Method for calculating pervious concrete double-layer grating arrangement parameters

Abstract

The invention relates to the technical field of road engineering material design and calculation, and discloses a calculation method for pervious concrete double-layer grating arrangement parameters. According to the method, a geogrid working performance coefficient, a grid interlayer spacing optimization factor, an effective permeability rate correction coefficient, an interlayer synergistic effect coefficient, a layered stress diffusion factor and a permeability comprehensive index are introduced for the first time, a quantitative evaluation model is constructed, and a multi-dimensional performance index and a structure response function are constructed. The structural mechanical behavior and permeability of the pervious concrete are comprehensively considered, and the double-layer arrangement position and interlayer spacing of the geogrid are determined. The blindness of traditional empirical layout is overcome, and the method is suitable for road structure design under medium and heavy traffic loads. According to the method, a scientific and computable double-layer arrangement parameter determination method is established, and collaborative optimization of the grid enhancement effect and the water permeability performance is achieved.

Description

Technical Field

[0001] This invention belongs to the field of road engineering material design and calculation technology, specifically involving a method for calculating the double-layer layout parameters of geogrids based on the synergistic optimization of mechanical properties and permeability. This method, by constructing a multi-index calculation model, accurately determines the optimal embedment depth and interlayer spacing of the geogrid in permeable concrete, and is applicable to the reinforcement design of sponge city pavements, parking lots, and other medium-to-heavy traffic load scenarios. Background Technology

[0002] In civil engineering construction, the placement of geogrids within permeable concrete can enhance its overall performance, enabling it to better mitigate urban flooding and the heat island effect, improve its mechanical properties, and solve its application challenges in medium- and heavy-duty traffic. However, current experiments on placing geogrids within permeable concrete rely on empirical trial and error for the double-layer arrangement, lacking theoretical calculation tools. This can easily lead to placement deviations from the stress core area and unreasonable layer spacing, resulting in stress concentration and decreased permeability. Therefore, there is an urgent need to establish a scientific and calculable method for determining the parameters of the double-layer arrangement to achieve synergistic optimization of the geogrid enhancement effect and permeability. Summary of the Invention

[0003] This invention proposes a calculation method for the arrangement parameters of permeable concrete double-layer grids. It comprehensively considers multiple factors such as flexural strength improvement, crack control, and permeability maintenance, establishes a series of quantitative calculation formulas, and proposes evaluation indicators for arrangement location, interlayer spacing, and interlocking effectiveness, forming a complete design calculation method.

[0004] To achieve the above objectives, the present invention provides the following technical solution:

[0005] The design calculation method of this invention takes the internal stress distribution, crack control requirements and permeability maintenance requirements of permeable concrete structures as its starting point, systematically proposes a process for determining layout parameters, and establishes a structural response function through five performance indicators to achieve scientific calculation and quantitative evaluation of the layout position, interlayer spacing and reinforcement effect of double-layer grids.

[0006] Step 1: Design Objectives and Basic Parameter Collection. Based on actual engineering needs, clarify the main control objectives for permeable concrete structure design, such as crack control, ductility improvement, and permeability maintenance. On this basis, collect the following material parameters and structural information: maximum coarse aggregate size D. max Concrete design strength grade, longitudinal elastic modulus E of geogrid g Effective stress-bearing area A of the grid g The size and laying method of the grid mesh, and the type of grid is not limited to polypropylene.

[0007] Step 2, lay out the preliminary design, based on D maxCalculate the minimum value S of the spacing between the two layers of grid. gmin Ensure that it meets S g ≥2×D max The spacing requirements are determined based on the concrete slab thickness h. Preliminary selections of arrangement combinations are made, such as h / 6+2h / 3, h / 3+7h / 10, etc., to ensure the grid is within the main tensile stress zone of the structure, maximizing the effectiveness of the reinforcing material.

[0008] Step 3, Calculation of Enhancement Effect Indicators: To scientifically quantify the impact of various aggregate combinations on structural performance, the following five core calculation indicators are introduced. The calculation formulas are applicable to different aggregate gradations:

[0009] Equation 1, Geogrid working efficiency coefficient η g This coefficient is used to evaluate the contribution of geogrids to the reinforcement of permeable concrete structures before and after the second peak load. It comprehensively considers the load increase ratio, material stiffness ratio, and load-bearing area ratio, and is expressed as follows: Among them, P peak1 and P peak2 E represents the peak load of the specimen at the first and second flexural failures, respectively. g and E c A represents the elastic modulus of geogrids and permeable concrete. g With A c This represents the area of ​​the grid and concrete that bear the load. The larger this coefficient is, the more significant the reinforcement effect of the grid.

[0010] Equation 2, the grid layer spacing optimization factor ψ, is used to control the stress interference between the upper and lower layers in a double-layer grid arrangement, ensuring maximum enhancement efficiency. The expression is as follows: Among them, S g D represents the vertical spacing between the upper and lower grid layers. max The maximum aggregate size in the concrete is given by σ, where Δσ is the stress gradient difference between the two layers. c ψ represents the compressive strength of concrete. When ψ ≥ 1.1, the interlayer stress distribution is more uniform, and the reinforcement efficiency is higher.

