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The impact of soil properties on the structural integrity of high-fill reinforced concrete culverts
Computers and Geotechnics 52 (2013) 46–53
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Technical Communication
The impact of soil properties on the structural integrity of high-fill reinforced concrete culverts Baoguo Chen a,⇑, Liang Sun b a
China University of Geosciences (Wuhan), Engineering Faculty, 388 Lu-mo Road, Hongshan District, Wuhan 430074, China Ecole Polytechnique Fédérale de Lausanne (EPFL), School of Architecture, Civil and Environmental Engineering (ENAC), Laboratory for Rock Mechanics (LMR), Station 18, CH-1015 Lausanne, Switzerland b
a r t i c l e
i n f o
Article history: Received 2 September 2012 Received in revised form 27 March 2013 Accepted 29 March 2013 Available online 24 April 2013 Keywords: Culvert Structural integrity High fill Ground bearing capacity Ground treatment
a b s t r a c t Reinforced concrete (RC) culverts under high fill have been widely used in the construction of expressways and railways. Based on the results of a field survey, various types of structural damage to RC culverts occur during construction and service periods. In this study, numerical simulation and field tests were conducted to investigate the impact of soil properties on the structural integrity of RC culverts under high fill. Important factors that influence culvert integrity, such as ground bearing capacity and ground treatment, have been analyzed in detail. Research findings indicate that damage to RC culverts under high fill is not typically caused by failure to the subgrade layer under the culvert foundation, due to the beneficial effects of foundation depth, foundation width and subgrade layer consolidation. Structural damage is probably caused by improper ground treatment strategies. Proper strategies for preventing integrity problems are recommended based on the research. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction High-fill reinforced concrete (HRC) culverts have been widely used as substructures for water, vehicle and pedestrian conveyance. The results of a random field survey of 102 HRC culverts, which were located on highways in five provinces (Hunan, Hubei, Sichuan, Shanxi and Henan) in China, demonstrated that structural problems occur frequently in culverts [1]. Typical characteristics of damaged HRC culverts are summarized in Table 1, which shows that the ratio of damaged culverts to total surveyed culverts is 59.8%. In particular, the damage ratios of slab culverts, arch culverts, pipe culverts and box culverts are 64.8%, 54.8%, 63.6% and 33.3%, respectively. Significant damage characteristics include structural cracks and differential settlements of culvert foundations. In this survey, the damaged culvert is defined as the crack width on the culvert is more than 0.2 mm or the differential foundation settlement is more than 30 mm based on the Chinese Code for Design of Highway Reinforced Concrete and Prestressed Concrete Bridges and Culverts [2]. These problems occur in HRC culverts for two important reasons: (1) vertical earth pressure on culverts and (2) impact of soil properties on culverts. Compression of the backfill mass at both sides of the culvert is larger than that of the RC culvert due to the differential stiffness. Thus, vertical earth pressure concentrates ⇑ Corresponding author. Tel.: +86 27 67883074; fax: +86 27 67883507. E-mail addresses: [email protected] (B. Chen), liang.sun@epfl.ch (L. Sun). 0266-352X/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.compgeo.2013.03.006
on the top of RC culverts [3,4]. The vertical earth pressure concentration on culverts will be more significant for a larger differential stiffness between a culvert and its adjacent backfill [5,6]. Marston pioneered the research concerning vertical earth pressure on culverts based on analytical and experimental methods [7,8]. Following the research of Marston, Spangler [9,10] analyzed the vertical earth pressure on rigid pipe culverts and discussed the key factors that influence the load on underground conduits. Karinski et al. [11] investigated vertical earth pressure on rigid culverts under fill and traffic loads through theoretical analysis and discussed the influence of structural deformation and dimension on vertical earth pressure. Kim and Yoo [12] examined vertical earth pressure on rectangular culverts under three different installation conditions (embankment installation, trench installation and imperfect trench installation) by numerical simulation. Bennett et al. [13] studied the structure stress states and vertical earth pressure on RC box culverts by conducting field tests and found that the height of the backfill over the culvert was the main factor that influenced vertical earth pressure and internal structural forces. Kang et al. [5,14,15] analyzed the soil–culvert interaction under two conditions, i.e., imperfect trench installation and embankment installation, using numerical simulation. Valsangkar et al. [16–18] investigated the backfill–culvert interaction and detected the earth pressure acting on culvert under embankment installation and induced trench installation conditions, using field and centrifuge test and numerical simulation. These studies thoroughly addressed the subject of vertical earth pressure on culverts and the relationship
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B. Chen, L. Sun / Computers and Geotechnics 52 (2013) 46–53 Table 1 Survey results of collapsed culverts. Culvert types
Culvert amount
Typical damage characteristics
Amount of damaged culverts
Damage ratio of different damage characteristics (%)
Damage ratio of different culvert types (%)
Slab culvert
54
Longitudinal crack on top slab Diagonal crack on culvert body Differential settlement of foundation Water permeation under foundation
14 10 7 4
25.9 18.5 13.0 7.4
64.8
Arch culvert
31
Diagonal crack on culvert body Longitudinal crack near the skewback Differential settlement of foundation Water permeation under the foundation
3 6 5 3
9.7 19.4 16.1 9.7
54.8
Pipe culvert
11
Large settlement at the center of pipe Longitudinal crack on culvert body Foundation crack and differential settlement
2 3 2
18.2 27.3 18.2
63.6
Box culvert
6
Differential settlement of foundation Foundation crack and gaps among culvert sections
1 1
20.0 20.0
33.3
between fill load and structural stress states. However, few studies have focused on the impact of soil properties on the structural integrity and stress states of HRC culverts. When investigating the structural integrity and stress states of HRC culverts, the mechanical properties of the subgrade layer cannot be disregarded [19–22]. The objective of this study is to discuss how the following two principal issues affect HRC culvert stress states and integrity: (1) the ground bearing capacity of HRC culverts and (2) ground treatment of HRC culverts.
possible point loads or other stress distortions induced by large size particles in the backfill. Eight earth pressure cells were placed at the foundation level (two under the culvert foundation and six at the sides of the culvert at the same level). 2.2. Numerical model Accordingly, the problem selected for the numerical analysis was based on the instrumented HRC culvert. A finite element analysis is carried out using the software PLAXIS to investigate the abovementioned issues. In the numerical model, the two side boundaries of the model were horizontally restrained, while the bottom of the model was fixed. The ground water surface was assumed to be located at the bottom line of the culvert foundation. The loading procedure followed an actual installation regulation. The 15-noded triangular elements were used to generate the mesh of the model. Fine meshing was chosen for the soil–culvert system. Slippage was allowed to occur between the soil and the culvert, where five pairs of interface elements were used to model the slippage between the soil and the structure. The interface elements have zero thickness and were modeled by an elastic–plastic relation with the Mohr–Coulomb criterion. The strength properties of the interfaces were defined as the strength properties of the corresponding soil layer multiplied by a strength reduction factor (Rinter). In this study, strength reduction factors of 0.8 and 0.5 were used for sand/gravel and clay, respectively [23].
2. Numerical simulation 2.1. Description of the instrumented culvert Field test results were used to validate the numerical model. The instrumented HRC culvert was 8 m high and 10 m wide. The instrumented section was located approximately in the center of the culvert length (Fig. 1a). The subgrade layers consisted of a layer of clay, a layer of fully weathered mudstone and a stiff layer of moderately weathered mudstone. During the construction procedure, the excavation depth of the clay layer, which was replaced by quartz sand, was 3.5 m. The backfill on the culvert was 18.0 m high and was filled step by step; each step was 0.5 m thick. During the backfilling procedure, the installation time was 10 days per layer. Vibrating-wire earth pressure cells (JMZX-50xxA, 210 mm diameter and 12 mm thickness) were used to record the foundation pressure and the embankment pressure at the foundation level (Fig. 1b). The pressure cells were fixed to the subgrade layer. A quick setting high strength grout pad was used to assure uniform contact between the pressure cells and the subgrade layer. Medium sand was used to cover the cell to protect the cell from
backfill
2.3. Material parameters The weathered mudstone layers and sand, as well as backfill over the culvert were modeled by Mohr–Coulomb elastoplastic
backfill
embankment centerline
b=10
fully weathered mudstone moderately weathered mudstone
(a) Cross section of embankment
clay
D x h=8
7.2
6
6
clay
4
culvert foundation
15
7.2 6
1
8
culvert
4 4 4
culvert pressure cells
Bx
foundation level Reinforced area 4 4 4
fully weathered mudstone moderately weathered mudstone
(b) Cross section of culvert
Fig. 1. Field layout of the instrumented culvert (units in meters). (a) Cross section of embankment. (b) Cross section of culvert.
