CN112632670B - Method for calculating anti-skid stability safety degree of arch seat of arch dam - Google Patents
Method for calculating anti-skid stability safety degree of arch seat of arch dam Download PDFInfo
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Abstract
The invention discloses a method for calculating the safety degree of the anti-skid stability of an arch support, which relates to the field of arch dam engineering and solves the problems that the safety degree calculation result is distorted and the engineering has safety risk or is uneconomical due to too rough determination of the material performance subentry coefficient in the existing anti-skid stability analysis of the arch support, and adopts the technical scheme that: the method for calculating the anti-sliding stability safety degree of the arch base of the arch dam comprises the steps of firstly determining a sliding block which can slide and a sliding surface of the sliding block; secondly, dividing sliding surfaces of sliding blocks into sub-regions according to rock mass classification lines and structural surface range boundary lines, and respectively calculating the area of each sub-region and the material performance subentry coefficient; then calculating the sliding force on the sliding surface and the total normal force vertical to the sliding direction, and decomposing the total normal force into normal forces borne by each sub-region according to the area ratio of each sub-region; and finally, judging whether the arch seat sliding block is safe according to a formula, and calculating the shearing resistance or shearing resistance safety degree of the arch seat sliding block. The invention is used for analyzing the anti-skid stability safety degree of the arch support.
Description
Technical Field
The invention relates to the technical field of arch dam engineering, in particular to a method for calculating the anti-slip stability safety of an arch abutment of an arch dam.
Background
The arch base stability analysis is one of the most important problems in arch dam design and is the most difficult problem to solve. Modern arch dam construction practices show that the real potential risk of the arch dam is the stability of the arch seats on both sides. Therefore, whether the arch support has enough anti-skid stability safety degree is always the key point of analysis and demonstration in the arch dam engineering design stage.
The numerical calculation method is a main calculation and analysis means widely used at home and abroad at present, and common numerical calculation methods can be classified into the following three categories: rigid body limit balancing method, rigid body spring element method, three-dimensional nonlinear finite element method. Wherein the rigid body poleThe limit balance method is a general calculation analysis method in most countries, is simple to use, clear in concept and long-term practical experience although the method is rough, and is an analysis method used by designers in various countries. The rigid body limit balance method is as follows: considering a mountain, cut into a wedge with several sliding surfaces, the wedge bears various specified loads, and the shear strength index f on each sliding surface 1 、C 1 、f 2 Determining a safety coefficient K after geological exploration and physical and mechanical experiments of rock mass, so that all f 1 、C 1 、f 2 After the value is divided by K, the wedge block just reaches the limit balance state under the action of external force (including dead weight), namely the shearing resistance on the sliding surface is just equal to the shearing force acting on the sliding surface, and the anti-sliding safety coefficient (or safety degree) of the wedge block is K.
At present, the existing methods for calculating and measuring the anti-skid stability and safety of the arch abutment of the arch dam based on the rigid body limit balance method mainly comprise two types, namely a water conservancy industry method and an energy (hydropower) industry method. The method recommended by the current standard of the water conservancy industry adopts a safety coefficient control thought of 'Dalao K', the method does not respectively research various relevant factors influencing the anti-sliding stability of the arch support, and the determination of the control standard of the method is mainly based on engineering experience and lacks the support of mathematical theories such as structural reliability, probability theory and the like, so the method is not in accordance with the mainstream development direction in the current world geotechnical field. The method for recommending the current standard in the energy (hydroelectric) industry adopts a calculation and analysis method of the subentry coefficient, the determined subentry coefficient is supported by mathematical theories such as structural reliability, probability theory and the like, and each subentry coefficient (structural importance coefficient gamma) with definite mathematical or physical meanings is respectively given 0 Design condition coefficient psi, structural coefficient gamma d1 、γ d2 Coefficient of material property division gamma m1f 、γ m1c 、γ m2f ) The method has relatively firm mathematical foundation and takes the existing engineering experience into consideration, so that the method is generally more advanced and practical.
The method in the energy (hydropower) industry is represented by a calculation method in concrete arch dam design specifications (DL/T5346-2006) of the existing power industry. When the arch abutment stability is analyzed by using a rigid body limit balance method, the 1-level and 2-level arch dams and the high arch dams meet the design formula a of the bearing capacity limit state, and the other arch dams meet the following design formula a or formula b of the bearing capacity limit state.
The formula a and the formula b can be converted to obtain a formula c and a formula d:
in the formula:
SF 1 the ratio of the resistance term to the action term (safety) in the formula a is greater than or equal to 1.0, and the requirement of the current specification is met.
