A Time-Varying Bearing Capacity Sensing and Prediction Method for Static Pressure Piles Based on Physical Information Networks

Abstract

This invention provides a method for sensing and predicting the time-varying bearing capacity of statically loaded piles based on Physical Information Networks (PINNs). The method includes: collecting pore pressure dissipation data using pile sensors; inputting the pore pressure dissipation data and calculation points into a PINNs integrated forward and inverse model, estimating excess pore water pressure during backpropagation to obtain the final consolidation coefficient; inputting the final consolidation coefficient and the calculation points into a PINNs integrated forward and inverse model, estimating excess pore water pressure during backpropagation; inputting a test set into the trained PINNs integrated forward and inverse model, outputting the excess pore water pressure dissipation degree of the pile side soil, and predicting the time-varying bearing capacity of the statically loaded pile based on this value. This invention can accurately invert and sense the soil consolidation coefficient using short-term pore pressure dissipation test data from pile pore pressure sensors, thereby predicting the degree of consolidation of the pile side soil and achieving accurate prediction of the time-varying bearing capacity of statically loaded piles.

Description

Technical Field

[0001] This invention belongs to the field of geotechnical mechanics and engineering technology, specifically relating to a method for sensing and predicting the time-varying bearing capacity of static pressure piles based on physical information networks. Background Technology

[0002] During static pressure pile driving in naturally saturated clay strata, the pile shears and compresses the soil, penetrating the foundation and causing remodeling of the surrounding soil, resulting in high excess pore water pressure. After pile driving, the effective stress of the surrounding soil gradually recovers and increases as the excess pore water pressure dissipates. Therefore, the bearing capacity of static pressure piles in saturated clay strata exhibits significant time-dependent characteristics. However, due to the complexity of the stress and strain history of the soil surrounding the static pressure pile, current research on the pile driving effect and bearing capacity time-dependent characteristics of static pressure piles in saturated soft soil foundations remains insufficient. The design and calculation of static pressure piles often fail to consider the increase in bearing capacity after pile driving caused by the dissipation of excess pore water pressure, leading to conservative designs and significant resource waste in practical engineering. Therefore, predicting and fully utilizing the time-dependent characteristics of the bearing capacity of static pressure piles has become a critical issue urgently needing to be addressed in current research on soft soil pile foundations.

[0003] Extensive research has been conducted by scholars both domestically and internationally on the time-varying bearing capacity of statically pressed piles. For example, Randolph et al. used undrained borehole expansion approximation to simulate the statically pressed pile driving process, conducting theoretical research on the pile driving effect and the reconsolidation of the surrounding soil in saturated clay. Skov et al. proposed an empirical formula for calculating the time-varying bearing capacity of statically pressed piles by analyzing measured data of the bearing capacity of statically pressed piles in clay over time. Cao Quan et al., based on the characteristics of static cone penetration tests and the penetration of statically pressed piles in soft clay, proposed a theoretical solution for calculating the time-varying bearing capacity of statically pressed piles in soft soil based on static cone penetration test parameters. While these studies have significant theoretical and engineering implications, most theoretical research neglects the in-situ mechanical properties of the soil, such as stress history and stress anisotropy, as well as the influence of soil stress relaxation during the reconsolidation process on the time-varying bearing capacity of statically pressed piles. Furthermore, most studies focus on a single aspect of the pile driving process or the reconsolidation of the surrounding soil, failing to systematically and comprehensively reflect the essence of the time-varying bearing capacity of statically pressed piles.

[0004] Therefore, accurately predicting the time-varying bearing capacity of static pressure piles has become a key technical challenge that urgently needs to be addressed. Summary of the Invention

[0005] To address the aforementioned problems in existing technologies, this invention provides a method for sensing and predicting the time-varying bearing capacity of statically loaded piles based on physical information networks. The technical problem to be solved by this invention is achieved through the following technical solution:

[0006] Firstly, a method for sensing and predicting the time-varying bearing capacity of statically pressed piles based on physical information networks includes:

[0007] S100 uses pile body sensors to collect pore pressure dissipation data; the pore pressure dissipation data includes the sensor deployment depth, the excess pore water pressure collected by the sensor, and the collection time.

[0008] S200, input the pore pressure dissipation data and calculation points into the PINNs forward and inverse integrated inversion model, and estimate the excess pore water pressure in the back propagation to obtain the final consolidation coefficient;

[0009] S300, input the final consolidation coefficient and calculation points into the PINNs integrated forward and inverse model, and estimate the excess pore water pressure in the back propagation to obtain the trained PINNs integrated forward and inverse model;

[0010] S400 inputs the test set into the trained PINNs forward and inverse integrated forward model, outputs the dissipation degree of excess pore water pressure in the soil side of the pile, and predicts the time-varying bearing capacity of the static pressure pile based on the dissipation degree of excess pore water pressure in the soil side of the pile. The test set consists of several calculation points that need to be predicted, and the calculation points include time and radial distance.

