High-compressibility soft soil permeability coefficient inversion method based on machine learning

Abstract

The invention discloses a high-compressibility soft soil permeability coefficient inversion method based on machine learning, and the method comprises the steps: building a nonlinear consolidation control equation through obtaining multi-source rock and soil parameters of high-compressibility soft soil, solving the equation through a finite difference method, and generating a sample data set containing a settlement-time curve and permeability model parameters; after standardizing the data set, screening effective parameter combinations by adopting a Latin hypercube sampling method to form a training sample set; a CNN-BiLSTM-Attention hybrid neural network model is constructed for training, an adaptive moment estimation algorithm is adopted to optimize parameters, and the generalization ability is improved through five-fold cross validation; and finally, inputting an actually measured settlement-time curve into the trained model, outputting an optimal combination of parameters of the penetration model, and performing inversion to obtain a penetration coefficient. According to the method, rapid and accurate inversion of the permeability coefficient is realized, the prediction efficiency is greatly improved, the traditional test cost is remarkably reduced, and the method has excellent engineering applicability.

Description

Technical Field

[0001] This invention relates to the field of geotechnical engineering investigation and soft soil foundation treatment technology, and in particular to a machine learning-based method for inverting the permeability coefficient of highly compressible soft soil. Background Technology

[0002] In geotechnical engineering, permeability coefficient is a key parameter for evaluating soil consolidation characteristics, seepage behavior, and settlement prediction. Traditional methods for determining permeability coefficient mainly rely on laboratory tests (such as consolidation tests and permeability tests), which suffer from problems such as long test cycles, high costs, and results being greatly affected by test conditions. Especially for highly compressible soft soils, the permeability coefficient varies significantly with stress level and void ratio, exhibiting strong nonlinear characteristics, further increasing the difficulty of accurately obtaining the permeability coefficient. Although existing research has proposed various empirical models (such as...) Models (such as logarithmic and double logarithmic models) are used to describe the relationship between permeability coefficient and parameters such as void ratio and liquid limit. However, these models still rely on specific assumptions and parameter fitting, have limited generalization ability, and are difficult to adapt to complex and ever-changing actual engineering conditions. Summary of the Invention

[0003] In view of this, the purpose of this invention is to propose a machine learning-based method for inverting the permeability coefficient of highly compressible soft soil.

[0004] To achieve the above-mentioned technical objectives, the technical solution adopted by this invention is: a machine learning-based method for inverting the permeability coefficient of highly compressible soft soil, comprising: Obtain multi-source soil and rock parameters for highly compressible soft soil, including initial void ratio, liquid limit void ratio, liquid limit water content, initial water content, and current effective stress. Nonlinear consolidation control equations are constructed based on multi-source soil and rock parameters, and the finite difference method is used to numerically solve the nonlinear consolidation control equations to generate a sample dataset containing settlement-time curves and permeability model parameters. The sample dataset is standardized, and the Latin hypercube sampling method is used to select effective parameter combinations that meet the preset permeability coefficient range to form a training sample set. A CNN-BiLSTM-Attention hybrid neural network model is constructed, in which a convolutional neural network is used to extract local features of the sedimentation-time curve, a bidirectional long short-term memory network is used to capture long-term dependencies of the time series, and an attention mechanism is used to enhance the feature weights of key time steps. The hybrid neural network model is trained using a training sample set, the model parameters of the hybrid neural network model are optimized using an adaptive moment estimation algorithm, and the generalization ability of the model is improved by five-fold cross-validation. The measured settlement-time curve of the soil to be inverted is input into the trained hybrid neural network model, which outputs the optimal combination of the corresponding permeability model parameters. Based on the optimal combination of permeability model parameters, the permeability coefficient of the soil to be inverted is obtained by inversion through nonlinear consolidation control equations.

[0005] In some embodiments, a nonlinear consolidation control equation is constructed based on multi-source soil and rock parameters, and the nonlinear consolidation control equation is numerically solved using the finite difference method to generate a sample dataset containing settlement-time curves and permeability model parameters, including: A nonlinear relationship model between the permeability coefficient and the void ratio is established. The nonlinear relationship model contains multiple undetermined permeability model parameters. A compression curve model that considers stress history is established. The compression curve model represents the evolution relationship between porosity and effective stress through multiple compression model parameters. By coupling the nonlinear relationship model and the compression curve model into the framework of Terzaghi's one-dimensional consolidation theory, a nonlinear partial differential governing equation with excess pore water pressure as the variable is derived. The nonlinear partial differential control equations are discretized in time and space using the Crank-Nicolson difference scheme to construct the corresponding difference equation system. A closed solution system is established by pre-setting boundary conditions and initial conditions. The difference equation system is solved by matrix iteration algorithm to obtain the distribution of excess pore water pressure at different time and space nodes. Based on the effective stress principle and compression curve model, the evolution process of porosity under the corresponding working conditions is calculated. Based on the evolution of the porosity, integral calculations are performed to generate sedimentation-time curve samples corresponding to the parameter combinations of each permeability model; The parameters of the permeability model are matched and correlated with the corresponding sedimentation-time curves to generate a sample dataset for training machine learning models.

[0006] In some embodiments, the nonlinear relationship model is represented by formula (1), which is as follows: ; In formula (1), Permeability coefficient, These are the parameters for the first penetration model. These are the parameters for the second penetration model. These are the parameters for the third penetration model. Porosity Liquid limit porosity; The compression curve model is represented by formula (2), which is as follows: ; In formula (2), The initial void ratio, For effective stress, These are the parameters for the first compression model. These are the parameters for the second compression model. These are the parameters for the third compression model; The nonlinear partial differential control equation is expressed by formula (3), which is as follows: ; In formula (3), The symbol is for partial differentials. The pressure of the superstatic pore water. For depth coordinates, For time, Indicates excess pore water pressure Second-order partial derivative along the depth direction, Indicates excess pore water pressure Over time rate of change, This represents the gradient of excess pore water pressure along the depth direction. The square of, The first coefficient related to soil parameters, The second coefficient is related to soil parameters. This can be expressed by formula (4). Equation (5) expresses Equation (4) as follows: ; In formula (4), For the specific gravity of water, This represents the current porosity. Formula (5) is as follows: .

[0007] In some embodiments, the sample dataset is standardized, and the Latin hypercube sampling method is used to select effective parameter combinations that meet a preset permeability coefficient range to form a training sample set, including: Normalization preprocessing is performed on the sedimentation-time curves in the sample dataset to obtain standardized sedimentation-time curves; Determine the reasonable range of values ​​for the permeability model parameters, based on the typical physical and mechanical properties of highly compressible soft soil; The Latin hypercube sampling method is used to generate uniformly distributed sample points in the multidimensional parameter space within the range of values. The permeability model parameters corresponding to each sample point are combined and input into the nonlinear consolidation control equation to calculate the corresponding permeability coefficient value. Establish screening criteria based on a reasonable range of penetration coefficients, and automatically eliminate invalid parameter combinations that exceed the preset screening threshold range; Cluster analysis was performed on the selected effective parameter combinations to ensure the uniformity and representativeness of the sample distribution in the parameter space; The selected effective parameter combinations are paired with the corresponding standardized sedimentation-time curves to construct a training sample set for neural network training.

