Transcript 응용토질역학15장 - 연세대학교 기초시스템연구실

Chapter 15
Soil-Bearing Capacity for Shallow
Foundations
연세대학교 지반공학연구실
Soil Substructure Interaction Lab.
개요
○ 구조물 기초 설계시 고려사항
1. 상부구조에 의해 기초에 전달되는 하중
2. 기초를 지지할 흙의 거동 및 응력과 관련된 변형조건
3. 흙의 토질공학적 조건
Soil Substructure Interaction Lab.
개요
- Foundation <기초>
1. Shallow FDN [ Df≤B , Df≤(3 ~ 4)B ]
• spread footing (확대기초)
• mat foundations (전면기초)
2. Deep FDN
• Pile FDN
• Caisson FDN
• Drilled shaft FDN
Soil Substructure Interaction Lab.
개요
- Two main characteristics for shallow foundations
1. Should be safe against overall shear failure
safe load
bearing capacity
2. Should not undergo excessive settlement
Allow. Settlement
Figure 15.1 Common types of foundations;
(a) spread footing; (b) mat foundation;
(c) pile foundation; (d) drilled shaft foundation
Soil Substructure Interaction Lab.
15.1 Ultimate Soil-Bearing Capacity for
Shallow Foundations
- 전단파괴의 3가지 형태 (Fig 15.3)
1. General shear failure (Ⅰ)
• Dense sand, stiff clay
• qu(단위 면적당 하중)에 도달시 흙에서 갑작스런
파괴가 일어나고 파괴면은 지표면까지 확장
Soil Substructure Interaction Lab.
15.1 Ultimate Soil-Bearing Capacity for
Shallow Foundations
2. Local shear failure (Ⅱ)
• Medium sand or clay
• 기초하중증가로 침하도 증가, 파괴면은 기초의
바깥방향으로 점차확산
• qu 의 최대치가 나타나지 않음
Soil Substructure Interaction Lab.
15.1 Ultimate Soil-Bearing Capacity for
Shallow Foundations
3. Punching shear failure <관입전단파괴>
• Fairly loose soil
• 파괴면이 지표면까지 확장되지 않음
• qu를 넘어서도 하중-침하곡선은 경사가 급하고
직선에 가깝다
Soil Substructure Interaction Lab.
15.1 Ultimate Soil-Bearing Capacity for
Shallow Foundations
•
qult : max load per unit area which the soil can
sustain without plastic failure
Soil Substructure Interaction Lab.
15.2 Terzaghi’s Ultimate Bearing Capacity
Equation
- Terzaghi (1943)
• 얕은기초의 극한지지력 산정이론 제안
• Df≤B
shallow foundation
• Continuous, strip footing 에 극한하중 작용시 전반
전단 파괴면 (General shear failure)
Soil Substructure Interaction Lab.
15.2 Terzaghi’s Ultimate Bearing Capacity
Equation
B
I
Df
H
G
Ⅲ
E
A
Ⅱ

Ⅰ

J
B
Ⅱ
Ⅲ
F
D
• Zone Ⅰ : Triangular elastic zone
Ⅱ : Radial shear zone bounded by logarithmic spiral
Ⅲ : Triangular Rankine passive zone
Soil Substructure Interaction Lab.
15.2 Terzaghi’s Ultimate Bearing Capacity
Equation
B
I
H
Df
G
Ⅲ
E
A
Ⅱ

Ⅰ
J

B
Ⅱ
Ⅲ
F
D
• 파괴면 GH, FI를 따라 생기는 전단저항은 무시
• Square FDN
• Circular FDN
Local shear failure
• (strip FDN)
• (square FDN)
• (circular FDN)
여기서 : 수정지지력계수
<table 15.2 참조>
-
Soil Substructure Interaction Lab.
15.2 Terzaghi’s Ultimate Bearing Capacity
Equation
• Equilibrium
q u 2b 1  W
 2C sin   2 P p
(15.1)
B
2
W  ABJ ( w.t of soil wedge), rb 2 tan 
where
b
C  cohensive force acting
•
AJ , BJ ,
2b  q u  2 P p  2bc tan   b 2 tan 
cb
cos 
(15.2)
Soil Substructure Interaction Lab.
15.2 Terzaghi’s Ultimate Bearing Capacity
Equation
Pp 
1
 b tan   2 K r  cb tan  K c  qb tan  K q
2
Kr , Kc , Kq
: earth PR. coefficients,
(15.3)
f n  
< Fig 15.6 참조 >
Soil Substructure Interaction Lab.
15.2 Terzaghi’s Ultimate Bearing Capacity
Equation
2b  q u  2 P p  2bc tan   b 2 tan 
Pp 
1
 b tan   2 K r  cb tan  K c  qb tan  K q
2
eq(15.3)
(15.2)
(15.3)
eq(15.2)
1
qu  c' N c  qN q  BN 
2
where
N c  tan ' K c  1
(15.5)
N q  K q tan  '
(15.6)
1
N   tan  ' K  tan  '1
2
(15.7)
<table 15.1 참조>
Soil Substructure Interaction Lab.
15.3 General Bearing Capacity Equation
- Terzaghi’s bearing capacity equation
• Not consider rectangular FDN, 0< B <1
L
• Not consider shear resistance
• Load inclination
•