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B. Chen, L. Sun / Computers and Geotechnics 52 (2013) 46–53
Average foundation pressure (kPa)
materials. The clay layer was modeled by Cam-Clay soft soil material. Although in nonconservative design, the RC culverts are designed to crack. The cracking means that the stiffness changes between the walls and the slab midspan, which lead to load redistribution on the box culvert. The stiffness of slab with cracks is impacted by crack width, crack length, crack spacing, etc. It varies with cracking degree. However, a tentative study was conducted using numerical simulation, which shows that the vertical load on culvert decreases by about 12% when the stiffness of culvert top slab reduces by 50%. This study is a first approximation, where reinforced concrete response was assumed to be linear and elastic. The material properties used in the numerical models are presented in Table 2.
550 500 450 400 350 300
Field test numerical simulation
250 200 3.0
6.0
9.0
12.0
15.0
18.0
Height of backfill over culvert (m) Fig. 2. Variation in average foundation pressure versus backfill height.
The numerical simulation was compared with the field tests. Fig. 2 presents the variations in the average foundation pressure at the centerline of the embankment versus the height of the backfill. Fig. 3 presents the distribution of the earth pressure at the foundation level. The difference between field test data and numerical results is about 10%. It is believed as a reasonable agreement because only qualitative comparison can be made due to the limitations of the field tests. The validation demonstrated that the numerical simulation could be used for further analysis. Results of the field test and numerical simulation revealed that the average foundation pressure increased with an increase in backfill height. The analysis showed that the earth pressure was unevenly distributed at the level of the culvert foundation. The embankment pressure at both sides of the culvert foundation was lower than the backfill overburden, due to the friction of the culvert sidewalls; however, the pressure approached the backfill overburden as the distance from the culvert axis increased.
Pressure at foundation level (kPa)
2.4. Validation 600
Field test
Numerical result H=16.5 m
450
H=10.5 m H=3.5 m
300
150 -20 -16 -12
-8
-4
0
4
8
12
16
20
Distance from the culvert axis (m) Fig. 3. Distribution of earth pressure at the culvert foundation level.
used in the numerical model are the same as the material properties presented in Table 2. 3.1. Effect of culvert foundation depth
3. Ground bearing capacity of HRC culverts A lower ground bearing capacity of HRC culverts may induce structural damage. The cone penetration test and dynamic sounding are the prevailing methods used to determine ground bearing capacity. However, these methods do not consider the following effects: (1) foundation depth, (2) foundation width and (3) loading rate of backfill. In this study, numerical simulations were conducted to analyze the influence of these factors on the ground bearing capacity of HRC culverts. The material model and numerical model in these simulations were the same as that of the former presented. The numerical model was shown in Fig. 4. In the numerical model, the dimensions of the culvert were the same as the instrumented culvert. For box culverts, foundation depth (d) was the sum of the culvert height (h) and the backfill height on culvert (H). The backfill on the culvert was filled step by step, and each step was filled in 10 days with a thickness of 0.5 m. The material properties
This section investigates the effect of foundation depth on ground bearing capacity. In the parametric study, the foundation depth (d/b) ranged from 1 to 6. For comparison purposes, two different types of subgrade layer (clay and sand) were considered in this analysis. Furthermore, a surface load was applied to the backfill to investigate the variation in foundation settlement versus average foundation pressure for different foundation depths. The surface load was increased sequentially by 50 kPa for each load grade. The characteristic value of ground bearing capacity is generally considered to be the main reference in culvert design. This value is determined by the average foundation pressure–settlement (p–s) curve. According to the Chinese Code for Design of Ground Base and Foundation of Highway Bridges and Culverts [24], the characteristic value of ground bearing capacity is equal to an average foundation pressure, which produces a specific foundation settlement ratio (i.e., s/b = 2%). The characteristic values of ground bearing capacity versus foundation depths for clay and sand ground are
Table 2 Parameters in the numerical analysis. Parameters
Unit
Culvert
Backfill
Clay
Sand
Fully weathered mudstone
Moderately weathered mudstone
Young’s modulus Poisson’s ratio Effective cohesion Effective friction angle Effective dilatancy angle Permeability Unit weight
MPa – kPa Degree Degree m/d kN/m3
30000.0 0.20 – – – – 25.0
28.0 0.27 6.0 29.5 5.0 1.20 19.6
6.8 0.35 16.6 14.7 0 0.01 17.9
19.6 0.30 0 33.5 2.0 25.0 19.5
42.0 0.25 26.0 19.0 4.0 1.00 20.2
56.0 0.24 30.0 28.0 8.0 0.70 21.8
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B. Chen, L. Sun / Computers and Geotechnics 52 (2013) 46–53
(2007) [24]. The results concluded that the effect of foundation width on the characteristic value of the ground bearing capacity of sand but not of clay should be considered in HRC culvert design.
load
culvert
d
h H
backfill
3.3. Effect of loading rate of backfill
10b
b
ground soil
20b Fig. 4. Numerical model for the ground bearing capacity analysis.
presented in Fig. 5. The characteristic values of ground bearing capacities for clay and sand increased nonlinearly with foundation depth and nearly approached a limiting value. The characteristic values of ground bearing capacity for clay and/or sand calculated by Chinese Code (2007) method [24] were 38.3% and/or 30.4% less than that of calculated by FEM, respectively, when the foundation depth b/d was equal to 6.0. However, the differences were only 29.5% and/or 16.4% for clay and/or sand ground based on two different calculation methods, respectively, when the foundation depth b/d was equal to 1.0. In the Chinese Code (2007), the effective culvert foundation depth was considered to be less than four times the foundation width. The characteristic value of the ground bearing capacity of HRC culverts, as calculated by the code, was underestimated. 3.2. Effect of culvert foundation width This section investigates the effect of foundation width on ground bearing capacity. For the parametric study, the culvert foundation width (b) ranged from 1 m to 14 m, and the foundation depth (d) remained constant at 10 m. To be noticed, in the Chinese Code (2007), the effective culvert foundation width varied from 2 m to 10 m [24]. To analyze the effect of culvert foundation width on the characteristic values of sand and clay ground bearing capacities, a ratio of s/b = 2% was used. Fig. 6 shows that the characteristic value of sand ground bearing capacity increased nonlinearly with foundation width. The characteristic value of sand ground bearing capacity increased by 44.8% and/or 50.4% for FEM and/or code method, respectively, when the culvert foundation width increased from 1 m to 14 m. However, the characteristic value of clay ground bearing capacity did not change significantly. These results were in reasonable agreement with the results calculated by the Chinese Code
This section investigates the effect of loading rate of backfill on ground bearing capacity. The backfill over the culvert was filled step by step during the construction of the HRC culvert. The subgrade layer of clay was compressed and consolidated gradually as the height of the backfill over the culvert increased. The ground bearing capacity can potentially improve with the consolidation of the soil during backfilling. For the parametric study, the waiting time for each step (0.5 m) ranged from a very small value to 50d. The subgrade layer fails when the backfill on the ground reaches a certain height. The failure pressure of the subgrade layer is considered as the limited ground bearing capacity, which is determined by the average foundation pressure–settlement (p–s) curve. According to the Chinese Code (2007) [24], it is equal to an average foundation pressure, which produces a specific foundation settlement ratio (i.e., s/b = 4% for high-fill RC culvert). The limited ground bearing capacity varied with loading rate of the backfill and permeability of the clay layer, as shown in Fig. 7. The limited ground bearing capacity decreased nonlinearly with the backfilling rate and decreased rapidly when the loading rate changed from 0.1 m/d to 100 m/d (e.g., it decreased by 62.2% when the permeability of the clay is equal to 0.01 m/d). Moreover, the limited ground bearing capacity decreased with a decrease in the permeability coefficient (k) of the clay. The influence of the permeability coefficient on ground bearing capacity became more evident with lower permeability coefficients. During backfilling, the maximum excess pore pressure was generated in the center of the clay layer under the centerline of the embankment. Fig. 8 shows that the maximum excess pore pressure increased nonlinearly with the backfilling rate (H = 6.0 m, the limit height of backfill was 6.0 m when the permeability was 0.001 m/d and the loading rate was fast enough). The maximum excess pore pressure increased rapidly when the loading rate increased from 0.1 m/d to 100 m/d (e.g., it increased by 95 times when the permeability of the clay is equal to 0.01 m/d). The maximum excess pore pressure increased when the permeability coefficient of the clay layer decreased. 3.4. Summary Engineers typically believe that insufficient ground bearing capacity under HRC culverts induces failure in the subgrade layer, which eventually results in integrity problems in HRC culverts. 1050
sand by FEM sand by code
3000
clay by FEM clay by code
Characteristic value of ground bearing capacity (kPa)
Characteristic value of ground bearing capacity (kPa)
3500
2500 2000 1500 1000 500 0
1
2
3
4
5
6
Foundation depth d/b Fig. 5. Variation in the characteristic value of ground bearing capacity versus foundation depth.
