Reinforcing material tensile strength design method of step type reinforced earth retaining wall

Abstract

The invention discloses a rib tensile strength design method for a stepped reinforced earth retaining wall, and provides a rib tensile force calculation method suitable for the stepped reinforced earth retaining wall on the basis of the upper limit theorem of limit analysis. According to the method, a strength reduction method is combined, the tension of the rib material in the given stability coefficient state and the corresponding potential fracture surface position can be calculated, and meanwhile the stable state of the actually given retaining wall can be judged. The calculation method can be suitable for the form of a multi-stage complex reinforced soil retaining wall, can analyze the conditions of different retaining wall heights, step widths and wall surface inclination angles of all stages and the influence of foundation soil, and provides scientific and reasonable guidance for the design of the step type reinforced soil retaining wall. The calculation method can reasonably predict the rib material tension lower limit value required by the reinforced earth retaining wall in the limit state, and provides guidance for selection of the rib material tensile strength in actual construction, so that the construction cost of the step type reinforced earth retaining wall is lower.

Description

Technical Field

[0001] The invention belongs to the technical field of road engineering, and specifically relates to a method for designing the tensile strength of reinforcement materials of a stepped reinforced earth retaining wall. Background Art

[0002] Reinforced earth retaining walls are widely used in road construction systems due to their good seismic performance, fast construction speed, low cost, and beautiful appearance. For example, they are used as retaining structures for ramps on both sides of urban viaducts, reinforced foundations supporting bridgeheads, and high reinforced embankments on mountain roads. As the height of the retaining wall increases, the tensile force of the reinforcement required to maintain the internal stability of the retaining wall will increase logarithmically, and thus a stepped reinforced earth retaining wall is proposed. It effectively reduces the tensile force of the reinforcement by setting the platform width, and has good economic benefits. However, compared with a single-stage reinforced earth retaining wall, the relatively complex structural structure and the interaction between adjacent retaining walls will cause the stress state of the reinforced earth retaining wall to change, and it is necessary to consider how to design the stepped reinforced earth retaining wall.

[0003] At present, the existing design specifications design secondary reinforced earth retaining walls based on lateral earth pressure, which will result in conservative design values ​​of reinforcement tension, and the influence of the number of grades and platform width of the retaining wall on its stability and failure mode is unclear. In addition, some scholars have conducted some design studies on multi-tiered retaining walls, such as the literature "Design guidelines for multi-tiered MSE walls" and "Study on the calculation method and influence law of reinforcement force required for the stability of stepped reinforced retaining walls", which preliminarily explored the influence of retaining wall structure (number of grades and platform width) and backfill shear strength on retaining wall stability based on the limit equilibrium method. However, the reinforcement tension obtained based on the limit equilibrium method is still conservative, and the interaction between the reinforcement and soil when the retaining wall is under working stress is not considered. Summary of the invention

[0004] In view of the shortcomings of the prior art, the technical problem to be solved by the present invention is to provide a design method for the tensile strength of reinforcements of a stepped reinforced earth retaining wall. The design method for the tensile strength of reinforcements of the present invention designs a method for optimizing the tensile strength of reinforcements based on the upper limit theorem of limit analysis during the design stage of the stepped reinforced earth retaining wall. The method can provide scientific and reasonable guidance for the actual construction of the stepped reinforced earth retaining wall.

[0005] The technical solution of the present invention to solve the technical problem is to design a method for designing the tensile strength of reinforcement materials of a stepped reinforced earth retaining wall, characterized in that the method comprises the following steps:

[0006] Step 1: Set the structure and dimensions of the stepped reinforced earth retaining wall, including the number of stepped reinforced earth retaining walls, the height of each level of retaining walls, the width of each level of platforms, the spacing between reinforcements, and the inclination of the wall panels; and determine the property parameters of the backfill soil and foundation soil, including the internal friction angle, cohesion, and gravity of the backfill soil and the internal friction angle, cohesion, and gravity of the foundation soil;

