CONSIDERATIONS ON DETERMINISTIC ANALYSIS MODEL OF SEEPAGE FLOW IN EARTH-ROCK DAM

Gu Chongshi,  Zhang Qianfei

 Hohai University, Nanjing, China

College of Water Conservancy & Hydropower Engineering,

Hohai University, 1,Xikang Road, Nanjing, 210098,China

Tel: +86-25-3713777 ext. 50957

Fax:+86-25-3713059

E-mail: zqf7586@sohu.com

Abstract: Aimed at the characteristic of seepage flow in earth-rock dam, the seepage flow deterministic analysis model is established based on the FEM for 3-D seepage flow together with observation data, and the separation of seepage’s amount for dam body, dam foundation and side banks is made theoretically. Practical computation example shows that the model’s precision is higher and the separation results are more objective and satisfactory.

Keywords: earth-rock dam, seepage, deterministic analysis model

1  INTRODUCTION

The condition of seepage in earth-rock dam is one of important factors that affect dam’s safety, and the observation of seepage is a primary item in the earth-rock dam’s prototype observations and its contents include the water level of piezometer and the amount of seepage in each part of dam. It is of significance to establish the seepage monitoring model of earth-rock dam reasonably by use of prototype observation data for analyzing and monitoring dam’s condition of seepage correctly and timely. At present, in the establishment of mathematic monitoring model of dam’s seepage for analyzing and monitoring dam’s condition of seepage, several hot point problems are following as:

(1) The observation value of seepage (such as the height of phreatic line) is variational continuously with the reservoir level, and besides, the seepage field of earth-rock dam is also affected by the risefall’s velocity of reservoir level. Thus, it is one of key tasks in the analysis of earth-rock dam’s seepage that how to simulate the practical status of seepage using mathematic models.

(2) As a result of lack of observation items, the prototype observation data are not enough to analyze and monitor the whole seepage situation of dam. For instance, there is only one survey point in the downstream that is made to measure the dam’s total amount of seepage in some earth-rock dams. In order to detect the dam’s hidden danger and take measures instantly, it is very important that how to analyze and monitor the seepage status of whole dam and its each part (ex. dam body, dam foundation and side banks) by use of fewer prototype observation data. This is another key problem in the field of dam’s seepage safety monitoring.

Aimed at the above-mentioned problem, the separation of seepage’s amount for dam body, dam foundation and side banks is made through 3-D seepage finite element method analysis, and thereby the seepage flow deterministic analysis model is established. It presents a new method to establish earth-rock dam’s seepage safety monitoring model reasonably.

2  PRINCIPIUM OF DETERMINISTIC ANALYSIS MODEL

The amount of seepage in earth-rock dam is mostly affected by the reservoir level, rainfall precipitation, temperature and time-effect. The seepage’s amount can then be expressed as

                          (1)

in which = the amount of seepage; , , , = the seepage’s component of hydraulic pressure, rainfall, temperature, and time-effect, respectively.

2.1  Hydraulic pressure component ( )

The hydraulic pressure component consists of the amount of dam body filtration ( ), dam foundation filtration ( ) and bypass seepage ( ), namely

                                        (2)

in which , and  are relevant to the first to third power of the depth of upstream[1], i.e.

, ,                              (3)

The hydraulic pressure component ( ) can then be expressed as

                                (4)

The amount of dam body filtration ( ), dam foundation filtration ( ) and bypass seepage( ) can be obtained through 3-D seepage finite element method computation in any depth of upstream ( =1,2,…,n, where n represents the group count of computation). The coefficients in formula (4), , and  are gained under optimization principium utilizing the data of  and , , (totally n groups). In this way, the mathematic expressions are obtained of the amount of dam body filtration ( ), dam foundation filtration ( ) and bypass seepage ( ), which vary with the reservoir level. Thereof, the dynamic variance curve is constructed to reflect the seepage amount’s variation with the reservoir level. Thus, the seepage field in the dam can be calculated in any reservoir level.

2.2  Rainfall component ( )

The seepage’s component of rainfall is primary affected by intraday (i.e. the surveying day) rainfall, and its expression is as follows

                                                (5)

in which = the daily precipitation of surveying day; = the regression coefficient of rainfall component.