[0008] In some embodiments, the preset screening threshold range is determined by the physical rationality of the permeability coefficient, which satisfies formula (6), as follows: ; Parameter combinations that exceed the preset screening threshold range are identified as invalid samples and are removed.

[0009] In some embodiments, a CNN-BiLSTM-Attention hybrid neural network model is constructed, wherein a convolutional neural network is used to extract local features of the sedimentation-time curve, a bidirectional long short-term memory network is used to capture long-term dependencies in the time series, and an attention mechanism is used to enhance the feature weights at key time steps, including: A one-dimensional convolutional neural network module is constructed. By setting multiple layers of convolutional kernels of different scales, multi-level feature extraction is performed on the input sedimentation-time curve to obtain a high-dimensional feature vector containing local fluctuation patterns and trend changes. A bidirectional long short-term memory network module is constructed to process high-dimensional feature vectors through both forward and backward channels, capturing the forward causal dependence and backward correlation characteristics of the sedimentation development process, and fusing them to generate a hidden state sequence containing complete temporal context information. An attention mechanism module is constructed, which calculates the weight coefficients of each time step in the hidden state sequence through a trainable parameter matrix, and performs a weighted summation of the hidden states based on the weight coefficients to highlight the characteristic contributions of the consolidation inflection point and the key stage of rate change during the settlement process. Construct a fully connected regression module to map the attention-weighted feature representations to the penetration model parameter space and output the optimal combination of penetration model parameters; Introducing residual connection mechanisms into hybrid neural network models can alleviate the gradient vanishing problem during deep network training. A hierarchical regularization strategy is adopted, applying Dropout operations to both the convolutional and recurrent layers to suppress the overfitting tendency of the model, thus obtaining a hybrid neural network model to be trained.

[0010] In some embodiments, the hybrid neural network model is trained using a training sample set, the model parameters of the hybrid neural network model are optimized using an adaptive moment estimation algorithm, and the generalization ability of the model is improved using a five-fold cross-validation method, including: The training sample set is randomly divided into five non-overlapping subsets. A rotational validation strategy is adopted, in which one subset is used as the validation set and the other four subsets are used as the training set, and five rounds of model training and validation are carried out. In each training round, the learning rate of the model parameters is dynamically adjusted using an adaptive moment estimation algorithm. The adaptive update of the model parameters is achieved by calculating the first-order moment estimate and the second-order moment estimate of the gradient. A composite loss function based on mean square error is established, which simultaneously considers the prediction accuracy of the permeability model parameters and the reconstruction error of the settlement-time curve. An early stopping strategy is implemented during training. Training is automatically terminated when the validation set loss function no longer decreases over several consecutive training cycles to prevent model overfitting. Gradient clipping is used to limit the range of gradient values ​​during backpropagation, ensuring numerical stability during training. After each round of training, model performance evaluation metrics are calculated based on the validation set, including the coefficient of determination, root mean square error, and mean absolute percentage error. By integrating the optimal model parameters from five rounds of cross-validation, a final model with the best generalization ability is obtained. The final model is optimized for hyperparameters by using a Bayesian optimization algorithm to search for the optimal combination of the number of convolutional kernels, the number of long short-term memory units, and the attention dimension.

[0011] In some embodiments, the composite loss function is expressed by formula (7), which is as follows: ; In formula (7), This represents the mean square error between the predicted values ​​and the actual values ​​of the permeability model parameters. These are the predicted values ​​of the penetration model parameters. These are the true values ​​of the penetration model parameters. This represents the mean square error between the reconstructed settlement-time curve and the measured settlement-time curve. To reconstruct the settlement-time curve, For the measured settlement-time curve, As the first weighting coefficient, This is the second weighting coefficient. .

[0012] In some embodiments, the measured settlement-time curve of the soil to be inverted is input into the trained hybrid neural network model, and the corresponding optimal combination of permeability model parameters is output, including: The measured settlement-time curves were preprocessed to be consistent with the training sample set. The preprocessed measured settlement-time curve is input into the trained hybrid neural network model, and the feature extraction and fusion process is carried out sequentially through the convolutional neural network module, the bidirectional long short-term memory network module, and the attention mechanism module through forward propagation calculation. In the attention mechanism module, key feature weights corresponding to the turning point of the primary consolidation stage and the starting point of the secondary consolidation stage in the measured sedimentation-time curve are automatically identified and enhanced. The fully connected regression module maps the attention-weighted feature representations to the initial predicted values ​​of the penetration model parameters. Based on the initial predicted values ​​of the permeability model parameters, the corresponding settlement-time curve is reconstructed through the nonlinear consolidation control equation, and is denoted as the reconstructed settlement-time curve. Calculate the similarity index between the reconstructed settlement-time curve and the measured settlement-time curve. When the similarity index does not reach the preset threshold, use an iterative optimization algorithm to fine-tune the initial predicted values ​​of the permeability model parameters. Repeat the reconstruction and fine-tuning process until the similarity index reaches the preset requirements, and output the current penetration model parameters as the optimal combination; The physical rationality of the optimal combination is verified to ensure that the permeability model parameters are within the typical range of highly compressible soft soil. The optimal combination that passes the physical rationality check is denoted as the final optimal combination of permeation model parameters.

[0013] In some embodiments, the permeability coefficient of the soil to be inverted is obtained by inversion using nonlinear consolidation control equations based on the optimal combination of permeability model parameters, including: By substituting the optimal combination of permeability model parameters into the preset permeability coefficient mathematical model, a quantitative relationship expression between porosity and permeability coefficient is established. Based on the measured physical state parameters of the soil to be inverted, determine the initial void ratio and current effective stress conditions required for the calculation. By inputting the initial void ratio and the current effective stress into the quantitative relationship expression, the current permeability coefficient of the soil to be inverted can be directly calculated. The consolidation development process of soil under load is simulated by nonlinear consolidation control equations to obtain the void ratio variation sequence at different consolidation stages. Based on the porosity change sequence, the corresponding permeability coefficient sequence is continuously calculated using a quantitative relationship expression to obtain the change law of permeability coefficient with time. A verification mechanism for the permeability coefficient inversion results was established. The calculated permeability coefficient was substituted into the nonlinear consolidation control equation to verify its matching degree with the measured settlement-time curve. When the verification results meet the preset accuracy requirements, the current permeability coefficient value of the soil to be inverted is output as the final permeability coefficient of the soil to be inverted.

