A multi-scale coupling analysis method for ballastless track pouring construction

Abstract

The present invention discloses a multi-scale coupling analysis method for ballastless track pouring construction, which relates to the technical field of high-speed railway ballastless track construction. The method comprises: obtaining the macroscopic flow parameters, rheological parameters and inter-particle surface energy parameters of self-compacting concrete; fitting a first fitting equation and a second fitting equation, performing simultaneous equations and obtaining a correlation relationship; optimizing the inter-particle surface energy combination, constructing an aggregate particle refinement model according to the optimized inter-particle surface energy combination, sphericity and angle index, and constructing a flexible multi-body dynamics model; coupling the aggregate particle refinement model and the flexible multi-body dynamics model to construct a multi-scale coupling model for pouring construction; and performing a multi-scale mechanical analysis of the ballastless track pouring construction process through the multi-scale coupling model for pouring construction to obtain a multi-scale coupling analysis result. The present invention can realize the mechanical interaction analysis between the self-compacting concrete and the track structure during the entire pouring construction process at the micro-aggregate scale.

Description

Technical Field

[0001] The present invention relates to the technical field of high-speed railway ballastless track construction, and in particular to a multi-scale coupling analysis method for ballastless track pouring construction. Background Art

[0002] As the core component of high-speed rail infrastructure, ballastless track structure has become the main track type for high-speed rail construction. New high-speed rail lines with speeds of 300km / h and above mainly use ballastless track. As a typical ballastless track structure, CRTS III slab ballastless track mainly consists of track slab, self-compacting concrete (SCC) filling layer, isolation layer and base plate. Among them, the pouring construction of SCC filling layer is the most important process in ballastless track laying. SCC can be simplified as a solid-liquid two-phase fluid composed of cement mortar and coarse aggregate, in which cement mortar is a submillimeter scale (0.35~0.5 MM ), coarse aggregate is millimeter scale (5~16 MM During ballastless track pouring construction, freshly mixed SCC flows from the reserved pouring holes in the track slab in a self-leveling manner to fill the enclosed space. Due to the discrete characteristics of SCC itself, the flat dimensions of the enclosed space (5.6 m × 2.5 m × 0.1 m), and the influence of the steel mesh on SCC flow, the mechanical mechanism of SCC on the track structure is very complex.

[0003] Existing analysis methods are primarily based on computational fluid dynamics theory, and most simplify SCC as a homogeneous fluid. This makes it difficult to accurately consider the discrete characteristics between coarse and fine aggregate particles in SCC, and to finely account for the interactions between cement mortar and aggregate particles, and between aggregate particles and steel mesh in SCC. This affects the accuracy of the simulation of the SCC flow state and the mechanical state of the track structure, and is insufficiently adaptable to the analysis of ballastless track pouring construction. Summary of the Invention

[0004] Based on this, it is necessary to provide a multi-scale coupling analysis method for ballastless track pouring construction to address the above technical issues.

[0005] An embodiment of the present invention provides a multi-scale coupling analysis method for ballastless track pouring construction, comprising:

[0006] Obtain the macroscopic flow parameters, rheological parameters and inter-particle surface energy parameters of self-compacting concrete;

[0007] The macroscopic flow parameters are fitted according to the rheological parameters to obtain a first fitting equation with the rheological parameters as independent variables and the macroscopic flow parameters as dependent variables; the macroscopic flow parameters are fitted according to the inter-particle surface energy parameters to obtain a second fitting equation with the inter-particle surface energy parameters as independent variables and the macroscopic flow parameters as dependent variables;

[0008] The first fitting equation and the second fitting equation are combined to obtain the correlation between the rheological parameters and the inter-particle surface energy; based on the correlation between the rheological parameters and the inter-particle surface energy, the inter-particle surface energy combination is optimized to obtain an optimized inter-particle surface energy combination;

[0009] Based on the morphological characteristics of self-compacting concrete aggregate particles, the sphericity and angular index are determined, and a refined aggregate particle model is constructed based on the optimized inter-particle surface energy combination, sphericity, and angular index. Based on the flexible multi-body dynamics theory, a flexible multi-body dynamics model is constructed to characterize the interaction between the track structure and the pouring construction equipment based on their geometric characteristics.

[0010] The aggregate particle refinement model and the flexible multi-body dynamics model are coupled to construct a multi-scale coupling model of pouring construction that reflects the interaction between self-compacting concrete particles and the track structure. The multi-scale coupling model of pouring construction is then used to conduct a multi-scale mechanical analysis of the ballastless track pouring construction process, and the multi-scale coupling analysis results are obtained.

[0011] Optionally, macroscopic flow parameters include slump spread and spread time T 500 The rheological parameters include yield stress and plastic viscosity, and the surface energy parameters between particles include the surface energy between coarse aggregate and coarse aggregate, the surface energy between coarse aggregate and mortar, and the surface energy between mortar and mortar.

[0012] Optionally, the macroscopic flow parameters are fitted according to the rheological parameters based on the following formula:

[0013] ;

[0014] ;

[0015] in, SF is the slump spread, T 500 To extend the time, η is the plastic viscosity, τ is the yield stress;

[0016] The macroscopic flow parameters are fitted according to the interparticle surface energy parameters based on the following formula:

[0017] ;

[0018] ;

[0019] in, AA is the surface energy between coarse aggregate and coarse aggregate, AM is the surface energy between coarse aggregate and mortar, MM is the surface energy between mortar and mortar.

