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Numerical stress-deformation analysis of cut-off wall in clay-core rockfill dam on thick overburden
Accepted Manuscript Numerical stress-deformation analysis of a cut-off wall in clay-core rockfill dam on thick overburden Si-hong Liu, Liu-jiang Wang, Zi-jian Wang, Erich Bauer PII:
S1674-2370(16)30041-2
DOI:
10.1016/j.wse.2016.11.002
Reference:
WSE 70
To appear in:
Water Science and Engineering
Please cite this article as: Liu, S.-h., Wang, L.-j., Wang, Z.-j., Bauer, E., Numerical stress-deformation analysis of a cut-off wall in clay-core rockfill dam on thick overburden, Water Science and Engineering (2016), doi: 10.1016/j.wse.2016.11.002. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Numerical stress-deformation analysis of a cut-off wall in clay-core rockfill dam on thick overburden Si-hong Liu a, Liu-jiang Wang a,*, Zi-jian Wang b, Erich Bauer c College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing 210098, China b
Zhejiang Design Institute of Conservancy and Hydroelectric Power, Hangzhou 310002, China c
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a
Institute of Applied Mechanics, Graz University of Technology, Graz 8010, Austria Received 12 September 2015; accepted 16 January 2016
Abstract
1. Introduction
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The cut-off wall in a clay-core rockfill dam built on a thick overburden layer is easily subjected to a great compressive pressure under the action of the loads such as the dead weight of both the dam and the overburden layer, the frictional force induced by the differential settlement between the cut-off wall and its surrounding soils as well as the water pressure. Thus, how to reduce the stress of the cut-off wall has become one of the main problems that need to be considered in the engineering design. In this paper, numerical analysis of a core rock-fill dam built on a thick overburden layer was conducted and some factors influencing the stress-strain behaviors of the cut-off wall were investigated. The factors include the improvement of the overburden layer, the modeling approach for interfacial contact between the cut-off wall and its surrounding soils, the modulus of the cut-off wall concrete, and the connected pattern between the cut-off wall and the clay core. The result shows that improving the overburden layer, selecting plastic concrete with a low modulus and a high strength, and optimizing the connection between the cut-off wall and the clay core of the dam are effective measures to reduce the deformations and compressive stresses of the cut-off wall. Besides, both the Goodman element and mud-layer element are suitable for simulating the interfacial contact between the cut-off wall and its surrounding soils. Keywords: Overburden layer; Core rockfill dam; Cut-off wall; Numerical analysis; Stress and deformation analysis
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In recent years, clay-core rockfill dams built on a thick overburden layer increase gradually. The anti-seepage treatment of the thick overburden layer is very important in the design of these dam projects in order to ensure the safe operation. In general, there are two ways to do this: one is to excavate the overburden deposits under the clay core, and the other is to build concrete cut-off walls inside the overburden deposits. The latter one is now widely used in China (Gao, 2000). As the concrete cut-off wall is built under the clay core, it is subjected to a large dead load of the upper dam body and the water head difference between upstream and downstream during the construction and impounding. As a result, the stress-deformation characteristics of cut-off walls are very complex. The centrifugal model test, field monitoring, and numerical analysis method were usually used to study the behavior of cut-off walls. For example, the interaction mechanism between the cut-off wall and surrounding soils in the upstream cofferdam of the Three Gorges Project was investigated through the centrifugal model test and numerical analysis (Bao, 2007). The strain and deformation of this cut-off wall were monitored (Zhang et al., 2000; Cheng, 2004). Many numerical analyses have been carried out to —————————————— This work was supported by the National Natural Science Foundation of China (Grant No. 51379066), the Fundamental Research Funds for the Central Universities (Grant No. 2016B03514), the National Key Technology Support Program (Grant No. 2015BAB07B05), and the Key Laboratory of Earth-Rock Dam Failure Mechanism and Safety Control Techniques (Grant No. YK913007). *Corresponding author. E-mail address: [email protected] (Liu-Jiang Wang)
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investigate the interaction characteristics between overburden soils and the cut-off wall, and the influence of the cut-off wall’s thickness, the properties of alluvium deposits, the valley boundary, and the cut-off wall construction sequence on the stress-deformation behaviors of cut-off walls (Lu and Wang, 1998; Wang et al., 2006; Li et al., 2007; Jia et al., 2008; Pan et al., 2013; Ding et al., 2013). In this study, numerical analysis of a clay-core rockfill dam built on a deep overburden layer was conducted and some factors affecting the stress-strain behaviors of the cut-off wall were investigated comprehensively. The factors investigated includes the improvement of the overburden layer, the modeling approach for interfacial contact between the cut-off wall and its surrounding soil, the modulus of cut-off wall concrete, and the connected pattern between the cut-off wall and the clay core.
2 Finite element analysis for rockfill dam
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In this study, two-dimensional finite element analysis was carried out on a clay-core rockfill dam, which was built on an overburden layer with a thickness ranging from 39.5 m to 81.3 m. Fig. 1 shows the typical cross-section of this rockfill dam. The dam had a height of 120 m and a crest width of 12 m. Both the upstream and downstream slopes were 1:2. The slopes of the core wall, filter zones, and transition zones were 1:0.25. The normal water storage level of the dam reservoir is 2485 m. The overburden layer of the dam foundation is composed of sand alluvium and talus deposit. Along the depth, the overburden foundation is divided into six layers: layer 1, spreading over the river bed, is composed of sand and gravel with a loose structure and moderate permeability; layer 2 is composed of silty clay with a percentage of silt of 54% and a percentage of clay of 26%; layers 3 and 4 are composed of coarse sand that contains gravel and gravel that contains mud, having a loose structure and moderate permeability; layer 5 is composed of coarse sand that contains gravel with a percentage of silt of 32% and a percentage of clay of 8%; and layer 6 is composed of gravel that contains mud with a loose structure and moderate permeability. In the project, layers 1 and 2 were excavated, and layer 3 was improved using vibro-replacement stone columns. Meanwhile, a 1.2 m-thick concrete cut-off wall, embedding into the bedrock with a depth of 0.5 m, was constructed inside the overburden layer. The curtain grouting was carried out in the bedrock under the cut-off wall to ensure a reliable connection between the cut-off wall and the bedrock. The cut-off wall was connected with the clay core of the dam through a gallery.