[0011] Secondly, the present invention provides a method for sensing and predicting the time-varying bearing capacity of statically loaded piles based on physical information networks, including:

[0012] The data acquisition module is used to collect pore pressure dissipation data using pile body sensors; the pore pressure dissipation data includes the sensor deployment depth, the excess pore water pressure collected by the sensor, and the acquisition time.

[0013] The inversion module is used to input pore pressure dissipation data and calculation points into the PINNs integrated forward and inverse inversion model, and estimate excess pore water pressure in the back propagation to obtain the final consolidation coefficient;

[0014] The forward modeling module is used to input the final consolidation coefficient and calculation points into the PINNs integrated forward and inverse modeling model, and estimate the excess pore water pressure in the back propagation to obtain the trained PINNs integrated forward and inverse modeling model.

[0015] The prediction module is used to input the test set into the trained PINNs forward and inverse integrated forward model, output the dissipation degree of excess pore water pressure in the soil along the pile, and predict the time-varying bearing capacity of the static pressure pile based on the dissipation degree of excess pore water pressure in the soil along the pile. The test set consists of several calculation points that need to be predicted, and the calculation points include time and radial distance.

[0016] Beneficial effects:

[0017] This invention provides a method for sensing and predicting the time-varying bearing capacity of statically loaded piles based on Physical Information Networks (PINNs). The method includes: collecting pore pressure dissipation data using pile sensors; inputting the pore pressure dissipation data and calculation points into a PINNs integrated forward and inverse model, estimating excess pore water pressure during backpropagation to obtain the final consolidation coefficient; inputting the final consolidation coefficient and calculation points into a PINNs integrated forward and inverse model, estimating excess pore water pressure during backpropagation to obtain the final excess pore water pressure; inputting a test set into the trained PINNs integrated forward and inverse model, outputting the excess pore water pressure dissipation degree of the pile side soil, and predicting the time-varying bearing capacity of the statically loaded pile based on this excess pore water pressure. This invention can accurately invert and sense the soil consolidation coefficient using short-term pore pressure dissipation test data from pile pore pressure sensors, thereby predicting the degree of consolidation of the pile side soil and achieving accurate prediction of the time-varying bearing capacity of statically loaded piles.

[0018] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0019] Figure 1 This is a flowchart illustrating a method for sensing and predicting the time-varying bearing capacity of static pressure piles based on a physical information network, provided in an embodiment of the present invention.

[0020] Figure 2 This is a schematic diagram of a static pressure pile and its sensor arrangement provided in an embodiment of the present invention;

[0021] Figure 3 This is a schematic diagram of a PINNs forward and inverse integrated model provided in an embodiment of the present invention;

[0022] Figure 4 This is a schematic diagram of the inversion consolidation coefficient results of a PINNs forward and inverse integrated model provided in an embodiment of the present invention;

[0023] Figure 5 This is a schematic diagram of the result of predicting the dissipation of excess pore water pressure using the PINNs forward and inverse integrated model, provided by an embodiment of the present invention.

[0024] Figure 6 This is a curve comparing the predicted bearing capacity of a PINNs static pressure pile with the measured bearing capacity, provided by an embodiment of the present invention. Detailed Implementation

[0025] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0026] Example 1

[0027] Given the challenges faced by current methods for predicting the time-varying bearing capacity of static piles, such as the failure to consider the in-situ mechanical properties of soil, such as stress history and stress anisotropy, as well as the influence of soil stress relaxation during the reconsolidation process around the pile on the time-varying bearing capacity of static piles, and the low efficiency of prediction, it is difficult to achieve rapid and accurate prediction of the time-varying bearing capacity of static piles in practical applications.

[0028] Therefore, please see Figure 1 , Figure 1 This is a flowchart illustrating a method for sensing and predicting the time-varying bearing capacity of statically loaded piles based on a physical information network, provided by an embodiment of the present invention. The method includes:

[0029] S100 uses pile body sensors to collect pore pressure dissipation data;

[0030] Among them, the pore pressure dissipation data includes the sensor deployment depth, the excess pore water pressure collected by the sensor, and the collection time.

[0031] Figure 2 The diagram shown illustrates a static pressure pile and its sensor arrangement according to an embodiment of the present invention. See also, as an example... Figure 2 A pore pressure sensor can be installed on the static pressure pile body, and then a pile driving test can be carried out to collect the pore water pressure at different depths through the pore pressure sensor.

[0032] To better illustrate the beneficial effects of the present invention, a centrifugation model experiment was conducted:

[0033] Specifically, the model pile used in the experiment was a pore pressure static cone penetrometer with an effective length L of 300 mm and an axial diameter D of 10 mm. The experimental procedure was as follows: First, the model pile was pushed into the soil sample at a constant speed of 90 mm / min until the specified depth of 240 mm was reached; then, the seepage process was stopped and a pore pressure dissipation test was conducted until the pore pressure reading decayed to the level of the static pore water pressure. During the experiment, the pore pressure dissipation data were recorded in detail.