[0007] Step 2: Based on the upper limit theorem of limit analysis, that is, on the basis of rigid-plastic and small deformation assumptions, for a given failure mode or deformation field, establish the virtual work equation shown in formula (1), that is, the internal energy dissipation rate along the failure surface inside the reinforced earth retaining wall is equal to the external force power under gravity load; the internal energy dissipation rate includes the energy dissipation rate of the reinforcement along the failure surface and the internal energy dissipation rate of the soil; and combine the strength reduction method of soil shear parameters to consider the stable state of the stepped reinforced earth retaining wall, and its calculation method is shown in formula (2);

[0008]

[0009] in: With the velocity field The coordinated strain rate field; σ ij is the external force F i The corresponding stress field; V1 is the volume domain of the sliding soil; c1 and c R are the cohesion of backfill soil before and after reduction respectively; and are the internal friction angles of backfill soil before and after reduction, respectively; FS is the stability coefficient;

[0010] For the calculation of the reinforcement tension of the stepped reinforced earth retaining wall, the following assumptions are made about the backfill soil, reinforcement and potential rupture surface:

[0011] (1) The backfill soil obeys the Mohr-Coulomb yield criterion and the kinematically associated flow law;

[0012] (2) The backfill soil that causes sliding is a rigid body;

[0013] (3) The potential rupture surface is a logarithmic spiral sliding surface;

[0014] (4) Ignore the compression and bending of the reinforcement;

[0015] (5) The length of the reinforcement bar ensures that the potential failure surface intersects each layer of reinforcement;

[0016] (6) The reinforcements of each level of retaining wall are placed vertically at equal intervals, and the vertical range of reinforcement is half of the spacing between reinforcements;

[0017] Due to the different properties of backfill soil and foundation soil, a double logarithmic spiral is used to assume the potential fracture surface form, and the relationship between the logarithmic spiral angle θ and the radius r is shown in formula (3);

[0018]

[0019] Where: r0 and r n Represents the logarithmic spiral relative to the angle θ0 and θ n The radius of the angle; θ0, θ n and θ h They are the logarithmic spiral angle when the spiral line passes through the top of the wall, the logarithmic spiral angle when it passes through the interface between the backfill soil and the foundation soil, and the logarithmic spiral angle when it passes through the exit of the foundation surface.

[0020] According to the multi-step reinforced earth retaining wall structure set in step 1, using the above formulas (1) and (2), the external force work is the work done by the sliding soil under the action of gravity W ex , the internal energy dissipation rate includes the energy dissipation rate of the reinforcement along the failure surface W re and the internal energy dissipation rate of the soil W in , the calculation formula is as follows:

[0021]

[0022] Where θ i is the logarithmic spiral angle when the logarithmic spiral line passes through the interface between the i-th retaining wall and the i+1-th retaining wall; V is the velocity discontinuity on the velocity discontinuity surface; Ω is the angular acceleration;

[0023]

[0024] in:

[0025]

[0026] Where: α i is the proportion of the i-th level retaining wall to the total wall height; H is the total height of the retaining wall; δ is the inclination angle of the wall panel; n is the number of levels of the retaining wall; D is the sum of the widths of the platforms at each level; D i is the platform width at the i-th retaining wall; L is the distance between the rupture surface of the wall top and the back of the wall panel; M is the distance between the rupture surface of the surface foundation soil and the toe of the lowest retaining wall; From the geometric relationship of the retaining wall, it can be known that D i , H, L, D and M and θ0, θ i ,θ h The relationship between , r0 and β` is as follows:

[0027]

[0028] Substituting formulas (4), (5) and (6) into formula (1), we can obtain the calculation formula for the reinforcement tension T:

[0029]

[0030]

[0031] In the formula and are the internal friction angles of backfill soil and foundation soil respectively; c1 and c2 are the cohesion of backfill soil and foundation soil respectively; γ1 and γ2 are the weights of backfill soil and foundation soil respectively;

