Soil Mechanics of Earthworks, Foundations and Highway Engineering

354 Pages·1988·9.35 MB·English

Handbook
of Soil Mechanics
Volume 3
Soil Mechanics of Earthworks, Foundations
and Highway Engineering
by
Ârpâd Kézdi
and
Lâszlo Réthâti
Elsevier
Amsterdam · Oxford · New York · Tokyo 1988
Joint edition published by Elsevier Science Publishers, Amsterdam,
and Akadémiai Kiado, Budapest
Handbook of Soil Mechanics
Vol. 1. Soil Physics
Vol. 2. Soil Testing
Vol. 3. Soil Mechanics of Earthworks, Foundations and Highway Engineering
Vol. 4. Application of Soil Mechanics in Practice: Examples and Case Histories
This is the revised and enlarged version of the German Handbuch der Bodenmechanik. Band 2: Bodenmechanik
im Erd-, Grund- und Straßenbau, published by Akadémiai Kiado, Budapest in co-edition
with VEB Verlag für Bauwesen, Berlin (GDR)
Translated by H. Héjj
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Library of Congress Cataloging-in-Publication Data
Kézdi, Arpâd
[Bodenmechanik im Erd-, Grund-, und Strassenbau. English]
Soil mechanics of earthworks, foundations, and highway engineering
by Ârpâd Kézdi and Lâszlo Réthâti; [translated by H. Héjj].
p. cm. — (Handbook of soil mechanics; v. 3)
Translation of the rev. & enl. version of: Bodenmechanik im Erd-,
Grund-, und Strassenbau, originally published as Bd. 2 of Hanbduch
der Bodenmechanik.
Bibliography: p.
Includes index.
ISBN 0-444-98929-3 (U.S.)
1. Soil mechanics — Handbooks, manuals, etc. I. Réthâti, Lâszlo.
II. Title. III. Series: Kézdi, Ârpâd. Handbuch der Bodenmechanik.
English: v. 3.
TA710.K4913 1979 vol. 3
624. Γ513 s—de 19 88-2363
[624. Γ5136] CIP
With 561 Illustrations and 46 Tables
© Akadémiai Kiado, Budapest 1988
All rights reserved.
No part of this publication may be reproduced, stored in a 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 Hungary by Akadémiai Kiado es Nyomda Vallalat, Budapest
Preface
The first and second volumes of the Handbook of
Soil Mechanics, published in 1974 and 1979, were
a great success in the field of soil mechanics. This
third volume deals mainly with practical problems.
This is a revised and enlarged version of the second
volume of the Handbuch der Bodenmechanik,
published in German jointly by the Akadémiai
Kiado and VEB Verlag für Bauwesen (GDR).
Unfortunately, the senior author, Ârpâd Kézdi
was unable to complete the initially planned four vol-
umes of this series due to his sickness and untimely
death. As a colleague and friend I have been most
honoured to help in updating this third volume
which has been based on the literature of the past
twenty years and on my own research having added
several new sections. As to the reference list we ask
the readers' understanding for its being incomplete
due to the untimely death of Professor Kézdi.
My aim in this book has been concordant with
Arpâd Kézdi's to summarize the results of soil
mechanics describing at the same time the trends
of development of this field.
The assistance and encouragement of the Aka-
démiai Kiado and Elsevier Science Publishers are
gratefully acknowledged.
LÄSZLO RÉTHAT1
Chapter 1.
