Quantitative collaborative design method for blast-resistant arch structure with flexible boundary considering soft backfill

Abstract

The application discloses a kind of anti-blast arch structure flexible boundary quantitative collaborative design method considering soft backfill, belong to the field of protective engineering anti-blast design.The method includes: the method includes: based on the resistance coefficient of surrounding rock, structure bottom and medium effective contact area calculate the equivalent stiffness of surrounding rock;Based on the deformation modulus of soft backfill material, soft backfill layer thickness, effective contact area calculate the equivalent stiffness of soft backfill layer;Based on the deformation modulus of straight wall material, straight wall height, effective contact area calculate the equivalent stiffness of straight wall;Based on the stiffness model of spring series connection, determine the equivalent stiffness of arch foot flexible boundary;Flexible boundary equivalent stiffness is input into arch structure anti-blast calculation analysis model, explosion load is applied to carry out time history analysis, and obtain structural dynamic response index;According to the preset anti-blast performance target optimization, determine the design parameters of soft backfill layer.The application can realize the quantitative characterization of the effect of surrounding rock, soft backfill layer and straight wall on arch structure flexible boundary, improve the scientificity and economy of protective engineering design.

Description

Technical Field

[0001] This invention relates to the field of blast-resistant design of underground structures in protective engineering, specifically to a quantitative collaborative design method for the flexible boundary of a blast-resistant arch structure, and in particular, a protective design method for blast-resistant arch structures that comprehensively considers the collaborative deformation effects of surrounding rock, soft backfill layer and straight wall. Background Technology

[0002] In blast protection engineering, the blast resistance design of arched lining structures is crucial. Studies have shown that the dynamic response of an arch structure is not only related to its own geometry, material strength, and stiffness, but also closely related to the boundary constraints at the arch foot. Existing blast resistance analysis methods typically simplify the arch foot boundary to an ideal hinged or fixed constraint. While this idealization facilitates analysis, it fails to accurately reflect the boundary stress and deformation characteristics under the combined action of the structure, backfill medium, and surrounding rock in actual engineering projects, thus affecting the accuracy of blast resistance performance assessment results.

[0003] Engineering practice and research have shown that placing a soft backfill layer, such as foamed concrete or clay, between the arch structure and the surrounding rock can reduce the peak transfer of explosive loads, decrease the dynamic response of the structure, and improve the overall protective capability of the structure by introducing a flexible boundary effect. However, existing soft backfill layer designs mostly rely on experience to determine their material parameters and structural dimensions, lacking a quantitative design method for the combined effects of the surrounding rock, soft backfill layer, and structure, making it difficult to achieve optimized design for specific blast resistance targets. Furthermore, for straight-wall arch structures with straight wall sections, the straight walls themselves will deform under explosive loads, affecting the overall flexibility of the arch foot boundary. Existing methods typically do not incorporate the elasticity of the straight walls into the boundary equivalence analysis, leading to discrepancies between the calculated results and actual conditions.

[0004] Therefore, it is necessary to propose a method that can quantify the mechanical effects of the surrounding rock, soft backfill layer and straight wall into the equivalent stiffness of the structural flexible boundary, and use this equivalent stiffness for blast-resistant dynamic analysis and soft backfill parameter optimization design, so as to improve the accuracy and economy of blast-resistant design of arch structures. Summary of the Invention

[0005] This invention proposes a quantitative collaborative design method for the flexible boundary of an blast-resistant arch structure that considers soft backfill. This method addresses the problems in existing technologies, such as oversimplification of the arch foot boundary, reliance on empirical selection of soft backfill layer parameters, and insufficient consideration of the influence of straight wall deformation. This method can comprehensively consider the influence of surrounding rock, soft backfill layer, and straight wall deformation, and establish a quantitative relationship from surrounding rock parameters, backfill material parameters, and straight wall parameters to the stiffness of the structural flexible boundary, thereby achieving accurate evaluation and optimized design of the blast-resistant performance of the arch structure.

[0006] The technical solution for achieving this invention is: a quantitative collaborative design method for the flexible boundary of an anti-blast arch structure considering soft backfill, comprising the following steps:

[0007] Step S1: Obtain the surrounding rock resistance coefficient, determine the effective contact area between the bottom of the structure and the adjacent medium along the load transfer direction, and calculate the equivalent stiffness of the surrounding rock based on the surrounding rock resistance coefficient and the effective contact area.