2.3  Temperature component ( )

The viscosity of water and the crack’s opening of bedrock are changed because of the temperature’s variance, and these changes make an influence on the seepage. The seepage’s component of temperature is primarily caused by the change of temperature of dam foundation and side banks’ bedrock. On the condition of the lack of temperature observation data of bedrock, we take the periodical items as the expression of temperature component, namely

                                       (6)

in which = the accumulative total days from beginning day to surveying day; , , = the regression coefficient of temperature component.

2.4  Time-effect component ( )

Time-effect is an important factor to work on seepage and it is also a key reference to appraise the condition of dam seepage. The reservoir sedimentation, the slow deformation of bedrock’s fissure due to seepage and the antiseepage behavior’s change of impervious barrier will also affect dam’s seepage status. The general rule of  time-effect is that it varies fast in the early days of first filling or one engineering measure and tends to smooth along with time lapse. The usual time-effect component is expressed as

                                                (7)

in which  and  represents the accumulative total days from beginning day to surveying day; , = the regression coefficient of time-effect component.

2.5  Mathematic expression of deterministic analysis model

From the above analysis, the deterministic analysis model of reservoir seepage is expressed as

                                   (8)

in which , , = the rectificative parameters for seepage amount of dam body, dam foundation and side banks, respectively; = the constant; and the other symbols have same meaning as formula (4) to formula (7).

2.6  Parameters’ calculation of deterministic analysis model

The formula (8) can also be expressed as

                                          (9)

 is calculated by substituting the observation value of and into formula (9) and  is the corresponding observation value, and is defined as

                              (10)

On the basis of the least squares, when reaches the minimum, there are

, , , , , , , , ,

                              (11)

From formula (11), the values are obtained of  and the coefficient of multiple correlation , residual mean square deviation . Thus, the parameters of deterministic analysis model in formula (8) are obtained.

3  MODEL APPLICATION AND RESULTS

3.1  Background

The model is applied in the reservoir seepage in one directional blasting rock-fill dam with inclined core. The maximal height of the dam is 81.3m, and the reservoir storage 1.2805 billion m³. The seepage observation is the primary content of the dam’s prototype observation. For observing the condition of reservoir seepage, a measuring weir is arranged in the downstream place where is away 250m from dam axis, and some bypass seepage piezometer orifices are planned in the side banks. On the whole, the observation items for seepage are not enough to analyze the seepage status of dam.

3.2  Fem model for 3-d seepage flow

Figure 1 shows the FEM model of the dam, which is a set of discrete elements with 15,012 elements and 16,846 nodes.

3.3  Deterministic analysis model for reservoir seepage

The regression coefficients of the model are obtained by use of stepwise regression method together with prototype observation data of reservoir seepage. Figure 2 shows the reservoir seepage hydrograph of the observation value, fitting value. The value of coefficient of multiple correlation is 0.9128 and residual mean square deviation  1.6967 L/s which is less than that of the 10% of mean annual seepage amount. The above values show that the model’s precision is higher.

3.4  Results analysis

From the above analysis, it is known that the model’s precision is higher and the model is available for analyzing and monitoring the seepage condition of dam. In view of the lack of observation data of the amount of dam body filtration, dam foundation filtration and bypass seepage, they are separated by utilizing deterministic analysis model and the dam’s seepage condition is analyzed and appraised based on the separation results.

It is known that the rainfall runoff is apt to lead the rapid increase of reservoir seepage. In order to lessen the rainfall runoff’s function on the reservoir seepage and analyze quantificationally the amount of dam body filtration, dam foundation filtration and bypass seepage caused by reservoir level, table 1 integrates the separation results of reservoir seepage’s maximal value and minimal value in the 11^th month with minor rainfall of each year since 1984 to 1996. In addition, in virtue of the separation results, figure 2 shows the hydrograph of the amount of dam body filtration, dam foundation filtration and bypass seepage due to the change of reservoir level and groundwater level, and figure 3 plots the relation curve of above components with reservoir level.

