Method for determining optimal water level heights of upstream and downstream of homogeneous earth dam

Abstract

The invention discloses a method for determining the upstream and downstream optimal water level height of a homogeneous earth dam, and belongs to the technical field of stability evaluation and disaster prevention and control of homogeneous earth dams. Comprising the following steps: establishing a homogeneous earth dam section mathematical model to obtain a homogeneous earth dam minimum safety coefficient contour map; a change curve between the upstream and downstream water level height possible value and the failure probability is obtained; and obtaining the upstream and downstream optimal water level height of the homogeneous earth dam according to the desired failure probability. According to the method, the concept of the failure probability is introduced into the homogeneous earth dam project, and the reliability of the homogeneous earth dam slope project is reflected through the failure probability. The upstream water level height and the downstream water level height are considered, the rule between the upstream water level height and the downstream water level height and the failure probability is effectively obtained, the safety of the earth dam slope is improved by adjusting the relation between the upstream water level and the downstream water level in the earth dam slope project, and a new idea and a new method for economically and controllably reducing the instability probability of the earth dam slope are provided.

Description

Technical Field

[0001] The present invention belongs to the technical field of stability evaluation and disaster prevention of homogeneous earth dams, and particularly relates to a method for determining optimal water level heights upstream and downstream of a homogeneous earth dam. Background Art

[0002] The scale and frequency of geological disasters caused by the instability of earth dams in reservoirs are increasing year by year, causing huge economic losses and casualties. At present, there are a large number of homogeneous earth dams in many small reservoirs in my country. The instability of earth dams is often caused by the change of water level difference between the upstream and downstream of the earth dams. Therefore, it is particularly important to control the influence of the upstream and downstream water level height on the stability of the earth dam. The main reason for the instability of homogeneous earth dams due to the upstream and downstream water level height is that the height of the infiltration line in the earth dam is different under different upstream and downstream water level heights, resulting in different sizes of excess pore water pressure in the earth dam. When the excess pore water pressure in the earth dam is greater, the anti-sliding force provided by the hydrostatic pressure outside the slope is smaller, which will easily cause the instability of the earth dam. In existing projects, the research on the influence of the upstream and downstream water level height stability of homogeneous earth dams is not comprehensive enough. At present, the way to improve the slope stability of the dam body is more to improve the material properties and reinforcement. There is little research on regulating the upstream and downstream water level height of homogeneous earth dams to achieve stable improvement. Therefore, a new idea and method for determining the optimal upstream and downstream water level height of homogeneous earth dams is urgently needed. Summary of the invention

[0003] In view of the above shortcomings, the object of the present invention is to provide a method for determining the optimal water level height upstream and downstream of a homogeneous earth dam.

[0004] The technical solution adopted by the present invention is: a method for determining the optimal water level height upstream and downstream of a homogeneous earth dam, the technical key points of which are as follows: Firstly, a mathematical model of the homogeneous earth dam section is established. According to the different upstream and downstream water levels of the homogeneous earth dam, the minimum safety factor of the homogeneous earth dam is calculated using the limit equilibrium method. The upstream and downstream water levels are changed, and the above calculation is repeated to obtain the contour map of the minimum safety factor of the homogeneous earth dam under different upstream and downstream water levels. According to the minimum allowable safety factor of the homogeneous earth dam, the possible values ​​of the upstream and downstream water level heights corresponding to the minimum allowable safety factor are queried on the contour map of the minimum safety factor of the homogeneous earth dam. Then, under different possible values ​​of the upstream and downstream water level heights, considering the uncertainty of the soil parameters of the homogeneous earth dam, the Monte Carlo sampling method combined with the response surface method is used to obtain the failure samples of the homogeneous earth dam section, and the change curve between the possible values ​​of the upstream and downstream water level heights of the homogeneous earth dam section and the failure probability is calculated; Finally, the optimal water level heights upstream and downstream of the homogeneous earth dam are obtained according to the expected failure probability.