[0008] Step S2: Obtain the deformation modulus of the soft backfill material and the thickness of the soft backfill layer. Based on the deformation modulus of the soft backfill material, the thickness of the soft backfill layer, and the effective contact area, calculate the equivalent stiffness of the soft backfill layer.

[0009] Step S3: When the arch structure is a straight-wall arch structure, obtain the deformation modulus of the straight-wall material and the height of the straight wall. Based on the deformation modulus of the straight wall, the height of the straight wall and the effective contact area, calculate the equivalent stiffness of the straight wall.

[0010] Step S4: Based on the spring series stiffness model, calculate the equivalent stiffness of the flexible boundary of the arch structure using the equivalent stiffness of the surrounding rock and the equivalent stiffness of the soft backfill layer; when considering the deformation of the straight wall, further calculate the equivalent stiffness of the flexible boundary of the arch structure by combining the equivalent stiffness of the straight wall.

[0011] Step S5: Establish a finite difference calculation and analysis model for the blast-resistant dynamic response of the arch structure, and determine the equivalent stiffness k of the flexible boundary of the arch structure. f As the spring stiffness input to the arch foot boundary of the analysis model, the vertical boundary conditions of the model are obtained:

[0012] (1).

[0013] Where s1 is micro-segment 1, its left side is section 0, its right side is section 1, p0 is the load perpendicular to the arch axis at section 0, and θ0 is the angle between the section and the vertical axis. Where is the length of segment 1, Q1 is the shear force at section 1, and N1 is the axial force at section 1. Let w be the mass per unit length of the member, and w0 be the vertical displacement at section 0. Z0 represents the vertical acceleration of section 0, and Z0 is the initial value of the vertical coordinate of section 0.

[0014] When considering the deformation of a straight wall, the boundary conditions of the model are:

[0015] (2).

[0016] Where Q0 is the shear force at section 0 and N0 is the axial force at section 0.

[0017] Using equations (1) and (2) as boundary conditions, considering equilibrium conditions, geometric relationships and material constitutive properties, an explosive load is applied and dynamic time history analysis is performed to obtain the structural dynamic response index.

[0018] Step S6: Adjust the thickness and material deformation modulus of the soft backfill layer, analyze the influence of the change in flexible boundary stiffness on the dynamic response index of the arch structure, and optimize and determine the design parameters of the soft backfill layer based on the preset anti-blast performance target.

[0019] Compared with the prior art, the significant advantages of this invention are:

[0020] (1) The combined effect of the surrounding rock, soft backfill layer and straight wall is uniformly equivalent to the structural flexible boundary stiffness, overcoming the error caused by the simplification of traditional hinged or consolidated boundaries.

[0021] (2) Establish a quantitative relationship between soft backfill layer parameters, boundary stiffness and structural blast resistance response, so that the design of soft backfill layer is transformed from empirical selection to target-oriented parameter optimization.

[0022] (3) On the basis of meeting the requirements of blast resistance, the material waste can be reduced and the engineering economy can be improved by optimizing the modulus and thickness of the soft backfill layer. Attached Figure Description

[0023] Figure 1 This is a flowchart of a quantitative collaborative design method for flexible boundaries of an anti-blast arch structure considering soft backfill, according to the present invention.

[0024] Figure 2 This is a simplified structural boundary model diagram of Embodiment 1 of the present invention.

[0025] Figure 3 This is a structural boundary force analysis diagram of Embodiment 1 of the present invention.

[0026] Figure 4 This is a graph showing the variation of the equivalent stiffness of the structural boundary with the thickness of the soft backfill in Embodiment 1 of the present invention.

[0027] Figure 5 This is a graph showing the variation of structural deflection response with soft backfill thickness in Embodiment 1 of the present invention.

[0028] Figure 6 This is a simplified structural boundary model diagram of Embodiment 2 of the present invention.

[0029] Figure 7 This is a structural boundary force analysis diagram of Embodiment 2 of the present invention.

[0030] Figure 8 This is a graph showing the variation of the equivalent stiffness of the structural boundary with the thickness of the soft backfill in Embodiment 2 of the present invention.

[0031] Figure 9 This is a graph showing the variation of structural deflection response with soft backfill thickness in Embodiment 2 of the present invention. Detailed Implementation

[0032] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. 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 of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0033] The technical solutions of the various embodiments of the present invention can be combined with each other, but only if they can be implemented by those skilled in the art. 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.

[0034] The following section will further introduce the specific implementation method, as well as the technical difficulties and inventive points of this invention, using this design example as an example.