[0034] S200, input the pore pressure dissipation data and calculation points into the PINNs forward and inverse integrated inversion model, and estimate the excess pore water pressure in the back propagation to obtain the final consolidation coefficient;

[0035] The PINNs integrated forward and inverse model includes a first neural network. The consolidation coefficient is obtained by training the first neural network. The training process includes: repeatedly inputting pore pressure dissipation data and calculation points into the first neural network and outputting the first estimated value of excess pore water pressure; using the first estimated value of excess pore water pressure to calculate the physical information-data loss function; and updating the weights and biases of the first neural network in reverse according to the physical information-data loss function until the training ends. The consolidation coefficient at the end of the training is taken as the final consolidation coefficient.

[0036] The first neural network of the present invention includes two first input layers and one first output layer. The two first input layers input depth and time, respectively, and the first output layer outputs the estimated excess pore water pressure. For example, the first neural network includes 5 hidden layers, each hidden layer has 30 neural network nodes, the selected activation function is Tanh, the optimizer is Adam, and the initial value of the consolidation coefficient to be inverted is set to 1.

[0037] Therefore, the calculation points are first input into the first neural network, and the excess pore water pressure is estimated during the backpropagation process, thus obtaining the first estimated value of the excess pore water pressure. Then, based on the first estimated value of the excess pore water pressure, the physical-data loss function is calculated using the chain rule, and the residual of the physical-data loss function is obtained. Then, based on the residual of the physical-data loss function, the weights and biases of the first neural network are continuously updated in reverse using the chain rule to generate the estimated value of the consolidation coefficient, so that the residual of the physical-data loss function is minimized, and the consolidation coefficient under this condition is taken as the final consolidation coefficient.

[0038] In a specific embodiment of the present invention, reference is made to... Figure 3 The training process of the first neural network includes:

[0039] a1, by inputting the collected pore pressure dissipation data and calculation points into the PINNs integrated forward and inverse inversion model, the first estimated value of excess pore water pressure is obtained; the first neural network includes: a first input layer, a first output layer and a first hidden layer;

[0040] b1, Calculate the physical information-data loss function based on the first estimate of the excess pore water pressure;

[0041] The physical information-data loss function includes the loss function of the first radial consolidation equation, the loss function of the first initial condition, the loss function of the first boundary condition, and the excess pore pressure dissipation data loss function;

[0042] The physical information-data loss function is expressed as:

[0043]

[0044] in, Represents the physical information-data loss function. The loss function representing the excess pressure dissipation data in the pores. This represents the loss function of the first radial consolidation equation. The loss function represents the first initial condition. The loss function represents the first boundary condition;

[0045] During the static pressure pile driving process, the excess pore pressure is mainly generated in the radial direction. Therefore, the radial consolidation equation is used to simulate the dissipation process of excess pore pressure in the soil along the pile side during static pressure pile driving. The radial consolidation equation can be characterized as follows:

[0046]

[0047] In the formula: G is the shear modulus, v′ is the effective Poisson's ratio, and c h denoted as the horizontal consolidation coefficient, z as the depth, t as the time, and u(z,t) as the excess pore water pressure at depth z and time t.

[0048] The loss function for constructing the first radial consolidation equation using the radial consolidation equation is expressed as:

[0049]

[0050] Where, λ P N represents the weights of the loss function in the radial consolidation equation. P This indicates the number of computational points from within the computational domain of the radial consolidation equation. This represents the i1th calculation point within the computational domain of the radial consolidation equation. This represents the radial distance to the i1th calculation point within the computational domain of the radial consolidation equation. This represents the time taken at the i1th calculation point within the computational domain of the radial consolidation equation. c represents the first estimate of the excess pore water pressure at the i1th calculation point within the computational domain of the radial consolidation equation. h Indicates the consolidation coefficient;

[0051] During the dissipation of excess pore pressure on the pile side, the pore pressure change at the radius of the elastic-plastic zone is minimal and can be considered as the drainage boundary; since the pile body is impermeable, the diameter of the pile can be set as the non-drainage boundary condition, thus:

[0052]

[0053] The loss function for the first boundary condition is expressed as:

[0054]

[0055] In the formula, The weights of the loss function representing the boundary conditions at the pile diameter are given. N represents the weight of the loss function for the boundary conditions at the elastoplastic radius. B This indicates the number of computation points from within the boundary condition computation domain. This represents the i2th calculation point within the boundary condition computation domain. This represents the radial distance to the i2th calculation point within the boundary condition computation domain. This represents the time taken at the i2th calculation point within the boundary condition computation domain. This represents the first estimated value of the excess pore water pressure at the i2th calculation point within the boundary condition computation domain;

[0056] Loss function with first initial conditions The loss function for the first initial condition is related to the initial pore water pressure and is therefore expressed as:

[0057]

[0058] Where, λ I N represents the weights of the loss function used to calculate the initial conditions. I This indicates the number of computation points originating from the initial condition computation domain. This represents the i3rd calculation point within the initial condition computation domain. This represents the radial distance to the i3th calculation point within the initial condition computation domain. This represents the pre-time of the i3th calculation point within the initial condition computation domain. This represents the first estimated value of the excess pore water pressure at the i3th calculation point within the initial conditions computational domain. This represents the initial pore water pressure at the i3th calculation point within the initial condition calculation domain;

