# Crack Risk Evaluation of Submerged Concrete Tunnel during Hardening Phase

Authors: G. M. Ji; T. Kanstad; Ø. Bjøntegaard
Journal: Advances in Civil Engineering
 (2018)

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## Abstract

Cracking of concrete structures during the hardening phase often seriously compromises not only structure integrity but also durability and long-term service life. Especially for large massive structures, for example, concrete submerged tunnel, the reliable crack risk evaluation at the hardening phase is critical to the successful design. Mineral additives such as silica fume (SF), blast furnace slag (BFS), and fly ash (FA) have been used extensively in production of high-performance concrete in the last decades. The mineral additives such as FA and BFS not only reduce the hydration heat during the hardening phase but also have significant influence on the development of mechanic and viscoelastic properties at an early age. The main objective of the research is to propose a design methodology to select the appropriate composition of concrete for construction of the submerged tunnel. The influence of mineral additives such as FA and BFS on the risk of cracking during the hardening phase was investigated for the massive concrete structure. Five types of concrete mixes denoted as SV40, 40% BFS, 60% BFS, 40% FA, and 60% FA concrete are considered in the current study, and the measurement to reduce the initial temperature is also considered for 60% FA concrete. First, the well-documented material models are verified by calibration of restraint stress development in the TSTM test by using the finite element method (FEM), and then the 3D thermal-structural analysis is performed to assess the cracking risk for the submerged tunnel during the hardening phase. Based on analysis results, the 60% FA concrete has both the lowest maximum temperature and the lowest stress/strength ratio, and the cracking-free design based on the current study ensures the successful construction of the submerged tunnel.


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## Body

## 1. Introduction

In the past, prediction of the early-age cracking was almost exclusively based on temperature criteria. The temperature development in the young concrete was calculated, and cracking was predicted from the maximal temperature difference in the massive concrete structure. To avoid cracking, limitations were applied to maximum temperature and temperature difference between the surface and the center of the structure and between the new and the older adjoining structures. These limitations were based on practical experience and experience from the laboratory. The main drawback of the temperature-based crack risk estimation is that the other important factors in stress calculation are not considered: restraint conditions, material properties, and shrinkage. Several researchers [1, 2] have shown that there is no general correlation between stresses and temperature. Whether young concrete will crack or not depends very much on restraint conditions and material properties.In North America, the second Midtown Tunnel built under the Elizabeth River from 2013 to 2016 is the first deepwater concrete immersed-tube tunnel and only the second all-concrete immersed tunnel in the U.S. The all-concrete tunnel design allows for a strong, durable structure with substantial economic savings compared to a more conventional design using a steel tube encased in concrete, and it is extensively used across Europe. The all-concrete tunnel design is also selected for the submerged tunnel built in Oslo.Cracking during the hardening phase is prone to occur in massive concrete structures, and it compromises not only structure integrity but also durability and long-term service life. The early-age cracking was observed in concrete bridge deck expansion joint repair sections [3]. The cracking risk at the hardening phase is the main concern in the design of the concrete submerged tunnel built in Oslo. The illustration of the submerged tunnel is shown in Figure 1. The total length of the tunnel is about 1110 m with three traffic lanes in each direction, and 675 m of it (30 sections) is submerged under the seawater.Figure 1
Bjørvika submerged tunnel.
(a)
(b)In recent years, an increased interest in cracking of hardening concrete has led to extensive research on this subject [4–9]. A large number of material models for young concrete have been presented and implemented in computer programs for the simulation of stress development. Simulation of the hardening structure in general has to take into account temperature development due to hydration, development of material properties, and restraint conditions of the particular structure [10, 11]. FEM simulation was performed to predict early thermal stress in second lining concrete of NATM tunnels, and the model was verified by field measurements [12]. The effect of reinforcement on the early-age cracking is investigated [13], and the results showed that the probability of cracking in highly reinforced structures is lower than that has been estimated in calculations where the effect of reinforcement is completely ignored. For quantifying the effect of reinforcement on the stress development due to restrained load-independent deformations, a “strain enhancement factor” has been introduced. From the experiments with HSC specimens reinforced with four rebars, this factor reached a mean value of 1.85. A simplified model is used to investigate the possible effect of a gradient concrete material distribution in mass concrete structures on crack reduction. The results of the analysis show that gradient concrete might contribute to lowering the constraint stresses and therefore the crack risk during concrete hardening [14]. The influence of gravel (consisting mainly of quartz), basalt, granite, and limestone aggregate on the temperature development, stress level, and cracking risk has been studied in the experimental and numerical tests [15]. The use of aggregates with appropriate thermal properties in concrete such as low specific heat, high thermal conductivity coefficient, and low coefficient of thermal expansion reduces the induced stresses and the cracking risk. The reinforcement concrete structure was studied by several authors by using software DIANA, ABAQUS, ANSYS, etc. [16–18].In the current study, a design methodology is proposed based on both comprehensive tests and advanced numerical simulations. The procedure of the design methodology is as follows:(i)
Suggest candidate concrete with different compositions(ii)
Establish material models through a comprehensive test program(iii)
Calibrate material models against temperature-stress testing machine (TSTM) tests(iv)
Perform advanced thermal-structural numerical simulation(v)
Recommend the concrete composition with lowest cracking risk