Fig. 1 Typical cross-section of rockfill dam
The static and dynamic analysis software for dam’s stress and seepage (Liu, 2008; Xiang et al., 1991) was used in this study, which was developed on the basis of the Biot consolidation theory for saturated soils to take into account the coupling between the seepage and the stress field. The finite element mesh for the dam body and the overburden foundation consisted of 2631 elements and 2523 nodes. As shown in Fig. 2, four columns of meshes are used for the 1.2 m-thick cut-off wall and 2
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136 contact elements are arranged between the cut-off wall and its surrounding soils. If the hollow junction was used for the connection between the cut-off wall and clay core, the modulus in the shadow area in the right figure of Fig. 2 was set to be 0. According to the processes of dam construction and impounding, 34 steps were set in the finite element calculation. The process of dam filling from the dam base to an elevation of 2440.0 m was simulated in the first 14 steps, which took 495 days. Then, the process of impounding from the riverbed to an elevation of 2437.0 m was simulated in steps 15 to 20, which took 30 days. After that, the process of the dam filling from the elevation 2440.0 m to an elevation of 2480.0 m was simulated in steps 21 to 28, which took 285 days. The process of impounding from the elevation 2437.0 m to 2475.0 m was simulated in the last five steps, which took 60 days. In the simulation of impounding, the water pressure and water head were applied on the upstream face of the clay core.
Fig. 2 Finite element mesh at top of cut-off wall
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The consolidated settlement of the overburden foundation has already been stable over hundred thousands of years. Thus, the displacement of the overburden foundation is set to zero at the beginning of the calculation. However, the initial earth stress of the overburden foundation should be considered, which was calculated using the unbalanced force iterative method. In the calculation, the linear elastic model was used for the concrete cut-off wall, with the elastic modulus E being 22 GPa and the Poisson’s ratio being 0.167. The Duncan-Chang (E-B) model was used for rockfill materials (Duncan and Chang, 1970). The Young’s modulus E and bulk modulus Bt of this constitutive model are expressed as n
Rf (σ 1 − σ 3 ) (1 − sin ϕ ) 1 − 2c cos ϕ + 2σ 3 sin ϕ
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σ E = Kpa 3 pa
2
(1)
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σ Bt = K b pa 3 pa Under unloading and reloading conditions, the elastic modulus E is expressed as n
(2)
σ E = K ur pa 3 (3) pa where σ 1 and σ 3 are the major and minor principle stresses, respectively; pa is the atmosphere pressure; Rf is the failure ratio; K is the modulus number; K b is the bulk modulus number; n and m are the exponents; K ur is the modulus number under unloading and reloading conditions; ϕ is the internal friction angle, and ϕ = ϕ0 − ∆ϕ lg (σ 3 pa ) , with ϕ0 being the initial internal friction angle and ∆ϕ being the increment of internal friction angle; and c is the cohesive strength. The parameters determined by laboratory tests are shown in Table 1, where ρ is the density and ks is the permeability coefficient.
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n
Kb
m
Kur
ϕ0
∆φ
c (kPa)
ρ (103 kg/m3)
ks (cm/s)
High plastic clay
0.78
140
0.22
56
0.36
210
27.0
0
24
1.98
2.55 × 10-6
Clay core
0.72
406
0.35
865
0.32
600
40.4
0
73
2.65
6.72 × 10-6
Filter 1
0.90
840
0.48
480
0.17
1260
52.2
10.0
0
2.12
9.55 × 10-2
Filter 2
0.80
600
0.42
400
0.25
900
45.0
8.8
0
2.10
5.98 × 10-3
Transition layer
0.88
840
0.43
480
0.17
1260
52.6
12.0
0
2.15
1.20 × 10-1
Rockfill 1
0.72
1490
0.24
683
0.10
2200
54.4
10.0
0
2.14
2.80 × 10-1
Rockfill 2
0.71
1400
0.18
470
0.15
2100
51.4
9.6
2.14
2.80 × 10-1
Sand and gravel
0.91
1000
0.45
630
0.04
1500
48.7
7.1
0
2.31
4.5 × 10-3
Sedimentary silt
0.67
160
0.43
87
0.25
240
27.5
0
52
2.00
1.89 × 10-6
Gravel that contains mud
0.81
610
0.44
550
0.15
910
45.0
5.6
0
2.50
3.35 × 10-4
Sand that contains gravel
0.70
250
0.44
72
0.26
375
40.9
4.0
0
2.31
4.5 × 10-3
Reinforced layer
0.70
800
0.44
350
0.05
1200
40.9
4.4
0
2.40
4.0 × 10-3
Goodman element
0.74
1500
0.66
11.0
0
15
Mud-layer element
0.50
100
0.45
10.0
0
3
3.1 Stress and deformation of dam
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Rf
Material
1.22
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Fig. 3 shows the contour distributions of the settlement and the major principal stress of the dam (including the overburden foundation) after impounding. The maximum settlement of the dam is 170 cm, occurring at the downstream side near the top surface of the overburden foundation. For the clay-core rockfill dam located on the hard bedrock, it is likely to induce an inconsistent deformation between the clay core and its adjacent rockfills due to their different deformation moduli. Therefore, the stress in the clay core will be partly transferred to the adjacent rockfills, which is so-called arching effect. However, for the dam analyzed in this study, due to the large compression deformation of the overburden layer and the uplift force from the cut-off wall, the arching effect between the clay core and the adjacent rockfill is not pronounced (Fig. 3). That is to say, the thick overburden layer plays an important role in reducing the arching effect.
