Multi-physics field coupling simulation method and system for reverse pouring of tunnel arch wall

Abstract

The application provides a kind of multi-physical field coupling simulation method and system for tunnel arch wall reverse pouring, method includes: constructing two-dimensional calculation domain and discretizing it;Adopt Herschel-Bulkley model containing thixotropy recovery mechanism and first-order differential equation to describe concrete shear stress and thixotropic evolution;Based on Arrhenius model and heat conduction equation, the coupling relationship between temperature, hydration degree and rheological parameter is established;Solve flow field by explicit projection method;Adopt VOF-PLIC algorithm to track concrete-air interface;Combine flow field and stress calculation template side pressure, and output distribution curve and extreme value;According to CFL criterion, dynamically control step length and cycle to set height or terminate;System contains modeling, material model, thermal-hydro coupling, flow field solving, interface tracking, side pressure evaluation and time control module;The application integrates multi-field coupling effect, improves the accuracy of reverse pouring whole process prediction and evaluation.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of tunnel construction simulation, and in particular to a multi-physical field coupling simulation method and system for reverse pouring of a tunnel arch wall. BACKGROUND

[0002] In the construction of tunnel lining concrete, the traditional arch wall pouring method is mostly from top to bottom or segmented pouring, and the related process and supporting design method are relatively mature, and a perfect construction specification has been formed in engineering practice. However, with the increasingly complex construction environment, in the conditions of limited terrain, narrow site or special working conditions, a reverse rapid pouring method advancing from the arch foot to the arch top has been gradually promoted in recent years. This method can significantly reduce high-altitude operation and shorten the construction period, but since the pouring direction is opposite to the traditional method, the concrete flow path, interface advancing mechanism and temperature distribution law are essentially different from the conventional working conditions, which brings new challenges to construction control and structural safety.

[0003] At the same time, the existing reverse pouring construction method lacks a professional simulation means that can truly reflect the multi-physical field coupling effect of concrete in the whole process of reverse pouring. This leads to the following problems in engineering practice:

[0004] 1. The compactness of concrete in the reverse pouring process is difficult to effectively control, and voids and cold joint defects are prone to occur;

[0005] 2. The formwork side pressure cannot be accurately predicted, resulting in overly conservative or insufficient formwork structure design;

[0006] 3. The early age temperature field prediction accuracy is low, and the temperature crack risk is difficult to evaluate and control in advance;

[0007] 4. The free liquid surface advancing form is difficult to predict, and the construction integrity and continuity cannot be effectively evaluated.

[0008] The existing simulation technical means have obvious deficiencies in multi-physical field synchronous coupling, construction dynamic process restoration and key construction parameter prediction accuracy, and cannot directly serve the construction optimization and risk prevention and control under the reverse pouring working condition. For example, the traditional free liquid surface tracking method, such as VOF or Level-set, is mostly applied to general flow working conditions, and does not consider the time-varying rheological parameters, so the accuracy of the simulation cannot be guaranteed; the conventional CAE fluid simulation process lacks integrated expression of the construction dynamic process and multi-physical field coupling effect, so the simulation prediction accuracy cannot be guaranteed.

[0009] Therefore, there is an urgent need for a multi-physical field coupling simulation method and system for reverse pouring of a tunnel arch wall, which can comprehensively consider the multi-field coupling effect of concrete and improve the accuracy of prediction and evaluation of the whole process of reverse pouring. SUMMARY

[0010] The application aims to provide a multi-physical field coupling simulation method and system for reverse pouring of a tunnel arch wall, aiming to solve the technical problem of lack of multi-physical field coupling simulation in reverse pouring, inaccurate dense degree, viscous stress tensor, lateral pressure, temperature control and interface prediction.

[0011] To achieve the above-mentioned purpose, in a first aspect, the application provides a multi-physical field coupling simulation method for reverse pouring of a tunnel arch wall, comprising the following steps:

[0012] S1, obtain the geometric parameters of the tunnel arch wall, construct a two-dimensional arch wall elevation calculation domain based on the geometric parameters, discretize the calculation domain and set boundary conditions; preferably, MAC staggered grid is used for discretization;

[0013] S2, define the concrete rheological constitutive and thixotropic evolution model: the Herschel-Bulkley model with thixotropic recovery mechanism is used to describe the shear stress behavior, and a first-order differential equation is used to characterize the recovery and destruction process of the thixotropic structure parameter;

[0014] S3, establish a coupled calculation model of temperature field and hydration kinetics: an Arrhenius type exponential model is used to describe the hydration degree evolution, and a heat conduction equation is used to consider the hydration heat release effect, and a coupling relationship of temperature, hydration degree and rheological parameter is established;

[0015] S4, solve the flow field by using the explicit projection method;

[0016] S5, use the geometric reconstruction method (Piecewise Linear Interface Calculation, PLIC) interface tracking algorithm based on the Volume of Fluid (Volume of Fluid, VOF) method to solve the space-time evolution process of the concrete-air free interface;

[0017] S6, calculate the template lateral pressure according to the flow field and stress distribution, and output the change curve and maximum value information of the lateral pressure with height;

[0018] S7, based on the CFL (Courant-Friedrichs-Lewy) stability criterion, dynamically control the time step, and cyclically execute steps S2 to S7 until the pouring simulation reaches the set height or the termination time.

[0019] As a further improvement of the above scheme, in step S1, the geometric parameters of the tunnel arch wall are obtained, including the arch foot position and spacing, the arch wall height H, the analysis width L along the wall direction, the lining thickness b, the pouring opening center coordinates and their size and quantity, the designed pouring height, the segmented pouring sequence and the single pouring amount.

[0020] As a further improvement to the above scheme, in step S1, in the MAC grid structure, pressure p, temperature T, and degree of hydration... Thixotropic structural parameters and volume fraction Arranged at the center of the grid cell, horizontal velocity The components are arranged at the center of the vertical plane of the unit, and the vertical velocity is... The components are arranged at the center of the unit's horizontal plane.

[0021] As a further improvement to the above scheme, in step S2, the shear stress model is as follows:

[0022] ;

[0023] in: Shear stress, unit: Pa;

[0024] The shear rate is calculated from the velocity gradient tensor.

[0025] Yield stress related to thixotropic structural parameters, in Pa;

[0026] The consistency coefficient (viscosity coefficient) related to the thixotropic structure parameters, in Pa·s. n ;

[0027] The liquidity index ( For shear-thinning fluids, It is of the Bingham type. (for shear-thickening fluids);

[0028] These are the parameters of the thixotropic structure. This indicates that the material structure has been fully restored and the viscosity is high. This indicates complete structural failure and maximum liquidity.

[0029] As a further improvement to the above scheme, yield stress and consistency coefficient according to They are represented as follows:

[0030] ;

[0031] ;

[0032] in All of these are material constants obtained through experimental calibration.

[0033] As a further improvement to the above scheme, in step S2, the thixotropic structural parameters... The evolution of the structure obeys the following equation:

[0034] ;

[0035] wherein: is the structure recovery coefficient, unit , indicating the speed of the structure recovering under the action of no shear;

[0036] is the shear damage coefficient, unit s, indicating the sensitivity of the shear rate to the structure damage;

[0037] The above model can reflect the characteristics of the arch foot area shear strength, structure damage, and strong fluidity, the upper part of the arch wall shear weakness, structure recovery, and fluidity decrease under the reverse pouring working condition.