Soil mechanics of earthwork
1.1 Introduction contingencies to be dealt with during the course
of construction on the basis of careful observation
Construction of earthworks involving billions of site conditions. Even a thorough soil survey
of cubic meters are carried out every year in con- might not detect some seemingly minor, but in
nection with civil engineering. They serve many fact important changes in soil conditions which,
purposes: they may be used as the foundation or if brought to light during construction, may
as a part of a structure, or they may be made necessitate a complete revision of the original
with the sole purpose of providing the necessary — and often only tentative — plans in order to
space for construction, as in the case of foundation match the changed conditions.
pits. The stability and durability of the earthwork Site observations should be extended not only
are prerequisites for the stability and durability to soil conditions but also to the geology, hydrol-
of the superstructure and for economy of con- ogy, meteorology and vegetation of the area in
struction. Shortsighted planning or poor work- question, and the combined effect of all these
manship in carrying out earthworks may have factors must be taken into consideration in stabil-
detrimental consequences: swelling or shrinkage ity analyses.
of the earth material, excessive deformation or This chapter deals with stability problems of
subsidence of the fill, slips of slopes, ground failure, various earthworks. The treatment is essentially
etc. Once the damage has occurred, reconstruc- theoretical and is based on mechanics. Neverthe-
tion or remedial measures usually cost a multiple less, we shall never omit to point out, where
of what would have been required for adequate appropriate, the importance of the influencing
preliminary soil exploration, design and con- factors mentioned in this paragraph.
struction.
During construction as well as after completion,
earthworks are constantly effected by weather 1.2 Stability of slopes
and exposed to atmospheric agents. Continually
changing temperature, precipitation, physical and 1.2.1 General remarks
chemical weathering, stagnant or flowing surface
water and groundwater, frost and ice are the most When an artifical earthwork, cutting or em-
important factors that endanger stability. Among bankment (Fig. 1) is to be constructed, the incli-
these the action of water deserves particular nation of its lateral boundary surfaces, called the
attention: earth stability problems are, as a rule, slopes, cannot be selected arbitrarily, since this
closely linked with those of drainage. Because of depends on the internal resistance of the earth
the ever-changing character of the influencing material. The inclination of a slope is usually
factors, stability problems should never be re- expressed as the tangent of its angle to the hori-
garded as static. The variation in soil conditions zontal. Tan β values are conveniently written in
and environment and the dynamic character of the form of a fraction whose numerator is always 1,
the factors must always be taken into consider- thus: 1 in 1 (ρ = cot β = 4/4), 1 in 1.5 (ρ = 6/4),
ation. 1 in 2 (ρ — 8/4) etc Typical uses of slopes are
Only this kind of approach will enable the civil those of embankments and cuts for roads, rail-
engineer to understand the manifold interactions ways, canals, waterways, excavations, foundation
between natural environment and man-made pits, spoil tips, and the like.
earthworks and to tackle stability problems suc- If a slope is made steeper than would be per-
cessfully. It should also be pointed out that even mitted by the available shear strength of the soil,
a most meticulous preliminary soil survey is not or if the intrinsic shear resistance of the soil in
likely to reveal all the hazards and influencing an originally stable slope has been reduced, for
factors and it is therefore impracticable to at- example through softening of the material, a slip
tempt to solve stability and drainage problems or slide results; part of the sloping soil mass
in advance in every detail. There will always be begins to move downward and outward as shown
12 Soil mechanics of earthworks
These maps are being elaborated in an ever-
widening range in most countries. During recent
years there has been a growing interest in hazard
and risk mapping, which is certainly due to an
increase of human activity in the realm of critical
areas. As geology surely plays an important role
in landslide development, the problem of mapping
has also been included on the agenda of the Inter-
national Association of Engineering Geology (Sym-
posium at Newcastle, 1979; Congress in Paris,
1980).
1.2.2 Cohesionless granular soils
In dry, clean sands the internal resistance is
entirely due to interparticle friction. An embank-
ment made of such soil remains stable, irrespective
of its height, as long as the angle of its slope β is
smaller than the angle of internal friction Φ
Fig. 1. Earthworks confined within slopes measured in the loose state of the soil. For this
case the safety factor ν against slip can be denned
as:
in Fig. 2. Similar movements — commonly tan Φ
known as landslides — occur in natural slopes and ν = .
on hillsides. tan β
The causes of instability of slopes are many, and When β = Φ, the slope is in a limiting state of
the resulting movements are very different in
equilibrium. In an infinite slope two sets of failure
character. An exhaustive discussion of this topic
planes are developed, one being parallel to the
is beyond the scope of this book. We shall there-
slope and the other vertical (See Vol. 1, Chapter 9).
