High-pressure water jet ground breaking depth time history prediction method based on dynamic erosion coefficient

Abstract

The invention discloses a high-pressure water jet ground breaking depth time history prediction method, and aims to solve the problem that the change of the ground breaking depth along with time cannot be accurately reflected in the prior art. The method comprises the following steps: firstly, obtaining corresponding data of ground breaking depth and time under different conditions through a jet flow ground breaking test, and further performing inversion analysis and constructing a dynamic erosion coefficient function changing along with a dimensionless stress ratio; and then the function is embedded into an ordinary differential equation representing ground breaking dynamics, and a prediction model is established. For a new construction scene, on the premise that jet flow working parameters and soil inherent attributes are known, the model is solved through numerical calculation, and a complete prediction curve that the ground breaking depth develops along with time can be simulated. According to the method, field test requirements can be remarkably reduced, a reliable basis is provided for scheme comparison and selection and parameter optimization in the early stage of construction, and accurate prediction of the ground breaking process is achieved.

Description

Technical Field

[0001] This invention relates to the field of high-pressure water jet soil breaking technology, and in particular to a calculation method that can accurately predict the continuous change of soil breaking depth over time. Background Technology

[0002] Accurately predicting the relationship between the penetration depth of high-pressure water jets and time is crucial for designing penetration parameters and optimizing construction efficiency. Existing prediction models, such as empirical formulas based on the final equilibrium state or static models based on a fixed erosion coefficient, cannot reflect the nonlinear changes in the penetration rate caused by the attenuation of jet velocity during the penetration process.

[0003] Specifically, while existing technologies can perform time iterations, their core parameter—the erosion coefficient—is assumed to be constant throughout the entire soil breaking process, which is clearly inconsistent with reality. The soil breaking process typically includes different stages such as severe impact, block erosion, and surface scouring, each with distinct breaking mechanisms and efficiencies. Using a fixed erosion coefficient leads to systematic deviations between the predicted curve and measured data over time, especially near stage transition points, failing to meet the requirements for high-precision time-history prediction. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method that can accurately reflect the dynamic characteristics of the entire soil breaking process and predict the nonlinear relationship between soil breaking depth and time.

[0005] To address the aforementioned technical problems, this invention provides a time-history prediction method for high-pressure water jet penetration depth based on a dynamic erosion coefficient. The core of this method lies in: constructing a dynamic erosion coefficient function that varies with penetration depth through experimental data inversion analysis, embedding it into the differential equation of penetration dynamics, and then numerically solving this equation to achieve accurate simulation of the penetration depth-time relationship. The specific steps are as follows:

[0006] S1. Determine the dynamic erosion coefficient function

[0007] S1.1. Conduct a standard high-pressure water jet soil breaking test: at different jet pressures (P jet Jet penetration tests were conducted under different soil types, and the penetration depth (H) and corresponding jet action time (t) under the j-th test condition were recorded at fixed time intervals to obtain depth-time series data {H}. ij ,t ij}, where i = 1, 2, 3, ..., n.

[0008] S1.2. Calculate the instantaneous soil breaking velocity: For the depth-time series data {H ij ,t ijNumerical differentiation is performed to calculate the value of {H} at each depth point. ij ,t ij The instantaneous soil breaking velocity (dH / dt) corresponding to} ij .

[0009] S1.3. Calculation of instantaneous jet shear stress: Based on jet dynamics theory, calculate H at each depth point. ij At the point where the jet acts on the soil surface, the instantaneous shear stress τ(H) ij The calculation formula is as follows:

[0010]

[0011] Among them, C s ρ is the shear stress coefficient, which can generally be taken as 0.16; ρ is the fluid density; U0 is the nozzle outlet jet velocity; d0 is the nozzle diameter.