[0038] As a further improvement of the above scheme, in step S3, the hydration kinetics equation is as follows:

[0039] ;

[0040] wherein: is the current hydration degree, dimensionless;

[0041] is the reference hydration rate constant before temperature correction, unit ;

[0042] is the apparent activation energy of the hydration reaction, unit J / mol;

[0043] is the gas constant, unit J / (mol·K);

[0044] is the absolute temperature, unit K;

[0045] is the final value of hydration, such as 0.8-0.9;

[0046] The temperature field satisfies the heat conduction and hydration heat coupling control equation, which is specifically as follows:

[0047] ;

[0048] wherein: is the density of concrete, unit ;

[0049] is the specific heat capacity of concrete, unit J / (kg·K);

[0050] ​ Effective thermal conductivity, unit W / (m·K);

[0051] Hydration heat release, unit , can be written as , wherein Unit mass hydration heat release potential, unit J / kg.

[0052] As a further improvement of the above solution, in step S3, the coupling relationship of the temperature, hydration degree and rheological parameter includes:

[0053] The temperature rise leads to the decrease of the concrete viscosity, which can be corrected by the following formula:

[0054] ;

[0055] , wherein Temperature sensitivity coefficient, Reference temperature;

[0056] The increase of the hydration degree makes the structure harden and the yield stress increase, which can be corrected by the following formula:

[0057] ;

[0058] , wherein Hydration strengthening coefficient;

[0059] Through the above modification, the strong coupling link of "temperature-hydration-rheology" is formed, and the comprehensive reflection of the early age performance evolution is realized.

[0060] As a further improvement of the above solution, in step S4, the step method of solving the flow field by using the explicit projection method is as follows:

[0061] S41, predicting the velocity field:

[0062] Under the premise that the velocity , apparent viscosity and shear stress of the previous time step are known, the predicted velocity without pressure term is calculated:

[0063] ;

[0064] , wherein: Time step, unit s;

[0065] Spatial convection term, preferably using first-order upwind difference or second-order MUSCL format to discretize;

[0066] σ nThe viscous stress tensor at the nth time step is given by the Herschel-Bulkley model, with units of Pa;

[0067] is the gravity acceleration vector, with units of ;

[0068] S42, solve the pressure Poisson equation:

[0069] To satisfy the incompressibility condition , the pressure Poisson equation is constructed as follows:

[0070] ;

[0071] where is the Laplace operator, preferably discretized using the five-point difference format on the MAC grid, and the pressure unknown is solved by Jacobi or Gauss-Seidel iteration.

[0072] S42, velocity correction:

[0073] After obtaining , the predicted velocity is corrected by projection as follows:

[0074] ;

[0075] where, Central difference is used for calculation, so that the corrected velocity field satisfies the mass conservation condition.

[0076] As a further improvement of the above scheme, in step S5, the step method for solving the space-time evolution process of the concrete-air free interface is as follows:

[0077] S51, the interface transport equation is as follows:

[0078] ;

[0079] where is the volume fraction of the concrete phase, is the velocity field at the current time step;

[0080] S52, at each time step, the volume fraction flux is calculated along each grid surface, and is updated, and the PLIC method is used for the elements of , according to the local gradient to reconstruct the linear interface, to obtain the geometric position and shape of the free surface;

[0081] S53, from The distribution calculation obtains: the average height of the free surface and the local rising velocity; the time and interface form of the left and right arch foot jets converging in the middle; and the volume ratio of the concrete in the wall.

[0082] As a further improvement of the above scheme, in step S6, the template side pressure The calculation formula is as follows:

[0083] ;

[0084] Wherein, P is the static pressure obtained in the unit, unit Pa;

[0085] σ is the viscous stress tensor;

[0086] is the outer normal vector of the template;

[0087] σ xy ,σ yy is the component of the viscous stress tensor;

[0088] is the equivalent side pressure acting on the template;

[0089] The distribution along the height direction of the arch wall is extracted The curve of the template side pressure changing with the height is drawn, and the maximum side pressure value and the corresponding height are output, which provides a quantitative basis for the template design, support system configuration and construction safety evaluation.

[0090] As a further improvement of the above scheme, in step S7, in order to ensure the numerical stability of the explicit time marching process, the time step is dynamically controlled according to the CFL condition, and the specific form is as follows:

[0091] ;

[0092] Wherein: is the Courant number safety factor, usually 0.2-0.5;

[0093] is the grid size;

[0094] is the maximum absolute value of the current time step velocity component;

[0095] is the maximum value of the global apparent viscosity.

[0096] Secondly, the application further provides a multi-physical field coupling simulation system for tunnel arch wall reverse pouring, which adopts the multi-physical field coupling simulation method for tunnel arch wall reverse pouring provided in the first aspect, and comprises:

[0097] a modeling module for establishing a two-dimensional calculation domain according to tunnel geometric parameters and discretizing the calculation domain and applying boundary conditions;

[0098] a material model module for implementing a Herschel-Bulkley rheological model with thixotropic recovery and a thixotropic evolution equation;

[0099] a thermal-hydric coupling module for calculating the interaction of hydration reaction and temperature field and the influence on rheological properties;

[0100] a flow field solving module for performing explicit solving of velocity field and pressure field based on a projection method;

[0101] an interface tracking module for simulating the change of a concrete-air interface by using a VOF-PLIC method;

[0102] a side pressure evaluation module for calculating the stress distribution of a formwork and outputting a pressure curve and an extreme value;

[0103] a time control module for dynamically adjusting a simulation step length according to a CFL condition and driving the modules to cooperatively operate until the simulation of the pouring process is completed.

[0104] Due to the above technical scheme, the present application has the beneficial effects as follows:

[0105] The present application provides a multi-physical field coupling simulation method for reverse pouring of a tunnel arch wall, which integrates a Herschel-Bulkley rheological model with a thixotropic recovery mechanism, a VOF-PLIC interface tracking algorithm, a temperature-hydric dynamics coupling model and formwork side pressure calculation in the same explicit time advancing framework, and constructs a CAE calculation process specially for arch wall reverse rapid pouring conditions. This CAE calculation process realizes closed-loop simulation from geometric modeling, material constitutive definition, field coupling solving to construction parameter output, can systematically reflect the interaction of flow field, temperature field and stress field in the reverse pouring process, and thus makes up for the lack of multi-physical field coupling simulation in the prior art.

[0106] Specifically, firstly, the present application can improve the prediction accuracy of fresh concrete fluidity and compactness. Since the Herschel-Bulkley model with a thixotropic recovery mechanism is adopted, and a first-order differential equation describing the recovery and destruction of structural parameters is introduced into the model, the spatiotemporal reconstruction behavior of thixotropic structure can be depicted according to different conditions of high shear at the arch foot and low shear on the upper segment of the arch wall. In combination with the concrete-air free interface evolution information obtained by the VOF-PLIC interface tracking (step S5), the flow front, filling state and possible void defects of concrete in the reverse pouring process can be accurately predicted, so as to improve the prediction reliability of compactness.

