- Email: [email protected]
Research on Section Form of Submerged Floating Tunnels Considering Structural Internal Force Optimization under Fluid Action
Available online at www.sciencedirect.com
ScienceDirect Procedia Engineering 166 (2016) 288 – 295
2nd International Symposium on Submerged Floating Tunnels and Underwater Tunnel Structures
Research on Section Form of Submerged Floating Tunnels Considering Structural Internal Force Optimization under Fluid Action Ke Li, Xinghong Jiang*† China Merchants Chongqing Communications Research &Design Institute Co., Ltd., Chongqing 400067, China
Abstract Submerged floating tunnel, as a new type traffic structure crossing different waters, has short research history. However, because of its novelty and superiority, it has been a hot research topic. This paper takes the tunnel structure form as the breakthrough point, firstly, gives space arrangement and dimension requirement of submerged floating tunnel from the design view, then, analyzes hydraulic property of two section forms combining with fluid calculation and compares influence of different section forms on structure stress by combining the structure calculation. The research concludes that the elliptical section has better fluid and structure property than the rectangular section. © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license © 2016 The Authors. Published by Elsevier Ltd. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of SUFTUS-2016. Peer-review under responsibility of the organizing committee of SUFTUS-2016 Keywords: submerged floating tunnel; section form; hydraulic property; structure property
1. Introduction The submerged floating tunnel, also called “Archimedes Bridge”, is a new traffic structure crossing different waters and is generally composed of main body, anchoring system, pipe joint and revetment structure [1]. Submerged floating tunnel can alleviate the influence of bad formation and bad weather, protect environment landscape, reduce slope degree of line, shorten length of tunnel, save engineering investment and have good development potential.
* Corresponding author. Tel.: +86-023-62653183; fax: +86-023-62653183. E-mail address:[email protected]
1877-7058 © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of SUFTUS-2016
doi:10.1016/j.proeng.2016.11.551
Ke Li and Xinghong Jiang / Procedia Engineering 166 (2016) 288 – 295
Substantial research on submerged floating tunnels started from 1960s. In 1966, Grant firstly took submerged floating tunnel as one of schemes crossing Italy Messina strait [2-4]. In 1968, ઼ veit put forward the submerged floating tunnel design first time. From 1984 to 1994, Italy and Norway researchers conducted deep research and discussion Development of submerged floating tunnel in China is late. Some key technologies of submerged floating tunnel have been deeply exchanged, discussed and researched by combining Jintang Straits and Qiongzhou Straits [4]. In general, development of submerged floating tunnel is still in theoretical accumulation and experimental verification stage. Most current researches simplify the structure into simple shape which is different from actual highway tunnel section. Therefore, it is necessary to research the hydraulic characteristics and structural characteristics of submerged floating tunnel by combining specific section parameter. This paper obtains section structure form of submerged floating tunnels with different lanes by combining building boundary and layout requirement of integral two-way four-lane, two-way six-lane and two-way eight-lane tunnels, analyzes influence of different lanes and different sections on interaction of submerged floating tunnel and water flow by calculation of water flow dynamics and finally analyzes pipe stress distribution characteristics under water flow and water pressure action by combining structure calculation. Nomenclature
xj
coordinate components
vj
fluid velocity
p
pressure
Re
U
Reynolds number of the flow density
g
acceleration of gravity
P
fluid viscosity, P 1.002 u 106 m 2 s
Pf
turbulent eddy viscosity,
k
turbulent kinetic energy turbulent energy dissipation rate turbulent Schmidt numbers
H G k , GH
V k , V H constant, V k C u , C1 , C 2
1.0 , V H
constant, Cu
1.33
0.09 , C1 1.44 , C2
1.92
