CN109800459A - Designing Method of Gravity Retaining Wall and device - Google Patents
Designing Method of Gravity Retaining Wall and device Download PDFInfo
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Abstract
The present invention provides a kind of Designing Method of Gravity Retaining Wall and devices, belong to Slope Prevention engineering field.The Designing Method of Gravity Retaining Wall includes: to establish soil body statistical parameter characteristic information；Simplify gravity retaining wall model and determines slope instability mode；According to requirement of engineering precision, discrete processes are carried out to the cross dimensions of gravity retaining wall；Determine stability against slope coefficient and stability against overturning coefficient；Using response phase method and iterative method is combined to calculate independent failure probability；Computing system failure probability；The minimum value for meeting the upper bottom width a and the sum of bottom width b of target reliability requirement is calculated according to obtained upper bottom width and corresponding bottom width data.Based on Reliability Theory, the calculating of gravity retaining wall reliability under relevant parameter is carried out, screening obtains sectional dimension that is most economical and meeting structural reliability requirement in all results, so that the design scheme of gravity retaining wall is more reasonable.
Description
Technical Field
The invention relates to the field of slope prevention and control engineering, in particular to a gravity type retaining wall design method and device.
Background
Gravity type retaining wall is a common side slope protection structure, and is the retaining wall that relies on wall body self gravity to resist soil body lateral pressure.
In the related design of the gravity retaining wall, a fixed value calculation method is still adopted in the aspect of stability calculation, uncertainty of rock-soil body parameters and related relation thereof cannot be considered, so that the design result of the gravity retaining wall is too conservative and is not reasonable in economic consideration.
Disclosure of Invention
The invention provides a gravity type retaining wall design method, and aims to improve the design of the existing gravity type retaining wall, so that the parameter design of the gravity type retaining wall is more economic and reasonable.
In a first aspect, an embodiment of the present invention provides a gravity retaining wall design method, including the following steps:
establishing soil body statistical parameter characteristic information: determining a random variable in design parameters of the gravity retaining wall, counting data of the random variable, obtaining a mean value and a standard deviation of the random variable and a correlation coefficient of the random variable, and determining a distribution form of the random variable;
simplifying a gravity type retaining wall model and determining a slope instability mode: the section of the gravity retaining wall is simplified into a trapezoid, the instability mode of the side slope is divided into a sliding instability mode and an overturning instability mode, the function functions of the sliding instability mode and the overturning instability mode are respectively determined,
wherein, supposing that the wall body of gravity type retaining wall does not produce the slip along the base and destroys, the mathematical expression of gravity type retaining wall antiskid function is:
PFsliding motion＝bCa-PahFormula-1
In the formula 1, b is the width of the lower bottom of the gravity retaining wall, Ca is the cohesive force of the soil body, and P isahIs the soil pressure component force along the horizontal direction;
assuming that the wall body of the gravity retaining wall does not generate the overturn damage around the toe of the wall, the mathematical expression of the anti-overturn function of the gravity retaining wall is as follows:
in formula 2: w1＝0.5γWall with a plurality of walls(b-a)H；W2＝γWall with a plurality of wallsaH; a, H are the width and height of the upper bottom of the gravity retaining wall respectively; gamma rayWall with a plurality of wallsThe gravity type retaining wall is heavy;
performing discrete processing on the section size of the gravity type retaining wall according to the engineering precision requirement to obtain discrete data of the upper bottom width a and the corresponding lower bottom width b of the gravity type retaining wall;
determining an anti-slip stability coefficient and an anti-overturning stability coefficient:
wherein, the mathematical expression of the anti-slip stability coefficient is as follows:
Fanti-skid＝FR/FsFormula-5
In formula 5, FAnti-skidTo an anti-slip stability factor, FRAnd FsRespectively, the sliding resistance and the sliding force;
the mathematical expression for deriving the anti-slip stability coefficient from equation 5 is:
Fanti-skid＝FR/Fs＝bCa/PahFormula-6
The mathematical expression of the anti-overturning stability coefficient is as follows:
Fanti-tilting＝MR/MSFormula-7
In formula 7, MRAnd MSThe device is divided into an anti-overturning moment and an overturning moment;
the mathematical expression for deriving the anti-overturning stability coefficient according to equation 7 is:
in formula 8, W1＝0.5γWall with a plurality of walls(b-a)H；W2＝γWall with a plurality of wallsaH；
Calculating independent instability probability by adopting a response surface method and combining an iteration method;
calculating the instability probability of the system: for a series system of curve equations with m extreme state equations, the mathematical expression for the probability of system instability is:
Pf，s＝1-P1，L，m≈1-Φm(β, R) formula-11
In formula 11: p1，mThe probability of the intersection of the m limit state curved surface safety zones; phim(β, R) is a cumulative distribution function of an m-dimensional standard normal distribution, R being a correlation coefficient between a plurality of failure modes, where m is 2;
and calculating the minimum value of the sum of the upper bottom width a and the lower bottom width b meeting the target reliability requirement according to the obtained upper bottom width and the corresponding lower bottom width data.