[0107] Secondly, the present application can realize temperature-hydration-rheology three-field strong coupling, and improve the prediction accuracy of lateral pressure and temperature control. Through the Arrhenius-type hydration kinetics equation and the heat conduction equation, and the temperature rise caused by hydration heat feedback to the rheological parameter correction, a closed-loop coupling mechanism of "temperature rise → hydration acceleration → yield stress and viscosity change" is formed. This mechanism can reflect the temperature gradient formed by hydration heat of early-age concrete and its influence on rheological property and formwork lateral pressure, so that the peak value of lateral pressure at different pouring stages and its distribution along the height can be more accurately predicted, which helps to optimize the formwork design and construction safety control.

[0108] Furthermore, the present application can accurately capture the free interface evolution and confluence characteristics of double-arch-foot reverse pouring. The VOF equation combined with PLIC geometric reconstruction can track the concrete-air interface of synchronous injection of left and right arch feet in real time under the explicit solution framework, and obtain the free surface shape, rising speed and spatiotemporal information of the confluence of the two streams in the middle. This technical feature solves the problem that the traditional method cannot predict the intersection position and time of the reverse pouring interface, and can provide quantitative basis for preventing cold joints and ensuring continuous pouring quality.

[0109] In addition, the present application can also improve the numerical stability and calculation efficiency. By dynamically controlling the time step based on the CFL stability criterion, and discretizing the calculation domain on the MAC staggered grid, the numerical divergence caused by improper step length can be avoided while ensuring the accuracy of the explicit projection method for solving the flow field, so that the simulation of long-time pouring process is stable and efficient, which is suitable for rapid iteration and scheme comparison in engineering application.

[0110] Through the organic combination of the above technical features, the present application forms a multi-physical field coupling simulation method that can simultaneously consider rheology, temperature, hydration and interface behavior, effectively improves the accuracy of density, lateral pressure, temperature control and interface prediction in the reverse pouring process of tunnel arch wall, and provides a reliable analysis tool for construction parameter optimization and safety control. BRIEF DESCRIPTION OF DRAWINGS

[0111] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or prior art description. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can also be obtained by those skilled in the art without creative labor based on the drawings shown.

[0112] Figure 1 A flowchart of a multi-physical field coupling simulation method for reverse pouring of tunnel arch wall according to the present application is shown in the figure.

[0113] Figure 2A MAC grid and variable arrangement schematic disclosed by the present application;

[0114] Figure 3 A VOF-PLIC free surface tracking schematic disclosed by the present application;

[0115] Figure 4 A temperature-hydration-rheology coupling relationship schematic disclosed by the present application;

[0116] Figure 5 A pouring geometry model and boundary condition schematic disclosed by the present application;

[0117] Figure 6 A Meizhou City, Guangdong Province, Changtian tunnel modeling area schematic disclosed by the present application, wherein Figure 6 (a) is a tunnel cross-section schematic, Figure 6 (b) is a single-sided arch wall analysis area schematic;

[0118] Figure 7 A curve schematic of the free surface height changing with time in the process of the reverse pouring simulation of the Meizhou City, Guangdong Province, Changtian tunnel disclosed by the present application;

[0119] Figure 8 A velocity field schematic of the t = 1.0h moment in the process of the reverse pouring simulation of the Meizhou City, Guangdong Province, Changtian tunnel disclosed by the present application;

[0120] Figure 9 A temperature field schematic of the t = 1.0h moment in the process of the reverse pouring simulation of the Meizhou City, Guangdong Province, Changtian tunnel disclosed by the present application;

[0121] Figure 10 A hydration degree distribution schematic of the t = 1.0h moment in the process of the reverse pouring simulation of the Meizhou City, Guangdong Province, Changtian tunnel disclosed by the present application;

[0122] Figure 11 A thixotropic structure parameter distribution schematic of the t = 1.0h moment in the process of the reverse pouring simulation of the Meizhou City, Guangdong Province, Changtian tunnel disclosed by the present application;

[0123] Figure 12 A formwork side pressure distribution schematic of the t = 1.0h moment in the process of the reverse pouring simulation of the Meizhou City, Guangdong Province, Changtian tunnel disclosed by the present application.

[0124] The purposes, functional features and advantages of the present application will be further described with reference to the embodiments and the accompanying drawings. DETAILED DESCRIPTION

[0125] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art without creative effort should fall within the protection scope of the present application.

[0126] It should be noted that the technical solutions among the various embodiments of the present application can be combined with each other, but it must be based on the fact that a person of ordinary skill in the art can realize the combination, and when the combination of the technical solutions appears contradictory or unachievable, it should be considered that the combination of the technical solutions does not exist and is not within the protection scope of the present application.

[0127] Embodiment 1

[0128] Referring to Figures 1-5 , the present application provides a multi-physical field coupling simulation method for reverse pouring of a tunnel arch wall, and steps of the method include:

[0129] S1, constructing a calculation domain and discretizing:

[0130] First, geometric parameters of the tunnel arch wall are obtained, and a calculation domain of the arch wall elevation is established in a two-dimensional plane according to the parameters (the height is H, the width L is taken along the wall, and the bottom edge is the arch foot line), and corresponding boundary conditions are set according to the actual construction boundary. In order to improve the numerical stability and accuracy, the MAC (Marker-and-Cell) staggered grid is preferably used to discretize the calculation domain, so that the velocity component and the pressure are arranged staggeredly at the grid nodes, which is convenient for mass conservation control when the subsequent explicit projection method is solved. This method can reduce numerical oscillation and ensure the stability and calculation efficiency of long-time pouring simulation.

[0131] In this embodiment, geometric parameters of the tunnel arch wall are obtained, including arch foot position and spacing, arch wall height H, analysis width L along the wall, lining thickness b, pouring port center coordinates and their size and quantity, designed pouring height, segmented pouring sequence and single pouring amount.

[0132] In the MAC grid structure, the pressure p, the temperature T, the hydration degree , the thixotropic structure parameter and the volume fraction are arranged at the center of the grid element, the horizontal velocity component is arranged at the center of the vertical surface of the element, and the vertical velocity component is arranged at the center of the horizontal surface of the element. Wherein: The unit of p is Pa; is the absolute temperature, the unit is K; is the dimensionless hydration degree, the value is 0~ ; is a dimensionless thixotropic structure parameter, taking value 0-1; is the volume fraction of concrete in the element, taking value 0 (air) -1 (completely filled with concrete). MAC staggered arrangement can effectively suppress numerical oscillation caused by pressure-velocity coupling, and improve the stability of free surface and pressure field solution. The boundary conditions are set as follows: at the arch foot pouring opening, the vertical inlet velocity is given and the mold temperature , the VOF value ; no slip condition , the temperature is treated according to the convective heat transfer condition; the upper opening adopts atmospheric pressure boundary.

[0133] S2, define the rheological constitutive and thixotropic evolution model of concrete:

[0134] In view of the characteristics that the concrete undergoes high shear (arch foot) and low shear (upper segment of arch wall) alternately in the reverse pouring process, the Herschel-Bulkley model with thixotropic recovery mechanism is used to describe the shear stress behavior, and the yield stress and apparent viscosity of which evolve with the thixotropic structure parameter, hydration degree and temperature. Further, the "recovery-damage" process of thixotropic structure is described by a first-order differential equation, so as to reflect the reconstruction and disintegration of the structure network of fresh concrete in time and space. This model can more truly predict the change of the fluidity of concrete at different pouring stages, help to improve the prediction accuracy of the compactness, and reduce the risk of voids or cold joints caused by the deviation of rheological property estimation.

