Microsoft Word - CET--006.docx


 CHEMICAL ENGINEERING TRANSACTIONS  
 

VOL. 59, 2017 

A publication of 

 
The Italian Association 

of Chemical Engineering 
Online at www.aidic.it/cet 

Guest Editors: Zhuo Yang, Junjie Ba, Jing Pan 
Copyright © 2017, AIDIC Servizi S.r.l. 
ISBN 978-88-95608- 49-5; ISSN 2283-9216 

Effect of Residual Deformation and Reinforcement on Double 
Column Bridge in Mined-out Area 

Yuxiao Zhu, Dongquan Wang, Ping Sheng 

College of Mechanics and Civil Engineering, China University of Mining & Technology, Xuzhou 221116, China 
Yuxiao Zhu@qq.com 

The residual deformation poses tremendous challenges to the safety of the newly built buildings and bridges 
in coal mined-out areas. In this paper, the residual deformation is predicted at the very beginning, followed by 
the investigation of the damages on the bridge piles due to the deformation. Multiple retrofitting and 
strengthening schemes are then proposed, including linking the piles with straining beams and increasing the 
cross sectional area of the cap beam. After that the optimized scheme is determined through FEM simulation.  

1. Introduction 
After the mining of underground coal seam, the mined-out area is formed in the rock mass, and the stress 
balance state of the surrounding rock mass is destroyed. The rock mass above the mined-out area is caving, 
fracture and bending (Guo et al., 2004). The mining rock mass will be naturally compacted by its own weight 
and ground stress to achieve a new balance. The residual voids, segregation and cracks in the rock mass 
cannot be fully compacted (Zhu et al., 2012). Under the influence of external factors, the surface will continue 
to deform. The deformation at this stage is small, namely, residual deformation. The amount has been far 
beyond the piers and abutments settlement value the bridge code allows. The residual deformation of the 
mined-out area not only lasts for a long time (maybe even 50 years after mining), but also has more crypticity 
and abruptness (Xu, 2015), which brings great potential safety hazard to the surface structure. Zhu (2012) and 
(Guo et al., 2004; Guo et al., 2002) studied the mechanism of surface residual deformation, the stability of 
mined-out area ground and the deformation and damage law of buildings, but the researches on bridge are 
little. Based on the prediction of residual deformation, through theoretical analysis and numerical simulation, 
this paper studies the adverse effect of surface residual deformation on the bridge and the damage of the 
bridge substructure. The reinforcement and reconstruction scheme for substructure is proposed and the 
optimal scheme is obtained through the numerical simulation method to ensure the safety of the new bridge in 
the process of residual deformation (Yin and Yu, 2016). 

2. Prediction of residual deformation at bridge site 
2.1 Bridge overview 

   
(a)                  (b) 

Figure 1: (a) The contrast graph between highway bridge and mining areas and (b) Arrangement for bridge 
substructure 

                               
 
 

 

 
   

                                                 
DOI: 10.3303/CET1759169

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Please cite this article as: Yuxiao Zhu, Dongquan Wang, Ping Sheng, 2017, Effect of residual deformation and reinforcement on double 
column bridge in mined-out area, Chemical Engineering Transactions, 59, 1009-1014  DOI:10.3303/CET1759169   

1009



The relationship between highway bridge and mining areas is shown in Figure 1(a), and the arrangement for 
bridge substructure is shown in Figure 1(b). 

