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SCALE EFFECT OF SPREAD FOUNDATION LOADING TESTS

USING VARIOUS SIZE PLATES

HIROFUMI FUKUSHIMAi), SATOSHINISHIMOTO

ii) and KOUICHI TOMISAWAiii)

ABSTRACT

With the revision of the Specification for Highway Bridges in 2002 (in Japanese), correction coefficients for scaleeffects were introduced for use in the calculation formula of the ultimate bearing capacity of spread foundation.

Meanwhile, soil moduli are often found using estimated formulas or other methods for practical reasons and arelikely to be underestimated. As a result, the bearing capacity may also be underestimated, thereby leading to the

design of uneconomical structures. Therefore, a proper understanding of appropriate design constants based onscale effects is of great importance.

In this study, therefore, plate loading tests of the ground with different-sized loading plates were conducted usingrock fills and gravel soils to examine the scale effect properties of the ultimate bearing capacity with changes in the

form of spread foundation.

The results of the tests were examined and compared with the ultimate bearing capacity formula. As a result, thefollowing were revealed:1) The same relationship of approximate expressions as in the Specification for Highway Bridges was recognized

for the correction coefficient Sof the bearing capacity coefficient N.

2) Because the parameter of the correction coefficient is not necessarily the same as the general value in theSpecification for Highway Bridges, it is necessary to study and calculate correction coefficients and soil moduliappropriate for on-site conditions.

3) The plate loading test with different-sized loading plates is effective as a method for studying design constants inthe design of spread foundation taking scale effects into consideration.

Key Words:Scale effect, Ultimate bearing capacity, Plate loading test

INTRODUCTION

Rapid progress in construction techniques andstructural analysis methods in recent years has allowed

the increase in scale of structures, which is needed dueto the promotion of high-standard arterial highway

projects, among other reasons. This is also the casewith the structure foundations: proper investigation,

design and construction methods for foundations thatare compatible with large structures are now required.The reduction in construction costs in publicundertakings, on the other hand, is strongly desired;

therefore, the establishment of more rational methods is

required in the design and construction of structures.Specifications for Highway Bridges with Instruction

Manual (IV - Base Structure Edition) (hereinafter called

specifications), revised in 2002, introduced thecorrection coefficients related to the scale effects of

bearing capacity coefficients to the ultimate bearing

capacity calculation formula of spread foundation

bottom ground1)

. The coefficients were designed to

properly consider the scale effects of the foundationshape, as the increase in foundation width tends toreduce ultimate bearing capacity. On the other hand,

it is common that soil constants (c and ) used in design

are obtained by general physical-property values,estimate equations, etc.; therefore, these constants tend

to be underestimated. This means that bearingcapacity can be underestimated and excessively large

structures be designed, bringing about the need to

identify more accurate design constants (c, , correctioncoefficients, etc.) that take into consideration scale

effects so that structures can be designed more

appropriately.The present study, with the aim of identifying

appropriate design constants that take into account scaleeffects, investigated the scale-effect properties of

i) Senior Research Engineer, Geotechnical Division, Civil Engineering Research Institute of Hokkaido, Hiragishi 1-3-1-34, Toyohira-ku, Sapporo,062-8602, JAPAN.ii) Director of Geotechnical Division, Civil Engineering Research Institute of Hokkaido.iii) Senior Research Engineer, Geotechnical Division, Civil Engineering Research Institute of Hokkaido.

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HIROFUMI FUKUSHIMA, SATOSHI NISHIMOTO and KOUICHI TOMISAWA

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ultimate bearing capacity that accompany the changesin the shape of spread foundation by conducting the

plate loading test on soft-rock ground, gravelly soil androck-fill embankment, where the dimensional shape of

loading plates are changed. In addition, studymethods on correction coefficients for soil strength

constants and scale effects that are necessary in thedesign of foundation structures are also considered.