In the scheme of the embodiment of the invention, the randomness and the correlation of soil body parameters are considered, the relation among different failure modes is fully considered, and the system failure probability under two typical failure modes is calculated. Based on the reliability theory, the reliability of the gravity retaining wall under corresponding parameters is calculated, and the section size which is most economical (namely the material consumption is minimum) and meets the requirement of the structural reliability is obtained by screening in all results, so that the design scheme of the gravity retaining wall is more reasonable.
In a specific embodiment, the random variables include the internal friction angle of the earth, cohesion, and back of the wall friction angle.
In a specific embodiment, the mean, standard deviation and correlation coefficient of the internal friction angle, cohesion and wall back friction angle are determined from the test results of the soil samples.
In a particular embodiment, the particular step of using the response surface method comprises
A quadratic polynomial is adopted to simulate a response surface, and under the condition of neglecting an error term and not containing a cross term, the quadratic polynomial assumed by 3 random variables of an internal friction angle, cohesive force and a wall back friction angle is as follows:
Z＝λ1+λ2X1+λ3X1 2+λ4X2+λ5X2 2+λ6X3+λ7X3 2formula-9
X in formula 91、X2、X3Respectively, the mean values of the internal friction angle, cohesive force and wall back friction angle, lambda1、λ2、λ3、λ4、λ5、λ6、λ7Are all undetermined coefficients;
in each response surface fitting process, 6 axial points and 1 central point are sampled according to the central composite design, so that 7 safety response values are obtained, 7 equations are established, 7 undetermined coefficients are solved, and a fitting response surface function is obtained.
In a specific embodiment, the specific steps of the iterative method include
S510, in the initial step, the mu is processedxAs center point of the sample, μxi±fσiAs a combined sample spot, where μxRepresents the mean value of the random variable, μxi±fσiThe method is characterized in that a point is diffused to the periphery by the central point, and the distribution range of the expansion points is influenced by the value of f;
s520, carrying out numerical calculation after sampling is finished, substituting the data of the mean value, the standard deviation and the correlation coefficient of each random variable, calculating the response value g of the function, and solving the approximate function by using a least square method or an equation solving method;
s530, after the fitted response surface function is obtained, calculating the reliability, and solving a design checking point x' and a corresponding reliability index by adopting a JC method;
s540, selecting the central point of the next sampling, and obtaining the central point X of the sample of the next sampling according to the following formula:
in the formula 10, x*Is the design check point found in the previous step, i.e. nearest to the center μ of the independent variablexApproximate limit state design point. Using xcAnd xci±fσiForming a new sample combination;
s550, performing numerical calculation, calculating a function value g at a newly-adopted sample point, and solving an approximate function, namely a response surface function;
s560, based on the new approximate limit state function, carrying out reliability calculation, and generally adopting JC method to solve new design check points and corresponding reliability indexes;
and S570, repeating the step S540 to the step S560 until the errors of the design check points of the two times are in a preset range.
In a specific embodiment, the discrete processing of the section size of the gravity retaining wall comprises the following steps:
setting size constraint conditions of the upper bottom width and the lower bottom width;
and discretizing the range of the admissible values of the upper bottom width a and the lower bottom width b which accord with the size constraint condition according to the requirement of the actual engineering precision.
In a specific embodiment, the dimensional constraints are defined according to the specifications of the branch structure design manual as follows:
in a specific embodiment, the dimensional constraints are defined according to the specifications of the branch structure design manual as follows:
in a specific embodiment, the step of obtaining the minimum value of the sum of the upper base width a and the lower base width b that meets the target reliability requirement comprises
Setting constraint conditions according to the design requirements of the gravity type retaining wall, wherein the constraint conditions are as follows:
β in formula 14System for controlling a power supplyFor system reliability, βTargetA target reliability is obtained;
solving the minimum value of the sum of the upper bottom width a and the lower bottom width b, namely an objective function: min (a + b).