[0012] S1.4. Inversion Calculation of Instantaneous Erosion Coefficient: Based on the basic formulas of erosion theory, the instantaneous erosion coefficient H at each depth point is inverted and calculated. ij The corresponding instantaneous erosion coefficient M ij The calculation formula is:

[0013]

[0014] Where, τ cr The critical shear stress of the soil can be obtained through a standard jet test combined with the formula in step S1.3.

[0015] S1.5. Define the dimensionless stress ratio: The instantaneous shear stress τ(H) from step S1.2... ij The critical shear stress τ of the soil in step S1.4 cr,j The ratio is defined as the dimensionless stress ratio σ, which is:

[0016]

[0017] S1.6. Fitting the dynamic erosion coefficient function: This involves fitting all data points (σ) from all experimental groups. ij M ij The data is collected and plotted in the σ-M coordinate system to form a data cloud map. A nonlinear regression algorithm is used to globally fit the dataset, resulting in a continuous function with the dimensionless stress ratio σ as the sole independent variable, namely the dynamic erosion coefficient function M(σ). This function preferably adopts an exponential growth model.

[0018] M(σ)=ae b·σ

[0019] a and b are model parameters determined through fitting.

[0020] S2. Construct a time-history prediction model for groundbreaking depth.

[0021] S2.1. Determine model variables and parameters: Establish the soil penetration depth H as the dependent variable of the model, i.e., the output quantity to be solved; establish the jet action time t as the independent variable of the model; and combine the dynamic erosion coefficient function M(σ) determined in step S1.6, the jet shear stress function τ(H) calculated based on jet dynamics, and the critical shear stress τ of the soil measured by standard tests. cr These are established as key input parameters for the model.

[0022] S2.2. Constructing the Main Body of the Differential Equation: Based on the fundamental principles of erosion theory, an ordinary differential equation is established concerning the variation of the penetration depth H with time t. Its expression is as follows:

[0023]

[0024] This equation incorporates the dynamic erosion coefficient function M(σ), the jet shear stress function τ(H), and the soil's inherent properties τ cr These factors, when combined, describe the dynamic process of the evolution of the soil penetration depth over time.

[0025] S2.3. Define initial conditions: Set a clear initial state for the differential equation. It is stipulated that the soil penetration depth is zero at the start of the jet action, i.e.:

[0026] H(t=0=0)

[0027] This initial condition, together with the differential equation, constitutes a complete initial value problem for an ordinary differential equation.

[0028] S3. Solve the depth-time curve.

[0029] For any new target construction scenario, given its jet working parameters and the critical shear stress τ of the target soil... cr Under the premise of solving the differential equation numerically, the steps are as follows:

[0030] S3.1. Initialize calculation parameters: Set the total time span T and calculation step size Δt for numerical solution. Initialize iteration variables: Set the iteration number n = 0, the initial time t0 = 0, and the initial soil breaking depth H0 = 0.

[0031] S3.2. Execute iterative calculation loop: when t is satisfied n Given that ≤T, repeat the following steps in a loop to calculate the next time step t. n+1 Breakthrough depth H n+1 :

[0032] a. Calculate the current stress state and erosion coefficient: based on the current depth H nAnd with new jet parameters, calculate the instantaneous jet shear stress τ(H) n Subsequently, the current dimensionless stress ratio σ is calculated. n =τ(H n ) / τ cr Based on this, the dynamic erosion coefficient function value M(σ) is calculated. n ).

[0033] b. Perform Runge-Kutta method single-step calculation: Calculate the four Runge-Kutta coefficients sequentially.

[0034] k1=Δt·M(σ n )·[τ(H n )-τ cr ]

[0035] k2=Δt·M(σ n2 )·[τ(H n +k1 / 2)-τ cr ]

[0036] k3=Δt·M(σ n3 )·[τ(H n +k2 / 2)-τ cr ]

[0037] k4=Δt·M(σ n4 )·[τ(H n +k3)-τ cr ]

[0038] Where, σ n2 σ n3 and σ n4 They are based on H n +k1 / 2、H n +k2 / 2 and H n +k3 is obtained through recalculation.

