Method and system for predicting deformation of solidified soil subgrade based on physical information neural network

Abstract

The present application relates to the technical field of subgrade health prediction, and particularly relates to a cured soil subgrade deformation prediction method and system based on a physical information neural network, the method comprising the following steps: obtaining multi-source monitoring data and soil property data of the cured soil subgrade, constructing a data set and generating an initial configuration point set; constructing a multi-physical field coupling control equation set as a physical constraint based on the soil property data, and embedding the equation set in a loss function of the physical information neural network; iteratively training the physical information neural network based on the data set and the initial configuration point set, and combining a self-adaptive configuration point dynamic adjustment strategy; taking the trained physical information neural network as a prediction model, and using the prediction model to predict the deformation of the cured soil subgrade at an arbitrary space-time coordinate. The present application embeds a multi-physical field constraint and adjusts the configuration point adaptively, so that the model focuses on the key area dynamically while meeting the physical law, and the accuracy and efficiency of the cured soil subgrade deformation prediction are improved.

Description

Technical Field

[0001] This invention relates to the field of roadbed health prediction technology, and in particular to a method and system for predicting deformation of solidified soil roadbeds based on physical information neural networks. Background Technology

[0002] Currently, many studies in the field of geotechnical engineering have introduced Physics-Informed Neural Networks (PINN) into the forward prediction and parameter inversion scenarios of consolidation problems. Some studies have verified the feasibility of PINN in solving one-dimensional and three-dimensional soft soil consolidation problems based on the classical Terzaghi consolidation theory, while other works have attempted to invert the physical parameters of soil using short-term monitoring data. However, most existing studies focus on ordinary homogeneous soft soil, and for the specific engineering object of solidified soil subgrades, the existing PINN prediction system still has the following technical shortcomings.

[0003] Under cement hydration, the unconfined compressive strength of solidified soil exhibits a significant nonlinear growth pattern with curing age. Furthermore, ambient temperature and internal moisture content directly regulate the hydration reaction rate, thus affecting the strength evolution process. Existing PINN consolidation models for ordinary soft soils have not yet established a mathematical description of the dynamic evolution of strength with age, temperature, and moisture content. This makes it difficult to accurately represent the core physical property of solidified soil—"gradual hardening with hydration"—ultimately leading to significant deviations in deformation predictions during the curing and long-term service periods.

[0004] Currently, most PINN consolidation studies only construct physical constraints around a single pore pressure dissipation equation. Although there have been some multi-field PINN explorations in general fields, temperature control equations with endogenous hydration heat and moisture migration control equations driven by temperature and humidity gradients have not been specifically incorporated, making it impossible to accurately characterize the multi-field linkage evolution law of solidified soil subgrade throughout the entire cycle.

[0005] The multiphysics gradients of solidified soil subgrades exhibit extremely uneven distribution across time and space: near drainage boundaries and during the early curing stage when hydration reactions are intense, the rates of change in pore pressure, temperature, and water content are much higher than in deeper internal regions and later stages of curing. Existing PINN models generally employ globally uniform or randomly configured sampling schemes, which waste significant computational resources in regions with gentle physical fields and are prone to insufficient sampling point density in high-gradient local areas, making it difficult to accurately capture local abrupt changes. Ultimately, this simultaneously limits both the model's prediction accuracy and convergence efficiency.

[0006] A few studies have extended PINN to solve three-dimensional Biot consolidation problems. However, the underlying physical framework of these general three-dimensional frameworks is still based on the consolidation assumption of ordinary homogeneous soil. They do not embed the hydration intensity evolution and multi-field coupling modules unique to solidified soil, and cannot directly support the full-cycle deformation prediction needs of solidified soil subgrades from the construction period to the long-term service period. Summary of the Invention

[0007] To address the shortcomings of existing technologies, this invention provides a method and system for predicting the deformation of solidified soil subgrade based on physical information neural networks.

[0008] To achieve the above objectives, in a first aspect, this invention provides a method for predicting the deformation of solidified soil subgrade based on a physical information neural network. The method includes the following steps: acquiring multi-source monitoring data and soil property data of the solidified soil subgrade, constructing a dataset, and generating an initial set of configuration points; constructing a set of multi-physics coupled control equations as physical constraints based on the soil property data, and embedding them into the loss function of the physical information neural network; iteratively training the physical information neural network based on the dataset and the initial set of configuration points, combined with an adaptive configuration point dynamic adjustment strategy; using the trained physical information neural network as a prediction model, and using the prediction model to predict the deformation of the solidified soil subgrade under arbitrary spatiotemporal coordinates. This invention, through the embedding of multi-physics constraints and adaptive adjustment of configuration points, enables the model to dynamically focus on key areas while satisfying physical laws, thereby improving the accuracy and efficiency of solidified soil subgrade deformation prediction.

[0009] Optionally, the multi-source monitoring data includes the spatial coordinates of different monitoring points in the solidified soil subgrade, as well as the three-dimensional displacement components, excess pore water pressure, temperature, and volumetric water content at different monitoring points.

[0010] Optionally, the soil property data includes the reference compression modulus, reference permeability coefficient, Poisson's ratio, thermal conductivity, specific heat capacity, density, cement hydration heat release rate curve, and unconfined compressive strength under different curing conditions of the solidified soil.

[0011] Optionally, the step of acquiring multi-source monitoring data and soil property data of solidified soil subgrade, constructing a dataset, and generating an initial configuration point set includes the following steps: Collect raw multi-source monitoring data and soil property data of solidified soil subgrade, preprocess the raw multi-source monitoring data to obtain the multi-source monitoring data and construct the dataset; Within the spatial range of the solidified soil subgrade, the initial configuration point set is generated using the Latin hypercube sampling method.

[0012] Optionally, the step of constructing a multiphysics coupled control equation set based on the soil property data as a physical constraint and embedding it into the loss function of the physical information neural network includes the following steps: Based on the soil properties data, temperature field equations, humidity field equations and stress field equations are constructed respectively to form a set of control equations coupled by multiple physical fields. Physical residual terms are constructed based on each partial differential equation in the governing equation set, and their sum of squares is used as a physical loss term, which is added to the loss function of the physical information neural network along with the boundary condition loss.

[0013] Optionally, the step of constructing a multiphysics coupled control equation set based on the soil property data as a physical constraint and embedding it into the loss function of the physical information neural network further includes: A coupled evolution equation for the unconfined compressive strength of solidified soil with respect to age, temperature, and moisture content is constructed, and then the constitutive parameters in the governing equation set are updated based on the coupled evolution equation.

[0014] Optionally, the iterative training of the physical information neural network based on the dataset and the initial set of configuration points, combined with an adaptive configuration point dynamic adjustment strategy, includes the following steps: Initialize the network parameters of the physical information neural network and the physical parameters to be inverted, and use the initial configuration point set as the current configuration point set; The physical information neural network is trained and validated based on the dataset, and then the network parameters and the physical parameters to be inverted are updated through backpropagation. Every preset number of training steps, the residual contribution of the configuration point is evaluated based on the physical residual at the configuration point in the current configuration point set; The configuration points are adaptively adjusted based on the residual contribution and the preset contribution threshold, thereby updating the current configuration point set; When the training causes the physical information neural network to reach the preset convergence condition, the trained physical information neural network can be obtained.