Fig. 3 Contours of settlement and major principal stress after impounding 4
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As the deformation modulus of the overburden layer is much lower than that of the concrete cut-off wall, the settlement of the overburden layer caused by dam filling and impounding will be larger than that of the concrete cut-off wall. Therefore, an uneven settlement exists between the cut-off wall and the foundation, resulting in a friction between the cut-off wall and the surrounding foundation. This friction is the major load affecting the stress and deformation of the cut-off wall. To reduce this uneven settlement, the overburden layer near the surface should be reinforced. In this project, layers 1 and 2 are excavated, and layer 3 composed of coarse sand that contains gravel is improved with the vibro-replacement stone columns. Based on the experiences from similar projects, the main parameters of the E-B model for the improved layer 3 are taken to be K = 800, Kb = 350, and m = 0.05. Meanwhile, a scheme without improvement of layer 3 is also investigated to verify the improvement effect, and the corresponding parameters are set to be K = 250, Kb = 72, and m = 0.26. Table 2 shows the comparison of the displacements at the top of cut-off wall with and without improvement of the overburden layer 3. It can be found that both the horizontal displacement and vertical displacement (settlement) are reduced significantly after the overburden layer 3 is improved. Table 3 shows the comparison of the principal stresses of the cut-off wall with and without improvement of the overburden layer 3. Fig. 4 shows the distribution of the major and minor principal stresses of the cut-off wall along the depth with and without improvement of the overburden layer 3 at completion of the dam. It can be seen that after the improvement of the overburden layer 3, the major principal stress (compression) of the cut-off wall is reduced significantly, with a mean decrease of 5 to 10 MPa along the depth. Therefore, the crushing of the cut-off wall can be diminished effectively with the improvement of layer 3. In the other hand, the minor principal stress of the cut-off wall changes slightly.
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Table 2 Comparison of displacements at top of cut-off wall with and without improvement of overburden layer 3 Horizontal displacement (cm)
Settlement (cm)
At dam
After
At dam
After
completion
impounding
completion
impounding
13.9
46.3
−13.7
−13.6
With improvement Without improvement
17.7
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60.0
−15.6
−15.2
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Table 3 Comparison of major and minor principal stresses of cut-off wall with and without improvement of overburden layer
Scheme
3 σ 1 (MPa)
At dam completion
σ 3 (MPa) After impounding
At dam completion
After impounding
Upside
Downside
Upside
Downside
Upside
Downside
Upside
Downside
With improvement
36.9
37.9
36.3
39.0
0.26
0.23
0.22
0.39
Without improvemen
41.2
41.1
40.6
41.7
0.18
0.24
0.32
0.35
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Fig. 4 Distribution of principal stresses of cut-off wall along depth with and without improvement of overburden layer 3 at
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completion of dam
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Figs. 5 and 6 show the settlements and the contours of major principal stress of the alluvium deposit with and without improvement of the overburden layer 3, respectively. As we can see from these two figures, the settlement in the improved overburden layer is reduced significantly, while the major principal stresses in the improved foundation increase. That is to say, when the foundation is improved, the stresses caused by the dam filling and impounding increase in the overburden layer and decrease in the cut-off wall, resulting in the decrease of arching effect between the cut-off wall and its surrounding rock/soils. Therefore, the improvement of the overburden layer is an effective measure to reduce the deformations and compressive stresses of the cut-off wall.
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Fig. 5 Comparison of settlement of alluvium deposit with and without improvement of overburden layer 3
Fig. 6 Contours of major principal stress in alluvium deposit with and without improvement of overburden layer 3 (units: MPa)
3.3 Influence of interface elements between cut-off wall and its surrounding soils on stress-strain behaviors of cut-off wall 6
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Due to large difference of the deformation moduli for different materials, the displacements of the cut-off wall and its surrounding soils are obviously inconsistent. Therefore, the way of simulating the interfacial contact between the cut-off wall and its surrounding soils is of great importance. In the present numerical study, three different interface elements were investigated: the Goodman element with a finite thickness (Goodman et al., 1968), the mud-layer element (Li et al., 2007), and the frictionless element. The Goodman element is the most wildly used to simulate interfacial contact between two materials that have greatly different moduli. The thickness of this element is zero. During the construction of the cut-off wall, a mud layer is usually produced between the cut-off wall and foundation, which influences the mechanical behavior of the interface and changes the loads on the cut-off wall and foundation. For the cofferdam in the Miyun Reservoir, it is found that the thickness of the mud layer at the interfacial contact between the cut-off wall and its surrounding soils is about 3−5 cm, and the mud adhered to the cut-off wall is under a plastic state with extremely low shear strength. In this analysis, the mud-layer element was adapted and the thickness of the mud-layer element was set to 3 cm. In order to evaluate the influence of the friction force on the cut-off wall, a frictionless element, by assuming that there is no friction between the cut-off wall and its surrounding soils, was used for contrasting. In this study, the parameters for both the Goodman element and the mud-layer element were respectively taken from the Pubugou Dam (Chen et al., 2005) and the cofferdam in the Three Gorges Project (Li and Cheng, 2005), as listed in Table 1. For the frictionless element, the shear modulus along the interface is set to zero. Table 4 shows the principal stresses of the cut-off wall simulated using three different interface elements. Fig. 7 shows the distribution of the principal stresses of the cut-off wall simulated using three different interface elements at completion of the dam. The results show that the principal stresses of the cut-off wall simulated using the frictionless elements distribute evenly along the depth and their values are smaller than those simulated using other two interface elements. When the frictionless elements are used, the stresses of the cut-off wall are mainly caused by the self-weight of the dam and the water pressure, neglecting the friction between the cut-off wall and its surrounding soils. The principal stresses in the cut-off wall simulated using the Goodman elements and the mud-layer elements are almost the same, indicating that these two interface elements are suitable for simulating the contact between the cut-off wall and its surrounding soils.