Soil Substructure Interaction Lab.
15.3 General Bearing Capacity Equation
-
지지력계수
( qu
1
 cN c  qN q  BN 
2
  45  

2
적용시 )
Reissner(1924)


N q  e  tan  tan 2  45  
2

Prandtl(1921)
N c  N q  1 cot 
Caquot and kerisel
N   2 N q  1 tan 




N   N q  1 tan1.4 



N   1.5 N q  1 tan 

Meyerhof
Hansen
Soil Substructure Interaction Lab.
15.3 General Bearing Capacity Equation
-
Meyerhof(1963)
1
q u  cN c  cs  cd  ci  qN q  qs  qd  qi  BN  s d i
2
where
 cs ,  qs ,  s  shape factors
 cd ,  qd ,  d  depth factors
 ci ,  qi ,  i  inclination factors
<table 15.5참조>
Soil Substructure Interaction Lab.
15.4 Effect of Groundwater Table
D1
D2
Df
Case 1
B
d
Case 2
 sat
• Case Ⅰ : 지하수위가 0≤D1≤Df 인 상태에 있을 때
q  D1    D2 ( sat   w )
1
1
BN    BN 
2
2
• Case Ⅱ : 지하수위가 0≤d≤B 인 상태에 있을 때
q  D f
 av    
d
    
B
• Case Ⅲ : 지하수위가 d≥B 위치에 있을 때 지하수위는
극한지지력에 영향을 주지 않음
Soil Substructure Interaction Lab.
15.5 Factor of Safety
1) 지지력에 대한 F·S
q all 
qu
FS
, 전허용지지력
Net stress increase on soil, , 순허용지지력
qall ( net ) 
qu  q
FS
, ( F·S는 적어도 3.0이상 )
Soil Substructure Interaction Lab.
15.5 Factor of Safety
2) 전단파괴에 대한 F·S (F·S. shear)
F·S. shear = 1.4 ~ 1.6
- 주어진 F·S. shear 에 대하여 순허용지지력을
계산하는 과정
① Developed cohesion. Cd &  d
Cd 
C
F  S shear
tan 



 d  tan 1 
 F  S shear 
② Cd와 를 이용하여 를 계산
1
q all  C d N c  qN q  BN 
2
N c , N q , N   bearing capacity factors for  d
Soil Substructure Interaction Lab.
15.5 Factor of Safety
③
q all ( net )  q all  q


1
C d N c  q N q  1  BN 
2
 Example 15.1
15.2
15.3
15.4
15.5
Soil Substructure Interaction Lab.
15.6 Ultimate Load for Shallow Foundations
under Eccentric Load
-
One-way Eccentricity
q
P
M
P M

y
A I
LB 3
I 
,M  Pe
12
where
B
L
+
=
P : Vertical Load
e : eccentricity of vertical load
B·L : Dimensions of footing
q : intensity of soil pressure
B
P P e B


A LB 3 2
12
P P e
  2
A LB
6
P 6 P  e P  6e 
 
 1
q
A A  B A  B  max
q
Soil Substructure Interaction Lab.
15.6 Ultimate Load for Shallow Foundations
under Eccentric Load
B
6
B
 0, e 
6
B
 0, e 
6
qmin  0, e 
for
qmin
qmin
if
e
B
6
q min  0
P
P
M
M
B
B
L
e P=R
B
e
6
tensile
stress
B
B
q max
B
6
e
X
e
qmin
e
Y
B
6
2
q
M
e
P
B B
 e
3
2
q
P   B   L
2
2P
2P
q

