Design method of earth-rock dam slope stability partial coefficient based on linearization of duncan nonlinear shear strength relationship

Abstract

The application discloses a kind of earth-rock dam slope stability design method based on Duncan nonlinear shear strength relation linearization, the method is first according to the linear shear strength index of assumed, using simplified method to carry out the analysis and calculation of dam slope stability coefficient method, obtain the initial safety margin η of dam slope stability coefficient method and the initial stress state of each soil strip bottom surface, and according to this, the linear shear strength index corresponding to Duncan nonlinear strength relation is calculated, and again using the strict method of stability analysis to carry out the analysis and calculation of dam slope stability coefficient method, through multiple iterations, until the safety margin of coefficient obtained in front and back is close, i.e. the final value of the safety margin of coefficient of dam slope stability can be obtained.The application is a beneficial supplement to the current roller compacted earth-rock dam design specification about dam slope and dam foundation anti-slide stability analysis coefficient method.

Description

Technical Field

[0001] This invention relates to the field of anti-sliding stability analysis of earth-rock dam slopes, specifically to a method for designing stability partial factors for earth-rock dam slopes based on the linearization of Duncan's nonlinear shear strength relationship. Background Technology

[0002] Slope stability analysis of earth-rock dams is an important part of earth-rock dam design. For face-faced rockfill dams and core-walled rockfill dams using coarse-grained materials such as rock and gravel, the cohesion of these materials is c=0. Therefore, the critical slip surface corresponding to the minimum safety factor obtained in slope stability analysis is usually a very shallow, meaningless arc. Thus, the Duncan nonlinear strength index should generally be used. The current design code for roller-compacted earth-rock dams (NB / T10872-2021) stipulates that for ultra-high dams, slope anti-sliding stability analysis should be performed using the partial factor method based on the probabilistic limit state design principle. The code also provides the linear strength index of the dam material (friction coefficient). With cohesion c) partial factor γ f γ c The suggested values ​​are provided, but no suggested values ​​or corresponding calculation methods are given for the material property partial factors corresponding to the Duncan nonlinear strength index.

[0003] When conducting partial factor design analysis and calculation for slope stability of face-panel rockfill dams and core-wall rockfill dams, the Duncan nonlinear strength index should be used for the rockfill material. Currently, the practice is to calculate the standard value of the corresponding friction coefficient using the Duncan nonlinear strength model based on the stress state of the bottom surface of each soil strip. Based on this, the corresponding design value of the friction coefficient is calculated. Then, a standard stability analysis is performed. Due to the friction coefficient... The partial factor γ f The partial factor γ of cohesion c c The recommended values ​​are different from those in the specifications, which can lead to some deviation in the final calculation results. Summary of the Invention

[0004] This invention addresses the shortcomings of existing methods by proposing a method to linearize the Duncan nonlinear strength index of coarse-grained materials and then use this linearization to perform calculations and analyses of the partial factor limit state method for the anti-sliding stability of earth-rock dam slopes. This method supplements and improves upon existing partial factor methods for the stability of earth-rock dam slopes.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] The present invention provides a design method for slope stability partial factors of earth-rock dams based on the linearization of Duncan's nonlinear shear strength relationship, comprising the following steps:

[0007] Step 1: Collect a wide range of basic data related to the slope stability of earth-rock dams, such as the dam's grade, type, basic profile, standard values ​​of physical and mechanical parameters of the dam body and foundation materials, and characteristic water levels of the reservoir.

[0008] Step 2: Using the seepage finite element analysis method, the seepage field and phreatic line distribution inside the dam body and foundation under different working conditions of the earth-rock dam are obtained, providing basic data for the next step of quantitative analysis of the slope anti-sliding stability;

[0009] Step 3: Based on the basic properties of the dam body and foundation materials and relevant engineering experience, determine the type of slip surface and the location of the initial slip surface;

[0010] Step 4: Vertically slice the sliding soil mass into m soil strips, and calculate the basic information of each soil strip (including the self-weight of the soil strip, the water pressure it is subjected to, the external forces such as seismic inertial force, and the type of material used on the bottom surface of the soil strip, etc.).

[0011] Step 5: Using a simplified method of stability analysis (for circular arc slip surfaces, the Swedish circular arc method is recommended; for non-circular arc slip surfaces, the Army Engineer Corps method is recommended), perform a stability analysis based on the assumed linear strength index to obtain the initial partial factor safety margin η0.