[0032] Step 3: Given a value of the stability coefficient, substitute this value and the retaining wall structure dimensions set in step 1, as well as the property parameters of the backfill soil and foundation soil, into the function of the reinforcement tension T, and obtain the reinforcement tension T as a function of θ0, θ i ,θ n and θ h function; by θ0, θ i ,θ n ,θ h A set of specific values ​​of θ0, θ i ,θ n and θ h The value range and size relationship of are shown in formula (22);

[0033]

[0034] Formula (22) is used as the slip surface, and the function of the reinforcement tension T is used as the objective function. Then, θ0, θ i ,θ n and θ h The value of and calculate the corresponding reinforcement tensile force value under the potential rupture surface;

[0035] Step 4: According to the θ0 and θ obtained in step 3 i ,θ n and θ h The value of is used to determine whether the obtained potential fracture surface angle meets the size limit of the retaining wall structure, as shown in formula (23); if the judgment condition is met, the next step is performed; if not, the angle of the slip surface needs to be searched again, and the process of step 3 is repeated until the judgment condition is met;

[0036]

[0037] Step 5: Since the fracture surface starts from the bottom of the wall and extends, according to the potential fracture surface position that meets the judgment conditions obtained in step 4, the horizontal distance U between the toe of each level of retaining wall and the potential fracture surface position is calculated from bottom to top.i , and its calculation formula is shown in (24):

[0038]

[0039] Step 6: When the horizontal distance between the toe of each retaining wall and the potential fracture surface is not less than 0, the corresponding reinforcement tension is used as the reference value; i <0, that is, there is a discontinuity point, and the whole multi-level retaining wall is split into two multi-level retaining walls at the discontinuity point, that is, the 1st to the i-th level are taken as the first multi-level retaining wall, and the i+1th to the n-th level are taken as the second multi-level retaining wall; then, according to the structure and size of each multi-level reinforced earth retaining wall, the process of step 3 to step 5 is repeated. If there is still a discontinuity point in the reinforced earth retaining wall after splitting, the splitting is still continued according to the above method until the horizontal distance between the toe of each level of the retaining wall and the potential rupture surface position of each multi-level reinforced earth retaining wall after splitting is not less than 0, and the corresponding number of reinforcement tension values ​​are obtained according to the number of multi-level reinforced earth retaining walls at this time, and the maximum value of the reinforcement tension value is taken as the reference value;

[0040] Step 7: Use the reference value of the reinforcement tensile force obtained in step 6 as the minimum value of the reinforcement tensile strength selected during the construction of the stepped reinforced earth retaining wall in step 1.

[0041] Compared with the prior art, the present invention has the following beneficial effects:

[0042] 1. Based on the upper limit theorem of limit analysis, this paper proposes a method for calculating the tension of reinforcements suitable for stepped reinforced earth retaining walls. This method combines the strength reduction method to calculate the tension of reinforcements and the corresponding potential rupture surface position under a given stability coefficient, and can also determine the stability state of an actual given retaining wall.

[0043] 2. This calculation method can be applied to the form of multi-level complex reinforced earth retaining walls. It can analyze the different heights, step widths, wall inclinations and the influence of foundation soil at each level of retaining walls, and provide scientific and reasonable guidance for the design of stepped reinforced earth retaining walls.

[0044] 3. This calculation method can reasonably predict the lower limit of the reinforcement tension required under the ultimate state of the reinforced earth retaining wall, provide guidance for the selection of the tensile strength of the reinforcement in actual construction, and make the construction cost of the stepped reinforced earth retaining wall more economical. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 The present invention is a structural schematic diagram of an embodiment of a stepped reinforced earth retaining wall.

[0046] Figure 2 The present invention is a flowchart of the steps of an embodiment of a method for designing the tensile strength of reinforcement materials of a stepped reinforced earth retaining wall.

