a study on the p-y curves by small-scale model tests

11
28 1C · 2008 1 41 地盤工學 大韓土木學會論文 28卷第1C 號· 20081pp. 41~51 모형실험을 통한 말뚝의 p-y 곡선에 관한 연구 A Study on the p-y Curves by Small-Scale Model Tests 김태식*·정상섬**·김영호*** Kim, Tae-Sik·Jeong, Sang-Seom·Kim, Young-Ho ····························································································································································································································· Abstract The load distribution and deformation of single piles which is embedded in Jumunjin sand and Kimhae clay are investigated, based on small scale model tests. Special attention is given to the consideration of flexural rigidity in laterally loaded piles. To consider the flexural rigidity of the pile, tests are performed with the aluminium piles of three different length under different relative densities and undrained shear strength. The test results indicate that the initial slope from the results of tests is pro- portional to the depth and pile-soil rigidity in both soils. But the increasing rate of the initial slope in the clay is less than in the sand. In addition, the soil resistance is more related to the depth and soil condition than the pile rigidity. Base on the test results, an empirical formula is proposed, which is good agreement with previously published small scale model test and field lateral load test. Keywords : p-y curve,pile-soil rigidity,initial slope,soil resistance ····························································································································································································································· 논문은 말뚝 기초지반의 강성이 수평재하말뚝의 거동에 미치는 영향을 알아보고자 주문진 표준사와 김해점토를 초지반으로 수평재하말뚝에 대한 실내실험을 실시하였다. 또한 실험 결과를 바탕으로 영향계수를 정량화 있는 경험식 산정하였다. 말뚝과 지반의 강성을 고려하기 위하여 길이가 다른 3 개의 알루미늄 모형말뚝을 제작하였으며 이를 사질토 점성토 지반에 설치한 기초지반의 상대밀도( 사질토 지반) 비배수전단강도( 점성토 지반) 변화시켜가며 수평재하 내실험을 수행하였다. 실험을 통하여 산정된 p-y 곡선의 초기기울기는 사질토와 점성토 지반 모두에서 깊이와 말뚝- 지반의 강성에 비례하였으나 점성토 지반의 경우 사질토 지반에 비하여 깊이에 따른 초기기울기의 증가율이 작은 경향을 나타내었 . 또한 극한 지반반력의 경우 모든 지반 조건에서 수평지반반력계수와 유사하게 깊이와 지반강성에 비례하여 증가하였으나 말뚝 강성에 대한 영향은 적게 나타났다. 이와 같은 특성을 고려하여 논문에서는 p-y 곡선의 초기기울기 산정 식을 험결과와 가장 유사한 형태를 지니는 쌍곡선으로 지반 조건에 따라 제시하였으며 제안된 식을 기존의 연구 현장재하시험 비교하여 제안 식의 적용성을 검증하였다. 핵심용어 : p-y 곡선, 말뚝- 지반의 강성, p-y 곡선의 초기기울기, 지반반력 ····························································································································································································································· 1. 최근 국내에는 인천대교를 비롯한 서·남해상의 장대교량, 대형 송전철탑 등이 빈번하게 설계, 시공되고 있다. 이러한 대형 구조물들은 풍하중, 온도하중, 충격하중, 지진하중 등에 의하여 상당한 크기의 수평하중을 받게 되며, 이는 지반 항력 감소 등을 초래하여 상부구조물의 설계에도 영향을 미치게 된다. 이러한 말뚝- 지반의 비선형 거동 cyclic 중에 의한 지반저항력 감소 등의 거동특성은 간단한 단부 지점조건의 모델링으로는 고려하기 어려우며 말뚝기초의 방향 거동에 관한 지반 공학적 측면에서의 정밀한 검토가 필요하다. 수평하중을 받는 단독말뚝을 해석하는 방법으로는 탄성지 상보 이론에 기초한 지반 반력법, 탄성해 방법 등이 으나 이러한 방법들은 모두 지반을 탄성으로 가정하고 . 이에 반하여 p-y 곡선법은 지반의 비선형거동을 고려할 있으므로 상대적으로 수평하중을 받는 탄소성 말뚝기 초의 해석기법으로 적절하다고 있다. 이에 따라 수십 년에 걸쳐 p-y곡선 산정을 위한 많은 연구가 수행되어 (Kubo, 1964; Matlock, 1970; Reese et al., 1975; Welch and Reese, 1972; Evans and Duncan, 1982; Murchisn and O'Neill, 1984; Georgiadis et al., 1992; Reese and Wang, 1997) 지금까지 다양한 지반과 하중조건을 고려한 p- y 곡선이 제안되고 있으나 이들 해석기법의 검증은 국외의 *정회원ㆍ고려개발 토목사업본부 사원 (E-mail : [email protected]) **정회원ㆍ교신저자ㆍ연세대학교 사회환경시스템공학부 교수 (E-mail : [email protected]) ***연세대학교 사회환경시스템공학부 박사과정 (E-mail : [email protected])

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28 1C · 2008 1 − 41 −

28 1C ·2008 1
pp. 41~51
A Study on the p-y Curves by Small-Scale Model Tests
*·**·***
·····························································································································································································································
Abstract
The load distribution and deformation of single piles which is embedded in Jumunjin sand and Kimhae clay are investigated, based on small scale model tests. Special attention is given to the consideration of flexural rigidity in laterally loaded piles. To consider the flexural rigidity of the pile, tests are performed with the aluminium piles of three different length under different relative densities and undrained shear strength. The test results indicate that the initial slope from the results of tests is pro- portional to the depth and pile-soil rigidity in both soils. But the increasing rate of the initial slope in the clay is less than in the sand. In addition, the soil resistance is more related to the depth and soil condition than the pile rigidity. Base on the test results, an empirical formula is proposed, which is good agreement with previously published small scale model test and field lateral load test.
Keywords : p-y curve,pile-soil rigidity,initial slope,soil resistance
·····························································································································································································································