[0014] Compared with existing technologies, the present invention, employing the above technical solution, has the following advantages: It provides a machine learning-based method for inverting the permeability coefficient of highly compressible soft soil. By acquiring multi-source soil and rock parameters of highly compressible soft soil, a nonlinear consolidation control equation is constructed and solved using the finite difference method, generating a sample dataset containing settlement-time curves and permeability model parameters. After standardizing the dataset, effective parameter combinations are selected using the Latin hypercube sampling method to form a training sample set. A CNN-BiLSTM-Attention hybrid neural network model is constructed for training, and an adaptive moment estimation algorithm is used to optimize the parameters. Five-fold cross-validation is used to improve generalization ability. Finally, the measured settlement-time curves are input into the trained model, and the optimal combination of permeability model parameters is output to invert the permeability coefficient. This method achieves rapid and accurate permeability coefficient inversion, significantly improves prediction efficiency, significantly reduces traditional experimental costs, and has excellent engineering applicability. Attached Figure Description

[0015] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0016] Figure 1 This is a schematic diagram of the overall process of the permeability coefficient inversion method described in the specific implementation method; Figure 2 This is a schematic diagram of the specific process of the permeability coefficient inversion method described in the specific implementation method; Figure 3 This is a schematic diagram of the structure of the CNN-BiLSTM-Attention hybrid neural network model described in the specific implementation method; Figure 4 This is a schematic diagram of the permeability coefficient of typical highly compressible soft soil. Figure 5 This is a schematic diagram of the curve fitting the calculated permeability coefficient of highly compressible soft soil. Figure 6 This is a comparison chart of the calculated permeability coefficient and the measured permeability coefficient. Detailed Implementation

[0017] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be particularly noted that the following embodiments are for illustrative purposes only and do not limit the scope of the invention. Similarly, the following embodiments are only some, not all, embodiments of the present invention, and all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0018] Please see Figures 1 to 6 This embodiment provides a machine learning-based method for inverting the permeability coefficient of highly compressible soft soil, including: Obtain multi-source soil and rock parameters for highly compressible soft soil, including initial void ratio, liquid limit void ratio, liquid limit water content, initial water content, and current effective stress. Nonlinear consolidation control equations are constructed based on multi-source soil and rock parameters, and the finite difference method is used to numerically solve the nonlinear consolidation control equations to generate a sample dataset containing settlement-time curves and permeability model parameters. The sample dataset is standardized, and the Latin hypercube sampling method is used to select effective parameter combinations that meet the preset permeability coefficient range to form a training sample set. A CNN-BiLSTM-Attention hybrid neural network model is constructed, in which a convolutional neural network is used to extract local features of the sedimentation-time curve, a bidirectional long short-term memory network is used to capture long-term dependencies of the time series, and an attention mechanism is used to enhance the feature weights of key time steps. The hybrid neural network model is trained using a training sample set, the model parameters of the hybrid neural network model are optimized using an adaptive moment estimation algorithm, and the generalization ability of the model is improved by five-fold cross-validation. The measured settlement-time curve of the soil to be inverted is input into the trained hybrid neural network model, which outputs the optimal combination of the corresponding permeability model parameters. Based on the optimal combination of permeability model parameters, the permeability coefficient of the soil to be inverted is obtained by inversion through nonlinear consolidation control equations.

[0019] In this embodiment, the multi-source soil parameters are a set of key indicators reflecting the physical state and mechanical properties of the soil, obtained from tests on highly compressible soft soil. The initial void ratio characterizes the degree of pore development in the soil when unloaded; the liquid limit void ratio reflects the pore characteristics of the soil under liquid limit conditions; the liquid limit water content and initial water content represent the water content of the soil in its flowing and initial states, respectively; and the current effective stress reflects the effective bearing capacity of the soil under the current stress conditions. These parameters are determined through indoor geotechnical tests. The void ratio is calculated by subtracting the volume of solid particles from the soil sample volume; the water content is determined using the drying method; and the effective stress is determined based on the difference between the external load and the pore water pressure. This step, by integrating the core parameters reflecting the compressibility and permeability of the soil, provides a comprehensive input data foundation for subsequent numerical simulations and machine learning.

[0020] The process of constructing nonlinear consolidation governing equations based on multi-source soil and rock parameters involves the in-depth application of soil consolidation theory. The nonlinear consolidation governing equations are partial differential equations established based on Terzaghi's one-dimensional consolidation theory, considering the nonlinear characteristics of permeability coefficient variation with void ratio. These equations describe the variation of excess pore water pressure with time and space by coupling a permeability model and a compression model. When using the finite difference method for numerical solution, the continuous partial differential equations are discretized into a system of difference equations. By setting reasonable spatial and time step sizes, the Crank-Nicolson implicit difference scheme ensures computational stability. The sample dataset includes settlement-time curves obtained through numerical calculations and corresponding permeability model parameter combinations. The settlement-time curves reflect the consolidation development process of the soil under different parameter combinations. This step, by establishing an accurate numerical calculation model, generates training samples covering various working conditions, providing ample learning data for the machine learning model.

[0021] Standardization of the sample dataset aims to eliminate the influence of different feature dimensions and numerical ranges on model training. The standardization process employs Z-score normalization, transforming each feature value into a distribution with a mean of 0 and a standard deviation of 1. Latin hypercube sampling generates uniformly distributed sample points within the parameter space, ensuring that the sampling results adequately cover the possible range of parameter values. The preset permeability coefficient range is determined based on the typical physical properties of highly compressible soft soil, and the selection of effective parameter combinations is based on the physical rationality of the permeability coefficient, eliminating abnormal samples that exceed the reasonable range. The formation of the training sample set also includes checking the balance of the sample distribution to ensure that each parameter interval has sufficient representative samples. This step, through a scientific sampling and selection mechanism, constructs a high-quality training dataset, laying a data foundation for model training.

[0022] The construction of the CNN-BiLSTM-Attention hybrid neural network model demonstrates the advantages of deep learning in time-series data processing. The convolutional neural network extracts local fluctuation features of the sedimentation-time curve through one-dimensional convolutional kernels, capturing the short-term change patterns of the curve. The bidirectional long short-term memory network comprehensively captures the long-term dependencies in the sedimentation development process through forward and backward time-series processing. The attention mechanism automatically focuses on key stages in the consolidation process, such as the primary consolidation inflection point and the secondary consolidation initiation point, by calculating the importance weights of each time step. The hybrid neural network model achieves an end-to-end mapping from the original curve to parameter prediction by cascading these three modules. This step, by designing a network structure specifically for the characteristics of the sedimentation-time curve, fully leverages the advantages of different neural network architectures.

[0023] When training a hybrid neural network model using the training sample set, the adaptive moment estimation algorithm accelerates model convergence and improves training stability by dynamically adjusting the learning rate. This algorithm combines first-order and second-order moment estimation of the gradient, adaptively adjusting the learning step size for each parameter. Five-fold cross-validation randomly divides the training sample set into five non-overlapping subsets, evaluating the model's performance on different subsets through alternating validation, effectively improving the model's generalization ability. An early stopping strategy is also employed during training to prevent overfitting; training is automatically terminated when the validation set loss no longer decreases for several consecutive epochs. This step, by comprehensively utilizing multiple training optimization techniques, ensures that the model maintains high accuracy while possessing good generalization performance.