[0011] Equation 3, effective permeability correction coefficient λ p To optimize the design of the reinforced structure without significantly reducing permeability, the following correction factor is introduced: Where n0 and k0 are the porosity and permeability coefficient in the unreinforced state, respectively, n eff k effThese are the corresponding parameters under enhanced conditions. This indicator can be used to verify whether the hydraulic performance of the enhanced scheme still complies with national standards.

[0012] Equation 4, interlayer synergy coefficient γ int This coefficient is used to quantify the overall effect of the synergistic effect of the double-layer grid, and its expression is as follows: in, This represents the second peak flexural strength under a double-layer grid configuration, with the denominator being the sum of the peak values ​​when using single-layer reinforcement at the same arrangement. If γ int A value >1 indicates a significant synergistic enhancement effect.

[0013] Equation 5, Layered stress diffusion factor ξ s To evaluate the stress transfer effect within the concrete layer under different arrangements, a diffusion factor is introduced: Where, θ total For the overall diffusion angle, θ top and θ bottom These are the stress diffusion angles of the upper and lower layers, respectively, σ avg For the mean stress, σ peak This represents the extreme value of the stress concentration point. The larger this factor is, the more uniform the stress distribution is, and the stronger the structural stability.

[0014] Step 4: Optimize and filter layout parameters. Substitute different layout schemes into the above index formula and select the parameter combination that simultaneously meets the following requirements: η g ≥0.005, ψ≥1.1, λ p ≥0.6, γ int >1, and ξ s ≥0.75 is close to 1, while achieving the optimal multi-objective of enhancing efficiency, interlayer synergy and permeability.

[0015] Step 5: Permeability performance verification and layout correction. The permeability performance of the selected optimal layout scheme is verified to ensure that the enhanced permeability coefficient k is correct. eff ≥0.5mm / s. If the standard requirements are not met, adjust the layout parameters, such as the burial depth of the lower layer grid and the grid mesh density, and repeat the above calculation process until the comprehensive performance design target is met.

[0016] The layout parameters determined by the calculation method of this invention, combined with reasonable construction techniques and base course design, can significantly improve the structural strength and ductility of permeable concrete. Its failure mode exhibits a multi-stage energy-dissipating fracture process, effectively inhibiting crack propagation rate and enhancing structural durability. Attached Figure Description

[0017] Figure 1 A flowchart illustrating the calculation method for the layout parameters of a double-layer grid for permeable concrete. Detailed Implementation

[0018] The following examples are provided to clearly and completely describe the present invention, but are not intended to limit the scope of the invention.

[0019] To verify the scientific validity and engineering applicability of the proposed method for calculating the layout parameters of the double-layer geogrid, a series of permeable concrete reinforcement tests were designed and implemented, covering different layout strategies and working conditions. Specific tests included typical embodiments and multiple comparative specimens, with tests covering key parameters such as flexural strength, crack propagation behavior, ductility, and permeability.

[0020] Example 1

[0021] The total thickness h of the specimen was 100 mm. Continuously graded crushed stone (particle size range 5–16 mm) was used as coarse aggregate, and the binder was a mixture of 42.5R cement and fly ash, with a water-cement ratio controlled at 0.30. The upper and lower layers of geogrid were embedded at h / 6 and 2h / 3 distances from the bottom surface, respectively. The geogrid material was biaxial polypropylene geogrid with a uniaxial ultimate tensile strength of 40 kN / m and a mesh size of 35 mm × 35 mm. The specimen was cast using a two-stage layering method and tamped twice to ensure effective embedding of the geogrid into the interface. After 28 days of standard curing, a three-point bending load was applied.

[0022] Geogrid working efficiency coefficient η g : It meets the requirements and has the ability to effectively enhance contributions.

[0023] Optimization factor for grid layer spacing ψ: The requirements are met, and inter-layer interference is well controlled.

[0024] Effective permeability correction factor λ p : The requirements are met, and the permeability is still considered acceptable.

[0025] Interlayer synergy coefficient γ int : It meets the requirements and has a positive synergistic enhancement effect.

[0026] Layered stress diffusion factor ξ s : And it is close to 1, which meets the requirements, and the structural force transmission is uniform and stable.

[0027] This implementation scheme is based on the layout parameter calculation process proposed in this invention. The upper and lower layers of geogrid are respectively embedded at positions h / 6 and 2h / 3, and a layered, segmented molding process is adopted to effectively anchor the geogrid within the main tensile stress zone of the structure. Experimental verification shows that the proposed layout scheme exhibits excellent performance in flexural strength, structural ductility, and permeability. All calculated results meet the design screening criteria and the permeability performance verification requirements, eliminating the need for further layout modifications.

[0028] Example 2

[0029] Change the layout parameters and embed the grid at positions h / 3 and 7h / 10. The remaining material and process parameters are the same as in Example 1.