[0047] Figure 3 It is a schematic diagram of the reinforcement tension and the corresponding potential failure surface obtained by using the method in Document 1 and a reinforcement tensile strength design method for a stepped reinforced earth retaining wall of the present invention in the scenario of the reinforced earth retaining wall in Document 1.

[0048] Figure 4 It is a schematic diagram of the reinforcement tension and the corresponding potential failure surface obtained by using the method in Document 2 and a reinforcement tensile strength design method for a stepped reinforced earth retaining wall of the present invention in the scenario of the reinforced earth retaining wall in Document 2.

[0049] Figure 5 It is a schematic diagram of the reinforcement tension and the corresponding potential failure surface obtained by using the method in Document 3 and a reinforcement tensile strength design method for a stepped reinforced earth retaining wall of the present invention in the scenario of the reinforced earth retaining wall in Document 3. DETAILED DESCRIPTION

[0050] The technical solution of the present invention is further described below in conjunction with specific embodiments and drawings.

[0051] The present invention provides a method for designing the tensile strength of reinforcement materials of a stepped reinforced earth retaining wall, the method comprising the following steps:

[0052] Step 1: Set the structure and dimensions of the stepped reinforced earth retaining wall, including the number of stepped reinforced earth retaining walls, the height of each level, the width of each level, the spacing between reinforcements, and the inclination angle of the wall panel; and determine the property parameters of the backfill soil and foundation soil, including the internal friction angle, cohesion, and density of the backfill soil and the internal friction angle, cohesion, and density of the foundation soil.

[0053] Step 2: Based on the upper limit theorem of limit analysis, that is, on the basis of rigid plasticity and small deformation assumptions, for a given failure mode or deformation field, establish the virtual work equation shown in formula (1), that is, the internal energy dissipation rate along the failure surface of the reinforced earth retaining wall is equal to the external force power under gravity load. The internal energy dissipation rate includes the energy dissipation rate of the reinforcement along the failure surface and the internal energy dissipation rate of the soil. In addition, the stability state of the stepped reinforced earth retaining wall is considered in combination with the strength reduction method of the soil shear parameter, and its calculation method is shown in formula (2).

[0054]

[0055] in: With the velocity field The coordinated strain rate field; σ ij is the external force F i The corresponding stress field; V1 is the volume domain of the sliding soil, such as Figure 1 The soil area included in OAEC. c1 and cR are the cohesion of backfill soil before and after reduction respectively; and are the internal friction angles of backfill soil before and after reduction; FS is the stability coefficient.

[0056] Combining the above-mentioned upper limit theorem of limit analysis with the soil shear parameter strength reduction method, three aspects can be calculated: (1) when the stability coefficient and the reinforcement tension are given, the upper limit of the total height of the reinforced earth retaining wall is obtained; (2) when the reinforced earth retaining wall structure and the stability coefficient are given, the lower limit of the reinforcement tension is obtained; (3) when the reinforced earth retaining wall structure and the reinforcement tension are given, the stability state (stability coefficient) of the retaining wall is determined. This embodiment only involves the calculation of the lower limit of the reinforcement tension.

[0057] For the calculation of the reinforcement tension of the stepped reinforced earth retaining wall, the following assumptions are made about the backfill soil, reinforcement and potential rupture surface:

[0058] (1) The backfill soil obeys the Mohr-Coulomb yield criterion and the kinematically associated flow law;

[0059] (2) The backfill soil that causes sliding is a rigid body;

[0060] (3) The potential rupture surface is a logarithmic spiral sliding surface;

[0061] (4) Ignore the compression and bending of the reinforcement;

[0062] (5) The length of the reinforcement bar ensures that the potential failure surface intersects each layer of reinforcement;

[0063] (6) The reinforcement of each level of retaining wall is placed vertically at equal intervals, and the vertical range of reinforcement is half of the spacing between the reinforcements.

[0064] Due to the different properties of backfill soil and foundation soil, a double logarithmic spiral is used to assume the potential fracture surface form, and the relationship between the logarithmic spiral angle θ and the radius r is shown in formula (3).

