1. ก ก ก F 15 12-14 2553
ก ก ก ก F F
PREDICTION OF RC BUILDING DAMAGE CATEGORIES RESPONSE TO TUNNEL
EXCAVATION INDUCED GROUND MOVEMENT
F (Suchatvee Suwansawat)1
(Chinawut Chanchaya)2
1
F F ก ก กF F F F ก
ก F กF F ก ( kssuchat@kmitl.ac.th)
2
ก .ก F ก ( ) (topcu_999@yahoo.com)
F : F ก กก ก F F F ก
ก F Stiffness F F F F Fก F
ก F ก 1-5 F F F ก F
F , F ก F
F ก Normalised Stiffness Ratio (NSR) Fก
F F F ʽ ก ก Sagging Hogging F ก
(Gaussian Curve) F F Bending Stiffness ( EI* ) Shear Stiffness ( GA* ) F ก
F ก F F F F กF F ก F
ก F ก F F F F
ก ก F ก กก ก F F
ABSTRACT : Building damage due to tunnel excavation-induced ground movement is general evaluated using deep elastic beam
method with various related stiffness and dimension length/height with unit thickness of building. Damage criterion based on
limit/critical tensile strain corresponding to building damage category 1-5 as commonly calculated the deflection ratio, horizontal
tensile strain of adjacent buildings in influence zone of tunnel excavation for risk assessment. This paper employed the approach of
Normalised Stiffness Ratio (NSR) related to the percentage of openings for the different of Reinforced Concrete (RC) buildings
within sagging and hogging zone of Gaussian Curve to evaluate the proper equivalent bending stiffness ( EI* ) and shear stiffness
( GA* ) by analytical calculations, which presented the chart of generalized RC building damage categories response to tunnel
excavation accurately between deflection ratio and horizontal tensile strain compared to critical strain for different L/H building.
KEYWORDS : Tunnel Excavation, Building Damage, Reinforced Concrete, Deflection Ratio, Normalised Stiffness Ratio

2. ก ก ก F 15 12-14 2553
1. ก F F F ก F
ˆ กF F F F F ก (1) (2)
ก ˈ ก ก d ∆ M P ( L 2)
2
= + (1)
dx 2 EI kGA
F F F F F ก ∆ PL2
=
 18EI  (2)
1 + L2GA 
ก ก ก F กF F F F L 48 EI  
∆ = F กF (Relative deflection)
Fก ก F ก Fก
M = F (Bending Moment)
F F ก F F
P = ก ˈ (Point Load)
F F ก F ก
L =
F F ก
EI = F F
ก F F F
GA = F
กF F F Fก
k = . . . (Shear Coefficient)
= 2/3 F
2. กก F F
F กF F กก F
ก
F 2 F ก Bending Moment
ก F Stiffness
Shearing F ก F
F F
กF Fก F
F 2 F 1
1 3 ก ก (3) (4)
1 F I, Cb Cs ก
1 ก กก F [1]
3ก FF I ก F ก [3]
∆
= Cbε b ,max (3)
2 ก FF F ก Point Load L
∆
= Cs ε d ,max (4)
L
ˈ ก (Deep beam) ก ก F ∆ = F กF F
L
ก ก ˈ (Point Load) 2 ก ε b,max = F ก Bending
F F F x ε d ,max = F ก

3. ก ก ก F 15 12-14 2553
ก ก F ε b,max ε d ,max F F F δL กก F F Stiffness Ratio Neutral
F F 2 ก (5) axis F F Deflection Ratio ก
F ε br ε dr ก (6) (7) F F F ก ก ˈ
δL =
∆δ L (5) Frame Structure (E/G=12.5) ก F Deflection Ratio กก F
L
ε br = ε b ,max + δ L (6) ก (Limit Tensile Strain) ก
 1 −ν  2  1 +ν 
2
(7) ก ก ก
ε dr = δ L   + δL   + ε d ,max
2
 2   2  ˈ F L F F ก 3.125
δL = F H
4(a) ก ก
ε br = F ก Bending
L F F ก 3.125 F ก
ε dr = F ก H
∆δ L = F กF 5 F กF F F F EI * GA* F
ν = F ˆ F
ก ก (3) (7) F F F ∆
L
ก ε limit F (L) ก F E
H G
F Neutral axis Sagging Hogging 4
5ก F
3. ก F Equivalent Stiffness
กกF F F F ʽ F
F F F ก F F F ʽ
(a) Neutral axis F กก Sagging
6 Fก F F Stiffness
(b) Neutral axis F F Hogging
4 F E/G Neutral axis F F Deflection Ratio [5]

4. ก ก ก F 15 12-14 2553
กF F EI * GA* กก ก
F Deflection Ratio ก F
(Tensile Strain) ก ก ก F
ก ˈ F
F L
 
