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Proceedings of the Fifteenth Canadian Soil Mechanics Conference: 8
and 9 November 1961
NA TIONAL RESEARCH COUNCIL OF CANADA
ASSOCIA TE COMMITTEE ON SOIL AND SNOW MECHANICS
PROCEEDINGS
OF THE
FIFTEENTH CANADIAN SOIL MECHANICS CONFERENCE
8 AND 9 NOVEMBER 1961
TECHNICAL MEMORANDUM NO. 73
Prepared by
E. Penner and Miss
J.
ButlerOTTAWA JUNE 1962
(i)
Preface
These are the proceedings of the Fifteenth Soil Mechanics Conference held at the Queen Elizabeth Hotel, Montreal, P. Q.,
Canada, on 8 and 9 November 1961. This was the first conference
to be sponsored jointly by the Soil Mechanics Subcommittee of the Associate Committee on Soil and Snow Mechanics of the National Re search Council and the Geotechnical Engineering Division of the Committee on Technical Operations of the Engineering Institute of Canada.
The technical sessions were devoted to two general subjects,
earth pressures and trench bracing. The various aspects of earth
pressures were dealt with in a number of separate papers. Trench
bracing was discussed by a panel of six members especially selected to represent a dive rsity of inte rest.
The details of the program were arranged by a committee selected from the Montreal Soil Mechanics Group under the
chair-manship of Mr. F. L. Peckover. The sponsoring organizations wish
to express their ,appreciation to the committee and also to Mr. Garnet T. Page and his staff at the Engineering Institute of Canada headquarters in Montreal for secretarial and administrative assistance.
8 NOVEMBER Section 1(a) Se ction 1 (b) Section l(c) Morning Session Section 2 Section 3 Section 4
(ii)
Table of ContentsOpening Remarks by the Conference Chairman, Professor J. E. Hurtubise, Ecole Polytechnique, Montreal.
Welcoming Remarks by Dr. R. F. Legget, Chairman, Associate Committee on Soil and Snow Mechanics, National Research Council, Ottawa, and of the Geotechnical Engineering Division of the Committee on Technical Operations of the Engineering Institute of Canada.
Welcoming Remarks by Mr. Harry Mullins, Chairman, Montreal Branch of the
Engineering Institute of Canada.
H. Q. Golder, Chairman
Earth Pressures 'on Structures and Mobilized Shear Resistance by P. Andre' Rochette.
Some Problems in the Design of Rigid Retaining Walls by G. G. Meyerhof.
Discussions by D. J. Bazett
J. E. Hurtubise and :;. Granger
C. B. Crawford
Closure by G. G. Meyerhof
The Performance of Some Steel Sheet Pile Bulkheads by P. J. Thompson and
M.A.J. Matich. Discussions by A. Ingram R.M. Hardy P. J. Harris R. P. Henderson N. E. Wilson and J. Schroeder Closure by M. A. J. Matich Page No.
1
1 1 359
70 74 7778
80
101 106 107 110 111 112(iii)
Afternoon Session N. D. Lea, Chairman
Page No.
Section 5
Section
6
Section 7
9 NOVEMBER
Earth Pressures on Multiple Tunnels by D. F. Coates and K. L. McRorie.
Discussions by G. Y. Sebastyan
J.C. Osler
N. E. Wilson and
J. Schroeder
Closure by D. F. Coates
Flexible Conduit.Per fo r ma nce by
R. M. Hardy.
Discussions by C. D. Smith R. Peterson and
N. L. Iverson Closure by R. M. Hardy
The Foundations Section of the National
Building Code (1960) by W. J. Eden.
Discussion by H.Q. Golder 115 132 133 135 135 138 147 148 150 156 161
Morning Session A. Baracos, Chairman
Section 8
Section 9 .
Surficial Geology and Soils of the Montreal Area by V. K. Prest. Discussions by J.A. Elson P. F. Karrow T. G. Tustin and JoE. Hurtubi se P. Andre Rochette Closure by V.K. Prest J. Hode Keyser
Case History of a Preloaded Foundation by C.E. Leonoff and C.F. Ripley.
Discussions by R. M. Hardy R.B. Beck H. G. Dutz K. Terzaghi
Closure by C. E. Leonoff and
C. F. Ripley 163 169 170 171 178 182 184 186 208 209 210 211 213
(iv)
Afternoon Session R. F. Legget, Moderator
Page No.
Section 10(a) Panel Discussion on Trench Bracing
Opening Remarks by:
-217
A. L. Bissonnette J.P. Ca r rf e r e G. Decarie H. Lapointe J. McNair - Legal Counsellor - Building Codes - General Contractor - Engineering Consultant - Labour Relations217
219
220
223
226
Section 10(b) Regional Reports Section 11(a)
(b)
(c)
(d)
(e)
(f)
(g)
APPENDIX "A"Brief resume of the Discussion on Trench Bracing.
Montreal Soil Mechanics Group Activities by R. F. Ogilvy.
Toronto Soil Mechanics Group Activities by F. A. DeLory.
Ottawa Soil Mechanics Group Activities by K. N. Burn.