SF 2 The ratio of the resistance term to the action term (safety for short) in the formula b is greater than or equal to 1.0, and the requirement of the current specification is met.
γ 0 And (4) taking 1.1,1.0,0.9 as the structural importance coefficients corresponding to buildings with the security levels I, II and III respectively.
Psi-design condition coefficient, corresponding to persistent, transient, occasional, take 1.00,0.95,0.85, respectively.
T-sliding force in the sliding direction.
N-normal force perpendicular to the sliding direction.
f 1 、f 2 Shear-break coefficient of friction and shear frictionAnd (4) the coefficient.
C 1 Shear cohesion.
A is the area of the sliding surface.
γ d1 、γ d2 For the structural coefficients of the two calculation cases, 1.2 and 1.1 are taken, respectively.
γ m1f 、γ m1c 、γ m2f And the coefficient of the material performance subentries of the two expressions is 2.4, 3.0 and 1.2 respectively.
The calculation formula of energy (water and electricity) industry specification stipulates the material performance subentry coefficient, namely gamma m1f 、γ m1c 、γ m2f The values of the three coefficients are respectively 2.4, 3.0 and 1.2. According to the definition of 'unified design standard for structure reliability of hydraulic and hydroelectric engineering' (GB 50199-2013), the material performance subentry coefficient reflects the unfavorable variation of the performance of the material (the material in the arch abutment anti-skid stability analysis is the various rock masses and the various structural surfaces of the dam foundation) to the standard value. For different types of rock masses and structural surfaces, the difference of the variation coefficients of the shear (break) strength indexes is large, and the rock masses and the structural surfaces are difficult to represent relatively accurately by using a uniform variation coefficient. Therefore, the coefficient of variation of the material is used as an independent variable, and the coefficient of the material performance subentry (namely gamma) is calculated according to a correlation formula of the unified design Standard for the reliability of Water conservancy and hydropower engineering (GB 50199-2013) m1f 、γ m1c 、γ m2f Etc.) are definitely different for different classes of rock mass and structural planes. Partial statistical data also shows that the calculated material performance polynomial coefficients have great difference for different types of rock masses and structural planes. For example, the relevant statistical data in the repair and edition of the design Specification of concrete arch dams are listed in Table 1.
TABLE 1 statistics of variation coefficient statistics and material performance polynomial coefficient calculation results of various rock masses and structural surfaces
For the material performance fractional coefficients which have relatively large variation range and are relatively obviously influenced by the rock mass type, determining a fixed value which is not associated with the rock mass type or the structural surface type is obviously unreasonable, and no matter what value is taken, the theoretical calculation result of the material performance fractional coefficients of the rock mass and the structural surface of each type can not be well matched with the theoretical calculation result of the material performance fractional coefficients of the rock mass and the structural surface of each type. Therefore, the rough and definite determination method for the material performance polynomial coefficient influences the accuracy of the calculation formula and the reasonability of the corresponding control standard, so that the safety degree calculation result analyzed according to the formula is sometimes difficult to avoid distortion. Under extreme conditions, the degree of distortion is higher, and even the objective evaluation of the anti-sliding stability safety degree of the arch end of the arch abutment by designers is influenced, so that the design of the arch dam is influenced.
Disclosure of Invention
The invention provides a method for calculating the anti-skid stability safety degree of an arch abutment of an arch dam, which solves the problem of material performance subentry coefficient gamma in the existing method for analyzing the anti-skid stability of the arch abutment m1f 、γ m1c 、γ m2f The determination of (1) is too hard and rough, so that the safety degree calculation result is distorted, and the engineering has safety risk or is not economical.
The technical scheme adopted by the invention is as follows: the method for calculating the anti-slip stability safety degree of the abutment of the arch dam comprises the following steps of:
s1, determining a sliding block capable of sliding and a sliding surface of the sliding block.
S2, dividing the sliding surface of the sliding block which can slide into a plurality of independent sub-areas according to the rock mass classification line and the structural surface range boundary line; wherein the number of subregions on a single sliding surface is a positive integer.
S3, respectively calculating the material performance subentry coefficient gamma corresponding to each subregion m1fi 、γ m1ci 、γ m2fi And counting the area A of each sub-region i 。
Specifically, the method comprises the following steps: coefficient of material property m1fi 、γ m1ci 、γ m2fi Values are taken according to any of the following methods.