fore be concerned primarily with the basic problem
The assumption of the Möhr failure theory that
of finding criteria for the stability of a given slope the intermediate principal stress (T is irrelevant
in a given soil, in order to ascertain what is the 2
to the state of failure is not fully satisfied in dry
safety factor against failure. It should be empha-
sands in that the limiting value of the slope angle
sized, however, that stability problems must never
seems to depend also on the state of stress, i.e.,
be treated mechanically without regard to environ-
on whether we have to do with a two-dimensional
mental effects. The geology of the area, the strat-
or a three-dimensional problem. When dry sand
ification of the soil and various external effects is heaped up to form a conical fill, σ > (σ = σ ),
such as surcharge, incidental loads, infiltration, λ 2 3
the safe angle of slope is smaller than it would be
groundwater seepage, the action of vegetation, for an infinite slope (plane strain, σ > a > tf).
should all be considered in their dialectic inter- 3 2 3
Finally, the slope will be steepest when a conical
action with due regard to their variations with
hollow is made in a semi-infinite horizontal sand
time. In this chapter we shall discuss the mechan- mass, in which case (σ = cr ) > σ (Fig. 3). Here
ical principles and methods necessary for stabil- 1 2 3
an arching effect also comes into play and it is
ity analysis.
more pronounced the smaller the top radius of
Concern frequently arises in the preliminary the hollow. This explains, in part, why vertical
design stage about the stability of natural or boreholes remain stable without casing to a con-
artifical slopes on hillsides or in mountainous siderable depth in moist sands having only a
areas. The efficiency of such engineering consid- slight cohesion.
erations can be largely enhanced by using the
The stability of slopes in sand may be greatly
maps of recorded landslides or sliding areas.
endangered by forces resulting from vibration and
seepage. Dynamic effects caused, for example, by
an earthquake or by pile driving may result, even
θ C in dry sands, in a radical reduction of the angle
of internal friction and as a consequence in the
flattening of the slope. In saturated or quasi-
saturated sands, quick-sand conditions may arise
(see Vol. 1, Section 6.2).
In the literature we find reports of catastrophic
landslides triggered by violent earthquakes. For
example, the 1923 earthquake in Japan caused
Fig. 2. Slope failure a huge mass of saturated and completely liquefied
Stability of slopes 13
Fig. 3. Inclination of free slopes as a function of stress conditions
soil to rush downslope at the enormous speed of cement powder will be reduced to a very small
one kilometre per minute (CASAGRANDE and value. Such peculiar conditions, on a large scale,
SHANON, 1948). A similar phenomenon known as might account for the devastating loess flow which
"mur" occurs frequently in the Alps; in this case, occurred in the Kansu province of China in 1922,
however, the seepage force of flowing ground- and which took a toll of well over 100 000 lives.
water also comes into play (see Vol. 1, Section 5.2). Following an earthquake, vast banks of loess over
It is interesting to note that quick condition 100 m in height completely lost their stability,
may occur even in dry cohesionless soils. We can collapsed and spread at an incredible speed over
easily produce this phenomenon if we open a several square kilometres of the valley floor. As a
cement bag and empty its content onto a smooth contemporary report described the case, . .vil-
plane surface so quickly that there is not enough lages became buried and rivers dammed up within
time for the air entrapped in the voids between seconds". A probable explanation, gathered from
the particles to escape. As a result a considerable the study of photographs of the catastrophe-
portion of the stresses has to be borne temporarily stricken area, was that the shear strength of the
eby the por air and the shear strength of the material had been reduced to a fraction of its
14 Soil mechanics of earthworks
original value within a very short time. As violent
shocks had destroyed the structure of the loess
(see Vol. 1, Section 3.4.2) a large portion of the
pore air became entrapped in the debris with
practically no time to escape. Thus a large portion
of the stresses due to the weight of the affected
mass was transferred to the pore air and caused l!