Vancouver Soil Mechanics Group Activities
by E. J. Klohn.
Winnipeg Soil Mechanics Group Activities by A. O. Dyregrov.
Soil Mechanics Activities in the Prairie Provinces by N. L. Iverson.
Soil Mechanics Activities in the Atlantic Provinces by G. G. Meyerhof. Registration List.
228
230
234
235
236
238
239
240
Section 1(a)
Opening Remarks by General Chairman of the Conference. Professor J. E. Hu r tub i s e of Ecole Polytechnique
Professor Hurtubise welcomed the guests on behalf of the Montreal Soil Mechanics Group of the Associate Committee on Soil and
Snow Mechanics. He said he was delighted with the good attendance and
briefly pointed out the joint sponsorship of this present conference. He hoped they would find the conference both stimulating and worthwhile.
***********
Section l(b)
Welcoming Remarks by R. F. Legget
Dr. Legget welcomed the guests to the Fifteenth Soil Mechanics Conference on behalf of the Associate Committee on Soil and Snow Mechanics of the National Research Council and the Geotechnical Engineering Division of the Committee on Technical Operations of the Engineering Institute of Canada under whose joi nt sponsorship this
conference was being held for the first time. Dr -. Legget expressed his
pleasure at the co-operative effort between the various sponsoring groups and hoped it would continue until the EIC could assume full responsibility for the organization of the confe r e nc e and publication of
its proceedings. He said the President of the National Research Council,
Dr. E. W. R. Ste a ci e , was following the development of the conference with great interest and had wished to have his greetings and best wishes conveyed to all those participating.
*****'(.'::;'**
Welcome and Introductory Rerna r-k s by Mr , Harry Mullins,
Chairman, Montreal Branch of i;he Engineering Institute of Canada Monsieur Ie President, Mesdames et Messieurs, au nom du chapitre au Montreal, l'Institut des Inge ni eu r s de Canada, c 'est avec grand plaisir
que je vous souhaite la bienvenue
a
la qui nzi erne Conference CanadienneGeotechnique, tenue conjointement avec Ie Conseil National des
Rescherches du Canada et l'Institut des Ingeni e u r s de Canada. Montreal
est une des villes les plus interessante pour l e touriste. Nous e s pe r o n s
que vous aurez l e temps de visiter quelques endroits historiques tel que l'Oratoire St. Joseph, la montagne du Mont Royal et le chalet. Nous
2.
vous souhaitons un s e jo u r a g r e ab le
a
Montreal et beaucoup de suc ce sa
votre conference.
* * *
Mr. Chairman, Ladies and Gentlemen, on behalf of the Montreal Branch of the E.!. C., it is indeed a pleasure to welcome you to this
15th Canadian Soil Mechanics Conference.
I think it most appropriate, and to our good fortune for you to have chosen Montreal, and more specifically the Queen Elizabeth Hotel, as your Conference Headquarters. I say this keeping in mind the many sky-scrapers of unique design which are in the process of construction in this
area. To you it might be more interesting if the work were in the
pre-liminary stage s of construction rather than nearing completion. However, for those of us located within a stone's throw from this building, we have had an excellent opportunity to witness Canadian engineers and construc-tion men complete an outstanding engineering accomplishment in record time.
I am looking forward shortly to the formation of a Soil Mechanics Division in the Civil Section of the MontrealBranch. Perhaps this confer-ence will stimulate the formation of this much needed technical section.
This year's International Soil Mechanics Conference was held in Paris and the number present here, including your interesting technical program, is evidence of the increasing status Soil Mechanics is achieving
as a vital part of modern civil engineering. It is gratifying to see the
increasing attention being given to Soil Mechanics on construction jobs. Perhaps the day is not too far away when plans and specifications sub-mitted for tender will contain a thorough geotechnical survey report. Certainly, modern construction practice demands the use of the following geotechnical
procedures:-1. Preliminary geological investigations at the building site.
Z. Execationof a well planned sub-surface investigation,
planned on the basis of geological information.
3. Accurate laboratory tests based on truly representative
soil samples.
4. Thorough control of all construction operations involving soil.
5. Development of the necessary instrumentation for observing
soil behaviour in the completed structure.
Montreal is a real tourist attraction. I hope that those of you who are visiting our city for the first time will find some time to visit a few
of the more important points of interest, such as St. JosephIs Oratory,
Mount Royal, and the lookout.
We sincerely hope you enjoy your stay in Montreal and trust that your conference will be most successful.
3.
Section 2
Earth Pressures on Structures and Mobilized Shear Resistance by
*
P. Andre Rochette
Summary
This paper discusses the fundamental mechanisms of earth
pres-sure development on structures. Emphasis is given to the importance
of the strain distribution and the extent of the rupture pattern which are a function of the wall displacement. Therefore, a variable resistance is mobilized along the rupture lines. A method of evaluation of the total resistance by utilizing an equivalent average for the mobilized resist-ance is proposed and illustrated by interpretation of published model test results.