[0024] When inputting the measured settlement-time curves of the soil to be inverted into the trained hybrid neural network model, the measured curves first need to undergo standardization preprocessing consistent with the training set. The model performs forward propagation calculations, sequentially passing through convolutional layers, bidirectional long short-term memory layers, and attention layers for feature extraction and fusion, finally outputting the predicted values ​​of the permeability model parameters at the fully connected layer. The optimal combination of permeability model parameters is determined based on the degree of matching between the predicted values ​​and the actual curves, and iterative optimization ensures the accuracy of the prediction results. The output process also includes verifying the physical rationality of the prediction results, ensuring that the parameter values ​​conform to the typical characteristics of highly compressible soft soil. This step achieves a rapid mapping from measured curves to model parameters through the trained model, providing a crucial input for permeability coefficient inversion.

[0025] The process of inverting the permeability coefficient based on the optimal combination of permeability model parameters is achieved by establishing a quantitative relationship between the parameters and the permeability coefficient. The optimal parameter combination is substituted into a pre-defined mathematical model of the permeability coefficient, and combined with the current physical state parameters of the soil to be inverted, the permeability coefficient value is directly calculated. The nonlinear consolidation governing equation is used in this process to verify the rationality of the inversion results, and the accuracy of the inversion is evaluated by comparing the degree of agreement between calculated and measured settlement. The permeability coefficient inversion results also include a sequence of permeability coefficient changes at different consolidation stages, reflecting the evolution of permeability characteristics during soil consolidation. This step, by combining machine learning prediction with physical model verification, ensures the accuracy and reliability of the inversion results.

[0026] This embodiment achieves accurate and rapid inversion of the permeability coefficient of highly compressible soft soil by constructing a complete technical process from data acquisition to parameter inversion. It comprehensively characterizes soil properties using multi-source geotechnical parameters, establishes an accurate numerical calculation model based on nonlinear consolidation theory, ensures sample representativeness through Latin hypercube sampling, designs a specialized hybrid neural network structure to effectively extract settlement-time curve features, and combines adaptive optimization and cross-validation to improve model performance. Finally, the rationality of the inversion results is ensured through physical model verification. This embodiment overcomes the limitations of traditional experimental methods, such as long cycles and high costs, and provides an efficient and reliable technical means for determining the permeability coefficient of highly compressible soft soil through the deep integration of machine learning and geotechnical theory.

[0027] In some embodiments, a nonlinear consolidation control equation is constructed based on multi-source soil and rock parameters, and the nonlinear consolidation control equation is numerically solved using the finite difference method to generate a sample dataset containing settlement-time curves and permeability model parameters, including: A nonlinear relationship model between the permeability coefficient and the void ratio is established. The nonlinear relationship model contains multiple undetermined permeability model parameters. A compression curve model that considers stress history is established. The compression curve model represents the evolution relationship between porosity and effective stress through multiple compression model parameters. By coupling the nonlinear relationship model and the compression curve model into the framework of Terzaghi's one-dimensional consolidation theory, a nonlinear partial differential governing equation with excess pore water pressure as the variable is derived. The nonlinear partial differential control equations are discretized in time and space using the Crank-Nicolson difference scheme to construct the corresponding difference equation system. A closed solution system is established by pre-setting boundary conditions and initial conditions. The difference equation system is solved by matrix iteration algorithm to obtain the distribution of excess pore water pressure at different time and space nodes. Based on the effective stress principle and compression curve model, the evolution process of porosity under the corresponding working conditions is calculated. Based on the evolution of the porosity, integral calculations are performed to generate sedimentation-time curve samples corresponding to the parameter combinations of each permeability model; The parameters of the permeability model are matched and correlated with the corresponding sedimentation-time curves to generate a sample dataset for training machine learning models.

[0028] In this embodiment, establishing a nonlinear relationship model between permeability coefficient and void ratio refers to constructing a mathematical expression containing multiple undetermined permeability model parameters to describe the nonlinear law of permeability coefficient variation with void ratio. This model transforms the complex nonlinear relationship into a tractable linear form by introducing a logarithmic transformation, where each undetermined parameter characterizes the degree of influence of different physical factors on the permeability coefficient. Establishing a compression curve model considering stress history quantifies the evolutionary relationship between void ratio and effective stress through multiple compression model parameters. These parameters collectively determine the compressibility characteristics of the soil under different stress states. The process of coupling these two models to Terzaghi's one-dimensional consolidation theory framework essentially involves embedding the material constitutive relation into classical consolidation theory, deriving a nonlinear partial differential equation with excess pore water pressure as the control variable through mathematical derivation.

[0029] When using the Crank-Nicolson difference scheme for spatiotemporal discretization, this scheme maintains computational stability and achieves second-order accuracy through weighted averaging across the time layers. The constructed difference equation system transforms continuous partial differential equations into a system of algebraic equations through spatial grid partitioning and time-step discretization. A closed solution system is established using preset boundary and initial conditions, where the boundary conditions include drained and undrained boundaries, and the initial conditions reflect the stress state at the initial loading moment. When solving the difference equation system using a matrix iteration algorithm, the preferred TDMA algorithm can efficiently handle the tridiagonal matrix and progressively calculate the excess pore water pressure distribution at each spatiotemporal node.

[0030] The porosity evolution process is calculated based on the effective stress principle and compression curve model. This involves using the constitutive relationship between effective stress and porosity, combined with the obtained excess pore water pressure distribution, to inversely deduce the porosity change at each point. Settlement-time curve samples are generated through integral calculations based on the porosity evolution process. This is achieved by numerically integrating the change in porosity along the soil depth direction to obtain the total settlement at different times. Finally, the permeability model parameters are matched and correlated with the corresponding settlement-time curves. This establishes a mapping relationship between the parameter space and the response space, forming a standardized sample dataset for training machine learning models.

[0031] This embodiment constructs a high-quality machine learning training sample library by establishing an accurate physical and mathematical model and an efficient numerical calculation method. The nonlinear relationship model and compression curve model accurately characterize the constitutive properties of the soil, while the Crank-Nicolson difference scheme ensures the accuracy and stability of the numerical solution. The complete solution process provides a reliable data foundation for subsequent machine learning training. This embodiment combines geotechnical mechanics theory with numerical calculation, providing solid theoretical support and data assurance for the inversion of the permeability coefficient of highly compressible soft soil.

[0032] In some embodiments, the nonlinear relationship model is represented by formula (1), which is as follows: ; In formula (1), Permeability coefficient, These are the parameters for the first penetration model. These are the parameters for the second penetration model. These are the parameters for the third penetration model. Porosity Liquid limit porosity; The compression curve model is represented by formula (2), which is as follows: ; In formula (2), The initial void ratio, For effective stress, These are the parameters for the first compression model. These are the parameters for the second compression model. These are the parameters for the third compression model; The nonlinear partial differential control equation is expressed by formula (3), which is as follows: ; In formula (3), The symbol is for partial differentials. The pressure of the superstatic pore water. For depth coordinates, For time, Indicates excess pore water pressure Second-order partial derivative along the depth direction, Indicates excess pore water pressure Over time rate of change, This represents the gradient of excess pore water pressure along the depth direction. The square of, The first coefficient related to soil parameters, The second coefficient is related to soil parameters. This can be expressed by formula (4). Equation (5) expresses Equation (4) as follows: ; In formula (4), For the specific gravity of water, This represents the current porosity. Formula (5) is as follows: .