2. Structure Form Section size of submerged floating tunnel is influenced by the number of lanes, structure form, section type and spatial layout. According to existing research experience, the highway floating tunnel generally adopts two-way lane horizontal arrangement, as shown in figure 1. By reference of immersed tube tunnel section, submerged floating tunnel generally adopts polygonal section. However, with the consideration of large influence of hydrostatic pressure and water flow, submerged floating tunnel can adopt elliptic section. By comparison, if rectangular section is adopted for submerged floating tunnel, span and height are relatively small, space availability is high and current obstruction area is small. However, due to sudden change of structure horizontal direction slope, high water pressure easily generates in upstream face and reflow easily generates in downstream face which aren’t benefit for stability of water flow. If elliptic section height increases, current obstruction area will also increase. However, the surface smoothness is good. Surface mutation characteristic is obvious. Hydraulic properties of these two section forms have their own advantages and disadvantages. Calculation shall be carried out for discussion. Height-span ratios of rectangular section and elliptic section are 0.40 and 0.47. Increase of height-span ratio improves pressure resistance capability. Besides, smooth
289
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Ke Li and Xinghong Jiang / Procedia Engineering 166 (2016) 288 – 295
surface is benefit for conducting force of structure. However, because section width is large, the general stress is also large. Therefore, it cannot simply conclude the advantage and disadvantage of stress of these two section forms. The further calculation and analysis shall be conducted. It can be seen from comprehensive comparison of their economical efficiencies that area of elliptical section is 537m2 and area of rectangular section is 419m2. Larger area of elliptical section will increase the cost. Un-straight surface will cause difficulty for transportation. Therefore, section form cannot be determined depending on one advantage. Comprehensive analysis is required. 34100 20600
3150
00 15
2350
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3200
4000 650 4500
500
4100
750
15 00
4300
00 15
1250 500
1000 2000
2650
7700
5100
750
1950
1500 1500
3150
13600 6000
500
6750
3550 400 3550
2200 500
1750 750 1600
0 0 65 150
4950
6750
25500 38000
4300
1950
Fig. 1. Section form of tunnel (unit: mm)
3. Calculation of Hydraulic Prosperities 3.1. Mathematical Model During calculation, assuming that the water is incompressible, Navier-Stokes equation, continuity equation and momentum equation of incompressible object are as follows:
wv 1 v v 'v p 0 Re wt
(1)
wU wU Uv j wt wx j
(2)
0
w w U v j vi Uk wt wx j
wp w wxi wx j
ª § wv j vi · º « Pe ¨¨ ¸¸ » U gi «¬ © wvi wv j ¹ »¼
(3)
P P f ˈ P f Cu U k 2 H . Turbulent calculation adopts k H standard two- equation mode: Wherein: Pe
w w Uk Uv jk wt wx j
w wx j
ª§ Pf «¨ P Vk ¬«©
· wk º » Pk UH ¸ ¹ wx j ¼»
(4)
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Ke Li and Xinghong Jiang / Procedia Engineering 166 (2016) 288 – 295
w w UH U v jH wt wx j
Pk
§ wvi
Pf ¨ ¨
© wv j
w wx j
ª§ P f · wH º H H2 «¨ P » C1 Pk C2 U ¸ V H ¹ wx j »¼ k k «¬©
wv j · wvi ¸ wvi ¸¹ wv j
(5)
(6)
3.2. Model and Boundary Conditions Submerged floating tunnels are same in vertical section forms. Because the calculation is mainly aimed at analysis of influence of different section forms on interaction of submerged floating tunnel and water flow, it is regarded that the seabed topography is flat and the sea surface wave influence is neglected. Two-dimensional calculation model is adopted to improve calculation efficiency. Structure dimension of different section forms and position relationship of two tunnel section are shown in figure 1. Grid division of different sections is shown in figure 2. Take the middle point on bottom of rectangular section as coordinate origin, horizontal direction as X-axis and vertical direction as Y-axis. Take rectangle in calculation area to simulate infinite flow field. Distance between upper boundary and origin is 80m and distance between lower boundary and origin is 60m. Distance between left/right boundary and origin is 120m. It is approximately regarded that incoming flow has no interference. During simulation, left boundary is entrance and the velocity is 2m/s. Right boundary is outflow type. Upper and lower boundaries are symmetric. Structure surface of tunnel adopts wall boundary. Turbulent calculation model adopts standard k H two equation model [5].
(a)
(b)
Fig. 2. Grid division of submerged floating tunnels: (a) Rectangular section; (a) Rectangular section.