[0065]

[0066] Where: r0 and r n Represents the logarithmic spiral relative to the angle θ0 and θ n The radius of the angle; θ0, θ n and θ h They are the logarithmic spiral angles when the spiral line passes through the top of the wall (such as Figure 1 The angle corresponding to the midpoint A), the logarithmic spiral angle passing through the interface between the backfill soil and the foundation soil (such as Figure 1 The angle corresponding to the midpoint C) and the logarithmic spiral angle at the exit through the foundation surface (such as Figure 1 The angle corresponding to the midpoint E).

[0067] According to the multi-step reinforced earth retaining wall structure set in step 1, using the above formulas (1) and (2), the external force work is the work done by the sliding soil under the action of gravity W ex , the internal energy dissipation rate includes the energy dissipation rate of the reinforcement along the failure surface W re and the internal energy dissipation rate of the soil W in , the calculation formula is as follows:

[0068]

[0069] Where θ i is the logarithmic spiral angle when the logarithmic spiral line passes through the interface between the i-th level retaining wall and the i+1-th level retaining wall (e.g. Figure 1 The angle corresponding to the midpoint B), and θ is the unified term for all angles, and θ i is the concretization of θ, specifically the logarithmic spiral angle when the spiral line passes through the interface of each level of retaining wall; V is the velocity discontinuity on the velocity discontinuity surface; Ω is the angular acceleration.

[0070]

[0071] in:

[0072]

[0073]

[0074] Where: α i is the proportion of the i-th level retaining wall to the total wall height; H is the total height of the retaining wall; δ is the inclination angle of the wall panel; n is the number of levels of the retaining wall; D is the sum of the widths of the platforms at each level; D i is the platform width at the i-th retaining wall; L is the distance between the rupture surface of the wall top and the back of the wall panel; M is the distance between the rupture surface of the surface foundation soil and the toe of the lowest retaining wall. From the geometric relationship of the retaining wall, it can be seen that D i , H, L, D and M and θ0, θ i ,θ h The relationship between , r0 and β` is as follows:

[0075]

[0076] Substituting formulas (4), (5) and (6) into formula (1), we can obtain the calculation formula for the reinforcement tension T (i.e. the tension borne by the reinforcement):

[0077]

[0078] In the formula and are the internal friction angles of backfill soil and foundation soil respectively; c1 and c2 are the cohesion of backfill soil and foundation soil respectively; γ1 and γ2 are the weights of backfill soil and foundation soil respectively.

[0079] Step 3: Given a value of the stability coefficient, substitute this value and the retaining wall structure dimensions set in step 1, as well as the property parameters of the backfill soil and foundation soil, into the function of the reinforcement tension T, and obtain the reinforcement tension T as a function of θ0, θ i ,θ n and θ h function; by θ0, θ i ,θ n ,θ h A set of specific values ​​of θ0, θ i ,θ n and θ h The value range and size relationship of are shown in formula (22).

[0080]

[0081] Formula (22) is used as the slip surface, and the function of the reinforcement tension T is used as the objective function. Then, θ0, θ i ,θ n and θ h and calculate the corresponding reinforcement tensile force under the potential rupture surface.

[0082] Step 4: According to the θ0 and θ obtained in step 3 i ,θ n and θ h The value of is used to determine whether the obtained potential fracture surface angle meets the size limit of the retaining wall structure, as shown in formula (23). If the judgment condition is met, proceed to the next step; if not, it is necessary to search for the angle of the slip surface again and repeat step 3 until the judgment condition is met.

