Support position optimization with safety factor in the demolition and rebuilding of a bridge using the SPMT method: A case study

Abstract

The accelerated bridge construction (ABC) method has become increasingly popular in recent decades because it creates few traffic disruptions, minimal environmental impacts, and lower cycle costs. The self-propelled modular transporter (SPMT) is an ABC method. In the SPMT method, the support position is a key factor during transportation because the support position changes the boundary conditions and consequently changes the stress distribution of the original bridge. Unreasonable stress distribution may cause a collapse of the demolished bridge and permanent damage to the new built bridge during the transportation process. In the present study, an overpass bridge is demolished and replaced due to the expansion of an expressway. The SPMT method is adopted for rapid demolition and construction because it can greatly reduce traffic interruptions and costs. An optimization strategy of SPMT support positions is proposed by introducing a safety factor. The influence of the support positions of the SPMT on the internal force, stress, deflection, and resistance to overturning of both the demolished and new built bridges during the transport process is considered in the safety factor. Finally, an overpass bridge is taken as a case study. The optimal support positions of both demolished and new built bridges are obtained, and the demolition and rebuilding of the bridge are successfully completed using the SPMT method.

Keywords

accelerated bridge construction method optimal support position SPMT transport bridge rebuilding

Introduction

Many old bridges in different countries have stood for decades and are approaching their useful service life. These old bridges need maintenance or rebuilding. According to a recent report, nearly 40% of American bridges are over 50 years old, and 9.1% of them have structural defects. At the end of 2018, China had approximately 833,000 highway bridges. Most of those built in the 1980s and 1990s have different levels of wear and need to be repaired, reinforced, or rebuilt. Moreover, with rapid economic development, highway networks are becoming denser, the demand for bridge expansion is increasing, and an increasing number of old bridges need to be rebuilt.

The rebuilding or replacement of old bridges has become a topic of interest in bridge engineering. The traditional replacement methods include blasting, mechanical chiseling, and cutting and hoisting. Most of these methods cause severe traffic congestion, long-term closures, high safety risks, and considerable social impacts. Russell et al. (2005) identified 10 technologies, including SPMT moving technology, that can minimize traffic disruption, lower environmental impacts, increase quality, and lower cycle costs. Culmo (2011) published an ABC manual at the sponsorship of the Federal Highway Administration. There are three main types of ABC methods: prefabricated bridge elements and systems (PBES), slide-in bridge construction (SIBC), and SPMTs (Attanayake and Aktan, 2018). ABC can reduce construction duration and decrease the environmental and socioeconomic impacts of repair and upgrade activities by minimizing traffic disruptions (Salem, 2018). Since then, the ABC method has become popular and has developed rapidly to reduce the effects on traffic (Nader, 2020).

The SPMT method has been widely used in the rebuilding of old bridges because it is cost effective and only interrupts traffic for a short time. Many researchers and engineers have reported on applications of the SPMT method in bridge construction. Ardani et al. (2010) documented the removal and replacement of the 4500 South Bridge by a SPMT in Salt Lake City during a weekend and confirmed that a SPMT can greatly shorten the construction time, reduce traffic impacts, and save on engineering costs. Rosvall et al. (2010) investigated the construction stresses caused by lifting and moving highway bridges during the movement of SPMTs. Pierce and Kirtan (2015) analyzed the I-84 bridge stress from differing support conditions at different construction stages and the worst-case scenario of a local loss of support during bridge movement by a SPMT. Yan et al. (2018) investigated the optimal transverse position for overweight trucks to cross simply supported multiple-girder bridges. Attanayake and Aktan (2018) developed a multicriteria decision-support model to identify the most preferable construction methods for selected sites. Dorafshan et al. (2019) studied the dynamic effects of SPMT movements on bridges during simulated bridge transport. Lavrikov et al. (2019) introduced the basic principles of operating a loosely coupled SPMT using modern information technologies. Zhu et al. (2020) proposed a simulation-based optimization method to lower the time cost and prevent loading failures. Partovi and Fanaie (2020) studied the effects of the distance from the support on the deflection of the mid-span in both simply supported and fixed supported girder bridges and obtained the appropriate distance from the support causing the minimum deflection. Previous research results have shown that the support position is a key factor during the transportation of the SPMT because the support position changes the stress distribution of the bridge. Unreasonable stress distribution may cause severe results, such as a collapse of the old bridge and permanent damage to the new bridge during the transportation process.

