Duncan nonlinear shear strength relation linearization-based earth and rockfill dam slope stability subitem coefficient design method

Abstract

The invention discloses a Duncan nonlinear shear strength relation linearization-based earth and rockfill dam slope stability subitem coefficient design method, which comprises the following steps of: firstly, according to an assumed linear shear strength index, carrying out dam slope stability subitem coefficient method analysis and calculation by adopting a simplification method; obtaining the initial subitem coefficient safety margin eta0 of dam slope stability and the initial stress state of each soil strip bottom surface, calculating a linear shear strength index corresponding to the Duncan nonlinear strength relationship according to the initial subitem coefficient safety margin eta0 and the initial stress state, carrying out dam slope stability subitem coefficient method calculation by adopting a strict stability analysis method again, and carrying out multiple iterations to obtain the stability of the dam slope. And obtaining the final value of the safety margin of the subitem coefficient of the dam slope stability of the earth and rockfill dam until the safety margins of the subitem coefficients obtained in two times are close. The method is a beneficial supplement for a dam slope and dam foundation anti-sliding stability analysis subitem coefficient method in existing rolling type earth and rockfill dam design specifications.

Description

Technical Field

[0001] The present invention relates to the field of anti - sliding stability analysis of earth - rock dam slopes, and specifically to a design method for partial factor of earth - rock dam slope stability based on the linearization of Duncan's non - linear shear strength relationship. Background Art

[0002] The stability analysis of earth - rock dam slopes is an important part of earth - rock dam design. For coarse - grained materials such as rockfill, gravel and sand in concrete - faced rockfill dams and core - wall rockfill dams, since the cohesion c of such materials is 0, the critical slip surface corresponding to the minimum safety factor obtained during the slope stability analysis is usually a very shallow arc without practical significance. Therefore, generally, Duncan's non - linear strength index should be adopted. The current design code for rolled earth - rock dams (NB / T 10872 - 2021) stipulates that for extremely high dams, the anti - sliding stability analysis of dam slopes should be checked by the partial factor method based on the principle of probability - limit state design. At the same time, the code gives the recommended values of partial factors γ for the linear strength indices (friction coefficient f and cohesion c), but does not give the recommended values of partial factors of material properties corresponding to Duncan's non - linear strength index and the corresponding calculation method. c When carrying out the analysis and calculation of the partial factor design method for the stability of concrete - faced rockfill dam and core - wall rockfill dam slopes, the Duncan non - linear strength index should be adopted for the rockfill material. The current practice is to calculate the standard value of the corresponding friction coefficient according to the stress state at the bottom of each soil strip using the Duncan non - linear strength model

[0003] and calculate the corresponding design value of the friction coefficient based on this and then carry out the conventional stability analysis. Since the recommended values of the partial factor γ of the friction coefficient and the partial factor γ f of the cohesion c are different in the code, this practice will bring certain deviations to the final calculation results. c Summary of the Invention

[0004] In view of the deficiencies of the existing methods, the present invention proposes a method for linearizing the Duncan non - linear strength index of coarse - grained materials and carrying out the calculation and analysis of the partial factor limit state method for the anti - sliding stability of earth - rock dam slopes, which is a supplement and improvement to the existing partial factor method for earth - rock dam slope stability.

[0005] To achieve the above object, the present invention provides the following technical solutions:

[0006] The design method for partial factor of earth - rock dam slope stability based on the linearization of Duncan's non - linear shear strength relationship provided by the present invention includes the following steps:​

[0007] Step 1: Extensively collect basic information related to the slope stability of earth-rock dams, such as the grade of earth-rock dams, dam types, basic profiles of dams, standard values of physical and mechanical parameters of dam body and foundation materials, characteristic water levels of reservoirs, etc.;

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

[0009] Step 3: Determine the type of slip surface and the initial position of the slip surface according to the basic characteristics of the dam body and foundation materials and relevant engineering experience;

[0010] Step 4: Vertically divide the sliding soil mass into further m soil strips, and calculate the basic information of each soil strip (including the self-weight of the soil strip, external forces such as water pressure and seismic inertia force received, and the material type used for the bottom surface of the soil strip, etc.);

