A method for designing blasting vibration reduction parameters of MICP in-situ solidification based on wave impedance regulation

Abstract

The present application relates to the technical field of biological rock and soil engineering, and more particularly to a MICP in-situ solidification blasting vibration reduction parameter design method based on wave impedance regulation, comprising: taking mineralization control parameters as front-end input, determining optimal mineralization control conditions through a first relationship model; then under the optimal mineralization control conditions, establishing a second relationship model between the consolidation round and the wave velocity, dynamic parameters and wave impedance of the solidified body; further establishing a third relationship model between the wave impedance difference and the vibration isolation efficiency; finally, according to the target vibration reduction index, the required mineralization control parameter conditions and the consolidation round are obtained by back calculation. The present application establishes a quantitative design relationship among the mineralization control parameters, the consolidation round, the wave impedance and the vibration isolation efficiency, and overcomes the problem that the parameters in the existing MICP vibration reduction design mainly depend on experience.

Description

Technical Field

[0001] This invention relates to the field of bio-geotechnical engineering technology, and in particular to a method for designing MICP in-situ solidification blasting vibration reduction parameters based on wave impedance regulation. Background Technology

[0002] As an efficient and economical method of rock and soil excavation, the drill-and-blast method is widely used in underground engineering construction. However, in urban underground engineering, deep foundation pit engineering, subway tunnel engineering, and construction of adjacent existing structures, the blasting vibration waves can easily have adverse effects on surrounding buildings, underground pipelines, and existing tunnels after propagating in the strata, thus placing higher demands on vibration isolation and reduction technology.

[0003] Existing vibration path control measures mainly include vibration damping trenches, vibration damping holes, pile banks, rigid vibration isolation walls, and grouting curtains. However, vibration isolation barriers formed by traditional materials often suffer from problems such as large construction disturbances, heavy environmental burdens, fixed material parameters, and difficulty in flexible control. Patent publication number CN119470088A discloses a method for a grouting curtain model test system for vibration control of underground pipelines. This method involves constructing a model test chamber according to similarity theory, selecting silty clay fill material and PVC buried pipelines, preparing simulated explosive charges, and developing a vibration-damping grouting curtain material using iron powder and rubber as functional components. Strain measuring points, acceleration sensors, and earth pressure sensors are arranged on the pipeline surface and in the soil. Through comparative blasting tests before and after grouting, the absorption and reflection mechanism of the grouting curtain on blasting vibrations is revealed. Test results show that the grouting curtain can reduce the overall strain of buried pipelines by approximately 40%. This technical solution represents a research approach that uses traditional grouting curtain materials for blasting vibration control. However, its research focuses on cement-based and rubber-modified grouting materials, emphasizing the influence of material ratio and curtain arrangement on the vibration response of buried pipelines.

[0004] Microbially Induced Carbonate Precipitation (MICP) technology boasts advantages such as good environmental compatibility, minimal construction disturbance, and strong permeability. Furthermore, it can form a calcium carbonate cemented structure in situ within soil through microbial mineralization, thereby altering the soil's density, stiffness, and wave propagation characteristics, theoretically possessing the potential to construct novel vibration-damping barriers. While existing MIP research has demonstrated that factors such as bacterial concentration, urea concentration, calcium source concentration, initial pH, and ambient temperature significantly affect mineralization efficiency, most studies remain focused on optimizing mineralization efficiency, improving strength, or enhancing general dynamic performance. A systematic design method is still lacking for quantitatively understanding the relationship between "mineralization control parameters, calcium carbonate yield, pore filling evolution, wave impedance, and vibration isolation efficiency," particularly how to deduce mineralization parameters and consolidation cycles based on target vibration reduction requirements. Moreover, the material properties of MICP solidified bodies are not only related to mineralization control factors but also closely linked to the initial pore structure of the original gravel skeleton and the evolutionary process of calcium carbonate gradually filling the pores with increasing consolidation cycles. If the initial porosity, the interstitial evolution process, and the wave impedance variation law cannot be integrated into the design framework, it will be difficult to establish a stable and calculable correspondence between material properties and vibration isolation efficiency. Summary of the Invention

[0005] In view of this, the present invention provides a design method for MICP in-situ solidification blasting vibration reduction parameters based on wave impedance regulation, in order to solve the problem that there is no quantitative correspondence between mineralization control parameters, consolidation cycles and vibration reduction effect in existing MICP blasting vibration reduction designs, and the design process mainly relies on experience.

[0006] The technical solution of this invention is implemented as follows: On the one hand, this invention provides a method for designing MICP in-situ solidification blasting vibration reduction parameters based on wave impedance regulation, comprising the following steps: S1. Determine the main factors affecting the mineralization and vibration reduction effects of the MIP solidified body. The main factors include at least the mineralization control factors, the initial porosity of the original gravel skeleton, and the number of consolidation cycles. S2. Conduct mineralization experiments based on mineralization control factors, establish a first-order relationship model between mineralization control factors and calcium carbonate yield, and obtain the optimal combination of mineralization control factors; S3. Under the condition of optimal combination of mineralization control factors, based on the initial porosity of the original gravel skeleton, establish a second relationship model between the consolidation cycle and the wave velocity, dynamic parameters and wave impedance of the solidified body. S4. Based on the wave propagation theory, establish a third relationship model between the wave impedance difference between the MIP solidified body and the surrounding undisturbed soil and the vibration isolation efficiency. S5. Based on the target vibration reduction index or allowable vibration threshold, the target wave impedance difference is deduced by combining the third relationship model, and the consolidation cycle that satisfies the target wave impedance difference is deduced by combining the second relationship model. The corresponding mineralization control parameter conditions are determined by combining the first relationship model, and the design results that meet the vibration reduction requirements are output.