[0135] S3, establish a coupled calculation model of temperature field and hydration kinetics:

[0136] According to the hydration reaction law of concrete, the Arrhenius type exponential model is used to calculate the evolution of hydration degree with time, and the temperature rise effect caused by hydration heat release is taken into account by combining with the heat conduction equation, to establish the coupling relationship between temperature field, hydration degree and rheological parameters, see Figure 4 . Specifically, the hydration heat release is taken as a heat source into the heat conduction equation, and after the temperature distribution is obtained, the yield stress and viscosity parameters of the Herschel-Bulkley model are feedback corrected, so as to form a closed loop coupling mechanism of "temperature rise→hydration acceleration→rheological property change". This way can reflect the temperature gradient of early age concrete and its influence on the hardening process and formwork side pressure, so as to improve the accuracy of temperature control and side pressure prediction.

[0137] S4, solve the flow field by using explicit projection method:

[0138] After the definition of the coupling relationship between the constitutive model and the field, the explicit projection method is used to solve the Navier-Stokes equation for time advancement to obtain the velocity field and pressure field distribution at each time. The explicit format is easy to synchronize with the VOF-PLIC interface tracking and thixotropic evolution equation, and can well maintain mass conservation with the MAC grid, and is suitable for numerical simulation of concrete reverse casting with large deformation and free surface flow.

[0139] S5, solve the free interface using VOF-PLIC interface tracking algorithm:

[0140] For the working condition of synchronous reverse casting of left and right arch feet, the volume fraction method (VOF) is combined with the piecewise linear interface calculation (PLIC) geometric reconstruction method to track the space-time of the concrete-air free interface. This method obtains the volume fraction distribution by solving the VOF transport equation, and then uses PLIC to geometrically reconstruct the interface to obtain the position, shape, rising speed of the free liquid surface, and the time and position of the convergence of the two streams in the middle, see Figure 3 Such a setting can accurately predict the advancement process of the casting interface, provide a basis for judging whether there is a cold joint and evaluating the filling uniformity, and further improve the engineering reliability of the density prediction.

[0141] S6, calculate the template side pressure and output the results:

[0142] Based on the flow field and corresponding stress distribution obtained in step S4, the side pressure of the template is calculated according to the superposition principle of fluid statics and dynamics, and the curve of the side pressure with the casting height is drawn, and the maximum value information is extracted. Since the side pressure is affected by the coupling of rheological properties, temperature field and interface shape, this method can accurately reflect the maximum side pressure and its distribution trend under different working conditions, thereby providing quantitative reference for template strength design and construction safety control.

[0143] S7, dynamically control the time step and loop calculation:

[0144] In order to ensure the stability of numerical calculation, the time step is dynamically determined according to the CFL (Courant-Friedrichs-Lewy) stability criterion, so that the explicit solution process meets the accuracy requirements while avoiding divergence. Then steps S2 to S7 are executed in a loop to continuously update the hydration degree, temperature, rheological parameters, flow field and interface position until the simulated casting height reaches the set value or the calculation time is reached. This method can maintain stable and efficient operation in long-time casting simulation, facilitating rapid iteration and comparative analysis of engineering schemes.

[0145] Through the organic combination of the above steps, the embodiment realizes the multi-physical field coupling simulation for the reverse pouring of the tunnel arch wall: the Herschel-Bulkley rheological model containing the thixotropic recovery, the VOF-PLIC interface tracking, the temperature-hydration dynamics coupling and the template side pressure calculation are unified in the explicit time advancement framework, and a complete CAE calculation process is formed. This process can synchronously reflect the interaction of the flow field, the temperature field, the stress field and the free interface, effectively overcomes the problem of the lack of multi-physical field coupling in the prior art, significantly improves the prediction accuracy of the dense degree, the side pressure, the temperature control and the interface position, and can guide the template design and the construction parameter optimization.

[0146] As a preferred embodiment, the shear constitutive and thixotropic evolution process of the fresh concrete are defined and calculated in the following manner during the implementation of the embodiment, so as to solve the problem of inaccurate prediction of fluidity and dense degree caused by the difference in the shear environment in the reverse pouring process.

[0147] S21, the Herschel-Bulkley model with a thixotropic recovery mechanism is adopted:

[0148] In step S2, the Herschel-Bulkley (HB) model with a thixotropic recovery mechanism is selected to describe the shear stress behavior of the fresh concrete, and the expression is as follows:

[0149] ;

[0150] Wherein: is the shear stress, with the unit of Pa;

[0151] is the shear rate, which is calculated from the velocity gradient tensor, with the unit of s -1 ;

[0152] is the yield stress related to the thixotropic structure parameter , with the unit of Pa;

[0153] is the consistency coefficient (viscosity coefficient) related to the thixotropic structure parameter , with the unit of Pa· ;

[0154] is the flow index is a shear thinning fluid, is a Bingham type, is a shear thickening fluid;

[0155] is the thixotropic structure parameter, indicates that the material structure is completely recovered, and the viscosity is high, represents complete structure destruction and the highest fluidity.

[0156] S22, parametric expression of yield stress and consistency coefficient:

[0157] To introduce the structure parameter λ into the constitutive relation, the embodiment further expresses the yield stress and the consistency coefficient as follows:

[0158] ;

[0159] ;

[0160] wherein are material constants calibrated by indoor rheological test. This expression makes the yield stress and the viscosity change continuously with the change of the thixotropic structure state, and can reflect the response of the concrete under different shear histories in numerical calculation.

[0161] S23, evolution equation of thixotropic structure parameter:

[0162] To depict the evolution of the structure parameter λ in time and space, the embodiment introduces the following first-order differential equation in step S2:

[0163] ;

[0164] wherein: is the structure recovery coefficient, with the unit , representing the speed of the structure recovery under no shear action;

[0165] is the shear damage coefficient, with the unit s, representing the sensitivity of the shear rate to the structure damage;

[0166] It can be known from the above that: when the shear rate is large (such as the arch foot area), the second term dominates, λ decreases rapidly, the structure damage is intensified, and the concrete shows low yield stress and low viscosity, i.e. the fluidity is enhanced; when the shear rate is small (such as the upper part of the arch wall), the first term A(1-λ) plays a significant role, λ gradually increases, the structure tends to recover, the viscosity rises, and the fluidity decreases.

[0167] ​​By introducing the specific expressions and evolution equations described above, the rheological model in this embodiment can accurately reflect the spatial shear differences under reverse casting conditions, thereby enabling precise prediction of concrete flowability changes with time and location in numerical simulations. Combined with subsequent VOF-PLIC interface tracking and lateral pressure calculations, it can effectively improve the accuracy of determining compactness during casting and reduce the risk of voids or cold joints caused by errors in flowability estimation. Furthermore, after coupling this model with temperature-hydration kinetics, the temperature rise caused by hydration exothermics can be fed back to… and The revision further improves the reliability of side pressure and temperature control analysis.

[0168] As a preferred embodiment, this embodiment establishes a coupled model in the following manner to overcome the problem that it is difficult to accurately predict the mutual influence of temperature gradient, hydration process and rheological properties of early-age concrete in reverse casting, thereby improving the reliability of temperature control, lateral pressure and compaction analysis.

[0169] S31. Hydration kinetic equation: The evolution of hydration degree over time is described using an Arrhenius-type exponential model, which takes the following form:

[0170] ;

[0171] in: The current degree of hydration is dimensionless.