[0015] Optionally, the step of evaluating the residual contribution of a configuration point based on the physical residual at the configuration point in the current configuration point set every preset number of training steps includes the following steps: Every preset number of training steps, for any one of the current configuration points in the set of configuration points, calculate the residuals of the temperature field equation, humidity field, equilibrium equation, and continuity at that configuration point. The sum of the absolute values ​​of the residuals of the temperature field equation, the humidity field, the equilibrium equation, and the continuity residual is taken as the residual contribution of the configuration point.

[0016] Optionally, the step of adaptively adjusting the configuration points based on the residual contribution and a preset contribution threshold, and then updating the current configuration point set, includes the following steps: The solidified soil subgrade is divided into multiple grid units in the spatiotemporal domain, and the residual threshold is determined. The residual threshold includes an upper limit of contribution and a lower limit of contribution. Configuration points whose residual contribution exceeds the upper limit of contribution are recorded as high residual configuration points, and configuration points whose residual contribution is lower than the lower limit of contribution are recorded as low residual configuration points. The number of high residual configuration points and low residual configuration points in each of the grid cells is counted, thereby determining the high residual region and the low residual region; Based on the number of configuration points in the current configuration point set and the number of high residual regions, the Latin hypercube sampling method is used to adaptively generate new configuration points. Based on the number of low residual regions and the number of newly added configuration points, remove the same number of configuration points located in the low residual regions from the current configuration point set.

[0017] Secondly, the present invention provides a solidified soil subgrade deformation prediction system based on a physical information neural network. The solidified soil subgrade deformation prediction system based on a physical information neural network includes: a data input device, a data output device, a processor, and a storage device. The storage device includes a computer-readable storage medium storing a computer program. The computer program includes program instructions. When the program instructions are executed by the processor, the processor implements the solidified soil subgrade deformation prediction method based on a physical information neural network provided by the present invention.

[0018] In summary, the present invention has at least the following beneficial effects: 1. This method embeds the multi-physics field coupled control equations into the loss function of the physical information neural network, so that the model training is subject to the dual constraints of monitoring data and physical laws, ensuring the physical rationality of the deformation prediction results; by dynamically adjusting the distribution of configuration points during the training process, the configuration points are gradually focused on the areas of drastic changes in the physical field, thereby improving the prediction accuracy and training efficiency.

[0019] 2. This method achieves unified quantification of multi-physics constraints by embedding the sum of squared residuals of the temperature field equation, humidity field equation, and stress field equation as physical loss terms into the total loss function; by constructing coupled evolution equations and updating constitutive parameters in the control equation set accordingly, the constitutive parameters change in real time with the curing process, reflecting the physical characteristics of "hardening with age" of the solidified soil.

[0020] 3. This method enables the model to automatically identify the optimal values ​​of physical parameters from monitoring data by jointly initializing and synchronously updating physical parameters and network parameters, thus overcoming the problem of parameters not matching the actual field conditions due to reliance on indoor test calibration. By evaluating the residual contribution of each configuration point at preset steps and making adaptive adjustments, the configuration point set is dynamically optimized during training, solving the problem that a fixed configuration point distribution cannot adapt to changes in the model error distribution and improving prediction accuracy.

[0021] 4. This method achieves quantitative assessment of the comprehensive deviation of multi-physics fields by using the sum of the absolute values ​​of each physical residual as the residual contribution of the configuration point; it achieves accurate positioning of high residual and low residual regions by dividing the roadbed into grid cells and counting the number of high and low residual configuration points in each grid; and it keeps the total number of configuration points constant by adding configuration points in high residual regions and removing the same number of configuration points from low residual regions, thus achieving efficient utilization of computing resources and ensuring prediction efficiency.

[0022] 5. A system adapted to this method was constructed. This system not only improves the practicality of this method, but also facilitates its promotion. Attached Figure Description

[0023] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of this application and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0024] Figure 1 This is a flowchart illustrating the deformation prediction method for solidified soil subgrade based on a physical information neural network according to an embodiment of the present invention. Figure 2 This is a schematic diagram of the framework of the solidified soil subgrade deformation prediction system based on physical information neural network according to an embodiment of the present invention. Detailed Implementation

[0025] Specific embodiments of the present invention will now be described in detail. It should be noted that the embodiments described herein are for illustrative purposes only and are not intended to limit the invention. In the following description, numerous specific details are set forth in order to provide a thorough understanding of the invention. However, it will be apparent to those skilled in the art that these specific details are not necessary to practice the invention. In other instances, well-known circuits, software, or methods have not been specifically described to avoid obscuring the invention.

[0026] Throughout this specification, references to "an embodiment," "an embodiment," "an example," or "an example" mean that a particular feature, structure, or characteristic described in connection with that embodiment or example is included in at least one embodiment of the invention. Therefore, the phrases "in an embodiment," "in an embodiment," "an example," or "an example" appearing in various places throughout the specification do not necessarily refer to the same embodiment or example. Furthermore, specific features, structures, or characteristics can be combined in one or more embodiments or examples in any suitable combination and / or sub-combination. Moreover, those skilled in the art will understand that the illustrations provided herein are for illustrative purposes and are not necessarily drawn to scale.

[0027] It should be noted in advance that, in one alternative embodiment, except for independent descriptions, the same symbols or letters appearing in all formulas have the same meaning.

[0028] In one optional embodiment, please refer to Figure 1 This invention provides a method for predicting the deformation of solidified soil subgrade based on a physical information neural network. The method includes the following steps: S1. Obtain multi-source monitoring data and soil property data of the solidified soil subgrade, construct a dataset and generate an initial configuration point set.

[0029] Step S1 specifically includes the following steps: S11. Collect the original multi-source monitoring data of the solidified soil subgrade and the soil property data, preprocess the original multi-source monitoring data to obtain the multi-source monitoring data and construct the dataset.

[0030] Specifically, in this embodiment, the multi-source monitoring data includes the spatial coordinates of different monitoring points in the solidified soil subgrade, as well as the three-dimensional displacement components, excess pore water pressure, temperature, and volumetric water content at different monitoring points. Soil property data includes the reference compression modulus, reference permeability coefficient, Poisson's ratio, thermal conductivity, specific heat capacity, density, cement hydration heat release rate curve, and unconfined compressive strength under different curing conditions for the solidified soil.

[0031] Based on the cross-sectional shape, geological conditions, and embankment height of the roadbed, representative monitoring sections are selected along the longitudinal direction of the route. Generally, the spacing between monitoring sections should be 50 to 100 meters. For critical sections with complex geological conditions or large embankment heights, the spacing of monitoring sections should be appropriately increased. On each monitoring section, monitoring points are set up at different depths along the cross-sectional direction of the roadbed at characteristic locations such as the center of the top surface of the roadbed, the shoulders on both sides, and the toe of the slope. Various sensors for collecting displacement, excess pore water pressure, temperature, and volumetric water content need to be simultaneously deployed near each monitoring point. Generally, the planar positions of various sensors within the same cross-section should be as close as possible to the corresponding monitoring point.

[0032] The longitudinal direction (i.e. the direction of route extension) of the solidified soil subgrade is taken as the X-axis, the transverse direction (i.e. perpendicular to the route direction and parallel to the subgrade cross section) of the solidified soil subgrade is taken as the Y-axis, and the direction perpendicular to the horizontal plane downward is taken as the Z-axis. The origin of the coordinate system is established by taking the center point of the top surface of the subgrade at the starting end section of the monitored road segment and the vertical projection point of the subgrade surface as the origin of the coordinate system.

