Analysis method for earth pressure on high toe wall during water storage period of dam structure

Abstract

The present invention discloses a method for analyzing the earth pressure on the high toe wall during the water storage period of a dam structure, belonging to the technical field of dam engineering, and capable of solving the problem that the earth pressure calculation method directly applied in the existing specifications has a large difference from the earth pressure distribution calculated by the finite element method. The method includes: S1, determining the earth pressure at the completion period on the interface between the high toe wall and the rockfill dam; S2, taking the ratio of the water storage depth to the height of the rockfill dam as the independent variable, and taking the ratio of the increase value of the earth pressure on the interface between the high toe wall and the rockfill dam during the water storage period to the earth pressure at the completion period as the dependent variable, and constructing an S-shaped growth curve equation; S3, determining the empirical parameters in the S-shaped growth curve equation, and determining the earth pressure on the interface between the high toe wall and the rockfill dam during the water storage period according to the S-shaped growth curve equation and its empirical parameters. The present invention is used for calculating the earth pressure on the high toe wall during the water storage period of the dam structure.

Description

Technical Field

[0001] The present invention relates to an analysis method for earth pressure on a high toe wall during the water storage period of a dam structure, belonging to the technical field of dam engineering. Background Art

[0002] In recent years, a large number of domestic projects have applied the concrete high toe wall technology to the face rockfill dam project to transform unfavorable topographic and geological conditions, connect the concrete face slab with the high toe wall, and form a complete anti-seepage system. The shape and structural stress conditions of the high toe wall are relatively complex. At the same time, as a component of the toe slab anti-seepage body of the concrete face rockfill dam, its safety and stability are extremely important for the normal operation of the face rockfill dam.

[0003] Most high toe walls are submerged type and are jointly affected by loads such as rockfill pressure and water pressure. Their working conditions are more complex than those of conventional retaining walls. In the prior art, the calculation of the rockfill pressure at the interface between the high toe wall and the rockfill body often uses the Coulomb earth pressure theory. Whether it is the active earth pressure or the passive earth pressure, this method assumes that the earth pressure varies in a triangular distribution law along the wall back and the wall height. However, the surface load form of the submerged high toe wall is distributed along the inclined surface of the dam body vertically. Directly applying the calculation method in the current specification has a large difference from the earth pressure distribution calculated by the finite element method. Summary of the Invention

[0004] The present invention provides an analysis method for earth pressure on a high toe wall during the water storage period of a dam structure, which can solve the problem that there is a large difference between directly applying the earth pressure calculation method in the current specification and the earth pressure distribution calculated by the finite element method in the prior art.

[0005] The present invention provides an analysis method for earth pressure on a high toe wall during the water storage period of a dam structure, and the method includes:

[0006] S1. Determine the earth pressure at the completion period on the interface between the high toe wall and the rockfill dam;

[0007] S2. Take the ratio of the water storage depth to the height of the rockfill dam as the independent variable, and take the ratio of the increase value of the earth pressure on the interface between the high toe wall and the rockfill dam during the water storage period to the earth pressure at the completion period as the dependent variable, and construct an S-shaped growth curve equation;

[0008] S3. Determine the empirical parameters in the S-shaped growth curve equation, and determine the earth pressure on the interface between the high toe wall and the rockfill dam during the water storage period according to the S-shaped growth curve equation and its empirical parameters.

[0009] Optionally, determining the empirical parameters in the S-shaped growth curve equation in S3 specifically includes:

[0010] Determine the first influencing factor group of the empirical parameters;

[0011] Determine the fitting formula of the empirical parameter according to the first influencing factor group.

[0012] Optionally, the first influencing factor group for determining the empirical parameter is specifically:

[0013] Determine the first influencing factor group of the empirical parameter according to the orthogonal test method.

[0014] Optionally, the determining the fitting formula of the empirical parameter according to the first influencing factor group is specifically:

[0015] According to the first influencing factor group, perform linear fitting on the empirical parameter by using the multiple linear regression method to obtain the fitting formula of the empirical parameter.