2 SCALE EFFECTS OF SPREAD FOUNDATION

ULTIMATE BEARING CAPACITY EQUATIONS

2.1 Outline of size effects

The phenomenon in which increased foundationwidth on the ground reduces the ultimate bearing

capacity of spread foundation was noted as early as inthe 1940s, and it is well known as a classic technical

theme

2)

. It has been referred to as the "scale effect"since the 1960s, when De Beer3)

reconfirmed it in

experiments and already established foundations.This phenomenon is understood in the bearing

capacity theory of Terzaghi: the bearing capacitycoefficient (N) decreases with foundation width.

Although various reasons have been suggested as thecause, the following three, or a combination of them,

are generally accepted:

1) Reduction in due to increased stress 4)2) Difference in among locations exerted on slip

bands along with the progress of failure5)

3) Impacts of the ratio of sand particles to

foundation width 6)So far, no clear indications of how much each of the

above factors affects bearing capacity have been

discovered. Therefore, in practice, field-loading tests

are conducted to correct the bearing capacity formula.

2.2 Scale effect correction in accordance with

Specifications for Highway Bridges with Instruction

Manual IV - Base Structure Edition

The specifications, revised in 2002, introduced the

ultimate bearing capacity equation of spread foundation

that allows for scale effect correction

1)

. The followingis the equation quoted from the specifications:

++= SNBSqNScNAQ eqqcceu 12

1 (1)

Qu: Ground ultimate bearing capacity thatconsiders the scale effects of bearing capacity

coefficients (kN)Ae: Effective loading area (m

2)

,: Shape coefficients of foundation

: Addition coefficients for penetration effects

c: Ground cohesion (kN/m2)

q: Top loading (kN/m2) q=2Df

Df:Effective penetration depth of foundation (m)

1, 2: Unit weight of bearing stratum andpenetration stratum (kN/m

3), Submerged unit

weight for under ground water levelBe: Effective foundation loading width that

considers load eccentricity (m)Be=B - 2eB

B: Foundation width (m)eB: Load eccentricity (m)

Nc,Nq,N: Bearing capacity coefficientsSc, Sq, S:

Correction coefficients related to the scaleeffects of bearing capacity coefficients

Sc=(c*), Sq=(q*)

, S=(B*)

c*=c/c01 c* 10, c0=10(kN/m2)

q*=q/q01 q* 10, q0=10(kN/m2)

B*=Be/B01B*,B0=1.0(m), , : Coefficients that describe the degree of

scale effects (the value -1/3 may be used)The correction coefficients significantly reduced

bearing capacity compared with that calculated usingthe conventional equation (1996 specifications)

7). As

for the application of the correction coefficients,conditions for the investigation and calculation methods

of soil constants (c, , etc.) are not mentioned.Cases where the correction coefficients reduced the

allowable bearing capacity by 40 to 60% in the design

of spread foundation with ordinal width have beenverified. This degree of reduction is not negligible inactual practice; appropriate bearing capacity assessment

where scale effects are strictly assessed is requiredthrough investigation and calculation of more accurate

soil constants (c, ).Also, correction-coefficient parameters (, , ) are

currently assigned general values not influenced by site

conditions; the identification and setting of propervalues for differing conditions are required.

Therefore, in this study, with the aim of identifying

appropriate design constants and correction coefficients

that take into account scale effects, plate loading testswere conducted on gravelly soil and rock-fill

embankment using loading plates of different scales to

examine the properties of ultimate bearing capacitywhen influenced by the effects of scale.

3. RELATIONSHIP BETWEEN SUBGRADE

REACTION COEFFICIENT AND

FOUNDATION-WIDTH SCALE

The specifications provide the following formula as

an estimate equation for subgrade reaction coefficients,which is based on the idea that subgrade reaction

coefficients are directly proportionate to foundation

width raised to the -3/4th power8)

.

43

03.0

= VVV Bkk (2)

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kV: Subgrade reaction coefficient (kN/m3)

kV0: Vertical subgrade reaction coefficientequivalent to the values of plate loading test

that uses 0.3-m-diameter rigid disks (kN/m3)

BV: Conversion loading width of foundation (m)

This relational expression was established based onloading test results conducted on sandy ground and theloamy layer of the Kanto Plain, where plate scale was

set at various levels between 300 and 1,200 mm9)

.It is quite likely that the formula will not necessarily

apply in all situations, depending on ground conditions.Therefore, we decided to summarize and examine the

relationship between loading plate scale and thesubgrade reaction coefficient to confirm the

applicability of the formula to materials with largeparticle size, such as those examined in this study.