In the present study, a bridge is rebuilt using the SPMT method. An optimization strategy of the support positions during SPMT transportation is proposed. The internal force, stress and deflection of both demolished and new built bridges are calculated by the finite element method when they are supported at different positions. Finally, the optimal support positions of both demolished and new built bridges are obtained through parametric analyses. The original bridge was successfully demolished and rebuilt using the SPMT method according to the optimization results.

Background of the engineering project

Introduction of the demolished and new built bridges

The demolished bridge crosses the Kaiyang expressway. The Kaiyang expressway is a section of the G15 Shen-hai expressway of the national highway network of China and carries heavy traffic loads, with an average daily traffic volume of 92,000 vehicles.

The demolished bridge is a three-span prestressed box girder (24 m + 34.4 m + 24 m) with a variable cross-section. It was built in 2003 according to the bound volume of Specifications for Design of Highway Bridges and Culverts and Technical Specifications for Construction of Highway Bridges and Culverts (JTJ041-2000). The design loads are steam-20 and hang-100, as shown in Figure 1. The bridge width is 8 m, the height of the cross-section at the mid-span is 1 m, and the bridge height is 2 m at the supports, as shown in Figure 2. The concrete grade of the box girder is C40, and the diameter of the steel strands is Φ 15.24 mm. The self-weight of the entire demolished bridge is calculated as 1500 t, and the removed part is approximately 632 t. The 1# pier is double column piers with a diameter of 120 cm and a height of 880 cm. The hollow thin wall piers 2# and 3# are 80 cm wide, 600 cm long, and 860 cm high. The length of abutment 4# is 780 cm. The concrete of the piers and abutment are grade of C30 and C15, respectively. The pier foundations are friction piles.

Figure 1.

Schematic diagram of design loads (unit: KN m).

Figure 2.

Schematic diagram of the original bridge: (a) span of the original bridge and (b) section of the original bridge (unit: cm).

As the Kaiyang expressway cannot meet the increasing traffic demand, the overpass bridge had to be demolished and rebuilt because the bridge piers of the overpass are located on the widened roadbed. The width of the rebuilt bridge enlarges from 8 m to 12 m to meet the requirement of the increasing traffic volume. The new built bridge is a two-span simply supported steel-concrete composite beam with a span of 30 m, as shown in Figure 3. The width and height of the new built bridge are 12 m and 2 m, respectively. The new built bridge is an equal-height combined double-box beam. The steel structure is 1.62 m in height, the thickness of the bottom plate $(t_{b})$ varies from 20 mm to 24 mm, and the thickness of the web $(t_{f})$ is 12 mm or 14 mm, using Q345qC steel. The steel main beams are fabricated in sections at the factory and assembled on site. The deck of the bridge is cast-in-place reinforced concrete with a grade of C50. The thickness of the bridge deck varies along the bridge and ranges from 0.25 m to 0.38 m. The full bridge weighs approximately 377 t. The bridge adopts column piers and cast-in-situ concrete piles.

Figure 3.

Schematic diagram of the new built bridge: (a) span of the new built bridge and (b) section of the new built bridge (unit: cm).

The design load of the new built bridge is highway-I, and the service life is 100 years. The new built bridge was designed according to General Specifications for Design of Highway Bridges and Culverts (JTGD60-2015), Specifications for Design and Construction of Highway Steel-concrete Composite Bridge (JTG/TD64-01-2015), and Specifications for Design of Highway Steel Bridge (JTGD64-2015).

In this special site, the traditional replacement method is not available because it requires closing the expressway for a long time, resulting in traffic congestion. The ABC method is a better choice because it only interrupts traffic for a short time. In addition, there was a suitable construction site for storing the demolished and new built bridges and an easy pathway for transportation. Finally, the SPMT method was adopted to demolish and rebuild the bridge after comprehensive consideration.