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Table 4 Major and minor principal stresses of cut-off wall simulated with different interface elements between cut-off wall and its surrounding soils
σ 1 (MPa)
At dam completion
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Contact simulation method
σ 3 (MPa) After impounding
At dam completion
After impounding
Upside
Downside
Upside
Downside
Upside
Downside
Upside
Downside
Goodman element
36.9
37.9
36.3
39.0
0.26
0.28
0.22
0.39
Frictionless element
26.5
27.5
27.1
31.0
0.18
0.19
0.21
0.41
Mud-layer element
39.1
40.3
38.3
39.5
0.31
0.31
0.42
0.44
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Fig. 7 Distribution of major and minor principal stresses of cut-off wall along depth calculated by different interface elements between cut-off wall and its surrounding soils at completion of dam
3.4 Influence of elastic modulus of cut-off wall concrete on stress-strain behaviors of cut-off wall
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There are two kinds of concretes that are frequently used for cut-off walls: the normal concrete and the plastic concrete. The elastic modulus of normal concrete is about 25.5 to 36.0 GPa, which is 5−10 times larger than that of plastic concrete. In this study, three different elastic moduli of cut-off wall concrete (10 GPa, 22 GPa, and 35 GPa) were selected to investigate their influence on the stress-strain behavior of the cut-off wall. Table 5 shows a comparison of the displacements at the top of the cut-off wall with different elastic moduli of concrete. It can be seen that the vertical displacement (settlement) of the cut-off wall increases with the decreasing elastic modulus of concrete, while the horizontal displacement of the cut-off wall changes slightly with different elastic moduli of concrete. Table 6 shows the principal stresses of the cut-off wall with different elastic moduli of concrete. Fig. 8 shows the distribution of the principal stresses of the cut-off wall with different elastic moduli of concrete at the completion of the dam. The results show that the major principal stress of the cut-off wall increases with the elastic modulus of concrete, while the minor principal stress is not much affected by the elastic modulus of concrete. The reduction of the major principal stress of the cut-off wall with a low elastic modulus of concrete is mainly attributed to the decrease of the relative settlement between cut-off wall and its surrounding soils. For the common concrete, the strength increases with the elastic modulus. In this case, although the compressive stress of the cut-off wall decreases when concrete with a lower elastic modulus is used, the crushing of the cut-off wall may occur if the compressive stress exceeds the compressive strength of the cut-off wall. Therefore, selection of a reasonable plastic concrete, preferably with a lower modulus and relatively higher compressive strength, is very important in the construction of cut-off walls. Table 5 Comparison of displacement at top of cut-off wall with different concrete elastic moduli Horizontal
Elastic modulus of
displacement (cm)
Settlement (cm)
cut-off wall
At dam
After
At dam
After
concrete (GPa)
completion
impounding
completion
impounding
10
13.9
46.1
−27.9
−27.5
22
13.9
46.3
−13.7
−13.6
35
13.8
46.5
−8.8
−8.9
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At dam completion
σ 3 (MPa)
After impounding
At dam completion
After impounding
Downside
Upside
Downside
Upside
Downside
Upside
10
23.7
24.3
23.7
24.4
0.41
0.39
0.49
Downside 0.42
22
36.9
37.9
36.3
39.0
0.26
0.23
0.32
0.35
35
44.7
45.5
43.8
50.1
0.17
0.18
0.24
0.30
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Upside
Fig. 8 Distribution of major and minor principal stresses of cut-off wall with different elastic moduli along depth at completion of dam
3.5 Influence of connection between cut-off wall and clay core on stress-strain behavior of cut-off wall
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In addition to the interfacial friction, the weight of the dam body and the water pressure are also the main loads acting on a cut-off wall. Thus, proper selection of the connection between the cut-off wall and the clay core is of importance to improve the stress states of the cut-off wall, especially near the connecting part. In practice, there may be three different connections between a cut-off wall and a clay core: the gallery junction, hollow junction, and direct plug-in connection, which induce different stresses in the cut-off wall. The gallery junction means that the top of the cut-off wall is directly connected to the bottom of a gallery. The hollow junction is to leave a 0.5-m space between the top of the cut-off wall and the bottom of the gallery and set the elastic modulus of the elements in the space to be zero, as shown in Fig. 2. The plug-in junction is to directly insert the cut-off wall into the clay core by 12 m. Fig. 9 shows the distributions of the calculated principal stresses of the cut-off wall along the depth under these three connections. It can be seen that the compressive stresses are produced in the cut-off wall under these three connections, and they gradually increase with the depth. The major principal stress produced in the cut-off wall is the lowest using the plug-in junction, and the highest using the gallery junction. The minor principal stress produced in the cut-off wall is the highest using the plug-in junction, and it is nearly the same using the other two junctions. Therefore, from the perspective of the stress of the cut-off wall, the plug-in junction is the best for the connection between the cut-off wall and the clay core. However, in practical engineering, the gallery is necessary for arrangement of instrumental equipment and the foundation grouting. When the gallery is applied, the hollow junction can effectively reduce the compressive stress near the upper bottom side of the cut-off wall, but its detailed design may be very complex. Thus, selection of a proper connection is important in the real project. 9
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Fig. 9 Distribution of principal stresses of cut-off wall along depth under different connections between cut-off wall and clay core
4 Conclusions
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In this paper, numerical analysis of a core rock-fill dam built on a thick overburden deposit was conducted, and the effects of some factors on the stress-strain behavior of the cut-off wall were studied. The main conclusions are as follows: (1) The uneven settlement exists between the cut-off wall and the foundation, resulting in a friction between the cut-off wall and the surrounding foundation. With the improvement of the overburden layer near the surface of the dam foundation, this uneven settlement and frictional force are effectively reduced, and the compressive stress of the cut-off wall along the depth is decrease by about 5 to 10 MPa. (2) The frictional force between the cut-off wall and its surrounding soils should be considered in the simulation of the stress-strain behavior of the cut-off wall to ensure the accuracy of the stress in the cut-off wall, and both the Goodman element and mud-layer element are suitable for simulating the interfacial contact. (3) With the decrease of the elastic modulus of concrete, the uneven settlement and fictional force between the cut-off wall and its surrounding soils decrease, resulting in the reduction of the compressive stress in the cut-off wall. Therefore, the low-modulus concrete whose stiffness is close to the foundation’s stiffness is recommended to use in the construction of the cut-off wall, if the compressive strength of concrete is larger enough to prevent crushing. (4) The compressive stress of the cut-off wall changes significantly using different connections between the cut-off wall and the clay core. Compared with gallery junction, the plug-in junction can effectively reduce the compressive stress of the cut-off wall along the depth, and the hollow junction can reduce the compressive stress near the upper bottom side of the cut-off wall.
Acknowledgements
We would like to express our appreciation to Yue-min Zhang and Wen Long at Beijing Guardian Water Power Engineering Co., Ltd. for giving some important suggestions for this paper.
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Liu, S.H., 2008. Research on the Visiable Finite Element Code for Rockfill Dam. Hohai University, Nanjing (in Chinese). Lu, T.H., Wang, R.D., 1998. Stress and deformation of concrete cut-off wall in Pubugou Earth-Rockfill Dam. Journal of Hohai University (Natural Sciences), 26(2), 41−44 (in Chinese).