[0011] Step 5: Adopt a simplified method for stability analysis (for circular slip surfaces, it is recommended to use the Swedish circle method; for non-circular slip surfaces, it is recommended to use the Army Corps of Engineers method), and conduct a stability analysis once according to the assumed linear strength index to obtain the initial partial factor safety margin η0;

[0012] Step 6: Calculate the effective normal stress and shear stress (i = 1, 2, …, m, where m is the total number of soil strips) at the bottom slip surface of each soil strip, and calculate the minor principal stress σ3 at the bottom surface of each soil strip;

[0013] Step 7: If the Duncan nonlinear strength parameters should be used for the bottom surface of a certain soil strip, calculate the linear strength index corresponding to the standard value of the Duncan nonlinear strength index according to the minor principal stress σ3 at the bottom surface of this soil strip;

[0014] Step 8: According to the standard value of the linear strength index c obtained in Step 7, combined with the friction coefficient recommended by the current specification and the material performance partial factor γ f of cohesion c, c calculate the design value of the linear strength index, and then adopt a strict method for stability analysis to calculate the partial factor safety margin η1 of the slope anti-slide stability of the dam, and at the same time calculate the stress state (including normal stress σ n , shear stress τ f and the corresponding minor principal stress σ3) at the bottom surface of each soil strip;

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

[0016] Step 10: Use optimization methods such as genetic algorithms and particle swarm algorithms to change the slip surface position, 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 solutions, the embodiments of the present invention can at least produce the following technical effects:

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

[0019] (2) The present invention fills the blank in the current code regarding the limit state design method of partial factors for Duncan non - linear strength indexes. By introducing the γ f and γ c partial factors recommended by the code, directly relating the design value to the standard value, the method not only meets the code requirements but also has engineering practicability. This method can seamlessly connect with the existing design process and provides a standardized solution for the dam slope stability analysis of extra - high dams and complex working conditions. Description of the Drawings

[0020] To more clearly illustrate the technical solutions in the embodiments of the present invention or in the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on the structures shown in these drawings.

[0021] Figure 1 is the flowchart of the partial factor design method for the dam slope stability of earth - rock dams based on the linearization of the Duncan non - linear shear strength model of the present invention;

[0022] Figure 2 is the schematic diagram of vertically dividing the sliding mass into several soil strips in the present invention;

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

[0024] Figure 4 This is a schematic diagram for calculating the minor principal stress σ3 according to the normal stress σ n and shear stress τ f at the bottom of the soil strip in the present invention. Specific implementation manners

[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, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention. In addition, the technical solutions between the various embodiments can be combined with each other, but it must be based on the fact that those of ordinary skill in the art can implement it. When the combination of the technical solutions is contradictory or cannot be implemented, it should be considered that such a combination of the technical solutions does not exist and is not within the protection scope required by the present invention.

[0026] The design method of the partial factor of the dam slope stability of the earth-rock dam based on the linearization of the Duncan nonlinear shear strength relationship mainly includes the following steps:

[0027] Step 1: Extensively collect the basic data related to the dam slope stability of the earth-rock dam, such as the grade of the earth-rock dam, the dam type, the basic profile of the dam, the standard values of the physical and mechanical parameters of the dam body and dam foundation materials, the characteristic water levels of the reservoir, etc.;

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

[0029] Step 3: Determine the type of the slip surface and the position of the initial slip surface according to the basic characteristics of the dam body and dam foundation materials and relevant engineering experience;

[0030] Step 4: According to the position of the initial slip surface, further divide 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, the seismic inertia force, and the material type used for the bottom slip surface of the soil strip, etc.;

[0031] Step 5: Adopt a simplified method for stability analysis (for a circular arc slip surface, it is recommended to use the Swedish circular arc method; for an arbitrarily shaped slip surface, it is recommended to use the Army Engineer Corps method), and according to the assumed standard value of the linear shear strength index c k , and according to the partial factor of the material performance recommended by the specification (γ f , γ c ), obtain the design value of the shear strength index c d, carry out the calculation of the partial factor method for slope stability to obtain 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 a linear strength for the stability calculation in advance to 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 according to the stress values 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 shear strength index of the material is:

[0034]

[0035] c d = c k / γ c (2);

[0036] In the formula, γ f , γ c are the partial factors of the material for the friction coefficient and the cohesion c respectively. The current design code for rolled earth-rock dams (NB / T 10872-2021) recommends that γ f = 1.1, γ c = 1.2.

