CN110598308B - Method for determining standard shearing-resistant subentry coefficient of concrete gravity dam - Google Patents
Method for determining standard shearing-resistant subentry coefficient of concrete gravity dam Download PDFInfo
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Abstract
The invention discloses a method for determining a standard shearing-resistant subentry coefficient of a concrete gravity dam, which comprises the following steps: 1) determining a shear-resistant friction coefficient and a cohesion standard value according to the mechanical properties of the sliding surface of the concrete gravity dam; 2) establishing a model for determining the coherence of the standard shear parameter subentry coefficient and the structural coefficient without single working condition safety and reliability constraint; 3) and solving the model according to the set value ranges of the dam height and the structural coefficient and the stepping interval to obtain a design subentry coefficient and a structural coefficient. The shear-resistant parameter subentry coefficient and the structural coefficient are adjusted together without sequence, and the shear-resistant parameter subentry coefficient and the structural coefficient are not limited by the dam under a single working condition to meet the requirement of the design on safety and reliability, and the specification subentry coefficient and the structural coefficient are obtained by adopting an optimization method to obtain the satisfactory design subentry coefficient and the satisfactory structural coefficient.
Description
Technical Field
The invention relates to a water conservancy construction technology, in particular to a method for determining a standard shearing-resistant subentry coefficient of a concrete gravity dam.
Background
When the probability characteristics of the design indexes such as material performance, action, size and the like, such as the statistical parameters of probability distribution type, mean value, coefficient of variation and the like, are fixed, the subentry coefficient and the structural coefficient determined by the structural limit state equation are referred to as a single conditional subentry coefficient and a structural coefficient according to the reliability theory. Wherein the polynomial coefficient comprises various design index polynomial coefficients including material performance, action and the like. It is obvious that "single condition" herein refers to a certain design index probability characteristic. When the probability characteristic of the design index is changed, the corresponding subentry coefficient and the structural coefficient are also changed.
Different from the structural single condition subentry coefficient and the structural coefficient which meet the target safety reliability, the subentry coefficient and the structural coefficient in the design method for the extreme state of the specification subentry coefficient, namely the design subentry coefficient and the structural coefficient, are required to meet the required safety and reliability level of the structures designed by the design subentry coefficient under the conditions of various material properties, actions and the like, or meet the required safety and reliability level on the whole, which is also the principle of determining the specification subentry coefficient.
To achieve the goal, at present, two approaches (or methods) are mainly adopted in the process of specification editing or compiling at home and abroad. The first approach is to calculate the fractional coefficient and the structural coefficient of each single extreme state equation with the structure meeting the target safety reliability, and then to use the average or other methods to provide the fractional coefficient and the structural coefficient for the specification. The shear-resistant parameter subentry coefficient and the structural coefficient are determined by adopting the method in the concrete gravity dam design specification (NB/T35026-. The research approach accords with logic, but has the defects that because the subentry coefficient and the structural coefficient of each single extreme state equation which correspondingly meets the target safety reliability generally have large changes (the calculation result of the subentry coefficient related to a single condition is slight due to space limitation), no matter what method is adopted to determine the design subentry coefficient and the structural coefficient, the safety reliability of the dam designed by adopting the subentry coefficient and the structural coefficient can meet the target safety reliability requirement only under a certain specific condition at most due to inherent deficiency, and the safety reliability of the dam designed by adopting the subentry coefficient and the structural coefficient cannot meet the target requirement when the condition is changed.
The second approach is to determine the design polynomial coefficients first and then the structure coefficients. This approach is the main method for determining design polynomial coefficients and structural coefficients by current specifications. For example, the division coefficient and the structural coefficient are determined by the method according to the specifications of the unified design standard for the structural reliability of the water conservancy and hydropower engineering (GB 50199-2013) and the design specification for the concrete arch dam in the power industry (DL/T5346-2006). On the one hand, the dispersion of the polynomial coefficient and the structural coefficient of the single extreme state equation is large, so that it is difficult (actually impossible) to determine the proper design polynomial coefficient in advance, and on the other hand, under the condition that, for example, in the anti-sliding stability analysis of a building with two material parameters, namely, the shear-resistant friction coefficient and the cohesion force, the predetermined design polynomial coefficient, for example, the ratio of the shear-resistant friction coefficient polynomial coefficient to the cohesion force polynomial coefficient has a great influence on whether the safety reliability of the design structure integrally meets the target requirements under various conditions. And only one structural coefficient is adjustable later, so that the design of the structural coefficient is difficult to ensure that the designed dam integrally meets the target safety and reliability requirements no matter what method is adopted to determine the design structural coefficient. Therefore, for the shear stability analysis with two material parameters, the second research approach cannot obtain satisfactory design polynomial coefficients and structural coefficients.