The embodiment of the invention also provides a gravity retaining wall design device, which comprises
The first module is used for establishing soil statistical parameter characteristic information;
a second module for determining a corresponding function according to the simplified model of the gravity retaining wall and the slope instability mode;
the third module is used for performing discrete processing on the section size of the gravity type retaining wall according to the engineering precision requirement to obtain discrete data of the upper bottom width a and the corresponding lower bottom width b of the gravity type retaining wall;
the fourth module is used for calculating the independent instability probability according to a response surface method and by combining an iteration method;
a fifth module to calculate a system reliability;
a sixth module to calculate an anti-slip stability coefficient and an anti-overturning stability coefficient; and
a seventh module, configured to solve a minimum value of a sum of the upper bottom width a and the lower bottom width b according to the system reliability and the target reliability.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings that are required to be used in the embodiments will be briefly described below, it should be understood that the following drawings only illustrate some embodiments of the present invention and therefore should not be considered as limiting the scope, and for those skilled in the art, other related drawings can be obtained according to the drawings without inventive efforts.
FIG. 1 is a flow chart of a method for designing a gravity retaining wall according to an embodiment of the present invention;
FIG. 2 is a schematic view of a gravity retaining wall according to an embodiment of the present invention;
fig. 3 is a front-back comparison diagram of discrete processing of data of the upper bottom width and the lower bottom width of the gravity retaining wall according to the embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be described clearly and completely with reference to the accompanying drawings of the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all embodiments of the present invention. All other embodiments, which can be obtained by a person skilled in the art without any inventive step based on the embodiments of the present invention, are within the scope of the present invention.
Thus, the following detailed description of the embodiments of the present invention, presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be obtained by a person skilled in the art without any inventive step based on the embodiments of the present invention, are within the scope of the present invention.
It should be noted that: like reference numbers and letters refer to like items in the following figures, and thus, once an item is defined in one figure, it need not be further defined and explained in subsequent figures.
Example 1
In the related design of the gravity retaining wall, a fixed value calculation method is still adopted in the aspect of stability calculation, uncertainty of rock-soil body parameters and related relation thereof cannot be considered, so that the design result of the gravity retaining wall is too conservative and is not reasonable in economic consideration. The existing gravity retaining wall design method has a space for further lifting and optimizing.
Therefore, the inventor provides a gravity retaining wall design method.
First, for a better understanding of the present invention, some of the terms used in connection with the present invention will be briefly described as follows:
gravity type retaining wall: is a retaining wall commonly used in China at present. The gravity type retaining wall maintains the stability of the retaining wall under the action of soil pressure by the self gravity of the retaining wall. Gravity retaining walls can be constructed of masonry or concrete and are generally made in a simple trapezoidal shape.
Reliability: the reliability theory is a theory and a method for analyzing the operation regularity of the research system and evaluating and controlling the research system. The reliability theory takes the probability theory as the analysis basis and combines the related function to carry out probability calculation on whether the structure is in failure or not and feed back the failure probability by using the reliability index.
The system reliability: system reliability generally refers to the ability/probability of a system to perform a specified function within a specified time and under specified operating conditions. Due to the progress of scientific technology, the composition of the system becomes more and more complex, and many engineering systems are composed of a plurality of subsystems. The failure probability of a system is related not only to the failure probability of individual subsystems, but also to the interrelationship between these subsystems. The accurate estimation of the actual performance of the system and the reduction of the system risk are of great practical significance.
Response surface method: the response surface method is also actually a reliability calculation method improved by the JC method (i.e., an equivalent normalization method, which is a method for indirectly solving a random variable of non-normal distribution by converting it into corresponding normal distribution). The content of the iterative computation check point of the response surface method is completely consistent with that of the JC method, and the difference is that the situation of adopting the response surface method to carry out reliability computation is usually a complex geotechnical engineering structure without or without writing an explicit expression of a functional function.
Referring to fig. 1, the method for designing a gravity retaining wall specifically includes the following steps:
s100: establishing soil body statistical parameter characteristic information: determining random variables in the design parameters of the gravity retaining wall, counting the data of the random variables, obtaining the mean value and standard deviation of the random variables and the correlation coefficient of the random variables, and determining the distribution form of the random variables.
The gravity type retaining wall meter mainly relates to 11 parameters of an internal friction angle of a soil body, cohesive force of the soil body, a wall back friction angle, a top slope of a retaining wall, a wall back inclination angle, a soil body weight, a wall body height, a base friction coefficient, an upper bottom width and a lower bottom width of the retaining wall, wherein the top slope of the retaining wall is the slope under most conditions, and the wall back inclination angle is 0 degree. Among these calculation parameters, the internal friction angle, the cohesion of the soil, and the back friction angle are highly uncertain and thus serve as random variables in the calculation. 4 parameters of soil mass gravity, wall body height and base friction coefficient are determinacy variables, and the width of the upper bottom and the width of the lower bottom of the retaining wall are designed target values.