[0007] Based on the above technical solutions, preferably, in step S1, the mineralization control factors include bacterial solution concentration, initial pH value, ambient temperature, urea concentration, and CaCl2 concentration.

[0008] Based on the above technical solutions, preferably, step S2 includes the following sub-steps: S21. Design multiple combinations of mineralization control factors, conduct mineralization experiments respectively, obtain the calcium carbonate yield corresponding to each combination, and form a calcium carbonate yield dataset. S22. Perform multi-factor regression analysis on the dataset to establish a first relationship model of calcium carbonate production with respect to the combination of mineralization control factors, and optimize the first relationship model to obtain the optimal combination of mineralization control factors that maximizes calcium carbonate production and the corresponding optimal calcium carbonate production.

[0009] Based on the above technical solution, preferably, in step S22, the first relational model is represented as: ; Where Y represents calcium carbonate production; For the i-th mineralization controlling factor, Let j be the controlling factor of mineralization; For constant terms, The coefficients of the linear terms of each factor are... The coefficients of the quadratic terms of each factor are... The coefficients for the interaction terms of each factor are given above, and all coefficients are determined by regression analysis of mineralization test data. By optimizing the above equation, the optimal combination of mineralization control factors that maximizes Y is determined. .

[0010] Based on the above technical solutions, preferably, step S3 includes the following sub-steps: S31. Under the condition of optimal combination of mineralization control factors, test the density, longitudinal wave velocity and transverse wave velocity of the solidified body under different consolidation cycles, and establish a wave velocity relationship model of the wave propagation characteristics of the solidified body with the consolidation cycle. S32. Based on density, longitudinal wave velocity and transverse wave velocity, calculate the elastic modulus, shear modulus and Poisson's ratio of the solidified body under each consolidation cycle, and establish a dynamic parameter relationship model for the evolution of dynamic parameters with the consolidation cycle. S33. Based on density and corresponding wave velocity, establish a wave impedance relationship model for the evolution of longitudinal wave impedance and transverse wave impedance with consolidation cycle. The wave velocity relationship model, the dynamic parameter relationship model, and the wave impedance relationship model together constitute a second relationship model with the consolidation cycle as the independent variable.

[0011] Based on the above technical solution, preferably, in step S31, the longitudinal wave velocity and transverse wave velocity after the Nth round of consolidation are expressed as follows: ; ; in, The longitudinal wave velocity after the Nth round of consolidation; The transverse wave velocity is the Nth consolidation round; N is the consolidation round number. , , , These are the fitting parameters for the P-wave velocity model. , , , These are the fitting parameters for the shear wave velocity model. All of the above fitting parameters were determined from mineralization consolidation test data. In step S32, the elastic modulus and shear modulus after the Nth round of consolidation are expressed as follows: ; ; in, The elastic modulus after the Nth consolidation round; The shear modulus after the Nth consolidation round; , , , These are the fitting parameters for the elastic modulus model. , , , These are the fitting parameters for the shear modulus model. All of the above fitting parameters were determined from mineralization consolidation test data.

[0012] Based on the above technical solution, preferably, in step S33, the longitudinal wave impedance and transverse wave impedance after the Nth round of consolidation are determined by the density of the solidified body and the corresponding wave velocity after that round of consolidation, respectively, and are expressed as follows: ; ; in, The density of the solidified body after the Nth round of consolidation. The longitudinal wave velocity after the Nth round of consolidation. The transverse wave velocity after the Nth round of consolidation; The longitudinal wave impedance after the Nth consolidation round is given. The transverse wave impedance after the Nth consolidation is given.

[0013] Based on the above technical solutions, preferably, step S4 specifically includes: S41. Simplify the undisturbed soil and the MIP solidified body into a one-dimensional plane wave normal propagation problem. Using the longitudinal wave impedance of the undisturbed soil and the longitudinal wave impedance of the MIP solidified body as basic parameters, define the impedance ratio as: ; in, The impedance ratio, The longitudinal wave impedance of the undisturbed soil mass. The longitudinal wave impedance of the MICP solidified body; S42. Based on wave propagation theory, establish energy transmittance under one-dimensional normal incidence conditions. and , The relationship between them, and thus the establishment of vibration isolation efficiency. and The relationship between them is used to obtain the third relationship model.

[0014] Based on the above technical solution, preferably, in step S42, under one-dimensional normal incidence conditions, the energy transmittance is... Vibration isolation efficiency They are represented as follows: ; ; in, The longitudinal wave impedance of the undisturbed soil mass. The longitudinal wave impedance of the MICP solidified body. This is the impedance ratio.