[0059] Loss function of excess pore pressure dissipation data The loss function for the excess porosity dissipation data, constructed from the excess porosity dissipation data collected by sensors, is therefore expressed as:

[0060]

[0061] Where, λ D N represents the weight of the loss function used to calculate the excess pore pressure dissipation data. D This indicates the number of calculation points within the calculation domain derived from the excess pore pressure dissipation data. This represents the i4th calculation point within the calculation domain of excess pore pressure dissipation data. This represents the radial distance of the i4th calculation point within the calculation domain of the excess pore pressure dissipation data. This represents the time at the i4th calculation point within the calculation domain of excess pore pressure dissipation data. This represents the excess porosity dissipation data at the i4th calculation point within the excess porosity pressure dissipation data calculation domain. This represents the first estimated value of the excess pore water pressure at the i4th calculation point within the excess pore pressure dissipation data calculation domain.

[0062] c1, based on the residual of the physical information-data loss function, and using the chain rule to update the weights and biases of the first neural network in reverse, and use it as the first neural network for the next iteration;

[0063] d1, repeat a1-c1 until the residual of the physical information-data loss function is less than the predetermined first criterion, then training is terminated, and the consolidation coefficient in the physical information-data loss function at the training termination is taken as the final consolidation coefficient.

[0064] refer to Figure 3 This invention can set up the PINNs forward and inverse integrated inversion model and the PINNs forward and inverse integrated forward model respectively in the inversion module and the forward module, and then call these two modules to execute the training process of the corresponding model.

[0065] In this embodiment, the weights and biases of the first neural network are updated based on the first estimated value of the excess pore water pressure, and the consolidation coefficient in the physical information-data loss function is calculated as the estimated value of the consolidation coefficient. The above steps are then repeated until the residual of the physical information-data loss function is less than a predetermined first standard. At this point, the consolidation coefficient in the physical information-data loss function is calculated as the final consolidation coefficient. It should be noted that the first standard can be set according to actual conditions; this embodiment does not specifically limit it. For example, the first standard could be e. -2 .

[0066] Furthermore, the PINNs integrated forward and inverse inversion model saves the consolidation coefficient c once every 1000 training iterations during the training process. V The estimated value is taken as the consolidation coefficient c from the last training iteration. v The final result of the inversion. To qualitatively measure the error between the true value and the inverted / predicted value, L is selected. w The relative error is used as a metric, and its calculation formula is as follows:

[0067]

[0068] In the formula, and y u These represent the inverted / predicted value and the actual value, respectively. This can represent the inverted / predicted and actual values ​​of excess pore water pressure, or the inverted / predicted and actual values ​​of the consolidation coefficient; N represents the number of inverted / predicted values. For example... Figure 4 As shown, after 40,000 training iterations, the consolidation coefficient c of the PINNs integrated forward and inverse inversion model is...v The inversion error is only 0.04, which indicates that the PINNs integrated forward and inverse inversion model constructed in this invention can quickly and accurately invert the consolidation coefficient c based on short-term pore water pressure and excess pore pressure dissipation data. h .

[0069] S300, input the final consolidation coefficient and calculation points into the PINNs integrated forward and inverse model, and estimate the excess pore water pressure in the back propagation to obtain the trained PINNs integrated forward and inverse model;

[0070] The PINNs integrated forward and inverse model includes a second neural network. The final excess pore water pressure is obtained by training the second neural network. The training process includes: repeatedly inputting pore pressure dissipation data and calculation points into the second neural network and outputting a second estimate of the excess pore water pressure; calculating the physical information loss function using the second estimate of the excess pore water pressure; and updating the weights and biases of the second neural network in reverse according to the physical information loss function until the training ends. The second estimate at the end of the training is taken as the final excess pore water pressure.

[0071] It is worth noting that the calculation points in steps S200 and S300 are randomly selected.

[0072] In a specific embodiment of the present invention, reference is made to... Figure 3 The training process of the second neural network includes:

[0073] a2, the final consolidation coefficient is used as the consolidation coefficient of the physical information loss function of the second neural network, and the calculation points are input into the second neural network to obtain the second estimate of the excess pore water pressure; the second neural network includes: a second input layer, a second output layer and a second hidden layer;

[0074] The second neural network in this step includes two second input layers and one second output layer. The two second input layers take depth and time as inputs, respectively, and the second output layer outputs the estimated excess pore water pressure. For example, the second neural network includes 5 hidden layers, each with 30 neural network nodes, using Tanh activation function and Adam optimizer.