[0005] In the above scheme, the steps to obtain the minimum safety factor contour map are: (1) Establish a mathematical model of the homogeneous earth dam section and determine the design based on the survey data. x The design values ​​of upstream water level are denoted as A1, A2, A3, ...A x , y The design values ​​of downstream water level are denoted as B1, B2, B3, ...B y ; (2) At the upstream water level height of a homogeneous earth dam section, A i , i =1,2,... x , change the downstream water level, and use the Slope / w module in Geo-studio to calculate (A i ,B j ) corresponds to the minimum safety factor FS ij , i =1,2,… x , j =1,2,...... y , using (A i , B j , FS ij ), i =1,2,… x , j =1,2,...... y , draw the contour map of the minimum safety factor of the homogeneous earth dam under the design combination value of the upstream and downstream water level height; In the above scheme, the steps to obtain the variation curve between the possible values ​​of the upstream and downstream water level heights and the failure probability of the homogeneous earth dam section are as follows: (1) According to the required minimum safety factor, obtain the minimum safety factor contour map of the homogeneous earth dam W The design combination value of the upstream and downstream water level height is recorded as (A k , B k ), k =1,2,3..... W ,exist W The upstream and downstream water level design combination value (A k , B k ) under the condition that the cohesion of the homogeneous earth dam soil c , internal friction angle φ Treated as a random variable ， Generated using Matlab software N parameter samples Q1, Q2, ..., Q N , Q1, Q2, ..., Q are calculated using the response surface methodology N The corresponding safety factor FS 1, FS 2,……, FS N ;like FS i <1, then Q i , ( i =1, 2, 3...... N ) is a failed sample, and the process is repeated to obtain n unstable samples, calculate the failure probability of homogeneous earth dam P fz = n / N , z =1,2,3...... W ; (2) Using the above-obtained W The design combination value of upstream and downstream water level height (A k , B k ) and the corresponding failure probability P fz , and draw the variation curve between the design combination values ​​of different upstream and downstream water level heights of the homogeneous earth dam and the failure probability.

[0006] In the above scheme, the desired expected failure probability is finally determined by querying the curve to determine the optimal water level height upstream and downstream of the homogeneous earth dam. The beneficial effects of the present invention are as follows: the method for determining the optimal water level height of the upstream and downstream of a homogeneous earth dam includes the steps of establishing a mathematical model of the homogeneous earth dam section to obtain a contour map of the minimum safety factor of the homogeneous earth dam; the step of obtaining a change curve between the possible values ​​of the upstream and downstream water level heights and the failure probability; and the step of obtaining the optimal water level height of the upstream and downstream of the homogeneous earth dam according to the desired expected failure probability. The method of introducing the failure probability takes the upstream and downstream water level heights into consideration, and effectively obtains the law between the upstream and downstream water level heights and the failure probability. In the earth dam slope engineering, the relationship between the upstream and downstream water levels is adjusted to improve the safety of the earth dam slope, and an economical and controllable method for reducing the probability of earth dam slope instability is provided. BRIEF DESCRIPTION OF THE DRAWINGS

[0007] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0008] Figure 1 A flow chart of a method for determining the optimal water level height upstream and downstream of a homogeneous earth dam in an embodiment of the present invention; Figure 2A cross-sectional model diagram of a homogeneous earth dam in an embodiment of the present invention; Figure 3 Contour line diagram of minimum safety factor at different upstream and downstream water level heights of a homogeneous earth dam in an embodiment of the present invention; Figure 4 A graph showing the failure probability of different upstream and downstream water level combinations of a homogeneous earth dam in an embodiment of the present invention. DETAILED DESCRIPTION

[0009] To make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the following is a brief description of the present invention in conjunction with the attached Figure 1-Figure 4 The present invention is further described in detail with reference to the accompanying drawings and specific embodiments.

[0010] In this embodiment, the cross-section height of the homogeneous earth dam is 10m, the bottom width is 53m, the slope is 1:2, the slope angle is 26.57°, the earth dam body is silt, its permeability coefficient is K=0.864m / d, the average value of the internal friction angle φ is 20°, the standard deviation is 6, the average value of the cohesion c is 6kpa, the standard deviation is 1.8, the bulk density γ is 20kN / m3, the saturated volume water content is 0.5m3m-3, and the residual water content is 0.05m3m-3.

