Proceedings of the First International Conference on Press-in Engineering 2018, Kochi

Evaluation of Bearing Capacity of a Small-Diameter Spiral Pile Subjected to
Combined Load Using Model Tests
Shuhei NAKAGAWA
Graduate student, Faculty of Engineering, Hokkaido University, Sapporo, JapanRyo YAMAUCHI
Graduate student, Faculty of Engineering, Hokkaido University, Sapporo, Japan

Koichi ISOBE
Associate Professor, Faculty of Engineering, Hokkaido University, Sapporo, Japan
Email: kisobe@eng.hokudai.ac.jp

Koichi TOMISAWA
Dr., Civil Engineering Research Institute for Cold Region, Sapporo, Japan

ABSTRACT
A spiral pile is a useful pile because it has high resistance against vertical load such as push-in and pull-out loading, but
it also has a problem that its horizontal resistance is relatively small, comparing to a steel pipe pile with the same diameter.
In addition, the conventional design has the following problems; 1) unifying effect of the surrounding ground by therevolving press-in has not been considered for safety design, 2) evaluation method for bearing capacity against combined
load is not established, and 3) inclination effect of loading has not been clarified.
In the previous research (Isobe and Yamauchi, 2017), a simple method is proposed to consider the unifying effect of thesurrounding ground due to the revolving press-in, based on the various loading test results such as push-in, pull-out andlateral loading tests for the spiral piles in soft clay ground. Then, the bearing capacity of the spiral pile subjected to
combined load was investigated with the numerical analysis method. In this paper, in order to verify this analysis, model
tests have been carried out in which model piles were revolving press-in a dry silica sandy ground and then loaded atsome arbitrary angles.
Key words: spiral pile, bearing capacity, combined loading, loading test, FEM

1. Introduction
Recently, demand for renewable energy has been

pile form because of the high resistance to the vertical loadincreasing and commercial photovoltaic power generation

problems; 1) unifying effect of the surrounding ground byhave become popular. In order to reduce production costs,

the rotary press fitting has not been considered for safety

the photovoltaic power generation facilities have to be

design, 2) evaluation method for bearing capacity against

massively invested even in the areas of poor conditions,combined load is not established, and 3) inclination effectlike lands full of slopes, though inexpensive. In general,of loading has not been clarified.

(push-in and pull-out), but there are the following

solar power generation equipment is constructed based on

In this study, combined loading tests on a single screw

concrete spread foundations, but for effectively utilizing

pile were conducted in the pull-out direction. The bearing

those aforementioned bad grounds, some techniques suchcapacity obtained by the model experiments is compared

as steel pipe piles with a small diameter, spiral piles, andwith the bearing capacity calculated by the proposed

batter piles are applied (Araki, 2013, Sato et al., 2015 andevaluation method in previous research (Isobe andHirata et al., 2005). In particular, the spiral pile is a useful

Yamauchi, 2017). Because the screw pile used in this tests- 117 -

Proceedings of the First International Conference on Press-in Engineering 2018, Kochi

was fitted with a spiral blade on the circumferential

the spiral pile, the effect of the spiral structure on thesurface of straight pile using glue, loading tests werebearing capacity of the pile was investigated. The screw

conducted for the straight pile with sand adhered on thepile has a shape with a spiral blade attached to thecircumferential surface in the same

circumferential surface of the straight pile by glue. The

manner forcomparison.

winding direction of a spiral blade is right, the pitch of the
spiral blade is 15 mm, and the blade adheres to the entire

2. Outline of previous study
In the previous research, vertical and horizontal

pile excluding the tip. Thus, the diameter of the screw pileloading tests were performed on a spiral pile, which wasloading tests were performed on the screw pile and thesubjected to twisting processing to flat steel pile andstraight pile to compare the influence of the blades.

was set to 1.3 mm considering the spiral blade. The

constructed on soft viscous ground. Based on these results,
correction coefficients were set for the parameters such as

40

80

70

60

50

pile diameter, soil strength and bending stiffness of the pile

40

Vertical load (kN)by adapting the conventional vertical bearing capacity
evaluation formula and Chang’s equation to calculate
horizontal resistance characteristics of the spiral pile.
Subsequently, three-dimensional elasto-plastic finite
element analysis with Drucker-Prager type of yieldfunction was carried out in consideration of correction