In the reliability calculation process, the mean and standard deviation of the random variables are the two most important parameters. However, in practice, due to the consideration of uncertainty of geotechnical engineering parameters, the source of the geotechnical uncertainty is complex and is affected by the soil variability, the measurement equipment and the precision of the relevant model, so when the test data is abundant, the mean value, the standard deviation and the relevant coefficient of the random variable should be calculated according to the test data measured by the soil body sample sampled actually. That is, the mean, the standard deviation and the correlation coefficient of the random variable can be obtained through a plurality of experiments.
In other embodiments, if the test data is insufficient, the values can be approximated according to other similar engineering test parameters. For example: the standard deviation of the random variables was also calculated from realistic statistical estimates of variability of soil properties established by Phoon and Kulhawy in 1999, although the statistical results were also based on the development of experiments on large numbers of samples. Referring to table 1, according to the statistical conclusion, three ranges of variability (low, medium, and high) of soil properties are sufficient for the reliability level test, and by selecting three options of high, medium, and low, corresponding coefficients of variation are obtained, and by using the formula σ ═ μ cov, where σ represents the standard deviation of the random variables, μ represents the mean of the random variables, and cov represents the coefficients of variation, the standard deviation of the random variables is calculated. The method for calculating the standard deviation of the random variable is suitable for the case of less test data, and the mean value of the random variable is still determined by the test data in the method.
TABLE 1 correspondence table of variation grade and variation coefficient
In addition, when the test data is relatively small, other calculation methods may be used for the correlation coefficient of the random variable. For example, according to an engineering experience method, multiple scholars study according to data of multiple groups of soil samples, and indicate that strong negative correlation exists among soil indexes, and linear correlation coefficients of the soil indexes are generally in an interval of [ -0.8, -0.6 ]. The correlation coefficient matrix recommended by the calculation method, as shown in table 2, can be set according to actual conditions, such as different data results obtained by experiments in actual engineering. The method is suitable for being selected under the condition of less test data. Under the condition of more test data, the correlation coefficient can also be directly calculated according to the test data.
TABLE 2 correlation coefficient matrix schematic table
Wherein,represents an internal friction angle, Ca represents cohesion,&representing the back friction angle of the wall.
Therefore, the method for acquiring the mean value, the standard deviation and the correlation coefficient of the internal friction angle, the cohesive force and the wall back friction angle can be determined according to the test data of the soil body sample sampled actually. Or by using similar engineering empirical data. It should be noted that similar engineering experience is applicable to the selection under the condition that the soil body sample actually sampled is small. When the actually sampled soil samples are more, the soil samples can be determined according to the test data of the actually sampled soil samples. Thus being closer to the actual situation of engineering.
According to the investigation, the distribution form of most variables in the field of gravity retaining wall engineering is mainly the following two types:
the first method comprises the following steps: the Normal distribution (also called "Normal distribution"), also known as Gaussian distribution (Gaussian distribution), is obtained by professor schneideri first according to the process of solving an asymptotic formula in the binomial distribution, and then the Gaussian is derived from another angle in combination with a measurement error. One of the most important distribution forms of normal distribution is widely applied in the fields of mathematics, physics, engineering and the like.
And the second method comprises the following steps: lognormal distribution, which is an obvious off-normal distribution form, is mainly applied to fatigue tests of materials at first and is a main distribution form for researching the service lives of materials and parts. In common durability design, the lognormal distribution mode can be used for both the material parameters used by the part and the initial crack size, and the like, and the method has the characteristics of convenient and simple use and capability of returning to a reliable confidence interval according to actual conditions, so the method is widely applied to the aspects of part service life research and the like. In addition, for the field of geotechnical engineering, the compression coefficient and the compression modulus of the soil body generally follow the lognormal distribution.
In the related literature, the common distribution forms of the geotechnical parameters are a lognormal distribution form and a normal distribution form, but in the actual reliability calculation process, the inventor finds that: if the normal distribution mode is adopted, a negative value is selected with a certain probability in the process of randomly selecting the sampling point, which is contrary to the practical situation. Because there is no constraint on both sides of the data of the normal distribution, so that there is no requirement that the data have to be positive values, unnecessary errors are easily generated by using the normal distribution as a distribution form in the actual calculation process.