[0016] Optionally, the empirical parameter includes the curve vertex value , growth rate and the position of the midpoint of the curve .

[0017] Optionally, the first influencing factor group includes the upstream slope ratio of the rockfill dam, the downstream slope ratio of the high toe wall, the height of the high toe wall, and the height of the rockfill dam.

[0018] Optionally, the S1 specifically includes:

[0019] Use the vertical plane passing through the bottom of the high toe wall and the horizontal plane passing through the top of the high toe wall to divide the rockfill dam into a first rockfill body located below the horizontal plane and adjacent to the high toe wall, a second rockfill body directly above the first rockfill body, a third rockfill body located above the horizontal plane and adjacent to the second rockfill body, and a fourth rockfill body directly below the third rockfill body;

[0020] Determine the gravity of the first rockfill body and the second rockfill body, as well as the uniform load applied by the third rockfill body on the top surface of the fourth rockfill body and the earth pressure coefficient of the dam body, and determine the earth pressure at the completion period on the interface between the high toe wall and the rockfill dam according to the gravity of the first rockfill body and the second rockfill body, the uniform load, and the earth pressure coefficient.

[0021] Optionally, the determining the uniform load applied by the third rockfill body on the top surface of the fourth rockfill body is specifically:

[0022] Determine the gravity of the third rockfill body and convert the gravity of the third rockfill body into the uniform load applied on the top surface of the fourth rockfill body.

[0023] Optionally, the determining the earth pressure coefficient of the dam body is specifically:

[0024] Determine the second influencing factor group of the earth pressure coefficient according to the orthogonal test method;

[0025] According to the second influencing factor group, a linear fitting of the earth pressure coefficient is performed by using the multiple linear regression method to obtain the fitting formula of the earth pressure coefficient.

[0026] Optionally, the second influencing factor group includes the upstream slope ratio of the rockfill dam, the downstream slope ratio of the high toe wall, the height of the high toe wall, and the height of the rockfill dam.

[0027] The beneficial effects that can be produced by the present invention include:

[0028] The analysis method for the earth pressure on the high toe wall during the water storage period of the dam body structure provided by the present invention constructs an S-shaped growth curve equation by using the ratio of the water storage depth to the height of the rockfill dam as the independent variable and the ratio of the increase in the earth pressure on the interface between the high toe wall and the rockfill dam during the water storage period to the earth pressure at the completion period as the dependent variable, and determines the earth pressure on the interface between the high toe wall and the rockfill dam during the water storage period by using this S-shaped growth curve equation. This method has a high fitting accuracy, and the change trend of the growth rate of the curve is consistent with the change trend of the finite element calculation results. Description of the Drawings

[0029] Figure 1 It is a flow chart of the analysis method for the earth pressure on the high toe wall during the water storage period of the dam body structure provided by the embodiment of the present invention;

[0030] Figure 2 It is a schematic diagram of the change of the earth pressure with the increase of the water storage depth provided by the embodiment of the present invention;

[0031] Figure 3 It is a schematic diagram of the fitting of the earth pressure with the increase of the water storage depth provided by the embodiment of the present invention;

[0032] Figure 4 It is the main effect diagram of the influence of each factor on the earth pressure coefficient provided by the embodiment of the present invention;

[0033] Figure 5 It is the main effect diagram of the influence of each factor on the empirical parameter provided by the embodiment of the present invention;

[0034] Figure 6 It is the main effect diagram of the influence of each factor on the empirical parameter provided by the embodiment of the present invention;

[0035] Figure 7 It is the main effect diagram of the influence of each factor on the empirical parameter provided by the embodiment of the present invention;

[0036] Figure 8 It is a schematic diagram of the structure of the high toe wall and the rockfill dam provided by the embodiment of the present invention;

[0037] Figure 9 Schematic diagram for comparing the calculated value of earth pressure during the impoundment period provided by the embodiment of the present invention with the finite element calculation result Specific implementation manners

[0038] The present invention will be described in detail below in conjunction with embodiments, but the present invention is not limited to these embodiments

[0039] The embodiment of the present invention provides an analysis method for the earth pressure on the high toe wall during the impoundment period of a dam structure, as Figure 1 shown, the method includes