[0012] Step 6: Calculate the effective normal stress on the bottom sliding surface of each soil strip according to the static equilibrium equation. With shear stress (i = 1, 2, ..., m, where m is the total number of soil strips), calculate the minor principal stress σ3 on the bottom surface of each soil strip;

[0013] Step 7: If the Duncan nonlinear strength parameter should be used for the bottom surface of a soil strip, calculate the Duncan nonlinear strength index based on the minor principal stress σ3 of the bottom surface of the soil strip. The linear strength index corresponding to the standard value The standard value of c;

[0014] Step 8: Based on the linear strength index obtained in Step 7 The standard value of c, combined with the friction coefficient recommended by current specifications. The material property partial factor γ related to cohesion c f γ c The design value of the linear strength index is calculated, and then the safety margin η1 of the partial factor for the anti-sliding stability of the dam slope is calculated using a rigorous stability analysis method. At the same time, the stress state of the bottom surface of each soil strip (including the normal stress σ) is calculated. n Shear stress τ f And the corresponding minor principal stress σ3);

[0015] Step 9: If the difference between the partial factor safety margin η0 obtained in the previous calculation and the partial factor safety margin η1 obtained in this calculation is within the allowable range, end the calculation; otherwise, repeat steps 7-9 until convergence is achieved.

[0016] Step 10: Using optimization methods, such as genetic algorithms or particle swarm optimization, change the position of the slip surface and repeat steps 4-9 to find the critical slip surface corresponding to the minimum partial factor safety margin η.

[0017] Based on the above technical solution, the embodiments of the present invention can produce at least the following technical effects:

[0018] (1) This invention effectively solves the deviation problem caused by the difference between the friction coefficient and cohesion partial factors in the existing partial factor method by linearizing the Duncan nonlinear shear strength relationship and combining it with an iterative calculation process, thus significantly improving the accuracy of the safety margin calculation of the partial factor for slope stability of earth-rock dams. Through multiple iterations until convergence, the stability and reliability of the calculation results are ensured, and it is especially suitable for materials with significant nonlinear characteristics such as coarse-grained soil.

[0019] (2) This invention fills the gap in the current specifications regarding the limit state design method with partial coefficients for the Duncan nonlinear strength index, by introducing the γ recommended in the specifications. f and γ c The partial factor directly correlates the design value with the standard value, ensuring that the method meets both specification requirements and engineering practicality. This method can be seamlessly integrated into existing design processes, providing a standardized solution for slope stability analysis of ultra-high dams and dams under complex conditions. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the structures shown in these drawings without creative effort.

[0021] Figure 1 This is a flowchart of the partial factor design method for slope stability of earth-rock dams based on the linearization of the Duncan nonlinear shear strength model, as described in this invention.

[0022] Figure 2 This is a schematic diagram illustrating the vertical division of the sliding body into several soil strips according to the present invention.

[0023] Figure 3 This is a schematic diagram of the normal stress and shear stress on the bottom surface of any soil strip according to the present invention;

[0024] Figure 4 The present invention is based on the normal stress σ on the bottom surface of the soil strip. n With shear stress τ f A schematic diagram for calculating the minor principal stress σ3. Detailed Implementation

[0025] The technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. In addition, the technical solutions of the various embodiments can be combined with each other, but this must be based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention.

[0026] The design method for slope stability partial factors of earth-rock dams based on the linearization of Duncan's nonlinear shear strength relationship mainly includes the following steps:

[0027] Step 1: Collect a wide range of basic data related to the slope stability of earth-rock dams, such as the dam's grade, type, basic profile, standard values ​​of physical and mechanical parameters of the dam body and foundation materials, and characteristic water levels of the reservoir.

[0028] Step 2: Using the seepage finite element analysis method, the seepage field and phreatic line distribution inside the dam body under different working conditions are obtained, providing basic data for the next step of slope anti-sliding stability analysis;

[0029] Step 3: Based on the basic properties of the dam body and foundation materials and relevant engineering experience, determine the type of slip surface and the location of the initial slip surface;

[0030] Step 4: Based on the initial slip surface location, further subdivide the sliding soil mass into several soil strips, and calculate the basic information of each soil strip, including the self-weight of the soil strip, the water pressure it is subjected to, the seismic inertial force, and the type of material used for the bottom slip surface of the soil strip, etc.

[0031] Step 5: Employ a simplified stability analysis method (for circular arc slip surfaces, the Swedish circular arc method is recommended; for slip surfaces of arbitrary shapes, the Army Engineer Corps method is recommended), and base the analysis on the assumed linear shear strength index standard value. c k According to the material performance partial factor (γ) recommended by the specification f γ c ), to obtain the design value of the shear strength index. c dThe partial factor method for dam slope stability was used to calculate the initial partial factor safety margin η0.