From Table 1, it is shown that the separation value by model is in proximity to the FEM computation value, so it is available to analyze the action of each part’s seepage on the whole dam’s seepage by use of deterministic analysis model. From table and figures, it is shown that:

(1) The reservoir seepage is mainly affected by the reservoir level, and consequently the amount of dam body filtration, dam foundation filtration and bypass seepage are also mainly affected by the change of reservoir level. All three components increase and decrease with the rise and recession of level.

(2) The large proportion of the total amount of reservoir seepage is dam foundation filtration, then bypass seepage, whereas the least proportion of that is dam body filtration. For instance, in November 14, 1990, the reservoir level is lower and the observation value of reservoir seepage is 13.46 L/s. The hydraulic pressure component is 10.1014 L/s and the other 2.5357 L/s. Among the hydraulic pressure component, the amount of dam body filtration, dam foundation filtration and bypass seepage are 0.4671 L/s, 6.5992 L/s, 3.0351 L/s respectively, which comprise 3.5%, 49.0%, 22.5% of the total reservoir seepage. This shows that the dam has lower saturation line and the reservoir seepage results mostly from the filtration of dam foundation and side banks.

(3) Figure 3 shows that the proportion of bypass seepage to the total reservoir seepage increases with the rise of water level, whereas that of dam foundation seepage decreases with the rise of water level after eliminating the influence of rainfall on the reservoir seepage. For instance, in November 9,1994, the reservoir level is higher and the observation value of reservoir seepage is 32.51 L/s. The hydraulic pressure component is 26.4748 L/s and the other 6.1788 L/s. Among the hydraulic pressure component, the amount of dam body filtration, dam foundation filtration and bypass seepage are 2.5878 L/s, 13.2780 L/s, 10.6090 L/s respectively, which comprise 7.5%, 38.3%, 30.8% of the total reservoir seepage. Compared with the above value occurring in November 14,1990, the proportion of side banks to the total seepage increases 8.3% and that of dam foundation seepage decreases 10.7%. This shows that the reservoir seepage is mostly produced through dam foundation filtration in lower water level (about 50%). However, in higher water level, the seepage through side banks holds considerable proportion (about 30%), and its influence on reservoir seepage can not be neglectable.

4  CONCLUSIONS

(1) Aimed at the lack of seepage observation items in earth-rock dam, the seepage’s amount of dam body, dam foundation and side banks are separated by utilizing FEM computation, and in this way the deterministic analysis model is established for analyzing and appraising the seepage condition of whole dam and its each part (dam body, dam foundation, side banks and as such).

(2) Practical example shows that the model has higher precision and good fitting effect and it is available to forecast the condition of dam seepage. It is of great significance for analyzing and monitoring the condition of dam seepage.

References

[1]  Desai, C. S. & G. C. I, “A residual flow procedure and application for free surface flow in porous media”, Advances in Water Resources, Vol 6, Mar. 1983.

[2]  Glover, R.E. “Groundwater movement.” Engineering Monograph 31,Bureau of Reclamation,U.S. 1964.

[3]  Mao Changxi, Duan Xiangbao and Li Zuyi, “Numerical computation in seepage flow and programs application”, Hohai University Press, Nanjing, Sep. 1999.

[4]  Martin J A, “Consulting engineering view on dams safety”, International Water Power & Dam Construction, UK, Nov. 1985.

[5]  Wu Zhongru, Shen Changsong and Ruan Huanxiang, “Theory and application of hydraulic structure safety monitoring”, Hohai University Press, Nanjing, Aut. 1990.

[6]  Wu Zhongru and Gu Chongshi, “Comprehensive appraisal expert system of dam safety”, Beijing Science and Technique Press, Beijing, Dec. 1997.

Table 1  Separation results of reservoir seepage’s maximal value and minimal value in the 11^th month

Note:  The sign “*” represents the seepage amount caused by reservoir level and groundwater level, not including the components of rainfall, temperature and time-effect.

Fig. 1  FEM model of the dam

Fig. 2  Hydrograph of the amount of dam body filtration, dam foundation filtration and bypass seepage (L/s)

Fig. 3  Curve of the amount of dam body filtration, dam foundation filtration
and bypass seepage (L/s) with reservoir level (m)