In order to avoid the problems, the gravity dam has a stable, safe and reliable level which is consistent with the specification of the water conservancy gravity dam under the conditions of different dam heights and different material mechanical characteristics, different previous new methods are provided for researching and determining the shearing-resistant parameter component coefficient and the structural coefficient of the specification of the gravity dam.
Disclosure of Invention
The invention aims to solve the technical problem of providing a method for determining the standard shearing-resistant component coefficient of a concrete gravity dam aiming at the defects in the prior art.
The technical scheme adopted by the invention for solving the technical problems is as follows: a method for determining the normalized shearing-resistant subentry coefficient of a concrete gravity dam comprises the following steps:
1) determining a shear-resistant friction coefficient and a cohesion standard value according to the mechanical properties of the sliding surface of the concrete gravity dam;
2) if the standard structural coefficient and the subentry coefficient of one material are determined, the step 2.1) is carried out; if the standard structural coefficient and the subentry coefficient of more than one material are determined, the step 2.2) is carried out;
2.1) establishing a model for determining the coherence of the standard shear-resistant parameter subentry coefficient and the structural coefficient without single working condition safety and reliability constraint; the model is as follows:
η(γf′,γc′,γd)＝1；
wherein, K'i(γf′,γc′,γd) The dam stability safety factor of the ith dam height is [ K']Designing a stable safety coefficient for water conservancy specifications; delta K'iDesigning a difference value of the stability safety coefficient of the dam of the ith dam height and the stability safety coefficient of the water conservancy specification; n is the number of dam heights from a low dam to a high dam; 1,2, …, n; eta (gamma)f′,γc′,γd) Is a resistance action ratio coefficient, and is a function of a material shear parameter subentry coefficient and a structure coefficient;
γdis a coefficient of structure, gammaf′Is a shear-resistant coefficient of friction, gammac′Is a shear-resistant cohesion polynomial coefficient;
2.2) establishing a model for determining the coherence of the standard shear-resistant parameter subentry coefficient and the structural coefficient without single working condition safety and reliability constraint; the model is as follows:
constraint conditions are as follows:
η(γf′,γc′,γd)＝1
wherein, K'ji(γf′,γc′,γd) When the jth combination is taken as the anti-shear parameter, the stable safety factor at the ith dam height is designed by a polynomial coefficient method, and the stable safety factor is [ K']Designing a stable safety coefficient for water conservancy specifications; delta K'jiWhen the jth combination is taken for the shear-resistant parameters, the difference value of the stable safety coefficient of the ith dam height dam and the stable safety coefficient of the water conservancy standard design is obtained; n is the number of dam heights from a low dam to a high dam; 1,2, …, n; m is the possible value combination number of each mechanical parameter of the material; j is 1,2, …, m; eta (gamma)f′,γc′,γd) Is a resistance action ratio coefficient, and is a function of a material shear parameter subentry coefficient and a structure coefficient;
γdis a coefficient of structure, gammaf′Is a shear-resistant coefficient of friction, gammac′Is a shear-resistant cohesion polynomial coefficient;
3) and obtaining a design item coefficient and a structural coefficient according to the model.
3.1) setting the value range and the stepping interval of the dam height and the structural coefficient; drawing up a series of dam heights and structural coefficients;
3.2) calculating and determining the corresponding optimal friction coefficient and cohesion coefficient for each structural coefficient:
3.2.1) in the possible value range of the shear-resistant friction coefficient polynomial coefficient and the cohesion coefficient polynomial coefficient, taking a series of shear-resistant friction coefficient polynomial coefficients and cohesion coefficient combinations;
3.2.2) combining each group of shearing-resistant friction coefficient polynomial coefficient and cohesion coefficient polynomial, combining the structural coefficient, adopting a polynomial coefficient extreme state design formula, and reversely calculating the downstream dam slope gradient of the dam under different dam heights by using a resistance action ratio coefficient of 1; wherein, the shearing resistant friction coefficient and the cohesion standard value are determined according to the common value of the materials.