[0037] Step 6: Calculate the effective normal stress and shear stress (i = 1, 2,..., m, where m is the total number of soil strips) at the bottom slip surface of each soil strip, and calculate the corresponding minor principal stress σ3;

[0038] Specifically, the derivation process of calculating the minor principal stress σ3 according to the effective normal stress σ n at the bottom slip surface of the soil strip is as follows (see Appendix Figure 2 ):

[0039] It is known that the bottom slip surface of the soil strip reaches the limit equilibrium state everywhere, that is, the effective normal stress σ n and the shear stress τ f satisfy the Mohr-Coulomb strength criterion:

[0040]

[0041] For cohesionless soil, since c = 0, the expression of the Mohr-Coulomb strength criterion is

[0042]

[0043] In the stress Mohr circle, 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 internal friction angle of the material. According to the physical meaning of the stress Mohr circle, we have:

[0044]

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

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

[0047]

[0048] Therefore

[0049]

[0050] Substitute Equation (8) and Equation (6) into Equation (4), we have

[0051]

[0052] Step 7: Calculate the linear strength index corresponding to the Duncan nonlinear strength index according to the minor principal stress σ3 at the bottom of the soil strip obtained in Step 6;

[0053] For coarse-grained soil, the nonlinear strength relationship proposed by Duncan is

[0054]

[0055] Substitute Equation (10) into Equation (4), we have

[0056]

[0057] According to Equation (11), under a certain normal force σ n,o the expression of the shear stress τ n,o is

[0058]

[0059] Expand Equation (11) at σ n,o using the Taylor series and neglect the second-order infinitesimal, we have

[0060] Expand Equation (13), we have

[0061]

[0062] In Equation (14), let σ n = 0, we have

[0063]

[0064] Substitute Equation (15) into (14), we get

[0065]

[0066] Therefore, we have

[0067]

[0068]

[0069] Further expand Equations (17) and (18), and combine with Equation (9), we get

[0070]

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

[0072] Substitute Equation (19) into Equations (17) and (18), and the expression of the linear strength index (standard value) corresponding to the Duncan nonlinear strength index (standard value) can be obtained as

[0073]

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

[0075]

[0076] c d = c k / γ c (23);

[0077] Step 8: Adopt a strict method for stability analysis to calculate the partial coefficient safety margin η1 of the dam slope anti-slide stability, and at the same time calculate the stress state (including the normal stress σ n , shear stress τ f and the corresponding minor principal stress σ3) at the bottom of each soil strip;

[0078] The strict method for stability analysis refers to the stability analysis method that simultaneously satisfies the force and moment equilibrium conditions. The current design code for rolled earth-rock dams (SL274-2020, NB / T10872-2021) stipulates that for the calculation of the dam slope anti-slide stability, for the circular slip surface, the simplified Bishop method considering the interaction between strips can be adopted; for the non-circular slip surface, the Morgenstern-Price method that satisfies the force and moment equilibrium conditions can be adopted.

[0079] Step 9: If the difference between the partial factor safety margin η0 obtained from the previous calculation and the partial factor safety margin η1 obtained from the current calculation is less than the allowable value, the calculation is terminated. Otherwise, based on the stress state at the bottom of the slice obtained in Step 8, Steps 7 - 9 are repeatedly executed until the convergence condition is satisfied, thereby obtaining the final value η of the partial factor safety margin for the dam slope stability.

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

[0081] The above shows and describes 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 by the above embodiments. What is described in the above embodiments and the specification only illustrates the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention will have various changes and improvements, and these changes and improvements all fall within the scope of the present invention claimed. The scope of the present invention claimed is defined by the appended claims and their equivalents.

