A method for calibrating simulation parameters of the whole process of shotcrete construction in a physical engine

Abstract

The application relates to a method for calibrating simulation parameters in the whole process of shotcrete construction in a physical engine, which comprises the following steps: obtaining to-be-calibrated parameters in the whole process of shotcrete construction, performing multi-stage parameter calibration on the to-be-calibrated parameters, and obtaining final calibration results; wherein the multi-stage parameter calibration comprises the following steps: basic fluid parameter calibration and basic solver parameter calibration in basic parameters, rheological parameter calibration and adhesion parameter calibration in a low-speed stage, and mass field parameter calibration and velocity field parameter calibration in a high-speed stage. The application realizes the system calibration of simulation parameters in the whole construction process.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of computer virtual simulation and drill-and-blast tunnel construction engineering, in particular to a method for calibrating simulation parameters of the whole process of shotcrete construction in a physical engine. BACKGROUND

[0002] Shotcrete, as a construction material for tunnel primary support, is widely used in tunnel engineering construction. However, due to the limited understanding of the shotcrete construction mechanism, a large amount of shotcrete is bounced back to the ground, causing resource waste.

[0003] To clarify the shotcrete construction mechanism, the traditional method mainly uses the discrete element method (DEM) to carry out shotcrete jet simulation. However, due to the limitations of algorithm convergence ability, robustness and other factors, it cannot be fully applied to the whole process simulation of high-speed shotcrete jet, and lacks accurate simulation parameter calibration means. Different concrete mixtures, nozzle types and construction environment variables will have a significant impact on the jet hydrodynamic characteristics. The traditional parameter calibration method only relies on experience or single experiment, which cannot meet the "just-in-time" demand, and the accuracy of the mechanism revealed is difficult to guarantee.

[0004] The physical engine provides a new simulation method for shotcrete simulation, which can meet the needs of high physical accuracy, robustness, real-time calculation and interactive simulation in the context of intelligent construction. It is urgent to form a supporting parameter calibration method for the physical engine.

[0005] In the prior art, although there are parameter calibration methods for discrete element (DEM) simulation, and they have been applied in particle materials and powder flow scenarios, the simulation of shotcrete using only DEM has no systematic parameter calibration method, and the simulation and corresponding accuracy need to be discussed. Moreover, DEM calibration often relies on dispersed field experiments and experience-based parameter adjustment. The high-dimensional coupling between parameters leads to long time-consuming manual adjustment and limited precision, making it difficult to achieve "just-in-time" and rapid migration between different concrete mixtures, nozzle types or construction environments.

[0006] Now, the real-time, high-robustness and interactive whole-process shotcrete construction simulation can be realized through the position-based dynamics (PBD) algorithm in the physical engine. However, there is no systematic and engineering parameter calibration method for the high-speed, multi-phase flow process simulation of shotcrete construction, which ensures the high physical accuracy of the simulation method.

[0007] The prior technical solution also discloses a discrete element parameter calibration method for a shared-node DEM-SPH sea ice model, and relates to the technical field of computer digital simulation, and in particular to a discrete element parameter calibration method for a shared-node DEM-SPH sea ice model, which comprises the following steps: selection of sea ice macroscopic mechanical parameters; selection of a sea ice and structure friction coefficient; uniaxial compression discrete element numerical simulation; three-point bending discrete element numerical simulation; secondary uniaxial compression discrete element numerical simulation; and sea ice sample discrete element parameter calibration. In this way, in the process of performing numerical simulation analysis on ice loads of marine structures, the influencing factors of the macroscopic strength of the structure to be simulated are comprehensively and comprehensively considered by combining theoretical analysis with numerical simulation, and a functional relationship between the microscopic parameters and the macroscopic parameters is established, so that the discrete element parameters of sea ice of different strengths can be quickly determined, and finally the results obtained by the discrete element parameter calibration are more comprehensive and efficient. However, this method is only applicable to the coupling of discrete elements and smooth particle hydrodynamics. There is no systematic method for real-time simulation parameter calibration of a physical engine based on a PBD algorithm.

[0008] Therefore, there is no systematic and reusable construction simulation parameter calibration method for the construction process of shotcrete in a physical engine. SUMMARY

[0009] To solve the problems of the prior art, the purpose of the present application is to provide a shotcrete construction whole-process simulation parameter calibration method in a physical engine, a shotcrete jet-attachment-rebound whole-process simulation multi-stage parameter calibration process based on a PBD algorithm, which realizes the systematic calibration of the whole-process simulation parameters. By setting five calibration nodes of basic fluid parameters, basic solver parameters, rheological parameters, adhesion parameters, mass field parameters and velocity field parameters, combined with virtual simulation-site experiment closed-loop feedback and optimization algorithm, through simulation parameter calibration, high-physical-accuracy simulation from low speed to high speed is realized. This method can significantly shorten the calibration period and reduce the experimental cost, and through a unified scripted workflow, efficient reuse across working conditions is ensured, providing reliable support for rapid simulation prediction and optimization in engineering sites.