3.2.3) calculating the stable safety coefficients of the dams with different dam heights by combining the shearing resistance friction coefficient polynomial coefficient and the cohesion coefficient polynomial coefficient of each group to obtain the difference value delta K 'between the stable safety coefficient of the dam and the stable safety coefficient of the design'i(ii) a Then calculating the sum of the absolute values of the relative differences of the whole dam deviating from the water conservancy standard design safety coefficient under the combination of the component item coefficients and the structural coefficients
3.2.4) comparing the integral deviation of the stability safety coefficient under the combination of each shear-resistant friction coefficient subentry coefficient and the cohesion coefficient-the sum of absolute values of relative differences, and taking the friction coefficient subentry coefficient and the cohesion coefficient corresponding to the minimum value as the optimal material subentry coefficient under the structural coefficient;
3.2.5) comparing the stable safety coefficient overall deviation corresponding to the optimal subentry coefficient combination under each proposed structural coefficient, and taking a group of subentry coefficients and structural coefficients with the minimum stable safety coefficient overall deviation as design subentry coefficients and structural coefficients.
In the scheme, the water conservancy standard stable design safety coefficient can be replaced by a target reliable index, and the corresponding stable safety coefficient is replaced by a shear-resistant stable and reliable index. Compared with the former (namely the standard subentry coefficient calculation method based on the design safety coefficient), the latter standard subentry coefficient calculation method (namely the standard subentry coefficient calculation method based on the target reliable index) can more accurately reflect the uncertainty of the shear-resistant parameter of the gravity dam material and measure the safety and reliability of the dam.
The invention has the following beneficial effects: the invention provides a novel method for determining a standard shear-resistant parameter subentry coefficient and a structural coefficient, which comprises the following steps: the method uses the minimum safe reliability of the whole deviation design (target) of the stable safe reliability of the dam as a target function, uses the resistance action ratio equal to 1 as a constraint condition, adjusts the shear-resistant parameter subentry coefficient and the structural coefficient together without any sequence, and obtains the satisfactory design subentry coefficient and the satisfactory structural coefficient by adopting an optimization method to standardize the subentry coefficient and the structural coefficient without the limitation of the safe reliability of the dam under the single working condition.
Drawings
The invention will be further described with reference to the accompanying drawings and examples, in which:
FIG. 1 is a flow chart of a method of an embodiment of the present invention;
fig. 2 is a comparison graph of the design method of the polynomial coefficient with the minimum and maximum overall average relative difference value and the stable safety line of the water conservancy standard according to the embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
As shown in fig. 1, a method for determining a normalized shearing-resistant polynomial coefficient of a concrete gravity dam includes the following steps:
1) determining the material of the concrete gravity dam sliding surface, and determining the shear-resistant friction coefficient and the cohesion standard value according to the material mechanical property of the concrete gravity dam sliding surface;
2) if the standard structural coefficient and the subentry coefficient of one material are determined, the step 2.1) is carried out; if the standard structural coefficient and the subentry coefficient of more than one material are determined, the step 2.2) is carried out;
2.1) establishing a model for determining the coherence of the standard shear-resistant parameter subentry coefficient and the structural coefficient without single working condition safety and reliability constraint; the model is as follows:
or
Constraint conditions
η(γf′,γc′,γd)＝1 (3)
Wherein, K'i(γf′,γc′,γd) The dam stability safety factor of the ith dam height is [ K']Designing a stable safety coefficient for water conservancy specifications; delta K'iDesigning a difference value of the stability safety coefficient of the dam of the ith dam height and the stability safety coefficient of the water conservancy specification; n is the number of dam heights from a low dam to a high dam; 1,2, …, n; eta (gamma)f′,γc′,γd) Is a resistance action ratio coefficient, and is a function of a material shear parameter subentry coefficient and a structure coefficient;
γdis a coefficient of structure, gammaf′Coefficient of friction against shear，γc′Is a shear-resistant cohesion polynomial coefficient;
2.2) establishing a model for determining the coherence of the standard shear-resistant parameter subentry coefficient and the structural coefficient without single working condition safety and reliability constraint; the model is as follows:
or
Constraint conditions
η(γf′,γc′,γd)＝1 (6)
Wherein, K'ji(γf′,γc′,γd) When the jth combination is taken as the anti-shear parameter, the stable safety factor at the ith dam height is designed by a polynomial coefficient method, and the stable safety factor is [ K']Designing a stable safety coefficient for water conservancy specifications; delta K'jiWhen the jth combination is taken for the shear-resistant parameters, the difference value of the stable safety coefficient of the ith dam height dam and the stable safety coefficient of the water conservancy standard design is obtained; n is the number of dam heights from a low dam to a high dam; 1,2, …, n; m is the possible value combination number of each mechanical parameter of the material; j is 1,2, …, m; eta (gamma)f′,γc′,γd) Is a resistance action ratio coefficient, and is a function of a material shear parameter subentry coefficient and a structure coefficient;
γdis a coefficient of structure, gammaf′Is a shear-resistant coefficient of friction, gammac′Is a shear-resistant cohesion polynomial coefficient;
3) and obtaining a design item coefficient and a structural coefficient according to the model.