2.2 Analysis of residual deformation at bridge site 

73d22 working face is not fully exploited mining, and the subsidence coefficient is only 0.406. After longwall 
face mining, the overburden would form collapse zone, fracture zone and bending zone. At the end of a 
certain period of time, the fractured rock layer reaches a new relative equilibrium, and the surface movement 
tends to stop. However, the overburden will have residual voids, cracks, segregation and broken rock mass in 
the mined-out area. Over time, the strength of the fractured rock mass will gradually decrease. Under the 
action of natural forces and external forces or disturbances (such as earthquakes, mining activities, loads, 
etc.), the relatively balanced mined-out area will cause structural deformation and compaction, leading to the 
occurrence of residual settlement, that is, to produce activation subsidence. The results of physical simulation, 
numerical simulation and field measurement (Guo et al., 2002; Guo et al., 2008) show that when the depth 
ratio exceeds a certain value (> 30), the active surface subsidence of the mined-out area appears as a 
continuous gradient, and does not appear abrupt and non-continuous subsidence. According to the residual 
settlement and deformation of the surface, we can take some structural anti-deformation measures to 
buildings, which is to ensure the safety of the buildings. The mining deep ratio of 73d22 working face surface is 
89>30. The subsidence distribution in the mined-out area is big in the middle and small at the edge like a 
basin. After that the residual settlement is stable, there will be large residual deformation at the bridge site. It 
will inevitably have a negative impact on the bridge built on it, and even affect the safety of the bridge. 

2.3 Prediction of surface residual deformation 

The residual deformation and subsidence law at the bridge site is the key to the research. The probability 
integral method (Liu et al., 2016) derived from the theory of granular media mechanics is the most widely used 
mining subsidence prediction method. It is assumed that under all kinds of factors, all the possible residual 
settlement in the mined-out area occurs. After the end of the rock movement, the internal gap are fully filled 
and compacted, and the formed surface movement basin is the ideal limit subsidence distribution, namely, the 
ideal subsidence curve can be expressed by Eq. (1): 












+










= 1

2
x

r
erf

mq
xW

π'
)('

 (1)

 

where, W′(x) means ideal subsidence curve, x denotes the distance from the boundary of mined-out area, m is 
mining thickness, r is main effect radius, q’ is limit subsidence coefficient. 
Under actual conditions, after the new stress balance that the overburden rocks in the mined-out area reached 
through broken structures, moving and deforming, the broken-down masonry beams are still present in the 
overburden. Therefore, the actual subsidence curve can be expressed by Eq. (2): 

( )











+










−= 1

2
)( Sx

r
erf

qm
xW

π

 (2)

 

where, W(x) means actual subsidence curve, q is the subsidence coefficient of current subsidence basin 
(q<q′<1), S is the inflection point offset. 
The maximum residual subsidence curve that may occur above the mined-out area can be expressed bt EQ. 
(3): 

)()()( ' xWxWxWe −= ( )











+










−−












+










= 1

2
1

2
00 Sx

r
erf

W
x

r
erf

W ππ'

 (3)

 

where, = 	  is the maximum surface residual subsidence value after coal seam mining of α,W =	  the maximum subsidence value after relative stabilization of coal seam mining of α. 
According to the first derivative of Eq. (4), the surface residual tilt above the mined-out area is: 

2

2

2

2

00 r

Sx

r

x

e e
r

W
e

r

W
xi

)('

)(
−

−−
−==

ππ

 (4)
 

The level movement of surface residual is: 

1010



2

2

2

2

0
’
0

r

Sx

r

x

e ebWebWxU
)(

)(
−

−−
−==

ππ

 (5)
 

The calculation formula of residual level deformation and residual curvature can be obtained (Liu et al., 2016). ( ) can be used as the maximum estimate of the residual settlement in the mined-out area. The bridge 
construction in the mined-out area should ensure the long-term safety of the bridge structure. Therefore, the 
maximum predictive value should be taken as the basis to study the anti-deformation structure of the bridge.  

3. Influence of residual deformation at bridge site on bridge 
3.1 Relationship between surface deformation and deformation of bridge foundation 

According to the measured data of bridge deformation and surface deformation (Tan et al., 2007), the bridge 
deformation is linear with the surface deformation. The bridge subsidence is slightly larger than the surface 
subsidence, and the bridge slope is slightly larger than the surface tilt, the difference is not big, and the tilt of 
the bridge caused by uneven subsidence is the main reason for the destruction (Zhu and Jiang, 2014). 

3.2 Prediction result and analysis of surface residual deformation at bridge site 

According to the spatial position relationship between the bridge pier and the working face, the predicted 
cross-section is set at the bridge pier and platform position, that is, on both sides of the abutment north and 
south (denoted by N and B), center line (denoted by Z), a total of 7 expected cross-section. The expected 
point arrangement is shown in Figure 2. 