[0172] The reference hydration rate constant before temperature correction, in units of ;

[0173] The apparent activation energy of the hydration reaction is expressed in J / mol.

[0174] is the gas constant, with units of J / (mol·K);

[0175] Absolute temperature, unit K;

[0176] This represents the final hydration value, such as 0.8–0.9.

[0177] The above equations demonstrate the significant effect of temperature on the hydration rate. Increased temperature accelerates the hydration reaction process, thus numerically creating a direct coupling between the temperature field and the degree of hydration.

[0178] S32. Early-age temperature field governing equations: The temperature field is jointly determined by heat conduction and heat release from hydration, satisfying the following coupled equations:

[0179] ;

[0180] wherein: is the density of concrete, unit ;

[0181] is the specific heat capacity of concrete, unit J / (kg·K);

[0182] is the effective thermal conductivity, unit W / (m·K);

[0183] is the hydration heat release term, unit , which can be written as wherein is the specific hydration heat release potential, unit J / kg;

[0184] The above equation converts the hydration kinetics calculated into a heat source term introduced into the heat conduction process, so as to reflect the temperature gradient formed inside the pouring body due to hydration heat release and its development over time.

[0185] S33, Coupling relationship of temperature, hydration and rheological parameters: in order to form a strong coupling link of “temperature-hydration-rheology”, the following correction relationship is further established in the embodiment:

[0186] Influence of temperature on rheological parameters: temperature rise will reduce the viscosity of concrete, and the following correction is adopted: ;

[0187] wherein is the temperature sensitivity coefficient, is the reference temperature; the correction makes the temperature rise caused by hydration heat release be able to be fed back to the consistency coefficient of Herschel-Bulkley model, thereby affecting the flow resistance and lateral pressure distribution.

[0188] Influence of hydration degree on rheological parameters: with the hydration, the concrete structure gradually hardens, and the yield stress increases, which is expressed as:

[0189] ;

[0190] wherein is the hydration strengthening coefficient; the relationship introduces the hydration degree into the yield stress calculation, so that the hardening process is embodied in numerical simulation.

[0191] Through the above modification, a strong coupling link of “temperature-hydration-rheology” is formed, and comprehensive reflection on the evolution of early age performance is realized.

[0192] By the modeling of S31-S33, the strong coupling of temperature field, hydration kinetics and rheological properties is realized in this embodiment: the hydration heat is included in the heat conduction calculation, which can accurately predict the temperature distribution and gradient change in the early age concrete; the temperature change directly affects the viscosity through exponential correction, and the hydration degree increases the yield stress, both of which change the flow and filling performance of concrete; the closed-loop coupling mechanism can reflect the chain reaction of "temperature rise → hydration acceleration → yield stress and viscosity evolution", so as to more realistically reproduce the side pressure change and interface advancing characteristics caused by hydration heat and structure hardening in the reverse casting process. Combined with the thixotropic HB model in step S2 and the side pressure calculation in step S6, this coupling method significantly improves the accuracy of temperature control and side pressure prediction, and helps to predict the influence of local flow difference caused by temperature gradient on the dense degree, providing a feasible numerical way to solve the problems of multi-physical field coupling simulation and inaccurate key parameter prediction in reverse casting.

[0193] As a preferred embodiment, to further clarify the implementation details of the explicit projection method in step S4, this embodiment combines the numerical characteristics of the reverse casting condition and completes the flow field solution in the following order to ensure that the calculation stability and mass conservation are considered on the premise of not introducing excessive complexity, thereby improving the prediction accuracy of the formwork side pressure, interface advancing and dense degree.

[0194] S41, predict the velocity field:

[0195] On the basis of the known velocity , apparent viscosity and shear stress at the last time step, the predicted velocity without pressure term is calculated first, and the discrete momentum equation is:

[0196] ;

[0197] Wherein: is the time step, unit s;

[0198] is the spatial convection term, and this embodiment preferably adopts first-order upwind difference or second-order MUSCL format for discretization to suppress numerical oscillation caused by convection dominance;

[0199] σ n is the viscous stress tensor given by the Herschel-Bulkley model at the nth time step, unit Pa;

[0200] is the gravity acceleration vector, unit ;

[0201] This step realizes the explicit promotion of inertia, convection, viscous shear and gravity, and provides a basic field for subsequent pressure correction.

[0202] S42, solve the pressure Poisson equation:

[0203] To meet the incompressible condition , the pressure Poisson equation needs to be constructed and solved, as follows:

[0204] ;

[0205] Where is the Laplace operator, and the five-point difference format is preferred for discretization on the MAC staggered grid, which can improve the discretization accuracy and facilitate boundary condition processing;

[0206] The pressure unknown is solved by Jacobi or Gauss-Seidel iteration until the residual satisfies the set convergence criterion.

[0207] The role of this step is to adjust the predicted velocity through the pressure field to satisfy the continuity equation, thereby avoiding numerical divergence and accurately reflecting the changes in lateral pressure due to flow restriction during the reverse pouring process.

[0208] S42, velocity correction:

[0209] After obtaining , the predicted velocity is projected and corrected according to the following formula:

[0210] ;

[0211] Where, Central difference calculation is adopted to ensure that the velocity field after correction has second-order accuracy in space and strictly satisfies mass conservation.

[0212] Through the above three-step explicit projection method, this embodiment realizes stable solution of the Navier-Stokes equation on the MAC staggered grid. The prediction step clearly shows the contribution of inertia, viscosity and gravity, which can accurately capture the difference between high flow velocity at the arch foot and slow flow at the upper section of the arch wall during reverse pouring; the solution of the pressure Poisson equation ensures the mass conservation of the velocity field, making the template lateral pressure calculated from the flow field (step S6) more reliable; the combination of explicit format and CFL dynamic time step control (step S7) can maintain numerical stability under conditions of large deformation and free surface flow, avoiding non-physical oscillation.

[0213] The above-mentioned embodiments can effectively improve the accuracy and stability of the flow field calculation, and cooperate with the thixotropic HB model in step S2 and the temperature-hydration-rheology coupling model in step S3, enabling the overall simulation method to more accurately predict the compaction degree, lateral pressure distribution, and interface advancement during the reverse pouring process, thereby directly providing a feasible numerical solution for the technical problems of "lack of multi-physics field coupling simulation and inaccurate prediction of relevant parameters".

[0214] As a preferred embodiment, to further clarify the calculation method of the spatio-temporal evolution of the concrete-air free interface in step S5, in this embodiment, for the working condition of synchronous feeding at the left and right springing of the reverse pouring, the interface tracking is implemented in the following order to improve the prediction accuracy of the interface advancement, material flow confluence, and filling state, thereby improving the judgment of the compaction degree and cold joint risk.

[0215] S51. Interface transport equation: The volume fraction method is used to describe the distribution of the concrete phase in the grid cell, and its interface transport equation is:

[0216] ;

[0217] where is the volume fraction of the concrete phase. F = 1 indicates that the cell is filled with concrete, F = 0 indicates that it is all air, and 0 < F < 1 indicates that there is an interface in the cell; u is the velocity field at the current time step, obtained by the explicit projection method in step S4. The above equation tracks the overall position of the concrete-air interface through convective transport and can adapt to the drastic deformation of the free surface during the reverse pouring process.