SPMT parameters

A SPMT is a self-propelled modular transport machine. It is capable of independent steering and height adjustment with various steering modes (FHA, 2007). A SPMT consists of a power pack unit (PPU), modules, a remote control, and other accessories, as shown in Figure 4.

Figure 4.

Photo of SPMT.

In the present project, SPMT modules with 4 axles and 6 axles are utilized to finish the transportation tasks. Their rated loads are 144 t and 216 t, respectively. The 4-axle SPMT module is 2.43 m wide and 5.6 m long, and the 6-axle SPMT module is 2.43 m wide and 8.4 m long. The design speed of the SPMT modules used in this project is 0.5 km/h, and the steering angle is 230°. The loading platform is 1500 mm in height, and the vertical lifting range can be adjusted up and down 350 mm.

Support optimization strategy

The demolished bridge was first cut into several parts with a diamond rope saw, and then transported to the beam storage site by the SPMT, and finally deconstructed on site. The rest of the original bridge was mechanically chipped away at the site and moved away. The key step for the demolition of the bridge was transportation. Support and transportation are the cores of the SPMT construction method.

During the transportation process, the cut beam is supported by the SPMT modular transporter and the bracket. The cut beam and support equipment form a new structural system, which is a simply supported beam with a cantilever on both sides. The support positions affect the span and internal force distribution of the new structural system. Therefore, it is necessary to find the optimal support position to ensure transportation safety and structural safety.

After the demolished bridge was removed, new built bridge construction began. The new built bridge is a simply supported bridge. It is first assembled and poured on the beam storage site, then transported to the bridge site, and finally built on site. The transportation of the new built bridge is also a key construction factor because if the support position is not reasonable, the internal forces generated during transportation may cause damage to the new built bridge. The support position should be optimized by considering the safety, economy, reasonable stress and other factors.

To qualitatively evaluate the influence of space, internal force, stress, deflection and overturning moment on the structural safety, a safety factor, k, is proposed as follows

k = k_{s p a c e} \times k_{c} \times k_{o} \times k_{s} \times k_{d}

(1)

where

k_{c}

is load capacity coefficient,

k_{o}

represents anti-overturning coefficient,

k_{s}

is stress coefficient,

k_{d}

represents deflection coefficient, and

k_{s p a c e}

is the allowable space safety factor

k_{c} = {\frac{\min (M_{\max} - M, M - M_{\min})}{0.5 (M_{\max} - M_{\min})} | (M < R); 0 | (M \geq R)

(2)

where M is the internal force of bending moment, R represents the bending resistance,

M_{\min}

and

M_{\max}

, are the minimal and maximal allowable bending moment. When the bending moment of the beam is greater than the resistance (M ≥ R)

k_{c}

is equal to 0, representing that the structure is unsafe. When M < R,

k_{c} \in (0,1)

, and higher

k_{c}

is better, representing that the structure is safer.

k_{c} = 1

means that M is located at the middle of the resistance range

k_{o} = \frac{M_{o}}{M_{m o}}

(3)

where

M_{o}

and

M_{m o}

are the anti-overturning moment and the maximum anti-overturning moment. The anti-overturning coefficient

k_{o} \in (0,1]

k_{o} = 0

means that the anti-overturning moment is very small and the structure is unstable, and larger

k_{o}

represents that the structure is more stable during the transportation

k_{s} = {\begin{matrix} 1, σ_{\max} < f_{d} \\ 0, σ_{\max} \geq f_{d} \end{matrix}

(4)

where

σ_{max}

is the maximal stress of the bridge and

f_{d}

is the design value of beam stress. When the maximum tensile and compressive stresses of concrete and steel are less than the design values

(σ_{\max} < f_{d})

k_{s}

is equal to 1, representing that the structure is safe. When

σ_{\max} \geq f_{d}

k_{s}

is equal to 0

k_{d} = {\begin{matrix} \frac{D - D_{\max}}{D_{\min} - D_{\max}}, D < D_{\lim i t} \\ 0, D \geq D_{\lim i t} \end{matrix}, D_{\lim i t} = \frac{l_{1}}{300} o r \frac{l_{2}}{500}

(5)

where

l_{1}

is the cantilever length,

l_{2}

is the mid-span length,

\frac{l_{1}}{300}

is deflection limit at the end of cantilever beam, and

\frac{l_{2}}{500}

is the deflection limit at the mid-span of simple supported bridge. When the deflection of bridge is greater than the deflection limit

(D \geq D_{l i m i t})

k_{d}

is equal to 0, it means that the structure is unsafe. When

D < D_{l i m i t}

k_{d} \in (0,1]

, and larger

k_{d}

is better.