## 2. Candidate Concrete

The concrete proposed in the current design includes one typical construction concrete (SV40) and four other concrete types with different percentages of mineral additives (FA or BFS), and the composition of concrete is presented in Table1. The materials tests and the mechanical properties do not include the steel reinforcement (bars, etc.).Table 1
Concrete compositions and mechanical properties at 28 days.
Materials
Concrete fraction (kg/m3), nominal values
SV40
40% BFS
60% BFS
40% FA
60% FA
Norcem Anleggsement (c)
404.1
263.4
232.5
263.7
232.9
Silica fume (s)
20.2
13.2
11.6
13.2
11.6
Fly ash (FA)
—
—
—
105.5
139.6
Blast furnace slag (BFS)
—
105.4
139.5
—
—
Water (w)
178
Norstone 0–8 mm
910
995
994
965
958
Norstone 8–16 mm
880
Sikament 92
1.9
Measured values: fresh concrete
Air (%)
4.3
1.6
1.6
1.4
1.1
Density (kg/m3)
2370
2410
2410
2410
2370
Slump (mm)
70
125
140
150
160
Binder composition (ratio and volumes)
s/c ratio
0.05
FA or BFS/c ratio
—
0.40
0.60
0.40
0.60
Binder and water volume (ltr)
317
305
306
316
321
w/(c + 2s + FA + BFS) ratio
0.40
0.45
0.45
0.45
0.45


## 3. Material Models

A comprehensive test program was performed at laboratories of Norwegian Public Roads Administration (SVV) and Norwegian University of Science and Technology (NTNU) to determine the following material parameters [19]:(i)
Heat of hydration(ii)
Mechanical properties (elastic modulus, compressive strength, and tensile strength)(iii)
Creep/relaxation properties under compressive loading(iv)
Volume change


### 3.1. Heat of Hydration

A semiadiabatic temperature test was performed to determine the hydration heat and thermal properties. The heat of hydration is expressed in the simple three-parameter equation, which is commonly used in engineering practice [20]:(1)Q=Q∞⋅exp−τteα,where Q∞ is the asymptotic value of the produced heat, while τ and α are model parameters which are determined from experimental data (Table 2). The activation energy is determined by strength development at several isothermal temperature histories. For temperature calculation, the most important input parameters, in addition to the produced heat and heat capacity, are the heat conductivity and the boundary conditions (connectivity and ambient air temperature) at the various surfaces of the structure.Table 2
Parameters for thermal properties.
Concrete type
Heat production
Activation energy (1/°K)
Thermal conductivity (kJ/ms°C)
Specific heat (J/kg°C)
Binder (kg/m3)1
Q
∞ (kJ/kg binder)
τ (h)
α
A
B
SV40
424
319
15.04
1.34
21966
2699
0.0026
1.06
40% BFS
382
286
18.95
0.84
0.0024
60% BFS
384
274
21.97
0.78
0.0024
40% FA
382
244
20.12
1.39
26574
1030
0.0024
1.07
60% FA
384
215
21.86
1.17
36192
1136
0.0024
1.07
60% FA (with initial temperature 11°C)
382
222
17.34
1.15
0.0024
1Binder = cement + silica fume + fly ash + blast furnace slag.