[0020] Alternatively, the sphericity can be determined based on the following formula according to the aggregate particle morphology characteristics of the self-compacting concrete:

[0021] ;

[0022] in, SPH is sphericity, L is the length of the major axis of the aggregate particles, W is the median length of the aggregate particles, T is the minor axis length of the aggregate particles;

[0023] The angle index is determined based on the following formula according to the aggregate particle morphology characteristics of self-compacting concrete:

[0024] ;

[0025] ;

[0026] in, AI is the angle index, e is the angle, P ( e ) is the frequency of the angle index change value of each vertex relative to the previous vertex within the set angle range, AI i is the angle index of each view, S i is the area of ​​the projection surface of each view.

[0027] Optionally, the method further includes normalizing the sphericity and the angular index based on the following formula:

[0028] ;

[0029] ;

[0030] in, SPH * is the normalized sphericity, AI * is the normalized angle index, SPH max is the maximum value of sphericity, SPH min is the minimum value of sphericity, AI max is the maximum value of the angle index, AI min is the minimum value of the angle index.

[0031] Optionally, the aggregate particle refinement model and the flexible multi-body dynamics model are coupled to construct a multi-scale coupling model of pouring construction that reflects the interaction between self-compacting concrete particles and the track structure, specifically including:

[0032] Obtaining contact pairs between aggregate particles and between aggregate particles and continuum structures;

[0033] Determine the contact forces between aggregate particles and between aggregate particles and the structure, as well as the motion parameters of aggregate particle units, and update the spatial position of the particles in this time step;

[0034] The forces transmitted by the discrete elements are used as boundary conditions to determine the deformation of the continuum structure, and the spatial position information of the multi-flexible body structure is updated by calculating the motion parameters of the structure to complete the calculation cycle of a single time step. After multiple iterations, a multi-scale coupling model of grouting construction is obtained.

[0035] Optionally, the aggregate particles are composed of a plurality of spherical units. j The spherical unit is in contact with the track plate flexible body, and the normal force between the aggregate particles and the track plate flexible body is:

[0036] ;

[0037] The tangential force between the aggregate particles and the track slab flexible body is:

[0038] ;

[0039] in, ni is the normal relative velocity between aggregate particles and the track slab flexible body, ti is the tangential relative velocity between aggregate particles and the track slab flexible body, n is the normal force between the aggregate particles and the track slab flexible body, t is the tangential force between aggregate particles and the track slab flexible body, is the normal overlap between aggregate particles and track slab flexible body, n is the damping coefficient in the normal direction, t is the tangential damping coefficient, n is the normal elastic coefficient, t is the tangential elastic modulus, n is the unit vector of the normal force between the aggregate particles and the track slab flexible body, tis the unit vector of the tangential force on the contact surface between aggregate particles and the track slab flexible body, j is the total number of spherical units, is the tangential force coefficient.

[0040] The multi-scale coupling analysis method for ballastless track pouring construction provided by the embodiment of the present invention has the following beneficial effects compared with the prior art:

[0041] The present invention realizes multi-scale collaborative simulation of materials, structures and equipment by constructing a refined model of aggregate particles (incorporating a combination of macroscopic flow parameters, rheological parameters and inter-particle surface energy) and a flexible multi-body dynamics model (characterizing the interaction between the track structure and the pouring construction equipment). By coupling the multi-scale coupling model constructed by the refined model of aggregate particles and the flexible multi-body dynamics model, accurate analysis of the interaction between self-compacting concrete and the track structure during the entire pouring construction process is achieved at the micro-aggregate scale level, which not only significantly improves the simulation accuracy of the entire construction process simulation, but also effectively ensures the adaptability of the ballastless track pouring construction analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 A schematic diagram of the slump expansion of self-compacting concrete according to a multi-scale coupling analysis method for ballastless track pouring construction provided in one embodiment;

[0043] Figure 2 A schematic diagram of the expansion time of self-compacting concrete in a multi-scale coupling analysis method for ballastless track pouring construction provided in one embodiment;

[0044] Figure 3 A distribution diagram of test points for a multi-scale coupling analysis method for ballastless track pouring construction provided in one embodiment;

[0045] Figure 4 A diagram showing the influence of normalized surface energy on slump spread in a multi-scale coupling analysis method for ballastless track pouring construction provided in one embodiment;

[0046] Figure 5 A schematic diagram of the effect of coarse aggregate-coarse aggregate / coarse aggregate-mortar on slump expansion in a multi-scale coupling analysis method for ballastless track pouring construction provided in one embodiment;

[0047] Figure 6 A schematic diagram of the effect of coarse aggregate-coarse aggregate / mortar-mortar on slump expansion in a multi-scale coupling analysis method for ballastless track pouring construction provided in one embodiment;

[0048] Figure 7A schematic diagram of the effect of coarse aggregate-mortar / mortar-mortar on slump expansion in a multi-scale coupling analysis method for ballastless track pouring construction provided in one embodiment;

[0049] Figure 8 A diagram showing the influence of normalized surface energy on expansion time in a multi-scale coupling analysis method for ballastless track pouring construction provided in one embodiment;