[0030] Geogrid working efficiency coefficient η g : It meets the requirements and has the ability to effectively enhance contributions.

[0031] Optimization factor for grid layer spacing ψ: The requirements are met, and inter-layer interference is well controlled.

[0032] Effective permeability correction factor λ p : The requirements are met, and the permeability is still considered acceptable.

[0033] Interlayer synergy coefficient γ int : It meets the requirements and has a positive synergistic enhancement effect.

[0034] Layered stress diffusion factor ξ s : And it is close to 1, which meets the requirements, and the structural force transmission is uniform and stable.

[0035] This implementation scheme is based on the layout parameter calculation process proposed in this invention. The upper and lower layers of geogrid are respectively embedded at positions h / 3 and 7h / 10, and a layered, segmented molding process is used to effectively anchor the geogrid within the main tensile stress zone of the structure. Experimental verification shows that the proposed layout scheme exhibits excellent performance in flexural strength, structural ductility, and permeability. All calculated results meet the design screening criteria and the permeability performance verification requirements, eliminating the need for further layout modifications.

[0036] Comparative Example 1

[0037] Change the layout parameters and embed the grid at positions h / 4 and h / 8. All other material and process parameters remain the same as in Example 1.

[0038] Geogrid working efficiency coefficient η g : The requirements are not met.

[0039] Optimization factor for grid layer spacing ψ: The requirements are not met.

[0040] Effective permeability correction factor λ p : The requirements are not met.

[0041] Interlayer synergy coefficient γ int : The requirements are not met.

[0042] Layered stress diffusion factor ξ s : The requirements are not met.

[0043] Test results showed a flexural strength of 5.69 MPa. The load-displacement curve exhibited typical linear brittle fracture characteristics, with rapid crack penetration and a peak displacement of only 0.663 mm, indicating a lack of ductility reserve and essentially zero post-cracking load-bearing capacity. The crack rapidly penetrated the entire specimen in the initial loading stage, leading to sudden fracture without slow crack propagation or post-cracking hysteresis; the failure mode was typical of brittle failure. This comparative example used upper and lower layers of grids at positions h / 8 and h / 4 to verify the impact of non-optimized parameter combinations on structural performance. Experimental calculations showed that this layout scheme failed to meet the calculated results for various indicators due to insufficient spacing and shallow placement.

[0044] The layout calculation method proposed in this invention allows for the selection of layout parameters based on mechanical performance targets. Examples demonstrate that double-layer grid reinforcement offers significant advantages in ductility control, post-cracking strength maintenance, and permeability compatibility, thus validating the rationality and optimality of the calculation method. Furthermore, comparative examples prove the engineering necessity and evaluation accuracy of the parameter selection method proposed in this invention.

Claims

1. A method for calculating the arrangement parameters of a double-layer permeable concrete grid, characterized in that, Includes the following steps: Step 1: Collect design parameters, including the maximum coarse aggregate particle size D. max Concrete design strength grade, geogrid elastic modulus E g Effective stress-bearing area A of the grid g Parameters such as the grid laying method and surface layer thickness h. Step 2, initial layout design, determine the minimum interlayer spacing S based on aggregate particle size. g ≥2D max And initially determine the grid layout position. Step 3: Calculate the five performance indicators. Geogrid working efficiency coefficient η g This indicates the grid's ability to enhance the peak load-bearing capacity of the structure. The grid layer spacing optimization factor ψ reflects the rationality of stress transfer between upper and lower grid layers: Effective permeability correction factor λ p This is used to measure the degree to which enhanced permeability is retained. Interlayer synergy coefficient γ int Used to evaluate the synergistic reinforcement effect of upper and lower grid layers: Layered stress diffusion factor ξ s This is used to measure the uniformity of crack propagation paths and multi-stage energy dissipation capacity. Step 4: Parameter optimization and screening. Substitute different layout schemes into the above index formula to achieve the multi-objective optimization of enhanced efficiency, inter-layer synergy and permeability. Step 5, Verification and Iterative Correction: Verify the permeability of the optimal solution to ensure it meets both structural mechanics and permeability performance objectives.

2. The method according to claim 1, wherein the grid working efficiency coefficient η g Used to characterize the increase in the second peak flexural strength of the grid structure after crack formation.

3. The method according to claim 1, wherein the interlayer synergy coefficient γ int When the value is greater than 1, it indicates that the upper and lower grid layers form a cooperative force-bearing mechanism, thereby significantly delaying the penetration of the main crack.

4. The method according to claim 1, wherein the arrangement position can be selected as h / 6 and 2h / 3 from the bottom of the concrete, or h / 3 and 7h / 10.

5. The method of claim 1, wherein the type of grating used in the method is not limited to polypropylene.

6. The method according to claim 1, wherein the calculation formula in the method is applicable to different aggregate gradations.

7. The method according to any one of claims 1-4, wherein the method is applicable to permeable concrete pavement structures with a thickness of 80-150 mm, and the base layer is a composite base layer with good stability.

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