Peng Yu， Liu Ming
Senior Engineer
Songhuajiang and Liaohe River Water Conservancy Commission, Changchun, China,
(86)-431-5607113
Sun Ying Teng Limei Chen Zhaohe
Lecturer Engineer Professor
Beijing Postgraduates School, North China Inst. of Water Resources & Hydropower, Beijing, China, (86)-10-63286960
Abstract:
The numerical simulation of 3-D seepage flow for Gong-Bo-Xia Hydropower Project
is described in this paper. Gong-Bo-Xia Hydropower Project is a large
multipurpose hydropower project, with total capacity of 1500MW, in Yellow River,
it is located in Qinghai Province, China, and composed of outlet works, dam,
intake of hydropower system, low-level outlet and concrete cutoff etc.. The
physical seepage space is very large. Its boundaries are such that the upstream
boundary is taken at 480m upstream from axis of dam; the downstream one is taken
at 900m downstream from axis of dam; the lowest bottom boundary is taken at
elev.1800m the left boundary is taken at 200m
outside of the left wall of the spillway and the right one is taken at 100m
outside the right end of the concrete cutoff. Considering the complexity of the
layout of the project and the seepage space, as well as the variety of the
seepage control measures, Boundary-Fitted Curvilinear Coordinates (BFCC)
transformation and domain decomposition technique has been used here to perform
the numerical simulation of 3-D seepage flow of several alternatives. According
to the results and analysis, some conclusions were made, which provide a useful
basis for the project design with reliable safety and economy.
Keywords: seepage flow, Boundary-Fitted Curvilinear Coordinates(BFCC), domain decomposition, numerical simulation, 3-D, hydropower project
Gong-Bo-Xia
Hydropower Project, the fourth cascade after Long-Yang-Xia, La-Xi-Wa and Li-Jia-Xia
Projects in Yellow River, is located in Qinghai Province, China. It is a large
multipurpose hydropower project with total capacity of 1500MW, and composed
mainly of five parts which from left to right bank are successively outlet
works, dam, intake of hydropower system, low-level outlet and concrete cutoff.
The dam is CFRD with maximum height of 139m, which creates a reservoir storage
of 6.2
. The elevation of dam crest is 2010m. Width of the crest is 10m and its length
is 423m. The whole length of the concrete cutoff is 548m which can cut off the
high permeability sand layer located in the right abutment. The layout of the
project, the location of every part, and their structure sizes, material
characteristics as well as engineeringgeology were all described in detail in
Ref.[1].
It is well known that seepage flow analyses is one of the important parts in hydraulic engineering design. Engineering practice shows that the safety and economy of the structure and project layout are mainly depended on the correctness of seepage flow analyses and the adequacy of the selection of seepage control measures.
The 3-D seepage space of Gong-Bo-Xia Project is not only very large, but also very complicated. Considering the complexity in configuration, the difference in structure sizes, the irregularity of the geometric boundaries, the anisotropy of materials and the inhomogeneity of engineeringgeology, numerical simulation of 3-D seepage flow for Gong-Bo-Xia Hydropower Project should be carried out by using BFCC transformation and domain decomposition technique which can make the boundary conditions be introduced accurately in complicated seepage space in order to ensure the accuracy of simulation.
In order to properly analyze the seepage flow of the project, the external boundaries of the seepage space can be selected as follows: 480m upstream of axis of dam, which can keep enough surface area for foundation seepage; 900m downstream of axis of dam, which can make seepage flow downstream freely; vertically down to elev.1800.0m; 200m outside the left wall of spillway as the left boundary and 100m outside the right end of concrete cutoff as right boundary. The internal boundaries of seepage space are composed of the multiple substructures boundaries respectively with the same physical and mechanical characteristics.
The governing equation of 3-D steady seepage flow in original physical space was adopted as follows:
(1)
where,
is piezometric head and
is coefficient of permeability
whose value varied for different layer of porous media. The subscripts X, Y, Z
denote the partial differentiation with respect to X, Y, Z axis respectively.
The boundary conditions are basically divided into two classes, i.e. the first class and second class of boundary conditions.
The first class of boundary conditions may be expressed as follows:
(2)
where
represents the first class boundary
considered, and
is the function known on
.
The second class of boundary conditions may be expressed as follows:
(3)
where
represents the second class
boundary considered,
is the known inflow (or outflow)
rate through unit area of
, and
,
,
are direction cosines of point
at
.
In order to transform the original physical space into the transformed domain, the BFCC transformation utilizes the following Poisson equations and boundary conditions:
(4)
(5)
where
are control functions and
represent external and internal
boundaries respectively.
Correspondingly, the governing equations and boundary conditions for physical space (1), (2) and (3) have to be transformed into the following transformed equations and corresponding boundary conditions:
(6)
o
(7)
(8)
where
and
are coefficients consisting of
first derivatives of
and
with respect to
and
;
is Jacobi determinant of the
transformation;
and
are corresponding to original
boundaries
and
respectively. In fact, the 3-D
seepage problem will be solved for equation (6), (7), (8) simultaneously in the
transformed domain.
The theory and engineering application of the BFCC transformation technique were described in detail in Ref.[2~5].