[0015] Based on the above technical solutions, preferably, in step S5, the engineering requirement is that the target vibration isolation efficiency is not less than... ,Will Substituting into the third relationship model, the target impedance ratio is obtained: ; in, The target impedance ratio, To preset the vibration isolation efficiency; Furthermore, from Determine the longitudinal wave impedance of the target solidified body ,in The longitudinal wave impedance of the undisturbed soil mass; then... Substituting into the second relational model, we obtain the result that satisfies... The minimum consolidation cycle N*, where The longitudinal wave impedance after the Nth round of consolidation is given; finally, the optimal combination of mineralization control factors is determined by combining the first relationship model. The final design output includes: the combination of target mineralization control factors. The target consolidation cycle N* and the corresponding target wave impedance range.

[0016] The present invention has the following advantages over the prior art: (1) This invention establishes a quantitative design relationship between mineralization control parameters, consolidation cycles, wave impedance and vibration isolation efficiency, overcoming the problem that parameters in existing MIP vibration reduction designs mainly depend on experience.

[0017] (2) This invention uses wave impedance as an intermediate bridge to link the evolution of solidified material properties with vibration reduction effect, so that the design of vibration reduction parameters has a clear physical basis.

[0018] (3) The present invention can output mineralization control parameters and consolidation cycles according to the target vibration reduction requirements, realize the quantitative design of vibration reduction parameters, and has good engineering application prospects. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0020] Figure 1 This is a flowchart of the method of the present invention; Figure 2 This is a schematic diagram illustrating the relationship between mineralization control factors and calcium carbonate yield in an embodiment of the present invention; Figure 3 This is a schematic diagram illustrating the relationship between the number of consolidation cycles and wave velocity evolution in an embodiment of the present invention; Figure 4 This is a schematic diagram illustrating the relationship between the number of consolidation cycles and the evolution of wave impedance in an embodiment of the present invention. Detailed Implementation

[0021] The technical solutions of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. 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.

[0022] like Figure 1 As shown, this invention provides a method for designing MICP in-situ solidification blasting vibration reduction parameters based on wave impedance modulation, comprising the following steps: S1. Determine the main factors affecting the mineralization and vibration reduction effects of the MIP solidified body. The main factors include at least the mineralization control factors, the initial porosity of the original gravel skeleton, and the number of consolidation cycles. S2. Conduct mineralization experiments based on mineralization control factors, establish a first-order relationship model between mineralization control factors and calcium carbonate yield, and obtain the optimal combination of mineralization control factors; S3. Under the condition of optimal combination of mineralization control factors, based on the initial porosity of the original gravel skeleton, establish a second relationship model between the consolidation cycle and the wave velocity, dynamic parameters and wave impedance of the solidified body. S4. Based on the wave propagation theory, establish a third relationship model between the wave impedance difference between the MIP solidified body and the surrounding undisturbed soil and the vibration isolation efficiency. S5. Based on the target vibration reduction index or allowable vibration threshold, the target wave impedance difference is deduced by combining the third relationship model, and the consolidation cycle that satisfies the target wave impedance difference is deduced by combining the second relationship model. The corresponding mineralization control parameter conditions are determined by combining the first relationship model, and the design results that meet the vibration reduction requirements are output.

[0023] This invention uses mineralization control parameters as front-end inputs and determines the optimal mineralization control conditions through a first relational model. Under the optimal mineralization control conditions, a second relational model is established based on the initial pore structure of the original gravel skeleton as the physical basis, relating the consolidation cycle to the wave velocity, dynamic parameters, and wave impedance of the solidified body. A third relational model is further established relating the difference in wave impedance between the solidified body and the surrounding undisturbed soil to the vibration isolation efficiency. Finally, the required consolidation cycle and mineralization control parameters are calculated based on the target vibration reduction index.

[0024] In one embodiment of the present invention, in step S1, the mineralization control factors include bacterial solution concentration, initial pH value, ambient temperature, urea concentration, and CaCl2 concentration. These mineralization control factors collectively determine the microbial mineralization capacity and calcium carbonate yield; the initial porosity of the original gravel skeleton determines the initial fillable space of calcium carbonate, which is the physical basis for the densification evolution of the solidified body; the consolidation rounds determine the cumulative filling degree of calcium carbonate in the pores. These factors collectively affect the density, wave velocity, and wave impedance of the solidified body, thereby affecting its vibration isolation efficiency. Here, the consolidation round N refers to the number of cementitious liquid injections; each completion of a cementitious liquid injection and mineralization reaction process is counted as one consolidation round; the initial porosity of the original gravel skeleton refers to the ratio of pore volume to total volume in the gravel medium before MIP treatment, and its magnitude determines the upper limit of usable pore space for the densification evolution of the solidified body.

[0025] For ease of description, in this embodiment, the combination of mineralization control factors is denoted as X, and the preferred combination of mineralization control factors is denoted as X. The yield of calcium carbonate is denoted as Y, and the yield of preferred calcium carbonate is denoted as Y. The number of consolidation rounds is denoted as N, and the density of the solidified body after the Nth consolidation round is denoted as... Longitudinal wave velocity is denoted as The transverse wave velocity is denoted as The longitudinal wave impedance is denoted as The transverse wave impedance is denoted as The longitudinal wave impedance of the undisturbed soil is denoted as . The longitudinal wave impedance of the MICP solidified body is denoted as Vibration isolation efficiency is denoted as .