The method comprises the following steps: under the condition that the shear-resistant mechanical test is not carried out on various rocks and structural surfaces of specific engineering, the material performance subentry coefficient is selected according to the table 2 according to the types of rocks or structural surfaces to which each subregion belongs.
TABLE 2 materials Property subentry coefficient values
The second method comprises the following steps: under the condition of carrying out shear resistance mechanical tests on various rock masses and structural planes of specific engineering, the variation coefficient delta of the material parameters of various rock masses and structural planes determined by the shear resistance mechanical tests m On the basis, material performance subentry coefficients corresponding to the types of rocks or structural surfaces of the subregions are calculated according to a method specified in article 8.4.4 in the unified design Standard for reliability of Water conservancy and hydropower engineering (GB 50199-2013).
S4, calculating sliding force T on the sliding surface and total normal force N perpendicular to the sliding direction according to acting load on the sliding block, and decomposing the total normal force N into normal force N borne by each sub-region according to the area ratio of each sub-region divided in the step S1 i ，N i The calculation formula of (2) is as follows:
and S5, judging whether the arch abutment sliding block is safe or not by using a formula 1 for the level 1 and level 2 arch dams and high arch dams, wherein the condition that the formula 1 is met is safety, and meanwhile, calculating the anti-shear safety degree of the possible sliding block of the arch abutment by using a formula 3.
For the arch dam of 3 grades and below, whether the arch seat sliding block is safe is judged by using a formula 1 or a formula 2, the safety is judged if the formula 1 or the formula 2 is met, and meanwhile, the shearing resistance or shearing resistance safety degree of the arch seat sliding block is calculated by using a formula 3 or a formula 4, wherein:
wherein: SF 1 The ratio of the resistance term to the action term in the formula 1, which is called the shear-resistant safety degree for short, is more than or equal to 1.0, so that the requirement is met;
SF 2 the ratio of the resistance term to the action term, namely the shear resistance safety degree for short in the formula 2 is more than or equal to 1.0, so that the requirement is met;
γ 0 the structural importance coefficient corresponding to buildings with safety levels I, II and III can be 1.1,1.0,0.9 respectively or other reasonable values after demonstration;
psi-design condition coefficient, corresponding to persistent, transient, occasional, may take 1.00,0.95,0.85, respectively, or other reasonable values as demonstrated;
γ d1 、γ d2 the structural coefficients of the two calculation formulas can be respectively 1.2 and 1.1, or other reasonable values after demonstration;
γ m1fi 、γ m1ci 、γ m2fi -a material property subentry coefficient corresponding to the type of rock or structural surface to which each subregion belongs;
t-sliding force in the sliding direction;
N i normal force vertical to the sliding direction is born by a single sub-area divided according to the rock mass type and the structural surface type on the sliding surface;
f 1i 、f 2i shearing-resistant friction coefficients and shearing-resistant friction coefficients corresponding to different rock mass types and structural surface types;
C 1i shearing-resistant cohesion of different rock mass types and structural surface types;
A i -the area of a single sub-area on the sliding surface divided according to rock mass type and structural surface type.
The invention has the beneficial effects that: the invention provides a set of calculation formula for the anti-sliding stability of an arch support and a matched analysis method thereof, wherein the calculation formula comprises material performance itemized coefficients capable of accurately reflecting the category differences of different rock masses and structural surfaces. In the prior art, a group of uniform material performance itemized coefficients are matched with different types of rock masses and structural surfaces, and under the condition that the shear (breaking) strength parameter variation coefficients of the different types of rock masses and the structural surfaces are large, the method inevitably takes account of the different types of rock masses and the structural surfaces. The invention provides different and more consistent material performance subentry coefficients aiming at different types of rock masses and structural surfaces, and further modifies the original method calculation formula correspondingly according to the thought, thereby avoiding the problems of safety degree calculation result distortion, safety risk of engineering or uneconomic engineering caused by the defects of the existing analysis method to the maximum extent. The invention also provides a suggested value of the material performance subentry coefficient, which can be selected under the condition that the shear resistance mechanical test is not carried out aiming at various rock masses and structural planes of specific engineering.
Detailed Description
The present invention is further described below.