3.3. Result Analysis After calculation, in order to analyze influence of submerged floating tunnel on water flow action, setting the inlet pressure of model is 0, pressure distribution of flow field of submerged floating tunnel is shown in figure 3. Velocity cloud atlas of flow field is shown in figure 4. It can be known from analysis that influenced by water flow, pressure distribution on pipe section greatly changes. Positive pressure and negative pressure appear. When left incoming flow encounters with top point of upstream face of pipe section, water flow is blocked and velocity changes to zero. In upstream face of pipe section, a small scope of stagnation flow region forms. Pressure on upstream face is positive and gradually reduces from wall to far position. After passing through top point, the incoming flow is divided into two branches. One branch flows to end from upper position and one branch flows to end from lower position. In intersection point of upper and lower surface of pipe section, separation of boundary layer appears. Then, it continuously flows to downstream. A certain scope of wake region forms behind the pipe body. At top and bottom of pipe section, high negative pressure region with accelerated flow forms. It represents that the adsorption capacity of side and downstream face gradually reduces from wall to far position. After passing through high negative pressure
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Ke Li and Xinghong Jiang / Procedia Engineering 166 (2016) 288 – 295
region, the pressure sharply reduces. A certain scope of wake region forms behind the pipe body. In the position at certain distance with pipe section, water flow generates reflow phenomenon. Regular vortex forms in wake region of downstream face. With increase of distance with pipe section, turbulence gradually attenuates, vortex gradually disappears and water flow recovers normal state. It can be seen from comparison of flow field pressure and velocity distribution cloud atlas of submerged floating tunnels with two sections that if the rectangular section is adopted, pressure distribution around the section is highly uneven. Pressure is in the left and pulling force is in the right. Difference is higher than 0.4kPa. Because the submerged floating tunnel can almost be regarded as shear beam in length direction and length of submerged floating tunnel is long, uneven pressure-pulling force may cause high lateral pressure-pulling force load. It can be seen from analysis of upper and lower pressure reduction value that upper pressure is less than the lower pressure. Floating up action is shown. The stress of anchor will increase, which adversely influences safety of structure. In case of elliptical tunnel, if the velocity is 2m/s, upstream face and downstream face are under same pressure, about 0.4kPa, which is benefit for keeping horizontal stability of tunnel structure. Upper pressure and lower pressure are the same. No additional load will generate on anchor cable structure. Therefore, its mechanical stability is better. 80
80
60
60
0
Pressure 40
-0.8
0
20 -0.8 -0.4
-20
-100
-50
0
50
1.6 1.2 0.8 0.4 0 -0.4 -0.8 -1.2 -1.6
20 0
-0.8
-20
-60
100
(a)
0
-0.8
-100
0
-0.4
0
-40
0
-40
0
Pressure
-0.4
40
0.4
0.4
0
-60
1.6 1.2 0.8 0.4 0 -0.4 -0.8 -1.2 -1.6
0.4
-0.4
0
-50
0
50
100
(b)
Fig. 3. Cloud atlas of pressure distribution in flow field of submerged floating tunnel section (unit: kPa): (a) Rectangular section; (b) Elliptic section 80
80 X Velocity
X Velocity
2.2
40
2
2.4
20
2
1.8
0
2
2.2
-20 2
-40 -60
-100
-50
0
50
100
2.6 2.4 2.2 2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2
60 2.2
2
40
2.4
2
20 1.8
2.6 2.4 2.2 2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2
60
0
1.8
2.4
-20
2
2
2 .2
-40 -60
-100
-50
0
50
100
(a) (b) Fig. 4. Cloud atlas of velocity distribution in flow field of submerged floating tunnel section (unit: m/s): (a) Rectangular section; (b) Elliptic section.
4. Structure Mechanical Properties 4.1. Model Definition In order to discuss the mechanical influence of water pressure action on submerged floating tunnel structure, hereby, section of submerged floating tunnel is selected for plane strain calculation. Grid division is shown in fig. 5. Material is C40 concrete. Load is water pressure load. Height of water head on top of section is 50m. During model building, it is regarded that middle column position is unchanged. Fixed boundary condition is selected.
Ke Li and Xinghong Jiang / Procedia Engineering 166 (2016) 288 – 295
(a)
(b)
Fig. 5. Grid division for structure calculation of submerged floating tunnel: (a) Rectangular section; (b) Elliptic section.