4. PLATE LOADING TEST WHERE LOADING

PLATE SCALE IS CHANGED

4.1 Outline of experiment

Loading plate tests were conducted on specificground types, where various loading plate scales were

used, to examine the scale effects of ultimate bearing

capacity in association with gravelly soil and rock-fillembankment (embankment created with debris from theexcavation of fine rock mass).

Loading plate tests were conducted for 17

conditions, where the scale shape of loading plates and

ground conditions were changed (Table 1).Four types of circular loading plates (300, 900,

1,200 and 1,500 mm in diameter) were prepared to

verify the scale effects in the ultimate bearing capacityequation of spread foundation, and one type of square

loading plate (B=1,500 mm) to confirm the shapecoefficient in the equation.

Loading directions and reaction-force devices werealtered for different ground conditions. Ground

anchors were used as a reaction-force device in verticalloading tests and were connected to loading burrs.

Adequate reaction force was assured against the designultimate load (Photo1). For soft-rock ground,

horizontal loading by test pit excavation was conductedto ensure adequate reaction force (Photo 2).

The multicycle loading method (4 cycles), as

described in Japanese Geotechnical Society's"Horizontal Loading Test Method for Piles and

Instruction Manual10)

," was adopted, and the test force

duration for virgin load was 30 minutes, and that forhysteretic load was 5 minutes.

There were three types of test ground - rock-fillembankment made of gneiss, boulder-mixed gravel,

and shale. Tables 2 through 4 show the summaries ofrespective ground materials.

In vertical loading tests, the ground surface was

leveled by spreading sand on it. In horizontal loadingtests, the gap between the ground surface and loading

plate was filled with non-shrinkage mortar to hold them

together.

Table 1 Test conditions

Circular SquareFY Ground type

Load

direction

Test

conditions 300 600 900 1200 1500 1,500

2004 Soft rock Horizontal 6 3 2 1

2003 Gravelly soil Vertical 4 1 1 1 1

Unreinforced

soil

Vertical 4 1 1 1 1

2002 Rock-fillGeogrid-

reinforcedVertical 3 1 1 1

Photo 1 Loading test (Vertical)

Photo 2 Loading test (Horizontal)

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Table 2 Summary of rock-fill embankment

material

Gneiss

Unit weight t (kN/m3) 27 (22 for rock fill)

Unconfined compressionstrength (kN/m2) 50,600

Table 3 Summary of gravelly soil

Boulder-mixed gravel

Unit weight t (kN/m3) 20

N value in standard

penetration test50+

Table 4 Summary of soft-rock ground

Shale

Unit weight t (kN/m3) 23

Unconfined compressionstrength (kN/m

2)

100

4.2 Results

(1) Estimation of ultimate bearing capacities

Ultimate bearing capacities were estimated by themethod of Uto et al.

11)in some situations, as the

loading in ultimate state could not be tested due to the

tilting of loading devices or other reasons.This estimation method reveals the relationshipbetween the load and settlement by the approximate

expression below and estimates the ultimate load Qmax,

standard displacement and other variables by theleast-squares method.

( )}1{ 0

/

max

mSS

eQQ= (3)

Q: Load

Qmax: Ultimate load

S: Displacement

S0: Standard displacement (displacement thatcorresponds to the yield load)

m: Displacement index

The coefficient of subgrade reaction was alsocalculated based on yield load and yield displacement

obtained using this method.

The load-settlement curves in rock-fill embankmentand reinforced soil are as shown below (Figure 1).