[0033] In this embodiment, the nonlinear relationship model shown in formula (1) establishes a quantitative relationship between the permeability coefficient and the pore structure parameters. Wherein, the first permeability model parameters... Characterizing the baseline permeability level, parameters of the second permeability model The third permeability model parameter reflects the sensitivity of the porosity to the permeability coefficient. This model reflects the corrective effect of the liquid limit void ratio. By introducing the dual influence of void ratio and liquid limit void ratio, it more accurately describes the nonlinear variation law of the permeability characteristics of highly compressible soft soil.

[0034] The compression curve model shown in formula (2) fully characterizes the evolution of porosity with effective stress using three compression model parameters. The first compression model parameter... The positional characteristics of the control curves are related to the structural strength of the soil; parameters of the second compression model. The shape of the curve determines the stress sensitivity of the soil; the third compression model parameters The curvature of the adjustment curve characterizes the magnitude of the compression index. This model can continuously describe the change in porosity under different stress states, avoiding the limitations of traditional piecewise models.

[0035] The nonlinear partial differential governing equation shown in formula (3) is derived based on Terzaghi's consolidation theory through a coupled permeation and compression model. The equation includes a spatiotemporal variation term for excess pore water pressure and a nonlinear gradient term, where the first coefficient... The second coefficient comprehensively reflects the coupled effect of soil compressibility and permeability. This characterizes the nonlinear characteristics caused by the change in permeability coefficient with porosity. These two coefficients are specifically expressed by formulas (4) and (5), respectively, where the specific weight of water is a known physical constant, and the current porosity is updated in real time during the solution process.

[0036] The terms in Equation (4) correspond to the combined effects of water density, compression model parameters, initial void ratio, stress level, and permeability coefficient, respectively, reflecting the interaction of various physical factors during the consolidation process. Equation (5) focuses on the coupling relationship between permeability model parameters and compression model parameters, characterizing the feedback effect of permeability characteristics on the consolidation process through the product relationship between parameters. The determination of these coefficients enables the governing equations to more realistically simulate the nonlinear consolidation behavior of highly compressible soft soil.

[0037] This embodiment provides a solid theoretical foundation for the inversion of permeability coefficients in highly compressible soft soils by establishing a precise mathematical model. Three core formulas comprehensively describe the mechanical behavior of the soil from three dimensions: permeability characteristics, compressibility characteristics, and consolidation process. The coupling relationships between parameters accurately reflect the complex interactions in actual engineering. The establishment of this mathematical model gives subsequent numerical calculations and machine learning training clear physical meaning and engineering applicability, laying an important foundation for achieving accurate inversion.

[0038] In some embodiments, the sample dataset is standardized, and the Latin hypercube sampling method is used to select effective parameter combinations that meet a preset permeability coefficient range to form a training sample set, including: Normalization preprocessing is performed on the sedimentation-time curves in the sample dataset to obtain standardized sedimentation-time curves; Determine the reasonable range of values ​​for the permeability model parameters, based on the typical physical and mechanical properties of highly compressible soft soil; The Latin hypercube sampling method is used to generate uniformly distributed sample points in the multidimensional parameter space within the range of values. The permeability model parameters corresponding to each sample point are combined and input into the nonlinear consolidation control equation to calculate the corresponding permeability coefficient value. Establish screening criteria based on a reasonable range of penetration coefficients, and automatically eliminate invalid parameter combinations that exceed the preset screening threshold range; Cluster analysis was performed on the selected effective parameter combinations to ensure the uniformity and representativeness of the sample distribution in the parameter space; The selected effective parameter combinations are paired with the corresponding standardized sedimentation-time curves to construct a training sample set for neural network training.

[0039] In this embodiment, the normalization preprocessing of the settlement-time curve refers to using the maximum-minimum normalization method to linearly transform the original settlement data to the [0,1] interval. Specifically, this is achieved by calculating the ratio of the settlement value at each time point to the maximum settlement value. This processing eliminates the influence of dimensions, making curves of different orders of magnitude comparable and providing standardized input data for subsequent machine learning models.

[0040] When determining the reasonable range of values ​​for permeability model parameters, empirical ranges for each parameter are obtained through statistical analysis of a large amount of experimental data, based on the typical physical and mechanical properties of highly compressible soft soil. Preferably, the range of values ​​should cover the actual parameter variation range of common highly compressible soft soils to ensure that the sampling results are representative of engineering applications.

[0041] When generating sample points using the Latin hypercube sampling method, the method uniformly divides the space into intervals along each parameter dimension and randomly samples within each interval, ensuring a uniform distribution of sample points in the multidimensional parameter space. Compared to simple random sampling, this method can better cover the entire parameter space with a smaller number of samples.

[0042] When calculating the permeability coefficient by inputting parameter combinations into the nonlinear consolidation control equation, the permeability coefficient value corresponding to each parameter combination is obtained through numerical solution methods. The calculation process considers the coupling effect between parameters to ensure that the obtained permeability coefficient has physical rationality.

[0043] When establishing screening criteria based on a reasonable range of permeability coefficients, the preset screening threshold range is determined according to the typical permeability characteristics of highly compressible soft soils. Preferably, this range should exclude physically unreasonable extreme values, such as those exceeding the practically possible range of permeability coefficients in engineering.

[0044] When performing cluster analysis on effective parameter combinations, the K-means clustering algorithm is used to divide the samples into several categories, and the balance of sample distribution in each category is checked. If some regions are found to have too few samples, supplementary sampling is performed to ensure the representativeness of the samples in the parameter space.

[0045] When the selected parameter combinations are paired with standardized curves, a one-to-one mapping relationship is established, forming a structured training sample set. Each sample contains a set of parameter values ​​and a corresponding standardized sedimentation-time curve, providing a complete data foundation for neural network training.

[0046] This embodiment constructs a high-quality training sample set through systematic data preprocessing and sampling screening. Normalization improves data quality, Latin hypercube sampling ensures thorough exploration of the parameter space, physical rationality screening guarantees the engineering value of the samples, and cluster analysis optimizes the sample distribution. This embodiment provides reliable data support for the machine learning model, ensuring the accuracy and generalization ability of the inversion model.

[0047] In some embodiments, the preset screening threshold range is determined by the physical rationality of the permeability coefficient, which satisfies formula (6), as follows: ; Parameter combinations that exceed the preset screening threshold range are identified as invalid samples and are removed.

[0048] In this embodiment, the preset screening threshold range is a physically reasonable range determined based on the actual permeability characteristics of highly compressible soft soil. The permeability coefficient range shown in formula (6) is... to The range covers typical values ​​from extremely low permeability clay to relatively high permeability soft clay. This range was derived through statistical analysis of a large amount of experimental data, ensuring the engineering applicability of the screening results. Parameter combinations outside this range do not physically conform to the basic characteristics of highly compressible soft soil and are therefore discarded as invalid samples.