4.2. Result Analysis After calculation, displacement distribution of tunnels with two section forms is shown in figure 6 and figure 7. It can be seen from figures that influenced by water pressure function and structure arrangement, upper and lower side of submerged floating tunnel mainly have vertical displacement and left and right side mainly have horizontal displacement. Vertical displacement is high. In rectangular section, maximum displacement is in middle position of bottom and is 20mm. In elliptic section, maximum displacement is in both sides of top and is 4mm. Thus it can be seen that elliptic section is benefit for restriction of structure deformation. However, internal space arrangement isn’t even, resulting in uneven structure deformation. Short board effect easily occurs. Full utilization of structure strength is influenced.
(a)
(b)
Fig. 6. Cloud atlas of displacement distribution of rectangular submerged floating tunnel structure: (a) Horizontal displacement; (b) Vertical displacement.
(a)
(b)
Fig. 7. Cloud atlas of displacement distribution of elliptical submerged floating tunnel structure: (a) Horizontal displacement; (b) Vertical displacement.
Based on calculation, principal stress distribution is shown in figure 8 and figure 9. It can be seen from analysis of cloud atlas of principal tensile stress that under water pressure action, principal tensile stress of rectangular submerged floating tunnel structure is high, especially at top and bottom and external side of structure. The region with maximum tensile stress higher than 1.5MPa is connected with internal high tensile stress region. Structure function is easily damaged. It can be seen from principal pressure stress that region with maximum pressure stress higher than 17.5MPa appears in structure connection place in rectangular section and is less in elliptical tunnel. It is mainly generated by
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stress in centralized way. Because the submerged floating tunnel directly connects with water body, the water proof requirement is extremely high. Bearing capacity of rectangular tunnel is low. During using, structure shall be optimized to reduce structure mutation, reinforcing steel bar proportion in transition region shall be increased and tensile strength of structure shall be improved. Bearing capacity of elliptical tunnel is high. However, uneven space layout influences the integral bearing capacity.
(a)
(b)
Fig. 8. Cloud atlas of main stress distribution of rectangular submerged floating tunnel structure: (a) Principal tensile stress; (b) Principal compressive stress.
(a)
(b)
Fig. 9. Principal stress distribution of elliptical submerged floating tunnel structure: (a) Principal tensile stress; (b) Principal compressive stress.
5. Conclusions This paper takes the tunnel structure form as the breakthrough point and analyzes characteristics of two-lane tunnel structure. Combined with fluid calculation, the paper obtains that as to rectangular tunnel, pressure on upstream face is obviously higher than that on downstream face and pressure on upper surface is less than that on lower surface, which generates horizontal thrust and upward lift force of tunnel. Therefore, both sides of tunnel and anchor structure are under pressure. Elliptical tunnel structure is benefit for keeping balance of pressure on upstream face, downstream face, upper surface and lower surface and for stability of flow field. Combined with structure calculation, rectangular section has high displacement and main stress. Internal and external regions with small tensile stress are connected. Therefore, structure function is easily damaged. Elliptical section has small thickness of concrete, small displacement and stress. So, it is benefit for structure stress. In design of submerged floating tunnel section, advantages of rectangular section and elliptical section shall be comprehensively utilized by combining characteristics of force to achieve optimization of cost, construction and performance, i.e. rectangular section is benefit for processing and transportation and elliptical section is benefit for stability of flow field. Acknowledgements This work has been supported by science and technology project of Ministry of Communications (2013318740050), National Natural Science Foundation of China (No. 41601574), Chongqing fundamental and advanced research program (cstc2014jcyjA30020, cstc2015jcyjBX0118), Chongqing application development program (cstc2013yykfB30005), Chongqing key scientific and technological project (cstc2012gg-yyjs30002).
Ke Li and Xinghong Jiang / Procedia Engineering 166 (2016) 288 – 295
References [1] Donna A. Submerged floating tunnels: a concept whose time has arrived. Tunneling and Underground Space Technology 1996; 11(4): 505510. [2] A. Fiorentino. Brief history of Archimedes bridge in the Strait of Messing. International Conference on Submerged Floating Tunnel. Sandnes, 1996; 29-30. [3] P. Tveit. Ideas on downward arched and other underwater concrete tunnels. Tunneling and Underground Space Technology 2000; 15(1): 6978. [4] Mai JT, Guan BS. A feasibility study on Qiongzhou strait submerged floating tunnel. Journal of railway engineering society 2003; 4: 93-96. [5] Li Y, Lin M. Hydrodynamic coefficients induced by waves and currents for submerged circular cylinder. Procedia Engineering 2010; 4: 253261.