F ก 3.125 ก ˈ 2 ก
 H critical
F F NSR ก L 7
H
• ก 1  L < L 
   
 H   H critical
(L H ) L (11)
A∗ = x
(L H ) critical
m  L
∑  t.H − (i A )



i =1 

o i 
(L H ) 
( )  + t. ( L.h − ( A ) ) .λ  (12)
3

n
 1  L.h j − ( Ao ) j  j o
∗
x ∑  xt. 
j
I = 
2
j 
(L H ) critical
j =1 12



L 

L 

• ก 2  L > L 
   
 H   H critical
L (13)
A∗ =
 
6 F ʽ 0%, 10%, 20% 30% [7] m
L
∑  t.H − (i A ) 

i =1 


3.1 F NSR F F I* A*
o i

( ) ( L.h − ( A ) ) .λ  (14)
3

n
 1  L.h j − ( Ao ) j 
F กF ก ก
j o
I = ∑  xt. 
∗ j
 + t. 2
j 
j =1 12  L  L 
   
(2) F F F Stiffness ก
A* = F F
F F ʽ ก (8) ก F ʽ
I* = F F F
ก (9) ก F Stiffness ก
L =
ก (10) F EI * GA*
Li = F F F F
1 (8)
K =
plain beam
L3 3L hj = F F F F
+
48EI 8GA
( Ao )i = F ʽ F F
1 (9)
K equivalent =
L3 3L ( Ao ) j = F ʽ F F
+
48 EI * 8GA*
λj = ก Neutral axis F
NSR =
K equivalent (10)
K plain beam F F ก
NSR = F Normalised Stiffness Ratio t =
K plain beam = F Stiffness ( ) F F NSR F Sagging
K equivalent = F Stiffness ( F ʽ ) Hogging 7 F ก 1 F กF F A, I
EI = F Bending Stiffness กก F NSR F
GA = F Shear Stiffness ก 2 F F กF F A, I ก F NSR
EI * = F Bending Stiffness F F ก ก F NSR F F
GA* = F Shear Stiffness F F F F ʽ กก
L =

5. ก ก ก F 15 12-14 2553
ก F Deflection Ratio กก ก F F Bending
Strain ( ε br ) Diagonal Strain ( ε dr ) F ก F F
(a) F NSR F Sagging
(a) F F Sagging
(b) F NSR F Hogging
7 F F F Nomalised Stiffness Ratio (NSR) ก F
F (L/H) F F F ʽ 0%, 10%, 20%, 30% (b) F F Hogging
3.2 F ก F ʽ ∆ δL
8 F F L ก (ก E
=12.5)
ก ก F ʽ ε limit ε lim it G
ก F Deflection Ratio F F F ʽ (No openings)
F ก F ก ก
ก ( F F ʽ )
ก ก (3) (7) F F Cb Cs ก
F ʽ ก ก (15) (16)
Cb =
L
+
3I *  E 
 
(15)
12λ 2λ LA*  G 
Cs = 1 +
L2 A*  G 
 
(16)
18I *  E 
F ก F Neutral axis ก
ก F ก ก F
ก F F ʽ F (a) F F Sagging
Deflection Ratio ก ε limit ก ก (3) (7)

6. ก ก ก F 15 12-14 2553
2 ก F ก [2]
ก กก ก F ก F
F Deflection Ratio ก F ʽ
ก F F ʽ F ก
(b) F F Hogging F F 10 กก F กF
9 F F
∆
L ก δL
(ก E
=12.5) F [4,6] ก
ε limit ε lim it
Fก ก
G
F ʽ (With opening) 30%
F ก
กก F
ก กก F Equivalent Stiffness
F F ˈ Theory of Elasticity
F EI * GA* Normalised
Stiffness Ratio, (NSR) L F
H
∆ δL
F F ε limit
L ก ε lim it
ก
ก ( E =12.5) ก F F ʽ (Plain beam)
G
8 ก F ʽ (Beam with openings) 30%
δL
9 F ε
ก F ก Diagonal
lim it
strain ( F ˈ F F) กF F ˈ
Bending strain ( F ˈ F ) ก ก
F εδL L F %Opening F
lim it H
F F Deflection Ratio ก ก ก
ก F Deflection Ratio F
ก ก F
ก ก
F ก (Limit Tensile Strain, ε limit )
2 F ˈ ก F
F ก กก
10 ก
ก กF F F F

7. ก ก ก F 15 12-14 2553
4.
ก ก
( F F ʽ ) F ʽ ก F
Deflection Ratio ( ∆ ) ก F (δ )
L
L
ก F ก ( ε limit ) ก
กก ก F ก
F Normalised Stiffness Ratio (NSR) F
Bending Stiffness ( EI * ) Shear Stiffness ( GA* )
Fก F F F ʽ F F F
Deflection Ratio ก ก
ก F Deflection Ratio
ก ก F
5. ก
[1] F , ก
2552. ก ก
F, ก ก ก F
14,
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Pentech Press, London, 611-654.
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(11), 1605-1619.
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Evaluating Damage Potential Buildings Affected by Excavations,
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Vol. 131 (10), 1199-1210.
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Simplified model for evaluating damage potential of buildings
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