[0010] To achieve the above purpose, the present application provides the following solutions:

[0011] A shotcrete construction whole-process simulation parameter calibration method in a physical engine, comprising:

[0012] Obtaining to-be-calibrated parameters of the shotcrete construction whole process, performing multi-stage parameter calibration on the to-be-calibrated parameters, and obtaining final calibration results;

[0013] The multi-stage parameter calibration includes: basic fluid parameter calibration and basic solver parameter calibration in basic parameters, rheological parameter calibration and adhesion parameter calibration in a low-speed stage, and mass field parameter calibration and velocity field parameter calibration in a high-speed stage.

[0014] Optionally, the basic fluid parameter calibration on the to-be-calibrated parameter includes:

[0015] Obtaining shotcrete gradation data, and obtaining a shotcrete mixture sample through the shotcrete gradation data, performing a bulk density test on the shotcrete mixture sample, and measuring a bulk density of the basic fluid parameter;

[0016] Obtaining an aggregate particle size distribution, determining an average particle size or a representative particle size of the aggregate based on the aggregate particle size distribution, and taking the average particle size or the representative particle size of the aggregate as a particle size of the basic fluid parameter.

[0017] Optionally, the basic solver parameter calibration on the to-be-calibrated parameter includes:

[0018] Setting an initial basic solver parameter, performing a shotcrete test spraying simulation by using the initial basic solver parameter, obtaining a particle number-simulation frame rate curve and an upper limit of particle velocity, and determining a sub-step number of the basic solver parameter;

[0019] Determining a fixed time step of the basic solver parameter by using the particle number-simulation frame rate curve;

[0020] Taking the upper limit of the particle velocity as a hibernation threshold of the basic solver parameter, and proving that a current particle is in a hibernation state and is fixed at a hibernation position if a modulus of the particle velocity is less than the hibernation threshold;

[0021] On the basis of the sub-step number, adjusting a constraint iteration number of the basic solver parameter by using a constraint stiffness priority, and obtaining a constraint iteration number corresponding to a physical response similar to a real spraying vision.

[0022] Optionally, the determination of the fixed time step of the basic solver parameter includes:

[0023]

[0024] wherein, is the fixed time step, is the target frame rate.

[0025] Optionally, the rheological parameter calibration on the to-be-calibrated parameter includes:

[0026] The rheological parameters are calibrated by performing a slump test in a field experiment and a virtual environment simultaneously: during the slump test, the concrete filled in a slump bucket collapses after being lifted out of the bucket to minimize the error between the slump-time curve and the slump radius-time curve in the field slump test and the virtual simulation test, and the rheological parameters are calibrated to achieve the target;

[0027] After the rheological parameters are calibrated, a smoothing radius of the rheological parameters is obtained according to the number of target neighbor particles and the particle spacing;

[0028] The viscosity coefficient and the surface tension of the rheological parameters are adjusted using the smoothing radius, and a virtual slump test is performed using the adjusted viscosity coefficient and the surface tension, the error between each set of simulated slump curves and the measured curves is calculated, and the slump-time and slump radius-time curve fitting degrees of the field experiment and the virtual experiment are greater than a target threshold, and the viscosity coefficient and the surface tension corresponding to the curve with the smallest error are obtained.

[0029] Optionally, obtaining the smoothing radius of the rheological parameters comprises:

[0030]

[0031] wherein, is the smoothing radius, is the particle spacing, is the number of target neighbor particles.

[0032] Optionally, calibrating the adhesion parameter of the parameter to be calibrated comprises:

[0033] The adhesion parameter is calibrated by a tilt plate experiment, the sliding mass and the adhesion behavior of the sprayed concrete within a certain time window are obtained under different inclination conditions, and a control experiment is constructed in the virtual environment according to the same inclination and operation sequence to obtain a simulated sliding mass.

[0034] The mean square error of the simulated sliding mass and the measured sliding mass of the multi-inclination data set is used as an optimization target to perform iterative optimization, in each iteration process, the parameter vector is updated according to the gradient of the objective function, and a constraint condition is applied, and when the objective function converges to a preset threshold on the multi-inclination data, the optimal adhesion parameter is output.

[0035] Optionally, calibrating the mass field parameter of the parameter to be calibrated comprises:

[0036] In the simulation side, the same nozzle-sampling surface arrangement as in the entity test is used, and during the entity test, the sprayed concrete spreads from the nozzle to the sprayed surface at a divergence angle, the area integral of the mass flux density on the honeycomb sampling plate is obtained, and the honeycomb sampling plate is discretized into several equivalent sampling units to obtain the spatial mass distribution ratio of the entity, and the simulation side is normalized by the same sampling to obtain the spatial mass distribution ratio of the simulation side;

[0037] The spatial characteristics of the simulation side and the entity test are determined by using the spatial mass distribution ratio, and if the spatial characteristics of the simulation side and the entity test are consistent, the random initial velocity direction of the mass field parameter is gradually adjusted to minimize the mean square error between the simulation spraying thickness distribution and the measured data, until the distribution form and peak position attenuation trend are consistent with the entity and reach a preset error threshold, and the calibrated random initial velocity direction is obtained.