[0033] During the curing phase of the solidified soil subgrade, some monitoring points are located on the top surface of the subgrade. In this case, a high-precision total station can be set up at control points with known coordinates, and reflecting prisms can be installed at each monitoring point. The total station measures the horizontal angle, vertical angle, and slope distance from the station point to the monitoring point using a laser beam. Based on this, the spatial coordinates of the monitoring point are calculated using the total station polar coordinate measurement method. Using the spatial coordinates of the monitoring point obtained from the previous measurement as the initial coordinates, the difference between the spatial coordinates of the monitoring point obtained from the next measurement and the initial coordinates represents the displacement components of that monitoring point in the three directions, reflecting the deformation of the solidified soil subgrade at the monitoring point. The time interval between two spatial coordinate measurements is recorded as the optimal sampling interval, preferably 24 hours.

[0034] For a monitoring point with a certain burial depth, its initial spatial coordinates can be obtained through the following steps: First, determine the projection point of the monitoring point on the surface of the monitored road section; obtain the three-dimensional coordinate position of the projection point in a spatial rectangular coordinate system using a total station polar coordinate measurement method; keeping the X-axis and Y-axis coordinates of the projection point unchanged, add the burial depth of the monitoring point to its Z-axis coordinate to obtain the initial spatial coordinates of the monitoring point. Furthermore, the displacement components of the monitoring point in the horizontal direction (X-axis and Y-axis directions) can be obtained using the inclinometer method, and the displacement component in the Z-axis direction can be obtained using the magnetic settlement ring method. Given the initial spatial coordinates of the monitoring point and its displacement components in the three coordinate axes, the spatial coordinates of the monitoring point after displacement can be obtained by calculating the sum of the initial coordinate values ​​of the monitoring point on the coordinate axes and its displacement components on those axes.

[0035] The excess pore water pressure is collected in real time by excess pore water pressure gauges buried at monitoring points, and the pressure gauges at each depth are led to a data acquisition box on the ground via cables. The temperature is collected in real time by temperature sensors buried at monitoring points, and the temperature sensor signals are led out via cables, sharing the data acquisition system with the excess pore water pressure gauges.

[0036] Volumetric moisture content is obtained in real time using time-domain reflectometry (TDRS) technology. A TDRS probe, consisting of two or three parallel metal rods, is embedded at each monitoring point and connected to a TDRS data acquisition unit on the ground via a coaxial cable. The acquisition unit emits a step voltage pulse to the probe, determines the propagation speed and attenuation characteristics of electromagnetic waves in the soil based on the reflected waveform, and calculates the volumetric moisture content at the monitoring point by combining this with the relationship curve between dielectric constant and volumetric moisture content established through indoor calibration tests.

[0037] After collecting multi-source monitoring data, preprocessing is required. Specifically, for data such as three-dimensional displacement components, excess pore water pressure, temperature, and volumetric water content, Laida's rule is used to identify and remove outliers. Then, linear interpolation is used to fill in missing values. Finally, the average values ​​of excess pore water pressure, temperature, and volumetric water content within the optimal sampling interval are calculated as the final values ​​for the optimal sampling interval.

[0038] In addition, the spatial coordinates and the acquisition time corresponding to the multi-source monitoring data need to be normalized according to the following formula:

[0039]

[0040] in, Represents the normalized spatial coordinates. This represents unnormalized spatial coordinates. The minimum X-axis coordinate value representing the spatial extent of the solidified soil subgrade. The minimum Y-axis coordinate value representing the spatial extent of the solidified soil subgrade. The minimum Z-axis coordinate value representing the spatial extent of the solidified soil subgrade. This represents the maximum X-axis coordinate value of the solidified soil subgrade spatial range. This represents the maximum Y-axis coordinate value of the solidified soil subgrade spatial range. This represents the maximum Z-axis coordinate value of the solidified soil subgrade. This represents the normalized collection time. This indicates the unnormalized collection time. This indicates the maximum monitoring coverage time, with the data collection time measured in days.

[0041] After data preprocessing, multi-source monitoring data from the same monitoring point at the same acquisition time are treated as a single data sample, and then all data samples are used to construct a dataset. Any single data sample can be represented as... , This represents the displacement component along the X-axis. This represents the displacement component along the Y-axis. This represents the displacement component along the Z-axis. The displacement components are represented by p, the excess pore water pressure, and the temperature. This represents the volumetric water content. The dataset is divided into a training set and a validation set in a 7:3 ratio for subsequent training and validation of the physical information neural network.

[0042] Soil property data acquisition must be completed indoors, and soil samples should be collected from the construction site before roadbed filling. The baseline compression modulus refers to the compression modulus of a soil sample under standard indoor curing conditions, determined through a standard consolidation test. The determination of permeability coefficient requires selecting an appropriate test method based on the permeability of the soil sample: for sandy soils with good permeability, a constant head permeability test is used; for cohesive soils with low permeability, a variable head permeability test is used. Test results should be converted to permeability coefficient values ​​at a standard temperature (usually 293.15 K). Poisson's ratio can be determined through a triaxial compression test. Under confining pressure, an axial load is applied to the sample, and axial and radial strains are measured simultaneously; the ratio of these two strains is used to calculate Poisson's ratio. Thermal conductivity can be determined using a thermal property analyzer. The prepared soil sample is placed under the instrument's test probe, and the thermal conductivity is measured using the transient plane heat source method. Specific heat capacity can be determined using differential scanning calorimetry (DSC), calculating the specific heat capacity by measuring the heat flow change of the soil sample during heating. Density was determined using the ring cutter method, in which undisturbed soil samples were cut with a ring cutter, the mass of the soil sample was weighed, and the mass per unit volume was calculated.

[0043] The determination of the cement hydration heat release rate curve needs to be completed indoors using isothermal calorimetry. The cement to be used in the solidified soil is mixed evenly with soil and water taken from the site according to the designed mix ratio. The mixture is then placed in an adiabatic or semi-adiabatic calorimeter, and the temperature change is continuously monitored for more than 72 hours under constant temperature conditions to plot the temperature change curve. Based on the temperature change curve, the change law of the cement hydration heat release rate over time is calculated, thus obtaining the cement hydration heat release rate curve.

[0044] The unconfined compressive strength of solidified soil subgrade under different curing conditions was obtained by preparing solidified soil subgrade specimens under different curing conditions and conducting unconfined compressive strength tests. The preparation method for solidified soil subgrade specimens is as follows: First, a mixture is prepared according to the mix design provided by the construction party. Then, the mixture is placed in three layers into a cylindrical mold with an inner diameter of 39.1 mm and a height of 80 mm. Each layer is compacted with a compaction hammer to a specified number of times to obtain the original solidified soil subgrade specimen. After demolding, the original solidified soil subgrade specimens are placed under different curing conditions to obtain the desired solidified soil subgrade specimens. These curing conditions include different curing temperatures (e.g., 5℃, 20℃, 40℃, 60℃), different air moisture contents, and different curing ages (e.g., 3 days, 7 days, 14 days, 28 days, 60 days, 90 days). After reaching the predetermined curing age, the solidified soil subgrade specimens are removed from the curing environment, and the unconfined compressive strength of the specimens is obtained through unconfined compressive strength tests. At least three parallel specimens were prepared under each set of curing conditions. The arithmetic mean of the unconfined compressive strength of the three specimens was taken as the final unconfined compressive strength of the solidified soil subgrade specimen under that curing condition.