3.1) setting the value range and the stepping interval of the dam height and the structural coefficient; drawing up a series of dam heights and structural coefficients;
3.2) calculating and determining the corresponding optimal friction coefficient and cohesion coefficient for each structural coefficient:
3.2.1) in the possible value range of the shear-resistant friction coefficient subentry coefficient and the cohesion force subentry coefficient, taking a series of friction coefficient subentry coefficients and cohesion force subentry coefficients to combine;
3.2.2) combining each group of shearing-resistant friction coefficient polynomial coefficient and cohesion coefficient polynomial, combining the structural coefficient, adopting a polynomial coefficient extreme state design formula, and reversely calculating the downstream dam slope gradient of the dam under different dam heights by using a resistance action ratio coefficient of 1; wherein, the shearing resistant friction coefficient and the cohesion standard value are determined according to the common value of the materials.
3.2.3) calculating the stable safety coefficients of the dams with different dam heights by combining the shearing resistance friction coefficient polynomial coefficient and the cohesion coefficient polynomial coefficient of each group to obtain the difference value delta K 'between the stable safety coefficient of the dam and the stable safety coefficient of the design'i(ii) a Then calculating the sum of the absolute values of the relative differences of the whole dam deviating from the water conservancy standard design safety coefficient under the combination of the component item coefficients and the structural coefficients
3.2.4) comparing the integral deviation of the stability safety coefficient under the combination of each shear-resistant friction coefficient subentry coefficient and the cohesion coefficient-the sum of absolute values of relative differences, and taking the friction coefficient subentry coefficient and the cohesion coefficient corresponding to the minimum value as the optimal material subentry coefficient under the structural coefficient;
3.2.5) comparing the stable safety coefficient overall deviation corresponding to the optimal subentry coefficient combination under each proposed structural coefficient, and taking a group of subentry coefficients and structural coefficients with the minimum stable safety coefficient overall deviation as design subentry coefficients and structural coefficients.
For the above method, it is to be noted that:
the shear-resistant friction coefficient subentry coefficient, the shear-resistant cohesion coefficient subentry coefficient and the structural coefficient can be adjusted independently, and when the material subentry coefficient and the structural coefficient are determined by adopting the formulas (1) to (6), a design value dereferencing method of the material parameter does not need to be specified in advance like a common method (similar to a method for determining the material subentry coefficient and the structural coefficient based on a single condition subentry coefficient and a structural coefficient statistical value, including a method used in specifications such as 'Water conservancy and hydropower engineering structure reliability design unified Standard' (GB 50199-2013)), so that the problem of how to take the design value can be avoided. The design value of the shear-resistant parameter is actually implicitly determined by the fact that the overall dam stability safety deviates from the target safety reliability by the minimum.
Secondly, regarding the shearing resistance friction coefficient and the cohesion standard value, the formula (1) to the formula (6) directly use the water conservancy standard design stability safety factor as the target safety degree, the specific numerical value determination method is consistent with the water conservancy standard, and the determination is comprehensively carried out according to the small value average value of the test and the combination of the field condition and similar engineering.