,X\\\\Vs\\\sf ^ . | ·^
a radical decrease in shear strength and an in-
stantaneous liquefaction of the soil.
Seepage of water induces neutral stresses in Fig. 4. Forces acting on the sliding mass
the slope. Since the total stresses in a given slope
are constant, an increase in the neutral stress
will result in an equal decrease in the effective soil whose compressive stress—strain diagram shows
stress. As a consequence, the stability of the slope a sharp definite failure (see Vol. 1, Fig. 239). Only
will also be reduced. An especially dangerous this case will be discussed in this chapter.
situation arises when water is suddenly removed Failure usually starts with the formation of
from the face of a submerged slope (rapid draw- tension cracks some distance from the crest of
down). the slope and this is followed by the sliding down
The effect of stagnant and percolating water of a large mass of soil on a rotational slip surface,
on the stability of slopes will be discussed in as was shown in Fig. 2. The slip surface resembles
Section 1.3. an elliptical arc, with the sharpest curvature near
the upper end and with a relatively flat central
section.
1.2.3 Slopes in homogeneous cohesive soils The forces that act on the sliding soil mass are
shown in Fig. 4. Sliding is caused by the weight
1.2.3.1 General remarks of the moving soil mass itself, while internal fric-
tion and cohesion mobilized along the slip surface
For cohesive soils the shear strength is given by tend to restrain motion.
the general Coulomb equation: In a homogeneous soil, failure may either take
the form of a slope failure along a slip surface
χ = a tan Φ + c . that passes through or sometimes above the toe A
of the slope (Fig. 5a) or it may occur along a slip
In such soils, cuts with vertical walls will stand surface that passes below the toe and intersects
without bracing up to a certain limiting height. the free surface at a point some distance from it
For greater heights the slope must be flattened. (base failure, Fig. 5b). The shape and position of
The stable height of the slope can thus be expressed the critical slip surface are governed by two
as a function of the slope angle: h = f(ß). The factors, the inclination of the slope and the shear
failure of a slope may occur in such a manner strength of the soil. (This is valid for homogeneous
that a body of soil breaks away from the adjacent soil only.)
soil mass and slips down on a single and well- In the design of slopes we usually have to
defined rupture surface. In other cases no such answer one of the following two questions: first,
definite slip surface exists. The first type of given the height and gradient of a slope and the
failure is characteristic of a stiff homogeneous shear strength of its material, what safety factor
(a)
Fig. 5. a — Toe failure; b — base failure in homogeneous subsoil
Stability of slopes 15
against failure exists, and second, given the height restraining forces are, according to Coulomb's
of the slope and the physical properties of the soil, failure theory, those due to internal friction and
what should the slope angle be to secure a required cohesion. In the limiting state of equilibrium:
safety factor. A number of methods, both ana-
lytical and graphical, are available for the solution T - C- Ν tan<Z> = 0.
of these problems. The most widely used is the
procedure in which we work with arbitrarily In order to find the most dangerous position of
selected slip surfaces, determine the conditions the slip surface AC, we have to determine the angle
under which failure along such surfaces just at which the force of cohesion required to maintain
occurs and find, by trial, the critical position of equilibrium is a maximum. The cohesive force
the slip surface along which the danger of failure can be written as the length of the slip surface
is greatest. The exact mathematical equation of multiplied by the cohesion, per unit area, of the
the slip surface is known only for certain particular soil: C = cl. The weight W of the sliding wedge
cases such as the semi-infinite half space with ABC, as well as its perpendicular components Ν
horizontal or sloping surface (see Vol. 1, Chapter 9). and Γ, can be expressed, by geometry, as functions
In practical stability analysis, the actual slip of the inclination angle of the rupture plane. The
surface is replaced by some relatively simple sur- weight can be written as:
face which is more amenable to mathematical or
graphical treatment. Such surfaces are, as is h2y
known from the theory of earth pressure, the W = —- (cot β — cot κ)
plane and the cylindrical surface with a circular 2
or a logarithmic spiral arc.