295
ScienceDirect Procedia Engineering 166 (2016) 288 – 295
2nd International Symposium on Submerged Floating Tunnels and Underwater Tunnel Structures
Research on Section Form of Submerged Floating Tunnels Considering Structural Internal Force Optimization under Fluid Action Ke Li, Xinghong Jiang*† China Merchants Chongqing Communications Research &Design Institute Co., Ltd., Chongqing 400067, China
Abstract Submerged floating tunnel, as a new type traffic structure crossing different waters, has short research history. However, because of its novelty and superiority, it has been a hot research topic. This paper takes the tunnel structure form as the breakthrough point, firstly, gives space arrangement and dimension requirement of submerged floating tunnel from the design view, then, analyzes hydraulic property of two section forms combining with fluid calculation and compares influence of different section forms on structure stress by combining the structure calculation. The research concludes that the elliptical section has better fluid and structure property than the rectangular section. © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license © 2016 The Authors. Published by Elsevier Ltd. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of SUFTUS-2016. Peer-review under responsibility of the organizing committee of SUFTUS-2016 Keywords: submerged floating tunnel; section form; hydraulic property; structure property
1. Introduction The submerged floating tunnel, also called “Archimedes Bridge”, is a new traffic structure crossing different waters and is generally composed of main body, anchoring system, pipe joint and revetment structure [1]. Submerged floating tunnel can alleviate the influence of bad formation and bad weather, protect environment landscape, reduce slope degree of line, shorten length of tunnel, save engineering investment and have good development potential.
* Corresponding author. Tel.: +86-023-62653183; fax: +86-023-62653183. E-mail address:[email protected]
1877-7058 © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of SUFTUS-2016
doi:10.1016/j.proeng.2016.11.551
Ke Li and Xinghong Jiang / Procedia Engineering 166 (2016) 288 – 295
Substantial research on submerged floating tunnels started from 1960s. In 1966, Grant firstly took submerged floating tunnel as one of schemes crossing Italy Messina strait [2-4]. In 1968, ઼ veit put forward the submerged floating tunnel design first time. From 1984 to 1994, Italy and Norway researchers conducted deep research and discussion Development of submerged floating tunnel in China is late. Some key technologies of submerged floating tunnel have been deeply exchanged, discussed and researched by combining Jintang Straits and Qiongzhou Straits [4]. In general, development of submerged floating tunnel is still in theoretical accumulation and experimental verification stage. Most current researches simplify the structure into simple shape which is different from actual highway tunnel section. Therefore, it is necessary to research the hydraulic characteristics and structural characteristics of submerged floating tunnel by combining specific section parameter. This paper obtains section structure form of submerged floating tunnels with different lanes by combining building boundary and layout requirement of integral two-way four-lane, two-way six-lane and two-way eight-lane tunnels, analyzes influence of different lanes and different sections on interaction of submerged floating tunnel and water flow by calculation of water flow dynamics and finally analyzes pipe stress distribution characteristics under water flow and water pressure action by combining structure calculation. Nomenclature
xj
coordinate components
vj
fluid velocity
p
pressure
Re
U
Reynolds number of the flow density
g
acceleration of gravity
P
fluid viscosity, P 1.002 u 106 m 2 s
Pf
turbulent eddy viscosity,
k
turbulent kinetic energy turbulent energy dissipation rate turbulent Schmidt numbers
H G k , GH
V k , V H constant, V k C u , C1 , C 2
1.0 , V H
constant, Cu
1.33
0.09 , C1 1.44 , C2
1.92