S200: simplifying a gravity type retaining wall model and determining a slope instability mode: the section of the gravity retaining wall is simplified into a trapezoid, the instability mode of the side slope is divided into a sliding instability mode and an overturning instability mode, the function functions of the sliding instability mode and the overturning instability mode are respectively determined,
the gravity retaining wall can be simplified into a trapezoid in actual design and construction, the height of the gravity retaining wall is determined by the height of an actual soil slope, the upper bottom width and the lower bottom width of the gravity retaining wall are mainly considered, and a simplified model thereof is shown in fig. 2. In the stability checking calculation, the anti-slip stability checking calculation and the anti-overturning stability checking calculation are mainly checked, so that two instability modes of slip and overturning are mainly considered in the calculation of the reliability. The target function is an anti-slip function and an anti-overturning function, and specific calculation methods of the anti-slip function and the anti-overturning function are briefly described below with reference to fig. 2 as an example of a gravity retaining wall.
Wherein, supposing that the wall body of gravity type retaining wall does not produce the slip along the base and destroys, the mathematical expression of gravity type retaining wall antiskid function is:
PFsliding motion＝bCa-PahFormula-1
In the formula 1, b is the width of the lower bottom of the gravity retaining wall, Ca is the cohesive force of the soil body, and P isahIs the soil pressure component force along the horizontal direction;
assuming that the wall body of the gravity retaining wall does not generate the overturn damage around the toe of the wall, the mathematical expression of the anti-overturn function of the gravity retaining wall is as follows:
in formula 2: w1＝0.5γWall with a plurality of walls(b-a)H；W2＝γWall with a plurality of wallsaH; a, H are the width and height of the upper bottom of the gravity retaining wall respectively; gamma rayWall with a plurality of wallsThe gravity retaining wall is heavy.
S300: according to the engineering precision requirement, the section size of the gravity type retaining wall is subjected to discrete processing, and discrete data of the upper bottom width a and the corresponding lower bottom width b of the gravity type retaining wall are obtained.
If a conventional calculation method for finding an optimal solution is adopted, for example, a planning solver in EXCEL, the calculated value is sometimes the optimal solution, but exceeds the engineering precision, for example, when the calculated optimal solution is 0.4359m of the upper bottom dimension, the accuracy is already 0.1mm, which is not realized in the actual construction, so that the discrete data of the upper bottom width a and the corresponding lower bottom width b of the gravity type retaining wall needs to be obtained by performing discrete processing on the section dimension of the gravity type retaining wall in combination with the engineering practice and under the condition of meeting the construction precision.
The discrete processing of the section size of the gravity retaining wall comprises the following steps:
s310: setting the size constraint conditions of the upper bottom width and the lower bottom width.
In a specific setting, relevant specifications can be combined, for example, according to relevant regulations in a branch structure design manual:
the top width of the retaining wall is generally H/12, and is not less than 0.4m or 0.2m according to different construction materials; the base width is generally (0.5-0.7) H. Wherein H also refers to the height of the gravity retaining wall.
Thus, the size constraint may be set to:
or
The values of the upper bottom width and the lower bottom width are restricted within a certain range by the size constraint condition.
S320: according to the requirement of the actual engineering precision, discretization is performed on the range of the obtainable values of the upper bottom width a and the lower bottom width b which meet the size constraint condition, please refer to fig. 3.
According to the requirement of actual engineering precision, the available value ranges of the upper bottom width a and the lower bottom width b obtained in the step S610 are converted into limited discrete data through discretization.
S400: determining an anti-slip stability coefficient and an anti-overturning stability coefficient:
wherein, the mathematical expression of the anti-slip stability coefficient is as follows:
Fanti-skid＝FR/FsFormula-5
In formula 5, FAnti-skidTo an anti-slip stability factor, FRAnd FsRespectively, the sliding resistance and the sliding force;
the mathematical expression for deriving the anti-slip stability coefficient from equation 5 is:
Fanti-skid＝FR/Fs＝bCa/PahFormula-6
The mathematical expression of the anti-overturning stability coefficient is as follows:
Fanti-tilting＝MR/MSFormula-7
In formula 7, MRAnd MSThe device is divided into an anti-overturning moment and an overturning moment;
the mathematical expression for deriving the anti-overturning stability coefficient according to equation 7 is:
in formula 8, W1＝0.5γWall with a plurality of walls(b-a)H；W2＝γWall with a plurality of wallsaH；
S500: and calculating the independent instability probability by adopting a response surface method and combining an iteration method.
Wherein the specific steps of adopting the response surface method comprise
And (2) simulating a response surface by using a quadratic polynomial, wherein the quadratic polynomial assumed by 3 random variables of the internal friction angle, the cohesive force and the wall back friction angle is as follows under the condition that an error term is ignored and no cross term is contained:
Z＝λ1+λ2X1+λ3X1 2+λ4X2+λ5X2 2+λ6X3+λ7X3 2formula-9
X in formula 91、X2、X3Respectively, the mean values of the internal friction angle, cohesive force and wall back friction angle, lambda1、λ2、λ3、λ4、λ5、λ6、λ7Are all undetermined coefficients;
in each response surface fitting process, 6 axial points and 1 central point are sampled according to the central composite design, so that 7 safety response values are obtained, 7 equations are established, 7 undetermined coefficients are solved, and a fitting response surface function is obtained.