900 750 600
sand by FEM sand by code
450
clay by FEM clay by code
300 150 0
0
2
4
6
8
10
12
14
Foundation width (m) Fig. 6. Variation in the characteristic value of ground bearing capacity versus foundation width.
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Limited ground bearing capacity (kPa)
500
400
300
200
k=0.100 (m/d) k=0.010 (m/d) k=0.001 (m/d)
100 1.E-02
1.E-01
1.E+00
1.E+01
1.E+02
1.E+03
Backfilling rate (m /d) Fig. 7. Variation in ultimate ground bearing capacity versus backfilling rate.
However, the results of the study in this section indicated that the foundation depth and foundation width have positive effects on ground bearing capacity. Moreover, slowly backfilling rate is beneficial to the consolidation of the subgrade layer, thus, enhance the ground bearing capacity. Therefore, if these factors are not considered, ground bearing capacity is usually underestimated. Moreover, the study in Section 2 shows that the difference of the average foundation and embankment pressures at the culvert foundation level decreased with the distance from the culvert axis. Based on the field test, when the distance was larger than the culvert foundation width, the differential pressure between average foundation and embankment pressures is less than 10%. Thus, it is highly unlikely that failure of the subgrade layer beneath the culvert foundation will occur if the subgrade layer can bear the dead weight of the fill mass adjacent to the culvert. Damage to HRC culverts are rarely caused by subgrade layer failure beneath the culvert foundation. In contrast, if the ground bearing capacity of an HRC culvert is underestimated, the adoption of an improper ground treatment method to reinforce the subgrade layer may result in structural damage. This issue is discussed in the next section. 4. Ground treatment under HRC culverts Ground treatments are often adopted to enhance the ground bearing capacity, due to the underestimation of the ground bearing capacity of HRC culverts. However, improper ground treatments have significant impacts on culvert stress states and may cause structural damage. Numerical simulations were conducted to investigate the impact of ground treatment on culvert stress states by considering three important issues: (1) reinforcement stiffness after ground treatment, (2) reinforced ground depth and (3) reinforced ground width.
In the numerical model, the reinforced ground area (Fig. 1b) under the culvert foundation was the clay layer which was replaced by stiffer materials (e.g., compressed graded gravel or a compressed mixture of sand, gravel and cement). The numerical model was the same as the instrumented culvert as show in Fig. 1. The constitutive models of the materials, meshing and interface elements, boundary and loading conditions are the equivalent for the previous numerical model discussed in Section 2. The height of the backfill over the culvert was 18.0 m and the traffic load was not considered. Young’s modulus of reinforcement Ex was assumed and the reinforced width and reinforced depth of ground were Bx and Dx, respectively. To analyze the influencing factors (i.e., Ex, Dx and Bx) on the internal forces of the culvert, the normal force, shear force and bending moment were converted into dimensionless variables that are defined as
KN ¼
Nmx ; N0
KQ ¼
Q mx Q0
and K M ¼
Mmx M0
ð1Þ
where KN is the coefficient of the culvert normal force; Nmx is the maximum normal force of the culvert when the values of the investigated influencing factors are equal to Ex, Dx or Bx; and N0 is the maximum normal force of the culvert when the values of the investigated influencing factors are equal to initial values (E0 = 10 MPa, D0 = 0 m or B0 = 10 m). KQ and KM are the coefficients of the culvert shear force and bending moment, respectively; Qmx and Mmx are the maximum shear force and maximum bending moment, respectively, of the culvert when the values of investigated influencing factors are equal to Ex, Dx or Bx; Q0 and M0 are the maximum shear force and maximum bending moment, respectively, of the culvert when the values of the investigated influencing factors are equal to initial values (E0 = 10 MPa, D0 = 0 m or B0 = 10 m). 4.1. Effect of reinforcement stiffness This section investigates the effect of Young’s modulus of reinforcement (Ex) on culvert stress states. The reinforced ground width was 10 m and the reinforced ground depth was 6 m. For the parametric study, Ex ranged from 10 MPa to 500 MPa, and the initial value of Young’s modulus E0 was equal to 10 MPa. The variations in vertical earth pressure on the culvert, average foundation pressure and internal force coefficients are presented in Fig. 9. Vertical earth pressure on the culvert and average foundation pressure initially increased nonlinearly with Young’s modulus of reinforcement and subsequently approached limiting values at higher Young’s moduli (Fig. 9a and b). Fig. 9c shows that the internal force coefficients of the culvert (KN, KQ, KM) increased nonlinearly with Young’s modulus of reinforcement and approached asymptotic values at higher Young’s moduli.
Maximum excess pore pressure (kPa)
4.2. Effect of reinforced ground depth 120
90
k=0.100 (m/d) k=0.010 (m/d) k=0.001 (m/d)
60
30
0 1.E-02
1.E-01
1.E+00
1.E+01
1.E+02
1.E+03
Backfilling rate (m /d) Fig. 8. Variation in maximum excess pore pressure versus backfilling rate (H = 6.0 m).
This section investigates the effect of reinforced ground depth on culvert stress states. For the parametric study, the reinforced ground depth (Dx) ranged from 0 m to 6 m. Other parameters include a reinforced ground width under the culvert of 10 m, Young’s modulus of reinforcement of 40 MPa and an initial value of the reinforced depth (D0) of 0 m. Variations in vertical earth pressure on the culvert, average foundation pressure and internal force coefficients versus reinforced ground depth are presented in Fig. 10. The vertical earth pressure and average foundation pressure increased nonlinearly with reinforced ground depth. However, the increase of vertical earth pressure on the culvert was more gradual than the increase of average foundation pressure. The culvert internal force coefficients also increased nonlinearly with reinforced ground depth.
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800
495
Average foundation pressure (kPa)
Vertical earth pressure on culvert (kPa)
500
490 485 480 475 470 465
0
200
400
750 700 650 600 550
600
0
Young's modulus of reinforcement (MPa) (a) Pressure on culvert
100
200
300
400
500
Young's modulus of reinforcement (MPa) (b) Average foundation pressure
Culvert’s internal force coefficients
1.40 1.30 1.20
KN KQ KM
1.10 1.00 0
100
200
300
400
500
Young's modulus of reinforcement (MPa) (c) Internal force coefficients
480
680
470
660
Average foundation pressure (kPa)
Vertical earth pressure on culvert (kPa)
Fig. 9. Influence of reinforcement stiffness on culvert stress states. (a) Pressure on culvert. (b) Average foundation pressure. (c) Internal force coefficients.