The optimization process of the support position of bridge transported by SPMT is summarized in Figure 5. Firstly, the supporting range of SPMT is determined according to the space size of the structure, and $k_{s p a c e}$ is obtained. Then, the bearing capacity safety factor $k_{c}$ , the stress safety factor $k_{s}$ , and the deflection safety factor $k_{d}$ are calculated according to the FEM simulation under different support conditions. The anti-overturning ability $k_{o}$ of the beam can be simultaneously calculated. Finally, the safety factor k is calculated under different support conditions, and the optimal support position of SPMT is obtained at the place of maximum safety factor.

Figure 5.

Support position optimization strategy.

Support optimization for the demolished bridge

For the demolished bridge, the stress and deflection are not considered, and the factors $k_{s}$ and $k_{d}$ are ignored in equation (1).

Available space for support points

For a beam with a variable section, the section load and the structural resistance vary along the bridge axis. The support position will change the distribution of the structural internal force. At the same time, the support point of the modular transporter is limited by its volume and the allowable space under the bridge. Therefore, it is necessary to find an optimal support position for modular transporters, considering both structural safety and allowable space.

According to the construction documents of the demolished bridge, the plane and elevation of the demolished bridge are cut in a V-shape to transport more easily, as shown in Figure 6. The weight of the cut beam is approximately 632 t. Four 6-axle modular transporters are used to transport the cut beam with a load capacity of 216×4=864 t. The top width of the demolished bridge is 8 m, the bottom width is 6 m, and the length of the 6-axle modular transporter is 8.4 m. Therefore, the 4 modular transporters are separated into two pairs and connected in parallel to move the cut beam. The width of each pair of modular transporters is 5.33 m after being connected together.

Figure 6.

Schematic diagram of support (unit: cm).

Figure 6 indicates that the modular transporters are symmetrically located against the mid-span section. The pavement width of the expressway under the bridge is 28.0 m, and the total length of the cut beam is l = 36.90 m. The horizontal distance from the inner side support point of the modular car to the mid-span is defined as x, which represents the support position.

When the modular transporters move, one should at least ensure that the external wheels are located on the road surface and the two supports should not collide. Therefore, the longest distance is calculated as $x_{\max} = W - B - T / 2$ and the shortest distance is calculated as $x_{\min} = C - T / 2$ , where W is the width of the road, B is the spacing between the inner and outer wheels of the SPMT, T is the spacing between the two support points, and C is the width of the support. $x_{\max}$ and $x_{\min}$ are calculated as 9.835 and 2.25 m, respectively. Therefore, a space size factor was defined as follows

k_{s p a c e} = {\begin{cases} 1,2.25 m < x < 9.835 m \\ 0, x \geq 9.835 m \cup x \leq 2.25 m \end{cases}

(6)

when

k_{s p a c e} = 1

, it means that the supports are within the allowable range.

As SPMTs need to work together during transportation, a smaller x should be a better choice. However, when the distance x is small, the cantilevers of the cut beam become longer, which affects the stability of the beam during transportation. To find the best support position, nine support cases are calculated when the distance x varies from 1 to 9 m with an interval of 1 m.

Structural safety

Using the above information, a finite element model was established in the commercial software MIDAS Civil to calculate the internal force of the demolished bridge, as shown in Figure 7. The demolished bridge is separated into 46 BEAM elements in the FEM model and the maximum length of elements is 1 m. The boundary conditions representing the support of the SPMTs are simulated by hinge joints.

Figure 7.

FEM model of the demolished bridge.