A basic method of earth pressure calculation, accounting for the type of wall displacement and consequent strain and resistance distribu-tion, and based on a proper use of the mobilized angles of soil or wall friction in the classical earth pressure theories, is briefly described. A review of the main solutions available to date for earth pres-sure computation, including assumptions and field of applicability, as well as results and accuracy obtained, is presented.
In the appendix, references to selected documents on earth pres-sure are given in the alphabetic order of the author's names. For prac-tical purposes, a bibliography for the various types of structures and
associated earth pressure problems, is submitted. A subject index is
also added for an easier appraisal of the bibliography.
1. Introduction: Definition and Mechanism of Earth Pressures
1) Active Earth Pressures
When a wall, under lateral pressure, moves away from the soil mass, the soil element near the wall tends to elongate horizontally and
in consequence shorten in height (Fig. I-a, left). The deformation is
re sisted by shear along adjacent soil elements and the lateral earth pressure drops to an active value smaller than the initial earth pressure at rest.
As the movement of the wall increases, the normal pressure on the wall continues to decrease until a value, (a) on Fig. I-a, which has a
4.
high enough differential to the vertical pressure (as represented by the circle of diameter (a) -p on the Coulomb-Mohr rupture diagram) for
failure to take place. Deformation and failure then extend to adjacent
and further elements until a wedge of soil, limited by the dashed line passing through the bottom of the wall, slides downward (Fig. l-b, left).
2) Minimum and intermediate active pressures
Figs. I -a and I -b show the total earth pressure against a wall, its components E and F, its angle 5 wi th a normal to the wall; also the total earth pressure envelope (the stress envelope being the envelope of the stresses acting on elements of rotating planes around the top of the wall) .
For equilibrium by friction along the wall, the angle of the stress acting on each wall element with the normal cannot exceed the angle of
wall friction
IIBw",
which in itself cannot be higher than the angle offric-tion of the soil near the wall ｾｷＧ if no rupture is to occur within a thin
layer of soil adjacent to the wall. As it will be noticed in Article II,
paras. I and 2, the ratio 5 w/pw only depends upon the soil-wall contact
conditions, i,e , roughness of the wall as well as nature and degree of
compaction of the soil, and also upon the contact changes with the wall movement or deformation.
For a given displacement of the wall, the actual angle of the earth
pressure "51 1 due to the weight of a frictional soil is related to the stress
envelope, Le , to the arigle of soil friction, the angle between the soil
sur-face and the wall, and the slope of the back wall. Loads applied at the
ground or wall surfaces, the soil cohesion "C" (the effect of which is to
hold the soil mass by an all-round compressive pressure H
=
ｃＯｴ｡ｮｾＩchange the total pressure envelope and the values of E, F and 5.
The pressure of a soil element adjacent to the wall varies from the "at rest" pressure in accordance with the wall displacement at the location of the element. The total earth pressure against a wall and its
components depend on the position of the centre of wall rotation (Fig. l vb},
In addition to the tilt of the wall, a vertical settlement or uplift modifies the value of the tangential earth pressure 'IF" by the amount of the shear resistance mobilized along the wall, and in consequence, the angle of the total active pressure 5 varies as shown on Fig. I-c.
As a result, an increase in the tangential component of the active earth pressure is equivalent to a reduction of the value of p on Fig. l s-a left, and the normal pressure (a) is decreased. Consequently, the higher the angle of the total pressure 5, the lower the total and normal active pressures: both pressures are a minimum when external loads or the wall displacement fully mobilize the wall friction (5 increases to 5 w );
5.
friction is higher
(Ow
tends towards ｾｷＩＮ On the other hand, the loadsand wall displacements may be such that the tangential component of the total pressure decreases, may even become negative and directed toward the top of the wall (as in the case of wall settlement; P is then increased by wall friction as is (a) on Fig. I-a, left); then the total active pressure
and its normal component increase. The maximum values are obtained
when
°
= - lowI,
and are higher if the wall is smoother and if the angleof soil friction is smaller. In the e xarn pl e of Fig. 6, the normal pressure
may vary between a minimum of 0.27 for 0 = ｾｷ and a maximum of 0.84
for
°
=
ＭｾｷＧ with a value of 0.33 for 0 = 0 (A. Caquot and J. Ke r i s e l ,1948).
*
3 ) Passive Earth Pres sures
Figs. l va, right and l-b, right show the passive earth pressure
which develops to resist the wall displacement toward the fill. Similar
considerations as before for active pressures would indicate the
defor-mation of the soil elements until a curved wedge slides upwards. The
normal pressure at failure takes a maximum value for fully mobilized
(0
= -
Ow) wall friction; the rougher the wall, the higher the soil frictionangle, the higher the maximum obtained. The rninirrrurn normal pressure
occurs for 0
=
+ow (Fig. l v c] and is lower for a smooth wall and forsmaller soil friction angles. In the case of Fig.
6,
the normal passivepressure decreases from 5.6 to 0.46 when 0 varies fr orn
-¢w
to Ｋｾｷand takes the value of 3.0 for no rnobiIi z ati o n of wall friction (A. Caquot
and J. Ke r i se I, 1948).