[0075] b2, Calculate the physical information loss function based on the second estimate;

[0076] The physical information loss function includes the loss function of the second partial differential equation, the loss function of the second initial condition, and the loss function of the second boundary condition;

[0077] The physical information loss function is expressed as:

[0078]

[0079] in, Represents the physical information loss function. This represents the loss function of the second radial consolidation equation. The loss function represents the second initial condition. The loss function representing the second boundary condition;

[0080] The loss function of the second radial consolidation equation is expressed as:

[0081]

[0082] Where, λ P N represents the weights of the loss function in the radial consolidation equation. P This indicates the number of computational points from within the computational domain of the radial consolidation equation. This represents the i5th calculation point within the computational domain of the radial consolidation equation, for example, set to 10000. This represents the radial distance to the i5th calculation point within the computational domain of the radial consolidation equation. This represents the time taken at the i5th calculation point within the computational domain of the radial consolidation equation. This represents the second estimate of the excess pore water pressure at the i5th calculation point within the computational domain of the radial consolidation equation;

[0083] The loss function for the second boundary condition is expressed as:

[0084]

[0085] In the formula, The weights of the loss function representing the boundary conditions at the pile diameter are given. N represents the weight of the loss function for the boundary conditions at the elastoplastic radius. B This indicates the number of computation points from within the boundary condition computation domain. This represents the i-th calculation point within the boundary condition computation domain, for example, set to 1000. This represents the radial distance to the i6th calculation point within the boundary condition computation domain. This represents the time taken at the i6th calculation point within the boundary condition computation domain. This represents the second estimate of the excess pore water pressure at the i6th calculation point within the boundary condition computation domain;

[0086] The loss function for the second initial condition is expressed as:

[0087]

[0088] Where, λ I This represents the weights of the loss function used to calculate the initial conditions; for example, it can be set to 1 or N. IThis indicates the number of computation points from the initial condition computation domain, for example, set to 1000. This represents the i7th calculation point within the initial condition computation domain. This represents the radial distance to the i7th calculation point within the initial condition computation domain. This represents the pre-time of the i7th computation point within the initial condition computation domain. This represents the second estimated value of the excess pore water pressure at the i7th calculation point within the initial condition computational domain. This represents the initial pore water pressure at the i7th calculation point within the initial condition calculation domain.

[0089] c2, based on the residual of the physical information loss function, and using the chain rule to update the weights and biases of the second neural network in reverse;

[0090] d2, repeat a2-c2 until the residual of the physical information loss function is less than the predetermined second criterion, then training ends.

[0091] In this embodiment, the weights and biases of the second neural network are updated based on the second estimate. Then, the above steps are continued until the residual of the physical information loss function is less than a predetermined second criterion, completing the training of the PINNs integrated forward and inverse model. It should be noted that the second criterion can be set according to actual conditions; this embodiment does not specifically limit it. For example, the second criterion could be e. -2 .

[0092] S400 inputs the test set into the trained PINNs forward and inverse integrated forward model, outputs the dissipation degree of excess pore water pressure in the soil side of the pile, and predicts the time-varying bearing capacity of the static pressure pile based on the dissipation degree of excess pore water pressure in the soil side of the pile. The test set consists of several calculation points that need to be predicted, and the calculation points include time and radial distance.

[0093] The test set consists of several calculation points that need to be predicted, including time and radial distance. The test set is input into the trained PINNs integrated forward and inverse model, which outputs the dissipation degree of excess pore water pressure in the pile side soil. The dissipation degree of excess pore water pressure in the pile side soil is then input into the calculation formula for the time-varying bearing capacity of the static pressure pile to calculate the time-varying bearing capacity of the static pressure pile.

[0094] The formula for calculating the time-varying bearing capacity of static pressure piles is as follows:

[0095]

[0096] In the formula, Q t (t), Q s (t) and Q b (t) represent the time-varying bearing capacity, pile side resistance, and pile end resistance of the statically pressed pile, respectively; h if represents the depth to which the pile is driven into the i-th layer of soil; si (t) and q bi (t) represent the unit pile side resistance and unit pile end resistance in the i-th soil layer, respectively; C s and A b These are the pile cross-sectional perimeter and the pile cross-sectional area, respectively.

[0097] Unit pile end resistance q b (t) is:

[0098]

[0099] In the formula, N c s is the end bearing capacity coefficient. u0tc denoted as the shear strength of the in-situ soil under triaxial compression conditions, Λ as the plastic volumetric strain ratio, OCR as the overconsolidation ratio, p′(t) as the average effective stress over time, and p′0 as the initial average effective stress.

[0100] The average effective stress p′(t) is:

[0101]

[0102] In the formula, u0-u t It is the dissipation rate of excess pore water pressure in the soil along the pile, where u0 is the initial excess pore water pressure in the soil along the pile. t This refers to the excess pore water pressure in the soil surrounding the pile.

[0103] Unit pile side resistance f s (t) is:

[0104]

[0105] In the formula, and ψ f Here, φ′ is the stress transformation parameter, φ′ is the effective internal friction angle, and M is the slope of the critical state line.