[0038] Optionally, the velocity field parameter calibration of the to-be-calibrated parameter comprises:

[0039] In the collision solving stage, the upper limit of the de-penetration velocity is set, so that the kinetic energy is controllably dissipated at the impact moment, and the speed evolution of deceleration, rebound, re-attachment and re-rebound is reproduced, the velocity field calibration takes the side wall spraying as the reference scene, uses the same nozzle as in the field, collects the three-dimensional trajectory and speed time sequence of representative particles through scripted particle tracking, and constructs a space-time velocity field data set, the space-time velocity field data set comprises: initial velocity, maximum de-penetration velocity, atmospheric drag coefficient related to particle-air interaction, wind field intensity and acceleration distance;

[0040] The consistency of the high-speed stage velocity curve of the field test and the simulation side is taken as the criterion, and the space-time velocity field data set is iteratively adjusted, so that the velocity decay amplitude, rebound peak value and time sequence of the simulation particles in the axial and edge regions are consistent with the measured data of the field test, and the calibrated velocity field parameter is obtained.

[0041] The beneficial effects of the present application are:

[0042] The present application significantly improves the precision and efficiency of shotcrete construction simulation through an end-to-end multi-stage closed-loop calibration process and an adaptive parameter search strategy. In the low-speed stage, the simulation and the on-site experiment dynamic slump experiment curve fitting degree reaches more than 90%, indicating that the calibrated viscosity coefficient and surface tension can highly restore the rheological properties of concrete; in the adhesion stage, the inclined plate simulation sliding mass and the measured data correlation coefficient R² reaches more than 0.90, fully showing that the friction coefficient and the adhesion force parameters accurately capture the particle-rock surface interaction; in the high-speed jet stage, the relative error between the side wall rebound rate simulation value and the on-site measured value is controlled within ± 15%, and the rebound error band is maintained within 15% in the spatial distribution, verifying the double calibration capability of the present method for the rebound velocity field and the jet mass field.

[0043] The present application can realize real-time simulation of 30+FPS in a 2m x 2m side wall scene relying on the numerical stability of the PBD algorithm in the physical engine, and can compress a number of traditional on-site experiments and manual parameter adjustment work that takes several days to complete to the level of several hours. The present application will provide a "just measure and adjust" rapid calibration capability for the tunnel construction site, not only greatly reducing the experimental material and labor costs, but also seamlessly integrating into the digital twin platform and intelligent jet control system, thereby promoting the intelligentization and digitization upgrade of tunnel shotcrete construction, and producing significant social, economic and technical value. BRIEF DESCRIPTION OF DRAWINGS

[0044] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments will be briefly introduced as follows. Obviously, the drawings in the following description only constitute some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0045] Figure 1 A physical engine shotcrete construction whole process simulation parameter calibration method schematic diagram of an embodiment of the present application;

[0046] Figure 2 An inclined plate experiment equipment schematic diagram of an embodiment of the present application;

[0047] Figure 3 A honeycomb plate device schematic diagram of an embodiment of the present application. DETAILED DESCRIPTION

[0048] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0049] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0050] like Figure 1 As shown in the figure, this embodiment discloses a method for calibrating simulation parameters of the entire process of shotcrete construction in a physics engine, including: obtaining the parameters to be calibrated for the entire process of shotcrete construction, performing multi-stage parameter calibration on the parameters to be calibrated, and obtaining the final calibration result; wherein, the multi-stage parameter calibration includes: calibration of basic fluid parameters and basic solver parameters in the basic parameters, calibration of rheological parameters and adhesion parameters in the low-speed stage, and calibration of mass field parameters and velocity field parameters in the high-speed stage.

[0051] Furthermore, the calibration of the basic fluid parameters for the parameters to be calibrated includes: obtaining shotcrete gradation data, obtaining shotcrete mixture samples using the shotcrete gradation data, conducting bulk density tests on the shotcrete mixture samples, and measuring the bulk density of the basic fluid parameters; obtaining aggregate particle size distribution, determining the average particle size or representative particle size of the aggregate based on the aggregate particle size distribution, and using the average particle size or representative particle size of the aggregate as the particle size of the basic fluid parameters.

[0052] The calibration of the basic solver parameters for the parameters to be calibrated includes: setting initial basic solver parameters; conducting a shotcrete test spraying simulation using the initial basic solver parameters to obtain the particle number-simulation frame rate curve and the upper limit of particle velocity, and determining the number of substeps for the basic solver parameters; using the particle number-simulation frame rate curve to determine the fixed time step of the basic solver parameters; using the upper limit of particle velocity as the dormancy threshold of the basic solver parameters; if the magnitude of particle velocity is less than the dormancy threshold, it proves that the current particle is in a dormant state and is fixed in the dormant position; based on the number of substeps, adjusting the constraint iteration number of the basic solver parameters through constraint stiffness priority to obtain the constraint iteration number corresponding to the physical response that is similar to the actual spraying visual appearance.

[0053] Specifically, the basic parameter calibration:

[0054] The basic parameters include: coverage, basic fluid parameters and basic solver parameters.

[0055] 1. Basic fluid parameters include particle size and density:

[0056] The calibration of basic fluid parameters was performed using small-scale aggregate screening and density testing in a field experiment. First, aggregate screening was used to obtain the shotcrete gradation data and aggregate particle size distribution. Particle size was defined as the average or representative particle size of the aggregate. Density was defined as the bulk density of the shotcrete mixture sample measured by a bulk density test. The calibration of the concrete cover and basic fluid parameters was completed through particle size and density calibration.

[0057] 2. The basic solver parameters include gravitational acceleration (-9.8 m / s²). 2 ), fixed time step, sleep threshold, number of substeps and number of constraint iterations.