[0011] The steps of the method for determining the optimal water level height upstream and downstream of a homogeneous earth dam adopted in this embodiment are as follows: The Seep / w module in Geo-studio software is used to establish a numerical model of the homogeneous earth dam section. Figure 2 As shown in the figure, the 4 upstream water level heights are designed as follows: A1=2m, A2=4m, A3=6m, A4=8m, and the 4 downstream water level heights are designed as follows: B1=2m, B2=4m, B3=6m, B4=8m; by designing orthogonal experiments, when the upstream water level height is A1=2m and the downstream water level height is B y , y =1,2,...,4, use the limit equilibrium method to calculate the corresponding minimum safety factor: FS 1=1.154, FS 2=1.171, FS 3=1.241, FS 4=1.4, change the upstream water level, and repeat the above steps until (A x , B y ) x =1,2,…,4, y =1,2,…,4 The corresponding minimum safety factor under orthogonal test combination FS i ( i =1,2...,16), using (A x , B y , FSi ) x =1,2,…,4, y =1,2,…4, i =1,2,…16, draw the minimum safety factor contour map under different combinations of upstream and downstream water level heights of homogeneous earth dam sections, such as Figure 3 As shown; According to the expected minimum safety factor of homogeneous earth dam section FS =1.163, and the five upstream and downstream water level height combinations are obtained in the minimum safety factor contour map: (A1, B1)=(2.51m, 3.47m), (A2, B2)=(3.07m,4.01m), (A3, B3)=(5.35m, 4.69m), (A4, B4)=(6.76m, 5.26m), (A5, B5)=(8m, 5.8m); Under a certain upstream and downstream water level height combination, the cohesion c and internal friction angle φ As a log-normal random variable, 10 random 5 soil parameter samples Q1, Q2, ..., Q 100000 , calculated based on the response surface methodology10 5 The parameter samples correspond to N =10 5 The safety factor is FS 1, FS 2,……, FS 100000 .exist N =10 5 Among the safety factors, if the safety factor FS i <1, = 1, 2, ..., 10 5 , then Q i For failed samples, repeat the process to obtain n unstable samples, according to the formula P f = n / 10 5 Calculate the failure probability corresponding to the homogeneous earth dam section, change the upstream and downstream water level height combination value, and repeat the above steps until the relationship curve between the upstream and downstream water level height combination value and the failure probability of the homogeneous earth dam is obtained. Figure 4 As shown in the figure, when the combined value of the upstream and downstream water levels is (A, B) = (2.51m, 3.47m), the corresponding failure probability P f =85.86%; when the combined value of the upstream and downstream water level height is (A, B)=(3.07m, 4.01m), the corresponding failure probability Pf =75.08%; when the combined value of the upstream and downstream water levels is (A, B)=(5.35m, 4.69m), the corresponding failure probability P f =72.72%; when the combined value of the upstream and downstream water levels is (A, B)=(6.76m, 5.26m), the corresponding failure probability P f =49.68%; when the combined value of the upstream and downstream water levels is (A, B) = (8m, 5.8m), the corresponding failure probability P f =12.23%. You can query based on the required minimum safety factor and expected failure probability. Figure 3 , 4 Relationship curve is used to determine the optimal combination of water level heights upstream and downstream of the homogeneous earth dam; for example, when the expected minimum safety factor is 1.163 and the expected failure probability is 49.68%, the optimal combination of water level heights upstream and downstream of the homogeneous earth dam is (6.76m, 5.26m).

[0012] Therefore, the comparison found that the influence of upstream and downstream water level on the safety of homogeneous earth dams is often ignored, resulting in incomplete consideration of the stability of homogeneous earth dams. The present invention designs different upstream and downstream water level combination values, uses the orthogonal test method, and uses the limit equilibrium method to calculate and obtain the minimum safety factor of the homogeneous earth dam and draws a contour map. According to the expected minimum safety factor, different upstream and downstream water level combination values ​​are obtained. Considering the variability of soil parameters, the relationship curve between the upstream and downstream water level combination value and the failure probability of the homogeneous earth dam is obtained, and the upstream and downstream water level combination value of the homogeneous earth dam is determined according to the required expected minimum safety factor and the expected failure probability. The engineering example verifies that when the expected minimum safety factor is 1.163, as the upstream and downstream water level combination value increases, the failure probability of the homogeneous earth dam section gradually decreases, which fully verifies the influence of the upstream and downstream water level on the stability of the homogeneous earth dam section. Finally, the optimal upstream and downstream water level of the homogeneous earth dam can be determined according to the required expected minimum safety factor and the expected failure probability. The effectiveness of the present invention is verified by comparative analysis of examples.