[0035] Combination Figure 1 A quantitative collaborative design method for flexible boundaries of blast-resistant arch structures considering soft backfill includes the following steps:

[0036] Step S1: Obtain the surrounding rock resistance coefficient, determine the effective contact area between the bottom of the structure and the adjacent medium along the load transfer direction, and calculate the equivalent stiffness of the surrounding rock based on the surrounding rock resistance coefficient and the effective contact area.

[0037] Obtain the resistance coefficient K of the surrounding rock where the arch structure is located. r Determine the effective contact area S between the bottom of the structure and the adjacent medium along the load transfer direction, and treat the constraint of the surrounding rock on the structural boundary as an equivalent spring action, then calculate the equivalent stiffness k of the surrounding rock. r :

[0038] k r = K r S;

[0039] Wherein, the surrounding rock resistance coefficient K r It can be obtained based on engineering specifications, in-situ testing, inversion analysis, theoretical calculation, or numerical simulation.

[0040] Step S2: Obtain the deformation modulus of the soft backfill material and the thickness of the soft backfill layer. Based on the deformation modulus of the soft backfill material, the thickness of the soft backfill layer, and the effective contact area, calculate the equivalent stiffness of the soft backfill layer.

[0041] A soft backfill layer is installed between the bottom of the structure and the surrounding rock. The deformation modulus of the soft backfill material is E. l The design value for the thickness of the soft backfill layer is h. l Treating the soft backfill layer as a stress-deformation spring along the load transfer direction, the equivalent stiffness k of the soft backfill layer is calculated. l :

[0042] k l = E l S h l -1 ;

[0043] Wherein, the equivalent deformation modulus E of the soft backfill material l It can be obtained based on material testing, empirical values, standard recommended values, or numerical analysis.

[0044] Step S3: When the arch structure is a straight-wall arch structure, obtain the deformation modulus of the straight-wall material and the height of the straight wall. Based on the deformation modulus of the straight wall, the height of the straight wall and the effective contact area, calculate the equivalent stiffness of the straight wall.

[0045] When the arch structure is a straight-walled arch, the influence of the straight walls is further considered, and the deformation modulus of the straight-wall material is E. w The height of the straight wall is h w The deformation of the straight wall in the main force direction is equivalent to the action of a spring, and the equivalent stiffness k of the straight wall is calculated. w :

[0046] k w = E w S h w -1 ;

[0047] Wherein, the deformation modulus E of the straight wall material w The equivalent stiffness can be determined based on material testing, design specifications, or numerical analysis. In a preferred embodiment, the calculation of the equivalent stiffness of the straight wall is applicable when the straight wall is mainly subjected to axial compressive deformation. When the bending or shear deformation of the straight wall has a significant impact, the modified equivalent stiffness can be used in subsequent calculations.

[0048] Step S4: Based on the spring series stiffness model, calculate the equivalent stiffness of the flexible boundary of the arch structure using the equivalent stiffness of the surrounding rock and the equivalent stiffness of the soft backfill layer; when considering the deformation of the straight wall, further calculate the equivalent stiffness of the flexible boundary of the arch structure by combining the equivalent stiffness of the straight wall.

[0049] The deformation effects of the surrounding rock, soft backfill layer, and straight wall on the arch foot boundary are considered as a series spring system. Based on the spring series stiffness model, the equivalent stiffness k of the flexible boundary of the arch structure is calculated. f .

[0050] When the deformation of straight walls is not considered, the calculation formula is:

[0051] k f = (k r -1 + k l -1 + k w-1 ) -1 ;

[0052] When considering the deformation of a straight wall, the calculation formula is:

[0053] k f = (k r -1 + k l -1 ) -1 ;

[0054] Step S5: Establish a finite difference calculation and analysis model for the blast-resistant dynamic response of the arch structure, and perform blast-resistant dynamic response analysis:

[0055] Establish a calculation and analysis model for the blast-resistant dynamic response of an arch structure, and incorporate the equivalent stiffness k of the flexible boundary step. f As the input model for the spring stiffness of the arch foot boundary, an explosive load is applied and dynamic time history analysis is performed to obtain the structural dynamic response index.