[0026] In one embodiment of the present invention, step S2 is used to establish a quantitative relationship between mineralization control factors and calcium carbonate yield. Preferably, a multi-factor experimental and regression analysis method is used to establish a calcium carbonate yield prediction model. Specifically, step S2 includes the following sub-steps: S21. Design multiple combinations of mineralization control factors, conduct mineralization experiments respectively, obtain the calcium carbonate yield corresponding to each combination, and form a calcium carbonate yield dataset.

[0027] S22. Perform multi-factor regression analysis on the dataset to establish a first relationship model of calcium carbonate yield with respect to the combination of mineralization control factors. Then, optimize the first relationship model to obtain the optimal combination of mineralization control factors that maximizes calcium carbonate yield and the corresponding optimal calcium carbonate yield. The first relationship model is expressed as follows: ; Where Y represents calcium carbonate production; For the i-th mineralization controlling factor, Let j be the controlling factor of mineralization; For constant terms, The coefficients of the linear terms of each factor are... The coefficients of the quadratic terms of each factor are... The coefficients for the interaction terms of each factor are given above, and all coefficients are determined by regression analysis of mineralization test data. By optimizing the above equation, the optimal combination of mineralization control factors that maximizes Y is determined. .

[0028] Specifically, such as Figure 2 As shown, the effects of different mineralization control factors on calcium carbonate production vary significantly. The main effect diagram reflects the changing trends of calcium carbonate production due to changes in the levels of each factor. Figure 2 (a) in the text resulted in a bacterial concentration of ( (a) The relationship between bacterial concentration, initial pH value, ambient temperature, urea concentration, and calcium source concentration and calcium carbonate production; (b) The relationship between initial pH value and calcium carbonate production; (c) The relationship between ambient temperature and calcium carbonate production; (d) The relationship between urea concentration and calcium carbonate production; (e) The relationship between calcium chloride concentration and calcium carbonate production. A first-order relationship model was established by performing regression analysis on calcium carbonate production data under different combinations of mineralization control factors. The first-order relationship model was used to characterize the relationship between bacterial concentration, initial pH value, ambient temperature, urea concentration, and calcium source concentration and calcium carbonate production, and optimization was performed through regression equations.

[0029] Let the calcium carbonate production be... The bacterial concentration is The initial pH value is The ambient temperature is The urea concentration is , concentration Then the first relational model can be fitted as:

[0030] In the formula: This represents calcium carbonate production, expressed in g / L. This refers to the bacterial concentration, in units of... ; This is the initial pH value; This refers to the ambient temperature, expressed in °C. This refers to the urea concentration, expressed in mol / L. for Concentration, in mol / L.

[0031] The sign of each coefficient reflects the direction of the corresponding factor's influence on calcium carbonate production. Among them, The coefficient is negative, indicating that the calcium carbonate production exhibits a downward-opening parabolic characteristic as the ambient temperature changes.

[0032] By optimizing the fitting equation of the first relational model, the optimal combination of mineralization control factors can be obtained. The corresponding calcium carbonate production is denoted as In a preferred embodiment, the preferred combination of mineralization control factors is: bacterial concentration. urea concentration , concentration Ambient temperature = 21.8°C Initial pH value Under these conditions, the theoretical maximum calcium carbonate yield is: The average measured value of the verification experiment was The relative error is controlled within The results indicate that the first relationship model has good predictive accuracy for calcium carbonate production.

[0033] The first relational model makes explicit the nonlinear correspondence between mineralization control factors and calcium carbonate production. It quantifies the main effects, secondary effects, and interaction effects of each factor through a unified framework, and supports the direct solution of optimal mineralization control conditions through numerical optimization algorithms. This avoids the inefficient practice of repeatedly adjusting single-factor experiments and provides a reliable mineralization control basis for subsequent prediction of solidified body performance.

[0034] In one embodiment of the present invention, step S3 involves obtaining a preferred combination of mineralization control factors. Based on this, the relationship between the consolidation cycle and the wave propagation characteristics and wave impedance of the solidified body is established. Step S3 includes the following sub-steps: During MICP consolidation, calcium carbonate deposition continuously fills the interparticle pores and enhances interparticle cementation, causing the internal structure of the sand to evolve from a loose to a dense and ordered state. Experimental results show that the calcium carbonate content generally increases with the number of consolidation rounds. The increase is rapid in the early stages (rounds 2-6), rising from 3.42% to 9.47%; the growth rate slows down in rounds 8-12, reaching 16.28% in the 12th round; and plateaus in rounds 14-18, with an overall average of 18.01% in the 18th round. Simultaneously, porosity generally decreases with increasing consolidation rounds, exhibiting distinct stages: the porosity decreases rapidly in the lower consolidation rounds, decreasing from 0.403 to 0.338, a drop of approximately 16%, while the rate of decrease gradually slows down after eight consolidation rounds. It should be noted that the above data on the evolution of calcium carbonate content and porosity correspond to a dry density of 1.5 g / cm³ for pure sand. 3 Optimal combination of mineralization control factors Under specific preconditions, the evolution law under different initial pore structures needs to be recalibrated. In the early stage of solidification, the cementing liquid is more likely to enter the connected channels and deposit in larger pores or particle contact areas. The new deposition in the later stage is more reflected in the thickening of the existing deposition layer or the filling of residual micropores. The above-mentioned pore structure and cementation evolution law provide a structural basis for the changes in wave velocity, dynamic parameters and wave impedance with the consolidation cycle.