Pan, Y., He, Y.L., Zhou, X.X., Cao, X.X., 2013. Analysis of effect of canyon terrain on stress and displacement of cutoff wall in dam foundation with deep overburden. Rock and Soil Mechanics, 34(7), 2023−2030 (in Chinese). Wang, G., Zhang, J.M., Pu, J.L., 2006. An evaluation of the factors influencing the stress and deformation of concrete diaphragm wall in dams. China Civil Engineering Journal, 39(4), 73−77 (in Chinese). Xiang, D.R., Shao, S.G., Liu, S.H., Zhu, J.G., 1991. 3D Finite Element Code TDAD for Rockfill Dam. Beijing Science and
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Technology Press, Beijing (in Chinese).
Zhang, X.P., Bao, C.G., Zhang, J.S., 2000. The displacement and operation of impervious cores in phase-
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Three Gorges Project. Journal of Hydraulic Engineering, 31(9), 91−96 (in Chinese).
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cofferdam of
S1674-2370(16)30041-2
DOI:
10.1016/j.wse.2016.11.002
Reference:
WSE 70
To appear in:
Water Science and Engineering
Please cite this article as: Liu, S.-h., Wang, L.-j., Wang, Z.-j., Bauer, E., Numerical stress-deformation analysis of a cut-off wall in clay-core rockfill dam on thick overburden, Water Science and Engineering (2016), doi: 10.1016/j.wse.2016.11.002. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Numerical stress-deformation analysis of a cut-off wall in clay-core rockfill dam on thick overburden Si-hong Liu a, Liu-jiang Wang a,*, Zi-jian Wang b, Erich Bauer c College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing 210098, China b
Zhejiang Design Institute of Conservancy and Hydroelectric Power, Hangzhou 310002, China c
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Institute of Applied Mechanics, Graz University of Technology, Graz 8010, Austria Received 12 September 2015; accepted 16 January 2016
Abstract
1. Introduction
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The cut-off wall in a clay-core rockfill dam built on a thick overburden layer is easily subjected to a great compressive pressure under the action of the loads such as the dead weight of both the dam and the overburden layer, the frictional force induced by the differential settlement between the cut-off wall and its surrounding soils as well as the water pressure. Thus, how to reduce the stress of the cut-off wall has become one of the main problems that need to be considered in the engineering design. In this paper, numerical analysis of a core rock-fill dam built on a thick overburden layer was conducted and some factors influencing the stress-strain behaviors of the cut-off wall were investigated. The factors include the improvement of the overburden layer, the modeling approach for interfacial contact between the cut-off wall and its surrounding soils, the modulus of the cut-off wall concrete, and the connected pattern between the cut-off wall and the clay core. The result shows that improving the overburden layer, selecting plastic concrete with a low modulus and a high strength, and optimizing the connection between the cut-off wall and the clay core of the dam are effective measures to reduce the deformations and compressive stresses of the cut-off wall. Besides, both the Goodman element and mud-layer element are suitable for simulating the interfacial contact between the cut-off wall and its surrounding soils. Keywords: Overburden layer; Core rockfill dam; Cut-off wall; Numerical analysis; Stress and deformation analysis
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In recent years, clay-core rockfill dams built on a thick overburden layer increase gradually. The anti-seepage treatment of the thick overburden layer is very important in the design of these dam projects in order to ensure the safe operation. In general, there are two ways to do this: one is to excavate the overburden deposits under the clay core, and the other is to build concrete cut-off walls inside the overburden deposits. The latter one is now widely used in China (Gao, 2000). As the concrete cut-off wall is built under the clay core, it is subjected to a large dead load of the upper dam body and the water head difference between upstream and downstream during the construction and impounding. As a result, the stress-deformation characteristics of cut-off walls are very complex. The centrifugal model test, field monitoring, and numerical analysis method were usually used to study the behavior of cut-off walls. For example, the interaction mechanism between the cut-off wall and surrounding soils in the upstream cofferdam of the Three Gorges Project was investigated through the centrifugal model test and numerical analysis (Bao, 2007). The strain and deformation of this cut-off wall were monitored (Zhang et al., 2000; Cheng, 2004). Many numerical analyses have been carried out to —————————————— This work was supported by the National Natural Science Foundation of China (Grant No. 51379066), the Fundamental Research Funds for the Central Universities (Grant No. 2016B03514), the National Key Technology Support Program (Grant No. 2015BAB07B05), and the Key Laboratory of Earth-Rock Dam Failure Mechanism and Safety Control Techniques (Grant No. YK913007). *Corresponding author. E-mail address: [email protected] (Liu-Jiang Wang)
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investigate the interaction characteristics between overburden soils and the cut-off wall, and the influence of the cut-off wall’s thickness, the properties of alluvium deposits, the valley boundary, and the cut-off wall construction sequence on the stress-deformation behaviors of cut-off walls (Lu and Wang, 1998; Wang et al., 2006; Li et al., 2007; Jia et al., 2008; Pan et al., 2013; Ding et al., 2013). In this study, numerical analysis of a clay-core rockfill dam built on a deep overburden layer was conducted and some factors affecting the stress-strain behaviors of the cut-off wall were investigated comprehensively. The factors investigated includes the improvement of the overburden layer, the modeling approach for interfacial contact between the cut-off wall and its surrounding soil, the modulus of cut-off wall concrete, and the connected pattern between the cut-off wall and the clay core.
2 Finite element analysis for rockfill dam
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In this study, two-dimensional finite element analysis was carried out on a clay-core rockfill dam, which was built on an overburden layer with a thickness ranging from 39.5 m to 81.3 m. Fig. 1 shows the typical cross-section of this rockfill dam. The dam had a height of 120 m and a crest width of 12 m. Both the upstream and downstream slopes were 1:2. The slopes of the core wall, filter zones, and transition zones were 1:0.25. The normal water storage level of the dam reservoir is 2485 m. The overburden layer of the dam foundation is composed of sand alluvium and talus deposit. Along the depth, the overburden foundation is divided into six layers: layer 1, spreading over the river bed, is composed of sand and gravel with a loose structure and moderate permeability; layer 2 is composed of silty clay with a percentage of silt of 54% and a percentage of clay of 26%; layers 3 and 4 are composed of coarse sand that contains gravel and gravel that contains mud, having a loose structure and moderate permeability; layer 5 is composed of coarse sand that contains gravel with a percentage of silt of 32% and a percentage of clay of 8%; and layer 6 is composed of gravel that contains mud with a loose structure and moderate permeability. In the project, layers 1 and 2 were excavated, and layer 3 was improved using vibro-replacement stone columns. Meanwhile, a 1.2 m-thick concrete cut-off wall, embedding into the bedrock with a depth of 0.5 m, was constructed inside the overburden layer. The curtain grouting was carried out in the bedrock under the cut-off wall to ensure a reliable connection between the cut-off wall and the bedrock. The cut-off wall was connected with the clay core of the dam through a gallery.