[0218] S52. Volume fraction update and PLIC interface reconstruction:

[0219] Within each time step, first calculate the volume fraction flux on each grid surface and update the distribution accordingly. For the mixed cells with 0 < F < 1, the Piecewise Linear Interface Calculation (PLIC) method is used for geometric reconstruction: Based on the local volume fraction gradient fit the plane equation of the interface within the cell to obtain the precise geometric position and shape of the interface.

[0220] Compared with the approximation that only depends on the volume fraction, PLIC can retain the interface curvature and normal information with higher accuracy, reduce the interface diffusion error; and can clearly present the confluence process of the jets at the left and right springing in the middle, providing an intuitive basis for judging whether there is a cold joint.

[0221] S53. Interface and filling state parameter extraction; Based on the updated distribution, the following can be quantitatively calculated:

[0222] Free surface average height and local rising velocity: The top position of the statistical concrete occupied unit is obtained to get the average height of the liquid surface and its rate of change along the height direction of the arch wall, reflecting the overall trend of the pouring front advance;

[0223] Time and interface morphology of left and right arch foot jets converging in the middle: Identify the time when the two sides of the flow volume fraction front meet for the first time in the middle of the wall and the corresponding interface shape, which can be used to evaluate the continuity of the double flow lap joint;

[0224] Volume ratio of concrete in the wall: integral The total volume ratio of the poured concrete is obtained, which helps to judge the pouring progress and dense filling degree.

[0225] This embodiment realizes high-precision tracking of the concrete-air free interface in the explicit time marching framework. Specifically, the VOF equation ensures the conservation of the overall convection transport of the interface, and the PLIC reconstruction retains the geometric details of the interface. The combination of the two can accurately predict the free surface morphology, rising velocity and convergence characteristics of the left and right arch foot flows in the middle; The obtained interface and filling parameters can be directly used to evaluate the dense degree in the reverse pouring process, and the cold joint or hollow defects that may be formed due to the delayed flow lap joint can be found in advance; The touch HB model of step S2, the temperature-hydration-rheological coupling model of step S3 and the calculation of step S6 side pressure are connected, so that the simulation method can reflect the mutual influence of rheology, thermodynamics and interface behavior in the same calculation process, thereby effectively solving the problems of missing multi-physical field coupling simulation and inaccurate prediction of key parameters in the prior art, and providing reliable numerical basis for template design, construction parameter optimization and quality control.

[0226] As a preferred embodiment, for the calculation of the template side pressure in step S6, this embodiment further gives the specific mechanical model and implementation method, so as to accurately obtain the distribution of the side pressure along the height of the arch wall in the reverse pouring simulation, thereby overcoming the problem of inaccurate side pressure prediction in the prior art and providing quantitative basis for template design and construction safety control.

[0227] S61, template side pressure calculation:

[0228] On the basis of the completed flow field and stress field solution, according to the static pressure P and viscous stress tensor σ in the unit, the equivalent side pressure acting on the unit template area is calculated according to the following formula :

[0229] ;

[0230] Wherein, P is the static pressure obtained in the unit, unit Pa;

[0231] σ is the viscous stress tensor, calculated by the Herschel-Bulkley constitutive model in step S2;

[0232] is the outer normal unit vector of the formwork;

[0233] σ xy ,σ yy is the component of the viscous stress tensor in the local coordinate system of the formwork;

[0234] is the equivalent lateral pressure acting on the formwork;

[0235] The lateral pressure of the formwork is composed of the combined effects of the hydrostatic pressure and the viscous shear stress in the normal direction, which can reflect the combined effects of the dynamic pressure and viscous resistance on the lateral formwork during the reverse pouring process due to the flow of concrete.

[0236] S62, lateral pressure distribution extraction and output:

[0237] In the direction of the arch wall height (y direction), the lateral pressure distribution is extracted cell by cell to form the curve of the lateral pressure change with height, and the maximum lateral pressure value and its corresponding height position are determined. This data can be directly used for:

[0238] Formwork structure strength and stiffness design to ensure the safety of the formwork under the maximum lateral pressure;

[0239] Support system arrangement and reinforcement scheme development to reasonably distribute the load;

[0240] Safety evaluation and monitoring of the construction process to prevent structural instability or formwork explosion risk caused by lateral pressure overrun.

[0241] Since the calculation combines the static pressure and viscous shear stress and takes into account the directionality of the outer normal of the formwork, it can more realistically reflect the differences in the effects of the flow state of concrete at different heights on the lateral formwork during the reverse pouring process.

[0242] As a preferred embodiment, for the numerical stability control of the explicit time marching process in step S7, this embodiment uses the CFL stability criterion to dynamically determine the time step Δt to avoid numerical divergence caused by excessively large step size, ensuring the stability and controllability of the calculation in long-time reverse pouring simulation, thereby supporting the reliability of the results of multi-physical field coupling.

[0243] In the calculation steps that need to be synchronized, such as explicit projection method and thixotropic evolution solution, the time step Δt must satisfy the following CFL condition:

[0244] :

[0245] where: Courant number safety factor, usually taken as 0.2-0.5, to leave enough numerical stability margin; Size of the computational domain grid in x, y direction; Maximum absolute value of the current time step velocity component, reflecting the fastest scale of convection transport; Maximum value of the global apparent viscosity, derived from the Herschel-Bulkley model calculation results, Density of concrete.

[0246] The three terms of the above formula correspond to the limiting conditions of convection stability, cross-grid propagation time and viscous diffusion stability respectively, and the minimum value is multiplied by the safety factor to obtain the maximum Δt allowed for this time step.

[0247] At the beginning of each cycle, the , and are calculated in real time according to the above formula, and the step length is used to advance the solution of steps S2-S6. In this way, under the premise of ensuring the stability of the explicit format, the largest step length is used as much as possible to improve the calculation efficiency.

[0248] To further illustrate the inventive concept of the present application, see Figures 6-12 , combined with specific application scenarios.

[0249] I. Geometry modeling and boundary condition setting:

[0250] Taking the Changtian Tunnel project in Meizhou City, Guangdong Province as the application background, see Figure 6 , a two-dimensional arch wall facade calculation domain with a height of 5.0m and a width of 6.0m is constructed, and the left wall is selected as the analysis area. The wall thickness is processed as two-dimensional unit thickness, the bottom edge = arch foot position (as pouring inlet), the left and right sides are formwork or initial support side wall, and the top edge is the arch top free surface.

[0251] See Figure 7 , 121x101 MAC staggered grid is used for discretization, in which pressure p, temperature T, hydration degree α, thixotropic parameter λ and volume fraction VOF(F) are arranged at the center of the element, and velocity components u, v are arranged at the vertical edge and horizontal edge of the element respectively, to avoid pressure oscillation and improve the stability of coupled fields.

[0252] The boundary conditions are set as shown in the following table:

[0253] ;

[0254] II. Material model and physical property parameter setting:

[0255] 1. Basic material properties of concrete: density p = 2350 kg / m3, specific heat c = 900 J / kg-K, thermal conductivity k = 1.7 W / m-K.

[0256] 2. Herschel-Bulkley thixotropic constitutive model: shear stress is expressed as wherein τ y0 = 100 Pa, K0= 18 Pa-s n , n = 0.45; the evolution equation of thixotropic structure parameter l is , the restitution coefficient = 0.20 s -1 , the failure coefficient = 1.8.