2. Structure Form Section size of submerged floating tunnel is influenced by the number of lanes, structure form, section type and spatial layout. According to existing research experience, the highway floating tunnel generally adopts two-way lane horizontal arrangement, as shown in figure 1. By reference of immersed tube tunnel section, submerged floating tunnel generally adopts polygonal section. However, with the consideration of large influence of hydrostatic pressure and water flow, submerged floating tunnel can adopt elliptic section. By comparison, if rectangular section is adopted for submerged floating tunnel, span and height are relatively small, space availability is high and current obstruction area is small. However, due to sudden change of structure horizontal direction slope, high water pressure easily generates in upstream face and reflow easily generates in downstream face which aren’t benefit for stability of water flow. If elliptic section height increases, current obstruction area will also increase. However, the surface smoothness is good. Surface mutation characteristic is obvious. Hydraulic properties of these two section forms have their own advantages and disadvantages. Calculation shall be carried out for discussion. Height-span ratios of rectangular section and elliptic section are 0.40 and 0.47. Increase of height-span ratio improves pressure resistance capability. Besides, smooth
289
290
Ke Li and Xinghong Jiang / Procedia Engineering 166 (2016) 288 – 295
surface is benefit for conducting force of structure. However, because section width is large, the general stress is also large. Therefore, it cannot simply conclude the advantage and disadvantage of stress of these two section forms. The further calculation and analysis shall be conducted. It can be seen from comprehensive comparison of their economical efficiencies that area of elliptical section is 537m2 and area of rectangular section is 419m2. Larger area of elliptical section will increase the cost. Un-straight surface will cause difficulty for transportation. Therefore, section form cannot be determined depending on one advantage. Comprehensive analysis is required. 34100 20600
3150
00 15
2350
18000
3200
4000 650 4500
500
4100
750
15 00
4300
00 15
1250 500
1000 2000
2650
7700
5100
750
1950
1500 1500
3150
13600 6000
500
6750
3550 400 3550
2200 500
1750 750 1600
0 0 65 150
4950
6750
25500 38000
4300
1950
Fig. 1. Section form of tunnel (unit: mm)
3. Calculation of Hydraulic Prosperities 3.1. Mathematical Model During calculation, assuming that the water is incompressible, Navier-Stokes equation, continuity equation and momentum equation of incompressible object are as follows:
wv 1 v v 'v p 0 Re wt
(1)
wU wU Uv j wt wx j
(2)
0
w w U v j vi Uk wt wx j
wp w wxi wx j
ª § wv j vi · º « Pe ¨¨ ¸¸ » U gi «¬ © wvi wv j ¹ »¼
(3)
P P f ˈ P f Cu U k 2 H . Turbulent calculation adopts k H standard two- equation mode: Wherein: Pe
w w Uk Uv jk wt wx j
w wx j
ª§ Pf «¨ P Vk ¬«©
· wk º » Pk UH ¸ ¹ wx j ¼»
(4)
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Ke Li and Xinghong Jiang / Procedia Engineering 166 (2016) 288 – 295
w w UH U v jH wt wx j
Pk
§ wvi
Pf ¨ ¨
© wv j
w wx j
ª§ P f · wH º H H2 «¨ P » C1 Pk C2 U ¸ V H ¹ wx j »¼ k k «¬©
wv j · wvi ¸ wvi ¸¹ wv j
(5)
(6)
3.2. Model and Boundary Conditions Submerged floating tunnels are same in vertical section forms. Because the calculation is mainly aimed at analysis of influence of different section forms on interaction of submerged floating tunnel and water flow, it is regarded that the seabed topography is flat and the sea surface wave influence is neglected. Two-dimensional calculation model is adopted to improve calculation efficiency. Structure dimension of different section forms and position relationship of two tunnel section are shown in figure 1. Grid division of different sections is shown in figure 2. Take the middle point on bottom of rectangular section as coordinate origin, horizontal direction as X-axis and vertical direction as Y-axis. Take rectangle in calculation area to simulate infinite flow field. Distance between upper boundary and origin is 80m and distance between lower boundary and origin is 60m. Distance between left/right boundary and origin is 120m. It is approximately regarded that incoming flow has no interference. During simulation, left boundary is entrance and the velocity is 2m/s. Right boundary is outflow type. Upper and lower boundaries are symmetric. Structure surface of tunnel adopts wall boundary. Turbulent calculation model adopts standard k H two equation model [5].
(a)
(b)
Fig. 2. Grid division of submerged floating tunnels: (a) Rectangular section; (a) Rectangular section.