[0056] The analytical model is established using the finite difference method, and the equivalent stiffness k of the flexible boundary of the arch structure is used. f As the spring stiffness input to the arch foot boundary of the analysis model, the vertical boundary conditions of the model are obtained:

[0057] (1);

[0058] Where s1 is micro-segment 1, its left side is section 0, its right side is section 1, p0 is the load perpendicular to the arch axis at section 0, and θ0 is the angle between the section and the vertical axis. Where is the length of segment 1, Q1 is the shear force at section 1, and N1 is the axial force at section 1. Let w be the mass per unit length of the member, and w0 be the vertical displacement at section 0. Let Z0 be the vertical acceleration at section 0, and Z0 be the initial vertical coordinate of section 0. Considering the deformation of the straight wall, the model boundary conditions are:

[0059] (2);

[0060] Where Q0 is the shear force at section 0 and N0 is the axial force at section 0.

[0061] Using equations (1) and (2) as boundary conditions, considering equilibrium conditions, geometric relationships and material constitutive properties, an explosive load is applied and dynamic time history analysis is performed to obtain the structural dynamic response index.

[0062] The explosive load can be applied in the form of triangular pulse, exponentially decaying pulse, equivalent overpressure time history, free field explosive load, or contact explosive equivalent load.

[0063] The dynamic response indicators include, but are not limited to, one or more of the following: structural displacement, deflection, acceleration, bending moment, axial force, shear force, degree of plastic development, and damage indicators.

[0064] Step S6: Adjust the thickness and material deformation modulus of the soft backfill layer, analyze the influence of the change in flexible boundary stiffness on the dynamic response index of the arch structure, and optimize and determine the design parameters of the soft backfill layer based on the preset anti-blast performance target.

[0065] By adjusting the design parameter h of the soft backfill layer thickness l and compressive modulus design parameter E l The study analyzed the changes in boundary stiffness and their impact on the structural dynamic response index, and optimized and determined the design parameters of the soft backfill layer based on the preset anti-blast performance target.

[0066] The optimization method can be parameter traversal analysis, iterative optimization analysis, or multi-scheme comparison analysis; preferably, under the premise of meeting the explosion-proof performance target, the design scheme with the minimum amount of soft backfill material, the minimum thickness, the optimal structural response, or the lowest overall cost is selected.

[0067] Example 1: Ground-level arch structure

[0068] Combination Figures 2-5 This embodiment is applicable to ground-level arch structures without straight walls.

[0069] Taking a concrete circular arch located in Class I surrounding rock as an example, with a span of 10 m and a rise of 2.5 m, the material used is C35 concrete with a density of ρ w = 2500 kg·m -3 Its elastic modulus is taken as its deformation modulus E. w = 31.5 GPa, lining thickness is 0.6 m, and the unit length along the longitudinal direction is 1 m. The effective contact area between the arch foot on one side and the adjacent medium is S = 0.6 m².

[0070] Step S1: Calculation of equivalent stiffness of surrounding rock

[0071] According to the "Railway Tunnel Design Code TB 10003-2016", the resistance coefficient K of Class I surrounding rock is obtained. r = 2000 MPa / m, calculate the equivalent stiffness of the surrounding rock:

[0072] k r = K r S = 1.2 × 10 9 N / m.

[0073] Step S2: Calculation of equivalent stiffness of soft backfill layer

[0074] The initial selection of soft backfill material is foamed concrete, and its lateral confined compression modulus is taken as the deformation modulus E. l = 300 MPa, preliminary design thickness h l = 0.2 m, calculate the equivalent stiffness of the soft backfill layer:

[0075] k l = E l S h l -1 = 9.0 × 10 8 N / m.

[0076] Step S3: Calculation of equivalent stiffness of flexible boundary of arch structure

[0077] This example focuses on a ground-supported arch, neglecting the elasticity of the straight wall. The surrounding rock and soft backfill layer are considered as a series of spring systems, and the equivalent stiffness of the flexible boundary is calculated:

[0078] k f = (k r -1 + k l -1 ) -1 ≈ 5.14 × 10 8 N / m.

[0079] Step S4: Explosion-resistant dynamic response analysis

[0080] A dynamic response analysis model for the arch structure is established using the finite difference method, with a stiffness of k set at the arch foot boundary. f =4.5×10 8 A linear spring with a strength of N / m was used. A typical sudden triangular uniformly distributed explosive load with a peak pressure of 0.1 MPa and a positive pressure duration of 5 ms was applied, and response indicators such as crown deflection and mid-span bending moment were obtained through dynamic time history analysis.