II. Resistance Parameters of the Soil
Fig. 2 shows a tentative interpretation by the writer of the well-known measurements obtained on large retaining-wall tests by Prof. K.
Terzaghi (Engineering News-Records, 1934, p.137). Tests Nos. 1 and 2
refer to a wall rotation around the lower edge (zR = -
%),
and to amove-ment normal to wall (translation) respectively. The angle of friction of the cornpa cte d dry sand fill is not given but could be evaluated at
approxi-mately 40" (on Fig. 2-b, point f and the at rest value of ｾｷ correspond
to laboratory test conditions). Fig. 2-b s ho w s how the angle of frictional
resistance varies with the soil deformation due to wall displacement, and Fig. 2-a enables de te rrni nati on of the average angle of friction
mobi-lized Ｈｾｭ on Fig. 3 -b , para. I-c) when the first rupture slip takes place:
- Test No.1, at failure: ｾｭ = 510
,
- Test No.2, at failure: ｾｭ = 44. SQ.
Figs. 3 -a and 3 -b illustrate a method of evaluating the equivalent angle of friction which is mobilized at failure and should be used in a
*
Complete references are given in the extended Bibliography at the end6.
stability analysis. In common practice, determination of the "coefficient
of utilization" for the laboratory cohesion or tanｾ data (actually an
addi-ti ve coefficient is often applied to ｾ instead of a multiplying factor to
tan
e },
and evaluation of ｾｭ only require a rough estimate of thedistribu-tion of the strains and resistance parameters. However, the blind use of results corresponding to unreal structure and stress conditions would
lead to misleading conclusions. Field or model measurements are of
great value; as an example, some findings from TerzaghiIS
retaining-wall tests are summarized as follows:
1) Mobilized wall roughness ratio During a test performance, the ratio
(mobilized wall roughness ratio) of the mobilized wall friction 0 to the
ｾｷ angle of friction of the soil adjacent to the wall, has a fairly constant
value independent of the wall movement. This important statement is
derived as follows: the required ｾｭ value for failure at displacement D
is computed from the Coulomb-Poncelet's condition
(E
as a function of ｾand
6),
using measured values of E and6;
results of ｾｭ in relation toD
are shown on Fig. 2-a. The Caquot and Ker i se l ' s method (E as a function
of ｾ and ｾＩＬ which is known to lead to similar results in the case of a
vertical wall with a horizontal ground surface, is then used with the
measured E and the computed
ｾｭＺ
insignificant scattering ofｾ
valuesis obtained when D varies.
The mobilized roughness ratio, which is constant during a given wall movement, depends on the fill density and wall roughness, but not, apparently, on the type of wall movement:
Test No. 1
=
rotation a:round the bottom (zR' 0)i dense sand, ｾ､=
400;f;.
=
o.
60.Test No.2
=
normal translation (zR(0);
dense sand, ｾ､=
40°; ｾ=
0.60.Test No.3 = rotation (same as Test 1); loose sand, ｾ､ = 310; ｾ
=
0.87.2) Mobilized angle of frictional resistance It is possible to compute the
mobilized angle of frictional resistance of the soil near the wall from the
measured value of 0 and the mobilized roughness ratio: the results are
given on Fig. 2-b and are valid for both Tests Nos. 1 and 2 on the dense sand:
Ｍｾｷ
=
1 ° to 30for zero or negligible wall displacement
Ｍｾｷ takes a ｭ｡ｸｾｭｵｭ value ｾｷ 1
=
62 ° for a deformationD l
=
0.5romr
Ｍｾｷ remains at a constant value ｾｷ｣
=
49° for any higherdeformation than Dc
=
2.5 h- when the wall movement
｣･｡ｳ･ｾｷ｣
drops with time tothe value of 40 ° .
7.
a) The rise of the
rPw
value, which develops as soon as wall motionbe-gins. and vanishes with time after complete displacement, is due to a
restraint to deformation and loosening of the soil near the wall, i ,e ,
to a "rigidification effect" c r e ate d ::>y soil deformation.
b) The value of 400 obtained with time at large deformations corresponds
to test conditions on samples and is therefore the angle of internal friction.
c) The angle of internal friction must be increased by a factor of
utiliza-tion "U!' to obtain the various soil conditions near the wall: the
maxi-mum resistance mobilized at low deformation through dilatancy, interlocking, and rigidification effects, corresponds to an angle of
friction higher, by U 1 = 220
, than the angle of internal friction.
d) The tentative relationship Uc/Ul = Z/3 of the roughness ratio
ｾ
enable s evaluation of the angle of friction
rP
c of the soil wadjacent to the wall at rupture.
e) The sand concerned has an ultimate angle of friction at rupture rPr =
32 to 340
(the ultimate angle corresponds to free deformation, there-fore to rupture with no further volume change). When it is compacted
to an internal angle of friction rPd = 400
, it is found that the maximum
increase of the angle of frictional resistance by dilatancy rPl -rPd
=
220is equal to three times the increase rPd - ｾ corresponding to the
com-paction. However, further tests are required to determine how these relationships may vary wi th the nature and density conditions of the
sand and also with the type of wall rnove rn e nt to failure.