[0049] This embodiment effectively filters out parameter combinations that do not conform to the actual soil characteristics by setting a clear physical rationality threshold, thereby improving the engineering representativeness and reliability of the training sample set and providing quality assurance for the accurate training of subsequent machine learning models.

[0050] In some embodiments, a CNN-BiLSTM-Attention hybrid neural network model is constructed, wherein a convolutional neural network is used to extract local features of the sedimentation-time curve, a bidirectional long short-term memory network is used to capture long-term dependencies in the time series, and an attention mechanism is used to enhance the feature weights at key time steps, including: A one-dimensional convolutional neural network module is constructed. By setting multiple layers of convolutional kernels of different scales, multi-level feature extraction is performed on the input sedimentation-time curve to obtain a high-dimensional feature vector containing local fluctuation patterns and trend changes. A bidirectional long short-term memory network module is constructed to process high-dimensional feature vectors through both forward and backward channels, capturing the forward causal dependence and backward correlation characteristics of the sedimentation development process, and fusing them to generate a hidden state sequence containing complete temporal context information. An attention mechanism module is constructed, which calculates the weight coefficients of each time step in the hidden state sequence through a trainable parameter matrix, and performs a weighted summation of the hidden states based on the weight coefficients to highlight the characteristic contributions of the consolidation inflection point and the key stage of rate change during the settlement process. Construct a fully connected regression module to map the attention-weighted feature representations to the penetration model parameter space and output the optimal combination of penetration model parameters; Introducing residual connection mechanisms into hybrid neural network models can alleviate the gradient vanishing problem during deep network training. A hierarchical regularization strategy is adopted, applying Dropout operations to both the convolutional and recurrent layers to suppress the overfitting tendency of the model, thus obtaining a hybrid neural network model to be trained.

[0051] In this embodiment, the one-dimensional convolutional neural network module scans the sedimentation-time curve using multiple convolutional kernels of different widths to capture short-term fluctuations and long-term trend features. Narrower convolutional kernels identify local detail changes, while wider kernels extract overall morphological features. After fusing multi-scale features, a high-dimensional feature vector is formed, comprehensively representing the local patterns of the curve.

[0052] The bidirectional long short-term memory network module employs two processing channels: a forward channel that analyzes the settlement development pattern in chronological order, and a backward channel that identifies the subsequent effects of the consolidation process. The latent states from both directions are fused through splicing or addition to form a feature sequence containing complete temporal information, accurately reflecting the correlation between the preceding and following stages of the settlement process.

[0053] The attention mechanism module calculates importance scores for each time step using a trainable weight matrix, focusing on enhancing the feature contributions of consolidation inflection points and rate abrupt change points. This module automatically identifies key stages in the settlement process, such as the critical point of transition from primary to secondary consolidation, improving the model's sensitivity to important features.

[0054] The fully connected regression module maps the weighted feature vectors to the permeability model parameter space, achieving the feature-to-parameter transformation through multiple nonlinear transformations. This module outputs the optimal combination of permeability model parameters, providing direct input for subsequent permeability coefficient calculations.

[0055] The residual connection mechanism establishes shortcut paths between network layers, enabling gradients to propagate directly in the backpropagation direction, effectively mitigating the vanishing gradient problem in deep networks. The hierarchical regularization strategy sets different dropout rates in convolutional and recurrent layers, randomly masking the outputs of some neurons to reduce overfitting of the model to the training data.

[0056] This embodiment fully leverages the advantages of different network structures by constructing a multi-module collaborative hybrid neural network. Convolutional networks extract local features, bidirectional recurrent networks capture long-term dependencies, attention mechanisms focus on key information, and residual connections and regularization techniques ensure training stability. This enables the model to accurately learn the complex mapping relationship between sedimentation-time curves and permeation parameters, providing reliable technical support for high-precision inversion.

[0057] In some embodiments, the hybrid neural network model is trained using a training sample set, the model parameters of the hybrid neural network model are optimized using an adaptive moment estimation algorithm, and the generalization ability of the model is improved using a five-fold cross-validation method, including: The training sample set is randomly divided into five non-overlapping subsets. A rotational validation strategy is adopted, in which one subset is used as the validation set and the other four subsets are used as the training set, and five rounds of model training and validation are carried out. In each training round, the learning rate of the model parameters is dynamically adjusted using an adaptive moment estimation algorithm. The adaptive update of the model parameters is achieved by calculating the first-order moment estimate and the second-order moment estimate of the gradient. A composite loss function based on mean square error is established, which simultaneously considers the prediction accuracy of the permeability model parameters and the reconstruction error of the settlement-time curve. An early stopping strategy is implemented during training. Training is automatically terminated when the validation set loss function no longer decreases over several consecutive training cycles to prevent model overfitting. Gradient clipping is used to limit the range of gradient values ​​during backpropagation, ensuring numerical stability during training. After each round of training, model performance evaluation metrics are calculated based on the validation set, including the coefficient of determination, root mean square error, and mean absolute percentage error. By integrating the optimal model parameters from five rounds of cross-validation, a final model with the best generalization ability is obtained. The final model is optimized for hyperparameters by using a Bayesian optimization algorithm to search for the optimal combination of the number of convolutional kernels, the number of long short-term memory units, and the attention dimension.

[0058] In this embodiment, the five-fold cross-validation method divides the training sample set into five non-overlapping subsets and uses a rotational validation approach to ensure that each subset serves as a validation set once. This strategy makes full use of limited data and comprehensively evaluates model performance through multiple training and validation cycles, effectively improving the model's generalization ability on unknown data.

[0059] The adaptive moment estimation algorithm dynamically adjusts the learning rate of each parameter by maintaining first-order and second-order moment estimates of the gradient. The first-order moment estimate reflects the direction of the gradient mean, while the second-order moment estimate characterizes the magnitude of gradient change. The combination of the two enables adaptive adjustment of parameter updates, accelerating convergence in the early stages of training and stabilizing the convergence process as it approaches the optimal solution.

[0060] The composite loss function includes two components: the parameter prediction error of the permeability model and the settlement-time curve reconstruction error. The former directly measures the accuracy of parameter prediction, while the latter indirectly verifies the rationality of the parameters by comparing the difference between the reconstructed curve and the true curve. This dual requirement ensures that the model accurately predicts parameters while conforming to physical laws.

[0061] The early stopping strategy monitors changes in the validation set loss and automatically terminates training when the loss value does not show a significant decrease over multiple consecutive training epochs. This mechanism effectively prevents the model from overfitting the training data, improving training efficiency while maintaining accuracy.

[0062] Gradient clipping, by setting a gradient threshold, limits excessively large gradient values ​​during backpropagation to a reasonable range. This avoids numerical instability caused by gradient explosion and ensures smooth convergence during training.

[0063] Model performance is evaluated using a comprehensive approach that incorporates three metrics: coefficient of determination, root mean square error (RMSE), and mean absolute percentage error (MAS). The coefficient of determination reflects the goodness of fit of the model, the RMSE measures the magnitude of prediction bias, and the MAS characterizes the level of relative error. This multi-faceted evaluation ensures the reliability of the model's performance.