Thirdly, the function component coefficient is still adopted according to the design specification of hydraulic structure load (DL 5077-1997).
And fourthly, when the target reliable index of the dam is adopted to determine the shear-resistant subentry coefficient, respectively changing the corresponding stable safety coefficient and the design stable safety coefficient in the formulas (1) to (6) into the stable reliable index and the target reliable index.
One embodiment is as follows:
the optimal structural coefficient and the subentry coefficient of the dam are respectively 1.1MPa and 1.1MPa when the shearing resistance friction coefficient and the cohesion standard value are respectively
The computer programs are prepared by the following equations (1) to (6). Through calculation, under the condition that the shear-resistant friction coefficient and the cohesion standard value are respectively 1.1MPa and 1.1MPa, the table 1 shows the optimal friction coefficient subentry coefficient and the cohesion subentry coefficient under each structural coefficient, and the sum of the relative difference absolute values of the high-stability safety coefficients of each dam and the integral average relative difference of each dam designed by adopting the corresponding structural coefficient and the subentry coefficient, wherein the calculation result that the structural coefficient is less than 1 is listed only for reflecting a change condition of deviation. Tables 2-3 also specifically show indexes of dam friction coefficient safety reserve, cohesion safety reserve, stability safety coefficient cumulative relative difference, integral average relative difference and the like under the combination of a plurality of structural coefficients and the fractional coefficients, and fig. 2 is a fractional system drawn according to the corresponding friction coefficient safety reserve and cohesion safety reserveAnd (3) comparing the stable safety line with the water conservancy standard stable safety line by using the limit state design method, wherein the comparison comprises a scheme for calculating the minimum deviation and the maximum deviation of the whole stable safety coefficient. The calculation formulas of the friction coefficient safety reserve and the cohesion safety reserve are respectively
In the formula: x + Y ═ K']Wherein [ K']To design a stable safety factor; sigma W is the sum of all normal actions on the dam basal plane; sigma P is the sum of all tangential actions on the dam base surface; a is the area of the dam foundation surface.
During calculation, designing a safety coefficient [ K' ] of the water conservancy specification to be 3; the structural importance coefficient is 1.0 for a dam with the dam height of 30 meters, 1.05 for the dam height of 50 meters and 1.1 for the dam height of more than 100 meters; the design condition coefficient is 1.0; the load division coefficient takes values according to the design code of hydraulic structure load (DL 5077-1999): the hydrostatic pressure polynomial coefficient of the upstream and downstream of the dam is 1, and the osmotic pressure reduction coefficient and the silt pressure polynomial coefficient of the front of the dam are 1.2.
In the optimization calculation, in order to reflect the influence of the dam body type, the following 3 dam section schemes are adopted:
dam section scheme 1: the upstream dam slope of the dam is vertical, the height and the top width of the dam are 5 meters for 30 meters, and the height and the top width of the other dams are 10 meters;
dam section scheme 2: the upstream dam slope of the dam is vertical, the height and the top width of the dam are 3 meters for 30 meters, and the height and the top width of the other dams are 10 meters;
dam section scheme 3: the upstream dam slope of the dam is 0.2, the slope breaking point of the upper dam surface is arranged at the high position of one third of the dam, the height and the top width of the dam are 30 meters, and the height and the top width of the other dams are 10 meters.
As can be seen from the table, fig. 2:
(1) the width of the dam crest and the gradient of the upstream dam are changed, and the optimal shearing-resistant parameter polynomial coefficient calculated under each structural coefficient is not influenced.
(2) The overall relative average difference value of the designed dam corresponding to the optimal friction coefficient and the cohesion polynomial coefficient under each structural coefficient is generally less than 2.5%, and the numerical value is very small. From the stable calculation results (tables 2 to 3) of the dams of the dam heights when the relative difference is maximum and minimum and the comparison of the made subentry coefficient design formula and the water conservancy specification in the figure 1, it can be seen that the stable safety coefficient of the dam designed by adopting each group of structural coefficients and subentry coefficients is better matched with the water conservancy specification.