B  L  3

 B  3e  L
2

4P
2P


3 L B  2e 
B

3 L  e 
2

R=P
Soil Substructure Interaction Lab.
15.6 Ultimate Load for Shallow Foundations
under Eccentric Load
-
Meyerhof(1953) : effective area method
①
e
M
,
P
qmax ,
qmin ,
e
B
6
qmax 
4P
3 LB  2e 
② Determine the effective dimensions
B′ = B-2e effective width
B′<L′
L′ = L
effective length
혹은 길이(L)방향으로 편심이 있을 때
B′=B , L′=L-2e
L′과 B′중 작은값이 기초의 유효폭이 된다
Soil Substructure Interaction Lab.
15.6 Ultimate Load for Shallow Foundations
under Eccentric Load
③
1
q u  cN c  cs  cd  ci  qN q  qs  qd  qi  B N  s d i
2
–  cs ,  qs , s
는 B′,L′ 사용하여 table 15.5 에서 결정
–  cd ,  qd , d
는 B를 사용하여 table 15.5 에서 결정
④ Qult  q u  B   L,
B   L  A  유효면적
⑤ 지지력 파괴에 대한 안전율
FS 
Q ult
Q
Soil Substructure Interaction Lab.
15.6 Ultimate Load for Shallow Foundations
under Eccentric Load
Two-Way Eccentricity
 Example 15.6
Soil Substructure Interaction Lab.
15.7 Bearing Capacity of Sand Based on
Settlement
• N치 : KSF – 2318
Split – spoon sampler를 지반에 관입시켜 그 저
항치를 기록하고 동시에 토질분류 및 실내시험을
위한 대표적인 시료를 채취하는 방법으로 규정
N값은 중량 64.5㎏ 의 Hammer를 76㎝의 높이
에서 자유낙하시켜 관입시험용 sampler를 지반에
30㎝ 관입시키는데 필요한 타격수
Soil Substructure Interaction Lab.
15.7 Bearing Capacity of Sand Based on
Settlement
-
According to Meyerhof’s theory, for 25 mm (1 in.) of estimated
maximum settlement,
 qall ( net ) (kN / m 2 )  11.98 N cor
(for B  1.22m)
 3.28B  1 
q
(
kN
/
m
)

7
.
99
N

 all ( net )
cor 
 3.28B 
2
2
(for >1.22 m)
where N cor  corrected standard penetration number
Soil Substructure Interaction Lab.
15.7 Bearing Capacity of Sand Based on
Settlement
 Se 

 25 
 qall ( net ) (kN / m 2 )  19.16 N cor Fd 
(for B  1.22m)
2
 qall ( net) (kN / m 2 )  11.98 N cor  3.28B  1 Fd  S e 
 3.28B 
 25 
(for > 1.22 m)
where Fd  depth factor = 1  0.33( D f / B)  1.33
S e  tolerable elastic settlement, in mm
Soil Substructure Interaction Lab.
15.8 Plate Load Test
- Plate load test
• Plates : 25㎜ thick 150∼762㎜ in diameter
• Hole : a minimum diameter 4B (B:diameter of the test plate)
to a depth of Df
• Loading : about of the estimated ultimate load elapsed one
hour between / each load application step
• Test : until failure or at least 25㎜ settlement
q
S
Soil Substructure Interaction Lab.
15.8 Plate Load Test
• Clay
q u F   q u P 
FDN Plate
independent of the plate size
• Sandy soils
q u F   q u P 
BF
,
BP
B F , B P : width of FDN & plate
• For load intensity , q0
SF  SP

BF
BP
B
S P  F
 BP
(clayey soil )




2
 3.28B P

 3.28B
F

 1 
 1 
2
( sandy soil )
where B P , BF m 

2 BF
 BF  B P
 S P 




2
Soil Substructure Interaction Lab.
15.9 Ultimate Bearing Capacity on Layered
Soil
Soil Substructure Interaction Lab.
15.10 Summary and General Comments
• Bearing capacity of foundations depends on few factors
1. Subsoil stratification
2. Shear strength parameters of the subsoil
3. Location of the groundwater table
4. Environmental factors
5. Building size and weight
6. Depth of excavation
7. Type of structure
Soil Substructure Interaction Lab.