30

20

20
10

0
-10
-20

-20

-30

coefficients. As a result, it reproduced the bearing capacity-40

of a spiral pile against the combined load in the vertical-80 -70 -60

-40
-40

and horizontal directions by the same analysis method. In-20this study, the ultimate resistance was defined as the load

-50

0
20
Lateral load (kN)40

at a time when the vertical or horizontal displacement ofFig. 1loading point reaches the displacement of 10% of pile

numerical analysis results (Isobe and Yamauchi, 2017)

Bearing capacity curve of spiral pile based on the

diameter.
Relationship between vertical and horizontal ultimate

Screw Pile

resistance for each loading angle based on the simulation

Straight Pile

25

results shown in Fig. 1 is an elliptical shape with the longside in the vertical load direction. The numbers shown in

PILE HEAD
SUS304100

this figure mean the loading angle (0 degree is horizontal
loading), positive and negative value indicate pulling-out
direction and pushing-in direction, respectively. It was

CORE MATERIAL
A1050, f6 × t0.5355suggested from Fig. 1 that the bearing capacity curve of

SPIRAL BLADE
SUS304, f13,250

the spiral pile subjected to combined load can be shownon the elliptical shape calculated from bearing capacity
subjected to load at 90, 0 and -90 degrees.

Winding direction : Right,
Pitch : 15mm

3. Outline of model test
TAPER
Tip angle : 60 degrees

5

3.1. Model pile

13

A miniaturized spiral pile was originally planned to
be used for the small-scale model tests, but it did not have

Fig. 2

6

Model pileenough rigidity to carry out the loading test in the small-First, bending tests were carried out for the screw pile

scale model tests. Therefore, in this series of tests, using

and the straight pile with a total length of 165 mm to

the screw pile having the spiral structure similar to that ofinvestigate the influence of the blades on the flexural- 118 -

Proceedings of the First International Conference on Press-in Engineering 2018, Kochi

rigidity in air. In these bending tests, the pile head washead is rotated along the spiral direction of screw pile andfixed and the load was applied on the pile tip, measuringpenetrated. According to the reference2), the screw pile canthe bending strain on the pile by strain gauges installed on

be constructed with less disturbing the ground by press-in

the circumference of pile. Fig. 3 shows that maximum

at the speed that length of penetration per one rotation isstrains were observed at around 20 mm from the pile headequal to the length per one pitch of the screw pile. In thesein both piles, and no difference is found between them. It

model tests also, the same speed is applied.

is, therefore, considered that the influence of the spiralblade on the flexural rigidity of the model pile is little.
Based on the results, the flexural rigidity of both piles, EI
can be regarded as 0.0053 (kN-m2).
模型杭 曲げ試験 比較

Rotating handle

1500

Removable guide

Straight Pile
Screw Pile
100

1000

Strain (*10 -6)500

Penetration assist
device

0
-500
-1000

○ 0.00067 kN□ 0.00402 kN◇ 0.00753 kN

-1500
0

20

40

60

80

250

Fig. 4 Penetration of the screw pile

100 120 140 160

Length from pile head (mm)Fig. 33.2.3.

Bending strain distribution on the model piles

Loading Procedure

A loading device shown in Fig. 5 can set optional
3.2. Model test procedureloading angle in the range of 0 to 90 degrees. Pull-out

3.2.1.

loading are applied by the loading motor up. The tensile

Model ground preparation

The soil chamber is a rectangular structure with depthload applied to the pile head was measured by the load cellof 250 mm, width of 700 mm and height of 500 mm as

attached between the motor and the pile head. The lateral

shown in Fig. 4 and Fig. 5. The model ground material

and vertical displacement and load of the pile head arewith the relative density, Dr of 70% was achieved with drymeasured at 90 mm from the ground surface because there

sand (Silica No. 7) by pluviation in air from height of 300

is little difference in the displacement of the model pile atmm.

the ground surface and the measurement point consideringthat the rigidity of the pile is high and there is little effect3.2.2.

on the displacement by the deformation of the pile. The

Penetration of model pile

Loading tests were carried out on piles constructed

pile head and loading motor was connected by a wire, andvertically to the flat model ground. The straight pile wasa pulley is installed at an optional position between them

installed to prescribed depth by press-in on the pile head.

to vary loading directions. As with the previous study, theFor the screw pile, the penetration assist device, in which

ultimate bearing capacity against combined loading was

revolving press-in is applied on the spiral pile head in

defined as the load at a time when the lateral or verticalpredetermined directions with the removable guides, anddisplacement at the loading point reaches 10% of pilethe direction of penetration can be freely adjusted, is useddiameter at the loading point. The combined loading of 0,(Fig. 4). The penetration direction is fixed by the30, 45, 60, 75, 80, and 90 degrees was tested three times

penetration assist device during the operation, and the pileeach.