(3) For better selection, when the excluded coefficient of structure is less than 1 (because the coefficient of structure and the coefficient of material component are both used to values greater than or equal to 1 in practical engineering), the optimal coefficient of structure, the coefficient of friction component and the coefficient of cohesion component are 1, 2.5 and 3 respectively, which are selected from table 1, according to the minimum overall deviation. The average integral relative difference of the stable safety coefficient of the dam corresponding to the optimal structural coefficient and the subentry coefficient is 1.39-1.83%. Because the deviation is very small, the dam stability safety degree of the first-in-first-out structural coefficient and the subentry coefficient is very close to the water conservancy specification (see comparison figure 2).
TABLE 1 calculation results based on the fractional coefficient and the structural coefficient for which the degree of stability safety deviates the least
TABLE 2. gammad＝1.0、γf′＝2.5、γc′Dam stability calculation of 3.0
(minimum integral deviation, vertical slope of upstream dam, height of 30 meters and width of top of dam 3 meters, height of the rest of the dam 10 meters)
TABLE 3. gammad＝1.8、γf′＝1.3、γc′Dam stability calculation of 1.8
(maximum integral deviation, vertical slope of upstream dam, height of 30 meters and width of top of dam 3 meters, height of the rest of the dam 10 meters)
The above results were obtained when the shear resistance friction coefficient and the standard value of the cohesion are 1.1 and 1.1MPa, respectively, i.e., the ratio of the cohesion to the friction coefficient is 1MPa, and in actual engineering, the ratio of the cohesion to the friction coefficient may vary. Table 4 shows the maximum and minimum values of the ratio of the cohesive force to the friction coefficient of each material obtained by calculating the shear resistance parameter values of the materials such as bedrock in the concrete gravity dam specification appendix. It can be seen from the table that for the three classes of materials concrete/bedrock, bedrock/bedrock, concrete/concrete, the cohesion to friction ratio is mostly greater than 0.5MPa (about 80%), with the exception that a small fraction of the iv and v classes of bedrock will appear to be less than 0.5MPa, the cohesion to friction ratios for the i to iii classes of bedrock and the concrete/concrete are all greater than 0.5MPa, with a maximum of 1.88MPa appearing in the iii class of bedrock and a minimum of 0.07 appearing in the v class of bedrock. For the soft and hard structural surfaces, the cohesion is generally low, and the ratio of the cohesion to the friction coefficient is mostly less than 0.5MPa, wherein the maximum value is 0.556, and the minimum value is 0.008. Obviously, for IV and V bedrocks, the ratio of the cohesive force to the friction coefficient of a part of materials is overlapped with that of a soft and hard structural surface.
TABLE 4 cohesion to friction ratio based on the concrete gravity dam specification annex shear resistance parameter values
In order to understand the influence of different shear-failure resistant friction coefficients and cohesion standard values, the applicant also determines the standard structural coefficient and shear-failure resistant parameter subentry coefficient by calculation and analysis of an optimization method aiming at concrete/bedrock, bedrock/bedrock, concrete/concrete and soft and hard structural surfaces, and the result is that: the standard shearing resistance friction coefficient, the cohesion coefficient and the structural coefficient of the concrete/bedrock, the bedrock/bedrock and the concrete/concrete are respectively 2.5, 3.0 and 1.0, and the standard shearing resistance friction coefficient, the cohesion coefficient and the structural coefficient of the soft and hard structural surface are respectively 2.7, 3.0 and 1.0.
It will be understood that modifications and variations can be made by persons skilled in the art in light of the above teachings and all such modifications and variations are intended to be included within the scope of the invention as defined in the appended claims.