. . 3 ( ) ( ) . p-y - . . p-y .
: p-y , - , p-y ,
·····························································································································································································································
, .
, , ,
,

. - cyclic



.
,

. p-y

.
p-y (Kubo, 1964; Matlock, 1970; Reese et al., 1975; Welch
and Reese, 1972; Evans and Duncan, 1982; Murchisn
and O'Neill, 1984; Georgiadis et al., 1992; Reese and
Wang, 1997) p-
y
* (E-mail : [email protected]) ** (E-mail : [email protected])
*** (E-mail : [email protected])
− 42 −
1998, 1999, 2000)
,
, ,
(2005) Pile-Bent ,


p-y



.

p-y
,
.
2.
.
2.1
,
, 2cm
1.0×1.5×1.0m ( 2.1
), 2cm
80cm× 1.0m ( 2.2 )
. Ring
type 25cm
.

.

2.1 2.2 .
2.3
EN AW 6063-T5 0.40
m, 0.65m, 0.85m 3 ,
European Aluminium Association
Physical & Elastic Properties ( 2.3
).
28 1C · 2008 1 − 43 −
2.3.2
-
.
( 2.4 ),
Davisson (1970)
( 2.4 ) 40% 80%
( 2.6 ).

Davisson
17kPa 40kPa
( 2.7 ).
) , .
2.4
.
ASTM D 3966-90(optional)
.
Traveling
spreader 3 Pluviation

( 2.8 ).
2.1. ( )

(mm) Dmin 0.075(No. 200)
10% (mm) D10 0.35
60% (mm) D60 0.57
Cu 1.63
Cc 1.02
Gs 2.63
(%) w 0
2.2. ()

Cu 1.82
Cc 0.111
Gs 2.604
(%) LL 63
(%) PL 29.3
(%) PI 33.7
2.3.
2.4. (Davisson, 1970)
nh
277 ~ 2770 t/m3
(peat) nh 6 t/m3
nh 67 cu
2.5. (Broms )

- 2.0 < ηL < 4.0
,
(L=0.40m) 1.75 1.94
(L=0.65m) 3.00 3.32
(L=0.85m) 4.00 4.43
2.7. ()
(L=0.40m) 1.14 1.58
(L=0.65m) 2.42 2.99
(m) (m)
(%)1 2 3
− 44 −
±1.8% .
2.4.2
17kPa 40kPa
.
Field vane test -
( 2.3 ),


.
10cm

.
(3.1) (
3.1 ) curve-fitting x-y
4 ( (3.2)~ (3.3) )
.
( 3.1 ) p-y
( 3.2 ).

.



( 3.3(a) ).



.
,
( 3.3(b)
).
(
3.4(a) ),
.


. 0.45L~
0.50L .

( 3.4(b) ).

.
cu=17kPa 0.40m
0.45L, 0.65m 0.5L, cu=40kPa
0.3L, 0.5L .
y
Kondner(1963)

M EIε y
p-y
p-y .

p-y
Palmer & Thompson(1948)
.
( 3.5(a) ).





( 3.5(b) ).


3.1
− 46 −
(1997) 6D 0.18m

( 3.1 ).
3.2 p-y
3.3
28 1C · 2008 1 − 47 −
3.6
S
.
,

.

.
3.4
3.5 p-y (kh)
3.1


− 48 −
p-y
,

. p-y


4.1
, Palmer & Thompson
(1948) .
z : (m)
(4.2) .
(4.2)
(4.3)
(4.4)
, B log
A . A B
.
4.1
4.2
4.1
A, B 4.3 .
kini nh z D ----=
B ×=
kini
Y BX logA+=

Terzaghi 700 ~ 2100 2100 ~ 7200 7200 ~ 14100
Reese 5500 16600 34600
2200 6700 18000
Dr=40% 12742 Dr=80% 22714
4.2. (kN/m3)
nh(kN/m3)
Terzaghi(1955) 4.7~97
cu=17kPa 50 cu=40kPa 90
28 1C · 2008 1 − 49 −
Davisson “
” 0%=2770, 100%=27700


.
.
4.2.1
(4.8)

4.2
A, B 4.4 .
4.2.2
,
.

(4.14) .
(4.15)
4.3 A
pu 3DγzKp=
pu cuNcD=
pu AcuDzB=
log pu
4.3. A, B
A B
67 1.486
4.4. A, B
A B
2.16 0.900
− 50 −

(2001)
p-y ,

.
(2001)
.
4.6 4.7
4.8 .
p-y .

( 4.4 ).

p-y .
4.9
4.10 ,

( 4.5 ).
p-y

p-y .
p-y ,

,
.
.
4.5. A, B
A B
2.87 0.547
(m)
4.7 ()
(g/)
(nh)
(m) (kh)
0.05 0.045 kg/ 0.027 kg/cm
0.10 0.168 kg/ 0.050 kg/cm
4.4 () 4.5. ()
4.9. ()
(m)
4.10. ()
(g/)
(nh)
28 1C · 2008 1 − 51 −
. ,
.

.
2.

.

.

.

.
,
.

.

, (1999e) , , , 15, 6, pp. 167-185
, (1999f) , 99 , , pp. 3-44
, (1999) p-y , , , 19 , -1, pp. 105-115.
, , (1999d) , , , 15, 6, pp. 29-44.
, , (2000) ,
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, (2001) , , , 17, 6, pp. 193-205.
, , (2005) Pile-Bent , 2005 , .
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(: 2007.9.3/: 2007.10.28/: 2007.12.28)