[0083]

[0084] Step 5: Since the fracture surface starts from the bottom of the wall and extends, according to the potential fracture surface position that meets the judgment conditions obtained in step 4, the horizontal distance U between the toe of each level of retaining wall and the potential fracture surface position is calculated from bottom to top. i , and its calculation formula is shown in (24):

[0085]

[0086] Step 6: When the horizontal distance between the toe of each retaining wall and the potential fracture surface is not less than 0, the corresponding reinforcement tension is used as the reference value; i<0, there is a discontinuous point (i.e., the potential fracture surface passes through the outside of the retaining wall or is a discontinuous potential fracture surface). At the discontinuous point, the whole multi-level retaining wall is split into two multi-level retaining walls, i.e., the 1st to the i-th level are taken as the first multi-level retaining wall, and the i+1st to the n-th level are taken as the second multi-level retaining wall; taking the 5-level retaining wall as an example, if U3<0, the upper three-level retaining walls are taken as a multi-level reinforced earth retaining wall, and the lower two-level retaining walls are taken as a multi-level reinforced earth retaining wall. Then, according to the structure and size of each multi-level reinforced earth retaining wall, the process of steps 3 to 5 is repeated. If there are still discontinuous points in the reinforced earth retaining wall after splitting, the splitting is continued according to the above method until the horizontal distance between the toe of each level of the retaining wall and the potential fracture surface position of each multi-level reinforced earth retaining wall after splitting is not less than 0. According to the number of multi-level reinforced earth retaining walls at this time, the corresponding number of reinforcement tension values ​​are obtained, and the maximum value of the reinforcement tension value is taken as the reference value.

[0087] Step 7: The reference value of the reinforcement tension obtained in step 6 is used as the minimum tensile strength of the reinforcement selected for the construction of the stepped reinforced earth retaining wall in step 1, which can meet the stability requirements of the retaining wall under the set conditions.

[0088] Example

[0089] The operation flow of the method for designing the tensile strength of reinforcement of a stepped reinforced earth retaining wall of the present invention is as follows: Figure 2 As shown in the figure, reference 1 - "Performance of geosynthetic-reinforced soil walls at failure", reference 2 - "Limit equilibrium analyses of geosynthetic-reinforced two-tiered walls: Calibration from centrifuge tests" and reference 3 - "Geosynthetic reinforced multitiered walls" are selected for comparison, and the calculation results of the reinforcement tension of specific retaining walls by different methods are analyzed.

[0090] Reference 1 is a centrifuge test of a single-stage reinforced earth retaining wall. The main parameters of the retaining wall structure are wall height H = 256 mm, reinforcement spacing S v =16mm, reinforcement length L = 168mm, wall inclination angle is 0°, and the shear strength parameters of backfill soil and foundation soil are both c1 = 0kPa. and γ1=15.02kN / m 3 , centrifugal acceleration at failure N f =26g.

[0091] Reference 2 is a centrifuge test of a secondary reinforced earth retaining wall. The main parameters of the retaining wall structure are wall height H = 240 mm, where H1 = 180 mm, H2 = 160 mm, and reinforcement spacing S v =20mm, reinforcement length L1=L2=192mm, platform width D1=40mm, wall inclination angles of all levels are 0°, and the shear strength parameters of backfill soil and foundation soil are both c1=0kPa. and γ1=15.02kN / m 3 , centrifugal acceleration at failure N f =16g.

[0092] Figure 3 and Figure 4 The reinforcement tension and corresponding potential failure surface under the limit state (FS=1) obtained by the reinforcement tension calculation method of the present invention and the centrifuge test under the gravity acceleration of the failure of different retaining walls are shown respectively. According to the results, it can be seen that the potential failure surface obtained by the present invention is close to the actual failure surface of the retaining wall. When the actual potential failure surface is generated in the centrifuge test, the retaining wall has already been destroyed and does not meet the basis of the small deformation assumption. Therefore, when calculating the limit state stability of the reinforced earth retaining wall, the centrifugal acceleration N at the time of failure is used. f The calculated reinforcement tensile force will be greater than the test reinforcement tensile force value.