 

Figure 2: Sketch map of residual deformation in bridge substructure 

From Figure 3 (a), it is shown that the bridge has a great sinking from west to east. The maximum sinking 
value of 235mm is far beyond the requirements of the specification. The North Bridge is smaller than the 
South Bridge. The residual deformation causes the bridge uneven settlement in the east-west direction. The 
uneven settlement difference of North Bridge is 6~10mm, while that of South Bridge is 3~7mm, which allows 
the bridge to produce additional longitudinal, and the value is less than the standard value of 0.2% (Liu et al., 
2014). Figure 3 (b) shows that both the north and south bridges produce large horizontal displacements (“-“ 
sign indicates southward movement). The maximum value is at the No. 0 platform of North Bridge and its 
value is 87mm. Because of the simple structure of the bridge system, the uneven subsidence and horizontal 
movement does not produce additional internal forces within the structure (including substructure and 
superstructure). 

   

(a)              (b) 

Figure 3: (a) Residual subsidence curve of the piers and abutments (mm) and (b) Residual horizontal 
movement curve of the piers-abutments in north-south direction(mm) 

1011



4. Influence of residual deformation on bridge substructure 
4.1 Numerical model 

Use ANSYS finite element analysis software to establish the real bridge model to study the impact of residual 
deformation, model size 50×14×57(m). Concrete used C30. According to the measured elastic modulus 
E=2.4×104MPa, Poisson's ratio μ = 0.2; The shear transfer coefficient of concrete crack is 0.5, the shear 
transfer coefficient of closed crack is 1.0, the uniaxial tensile strength of concrete is 1.43MPa and the uniaxial 
compressive strength is 14.3MPa. Calculation model and mesh division is shown in Figure 4, the concrete unit 
used solid65 unit, reinforced role used dispersion model.  

 

Figure 4: The model and FEM mesh 

4.2 Analysis of calculation results 

The calculation results of four kinds of working conditions are analyzed (1) The substructure of the bridge is in 
good condition and normal work under condition 1 and condition 2 (2) Under condition 3, the concrete 
structure of the bridge is slightly damaged (3) Under condition 4, 80% of the pile body concrete is severely 
damaged, the upper and the outer pile body of the middle pile is slightly damaged, but it can no longer work. 
Table 1 lists the maximum compressive stress and maximum tensile stress of the structure situation under 
conditions 1 and 4.  

Table 1: Comparison of the initial stress due to residual deformation 

Maximum stress 
(MPa) 

Cap beam Piers Pile foundation 
1 4 1 4 1 4 

Maximum compressive stress 
Value 0.86 0.865 1.11 1.99 1.08 1.63 
Increasing amount 0.58% 79.28% 50.93% 

Maximum tensile stress 
Value 1.14 1.30 0.11 0.70 0.952 2.54 
Increasing amount 14.04% 536.36% 166.81% 

5. Reinforcement scheme analysis for substructure of bridge 
5.1 Structural reinforcement scheme 

Setting up cross-beam between the two columns can effectively improve the overall structure and reduce the 
impact of uneven settlement (Liu et al., 2014). According to the force condition of substructure under the 
impact of residual deformation, we proposed the reinforcement measures of adding cross-beam between the 
piers and increasing the cross-section including four programs (see Table 2). Scheme A adds a transverse 
beam at the position 0.6H (H is the height of the pier) at the bottom of the pier column, and scheme B adds 
the cross-beam at the position 0.3H and 0.8H from the bottom of the pier column respectively. The beam 
cross-section of the scheme C and D is the same as the scheme A and B, but the cross-sectional dimension 
of the cap beam and the cross-beam is appropriately increased in consideration of the non-uniform 
subsidence requirements. 