[0081] Fixed E l = 300 MPa, with the arch deflection as the optimization objective, the influence of soft backfill thickness is analyzed, and h is calculated respectively. l Boundary stiffness and structural response at 0~0.5 m (0.1 m intervals). It was found that as the thickness of the soft backfill layer increases, the flexible boundary stiffness of the arch structure decreases, the deflection at the arch crown gradually decreases, and the structural resistance gradually increases.

[0082] Step S5: Optimization design of soft backfill layer parameters.

[0083] The preset blast resistance performance target is: the first peak value of the arch deflection response does not exceed 0.15 mm. Calculations show that under the working conditions set in this embodiment, when h lWhen the arch deflection response is ≥ 0.2m, it meets the blast resistance performance target. Therefore, the preferred soft backfill layer parameters in this embodiment are:

[0084] E l = 300 MPa foamed concrete, h l = 0.2 m.

[0085] Example 2: Straight-wall arch structure

[0086] Combination Figures 6-9 This embodiment is applicable to straight-wall arch structures, considering the influence of the elastic deformation of the straight wall on the flexible boundary, and treating the straight wall as a member that only undergoes axial tensile and compressive deformation. It is suitable for simplified calculations based on the axial force of the straight wall.

[0087] Based on Example 1, the structure is augmented with a straight wall of height h. w = 3.0 m, thickness t w = 0.6 m, and the effective contact area per unit length along the longitudinal direction is still S = 0.6 m².

[0088] Steps S1 and S2:

[0089] Same as in Example 1, k r = 1.2×10 9 N / m, k l = 9.0 × 10 8 N / m.

[0090] Step S3: Calculation of equivalent stiffness of straight wall

[0091] Assuming the material of the straight wall is the same as that of the arch, calculate the equivalent stiffness k of the straight wall. w :

[0092] k w = E w S h w -1 = 6.3×10 9 N / m.

[0093] Step S4: Calculation of equivalent stiffness of flexible boundary of arch structure

[0094] This example focuses on a straight-wall arch, treating the surrounding rock, soft backfill layer, and straight wall as a series spring system, and calculating the equivalent stiffness of the flexible boundary:

[0095] k f = (k r -1 + k l -1 + k w -1) -1 ≈ 5.10×10 8 N / m.

[0096] Step S5: Explosion-resistant dynamic response analysis

[0097] A dynamic response analysis model for the arch structure is established using the finite difference method, with a stiffness of k set at the arch foot boundary. f =4.8×10 8 A linear spring with mass m. If a concentrated mass block fixed to the arch is included in the model to account for the mass of a straight wall, its mass m... w The calculation is as follows:

[0098] m w = ρ w h w S = 4500 kg.

[0099] A typical sudden triangular uniformly distributed explosive load with a peak value of 1 MPa and a positive pressure duration of 5 ms was applied, and response indicators such as crown deflection and mid-span bending moment were obtained through nonlinear dynamic time history analysis.

[0100] Fixed E l = 300 MPa, with the arch deflection as the optimization objective, the influence of soft backfill thickness is analyzed, and h is calculated respectively. l Boundary stiffness and structural response at 0~0.5 m (0.1 m intervals). It was found that as the thickness of the soft backfill layer increases, the flexible boundary stiffness of the arch structure decreases, the deflection at the arch crown gradually decreases, and the structural resistance gradually increases.

[0101] Step S6: Optimization design of soft backfill layer parameters.

[0102] The preset blast resistance performance target is: the first peak value of the arch deflection response does not exceed 0.25 mm. Calculations show that under the working conditions set in this embodiment, when h l When the arch deflection response is ≥ 0.2m, it meets the blast resistance performance target. Therefore, the preferred soft backfill layer parameters in this embodiment are:

[0103] E l = 300 MPa foamed concrete, h l = 0.2 m.