- 119 -

Proceedings of the First International Conference on Press-in Engineering 2018, Kochi

ストレート杭 鉛直変位ー水平変位

Normalized vertical displacementby pile diameter

0.5

Wire
Displacement
meter

500

Pulley100

Load cell

Motor
Loading
Device

0.4

0.3

0.2

0.1

400

700

90 ①
90 ②
90 ③
80 ①
80 ②
80 ③
75 ①
75 ②
75 ③
60 ①
60 ②
60 ③
45 ①
45 ②
45 ③
30 ①
30 ②
30 ③
0 ①
0 ②
0 ③

0.0
0.0

0.1

0.2

0.3

0.4

0.5

Normalized lateral displacement by pile diameter

Fig. 5

Loading device

Fig. 6

Vertical displacement- lateral displacement for thestraight pile

4. Test Results
スパイラル杭 鉛直変位ー水平変位

Figs. 6 and 7 show vertical displacement - lateral

0.5

respectively. As shown in Fig. 6, for the straight pile,
lateral displacement is dominant in the case of loading
direction close to horizontal (0 and 30 degrees) andvertical displacement is dominant in the case of loading
direction close to vertical (60 to 90 degrees). Therefore,
ultimate bearing capacity was judged by the lateraldisplacement in the cases of the loading direction of 0 andNormalized vertical displacementby pile diameter

displacement for the straight pile and the screw pile,
0.4

90 ①
80 ①
80 ②
80 ③
75 ①
75 ②
75 ③
60 ①
60 ②
60 ③
45 ①
45 ②
45 ③
30 ①
30 ②
30 ③
0 ①

0.3

0.2

0.1

30 degrees, and was judged by the vertical displacement
0.0
0.0

in the cases of the loading direction of 60 to 90 degrees. In

0.1

0.2

0.3

0.4

0.5

Normalized lateral displacement by pile diameterthe case with the loading angle of 45 degrees, theintermediate behavior was observed unlike other cases.

Fig. 7 Vertical displacement- lateral displacement for the screw

Therefore, the bearing capacity of the straight pile with thepileloading angle of 45 degrees is judged by both verticaldisplacement and horizontal displacement. As shown in(6 mm). According to Fig. 8, in the case of the loading

Fig. 7, for the screw pile, the increase of the verticalangle of 60 to 90 degrees, the maximum values werebearing capacity due to the spiral blade was observed, so

observed in the range of the normalized displacement ofthat vertical displacement did not occur much at all load

0.1 to 0.3, after that the resistance shows a tendency toangle. Thus, for the screw pile, the ultimate bearing

keep constant. Thus, the pile was considered to becapacity was judged based on the horizontal displacement.

withdrawn in the vertical direction.

Fig. 8 shows vertical load – vertical displacement for

The case with the loading angle of 45 degrees shows

the straight pile in the cases with the loading angle of 45

a different tendency from the cases with the loading angle

to 90 degrees, and Fig. 9 shows lateral load – lateralof 60 to 90 degrees, due to the influence of the lateraldisplacement for the straight pile in the cases of thesubgrade reaction, resulting in the continuing increase ofloading angle of 0 to 45 degrees. The horizontal axis

the resistance. Also in Fig. 9, larger resistance wasindicates the displacement normalized by the pile diameter

observed in the case with the loading angle of 45 degrees
due to the influence of the vertical resistance, comparing
to the results for the loading angle of 0 degree. Therefore,
it is found that the variation of the results in the case with- 120 -

Proceedings of the First International Conference on Press-in Engineering 2018, Kochi

the loading angle of 45 degrees is considered to be due to

ストレート杭鉛直変位～鉛直荷重
90 ① 引抜方向 80③
60

the mutual influence of vertical and lateral resistance

0.008

during loading.
0.007

Fig.10 shows lateral load – lateral displacement of

②
③
①
②

75
75
75
60

①
②
③
①

60
45
45
45

②
③
①
②
③

0.006

Vertical load (kN)

the screw pile. In this figure also, the displacement was
normalized by the pile diameter (the outer diameter of theblade, 13 mm). In the displacement range of 0.1 (= 10%D)or less, as the loading angle is closer to lateral direction,
the bearing capacity becomes larger.