[0050] Figure 9 A schematic diagram of the effect of coarse aggregate-coarse aggregate / coarse aggregate-mortar on expansion time in a multi-scale coupling analysis method for ballastless track pouring construction provided in one embodiment;

[0051] Figure 10 A schematic diagram of the effect of coarse aggregate-coarse aggregate / mortar-mortar on expansion time in a multi-scale coupling analysis method for ballastless track pouring construction provided in one embodiment;

[0052] Figure 11 A schematic diagram of the effect of coarse aggregate-mortar / mortar-mortar on expansion time in a multi-scale coupling analysis method for ballastless track pouring construction provided in one embodiment;

[0053] Figure 12 A DEM model diagram of spherical aggregate particles for a multi-scale coupling analysis method for ballastless track pouring construction provided in one embodiment;

[0054] Figure 13 A DEM model diagram of columnar aggregate particles for a multi-scale coupling analysis method for ballastless track pouring construction provided in one embodiment;

[0055] Figure 14 A DEM model diagram of tapered aggregate particles for a multi-scale coupling analysis method for ballastless track pouring construction provided in one embodiment;

[0056] Figure 15 A DEM model diagram of flaky aggregate particles for a multi-scale coupling analysis method for ballastless track pouring construction provided in one embodiment;

[0057] Figure 16 A diagram of a contact model between self-compacting concrete aggregate particles and track slabs in a multi-scale coupling analysis method for ballastless track pouring construction provided in one embodiment;

[0058] Figure 17 A DEM-MFBD coupling calculation flow chart of a multi-scale coupling analysis method for ballastless track pouring construction provided in one embodiment;

[0059] Figure 18A schematic diagram of a CRTS III ballastless track pouring construction coupling model for a multi-scale coupling analysis method for ballastless track pouring construction provided in one embodiment;

[0060] Figure 19 The present invention is a flow chart of a multi-scale coupling analysis method for ballastless track pouring construction provided in one embodiment. DETAILED DESCRIPTION

[0061] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0062] As a core component of high-speed rail infrastructure, ballastless track has become the predominant track type in high-speed rail construction. New high-speed rail lines with speeds of 300 km / h and above primarily utilize ballastless track. CRTS III slab track, a typical ballastless track structure, primarily consists of a track slab, a self-compacting concrete (SCC) infill layer, an isolation layer, and a base plate. The pouring of the SCC infill layer is the most critical step in ballastless track construction. During pouring, freshly mixed SCC flows through pre-reserved holes in the track slab in a self-leveling manner to fill the enclosed space. Due to the SCC's inherent discrete properties, the flat dimensions of the enclosed space (5.6 m × 2.5 m × 0.1 m), and the influence of steel mesh on SCC flow, the mechanical interaction mechanism of SCC on the track structure is complex. Even with pre-installed clamping devices, the track slab will still float upward, affecting the track slab's fine-tuning and, in turn, the smoothness of the high-speed rail line. Currently, grouting construction relies heavily on manual labor. The setting of SCC material parameters and the adjustment of grouting process parameters are often based on the experience and judgment of on-site construction personnel, lacking scientific theoretical guidance. This often overlooks the impact of microscopic material parameters, such as aggregate particle size and gradation, on the SCC flow state and mechanical behavior of the track structure during the grouting process. As a result, some lines have experienced initial damage during SCC maintenance, such as interlayer delamination, track slab edge fracturing and block loss, and base plate cracking. These damages have severely deteriorated the service life of the track structure and impacted the safe operation of high-speed trains. Consequently, these initial damages have necessitated the removal of the slabs and re-construction on-site, significantly wasting manpower, material, and financial resources.

[0063] During pouring, freshly mixed SCC flows through the reserved pouring holes in the track slab in a self-leveling manner to fill the enclosed space. Due to the discrete characteristics of SCC itself, the flat dimensions of the enclosed space (5.6 m × 2.5 m × 0.1 m), and the influence of the steel mesh on SCC flow, the mechanical interaction mechanism of SCC on the track structure is very complex. Even with the preset clamping device, the track slab will still float upward, affecting the fine-tuning effect of the track slab and, in turn, the smoothness of the high-speed rail line.

[0064] Most existing studies simplify SCC as a homogeneous fluid, making it difficult to accurately consider the discrete characteristics between coarse and fine aggregate particles in SCC, unable to finely consider the microscopic mechanical properties of aggregate particles on the track structure, and difficult to accurately analyze the mechanical response of the track structure and construction equipment during pouring construction.

[0065] The embodiment of the present invention provides a multi-scale coupling analysis method for ballastless track pouring construction, such as Figure 19 As shown, specifically including:

[0066] The macroscopic flow parameters, rheological parameters and inter-particle surface energy parameters of self-compacting concrete were obtained.

[0067] Macroscopic flow parameters were fitted according to rheological parameters, resulting in a first fitting equation with rheological parameters as independent variables and macroscopic flow parameters as dependent variables. Macroscopic flow parameters were fitted according to interparticle surface energy parameters, resulting in a second fitting equation with interparticle surface energy parameters as independent variables and macroscopic flow parameters as dependent variables.

