks. For this reason, in modern rock mass mech
anics, the methods for evaluating the physical properties of rocks from the
point of view of mining engineering are considered to be most important.
Extensive theoretical, laboratory, and in-situ investigations carried out
in many countries (including Poland), where coal production has been greatly
developed, have resulted in considerable achievements in the field of rock
mass mechanics. It is impossible to include all these achievements in a single
monograph, and therefore in the present book the author has attempted to
construct a synthetic mathematical description of the rock mass movements
and of the strain and stress state induced by mining, in particular when extract
ing mineral deposits. Studying the available literature on the subject, we can
distinguish three major trends in the development of rock mass mechanics:
2 INTRODUCTION
— The first approach, based on empirical investigations (carried out by
Dumont, Goldreich, Szulz, Sparry, Hausse, Banneax, Thririart, and others),
has developed integral-geometrical theories which using in-situ measurements
of the profile of the so-called subsidence trough represent this profile by approxi
mative integral functions. The required accuracy of this approximation can
be achieved by appropriately assuming the form of the influence function
which occurs as the kernel of the integral. This approach is represented by
Bals (1931/1932), Beyer (1945), Brauner (1959), Flaschentrager (1938), Kein-
horst (1925), Kuothe (1953), King and Whetton (1957), Kochmanski (1956),
Perz (1948), and others. Their results have found wide practical applications
in mining works carried out in protective pillars and in studying effects that
this mining exerts upon the ground surface.
— The second approach was initiated by Litwiniszyn (1953) who by com
bining the Avershin hypothesis with the parabolic form of the continuity
equation obtained a solution consistent with the Rnothe integral solution that
involves the Gauss function. This inspired Litwiniszyn with the idea that a rock
mass set in motion can be treated as a medium governed by certain rules of
the probability calculus. As the model of the rock mass, he adopted a granular
medium composed of isolated elements which, when in motion, may lose
contact between one another. To describe movements of the grains of this
granular medium placed in the gravity field and unbalanced, and the random
movements of the voids formed when a certain number of the grains have been
removed from the medium, Litwiniszyn used the probabilistic methods.
Assuming that the displacement components are random variables dependent
on a parameter, he has shown that the development of subsidences in a rock
mass is a stochastic process. Litwiniszyn has created what is known as the
kinetics of a stochastic medium, which may be modelled by a granular medium
(Litwiniszyn, 1954, 1956, 1961). A movement of such a medium is governed
by the "transition function". In a two-dimensional case (Litwiniszyn, 1956)
this function satisfies an integral equation, analogous to Smoluchowski's
equation known in the theory of diffusion and stochastic processes. In their
several works Litwiniszyn and Smolarski (1962, 1964) and Smolarski (1967)
have determined all the components of the displacement field induced in a sto
chastic medium. They have shown that the transition functions satisfy a set
of integral equations equivalent to Smoluchowski's equations. To find certain
classes of solutions of this set, Litwiniszyn uses the Fourier transforms and
shows that the set of integral equations can be reduced to a set of functional
equations. Smolarski makes use of Kolmogorov's method for the solution
of a single Smoluchowski equation and derives a set of second order partial
differential equations whose integrals satisfy the set of Smoluchowski equa-
DEVELOPMENT OF ROCK MASS MECHANICS 3
tions. Based on the equations of the stochastic model, Litwiniszyn (1956),
Smolarski (1964) and also other investigators (Brauner, 1959; Klein, 1973,
1978; Ryncarz, 1968; Trutwin, 1962) solved several boundary value problems
important for engineering practice.
— The third approach uses the methods of the mechanics of continuous
media, especially those of elasticity, viscoelasticfty, and plasticity. The state
equations derived for an adopted model of the rock mass and describing the
relations between stresses, strains and the rate of their variation, in conjunction
with the equations of equilibrium subjected to assumed initial and boundary
conditions, enable us to find not only the components of the displacement
vector and of the strain tensor, but also those of the stress tensor.
The fundamental assumptions underlying several solutions thus far ob
tained using the continuous model are those of continuity, homogeneity, and
isotropy of the rock mass which, in view of the well-known complexity of
rock masses are far-fetched idealizations. Nevertheless, these solutions are
very important since based on them we can examine the structure (e.g., strati
fied) and the character (e.g., elasticoplastic) of deformation of more complex
rock masses.
In Poland, significant contributions to the development of this line of
research were made by Salustowicz (1955, 1956) who determined the distribu
tion of stress and displacement around drifts and mining excavations. Berry
(1964), Barenblatt and Khrystyanovich (1955), Gerard and Harisson (1970),
Dymek (1967, 1969), Golecki and Jozkiewicz (1963), Gupta (1967), Lisowski
(1957), Mirsa and Sen (1976), Sales and Berry (1962), Salomon (1965), Szefer
(1964, 1965), and other investigators used the elastic model of the rock mass
in considering the distributions of stress and displacement.
The visco-elastic model was first used for examining the movements of
rock masses by Salustowicz (1958) and Litwiniszyn (1955), and later by Mar
shall and Berry (1968) and others. In Poland, later studies based chiefly on the
"standard" model were conducted by Filcek (1963), Gil and Kraj (1972, 1974),
Krzyzowski (1976), Jaworski (1979), Dymek (1973, 1976), Zaj^c (1971),
and Szefer (1964).
Z. Yerzhanov applied the phenomenological theory of hereditary creep to
studies on rocks. In this case, the state equation is the Boltzmann-Volterra inte
gral equation with the kernel of Rabotnov's type, the constants that characterize
the kernel being determined from a creep test. This model has mainly been
applied to problems associated with the construction of underground structures.