[0045] S12. Within the spatial range of the solidified soil subgrade, the initial configuration point set is generated using the Latin hypercube sampling method.

[0046] Specifically, in this embodiment, the Latin hypercube sampling method is used to generate the initial set of placement points. The initial set of placement points includes a boundary set of placement points and a body set of placement points. The boundary set of placement points includes a first type of boundary set and a second type of boundary set.

[0047] The computational domain of the solidified soil subgrade is extended in three spatial dimensions and one temporal dimension to form a four-dimensional parameter space. The Latin hypercube sampling method divides each dimension of this four-dimensional space into N (preferably 10000) equally probable intervals, and randomly selects a sample point in each dimension of each interval. Then, the sample points of each dimension are randomly combined to generate N initial configuration points that are uniformly distributed in the four-dimensional space. The set of these configuration points is the in-body configuration point set.

[0048] Similarly, for the top surface of a solidified soil subgrade, the Latin hypercube sampling method can be used to generate N surface configuration points. The set of these surface configuration points is the first type of boundary configuration point set. For the bottom and sides of the solidified soil subgrade, the same Latin hypercube sampling method is used to generate N surface configuration points. The set of these surface configuration points is the second type of boundary configuration point set.

[0049] S2. Based on the soil properties data, construct a set of multiphysics field coupled control equations as physical constraints, and embed them into the loss function of the physical information neural network.

[0050] Step S2 specifically includes the following steps: S21. Based on the soil properties data, construct the temperature field equation, humidity field equation and stress field equation respectively to form a set of control equations coupled by multiple physical fields.

[0051] Specifically, in this embodiment, the temperature change inside the solidified soil is jointly controlled by heat conduction and the heat release from cement hydration, as shown in the following equation:

[0052] in, represents the density of the solidified soil, and c represents the specific heat capacity of the solidified soil. This indicates the thermal conductivity of the solidified soil. Represents the gradient operator. The t represents the rate of heat release during cement hydration, and t represents time. The rate of heat release during cement hydration satisfies the following relationship:

[0053] in, It represents the total heat of hydration, which depends on the type and amount of cement. It is equal to the product of the heat of hydration of cement and the amount of cement used. The heat of hydration of ordinary Portland cement is about 250~461 kJ / kg. The shape parameter is typically 0.5 to 2.0, and is obtained by recording the cement hydration heat release rate curve through isothermal calorimetry and fitting the curve. The hydration half-life is typically 0.5 to 3 days (depending on the type of cement and temperature). It is obtained by recording the heat release rate curve of cement hydration through isothermal calorimetry and fitting the curve. The acceleration factor of temperature on the hydration rate is calculated using the Arrhenius formula.

[0054] The boundary conditions for the temperature field are as follows: If the top surface of the solidified soil subgrade is in contact with the atmosphere, the boundary condition is set as a known temperature boundary, i.e., the average air temperature within the optimal sampling interval; for the bottom surface, sides, and top surface of the solidified soil subgrade under non-curing conditions, the boundary condition is set as a known ground temperature boundary. This can be achieved by burying temperature sensors on the bottom surface, sides, and top surface of the subgrade, and calculating the average temperature within the optimal sampling interval for each of the bottom surface, sides, and top surface as the boundary condition value given for the corresponding surface within the sampling interval.

[0055] Moisture migration within solidified soil is driven by both humidity and temperature gradients, as shown in the following equation:

[0056] in, The water diffusion coefficient is calculated using the empirical formula for exponential diffusion, i.e. ; Indicates the baseline moisture diffusion coefficient. Indicates the water diffusion sensitivity coefficient. and It is obtained by performing soil-water characteristic curve tests and unsaturated permeability tests on solidified soil and fitting the test data. Indicates the thermal diffusivity; This indicates the rate of water consumption in the hydration reaction. , This represents the water consumption coefficient. The water consumption coefficient is obtained as follows: Prepare solidified soil samples identical to those used in isothermal calorimetry tests; terminate the hydration reaction of the solidified soil samples at different hydration times, then test the chemically bound water content using TGA, and plot the chemically bound water content versus time; differentiate the chemically bound water content with time to obtain the water consumption rate of the hydration reaction versus time curve; perform a linear regression between the water consumption rate of the hydration reaction at different times and the corresponding cement hydration heat release rate, and the slope is the water consumption coefficient. .

[0057] The boundaries of the humidity field and the temperature field coincide, both being the surfaces of the solidified soil subgrade. The boundary conditions for the humidity field are as follows: if the top surface of the solidified soil subgrade is in contact with the atmosphere, the boundary condition is set to a known moisture content boundary, which is the daily average air moisture content within the optimal sampling interval; the bottom surface of the solidified soil subgrade is set as an impermeable boundary; the boundary conditions for the humidity field on the sides of the solidified soil subgrade need to be set according to the drainage conditions. Alternatively, the average moisture content within the optimal sampling interval can be measured and calculated using a humidity sensor as the boundary condition value given for the sides of the solidified soil subgrade within the optimal sampling interval.

[0058] It should be noted that the temperature and moisture content boundaries of the top surface of the solidified soil subgrade are Class I boundary conditions (given boundary condition values, i.e., given values), and their errors are included in the total loss through subsequent temperature and humidity boundary condition losses. The temperature and moisture content boundaries of the bottom and side surfaces are Class II boundary conditions (given normal flux, adiabatic / impermeable), and their errors are included in the total loss through subsequent boundary condition losses of the bottom and side surfaces of the solidified soil subgrade. Class I and Class II boundary conditions are not interchangeable.

[0059] The stress field equations are described using the three-dimensional Biot consolidation theory. This theory comprises two sets of equations: equilibrium equations and continuity equations. The equilibrium equations and continuity equations along the X, Y, and Z axes are shown below:

[0060]

[0061]

[0062]

[0063] in, hour, This represents the shear stress along the j-axis in the plane along the i-axis direction. hour, This represents the normal stress in the plane along the i-axis direction; , ; , and These represent the body force components along the X, Y, and Z axes, respectively. , m represents the soil weight; , This represents the total length of the entire computational domain in the X direction; similarly, it can be obtained... and ; Indicates volumetric strain. ; The unit weight of water is given by ; k represents the permeability coefficient of the solidified soil. , Represents the baseline permeability coefficient. This represents the attenuation coefficient. Shear stress is calculated from strain using the generalized Hooke's law:

[0064] in, This represents the unconfined compressive strength in the current spatial coordinates. express The compression modulus below, , representing the strength-modulus mapping index; Indicates and The corresponding strain, , This represents the displacement component along the i-axis. This represents the displacement component along the j-axis. This represents the partial derivative of the displacement component along the i-axis with respect to the j-axis coordinate; This indicates the Poisson's ratio of the solidified soil. Indicates the baseline compression modulus of the solidified soil; This represents the Biot coefficient, determined by triaxial compression tests on solidified soil, and is typically taken as 0.9 to 1.0. The benchmark unconfined compressive strength of solidified soil is the unconfined compressive strength of the original solidified soil subgrade specimen after curing for 28 days at 20℃ and 95% relative humidity. Represents the Kronecker symbol. hour , At that time .