[0068] The first fitting equation and the second fitting equation are combined to obtain the correlation between the rheological parameters and the inter-particle surface energy. Based on the correlation between the rheological parameters and the inter-particle surface energy, the inter-particle surface energy combination is optimized to obtain the optimized inter-particle surface energy combination;

[0069] Based on the morphological characteristics of self-compacting concrete aggregate particles, the sphericity and angular index were determined. A refined aggregate particle model was constructed based on the optimized inter-particle surface energy combination, sphericity, and angular index. Based on flexible multi-body dynamics theory, a flexible multi-body dynamics model was constructed to characterize the interaction between the track structure and the pouring equipment, taking into account their geometric characteristics.

[0070] By coupling the refined aggregate particle model with a flexible multibody dynamics model, a multiscale coupling model of pouring construction was constructed to reflect the interaction between self-compacting concrete particles and the track structure. This model was then used to conduct a multiscale mechanical analysis of the ballastless track pouring construction process, yielding the results of this multiscale coupling analysis.

[0071] Specific implementation includes:

[0072] Obtain the macroscopic flow parameters and rheological parameters of self-compacting concrete, where the macroscopic flow parameters mainly include slump expansion and expansion time T 500 , and the rheological parameters are yield stress and plastic viscosity. Since the macroscopic flow parameters of each group of self-compacting concrete strictly correspond to the rheological parameters, in order to clarify the correspondence between the macroscopic flow parameters and the rheological parameters, the rheological parameters are used to fit the macroscopic flow parameters, and the slump expansion and expansion time after fitting are obtained.T 500 The equations for rheological parameters are shown in Equations (1) and (2). Furthermore, in order to more intuitively analyze the relationship between macroscopic working performance and rheological parameters, the experimental results of slump spread are integrated with the fitting equations as follows: Figure 1 As shown, the time will be extended T 500 The experimental results are integrated with the fitting equation as shown in Figure 2 shown.

[0073] (1)

[0074] (2)

[0075] in, SF is the slump flow, in units of MM ; T 500 is the expansion time, in seconds; η is the plastic viscosity, in Pa·s; τ is the yield stress, in Pa.

[0076] Depend on Figure 1 and Figure 2 It can be seen that the expansion and T 500 Both have good nonlinear relationships with yield stress and plastic viscosity, and are affected by the synergistic effects of yield stress and plastic viscosity. The correlation coefficient R between the proposed expansion fitting equation and the experimental data 2 0.9420, expansion time T 500 The correlation coefficient between the fitting model and the experimental data is 0.9815, and the fitting equation and the experimental data are in good agreement. Figure 1 It can be seen that the expansion decreases with the increase of yield stress and plastic viscosity. Yield stress is the main influencing factor of expansion, and plastic viscosity has the second largest influence on expansion. When the yield stress is large, the influence of plastic viscosity on expansion is small, and when the yield stress is small, the influence of plastic viscosity on expansion is large. T 500 ,Depend on Figure 2 It can be seen that the expansion time T 500 With the increase of yield stress and plastic viscosity, the plastic viscosity has a greater effect on the expansion time than the yield stress. T 500 Specifically, when the plastic viscosity is small, the yield stress has a greater impact on T 500 When the plastic viscosity is large, the influence of yield stress increases significantly.

[0077] In order to improve the efficiency of model parameter calibration and accurately obtain the surface energy parameter combination that reflects the flow state of self-compacting concrete, the star point design method in the response surface method is used to optimize the surface energy combination, where the independent variables are the surface energy between coarse aggregate and coarse aggregate ( x 1: AA ), surface energy between coarse aggregate and mortar ( x 2: AM ) and the surface energy between mortar and mortar ( x 3: MM ), the experimental scheme was designed based on the three-factor five-level central design method, including 2 k Factor points, 2 k extreme points and n center points. Among them, k is the number of independent variables, which is 3 in this embodiment. Therefore, there are 8 factor points, 6 axial points and 6 center points in this embodiment (such as Figure 2 Combined with the results of the previous literature survey, the value range and coding value of each input variable were determined, as shown in Table 1.

[0078] Table 1 Comparison table of independent variables and coding values

[0079]

[0080] Note: .

[0081] Combine Figure 3 As shown in Table 1, the circular points are factor points, which are the corner points of the cube. The coding value of each factor is 1 or -1, which is mainly used to evaluate the interaction terms and linear terms between factors; the star points are extreme points, with coding values ​​of 1.682 or -1.682, which are mainly used to evaluate the nonlinear relationship between factors; the triangular points are the center points, located at the center of the cube, with coding values ​​of 0, which are mainly used to reduce the deviation of the regression coefficient and improve the accuracy of the response surface model.

[0082] The variance analysis was used to evaluate the individual variables and the interaction between the individual variables. When the p value of the influencing factor was less than 0.05, it was considered that the influencing factor had a significant effect. As shown in Table 2, the surface energy between coarse aggregate and coarse aggregate ( x 1: AA ), surface energy between coarse aggregate and mortar ( x 2: AM ) and the surface energy between mortar and mortar ( x 3: MM ) all significantly affect the slump expansion of self-compacting concrete, and there is a strong linear relationship between the expansion and the three independent variables. The equation after linear fitting is as follows (3):

[0083] (3)

[0084] Table 2 ANOVA results of the fitting equation

[0085]

[0086] As can be seen from Table 2, the p-value of the established expansion fitting model is less than 0.0001, indicating that the model has high statistical significance, and the model's goodness of fit R 2 The value of 0.9624 indicates that more than 96.2% of the changes in the model response value are related to the three independent variables. The low CV value also confirms this. In addition, the model's corrected correlation coefficient is highly consistent with the predicted correlation coefficient, which is significantly lower than the statistical recommendation that the difference between the two values ​​is less than 20%, indicating that the model's predicted value is in good agreement with the test value, and the established prediction model is reasonable and effective. On this basis, the independent and interactive influence relationships of each variable on the expansion degree are extracted, as shown in Figure 2. Figure 4 、 Figure 5 、 Figure 6 and Figure 7 shown.