### 3.2. Mechanical Properties

The modified version of CEB-FIP MC 1990 is used to describe the development of the compressive strength, tensile strength, and modulus of elasticity [21]:(2)fcte=fc28⋅exps⋅1−28te−t0,ftte=ft28⋅exps⋅1−28te−t0nt,Ecte=Ec28⋅exps⋅1−28te−t0nE,in which t0 is introduced to identify the start of significant mechanical properties development, and it might be determined from a TSTM test; it is the time at which stiffness achieves a value high enough to produce measurable stresses. The parameter s was determined from the compressive strength development, whereas parameters nt and nE were determined from the tensile strength and elastic modulus tests, respectively (Table 3).Table 3
Model parameters for mechanical properties.
Concrete
f
c
28 (MPa)
f
t
28 (MPa)
E
c
28 (MPa)
s
n
E
n
t
t
0 (hrs)
SV40
65.1
3.86
31700
0.197
0.421
0.722
8.0
40% BFS
54.8
3.89
33700
0.368
0.300
0.605
8.8
60% BFS
52.8
3.34
32200
0.433
0.327
0.604
8.8
40% FA
47.2
3.32
32900
0.363
0.253
0.623
9.5
60% FA
41.2
3.20
33360
0.418
0.251
0.561
10.5


### 3.3. Creep in Compression

The creep of concrete at the constant moisture and thermal state may be well described by power curves of load durationst−t′ and by inverse power curves of age t′ at loading. This leads to the most well-known compliance function double power law [22, 23]:(3)Jt,t′=1E0+φ1E0t′−m+αt−t′n.The double power law (DPL) is originally proposed for hardened concrete. It was modified to describe the creep property of early-age concrete by taking into account the aging characteristics of young concrete [24, 25]:(4)Jt,t′=1Ect′1+φt′−dt−t′p,where Jt,t′ = compliance function, t′ = concrete age at loading (days), t = concrete age (days), Ect′ = modulus of elasticity at loading time, and φ, d, and p = creep model parameters.From the previous study [19], it can be seen that the combined compressive and tensile creep data give best correspondence with the measured stress developments in the TSTM tests, and using only the compressive DPL parameters gives better agreement with the test results than using only the tensile DPL parameters. For the FEM program DIANA which is used in the current study, only one set of DPL parameters could be specified in the input file, and then the compressive creep data as shown in Table 4 are used in the analysis.Table 4
Creep parameters in DPL for the compressive creep tests.
Concrete
Creep model parameters
φ
d
p
SV40
0.98
0.18
0.19
40% BFS
1.05
0.30
0.32
60% BFS
0.77
0.30
0.32
40% FA
1.23
0.28
0.30
60% FA
1.47
0.24
0.24


### 3.4. Volume Change

The thermal dilation (TD) and the autogenous deformation (AD), which are the driving forces to the restraint stress, were determined from the dilation rig test [26]. The sum of the two properties is measured directly and then separated into TD and AD. But this separation is only valid for that particular temperature history. The practical solution is simply to assume that the thermal dilation coefficient is a constant, and then the autogenous deformation is determined by subtracting thermal dilation from the total deformation measured under one realistic temperature history.The imposed temperatures and measured total deformations for five concrete types are shown in Figure2. The constant coefficients of thermal expansion (CTEs) used to separate AD and TD and autogenous deformation (AD) after 12 days are presented in Table 5. The separated AD and TD are also shown in Figure 2.Figure 2
Free deformation and separated thermal dilation and autogenous deformation: (a) SV40; (b) 40% FA; (c) 60% FA; (d) 60% FA (11°C); (e) 40% BFS; (f) 60% BFS.
(a)
(b)
(c)
(d)
(e)
(f)Table 5
Constant coefficient of thermal expansion (CTE) and autogenous deformation (AD) after 12 days.
Concrete type
Maximum temperature (oC)
CTE (10−6)
AD (10−6)
SV40
56.0
10.54
150
40% FA
48.7
8.70
100
60% FA
44.4
8.35
80
60% FA-11°C
33.0
8.35
38
40% BFS
50.4
9.43
152
60% BFS
47.5
9.41
150