Table 5 Results of plate loading test

Circular

Loadingplatescale

B 600 900 1,200

Qu 1,197 1,150 1,092 2,434 2,668 4,491Ultimatebearing

capacityqu 4,234 4,067 3,862 3,826 4,194 3,971

Soft rock

Soil

constant

c

38.7

100

38.3

100

37.8

100

37.3

100

38.3

100

37.5

100

Circular Square

Loadingplate

scale

B 300 600 900 1,500 1,500

Qu 619 1,506 4,163 14,843 -Ultimate

bearingcapacity qu 8,761 5,326 6,543 8,399 -Gravelly

soilSoil

constant

c

44.950

42.850

43.750

44.750

--

Qu 193 - 1,878 4,504 4,581Ultimate

bearingcapacity

qu 2,735 - 2,952 2,549 2,036

Rock-fill

embankment

Unreinforced

Soilconstant

c

51.10

--

48.40

46.30

45.30

Qu 316 - 2,539 5,266 -Ultimate

bearingcapacity

qu 4,476 - 3,992 2,980 -

Rock-fill

embankment

Reinforced soil Soilconstantc

51.12.8 -- 48.42.3 46.31.0 --

Units are:B: mmQu: kNqu:kN/m2: oc: kN/m2

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(2) Estimation of soil constants

Subgrade reaction coefficients were calculated

based on yield load and yield displacement obtained bythe method of Uto et al.

Soil constants were calculated from ultimate bearingcapacity using the following formula:

( )

SNBScNB

Q ccu 1

2

3.03.14

+= (4)

(Specifications IV [Instruction 10.3.6])

The following assumptions were made:1) Cohesion is ignored for unreinforced soil (c=0).2) Reinforced soil functions as dummy cohesion

effects in geogrid-reinforced soil.3) The cohesion of gravelly soil is set at 50kN/m2

based on the results of geological surveys.

4) The general value set in the specifications (-1/3)is used for correction coefficient parameters

and .

5) , B*and c* are used as they are, though theyare outside the ranges set in the specifications

( 45o, 1B*, 1 c* 10)Table 6 shows ultimate bearing capacities and soil

constants obtained for different conditions by the

plate-loading test.

The test results confirmed that the soil constant

tends to decrease as loading-plate scale increases.

One possible reason is that the bearing capacitycoefficient, which is supposed to be constant based on

the correction coefficient of scale effects (S), was notappropriately corrected under the conditions tested.

Therefore, it is necessary to examine the approximate

expression of scale effect correction and theparameters.

5. DISCUSSION

5.1 Scale effects of bearing capacity coefficient N

(1) Summary by normalized ultimate bearing capacity

The ultimate bearing capacity for each study groundwas normalized using the following formula and

summarized by the relation with loading plate scale(Figure 2).

( ) 00 BBNN cc = (5)Nc: Combined bearing capacity coefficient

(Normalized ultimate bearing capacity)Nc0: Standard bearing capacity coefficient

(Bearing capacity coefficient whenB=B0)B0: B0=1.0 m

Table 6 Test results

Ground

type

Soft rock

(2004 study

Gravelly soil

(2003 study)

Rock-fill embankment

(2002 study)

Estimates

=37.7 c=100.0

N=50.9 =-1.26

Nc=60.0 =-1/3

=45.6 c=50.0

N=252.0 =-1.18

Nc=144.6 =-1/3

=47.4 c=0: Unreinforced

c=3.3: Reinforced

N=380.2 =-1.11

Nc=184.4 =-1/3

Approx.

expression

26.13/1

0.13.0

103.1

+

=B

NBc

cNqcu

18.13/1

0.13.0

103.1

+

=

BNB

ccNq

cu

Unreinforced11.1

0.13.0

=B

NBqu

Reinforced soil 11.13/1

0.13.0

103.1

+

=B

NBc

cNqcu

0

50

100

150

200

250

300

350

0 10 20 30 40 50

S(mm)

Q(kN)

B=300 Rock-Fi ll Fi tt ed Line

B=300 Reinforced Fitted Line

0

500

1000

1500

2000

2500

3000

0 50 100 150

S(mm)

Q(kN)

B=900 Rock-Fil l Fi tt ed Line

B=900 Reinforced Fitted Line

0

1000

2000

3000

4000

5000

6000

0 50 100 150 200

S(mm)

Q(kN)

B=1500 Rock-Fi ll Fi tt ed LineB=1500(Square) Rock-Fill Fitted LineB=1500 Reinforced Fitted Line

Figure 1 Estimation of the load-settlement curves and ultimate bearing capacities (rock-filled embankment)