[0058] The solver is the solution engine of the PBD algorithm, typically employing Gauss-Seidel iterative or Jacobi iterative methods. Gravity: Gravitational acceleration, the magnitude of the gravitational force acting on the particle. Fixed time step: The fixed time step size used in the simulation. Sleep threshold: The velocity threshold at which a particle transitions to a sleep state. Substeps: The number of substeps, where each physical time step can be further divided into smaller substeps to improve stability and accuracy. Constraint iterations: The number of constraint iterations performed in each substep.

[0059] Calibration steps: First, set a set of initial basic solver parameters, conduct a test spraying simulation of shotcrete, and observe the particle number-simulation frame rate curve. It is required that under a set of basic solver parameter configurations, the frame rate for simulating a certain number of particles should exceed a certain number of frames.

[0060] There is no strict analytical formula for a fixed time step; instead, it is chosen based on numerical stability and simulation accuracy. The main considerations are: too large a time step results in excessively long particle displacements, preventing the constraint iterations from converging in time, leading to numerical oscillations and instability. Too small a time step results in excessive computation but greater stability. A fixed time step can be determined using the following formula: . This refers to the target frame rate.

[0061] Sleep threshold This is the upper limit of particle velocity; if the particle velocity modulus... The particles are considered to be in a dormant state and are fixed in their dormant position. Generally, the speed is taken as 1%–5% of the typical motion speed in the simulation.

[0062] Coordinating the number of substeps and the number of constraint iterations is crucial, as these iterations directly affect the stiffness of the simulated material. First, a simulated spray test is performed with a preset sub-layout number of 4, increasing by 1 each time until a stable frame rate is obtained with no abnormal rebound or other physical phenomena; this is then determined as the final substep number. Next, by observing the constraint stiffness priority, the number of constraint iterations is adjusted to achieve a physical response that closely approximates the visual appearance of a real spray.

[0063] Furthermore, the rheological parameter calibration of the parameters to be calibrated includes: calibrating the rheological parameters by simultaneously performing slump tests in both on-site and virtual environments; during the slump test, the concrete filled in the slump bucket collapses after the bucket is lifted, with the goal of minimizing the errors in the slump-time curve and slump radius-time curve in both the on-site and virtual simulation tests; after calibrating the rheological parameters, obtaining the smoothing radius of the rheological parameters based on the number of particles in the target neighborhood and the particle spacing; adjusting the viscosity coefficient and surface tension of the rheological parameters using the smoothing radius, conducting virtual slump tests using the adjusted viscosity coefficient and surface tension, calculating the error between each set of simulated slump curves and measured curves, and ensuring that the goodness of fit of the slump-time and slump radius-time curves in both the on-site and virtual experiments is greater than the target threshold, obtaining the viscosity coefficient and surface tension corresponding to the curve with the smallest error.

[0064] The adhesion parameter calibration process includes: calibrating the adhesion parameters through inclined plate experiments; obtaining the slip mass and adhesion behavior of shotcrete within a certain time window under different inclination angles; constructing a control experiment in a virtual environment with the same inclination angle and operation sequence to obtain the simulated slip mass; iterative optimization using the mean square error between the simulated slip mass and the measured slip mass of the multi-inclination angle dataset as the optimization objective; updating the parameter vector according to the gradient of the objective function in each iteration and applying constraints; and outputting the optimal adhesion parameters when the objective function converges to a preset threshold on the multi-inclination angle data.

[0065] Specifically, the low-speed phase:

[0066] The low-speed phase includes basic solver parameters, rheological parameters, and adhesion parameters.

[0067] 3. Rheological parameters include smooth radius, viscosity, and surface tension.

[0068] The rheological properties of shotcrete in the low-velocity phase need to be calibrated by simultaneously performing slump tests in both field and virtual environments. In the slump test, concrete poured into a slump cone collapses after the cone is lifted, and the slump value and the radius of the accumulated material (slump radius) can be observed using a high-speed camera. To minimize errors in the slump-time and slump radius-time curves in both field and virtual simulation experiments, the adjusted rheological parameters include the smoothing radius, viscosity, and polarity. Smoothing radius: The neighborhood search radius used for fluid density calculation. Viscosity: A parameter used to smooth the velocity field during fluid particle motion. Polarity: A parameter used to control the surface tension of the fluid.

[0069] The smooth radius (h) is calculated based on the number of particles in the target neighborhood N* and the particle spacing Δx.

[0070] Generally, N* is between 30 and 45, so h≈ (1.5~2.0)Δx. The particle spacing Δx can be taken as a multiple of the diameter, assuming that the particles are actually in contact on the surface.

[0071] Based on a determined smooth radius, the viscosity and surface tension are adjusted using the Taguchi method. In the Taguchi matrix, the safe range for viscosity is [0-1.5] with a step size of 0.02. The adjustment range for surface tension is [0-0.1] with a step size of 0.01. By iterating through the combined matrix values ​​of viscosity and surface tension, slump tests are simulated under all parameter combinations. The error between each simulated slump curve and the measured curve is calculated, ensuring that the goodness of fit between the slump-time and slump radius-time curves of both the field and virtual experiments is ≥95%. All simulation steps are automated by a scripting plugin. The set of simulation parameters with the smallest error is selected as the calibrated viscosity and surface tension.