[0064] Parameter ensemble is a weighted average of the optimal model parameters obtained from five rounds of cross-validation, which combines the advantages of each training iteration to obtain a final model with better stability.

[0065] Hyperparameter optimization employs a Bayesian optimization algorithm, which efficiently searches for the optimal combination of the number of convolutional kernels, the number of long short-term memory units, and the attention dimension by establishing a surrogate model and a sampling function. This algorithm finds a better solution with fewer iterations, improving the efficiency of hyperparameter tuning.

[0066] This embodiment constructs a stable and reliable model training process through a systematic training strategy and optimization techniques. Cross-validation ensures generalization ability, adaptive optimization accelerates convergence, composite loss ensures prediction accuracy, early stopping and gradient pruning maintain training stability, multi-metric evaluation comprehensively assesses performance, and parameter ensemble and Bayesian optimization further improve model quality.

[0067] In some embodiments, the composite loss function is expressed by formula (7), which is as follows: ; In formula (7), This represents the mean square error between the predicted values ​​and the actual values ​​of the permeability model parameters. These are the predicted values ​​of the penetration model parameters. These are the true values ​​of the penetration model parameters. This represents the mean square error between the reconstructed settlement-time curve and the measured settlement-time curve. To reconstruct the settlement-time curve, For the measured settlement-time curve, As the first weighting coefficient, This is the second weighting coefficient. .

[0068] In this embodiment, the composite loss function organically combines two key error terms through formula (7). First The second item directly measures the prediction accuracy of the penetration model parameters, ensuring that the parameter combination output by the model is close to the true value; The degree of agreement between the reconstructed settlement-time curve and the measured curve is evaluated to verify the rationality of the parameters from the perspective of physical laws. First weighting coefficient. Second weighting coefficient The constraint that the contribution ratios of the two errors are adjusted to a sum of 1 ensures the balance of the loss function. Preferably, this can be determined through grid search. and The optimal value of is used to achieve the best balance between parameter prediction and curve reconstruction in the model.

[0069] This embodiment designs a dual-objective loss function, which ensures both the accuracy of parameter prediction and compliance with physical laws, so that the trained model has both mathematical accuracy and engineering practicality, providing an effective optimization objective for high-precision inversion.

[0070] In some embodiments, the measured settlement-time curve of the soil to be inverted is input into the trained hybrid neural network model, and the corresponding optimal combination of permeability model parameters is output, including: The measured settlement-time curves were preprocessed to be consistent with the training sample set. The preprocessed measured settlement-time curve is input into the trained hybrid neural network model, and the feature extraction and fusion process is carried out sequentially through the convolutional neural network module, the bidirectional long short-term memory network module, and the attention mechanism module through forward propagation calculation. In the attention mechanism module, key feature weights corresponding to the turning point of the primary consolidation stage and the starting point of the secondary consolidation stage in the measured sedimentation-time curve are automatically identified and enhanced. The fully connected regression module maps the attention-weighted feature representations to the initial predicted values ​​of the penetration model parameters. Based on the initial predicted values ​​of the permeability model parameters, the corresponding settlement-time curve is reconstructed through the nonlinear consolidation control equation, and is denoted as the reconstructed settlement-time curve. Calculate the similarity index between the reconstructed settlement-time curve and the measured settlement-time curve. When the similarity index does not reach the preset threshold, use an iterative optimization algorithm to fine-tune the initial predicted values ​​of the permeability model parameters. Repeat the reconstruction and fine-tuning process until the similarity index reaches the preset requirements, and output the current penetration model parameters as the optimal combination; The physical rationality of the optimal combination is verified to ensure that the permeability model parameters are within the typical range of highly compressible soft soil. The optimal combination that passes the physical rationality check is denoted as the final optimal combination of permeation model parameters.

[0071] In this embodiment, the same normalization parameters as those used in the training phase are employed during the standardized preprocessing of the measured settlement-time curves to ensure that the input data and training data have consistent dimensions and distribution characteristics. This process guarantees the uniformity of the model input conditions and avoids prediction bias caused by differences in data scale.

[0072] During forward propagation computation, the preprocessed curve sequentially undergoes local feature extraction by the convolutional neural network module, temporal dependency capture by the bidirectional long short-term memory network module, and key information enhancement by the attention mechanism module. These modules work collaboratively to gradually extract deep feature representations closely related to the parameters of the permeation model.

[0073] In the attention mechanism module, the system automatically identifies key time points in the settlement process, especially the turning points of the primary consolidation stage and the starting points of secondary consolidation. These key stages play an important indicative role in permeability characteristics, and by increasing their weight coefficients, the model's sensitivity to key features is enhanced.

[0074] The fully connected regression module maps the optimized feature vectors to initial predicted values ​​for the permeation model parameters. This module achieves the transformation from the high-dimensional feature space to the parameter space through multi-level nonlinear transformations, outputting preliminary parameter estimation results.

[0075] When reconstructing the settlement-time curve based on the initial predicted values, the parameters are substituted into the nonlinear consolidation control equation for forward modeling. The similarity between the reconstructed curve and the measured curve is evaluated using preset quantitative indicators, such as the coefficient of determination or root mean square error.

[0076] When the similarity does not meet the requirements, an iterative optimization algorithm is used to fine-tune the parameters. This process gradually improves the prediction accuracy by repeatedly adjusting the parameter values ​​and reconstructing the curve until the preset similarity threshold is met.

[0077] Physical rationality verification ensures that the final parameter combination conforms to the typical characteristic range of highly compressible soft soil, excludes physically unreasonable prediction results, and guarantees the engineering applicability of the inversion results.

[0078] This embodiment establishes a complete prediction-verification-optimization process, achieving an accurate mapping from measured curves to parameter combinations. Standardization ensures data consistency, multi-module networks extract effective features, iterative optimization improves prediction accuracy, and physical verification ensures result reliability, providing a stable and reliable inversion method for practical engineering applications.

[0079] In some embodiments, the permeability coefficient of the soil to be inverted is obtained by inversion using nonlinear consolidation control equations based on the optimal combination of permeability model parameters, including: By substituting the optimal combination of permeability model parameters into the preset permeability coefficient mathematical model, a quantitative relationship expression between porosity and permeability coefficient is established. Based on the measured physical state parameters of the soil to be inverted, determine the initial void ratio and current effective stress conditions required for the calculation. By inputting the initial void ratio and the current effective stress into the quantitative relationship expression, the current permeability coefficient of the soil to be inverted can be directly calculated. The consolidation development process of soil under load is simulated by nonlinear consolidation control equations to obtain the void ratio variation sequence at different consolidation stages. Based on the porosity change sequence, the corresponding permeability coefficient sequence is continuously calculated using a quantitative relationship expression to obtain the change law of permeability coefficient with time. A verification mechanism for the permeability coefficient inversion results was established. The calculated permeability coefficient was substituted into the nonlinear consolidation control equation to verify its matching degree with the measured settlement-time curve. When the verification results meet the preset accuracy requirements, the current permeability coefficient value of the soil to be inverted is output as the final permeability coefficient of the soil to be inverted.