[0087] from Figure 4 、 Figure 5 、 Figure 6 and Figure 7 It can be seen that within the selected surface energy range, the surface energy between mortar particles has the greatest impact on expansion, followed by the surface energy between mortar and coarse aggregate particles. The surface energy between coarse aggregate particles has the least impact on expansion. This is primarily because mortar particles significantly outnumber coarse aggregate particles in the aggregate-mortar two-phase system of self-compacting concrete. Therefore, the strength of the surface energy between mortar particles directly affects the expansion of self-compacting concrete. As the surface energy between particles increases, the expansion decreases. This is because the increase in interparticle surface energy increases the interparticle resistance that self-compacting concrete must overcome to flow, which in turn leads to a decrease in expansion.

[0088] Furthermore, from Table 2, we can see that the expansion time T 500 There is also a strong linear relationship between the independent variable and the fitted equation is shown in Equation (4). According to the variance analysis, the fitted equation has a high statistical significance, among which the p value is less than 0.0001 and the goodness of fit R 2 is 0.9663, indicating that the established fitting model is accurate and effective. T 500 The independent influence relationship between them is described by a three-dimensional response surface diagram to describe the expansion time under the coupling effect of various factors. T 500 Changes, such as Figure 8 、 Figure 9 、 Figure 10 and Figure 11 shown.

[0089] (4)

[0090] from Figure 8 、 Figure 9 、 Figure 10 and Figure 11 It can be seen that similar to the influence of each variable on the expansion degree, the surface energy between mortar particles has an influence on the expansion time. T 500 The largest influence is the surface energy between coarse aggregate and mortar. The surface energy between coarse aggregate particles has a great influence on T 500 The effect is minimal. As the surface energy between particles increases, the T 500 It also gradually increases, which is also due to the increase in surface energy between particles. The resistance that the self-compacting concrete needs to overcome increases, thereby slowing down the flow speed of the self-compacting concrete itself.

[0091] After clarifying the relationship between the macroscopic flow parameters of self-compacting concrete and the surface energy between particles, the correlation between the rheological parameters of self-compacting concrete and the surface energy between particles can be obtained by combining equations 1 and 3 and equations 2 and 4. Furthermore, combined with construction requirements, specification requirements and model calculation efficiency, the surface energy combination between particles is optimized with the macroscopic flow test results and rheological test results of self-compacting concrete as the target values ​​(Table 3), and the corresponding surface energy combination between particles can be calculated. Specifically, the surface energy between coarse aggregate and coarse aggregate, the surface energy between coarse aggregate and mortar, and the surface energy between mortar and mortar are 0.89 J / m 2 , 0.7 J / m 2 and 1.1 J / m 2 .

[0092] Table 3 Target values ​​of surface energy combination optimization for self-compacting concrete

[0093]

[0094] Since the morphology of aggregate particles varies and the morphology of aggregate directly affects the flow state of self-compacting concrete, the parameters that characterize the morphology of aggregate mainly include shape parameters, angle parameters and surface texture parameters according to the differences in characteristic scales. Among them, the shape parameters reflect the aggregation state of aggregate at the macro scale, the angle parameters reflect the angle change of aggregate at the micro scale, and the surface texture parameters reflect the surface roughness of aggregate particles at the micro scale. Existing studies mainly use the needle index and flake index in the shape parameters to characterize the aggregate morphology. This method accurately reflects the overall macro morphology of the aggregate, but does not consider the surface angle of the aggregate at the micro scale. In order to more finely characterize the morphological characteristics of aggregate particles, the sphericity (Sphericity, SPH ) and the Angularity index in the angle parameter. AI ) to characterize the aggregate morphology.

[0095] Sphericity reflects the similarity between the overall form of the aggregate and a sphere and is calculated by the minimum circumscribed cuboid, e.g. Figure 4 As shown in Equation 5. It can be seen from the equation that the range of sphericity is 0~1. The closer the aggregate morphology is to sphericity, the closer the sphericity is to 1; conversely, the aggregate morphology is often flaky or strip-like.

[0096] (5)

[0097] Where, SPH represents sphericity, L 、 W and T They represent the lengths of the major axis, median axis and minor axis of the aggregate particles respectively.

[0098] The angle index reflects the intensity of the change in the aggregate profile angle and has both two-dimensional and three-dimensional scales. In the calculation, the two-dimensional angle index of the aggregate particles on the projection surface is first obtained. AI i , then the front view, side view and top view Figure 3 Orthogonal directions AI i The weighted average of the values ​​gives the three-dimensional angle index AI , the weighting basis is the area occupied by each view, as shown in Equations 6 and 7. Generally speaking, the larger the angle index, the more dramatic the angle change of the aggregate morphology; the smaller the angle index, the smoother the contour curve of the aggregate.

