Academic Journal of Science and Technology 
ISSN: 2771-3032 | Vol. 15, No. 2, 2025 

 

162 

Research	on	the	Effect	of	the	Sequence	of	Exterior	
Concrete	Placement	on	the	Stability	of	Reinforced	
Concrete	Arches	with	Rigid	Skeleton	
Yi Cai 

College of Civil Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China 

 

Abstract: In the process of casting concrete in the outer package of reinforced concrete arch bridge with strong skeleton, the 
force state of the main arch ring will be constantly changed with the advancement of concrete casting, and this dynamic load 
distribution makes the mechanical properties of the main arch ring extremely complicated. It is a key issue in the construction 
of reinforced concrete arch bridges with strong skeleton to study the influence of different pouring sequences on the linearity 
and stability of the arch ring. This paper takes a reinforced concrete arch bridge with strong skeleton on the Sichuan-Tibet line 
as the engineering background, and simulates the influence of different pouring sequences of exterior concrete on the stability 
of the strong skeleton concrete arch ring. Based on the optimal working surface (eight working surfaces) and the optimal pouring 
method (ring-segmented pouring), 24 first pouring schemes are numerically simulated, and the optimal location of the first 
pouring section is determined through the analysis and comparison of stability and deflection analyses. The study shows that the 
first-order flexural modal coefficient of Scheme 4 (simultaneous casting of 1-1, 3-1, 5-1 and 7-1 bottom slabs) reaches 22.51, 
which is the highest value of all the schemes, indicating that its ability to resist instability is significantly enhanced. In addition, 
the deflections of scheme 4 in all critical sections are at the lowest level, and the maximum deflection is 86.9% lower than the 
worst scheme, and the distribution shows a gradual growth characteristic, which avoids the risk of local abrupt changes in the 
high deflection scheme. 

Keywords: Rigid Skeleton Main Arch Circle; Pouring Working face; Sequence of Pouring Concrete for Outsourcing; Stability; 
Nonlinear analysis. 

 

1. Introduction 
Bergmeister K, Capsoni A and Corradi L[1] investigated the 

effect of deck girder slenderness on transverse buckling loads 
of arch steel bridges. Fangcun Song and Hu Jia[2] numerically 
simulated the linear elastic response and geometrically 
nonlinear load carrying performance of steel arch bridges by 
constructing a three-dimensional solid finite element model 
with parametric analysis method through engineering 
examples. Shangying Xie[3], Dongsheng Qian and Anbang 
Gu[3] studied the stability of a 180m span steel pipe concrete 
strong skeleton arch bridge, and the analysis showed that the 
influence of nonlinearity, especially the material nonlinearity, 
should be considered when the stability calculation of the 
large span steel pipe concrete strong skeleton arch bridge is 
carried out. Gangruo Wu[5] and Bingcheng Yang[6] establish 
finite element models of Pingyikou Bridge and Ziyang 
Hanjiang Bridge based on ANSYS to reveal the dynamic 
folding mechanism of the stiffness of the stiffness skeleton 
under the action of double nonlinear coupling, and the study 
shows that the construction of the split ring enhances the 
sensitivity to material nonlinearity by 18.7%, and the 
geometrical nonlinear increment induced by segmental 
construction is exponentially correlated with the span 
diameter. Chen Xiaobo[7] found that the sequence of concrete 
filling in the steel pipe had little effect on the stress of the 
stringers through the calculation and analysis of the 
construction process, and the three-ring pouring scheme for 
the outer concrete could avoid the appearance of tensile stress. 
The stability coefficients of the maximum cantilever stage of 
the steel pipe and after pouring concrete are more than 4, 
which meet the specification requirements. This kind of 

structural system with compression bending force as the main 
force, its stable bearing capacity is significantly affected by 
the construction timing effect. Therefore, it is important to 
study the stability of the main arch ring during the casting of 
the outer concrete. 

2. Model 

2.1. Establishment of foundation pit model 
The construction phase analysis of the main arch ring of the 

strong skeleton was simulated using Midas Civil finite 
element computational simulation software. Among them, the 
main arch ring of the strong skeleton and the outsourced 
concrete are simulated by beam unit, and the steel pipe 
concrete is simulated by joint section method, and the beam 
unit of the strong skeleton and the beam unit of the outsourced 
concrete are coupled with each other through the common 
unit section, and the whole model of the main arch ring of the 
strong skeleton contains 460 nodes and 1588 units, and the 
main arch ring of the strong skeleton is simulated by Midas 
Civil finite element calculation and simulation software. The 
grid division is shown. 