[0035] S31. Under the condition of optimal combination of mineralization control factors, test the density, longitudinal wave velocity and transverse wave velocity of the solidified body under different consolidation cycles, and establish a wave velocity relationship model of the evolution of wave propagation characteristics of the solidified body with the consolidation cycle.

[0036] Density is obtained by the ratio of sample mass to volume; longitudinal and transverse wave velocities are directly measured by ultrasonic testing instruments. Wave velocity, as a sensitive parameter reflecting the elastic properties and structural integrity of the medium, can characterize the curing effect based on its variation. For example... Figure 3 As shown, with each consolidation cycle The increase in P-wave velocity With transverse wave velocity All showed a significant growth trend, and the growth process could be well fitted by a logistic function, with a correlation coefficient of [missing information]. All values ​​were greater than 0.98. This result indicates that the MIP solidification effect is most significant in the initial stage, and the wave velocity growth gradually slows down with the further increase of solidification cycles, reflecting the transition of the cemented structure from a rapid formation stage to a stable development stage.

[0037] The longitudinal wave velocity and transverse wave velocity after the Nth round of consolidation are expressed as follows: ; ; in, The longitudinal wave velocity after the Nth round of consolidation is expressed in m / s. The transverse wave velocity after the Nth consolidation round is expressed in m / s; N is the consolidation round number. , , , These are the fitting parameters for the P-wave velocity model. , , , These are the fitting parameters for the shear wave velocity model. All of the above fitting parameters were determined from mineralization consolidation test data. Among them, and These represent the upper saturation limits that the longitudinal and transverse wave velocities approach with the number of consolidation cycles, respectively. and These respectively characterize the wave velocity difference between the unconsolidated state and the saturated state. and The characteristic cycle parameters that affect the growth rate, and Shape parameters are used to control the shape of the growth curve.

[0038] In one specific embodiment, based on the dry density of pure sand of 1.5 g / cm³ 3 Optimal combination of mineralization control factors Based on the consolidation test data under the given conditions, regression fitting was performed on the above model, and the values ​​of each parameter are as follows. The fitting result for the longitudinal wave velocity is: ; The fitting results for the transverse wave velocity are as follows: ; The parameters in the formula have the same meaning as before, and the correlation coefficient between the two formulas is... All values ​​are greater than 0.98. The above fitting results show that as the number of consolidation cycles increases, the longitudinal wave velocity approaches the saturation value of 2822 m / s from the initial value of approximately 1216 m / s, and the transverse wave velocity approaches the saturation value of 1673 m / s from the initial value of approximately 633 m / s. The wave velocity increases rapidly in the early stage and tends to saturate in the later stage.

[0039] S32. Based on density, longitudinal wave velocity and transverse wave velocity, calculate the elastic modulus, shear modulus and Poisson's ratio of the solidified body under each consolidation cycle, and establish a dynamic parameter relationship model for the evolution of dynamic parameters with the consolidation cycle.

[0040] Specifically, based on the average wave velocity and density data, the dynamic parameter relationships can be further obtained. The elastic modulus and shear modulus are obtained by converting density with longitudinal and transverse wave velocities, and the calculation relationship is as follows: ; ; Poisson's ratio It is derived from the ratio of P-wave to S-wave velocity: ; The experimental results show that the shear modulus With elastic modulus As the number of consolidation stages continues to increase, the Poisson's ratio... The overall trend is downward, indicating that MIP solidification significantly improves the dynamic stiffness of the soil and relatively limits its lateral deformation capacity. Taking typical data as an example: when... hour, , , , , , ;when hour, , , , , , .

[0041] Both the elastic modulus and the shear modulus are represented by saturated functions with the same structure as the wave velocity model, and are as follows: ; ; In the formula, This is the elastic modulus after the Nth consolidation round, in GPa. This is the shear modulus after the Nth consolidation round, in GPa. , , , These are the fitting parameters for the elastic modulus model. , , , These are the fitting parameters for the shear modulus model. All of the above fitting parameters were determined from mineralization consolidation test data.

[0042] In one specific implementation, based on the same consolidation test dataset, regression fitting is performed on the elastic modulus and shear modulus models to obtain the elastic modulus fitting result as follows: ; The fitting results for the shear modulus are as follows: ; The parameters in the formula have the same meaning as before, and the unit is GPa. The above fitting results show that the elastic modulus approaches the saturation value of 12.01 GPa from the initial value of approximately 1.85 GPa, and the shear modulus approaches the saturation value of 4.87 GPa from the initial value of approximately 0.71 GPa. This is consistent with the wave velocity evolution law, both showing a rapid increase in the early stage and a tendency to saturate in the later stage. The growth law of dynamic parameters with the consolidation cycle indicates that the contribution of calcium carbonate cement to soil stiffness accumulates continuously throughout the solidification process, with the most significant increase in the initial stage. The dynamic parameter relationship model plays an auxiliary supporting role in the second relationship model system. Its growth law provides a mechanical explanation for the increase in wave velocity and wave impedance, and can be used for independent evaluation of the mechanical properties of the solidified body.

