3D dynamic finite element calculation is carried out for a 161 m high geomembrane faced soft rockfill dam on overburden in a strong earthquake area. The dynamic response of the dam is obtained. The horizontal dynamic displacement is relatively more significant. The maximum vertical permanent deformation and deflection of geomembrane occur at the dam crest near the maximum dam cross section. The tensile strain of geomembrane increases significantly at the dig-fill junction and the reverse arc section. The maximum tensile strain of geomembrane is 1.52%, and the safety factor of geomembrane tensile strain is greater than the allowable value. Even subjected to the strong earthquake, the geomembrane slab can effectively coordinate the deformation with the dam body and deep overburden and the dam can be in a safe operation state.
1 Introduction
The number and height of dams have been greatly improved with the booming of dam industry in China [1]. Currently, there are fewer suitable sites for building high dams and large reservoirs. The remaining projects to be developed often face complex and harsh dam-building conditions such as deep overburden, high seismic intensity, soft dam materials and lack of impervious clay, thus concrete dams or conventional earth-rock dams are not the best choice.
Compared with clay and asphalt concrete, geomembrane has the advantages of low permeability, strong adaptability to deformation, convenient construction and low cost [2]. If a rockfill dam adopts flexible geomembrane as the impervious barrier, it may be well adapted to the large earthquake reciprocating deformation and avoid the impervious barrier damage when subjected to strong earthquake [3]. In addition, the geomembrane is especially suitable for impervious barrier of high rockfill dams filled with soft rock on the overburden [4], which can effectively coordinate the deformation with the dam body and overburden. Thus, the geomembrane faced rockfill dam is especially suitable for the above complex and harsh dam-building conditions. At present, geomembranes have been used in seepage control of more than 160 rockfill dams internationally, among which more than 40 dams have been built in China. However, most of the geomembrane faced rockfill dams are faced with low water heads, and are not built on the overburden in strong earthquake areas. Therefore, it is of great significance to investigate the seismic safety of high geomembrane faced soft rockfill dam built on the overburden subjected to strong earthquake.
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A pumped storage power station in southwest China is located in a strong earthquake area where the basic seismic intensity is VII and the design intensity is VIII. The upper reservoir dam of the power station is a geomembrane faced soft rockfill dam, with a maximum dam height of 161 m, a dam crest elevation of 3786 m, on a 30 ~ 68 m thick overburden. The filling material of the dam are mainly divided into cushion layer, transition layer, rockfill I and rockfill II from upstream to downstream. The rockfill materials are mainly composed of slate whose saturated compressive strength and softening coefficient are low. The geomembrane is also used as impervious body at the bottom of the reservoir, which is connected with the geomembrane of dam surface in a reverse arc section. In this study, 3D dynamic finite element method is carried out to demonstrate the feasibility of the construction of the high geomembrane faced soft rockfill dam on deep overburden subjected to strong earthquake from the perspective of stress, deformation and seismic response. It provides reference for the design and construction of similar projects.
2 Calculation Model and Calculation Conditions
2.1 Finite Element Model
According to the topographic and geological conditions of the dam site area and dam design, the calculation domain is reasonably selected. Figure 1 shows the 3D finite element model of the high geomembrane faced soft rockfill dam. The finite element mesh is mainly composed of eight-node hexahedral elements with 19,333 nodes and 21,697 elements, including 631 geomembrane elements.
Two 3 D diagrams a and b depict a dam structure and geomembrane slab, respectively. The dam section includes a geomembrane on the surface and reservoir bottom, with labeled points A through D for reference.
Fig. 1
3D finite element mesh of the geomembrane faced soft rockfill dam
×
2.2 Calculation Parameters of Dam Materials
The equivalent nonlinear viscoelastic model is used to simulate the dynamic stress–strain relationship of the dam materials, and the Shen Zhujiang model is used for earthquake permanent deformation [5]. Table 1 shows the results of large-scale indoor triaxial tests for dynamic calculation parameters of dam materials.
Table 1
Dynamic calculation parameters of dam materials
Materials
K2
λ
n
c1
c2
c3
c4
c5
Cushion layer
1950
0.21
0.38
0.75
0.86
0
6.99
0.85
Transition layer
2100
0.22
0.38
0.77
0.88
0
6.95
0.87
Rockfill I
2035
0.21
0.33
0.73
0.82
0
6.90
0.90
Rockfill II
1875
0.23
0.35
0.84
0.83
0
7.40
0.91
2.3 Properties of the Geomembrane
Smooth HDPE geomembranes with a thickness of 1.5 mm was employed in the soft rockfill dam. Table 2 shows the mechanical properties of the geomembrane.
Table 2
Mechanical properties of the geomembrane
Density (g/cm3)
Yield strength (MPa)
Yield strain (%)
Breaking strength (MPa)
Breaking strain (%)
0.94
11.52
13.00
11.46
610.32
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2.4 Dynamic Interface Model of Geomembrane-Sandy Gravel
The cyclic secant shear stiffness K is defined as the ratio of the shear stress to the corresponding shear-displacement amplitude u, i.e.:
$$K = \frac{\tau }{u} = \frac{1}{a + bu}$$
(1)
where, a and b are the model parameters obtained by experiments.
The following model is widely used in soil dynamics:
where the ultimate damping ratio λult is related to the asymptotical value under an theoretically infinitely large shear-displacement amplitude u.
To reasonably take into account the damping behavior of a geomembrane-sandy gravel interface under small cyclic shear displacements, the following modified model [6] for the pressure dependent damping ratio is proposed based on (2):
where, λ0 is the damping ratio for u = 0; λult is the ultimate value of the damping ratio for u → ∞; n is the vertical stress; k, α1 and α2 are constitutive parameters.
