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Relationships between applied loads, surface defections, traffic
volumes, and thicknesses of flexible pavements - Relations entre les
charges appliquées, les fléchissements en surface, les volumes de
circulation, et les épaisseurs des revêtements souples
The Associate Committee on Soil and Snow
Mechanics is one of about thirty special committees which
assist the National Research Council in its work.
Formed
in 1945 to deal with an urgent wartime problem involving
soil and snow, the Committee is now perfonning its intended
ta sk of co-ordinating Canadian research studies concerned
with the physical and mechanical properties of the terrain
of the Dominion.
It
does this through subcommittees on
Snow and Ice, Soil Mechanics, Muskeg and Pennafrost.
The Committee, which consists of about twenty-five Canadians
appointed as individuals and not as representatives. each for
a 3-year term, has funds available to it for making research
grants for work in its fields of interest.
Inquiries
wi
11 be
welcomed and should be addressed to: The Secretary, Associate
Committee on Soil and Snow Mechanics, c/o Division of
Building Research, National Research Council, Ottawa, Ontario.
This publication is one of a series being produced by the
Associate Committee on Soil and Snow Mechanics of the National Research
Council.
It
may therefore be reproduced, without amendment, provided
that the Division
i
s t o ld in advance and that full and due acknowledgment
of this publication is always made.
No abridgment of this report may
be published without the written authority of the Secretary of the ACSSM.
NATIONAL RESEARCH COUNCIL
CANADA
ASSOCIA TE COMMITTEE ON SOIL AND SNOW MECHANICS
CANADIAN PAPERS PRESENTED AT THE FIFTH
INTERNA TIONAL CONFERENCE ON SOIL MECHANICS
AND FOUNDATION ENGINEERING,
PARIS,
JULY 1961
TECHNICAL MEMORANDUM NO.72
OTTAWA
JANUARY 1962
PREFACE
The Fifth International Conference on Soil Mechanics
and Foundation Engineering was held in Paris, France, from 17 to
22 July 1961.
The first such conference was held in 1936 as a part
of the tercentenary celebrations of Harvard University, Cambridge,
Mass.
The incidence of war necessitated the gap of twelve years
between the first two meetings.
The second conference was held in
Rotterdam in 1948, and the third was held in Zurich in 1953.
The
fourth was held in London in 1957.
Seven Canadians were present at the Harvard rn e e
ti.ng,
This number has increased over the years and over 25 were present
at the conference in Paris.
The Associate Committee on Soil and
Snow Mechanics of the National Research Council is pleased to publish
the reprints of the eleven Canadian papers which were included in the
official proceedings.
The International Society of Soil Mechanics and Foundation
Engineering is composed of national sections.
The executive body for
the Canadian Section is the Associate Committee on Soil and Snow
Mechanics of the National Research Council.
The principal function of
the Canadian Section is to assist in the further development and
appli-cation of soil mechanics throughout Canada.
Enquiries with regard to
its work will be welcome; they may be addressed to the Secretary,
Associate Committee on Soil and Snow Mechanics, National Research
Council, Ottawa 2, Canada.
Robert F. Legget,
Chairman.
Ottawa
4/14
Relationships Between Applied Loads, Surface Deflections,
Traffic Volumes, and Thicknesses of Flexible Pavements
Relations entre les charges appliquees, les flechissernents en surface, les volumes de
CIrcu-lation, et les epaisseurs des revetements souples
by NORMANW. McLEOD, AsphaltConsultant, Imperial Oil Limited, Toronto, Canada
Summary
On the basis of the Canadian Department of Transport's load test data, a method for calculating the surface deflection of an existing flexible pavement under a loaded rigid bearing plate is described. When all other factors are equal, the surface deflection depends upon (a) the thickness of flexible pavement, and (b) the subgrade strength. For any specified traffic volume (less than un-limited) of a given design wheel load and tire inflation pressure, the permissible surface deflection when measured by means of a rigid bearing plate carrying the same total load and unit pressure, must be varied with the strength of the underlying subgrade. This implies that for flexible pavements not strong enough to carry unlimited traffic, a given Benkelman beam deflection under a specified wheel load does not indicate the same ability to carry traffic, if the strengths of the underlying subgrades are different.