460 450 440 430 420 410 400
0
1
2
3
4
5
640 620 600 580 560 540
6
0
1
2
3
4
5
6
Reinforced ground depth (m)
Reinforced ground depth (m)
(b) Average foundation pressure
(a) Pressure on culvert
Culvert’s internal force coefficients
1.40
KN KQ KM
1.30 1.20 1.10 1.00 0
1
2
3
4
5
6
Reinforced ground depth (m) (c) Internal force coefficients Fig. 10. Influence of reinforced ground depth on culvert stress states. (a) Pressure on culvert. (a) Pressure on culvert. (c) Internal force coefficients.
4.3. Effect of reinforced ground width This section investigates the effect of reinforced ground width on culvert stress states. For the parametric study, the reinforced ground width (Bx) ranged from b to (b + 6h). Other parameters
include a reinforced ground depth of 6 m, Young’s modulus of reinforcement (Ex) of 40 MPa and initial value of reinforced width (B0) of 10 m, which is equal to b. Variations in vertical earth pressure on the culvert, average foundation pressure and internal force coefficients versus
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700
470
Average foundation pressure (kPa)
Vertical earth pressure on culvert (kPa)
480
460 450 440
Bx=b+3h =
430 420 10
20
30
40
50
650 600 550
Bx=b+3h
500 450 10
60
Reinforced ground width (m)
20
30
40
50
60
Reinforced ground width (m) (b) Average foundation pressure
(a) Pressure on culvert
Culvert’s internal force coefficients
1.00
KN KQ KM
0.95 0.90 0.85
Bx=b+3h h
0.80 0.75 0.70 10
20
30
40
50
60
Reinforced ground width (m) (c) Internal force coefficients Fig. 11. Influence of reinforced ground width on culvert stress states. (a) Pressure on culvert. (b) Average foundation pressure. (c) Internal force coefficients.
reinforced ground width are presented in Fig. 11. Fig. 11a and b illustrates that the vertical earth pressure and average foundation pressure decreased nonlinearly with reinforced ground width and approach limiting values at higher reinforced ground widths. The results indicated that the vertical earth pressure concentration on the culvert gradually decreased with an increase in reinforced ground width. However, this trend is not apparent at larger reinforced ground widths. Fig. 11c shows that the culvert internal force coefficients (KN, KQ and KM) decrease nonlinearly with reinforced ground width and approached asymptotic values at higher reinforced ground widths. When Bx increased from b to (b + 3h), the coefficients of normal force, shear force and bending moment decreased by 20%, 24% and 27%, respectively. However, the increments are less than 1.5% when Bx increased from (b + 3h) to (b + 6h). 4.4. Summary In current engineering design, culvert integrity is believed to benefit from ground treatment because it increases ground bearing capacity. However, this finding was not always evident from the study discussed in this section. Generally, the vertical load acting on the culvert, average foundation pressure and culvert internal forces significantly increase with reinforcement stiffness and reinforcement thickness. Culvert damage tends to occur easily if the subgrade layer after treatment is extremely stiff. A stiffer and thicker reinforcement is neither safe nor economical. Therefore, proper ground treatments should not only consider ground bearing capacity and allowable settlement but also culvert stress states. This section also investigated reinforcement width, which is another aspect of ground treatment. Loads acting on the culvert and culvert internal forces generally decreased with reinforcement width. A wider reinforcement width is beneficial to culvert integrity, although the benefits are not cost-effective when the width is excessively large (e.g., larger than b + 3h). Overall, when considering similar budgets, a wide and shallow reinforced area in the subgrade layer with proper stiffness is
suggested instead of a narrow and deep reinforcement with excessive stiffness. 5. Conclusions and suggestions Based on the results of the field survey, structural damage to HRC culverts occur frequently. This study was performed to investigate the influence of soil properties on the integrity of HRC culverts. A numerical method was adopted to conduct a parametric analysis. A basic numerical model was established and validated based on field tests. Subsequently, the numerical model was expanded to investigate two important issues: ground bearing capacity and ground treatment. In Section 3, the ground bearing capacity of an HRC culvert was determined generally to increase with foundation depth and foundation width. A lower loading rate of backfilling was also determined to be beneficial to ground bearing capacity, due to the consolidation of the subgrade layer. Therefore, the ground bearing capacity is underestimated if these factors are not considered. In Section 4, the influence of ground treatment on culvert stress state was investigated. A wide and shallow reinforced area in the subgrade layer with proper stiffness is superior to a narrow and deep reinforced area with excessive stiffness because the latter produces a higher stress concentration on the culvert. To be noted, the box culvert wall thickness has effect on the slab stiffness, and this effect may influence the vertical load on the top of culvert. However, this paper mainly focuses on the impact of soil properties on structural stress states of culvert. The factor of culvert wall thickness will be considered in further researches. In summary, through the comprehensive analysis performed in this study, the ground bearing capacity in HRC culvert design should consider the effects of foundation depth, foundation width and subgrade layer consolidation. Overemphasizing reinforcement stiffness and thickness has the potential to produce additional internal forces in the culvert which can result in potential structural damage. Moreover, the selection of ground treatments should
B. Chen, L. Sun / Computers and Geotechnics 52 (2013) 46–53
include consideration of foundation uniformity with regards to total settlement requirements. Acknowledgments This work was supported by the National Natural Science Foundation of China (Grant No. 51108434), the Natural Science Foundation of Hubei Province of China (Grant No. 2010CDB04201) and theFundamental Research Funds for the Central Universities (Grant No. CUG130408). The authors would like to express their appreciation for these foundations’ financial assistance. The authors would also like to thank J. Zhao of the Ecole Polytechnique Fédérale de Lausanne for useful discussions, which helped to improve the quality of this paper. References [1] Zhang SB, Zheng, JJ, Chen BG, et al. Study and application of structure stress characteristics and ground treatment under high fill of expressway in mountain area. Technical report, Wuhan; 2008 [in Chinese]. [2] China Highway Planning and Design Institute. Code for design of highway reinforced concrete and prestressed concrete bridges and culverts (JTG D62). Beijing: China Communications Press; 2004 [in Chinese]. [3] Dasgupta A, Sengupta B. Large-scale model test on square box culvert backfilled with sand. J Geotech Eng 1991;117(1):156–61. [4] Zheng JJ, Zhao JB, Chen BG. Vertical earth pressure on culverts under high embankments. Chin J Geotech Eng 2009;31(7):1009–13 [in Chinese]. [5] Kang J, Parker F, Yoo CH. Soil–structure interaction for deeply recess corrugated steel pipes Part I: embankment installation. Eng Struct 2008;30(2):384–92. [6] Elachachi SM, Breysse AD. The effects of soil spatial variability on the reliability of rigid buried pipes. Comput Geotech 2012;43:61–71. [7] Marston A, Anderson AO. The theory of loads on pipes in ditch and tests of cement and clay drain tile and sever pipe. Bulletin No. 31. Ames: Iowa Engineering Experiment Station; 1913.
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[8] Marston A. The theory of external loads on closed conduits in the light of the latest experiments. Bulletin No. 96. Ames: Iowa Engineering Experiment Station; 1930. [9] Spangler MG. The supporting strength of rigid pipe culverts. Bulletin No. 112. Iowa: Iowa State College; 1933. [10] Spangler MG. A theory on loads on negative projecting conduits. In: Proc highway research board, Washington (DC); 1950. p. 153–61. [11] Karinski YS, Dancygier AN, Leviathan I. An analytical model to evaluate the static soil pressure on a buried structure. Eng Struct 2003;25(1):91–101. [12] Kim K, Yoo CH. Design loading on deeply buried box culverts. J Geotech Geoenviron Eng 2005;131(1):20–7. [13] Bennett RM, Wood SM, Drumm EC, Rainwater NR. Vertical loads on concrete box culverts under high embankments. J Bridge Eng 2005;10(6):643–9. [14] Kang J, Parker F, Yoo CH. Soil–structure interaction and imperfect trench installations for deeply buried concrete pipes. J Geotech Geoenviron Eng 2007;133(3):277–85. [15] Kang J, Parker F, Yoo CH. Soil–structure interaction for deeply buried corrugated steel pipes Part II: Imperfect trench installation. Eng Struct 2008;30(3):588–94. [16] McGuigan BJ, Valsangkar AJ. Earth processes on twin positive projecting and induced trench box culverts under high embankments. Can Geotech J 2011;48(2):173–85. [17] McGuigan BJ, Valsangkar AJ. Centrifuge testing and numerical modeling of box culverts installed in induced trench. Can Geotech J 2010;47(2):147–63. [18] McAffee RP, Valsangkar AJ. Field performance, centrifuge testing, and numerical modelling of an induced trench installation. Can Geotech J 2008;45(1):85–101. [19] Heger FJ, McGrath TJ. Design method for reinforced concrete pipe and box sections. Vienna: American Concrete Pipe Association; 1982. [20] Chen BG, Zheng JJ, Zhang SB, Ma Q, Zhao JB. Field test and numerical simulation of ground treatment for culverts under high embankments. Rock Soil Mech 2009;30(5):1483–9 [in Chinese]. [21] Chen BG, Zheng JJ, Lu YE. Soil–structure interaction of unsymmetrical trench installation culvert. J Southeast Univ 2009;25(1):94–8. [22] Chen BG, Zheng JJ, Han J. Experimental study and numerical simulation on concrete box culverts in trenches. J Perform Constr Fac 2010;24(3):223–34. [23] Vermeer PA, Brinkgreve RBJ. Finite element code for soil and rock analysis. Rotterdam: Balkema A.A.; 1998. [24] China Highway Planning and Design Institute. Code for design of ground base and foundation of highway bridges and culverts (JTG-D63). Beijing: China Communications Press; 2007 [in Chinese].