[0032] The Duncan nonlinear strength index is related to the minor principal stress σ3. Since the stress state of the bottom slip surface is unknown before the safety factor is calculated, it is necessary to assume linear strength in advance to perform stability calculations, obtain the stress state of the bottom slip surface of each soil strip, and then calculate the strength parameters of the bottom slip surface of each soil strip based on the stress value of the bottom surface of the soil strip obtained from the calculation.

[0033] The relationship between the standard value and the design value of the material's shear strength is as follows:

[0034]

[0035] c d =c k / γ c (2);

[0036] In the formula, γ f γ c These are the coefficients of friction. The material partial factor for cohesion c, as suggested in the current design code for roller-compacted earth-rock dams (NB / T10872-2021), is γ. f =1.1, γ c =1.2.

[0037] Step 6: Calculate the effective normal stress on the bottom sliding surface of each soil strip according to the static equilibrium equation. With shear stress (i = 1, 2, ..., m, where m is the total number of soil strips), and calculate the corresponding minor principal stress σ3;

[0038] Specifically, based on the effective normal stress σ of the bottom sliding surface of the soil strip n The derivation process for calculating the minor principal stress σ3 is as follows (see appendix). Figure 2 ):

[0039] It is known that the slip surface at the bottom of the soil strip is in a state of limit equilibrium, i.e., the effective normal stress σ n With shear stress τ f Satisfying the Mohr-Coulomb strength criterion:

[0040]

[0041] For cohesionless soils, since c = 0, the expression for the Mohr-Coulomb strength criterion is:

[0042]

[0043] In the Mohr circle of stress, for cohesionless soil, the Mohr-Coulomb strength envelope is a straight line passing through the origin, and the angle between it and the positive x-axis is the material's internal friction angle. Based on the physical meaning of the Mohr's circle of stress, we have:

[0044]

[0045] In the formula, σ1 and σ3 are the major principal stress and minor principal stress, respectively.

[0046] According to equation (5), we have

[0047]

[0048] Therefore

[0049]

[0050] Substituting equations (8) and (6) into equation (4), we have

[0051]

[0052] Step 7: Based on the minor principal stress σ3 obtained in Step 6, calculate the linear strength index corresponding to the Duncan nonlinear strength index;

[0053] For coarse-grained soils, Duncan proposed the following nonlinear strength relationship:

[0054]

[0055] Substituting equation (10) into equation (4), we have

[0056]

[0057] According to equation (11), under a certain normal force σ n,o Lower shear stress τ n,o The expression is

[0058]

[0059] Equation (11) is applied to σ n,o Using Taylor series expansion and ignoring second-order infinitesimals, we have:

[0060] Expanding equation (13), we have

[0061]

[0062] In equation (14), let σ n =0, there is

[0063]

[0064] Substituting equation (15) into equation (14), we have

[0065]

[0066] Therefore there is

[0067]

[0068]

[0069] Expanding equations (17) and (18) further, and combining them with equation (9), we have:

[0070]

[0071] In the formula, This is the friction angle corresponding to the Duncan nonlinear strength model.

[0072] Substituting equation (19) into equations (17) and (18), we can obtain the expression for the linear strength index (standard value) corresponding to the Duncan nonlinear strength index (standard value).

[0073]

[0074] Once the standard value of the linear strength parameter of the bottom slip surface is known, its design value is...

[0075]

[0076] c d =c k / γ c (twenty three);

[0077] Step 8: Using rigorous stability analysis methods, calculate the partial factor safety margin η1 for the anti-sliding stability of the dam slope, and simultaneously calculate the stress state (including normal stress σ) at the bottom of each soil strip. n Shear stress τ f And the corresponding minor principal stress σ3);

[0078] The rigorous method of stability analysis refers to the stability analysis method that simultaneously satisfies the force and moment equilibrium conditions. The current design code for roller-compacted earth-rock dams (SL274-2020, NB / T10872-2021) stipulates that for the calculation of the anti-sliding stability of the dam slope, for circular arc slip surfaces, the simplified Bishop method that takes into account the forces between the blocks can be used; for non-circular arc slip surfaces, the Morgenstern-Price method that satisfies the force and moment equilibrium conditions can be used.