Table 2: Reinforcement plans for Substructure 

Scheme 
Cross-beam Cap beam 

b×h(m) Number Cross-section b×h(m) 
A 1  1.2×1.2 1.7×1.5 
B 2  1.2×1.2 1.7×1.5 
C 1  1.2×2.0 2.0×2.0 
D 2  1.2×2.0 2.0×2.0 

1012



5.2 Calculation result and analysis of reinforcement 

5.2.1 Influence of cross - beam installation on internal force of substructure 
Comparing the reinforcement schemes, A and B in Table 3, it can be seen that a transverse beam is added 
between the piles, which greatly improves the stress state of the structure and reduces the additional internal 
forces under the influence of the residual inclination of the pile foundation and piers, especially moment and 
additional shear force, in which the reduction range of pile foundation is 20~30%, and the reduction range of 
piers is 15~20%. The additional bending moment and the additional shear force of the upper and lower 
crossbeams are greatly improved, and the bending moment is the most obvious. And the number of the 
additional beam has little effect on the maximum bending moment and the maximum shear force of the cap 
beam. Similarly, the similar results can be obtained by comparing the internal forces of the structures under C 
and D with residual tilting deformation. It can be seen that the strengthening scheme of the double-tie beam 
makes the force of the substructure reasonable. Correspondingly, after the addition of a cross-beam, the pillar 
of the axial force has increased with the change rate of about 10%. 

Table 3: Comparison of the internal forces between scheme A and scheme B 

Structure name 
Torque (kN˙m) Force (kN) 
Scheme A Scheme B Variation (%) Scheme A Scheme B Variation (%)

Pile foundation 

Inside the pile 
-992.1 -764.9 22.90 

428.4 320.7 25.14  
991.1 678.8 31.51  

In the pile 
-678.1 -520.7 23.21  

407.1 323.7 20.49  
999.6 707.6 29.21  

Lateral pile 
-997.7 -802.1 19.61 

388.0 283.1 27.04  
1061.4 744.0 29.90  

Piers 
Medial column -665.2 -548.3 17.57 312.3 257.6 17.52  
In the column -1311.5 -1097.6 16.31  49.8 39.2 21.29  
Lateral column -747.3 -636.9 14.77  435.3 347.5 20.17  

Straining beam 
Up beam 

-612.3 -345.1 43.64 267.2 197.9 25.94  
474.4 262.2 44.73  79.6 66.1 16.96 

Down beam 
 -329.4 46.20   212.0 20.66 
 387.1 18.40   51.2 35.68 

Cap beam 
-1324.0 -1253.2 5.35  1824.6 1824.6 0  
1291.8 1286.7 0.39  -1824.6 -1824.6 0 

 
5.2.2 Influence of increasing cross section on internal force of substructure 

Table 4: Comparison of the internal forces about the sectional dimension of cap beam and straining beam 

Structure name 
Torque (kN˙m) Force (kN) 
Scheme D Scheme B Variation (%) Scheme D Scheme B Variation (%)

Pile foundation 

Inside the pile 
-786.0 -764.9 2.68 

320.7 320.7 0  
679.0 678.7 0.04 

In the pile 
-533.6 -520.7 2.42 

324.0 323.7 0.09 
707.6 707.6 0 

Lateral pile 
-825.2 -802.1 2.79 

283.0 283.1 -0.04  
744.1 744.0 0.01 

Piers 
Medial column -574.0 -548.3 4.48 282.0 257.6 8.65 
In the column -1200.0 -1097.6 8.53 -659.0 -623.1 5.45 
Lateral column -671.0 -636.9 5.08 377.0 365.5 3.05 

Straining beam 
Up beam -402.3 -345.1 14.23 186.3 126.1 32.31 
Down beam -395.1 -329.4 16.63 323.1 242 25.10 

Cap beam 1480.0 1286.7 13.06 1879.3 1824.6 2.91 
 
Table 4 shows that the internal forces of the substructure will change after the enlarged cross and beam: (1) 
the internal force extremum increment of the pile is less than 3%, which is not affected; (2) Column internal 
force value increased obviously with bending moment of 6% and shear force of 5.7%; (3) The bending 
moment of transverse beam increased by 15.4% and the shear force increased by 28.7% on average; (4) The 
bending moment of the cap beam increased by 13.1%, and the shear force increased 2.9%. Similarly, a 
comparison of the internal forces of schemes C and A yields similar results. It can be seen that the 

1013



reinforcement scheme with the enlarged section will increase the internal force of the substructure with varying 
degrees. 