0.005
0.004
0.003
0.002

Fig. 11 shows the lateral load – lateral displacement

0.001

for the straight and spiral piles subjected lateral loading

0.000
0.0

(the loading angle of 0 degree). According to this figure,

0.1

0.2

0.3

0.4

0.5

Normalized vertical displacement by pile diameterwithin the range of the criterion displacement (10% of the
spiral pile diameter, 1.3 mm), no significant difference in

90
90
80
80

Fig. 8 Vertical load – vertical displacement for the straight pilethe relationship was observed. It infers that there was little

0.008

difference in their flexural rigidity and loading width in0.007

the same as the result of the bending test to both piles.

水平荷重～変位関係
45 ストレート杭
①
30 ①
45 ②
30 ②
45 ③
30 ③

0 ①
0 ②
0 ③

0.006

Laterall load (kN)

Figs. 12 and 13 show the bearing capacity against the
combined loading for the straight pile and the screw pile,
respectively. The ratio of V / H (V: bearing capacity of 90
degrees, H: bearing capacity of 0 degree) is 2.26 for thestraight pile and 9.15 for the screw pile, respectively. Since

0.005
0.004
0.003
0.002

there is no difference in the bearing capacity of both piles
0.001

subjected to only lateral load, the vertical bearing capacity

0.000
0.0

in pulling-out direction was increased by about 4 times by
bearing capacity by spiral blade is remarkable.

Fig. 9

0.2

0.3

0.4

0.5

Lateral load – lateral displacement for the straight pileFigs. 14 and 15 respectively show the bearing
capacity curve of the straight pile and the screw pile

0.008

normalized by the vertical bearing capacity of 90 degrees
0.007

and the lateral bearing capacity of 0 degrees. The bearing

90
80
80
80
75
75

①

75 ③
60 ①

③
①
②

60 ③
45 ①
45 ②

45 ③
30 ①
30 ②
30 ③
0 ①

データ
② 1 20:59:04602018/01/11
②

0.006

Lateral load (kN)capacity envelopes also were shown in the same figure
based on the method shown in the previous research (Isobeand Yamauchi, 2017). It was found that the averagebearing capacity against the combined loading for thestraight pile was in the envelope and the average value for

0.005
0.004
0.003
0.002

the screw pile was outside of the envelope. It is assumed
that the area where the spiral blade passes through the

0.001

surrounding ground was slightly disturbed during the

0.000
0.0

installing operation. On the other hand, for the straight pile,the surrounding ground was densified during the

0.1

Normalized lateral displacement by pile diameter

the spiral blade. The influence on improvement of vertical

0.1

0.2

0.3

0.4

0.5

Normalized lateral displacement by pile diameter

Fig. 10 Lateral load – lateral displacement for the screw pile

installation procedure. However, the influence was notconsidered in the estimation method. Thus, it was thoughtthat the different tendency was observed due to thedifference of how to install.

- 121 -

Proceedings of the First International Conference on Press-in Engineering 2018, Kochi
水平のみの載荷比較

ストレート杭 支持力曲線 正規化 引抜方向のみ

0.008

2.0

Straight pile
Screw pile

0.007

Estimate
Average
90 degrees
80 degrees
75 degees

Normalized Vertical load

Lateral load (kN)

0.006
0.005
0.004
0.003
0.002
0.001
0.000
0.0

1.0 1.3

2.0

3.0

4.0

1.5
80

75

30

1.0

0.5

0.0
0.0

Fig. 11 Lateral load – lateral displacement for both the straight

0.5

75

pile

60

45

2.0

スパイラル杭 支持力曲線 正規化 引抜方向のみ

2.0
Estimate
Average
90 degrees
80 degrees
75 degees

Normalized Vertical load

0.015

Vertical load (kN)

1.5

Fig. 14 Normalized bearing capacity envelope for the straight

ストレート杭 支持力曲線 引抜方向

30
0.010

Estimate
Average
90 degrees
80 degrees
75 degrees
60 degrees
45 degrees
30 degrees
0 degrees