and hence, by using equilibrium conditions, we
In this chapter we first discuss an early method
obtain the cohesion required to just maintain
based on a plane surface of sliding, then we deal
equilibrium:
with more advanced methods which assume cir-
cular slip surfaces.
hy sin (β — κ) sin (κ — Φ) ^
2 sin β cos Φ
1.2.3.2 Stability analysis using a plane slip surface
To find the maximum of c we differentiate the
The first attempt to treat the problem of slope above expression with respect to κ and then solve
stability mathematically was made by CULMANN the equation dc/άκ = 0, whence
(1866). He assumed a plane slip surface. As was
shown in the introduction to this chapter, such β + φ
an oversimplified assumption by no means reflects κ = .
reality, since slope failures, particularly in homo- 2
geneous cohesive soil masses, invariably occur In words, the most dangerous failure plane bisects
along curved rotational surfaces. Culmann's plane the angle between the slope and the "natural
slip surface theory is therefore mainly of historical slope" i.e. the line with an inclination of Φ.
significance. By substituting this value of the angle κ in
Given a slope of height Λ, making an angle β the expression for c and solving it for Λ, we obtain
with the horizontal (Fig, 6) let us find the plane the following relationship which furnishes for any
of rupture AB along which the resistance to given slope angle β, the maximum height h at
sliding is a minimum. The force that causes the which the slope is just in a limiting state of
slope to fail is the weight of the wedge ABC, The equilibrium:
4c sin β cos Φ
Β Ç (2)
γ 1 — cos (β — Φ)
Here c is the cohesion and γ is the unit weight of
the soil.
From Eq. (2) it can be shown that for slopes in
a limiting state of equilibrium, the locus of point .B,
as the slope angle β changes, is a parabola, known
as Culmann's cohesion parabola. Its focus coincides
with the toe A of the slope and its axis makes an
angle Φ with the horizontal. The distance from
the focus to the directrice is equal to:
4c _
q = — cos Φ .
Fig. 6. Stability analysis on a plane y
16 Soil mechanics of earthworks
If the height of the slope is smaller than & , even
0
Culmann's parabola yj£\\\\V< a slightly overhanging slope may remain stable.
JÂKY (1925) has shown on the basis of the cohe-
sion parabola that the theoretical profile of a slope
in the limiting state of equilibrium is curved. Let
h denote the limiting height of a slope inclined at
an angle β to the horizontal (Fig. 8). If we con-
sider an upper part of height /i separately from
x
the rest of the slope, this part would stand in a
slope steeper than the overall slope corresponding
to the total height h. Let us now divide the height
h into, say, four equal parts. Using the Culmann
parabola we can construct the limiting slope angles
corresponding to heights fc/4, ft/2,3/i/4, respectively.
Clearly, the lower the slope in question, the
steeper it can be. By drawing the respective slope
for each height in such a manner that the total
ß=90°
2 weight of the sliding wedge does not change, we
h2=h5 = 4£tan(45°+<P/2) obtain a profile made up of broken lines (Fig. 8).
If we use sufficiently small divisions and continue
the construction in the manner previously de-
scribed, eventually a smooth curve results. This is
Fig. 7. Culmann's cohesion parabola called the theoretical slope. From first principles,
JAKY also derived the mathematical equation of
the theoretical slope and he developed a method
for its construction.
Using polar co-ordinates, the equation of the
In practice, it would be rather awkward to form
parabola becomes:
a slope exactly to such a profile. Nevertheless,
bell-shaped and bowl-shaped slopes, which ap-
proximate the theoretical profile fairly well, are
1 - cos (β - Φ)
often used for high embankments and deep cut-
tings, respectively, in order to minimize the land
(For notation see Fig. 7.)
area occupied.