[0093] Reference 3 is a numerical simulation of a three-level reinforced earth retaining wall. The main parameters of the retaining wall structure are wall height H = 9m, where H1 = H2 = H3 = 3m, and reinforcement spacing S v =0.6m, reinforcement length L1=L2=L3=6.3m, platform width D1=D2=1.2m, wall inclination angle of each level is 0°, backfill soil shear strength parameter c1=0kPa, γ1=18kN / m 3 , the shear strength parameter of foundation soil c2=10kPa, γ2=18kN / m 3 .

[0094] Figure 5 The reinforcement tension and corresponding potential failure surface under the limit state (FS=1) obtained by the reinforcement tension calculation method and numerical simulation of the present invention are compared with the reinforcement tension values ​​obtained by the centrifuge and numerical simulation (limit equilibrium method). The method of the present invention not only satisfies the equilibrium condition but also considers the stress field that does not violate the limit condition, which is closer to the stress state and reinforcement-soil interaction state under the limit state of the soil. Therefore, it can be seen that the reinforcement tension value obtained by the method of the present invention is smaller than that of the limit equilibrium method.

[0095] In summary, the potential fracture surface obtained by the method of the present invention is consistent with that obtained by the prior art methods and tests, and the reinforcement tension values ​​are close. In addition, the result obtained by the reinforcement tension calculation method proposed in the present invention is closer to the actual situation and has practical application value.

[0096] Any matters not described in the present invention are applicable to the prior art.