Contents lists available at SciVerse ScienceDirect
Computers and Geotechnics journal homepage: www.elsevier.com/locate/compgeo
Technical Communication
The impact of soil properties on the structural integrity of high-fill reinforced concrete culverts Baoguo Chen a,⇑, Liang Sun b a
China University of Geosciences (Wuhan), Engineering Faculty, 388 Lu-mo Road, Hongshan District, Wuhan 430074, China Ecole Polytechnique Fédérale de Lausanne (EPFL), School of Architecture, Civil and Environmental Engineering (ENAC), Laboratory for Rock Mechanics (LMR), Station 18, CH-1015 Lausanne, Switzerland b
a r t i c l e
i n f o
Article history: Received 2 September 2012 Received in revised form 27 March 2013 Accepted 29 March 2013 Available online 24 April 2013 Keywords: Culvert Structural integrity High fill Ground bearing capacity Ground treatment
a b s t r a c t Reinforced concrete (RC) culverts under high fill have been widely used in the construction of expressways and railways. Based on the results of a field survey, various types of structural damage to RC culverts occur during construction and service periods. In this study, numerical simulation and field tests were conducted to investigate the impact of soil properties on the structural integrity of RC culverts under high fill. Important factors that influence culvert integrity, such as ground bearing capacity and ground treatment, have been analyzed in detail. Research findings indicate that damage to RC culverts under high fill is not typically caused by failure to the subgrade layer under the culvert foundation, due to the beneficial effects of foundation depth, foundation width and subgrade layer consolidation. Structural damage is probably caused by improper ground treatment strategies. Proper strategies for preventing integrity problems are recommended based on the research. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction High-fill reinforced concrete (HRC) culverts have been widely used as substructures for water, vehicle and pedestrian conveyance. The results of a random field survey of 102 HRC culverts, which were located on highways in five provinces (Hunan, Hubei, Sichuan, Shanxi and Henan) in China, demonstrated that structural problems occur frequently in culverts [1]. Typical characteristics of damaged HRC culverts are summarized in Table 1, which shows that the ratio of damaged culverts to total surveyed culverts is 59.8%. In particular, the damage ratios of slab culverts, arch culverts, pipe culverts and box culverts are 64.8%, 54.8%, 63.6% and 33.3%, respectively. Significant damage characteristics include structural cracks and differential settlements of culvert foundations. In this survey, the damaged culvert is defined as the crack width on the culvert is more than 0.2 mm or the differential foundation settlement is more than 30 mm based on the Chinese Code for Design of Highway Reinforced Concrete and Prestressed Concrete Bridges and Culverts [2]. These problems occur in HRC culverts for two important reasons: (1) vertical earth pressure on culverts and (2) impact of soil properties on culverts. Compression of the backfill mass at both sides of the culvert is larger than that of the RC culvert due to the differential stiffness. Thus, vertical earth pressure concentrates ⇑ Corresponding author. Tel.: +86 27 67883074; fax: +86 27 67883507. E-mail addresses: [email protected] (B. Chen), liang.sun@epfl.ch (L. Sun). 0266-352X/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.compgeo.2013.03.006
on the top of RC culverts [3,4]. The vertical earth pressure concentration on culverts will be more significant for a larger differential stiffness between a culvert and its adjacent backfill [5,6]. Marston pioneered the research concerning vertical earth pressure on culverts based on analytical and experimental methods [7,8]. Following the research of Marston, Spangler [9,10] analyzed the vertical earth pressure on rigid pipe culverts and discussed the key factors that influence the load on underground conduits. Karinski et al. [11] investigated vertical earth pressure on rigid culverts under fill and traffic loads through theoretical analysis and discussed the influence of structural deformation and dimension on vertical earth pressure. Kim and Yoo [12] examined vertical earth pressure on rectangular culverts under three different installation conditions (embankment installation, trench installation and imperfect trench installation) by numerical simulation. Bennett et al. [13] studied the structure stress states and vertical earth pressure on RC box culverts by conducting field tests and found that the height of the backfill over the culvert was the main factor that influenced vertical earth pressure and internal structural forces. Kang et al. [5,14,15] analyzed the soil–culvert interaction under two conditions, i.e., imperfect trench installation and embankment installation, using numerical simulation. Valsangkar et al. [16–18] investigated the backfill–culvert interaction and detected the earth pressure acting on culvert under embankment installation and induced trench installation conditions, using field and centrifuge test and numerical simulation. These studies thoroughly addressed the subject of vertical earth pressure on culverts and the relationship
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B. Chen, L. Sun / Computers and Geotechnics 52 (2013) 46–53 Table 1 Survey results of collapsed culverts. Culvert types
Culvert amount
Typical damage characteristics
Amount of damaged culverts
Damage ratio of different damage characteristics (%)
Damage ratio of different culvert types (%)
Slab culvert
54
Longitudinal crack on top slab Diagonal crack on culvert body Differential settlement of foundation Water permeation under foundation
14 10 7 4
25.9 18.5 13.0 7.4
64.8
Arch culvert
31
Diagonal crack on culvert body Longitudinal crack near the skewback Differential settlement of foundation Water permeation under the foundation
3 6 5 3
9.7 19.4 16.1 9.7
54.8
Pipe culvert
11
Large settlement at the center of pipe Longitudinal crack on culvert body Foundation crack and differential settlement
2 3 2
18.2 27.3 18.2
63.6
Box culvert
6
Differential settlement of foundation Foundation crack and gaps among culvert sections
1 1
20.0 20.0
33.3
between fill load and structural stress states. However, few studies have focused on the impact of soil properties on the structural integrity and stress states of HRC culverts. When investigating the structural integrity and stress states of HRC culverts, the mechanical properties of the subgrade layer cannot be disregarded [19–22]. The objective of this study is to discuss how the following two principal issues affect HRC culvert stress states and integrity: (1) the ground bearing capacity of HRC culverts and (2) ground treatment of HRC culverts.
possible point loads or other stress distortions induced by large size particles in the backfill. Eight earth pressure cells were placed at the foundation level (two under the culvert foundation and six at the sides of the culvert at the same level). 2.2. Numerical model Accordingly, the problem selected for the numerical analysis was based on the instrumented HRC culvert. A finite element analysis is carried out using the software PLAXIS to investigate the abovementioned issues. In the numerical model, the two side boundaries of the model were horizontally restrained, while the bottom of the model was fixed. The ground water surface was assumed to be located at the bottom line of the culvert foundation. The loading procedure followed an actual installation regulation. The 15-noded triangular elements were used to generate the mesh of the model. Fine meshing was chosen for the soil–culvert system. Slippage was allowed to occur between the soil and the culvert, where five pairs of interface elements were used to model the slippage between the soil and the structure. The interface elements have zero thickness and were modeled by an elastic–plastic relation with the Mohr–Coulomb criterion. The strength properties of the interfaces were defined as the strength properties of the corresponding soil layer multiplied by a strength reduction factor (Rinter). In this study, strength reduction factors of 0.8 and 0.5 were used for sand/gravel and clay, respectively [23].