[0099] (6)

[0100] (7)

[0101] in, e is the angle, e= 0°, 10°, 20°, …, 170°, P ( e ) is the angle range for each vertex relative to the set angle range ( e arrive( e Frequency of change in the angle index of the previous vertex within +10°), AI i is the angle index of each view, S i is the area of ​​the projection surface of each view.

[0102] In order to accurately obtain the three-dimensional morphology of aggregate particles, a three-dimensional laser scanner was used to scan randomly selected aggregate particles. It should be noted that the specification (Q / CR 596-2017) requires that the coarse aggregate of self-compacting concrete used for ballastless track pouring construction should be 5~10 MM and 10~16 MM In order to balance the refinement degree of self-compacting concrete and the calculation efficiency, dozens of particles with a larger particle size of 10~16 were randomly selected. MM Aggregate particles are scanned. The sphericity and angular index of the aggregate particles are calculated respectively, and the sphericity and angular index are normalized according to formula (8) and formula (9).

[0103] (8)

[0104] (9)

[0105] Where, SPH * and AI * represent the normalized sphericity and normalized angular index, respectively. SPH max and SPH min represent the maximum and minimum values ​​of sphericity, respectively. AI max and AI min Represent the maximum and minimum values ​​of the angle index respectively.

[0106] Furthermore, based on the clear classification standards of aggregate morphology, the distribution patterns of different particles in sphericity and angular index were statistically analyzed. Based on this, the scanned aggregate particles were divided into four categories, including:

[0107] (1) Spherical aggregate particles: The surface of the aggregate particles is smooth and the overall shape is close to a sphere. The normalized sphericity is in the range of 0.5 to 1, and the normalized angle index is in the range of 0 to 0.5.

[0108] (2) Columnar aggregate particles: The surface of the aggregate particles is smooth, but the angle of the aggregate profile varies greatly. The normalized sphericity and normalized angle index of this type of aggregate are both in the range of 0~0.5.

[0109] (3) Conical aggregate particles: The overall shape of the aggregate particles is close to that of a sphere, but the angle of the aggregate contour varies greatly and the edges and corners are distinct. The normalized sphericity and normalized angle index of this type of aggregate are both in the range of 0.5 to 1.

[0110] (4) Flaky aggregate particles: The aggregate particles are flat and the angle of the aggregate profile varies greatly. The normalized sphericity of this type of aggregate is in the range of 0 to 0.5, and the normalized angle index is in the range of 0.5 to 1.

[0111] Finally, the real morphology of aggregate particles is accurately simulated by discrete element spheres to obtain the refined model of classified aggregate particles. Figure 12 、 Figure 13 、 Figure 14 and Figure 15 According to the morphological characteristics of aggregate particles in self-compacting concrete, the sphericity and angular index are determined, and a refined aggregate particle model (Discrete Element Method, DEM) is constructed based on the optimized inter-particle surface energy combination, sphericity, and angular index.

[0112] The flexible multi-body dynamics model (MFBD) method can accurately express the structural deformation caused by contact forces. It mainly constructs the motion equation by calculating the position change of the node. i , whose spatial position can be determined by the node i -1's spatial position and relative deformation calculation:

[0113] (10)

[0114] Where, r i is the node in the inertial coordinate system i spatial location, r i-1 is the origin space position of the floating coordinate system, A i-1 is the direction cosine matrix from the floating coordinate system to the inertial coordinate system, s (i-1)i is the node in the inertial coordinate system when the flexible body is not deformed i Compared to nodes i A position vector of -1, u (i-1)i For nodes i Compared to nodes iA deformation vector of -1.

[0115] According to the virtual displacement principle, the node i With node i The virtual displacement relationship between -1 can be expressed as:

[0116] (11)

[0117] Where, δZ i and δZ i-1 Node i With node i A virtual displacement of -1, and H (i-1)i is the transformation matrix, δ q (i-1)i For nodes i Compared to nodes i -1 displacement and rotation vector matrices.

[0118] By iterating equation (11) along the path, the virtual displacement of the system can be obtained:

[0119] (12)

[0120] Furthermore, by differentiating the position and angle vector of the node in the inertial coordinate system, the node velocity in the inertial coordinate system can be obtained as:

[0121] (13)

[0122] Where, V is the node velocity in the inertial coordinate system, C is the transformation matrix, is the node velocity in the floating coordinate system.

[0123] The basic motion equation of the system in the inertial coordinate system is:

[0124] (14)

[0125] Where, M is the generalized mass matrix, Φ is the constraint equation, λ is the Lagrange multiplier, Q It is a general force.

[0126] Substituting formula (12) into formula (14), we can obtain:

[0127] (15)

[0128] because δq With arbitrariness, the dynamic equation of the system can be obtained as:

[0129] (16)

[0130] It can be seen that the multi-flexible body system mainly describes the deformation by calculating the relative coordinates between nodes, which has a higher calculation accuracy.

[0131] During the pouring construction of self-compacting concrete, the self-compacting concrete flows in the closed and narrow space formed by the lower surface of the track slab, the upper surface of the base plate and the self-compacting formwork. Its flow will generate a large force on the track structure and the self-compacting formwork, resulting in uneven deformation of the track structure. Therefore, a multi-flexible body dynamics method is used to construct a ballastless track structure model to obtain the stress and deformation characteristics of the structure during the pouring construction process.