3.3. Result Analysis After calculation, in order to analyze influence of submerged floating tunnel on water flow action, setting the inlet pressure of model is 0, pressure distribution of flow field of submerged floating tunnel is shown in figure 3. Velocity cloud atlas of flow field is shown in figure 4. It can be known from analysis that influenced by water flow, pressure distribution on pipe section greatly changes. Positive pressure and negative pressure appear. When left incoming flow encounters with top point of upstream face of pipe section, water flow is blocked and velocity changes to zero. In upstream face of pipe section, a small scope of stagnation flow region forms. Pressure on upstream face is positive and gradually reduces from wall to far position. After passing through top point, the incoming flow is divided into two branches. One branch flows to end from upper position and one branch flows to end from lower position. In intersection point of upper and lower surface of pipe section, separation of boundary layer appears. Then, it continuously flows to downstream. A certain scope of wake region forms behind the pipe body. At top and bottom of pipe section, high negative pressure region with accelerated flow forms. It represents that the adsorption capacity of side and downstream face gradually reduces from wall to far position. After passing through high negative pressure
292
Ke Li and Xinghong Jiang / Procedia Engineering 166 (2016) 288 – 295
region, the pressure sharply reduces. A certain scope of wake region forms behind the pipe body. In the position at certain distance with pipe section, water flow generates reflow phenomenon. Regular vortex forms in wake region of downstream face. With increase of distance with pipe section, turbulence gradually attenuates, vortex gradually disappears and water flow recovers normal state. It can be seen from comparison of flow field pressure and velocity distribution cloud atlas of submerged floating tunnels with two sections that if the rectangular section is adopted, pressure distribution around the section is highly uneven. Pressure is in the left and pulling force is in the right. Difference is higher than 0.4kPa. Because the submerged floating tunnel can almost be regarded as shear beam in length direction and length of submerged floating tunnel is long, uneven pressure-pulling force may cause high lateral pressure-pulling force load. It can be seen from analysis of upper and lower pressure reduction value that upper pressure is less than the lower pressure. Floating up action is shown. The stress of anchor will increase, which adversely influences safety of structure. In case of elliptical tunnel, if the velocity is 2m/s, upstream face and downstream face are under same pressure, about 0.4kPa, which is benefit for keeping horizontal stability of tunnel structure. Upper pressure and lower pressure are the same. No additional load will generate on anchor cable structure. Therefore, its mechanical stability is better. 80
80
60
60
0
Pressure 40
-0.8
0
20 -0.8 -0.4
-20
-100
-50
0
50
1.6 1.2 0.8 0.4 0 -0.4 -0.8 -1.2 -1.6
20 0
-0.8
-20
-60
100
(a)
0
-0.8
-100
0
-0.4
0
-40
0
-40
0
Pressure
-0.4
40
0.4
0.4
0
-60
1.6 1.2 0.8 0.4 0 -0.4 -0.8 -1.2 -1.6
0.4
-0.4
0
-50
0
50
100
(b)
Fig. 3. Cloud atlas of pressure distribution in flow field of submerged floating tunnel section (unit: kPa): (a) Rectangular section; (b) Elliptic section 80
80 X Velocity
X Velocity
2.2
40
2
2.4
20
2
1.8
0
2
2.2
-20 2
-40 -60
-100
-50
0
50
100
2.6 2.4 2.2 2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2
60 2.2
2
40
2.4
2
20 1.8
2.6 2.4 2.2 2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2
60
0
1.8
2.4
-20
2
2
2 .2
-40 -60
-100
-50
0
50
100
(a) (b) Fig. 4. Cloud atlas of velocity distribution in flow field of submerged floating tunnel section (unit: m/s): (a) Rectangular section; (b) Elliptic section.
4. Structure Mechanical Properties 4.1. Model Definition In order to discuss the mechanical influence of water pressure action on submerged floating tunnel structure, hereby, section of submerged floating tunnel is selected for plane strain calculation. Grid division is shown in fig. 5. Material is C40 concrete. Load is water pressure load. Height of water head on top of section is 50m. During model building, it is regarded that middle column position is unchanged. Fixed boundary condition is selected.
Ke Li and Xinghong Jiang / Procedia Engineering 166 (2016) 288 – 295
(a)
(b)
Fig. 5. Grid division for structure calculation of submerged floating tunnel: (a) Rectangular section; (b) Elliptic section.