2.5 Simulation of Dam Filling by Stages
This calculation simulates the dam filling and water storage process in detail. The 1st–47th steps simulate the dam filling from the bottom to the top. The 48th step simulates the placement of geomembrane. The 49th–58th steps simulate the reservoir storing water to the normal water level of 3780 m.
2.6 Input Seismic Parameters
The seismic intensity at the dam site is VII, and the peak ground acceleration is 0.396 g. Table 3 shows the parameters of the design standard response spectrum. Figure 2 shows the time histories of acceleration for seismic input.
Table 3
The design standard response spectrum parameters
Amax
βm
T0
T1
Tg
C
αmax
396
2.6
0.04
0.10
0.50
0.9
1.030
Three line graphs a to c display acceleration over time in three directions, such as along the valley, dam axial, and vertical directions, with time plotted in seconds and acceleration in meters per second squared.
Fig. 2
Time histories of acceleration
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3 Results and Analysis
3.1 Dynamic Displacement of Dam
Figure 3 shows the 3D dynamic displacement distribution of the dam. The dynamic displacement increases with the increasing elevation and decreases from the valley center to two banks. The maximum dynamic displacement occurs near the top of the dam with the maximum cross section, which are 39.37, 40.86 and 27.36 cm at valley direction, dam axial direction and vertical direction, respectively. The horizontal dynamic displacement of the dam is relatively more significant.
Three 3 D contour plots a to c illustrate stress distribution along the valley, dam axial, and vertical directions, with varying intensity levels mapped across each direction.
Fig. 3
3D dynamic displacement distribution of the dam (unit: cm)
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3.2 Dynamic Response of the Geomembrane
The geomembrane is deformed with the dam body and the overburden subjected to the earthquake, and the subordinate deformation and strain are generated. Figure 4 shows the vertical permanent deformation and deflection distribution of geomembrane at dam surface and reservoir bottom. The vertical permanent deformation of geomembrane increases with the increasing elevation which is in concordance with the deformation of the dam body. The maximum vertical permanent deformation and deflection of geomembrane are 36.83 and 39.79 cm, respectively. They are located at the dam crest near the maximum dam cross section.
Two contour plots represent vertical permanent deformation and deflection across a dam section. It has varying deformation levels indicated by the scale below each plot.
Fig. 4
Vertical permanent deformation and deflection distribution of geomembrane (unit: cm)
×
Figure 5 shows the principal tensile strain distribution of the geomembrane. The tensile strain is relatively larger at the boundary of dig-fill junction in reservoir and the reverse arc section. The maximum tensile strain of geomembrane is 1.52%, which occurs on the dam surface at the right bank. According to (4), the value of tensile strain safety factor k is 8.6, which is greater than the allowable value of 5.0. Thus, the geomembrane is safe subjected to the strong earthquake.
A contour plot illustrates stress distribution across a dam section with varying intensity levels indicated by the scale at the bottom.
Fig. 5
Principal tensile strain distribution of the geomembrane (unit: %)
where, εy is the yield strain of geomembrane, its value is 13.0 in Table 2; εmax is the maximum tensile strain of geomembrane.
×
Figure 6 shows the principal strain distribution of the geomembrane along particular paths. Figure 1b shows the particular paths, in which the path AB is perpendicular to the dam axis, and the path CD is located at the reverse arc section and parallel to the dam axis.
Two line graphs a and b represent tensile strain along two paths, A B and C D. Path A B includes a reverse arc section, with strain variations plotted over distance in meters.
Fig. 6
Principal strain distribution of geomembrane along particular paths
×
The tensile strain of geomembrane increases significantly at the dig-fill junction and the reverse arc section, while the strain in other parts is small and the change range is not significant. The geomembrane at the reverse arc section is subjected to water pressure to produce tensile deformation to both sides, which results in relatively larger tensile strains. The vertical depth of the filling material at the dig-fill junction is different, which is easy to produce uneven deformation, resulting in a significant increase in the tensile strain of the geomembrane. Although, the tensile strain safety factor of the geomembrane is greater than the allowable value, it is necessary to diminish the tensile strain of geomembrane as much as possible in view of the above causes. Therefore, some reasonable engineering measures can be taken such as increasing the compaction quality of rockfill materials at the cut-and-fill junction during construction and improving the quality of backfill materials.
4 Conclusions
3D dynamic finite element method is carried out for a high geomembrane faced soft rockfill dam on overburden subjected to strong earthquake. The following conclusions are drawn from the analysis of dynamic response of dam body and geomembrane:
(1)
The dynamic response of the dam increases with the increasing elevation, and the whipping effect near the dam crest is significant. The maximum dynamic displacement along valley direction, dam axis direction and vertical direction are 39.37, 40.86 and 27.36 cm, respectively.
(2)
The maximum vertical permanent deformation and deflection of geomembrane occur at the dam crest near the maximum dam cross section. The maximum tensile strain of geomembrane is 1.52%, which is located on the dam surface at the right bank. The tensile strain safety factor of geomembrane is greater than the allowable value. Thus, the geomembrane is safe subjected to the strong earthquake.
(3)
The tensile strain of geomembrane increases significantly at the dig-fill junction and the reverse arc section. Some engineering measures can be taken to diminish the tensile strain, such as paying attention to the compaction quality of rockfill materials at the cut-and-fill junction during construction and improving the quality of backfill materials.
(4)
Subjected to the strong earthquake, the geomembrane can effectively coordinate the deformation with the dam body and deep overburden. Therefore, it is feasible to build high geomembrane faced soft rockfill dams on the overburden in strong earthquake area.
Acknowledgements
The authors wish to thank the Open Research Fund of Hunan Provincial Key Laboratory of Hydropower Development Key Technology (Grant No. PKLHD202004).
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