As the cutting inclination has little effect on the internal force and structural resistance of the cut beam, it is ignored in the model to simplify the calculation. As the prestressed steel is cut off with the demolished bridge, the equivalent prestress loss of prestressed steel at the end of the beam should be considered in the model (Zhou et al., 2019). The prestress at the beam end is equal to 0. Due to the friction effect between the steel bundle and the concrete, the prestress gradually increases and reaches the original prestress after an anchoring length. The prestress at the middle span is treated as the post-tensioning prestress. At both ends of the beam, the prestress distribution is similar to that of pre-tensioning. The anchoring length is calculated as $l_{t r} = 67 \times d \times \frac{σ_{p e}}{1000} (m m)$ , in which $σ_{p e}$ is the effective prestress value of the prestressed steel and d is the diameter of the reinforcement. $l_{t r}$ is calculated according to the actual prestress at the cutting place of the steel bundle. Finally, the prestress is applied at the section $0.25 l_{t r}$ away from the beam ends and gradually increases from 0 to the original prestress at the section of $l_{t r}$ . To simplify the FEM model, the actual change in the prestress is simulated by the length variation of prestressed steel, as shown in Figure 8(a). The actual end prestress of all bundles is set as the control tensioning stress, and prestress is applied by the post-tensioning method. The beam is supported by an I-shaped steel beam on the bracket. Therefore, the beam has four strips of support. In the software, vertical support is used to simulate the striped support, as shown in Figure 8(a). The boundary conditions of the cut beam and prestressed steel bundle arrangement are shown in Figure 8(b). The steel bundle information is shown in Table 1.

Figure 8.

Boundary conditions of support points and prestressed steel bundle arrangement: (a) Simulated prestressing and support and (b) prestressed steel bundle layout (unit: cm).

Table 1.

Steel bundle information sheet.

Serial number		Specification	Tension controls stress (MPa)	Length (m)	Location
A1-A3	Strand-1860	$Φ 15.24 - 19$	986.52-986.2	36.93	Web
B1-B3	Strand-1860	$Φ 15.24 - 19$	997.93-997.6	36.90	Web
C1-C4	Strand-1860	$Φ 15.24 - 5$	1095.52-1022.96	7.25	Roof
D1-D4	Strand-1860	$Φ 15.24 - 5$	1110.63-1046.82	9.25	Roof
F1-F4	Strand-1860	$Φ 15.24 - 5$	1023.47-1095.91	7.25	Roof
G1-G4	Strand-1860	$Φ 15.24 - 5$	1047.22-1111.01	9.25	Roof

Figure 9 shows the calculated internal force and structural resistance (Li et al. 2020) of the cut beam when the support position varies from 1 m to 9 m. The results show that the internal force extremum increases when the support distance x decreases. When the support distance x is less than 5 m, the cut beam cannot bear the internal force because the cantilever is too long and the internal force at the support section is too large. When the support distance x is greater than 5 m, the internal force of the demolished bridge is lower than its structural resistance. Consequently, the allowable distance x is in the range of 6 m to 9 m.

Figure 9.

Comparison of internal force and structural resistance.

Resistance to overturning

When the cut beam is transported by the SPMT, the cutting section of the demolished bridge is treated as a simply supported cantilever structure, as shown in Figure 6. The lower bracket of the beam body is a temporary structure. During the moving process, the beam body is prone to disturbance due to uneven ground and starting, braking or steering factors, so there is a risk of overturning during transportation, and its overturning possibility varies with different support positions.

It is generally accepted that when the bearing force of the supports reduces to a critical value, the bridge system reaches a critical state of overturning. There are 4 supports in the SPMT module according to the real situation, as shown in Figure 7. A bending moment is applied on the bridge, and the bearing force of the supports is calculated using the FEM. The critical overturning moment of the beam is calculated when the bearing forces of the left supports decrease by 50%. Figure 10 shows the calculated critical overturning moment of the cut beam when the distance x varies from 1 m to 9 m.

Figure 10.

Critical overturning bending moment of the beam.

The result shows that the critical overturning moment of the beam gradually increases with increasing x, which means that the cut beam is more stable when x is larger. To ensure the stability of the beam in the process of transport, a larger x is better.

Optimization

The safety factor k of the demolished bridge is calculated when the distance x varies from 1 m to 9 m, and the results are shown in Figure 11 and Table 2. According to the load capacity coefficient, the allowable location ranges 5 m to 9 m. In addition, the maximum safety factor is obtained when x = 9 m.