Claims

1. A design method for partial coefficients of earth-rock dam slope stability based on the linearization of Duncan's nonlinear shear strength relationship, characterized in that: The following steps are involved: Step 1: Collect basic information of earth-rock dam, including dam body grade, dam type, profile parameters, standard values ​​of material physical and mechanical parameters and reservoir characteristic water level; Step 2: Through the seepage finite element analysis, obtain the seepage field and infiltration line distribution of the dam body and dam foundation under different working conditions; Step 3: Determine the type of sliding surface and the location of the initial sliding surface based on the material properties of the dam body and foundation and engineering experience; Step 4: Divide the sliding soil into several soil strips, calculate the external force on each soil strip and the material type at the bottom of the soil strip; Step 5: Using the simplified method of dam slope stability analysis, calculate the initial partial factor safety margin η0 based on the assumed standard value of the linear shear strength index; Step 6: Calculate the initial effective normal stress σ at the bottom of each soil strip through the static equilibrium equation of each soil strip n,0 , shear stress τ f,0 and minor principal stress σ 3,0 ; Step 7: Calculate the standard value of linear shear strength corresponding to Duncan nonlinear strength index based on the minor principal stress at the bottom of the soil strip and c k ; Step 8: Material performance partial factor γ according to the specification recommendations f and γ c , calculate the linear strength design value and c d , the partial factor safety margin η1 is recalculated using a rigorous method of stability analysis, and the stress state at the bottom of the soil strip is calculated, including the effective normal stress σ n , shear stress τ f and minor principal stress σ3; Step 9: Iterate steps 7 to 8 until the difference between η1 and η0 is less than the convergence condition, and output the final partial coefficient safety margin; Step 10: Adjust the position of the slip surface through the optimization algorithm, repeat steps 4 to 9, and determine the critical slip surface position corresponding to the minimum safety margin.

2. The method for designing partial coefficients of earth-rock dam slope stability based on linearization of Duncan's nonlinear shear strength relationship according to claim 1 is characterized in that: In step 5, the simplified method of the stability analysis is: When the sliding surface is an arc, the Swedish arc method is used to calculate the initial partial factor safety margin η0 of the dam slope stability according to the assumed standard value of the linear shear strength index; When the sliding surface is a non-circular arc, the Army Engineer Corps method is used to calculate the initial partial factor safety margin η0 of the dam slope stability based on the assumed standard value of the linear shear strength index.

3. The method for designing partial coefficients of earth-rock dam slope stability based on linearization of Duncan's nonlinear shear strength relationship according to claim 1 is characterized in that: The specific calculation process in step 7 is: For coarse-grained soil, Duncan proposed a nonlinear strength relationship: Where: is the Duncan nonlinear strength index, σ3 is the minor principal stress, is the friction angle corresponding to Duncan nonlinear strength model, p a is atmospheric pressure; Combined with the Mohr-Coulomb strength criterion for linearization, the linear shear strength index is obtained by Taylor series expansion and ignoring the second-order infinitesimal quantity. The expressions of and ck are:

4. The method for designing partial coefficients of earth-rock dam slope stability based on linearization of Duncan's nonlinear shear strength relationship according to claim 1 is characterized in that: In step 8, the strict method of stability analysis is: When the sliding surface is an arc, the simplified Bishop method is used; When the slip surface is non-circular, the Morgenstern-Price method is used.

5. The method for designing partial coefficients of earth-rock dam slope stability based on linearization of Duncan's nonlinear shear strength relationship according to claim 1 is characterized in that: The convergence condition in step 9 is that the absolute value of the difference between the safety margins of the two partial coefficients calculated before and after is less than ε, which is generally 1.0×10 -5 , that is, |η1-η0|≤ε.

6. The method for designing partial coefficients of earth-rock dam slope stability based on linearization of Duncan's nonlinear shear strength relationship according to claim 1 is characterized in that: In step 10, the optimization algorithm is a genetic algorithm or a particle swarm algorithm.

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