0.005

0.000
0.000

1.0

Normalized Lateral load

pile and the screw pile

80

45

5.0

Lateral displacement (mm)

0.020

60

60 degrees
45 degrees
30 degrees
0 degree

0.005

0.010

0.015

1.5
80

75

60

60 degrees
45 degrees
30 degrees
0 degree
45
30

1.0

0.5

0.020

Lateral load (kN)
Fig. 120.0
0.0

Bearing capacity envelope for the straight pile

0.5

1.0

1.5

2.0

Normalized Lateral load
スパイラル杭 変位自由 引抜方向0.020

Fig. 15 Normalized bearing capacity envelope for the screw
80

75

60

45

5. Discussion

0.015

Vertical load (kN)pile

5.1. Inverse calculation of friction resistance angle
30
0.010

Estimate
Average
90 degrees
80 degrees
75 degrees
60 degrees
45 degrees
30 degrees
0 degrees

0.005

0.000
0.000

0.005

0.010

0.015

0.020

Lateral load (kN)
Fig. 13 Bearing capacity envelope for the screw pile

between ground and pileThe

friction

resistanceangle

betweenthesurrounding ground and the pile was inversely calculated
from the bearing capacity in the direction of verticalpulling-out for the straight pile obtained from the model
test. The general vertical bearing capacity formula of a pileis as follows;
Ru = q A + L f(1)
where, Ru: ultimate vertical bearing capacity (kN), q:
ultimate bearing capacity of ground of pile tip (kN/m2), A:- 122 -

Proceedings of the First International Conference on Press-in Engineering 2018, Kochi

area of pile tip (m2), : skin frictional force per unit area
(kN/m2), L: pile length in this study (m), f: circumferential

displacement yt = 0.6 mm and the bearing capacity of thelength of pile (m). Since the bearing capacity of pile tip is

straight pile subjected to only lateral load H = 1.059*10-

not involved in evaluating the pull-out resistance, the first3

term of right side of Eq. (1) is assumed to be 0.

reaction coefficient kh is calculated as follows;First,

thestraight

pile,

using

criterion(kN) and substituting the values in Table 2, lateral groundRu / f L(2)Skin frictional force per circumference area,  isforkh = 4841 (kN/m3)
Then, for the screw pile, the lateral displacement of theobtained by the following equation;

pile head is evaluated by Eq. (6) using the inversely

 = 0.5  L K0tan3where, : unit volume weight of the ground (kN/m ), K0:

calculated kh. Incidentally, as can be seen in Fig. 11, thecoefficient of earth pressure at rest (Jaky's equation, 1 -screw pile are similar in the measurement range (0 mm <sinf), friction resistance angle between ground andy < 1.3 mm). In order to compare both piles under similar

pile. Eq. (4) is derived by combining Eqs. (2) and (3).

conditions, the value of the lateral loading H and thetan = Ru / (0.5  (1-sinfL f)2

load-displacement relationship of the straight pile and thedisplacement y were set 1.059*10-3 (kN) and 0.6 (mm) as(4)

Substituting the values in Table 1, is 37.4 degrees for thestraight pile and 70.4 degrees for the spiral pile. Thus, thethe same value of the above calculation, respectively.

increase due to the spiral blade can be confirmed.

substituting the inverse calculated kh into Eqs. (5) and (6),The calculated displacement of the pile by
β = 7.24 (m-1)

However, since the frictional resistance angle between
ground and screw pile which was inversely calculated isyt = 0.29 (mm)not a realistic value, it is necessary to make a realistic

However, the target displacement of yt is 0.6 mm. So, it isassumption of slip surface by pulling-out force in dry

necessary to set the correction coefficient for the pile

sandy ground.

diameter so as to decrease . The modified  inconsideration of  is expressed by the following;’= (kh D / 4 EI)1/4 = 1/4 

5.2. Inverse calculation of lateral ground reaction
coefficient
The lateral ground reaction coefficient kh is inversely(7)

Based on the above calculation, the obtained

calculated from Eq. (5) using the characteristic value ofcorrection coefficient for the pile diameter,  is 0.46. Thatis, in dry sandy ground, if the outer diameter of the spiral

pile β obtained by the equation shown in Eq. (6).