Claims (2)
1. A method for determining the normalized shearing-resistant subentry coefficient of a concrete gravity dam is characterized by comprising the following steps:
1) determining a shear-resistant friction coefficient and a cohesion standard value according to the mechanical properties of the sliding surface of the concrete gravity dam;
2) if the standard structural coefficient and the subentry coefficient of one material are determined, the step 2.1) is carried out; if the standard structural coefficient and the subentry coefficient of more than one material are determined, the step 2.2) is carried out;
2.1) establishing a model for determining the coherence of the standard shear-resistant parameter subentry coefficient and the structural coefficient without single working condition safety and reliability constraint; the model is as follows:
η(γf′,γc′,γd)＝1；
wherein, K'i(γf′,γc′,γd) Designed for designing method based on limit state of polynomial coefficientDam stability safety factor under ith dam height, [ K']Designing a stable safety coefficient for the current water conservancy standard of raw water; delta K'iDesigning a difference value of the stability safety coefficient of the dam of the ith dam height and the stability safety coefficient of the water conservancy specification; n is the number of dam heights from a low dam to a high dam; 1,2, …, n; eta (gamma)f′,γc′,γd) Is a resistance action ratio coefficient, and is a function of a material shear parameter subentry coefficient and a structure coefficient;
γdis a coefficient of structure, gammaf′Is a shear-resistant coefficient of friction, gammac′Is a shear-resistant cohesion polynomial coefficient;
2.2) establishing a model for determining the coherence of the standard shear-resistant parameter subentry coefficient and the structural coefficient without single working condition safety and reliability constraint; the model is as follows:
constraint conditions
η(γf′,γc′,γd)＝1
Wherein, K'ji(γf′,γc′,γd) When the jth combination is taken as the anti-shear parameter, the stable safety factor at the ith dam height is designed by a polynomial coefficient method, and the stable safety factor is [ K']Designing a stable safety coefficient for water conservancy specifications; delta K'jiWhen the jth combination is taken for the shear-resistant parameters, the difference value of the stable safety coefficient of the ith dam height dam and the stable safety coefficient of the water conservancy standard design is obtained; n is the number of dam heights from a low dam to a high dam; 1,2, …, n; m is the possible value combination number of each mechanical parameter of the material; j is 1,2, …, m; eta (gamma)f′,γc′,γd) Is a resistance action ratio coefficient, and is a function of a material shear parameter subentry coefficient and a structure coefficient;
γdis a coefficient of structure, gammaf′Is a shear-resistant coefficient of friction, gammac′Is a shear-resistant cohesion polynomial coefficient;
3) solving the model according to the set value ranges of the dam height and the structural coefficient and the stepping interval to obtain a design subentry coefficient and a structural coefficient;
the method comprises the following specific steps:
3.1) setting the value range and the stepping interval of the dam height and the structural coefficient; drawing up a series of dam heights and structural coefficients;
3.2) calculating and determining the corresponding optimal shearing-resistant friction coefficient component coefficient and the corresponding cohesion component coefficient for each structural coefficient:
3.2.1) in the possible value range of the shear-resistant friction coefficient polynomial coefficient and the cohesion coefficient polynomial coefficient, taking a series of shear-resistant friction coefficient polynomial coefficients and cohesion coefficient combinations;
3.2.2) combining each group of shearing-resistant friction coefficient polynomial coefficient and cohesion coefficient polynomial, combining the structural coefficient, adopting a polynomial coefficient extreme state design formula, and reversely calculating the downstream dam slope gradient of the dam under different dam heights by using a resistance action ratio coefficient of 1; wherein, the shear-resistant friction coefficient and the cohesion standard value are determined according to the common values of the materials;
3.2.3) calculating the stable safety coefficients of the dams with different dam heights by combining the shearing resistance friction coefficient polynomial coefficient and the cohesion coefficient polynomial coefficient of each group to obtain the difference value delta K 'between the stable safety coefficient of the dam and the stable safety coefficient of the design'i(ii) a Then calculating the sum of the absolute values of the relative differences of the whole dam deviating from the water conservancy standard design safety coefficient under the combination of the component item coefficients and the structural coefficients
3.2.4) comparing the integral deviation of the stable safety coefficient under the combination of each shear-resistant friction coefficient subelement coefficient and the cohesion coefficient, namely the sum of absolute values of relative differences, and taking the shear-resistant friction coefficient subelement coefficient and the cohesion coefficient corresponding to the minimum value as the optimal material subelement coefficient under the structural coefficient;
3.2.5) comparing the stable safety coefficient overall deviation corresponding to the optimal subentry coefficient combination under each proposed structural coefficient, and taking a group of subentry coefficients and structural coefficients with the minimum stable safety coefficient overall deviation as design subentry coefficients and structural coefficients.