Sommaire
Une methode basee sur lcs donnees des essais de chargement du Departernent des Transports du Canada est decrite. Elle permet de calculer Ie flechissement en surface d'un revetement flexible deja construit en Ie soumettant a un essai avec une plaque rigide de chargement. Lorsque tous les autres facteurs sont egaux, Ie flechissernent en surface depend (a) de l'epaisseur du revetement flexible et (b) de la resistance du sol de fondation. Pour n'importe quel volume de circulation specifie (moindre qu'illimite) d'une roue ayant une certaine charge, Ie pneu etant gonfle a une pres-sion donnee, Ie flechissement admissible en surface change avec la resistance du sol de fondation lorsque ce flechissement est mesure au moyen dune plaque rigide de chargement portant la meme charge totale, a la merne pression unitaire, Ceci suggere que pour des revetements flexibles qui ne sont pas assez resistants pour supporter une circulation illimitee, un flechissement donne, tel qu'indique par la poutrelle de Benkelman, sous une charge sur roue specifiee, n'indique pas fa meme aptitude a supporter la circulation, si la resistance des sols de fondation est differente
By convention, "h" is the symbol ordinarily used to indicate the thickness of a portland cement concrete pavement slab. In this paper therefore, the symbol "T" has been used to indicate total thickness of flexible pavement above the sub-grade. This includes the thickness of sub-base, base course, and bituminous surface. The symbols "h" and" T" have been used in this way in the new book by E.J. Yoder, "Principles of Pavement Design", published by John Wiley and Sons Inc.
Introduction
A number of methods are currently employed to determine the thicknesses of flexible pavements required to support various wheel loads over subgrades of widely different strengths. Emphasis is usually placed on thickness requir-ements for unlimited traffic, for example, Fig. 1. However, the Canadian Department of Ttransport [1] has recommended the following thickness reductions for three lesser categories of traffic volume :
(a) light traffic - 50 per cent of the thickness for unlimited traffic.
(b) medium traffic - 75 per cent of the thickness for
unlimited traffic
(c) heavy traffic - 90 per cent of the thickness for unlimited traffic.
The Asphalt Institute [2] also employs this method for
reducing flexible pavement thickness requirements with
respect to traffic volumes. The U.S. Corps of Engineers uses a similar approach [3].
Establishing Relationships Between Load, Thickness, Surface Deflection, and Traffic Volume
Analysis of the data from many hundreds of plate bearing tests conducted by the Department of Fransport, has led to the method to be described in this paper for calculating the deflection of a loaded rigid bearing plate on the surface of a flexible pavement for any combination of load, thickness, and subgrade strength. The required items of information for this purpose are:
(a) The P/ A ratio diagram of Fig. 2.
(b) average relationships between loads and deflections for rigid bearing plates, Fig. 3. (Note. due to the uncer-tainties of extrapolation, Fig. 3 is probably not very accurate for: deflections larger than 1'5 inch.)
P
,
:
--I ' ' J 4 5 6 8 10'It
--! 1---iInfluence of bearing plate diameter on value of "K " in flexible pavement design equation.
Influence du diametre de la plaque de chargement sur la valeur de " K" dans l'equation pour Ie calcul de l'epaisseur d'un revetement flexible.
1 0 1 1 -9 0 , - - - , - - - , - - - - r - - - - r - - r - - , - - - - r - - - ,
801--;---ｾＺＺ
i
ＮｾＭＭｉＮｲ｟｟｟｟ｉ
ｉｾ
1-ｾ
/' r
I
I
8
50Ｍｾ｟｟｟｟ＫＡＭＭＧＭＯＭＬＭｌＭＭ
I'
l=-r--j-+-r
oｾ
I I I I 1 I8
30ｲＭＭＭＭｾＧ-ｾ
201----:--1
!
Ir-
f-
I
Ａｾ［
i
I -IＭｉｾＭｾＺｉＭＭ
5 10 15 20 25 30 35 40 45 50BEARING PLATE DIAMETER IN INCHES
Fig. 4
Fig. 3 Average relationship between load and deflection for rigid bearing plates.