## 3.1. Heat of Hydration

A semiadiabatic temperature test was performed to determine the hydration heat and thermal properties. The heat of hydration is expressed in the simple three-parameter equation, which is commonly used in engineering practice [20]:(1)Q=Q∞⋅exp−τteα,where Q∞ is the asymptotic value of the produced heat, while τ and α are model parameters which are determined from experimental data (Table 2). The activation energy is determined by strength development at several isothermal temperature histories. For temperature calculation, the most important input parameters, in addition to the produced heat and heat capacity, are the heat conductivity and the boundary conditions (connectivity and ambient air temperature) at the various surfaces of the structure.Table 2
Parameters for thermal properties.
Concrete type
Heat production
Activation energy (1/°K)
Thermal conductivity (kJ/ms°C)
Specific heat (J/kg°C)
Binder (kg/m3)1
Q
∞ (kJ/kg binder)
τ (h)
α
A
B
SV40
424
319
15.04
1.34
21966
2699
0.0026
1.06
40% BFS
382
286
18.95
0.84
0.0024
60% BFS
384
274
21.97
0.78
0.0024
40% FA
382
244
20.12
1.39
26574
1030
0.0024
1.07
60% FA
384
215
21.86
1.17
36192
1136
0.0024
1.07
60% FA (with initial temperature 11°C)
382
222
17.34
1.15
0.0024
1Binder = cement + silica fume + fly ash + blast furnace slag.


## 3.2. Mechanical Properties

The modified version of CEB-FIP MC 1990 is used to describe the development of the compressive strength, tensile strength, and modulus of elasticity [21]:(2)fcte=fc28⋅exps⋅1−28te−t0,ftte=ft28⋅exps⋅1−28te−t0nt,Ecte=Ec28⋅exps⋅1−28te−t0nE,in which t0 is introduced to identify the start of significant mechanical properties development, and it might be determined from a TSTM test; it is the time at which stiffness achieves a value high enough to produce measurable stresses. The parameter s was determined from the compressive strength development, whereas parameters nt and nE were determined from the tensile strength and elastic modulus tests, respectively (Table 3).Table 3
Model parameters for mechanical properties.
Concrete
f
c
28 (MPa)
f
t
28 (MPa)
E
c
28 (MPa)
s
n
E
n
t
t
0 (hrs)
SV40
65.1
3.86
31700
0.197
0.421
0.722
8.0
40% BFS
54.8
3.89
33700
0.368
0.300
0.605
8.8
60% BFS
52.8
3.34
32200
0.433
0.327
0.604
8.8
40% FA
47.2
3.32
32900
0.363
0.253
0.623
9.5
60% FA
41.2
3.20
33360
0.418
0.251
0.561
10.5


## 3.3. Creep in Compression

The creep of concrete at the constant moisture and thermal state may be well described by power curves of load durationst−t′ and by inverse power curves of age t′ at loading. This leads to the most well-known compliance function double power law [22, 23]:(3)Jt,t′=1E0+φ1E0t′−m+αt−t′n.The double power law (DPL) is originally proposed for hardened concrete. It was modified to describe the creep property of early-age concrete by taking into account the aging characteristics of young concrete [24, 25]:(4)Jt,t′=1Ect′1+φt′−dt−t′p,where Jt,t′ = compliance function, t′ = concrete age at loading (days), t = concrete age (days), Ect′ = modulus of elasticity at loading time, and φ, d, and p = creep model parameters.From the previous study [19], it can be seen that the combined compressive and tensile creep data give best correspondence with the measured stress developments in the TSTM tests, and using only the compressive DPL parameters gives better agreement with the test results than using only the tensile DPL parameters. For the FEM program DIANA which is used in the current study, only one set of DPL parameters could be specified in the input file, and then the compressive creep data as shown in Table 4 are used in the analysis.Table 4
Creep parameters in DPL for the compressive creep tests.
Concrete
Creep model parameters
φ
d
p
SV40
0.98
0.18
0.19
40% BFS
1.05
0.30
0.32
60% BFS
0.77
0.30
0.32
40% FA
1.23
0.28
0.30
60% FA
1.47
0.24
0.24