blade is evaluated as pile diameter, it leads tooverestimation of the horizontal resistance. It is, therefore,

= (kh D / 4 EI)1/4
𝑦𝑡 =

1
2𝐸𝐼𝛽3

necessary to evaluate using the pile diameter excluding the(5)(𝑐1 + 𝑐2 )spiral blade portion, which is equal to the pile diameter of(6)𝐻

𝑐1 = [(1 − 𝑠𝑖𝑛2𝛽𝑙)𝑒−2𝛽𝑙 − 𝑒−4𝛽𝑙 ]𝐻𝑐2 = ∆ [1 − (1 + 𝑠𝑖𝑛2𝛽𝑙)𝑒−2𝛽𝑙 ]∆= 1 − 2(2 − cos2βl)𝑒+𝑒

In the previous research, it was necessary to estimate

(7)

∆

−2𝛽𝑙

the straight pile.
the vertical and horizontal bearing capacity for the spiral
pile installed in soft viscous ground by using the assumed

(8)
−4𝛽𝑙

pile diameter larger than the actual pile diameter. This wasdue to the fact that the spiral pile and the surrounding(9)

ground were integrated. On the other hand, in dry sandy
where, 𝛽 : characteristic value of pile (m-1), D: pile
diameter

(m),

EI:

flexuralrigidity2(kN-m ),

yt:displacement at the pile head (m), H: lateral load (kN), l:

ground, it was confirmed that the effect of integratingscrew pile with the surrounding ground can’t be expectedagainst the horizontal load.

pile length (m).

- 123 -

Proceedings of the First International Conference on Press-in Engineering 2018, Kochi

Table 1.

Summary of information concerning inverse calculation of friction resistance angle between ground and pile
Unit
Ru

kN

A

2

mm

Straight pile

Screw pile

Ultimate Vertical bearing capacity

0.002

0.019

Area of pile tip

28.27

L

mm

Pile lengthfmmPeripheral length of pile



3

kN/m

K0


Table 2.

°132.73255.00

18.85

40.84

Unit volume weight of ground

13.33

Coefficient of earth pressure at rest

0.36

Friction resistance angle between ground and pile

37.40

70.40

Summary of information concerning inverse calculation of level ground reaction coefficient
Unit
D
EI

m

Pile diameter
Flexural rigidity

yt

kN-m2
mm

Displacement of pile head

H
L

kN
m

Lateral load
Pile length



-1

kh

Screw pile

0.006

0.013
0.006
0.60
0.001
0.255

Characteristic value of pilem
kN/m3 Lateral ground reaction coefficient6. Conclusion
The following conclusions are obtained from this

Straight pile

5.964

7.236
4841

References
Araki, K. 2013. Simplifted foundation method subject tostudy;

small - scale structure “PIN FOUNDATION

1)

The bearing capacity in the vertical direction is

METHOD”. The Japanese Geotechnical Society. Vol.

increased by the spiral blade, but there is not much

61, No. 8, pp. 32-33. (in Japanese)

influence on the bearing capacity in the horizontal
2)

3)

Hirata, A., Kokaji, S. and Goto, T. 2005. Study on the

direction in dry sand.

estimation of the axial resistance of spiral bar based

The horizontal resistance of the screw pile wason interaction with ground. Shigen-to-Sozai, Vol. 121,

expected to increase by integration with thepp. 370-377. (in Japanese)surrounding ground in the soft viscous ground, but in

Isobe, K. and Yamauchi, R. 2017. Numerical simulation

the dry sandy ground there was no effect ofon bearing capacity of a small diameter spiral pile inintegration with the surrounding ground. It is,

soft ground subjected to combined load, Proceedings

therefore, necessary to evaluate the shape excludingof the 15th International Conference of the

spiral blade.

International Association for Computer Methods and

The influence of the ground disturbance during theAdvances in Geomechanics (USB).

installation operation and the type of ground was not

Sato, T., Harada, T., Iwasaki, N., Hayashi, S. and Ohtani,

considered in the proposed estimation method in the

J. 2015. Effect of shaft rotation of spiral piles underprevious research (Isobe and Yamauchi, 2017),

its installation on vertical bearing capacity. Japanese

resulting in the errors for the estimation of the

Geotechnical Journal, Vol. 10, No. 2, pp. 253-265. (inbearing capacity against the combined loading.

Japanese)- 124 -