2. Numerical simulation 2.1. Description of the instrumented culvert Field test results were used to validate the numerical model. The instrumented HRC culvert was 8 m high and 10 m wide. The instrumented section was located approximately in the center of the culvert length (Fig. 1a). The subgrade layers consisted of a layer of clay, a layer of fully weathered mudstone and a stiff layer of moderately weathered mudstone. During the construction procedure, the excavation depth of the clay layer, which was replaced by quartz sand, was 3.5 m. The backfill on the culvert was 18.0 m high and was filled step by step; each step was 0.5 m thick. During the backfilling procedure, the installation time was 10 days per layer. Vibrating-wire earth pressure cells (JMZX-50xxA, 210 mm diameter and 12 mm thickness) were used to record the foundation pressure and the embankment pressure at the foundation level (Fig. 1b). The pressure cells were fixed to the subgrade layer. A quick setting high strength grout pad was used to assure uniform contact between the pressure cells and the subgrade layer. Medium sand was used to cover the cell to protect the cell from
backfill
2.3. Material parameters The weathered mudstone layers and sand, as well as backfill over the culvert were modeled by Mohr–Coulomb elastoplastic
backfill
embankment centerline
b=10
fully weathered mudstone moderately weathered mudstone
(a) Cross section of embankment
clay
D x h=8
7.2
6
6
clay
4
culvert foundation
15
7.2 6
1
8
culvert
4 4 4
culvert pressure cells
Bx
foundation level Reinforced area 4 4 4
fully weathered mudstone moderately weathered mudstone
(b) Cross section of culvert
Fig. 1. Field layout of the instrumented culvert (units in meters). (a) Cross section of embankment. (b) Cross section of culvert.
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B. Chen, L. Sun / Computers and Geotechnics 52 (2013) 46–53
Average foundation pressure (kPa)
materials. The clay layer was modeled by Cam-Clay soft soil material. Although in nonconservative design, the RC culverts are designed to crack. The cracking means that the stiffness changes between the walls and the slab midspan, which lead to load redistribution on the box culvert. The stiffness of slab with cracks is impacted by crack width, crack length, crack spacing, etc. It varies with cracking degree. However, a tentative study was conducted using numerical simulation, which shows that the vertical load on culvert decreases by about 12% when the stiffness of culvert top slab reduces by 50%. This study is a first approximation, where reinforced concrete response was assumed to be linear and elastic. The material properties used in the numerical models are presented in Table 2.
550 500 450 400 350 300
Field test numerical simulation
250 200 3.0
6.0
9.0
12.0
15.0
18.0
Height of backfill over culvert (m) Fig. 2. Variation in average foundation pressure versus backfill height.
The numerical simulation was compared with the field tests. Fig. 2 presents the variations in the average foundation pressure at the centerline of the embankment versus the height of the backfill. Fig. 3 presents the distribution of the earth pressure at the foundation level. The difference between field test data and numerical results is about 10%. It is believed as a reasonable agreement because only qualitative comparison can be made due to the limitations of the field tests. The validation demonstrated that the numerical simulation could be used for further analysis. Results of the field test and numerical simulation revealed that the average foundation pressure increased with an increase in backfill height. The analysis showed that the earth pressure was unevenly distributed at the level of the culvert foundation. The embankment pressure at both sides of the culvert foundation was lower than the backfill overburden, due to the friction of the culvert sidewalls; however, the pressure approached the backfill overburden as the distance from the culvert axis increased.
Pressure at foundation level (kPa)
2.4. Validation 600
Field test
Numerical result H=16.5 m
450
H=10.5 m H=3.5 m
300
150 -20 -16 -12
-8
-4
0
4
8
12
16
20
Distance from the culvert axis (m) Fig. 3. Distribution of earth pressure at the culvert foundation level.
used in the numerical model are the same as the material properties presented in Table 2. 3.1. Effect of culvert foundation depth
3. Ground bearing capacity of HRC culverts A lower ground bearing capacity of HRC culverts may induce structural damage. The cone penetration test and dynamic sounding are the prevailing methods used to determine ground bearing capacity. However, these methods do not consider the following effects: (1) foundation depth, (2) foundation width and (3) loading rate of backfill. In this study, numerical simulations were conducted to analyze the influence of these factors on the ground bearing capacity of HRC culverts. The material model and numerical model in these simulations were the same as that of the former presented. The numerical model was shown in Fig. 4. In the numerical model, the dimensions of the culvert were the same as the instrumented culvert. For box culverts, foundation depth (d) was the sum of the culvert height (h) and the backfill height on culvert (H). The backfill on the culvert was filled step by step, and each step was filled in 10 days with a thickness of 0.5 m. The material properties
This section investigates the effect of foundation depth on ground bearing capacity. In the parametric study, the foundation depth (d/b) ranged from 1 to 6. For comparison purposes, two different types of subgrade layer (clay and sand) were considered in this analysis. Furthermore, a surface load was applied to the backfill to investigate the variation in foundation settlement versus average foundation pressure for different foundation depths. The surface load was increased sequentially by 50 kPa for each load grade. The characteristic value of ground bearing capacity is generally considered to be the main reference in culvert design. This value is determined by the average foundation pressure–settlement (p–s) curve. According to the Chinese Code for Design of Ground Base and Foundation of Highway Bridges and Culverts [24], the characteristic value of ground bearing capacity is equal to an average foundation pressure, which produces a specific foundation settlement ratio (i.e., s/b = 2%). The characteristic values of ground bearing capacity versus foundation depths for clay and sand ground are
Table 2 Parameters in the numerical analysis. Parameters
Unit
Culvert
Backfill
Clay
Sand
Fully weathered mudstone
Moderately weathered mudstone
Young’s modulus Poisson’s ratio Effective cohesion Effective friction angle Effective dilatancy angle Permeability Unit weight
MPa – kPa Degree Degree m/d kN/m3
30000.0 0.20 – – – – 25.0
28.0 0.27 6.0 29.5 5.0 1.20 19.6
6.8 0.35 16.6 14.7 0 0.01 17.9
19.6 0.30 0 33.5 2.0 25.0 19.5
42.0 0.25 26.0 19.0 4.0 1.00 20.2
56.0 0.24 30.0 28.0 8.0 0.70 21.8
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B. Chen, L. Sun / Computers and Geotechnics 52 (2013) 46–53
(2007) [24]. The results concluded that the effect of foundation width on the characteristic value of the ground bearing capacity of sand but not of clay should be considered in HRC culvert design.
load
culvert
d
h H
backfill
3.3. Effect of loading rate of backfill
10b
b
ground soil
20b Fig. 4. Numerical model for the ground bearing capacity analysis.