[0132] It should be noted that since the coarse aggregate particle size of self-compacting concrete is 10-16mm, which is close to the 14mm or 12mm diameter of the gate bars and steel mesh, the layout of the steel mesh in the enclosed space will directly affect the flow behavior of the self-compacting concrete, and thus the stress state of the track structure and formwork. To improve the simulation accuracy of the self-compacting concrete flow process, the track slab gate bars, self-compacting concrete steel mesh, and the reinforced steel mesh with limited grooves were restored according to the ballastless track design drawings. Furthermore, five sets of clamping devices were installed on the upper surface of the track slab to limit the spatial displacement of the track slab caused by the flow of self-compacting concrete. A self-compacting concrete formwork was installed between the track slab and the base plate. A pouring pipe and an overflow prevention pipe were installed at the pouring hole and observation hole respectively, and a pouring hopper was installed above the pouring pipe.

[0133] During the pouring construction process, self-compacting concrete particles will come into direct contact with the track structure, causing deformation of the track structure. Therefore, the DEM-MFBD coupling method is used to calculate the mechanical effects of self-compacting concrete particles on the track structure during the pouring process, and then a multi-scale coupling model of the pouring construction is constructed.

[0134] Similar to the contact between self-compacting concrete particles, the contact between self-compacting concrete particles and the track structure is also calculated using the Hertz-Mindlin model with the JKR contact model. Figure 16 shown.

[0135] Depend on Figure 16 It can be seen that at the contact boundary between the aggregate particles and the track plate, the particle unit and the continuous surface of the track plate are connected through spring damping, where n and trepresent the normal elastic coefficient and the tangential elastic coefficient, respectively. n and t represent the normal damping coefficient and the tangential damping coefficient, respectively. represents the friction coefficient between the particles and the flexible body, represents the surface energy between the two, Represents the normal overlap between aggregate particles and the track slab flexible body, which can be calculated by the following formula:

[0136] (17)

[0137] Where, i is the particle sphere radius, P is the node coordinate of the flexible body, O are the coordinates of the center of the sphere, n is the unit vector of the contact surface between the particle and the flexible body, is the radius of the circular contact area formed between the particle and the flexible body.

[0138] Since the aggregate particles of self-compacting concrete are composed of multiple spherical units, there is j The spherical elements are in contact with the track plate flexible body, so the normal force between the aggregate particles and the track plate flexible body is:

[0139] (18)

[0140] Similarly, the tangential force between the aggregate particles and the track slab flexible body can be obtained as:

[0141] (19)

[0142] Where, ni is the normal relative velocity between aggregate particles and the track slab flexible body, ti is the tangential relative velocity between aggregate particles and the track slab flexible body, n is the normal force between the aggregate particles and the track slab flexible body, t is the tangential force between aggregate particles and the track slab flexible body, n is the unit vector of the normal force between the aggregate particles and the track slab flexible body, t is the unit vector of the tangential force on the contact surface between aggregate particles and the track slab flexible body, j is the total number of spherical units, is the tangential force coefficient.

[0143] The above formula can be used to calculate the motion behavior of aggregate particles and track plate structure respectively. The specific coupling calculation process is as follows: Figure 17 shown.

[0144] Depend on Figure 17 It can be seen that in the discrete element module, the contact pairs between particles and between particles and continuum structures are first determined, and the contact forces between particles and between particles and structures and the motion parameters of the particle units such as velocity, acceleration, and displacement are calculated in sequence. The spatial position of the particles for this time step is then updated, and the forces between the particles and the continuum structure are then transmitted to the multi-flexible body dynamics module. In the multi-flexible body dynamics module, the forces transmitted by the discrete element are used as boundary conditions to calculate the deformation of the continuum structure. The spatial position information of the multi-flexible body structure is then updated by calculating the motion parameters of the structure. The updated spatial position of the geometric structure is then transmitted back to the discrete element calculation module, completing a calculation cycle for one time step. In the calculation process, the real-time transmission of discrete element data and multi-flexible body dynamics data, after multiple iterations, realizes the coupled calculation of the DEM-MFBD module.

[0145] For pouring construction, during the pouring construction process, the self-compacting concrete will flow from the center of the track plate along the pouring hopper and the pouring pipe into the closed space between the track plate and the base plate. During this process, the self-compacting concrete particles will directly contact the track plate, steel mesh and other components, and will also indirectly cause the buckling device to be stressed. This is very suitable for using the DEM-MFBD coupling method to calculate the interaction between the self-compacting concrete particles and the track structure. For this purpose, the DEM-MFBD coupling method is used to construct the CRTS III type slab track pouring construction coupling model, as shown in the figure. Figure 18 shown.

[0146] The coupled model for the CRTS III slab track pouring construction considers only gravity. The lower surface of the base plate is completely fixed, and simplified support devices are installed at the track plate's lifting holes to prevent the track plate from falling under its own weight. The lower portion of the clamping device is bound to the base plate, and the contact surface between the clamping device and the track plate is "hard contact" in the normal direction and friction contact in the tangential direction. Self-compacting concrete particles continuously flow from the opening above the pouring hopper, enabling simulation of the mechanical response of various track structure components during pouring construction.

[0147] The above-described embodiments merely illustrate several implementations of the present invention. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that a person skilled in the art would be able to make numerous variations and improvements without departing from the spirit of the present invention, and all such variations and improvements fall within the scope of protection of the present invention.