[0106] For example, the test set consists of 100 sets of computation points, with a range of [t∈(0,100), z=0.25]. Figure 5 The results of excess pore water pressure dissipation prediction using the PINNs integrated forward and inverse model are presented. It can be seen that the PINN prediction results agree well with the measured solutions, indicating that PINN can accurately predict the excess pore water pressure dissipation degree in the pile side soil. The excess pore water pressure dissipation degree in the pile side soil is then input into the calculation formula for the time-varying bearing capacity of statically pressed piles to predict the time-varying bearing capacity of the statically pressed piles. Figure 6The comparison between the predicted and measured bearing capacity of the PINNs static pressure pile is presented, with an error of only 0.01. It can be seen that the prediction results of the PINNs prediction model established in this invention are in good agreement with the measured values, proving that the method of this invention can accurately invert and perceive the soil consolidation coefficient through short-term pore pressure dissipation test data from pile pore pressure sensors, and thus predict the degree of consolidation of the soil along the pile, thereby achieving accurate prediction of the time-varying bearing capacity of the static pressure pile.

[0107] This invention provides a method for sensing and predicting the time-varying bearing capacity of statically loaded piles based on Physical Information Networks (PINNs). The method includes: collecting pore pressure dissipation data using pile sensors; inputting the pore pressure dissipation data and calculation points into a PINNs integrated forward and inverse model, estimating excess pore water pressure during backpropagation to obtain the final consolidation coefficient; inputting the final consolidation coefficient and calculation points into a PINNs integrated forward and inverse model, estimating excess pore water pressure during backpropagation; inputting a test set into the trained PINNs integrated forward and inverse model, outputting the excess pore water pressure dissipation degree of the pile side soil, and predicting the time-varying bearing capacity of the statically loaded pile based on this value. This invention can accurately inversely sense the soil consolidation coefficient using short-term pore pressure dissipation test data from pile pore pressure sensors, thereby predicting the degree of consolidation of the pile side soil and achieving accurate prediction of the time-varying bearing capacity of statically loaded piles.

[0108] This invention also provides a method for sensing and predicting the time-varying bearing capacity of static pressure piles based on physical information networks, comprising:

[0109] The data acquisition module is used to collect pore pressure dissipation data using pile body sensors; the pore pressure dissipation data includes the sensor deployment depth, the excess pore water pressure collected by the sensor, and the acquisition time.

[0110] The inversion module is used to input pore pressure dissipation data and calculation points into the PINNs integrated forward and inverse inversion model, and estimate excess pore water pressure in the back propagation to obtain the final consolidation coefficient;

[0111] The forward modeling module is used to input the final consolidation coefficient and calculation points into the PINNs integrated forward and inverse modeling model, and estimate the excess pore water pressure in the back propagation to obtain the trained PINNs integrated forward and inverse modeling model.

[0112] The prediction module is used to input the test set into the trained PINNs forward and inverse integrated forward model, output the dissipation degree of excess pore water pressure in the soil along the pile, and predict the time-varying bearing capacity of the static pressure pile based on the dissipation degree of excess pore water pressure in the soil along the pile. The test set consists of several calculation points that need to be predicted, and the calculation points include time and radial distance.

[0113] This invention provides a device for sensing and predicting the time-varying bearing capacity of statically loaded piles based on Physical Information Networks (PINNs). It utilizes pile sensors to collect pore pressure dissipation data; inputs the pore pressure dissipation data and calculation points into a PINNs integrated forward and inverse model, and estimates the excess pore water pressure during backpropagation to obtain the final consolidation coefficient; inputs the final consolidation coefficient and calculation points into a PINNs integrated forward and inverse model, and estimates the excess pore water pressure during backpropagation; inputs a test set into the trained PINNs integrated forward and inverse model, outputs the excess pore water pressure dissipation degree of the pile side soil, and predicts the time-varying bearing capacity of the statically loaded pile based on this value. This invention can accurately invert and sense the soil consolidation coefficient using short-term pore pressure dissipation test data from pile pore pressure sensors, thereby predicting the degree of consolidation of the pile side soil and achieving accurate prediction of the time-varying bearing capacity of statically loaded piles.

[0114] It is worth noting that the terms "first" and "second" in this invention are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0115] Although this application has been described herein in conjunction with various embodiments, those skilled in the art will understand and implement other variations of the disclosed embodiments by reviewing the accompanying drawings, the disclosure, and the appended claims in carrying out the claimed application. In the claims, the word "comprising" does not exclude other components or steps, and "a" or "an" does not exclude a plurality.