[0065] Furthermore, a mapping relationship is established between the unconfined compressive strength and the constitutive parameters of the solidified soil, namely, a coupled evolution equation of the unconfined compressive strength of the solidified soil with age, temperature, and moisture content. Then, the constitutive parameters of the solidified soil are updated in real time based on the calculated current unconfined compressive strength, allowing the constitutive parameters of the stress field equation to dynamically evolve over time. The constitutive parameters include the compressibility modulus and permeability coefficient in the stress field equation. The coupled evolution equation is shown below:

[0066]

[0067]

[0068]

[0069] in, This represents the unconfined compressive strength of solidified soil at different ages, temperatures, and moisture contents. This represents the age-related influence function; b represents the age-related influence coefficient; b represents the age-related influence constant. Indicates a unit of time. sky; This represents the function that influences moisture content; The apparent activation energy, which reflects the acceleration sensitivity of the hydration reaction to temperature, is usually taken as 20,000 to 40,000 J / mol; R represents the gas constant, which is taken as 8.314 J / (mol·K). This represents the standard temperature, taken as 293.15 K, corresponding to 20℃; This indicates the reference moisture content, which is usually taken as the initial moisture content of the stabilized soil. The strength-moisture content damage index represents the strength-moisture content damage index. The age influence coefficient, age influence constant, and strength-moisture content damage index are obtained by fitting the unconfined compressive strength under different curing conditions.

[0070] S22. Construct physical residual terms based on each partial differential equation in the governing equation set, and add their sum of squares as physical loss terms, along with boundary condition loss, to the loss function of the physical information neural network.

[0071] Specifically, in this embodiment, the physical residuals include the residuals of the temperature field equation, the humidity field equation, the stress balance equation, and the continuity equation. For each configuration point, the sum of the squares of their physical residuals is used as the physical loss term and added to the loss function of the physical information neural network. The loss function of the physical information neural network satisfies the following relationship:

[0072]

[0073]

[0074]

[0075] Where Loss represents the total loss; Indicates data loss; Indicates the number of monitoring points in a batch; This represents the physical constraint weight coefficient, with a value of 1. This represents the spatial coordinates of the h-th monitoring point, i.e. , This represents the X-axis coordinate of the h-th monitoring point. This represents the Y-axis coordinate of the h-th monitoring point. This represents the Z-axis coordinate of the h-th monitoring point; This represents the displacement loss corresponding to the h-th monitoring point at time t; This represents the pore water pressure loss at the h-th monitoring point at time t; This represents the temperature loss at the h-th monitoring point at time t; This represents the moisture loss at the h-th monitoring point at time t; Indicates physical loss; , , and These represent the normalized weighting coefficients for displacement loss, pore water pressure loss, temperature loss, and water content loss, respectively. Their values ​​are the normalized values ​​of the reciprocals of the measured values ​​of displacement component, excess pore water pressure, temperature, and volumetric water content, respectively, used to eliminate the influence of the dimensional differences of each physical quantity on gradient updates. This indicates the number of configuration points in a batch, and that the configuration points belong to the body configuration point set; The spatial coordinates of the w-th placement point in the body placement point set are generated by the Latin hypercube sampling method. This represents the residual of the temperature field equation corresponding to the h-th placement point at time t; Let represent the residual of the humidity field equation corresponding to the h-th placement point at time t; Let represent the residual of the stress balance equation corresponding to the h-th placement point at time t; Let represent the residual of the continuity equation corresponding to the h-th placement point at time t; , , and These represent the weighting coefficients for the temperature field, humidity field, stress equilibrium field, and continuity equation, respectively, and are calculated for each configuration point in the first batch after training begins. , , and Then calculate the contents of each batch. The reciprocal of the average is used as ,calculate The reciprocal of the average is used as ,calculate The reciprocal of the average is used as ,calculate The reciprocal of the average is used as , , , and Maintain a constant value during subsequent training to stabilize the scale of physical loss; This represents the boundary loss weighting coefficient, with a value of 1. Indicates boundary condition loss; This represents the loss due to temperature boundary conditions; Indicates the loss due to humidity boundary conditions; This indicates the boundary condition loss of the solidified soil subgrade surface and sides.

[0076] For any monitoring point at any given time, the corresponding displacement loss pore water pressure loss Temperature loss and moisture loss The calculations can be performed sequentially according to the following formulas:

[0077]

[0078]

[0079]

[0080] in, This represents the prediction results for the three-dimensional displacement components; This represents the measured results of the three-dimensional displacement components; This indicates the predicted result of excess pore water pressure; This represents the measured results of excess pore water pressure. This indicates the predicted temperature. Indicates the measured temperature result; This indicates the predicted volumetric moisture content. This represents the measured result of the volumetric moisture content.

[0081] For any configuration point at any time, the residual of the corresponding temperature field equation Humidity field equation residuals Stress equilibrium equation residuals and the residuals of the continuity equation The calculations can be performed sequentially according to the following formulas:

[0082]

[0083]

[0084]

[0085] in, , and These represent the residuals of the stress balance equations in the X, Y, and Z axes, respectively. , , .

[0086] The boundary condition losses due to temperature, humidity, and solidified soil subgrade and side surfaces can be calculated using the following formulas:

[0087]

[0088]

[0089] in, This indicates the number of configuration points in a batch, and the configuration points belong to the first type of boundary configuration point set; Indicates the first in a batch The spatial coordinates of a configuration point, and the configuration point belongs to the first type of boundary configuration point set; Represents the first type of boundary configuration point set at time t. Predicted temperature results for each configuration point; This represents the temperature of the top surface of the solidified soil at time t. Represents the first type of boundary configuration point set at time t. The configuration point (the first type of boundary configuration point set) The predicted volumetric moisture content of each configuration point; This represents the moisture content of the top surface of the solidified soil at time t. This indicates the number of configuration points in a batch, and that the configuration points belong to the second type of boundary configuration point set; This represents the spatial coordinates of the Gth configuration point in a batch, and this configuration point belongs to the second type of boundary configuration point set; This represents the Gth configuration point in the set of second-type boundary configuration points at time t. The partial derivative along the direction n, which is the outward normal to the boundary; This represents the Gth configuration point in the set of second-type boundary configuration points at time t. The partial derivative along the direction of the outer normal n of the boundary.

[0090] S3. Based on the dataset and the initial set of configuration points, the physical information neural network is iteratively trained using an adaptive configuration point dynamic adjustment strategy.

[0091] Step S3 specifically includes the following steps: S31. Initialize the network parameters of the physical information neural network and the physical parameters to be inverted, and use the initial configuration point set as the current configuration point set.

[0092] Specifically, in this embodiment, the input to the physical information neural network is the four-dimensional spatiotemporal coordinates of the monitoring point. The output is a prediction of the three-dimensional displacement components, excess pore water pressure, temperature, and volumetric water content at the monitoring point. The physical information neural network employs a fully connected feedforward neural network, comprising an input layer, hidden layers, and an output layer. The input layer has four neurons, corresponding to the normalized four-dimensional spatiotemporal coordinates; the hidden layers have six layers, each with 80 neurons, and use the Swish activation function; the output layer has six neurons, corresponding to the three-dimensional displacement components, excess pore water pressure, temperature, and volumetric water content, respectively.