[0257] 3. Hydration kinetics model: Arrhenius type equation is used wherein = 3 x 10 4 , E = 40 kJ / mol, = 0.85.

[0258] 4. Temperature field control equation: , hydration heat source , hydration latent heat H h = 280 kJ / kg.

[0259] III. Explicit time advancing calculation process:

[0260] Step S1, initialization of calculation domain:

[0261] Generate a two-dimensional geometric model and MAC grid, initialize the velocity field, temperature field, hydration degree and thixotropic parameters.

[0262] Step S2, shear rate calculation:

[0263] Calculate the shear rate based on the velocity gradient tensor , which provides input for thixotropic model updating.

[0264] Step S3, thixotropic structure parameter l n+1 updating:

[0265] Update the l distribution according to the evolution equation . See Figure 11 , the simulation results show that the l in the high shear zone of the arch foot decreases to 0.1-0.3 (structure failure), and the l in the upper low shear zone recovers to 0.95-1.0, reflecting the spatio-temporal differentiation characteristics of "shear failure-structure recovery".

[0266] Step S4, hydration degree a evolution calculation:

[0267] Through Arrhenius model Update hydration degree for temperature field and rheological parameter coupling calculation, see Figure 10 .

[0268] Step S5, rheological parameter correction:

[0269] Update yield stress according to λ and α And consistency coefficient , where C1=1.2, C2=2.6.

[0270] Step S6, flow field solution (explicit projection method):

[0271] Predicted velocity: ;

[0272] Pressure Poisson equation: Solved by Jacobi iteration;

[0273] Velocity correction: .

[0274] Step S7, VOF-PLIC interface tracking:

[0275] Solve volume fraction transport equation And use PLIC geometric reconstruction interface to extract free liquid surface height h(t). See Figure 7 , simulation results show that the liquid surface rises nearly linearly in the early stage (0-1h), and the increase slows down in the later stage due to thixotropic recovery, and finally stabilizes at the vault height of 5m.

[0276] Step S8, temperature field update:

[0277] Calculate temperature distribution through heat conduction and hydration exothermic coupling equation See Figure 9 , the simulation presents a layered trend of "hot at the bottom and cold at the top", with the bottom temperature rising to 28-29℃ and the hydration degree reaching 0.25-0.30.

[0278] Step S9, side pressure extraction and output:

[0279] Calculate the side pressure of the template according to the formula Generate a height distribution curve. See Figure 12 , in the simulation of Changtian Tunnel, the maximum side pressure is 60-65kPa, and it rises approximately linearly in the range of 0-2m depth. Thixotropic recovery leads to a significant decrease in the upper side pressure.

[0280] Four, time step control and loop termination:

[0281] The time step is dynamically controlled based on the CFL stability criterion to ensure the numerical stability of the explicit solution process. Steps S2 to S9 are executed in a loop until the pouring height reaches 5m or the simulation time is terminated.

[0282] Embodiment 2

[0283] The application also provides a multi-physical field coupling simulation system for reverse pouring of a tunnel arch wall, which adopts the simulation method described in Embodiment 1 and is composed of several functional modules that work cooperatively according to a predetermined logic to realize full-process calculation from geometric modeling to pouring process simulation, thereby solving the problems of lack of multi-physical field coupling simulation, low density, side pressure, inaccurate temperature control and interface prediction in reverse pouring. The composition and implementation mode of the system are described below.

[0284] Specifically, it comprises:

[0285] The modeling module is used to establish a two-dimensional arch wall elevation calculation domain according to the obtained geometric parameters of the tunnel arch wall, and to apply boundary conditions consistent with actual construction in the calculation domain. The module preferably uses MAC staggered grids to discretize the calculation domain to obtain the numerical advantage of staggered arrangement of velocity and pressure fields at grid nodes, which is beneficial to mass conservation control during subsequent explicit projection method solving. This processing method can reduce numerical oscillation and ensure the stability and calculation efficiency of long-time simulation.

[0286] The material model module is used to implement the Herschel-Bulkley rheological model with thixotropic recovery mechanism and the thixotropic evolution equation. The module has a built-in parametric form of yield stress and consistency coefficient , and describes the recovery and destruction process of thixotropic structure parameter λ according to a first-order differential equation. Through this module, the working condition characteristics of arch foot high shear leading to structure destruction and flowability enhancement, and low shear of the upper segment of the arch wall promoting structure recovery and flowability decrease can be reflected in the simulation, thereby improving the prediction accuracy of concrete flowability and density.

[0287] The thermal-chemical coupling module is used to calculate the interaction of hydration reaction and temperature field and its influence on rheological properties. The module solves the evolution of hydration degree α based on the Arrhenius type exponential model, and counts the hydration heat release effect through the heat conduction equation to form coupled calculation of temperature field and hydration degree. Further, temperature and α are fed back to the rheological parameter (viscosity and yield stress) correction formula to establish a closed-loop coupling mechanism of "temperature rise → hydration acceleration → rheological property change", thereby improving the accuracy of side pressure and temperature control prediction of early age temperature gradient and hardening process.

[0288] A flow field solving module is configured to solve the velocity field and the pressure field based on an explicit projection method. The module sequentially completes the prediction velocity calculation without a pressure term, the pressure field solving to meet the incompressible condition, and the projection correction of the velocity field in the steps of prediction-pressure Poisson-velocity correction, so as to ensure the mass conservation and accurately capture the difference between the high-speed flow at the arch foot and the slow flow at the upper section in the reverse pouring. The module cooperates with the material model module to introduce the Herschel-Bulkley stress tensor into the momentum equation, thereby improving the consistency between the flow field and the real pouring process.

[0289] An interface tracking module is configured to simulate the space-time evolution of the concrete-air free interface by using the VOF-PLIC method. The module solves the volume fraction transport equation in each time step, updates the concrete phase distribution, and obtains the interface position and morphology by the PLIC geometric reconstruction for the mixed cell, so as to accurately output the average height of the free liquid surface, the local rising velocity, the time of the left and right arch foot jets converging in the middle, and the interface morphology and other information, thereby providing the basis for judging the filling uniformity and cold joint risk, and improving the reliability of the dense degree prediction.

[0290] A side pressure evaluation module is configured to calculate the stress distribution of the formwork and output the pressure curve and the extreme value. The module calculates the equivalent side pressure according to the flow field and the stress distribution, and extracts the distribution data along the height direction of the arch wall, draws the change curve, and outputs the maximum side pressure value and the corresponding height, so as to provide a quantitative basis for the formwork structure design, the support system configuration, and the construction safety evaluation.

[0291] A time control module is configured to dynamically adjust the simulation step length according to the CFL stability criterion, and drive the collaborative operation of each module until the pouring process simulation is completed. The module calculates the maximum time step allowed according to the CFL condition based on the current maximum velocity component and the apparent viscosity in each cycle step, so as to ensure the numerical stability of the explicit solving process, and at the same time, as large as possible step length is used to improve the calculation efficiency. The stable control of the module makes the long-time multi-physical field coupling simulation feasible, and avoids the influence of numerical divergence on the prediction accuracy of the side pressure and the interface.