## 3.4. Volume Change

The thermal dilation (TD) and the autogenous deformation (AD), which are the driving forces to the restraint stress, were determined from the dilation rig test [26]. The sum of the two properties is measured directly and then separated into TD and AD. But this separation is only valid for that particular temperature history. The practical solution is simply to assume that the thermal dilation coefficient is a constant, and then the autogenous deformation is determined by subtracting thermal dilation from the total deformation measured under one realistic temperature history.The imposed temperatures and measured total deformations for five concrete types are shown in Figure2. The constant coefficients of thermal expansion (CTEs) used to separate AD and TD and autogenous deformation (AD) after 12 days are presented in Table 5. The separated AD and TD are also shown in Figure 2.Figure 2
Free deformation and separated thermal dilation and autogenous deformation: (a) SV40; (b) 40% FA; (c) 60% FA; (d) 60% FA (11°C); (e) 40% BFS; (f) 60% BFS.
(a)
(b)
(c)
(d)
(e)
(f)Table 5
Constant coefficient of thermal expansion (CTE) and autogenous deformation (AD) after 12 days.
Concrete type
Maximum temperature (oC)
CTE (10−6)
AD (10−6)
SV40
56.0
10.54
150
40% FA
48.7
8.70
100
60% FA
44.4
8.35
80
60% FA-11°C
33.0
8.35
38
40% BFS
50.4
9.43
152
60% BFS
47.5
9.41
150


## 4. Verification of Material Models

Stress development in restraint specimens exposed to realistic temperature histories was measured in the temperature-stress testing machine (TSTM) for all five concrete types. A numerical study was performed by the 3D finite element program DIANA [27] to verify the test results.The calculated stress developments of concrete containing 40% and 60% BFS have very good agreement with the test results, and the maximum deviation in both compression and tension is about 0.2 MPa (Figure3). The calculated compressive stress of the concrete containing 40% and 60% FA with 20°C initial temperature is higher than the measured ones, and the calculated tensile stress of the 60% FA concrete is lower than the test results, while the calculated tensile stress of the 40% FA concrete is lower than the test results at first 10 days; afterwards, it becomes higher than the test results. The calculated compressive stress and tensile stress of the 60% FA concrete with 11°C initial temperature are higher than the test results. The calculated compressive stress of the SV40 concrete is higher than the test results, and the calculated tensile stress is lower than the test results until 14 days.Figure 3
Calculated and measured stress development for the TSTM tests: (a) SV40; (b) 40% FA; (c) 60% FA; (d) 60% FA (11°C); (e) 40% BFS; (f) 60% BFS.
(a)
(b)
(c)
(d)
(e)
(f)All the model parameters used in the analysis were determined from independent tests, and no parameters are adjusted to achieve better fit with the test results. It can be concluded that the model parameters used in the analysis make reasonably accurate prediction of the stress development for the concrete containing different percentages of FA and BFS, but the deviation for the SV40 concrete is high especially for the tensile stress at 3 days; this is probably due to the low elastic modulus of the SV40 concrete from the test. The maximum compressive and tensile stresses are summarized in Table6 with the maximum deviation of compressive and tensile stresses. The deviation between the calculated and measured maximum stresses after 12–17 days is less than 12%, and in most cases, the calculations overestimate the maximum tensile stresses.Table 6
Calculated and measured stresses in the TSTM tests.
Concrete type
Maximum compressive stress (MPa)
Maximum tensile stress (MPa)
Time (days)
TSTM
DIANA
Ratio
Time (days)
TSTM
DIANA
Ratio
SV40
1.5
1.27
1.59
0.79
15
2.75
2.72
0.99
40% FA
1.5
0.62
0.92
0.67
17
2.50
2.67
1.07
60% FA
1.6
0.70
0.82
0.85
17
2.17
2.16
1.00
60% FA-11°C
2
0.30
0.45
0.67
17
2.44
2.73
1.12
40% BFS
1.5
1.50
1.25
1.20
12
2.46
2.57
1.04
60% BFS
1.7
1.0
0.80
1.25
13
2.47
2.67
1.08


## 5. Numerical Simulation

In the design process, the temperature and stress development in the submerged tunnel have been predicted by thermal-structural analysis to assess the risk of through cracking in the hardening phase. The numerical simulation provides reliable insight into the temperature and stress evolution in massive concrete from the casting to 28 days when the properties of concrete are stabilized, and it is essential for the environmental and cost friendly design of the submerged concrete tunnel.