[0093] Before iteratively training the physical information neural network, initial values ​​need to be assigned to all adjustable parameters in the network. Specifically, firstly, the Xavier initialization method is used to initialize the trainable network parameters of the neural network itself. These network parameters include the connection weights and bias terms between neurons in each layer, keeping the variance of the output of each layer within a reasonable range, thereby avoiding the vanishing or exploding gradient problem. Secondly, initial values ​​are assigned to the physical parameters to be inverted. These physical parameters include at least the baseline permeability coefficient, apparent activation energy, moisture diffusion sensitivity coefficient, intensity-water content damage index, age influence coefficient, age influence constant, intensity-modulus mapping index, and decay coefficient. During the iterative training of the physical information neural network, these parameters participate in backpropagation optimization synchronously with the network parameters, adaptively learning their optimal values ​​from the monitoring data. The initial values ​​for the apparent activation energy are set to 30,000 J / mol, the initial values ​​for the moisture diffusion sensitivity coefficient and the strength-moisture content damage index are set to 0.5, the initial value for the age-related influence coefficient is set to 0.3, the initial value for the strength-modulus mapping index is set to 0.5, and the initial value for the decay coefficient is set to 0.01 kPa. -1 .

[0094] Furthermore, to ensure that the prediction results of the physical information neural network strictly meet the boundary conditions of each physical field, this embodiment performs hard constraint encapsulation on the output layer.

[0095] Considering the drainage conditions of the solidified soil subgrade, the top surface (z=0) is a permeable boundary with excess pore water pressure p=0; the bottom surface (z=H, where the absolute value of H represents the thickness of the solidified soil layer) is an impermeable boundary, satisfying... For the above boundary conditions, the original output of the physical information neural network on the excess pore water pressure is encapsulated using the following formula to obtain the encapsulated prediction result of the pore water pressure:

[0096] in, This represents the raw output of the physical information neural network for the pressure of ultrastatic pore water.

[0097] Based on the displacement boundary conditions of the solidified soil subgrade, the bottom surface (at z=H) is a fixed boundary with zero displacement in all three directions; the top surface (at z=0) is a free boundary without constraints. For these boundary conditions, the raw output of the physical information neural network for the three-dimensional displacement components is encapsulated using the following formula:

[0098] in, This represents the raw output of the physical information neural network for the three-dimensional displacement components; This represents the normalized result of H, with the normalization method referring to that of z. It should be noted that this encapsulation method is suitable for roadbed surfaces located on hard bedrock or strata that do not undergo significant deformation (such as rock strata). In other alternative embodiments, for ordinary foundation soil, the bottom surface may experience some settlement deformation. In this case, a soft constraint method (i.e., applying weak constraints through boundary loss terms) can be used to avoid forced zeroing, which would cause the predicted results to deviate significantly from the measured data.

[0099] The boundary conditions of the temperature and humidity fields are handled using soft constraints, i.e., the boundary loss in the loss function of step S22. Since the boundary conditions of the temperature and humidity fields are relatively simple, and the boundary data can be directly obtained from sensors, the soft constraint method can guarantee sufficient accuracy.

[0100] S32. The physical information neural network is trained and validated based on the dataset, and then the network parameters and the physical parameters to be inverted are updated through backpropagation.

[0101] Specifically, in this embodiment, a training set is used to iteratively train the physical information neural network. The training process employs a mini-batch gradient descent method. In each training round, sample data of a preset batch size is randomly extracted from the training set. Simultaneously, configuration points of the same batch size are randomly extracted from both the boundary configuration point set and the in-body configuration point set of the current configuration point set, and combined to form the current training batch. For monitoring points, their four-dimensional spatiotemporal coordinates are input into the physical information neural network, which outputs the predicted results of the three-dimensional displacement components, excess pore water pressure, temperature, and volumetric water content at the monitoring point, and calculates the data loss for that batch.

[0102] For each configuration point, its four-dimensional spatiotemporal coordinates are input into the physical information neural network, which outputs the corresponding prediction results. Then, the processing is differentiated according to the configuration point type: if the configuration point belongs to the in-body configuration point set, the prediction results are substituted into the governing equations based on the neural network's automatic differentiation technique to calculate the physical loss for that batch; if the configuration point belongs to the boundary configuration point set, the boundary loss is calculated using the prediction results and the measured results on the solidified soil subgrade boundary. The total loss for that batch is calculated using the data loss, physical loss, and boundary loss obtained from the current training batch.

[0103] Subsequently, using the automatic differentiation function of the deep learning framework, the gradient of the total loss with respect to the network parameters and the physical parameters to be inverted is calculated. Then, the Adam optimizer is used to update all the trainable parameters according to a preset learning rate of 0.001. This process is repeated until a complete training cycle is completed, meaning that all sample data in the training set and the configuration points in the initial configuration point set have been traversed once.

[0104] After each training round, the physical information neural network is validated using a validation set, and the data loss of the physical information neural network on the validation set is calculated to monitor whether the physical information neural network is overfitting.

[0105] S33. Every preset number of training steps, evaluate the residual contribution of the configuration point based on the physical residual at the configuration point in the current configuration point set.

[0106] Step S33 specifically includes the following steps: S331. Every preset number of training steps, for any one of the current configuration points in the current configuration point set, calculate the residuals of the temperature field equation, humidity field, equilibrium equation, and continuity at that configuration point.

[0107] Specifically, in this embodiment, the preset training steps are set to 500 steps. That is, after the physical information neural network completes 500 parameter iterations, for any configuration point in the current configuration point set, its four-dimensional spatiotemporal coordinates are obtained and input into the physical information neural network in the current state. After forward propagation, the network outputs the predicted results of the three-dimensional displacement components, excess pore water pressure, temperature, and volumetric water content corresponding to the four-dimensional spatiotemporal coordinates. Subsequently, using the automatic differentiation technique of the neural network, the predicted results are substituted into the governing equations to calculate the residuals of the temperature field equation, humidity field equation, stress balance equation, and continuity equation for that configuration point.

[0108] S332. The sum of the absolute values ​​of the temperature field equation residual, the humidity field residual, the equilibrium equation residual, and the continuity residual is taken as the residual contribution of the configuration point.

[0109] Specifically, in this embodiment, at a given time t, for any given point in the current set of points within the bulk set of points, the sum of the absolute values ​​of its temperature field equation residual, humidity field residual, equilibrium equation residual, and continuity residual is calculated, and the calculation result is used as the residual contribution. The larger the residual contribution, the greater the degree of violation of the physical equations by the physical information neural network at the current point of configuration.

[0110] S34. The configuration points are adaptively adjusted according to the residual contribution and the preset contribution threshold, thereby updating the current configuration point set.

[0111] This step only adaptively adjusts the configuration points within the body of the current configuration point set, while leaving the configuration points in the boundary configuration point set unchanged. Step S34 specifically includes the following steps: S341. Divide the solidified soil subgrade into multiple grid units in the spatiotemporal domain, and determine the residual threshold, which includes an upper limit and a lower limit of contribution.

[0112] Specifically, in this embodiment, the normalized spatiotemporal domain of the solidified soil subgrade (including...) is... and The data is divided into multiple four-dimensional grid cells. To maintain fairness in the statistics across all dimensions, each of the four dimensions is divided at equal intervals. , , and Each of the four dimensions is divided into 10 equally spaced intervals, thus forming multiple four-dimensional hypercube grid cells (referred to as grid cells) of the same size, which are used for region identification and placement point statistics.