Claims

1. A quantitative collaborative design method for flexible boundaries of blast-resistant arch structures considering soft backfill, characterized in that, Includes the following steps: Step S1: Obtain the surrounding rock resistance coefficient, determine the effective contact area between the bottom of the structure and the adjacent medium along the load transfer direction, and calculate the equivalent stiffness of the surrounding rock based on the surrounding rock resistance coefficient and the effective contact area. Step S2: Obtain the deformation modulus of the soft backfill material and the thickness of the soft backfill layer. Based on the deformation modulus of the soft backfill material, the thickness of the soft backfill layer, and the effective contact area, calculate the equivalent stiffness of the soft backfill layer. Step S3: When the arch structure is a straight-wall arch structure, obtain the deformation modulus of the straight-wall material and the height of the straight wall. Based on the deformation modulus of the straight wall, the height of the straight wall and the effective contact area, calculate the equivalent stiffness of the straight wall. Step S4: Based on the spring series stiffness model, calculate the equivalent stiffness of the flexible boundary of the arch structure using the equivalent stiffness of the surrounding rock and the equivalent stiffness of the soft backfill layer; when considering the deformation of the straight wall, further calculate the equivalent stiffness of the flexible boundary of the arch structure by combining the equivalent stiffness of the straight wall. Step S5: Establish a finite difference calculation and analysis model for the blast-resistant dynamic response of the arch structure, and determine the equivalent stiffness k of the flexible boundary of the arch structure. f As the spring stiffness input to the arch foot boundary of the analysis model, the vertical boundary conditions of the model are obtained: (1)； Where s1 is micro-segment 1, its left side is section 0, its right side is section 1, p0 is the load perpendicular to the arch axis at section 0, and θ0 is the angle between the section and the vertical axis. Where is the length of segment 1, Q1 is the shear force at section 1, and N1 is the axial force at section 1. Let w be the mass per unit length of the member, and w0 be the vertical displacement at section 0. Z0 represents the vertical acceleration at section 0, and Z0 is the initial value of the vertical coordinate at section 0. When considering the deformation of a straight wall, the boundary conditions of the model are: (2)； Where Q0 is the shear force at section 0 and N0 is the axial force at section 0; Using equations (1) and (2) as boundary conditions, considering equilibrium conditions, geometric relationships and material constitutive properties, an explosive load is applied and dynamic time history analysis is performed to obtain the structural dynamic response index. Step S6: Adjust the thickness and material deformation modulus of the soft backfill layer, analyze the influence of the change in flexible boundary stiffness on the dynamic response index of the arch structure, and optimize and determine the design parameters of the soft backfill layer based on the preset anti-blast performance target.

2. The method according to claim 1, characterized in that, In step S1, the equivalent stiffness k of the surrounding rock r The calculation formula is: k r = K r S ; In the formula, K r is the resistance coefficient of the surrounding rock, and S is the effective contact area between the bottom of the structure and the adjacent medium along the load transfer direction.

3. The method according to claim 2, characterized in that, In step S2, the equivalent stiffness k of the soft backfill layer l The calculation formula is: k l = E l S h l -1 ; In the formula, E l h represents the deformation modulus of the soft backfill material. l S represents the thickness of the soft backfill layer, and S represents the effective contact area.

4. The method according to claim 3, characterized in that, In step S3, the equivalent stiffness k of the straight wall w The calculation formula is: k w = E w S h w -1 ; In the formula, E w h is the elastic modulus of the straight wall material. w Where S is the height of the vertical wall, and S is the effective contact area between the bottom of the structure and the adjacent medium along the load transfer direction.

5. The method according to claim 4, characterized in that: In step S4, the equivalent stiffness k of the flexible boundary of the arch structure f The calculation method is as follows: When the deformation of straight walls is not considered, the calculation formula is: k f = (k r -1 + k l -1 + k w -1 ) -1 ; When considering the deformation of a straight wall, the calculation formula is: k f = (k r -1 + k l -1 ) -1 ; In the formula, k r k is the equivalent stiffness of the surrounding rock. l For the equivalent stiffness of the soft backfill layer, k w The equivalent stiffness of a straight wall.

6. The method according to claim 5, characterized in that: The soft backfill material is one or more of the following: foamed concrete, foamed mortar, clay, low modulus cement-based materials, and polymer buffer materials.

7. The method according to claim 6, characterized in that: The surrounding rock resistance coefficient, the deformation modulus of the soft backfill material, and the elastic modulus of the straight wall material in step S1 can all be obtained by consulting engineering specifications, conducting material tests, numerical simulations, or theoretical calculations.

8. The method according to claim 7, characterized in that, The blast-resistant dynamic response analysis model in step S5 is established using the finite element method and finite difference method.

9. The method according to claim 8, characterized in that, The structural dynamic response indices in step S5 include one or more of the following: structural displacement, deflection, acceleration, bending moment, axial force, shear force, degree of plastic development, and damage index.

10. The method according to claim 9, characterized in that, The optimization determination in step S6 includes: parameterizing the combination of soft backfill layer thickness and material deformation modulus, establishing the correspondence between the equivalent stiffness of the flexible boundary and the structural dynamic response index, and selecting the design scheme with the minimum material consumption, optimal structural response, or lowest overall cost from the parameter combinations that meet the preset anti-blast performance target.

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