Claims

1. A method for designing the tensile strength of reinforcement for a stepped reinforced earth retaining wall, characterized in that: The method comprises the following steps: Step 1: Set the structure and dimensions of the stepped reinforced earth retaining wall, including the number of stepped reinforced earth retaining walls, the height of each level of retaining walls, the width of each level of platforms, the spacing between reinforcements, and the inclination angle of the wall panels; and determine the property parameters of the backfill soil and foundation soil, including the internal friction angle, cohesion, and gravity of the backfill soil and the internal friction angle, cohesion, and gravity of the foundation soil; Step 2: Based on the upper limit theorem of limit analysis, that is, on the basis of rigid-plastic and small deformation assumptions, for a given failure mode or deformation field, establish the virtual work equation shown in formula (1), that is, the internal energy dissipation rate along the failure surface inside the reinforced earth retaining wall is equal to the external force power under gravity load; the internal energy dissipation rate includes the energy dissipation rate of the reinforcement along the failure surface and the internal energy dissipation rate of the soil; and combine the strength reduction method of soil shear parameters to consider the stable state of the stepped reinforced earth retaining wall, and its calculation method is shown in formula (2); in: With the velocity field The coordinated strain rate field; σ ij is the external force F i The corresponding stress field; V1 is the volume domain of the sliding soil; c1 and c R are the cohesion of backfill soil before and after reduction respectively; and are the internal friction angles of backfill soil before and after reduction, respectively; FS is the stability coefficient; For the calculation of the reinforcement tension of the stepped reinforced earth retaining wall, the following assumptions are made about the backfill soil, reinforcement and potential rupture surface: (1) The backfill soil obeys the Mohr-Coulomb yield criterion and the kinematically associated flow law; (2) The backfill soil that causes sliding is a rigid body; (3) The potential rupture surface is a logarithmic spiral sliding surface; (4) Ignore the compression and bending of the reinforcement; (5) The length of the reinforcement bar ensures that the potential failure surface intersects each layer of reinforcement; (6) The reinforcements of each level of retaining wall are placed vertically at equal intervals, and the vertical range of reinforcement is half of the spacing between reinforcements; Due to the different properties of backfill soil and foundation soil, a double logarithmic spiral is used to assume the potential fracture surface form, and the relationship between the logarithmic spiral angle θ and the radius r is shown in formula (3); Where: r0 and r n Represents the logarithmic spiral relative to the angle θ0 and θ n The radius of the angle; θ0, θ n and θ h They are the logarithmic spiral angle when the spiral line passes through the top of the wall, the logarithmic spiral angle when it passes through the interface between the backfill soil and the foundation soil, and the logarithmic spiral angle when it passes through the exit of the foundation surface. According to the multi-step reinforced earth retaining wall structure set in step 1, using the above formulas (1) and (2), the external force work is the work done by the sliding soil under the action of gravity W ex , the internal energy dissipation rate includes the energy dissipation rate of the reinforcement along the failure surface W re and the internal energy dissipation rate of the soil W in , the calculation formula is as follows: Where θ i is the logarithmic spiral angle when the logarithmic spiral line passes through the interface between the i-th retaining wall and the i+1-th retaining wall; V is the velocity discontinuity on the velocity discontinuity surface; Ω is the angular acceleration; in: Where: α i is the proportion of the i-th level retaining wall to the total wall height; H is the total height of the retaining wall; δ is the inclination angle of the wall panel; n is the number of levels of the retaining wall; D is the sum of the widths of the platforms at each level; D i is the platform width at the i-th retaining wall; L is the distance between the rupture surface of the wall top and the back of the wall panel; M is the distance between the rupture surface of the surface foundation soil and the toe of the lowest retaining wall; From the geometric relationship of the retaining wall, it can be known that D i , H, L, D and M and θ0, θ i ,θ h The relationship between , r0 and β` is as follows: Substituting formulas (4), (5) and (6) into formula (1), we can obtain the calculation formula for the reinforcement tension T: In the formula and are the internal friction angles of backfill soil and foundation soil respectively; c1 and c2 are the cohesion of backfill soil and foundation soil respectively; γ1 and γ2 are the weights of backfill soil and foundation soil respectively; Step 3: Given a value of the stability coefficient, substitute this value and the retaining wall structure dimensions set in step 1, as well as the property parameters of the backfill soil and foundation soil, into the function of the reinforcement tension T, and obtain the reinforcement tension T as a function of θ0, θ i ,θ n and θ h function; by θ0, θ i ,θ n ,θ h A set of specific values ​​of θ0, θ i ,θ n and θ h The value range and size relationship of are shown in formula (22); Formula (22) is used as the slip surface, and the function of the reinforcement tension T is used as the objective function. Then, θ0, θ i ,θ n and θ h The value of and calculate the corresponding reinforcement tensile force value under the potential rupture surface; Step 4: According to the θ0 and θ obtained in step 3 i ,θ n and θ h The value of is used to determine whether the obtained potential fracture surface angle meets the size limit of the retaining wall structure, as shown in formula (23); if the judgment condition is met, the next step is performed; if not, the angle of the slip surface needs to be searched again, and the process of step 3 is repeated until the judgment condition is met; Step 5: Since the fracture surface starts from the bottom of the wall and extends, according to the potential fracture surface position that meets the judgment conditions obtained in step 4, the horizontal distance U between the toe of each level of retaining wall and the potential fracture surface position is calculated from bottom to top. i , and its calculation formula is shown in (24): Step 6: When the horizontal distance between the toe of each retaining wall and the potential fracture surface is not less than 0, the corresponding reinforcement tension is used as the reference value; i <0, that is, there is a discontinuity point, and the whole multi-level retaining wall is split into two multi-level retaining walls at the discontinuity point, that is, the 1st to the i-th level are taken as the first multi-level retaining wall, and the i+1th to the n-th level are taken as the second multi-level retaining wall; then, according to the structure and size of each multi-level reinforced earth retaining wall, the process of step 3 to step 5 is repeated. If there is still a discontinuity point in the reinforced earth retaining wall after splitting, the splitting is still continued according to the above method until the horizontal distance between the toe of each level of the retaining wall and the potential rupture surface position of each multi-level reinforced earth retaining wall after splitting is not less than 0, and the corresponding number of reinforcement tension values ​​are obtained according to the number of multi-level reinforced earth retaining walls at this time, and the maximum value of the reinforcement tension value is taken as the reference value; Step 7: Use the reference value of the reinforcement tensile force obtained in step 6 as the minimum value of the reinforcement tensile strength selected during the construction of the stepped reinforced earth retaining wall in step 1.

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