Figure 11.

Safety factor under different support locations.

Table 2.

Safety factor of demolished bridge.

x (m)	1	2	3	4	5	6	7	8	9
$k_{s p a c e}$	0.00	0.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00
$k_{c}$	0.00	0.00	0.00	0.00	0.01	0.30	0.85	0.44	0.91
$k_{o}$	0.60	0.73	0.82	0.89	0.93	0.95	0.97	0.99	1.00
K	0.00	0.00	0.00	0.00	0.01	0.29	0.83	0.43	0.91

According to the above analysis, the optimal support position of SPMT was obtained at 9 m and the demolished bridge was cut and smoothly transported to the beam storage site by the SPMT models under this support position. Figure 12 shows the picture of the transportation process. Both straight line and turning were conducted in the movement the cut beam.

Figure 12.

Transportation of the demolished bridge: (a) turning and (b) straight line.

Support optimization for the installation of the new rebuilt bridge

Available space for support points

The new built bridge is a steel-concrete composite beam. The main body of the composite beam consists of two steel box girders. The bridge deck is made of concrete slabs. The width of bridge deck is 12 m, the bottom plates of the two box girders are 2.3 m wide, and the whole width is 8.7 m. The 6-axle module is 8.4 m long and thus not enough, so a series of 4-axle modules are adopted to transport the new built bridge. According to the construction document, the steel beam is made of a Q345qC steel plate, which is prefabricated at the factory and assembled on site. The bridge deck is made of C50 cast-in-place concrete. The self-weight of the new built bridge is approximately 550 t. The load capacity of the 4-axle SPMT is 144 t. Therefore, four 4-axle SPMT transporters are adopted to transport the new built bridge, as shown in Figure 13. Similarly, straight lines and turning was used to move the new built bridge to its position, as shown in Figure 14. The load of the new bridge during the transportation process is the self-weight of the beam. The safety factor is set as 1.2.

Figure 13.

Schematic diagram of new built bridge transportation: (a) span of the new built bridge and (b) section of the new built bridge (unit: cm).

Figure 14.

Photos of the movement of the new built bridge.

The four 4-axle SPMTs are symmetrically arranged during transport, and the distance between the inner support point and the mid-span section is set as y.

Because the support should not contact the pier and the two supports should not collide, the maximal and minimal space are calculated as $y_{\max} = L - R - C - T / 2$ and $y_{\min} C - T / 2$ . L is the length of the beam and R is the diameter of the pier. $y_{\max}$ and $y_{\min}$ are calculated as 11.64 m and 1.59 m, respectively. A space size function was defined as follows

k_{s p a c e} = {\begin{cases} 1,1.59 m < y < 11.64 m \\ 0, y \geq 11.64 m \cup y \leq 1.59 m \end{cases}

(7)

Internal force

To obtain the optimal supporting position, FEM models are established when the distance y is varied from 1 m to 11 m, as shown in Figure 15. The model was established as a composite structure which is composed of steel and concrete. The FEM model has 120 BEAM elements with a maximum length of 0.5 m. The boundary conditions representing the support of the SPMTs are simulated by hinge joints.

Figure 15.

FE model of new built bridge.

The internal force of the beam was calculated when the support distance varied from 1 m to 11 m. Figure 16 compares the internal force of the beam and its resistance. Since the two beams have the same internal forces, only one of them is listed. The results show that the carrying capacity of the beam is lower than the internal forces when the support distance is less than 5 m. This means that the beam cannot meet the carrying capacity requirements during the transportation process when the support distance is less than 5 m. When the support distance is in a range of 6 m to 11 m, the carrying capacity of the beam is always higher than the internal forces. This means that the new built bridge will not be damaged during the transportation process if the support distance is greater than 5 m.

Figure 16.

Internal force diagram of new built bridge.