[0072] 4. Adhesion parameters include: static friction coefficient, dynamic friction coefficient, stickiness, and stick distance.

[0073] Static friction coefficient: Controls the tangential resistance a particle must overcome before it begins to slide. Dynamic friction coefficient: Adjusts the tangential resistance a particle experiences during sliding. Stickiness: Controls the normal adhesive force applied between the particle and the solid surface. Stick distance: Defines the maximum distance at which adhesion can be triggered between the particle and the rock surface.

[0074] like Figure 2 As shown, adhesion parameters were calibrated using tilt plate experiments: under different tilt angles, the slip mass and adhesion behavior of shotcrete were recorded within a certain time window; and a control experiment was constructed in a virtual environment with the same tilt angle and operation sequence to obtain the simulated slip mass. The mean square error (MSE) of the simulated-measured slip mass on the multi-tilt angle dataset was used as the optimization objective to complete parameter inversion.

[0075] Let the parameter vector θ = [μ] d ,μ s ,k stick ,d stick The RMS Prop strategy is employed to dynamically adjust parameters based on the error reduction trend, updating the parameters according to the gradient of the objective function in each iteration. To ensure physical feasibility, the following constraint is preferably applied: μ d : Coefficient of kinetic friction (0≤μ d ≤1); M s The static friction coefficient (0≤μ) s ≤1, and μ d ≤μ s ); k stick Normal adhesion coefficient / strength (dimensionless within the engine or defined according to engine unit system, k) stick ≥0); d stick Adhesion distance (m, 0) <d stick ≤h)(h is the neighborhood radius);

[0076] Once the objective function converges to a preset threshold on multi-angle data, the output parameters are fixed into subsequent high-speed jet simulations.

[0077] Furthermore, the mass field parameter calibration of the parameters to be calibrated includes: under the same nozzle-sampling surface arrangement in the simulation and the physical test, during the physical test, the sprayed concrete diffuses from the nozzle to the sprayed surface at a divergence angle, obtaining the area integral of the mass flux density on the honeycomb sampling plate, and discretizing the honeycomb sampling plate into several equivalent sampling units to obtain the spatial mass distribution ratio of the physical test. The simulation side is processed with the same sampling and normalization to obtain the spatial mass distribution ratio of the simulation side. The spatial mass distribution ratio is used to determine whether the spatial characteristics of the simulation side and the physical test are consistent. If the spatial characteristics of the simulation side and the physical test are consistent, the random initial velocity direction of the mass field parameters is gradually adjusted with the goal of minimizing the mean square error between the simulated spray thickness distribution and the measured data, until the distribution pattern and peak attenuation trend are consistent with the physical test and reach the preset error threshold, thus obtaining the calibrated random initial velocity direction.

[0078] The calibration of velocity field parameters for the parameters to be calibrated includes: setting an upper limit on the penetration velocity during the collision calculation stage, so as to controllably dissipate kinetic energy at the moment of impact, and reproducing the velocity evolution of deceleration, rebound, reattachment, and rebound. The velocity field calibration uses sidewall spray as the benchmark scenario and adopts nozzles consistent with those in the field. The three-dimensional trajectory and velocity sequence of representative particles are collected through scripted particle tracking to construct a spatiotemporal velocity field dataset. The spatiotemporal velocity field dataset includes: initial velocity, maximum penetration velocity, atmospheric drag coefficient related to particle-air interaction, wind field intensity, and acceleration distance. The consistency between the velocity curves of the high-speed stage in the field test and the simulation is used as the criterion to iteratively adjust the spatiotemporal velocity field dataset so that the velocity attenuation amplitude, rebound peak, and timing of the simulated particles in the axial and edge regions are consistent with the measured data of the field test, and the calibrated velocity field parameters are obtained.

[0079] Specifically, the high-speed phase:

[0080] The high-speed phase includes adhesion parameters, mass field parameters, and velocity field parameters.

[0081] 5. Mass field parameters:

[0082] The mass field parameter is the random initial velocity direction, which determines the randomness of the particles emitted by the particle emitter.

[0083] Mass field calibration involves only the parameter of random initial velocity direction (equivalent to controlling the jet divergence angle). The procedure is as follows: with the same nozzle-sampling surface arrangement as the physical test, the spatial mass distribution ratio of the physical test is obtained using a honeycomb sampling plate; the spatial mass distribution ratio of the simulation side is obtained using the same sampling and normalization method; using the difference between the two distributions as the evaluation index, the random initial velocity direction is gradually adjusted until the distribution pattern and peak position / attenuation trend are consistent with the physical test and reach the preset error threshold; the converged parameters are then fixed for subsequent high-speed jet simulation.

[0084] Details:

[0085] When shotcrete diffuses from the nozzle toward the sprayed surface at a divergence angle, neglecting dust loss, the total sprayed mass M is... Total Equal to the area integral of the mass flux density g(x,y) on the sprayed surface:

[0086]

[0087] in, This represents the local area of ​​the sprayed surface.

[0088] To facilitate the measurement of mass density, an equivalent expression method is adopted, discretizing the sprayed surface into several equivalent sampling units, and measuring the local cumulative mass m of each unit within a given time window. i Define the dimensionless mass field distribution ratio:

[0089]

[0090] Where N is the number of the smallest receiving quality units.