Fig. 1 Typical cross-section of rockfill dam
The static and dynamic analysis software for dam’s stress and seepage (Liu, 2008; Xiang et al., 1991) was used in this study, which was developed on the basis of the Biot consolidation theory for saturated soils to take into account the coupling between the seepage and the stress field. The finite element mesh for the dam body and the overburden foundation consisted of 2631 elements and 2523 nodes. As shown in Fig. 2, four columns of meshes are used for the 1.2 m-thick cut-off wall and 2
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136 contact elements are arranged between the cut-off wall and its surrounding soils. If the hollow junction was used for the connection between the cut-off wall and clay core, the modulus in the shadow area in the right figure of Fig. 2 was set to be 0. According to the processes of dam construction and impounding, 34 steps were set in the finite element calculation. The process of dam filling from the dam base to an elevation of 2440.0 m was simulated in the first 14 steps, which took 495 days. Then, the process of impounding from the riverbed to an elevation of 2437.0 m was simulated in steps 15 to 20, which took 30 days. After that, the process of the dam filling from the elevation 2440.0 m to an elevation of 2480.0 m was simulated in steps 21 to 28, which took 285 days. The process of impounding from the elevation 2437.0 m to 2475.0 m was simulated in the last five steps, which took 60 days. In the simulation of impounding, the water pressure and water head were applied on the upstream face of the clay core.
Fig. 2 Finite element mesh at top of cut-off wall
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The consolidated settlement of the overburden foundation has already been stable over hundred thousands of years. Thus, the displacement of the overburden foundation is set to zero at the beginning of the calculation. However, the initial earth stress of the overburden foundation should be considered, which was calculated using the unbalanced force iterative method. In the calculation, the linear elastic model was used for the concrete cut-off wall, with the elastic modulus E being 22 GPa and the Poisson’s ratio being 0.167. The Duncan-Chang (E-B) model was used for rockfill materials (Duncan and Chang, 1970). The Young’s modulus E and bulk modulus Bt of this constitutive model are expressed as n
Rf (σ 1 − σ 3 ) (1 − sin ϕ ) 1 − 2c cos ϕ + 2σ 3 sin ϕ
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σ E = Kpa 3 pa
2
(1)
m
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σ Bt = K b pa 3 pa Under unloading and reloading conditions, the elastic modulus E is expressed as n
(2)
σ E = K ur pa 3 (3) pa where σ 1 and σ 3 are the major and minor principle stresses, respectively; pa is the atmosphere pressure; Rf is the failure ratio; K is the modulus number; K b is the bulk modulus number; n and m are the exponents; K ur is the modulus number under unloading and reloading conditions; ϕ is the internal friction angle, and ϕ = ϕ0 − ∆ϕ lg (σ 3 pa ) , with ϕ0 being the initial internal friction angle and ∆ϕ being the increment of internal friction angle; and c is the cohesive strength. The parameters determined by laboratory tests are shown in Table 1, where ρ is the density and ks is the permeability coefficient.
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n
Kb
m
Kur
ϕ0
∆φ
c (kPa)
ρ (103 kg/m3)
ks (cm/s)
High plastic clay
0.78
140
0.22
56
0.36
210
27.0
0
24
1.98
2.55 × 10-6
Clay core
0.72
406
0.35
865
0.32
600
40.4
0
73
2.65
6.72 × 10-6
Filter 1
0.90
840
0.48
480
0.17
1260
52.2
10.0
0
2.12
9.55 × 10-2
Filter 2
0.80
600
0.42
400
0.25
900
45.0
8.8
0
2.10
5.98 × 10-3
Transition layer
0.88
840
0.43
480
0.17
1260
52.6
12.0
0
2.15
1.20 × 10-1
Rockfill 1
0.72
1490
0.24
683
0.10
2200
54.4
10.0
0
2.14
2.80 × 10-1
Rockfill 2
0.71
1400
0.18
470
0.15
2100
51.4
9.6
2.14
2.80 × 10-1
Sand and gravel
0.91
1000
0.45
630
0.04
1500
48.7
7.1
0
2.31
4.5 × 10-3
Sedimentary silt
0.67
160
0.43
87
0.25
240
27.5
0
52
2.00
1.89 × 10-6
Gravel that contains mud
0.81
610
0.44
550
0.15
910
45.0
5.6
0
2.50
3.35 × 10-4
Sand that contains gravel
0.70
250
0.44
72
0.26
375
40.9
4.0
0
2.31
4.5 × 10-3
Reinforced layer
0.70
800
0.44
350
0.05
1200
40.9
4.4
0
2.40
4.0 × 10-3
Goodman element
0.74
1500
0.66
11.0
0
15
Mud-layer element
0.50
100
0.45
10.0
0
3
3.1 Stress and deformation of dam
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0.20
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Rf
Material
1.22
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Fig. 3 shows the contour distributions of the settlement and the major principal stress of the dam (including the overburden foundation) after impounding. The maximum settlement of the dam is 170 cm, occurring at the downstream side near the top surface of the overburden foundation. For the clay-core rockfill dam located on the hard bedrock, it is likely to induce an inconsistent deformation between the clay core and its adjacent rockfills due to their different deformation moduli. Therefore, the stress in the clay core will be partly transferred to the adjacent rockfills, which is so-called arching effect. However, for the dam analyzed in this study, due to the large compression deformation of the overburden layer and the uplift force from the cut-off wall, the arching effect between the clay core and the adjacent rockfill is not pronounced (Fig. 3). That is to say, the thick overburden layer plays an important role in reducing the arching effect.