 

	
Figure 2.1 Finite element calculation model diagram of the 

main arch ring of the strong skeleton 



 

163 

The outer concrete was poured in sections and rings as shown below: 
	

	 	
Figure 2.2 Bottom slab pouring Figure 2.3 Web casting 

 
Eight working faces means that the outer concrete of the 

main arch ring is divided into 8 working faces, and each 
working face is divided into 3 small sections, with a total of 
24 working sections, and the pouring method is divided into 

ring section pouring and section direct pouring, and the 
pouring sequence is symmetrical pouring, as shown in Fig. 
2.4 below, and the construction program is shown in Table 4.3 
below. 

 

 
Figure 2.4. Division of eight working sections 

 

2.2. Selection of finite element support scheme 
The study will simulate the symmetrical pouring from 4 

working sections simultaneously, and select the optimal first 

pouring section by comparing the deflection and stability of 
the arch ring, listing 24 pouring schemes in the following 
Table 2.1, and deriving the optimal first pouring section by 
simulating multiple pouring schemes. 
 

Table 2.1 First pour program 
Program Casting section Program Casting section 

1 1-1、2-1、5-1 and 6-1 13 2-1、3-2、6-1 and 7-2 
2 1-2、2-2、5-2 and 6-2 14 2-1、3-3、6-1 and 7-3 
3 1-3、2-3、5-3 and 6-3 15 2-2、3-1、6-2 and 7-1 
4 1-1、3-1、5-1 and 7-1 16 2-2、3-3、6-2 and 7-2 
5 1-2、3-2、5-2 and 7-2 17 2-3、3-1、6-3 and 7-1 
6 1-3、3-3、5-3 and 7-3 18 2-3、3-2、6-3 and 7-2 
7 1-1、4-1、5-1 and 8-1 19 2-1、4-1、6-1 and 8-1 
8 1-2、4-2、5-2 and 8-2 20 2-2、4-2、6-2 and 8-2 
9 1-3、4-3、5-3 and 8-3 21 2-3、4-3、6-3 and 8-3 

10 2-1、3-1、6-1 and 7-1 22 3-1、4-1、7-1 and 8-1 
11 2-2、3-2、6-2 and 7-2 23 3-2、4-2、7-2 and 8-2 
12 2-3、3-3、6-3 and 7-3 24 3-3、4-3、7-3 and 8-3 

 

 

 



 

164 

 

3. Analysis of the First Pouring of 
Outsourced Concrete Working Face 

3.1. Stability analysis 
In order to study the different pouring sequences of the 

eight working faces, the first pouring section should be 
determined, and the first pouring section should be selected at 
the location where the structural stress is more uniform and 
has less influence on the overall stability, so as to avoid the 
structural instability due to the concentration of local stress, 
and to effectively control the position of the main arch ring 
line shape, so as to make sure that the line shape of the 
subsequent pouring section is in accordance with the design 
requirements. The construction progress should also be 

considered to ensure that the subsequent casting section can 
be carried out according to the plan to avoid the overall 
progress being affected by the delay in the construction of the 
first casting section. After determining the first pouring 
section, different pouring sequences for the 8 working faces 
are further studied, such as from the top of the arch to the foot 
of the arch, from the foot of the arch to the top of the arch, or 
alternating pouring, etc. The optimal pouring sequence is 
determined through numerical simulation to ensure that the 
line shape and stability of the main arch ring meets the design 
requirements. Table 3.1 below shows the first-order buckling 
modal coefficients for linear buckling analysis for each of the 
24 casting scenarios simulated separately, and Figure 3.1 
shows the first-order modal coefficients for each scenario for 
the first casting. 
 

Table 3.1 First-order flexural modal coefficients for each scenario of the first casting 
Program Buckling mode coefficient Program Buckling mode coefficient Program Buckling mode coefficient 

1 12.83 9 13.92 17 16.47 
2 13.98 10 18.07 18 9.34 
3 18.09 11 15.61 19 8.63 
4 22.51 12 11.54 20 10.31 
5 19.37 13 17.89 21 6.43 
6 15.25 14 13.12 22 7.00 
7 14.41 15 17.14 23 6.56 
8 13.41 16 9.87 24 6.20 

 

0 2 4 6 8 10 12 14 16 18 20 22 24
0

10

20

30

F
ir

st
 O

rd
er

 B
uc

kl
in

g 
M

od
es

First pour program 	
Figure 3.1. First-order flexural modal coefficients for each scenario of the first casting 