6. Conclusions 
(1) Under the action or perturbation of natural force and external force, the mined-out area in the relatively 
balance will produce structural deformation and compaction, resulting in the surface residual deformation. The 
bridge deformation is similar to surface deformation, appearing residual settlement, residual inclination, and 
residual horizontal movement and so on, and the bridge structure will be destroyed.  
(2) Residual tilting deformation will cause great additional internal forces on the substructure of the bridge, 
resulting in the destruction of the substructure (especially the pile foundation and pier columns). The 
reinforcement measures should be taken to the influence of the residual deformation on the substructure of 
the bridge. 
(3) The addition of transverse beams between piles can greatly reduce the internal force extremes of pile 
foundation, pier column and transverse beam, and it can also reduce the additional stress the adverse 
influence of residual tilting deformation on the substructure. Section reinforcement schemes C and D, and 
reinforcement schemes A and B can all meet the requirements of residual deformation of the ground surface, 
but the internal force of the substructure will increase to some extent when the section is enlarged. Therefore, 
reinforcement scheme B is a preferable scheme. 
(4) The length of the pile body should be reinforced according to the internal force of the pile to strengthen the 
bending reinforcement at the bottom and the top of the pile body. At the same time, it is suggested to 
strengthen the reinforcement check of the pier column, the cross beam and the cap beam according to the 
increment of internal force value of the residual tilting deformation, so as to ensure that the subpart of the 
bridge has sufficient resistance to deformation. 

Reference  

Guo G., Deng K., Tan Z., 2002, Study on the prediction method of ground residual subsidence in the deep 
abandoned longwall goaf and its application, Journal of Liaoning Technical University (Natural Science), 
21(1), 1-3. 

Guo G., Duan R., Du D., 2008, Discussion on the influence of residual surface movement and deformation on 
buildings in Goaf, Coal Engineering, 5, 72-74, DOI: 10.3969/j.issn.1671-0959.2008.05.029 

Guo G., Zhang G., Liu B., 2004, Critical disturbance depth and its influence of ground load on the 
underground mined out area, Ground Pressure and Strata Control, 1, 72-74, DOI: 10.3969/j.issn.1673-
3363.2004.01.030. 

Lan F., Wang K., 2011, Influence of collar beam of double column high-rise pile bridge with shortspan on 
seismic performance, Journal of Highway and Transportation Research and Development, 5, 92-97. 

Liu C., Sun Z., Shi K., 2016, Mixed H2/H∞ Control Approach and Its application in Satellite Attitude Control 
System, International Journal of Engineering Research in Africa, 25, 89-97, DOI: 
10.4028/www.scientific.net/JERA.25.89. 

Liu C., Wang F., Shi K., Wang X., Sun Z., 2014, Robust H∞ control for satellite attitude control system with 
uncertainties and additive perturbation, International Journal of Science, 1(2), 1-9. 

Liu L., Ma J., 2014, Research on the reasonable arrangement mode of the double column frame bridge piers, 
Journal of China & Foreign Highway, 34(4), 153-157. 

State Coal Industry Administration. Buildings, water bodies, railways and the main roadway pillars set and coal 
mining regulations, Beijing, China Coal Industry Publishing House, 2004. 

Tan Z., Yang H., Deng K., 2007, Field measurement on movement and deformation rule of mining induced 
railway bridge, Journal of Mining ＆ Safety Engineering, 24(2), 243-247. 

Xu P., Mao X., Zhang M., 2015, Deformation mechanism and detection analysis for mining residual cavities 
under buildings additional stress, Journal of Henan Polytechnic University (Natural Science), 34, 1, 25-29. 

Yin C.B., Yu F., 2016, Study on fatigue performance of concrete highway bridge under corrosive environment, 
Chemical Engineering Transactions, 55, 373-378, DOI: 10.3303/CET1655063. 

Zhu Q., Jiang J., 2014, Influence of mining subsidence on bridge-buildings. Science of Surveying and 
Mapping, 39(4), 88-91. 

Zhu G., Jie C., Dou M., 2012, Effect of old mined-out areas and surface residual deformation on buildings, 
Journal of Shenyang University (Natural Science), 24(3), 70-74. 

1014