Relation moyenne entre la charge et Ie Ilechisscment pour des plaques de chargement rigides.
Step I The contact area for a wheel load of 10,000 lb. at 70 p.s.i. inflation pressure is approximately equivalent to a circle with a radius of 6'74 inches and a PIA ratio of 0'297, Fig. 2.
Step 2 Subgrade support of 2,800 lb. on a 12-inch bearing plate (PI A ratio = 0'333) corresponds to a unit pressure of 24·7 p.s.i.
Step 3 A unit load of 24'7 p.s.i. for a PI A ratio of 0'333 corresponds to a unit load of 22.5 p.s.i, for a PIA ratio of 0'297, both at 0'2 inch deflection, Fig. 2.
Step 4 For unlimited traffic by a wheel load of 10,000 lb. at 70p.s.i, tire pressure, and for the subgrade strength given, the thickness requirement is 18 inches, Fig. 1.
Step 5 50 per cent of this thickness requirement is 9 inches, which will just support a light volume of traffic by a 10,000 lb. wheel load over this subgrade.
Step 6 Substituting in the design equation, and solving for P, (K= 37 from Fig. 4), P = 39·4 p.s.i.
Step 7 Therefore, a 13'48 inch diameter rigid bearing plate on a flexible pavement thickness of 9 inches over this subgrade will support only 39'4 p.s.i. at 0'2 inch deflection
ｩｃﾧＳｾｾｾｩｬｬｄ
sl---·t_ zr---
----j-1 0 6- 1 : + + ,
: i=51----+-t--++t-+t-++--+----+-+-++++-H-
'--'-Ｇｾｉｾ 4 -- - - .l.I:
+/'--J---liﾧｯｾＧｬｩｾｯ［ＺＺ［Ｇ
:r----
ｉＭＭｾＢ
/ / - - . J
-
l :
I! I tii:;, I 1'" ' / I ' ｾ loVe 1 - - i i i / . ._._ __-+-c_--L-+-t---1sis
ｾ fｦＭｾＭＺＺＧ］ i)- .r": : _ - - '-i,:
｟ＺＺｾ ｴｾ :::.;:jｾ
0'. ···1---br-lf
1ｲＭＭＭＭＭｾ
-c-ＺＺＺＺ］ｾＭＭＭ
...'-ｾ
3 / ' I , I 1 '-,+1-'3 0 2 - - - ' . I i I Ir
Illi
JJJil1
ｾ 001 0 02 003004 006 0080 I 02 0j 0 4 ＭｏｾＢ｢ 0;-"''''6-!c,uc---c----+--+--!-'---"--!c.LJ, ｄｅｆｌｅｃｔｉｏｾ IN INCHES,,'
OOA 0' 02PERIMETER-AREA RATIO PtA
,.'
,...
o OJ ＴｄＧｴＭｈＭＭＧＭＭｾＭＭﾷｾＭ｟｟｟ｩＭ｟ＫＭＭＭＭＭ｟｟ｲＭＭ ＧｏｾＧＧＺＧＺＲＧＭＭＺＺＧＧＺＺＭＧ --:.a-=----:::---::---.,......
- -
ArfGl[ '" ｴＢＧｾｾｔＬｏＢ "t 9 ' '0 " zo " '0ＧｎＩｩｩｾａｌ s» ec '". .
flflD '"' ,.
'0 " " ,.
re eo"'CUSfl PU.IcTRQM[T(R NO0' BLO"'Sr cso''<(;HHｲＮｾ Tｾｾｔ ''''1
, ro
" eo " ｾＺＩ
" '0 "
CONF Bf/lIM,C, PSI
,00 '00 "'0 '00 ':-00 Ｖｾ J rr·n !IOU
ＵｵｧｃＮｨａｾ｛ 5Ul'PORf,... ,p,>
" o ,' .. (Hl>UL£V'C.N
" ,·,Co< '>6...ｐｾＢｾｦＺ o ｾＡ HｾＬｬ［Ｈ［ＧｖＧ［
Fig. 2 Ratio of subgrade support at deflection" D " for bear-ing plates of any diameter over subgrade support at 0·2" deflection on 30 inch. diameter plate versus perimeter area ratio.