As mentioned above, the sizes of different zones in 3-D seepage space for Gong-Bo-Xia Hydropower Project are different largely. If the grid system had been generated in the whole space according to the requirement of computation for the smallest zone, it would be the case that a great number of work will be done unnecessarily for the other zones. On the other hand, if the system had been generated in the whole space according to the requirements for the larger ones, the case would be that the smaller ones may not be solved accurately. Against the above contradictories, we have to utilize the domain decomposition and coupling technique along with BFCC, i.e. the whole seepage space was decomposed into many subdomains, then transformed with BFCC according to their own grid systems respectively, and comparisons should be made continually during the iterative computations for the interfaces of the subdomains until satisfied. This technique has been applied successfully on a clay core dam with the results very close to those from laboratory tests. Practice shows that the domain decomposition technique is successful in quickness, efficiency and accuracy[3~5].
Several design alternatives have been simulated[5], but only the suggested alternative is presented herein due to space limitation.
Under the simultaneous actions of foundation and both sides of river channel as well as the drainage facilities of hydropower station, the equipotential lines behind grouting curtain turn to river bed with the general concave tendency and directed downward to supply the seepage in dam body and the foundation underneath the powerhouse, and concentrated in the dam near the rear of the concrete face and the drainage facilities, so a 3-D pattern is obviously presented for the whole seepage space as shown in Fig.1 and Fig.3. The seepage in the zone under power station is both under pressure and with water table, whereas the major is seepage with water table and only a small part, such as the bottom of powerhouse has a water head of about 20m. As shown in Fig.2, the infiltration distributed at the bottom of the steel penstocks is mainly located under the fissures with low-angle dip, though a small part went into it, but did not run through, the slide stability would not be influenced. If the pumping and drainage measures were not used at the foundation beneath the steel penstocks, the infiltration distributed there would all be located upon the fissures with low-angle dip, which would bring potential danger for the structure’s foundation[5]. To sum up, a remarkable effect can be achieved by using the drainage facilities in dam as well as pumping and drainage facilities in the foundation beneath the steel penstocks.
Besides, if six pumping and horizontal drainage tunnels are set up beneath the foundation of intake and steel penstocks, the design requirement can be satisfied, but not economic and the horizontal drainage tunnel located beneath the foundation of intake is ineffective. In order to make the design be technical feasible and be rational in economy, four pumping and horizontal drainage tunnels were suggested to be set up, which may satisfy all the requirements of the project.
For the concrete cutoff, although the seepage head was only reduced 38%~10% under the influence of water table of the surrounding mountains, the infiltration is lower than that in sand-gravel-pebble layer in right-bank terrace of class Ⅲ, and it fulfills the design requirements.
As shown in Fig.2 and 3, the effect of the grouting curtain for lowering the seepage pressure is not remarkable due to mainly the small ratio of permeability coefficients between the grouting curtain and underground part. Nevertheless, the grouting curtain performs certain actions in seepage control. Considering the large scale of the project and its operation safety, it is still necessary to set up the grouting curtain.
The computed total
seepage for the suggested design is 8035.2
, which equals 0.129‰
of the annual discharge in the river reach. The seepage flow is 129.6
through the concrete face of the dam, 6393.6
in the foundation of spillway, dam and intake, 302.4
in left-bank (left side of spillway), 1209.6
in right-bank (right side of unit 1#). The maximum seepage slope is
0.517 in the left-bank, 0.102 in the right-bank, 140.4 in the concrete face of
dam, 21.5 in the cushion layer and transition zone, 8.7 in the plinth of
foundation and 66.91 in the right-bank concrete cutoff, all of the seepage
slopes are smaller than allowable slope, and thereby the seepage stability is
guaranteed.
For Gong-Bo-Xia Hydropower Project constructed in “U” shape valley, considering the complexity of its general layout of structures and hydrogeological conditions as well as the seepage control measures, the seepage is three dimensional and exists with water table and/or under pressure.
It can be concluded from the computed results that the effects of concrete face and the drainage facilities in dam as well as the pumping and horizontal drainage tunnels set up beneath the foundation of steel penstocks, are remarkable. The effect of the grouting curtain for lowering the seepage pressure is not remarkable. Nevertheless, the grouting curtain performs certain action in seepage control. Considering the large scale of the project and its operation safety, it is still necessary to set up the grouting curtain. All of the computed seepage slopes are lower than allowable ones, and the seepage stability is guaranteed.
References
[1] The requirements for layout and geology of the Gong-Bo-Xia Hydropower Project for 3-D seepage flow computation. Northwest China Electric Power Investigation, Design and Research Institute, National Electric Power Co., 1998.11(in Chinese).
[2] FANG Fangxin, QI Li, PENG Yu and CHEN Zhaohe, Computer Application to 3-D Seepage Flow Analysis for La-Xi-Wa Hydropower Project, The Eighth Congress, APD-IAHR, Oct., 1992. Pune, India.
[3] PENG Yu, CHEN Zhaohe, Numerical 3-D seepage flow for Gong-Bo-Xia hydropower project using BFCC transformation and domain decomposition techniques, International symposium on high earch-rockfill dams, Oct., 1993, Beijing, China.
[4] CHEN Zhaohe, SUN Yongjuan, PENG Yu, et.la, Three dimensional seepage flow analyses for the upper pond of a large pumped storage station, Proceedings of Hydropower ’96, 1996.11.
[5] CHEN Zhaohe, PENG Yu, SUN Ying, et.la, Resesrch Report-Numerical Simulation of 3-D Seepage Flow in Gong-Bo-Xia Hydropower Project, School of Postgraduates, North China Inst. of Water Conservancy & Hydropower, 1999.10 (in Chinese).