### 5.1. Numerical Method

The detailed numerical method is described in [28]. In the FE analyses, the thermal-structural problem is decoupled and solved in sequence by the finite element program DIANA. The temperature distribution over time is solved first, and these results are used as input for the subsequent stress calculation. The temperature gradient mainly depends on the total quantity of hydration heat, boundary conditions, thermal properties, and discontinuity in geometry and material properties. The stress gradient depends on temperature distribution, mechanical properties, restraint conditions, discontinuity in geometry and material properties, etc. It is more convenient to simulate the mass structure without reinforcement, and the results are conservative. In the current study, the steel reinforcement (bars, etc.) is not included in the numerical model.Stress calculations need finer mesh than temperature calculations, the element in stress analysis has to be of higher order than the element in temperature analysis, and the requirements of stress analysis are usually decisive for element selection. The compatibility of the element type used in temperature and stress analysis is automatically handled by DIANA.


### 5.2. Finite Element Modelling

The tunnel consists of 50 sections, and the length of each section is 22 m. The cross section of the tunnel is not exactly symmetric, and the width between left side and middle wall is slightly different from the width between right side and middle wall. In the current study, the cross section is treated as symmetric, only half of the section is used in numerical analysis, it is considered that the simplification reduces the elements used in the finite element analysis (FEA) by 50%, and analysis results are still accurate enough for the design purpose. The boundary condition at the symmetry plane is fixed in the horizontal direction and has no heat transformation. The main dimensions of the tunnel structure are shown in Figure4. The element mesh of the 3D model used in the analyses is shown in Figure 5. Due to symmetry conditions, only one-fourth of the structure between the dilation joints is modelled. The bottom slab is modelled as hardened concrete, while it is assumed that the walls and top slab are cast in one operation.Figure 4
Geometry of the submerged tunnel (half of the cross section treated as symmetric).Figure 5
3D finite element model of ¼ tunnel structure.The boundary conditions used in analysis are the following:(i)
Fresh concrete temperature: 20°C(ii)
Ambient air temperature: 20°C(iii)
Wind velocity: 1 m/s(iv)
Vertical walls (21 mm plywood formwork; convectivity: 0.0033 kJ/m2s°C)(v)
Top slab (plastic foil; convectivity: 0.0076 kJ/m2s°C)(vi)
Time for formwork and plastic foil removal: 7 days (convectivity: 0.0133 kJ/m2s°C)The 20-node solid element CHX60 is used to model the concrete, and the element is automatically converted to 8-node HX8HT in the heat analysis. The 4-node boundary element BQ4HT is used to model the boundary conditions in the heat analysis.


## 5.1. Numerical Method

The detailed numerical method is described in [28]. In the FE analyses, the thermal-structural problem is decoupled and solved in sequence by the finite element program DIANA. The temperature distribution over time is solved first, and these results are used as input for the subsequent stress calculation. The temperature gradient mainly depends on the total quantity of hydration heat, boundary conditions, thermal properties, and discontinuity in geometry and material properties. The stress gradient depends on temperature distribution, mechanical properties, restraint conditions, discontinuity in geometry and material properties, etc. It is more convenient to simulate the mass structure without reinforcement, and the results are conservative. In the current study, the steel reinforcement (bars, etc.) is not included in the numerical model.Stress calculations need finer mesh than temperature calculations, the element in stress analysis has to be of higher order than the element in temperature analysis, and the requirements of stress analysis are usually decisive for element selection. The compatibility of the element type used in temperature and stress analysis is automatically handled by DIANA.