[0079] Step 9: If the difference between the partial factor safety margin η0 obtained in the previous calculation and the partial factor safety margin η1 calculated in this calculation is less than the allowable value, then the calculation ends. Otherwise, based on the stress state of the bottom surface of the block obtained in Step 8, Steps 7-9 are repeated until the convergence condition is met, thereby obtaining the final value η of the partial factor safety margin for dam slope stability.

[0080] Step 10: Using optimization methods, such as genetic algorithms or particle swarm optimization, change the position of the slip surface and repeat steps 4-9 to find the critical slip surface corresponding to the minimum partial factor safety margin η.

[0081] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of the present invention is defined by the appended claims and their equivalents.

Claims

1. A design method of earth-rockfill dam slope stability partial factor based on linearization of Duncan nonlinear shear strength relationship, characterized in that, The method comprises the following steps: Step 1: collecting basic information of the earth-rock dam, including dam body level, dam type, profile parameters, standard values of material physical and mechanical parameters, and reservoir characteristic water level; Step 2: obtaining seepage fields and phreatic line distributions of the dam body and dam foundation under different working conditions through seepage finite element analysis; Step 3: determining the type and initial position of the sliding surface according to the material properties of the dam body and dam foundation and engineering experience; Step 4: dividing the sliding soil into a plurality of soil strips, and calculating the external force borne by each soil strip and the material type of the bottom surface of the soil strip; Step 5: calculating the initial partial factor safety margin η0 based on the assumed standard value of the linear shear strength index by using a simplified method of dam slope stability analysis; Step 6: Calculate the initial effective normal stress σ on the bottom surface of each soil strip using the static equilibrium equations of each soil strip. n,0 Initial shear stress τ f,0 and initial minor principal stress σ 3,0 ; Step 7: Calculate the linear shear strength criterion value corresponding to the Duncan nonlinear strength index according to the minor principal stress on the bottom surface of the soil strip and c k ; Step 8: Calculate the linear strength design value f and γ c according to the material property partial coefficient suggested by the code and c d Recalculate the partial coefficient safety margin η1 using the strict method of stability analysis, and at the same time calculate the stress state of the soil strip bottom surface, including the effective normal stress σ n , shear stress τ f and minor principal stress σ3; Step 9: iteratively performing steps 7 to 8 until the difference between η1 and η0 is less than the convergence condition, and outputting the final partial factor safety margin; Step 10: adjusting the position of the sliding surface by using an optimization algorithm, repeating steps 4 to 9, and determining the critical sliding surface position corresponding to the minimum safety margin.

2. The design method of earth-rockfill dam slope stability partial factor based on linearization of Duncan nonlinear shear strength relationship according to claim 1, characterized in that, In step 5, the simplified method of stability analysis is: When the sliding surface is a circular arc, the initial partial factor safety margin η0 of the dam slope stability is calculated according to the assumed standard value of the linear shear strength index by using the Swedish circular arc method; When the sliding surface is a non-circular arc, the initial partial factor safety margin η0 of the dam slope stability is calculated according to the assumed standard value of the linear shear strength index by using the Corps of Engineers method.

3. The design method of earth-rockfill dam slope stability partial factor based on linearization of Duncan nonlinear shear strength relationship according to claim 1, characterized in that, The specific calculation process in step 7 is: For coarse-grained soil, the nonlinear strength relationship formula proposed by Duncan is: wherein: Duncan nonlinear strength index, σ3 is the minor principal stress, friction angle corresponding to the Duncan nonlinear strength model, p a atmospheric pressure; Based on the Mohr-Coulomb strength criterion, the linear shear strength index c and ck are obtained by Taylor series expansion and ignoring the second-order infinitesimal The expressions of c and ck are as follows:

4. The design method of earth-rockfill dam slope stability partial factor based on linearization of Duncan nonlinear shear strength relationship according to claim 1, characterized in that, In step 8, the strict method of stability analysis is: When the sliding surface is a circular arc, the simplified Bishop method is used; When the sliding surface is a non-circular arc, the Morgenstern-Price method is used.

5. The design method of earth-rockfill dam slope stability partial factor based on linearization of Duncan nonlinear shear strength relationship according to claim 1, characterized in that, The convergence condition in step 9 is that the absolute value of the difference between the partial coefficient of the previous calculation and the current calculation is less than ε, and ε is generally taken as 1.0 x 10 -5 , that is, |η1-η0|≤ε.

6. The design method of earth-rockfill dam slope stability partial factor based on linearization of Duncan nonlinear shear strength relationship according to claim 1, characterized in that, In step 10, the optimization algorithm is a genetic algorithm or a particle swarm algorithm.

Images