With the aid of the Culmann parabola, the
The idea of the theoretical slope, although it
limiting height can readily be determined for any
was originally developed on the assumption of
given slope angle ß. An important value is the
a plane surface of failure, can readily be applied
limiting height at which a vertical bank in cohe-
to other, more realistic, curved slip surfaces.
sive soil stands without lateral support. Incor-
Providing a graph relating the limiting height to
porating β = 90° in Eq. (2) gives
the slope angle is available, a theoretical profile
can always be constructed by the procedure
4C Lro . Φ illustrated in Fig. 8. This can then be used to
(3)
h = tan 45° -\ design safe and economic curved slopes.
0
γ [ 2
q=^j-cos Φ
Fig. 8. The theoretical slope constructed using Culmann's parabola
Stability of slopes 17
1.2.3.3 Stability analysis based on the assumption
that Φ = 0
The assumption that the slip surface is plane
offers a simple solution to the problem of slope
stability, but it is certainly not a satisfactory one
since experience has shown that actual slip sur-
faces deviate considerably from the plane. Yet,
considering the many uncertainties in the values
of the soil properties on which the calculation is
based, this discrepancy would seem to be of minor
significance as long as the results obtained are on
the safe side. However, this is not so: for given
soil properties and geometry, the analysis based
on a curved slip surface always leads to smaller
safety heights than are obtainable by the slip
plane assumption. Safety is thus the main factor Fig. 9. Circular sliding surface beneath the slope
which justifies the introduction of curved slip
surfaces into the following discussion.
If the soil of a slope is such that it has a con- the moment equation of equilibrium,
stant un drained shear strength, i.e. Φ = 0 and
Wa - Cz = 0 . (4)
τ — c, the stability of the slope can be investigated
by using a circular slip surface. For this particular C is the resultant of the elementary cohesive
case the circular cylinder is the exact solution, as forces acting along the arc AC. Its magnitude is
has been shown by the senior author. The Φ = 0 proportional to the length of the chord AC : C =
condition applies to the undrained shear of homo- = cl and the distance of its action line from the
geneous, saturated clays, when their shear strength centre of rotation 0 is ζ = rl /l (see Vol. 1, Section
is given as a function of the total normal stress. a c
10.5.2).
The circular slip surface was assumed, on the
From Eq. (4) the cohesion per unit area required
basis of previous observations, in some early
to prevent rotational sliding along the surface AC
investigations and was first used for the Φ = 0
is obtained as
analysis by FELLENIUS (1927, 1936). The method
Wa
became known as the Swedish method.
c = —- . (5)
According to this method, as a first step we
have to find the position and radius of that circle
The quantities a and l can be expressed
which replaces the actual slip surface. This circle, a
by geometry (Fig. 9). Substituting the resulting
known as the critical circle, must satisfy the
expressions into Eq. (5) gives
condition that the ratio of the moment of restrain-
ing forces acting along the slip surface to the
moment of driving forces be a minimum. The c = hy (6)
ratio obtained is then taken as the safety factor.
If it has a value equal to 1, the slope is on the where γ = unit weight of soil,
verge of imminent failure. For stable slopes the
safety factor must be ν >> 1. h = stable height of slope,
Figure 9 shows a slope AB inclined at angle β to /(α, β, θ) = a dimensionsless number.
the horizontal. Let AC be the arc of a trial slip
The most dangerous or critical circular ship surface
surface. Its position in relation to the slope is is the one along which the cohesive resistance
determined by two angles: the central angle 2Θ, needed for stability is maximum. For a given
and the angle α which the chord AC makes with slope the angle β is constant and the position of
the horizontal. the critical circle is thus governed by the equations:
Let W = weight of mass tending to slide,
= 0,
a = lever arm of force W with respect to
centre of slip surface, (?)
r = radius of slip circle, = 0,
l — length of slip surface,
a
l = length of chord of slip surface, If we solve Eqs (7) and substitute the resulting
c
c = cohesion on slip surface. values of α and θ into Eq. (6), we obtain:
Since there is no friction, the only force tending c = hy = hN (8)
Y e
to restrain sliding is the cohesive force C Writing f{«,ß, β)
2 Â. Kézdi and L. Réthâti: Handbook