Elastic-plastic and pure plastic models have also been used, based on the
known works of Ilyushin (1948, 1978), Sokolovski (1969), Kachnov (1969,
1974), Khrystyanovich and Shemyakin (1967), and others. These models also
4 INTRODUCTION
include failure of the rocks surrounding the contour of an excavation (Ruppe-
neit, 1954; Ruppeneit and Liberman, 1960; Iiberman, 1962, 1969; Protosenia,
1964; Olevyannyi and Amusin, 1974; Amusin, 1977; Alimzhanov, 1977;
Fisenko, 1972; Guz, 1977).
Mroz and Staroo (1977) proposed using the continuous model to describe
the brittle-plastic properties of rocks. This model simulates the time-indepen
dent properties of a progressively cracking medium.
In studies based on the elastic model numerical methods have extensively
been used and developed. They will not, however, be discussed in this book.
We shall mention here the finite element method, which is broadly discussed
by Zienkiewicz (1972), and the limit-element method devised by Brady and
Bray (1977). These methods have found wide application in rock mass mech
anics in solving two- and three-dimensional boundary problems, especially
those involving excavations of complex shapes. Another numerical method
for studying three-dimensional problems of rock mass mechanics based on
the theory of elasticity has been proposed by Deist, Salomon and Georgiadis
(1974).
Although using two basic models of the rock mass, these studies have
explained several phenomena that accompany mining, many vital problems
encountered in modern mining have not been solved. Among them we may
mention rock bursts in mines, gas-rock eruptions in rock masses that contain
free or absorbed gases, and the influence of faults on the rock mass and on the
ground surface. Moreover, laboratory examinations carried out on rock
samples have proved that plastic deformations develop in rocks from the very
beginning of load application. To deal with all these problems, the author
proposes a model based on the continuous dislocation theory, which describes
the elastic-plastic state of deformation developed in a rock mass. As applied
to problems of rock mass mechanics this model belongs to the group of con
tinuous elastic models that contain internal stress sources. It has two basic
features:
1. It does not assume that plastic deformations in a rock mass can only
be induced when the stress acting in it exceeds a certain definite value.
2. It assumes that the distribution of the Burgers vector in the rock mass
is continuous.
As to the first feature, the model is identical to Gilman's (1965) model
proposed for describing dislocation movements and verified experimentally
for certain Carboniferous rocks. The second feature implies that the tensor
of plastic strain in the rock mass be known and that the tensor of dislocation
density be expressed in terms of this tensor.
MECHANICS OF ROCK MASSES AND CONTINUOUS MEDIA 5
0.2 Interrelation between the mechanics of rock masses and the mechanics of
continuous media
The development of the separate line of research in rock mass mechanics
that makes use of continuous mathematical models provides a sufficient
proof that the methods of the mechanics of continuous media can be used
successfully in rock mass mechanics. The development of the mechanics of
continuous media, in particular the theory of elasticity, rheology, the theory of
plasticity, and the dislocation theory, contributes to the development of rock
mass mechanics. The methods developed by these disciplines enable us to
describe the complex phenomena occurring in rock masses more and more
precisely.
It should, however, be noted that none of the models so far constructed
describes the behaviour of a rock mass disturbed by mining to an accuracy
sufficient for practical purposes. The individual models do, however, permit
us to study the behaviour of rocks in selected regions of the rock mass. For
example, the process of unloading of the rock mass that surrounds narrow
excavations is a typical elastic process and has successfully been examined
using linear elastic models. The behaviour of rocks in the vicinity of longwalls
is sufficiently represented by visco-elastic models. The elastic-plastic properties
of seams when plastic and elastic deformations developed in them are of the
same order of magnitude can be described by the dislocation model. Finally,
the effect of cracking is well represented by the brittle-plastic model. The
mining engineer supervising a mining project constructed under complex
geological conditions may use several different models and combine them to
obtain the required accuracy.
1. Rock masses disturbed by mining
1.1 General characteristics of rock masses
As defined from the point of view of rock mechanics, a rock mass is that
portion of the Earth's crust in which man carries out or plans to carry out
mining of deposits. The rock mass is a medium showing a great variety of
distinct properties which depend not only on the properties of the individual
rocks of which it is built up but also on its entire mass. This means that the
phenomena occurring in rocks manifest themselves in the laboratory in ways
other than in nature.
Rocks have a very complex structure. They are heterogeneous and de­
formed, which affects the properties of the rock mass to a great extent. If the
rock mass is, in addition, saturated with water, its strength is considerably
reduced.
One of the most characteristic structural features of a rock mass is that it
contains planes of reduced cohesion, such as planes of stratification and cleav­
age. These planes form an almost orthogonal system cutting the rock mass
into blocks parallelepipedal in shape. A cross-section cut through one such
plane shows traces of the remaining planes, forming a net. This net may be
dense or loose. Dense nets may be found in weak rocks such as schists or car­
bons, whereas loose nets occur in very strong rocks such as sandstones with
a silica cement.
The pattern in which the planes of reduced cohesion are distributed in
a rock mass essentially affects the behaviour of rocks surrounding mining
excavations made in it. This is so since the tensile and shear strength of the
rock is greatly reduced in these planes.
Other important properties of rock masses are their stratification and pri­
mary stressing. Rock layers of considerable strength occur alternately with
layers of weak rocks, so that the properties of adjacent layers of a rock mass
differ in a step-wise manner. In Poland, the stress component acting in the
direction of gravity increases by about 245 χ 104 N/m2 per each 100 m depth.
This is the cause of the primary stressing of rocks.