Fig. 3 Contours of settlement and major principal stress after impounding 4
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As the deformation modulus of the overburden layer is much lower than that of the concrete cut-off wall, the settlement of the overburden layer caused by dam filling and impounding will be larger than that of the concrete cut-off wall. Therefore, an uneven settlement exists between the cut-off wall and the foundation, resulting in a friction between the cut-off wall and the surrounding foundation. This friction is the major load affecting the stress and deformation of the cut-off wall. To reduce this uneven settlement, the overburden layer near the surface should be reinforced. In this project, layers 1 and 2 are excavated, and layer 3 composed of coarse sand that contains gravel is improved with the vibro-replacement stone columns. Based on the experiences from similar projects, the main parameters of the E-B model for the improved layer 3 are taken to be K = 800, Kb = 350, and m = 0.05. Meanwhile, a scheme without improvement of layer 3 is also investigated to verify the improvement effect, and the corresponding parameters are set to be K = 250, Kb = 72, and m = 0.26. Table 2 shows the comparison of the displacements at the top of cut-off wall with and without improvement of the overburden layer 3. It can be found that both the horizontal displacement and vertical displacement (settlement) are reduced significantly after the overburden layer 3 is improved. Table 3 shows the comparison of the principal stresses of the cut-off wall with and without improvement of the overburden layer 3. Fig. 4 shows the distribution of the major and minor principal stresses of the cut-off wall along the depth with and without improvement of the overburden layer 3 at completion of the dam. It can be seen that after the improvement of the overburden layer 3, the major principal stress (compression) of the cut-off wall is reduced significantly, with a mean decrease of 5 to 10 MPa along the depth. Therefore, the crushing of the cut-off wall can be diminished effectively with the improvement of layer 3. In the other hand, the minor principal stress of the cut-off wall changes slightly.
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Table 2 Comparison of displacements at top of cut-off wall with and without improvement of overburden layer 3 Horizontal displacement (cm)
Settlement (cm)
At dam
After
At dam
After
completion
impounding
completion
impounding
13.9
46.3
−13.7
−13.6
With improvement Without improvement
17.7
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60.0
−15.6
−15.2
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Table 3 Comparison of major and minor principal stresses of cut-off wall with and without improvement of overburden layer
Scheme
3 σ 1 (MPa)
At dam completion
σ 3 (MPa) After impounding
At dam completion
After impounding
Upside
Downside
Upside
Downside
Upside
Downside
Upside
Downside
With improvement
36.9
37.9
36.3
39.0
0.26
0.23
0.22
0.39
Without improvemen
41.2
41.1
40.6
41.7
0.18
0.24
0.32
0.35
5
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Fig. 4 Distribution of principal stresses of cut-off wall along depth with and without improvement of overburden layer 3 at
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completion of dam
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Figs. 5 and 6 show the settlements and the contours of major principal stress of the alluvium deposit with and without improvement of the overburden layer 3, respectively. As we can see from these two figures, the settlement in the improved overburden layer is reduced significantly, while the major principal stresses in the improved foundation increase. That is to say, when the foundation is improved, the stresses caused by the dam filling and impounding increase in the overburden layer and decrease in the cut-off wall, resulting in the decrease of arching effect between the cut-off wall and its surrounding rock/soils. Therefore, the improvement of the overburden layer is an effective measure to reduce the deformations and compressive stresses of the cut-off wall.
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Fig. 5 Comparison of settlement of alluvium deposit with and without improvement of overburden layer 3
Fig. 6 Contours of major principal stress in alluvium deposit with and without improvement of overburden layer 3 (units: MPa)
3.3 Influence of interface elements between cut-off wall and its surrounding soils on stress-strain behaviors of cut-off wall 6
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Due to large difference of the deformation moduli for different materials, the displacements of the cut-off wall and its surrounding soils are obviously inconsistent. Therefore, the way of simulating the interfacial contact between the cut-off wall and its surrounding soils is of great importance. In the present numerical study, three different interface elements were investigated: the Goodman element with a finite thickness (Goodman et al., 1968), the mud-layer element (Li et al., 2007), and the frictionless element. The Goodman element is the most wildly used to simulate interfacial contact between two materials that have greatly different moduli. The thickness of this element is zero. During the construction of the cut-off wall, a mud layer is usually produced between the cut-off wall and foundation, which influences the mechanical behavior of the interface and changes the loads on the cut-off wall and foundation. For the cofferdam in the Miyun Reservoir, it is found that the thickness of the mud layer at the interfacial contact between the cut-off wall and its surrounding soils is about 3−5 cm, and the mud adhered to the cut-off wall is under a plastic state with extremely low shear strength. In this analysis, the mud-layer element was adapted and the thickness of the mud-layer element was set to 3 cm. In order to evaluate the influence of the friction force on the cut-off wall, a frictionless element, by assuming that there is no friction between the cut-off wall and its surrounding soils, was used for contrasting. In this study, the parameters for both the Goodman element and the mud-layer element were respectively taken from the Pubugou Dam (Chen et al., 2005) and the cofferdam in the Three Gorges Project (Li and Cheng, 2005), as listed in Table 1. For the frictionless element, the shear modulus along the interface is set to zero. Table 4 shows the principal stresses of the cut-off wall simulated using three different interface elements. Fig. 7 shows the distribution of the principal stresses of the cut-off wall simulated using three different interface elements at completion of the dam. The results show that the principal stresses of the cut-off wall simulated using the frictionless elements distribute evenly along the depth and their values are smaller than those simulated using other two interface elements. When the frictionless elements are used, the stresses of the cut-off wall are mainly caused by the self-weight of the dam and the water pressure, neglecting the friction between the cut-off wall and its surrounding soils. The principal stresses in the cut-off wall simulated using the Goodman elements and the mud-layer elements are almost the same, indicating that these two interface elements are suitable for simulating the contact between the cut-off wall and its surrounding soils.