3) Changes in the angle of frictional resistance with the deformation of
the soil The soil deformation near the wall is measured by the wall
displacement. After each given displacement.
rPw
drops with time to thevalue obtained in the laboratory; the dashed curve df on Fig. 2-b shows
the resistance-strain characteristics of the dense sand (Test No.1):
(a) existence of a certain strain €c
(r.ot
determined in the test;corresponding to Dc
=
2.5 1 ho.o )
after which the angle offriction remains constant
ｵｮｾｬＱ
failure at 400(angle of internal friction),
(b) the maximum friction due to dilatancy has not been drawn
on the dashed curve but could be as high as 620 for a strain
f €c
o
e
1=
""5'"""'
(c) in the case of loose sand, the dashed curve ce shows that
the angle of friction increases rapidly from the value of 260
•
at a negligible strain, to the internal friction of 31 0
obtained for a strain at least five times smaller than the
correspond-ing strain of dense sand (€c loose
］ｾ
dense=
€l dense).It would be valuable to compare the changes in the friction angle with the soil deformation (curve df unfortunately not plotted for D
8.
smalle r than
I
gOU)
to the r e sults obtained from cell te sts on sample s,as both cases represent the resistance deformation curves mentioned on Fig. 3-a, paras. 2-c and 3.
4) Evaluation of the equivalent angle of friction in relation to the wall
displacement The equivalent angle of fr i cti o n ｾｭＧ defined on Fig. 3-b,
para. l-c, is derived from the distribution of the angles of friction in the rupture zone or line for each given wall displacement.
a) Fig. 2-a give s the required e qui valent angle of friction l6'm at rupture in relation to the wall displacement. When the first slip takes place, l6'm is the actual angle of friction mobilized at rupture for the test conditions:
Test No.1, at failure (l6'm)f = 510
Df = 2.7
n¥ou
Test No.2, at failure (l6'm)f
=
44.50Df
=
5.0nfuo
b) At small wall di sp lac emente.D«
ＲＮＵＱＰｾ
, the deformation of the sandtakes place first mainly in the vicimty fbf the wall, until a value of 490
for l6'w is reached (see Fig. 2-b). For further wall displacements, the
strains proceed deeper inside the potential zone of rupture; the sand behind the wall no longer deforms, but follows the wall movement as
a block, and has an angle l6'w = 490
in the case of Te st No.1 as well as Test No.2.
c) The redistribution of the angles of friction with time is most
pro-nounced at the wall (decrease of 90
) but far less along the line of
rupture; l6'm is reduced by only 20
, whether the sand is dense or loose.
d) For any displacement D>D c' the required equivalent angle of friction
for rupture is higher by 30
in the case of rotation than for the
trans-lation of Test No.2. For the same value of the displacement D at
mid-height of the wall, the volume expansion of the soil is the same.
How-ever, deformation is restrained in the lower half of the soil mass, more in Test No.1 than Test No.2, and the subsequent increase of the angle of dilatant friction exceeds the loss obtained in the higher half
by 30
at Test No.1. On the contrary, for D
=
DcI the required l6'm forfailure is equal to the wall friction (l6'w)c and failure would take place
as if the angle of friction is 490
in the whole rupture zone.
e) Test No. 1 shows a linear variation of the strains along the wall. When the final distribution of the angles of friction is established for D> Dc"
the angles of friction vary between the extreme values of l6' 1 = 620
,
near the bottom of the wall, to the angle of internal friction l6'd = 400
,
at the top of the wall. In this case of linear change, the equivalent
angle of friction at failure is equal to the arithmetic mean 62
±
40=
51 09.
5) Conditions at failure The equivalent angle of friction decreases
dur-ing the wall displacement, but the problem is at what displacement will failure take place?
a) Terzaghi recognized in a later paper (K. Terzaghi, 1936) that the failure is related to the displacement of the top of the wall.
b) It is thought that local rupture occurs when the deformation exceeds a ce rtain strain, and proceeds from that point to a total slip. In both Tests Nos. 1 and 2. the maximum deformation happens at the top of the wall and an apparent slip takes place when this deformation is
equal to 5
n¥uu-,
with displacement values at mid-height of the wall of2.7
llfoo
and 5llfoo
respectively.c) In the case of Test No.1. failure occurs when the displacement is approximately equal to Dc; the equivalent angle of friction at rupture is therefore nearly equal to the angle mobilized at this deformation Dc; from para. 4-e (above), it co r r e sponds to an increase of the angle
of inte rnal friction by half the dilatancy rise viz. 40
+
¥
= 51 0•
d) When rupture occurs, at the same maximum displacement of the top of the wall in both tests, the volume deformation in the wall translation is twice that of Test No.1; the loosening effects are therefore doubled in Test No.2. and the equivalent angle of friction mobilizes only half
of the rise exhibited in Test No.1; it is equal to 40
+
¥
=
45.50•
e) Another way to visualize the friction angle distribution in Test No.2 is to consider that a translation normal to the wall creates a constant strain condition in the planes of the soil mass parallel to the wall. This is equivalent to assume that the increase in stress with depth due
to the overburden is exactly compensated at D ｾ Dc by the horizontal
frictional resistance to rupture exerted by the lower part of the fill which does not slide. The friction angle then varies from 49° near the wall to the angle of internal friction at the location where failure
begins, ｡ｾ､ the ･ｾｵｩｶ｡ｬ･ｮｴ angle of friction at the first slip takes the
mean value ＴＹｾＴ
=
44.5°.Paragraphs 1 to 6 are examples of the unlimited value of model tests, field measurements after construction, and case records. when measurements of the resistance parameters are made with time and in
the various zones where the parameters take different values, Results
from the single test here investigated can be useful only as working
assumptions in further research. More tests are required to provide a
ｧ･ｮ･ｲ｡ｾ picture of behaviour, even in simple cases. rather than having partial answers at arbitrary locations or specific periods. for a compli-cated system in unknown conditions. Quantitative equivalents to the actual variable parameter distributions should be developed rather than speculating on confusing reasons for suspecting the applicability of classical or experienced methods.