[0091] Used to describe spatially normalized distributions, and comparable under steady-state conditions. If η is obtained from physical experiments and virtual experiments... i If the distribution is consistent, it is considered that the simulated mass field accurately reproduces the spatial characteristics of the jet flow.

[0092] like Figure 3 As shown, a "honeycomb" sampling surface configuration is used to completely capture the spray cross-section: it consists of several detachable, uniformly cross-sectional cylindrical units arranged in a ring (or grid) array. Spraying stops when the central unit reaches the set filling condition (the central unit is full).

[0093] After normalizing the mass field, a Gaussian amplitude model (GaussAmp) is used for fitting, and its classic expression is as follows:

[0094]

[0095] Where y0, A, w, x c These are the coefficients of the GaussAmp model.

[0096] By adjusting the random initial velocity direction to minimize the mean square error between the simulated jet thickness distribution and the measured data, the fitting correlation coefficient R² is ultimately made to meet the requirements, ensuring that the simulated mass field has a high degree of consistency with the measured model.

[0097] 6. Velocity field parameters:

[0098] The velocity field parameters are: initial speed, maximum depenetration, atmospheric drag coefficient, wind intensity, and acceleration distance, which are related to particle-air interaction.

[0099] The maximum depenetration velocity is used for elastic collision correction: an upper limit is set on the depenetration velocity during the collision calculation stage, thereby controlling the dissipation of kinetic energy at the moment of impact and reproducing the velocity evolution of "deceleration-rebound-reattachment / rebound". Velocity field calibration uses sidewall jetting as the baseline scenario, employing nozzle-received surface geometry and boundaries consistent with the actual field. A spatiotemporal velocity field dataset is constructed by collecting the 3D trajectories and velocity sequences of representative particles through scripted particle tracking. The parameters to be calibrated include: initial velocity, maximum depenetration velocity, and atmospheric drag coefficient, wind intensity, and acceleration distance related to particle-air interaction. Using the "consistency of velocity curves in key stages" as the criterion (nozzle acceleration, high-speed jet deceleration, impact-rebound, rebound flight), the above parameters are iteratively adjusted to ensure that the velocity attenuation magnitude, rebound peak, and timing of simulated particles in the axial and edge regions are consistent with actual measurements. After completing the calibration of the six parameters, a comprehensive rebound verification was carried out.

[0100] 7. Comprehensive rebound verification:

[0101] To verify the rebound prediction capability of the calibrated model, a "field-virtual" comparison approach was adopted: a test area was demarcated on the tunnel sidewall, and a detachable rebound collector array was deployed. Rebound mass was measured at each location under uniform operating conditions. In the virtual environment, the sidewall geometry, nozzle-air zone-collision boundary, and collector arrangement were replicated at a 1:1 scale, and the rebound mass percentage at corresponding locations was simultaneously calculated. The consistency between the two models at corresponding sampling locations was used as the judgment criterion. If the preset error requirements were met, the parameter set was solidified for engineering simulation.

[0102] This embodiment discloses a method for calibrating simulation parameters of the entire process of shotcrete construction in a physics engine, including:

[0103] A. Basic parameter calibration: Basic parameters include coverage, basic fluid parameters and basic solver parameters.

[0104] 1. Basic fluid parameters:

[0105] In practical applications, the following mix proportion is used as an example: C25 grade shotcrete is provided by a building materials group and meets the requirements of Chinese National Standard GB / T 50080-2016 "Test Methods for Performance of Ordinary Concrete Mixtures". The density of this concrete mixture is 2280 kg / m³, and its detailed mix proportion (kg / m³) is as follows:

[0106] Cement: 446, Sand: 918, Crushed stone (5~10mm): 751, Water: 165, Water reducing agent: 4.46, Accelerating agent: 26.76, and particle size is set with a representative particle size of 10mm.

[0107] 2. Basic solver parameters: In practical applications, when conducting test spraying simulations of shotcrete and observing the particle count-simulation frame rate curve, it is required that under a set of basic solver parameter configurations, the frame rate for calculating 10,000 particles exceeds 60 FPS.

[0108] The fixed time step is based on the desired frame rate of 60 FPS, and is substituted into the formula. The calculated fixed time step is 0.0167s, which is rounded down to 0.01s.

[0109] The attention velocity of low-speed shotcrete can be assumed to be 0.1 m / s, and the dormancy threshold is calculated to be 0.1 * 1% = 0.001 m / s.

[0110] A total of 12 substeps are used within each fixed time step to provide sufficient constraint projection iterations while ensuring real-time computation performance per frame is less than 16 milliseconds. The constraint iteration priorities were determined based on simulation requirements, as follows: density constraints (5 iterations), collision constraints (3 iterations), and friction constraints (1 iteration). This combination effectively captures the overall behavior and particle interaction response of shotcrete, achieving the dual goals of simulation accuracy and computational efficiency.

[0111] B. Low-speed stage: The low-speed stage includes basic solver parameters, rheological parameters, and adhesion parameters.