[0040] S1. Determine the earth pressure at the completion period on the interface between the high toe wall and the rockfill dam

[0041] The embodiment of the present invention does not limit the method for determining the earth pressure at the completion period. For example, it can be obtained by using the finite element simulation method or by calculating with the theoretical formula

[0042] S2. Take the ratio of the impoundment depth to the height of the rockfill dam as the independent variable, and take the ratio of the increase value of the earth pressure on the interface between the high toe wall and the rockfill dam during the impoundment period to the earth pressure at the completion period as the dependent variable, and construct an S-shaped growth curve equation

[0043] Among them, the expression of the S-shaped growth curve equation is as follows

[0044] ;

[0045] In the formula, the independent variable is , representing the ratio of the impoundment depth to the height of the rockfill dam, and the dependent variable is , which is the ratio of the increase value of the earth pressure caused by impoundment to the earth pressure at the completion period; is the earth pressure during the impoundment period on the interface between the high toe wall and the rockfill dam after impoundment; is the earth pressure at the completion period on the interface between the high toe wall and the rockfill dam after completion; is the impoundment depth; is the height of the rockfill dam; is the empirical parameter in the S-shaped growth curve equation

[0046] S3. Determine the empirical parameter in the S-shaped growth curve equation, and determine the earth pressure during the impoundment period on the interface between the high toe wall and the rockfill dam according to the S-shaped growth curve equation and its empirical parameter

[0047] Among them, determining the empirical parameter in the S-shaped growth curve equation specifically includes

[0048] First, determine the first influencing factor group of the empirical parameter; specifically, determine the first influencing factor group of the empirical parameter according to the orthogonal test method

[0049] Then, determine the fitting formula of the empirical parameters according to the first influencing factor group; specifically, according to the first influencing factor group, use the multiple linear regression method to perform linear fitting on the empirical parameters to obtain the fitting formula of the empirical parameters.

[0050] The above-mentioned empirical parameters include the curve vertex value , growth rate and the curve midpoint position .

[0051] The above-mentioned first influencing factor group includes the upstream slope ratio of the rockfill dam , the downstream slope ratio of the high toe wall , the height of the high toe wall and the height of the rockfill dam .

[0052] Use the orthogonal test method and the multiple linear regression method to obtain the determination formula of the empirical parameters:

[0053] When the rockfill material is soft rock, calculate according to the following formulas respectively.

[0054] ;

[0055] ;

[0056] .

[0057] When the rockfill material is limestone or gravel, calculate according to the following formulas respectively.

[0058] ;

[0059] ;

[0060] .

[0061] After determining the values of the empirical parameters , substitute the values of the empirical parameters into the S-shaped growth curve equation, and the earth pressure during the water storage period can be obtained.

[0062] When calculating the earth pressure at the completion stage using the theoretical formula, S1 specifically includes:

[0063] (1) The rockfill dam is divided into a first rockfill body located below the horizontal plane and adjacent to the high toe wall, a second rockfill body directly above the first rockfill body, a third rockfill body located above the horizontal plane and adjacent to the second rockfill body, and a fourth rockfill body directly below the third rockfill body by using a vertical plane passing through the bottom of the high toe wall and a horizontal plane passing through the top of the high toe wall.

[0064] Reference Figure 8 As shown, ABGF is the high toe wall and AHIJB is the rockfill dam. Make an imaginary vertical plane BD along the bottom of the high toe wall and an imaginary horizontal plane AE along the top of the high toe wall to divide the backfill of the rockfill dam into four parts: the first rockfill body Ⅰ below the AE plane and to the left of the BD plane, the second rockfill body Ⅱ above the AE plane and to the left of the BD plane, the third rockfill body Ⅲ above the AE plane and to the right of the BD plane, and the fourth rockfill body Ⅳ below the AE plane and to the right of the BD plane.

[0065] (2) Determine the gravity of the first and second rockfill bodies, as well as the uniform load applied by the third rockfill body on the top surface of the fourth rockfill body and the earth pressure coefficient of the dam body.