[0113] Furthermore, a residual threshold is determined based on the residual contribution distribution of each configuration point. This residual threshold includes an upper and lower contribution limit. Specifically, the residual contribution values ​​of all current configuration points are sorted from largest to smallest. The residual contribution values ​​in the top 20% of the sorted values ​​are taken as the upper contribution limit, and the residual contribution values ​​in the bottom 20% of the sorted values ​​are taken as the lower contribution limit. For example, when there are 10,000 configuration points, the value ranked 2000th is taken as the upper contribution limit, and the value ranked 8000th is taken as the lower contribution limit. This dynamic threshold determination method can adapt to changes in the residual contribution distribution at different training stages, avoiding the problem of using a fixed threshold that leads to an excessively high threshold in the early stages, failing to identify high residual configuration points, or an excessively low threshold in the later stages, misclassifying many normal configuration points as high residual configuration points.

[0114] S342. The configuration points whose residual contribution exceeds the upper limit of contribution are recorded as high residual configuration points, and the configuration points whose residual contribution is lower than the lower limit of contribution are recorded as low residual configuration points.

[0115] Specifically, in this embodiment, for any configuration point in the current configuration point set, the residual contribution of the configuration point is first read, and then compared with the upper and lower limits of the contribution. If the residual contribution is greater than the upper limit, the configuration point is marked as a high residual configuration point; if the residual contribution is less than the lower limit, the configuration point is marked as a low residual configuration point; if the residual contribution is between the upper and lower limits, the configuration point is not marked.

[0116] S343. Count the number of high residual configuration points and low residual configuration points in each of the grid cells, and then determine the high residual region and the low residual region.

[0117] Specifically, in this embodiment, for any given grid cell, all configuration points falling within that grid cell are traversed, and the number of configuration points marked as high residual and low residual are counted respectively. If the proportion of high residual configuration points in a grid cell exceeds 40% of the total number of configuration points in that grid cell, then that grid cell is determined to be a high residual region. If the proportion of low residual configuration points in a grid cell exceeds 40% of the total number of configuration points in that grid cell, then that grid cell is determined to be a low residual region. If the proportions of both high and low residual configuration points in a grid cell exceed 40%, then the numbers of high and low residual configuration points are compared: if the number of high residual configuration points is greater than or equal to the number of low residual configuration points, then that grid cell is determined to be a high residual region; if the number of high residual configuration points is less than the number of low residual configuration points, then that grid cell is determined to be a low residual region. For grid cells where the proportions of both high and low residual configuration points do not exceed 40%, no region label is assigned. After traversing all grid cells, the set of all grid cells that are determined to be high residual regions constitutes the high residual region set, and the set of all grid cells that are determined to be low residual regions constitutes the low residual region set.

[0118] S344. Based on the number of configuration points in the current configuration point set and the number of high residual regions, new configuration points are adaptively generated using the Latin hypercube sampling method.

[0119] Specifically, in this embodiment, the initial total number of newly added configuration points is first determined, which is preferably 8% (rounded down) of the total number of configuration points in the current configuration point set. Then, the number of newly added configuration points to be allocated to each high residual region is calculated according to the following formula:

[0120] in, This represents the number of newly added configuration points in the d-th high residual region within the set of high residual regions; This indicates the initial total number of newly added configuration points; This represents the number of high residual configuration points in the d-th high residual region; D represents the total number of high residual regions. This indicates rounding up. The sum of the actual number of newly added configuration points obtained in each high residual region is the final number of newly added configuration points.

[0121] Furthermore, for each high residual region that requires additional configuration points, a corresponding number of new configuration points are generated within the spatiotemporal range formed by its spatial range and the time range of the entire computational domain, using the Latin hypercube sampling method.

[0122] S345. Based on the number of low residual regions and the number of newly added configuration points, remove the same number of configuration points located in the low residual regions from the current configuration point set.

[0123] Specifically, in this embodiment, the total number of configuration points to be removed is first determined. This total number is equal to the final number of newly added configuration points in S344, so as to keep the total number of configuration points unchanged before and after the adaptive adjustment, and avoid the continuous increase in the number of configuration points as the number of iterations increases, which would lead to a continuous increase in computational cost. Then, all configuration points located in the low residual region are selected from the current configuration point set to form a candidate set to be removed. If the number of configuration points in the candidate set to be removed is greater than or equal to the total number of configuration points to be removed, then the required number of configuration points to be removed are randomly selected from the candidate set to be removed and removed. If the number of configuration points in the candidate set to be removed is less than the total number of configuration points to be removed, then all configuration points in the candidate set to be removed are removed first, and then the remaining configuration points are supplemented in order of residual contribution from small to large to make up the number of configuration points still to be removed, that is, those configuration points with the lowest residual contribution are removed, until the total number of removals meets the requirements, thus realizing the update of the current configuration point set. The elimination mechanism of this configuration point ensures that computing resources are transferred from the low residual region where the model has already learned to the high residual region where it has not yet learned, thereby achieving adaptive optimization of configuration point allocation.

[0124] S35. When the training enables the physical information neural network to reach the preset convergence condition, the trained physical information neural network can be obtained.

[0125] Specifically, in this embodiment, the convergence condition consists of the following two conditions: First, the relative change in data loss of the physical information neural network on the validation set does not exceed 1% over 50 consecutive rounds; second, a preset maximum number of training iterations is reached, which is 20,000 steps. The first condition serves as an early stopping mechanism and the primary convergence criterion; the second condition acts as a fallback condition to prevent infinite loops. When the convergence condition is met, training of the physical information neural network is stopped, and the network parameters corresponding to the minimum data loss on the validation set are output as the final network parameters of the physical information neural network, resulting in the trained physical information neural network.

[0126] S4. Use the trained physical information neural network as a prediction model, and use the prediction model to predict the deformation of the solidified soil subgrade under arbitrary time and space coordinates.

[0127] Specifically, in this embodiment, after training the physical information neural network, it can be used as a prediction model, and then the prediction model can be used to predict the deformation of the solidified soil subgrade in any four-dimensional spatiotemporal coordinates.

[0128] It should be noted that in some cases, the actions described in the specification can be performed in different orders and still achieve the desired results. In this embodiment, the order of steps is given only to make the embodiment clearer and easier to explain, and not to limit it.

[0129] In an optional embodiment, to improve the practicality and facilitate the promotion of this method, please refer to [link to relevant documentation]. Figure 2 The present invention also provides a solidified soil subgrade deformation prediction system based on physical information neural network. The solidified soil subgrade deformation prediction system based on physical information neural network includes: a data input device 1, a data output device 2, a processor 3, and a storage device 4. The storage device 4 includes a computer-readable storage medium storing a computer program. The computer program includes program instructions. When the program instructions are executed by the processor 3, the processor 3 performs the contents described in steps S1 to S4.

[0130] In summary, the present invention has at least the following beneficial effects: 1. This method embeds the multi-physics field coupled control equations into the loss function of the physical information neural network, so that the model training is subject to the dual constraints of monitoring data and physical laws, ensuring the physical rationality of the deformation prediction results; by dynamically adjusting the distribution of configuration points during the training process, the configuration points are gradually focused on the areas of drastic changes in the physical field, thereby improving the prediction accuracy and training efficiency.