[0112] 3. Rheological Parameters: In practical applications, since the particle diameter used is 0.01m, the smooth radius h = 2.0 * 0.01 = 0.02m is taken. A physical test is conducted according to standard procedures, recording the transient deformation during the cone lifting process. A virtual test process is simultaneously constructed, including equipment preparation, spraying, layered compaction, surface leveling, cone lifting, and slump reading. A real-time acquisition system developed based on C# acquires the three-dimensional coordinates of the sprayed concrete particles at each time step, and compares the consistency between the physical and virtual results under multiple parameter combinations to determine the optimal parameters for low-speed spraying. The final calibration values ​​are: smooth radius h = 0.02m, viscosity coefficient 1.3, and surface tension 0.05.

[0113] 4. Adhesion parameters:

[0114] In practical applications, the device consists of an adjustable steel plate (0.4m × 0.4m), an electronic inclinometer, and an electronic scale. The inclination angle is continuously adjustable from 0° to 90°. Rock slabs from the tunnel site (andesite in this example) can be fixed on the steel plate to simulate different contact surface conditions. Before the test, 3kg of freshly mixed shotcrete was evenly spread on the surface of the horizontal rock slab, tilted at a set rate to the target angle, and the mass of the slab sliding down within 20 seconds was recorded. The experimental process was then reproduced in a virtual environment, and the collision parameters were determined by comparing the flow and accumulation behavior under different parameter combinations. The calibration results under low-speed shotcreting conditions were: dynamic friction coefficient 0.25, static friction coefficient 0.535, adhesion coefficient (stickiness) 0.0044, and adhesion distance (stick distance) 0.001m.

[0115] C. High-speed phase: The high-speed phase includes adhesion parameters, mass field parameters, and velocity field parameters.

[0116] 5. Mass field parameters:

[0117] In practical applications, a ring arrangement of 110 detachable steel pipes (30mm×30mm×180mm) is used, with the nozzles 1m above the plate surface. A wet spraying trolley is employed, spraying through rigid rubber nozzles (450mm long, 50mm inner diameter, 30m³ / h flow rate), stopping once the central pipe is full. The filling height of each pipe is recorded, and the normalized mass distribution ratio η is calculated. i Gaussian amplitude fitting was performed on the cross section at Y=17.5cm, and the goodness of fit R0 was [value missing]. 2 =0.99. The simulation side maintained the same layout and sampling method, with the initial particle velocity at the nozzle set to 35 m / s. Only the random initial velocity direction was adjusted to control the divergence angle, and the optimal value of 0.435 (approximately 10°) was obtained through iteration. The final simulated and measured mass field distribution showed good consistency R. 2 =0.89, and based on this, the parameter is fixed for velocity field calibration under high-speed injection conditions.

[0118] 6. Velocity field parameters:

[0119] In practical applications, during tunnel sidewall spraying tests, the nozzle was positioned 1.0m from the sidewall, perpendicular to the sprayed surface, with an initial particle velocity of 35m / s and a continuous spraying duration of 2s. A C# script was written to track the trajectories of representative particles and generate velocity field data. After calibration, with MaxDepenetration=5.0m / s, Atmosphericdrag=1.0, Windintensity=3000, and Accelerationdistance=0.5m, the virtual test was able to reproduce the characteristics of the actual jet flow: particles near the spray axis exhibited significant velocity decay upon impact and rebounded at approximately 6m / s, while edge particles maintained a higher residual velocity (approximately 17m / s), forming a clear spatial gradient.

[0120] 7. Comprehensive rebound verification:

[0121] In practical application, a 2m × 2m test area was designated near the bottom of the side wall, and a portable collector array (multi-point, distance-based data collection) was deployed. Nozzles were positioned 1.0m from the wall surface, spraying normally, using the same wet spraying equipment and materials as previously calibrated. A virtual side was modeled at a 1:1 scale, with a total mass counter and corresponding rebound collection points from the field. The percentage of rebound mass captured at each point was recorded and compared with field data. The overall rebound error was less than 15%, meeting the engineering simulation requirements.

[0122] Parameter summary: Particle size 0.01m; Static density 2280kg / m³; Smooth radius 0.02m; Viscosity 1.3; Polarity 0.05; Atmospheric drag coefficient 1. Wind field intensity 3000; Initial velocity 10m / s; Random initial velocity direction 0.435. Dormancy threshold 0.01m / s. Dynamic friction 0.25; Static friction 0.535; Adhesion coefficient 0.0044; Adhesion distance 0.001m; Maximum penetration velocity 5.0m / s. Fixed time step 0.01s; Number of substeps 12; Number of constraint iterations (density 5, collision 3, friction 1); Gravity 9.8m / s².