[0043] As the number of consolidation cycles increases, the shear modulus... With elastic modulus The continuous increase indicates a sustained enhancement in the overall stiffness of the solidified body. The growth of these dynamic parameters provides a mechanical basis for the increase in wave velocity and wave impedance, and helps explain the evolution of wave propagation characteristics in the second relational model. Specifically, the transverse wave velocity and shear modulus satisfy the following: ; The transverse wave impedance can be further expressed as: ; The above relationship is used to illustrate the supporting role of shear modulus growth in transverse wave propagation characteristics.

[0044] S33. Based on density and corresponding wave velocity, establish a wave impedance relationship model for the evolution of longitudinal wave impedance and transverse wave impedance with consolidation cycle. The wave velocity relationship model, the dynamic parameter relationship model, and the wave impedance relationship model together constitute a second relationship model with the consolidation cycle as the independent variable.

[0045] Specifically, wave impedance is a comprehensive parameter describing the resistance characteristics of a medium to the propagation of elastic waves; its magnitude is determined by both the medium density and the wave velocity. For example... Figure 4As shown, Figure 4 The upper figure shows the relationship between consolidation stage and longitudinal wave impedance evolution, while the lower figure shows the relationship between consolidation stage and transverse wave impedance evolution. As the consolidation stage increases, the longitudinal wave impedance... With transverse wave impedance All showed a significant upward trend, and the growth process maintained good consistency with changes in wave velocity and density. This phenomenon indicates that MICP solidification continuously enhances the soil's resistance to elastic wave propagation by increasing the medium density and strengthening the material stiffness. Specifically, the increase in dynamic parameters provides mechanical support for the evolution of wave velocity and wave impedance; according to the normalized growth rate analysis, the increase in wave impedance is still dominated by wave velocity. Further comparison of the growth rates of P-wave and S-wave impedance reveals that... The overall increase was greater than This indicates that longitudinal compressive deformation is more sensitive to the evolution of the cemented structure. With increasing calcium carbonate content, and All significantly improved.

[0046] Therefore, the first Longitudinal wave impedance after wheel consolidation With transverse wave impedance They are represented as follows: ; ; In the formula: For the first Density of the solidified body after wheel consolidation; For the first Longitudinal wave impedance after wheel consolidation; For the first Transverse wave impedance after wheel solidification.

[0047] Therefore, the second relationship model can be expressed as: in the optimal combination of mineralization control factors Under the conditions, consolidation cycle The first model determines the evolution of density, wave velocity, and wave impedance of the solidified body, thereby determining its wave propagation characteristics. The second model uses the consolidation cycle as the core independent variable, employing a saturated function to uniformly describe the evolution of wave velocity, dynamic parameters, and wave impedance. This transforms previously discrete experimental observations into continuous and calculable analytical expressions, making the changes in solidified material properties as the consolidation process predictable. In practical engineering applications, the model parameters can be recalibrated based on the initial pore structure and mineralization conditions of a specific site to ensure prediction accuracy and provide a quantitative basis for subsequent back-design.

[0048] In one embodiment of the present invention, step S4 is used to establish the relationship between the wave impedance difference between the solidified body and the surrounding undisturbed soil and the vibration isolation efficiency. Step S4 specifically includes: S41. Simplify the undisturbed soil and the MIP solidified body into a one-dimensional plane wave normal propagation problem. Using the longitudinal wave impedance of the undisturbed soil and the longitudinal wave impedance of the MIP solidified body as basic parameters, define the impedance ratio as: ; in, The impedance ratio, The longitudinal wave impedance of the undisturbed soil mass. Longitudinal wave impedance of MICP solidified body S42. Based on wave propagation theory, establish energy transmittance under one-dimensional normal incidence conditions. and , The relationship between them, and thus the establishment of vibration isolation efficiency. and The relationship between them is used to obtain the third relationship model.

[0049] To facilitate the establishment of an explicit model, the undisturbed soil and the MIP solidified body are simplified into a one-dimensional plane wave normal propagation problem. This simplification is based on the following considerations: in the near field of blasting, the propagation direction of the vibration wave is basically perpendicular to the interface of the solidified body barrier; the one-dimensional normal incidence model can provide a conservative estimate; and an explicit analytical relationship between the wave impedance difference and the vibration isolation efficiency can be established. Let the longitudinal wave impedance of the undisturbed soil be... The longitudinal wave impedance of the MICP solidified body is Then the impedance ratio Defined as: ; In the formula, It is the impedance ratio; The longitudinal wave impedance of the undisturbed soil mass; The longitudinal wave impedance of the MICP solidified body. Impedance ratio. The increase in wave propagation impedance of the solidified body relative to the undisturbed soil is a core intermediate parameter that quantifies the relationship between solidification effect and vibration isolation efficiency.