[0039] c. Update system status: Update the soil penetration depth using the weighted average method: H n+1 =H n +(k1+2k2+2k3+k4) / 6, with time updated simultaneously: t n+1 =t n +Δt.

[0040] S3.3. Output the prediction results: Repeat step S3.2 until t n >T, the loop terminates. Finally, output all calculated time-depth data (t). n H n This data sequence constitutes the predicted breakthrough depth-time curve for the new construction scenario. This curve can be directly used to guide construction and precisely control the jet action time to achieve the target depth.

[0041] The beneficial effects of this invention are:

[0042] (1) Traditional methods require extensive field tests for each new jet parameter combination to determine the construction parameters, which is time-consuming, labor-intensive, and costly. This invention determines the universal dynamic erosion coefficient function through indoor tests, which can accurately predict the on-site soil breaking effect and significantly shorten the project preparation time.

[0043] (2) During the construction design phase, this model can be used to quickly compare multiple schemes, such as simulating the soil breaking efficiency curves under different jet pressures and different nozzle diameter combinations, so as to find the best balance between soil breaking effect, equipment energy consumption and nozzle wear cost, change the previous extensive parameter selection mode that mainly relied on engineers' experience, and realize the optimal design of construction scheme. Attached Figure Description

[0044] Figure 1 This is a schematic diagram of the time history prediction method for the soil penetration depth of high-pressure water jet.

[0045] Figure 2 This is a diagram of a standard high-pressure water jet soil breaking test device.

[0046] Figure 3 This is a fitting graph of the dynamic erosion coefficient function.

[0047] Figure 4 This is a comparison chart of the predicted results and experimental data.

[0048] Figure 2 The components are: 1. Vertical lifting column, 2. Test soil box, 3. Submerged water environment, 4. Horizontal beam, 5. Guide rail, 6. Transmission mechanism, 7. Nozzle, 8. Electromagnetic flow meter, 9. Pressure transmitter, 10. Computer, 11. High-pressure hose, 12. Pressure regulating valve, 13. High-pressure plunger pump, 14. Water tank. Detailed Implementation

[0049] The technical solution of the present invention will be further described below with reference to embodiments, but it should not be construed as a limitation of the present invention:

[0050] In implementing this invention, it is first necessary to systematically set up multiple sets of differentiated test conditions to construct a basic dataset for determining the dynamic erosion coefficient function. This embodiment uses cohesive soil and prepares three types of remolded samples with dry densities of 1.65, 1.70, and 1.75 g / cm³ by controlling the compaction degree, aiming to obtain different critical shear stresses τ in the soil. crThe jet operating parameters are determined by adjusting the jet pressure. In this embodiment, three jet pressure levels of 5, 7.5, and 10 MPa were selected, along with three standard circular nozzles with diameters of 1.0, 1.5, and 2.0 mm. Finally, by combining the above three soil samples, jet pressures, and nozzle diameters, a total of 27 sets of test conditions were formed to ensure that the erosion coefficient function M(σ) obtained through subsequent fitting has sufficient representativeness and wide applicability.