Because the curve error of the response surface obtained by only adopting one-time sampling fitting is large, if the extreme state surface is relatively complex or comprises high-frequency terms, the fitting effect is not good, because the accuracy of the sampling fitting is related to the distance between the sampling central point and the extreme state surface, and if the distance is far, the error is large, the simulation precision of the response surface near the design checking point needs to be improved, so that the purpose of improving the precision of the reliability calculation is achieved.
In order to improve the accuracy of fitting, an iterative solution scheme of a response surface method can be adopted, and according to the Taylor expansion principle of the response surface method, the purpose of accurately simulating the extreme state surface near the design check point can be achieved only when the sampling point is very close to the design check point, so that the requirement can be met in an iterative mode.
Wherein the iteration method comprises the following specific steps
S510, in the initial step, the mu is processedxAs center point of the sample, μxi±fσiAs a combined sample spot, where μxRepresents the mean value of the random variable, μxi±fσiMeans that each point is spread around the center point. The value of f influences the distribution range of the expansion points, if the range is too large, the distance between the sampling point and the design check point is possibly far, the fitting result is poor, and the phenomenon that the design check point is not in the sampling range can be caused if the range is too small. Normally, the initial value of f is 2, and the iterative process is reduced continuously.
And S520, carrying out numerical calculation after sampling is finished, substituting the data of each sample point and calculating a response value g of the function, and solving the approximate function by using a least square method or an equation solving method. The data of each sample point as used herein refers to the data of the mean, standard deviation and correlation coefficient of the random variable.
S530, after the fitted response surface function is obtained, calculating the reliability, and solving a design checking point x' and a corresponding reliability index by adopting a JC method;
s540, selecting the central point of the next sampling, and obtaining the central point X of the sample of the next sampling according to the following formula:
in the formula 8, x*Is the design check point found in the previous step, i.e. nearest to the center μ of the independent variablexApproximate limit state design point. Using xcAnd xci±fσiAnd forming a new sample combination.
S550, performing numerical calculation, calculating a function value g at a newly-adopted sample point, and solving an approximate function, namely a response surface function;
s560, based on the new approximate limit state function, carrying out reliability calculation, and generally adopting JC method to solve new design check points and corresponding reliability indexes;
and S570, repeating the step S540 to the step S560 until the errors of the design check points of the two times are in a preset range.
S600: calculating the instability probability of the system: for a series system of curve equations with m extreme state equations, the mathematical expression for the probability of system instability is:
Pf，s＝1-P1，L，m≈1-Φm(β, R) formula-11
In formula 11: p1，mThe probability of the intersection of the m limit state curved surface safety zones; phim(β, R) is a cumulative distribution function of the m-dimensional standard normal distribution, and R is a correlation coefficient between failure modesIn the calculation of the degree, two instability modes of slippage and overturning are mainly considered, and at this time, the value of m is 2, that is, m is 2.
When m is 2, the cumulative distribution function of the two-dimensional standard normal distribution is:
in the formula 10, β 1 and β 2 represent the independent instability reliability of the two instability modes of slippage and overturning respectively, and the interrelation of the independent instability reliability of the two instability modes of P slippage and overturning can be converted into
The formula converts the cumulative distribution function of the two-dimensional standard normal distribution into one-dimensional integral, so that the one-dimensional integral is solved by adopting a trapezoidal area formula.
S700: and calculating the minimum value of the sum of the upper bottom width a and the lower bottom width b meeting the target reliability requirement according to the obtained upper bottom width and the corresponding lower bottom width data.
As a slope protection structure, when considering the minimum value of the sum of the upper bottom width a and the lower bottom width b, the gravity retaining wall should also consider the structural stability, that is, meet the target reliability, where the target reliability is determined by the actual engineering design requirements.
The step of obtaining the minimum value of the sum of the upper bottom width a and the lower bottom width b satisfying the target reliability requirement includes
Setting constraint conditions according to the design requirements of the gravity type retaining wall, wherein the constraint conditions are as follows:
β in formula 14System for controlling a power supplyFor system reliability, βTargetA target reliability is obtained;
solving the minimum value of the sum of the upper bottom width a and the lower bottom width b, namely: an objective function: min (a + b).
