This book is included in the Self Reliance Water & Wells section.
Preface
OVER a century ago, Coulomb formulated the laws of friction
and cohesion as affecting a mass of earth, and devised the "sliding wedge"
hypothesis to effect the computation of earth thrust
against a wall. For some reason doubtless on account of the
complexity of the analysis and lack of experimental determination
of the coefficients of cohesion the theory of earth pressure
was subsequently developed by many noted authors (Poncelet,
Weyrauch, and others) after Coulomb's hypothesis, but for an
earth supposed to be devoid of cohesion.
In 1856, Rankine published his notable theory of earth
pressure, deriving it from considerations pertaining to the
equilibrium of an infinitesimal wedge of earth in the interior of
a mass of homogeneous earth, supposed to have a free plane
surface. Again, the earth was supposed to be devoid of cohesion
and likewise to be subjected to no other external force but its
own weight.
All of these theories strictly pertain to such materials as dry
sand, clean gravel, or loose rock, which are practically devoid of
cohesion and affected only by friction between the particles.
Although ordinary earth in bank is endowed with both cohesion
and friction, it was assumed, when this earth was excavated,
more or less pulverized, and placed behind a retaining wall, that
the cohesion was temporarily destroyed, so that the theory
of earth endowed with friction alone considering the angle of
friction as the angle of repose for the loose earth could be safely
employed; since the filling, under the influence of rains, settlement,
and cohesive and chemical affinities, would regain by
degrees a large part of the cohesion temporarily lost, so that the
thrust would ultimately be less than for the pulverized earth.
This, of course, tacitly assumes that the coefficient of friction
would not be lowered during the consolidation.
For many years, engineers have expressed their dissatisfaction
with a theory thus restricted and which, when applied to
earth more or less consolidated especially clay was so deficient
"in the most vital elements existent in fact." It was
thus natural that the pendulum should swing back, so that, in
very recent years, the treatment of pressures in coherent earth
has been based on Coulomb's original laws. Thus in Resal's
comprehensive work, the subject is treated analytically in great
generality.
The author was also led, in the course of a discussion of certain
experiments on retaining boards backed by earth and an
analysis of the pressures exerted on the bracing of trenches, to
develop a complete graphical method for finding the' pressures
in coherent earth. More recently, Mr. A. L. Bell, M. Inst.
C. E., has added to pure knowledge of the subject by experiments
on clays and an analysis concerning the supporting power of
foundations,
From all of the experiments that have been made (as given
in Chapter I), the laws of Coulomb seem to be approximately
verified, but it is evident that extensive experimenting upon
every kind of earth is needed to give confidence. Partly
from this lack of experimental data, though mainly because
the theory of earth devoid of cohesion is strictly applicable to a
granular material, as clean, dry sand, gravel or rip-rap, the
theory for such earth is fully developed in Chapters II and III,
and numerous applications are made in Chapter IV to the design
of retaining walls of stone or reinforced concrete.
It will be found that the analysis of Chapters II-IV is more
critical and extended than usual. In Chapter XXI the discussion
by the "ellipse of stress" method leads up to Mohr's "circular
diagram of stress," which is afterward used in Chapter V in
treating coherent earth. The author first developed the theory
for coherent earth by the analytical method, but eventually
decided to use the Mohr diagram, because it not only led to the
same results, but gave numerical values with much greater facility
than the formulas for the general case, where the earth surface
is inclined.
In this chapter, the subjects of earth pressures in coherent
earth, surfaces of rupture, stable slopes, foundations, the thrust
against a retaining wall, the bracing of trenches, and the pressures
on tunnel linings, are treated; besides, there is added an
independent graphical method for evaluating earth thrust.
The theory of deep bins is given in Chapter VI, and the
attempt is made there to reach fairly good results in the vexed
subject of the thrusts on the walls of shallow bins filled with
coal.
The case of stresses in wedge-shaped reinforced-concrete beams
finds an approximate solution in Appendix I, in which a number
of diagrams are added to facilitate computation.
Finally, in Appendix II, the results of certain experiments on
model retaining walls are added, the discussion of which may
prove instructive.
It must be borne in mind that the theory of earth pressures
has been necessarily developed for a supposed homogeneous
earth, so that it is understood that its indications, for an actual
earth, must always be supplemented by the practical judgment
of the experienced engineer.
WM. CAIN.
CHAPEL HILL, N.C.
Feb. 6, 1916.
CHAPTER I LAWS OF FRICTION AND COHESION. TABLES, DIRECTION, AND DISTRIBUTION OF STRESS 1. Friction and Cohesion in Earth 2. Laws of Friction and Cohesion 3. Experimental Method 4. Earth Endowed Only with Friction 5. Angle of Repose, Rankine's Law as to the Stability of a Granular Mass 6-8. Coefficients of Friction and Cohesion. Tables 9. Weight of Earth in Water 10. Exceptional Case of Earth Thrust 11. Direction of Pressure 12. Direction of Pressure Against a Wall 13. Direction of Pressure from Experiments 14. Direction of Pressure for Stable Walls. Factors of Safety 15. Distribution of Stress on Base 16. Factors of Safety Against Overturning and Sliding 17. Middle Third Requirement, Etc CHAPTER II THRUSTS OF NON-COHERENT EARTH. GRAPHICAL METHODS 18. Surface of Rupture 19. Sliding Wedge Theory 20. Active and Passive Thrust 21. Graphical Determination of Active Earth Thrust Against a Wall 22. Variation of E with ɸ' 23. Examples 24. Center of Pressure 25. Definition and Use of K and K1 26. Thrust on a Vertical Plane in an Unlimited Mass 27. Limiting Plane λ =/< ɸ' 28. Wall Above Limiting Plane 29. Wall Below Limiting Plane, λ < ɸ' 30. Summary 31. Tables for K, β and ɤ 32. Construction for Thrust on a Surcharged Wall APPENDIX I STRESSES IN WEDGE-SHAPED REINFORCED CONCRETE BEAMS 1-6. Introductory 7-10. Stresses Due to Bending; General Solution 10-11. Applications to Counterfort and to Heel 12. β = o. Bars in One Plane 13. β > o. Bars in One Horizontal Plane 14. Prismatic Beams 15. Comparison of Stresses in Concrete by Two Methods 16. Shear at Neutral Axis 17-18. Bond Stress 19. Variation in Shear-Over Section 20. Spacing of Bars 21. Compressive Stresses in Concrete Due to Bent Bars Under Tension 22. Length of Embedment of Bars 23. Working Stresses Recommended APPENDIX II DISCUSSION OF EXPERIMENTS ON MODEL RETAINING WALLS
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