presented in Fig. 5. The characteristic values of ground bearing capacities for clay and sand increased nonlinearly with foundation depth and nearly approached a limiting value. The characteristic values of ground bearing capacity for clay and/or sand calculated by Chinese Code (2007) method [24] were 38.3% and/or 30.4% less than that of calculated by FEM, respectively, when the foundation depth b/d was equal to 6.0. However, the differences were only 29.5% and/or 16.4% for clay and/or sand ground based on two different calculation methods, respectively, when the foundation depth b/d was equal to 1.0. In the Chinese Code (2007), the effective culvert foundation depth was considered to be less than four times the foundation width. The characteristic value of the ground bearing capacity of HRC culverts, as calculated by the code, was underestimated. 3.2. Effect of culvert foundation width This section investigates the effect of foundation width on ground bearing capacity. For the parametric study, the culvert foundation width (b) ranged from 1 m to 14 m, and the foundation depth (d) remained constant at 10 m. To be noticed, in the Chinese Code (2007), the effective culvert foundation width varied from 2 m to 10 m [24]. To analyze the effect of culvert foundation width on the characteristic values of sand and clay ground bearing capacities, a ratio of s/b = 2% was used. Fig. 6 shows that the characteristic value of sand ground bearing capacity increased nonlinearly with foundation width. The characteristic value of sand ground bearing capacity increased by 44.8% and/or 50.4% for FEM and/or code method, respectively, when the culvert foundation width increased from 1 m to 14 m. However, the characteristic value of clay ground bearing capacity did not change significantly. These results were in reasonable agreement with the results calculated by the Chinese Code
This section investigates the effect of loading rate of backfill on ground bearing capacity. The backfill over the culvert was filled step by step during the construction of the HRC culvert. The subgrade layer of clay was compressed and consolidated gradually as the height of the backfill over the culvert increased. The ground bearing capacity can potentially improve with the consolidation of the soil during backfilling. For the parametric study, the waiting time for each step (0.5 m) ranged from a very small value to 50d. The subgrade layer fails when the backfill on the ground reaches a certain height. The failure pressure of the subgrade layer is considered as the limited ground bearing capacity, which is determined by the average foundation pressure–settlement (p–s) curve. According to the Chinese Code (2007) [24], it is equal to an average foundation pressure, which produces a specific foundation settlement ratio (i.e., s/b = 4% for high-fill RC culvert). The limited ground bearing capacity varied with loading rate of the backfill and permeability of the clay layer, as shown in Fig. 7. The limited ground bearing capacity decreased nonlinearly with the backfilling rate and decreased rapidly when the loading rate changed from 0.1 m/d to 100 m/d (e.g., it decreased by 62.2% when the permeability of the clay is equal to 0.01 m/d). Moreover, the limited ground bearing capacity decreased with a decrease in the permeability coefficient (k) of the clay. The influence of the permeability coefficient on ground bearing capacity became more evident with lower permeability coefficients. During backfilling, the maximum excess pore pressure was generated in the center of the clay layer under the centerline of the embankment. Fig. 8 shows that the maximum excess pore pressure increased nonlinearly with the backfilling rate (H = 6.0 m, the limit height of backfill was 6.0 m when the permeability was 0.001 m/d and the loading rate was fast enough). The maximum excess pore pressure increased rapidly when the loading rate increased from 0.1 m/d to 100 m/d (e.g., it increased by 95 times when the permeability of the clay is equal to 0.01 m/d). The maximum excess pore pressure increased when the permeability coefficient of the clay layer decreased. 3.4. Summary Engineers typically believe that insufficient ground bearing capacity under HRC culverts induces failure in the subgrade layer, which eventually results in integrity problems in HRC culverts. 1050
sand by FEM sand by code
3000
clay by FEM clay by code
Characteristic value of ground bearing capacity (kPa)
Characteristic value of ground bearing capacity (kPa)
3500
2500 2000 1500 1000 500 0
1
2
3
4
5
6
Foundation depth d/b Fig. 5. Variation in the characteristic value of ground bearing capacity versus foundation depth.
900 750 600
sand by FEM sand by code
450
clay by FEM clay by code
300 150 0
0
2
4
6
8
10
12
14
Foundation width (m) Fig. 6. Variation in the characteristic value of ground bearing capacity versus foundation width.
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B. Chen, L. Sun / Computers and Geotechnics 52 (2013) 46–53
Limited ground bearing capacity (kPa)
500
400
300
200
k=0.100 (m/d) k=0.010 (m/d) k=0.001 (m/d)
100 1.E-02
1.E-01
1.E+00
1.E+01
1.E+02
1.E+03
Backfilling rate (m /d) Fig. 7. Variation in ultimate ground bearing capacity versus backfilling rate.
However, the results of the study in this section indicated that the foundation depth and foundation width have positive effects on ground bearing capacity. Moreover, slowly backfilling rate is beneficial to the consolidation of the subgrade layer, thus, enhance the ground bearing capacity. Therefore, if these factors are not considered, ground bearing capacity is usually underestimated. Moreover, the study in Section 2 shows that the difference of the average foundation and embankment pressures at the culvert foundation level decreased with the distance from the culvert axis. Based on the field test, when the distance was larger than the culvert foundation width, the differential pressure between average foundation and embankment pressures is less than 10%. Thus, it is highly unlikely that failure of the subgrade layer beneath the culvert foundation will occur if the subgrade layer can bear the dead weight of the fill mass adjacent to the culvert. Damage to HRC culverts are rarely caused by subgrade layer failure beneath the culvert foundation. In contrast, if the ground bearing capacity of an HRC culvert is underestimated, the adoption of an improper ground treatment method to reinforce the subgrade layer may result in structural damage. This issue is discussed in the next section. 4. Ground treatment under HRC culverts Ground treatments are often adopted to enhance the ground bearing capacity, due to the underestimation of the ground bearing capacity of HRC culverts. However, improper ground treatments have significant impacts on culvert stress states and may cause structural damage. Numerical simulations were conducted to investigate the impact of ground treatment on culvert stress states by considering three important issues: (1) reinforcement stiffness after ground treatment, (2) reinforced ground depth and (3) reinforced ground width.
In the numerical model, the reinforced ground area (Fig. 1b) under the culvert foundation was the clay layer which was replaced by stiffer materials (e.g., compressed graded gravel or a compressed mixture of sand, gravel and cement). The numerical model was the same as the instrumented culvert as show in Fig. 1. The constitutive models of the materials, meshing and interface elements, boundary and loading conditions are the equivalent for the previous numerical model discussed in Section 2. The height of the backfill over the culvert was 18.0 m and the traffic load was not considered. Young’s modulus of reinforcement Ex was assumed and the reinforced width and reinforced depth of ground were Bx and Dx, respectively. To analyze the influencing factors (i.e., Ex, Dx and Bx) on the internal forces of the culvert, the normal force, shear force and bending moment were converted into dimensionless variables that are defined as
KN ¼
Nmx ; N0
KQ ¼
Q mx Q0
and K M ¼
Mmx M0
ð1Þ
where KN is the coefficient of the culvert normal force; Nmx is the maximum normal force of the culvert when the values of the investigated influencing factors are equal to Ex, Dx or Bx; and N0 is the maximum normal force of the culvert when the values of the investigated influencing factors are equal to initial values (E0 = 10 MPa, D0 = 0 m or B0 = 10 m). KQ and KM are the coefficients of the culvert shear force and bending moment, respectively; Qmx and Mmx are the maximum shear force and maximum bending moment, respectively, of the culvert when the values of investigated influencing factors are equal to Ex, Dx or Bx; Q0 and M0 are the maximum shear force and maximum bending moment, respectively, of the culvert when the values of the investigated influencing factors are equal to initial values (E0 = 10 MPa, D0 = 0 m or B0 = 10 m). 4.1. Effect of reinforcement stiffness This section investigates the effect of Young’s modulus of reinforcement (Ex) on culvert stress states. The reinforced ground width was 10 m and the reinforced ground depth was 6 m. For the parametric study, Ex ranged from 10 MPa to 500 MPa, and the initial value of Young’s modulus E0 was equal to 10 MPa. The variations in vertical earth pressure on the culvert, average foundation pressure and internal force coefficients are presented in Fig. 9. Vertical earth pressure on the culvert and average foundation pressure initially increased nonlinearly with Young’s modulus of reinforcement and subsequently approached limiting values at higher Young’s moduli (Fig. 9a and b). Fig. 9c shows that the internal force coefficients of the culvert (KN, KQ, KM) increased nonlinearly with Young’s modulus of reinforcement and approached asymptotic values at higher Young’s moduli.
Maximum excess pore pressure (kPa)
4.2. Effect of reinforced ground depth 120
90
k=0.100 (m/d) k=0.010 (m/d) k=0.001 (m/d)
60
30
0 1.E-02
1.E-01
1.E+00
1.E+01
1.E+02
1.E+03
Backfilling rate (m /d) Fig. 8. Variation in maximum excess pore pressure versus backfilling rate (H = 6.0 m).