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Table 4 Major and minor principal stresses of cut-off wall simulated with different interface elements between cut-off wall and its surrounding soils
σ 1 (MPa)
At dam completion
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Contact simulation method
σ 3 (MPa) After impounding
At dam completion
After impounding
Upside
Downside
Upside
Downside
Upside
Downside
Upside
Downside
Goodman element
36.9
37.9
36.3
39.0
0.26
0.28
0.22
0.39
Frictionless element
26.5
27.5
27.1
31.0
0.18
0.19
0.21
0.41
Mud-layer element
39.1
40.3
38.3
39.5
0.31
0.31
0.42
0.44
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Fig. 7 Distribution of major and minor principal stresses of cut-off wall along depth calculated by different interface elements between cut-off wall and its surrounding soils at completion of dam
3.4 Influence of elastic modulus of cut-off wall concrete on stress-strain behaviors of cut-off wall
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There are two kinds of concretes that are frequently used for cut-off walls: the normal concrete and the plastic concrete. The elastic modulus of normal concrete is about 25.5 to 36.0 GPa, which is 5−10 times larger than that of plastic concrete. In this study, three different elastic moduli of cut-off wall concrete (10 GPa, 22 GPa, and 35 GPa) were selected to investigate their influence on the stress-strain behavior of the cut-off wall. Table 5 shows a comparison of the displacements at the top of the cut-off wall with different elastic moduli of concrete. It can be seen that the vertical displacement (settlement) of the cut-off wall increases with the decreasing elastic modulus of concrete, while the horizontal displacement of the cut-off wall changes slightly with different elastic moduli of concrete. Table 6 shows the principal stresses of the cut-off wall with different elastic moduli of concrete. Fig. 8 shows the distribution of the principal stresses of the cut-off wall with different elastic moduli of concrete at the completion of the dam. The results show that the major principal stress of the cut-off wall increases with the elastic modulus of concrete, while the minor principal stress is not much affected by the elastic modulus of concrete. The reduction of the major principal stress of the cut-off wall with a low elastic modulus of concrete is mainly attributed to the decrease of the relative settlement between cut-off wall and its surrounding soils. For the common concrete, the strength increases with the elastic modulus. In this case, although the compressive stress of the cut-off wall decreases when concrete with a lower elastic modulus is used, the crushing of the cut-off wall may occur if the compressive stress exceeds the compressive strength of the cut-off wall. Therefore, selection of a reasonable plastic concrete, preferably with a lower modulus and relatively higher compressive strength, is very important in the construction of cut-off walls. Table 5 Comparison of displacement at top of cut-off wall with different concrete elastic moduli Horizontal
Elastic modulus of
displacement (cm)
Settlement (cm)
cut-off wall
At dam
After
At dam
After
concrete (GPa)
completion
impounding
completion
impounding
10
13.9
46.1
−27.9
−27.5
22
13.9
46.3
−13.7
−13.6
35
13.8
46.5
−8.8
−8.9
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At dam completion
σ 3 (MPa)
After impounding
At dam completion
After impounding
Downside
Upside
Downside
Upside
Downside
Upside
10
23.7
24.3
23.7
24.4
0.41
0.39
0.49
Downside 0.42
22
36.9
37.9
36.3
39.0
0.26
0.23
0.32
0.35
35
44.7
45.5
43.8
50.1
0.17
0.18
0.24
0.30
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Upside
Fig. 8 Distribution of major and minor principal stresses of cut-off wall with different elastic moduli along depth at completion of dam
3.5 Influence of connection between cut-off wall and clay core on stress-strain behavior of cut-off wall
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In addition to the interfacial friction, the weight of the dam body and the water pressure are also the main loads acting on a cut-off wall. Thus, proper selection of the connection between the cut-off wall and the clay core is of importance to improve the stress states of the cut-off wall, especially near the connecting part. In practice, there may be three different connections between a cut-off wall and a clay core: the gallery junction, hollow junction, and direct plug-in connection, which induce different stresses in the cut-off wall. The gallery junction means that the top of the cut-off wall is directly connected to the bottom of a gallery. The hollow junction is to leave a 0.5-m space between the top of the cut-off wall and the bottom of the gallery and set the elastic modulus of the elements in the space to be zero, as shown in Fig. 2. The plug-in junction is to directly insert the cut-off wall into the clay core by 12 m. Fig. 9 shows the distributions of the calculated principal stresses of the cut-off wall along the depth under these three connections. It can be seen that the compressive stresses are produced in the cut-off wall under these three connections, and they gradually increase with the depth. The major principal stress produced in the cut-off wall is the lowest using the plug-in junction, and the highest using the gallery junction. The minor principal stress produced in the cut-off wall is the highest using the plug-in junction, and it is nearly the same using the other two junctions. Therefore, from the perspective of the stress of the cut-off wall, the plug-in junction is the best for the connection between the cut-off wall and the clay core. However, in practical engineering, the gallery is necessary for arrangement of instrumental equipment and the foundation grouting. When the gallery is applied, the hollow junction can effectively reduce the compressive stress near the upper bottom side of the cut-off wall, but its detailed design may be very complex. Thus, selection of a proper connection is important in the real project. 9
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Fig. 9 Distribution of principal stresses of cut-off wall along depth under different connections between cut-off wall and clay core
4 Conclusions
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In this paper, numerical analysis of a core rock-fill dam built on a thick overburden deposit was conducted, and the effects of some factors on the stress-strain behavior of the cut-off wall were studied. The main conclusions are as follows: (1) The uneven settlement exists between the cut-off wall and the foundation, resulting in a friction between the cut-off wall and the surrounding foundation. With the improvement of the overburden layer near the surface of the dam foundation, this uneven settlement and frictional force are effectively reduced, and the compressive stress of the cut-off wall along the depth is decrease by about 5 to 10 MPa. (2) The frictional force between the cut-off wall and its surrounding soils should be considered in the simulation of the stress-strain behavior of the cut-off wall to ensure the accuracy of the stress in the cut-off wall, and both the Goodman element and mud-layer element are suitable for simulating the interfacial contact. (3) With the decrease of the elastic modulus of concrete, the uneven settlement and fictional force between the cut-off wall and its surrounding soils decrease, resulting in the reduction of the compressive stress in the cut-off wall. Therefore, the low-modulus concrete whose stiffness is close to the foundation’s stiffness is recommended to use in the construction of the cut-off wall, if the compressive strength of concrete is larger enough to prevent crushing. (4) The compressive stress of the cut-off wall changes significantly using different connections between the cut-off wall and the clay core. Compared with gallery junction, the plug-in junction can effectively reduce the compressive stress of the cut-off wall along the depth, and the hollow junction can reduce the compressive stress near the upper bottom side of the cut-off wall.
Acknowledgements
We would like to express our appreciation to Yue-min Zhang and Wen Long at Beijing Guardian Water Power Engineering Co., Ltd. for giving some important suggestions for this paper.
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cofferdam of