Rock mass classification is divided into five categories of I, II, III, IV, V and the like according to the national standard geological survey specification of hydroelectric power generation engineering (GB 50287-2016); the structural surfaces can be generally divided into two categories, namely rigid structural surfaces and weak structural surfaces. That is, the geological categories to which different regions on the sliding surface of the possible sliding blocks are related in the calculation of the sliding resistance of the arch base belong can only be one or a combination of the seven categories. According to the statistical data of the material parameters of different types of rock masses and structural surfaces, the relatively accurate shear (break) strength variation coefficient corresponding to each type of rock mass or structural surface can be obtained respectively, and further the relatively accurate material performance subentry coefficient corresponding to each type of rock mass or structural surface is calculated. Specifically, corresponding to a specific sliding surface of a specific sliding block, the material performance coefficients corresponding to the types of rocks or structural surfaces belonging to different areas are respectively expressed by gamma m1fi 、γ m1ci 、γ m2fi It is shown that m1f, m1c, m2f in the subscript have the same meaning as in the specification of concrete arch dam design (DL/T5346-2006), i.e. the same meaning as formula a and formula b in the present application, and i =1 and 2 … … in the subscript are the codes of the rock types or structural surface types belonging to different regions on the sliding surface, respectively.
On the basis, the method for calculating the anti-skid stability safety degree of the arch support of the arch dam comprises the following steps of:
s1, determining a sliding block capable of sliding and a sliding surface of the sliding block. The step is determined by the existing method.
S2, dividing the sliding surface of the sliding block which can slide into a plurality of independent sub-areas according to the rock mass classification line and the structural surface range boundary line; wherein the number of subregions on one sliding surface is a positive integer.
S3, respectively calculating the material performance subentry coefficient gamma corresponding to each subregion m1fi 、γ m1ci 、γ m2fi And counting the area A of each sub-region i . Coefficient of material property m1fi 、γ m1ci 、γ m2fi The value of (a) can be determined alternatively according to the two methods.
S4, calculating sliding force T on the sliding surface and total normal force N perpendicular to the sliding direction according to acting load on the sliding block, and decomposing the total normal force N into normal force N borne by each sub-region according to the area ratio of each sub-region divided in the step S1 i ，N i The calculation formula of (2) is as follows:
s5, according to the determined each subelement coefficient (including the material performance subelement coefficient corresponding to the rock mass classification or the structural surface type of each subregion), the mechanical parameter f of the rock class or the structural surface type of each subregion 1i 、C 1i 、f 2i (the mechanical parameters determined by geological survey are corresponding to the types of rocks and structural surfaces), and the normal force N of each subarea i And the area A of each sub-region i And judging whether the arch seat sliding block is safe or not by using a formula 1 or a formula 2, and calculating the shearing resistance and the shearing resistance safety degree by using a formula 3 or a formula 4.
When the method is used for analysis and calculation, the material performance subentry coefficient can be directly selected according to the rock class or structure surface type comparison table 2 to which each sub-area actually divided on the sliding surface belongs. The engineering of shear (break) resisting physical mechanical tests of a large number of rock masses and structural surfaces can be carried out conditionally, and the variation coefficient delta of the shear (break) resisting strength parameter of a specific engineering can be calculated based on the results of the shear (break) resisting physical mechanical tests and by a statistical method m And then calculating the material performance subentry coefficient corresponding to the type of the rock or the structural surface to which each subarea belongs by adopting a method specified in item 8.4.4 in the unified design Standard for reliability of Water conservancy and hydropower engineering (GB 50199-2013).
Although the expression form is similar to that of the formula 1 and the formula 2 proposed by the invention, the formula a and the formula b in the existing method (specification of concrete arch dam design (DL/T5346-2006)) have essential differences. Taking formula a as an example, if the safety of the arch seat sliding block is judged according to the formula a, the shearing-resistant friction coefficient f of the sliding surface is actually 1 Multiplied by the total normal force on the sliding surface and divided by a uniform material fraction factor gamma m1f (ii) a While suppressing the cohesive force C of the sliding surface 1 Multiplied by the total area of the sliding surface and divided by a uniform material fraction coefficient gamma m1c . In general, the coefficient of friction f against shear for different sub-areas on the sliding surface 1 And cohesion force C 1 Is different in order to obtain f on a sliding surface 1 The uniform representative value of (a) needs to be weighted average or other methods, and distortion inevitably occurs in order to keep the coefficient values uniform.