[0050] Under one-dimensional normal incidence conditions, the energy transmittance of an elastic wave at the interface between two media is expressed as: ; Vibration isolation efficiency is defined as the proportion of energy reflected or dissipated by the barrier, expressed as: ; Further using impedance ratio Substituting, we get: ; In the formula, Energy transmittance, This represents the vibration isolation efficiency. The above two equations constitute the third relational model. This model shows that, under the approximate condition of normal incidence, the greater the difference in wave impedance between the solidified body and the undisturbed soil, the smaller the transmittance and the higher the vibration isolation efficiency. When the longitudinal wave impedance obtained from the second relational model is used... Replace solidified body impedance At that time, the first Vibration isolation efficiency corresponding to wheel-fixed junction It can be represented as: ; Then Substituting the calculation formula into the above formula, we get: ; In the formula, Let be the vibration isolation efficiency after the Nth consolidation round. This formula gives an explicit correspondence between the number of consolidation rounds, the density of the solidified body, the wave velocity, and the vibration isolation efficiency.

[0051] Further Substituting the fitting result into the above equation, we get: ; The third relational model directly links the material evolution characteristics of the solidified body (reflected by wave impedance) with the engineering vibration isolation target. The one-dimensional normal incident energy transmission model adopted has clear physical meaning, and the derivation process does not need to rely on empirical coefficients, making the theoretical prediction of vibration isolation efficiency verifiable. At the same time, it provides an analytical calculation entry point for the reverse design in step S5.

[0052] In one embodiment of the present invention, step S5 is used to back-calculate the mineralization control parameters and consolidation cycles based on the target vibration reduction index. Assume the project requires a target vibration isolation efficiency of not less than... ,Will Substituting into the third relationship model, the target impedance ratio is obtained: ; Further solutions yield: ; in, The target impedance ratio, To preset the vibration isolation efficiency; Let the longitudinal wave impedance of the undisturbed soil be... The longitudinal wave impedance of the target solidified body for: ; Determine the longitudinal wave impedance of the target solidified body ,in The longitudinal wave impedance of the undisturbed soil mass; then... Substituting into the second relational model, we obtain the result that satisfies... The minimum consolidation cycle N*, where The longitudinal wave impedance after the Nth round of consolidation is given; finally, the optimal combination of mineralization control factors is determined by combining the first relationship model. The final design output includes: the combination of target mineralization control factors. The target consolidation cycle N* and the corresponding target wave impedance range.

[0053] In a specific application scenario, suppose in a blasting vibration control project, the longitudinal wave impedance of the undisturbed soil is determined to be... The project requires that the target vibration isolation efficiency at the control points be no less than [a certain percentage]. First, the target impedance ratio is obtained using the above formula. Then by Determine the longitudinal wave impedance of the target solidified body ; then Substituting into the second relational model, we obtain the result that satisfies... The minimum consolidation stage N*; finally, the optimal combination of mineralization control factors is determined by combining the first relational model. The method outputs design results that meet the target vibration isolation requirements. In summary, the method described in this embodiment takes the screening of mineralization control parameters as the starting point, the evolution of wave velocity, dynamic parameters and wave impedance under the action of consolidation cycles as the intermediate bridge, and the vibration isolation efficiency as the target output, thus realizing the quantitative design of vibration reduction parameters. It has clear physical significance and engineering application prospects.

[0054] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for designing vibration reduction parameters for in-situ solidification blasting of MICP based on wave impedance modulation, characterized in that, Includes the following steps: S1. Determine the main factors affecting the mineralization and vibration reduction effects of the MIP solidified body. The main factors include at least the mineralization control factors, the initial porosity of the original gravel skeleton, and the number of consolidation cycles. S2. Conduct mineralization experiments based on mineralization control factors, establish a first-order relationship model between mineralization control factors and calcium carbonate yield, and obtain the optimal combination of mineralization control factors; S3. Under the condition of optimal combination of mineralization control factors, based on the initial porosity of the original gravel skeleton, establish a second relationship model between the consolidation cycle and the wave velocity, dynamic parameters and wave impedance of the solidified body. S4. Based on the wave propagation theory, establish a third relationship model between the wave impedance difference between the MIP solidified body and the surrounding undisturbed soil and the vibration isolation efficiency. S5. Based on the target vibration reduction index or allowable vibration threshold, the target wave impedance difference is deduced by combining the third relationship model, and the consolidation cycle that satisfies the target wave impedance difference is deduced by combining the second relationship model. The corresponding mineralization control parameter conditions are determined by combining the first relationship model, and the design results that meet the vibration reduction requirements are output.

2. The method for designing MICP in-situ solidification blasting vibration reduction parameters based on wave impedance regulation as described in claim 1, characterized in that, In step S1, the mineralization control factors include bacterial concentration, initial pH value, ambient temperature, urea concentration, and CaCl2 concentration.

3. The method for designing MICP in-situ solidification blasting vibration reduction parameters based on wave impedance regulation as described in claim 2, characterized in that, Step S2 includes the following sub-steps: S21. Design multiple combinations of mineralization control factors, conduct mineralization experiments respectively, obtain the calcium carbonate yield corresponding to each combination, and form a calcium carbonate yield dataset. S22. Perform multi-factor regression analysis on the dataset to establish a first relationship model of calcium carbonate production with respect to the combination of mineralization control factors, and optimize the first relationship model to obtain the optimal combination of mineralization control factors that maximizes calcium carbonate production and the corresponding optimal calcium carbonate production.