Rapport entre Ie support du sol de fondation au fle-chissement " D " pour des plaques de chargement d'un diametre quelconque et Ie support du sol de fondation au flechissernent de 0·2 pouce pour une plaque de 30pouces de diametre en fonction du rapport entre Ie perimetre et la surface.
"L----l.----l_--"---'- _
Fig. Design curves for flexible pavements for highway
wheel loadings for highest traffic capacity (single wheel),
Abaques donnant l'epaisseur des revetements f1exibles en fonction des charges pour des routes ayant une circulation maximum (une seule roue).
(d) relationship between base course constant K and
bearing plate diameter, Fig. 4.
Suppose for example, a flexible pavement is to be designed to just support light traffic (50 per cent of the thickness required for unlimited traffic) by a wheel load of 10,000 lb. at 70 p.s.i. tire inflation pressure. The subgrade strength is 2,800 lb. on a 12-incb bearing plate at 0'2 inch deflection for 10 repetitions of load (in-place eB.R. = 3). Calculate the surface deflection of this flexible pavement under a rigid bearing plate carrying 10,000 lb. at 70 p.s.i.
ｾＧ［ｆＢｉｍａｔｅ T[bTAL LOADIN KIPSｏＬｾ 12 IN. DIAMETER RIGIDｂｅｾＧ［ｪｎｇ PLATE
ｾｾｐｐｒＺｩＬＢＧｍａｔｦＵ TOTALｌｏｾ IN KIPSＰｾｬＴ INDIAMETER;'GIO BEARINGｐｌＺｾｅ
ｯａｲｴｾｧｘｉｾｔｅ ｾｔａｌ ｾｏ INｋＧｦｾ ON 30ｾ ｏｉａｍｅｔｾ RIGIDｂｅａｾｇ PLATE
I
TOTAl,. LOAD IN Kirs ON CIRCULAR RIGID BEARING PLATE AT 70 PS.IOR
WHEEL LOAD IN KIPS AT 70 P$.l
ｾ W 30 ｾ ro
Fig. 5 Interrelationship between load, surface deflection, flexible pavement thickness, and traffic volume category (weak subgrade).
Relations entre la charge, Ie flechissement en surface, l'epaisseur du revetement flexible, et la categoric de volume de circulation (sol de fondation de faible resistance).
for 10 repetitions of load. However, the deflexion under a unit load of 70 p.s.i. is required.
Step 8 For a load ratio of
ｾ
= 1'78, a deflection of 39'20'59 inch will occur, Fig. 3.
Consequently, on this weak subgrade, for a flexible pave-ment thickness (9 inches) that is only 50 per cent of that required for unlimited traffic by a wheel load of 10,000 lb. at 70 p.s.i. inflation pressure, the calculated surface deflection under a rigid bearing plate, loaded to 10,000 lb. at 70 p.s.i., is 0'59 inch for 10 repetitions of load, Point A in Fig. 5.
Surface deflections can be calculated by this procedure for other applied loads, other categories of traffic volume, and for any specific thickness of flexible pavement. For a relat-ively weak sub grade supporting only 2,800 lb. on a 12-inch bearing plate at 0.2 inch deflection for 10 repetitions of load (in-place CBR = 3), the chart of Fig. 5 is obtained. Fig. 6 is
a similar diagram based upon a subgrade of medium strength capable of supporting 5,600 lb. on a 12-inch bearing plate at
0·2 inch deflection for 10 repetitions of load (in-place
CBR = 10).
In Figures 5 and 6, the horizontal line through a surface deflection of 0'2 inch, numbered "1" and labelled"T", ind-icates the thicknesses of flexible pavement required for unlimited traffic by the wheel loads shown. The broken line
curves numbered 2, 3, and 4, and labelled 0'9T, 0'75 T,
and 0'5 T, show the minimum thicknesses needed for the heavy, medium, and light categories of traffic for each wheel load listed along the top of the diagram.