It should be noted that the minimum value of the sum of the upper bottom width a and the lower bottom width b, which we find here, is the minimum value of the sum of the upper bottom width a and the lower bottom width b, which is based on the reliability theory and takes into consideration the factors of the actual engineering precision requirement. From this point of view, the cross-sectional dimensions that give the most economical (i.e. the least amount of material used) and meet the structural reliability requirements are selected among all the results, which can be considered as the optimal design.
Example 2
A gravity type retaining wall design device comprises
The first module is used for establishing soil statistical parameter characteristic information;
a second module for determining a corresponding function according to the simplified model of the gravity retaining wall and the slope instability mode;
the third module is used for performing discrete processing on the section size of the gravity type retaining wall according to the engineering precision requirement to obtain discrete data of the upper bottom width a and the corresponding lower bottom width b of the gravity type retaining wall;
the fourth module is used for calculating the independent instability probability according to a response surface method and by combining an iteration method;
a fifth module to calculate a system reliability;
a sixth module to calculate an anti-slip stability coefficient and an anti-overturning stability coefficient; and
a seventh module, configured to solve a minimum value of a sum of the upper bottom width a and the lower bottom width b according to the system reliability and the target reliability.
The design method of the gravity type retaining wall provided by the invention considers the randomness and the correlation of soil body parameters, fully considers the relation among different failure modes and calculates the system failure probability under two typical failure modes. Based on the reliability theory, the reliability of the gravity retaining wall under corresponding parameters is calculated, and the section size which is most economical (namely the material consumption is minimum) and meets the requirement of the structural reliability is obtained by screening in all results, so that the design scheme of the gravity retaining wall is more reasonable.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (10)
1. A gravity type retaining wall design method is characterized in that: comprises the following steps
Establishing soil body statistical parameter characteristic information: determining a random variable in design parameters of the gravity retaining wall, counting data of the random variable, obtaining a mean value and a standard deviation of the random variable and a correlation coefficient of the random variable, and determining a distribution form of the random variable;
simplifying a gravity type retaining wall model and determining a slope instability mode: the section of the gravity retaining wall is simplified into a trapezoid, the instability mode of the side slope is divided into a sliding instability mode and an overturning instability mode, the function functions of the sliding instability mode and the overturning instability mode are respectively determined,
wherein, supposing that the wall body of gravity type retaining wall does not produce the slip along the base and destroys, the mathematical expression of gravity type retaining wall antiskid function is:
PFsliding motion＝bCa-PahFormula-1
In the formula 1, b is the width of the lower bottom of the gravity retaining wall, Ca is the cohesive force of the soil body, and P isahIs the soil pressure component force along the horizontal direction;
assuming that the wall body of the gravity retaining wall does not generate the overturn damage around the toe of the wall, the mathematical expression of the anti-overturn function of the gravity retaining wall is as follows:
in formula 2: w1＝0.5γWall with a plurality of walls(b-a)H；W2＝γWall with a plurality of wallsaH; a, H are the width and height of the upper bottom of the gravity retaining wall respectively; gamma rayWall with a plurality of wallsThe gravity type retaining wall is heavy;
performing discrete processing on the section size of the gravity type retaining wall according to the engineering precision requirement to obtain discrete data of the upper bottom width a and the corresponding lower bottom width b of the gravity type retaining wall;
determining an anti-slip stability coefficient and an anti-overturning stability coefficient:
wherein, the mathematical expression of the anti-slip stability coefficient is as follows:
Fanti-skid＝FR/FsFormula-5
In formula 5, FAnti-skidTo an anti-slip stability factor, FRAnd FsRespectively, the sliding resistance and the sliding force;
the mathematical expression for deriving the anti-slip stability coefficient from equation 5 is:
Fanti-skid＝FR/Fs＝bCa/PahFormula-6
The mathematical expression of the anti-overturning stability coefficient is as follows:
Fanti-tilting＝MR/MSFormula-7
In formula 7, MRAnd MSThe device is divided into an anti-overturning moment and an overturning moment;
the mathematical expression for deriving the anti-overturning stability coefficient according to equation 7 is:
in formula 8, W1＝0.5γWall with a plurality of walls(b-a)H；W2＝γWall with a plurality of wallsaH；
Calculating independent instability probability by adopting a response surface method and combining an iteration method;
calculating the instability probability of the system: for a series system of curve equations with m extreme state equations, the mathematical expression for the probability of system instability is:
Pf，s＝1-P1，L，m≈1-Φm(β, R) formula-11
In formula 11: p1，mThe probability of the intersection of the m limit state curved surface safety zones; phim(β, R) is a cumulative distribution function of an m-dimensional standard normal distribution, R being a correlation coefficient between a plurality of failure modes, where m is 2;
and calculating the minimum value of the sum of the upper bottom width a and the lower bottom width b meeting the target reliability requirement according to the obtained upper bottom width and the corresponding lower bottom width data.