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In all tested conditions, normalized ultimate bearingcapacity (Nc) tended to decrease as the foundation

width B increased. Also, it was generally in a linearrelationship with the correction factor (S) set in the

specifications, and no significant gap was found in thecorrection coefficient parameter () among ground

types.

y = 1178.1x-1.0189

y = 380.19x-1.1114

y = 531.94x-1.2292

y = 578.8x-1.0283

100

1000

10000

0.1 1 10

B (m)

Ncr

Ncr: Gravelly soil

Ncr: Rock-fill (Unreinforced)

Ncr: Rock-fill (Reinforced)

Ncr: Soft rock

Approx. expression: Graverry soil

Approx. expression: Rock-fill (Unreinforced)

Approx. expression: Rock-fill (Reinforced)

Approx. expression: Soft rock

Figure 2 Relationship between loading width B and

combined subgrade reaction coefficientNc

(2) Scale effects in rock-fill embankment

Normalized ultimate bearing capacityNc equalsN

of Terzaghi's bearing capacity equation, as cohesion ccan be ignored in rock-fill embankment (unreinforced).The relationship can be expressed as N = 380.2

(=47.4o), = -1.11, and it was confirmed that the

correction coefficient parameter does not necessarily

correspond with the general value of -1/3 set in the

specifications.As for rock-fill embankment (reinforced soil),

cohesion c was estimated by assuming the increase inbearing capacity by geogrid as dummy cohesion c (Fig.3). Cohesion was estimated using the least-squares

method from the relationship between the normalized

Terzaghi's bearing capacity formula and loading platescale. The scale-effect parameter was -1/3 as set inthe specifications, since the correction coefficient of

cohesion has no relation with foundation-width scale

and cannot be estimated by the changes in loading-platescale. In this case, c was estimated to be 3.3kN/m

2.

(3) Scale effects in gravelly soil

The soil constant and scale-effect correctioncoefficient were estimated by the test results on

gravelly soil. They were estimated for the normalized

Terzaghi's bearing capacity formula using the

least-squares method with the multiplier ofloading-plate scale and the correction coefficient as the

parameter (Fig. 4). The cohesion of 50kN/m2, which

100

1000

10000

0.1 1 10

B (m)

Ncr

Rock-fill (Unreinforced)

Rock-fill (Reinforced)

Approx. expression (Unreinforced)

Approx. expression (Reinforced)

=47.4-1.11

c = 0 = -1/3

=47.4-1.11c = 3.3 = -1/3

Figure 3 Relationship between test values and

approximate expression in rock-fill

100

1000

10000

0.1 1 10

B (m)

Ncr

Gravelly soil

Approx. expression:Graverry soil

=45.6 =-1.18

c = 50 =-1/3


approximate expression in Gravelly soil

100

1000

10000

0.1 1 10

B (m)

Ncr

Soft rock

Approx. expression(Soft rock)

=37.7 =-1.26

c = 100 =-1/3


approximate expression in Soft-rock

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the Kanto Plain and sandy ground. The ground types

studied have relatively large particle sizes, andtherefore require careful considerations in setting the

constant in the design stage.

5.3 The idea of regulations of the Specifications for

Highway Bridges

In the current specifications, many designconstants are determined using the plate-loading test

with a 300-mm loading plate. This study, however,

revealed that the results of the plate-loading test werenot necessarily consistent with the regulations of thespecifications. Under ground conditions where

ground is used as a bearing stratum for spread

foundation of bridge structures, it is considerednecessary to conduct investigations suitable to siteconditions through loading and other tests.

While there has been close relationship between

the processes of ground survey methods/results anddesign conditions/methods, it is important to respect the

expertise of both ground surveys and structural designand further promote cooperation between the two fields

considering the current idea of performancespecification-type design.