In 1950, the Corps of Engineers published a diagram [3]
relating flexible pavement thickness to traffic volume for airport runways, which implies that about 18 per cent of the thickness required for unlimited traffic by any specified wheel load will support just one coverage (one trip) of that
wheel load without causing pavement failure. Curve 5,
labelled 0·25T,in Fig. 5 and 6, is somewhat more conservative than the Corps of Engineers' finding, and assumes that 25 per cent of the thickness needed for unlimited traffic by a given wheel load, Fig. I, will, support just one trip by that wheel load without causing failure of the pavement. Therefore, flexible pavement thicknesses to the left of curve number 5
(0'25T) in Figs. 5 and 6, are in the zero traffic category. The solid line curves crossing the diagrams of Fig. 5 and 6 from upper left toward lower right pertain to specific thicknesses of flexible pavement, and have been labelled 5 inches, 10 inches, etc.
Figs 5 and 6, therefore indicate relationships between total loads at 70 p.s.i. on a rigid bearing plate, deflections for 10 repetitions of load, flexible pavement thicknesses, and categories of traffic volume. It is assumed that the loads on rigid bearing plates in this case are identical with the wheel loads at 70 p.s.i. tire inflation pressure that can be supported for each traffic category shown.
Figs 5 and 6 are restricted to unit pressures of 70 p.s.i. For any given total load, higher and lower unit pressure than 70 p.s.i. will provide higher and lower deflections respectively, than those shown in Fig. 5 and 6, when all other factors are equal.
Along the tops of Figs 5 and 6, corresponding total loads on 12-inch, 24-inch, and 30-inch diameter bearing plates are shown. The relationship is approximate, and the size of
ｾａｐｐＹｒｏｘｉｍａｔｅ igTAL LOAD IN KIPS＿ｾ 12 IN DIAMETER RIGID BEttiNG PLATE
｢ａ［ｐｒｾｘｉｍａｔｾＵ TOTALｌｾｾｄ IN KIPSＰｾＵ 24 IN DIAMETE 3RO
RIGID BEARING PL3AlE
ａｩ｢ｒｾｘｉｍＲＢＶｅ ｩｾｔａｌ ｌｾｾｄ IN Klfg ONＳＰＴｾ DIAMET:; RIGIDｂｾｾｎｇ PLATE TOTAL LOAD IN KIPS ON CIRCULAR RIGID BEARING PLATE AT 70 PSJ.
OR
WHEEL LOAD IN KIPS AT 70 PSJ.
W ｾ ｾ w <I)
ｾ
0.. 0 I t--'I-Tt-'<.---'I"oo.----',""",:-ｾ Q:..
ｾ 02 o <5 ii: isｄﾷＳｦＭＭＭＭＭＭｪｾｈＪｱＭＮＮ［g
-'ＰＴＯＭＭｾｦＭＭ｟ｉＭ＾ＬＮＭＫＧＢ u, o <I) ｾ ｯＭＵＱＭＭＱＭＭＱＭＭＭ｜ｾＮＭＭＭＧｋＮＧ ;:: ;:: !oJ 0.. l;! 06P--CC-.-1---1---1---'" QFig. 6 Interrelationship between load, surface deflection, flexible pavement thickness, and traffic volume cate-gory (medium strengthsubgrade),
Relations entre la charge, Ie flechissement en surface, I'epaisseur du revetement flexible, et la categoric de volume de circulation (sol de fondation de resistance moyenne).
ｾ
...
ｾＭＭｪＭＭＭｦＭ
NOTE:
LOAD VALUES SHOWN ON CuRVES PERTAIN TO WHEEL LOAD AT 70 PS.I. FOR TRAFFIC CATEGORY INDICATED,OR TO TOTAL LOAD ON A CIRCULAR RIGID BEARING PLATE' AT 70 PS.I.