2. A gravity retaining wall design method according to claim 1 wherein the random variables include the internal friction angle of the earth mass, cohesion and wall back friction angle.
3. A gravity retaining wall design method according to claim 2, wherein the mean, standard deviation and correlation coefficient of the internal friction angle, cohesion and wall back friction angle are determined from the test results of the soil samples.
4. A gravity retaining wall design method according to claim 1, wherein: the specific steps of adopting the response surface method comprise
A quadratic polynomial is adopted to simulate a response surface, and under the condition of neglecting an error term and not containing a cross term, the quadratic polynomial assumed by 3 random variables of an internal friction angle, cohesive force and a wall back friction angle is as follows:
Z＝λ1+λ2X1+λ3X1 2+λ4X2+λ5X2 2+λ6X3+λ7X3 2formula-9
X in formula 91、X2、X3Respectively, the mean values of the internal friction angle, cohesive force and wall back friction angle, lambda1、λ2、λ3、λ4、λ5、λ6、λ7Are all undetermined coefficients;
in each response surface fitting process, 6 axial points and 1 central point are sampled according to the central composite design, so that 7 safety response values are obtained, 7 equations are established, 7 undetermined coefficients are solved, and a fitting response surface function is obtained.
5. A gravity retaining wall design method according to claim 1, wherein: the specific steps of the iterative method comprise
S510, in the initial step, the mu is processedxAs center point of the sample, μxi±fσiAs a combined sample spot, where μxRepresents the mean value of the random variable, μxi±fσiThe method is characterized in that a point is diffused to the periphery by the central point, and the distribution range of the expansion points is influenced by the value of f;
s520, carrying out numerical calculation after sampling is finished, substituting the data of the mean value, the standard deviation and the correlation coefficient of each random variable, calculating the response value g of the function, and solving the approximate function by using a least square method or an equation solving method;
s530, after the fitted response surface function is obtained, calculating the reliability, and solving a design checking point x' and a corresponding reliability index by adopting a JC method;
s540, selecting the central point of the next sampling, and obtaining the central point X of the sample of the next sampling according to the following formula:
in the formula 10, x*Is the design check point found in the previous step, i.e. nearest to the center μ of the independent variablexApproximate limit state design point. Using xcAnd xci±fσiForming a new sample combination;
s550, performing numerical calculation, calculating a function value g at a newly-adopted sample point, and solving an approximate function, namely a response surface function;
s560, based on the new approximate limit state function, carrying out reliability calculation, and generally adopting JC method to solve new design check points and corresponding reliability indexes;
and S570, repeating the step S540 to the step S560 until the errors of the design check points of the two times are in a preset range.
6. A gravity retaining wall design method according to claim 1 wherein the discrete processing of the cross-sectional dimensions of the gravity retaining wall comprises the steps of:
setting size constraint conditions of the upper bottom width and the lower bottom width;
and discretizing the range of the admissible values of the upper bottom width a and the lower bottom width b which accord with the size constraint condition according to the requirement of the actual engineering precision.
7. A gravity retaining wall design method according to claim 6, wherein the dimensional constraints are defined as follows according to the support structure design Manual specifications:
8. a gravity retaining wall design method according to claim 6, wherein the dimensional constraints are defined as follows according to the support structure design Manual specifications:
9. a gravity retaining wall design method according to claim 7 or 8 wherein the step of obtaining the minimum value of the sum of the upper base width a and the lower base width b that meets the target reliability requirement comprises
Setting constraint conditions according to the design requirements of the gravity type retaining wall, wherein the constraint conditions are as follows:
β in formula 14System for controlling a power supplyFor system reliability, βTargetA target reliability is obtained;
solving the minimum value of the sum of the upper bottom width a and the lower bottom width b, namely: an objective function: min (a + b).
10. A gravity retaining wall design device is characterized by comprising
The first module is used for establishing soil statistical parameter characteristic information;
a second module for determining a corresponding function according to the simplified model of the gravity retaining wall and the slope instability mode;
the third module is used for performing discrete processing on the section size of the gravity type retaining wall according to the engineering precision requirement to obtain discrete data of the upper bottom width a and the corresponding lower bottom width b of the gravity type retaining wall;
the fourth module is used for calculating the independent instability probability according to a response surface method and by combining an iteration method;
a fifth module to calculate a system reliability;
a sixth module to calculate an anti-slip stability coefficient and an anti-overturning stability coefficient; and
a seventh module, configured to solve a minimum value of a sum of the upper bottom width a and the lower bottom width b according to the system reliability and the target reliability.
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