[0066] The following formula is used to determine the gravity of the first rockfill body.

[0067] ;

[0068] In the formula, is the gravity of the first rockfill body; is the unit weight of the rockfill; is the downstream slope ratio of the high toe wall; is the height of the high toe wall.

[0069] The following formula is used to determine the gravity of the second rockfill body.

[0070] ;

[0071] In the formula: is the gravity of the second rockfill body; is the unit weight of the rockfill; is the downstream slope ratio of the high toe wall; is the upstream slope ratio of the rockfill dam; is the height of the high toe wall.

[0072] Determine the uniform load applied by the third rockfill body on the top surface of the fourth rockfill body, specifically: determine the gravity of the third rockfill body and convert the gravity of the third rockfill body into the uniform load applied on the top surface of the fourth rockfill body.

[0073] Determine the earth pressure coefficient of the dam body, specifically: First, determine the second influencing factor group of the earth pressure coefficient according to the orthogonal test method; then, based on the second influencing factor group, use the multiple linear regression method to perform linear fitting on the earth pressure coefficient to obtain the fitting formula of the earth pressure coefficient.

[0074] The above-mentioned second influencing factor group includes the upstream slope ratio of the rockfill dam , the downstream slope ratio of the high toe wall , the height of the high toe wall and the height of the rockfill dam .

[0075] For the earth pressure coefficient , the determination formula can be obtained by using the orthogonal test method and the multiple linear regression method.

[0076] When the rockfill material is soft rock, the value is as shown in the following formula:

[0077] ;

[0078] When the rockfill material is gravel or limestone, the value is as shown in the following formula:

[0079] ;

[0080] In the formula, is the earth pressure coefficient, is the upstream slope ratio of the rockfill dam; is the height of the high toe wall; is the height of the rockfill dam, is the downstream slope ratio of the high toe wall.

[0081] (3) Determine the earth pressure at the completion stage on the interface between the high toe wall and the rockfill dam according to the gravity of the first rockfill body and the second rockfill body, the uniform load, and the earth pressure coefficient.

[0082] Use the following formula to determine the earth pressure at the completion stage.

[0083]

[0084] In the formula: is the earth pressure at the completion stage; is the gravity of the first rockfill body; is the gravity of the second rockfill body; is the unit weight of the rockfill; is the height of the high toe wall; is the uniform load applied to the top surface of the fourth rockfill body, is the earth pressure coefficient.

[0085] The derivation process of the calculation formula for the earth pressure during the water storage period at the interface between the high toe wall and the rockfill dam is described in detail below.

[0086] Figure 2 Figure 4 is the diagram of the variation of earth pressure with the increase of water storage elevation statistically analyzed in combination with the monitoring data of a certain project. The elevation of the top of the high toe wall is 1510.00m. It can be seen from Figure 2 that there is no clear functional relationship between the normal force at the interface between the high toe wall and the rockfill body and the reservoir water pressure, but the characterization feature law conforms to the S-shaped growth curve equation. Therefore, the S-shaped growth curve equation is used to fit the normal force at the interface.

[0087] ;

[0088] In the formula, the independent variable is , which represents the ratio of the water storage depth to the height of the rockfill dam. The dependent variable is , which is the ratio of the increase in earth pressure caused by water storage to the earth pressure at the completion stage; is the earth pressure during the water storage period at the interface between the high toe wall and the rockfill dam after water storage; is the earth pressure at the completion stage at the interface between the high toe wall and the rockfill dam after completion; is the water storage depth; is the height of the rockfill dam; is the empirical parameter in the S-shaped growth curve equation.

[0089] After the water storage of the project under study, when , the earth pressure formula is as follows, and the fitting curve is as shown in Figure 3 . The fitting curve is very close to the finite element calculation result, and the correlation coefficient is about 0.9978, with a high fitting accuracy, and the change trend of the growth rate of the curve is consistent with that of the finite element calculation result. The fitting formula well simulates the change and development of the earth pressure at the interface between the high toe wall and the rockfill body after water storage, and the effect is good.

[0090] .