## 5.2. Finite Element Modelling

The tunnel consists of 50 sections, and the length of each section is 22 m. The cross section of the tunnel is not exactly symmetric, and the width between left side and middle wall is slightly different from the width between right side and middle wall. In the current study, the cross section is treated as symmetric, only half of the section is used in numerical analysis, it is considered that the simplification reduces the elements used in the finite element analysis (FEA) by 50%, and analysis results are still accurate enough for the design purpose. The boundary condition at the symmetry plane is fixed in the horizontal direction and has no heat transformation. The main dimensions of the tunnel structure are shown in Figure4. The element mesh of the 3D model used in the analyses is shown in Figure 5. Due to symmetry conditions, only one-fourth of the structure between the dilation joints is modelled. The bottom slab is modelled as hardened concrete, while it is assumed that the walls and top slab are cast in one operation.Figure 4
Geometry of the submerged tunnel (half of the cross section treated as symmetric).Figure 5
3D finite element model of ¼ tunnel structure.The boundary conditions used in analysis are the following:(i)
Fresh concrete temperature: 20°C(ii)
Ambient air temperature: 20°C(iii)
Wind velocity: 1 m/s(iv)
Vertical walls (21 mm plywood formwork; convectivity: 0.0033 kJ/m2s°C)(v)
Top slab (plastic foil; convectivity: 0.0076 kJ/m2s°C)(vi)
Time for formwork and plastic foil removal: 7 days (convectivity: 0.0133 kJ/m2s°C)The 20-node solid element CHX60 is used to model the concrete, and the element is automatically converted to 8-node HX8HT in the heat analysis. The 4-node boundary element BQ4HT is used to model the boundary conditions in the heat analysis.


## 6. Analysis Results and Discussion

The typical temperature and stress contour distribution in the middle section of the tunnel is shown in Figures6 and 7 for SV concrete, and all the other four concrete types have similar temperature and stress contour distribution. The maximum temperature appears at the corner between the inner wall and the top slab, while the critical locations, regarding the risk of through cracking determined as the ratio between maximum tensile stress and tensile strength, are in the center of the inner wall and approximately 0.6–1.2 m above the foundation slab. For the design of the submerged tunnel, the cracking in the outer wall is most critical to structure integrity and functionality, and the discussion of cracking risk will focus on the outer wall. In general, risk needs to take into account the hazard, exposure, and vulnerability over the time period. In the current study, the cracking risk is evaluated quantitatively, and the cracking index is defined as the ratio between stress and tensile strength of concrete. The maximum temperatures in outer and middle walls, in addition to the maximum temperatures in the whole structure, are presented in Table 7.Figure 6
Calculated temperature developments of SV40 concrete: (a) temperature contour (48 h after casting); (b) maximum temperature in the structure and temperature developments in the inner and outer walls.
(a)
(b)Figure 7
Calculated stress developments of SV40 concrete: (a) stress contour (336 h after casting); (b) stress developments in the inner and outer walls.
(a)
(b)Table 7
Calculated temperatures and the increase of temperature.
Concrete
Temperature (°C)
Outer wall
Inner wall
Whole structure
T
max_out
ΔT
max_out
T
max_middle
ΔT
max_middle
T
max_whole
ΔTmax_whole
SV40
60.7
40.7
60.3
40.3
69.0
49.0
40% FA
46.5
26.5
46.2
26.2
53.1
33.1
60% FA
42.2
22.2
41.9
21.9
48.4
28.4
60% FA-11°C
36.5
25.5
36.4
25.4
41.3
30.3
40% BFS
45.6
25.6
45.2
25.2
53.8
33.8
60% BFS
44.9
24.9
44.7
24.7
50.6
30.6The temperature and stress developments for 40% and 60% FA and 40% and 60% BFS concrete are shown in Figures8–12. The calculated tensile strength after 2 weeks is presented in Table 8, and the corresponding stress/strength ratios at 14 days are summarized in Table 9 for the five types of concrete.Figure 8
Calculated temperature (a) and stress (b) developments of 40% FA concrete.
(a)
(b)Figure 9
Calculated temperature (a) and stress (b) developments of 60% FA concrete.
(a)
(b)Figure 10
Calculated temperature (a) and stress (b) developments of 60% FA concrete with initial temperature 11°C.
(a)
(b)Figure 11
Calculated temperature (a) and stress (b) developments of 40% BFS concrete.
(a)
(b)Figure 12
Calculated temperature (a) and stress (b) developments of 60% BFS concrete.
(a)
(b)Table 8
Tensile strength at 14 days after casting.
Concrete
f
t28 (N/mm2)
Maturity time at 14 days after casting (days)
Tensile strength at critical time (N/mm2)
SV40
3.86
22.2
3.79
40% FA
3.32
20.7
3.19
60% FA
3.00
22.5
2.91
60% FA-11°C
3.00
19.7
2.86
40% BFS
3.89
20.7
3.74
60% BFS
3.34
21.0
3.20Table 9
Calculated stress/strength ratios at inner and outer walls at 14 days.
Concrete
Outer wall
Middle wall
Tensile strength
σt/ft outer wall
σt/ft inner wall
σtensile, max
σtensile, max
SV 40
3.91
4.40
3.79
1.04
1.18
40% FA
2.69
2.99
3.19
0.86
0.96
60% FA
2.14
2.38
2.91
0.74
0.82
60% FA-11°C
1.49
1.66
2.86
0.52
0.58
40% BFS
3.35
3.71
3.74
0.90
1.01
60% BFS
3.19
3.60
3.20
1.00
1.13The results show that the risk of cracking is about 6–14% higher in the inner wall compared to the outer wall due to the higher degree of restraint in the inner wall, but the consequences of through cracking are most serious in the outer wall which therefore should have to meet the design crack criterion. It is seen that, for the initial temperature of 20°C, concrete with 60% FA achieves both the lowest maximum temperature (42.2°C/temperature rise 22.2°C) and the lowest risk of cracking (0.74) in the outer wall. The replacement of cement with FA or BFS reduces the maximum temperature and temperature rise significantly. The temperature rise at the critical location of the outer wall during hardening is 40.7°C for SV40 concrete, 26.5°C for 40% FA concrete, 25.6°C for 40% BFS concrete, and 24.9°C for 60% BFS concrete. The comparison of the crack index at the outer wall for different concrete is shown in Figure13 and Table 9. Controlling of the initial temperature is the effective method to reduce the cracking risk for the massive concrete structure. The reduction of the fresh concrete temperature from 20 to 11oC results in a reduction of maximum temperature of 5.7°C, while the stress/strength ratio is reduced from 0.74 to 0.52 in the outer wall.Figure 13
Crack index at the outer wall for different concrete.