1
"
0.
A qualitative, theoretical understanding of the pressure and resist-ance distribution behind a wall can be obtained by considering the possi-bility of "transfer" of the pressures to locations of lesser yield by such
phenomena as arching, shear stresses, or boundary effects. On the
con-trary, the resistance-deformation relationship indicated by appropriate testing contains the quantitative effects of all possible phenomena of action and interaction of the soil particles, and it applies to the direct deter-mination of the re sistance mobilized by the wall di splacement or deforma-tion. In cases where the distributions are vaguely determined, it is how-ever less detrimental to make an error of 50% or more on the coefficient of utilization than to omit it entirely, and use the angle of internal friction for all failure conditions.
III. Earth Pressure Computations
As a practical method of evaluation of resistance and earth pres-sure parameters, with a simplified procedure for routine purposes, are to be published in a next paper, only a brief summary of the basic method of computation is given
below:-I} Measure the resistance parameters of the soil in relation to its defor-mation (see proposed method on Fig. 3-a, paras. 1,2, and 3).
2} Estimate approximately the amount of wall displacement, free or restrained, depending upon the design and construction conditions; estimate the location of the centre of wall rotation.
3} Determine the type of rupture pattern resulting from wall displacement. Fig. 4 illustrates how the figures vary with the location of the centre of rotation and with the amount of cohesion and friction.
4} Evaluate the resistance parameters of the soil in relation to the actual wall displacement (Fig. 3-b, para. I).
Full mobilization for passive pressures requires a displacement of 10 to 100 times greater than that for active pressures; that is why it is sometimes assumed that at failure the active pressure on one side of a sheet-pile wall is fully mobilized while only two-thirds of the passive
pressure on the other side of the pile is developed; e.g. it is recommended by P.W. Rowe, 1952, to evaluate the mobilized pressure by applying a co-efficient of utilization of 2/3 to the maximum passive pre ssure.
5} Evaluate the mobilized angle of wall friction O.
- Fig. 9, para. d, relates Of at failure to the angle of internal friction ,6d' In the case of wa l l rotation without vertical displacement, Figs. 6 and 7 demonstrate the influence of the location of the centre of
rotation
Of
0 and on the pressure itself. For each assumed value of11.
.
0
can be chosen corresponding to the wall roughness ratio
(ifli-).
Theco-ordinates of this point are the mobilized ratio
t
and thJ"normalpressure. d
- It is seen that in Terzaghi' s 1934 tests, the only case investigated
Z
was
;{i
<
0, andfd
was found approximately equal to 0.75 (seeFig.
9,
para. d). d Fig.6,
right, shows thatf;
=
ｾ
in the Terzaghi'stests; it is concluded that an ordinary
｣ｯｮ｣ｲ･ｴｾ
waIT has a roughnessｲ｡ｴｩｯｾＮ
equal to 0.75. Special surface conditions are thereforerequired in practice to enable consideration of the wall as "perfectly" rough in the case of a rotation around the base.
- The above values of
0
are increased by vertical wall displacement(modified Figs. 6 and 7 are then used, as it will be shown in a next paper).
6) Compute the earth pressure from known values of the resistance
parameters and of the mobilized angle of wall friction:
- The earth pressure is approximately equal to the sum of the various effects independently produced by the weight of the soil, the surcharge load, and the cohesion (which is equivalent to an all-around
compres-sive surcharge H = ｾ｣ ). For instance, the normal pressure per
. tg
linear foot of width of he wall is:
E =
1
Y h 2 Ey
+
qhEq+
chE c .- Figs. 6 and 7 refer to the E
y
and E q parameters in relation to thelocation of the centre of rotation and to the mobilized roughness of the wall.
- Fig. 9, para. e , indicates what is the influence of the wall flexibility and how it can be taken into consideration in the classical methods of pressure calculation.