The formula 1 provided by the invention is used for judging whether the arch abutment sliding block is safe or not, and actually, the shearing-resistant friction coefficient f of each subarea on the sliding surface 1i With normal force N borne on each sub-region i Multiplying, and dividing by the material fractional coefficient gamma corresponding to the type of the rock class or the structural surface to which each subregion belongs m1fi Finally, different seeds are put inThe results of the regions are summed. At the same time, the cohesive force C of each subregion on the sliding surface 1i And the area A of each sub-region i Multiplying, and dividing by the material fractional coefficient gamma corresponding to the type of the rock class or the structural surface to which each subregion belongs m1ci And finally summing the results of the different sub-regions. The formula a is similar to the formula 1 in expression form, and the expression significance is substantially different. As mentioned above, compared with formula a, the formula 1 is adopted to analyze and judge the stability and safety of the abutment slide block to better conform to the basic principle of rock mechanics, the accuracy and the rationality of judgment can be obviously improved, and the stable safety state of the abutment slide block can be reflected more objectively and truly, which has a positive effect on the design of the arch dam. The difference between equation b and equation 2 is also the same, and the description is omitted here.
Claims (4)
1. The method for calculating the anti-skid stability safety degree of the arch seat of the arch dam is characterized by comprising the following steps of: the method comprises the following steps:
s1, determining a sliding block capable of sliding and a sliding surface of the sliding block;
s2, dividing the sliding surface of the sliding block which can slide into a plurality of independent sub-areas according to the rock mass classification line and the structural surface range boundary line; wherein the number of subregions on a single sliding surface is a positive integer;
s3, calculating the material performance subentry coefficient gamma corresponding to each subregion m1fi 、γ m1ci 、γ m2fi And counting the area A of each sub-region i ；
S4, according to the acting load on the sliding block, calculating sliding force T on the sliding surface and total normal force N perpendicular to the sliding direction, and then decomposing the total normal force N into normal force N born by each sub-region according to the area ratio of each sub-region divided in the step S1 i ，N i The calculation formula of (2) is as follows:
s5, judging whether the arch abutment sliding block is safe or not by using a formula 1 for the level 1 and level 2 arch dams and high arch dams, wherein the condition that the formula 1 is safe is met, and meanwhile, calculating the anti-shear safety degree of the possible sliding block of the arch abutment by using a formula 3;
for the arch dam of 3 grades and below, whether the arch seat sliding block is safe is judged by using a formula 1 or a formula 2, the safety is judged if the formula 1 or the formula 2 is met, and meanwhile, the shearing resistance or shearing resistance safety degree of the arch seat sliding block is calculated by using a formula 3 or a formula 4, wherein:
wherein: SF 1 The ratio of the resistance term to the action term in the formula 1 is referred to as the shear-resistant safety degree for short;
SF 2 the ratio of the resistance term to the action term, referred to as shear safety for short, in equation 2;
γ 0 -a structural importance coefficient;
psi-design condition coefficient;
γ d1 、γ d2 -structural coefficients for two calculation formulas;
γ m1fi 、γ m1ci 、γ m2fi -a material property polynomial coefficient corresponding to the type of the rock or structural surface to which each sub-region belongs;
t-sliding force in the sliding direction;
N i normal force vertical to the sliding direction is born by a single sub-area divided according to the rock mass type and the structural surface type on the sliding surface;
f 1i 、f 2i shear-resistant friction coefficients and shear-resistant friction coefficients corresponding to different rock mass types and structural surface types are obtained;
C 1i shearing-resistant cohesion of different rock mass types and structural surface types;
A i the area of a single sub-area on the sliding surface divided according to the rock mass type and the structural surface type.
2. A method for calculating the safety of the anti-skid stability of the abutment of an arch dam as claimed in claim 1, wherein: in step S3, the material performance subentry coefficient gamma m1fi 、γ m1ci 、γ m2fi The values are taken according to the table 2,
TABLE 2 material Property subentry coefficients
3. A method for calculating the safety of the anti-skid stability of the abutment of an arch dam as claimed in claim 1, wherein: in step S3, the material performance subentry coefficient gamma m1fi 、γ m1ci 、γ m2fi Taking values according to the following method: the variation coefficient delta of the material parameters of various rock masses and structural surfaces determined by shear mechanical tests m On the basis, material performance subentry coefficients corresponding to the types of rocks or structural surfaces of the subregions are calculated according to a method specified in article 8.4.4 in the unified design Standard for reliability of Water conservancy and hydropower engineering (GB 50199-2013).
4. A method for calculating the safety of the anti-skid stability of the abutment of an arch dam as claimed in claim 1, 2 or 3, wherein: in step S5, the values of partial coefficients are:
γ 0 the structural importance coefficient is 1.1,1.0,0.9 corresponding to buildings with the security levels I, II and III respectively;
psi-design condition coefficient corresponding to persistent condition, transient condition, accidental condition, respectively 1.00,0.95,0.85;
γ d1 、γ d2 and the structural coefficients of the two calculation formulas are respectively 1.2 and 1.1.
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