6. SUMMARY

We conducted plate-loading tests on soft-rockground, gravelly soil and rock-fill embankment, in

which loading-plate scale was changed, to examine thescale effects of ultimate bearing capacity and subgrade

reaction coefficient. The results were as follows:1) A relationship similar to the approximate

expression suggested in the specifications wasconfirmed in the correction coefficient S of

bearing capacity coefficientN.2) The correction coefficient parameter was not

necessarily consistent with the general value thatappeared in the specifications (-1/3); it is therefore

necessary to further investigate it and calculate anappropriate correction coefficient depending on site

conditions. It is also crucial to further research

and calculate appropriate soil constants (c and )

based on scale-effect correction.3) The subgrade reaction coefficients obtained in the

tests established an approximate relationship

similar to the estimate equation suggested in thespecifications. However, the parameters were notnecessarily consistent with the value set in the

specifications (3/4th power).

4) Plate loading tests, in which loading-plate scale ischanged, are practical as an investigation methodof design constants that take into consideration the

scale effects in spread-foundation design.

Based on the above conclusions, we consider the

following items essential to establish rational

next-generation design and construction methods that

take into account the properties of different groundtypes.

1) The same study method should be applied to otherground types (hard rock, volcanic ash, hard elasticsoil, etc.) to identify the scale effect properties of

yet more ground types. Rock mass in particularneeds to be investigated, as that ground type is

often used as a bearing stratum for spreadfoundation structures.

2) The scale effect properties of bearing capacitycoefficients (Nc, Nq) related to the effects ofcohesion c and top load q must be examined.

References1) Japan Road Association (2002): Specifications for Highway

Bridges (I - General Edition, IV - Base Structure Edition)

with Instruction Manual, pp. 269-279. (in Japanese)2) Japanese Geotechnical Society (1990): Introduction to

Bearing Power, pp. 102-103. (in Japanese)

3) De Beer, E. E. (1965): Bearing Capacity and Settlement ofShallow Foundations on Sand, Proceedings of a Symposiumheld at Duke University, Durham, USA, pp. 15-33.

4) Kusakabe, O., Maeda, Y., Shiroishi, S. and Kawai, N. (1990):Loading test analysis of large three-dimensional foundation

using expanded Kotter equation," Collection of Papers for25th Geotechnical Engineering Academic Lecture Meeting,

pp. 1243-1246. (in Japanese).5) Yamaguchi, H., Kimura, T. and Fujii, N. (1975): Bearing

capacity experiment on shallow foundation by centrifugaldevices, Proceedings of the Japan Society of Civil Engineers,

No.233, pp. 71-85. (in Japanese)6) Tatsuoka, F. et al. (1989): Relationship among shear strength,

experimental data and design calculation formula in the

bearing capacity problems of ground, 34th GeotechnicalEngineering Symposium, pp. 17-22. (in Japanese)7) Japan Road Association (1996): Specifications for Highway

Bridges (I - General Edition, IV - Base Structure Edition)with Instruction Manual, pp. 250-258. (in Japanese)

8) Japan Road Association (2002): Specifications for HighwayBridges (I - General Edition, IV - Base Structure Edition)with Instruction Manual, pp. 254-257. (in Japanese)

9) Yoshinaka, R. (1968): Lateral Subgrade Reaction Coefficient,Civil Engineering Techniques Vol.10, No.1, pp. 32-37. (in

Japanese)10)Japanese Geotechnical Society (1983): Plate Loading Test

Methods and Instruction Manual, pp. 41-45. (in Japanese)

11)Uto, K. et al. (1982): A summary method for loading testresults of the pile, Foundation Engineering Vol.10, No.9, pp.

21-30. (in Japanese)12)Japan Road Association (1996): Specifications for Highway

Bridges (I - General Edition, IV - Base Structure Edition)

with Instruction Manual, pp. 236. (in Japanese)13)Kawamura, Y., Kadotani, T., Ouchi, M. and Motegi, K.

(1990): Planning and execution of large-scale loading tests ofspread foundation using the self-weight of caissons, 25th

Geotechnical Engineering Academic Lecture Meeting,pp.1239-1240. (in Japanese)

14)Maeda, Y., Kusakabe, O., Shiroishi, S. and Ouchi, M. (1990):Bearing capacity properties and destruction properties of

large three-dimensional foundations on the thick scoria layer,25th Geotechnical Engineering Academic Lecture Meeting,

pp.1241-1242. (in Japanese)

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