[0013] In actual projects, the optimal upstream and downstream hydrological difference is achieved by controlling and adjusting the upstream and downstream water level heights, thereby maximizing the stability of the slope. On this basis, corresponding reinforcement is carried out to reduce the use of reinforcement materials, reduce project costs, and improve the utilization rate of support materials.

[0014] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art can easily think of changes or substitutions within the technical scope disclosed by the present invention, which should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A method for determining the optimal water level height upstream and downstream of a homogeneous earth dam, characterized in that: The following steps are involved: Firstly, a mathematical model of the homogeneous earth dam section is established. According to the different upstream and downstream water levels of the homogeneous earth dam, the minimum safety factor of the homogeneous earth dam is calculated using the limit equilibrium method. The upstream and downstream water levels are changed, and the above calculation is repeated to obtain the contour map of the minimum safety factor of the homogeneous earth dam under different upstream and downstream water levels. According to the minimum allowable safety factor of the homogeneous earth dam, the possible values ​​of the upstream and downstream water level heights corresponding to the minimum allowable safety factor are queried on the contour map of the minimum safety factor of the homogeneous earth dam. Then, under different possible values ​​of the upstream and downstream water level heights, considering the uncertainty of the soil parameters of the homogeneous earth dam, the Monte Carlo sampling method combined with the response surface method is used to obtain the failure samples of the homogeneous earth dam section, and the change curve between the possible values ​​of the upstream and downstream water level heights of the homogeneous earth dam section and the failure probability is calculated; Finally, the optimal water level heights upstream and downstream of the homogeneous earth dam are obtained according to the expected failure probability.

2. A method for determining the optimal water level of a homogeneous earth dam upstream and downstream as claimed in claim 1, characterized in that ,The steps to obtain the minimum safety factor contour map are: (1) Establish a mathematical model of the homogeneous earth dam section and determine the design based on the survey data. x The design values ​​of upstream water level are denoted as A1, A2, A3, ...A x , y The design values ​​of downstream water level are denoted as B1, B2, B3, ...B y ; (2) At the upstream water level height of a homogeneous earth dam section, A i , i =1,2,... x , change the downstream water level, and use the Slope / w module in Geo-studio to calculate (A i ,B j ) corresponds to the minimum safety factor FS ij , i =1,2,… x , j =1,2,...... y , using (A i , B j , FS ij ), i =1,2,… x , j =1,2,...... y , draw the contour map of the minimum safety factor of the homogeneous earth dam under the design combination value of the upstream and downstream water level height.

3. A method for determining the optimal water level of upstream and downstream of a homogeneous earth dam as claimed in claim 1, characterized in that ,The steps to obtain the variation curve between the possible values ​​of upstream and downstream water level heights and failure probability of homogeneous earth dam sections are: (1) According to the required minimum safety factor, obtain the minimum safety factor contour map of the homogeneous earth dam W The design combination value of the upstream and downstream water level height is recorded as (A k , B k ), k =1,2,3..... W ,exist W The upstream and downstream water level design combination value (A k , B k ) under the condition that the cohesion of the homogeneous earth dam soil c , internal friction angle φ Treated as a random variable ， Generated using Matlab software N parameter samples Q1, Q2, ..., Q N , Q1, Q2, ..., Q are calculated using the response surface methodology N The corresponding safety factor FS 1, FS 2,……, FS N ;like FS i <1, then Q i , ( i =1, 2, 3...... N ) is a failed sample, and the process is repeated to obtain n unstable samples, calculate the failure probability of homogeneous earth dam P fz = n / N , z =1,2,3...... W ; (2) Using the above-obtained W The design combination value of upstream and downstream water level height (A k , B k ) and the corresponding failure probability P fz , and draw the variation curve between the design combination values ​​of different upstream and downstream water level heights of the homogeneous earth dam and the failure probability.

4. A method for determining the optimal water level of upstream and downstream of a homogeneous earth dam as claimed in claim 1, characterized in that ,Finally, according to the required expected failure probability, it means: the query curve is used to determine the optimal water level height upstream and downstream of the homogeneous earth dam.

Images