2. A method for determining the normalized shearing-resistant subentry coefficient of a concrete gravity dam is characterized by comprising the following steps:
1) determining a shear-resistant friction coefficient and a cohesion standard value according to the mechanical properties of the sliding surface of the concrete gravity dam;
2) if the standard structural coefficient and the subentry coefficient of one material are determined, the step 2.1) is carried out; if the standard structural coefficient and the subentry coefficient of more than one material are determined, the step 2.2) is carried out;
2.1) establishing a model for determining the coherence of the standard shear-resistant parameter subentry coefficient and the structural coefficient without single working condition safety and reliability constraint; the model is as follows:
η(γf′,γc′,γd)＝1；
wherein, betai(γf′,γc′,γd) Beta is a reliable index of shearing resistance of the dam at the ith dam height designed based on a polynomial coefficient methodTIs a target reliability index; delta betaiThe difference value of the shear-resistant reliable index and the target reliable index of the ith dam height dam is obtained; n is the number of dam heights from a low dam to a high dam; 1,2, …, n; eta (gamma)f′,γc′,γd) Is a resistance action ratio coefficient, and is a function of a material shear parameter subentry coefficient and a structure coefficient;
γdis a coefficient of structure, gammaf′Is a shear-resistant coefficient of friction, gammac′Is a shear-resistant cohesion polynomial coefficient;
2.2) establishing a model for determining the coherence of the standard shear-resistant parameter subentry coefficient and the structural coefficient without single working condition safety and reliability constraint; the model is as follows:
constraint conditions
η(γf′,γc′,γd)＝1；
Wherein, betaji(γf′,γc′,γd) When the jth combination is taken for the anti-shear parameters, the anti-shear reliable index, beta, under the ith dam height is designed by adopting a subentry coefficient methodTIs a target reliability index; delta betajiWhen the jth combination is taken for the shear-resistant parameters, the difference value of the stable safety coefficient of the ith dam height dam and the stable safety coefficient of the water conservancy standard design is obtained; n is the number of dam heights from a low dam to a high dam; 1,2, …, n; m is the possible value combination number of each mechanical parameter of the material; j is 1,2, …, m; eta (gamma)f′,γc′,γd) Is a resistance action ratio coefficient, and is a function of a material shear parameter subentry coefficient and a structure coefficient;
γdis a coefficient of structure, gammaf′For an optimum coefficient of friction, gammac′Is the optimal cohesion polynomial coefficient;
3) solving the model according to the set value ranges of the dam height and the structural coefficient and the stepping interval to obtain a design subentry coefficient and a structural coefficient;
the method comprises the following specific steps:
3.1) setting the value range and the stepping interval of the dam height and the structural coefficient; drawing up a series of dam heights and structural coefficients;
3.2) calculating and determining the corresponding optimal friction coefficient and cohesion coefficient for each structural coefficient:
3.2.1) in the possible value range of the shear-resistant friction coefficient polynomial coefficient and the cohesion coefficient polynomial coefficient, taking a series of shear-resistant friction coefficient polynomial coefficients and cohesion coefficient combinations;
3.2.2) combining each group of shearing-resistant friction coefficient polynomial coefficient and cohesion coefficient polynomial, combining the structural coefficient, adopting a polynomial coefficient extreme state design formula, and reversely calculating the downstream dam slope gradient of the dam under different dam heights by using a resistance action ratio coefficient of 1; wherein, the shear-resistant friction coefficient and the cohesion standard value are determined according to the common values of the materials;
3.2.3) calculating the stable safety coefficients of the dams with different dam heights by combining the shearing resistance friction coefficient polynomial coefficient and the cohesion coefficient polynomial coefficient of each group to obtain the difference value delta K 'between the stable safety coefficient of the dam and the stable safety coefficient of the design'i(ii) a Then calculating the sum of the absolute values of the relative differences of the whole dam deviating from the water conservancy standard design safety coefficient under the combination of the component item coefficients and the structural coefficients
3.2.4) comparing the integral deviation of the stability safety coefficient under the combination of each group of shear-resistant friction coefficient subelement coefficients and the cohesion coefficient subelement coefficient, namely the sum of absolute values of relative differences, and taking the friction coefficient subelement coefficient and the cohesion coefficient corresponding to the minimum value as the optimal material subelement coefficient under the structural coefficient;
3.2.5) comparing the stable safety coefficient overall deviation corresponding to the optimal subentry coefficient combination under each proposed structural coefficient, and taking a group of subentry coefficients and structural coefficients with the minimum stable safety coefficient overall deviation as design subentry coefficients and structural coefficients.
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