- The four main classical methods of earth pressure computation are
summarized on Figs. ＸＭｾＬ b, and c , which indicate the assumptions
made, the kind of results derived, and the accuracy obtained. It is seen that among the extreme methods (Fig. 8-a), the
Coulomb-Poncelet's values for total pressure apply to any wall roughness and wall displacement, but are restricted to the active pressure of a horizontal fill on a vertical wall. The plastic theory (Fig. 8-b) was progressively elaborated and improved, in both cases of active and passive pressures, for the "Rankine" zone at first, and later in the wall vicinity to allow for the correct value of mobilized wall friction. When active and passive pressures develop simultaneously on the same wall, the resultant pressure is evaluated from the pattern of rupture lines which depends on the location of the centre of rotation,
12.
and should satisfy the static, kinematic and plastic (ex. Kb tte r ls
equation) conditions of equilibrium. Ultimate equilibrium methods
(Fig.
s-e)
are most promising but are still not sufficiently completefor practical use and appreciation.
IV. Conclusions
The two main conclusions of this paper concerning earth pressures are based upon:
- an analysis of published field and model test data related to the
application of the results of standard laboratory tests;
- a review of the main methods of calculation which indicate the
various phenomena which influence the te sting procedure and results as well as the observation of field behaviour.
1) Earth pressure measurements reveal that the angle of shear
resist-ance Ｈｾｭ
*)
computed at failure by methods of earth pressure calculationmay vary from the angle of internal friction Ｈｾ､ＩＧ Ex.: large scale model
tests by K. Terzaghi, 1934, investigating active pressures of dry clean
sand Ｈｾ､ = 40°, Test No.1, see Fig. 2-a) against a rigid vertical wall.
ｾｭ was found of the orde r of 51 ° by appli cation of the Rankine Fo rmulae.
As all theories lead to the same result in this particular case of a rigid vertical wall, what then is the relationship between standard shear test results and the values to be applied in the classical theories in order to calculate the correct earth pressures?In other words, classical theories and standard tests constitute the most accurate, economical and practical approach to the soil problems; however, this does not pay enough attention to two main phenomena, viz. deformation (changes in soil system L.e .
shear, compressibility, etc.) and time (rigidification during movement
stress and cohesion relaxation, etc.). Might a "coefficient of utilization"
be applied to the test data to obtain better agreement of the theoretical solutions with field behaviour?
a) Measurement of the angle of mobilized wall friction 0 during the
wall displacement indicate s that the angle of friction ｾｷ for the soil
adjacent to the wall varies with the soil strain as measured by the wall
displacement (see paras. II -2 and II -3). The knowledge of the variation
in the value of ｾ at low and intermediate strains is not new (MIT summer
lectures, ASCE Conference at Boulder on shear strengths, 1960, e tc , }. This is not in conflict with the existence of a constant angle of friction
Ｈｾ｣ or ｾ､Ｇ Fig. 10-a) at high strains and failure conditions which depends
only on the sample density and test procedure. Fig. 2-b shows the shape
of the "strain-angle of friction" curve for a non-cohesive soil. This curve
provides quanti tati ve re suits for this fundamental phenomenon which cannot be obtained readily by normal laboratory shear tests.
13.
b) The mechanism of the frictional resistance mobilized with the strain is described as follows:
The main phases are derived from model tests: rapid strength changes at low strain, plastic flow at constant shear resistance and
ulti-mate residual resistarice , Characteristic strains Dc, Dr' D l' are then
defined (para. II-3, Figs. 2-b and IO-a). The related angles of friction
ｾ｣Ｇ ｾｲＧ and ｾｬ are derived (Figs. IO-a and
z-s).
Two values of the frictional resistance are associated with each
deformation (paras. II-2a and b; Fig. IO-a). (1) The angle of "internal"
friction appears either in the at rest and slow failure conditions, or in a soil mass which is too small to be influenced by rigidification or time lag,
ex. laboratory samples. (2) The angle of friction mobilized during
con-tinuous deformation or quick rupture is higher, by a few degrees, when measured in terms of effective stress, than the angle of internal friction (extra resistance necessary to overcome inertia, rigidification, local or micro-arching, etc.).
Typical determination and order of magnitude of the basic
IIresistance-deformation" parameters are given on Fig. 100b which is
derived from model tests: see paras. II -2c to e; also refer to the subject
index of the appendix: "Resistance mobilized". This enables construction
of the " a n gle of friction-strain" curve for the sample and test involved. The resistance-deformation curve obtained for a tested sample should be corrected so as to be representative of the field soil and stress conditions; corrected for test procedure (Fig. 3-a, para. 2 and upper figure), and for sample disturbance (Fig. 3-a, para. 3 and lower figure).
c) What is the relationship of the mobilized frictional resistance of a soil mass behind a structure with the displacement of the structure?
Variable strains are created by a wall di splacement along a unique
potential sliding line. Use of the friction angle-strain curve of the
mate-rial obtained at para. IV -lb would lead to a variable distribution of the friction angles along the rupture line. The earth pressure which should be computed from the variable friction angles can be calculated by the use of a constant average angle of friction. This average hypothetical "equivalent" or "mobilized" angle friction, well defined for each given wall displacement (Fig. 3-b, para. 1), is used to simplify earth pressure
calculations (Fig.
z-s).