4. The method for designing MICP in-situ solidification blasting vibration reduction parameters based on wave impedance regulation as described in claim 3, characterized in that, In step S22, the first relational model is represented as: ； Where Y represents calcium carbonate production; For the i-th mineralization controlling factor, Let j be the controlling factor of mineralization; For constant terms, The coefficients of the linear terms of each factor are... The coefficients of the quadratic terms of each factor are... The coefficients for the interaction terms of each factor are given above, and all coefficients are determined by regression analysis of mineralization test data. By optimizing the above equation, the optimal combination of mineralization control factors that maximizes Y is determined. .

5. The method for designing MICP in-situ solidification blasting vibration reduction parameters based on wave impedance regulation as described in claim 1, characterized in that, Step S3 includes the following sub-steps: S31. Under the condition of optimal combination of mineralization control factors, test the density, longitudinal wave velocity and transverse wave velocity of the solidified body under different consolidation cycles, and establish a wave velocity relationship model of the wave propagation characteristics of the solidified body with the consolidation cycle. S32. Based on density, longitudinal wave velocity and transverse wave velocity, calculate the elastic modulus, shear modulus and Poisson's ratio of the solidified body under each consolidation cycle, and establish a dynamic parameter relationship model for the evolution of dynamic parameters with the consolidation cycle. S33. Based on density and corresponding wave velocity, establish a wave impedance relationship model for the evolution of longitudinal wave impedance and transverse wave impedance with consolidation cycle. The wave velocity relationship model, the dynamic parameter relationship model, and the wave impedance relationship model together constitute a second relationship model with the consolidation cycle as the independent variable.

6. The method for designing MICP in-situ solidification blasting vibration reduction parameters based on wave impedance regulation as described in claim 5, characterized in that, In step S31, the longitudinal wave velocity and transverse wave velocity after the Nth round of consolidation are expressed as follows: ； ； in, The longitudinal wave velocity after the Nth round of consolidation; The transverse wave velocity is the Nth consolidation round; N is the consolidation round number. , , , These are the fitting parameters for the P-wave velocity model. , , , These are the fitting parameters for the shear wave velocity model. All of the above fitting parameters were determined from mineralization consolidation test data. In step S32, the elastic modulus and shear modulus after the Nth round of consolidation are expressed as follows: ； ； in, The elastic modulus after the Nth consolidation round; The shear modulus after the Nth consolidation round; , , , These are the fitting parameters for the elastic modulus model. , , , These are the fitting parameters for the shear modulus model. All of the above fitting parameters were determined from mineralization consolidation test data.

7. The method for designing MICP in-situ solidification blasting vibration reduction parameters based on wave impedance regulation as described in claim 6, characterized in that, In step S33, the longitudinal wave impedance and transverse wave impedance after the Nth round of consolidation are determined by the density of the solidified body and the corresponding wave velocity after that round of consolidation, respectively, and are expressed as follows: ； ； in, The density of the solidified body after the Nth round of consolidation. The longitudinal wave velocity after the Nth round of consolidation. The transverse wave velocity after the Nth round of consolidation; The longitudinal wave impedance after the Nth consolidation round is given. The transverse wave impedance after the Nth consolidation is given.

8. The method for designing MICP in-situ solidification blasting vibration reduction parameters based on wave impedance regulation as described in claim 1, characterized in that, Step S4 specifically includes: S41. Simplify the undisturbed soil and the MIP solidified body into a one-dimensional plane wave normal propagation problem. Using the longitudinal wave impedance of the undisturbed soil and the longitudinal wave impedance of the MIP solidified body as basic parameters, define the impedance ratio as: ； in, The impedance ratio, The longitudinal wave impedance of the undisturbed soil mass. The longitudinal wave impedance of the MICP solidified body; S42. Based on wave propagation theory, establish energy transmittance under one-dimensional normal incidence conditions. and , The relationship between them, and thus the establishment of vibration isolation efficiency. and The relationship between them is used to obtain the third relationship model.

9. The method for designing MICP in-situ solidification blasting vibration reduction parameters based on wave impedance regulation as described in claim 8, characterized in that, In step S42, under one-dimensional normal incidence conditions, the energy transmittance Vibration isolation efficiency They are represented as follows: ； ； in, The longitudinal wave impedance of the undisturbed soil mass. The longitudinal wave impedance of the MICP solidified body. This is the impedance ratio.

10. The method for designing MICP in-situ solidification blasting vibration reduction parameters based on wave impedance regulation as described in claim 1, characterized in that, In step S5, the engineering requirement is that the target vibration isolation efficiency is not lower than ,Will Substituting into the third relationship model, the target impedance ratio is obtained: ； in, The target impedance ratio, To preset the vibration isolation efficiency; Furthermore, from Determine the longitudinal wave impedance of the target solidified body ,in The longitudinal wave impedance of the undisturbed soil mass; then... Substituting into the second relational model, we obtain the result that satisfies... The minimum consolidation cycle N*, where The longitudinal wave impedance after the Nth round of consolidation is given; finally, the optimal combination of mineralization control factors is determined by combining the first relationship model. The final design output includes: the combination of target mineralization control factors. The target consolidation cycle N* and the corresponding target wave impedance range.

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