Claims

1. A multi-scale coupling analysis method for ballastless track pouring construction, characterized in that: include: Obtain the macroscopic flow parameters, rheological parameters and inter-particle surface energy parameters of self-compacting concrete; The macroscopic flow parameters are fitted according to the rheological parameters to obtain a first fitting equation with the rheological parameters as independent variables and the macroscopic flow parameters as dependent variables; the macroscopic flow parameters are fitted according to the inter-particle surface energy parameters to obtain a second fitting equation with the inter-particle surface energy parameters as independent variables and the macroscopic flow parameters as dependent variables; The first fitting equation and the second fitting equation are combined to obtain the correlation between the rheological parameters and the inter-particle surface energy; based on the correlation between the rheological parameters and the inter-particle surface energy, the inter-particle surface energy combination is optimized to obtain an optimized inter-particle surface energy combination; Based on the morphological characteristics of self-compacting concrete aggregate particles, the sphericity and angular index are determined, and a refined aggregate particle model is constructed based on the optimized inter-particle surface energy combination, sphericity, and angular index. Based on the flexible multi-body dynamics theory, a flexible multi-body dynamics model is constructed to characterize the interaction between the track structure and the pouring construction equipment based on their geometric characteristics. The refined aggregate particle model and the flexible multi-body dynamics model are coupled to construct a multi-scale coupling model of pouring construction that reflects the interaction between self-compacting concrete particles and the track structure. The multi-scale coupling model is then used to conduct a multi-scale mechanical analysis of the ballastless track pouring construction process, and the multi-scale coupling analysis results are obtained. The method of coupling the aggregate particle refinement model and the flexible multi-body dynamics model to construct a multi-scale coupling model of pouring construction that reflects the interaction between self-compacting concrete particles and the track structure specifically includes: Obtaining contact pairs between aggregate particles and between aggregate particles and continuum structures; Determine the contact forces between aggregate particles and between aggregate particles and the structure, as well as the motion parameters of aggregate particle units, and update the spatial positions of particles; The forces transmitted by the discrete elements are used as boundary conditions to determine the deformation of the continuum structure, and the spatial position information of the multi-flexible body structure is updated by calculating the motion parameters of the structure to complete the calculation cycle of a single time step. After multiple iterations, a multi-scale coupling model of grouting construction is obtained.

2. The multi-scale coupling analysis method for ballastless track pouring construction according to claim 1, characterized in that: The macroscopic flow parameters include slump spread and expansion time T 500 The rheological parameters include yield stress and plastic viscosity, and the inter-particle surface energy parameters include surface energy between coarse aggregate and coarse aggregate, surface energy between coarse aggregate and mortar, and surface energy between mortar and mortar.

3. The multi-scale coupling analysis method for ballastless track pouring construction according to claim 1, characterized in that: The macroscopic flow parameters are fitted according to the rheological parameters based on the following formula: ； ； in, SF is the slump spread, T 500 To extend the time, η is the plastic viscosity, τ is the yield stress; The macroscopic flow parameters are fitted according to the interparticle surface energy parameters based on the following formula: ； ； in, AA is the surface energy between coarse aggregate and coarse aggregate, AM is the surface energy between coarse aggregate and mortar, MM is the surface energy between mortar and mortar.

4. The multi-scale coupling analysis method for ballastless track pouring construction according to claim 1, characterized in that: The sphericity of the aggregate particles of self-compacting concrete is determined based on the following formula: ； in, SPH is sphericity, L is the length of the major axis of the aggregate particles, W is the median length of the aggregate particles, T is the minor axis length of the aggregate particles; The angle index is determined based on the following formula according to the aggregate particle morphology characteristics of self-compacting concrete: ； ； in, AI is the angle index, e is the angle, P ( e ) is the frequency of the angle index change value of each vertex relative to the previous vertex within the set angle range, AI i is the angle index of each view, S i is the area of ​​the projection surface of each view.

5. The multi-scale coupling analysis method for ballastless track pouring construction according to claim 4, characterized in that: It also includes normalization of sphericity and angular index based on the following formula: ； ； in, SPH * is the normalized sphericity, AI * is the normalized angle index, SPH max is the maximum value of sphericity, SPH min is the minimum value of sphericity, AI max is the maximum value of the angle index, AI min is the minimum value of the angle index.

6. The multi-scale coupling analysis method for ballastless track pouring construction according to claim 1, characterized in that: The aggregate particles are composed of multiple spherical units. j The spherical unit is in contact with the track plate flexible body, and the normal force between the aggregate particles and the track plate flexible body is: ； The tangential force between the aggregate particles and the track slab flexible body is: ； in, ni is the normal relative velocity between aggregate particles and the track slab flexible body, ti is the tangential relative velocity between aggregate particles and the track slab flexible body, n is the normal force between the aggregate particles and the track slab flexible body, t is the tangential force between aggregate particles and the track slab flexible body, is the normal overlap between aggregate particles and track slab flexible body, n is the damping coefficient in the normal direction, t is the tangential damping coefficient, n is the normal elastic coefficient, t is the tangential elastic modulus, n is the unit vector of the normal force between the aggregate particles and the track slab flexible body, t is the unit vector of the tangential force on the contact surface between aggregate particles and the track slab flexible body, j is the total number of spherical units, is the tangential force coefficient.

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