[0091] Based on the above formula derivation, accurately determining the value of is the key to calculating the earth pressure on the back of the high toe wall during the water storage period.

[0092] For the value of , the orthogonal test method is first used to determine it.

[0093] The orthogonal table has the construction principles of "balanced dispersion" and "neat comparability". The number of tests designed according to this method is small, and it can reflect the change law of objective things. Select orthogonal table to design the orthogonal test. The orthogonal test is determined as follows:

[0094] Each factor replaces the corresponding design parameter value in the orthogonal array according to its different levels, which is the corresponding orthogonal test table. According to the values of each factor in each test scheme, calculations are performed based on the established finite element model. The earth pressure behind the wall is obtained through integral calculation, and then the value of is calculated. The calculation results are shown in Table 1.

[0095] Table 1 Orthogonal test scheme and calculation results

[0096]

[0097] The difference in different levels of a factor is called the main effect of that factor. From Figure 4 analysis, it can be seen that the main effects of the three factors on are quite different. As increases, gradually decreases, and there is a good linear negative correlation between and ; as increases, gradually increases, and there is a good linear positive correlation between the two; as increases, gradually increases, and there is a good linear positive correlation between and .

[0098] From Figure 5 , Figure 6 , Figure 7 analysis, it can be seen that the main effects of the three factors on are quite different. As increases, and gradually increase, gradually decreases; as increases, gradually decreases, gradually increases; as increases, and gradually increase, gradually decreases. The three factors and The three indicators can be approximately considered to have a linear relationship.

[0099] Based on the above, the multiple linear regression method is used for further analysis. Based on Figures 4 to 7 the law and characteristic performance, the upstream slope ratio of the rockfill dam , the ratio of the height of the high toe wall to the height of the rockfill dam , the downstream slope ratio of the high toe wall These three factors act together on , assuming there is no mutual influence among the three variables, the functional forms are respectively set as:

[0100] ;

[0101] In the formula, is any one of ; A is the upstream slope ratio of the rockfill dam ; B is the ratio of the height of the high toe wall to the height of the rockfill dam ; C is the downstream slope ratio of the high toe wall is the corresponding coefficient; is the constant term.

[0102] Perform linear fitting on the 16 groups of data in the orthogonal test table, and respectively establish the calculation models of the upstream slope ratio of the rockfill dam, the ratio of the height of the high toe wall to the height of the rockfill dam, and the downstream slope ratio of the high toe wall for these three parameters with respect to .

[0103] When the dam building material is gravel or limestone, the fitting expressions are respectively as follows:

[0104] ;

[0105] ;

[0106] ;

[0107] .

[0108] When the dam building material is soft rock, the fitting expressions are respectively as follows:

[0109] ;

[0110] ;

[0111] ;

[0112] .

[0113] Next, combined with a certain project of an inlaid concrete face rockfill dam, monitor the prototype observation data and the finite element simulation results, and compare them with the calculation results of the above theoretical formulas.

[0114] The filling material of the dam body is basically limestone, the upstream slope ratio of the rockfill dam, the ratio , the downstream slope ratio of the high cut-off wall , which can be calculated according to the formula proposed by the present invention . It is calculated by the following formula.

[0115] .

[0116] After impoundment, the S-shaped growth curve equation is used to calculate the ratio of the increase in earth pressure caused by impoundment to the earth pressure at the completion period. It can be calculated according to the formula proposed by the present invention: , , . These three empirical parameters are calculated by the following formula.

[0117] ;

[0118] ;

[0119] .

[0120] Substituting into the S-shaped growth curve equation, the earth pressure during the impoundment period on the back of the high cut-off wall after impoundment is obtained. As Figure 9 shown, whether it is the dead water level or the normal impoundment level, the absolute error between the theoretical formula calculation value and the finite element calculation value is very small. It can be seen that the theoretical formula proposed by the present invention well simulates the change and development of the earth pressure during the impoundment period at the interface between the high cut-off wall and the rockfill body after impoundment, and has a high accuracy.