[0051] To obtain the experimental data required for constructing the dynamic erosion coefficient function, a standard high-pressure water jet soil breaking test was conducted as follows: First, test preparation was carried out. The nozzle 7 was fixed tightly against the transparent wall of the test soil tank 2, ensuring that the jet axis was perpendicular to the soil surface. This arrangement facilitates direct observation and recording of the cross-sectional morphology of the pit formed by jet erosion. Water was injected into the test soil tank 2 to create a stable submerged water environment 3. To further enhance the clarity of observation, blue ink was added to the submerged water environment, which can effectively mitigate the adverse effects on observation caused by water turbidity during the soil breaking process. The test setup is as follows: Figure 2 As shown. Then, the jet is set and started. The jet pressure is adjusted and stabilized at a predetermined value by the pressure regulating valve 12 of the control system. This pressure value is monitored in real time by the pressure transmitter 9 and transmitted to the computer 10. At the same time, the jet flow rate is monitored and recorded by the electromagnetic flowmeter (8). Next, the soil breaking process is performed and the data is recorded. The high-pressure plunger pump 13 is started to generate a stable high-pressure jet that acts on the soil. During the entire jet soil breaking process, the development of erosion pits on the side wall of the soil box is continuously recorded using a high-definition camera. For scale calibration, a ruler is placed close to the observation area on the side wall of the soil box. Finally, the data is processed to obtain depth-time series data. After the experiment, the video sequence is analyzed by an image processing program. The program converts pixels to actual size based on the ruler size on the side wall of the soil box, automatically identifies and extracts the precise soil breaking depth corresponding to different jet action times, thereby obtaining depth-time series data for subsequent inversion analysis.

[0052] After obtaining the soil breaking depth-time series data under different conditions through the aforementioned experimental method, according to the method described in this invention, the dynamic erosion coefficient function is calculated and established according to the following steps: (1) Calculate the instantaneous soil breaking velocity: Perform numerical differentiation processing on the depth-time series data obtained from the experiment, and use the central difference method to calculate the instantaneous soil breaking velocity corresponding to each data point. (2) Calculate the instantaneous jet shear stress: Based on the jet dynamics theory, convert the jet pressure recorded in the experiment into the initial flow velocity, etc., and calculate the instantaneous soil breaking velocity at each soil breaking depth H using the formula in step S1.3. ij At the point where the jet acts on the soil surface, the instantaneous shear stress τ(H) ij (3) Determine the critical shear stress of the soil: the critical shear stress τ of the soil crThis can be determined by analyzing standard jet test data. Specifically, the jet shear stress at which the soil breaking process tends to stop (i.e., the instantaneous breaking velocity approaches zero) can be considered as the critical shear stress τ of the soil. cr (4) Inversion calculation of instantaneous erosion coefficient: According to the formula in step 1.4, inversion calculation is performed for each valid data point to obtain the corresponding instantaneous erosion coefficient M. ij (5) Calculate the dimensionless stress ratio and fit the function: The instantaneous shear stress τ(H) obtained in step S1.3 is used as the ratio of the stresses. ij The critical shear stress τ determined in step S1.4 cr By analogy, the dimensionless stress ratio σ is obtained. ij Subsequently, the pairs (σ) obtained from the inversion of all experimental group data were... ij M ij The data is collected and formed into a point cloud in the σ-M coordinate system, such as... Figure 3 As shown. By globally fitting the dataset using an exponential growth model, the dynamic erosion coefficient function is obtained as M(σ)=2.298*exp(0.036*σ), with a coefficient of determination R0. 2 The accuracy rate is 98.78%, indicating that the selected model has a good fit.