Model tests reveal that, even in the cases of rigid walls, the loca-tion of the earth pressure centre (K. Terzaghi, 1934; P.W. Rowe, 1952, etc.)
and the shape and extent of the rupture lines
(J.
B. Hansen, 1953) varywith the location of the centre of rotation (see Fig. 5). Furthermore,
they vary during rotation around the same centre
(A.
Kezdi, 1958).Therefore, the mobilized equivalent angle of friction ｾｭ must be evaluated
in relation to the location of the centre of rotation and the amount of wall displacement.
14.
When the wall is not acted upon simultaneously by active and passive pressures and when the wall displacement is not restrained,
failure generally proceeds from a point where ｾ = ｾ｣ (para. II-5b). The
earth pressure is then said to be fully mobilized. In this case, a typical
determination of ｾｭ is given on Fig. 9 (para. c and Fig. 9-b). On the
other hand, when active and passive pressures exist (see Fig. 5 for re-taining walls; refer to other structures in the selected bibliography), failure takes place in the active zone at a structure displacement D m a
when ｾ｣ is reached locally. Then ｾｭ takes a value ｾｭ｡Ｇ The potential
rupture zone for passive pressures has a greater extent and is in
com-pression. So when failure occurs in the active zone, at deformation D m a,
the passive pressures and the angle of friction are not yet completely mobilized (see para. III -4; also in the selected bibliography: paras. 3A 1
and 3B 2). ｾｭｰ can be de ri ved from the fri ction angle - strain curve
(reference is made to model test results for various structures in the selected bibliography, see subject index: "Resistance Mobilized with
Structure Displacement"). The evaluation of the equivalent angle should
therefore be based on the ｾ｣ values rather than on the angle of internal
friction ｾ､ (except for longterm analysis). and on the friction angle
-deformation curve when failure occurs at low wall di splacement. The
conditions and interpretation of the sudden occurrence of a slip during the displacement have been analyzed in para. II -5 and in the selected
bibliography (paras. 3AI and 3B2). The factor of safety to be applied
depends on the wall displacement which cause s a structure or soil failure, whichever occurs first. and is selected to take account of the inaccuracy in the equivalent friction angle determination and of the soil or test uncertainties (Fig. 3-b, para. 2).
The influence of the wall roughness as well as the evaluation of the mobilized angle of the earth pressure resultant with the normal to the wall have been described in paras. II-I, III-5, and illustrated in Fi g s , 6, 7. and 9-d.
2) The various phenomena associated with ea.rth pressures are
empha-sized differently by the earth pressure theories. A review of the methods is made, see Figs. 8-a, b , and c , to demonstrate the influence of these phenomena on model or laboratory tests, and to assist in a more realistic determination of the mobilized wall roughness and equivalent angle of friction.
When the type of rno verne nt of the structure is unknown. no reli-able earth pressure computation is feasible, so much do the earth pres-sures depend on the structure displacement. The knowledge of forces applied to the structure, the restrictions to free movement, the com-pressibility of the fill and bearing strata, and the use of a diagram show-ing the earth pressures in relation to the centre of wall rotation (Fig. 5) permits determination of the centre of rotation at least within certain
15.
acceptable limits. In complicated cases, an approximate method by
successive trials is used to obtain the most critical wall displacement (e.g. J.B. Hansen, 1953), or a semi-empirical corrective factor derived from rotation (anchorage, fixed earth support, etc.) - see these methods for the various structures in the selected bibliography.
Fig. 4 illustrates the changes in rupture pattern with the type of wall displacement. The strain distribution along the rupture line is ap-proximated by the pressure conditions exhibited in Fig. 5 and the distri-bution of the mobilized friction is derived from the friction angle - strain curves of the materials through which the line passes. The average
friction is then estimated. Para. II -5 shows that, in practice, the
appre-ciation of the distribution can be simplified without excessive error to the value of the equivalent angle of friction.
Figs. 6 and 7 illustrate quantitatively how the angle of the total earth pressure with the normal to the wall depends more on the type of wall displacement than on the wall roughness.
The influence of the flexibility and yielding of a model test or field structure on the earth pressure data has been described for the main types of structures in the selected bibliography.
This paper is an attempt to review the mechanics of shear
resist-ance associated with earth pressure experiments and calculations. The
understanding of this mechanism simplifies the evaluation of the mobilized resistance and earth pressures in practical problems, by the app-ropriate selection of the dominant factors for each individual case. It is hoped that the paper will stimulate further research in the understanding of shear problems, and will assist practitioners by demonstration of the agreement between classical methods of computation and field or model behaviour.
Acknowledgements
The author gratefully acknowledges Professor J. E. Hurtubise,
Ecole Polytechnique de Montreal, and Mr. F. L. Peckover, Canadian
National Railways, for their encouragement and guidance. The research
was carried out under a grant from the National Research Council of Canada and with the assistance of most of the staff of the Civil
Engineer-ing Department of l'Ecole Polytechnique. The correctness of the English
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