SUBGRADE STRENGTH 5600 LBS. ON 12 IN. DIAMETER RIGID BEARING PLATE 02 IN DEFLEOTION, 10 REPETiTiONS OF LOAD
ON-PLACE C.B.R 10) I
8 Interrelationship between load, surface deflection, and additional thickness required to improve an existing flexible pavement from a lower to the unlimited traffic category (medium strength subgrade). Relations entre la charge, Ie flechissement en surface
et l'epaisseur additionnelle requise pour ameliorer une route existante de facon
a
la faire passer d'une circulation reduitea
une circulation illimitee (sol de fondation de resistance moyenne).ｾ -5 lL
..
II: .... ｾ ｏﾰｲＭＭＭＭＺｾＭ｟ＧｬｩＺＭＮＮＮＮＺＺＺｴ［ＮＮＮＮＮＮＮＮＮ［［［ｉＢＧ｟｟｟ＭＭＭＺｾＭＢＢｦ｟ＭｾＭＮＮＮ［［［ｲＢ｟ＮＮＬＮＮＮＭｔ｟ＭＬＮＬＮ ....-i :::; z ::;) ｾ 5 II:..
..,
12 o 10 w II: 5 8 II: en 15 w x 'o ｾ ｾ ＲＰＱＭＭＭＫＭＭＭＫＭＭＭＭＫＭＭｴＭＭＭＫＭＭＭｦｾｹ｟ ,C>o;,( en en w Z'"
ｾ 25 .... ...J..
Z ｾ 301--+----I---+-.-j1--+---+---+----.J--+---j 5 o..
Fig. -IO ...-..rTT-....,----,---..--..,...--...,---,---..--,--..,
flexible pavements showing higher Benkelman beam deflec-tions for the design wheel load, for example 0'06 inch, are considered adequate for only some smaller traffic volume category.
There is a current tendency to assume that all weaker flexible pavements that exhibit the same Benkelman beam deflection, for example0·05 inch, have the same traffic volume rating with respect to a specified wheel load.
Figs 7 and 8 warn that this assumption may be in serious error. For example, Fig. 7 indicates that for a surface deflec-tion of0·4 inch under a rigid bearing plate loaded to 9,000 lb. at 70 p.s.i., an existing flexible pavement over a weak
sub-grade (in-place CBR
=
3) will support light traffic by awheel load of 9,000 lb. at 70 p.s.i. tire inflation pressure. On the other hand, Fig. 8 shows that for a surface deflection of 0·4 inch under a rigid bearing plate loaded to 9,000 lb. at 70 p.s.i., a flexible pavement over a subgrade of medium
strength (in-place CBR = 10) will support less than one
coverage of a wheel load of9,000 lb. at 70 p.s.i. tire inflation pressure, that is, its traffic category is zero for this wheel load. This difference in traffic volume ratings for weaker flexible pavements ha vmg the same surface deflection is much greater for wider differences in the strength of the underlying subgrades.
Figs 7 and 8 suggest that for a given design wheel load, the
permissible Benkelman beam deflection at the surface of an existing flexible pavement for any specified traffic volume category less than unlimited must be varied with the strength
of the underlying subgrade.
Figs 7 and 8 indicate that all weak flexible pavements having the same surface deflection under a given loaded rigid bearing plate, require the same additional thickness of granular material or equivalent to upgrade them to the unlimited traffic category for the same wheel load. This
2C
Interrelationship between load, surface deflection, and additional thickness required to improve an existing flexible pavement from a lower to the unlimited traffic category (weak subgrade).
Relations entre la charge, leflechissernent en surface et l'epaisseur additionnelle requise pour ameliorer une route existante de facon
a
la faire passer d'une cir-culation reduitea
une circulation illimitee (sol de fondation de faible resistance).Fig. 7
SUBGRADE STRENGTH 2BOOLBS DN 12 IN DIAMETER RIGID BEAR"G PLATE 0'2 IN. DEFLECTION, 10 REPETITIONS OF LOAD
(IN-PLACE C.BR 3)
351---+---+---+--1---+---+---+--1---+----1
NOTE:
25 LOAD VALUES SHDWN ON CURVES PERTAIN TO WHEEL LDAD AT 7D PSI. FOR TRAFFIC CATEGORY INDICATED, OR TO TOTAL LOAD ON A CIRCULA R RIGID BEARING 30 PLATE AT lOPS I ＭＫＭＭＭＭＱＭＭＫＭＭＭＫＭＭＭＫｾ IS 4 0 ' - - - - ' - - - ' - - - ' - - - - ' - - - ' - - - - ' - - - ' - - - ' - -...- ... 5 -5I- -t---t---+--j----t---t---+--I---t---l 10 -10 ... _ , . - - . . . . , - - - - , - - - , . . - - . , . . - . . . . , - - - - , - - - , . . - - . , . . -...