[0292] ​The system combines functions such as geometric modeling, material constitutive, thermal-chemical coupling, flow field solving, interface tracking, side pressure evaluation and time control through modular design, and forms a complete simulation platform that can run in the same explicit time advancing framework. The parameter transmission and coupling calculation between modules enable the synchronous update of rheology, temperature, hydration, interface and stress field, making up for the problem of the lack of multi-physical field coupling simulation in the prior art; the linkage of the material model and the thermal-chemical coupling module can truly reproduce the changes of fluidity and side pressure of early-age concrete caused by hydration heat release and structural hardening; the combination of the interface tracking module and the side pressure evaluation module can provide quantitative data of filling state and formwork stress, significantly improving the prediction accuracy of compactness, side pressure, temperature control and interface position; the time control module ensures the stability and efficiency of long-time simulation, so that the system can be practically applied to engineering scheme comparison and construction safety evaluation. The system corresponds to the simulation method of embodiment 1 in structure, and realizes the multi-physical field coupling simulation for tunnel arch wall reverse pouring through the cooperative work of each functional module, which can effectively solve the technical problem of inaccurate prediction of key parameters in reverse pouring, and provide a reliable analysis tool for formwork design and construction control.

[0293] The above is only the preferred embodiment of the present application, and does not limit the patent scope of the present application, and any equivalent structural transformation made under the inventive concept of the present application, using the content of the present application specification and drawings, or directly / indirectly applied in other related technical fields are included in the patent protection scope of the present application.

Claims

1. A multiphysics coupling simulation method for reverse casting of tunnel arch walls, characterized in that, The steps include: S1. Obtain the geometric parameters of the tunnel arch wall, construct a two-dimensional arch wall elevation calculation domain based on the geometric parameters, discretize the calculation domain and set boundary conditions; S2. The Herschel-Bulkley model, which incorporates a thixotropic recovery mechanism, is used to describe the shear stress behavior. The formula is as follows: And through the first-order differential equation Characterizing thixotropic structural parameters The process of restoration and destruction, including: For shear stress, For shear rate, The yield stress is related to the parameters of the thixotropic structure. The consistency coefficient is related to the thixotropic structure parameters. For liquidity index, These are the parameters of the thixotropic structure. The structural restitution coefficient is... The shear failure factor; S3. Using an Arrhenius-type exponential model The evolution of hydration degree is described, and the exothermic effect of hydration is considered in conjunction with the heat conduction equation. A coupling relationship between temperature, hydration degree, and rheological parameters is established. The current degree of hydration, The baseline hydration rate constant before temperature correction. It is the apparent activation energy of the hydration reaction. The gas constant is... Absolute temperature This is the final value of hydration; S4. Based on the shear stress behavior described in step S2 and the coupling relationship described in step S3, the flow field velocity and pressure in the computational domain described in step S1 are solved using the explicit projection method. S5. The PLIC interface tracing algorithm based on the VOF method is used to solve the spatiotemporal evolution process of the concrete-air free interface. S6. Calculate the template side pressure based on the static pressure P obtained in step S4 and the viscous stress tensor σ obtained from the model calculation in step S2. It also outputs the curve of lateral pressure variation with height and the maximum value information; S7. Based on the CFL stability criterion, dynamically control the time step and execute steps S2 to S7 repeatedly until the casting simulation reaches the set height or the termination time.

2. The multiphysics coupling simulation method for reverse casting of tunnel arch walls according to claim 1, characterized in that, In step S1, the geometric parameters of the tunnel arch wall are obtained, including the arch foot position and spacing, arch wall height H, analysis width L along the wall direction, lining thickness b, center coordinates of the pouring opening and its size and quantity, design pouring height, segmented pouring sequence and single pouring volume.

3. The multiphysics coupling simulation method for reverse casting of tunnel arch walls according to claim 1 or 2, characterized in that, In step S3, the temperature field satisfies the coupled control equations of heat conduction and hydration heat release, as shown below: ； in, For concrete density, The specific heat capacity of concrete, For effective thermal conductivity, This is the heat release term for hydration.

4. The multiphysics coupling simulation method for reverse casting of tunnel arch walls according to claim 1 or 2, characterized in that, In step S3, the temperature-related correction relationship for rheological parameters is introduced: The consistency coefficient of concrete is corrected using the following formula: ； The yield stress is corrected using the following formula: ； in, For temperature sensitivity coefficient, For reference temperature; The hydration enhancement coefficient is... This refers to absolute temperature.

5. The multiphysics coupling simulation method for reverse casting of tunnel arch walls according to claim 1 or 2, characterized in that, In step S4, the steps for solving the flow field using the explicit projection method are as follows: S41. Predicted velocity field: Given the velocity at the previous time step. Apparent viscosity and shear stress Under the premise of calculating the prediction rate without the stress term : ； in: For time step, For space convection, σ n Let be the viscous stress tensor at the nth time step. This is the vector of gravitational acceleration; S42. Construct and solve the pressure Poisson equation: To satisfy the incompressibility condition The pressure Poisson equation is constructed as follows: ； in, For the Laplace operator; Unknown pressure Solve using Jacobi or Gauss–Seidel iterations; S43, Speed ​​Correction: After obtaining... Then, the predicted velocity is projected and corrected using the following formula: ； in, Central difference calculation is used to ensure that the corrected velocity field satisfies the mass conservation condition.

6. The multiphysics coupling simulation method for reverse casting of tunnel arch walls according to claim 1 or 2, characterized in that, In step S5, the steps and methods for solving the spatiotemporal evolution process of the concrete-air free interface are as follows: S51. The interface transport equations are as follows: ； in This represents the volume fraction of the concrete phase. The velocity field at the current time step; S52. At each time step, calculate the volume fraction flux along each grid surface. Update and The unit uses the PLIC method, based on local gradients. Reconstruct the linear interface to obtain the geometric position and shape of the free liquid surface; S53, by The distribution calculations yielded: the average height of the free surface and the local rising velocity; the time and interface morphology of the jets converging at the middle of the left and right arch feet; and the volume percentage of concrete within the wall.

7. The multiphysics coupling simulation method for reverse casting of tunnel arch walls according to claim 1 or 2, characterized in that, In step S6, the template side pressure The calculation formula is as follows: ； Where P is the static pressure obtained within the element, and σ is the viscous stress tensor; σ is the template's outward normal vector; xy， σ yy These are the components of the stress tensor; This is the equivalent lateral pressure acting on the template; Extract along the height of the arch wall The distribution is plotted, the curve of the template lateral pressure changing with height is drawn, and the maximum lateral pressure value and its corresponding height are output.

8. A multiphysics coupling simulation system for reverse casting of tunnel arch walls, employing the multiphysics coupling simulation method for reverse casting of tunnel arch walls as described in any one of claims 1-7, characterized in that, include: The modeling module is used to establish a two-dimensional computational domain based on the tunnel's geometric parameters, discretize the computational domain, and apply boundary conditions. The material model module is used to implement the Herschel-Bulkley rheological model with thixotropic recovery and the thixotropic evolution equation; The thermo-chemical coupling module is used to calculate the interaction between hydration reaction and temperature field and its effect on rheological properties; The flow field solution module is used to explicitly solve the velocity and pressure fields based on the projection method. The interface tracking module is used to simulate changes in the concrete-air interface using the VOF-PLIC method. The lateral pressure assessment module is used to calculate the stress distribution on the template and output the pressure curve and extreme values; The time control module is used to dynamically adjust the simulation step size according to the CFL conditions, driving the modules to run in coordination until the simulation of the pouring process is completed.

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