[0116] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A method for sensing and predicting the time-varying bearing capacity of static pressure piles based on physical information networks, characterized in that, include: S100, using pile body sensors to collect pore pressure dissipation data; the pore pressure dissipation data includes the sensor deployment depth, the excess pore water pressure collected by the sensor, and the collection time; S200, input the pore pressure dissipation data and calculation points into the PINNs forward and inverse integrated inversion model, and estimate the excess pore water pressure in the reverse propagation to obtain the final consolidation coefficient; S300, input the final consolidation coefficient and the calculation point into the PINNs forward and inverse integrated forward model, and estimate the excess pore water pressure in the back propagation to obtain the trained PINNs forward and inverse integrated forward model; S400, input the test set into the trained PINNs forward and inverse integrated forward model, output the excess pore water pressure dissipation degree of the pile side soil, and predict the time-varying bearing capacity of the static pressure pile based on the excess pore water pressure dissipation degree of the pile side soil. The test set consists of several calculation points that need to be predicted, and the calculation points include time and radial distance. The PINNs integrated forward and inverse inversion model includes a first neural network; The consolidation coefficient is obtained by training the first neural network. The training process includes: repeatedly inputting pore pressure dissipation data and calculation points into the first neural network and outputting a first estimated value of excess pore water pressure; using the first estimated value of excess pore water pressure to calculate the physical information-data loss function; and updating the weights and biases of the first neural network in reverse according to the physical information-data loss function until the training ends; and taking the consolidation coefficient at the end of the training as the final consolidation coefficient. The training process of the first neural network includes: a1, by inputting the collected pore pressure dissipation data and calculation points into the PINNs integrated forward and inverse inversion model, the first estimated value of excess pore water pressure is obtained; the first neural network includes: a first input layer, a first output layer and a first hidden layer; b1, Calculate the residual of the physical information-data loss function based on the first estimated value of the excess pore water pressure; c1, based on the residual of the physical information-data loss function, and using the chain rule to update the weights and biases of the first neural network in reverse, and use it as the first neural network for the next cycle; d1, repeat a1-c1 until the residual of the physical information-data loss function is less than the predetermined first standard, then the training ends, and the consolidation coefficient in the physical information-data loss function at the time of training end is taken as the final consolidation coefficient; The PINNs integrated forward and inverse model includes a second neural network; the training process of the PINNs integrated forward and inverse model includes: repeatedly inputting calculation points into the second neural network and outputting a second estimate of the excess pore water pressure, calculating the physical information loss function using the second estimate of the excess pore water pressure, and updating the weights and biases of the second neural network in reverse according to the physical information loss function until training ends. The training process of the second neural network includes: a2, the final consolidation coefficient is used as the consolidation coefficient of the physical information loss function of the second neural network, and the calculation point is input into the second neural network to obtain a second estimate of the excess pore water pressure; the second neural network includes: a second input layer, a second output layer and a second hidden layer; b2, Calculate the physical information loss function based on the second estimate; c2, based on the residual of the physical information loss function, and using the chain rule to update the weights and biases of the second neural network in reverse; d2, repeat a2-c2 until the residual of the physical information loss function is less than the predetermined second criterion, then the training ends and the trained PINNs integrated forward and inverse model is obtained.

2. The method for sensing and predicting the time-varying bearing capacity of static pressure piles based on physical information networks according to claim 1, characterized in that, The physical information-data loss function includes the loss function of the first radial consolidation equation, the loss function of the first initial condition, the loss function of the first boundary condition, and the excess pore pressure dissipation data loss function. The physical information-data loss function is expressed as follows: ； in, Represents the physical information-data loss function. The loss function representing the excess pressure dissipation data in the pores. This represents the loss function of the first radial consolidation equation. The loss function represents the first initial condition. The loss function represents the first boundary condition; The loss function of the first radial consolidation equation is expressed as: ； in, The weights represent the loss function of the radial consolidation equation. This indicates the number of computational points from within the computational domain of the radial consolidation equation. The first term in the computational domain of the radial consolidation equation represents the... One calculation point, Represents the first radial consolidation equation in the computational domain. The radial distance between each calculation point Represents the first radial consolidation equation in the computational domain. The time for each calculation point The first term in the computational domain of the radial consolidation equation represents the... The first estimate of excess pore water pressure at each calculation point Indicates the consolidation coefficient; The loss function for the first boundary condition is expressed as: ； In the formula, The weights of the loss function representing the boundary conditions at the pile diameter are given. The weights of the loss function representing the boundary conditions at the elastic-plastic radius are given. This indicates the number of computation points from within the boundary condition computation domain. The first boundary condition within the computational domain represents the boundary condition. One calculation point, Indicates the boundary conditions within the computational domain. The radial distance between each calculation point Indicates the boundary conditions within the computational domain. The time for each calculation point The first boundary condition within the computational domain represents the boundary condition. The first estimate of excess pore water pressure at each calculation point; The loss function for the first initial condition is expressed as: ； in, This represents the weights of the loss function used to calculate the initial conditions. This indicates the number of computation points originating from the initial condition computation domain. Represents the first condition within the computational domain. One calculation point, Represents the first condition within the computational domain. The radial distance between each calculation point Represents the first condition within the computational domain. Pre-time for each calculation point Represents the first condition within the computational domain. The first estimate of excess pore water pressure at each calculation point Represents the first condition within the computational domain. Initial pore water pressure at each calculation point; The loss function for the excess porosity pressure dissipation data is expressed as: ； in, The weights represent the weights of the loss function used to calculate the excess pore pressure dissipation data. This indicates the number of calculation points within the calculation domain derived from the excess pore pressure dissipation data. The first data in the calculation domain representing the excess pore pressure dissipation data One calculation point, The first data in the calculation domain representing the excess pore pressure dissipation data The radial distance between each calculation point The first data in the calculation domain representing the excess pore pressure dissipation data The time for each calculation point The first data in the calculation domain representing the excess pore pressure dissipation data Data on excess porosity dissipation at each calculation point The first data in the calculation domain representing the excess pore pressure dissipation data The first estimate of the excess pore water pressure at each calculation point.