[0123] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for calibrating simulation parameters of the entire process of shotcrete construction in a physics engine, characterized in that, include: The parameters to be calibrated throughout the entire process of shotcrete construction are obtained, and the parameters to be calibrated are calibrated in multiple stages to obtain the final calibration results. The multi-stage parameter calibration includes: calibration of foundation fluid parameters and foundation solver parameters in the foundation parameters, calibration of rheological parameters and adhesion parameters in the low-speed stage, and calibration of mass field parameters and velocity field parameters in the high-speed stage. The basic solver parameter calibration for the parameters to be calibrated includes: Set initial basic solver parameters, use the initial basic solver parameters to carry out sprayed concrete test spraying simulation, obtain particle number-simulation frame rate curve and upper limit of particle velocity, and determine the number of substeps of the basic solver parameters; Using the particle number-simulation frame rate curve, the fixed time step of the basic solver parameters is determined; The upper limit of the particle velocity is used as the dormancy threshold of the basic solver parameters. If the magnitude of the particle velocity is less than the dormancy threshold, it proves that the current particle is in a dormant state and is fixed in the dormant position. Based on the number of substeps, the constraint iteration number of the basic solver parameters is adjusted by the constraint stiffness priority to obtain the constraint iteration number corresponding to the physical response that is similar to the actual spraying vision. Mass field parameter calibration of the parameter to be calibrated includes: With the same nozzle-sampling surface arrangement in the simulation and the physical test, during the physical test, sprayed concrete diffuses from the nozzle to the sprayed surface at a divergence angle, and the area integral of the mass flux density on the honeycomb sampling plate is obtained. The honeycomb sampling plate is then discretized into several equivalent sampling units to obtain the spatial mass distribution ratio of the physical test. The simulation side is processed with the same sampling and normalization to obtain the spatial mass distribution ratio of the simulation side. The spatial mass distribution ratio is used to determine whether the spatial characteristics of the simulation side and the physical test are consistent. If the spatial characteristics of the simulation side and the physical test are consistent, the random initial velocity direction of the mass field parameters is gradually adjusted with the goal of minimizing the mean square error between the simulated spray thickness distribution and the measured data, until the distribution pattern and peak attenuation trend are consistent with the physical test and reach the preset error threshold, thus obtaining the calibrated random initial velocity direction.

2. The method for calibrating simulation parameters of the entire process of shotcrete construction in a physics engine according to claim 1, characterized in that, The basic fluid parameter calibration of the parameter to be calibrated includes: Obtain shotcrete gradation data, obtain shotcrete mixture samples using the shotcrete gradation data, perform bulk density tests on the shotcrete mixture samples, and measure the bulk density of the basic fluid parameters. Obtain the aggregate particle size distribution, and based on the aggregate particle size distribution, determine the average particle size or representative particle size of the aggregate, and use the average particle size or representative particle size of the aggregate as the particle size of the basic fluid parameter.

3. The method for calibrating simulation parameters of the entire process of shotcrete construction in a physics engine according to claim 1, characterized in that, Determining the fixed time step for the basic solver parameters includes: in, For a fixed time step, The target frame rate.

4. The method for calibrating simulation parameters of the entire process of shotcrete construction in a physics engine according to claim 1, characterized in that, The rheological parameter calibration of the parameter to be calibrated includes: The rheological parameters were calibrated by simultaneously performing slump tests in a field experiment and a virtual environment: during the slump test, the concrete filled in the slump bucket slumped after the bucket was lifted, and the rheological parameters were calibrated with the goal of minimizing the errors of the slump-time curve and slump radius-time curve in the field slump test and the virtual simulation test. After calibrating the rheological parameters, the smooth radius of the rheological parameters is obtained based on the number of target neighborhood particles and the particle spacing. The viscosity coefficient and surface tension of the rheological parameters are adjusted using the smooth radius. Virtual slump tests are conducted using the adjusted viscosity coefficient and surface tension. The error between each set of simulated slump curves and measured curves is calculated. The goodness of fit of the slump-time and slump radius-time curves of the field experiment and the virtual experiment is greater than the target threshold. The viscosity coefficient and surface tension corresponding to the curve with the smallest error are obtained.

5. The method for calibrating simulation parameters of the entire process of shotcrete construction in a physics engine according to claim 4, characterized in that, Obtaining the smooth radius of the rheological parameters includes: in, For smooth radius, For particle spacing, The number of particles in the target neighborhood.

6. The method for calibrating simulation parameters of the entire process of shotcrete construction in a physics engine according to claim 1, characterized in that, The adhesion parameter calibration of the parameter to be calibrated includes: The adhesion parameters were calibrated by tilt plate experiments. Under different tilt angles, the slippage mass and adhesion behavior of shotcrete within a certain time window were obtained. A control experiment was constructed in a virtual environment with the same tilt angle and operation sequence to obtain the simulated slippage mass. The mean square error between the simulated and measured slip mass of the multi-angle dataset is used as the optimization objective for iterative optimization. In each iteration, the parameter vector is updated according to the gradient of the objective function and constraints are applied. When the objective function converges to a preset threshold on the multi-angle data, the optimal adhesion parameters are output.

7. The method for calibrating simulation parameters of the entire process of shotcrete construction in a physics engine according to claim 1, characterized in that, The velocity field parameter calibration of the parameter to be calibrated includes: In the collision calculation stage, an upper limit is set on the penetration velocity to controllably dissipate kinetic energy at the moment of impact, reproducing the velocity evolution of deceleration, rebound, reattachment, and rebound. The velocity field parameter calibration is based on the sidewall spraying scenario, using nozzles consistent with the field. The three-dimensional trajectory and velocity sequence of representative particles are collected through scripted particle tracking to construct a spatiotemporal velocity field dataset. The spatiotemporal velocity field dataset includes: initial velocity, maximum penetration velocity, atmospheric drag coefficient related to particle-air interaction, wind field intensity, and acceleration distance. Using the consistency between the high-speed phase velocity curves of the field test and the simulation as the criterion, the spatiotemporal velocity field dataset is iteratively adjusted so that the velocity attenuation amplitude, rebound peak and timing of the simulated particles in the axial and edge regions are consistent with the measured data of the field test, and the calibrated velocity field parameters are obtained.

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