## 7. Conclusion

In the design of the massive concrete structure, the cracking risk in the hardening phase is the most critical for the integrity and durability of the structure. The proposed design methodology ensures that the appropriate composition of concrete is selected for the construction of the concrete submerged tunnel. The numerical method proposed here is based on the finite element method, and it has the potential to be used as a design tool in the important submerged concrete tunnel project.The risk of through cracking for the concrete submerged tunnel is determined for five types of concrete mixes denoted as SV40, 40% FA, 60% FA, 40% BFS, and 60% BFS concrete. The maximum temperature appears at the corner between the inner wall and the top slab, while the critical locations, regarding the risk of through cracking determined as the ratio between maximum tensile stress and tensile strength, are at the center of the inner wall and approximately 0.6–1.2 m above the foundation slab. The temperature development is similar in the critical locations of the inner and outer walls, but the stresses and the risk of cracking are 12% higher in the inner walls due to a larger degree of restraint. However, only the outer wall will experience water pressure, and therefore, the results of the outer wall are given most attention. It is seen that concrete with 60% FA has both the lowest maximum temperature (42.2°C/temperature rise 22.2°C) and the lowest risk of cracking (0.74) in the outer wall. The temperature rise during hardening is 30.7°C for SV40 concrete, 26.5°C for 40% FA concrete, 25.6°C for 40% BFS concrete, and 24.9°C for 60% BFS concrete. Furthermore, it is seen that the reduction in fresh concrete temperature from 20°C to 11°C results in a reduction of maximum temperature of 5.7°C, while the stress/strength ratio is reduced from 0.74 to 0.52.



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*Source: 7354025-2018-12-23.xml*