3. The method for sensing and predicting the time-varying bearing capacity of static pressure piles based on physical information networks according to claim 1, characterized in that, The physical information loss function includes the second partial differential equation loss function, the second initial condition loss function, and the second boundary condition loss function. The physical information loss function is expressed as follows: in, Represents the physical information loss function. This represents the loss function of the second radial consolidation equation. The loss function represents the second initial condition. The loss function representing the second boundary condition; The loss function of the second radial consolidation equation is expressed as: in, The weights represent the loss function of the radial consolidation equation. This indicates the number of computational points from within the computational domain of the radial consolidation equation. The first term in the computational domain of the radial consolidation equation represents the... One calculation point, Represents the first radial consolidation equation in the computational domain. The radial distance between each calculation point Represents the first radial consolidation equation in the computational domain. The time for each calculation point The first term in the computational domain of the radial consolidation equation represents the... The second estimate of excess pore water pressure at each calculation point; The loss function for the second boundary condition is expressed as: In the formula, The weights of the loss function representing the boundary conditions at the pile diameter are given. The weights of the loss function representing the boundary conditions at the elastic-plastic radius are given. This indicates the number of computation points from within the boundary condition computation domain. The first boundary condition within the computational domain represents the boundary condition. One calculation point, Indicates the boundary conditions within the computational domain. The radial distance between each calculation point Indicates the boundary conditions within the computational domain. The time for each calculation point The first boundary condition within the computational domain represents the boundary condition. The second estimate of excess pore water pressure at each calculation point; The loss function for the second initial condition is expressed as: in, This represents the weights of the loss function used to calculate the initial conditions. This indicates the number of computation points originating from the initial condition computation domain. Represents the first condition within the computational domain. One calculation point, Represents the first condition within the computational domain. The radial distance between each calculation point Represents the first condition within the computational domain. Pre-time for each calculation point Represents the first condition within the computational domain. The second estimate of excess pore water pressure at each calculation point Represents the first condition within the computational domain. The initial pore water pressure at each calculation point.

4. The method for sensing and predicting the time-varying bearing capacity of static pressure piles based on physical information networks according to claim 1, characterized in that, The S400 includes: The test set is input into the trained PINNs integrated forward and inverse model, and the excess pore water pressure dissipation degree of the pile side soil is output. This excess pore water pressure dissipation degree of the pile side soil is then input into the calculation formula of the time-varying bearing capacity of the static pressure pile to obtain the predicted time-varying bearing capacity of the static pressure pile.

5. The method for sensing and predicting the time-varying bearing capacity of static pressure piles based on physical information networks according to claim 4, characterized in that, The formula for calculating the time-varying bearing capacity of the static pressure pile is expressed as follows: ； In the formula, , and These represent the time-varying bearing capacity, pile side resistance, and pile end resistance of a static pressure pile, respectively. Indicates the number of piles driven into the ground. The depth of the soil layer; and They represent the first Unit pile side resistance and unit pile end resistance in the soil layer; and These are the pile cross-sectional perimeter and the pile cross-sectional area, respectively. The unit pile end resistance for: ； In the formula, The bearing capacity coefficient at the end. This represents the shear strength of the in-situ soil under triaxial compression conditions. The plastic volumetric strain ratio, It is an over-consolidation ratio. The average effective stress varies with time. The initial average effective stress; The average effective stress for: ； In the formula, It is the dissipation degree of excess pore water pressure in the soil along the pile. The initial excess pore water pressure in the soil around the pile. This refers to the excess pore water pressure in the soil surrounding the pile. The unit pile side resistance for: ； In the formula, and For stress transformation parameters, For the effective internal friction angle, is the slope of the critical state line.

6. A device for sensing and predicting the time-varying bearing capacity of static pressure piles based on physical information networks, characterized in that, The apparatus for implementing the time-varying bearing capacity sensing and prediction method for static pressure piles based on physical information networks as described in any one of claims 1 to 5 includes: The data acquisition module is used to collect pore pressure dissipation data using pile body sensors; the pore pressure dissipation data includes the sensor deployment depth, the excess pore water pressure collected by the sensor, and the acquisition time. The inversion module is used to input the pore pressure dissipation data and calculation points into the PINNs forward and inverse integrated inversion model, and estimate the excess pore water pressure in the back propagation to obtain the final consolidation coefficient. The forward modeling module is used to input the final consolidation coefficient and the calculation points into the PINNs integrated forward and inverse modeling model, and to estimate the excess pore water pressure in the back propagation to obtain the trained PINNs integrated forward and inverse modeling model. The prediction module is used to input the test set into the trained PINNs forward and inverse integrated forward model, output the dissipation degree of excess pore water pressure in the pile side soil, and predict the time-varying bearing capacity of the static pressure pile based on the dissipation degree of excess pore water pressure in the pile side soil. The test set consists of several calculation points that need to be predicted, and the calculation points include time and radial distance.

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