[0121] The analysis method of the earth pressure on the high cut-off wall during the impoundment period of the dam body structure provided by the present invention constructs an S-shaped growth curve equation by taking the ratio of the impoundment depth to the height of the rockfill dam as the independent variable and the ratio of the increase in earth pressure at the interface between the high cut-off wall and the rockfill dam during the impoundment period to the earth pressure at the completion period as the dependent variable, and uses this S-shaped growth curve equation to determine the earth pressure during the impoundment period at the interface between the high cut-off wall and the rockfill dam. This method has a high fitting accuracy, and the change trend of the growth rate of the curve is consistent with the change trend of the finite element calculation results.

[0122] The calculation idea of the earth pressure during the impoundment period determined by the present invention is proposed for the first time, with clear physical meaning, providing guarantee for the safety of the high cut-off wall project of the concrete face rockfill dam.

[0123] The above are only several embodiments of the present application, and do not impose any form of limitation on the present application. Although the present application is disclosed with preferred embodiments as above, it is not intended to limit the present application. Any person skilled in the art, without departing from the scope of the technical solution of the present application, makes some changes or modifications using the technical content disclosed above, which are equivalent to equivalent implementation cases and all fall within the scope of the technical solution.

Claims

1. A method for analyzing the earth pressure on the high toe wall during the water storage period of a dam structure, characterized in that, The method includes: S1. Determine the earth pressure at the completion stage on the interface between the high toe wall and the rockfill dam; S2. Use the ratio of the water storage depth to the height of the rockfill dam as the independent variable, and the ratio of the increase in earth pressure on the interface between the high toe wall and the rockfill dam during the water storage period to the earth pressure at the completion stage as the dependent variable to construct an S-shaped growth curve equation; S3. Determine the empirical parameters in the S-shaped growth curve equation, and determine the earth pressure during the water storage period on the interface between the high toe wall and the rockfill dam according to the S-shaped growth curve equation and its empirical parameters; wherein, the empirical parameters include the curve vertex value a, the growth rate k, and the curve midpoint position x c ; Determining the empirical parameters in the S-shaped growth curve equation in S3 specifically includes: Determine the first influencing factor group of the empirical parameters according to the orthogonal test method; According to the first influencing factor group, and use the multiple linear regression method to perform linear fitting on the empirical parameters to obtain the fitting formula of the empirical parameters; Wherein, the first influencing factor group includes the upstream slope ratio of the rockfill dam, the downstream slope ratio of the high toe wall, the height of the high toe wall, and the height of the rockfill dam.

2. The method according to claim 1, wherein S1 specifically includes: Use the vertical plane passing through the bottom of the high toe wall and the horizontal plane passing through the top of the high toe wall to divide the rockfill dam into a first rockfill body located below the horizontal plane and adjacent to the high toe wall, a second rockfill body directly above the first rockfill body, a third rockfill body located above the horizontal plane and adjacent to the second rockfill body, and a fourth rockfill body directly below the third rockfill body; Determine the gravity of the first rockfill body and the second rockfill body, as well as the uniform load applied by the third rockfill body on the top surface of the fourth rockfill body and the earth pressure coefficient of the dam body, and determine the earth pressure at the completion stage on the interface between the high toe wall and the rockfill dam according to the gravity of the first rockfill body and the second rockfill body, the uniform load, and the earth pressure coefficient.

3. The method according to claim 2, wherein Determining the uniform load applied by the third rockfill body on the top surface of the fourth rockfill body specifically is: Determine the gravity of the third rockfill body and convert the gravity of the third rockfill body into a uniform load applied on the top surface of the fourth rockfill body.

4. The method according to claim 2, wherein Determining the earth pressure coefficient of the dam body specifically is: Determine the second influencing factor group of the earth pressure coefficient according to the orthogonal test method; According to the second influencing factor group, and use the multiple linear regression method to perform linear fitting on the earth pressure coefficient to obtain the fitting formula of the earth pressure coefficient.

5. The method according to claim 4, wherein The second influencing factor group includes the upstream slope ratio of the rockfill dam, the downstream slope ratio of the high toe wall, the height of the high toe wall, and the height of the rockfill dam.

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