This section investigates the effect of reinforced ground depth on culvert stress states. For the parametric study, the reinforced ground depth (Dx) ranged from 0 m to 6 m. Other parameters include a reinforced ground width under the culvert of 10 m, Young’s modulus of reinforcement of 40 MPa and an initial value of the reinforced depth (D0) of 0 m. Variations in vertical earth pressure on the culvert, average foundation pressure and internal force coefficients versus reinforced ground depth are presented in Fig. 10. The vertical earth pressure and average foundation pressure increased nonlinearly with reinforced ground depth. However, the increase of vertical earth pressure on the culvert was more gradual than the increase of average foundation pressure. The culvert internal force coefficients also increased nonlinearly with reinforced ground depth.
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B. Chen, L. Sun / Computers and Geotechnics 52 (2013) 46–53
800
495
Average foundation pressure (kPa)
Vertical earth pressure on culvert (kPa)
500
490 485 480 475 470 465
0
200
400
750 700 650 600 550
600
0
Young's modulus of reinforcement (MPa) (a) Pressure on culvert
100
200
300
400
500
Young's modulus of reinforcement (MPa) (b) Average foundation pressure
Culvert’s internal force coefficients
1.40 1.30 1.20
KN KQ KM
1.10 1.00 0
100
200
300
400
500
Young's modulus of reinforcement (MPa) (c) Internal force coefficients
480
680
470
660
Average foundation pressure (kPa)
Vertical earth pressure on culvert (kPa)
Fig. 9. Influence of reinforcement stiffness on culvert stress states. (a) Pressure on culvert. (b) Average foundation pressure. (c) Internal force coefficients.
460 450 440 430 420 410 400
0
1
2
3
4
5
640 620 600 580 560 540
6
0
1
2
3
4
5
6
Reinforced ground depth (m)
Reinforced ground depth (m)
(b) Average foundation pressure
(a) Pressure on culvert
Culvert’s internal force coefficients
1.40
KN KQ KM
1.30 1.20 1.10 1.00 0
1
2
3
4
5
6
Reinforced ground depth (m) (c) Internal force coefficients Fig. 10. Influence of reinforced ground depth on culvert stress states. (a) Pressure on culvert. (a) Pressure on culvert. (c) Internal force coefficients.
4.3. Effect of reinforced ground width This section investigates the effect of reinforced ground width on culvert stress states. For the parametric study, the reinforced ground width (Bx) ranged from b to (b + 6h). Other parameters
include a reinforced ground depth of 6 m, Young’s modulus of reinforcement (Ex) of 40 MPa and initial value of reinforced width (B0) of 10 m, which is equal to b. Variations in vertical earth pressure on the culvert, average foundation pressure and internal force coefficients versus
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700
470
Average foundation pressure (kPa)
Vertical earth pressure on culvert (kPa)
480
460 450 440
Bx=b+3h =
430 420 10
20
30
40
50
650 600 550
Bx=b+3h
500 450 10
60
Reinforced ground width (m)
20
30
40
50
60
Reinforced ground width (m) (b) Average foundation pressure
(a) Pressure on culvert
Culvert’s internal force coefficients
1.00
KN KQ KM
0.95 0.90 0.85
Bx=b+3h h
0.80 0.75 0.70 10
20
30
40
50
60
Reinforced ground width (m) (c) Internal force coefficients Fig. 11. Influence of reinforced ground width on culvert stress states. (a) Pressure on culvert. (b) Average foundation pressure. (c) Internal force coefficients.
reinforced ground width are presented in Fig. 11. Fig. 11a and b illustrates that the vertical earth pressure and average foundation pressure decreased nonlinearly with reinforced ground width and approach limiting values at higher reinforced ground widths. The results indicated that the vertical earth pressure concentration on the culvert gradually decreased with an increase in reinforced ground width. However, this trend is not apparent at larger reinforced ground widths. Fig. 11c shows that the culvert internal force coefficients (KN, KQ and KM) decrease nonlinearly with reinforced ground width and approached asymptotic values at higher reinforced ground widths. When Bx increased from b to (b + 3h), the coefficients of normal force, shear force and bending moment decreased by 20%, 24% and 27%, respectively. However, the increments are less than 1.5% when Bx increased from (b + 3h) to (b + 6h). 4.4. Summary In current engineering design, culvert integrity is believed to benefit from ground treatment because it increases ground bearing capacity. However, this finding was not always evident from the study discussed in this section. Generally, the vertical load acting on the culvert, average foundation pressure and culvert internal forces significantly increase with reinforcement stiffness and reinforcement thickness. Culvert damage tends to occur easily if the subgrade layer after treatment is extremely stiff. A stiffer and thicker reinforcement is neither safe nor economical. Therefore, proper ground treatments should not only consider ground bearing capacity and allowable settlement but also culvert stress states. This section also investigated reinforcement width, which is another aspect of ground treatment. Loads acting on the culvert and culvert internal forces generally decreased with reinforcement width. A wider reinforcement width is beneficial to culvert integrity, although the benefits are not cost-effective when the width is excessively large (e.g., larger than b + 3h). Overall, when considering similar budgets, a wide and shallow reinforced area in the subgrade layer with proper stiffness is
suggested instead of a narrow and deep reinforcement with excessive stiffness. 5. Conclusions and suggestions Based on the results of the field survey, structural damage to HRC culverts occur frequently. This study was performed to investigate the influence of soil properties on the integrity of HRC culverts. A numerical method was adopted to conduct a parametric analysis. A basic numerical model was established and validated based on field tests. Subsequently, the numerical model was expanded to investigate two important issues: ground bearing capacity and ground treatment. In Section 3, the ground bearing capacity of an HRC culvert was determined generally to increase with foundation depth and foundation width. A lower loading rate of backfilling was also determined to be beneficial to ground bearing capacity, due to the consolidation of the subgrade layer. Therefore, the ground bearing capacity is underestimated if these factors are not considered. In Section 4, the influence of ground treatment on culvert stress state was investigated. A wide and shallow reinforced area in the subgrade layer with proper stiffness is superior to a narrow and deep reinforced area with excessive stiffness because the latter produces a higher stress concentration on the culvert. To be noted, the box culvert wall thickness has effect on the slab stiffness, and this effect may influence the vertical load on the top of culvert. However, this paper mainly focuses on the impact of soil properties on structural stress states of culvert. The factor of culvert wall thickness will be considered in further researches. In summary, through the comprehensive analysis performed in this study, the ground bearing capacity in HRC culvert design should consider the effects of foundation depth, foundation width and subgrade layer consolidation. Overemphasizing reinforcement stiffness and thickness has the potential to produce additional internal forces in the culvert which can result in potential structural damage. Moreover, the selection of ground treatments should
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include consideration of foundation uniformity with regards to total settlement requirements. Acknowledgments This work was supported by the National Natural Science Foundation of China (Grant No. 51108434), the Natural Science Foundation of Hubei Province of China (Grant No. 2010CDB04201) and theFundamental Research Funds for the Central Universities (Grant No. CUG130408). The authors would like to express their appreciation for these foundations’ financial assistance. The authors would also like to thank J. Zhao of the Ecole Polytechnique Fédérale de Lausanne for useful discussions, which helped to improve the quality of this paper. References [1] Zhang SB, Zheng, JJ, Chen BG, et al. Study and application of structure stress characteristics and ground treatment under high fill of expressway in mountain area. Technical report, Wuhan; 2008 [in Chinese]. [2] China Highway Planning and Design Institute. Code for design of highway reinforced concrete and prestressed concrete bridges and culverts (JTG D62). Beijing: China Communications Press; 2004 [in Chinese]. [3] Dasgupta A, Sengupta B. Large-scale model test on square box culvert backfilled with sand. J Geotech Eng 1991;117(1):156–61. [4] Zheng JJ, Zhao JB, Chen BG. Vertical earth pressure on culverts under high embankments. Chin J Geotech Eng 2009;31(7):1009–13 [in Chinese]. [5] Kang J, Parker F, Yoo CH. Soil–structure interaction for deeply recess corrugated steel pipes Part I: embankment installation. Eng Struct 2008;30(2):384–92. [6] Elachachi SM, Breysse AD. The effects of soil spatial variability on the reliability of rigid buried pipes. Comput Geotech 2012;43:61–71. [7] Marston A, Anderson AO. The theory of loads on pipes in ditch and tests of cement and clay drain tile and sever pipe. Bulletin No. 31. Ames: Iowa Engineering Experiment Station; 1913.
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