	
As can be seen from Table 3.1 and Figure 3.1, Option 4 has 

the highest value of 22.51, which is significantly higher than 
the other options, and therefore can be considered as the 
optimal solution for placing the exterior concrete. The 
corresponding pouring location of this scheme is 
“simultaneous pouring of 1-1, 3-1, 5-1 and 7-1 base slabs”. 
The first-order flexural modal coefficient is an important 
index for evaluating the ability of the structure to resist 
deformation under stress. The coefficient for Option 4 (22.51) 
is much higher than the average of 24.24, indicating that this 
pour sequence provides the best structural stability. The 
pouring locations “1-1, 3-1, 5-1 and 7-1” for option 4 can be 
found to show a balanced distribution of these locations. This 

distribution may have resulted in more uniform shrinkage 
stresses after the concrete was poured, reducing stress 
concentrations within the structure. The locations chosen for 
Option 4 may have created a more reasonable stress transfer 
path, which contributes to the uniform distribution and 
transfer of structural forces. In contrast, the first-order 
flexural modal coefficients of Option 19 (18.63), Option 22 
(17.00), Option 23 (14.56), and Option 24 (16.20) are lower, 
indicating that the structural stability of these pouring options 
is relatively poor, and all of them have a pouring section at 
the pouring location close to the vault. 

In summary, the first casting scheme is to cast 1-1, 3-1, 5-
1 and 7-1 bottom slabs at the same time, and Figures 3.2 and 



 

165 

3.3 show the first-order and second-order flexural modes of the main arch ring during the first casting, respectively. 
 

  

Figure 3.2. First-order flexural modes Figure 3.3. Second-order flexural modes 
 

3.2. Iinear analysis 
Through the Midas Civil software simulated the first time 

of outsourcing concrete bottom slab casting of 24 casting 
schemes, respectively, the foot of the arch, half-arch 1/8 
cross-section, half-arch 1/4 cross-section, half-arch 3/8 cross-
section, half-arch 1/2 cross-section, as well as the top of the 
arch cross-section of the deflection at the comparative 

analysis combined with the deflection value of the extreme 
value, the sum, the average value and distribution of the 
equilibrium, the comprehensive screening out of the optimal 
casting scheme. Fig. 3.4-Fig. 3.8 show the deflection 
distribution of 24 casting schemes at 1/8 cross-section, 1/4 
cross-section, 3/8 cross-section, 1/2 cross-section, and vault 
cross-section, respectively. 

	

0 5 10 15 20 25
0

5

10

15

20

25

30

35

40

45

T
or

si
on

（
m

m
）

Program 

Deflection Curve

 

0 5 10 15 20 25
0

10

20

30

40

50

60

70

80

T
or

si
on

（
m

m
)

Program

Deflection Curve

 
Figure 3.4 Deflection for scheme of 1/8 section Figure 3.5 Deflection for scheme of 1/4 section 

	

0 5 10 15 20 25

10

20

30

40

50

60

70

80

T
or

si
on

（
m

m
)

Program

 Deflection Curve

 

0 5 10 15 20 25

10

20

30

40

50

60

70

80

T
or

si
on

（
m

m
)

Program

Deflection Curve

 
Figure 3.6 Deflection for scheme of 3/8 section Figure 3.7 Deflection for scheme of 1/2 section 

	



 

166 

0 5 10 15 20 25

20

40

60

80

100

120

140

160

T
or

si
on

（
m

m
)

Program

 Deflection Curve

 
Figure 3.8 Deflection for scheme of the vault section 

 
 

The results of the deflection of the cross-section of each 
scheme of the first pouring from Fig. 3.4 to Fig. 3.8 show that 
Scheme 4 (simultaneous pouring of 1-1, 3-1, 5-1 and 7-1 
footings) has the most outstanding performance in terms of 
the overall deformation control and deflection equilibrium of 
each cross-section. The minimum deflection value is a key 
parameter to evaluate the stability of the structure, and the 
deflection of each section of scheme 4 is at a low level, 
including the deflection of the foot of the arch is 0 mm (no 
deformation due to the constraints), the 1/8 section is only 
2.32 mm, the 1/4 section is 6.97 mm, the 3/8 section is 21.08 
mm, the 1/2 section is 23.38 mm, and the top of the arch 
section is 22.13 mm. the maximum deflection occurs in the 
1/1/2 section (23.38 mm), and the maximum deflection occurs 
in the 1/1/1 section (23.38 mm). 2 section (23.38 mm), which 
is significantly lower than the extreme values of the other 
schemes (e.g., the deflection of the vault reaches 168.56 mm 
for scheme 23 and 155.76 mm for scheme 24). In addition, 
the deflection distribution of Scenario 4 shows a gentle 
transition, and there is no local mutation or peak, for example, 
the difference in deflection from 3/8 to the vault section is 
only 1.3 mm (21.08 mm to 22.13 mm), while the difference 
in the same interval of Scenario 23 is as high as 87.68 mm 
(68.8 mm to 155.76 mm), which indicates that the stress 
distribution of Scenario 4 is more uniform, and the structural 
stress caused by excessive local deflection can be effectively 
avoided. The risk of structural cracking due to excessive local 
deformation is effectively avoided. 