Stress and deflection of beam

The maximum stresses in the upper and lower flanges of the steel beam and concrete bridge deck were calculated when the support distance varied from 1 m to 11 m. Figure 17 shows the calculated results. When the support distance varies from 1 m to 11 m, the tensile stress and compressive stress first decrease and then increase. The maximum tensile stress of the steel beam is 15 MPa when the support distance is 11 m. The maximum compressive stress of the steel beam is −55 MPa when the support distance is 1 m. The minimum compressive stress of the steel beam is −13.6 MPa when the support distance is 8 m. Both the tensile stress and compressive stress are lower than the design stress. The tensile stress and compressive stress of bridge deck concrete first decrease and then increase when the support distance varies from 1 m to 11 m. The concrete tensile stress of the bridge deck exceeds the design value when the support distance is less than 5 m and is close to the design value when the support distance is equal to 5 m and 11 m. The maximum compressive stress of the concrete is −1.0 MPa, much smaller than the design value.

Figure 17.

Stress and deflection of the composite beam: (a) steel stress, (b) concrete stress and (c) beam deflection.

Figure 17(c) shows the deflection of the composite beam. The upward deflection is much smaller than that of the downward deflection. Both of them first decrease and then increase. The maximum downward deflection is −18 mm when the support distance is equal to 1 m. When the support distance is equal to 7 and 8 m, the downward deflection reaches the minimum value. According to the above analyses, the allowable support distance is in a range of 5 ∼ 11 m.

Resistance to overturning

The new built bridge also has a risk of overturning during the transportation process. The critical overturning moment is calculated similarly to that for the cut beam. Figure 18 shows the critical overturning moment of the new built bridge when the support distance varies from 1 m to 11 m. The critical overturning bending moment of the beam almost linearly increases with the support distance. Therefore, the new built bridge will be more stable during the transport process when using a greater support distance.

Figure 18.

Overturning bending moment of the new built bridge.

Optimization

According equation (1), the safety factor k of the new built bridge is calculated when the distance x varies from 1 m to 11 m. The results are shown in Figure 19 and Table 3. According to the load capacity coefficient, the allowable location ranges 6 m to 11 m. In addition, the safety factor increases first and reaches the maximum value at x = 8 m, then decreases when the distance x becomes larger.

Figure 19.

Diagram of new built bridge safety factor.

Table 3.

Safety factor of new built bridge.

x (m)	1	2	3	4	5	6	7	8	9	10	11
$k_{s p a c e}$	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00
$k_{c}$	0.00	0.00	0.00	0.00	0.00	0.02	0.07	0.09	0.09	0.07	0.05
$k_{s}$	0.00	0.00	0.00	0.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00
$k_{d}$	0.20	0.28	0.37	0.46	0.55	0.63	0.72	0.80	0.87	0.94	1.00
$k_{o}$	0.00	0.18	0.36	0.54	0.72	0.87	0.99	1.00	0.91	0.78	0.65
K	0.00	0.00	0.00	0.00	0.00	0.02	0.05	0.08	0.07	0.06	0.04

Based on the above analyses, the optimal support distance is set as 8 m and the new built bridge was successfully transported in place using the SPMT method, as shown in Figure 20.

Figure 20.

Photos of the demolition and construction of the bridge.

Economic benefits

The SPMT method has the characteristics of low traffic closure impact, safety and environmental protection, and no damage to the existing road. In this special case, the transportations of both demolished bridge and rebuilt bridge were finished within 3 hours. Compared with the traditional blasting demolition, the SPMT method saved approximately 1.621950 million Chinese yuan for this special case.

The SPMT method saved the cost of repairing and cleaning of the road approximately 134,400 Chinese Yuan, reduced the traffic closure by 75%, and earned toll fee approximately 1,524,775 Chinese Yuan. The rental fees of the SPMT were 40,000 Chinese Yuan.

Conclusions

In the present study, the SPMT method was adopted to demolish and rebuild an expressway bridge. An optimization strategy of SPMT support positions is proposed by introducing a safety factor, in which the influence of the support positions on the internal force, stress, deflection and resistance to overturning of bridges are considered. The proposed optimization strategy is adopted in the demolition and rebuild of an overpass bridge as a case study. The optimal support positions of both demolished bridge and new built bridges were obtained by finding the maximum safety factor k. Finally, the demolition and rebuild of the overpass bridge were successfully completed using the SPMT method. In this special case, the SPMT method saved approximately 1.62 million Chinese Yuan.

Footnotes

ORCID iDs

Xiangdong Yu

Haiquan Jing

References

Ardani

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