4.2. Result Analysis After calculation, displacement distribution of tunnels with two section forms is shown in figure 6 and figure 7. It can be seen from figures that influenced by water pressure function and structure arrangement, upper and lower side of submerged floating tunnel mainly have vertical displacement and left and right side mainly have horizontal displacement. Vertical displacement is high. In rectangular section, maximum displacement is in middle position of bottom and is 20mm. In elliptic section, maximum displacement is in both sides of top and is 4mm. Thus it can be seen that elliptic section is benefit for restriction of structure deformation. However, internal space arrangement isn’t even, resulting in uneven structure deformation. Short board effect easily occurs. Full utilization of structure strength is influenced.
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Fig. 6. Cloud atlas of displacement distribution of rectangular submerged floating tunnel structure: (a) Horizontal displacement; (b) Vertical displacement.
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Fig. 7. Cloud atlas of displacement distribution of elliptical submerged floating tunnel structure: (a) Horizontal displacement; (b) Vertical displacement.
Based on calculation, principal stress distribution is shown in figure 8 and figure 9. It can be seen from analysis of cloud atlas of principal tensile stress that under water pressure action, principal tensile stress of rectangular submerged floating tunnel structure is high, especially at top and bottom and external side of structure. The region with maximum tensile stress higher than 1.5MPa is connected with internal high tensile stress region. Structure function is easily damaged. It can be seen from principal pressure stress that region with maximum pressure stress higher than 17.5MPa appears in structure connection place in rectangular section and is less in elliptical tunnel. It is mainly generated by
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stress in centralized way. Because the submerged floating tunnel directly connects with water body, the water proof requirement is extremely high. Bearing capacity of rectangular tunnel is low. During using, structure shall be optimized to reduce structure mutation, reinforcing steel bar proportion in transition region shall be increased and tensile strength of structure shall be improved. Bearing capacity of elliptical tunnel is high. However, uneven space layout influences the integral bearing capacity.
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Fig. 8. Cloud atlas of main stress distribution of rectangular submerged floating tunnel structure: (a) Principal tensile stress; (b) Principal compressive stress.
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Fig. 9. Principal stress distribution of elliptical submerged floating tunnel structure: (a) Principal tensile stress; (b) Principal compressive stress.
5. Conclusions This paper takes the tunnel structure form as the breakthrough point and analyzes characteristics of two-lane tunnel structure. Combined with fluid calculation, the paper obtains that as to rectangular tunnel, pressure on upstream face is obviously higher than that on downstream face and pressure on upper surface is less than that on lower surface, which generates horizontal thrust and upward lift force of tunnel. Therefore, both sides of tunnel and anchor structure are under pressure. Elliptical tunnel structure is benefit for keeping balance of pressure on upstream face, downstream face, upper surface and lower surface and for stability of flow field. Combined with structure calculation, rectangular section has high displacement and main stress. Internal and external regions with small tensile stress are connected. Therefore, structure function is easily damaged. Elliptical section has small thickness of concrete, small displacement and stress. So, it is benefit for structure stress. In design of submerged floating tunnel section, advantages of rectangular section and elliptical section shall be comprehensively utilized by combining characteristics of force to achieve optimization of cost, construction and performance, i.e. rectangular section is benefit for processing and transportation and elliptical section is benefit for stability of flow field. Acknowledgements This work has been supported by science and technology project of Ministry of Communications (2013318740050), National Natural Science Foundation of China (No. 41601574), Chongqing fundamental and advanced research program (cstc2014jcyjA30020, cstc2015jcyjBX0118), Chongqing application development program (cstc2013yykfB30005), Chongqing key scientific and technological project (cstc2012gg-yyjs30002).
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References [1] Donna A. Submerged floating tunnels: a concept whose time has arrived. Tunneling and Underground Space Technology 1996; 11(4): 505510. [2] A. Fiorentino. Brief history of Archimedes bridge in the Strait of Messing. International Conference on Submerged Floating Tunnel. Sandnes, 1996; 29-30. [3] P. Tveit. Ideas on downward arched and other underwater concrete tunnels. Tunneling and Underground Space Technology 2000; 15(1): 6978. [4] Mai JT, Guan BS. A feasibility study on Qiongzhou strait submerged floating tunnel. Journal of railway engineering society 2003; 4: 93-96. [5] Li Y, Lin M. Hydrodynamic coefficients induced by waves and currents for submerged circular cylinder. Procedia Engineering 2010; 4: 253261.
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