bearing plate selected should be that nearest the actual size of the contact area for the design wheel load and tire inflation pressure specified.
For deflections exceeding about 2·0 inches in Fig. 5, the data may not be significant, since the Hybla Valley investiga-tion [4] indicated that deflecinvestiga-tions larger than these tend to be above those associated with the ultimate strength of the layered system represented by a flexible pavement structure. Figs 7 and 8, which are derived from Figs 5 and 6 respect-ively, indicate the additional thickness of flexible pavement required to upgrade the traffic carrying capacity of an existing flexible pavement from a lower traffic volume rating for a specified wheel load to the unlimited category. The change in surface deflection accompanying this improvement in capacity to carry more traffic can also be read off directly from Figures 7 and 8. For example, Fig. 7 shows that to raise the traffic volume category for a 15,000 lb. wheel load at 70 p.s.i., tire inflation pressure from the lower limit of the light traffic category band, to the unlimited rating, an additio-nal thickness of 11'8 inches of granular base or equivalent must be placed on an existing flexible pavement over this
weak aubgrade (in-place CBR = 3). At the same time, the
surface deflection under a rigid bearing plate loaded to 15,000 lb. at 70 p.s.i. would decrease from 0·68 to 0'2 inch.
The Benkelman beam, which was invented in 1953 (5),
or some modification of its principle, is being employed by a number of organizations to investigate the strength of existing flexible pavements. A Benkelman beam deflection in the vicinity of0'02 to 0'03 inch for the design wheel load (5,6) is believed to indicate that a flexible pavement will carry unlimited traffic of this wheel load or equivalent. Weaker 4
implies that this can also be expected for existing weak flexible pavements that show the same Benkelman beam deflections.
Figs 5, 6, 7, and 8 pertain to highway traffic. Similar dia-grams can be prepared for airport runway design. Further-more, Figs 1 to 8 are based on load test data for Canadian soils, and somewhat different relationships may be found elsewhere.
Limitations of space prevent additional comments on Figs 5, 6, 7, and 8.
Acknowledgments
This paper represents part of an extensive investigation of airports in Canada that was begun by the Canadian Depart-ment of Transport in 1945. Air Vice-Marshall A. de Niver-ville, Director-General Air Services, has the general admi-nistration of this investigation. It comes under the direct administration of Mr. Harold J. Connolly, Director, Air Ser-vices Construction, and Mr. George W. Smith, Chief Engineer. In their respective territories, the investigation is carried on
with the cooperation of Regional Construction Engineers
G. T. Chilcott, V. E. Currie, L. Millidge, R. A. Bradley,
R. L. Davies, and W. G. D. Stratton.
Grateful acknowledgment is made to Mr. C. L. Perkins
for his assistance with the calculations for the charts, and for his skilful drafting of the diagrams.
References
[I] NORMAN W. McLEOD (1956). Flexible Pavement Thickness
Requirements. Proceedings Association of Asphalt Paving Technologists, vol. 25.
[2] The Asphalt Institute, Thickness Design, (1959) Manual
Series No. J, June.
[3] U.S. Corps of Engineers Closing Discussion, (1950)
Trans-actions American Society of Civil Engineers, vol. liS. [4] Highway Research Board, Special Report46, (1959).A
Coop-erati ve Study of Structural Design of Nonrigid Pavements,
[5] Highway Research Board, (1955) Special Report 22, The
W.A.S.H.O. Road Test, Part. 2,
[6] F. N. HVEEM (1955). Pavement Deffiections and Fatigue Failures. Highway Research Board Bulletin 1/4.