[0131] 2. This method achieves unified quantification of multi-physics constraints by embedding the sum of squared residuals of the temperature field equation, humidity field equation, and stress field equation as physical loss terms into the total loss function; by constructing coupled evolution equations and updating constitutive parameters in the control equation set accordingly, the constitutive parameters change in real time with the curing process, reflecting the physical characteristics of "hardening with age" of the solidified soil.

[0132] 3. This method enables the model to automatically identify the optimal values ​​of physical parameters from monitoring data by jointly initializing and synchronously updating physical parameters and network parameters, thus overcoming the problem of parameters not matching the actual field conditions due to reliance on indoor test calibration. By evaluating the residual contribution of each configuration point at preset steps and making adaptive adjustments, the configuration point set is dynamically optimized during training, solving the problem that a fixed configuration point distribution cannot adapt to changes in the model error distribution and improving prediction accuracy.

[0133] 4. This method achieves quantitative assessment of the comprehensive deviation of multi-physics fields by using the sum of the absolute values ​​of each physical residual as the residual contribution of the configuration point; it achieves accurate positioning of high residual and low residual regions by dividing the roadbed into grid cells and counting the number of high and low residual configuration points in each grid; and it keeps the total number of configuration points constant by adding configuration points in high residual regions and removing the same number of configuration points from low residual regions, thus achieving efficient utilization of computing resources and ensuring prediction efficiency.

[0134] 5. A system adapted to this method was constructed. This system not only improves the practicality of this method, but also facilitates its promotion.

[0135] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention, and they should all be covered within the scope of the claims and specification of the present invention.

Claims

1. A method for predicting deformation of solidified soil subgrade based on physical information neural networks, characterized in that, Includes the following steps: Acquire multi-source monitoring data and soil property data of solidified soil subgrade, construct dataset and generate initial configuration point set; Based on the soil property data, a set of multiphysics coupled control equations is constructed as physical constraints and embedded into the loss function of the physical information neural network. Based on the dataset and the initial set of configuration points, the physical information neural network is iteratively trained using an adaptive configuration point dynamic adjustment strategy. The trained physical information neural network is used as a prediction model, and the prediction model is used to predict the deformation of the solidified soil subgrade under arbitrary spatiotemporal coordinates.

2. The method for predicting the deformation of solidified soil subgrade based on physical information neural networks according to claim 1, characterized in that: The multi-source monitoring data includes the spatial coordinates of different monitoring points in the solidified soil subgrade, as well as the three-dimensional displacement components, excess pore water pressure, temperature, and volumetric water content at different monitoring points.

3. The method for predicting deformation of solidified soil subgrade based on physical information neural network according to claim 1, characterized in that: The soil properties data include the reference compression modulus, reference permeability coefficient, Poisson's ratio, thermal conductivity, specific heat capacity, density, cement hydration heat release rate curve, and unconfined compressive strength under different curing conditions of the solidified soil.

4. The method for predicting deformation of solidified soil subgrade based on physical information neural network according to claim 1, characterized in that, The process of acquiring multi-source monitoring data and soil property data of solidified soil subgrade, constructing a dataset, and generating an initial configuration point set includes the following steps: Collect raw multi-source monitoring data and soil property data of solidified soil subgrade, preprocess the raw multi-source monitoring data to obtain the multi-source monitoring data and construct the dataset; Within the spatial range of the solidified soil subgrade, the initial configuration point set is generated using the Latin hypercube sampling method.

5. The method for predicting deformation of solidified soil subgrade based on physical information neural network according to claim 1, characterized in that, The process of constructing a multiphysics coupled control equation set based on the soil property data as a physical constraint and embedding it into the loss function of the physical information neural network includes the following steps: Based on the soil properties data, temperature field equations, humidity field equations and stress field equations are constructed respectively to form a set of control equations coupled by multiple physical fields. Physical residual terms are constructed based on each partial differential equation in the governing equation set, and their sum of squares is used as a physical loss term, which is added to the loss function of the physical information neural network along with the boundary condition loss.

6. The method for predicting deformation of solidified soil subgrade based on physical information neural network according to claim 1, characterized in that, The step of constructing a multiphysics coupled control equation set based on the soil property data as a physical constraint and embedding it into the loss function of the physical information neural network also includes: A coupled evolution equation for the unconfined compressive strength of solidified soil with respect to age, temperature, and moisture content is constructed, and then the constitutive parameters in the governing equation set are updated based on the coupled evolution equation.

7. The method for predicting deformation of solidified soil subgrade based on physical information neural network according to claim 1, characterized in that, The iterative training of the physical information neural network based on the dataset and the initial set of configuration points, combined with an adaptive configuration point dynamic adjustment strategy, includes the following steps: Initialize the network parameters of the physical information neural network and the physical parameters to be inverted, and use the initial configuration point set as the current configuration point set; The physical information neural network is trained and validated based on the dataset, and then the network parameters and the physical parameters to be inverted are updated through backpropagation. Every preset number of training steps, the residual contribution of the configuration point is evaluated based on the physical residual at the configuration point in the current configuration point set; The configuration points are adaptively adjusted based on the residual contribution and the preset contribution threshold, thereby updating the current configuration point set; When the training causes the physical information neural network to reach the preset convergence condition, the trained physical information neural network can be obtained.

8. The method for predicting deformation of solidified soil subgrade based on physical information neural network according to claim 7, characterized in that, Every preset number of training steps, the residual contribution of each configuration point is evaluated based on the physical residual at the current configuration point set, including the following steps: Every preset number of training steps, for any one of the current configuration points in the set of configuration points, calculate the residuals of the temperature field equation, humidity field, equilibrium equation, and continuity at that configuration point. The sum of the absolute values ​​of the residuals of the temperature field equation, the humidity field, the equilibrium equation, and the continuity residual is taken as the residual contribution of the configuration point.

9. The method for predicting deformation of solidified soil subgrade based on physical information neural network according to claim 8, characterized in that, The step of adaptively adjusting the configuration points based on the residual contribution and a preset contribution threshold, and then updating the current configuration point set, includes the following steps: The solidified soil subgrade is divided into multiple grid units in the spatiotemporal domain, and the residual threshold is determined. The residual threshold includes an upper limit of contribution and a lower limit of contribution. Configuration points whose residual contribution exceeds the upper limit of contribution are recorded as high residual configuration points, and configuration points whose residual contribution is lower than the lower limit of contribution are recorded as low residual configuration points. The number of high residual configuration points and low residual configuration points in each of the grid cells is counted, thereby determining the high residual region and the low residual region; Based on the number of configuration points in the current configuration point set and the number of high residual regions, the Latin hypercube sampling method is used to adaptively generate new configuration points. Based on the number of low residual regions and the number of newly added configuration points, remove the same number of configuration points located in the low residual regions from the current configuration point set.

10. A deformation prediction system for solidified soil subgrade based on physical information neural networks, characterized in that, The solidified soil subgrade deformation prediction system based on physical information neural network includes: a data input device, a data output device, a processor, and a storage device. The storage device includes a computer-readable storage medium storing a computer program. The computer program includes program instructions, which, when executed by the processor, cause the processor to implement the solidified soil subgrade deformation prediction method based on physical information neural network as described in any one of claims 1-9.

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