Comparing with other candidate solutions, although 
Solution 14 performs slightly better in the deflection of the 
vault (23.12 mm) and 1/2 section (18.89 mm), its deflection 
of 1/8 and 1/4 section (4.75 mm, 9.17 mm) is significantly 
higher than that of Solution 4 (2.32 mm, 6.97 mm), and the 
sum (78.36 mm) and the average value (15.67 mm) are higher. 
Balance is not enough. Although the deflection of 1/2 section 
(23.26 mm) of Scheme 16 is close to that of Scheme 4, the 
deflections of 1/8 and 1/4 sections (6.79 mm, 9.68 mm) are 
higher, and the sum reaches 80.83 mm, which further 
emphasizes the advantage of Scheme 4. In addition, some 
schemes such as schemes 23 and 24 have lower deflections in 
the early sections (e.g., 1/8 and 1/4), but the deflections at the 
vault increased abruptly to 155.76 mm and 168.56 mm, which 
indicates that there is a serious imbalance in the pouring 
sequence or load distribution, and it may lead to the instability 

of the structure. The deflection from the foot of arch to the top 
of arch increases gradually through the reasonable design of 
casting process, which is in line with the law of gradual 
increase of bending moment in the force characteristics of 
arch bridges, and thus improves the durability of the structure 
while guaranteeing the construction safety. 

4. Conclusion 
Based on the first pouring of concrete outside the eight 

working faces, the first-order flexural modal coefficient of 
Scheme 4 (simultaneous pouring of 1-1, 3-1, 5-1 and 7-1 
bottom slabs) reaches 22.51, which is the highest value of all 
the schemes, indicating that its ability to resist destabilization 
is significantly enhanced. In contrast, the flexural modal 
coefficient of Option 23 (4.56) and Option 24 (6.20) was only 
1/5~1/3 of that of Option 4 due to insufficient confinement of 
the casting section close to the vault, and there was a 
significant risk of instability. The deflections of Scheme 4 
(simultaneous casting of 1-1, 3-1, 5-1, and 7-1 base slabs) 
were at the lowest level in all critical sections: 1/8 section 
(2.32 mm), 1/4 section (6.97 mm), 3/8 section (21.08 mm), 
1/2 section (23.38 mm), and vault (22.13 mm), with 
maximum deflections 86% lower than those of the worst 
scheme (Scheme 24 vault 168.56 mm) by 86.9%. 

References 
[1] Bergmeister K, Capsoni A, Corradi L, et al. Lateral elastic 

stability of slender arches for bridges including deck 
slenderness[J]. Structural engineering international, 2009, 
19(2): 149-154. 

[2] Song F, Jia H. Numerical simulation of overall stability of 
concrete filled steel tube arch bridge[C]//2010 International 
Conference on Computer Application and System Modeling 
(ICCASM 2010). 

[3] Xie Shangying, Qian Dongsheng. Nonlinear Stability Analysis 
of Stiff Skeleton Concrete Arch Bridges during Construction 
Phase[J]. Journal of Civil Engineering, 2000, 33(01): 23-26. 

[4] Gu Anbang, Wang Rong, Liu Xiangjiang, et al. Stability study 
of large-span steel-tube-concrete rigid ribbed arch bridges[J]. 
Proceedings of the Chinese Highway Society 2001, 2001. 

[5] Wu Gangruo. Nonlinear analysis of mega-span arch bridges 
[D]. Xi'an:Chang'an University, 2006. 



 

167 

[6] YANG Bingcheng, WU Gangruo, LIU Jian. Nonlinear analysis 
of large-span steel-tube-concrete reinforced skeleton arch 
bridges[J]. Bridge Construction, 2006 (1): 5-7. 

[7] Chen Xiaobo. Analysis of forces and stability of large-span 
steel pipe concrete strong skeleton arch ribs during 
construction stage[J]. Chinese and foreign highways, 2015, 
35(01): 134-138.