[0053] After successfully fitting the dynamic erosion coefficient function, a specific prediction example was conducted to verify the effectiveness and accuracy of the prediction method proposed in this invention: (1) Setting prediction scenario parameters: Select a scenario with known soil properties and jet parameters as the prediction object. The specific parameters are as follows: the jet pressure is 8MPa, the nozzle diameter is 1.5mm, the critical shear stress of the soil is 7.85Pa, and the initial target distance is 2cm. (2) Substitute the above parameters and the determined dynamic erosion coefficient function M(σ) into the soil breaking dynamic differential equation established in this invention. Subsequently, the fourth-order Runge-Kutta method is used to numerically solve the initial value problem of the ordinary differential equation. The specific steps are as follows: a) Model initialization: Set the total time span T of the numerical solution to 50s and the calculation step Δt to 2s. Initialize the iteration variables: Let the iteration number n = 0, the initial time t0 = 0, and the initial soil breaking depth H0 be the initial target distance (0.02m in this example). b) Iterative calculation loop: At time t n If the total time T is not exceeded, step S3.2 is executed repeatedly to obtain the soil breaking depth at different times. c) Output the prediction result: Repeat step S3.2 until t. n>T, the loop terminates. Finally, all calculated time-depth data sequences are output, which constitute the predicted soil breaking depth-time curve under the new construction scenario. (3) Model verification and effect comparison: In order to verify the prediction effect, an actual jet soil breaking test was carried out under the same parameter conditions, and the real soil breaking depth-time data were recorded. The data points measured in the test and the predicted curve calculated in step S3 were plotted on the same coordinate system for comparison. The results are as follows. Figure 4 As shown. Coefficient of determination R 2 The accuracy rate was 84.71%, indicating that the predicted curve obtained by the method of this invention basically matches the actual experimental data points, with consistent trends and relatively small errors throughout the entire time history. This comparative result strongly demonstrates that the time history prediction method for soil breaking depth based on dynamic erosion coefficient can accurately reflect the dynamic characteristics of the soil breaking process and achieve reliable quantitative prediction of soil breaking effects under different jet parameters and soil conditions.

Claims

1. A time-history prediction method for the penetration depth of high-pressure water jet based on dynamic erosion coefficient, characterized in that, Includes the following steps: S1. Determine the dynamic erosion coefficient function: By analyzing the high-pressure water jet soil breaking test data, a dynamic erosion coefficient function with dimensionless stress ratio as the independent variable is obtained through inversion and fitting. S2. Construct a time history prediction model for soil penetration depth: Based on erosion theory, combine the dynamic erosion coefficient function, jet shear stress function and soil critical shear stress to establish an ordinary differential equation describing the evolution of soil penetration depth over time. S3. Solving the penetration depth-time curve: For the target construction scenario, based on its specific jet working parameters and the critical shear stress of the soil, the ordinary differential equation is solved using numerical methods to obtain the curve of the predicted penetration depth changing with time.

2. The method according to claim 1, characterized in that, Step S1 specifically includes: (1) Conduct standard high-pressure water jet soil breaking test to obtain sequential data of soil breaking depth and jet action time under different jet pressures and different soil types; (2) Perform numerical differentiation on the sequence data to calculate the corresponding instantaneous soil breaking velocity; (3) Based on the jet dynamics theory, calculate the instantaneous shear stress of the jet acting on the soil surface at different penetration depths; (4) Based on the basic formula of erosion theory, the instantaneous soil breaking velocity, instantaneous shear stress and critical shear stress of soil are used to calculate the corresponding instantaneous erosion coefficient. (5) The ratio of instantaneous shear stress to critical shear stress of soil is defined as the dimensionless stress ratio; (6) Collect all experimental data and perform global fitting using an exponential growth model in the coordinate system of dimensionless stress ratio and instantaneous erosion coefficient to obtain the dynamic erosion coefficient function.

3. The method according to claim 1, characterized in that, In step S2, the ordinary differential equation is expressed as follows: the derivative of the soil penetration depth with respect to time is equal to the product of the function value of the dynamic erosion coefficient function at the dimensionless stress ratio corresponding to the current depth and the difference between the jet shear stress at the current depth and the critical shear stress of the soil.

4. The method according to claim 1, characterized in that, The numerical method used in step S3 is the Runge-Kutta method, and the specific implementation steps of the Runge-Kutta method include: (1) Initialize the calculation parameters, including the total time span, calculation step size, initial time and initial soil breaking depth; (2) Execute an iterative calculation loop. In each iteration: calculate the ratio of the current jet shear stress to the dimensionless stress based on the current soil penetration depth, and then determine the dynamic erosion coefficient function value; calculate four Runge-Kutta coefficients; and use the Runge-Kutta coefficients to update the soil penetration depth and time at the next moment. (3) After the loop terminates, output all the calculated time-depth data sequences, which constitute the predicted soil breaking depth-time curve.

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