Citation: Zhang, Y.; Li, R.; Chen, J.
The Cooperative Control of Subgrade
Stiffness on Symmetrical
Bridge–Subgrade Transition Section.
Symmetry 2022, 14, 950. https://
doi.org/10.3390/sym14050950
Academic Editors: Victor A.
Eremeyev and Sergei D. Odintsov
Received: 17 March 2022
Accepted: 26 April 2022
Published: 6 May 2022
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Article
The Cooperative Control of Subgrade Stiffness on Symmetrical
Bridge–Subgrade Transition Section
Yang Zhang
1
, Rui Li
2,
* and Jun Chen
3
1
Jinhua Highway and Transportation Management Center, Jinhua 321000, China; zhangyangzj@outlook.com
2
Highway School, Chang’an University, Xi’an 710064, China
3
Jinhua Wucheng District Highway and Transportation Management Center, Jinhua 321000, China;
chenjunzj@outlook.com
* Correspondence: lirui@chd.edu.cn
Abstract:
In the field of civil engineering and architecture, the concept of symmetry has been widely
accepted. The bridge can be treated as a typical symmetrical structure of civil engineering buildings.
Among them, the Subgrade can be identified as an important part to bear the vehicle loads. Severe
pavement problems and bridge service capabilities will be caused by problems of the bridge–subgrade
transition section. Therefore, setting the rigid–flexible transition is an important method to solve this
problem. The bridge–subgrade transition section has been set at both ends of the bridge, which can be
regarded as a typical symmetrical structure. Based on nonlinear finite element numerical simulation
and synergistic theory, the cooperative control problems of the bridge–subgrade transition section
were studied in this work. The change rule of the stiffness of the transition section was discussed and
the influence of stiffness variation of the bridge–subgrade transition section on the stress state of the
structure was also analyzed. Furthermore, the influence of subgrade stiffness change on the stress
and strain field was analyzed. A permanent strain prediction model was established and stiffness or
subsidence difference coordination control was also discussed.
Keywords:
bridge–subgrade transition section; rigidity–flexibility transition; permanent deformation;
stiffness difference; settlement difference
1. Introduction
The bridge–subgrade transition section is the connection between bridge and pave-
ment. The transition section is set at the bridge head and tail, so it can be regarded as a
typical symmetrical structure. This section can balance the stiffness difference and settle-
ment difference of the two structures and increase the pavement’s integral continuity. Due
to the lack of processing bridge–subgrade transition sections during the engineering design
process, construction control is not effective, and the problems of operation or maintenance
technology are unreasonable. It will lead to the following two kinds of problems in tran-
sition section, widely. First, the pavement structure of the transition section produces a
settlement or fracture in retailing backwall. Second, the vehicles have obvious bumps when
they pass the transition section, which is the so-called “bump at bridge-head”. Because the
bridge–subgrade transition section is set symmetrically, the “bump at bridge-head” occurs
when the driver drives into and out of the bridge.
Wahls thought the step height of 1.2 cm would produce the bump effect [
1
].
Strak et al.
found the step height of 2.5 cm would produce the bump effect [
2
,
3
]. This problem
would bring many undesirable results such as affecting driving comfort, forcing vehicle
deceleration, influencing pavement service performance and transportation efficiency,
affecting service life of the vehicle, and leading to traffic accidents [
4
]. The problems of
the bridge–subgrade transition section have become one of the important factors that
affect pavement service ability seriously. Therefore, it is necessary to put forward a more
reasonable design method to solve the problem of the bridge–subgrade transition section.
Symmetry 2022, 14, 950. https://doi.org/10.3390/sym14050950 https://www.mdpi.com/journal/symmetry