[0080] In this embodiment, the quantitative relationship between void ratio and permeability coefficient directly reflects the intrinsic connection between soil microstructure and macroscopic permeability characteristics, providing a theoretical basis for permeability coefficient calculation.

[0081] When determining the calculation conditions based on the measured physical state parameters of the soil to be inverted, the initial void ratio is determined through laboratory tests, and the current effective stress is calculated based on field monitoring data. These parameters characterize the actual state of the soil under the current working conditions, ensuring that the permeability coefficient calculation conforms to the actual engineering situation.

[0082] The current permeability coefficient is calculated by inputting the initial void ratio and the current effective stress into a quantitative relationship expression. This is achieved by directly substituting the measured parameters into the established mathematical relationship to obtain the permeability coefficient value under the current state, avoiding a complex iterative process and improving computational efficiency.

[0083] When simulating the consolidation development process using nonlinear consolidation governing equations, numerical methods are employed to solve the governing equations and obtain the void ratio distribution at different time points. This simulation process reproduces the entire consolidation deformation process of soil under load, providing a data foundation for analyzing the variation law of permeability coefficient.

[0084] The permeability coefficient sequence is calculated based on the porosity change sequence by substituting the porosity at each time step into a quantitative relationship expression and continuously calculating the corresponding permeability coefficient value. This method can fully reflect the dynamic change characteristics of the permeability coefficient during the consolidation process.

[0085] When establishing a verification mechanism, the calculated permeability coefficient is substituted into the nonlinear consolidation control equation for forward modeling to obtain the theoretical settlement curve. The reliability of the inversion results is evaluated by comparing the degree of agreement between the theoretical curve and the measured curve. Preferably, verification indicators may include statistical measures such as the coefficient of determination.

[0086] When the verification results meet the preset accuracy requirements, it indicates that the permeability coefficient obtained by inversion can accurately reflect the actual characteristics of the soil. At this time, the current permeability coefficient is output as the final result, and the entire inversion process is completed.

[0087] This embodiment achieves accurate inversion of the permeability coefficient by establishing a complete calculation-verification process. The mathematical model provides theoretical support, the measured parameters ensure the accuracy of the calculation conditions, the numerical simulation reproduces the consolidation process, and the verification mechanism guarantees the reliability of the results, providing an effective method for determining the permeability coefficient in engineering practice.

[0088] Furthermore, the above technical solution can be understood in conjunction with the following example: Data collection and preprocessing: The test data obtained from highly compressible soft soil constitute the original dataset, as shown in List 1 below. Each data sample includes, but is not limited to, the following input features: void ratio. Liquid limit porosity Initial porosity Liquid limit Initial moisture content Effective stress etc., among which, This refers to the moisture content.

[0089]

[0090] Table 1 Data on soft soil grouting and settlement from multiple engineering projects were collected, with a particular focus on the permeability characteristics of highly compressible soft soils. The data included the following parameters: void ratio. Liquid limit porosity Initial porosity Liquid limit Initial moisture content Effective stress For data such as expansion modulus and loading strength, missing values ​​and outliers are handled and removed to ensure data accuracy; interpolation is used to fill missing values ​​and standard deviation is used to remove outliers.

[0091] By calculating the correlation matrix, the correlation between various parameters is analyzed to screen out features that have a greater impact on the permeability coefficient; feature scaling is performed to convert them to the same dimension so that the input data is suitable for the requirements of the machine learning model; new features are created, such as using the ratio of the porosity to the effective stress of each sample as a new feature term to further improve the expressive power of the model.

[0092] Mathematical model establishment: Based on a one-dimensional consolidation permeability test, a formula for the relationship between the permeability coefficient and the void ratio is established, which is a nonlinear relationship model, and is expressed by formula (1) as follows: ; In formula (1), Permeability coefficient, These are the parameters for the first penetration model. These are the parameters for the second penetration model. These are the parameters for the third penetration model. Porosity The liquid limit porosity is denoted as .

[0093] To avoid discontinuities in the compression curves under different stress levels, a compression curve model is adopted, which is expressed by formula (2) as follows: ; In formula (2), The initial void ratio, For effective stress, These are the parameters for the first compression model. These are the parameters for the second compression model. The third compression model parameter is used. The first, second, and third compression model parameters are usually obtained by fitting measured data.

[0094] Derivation and solution of governing equations: Substituting equations (1) and (2) into Terzaghi's one-dimensional nonlinear consolidation control equation, we obtain the result based on the excess pore water pressure. u The nonlinear partial differential control equation with variable A is expressed by formula (3) as follows: ; In formula (3), The symbol is for partial differentials. The pressure of the superstatic pore water. For depth coordinates, For time, Indicates excess pore water pressure Second-order partial derivative along the depth direction, Indicates excess pore water pressure Over time rate of change, This represents the gradient of excess pore water pressure along the depth direction. The square of, The first coefficient related to soil parameters, The second coefficient is related to soil parameters. This can be expressed by formula (4). Equation (5) expresses the following: Equation (4) is as follows: ; In formula (4), For the specific gravity of water, This represents the current porosity. The formula (5) is as follows: .

[0095] In the subsequent numerical solution process, the porosity ratio will be... At time step Spatial nodes The value is denoted as the current porosity. ,Right now .

[0096] The Crank-Nicolson difference is used to discretize formula (3). First, the depth coordinates are... Discretized There are nodes, and the distance between nodes is the spatial step size. Time Discretized Each time step has a step size of time steps. Thus, the discrete equation is obtained, which can be expressed by formula (8) as follows: ; In formula (8), This is the current time step number. This refers to the spatial node number. For the first The spatial node at the _ Numerical solution of excess pore water pressure at each time step. For the difference scheme coefficients, and , For time step, For spatial step size, This represents the total number of discrete nodes in the space. The boundary conditions of formula (8) are expressed by formula (9) as follows: ; In formula (9), For the top drainage boundary ( (place) in the The excess pore water pressure at each time step (set to 0). Indicates the bottom non-drainage boundary ( place, Symmetry condition (for the total thickness of the soil layer), For the first At the initial time (i) The excess pore water pressure, This refers to the instantaneous external load applied to the top of the soil. By combining the boundary conditions, formula (8) can be rewritten in terms of the unknown quantity. The system of linear equations is expressed in matrix form as shown in formula (10) as follows: ; In formula (10), The coefficient matrix, For the coefficient matrix and the first The diagonal elements corresponding to each spatial node For the first The ultrastatic pore water pressure at each spatial node The vector of terms on the right-hand side. For the right-hand term vector, the term is related to the first term. The elements corresponding to each spatial node; Wherein, the coefficient matrix and the right-hand term vector The elements in the formula are defined by the following formula: ; Based on this, a corresponding calculation program was written to perform calculations at each time step. Solve the linear equation system shown in formula (10) to obtain the excess pore water pressure at each spatial node in the soil sample at this time step. Then, the void ratio is obtained through the effective stress principle and formula (2), and finally the corresponding settlement is obtained by integrating the soil layer depth, thereby generating a settlement-time curve sample.

[0097] Sample generation and dataset construction: The Latin hypercube sampling (LHS) method was used to generate parameter combinations within the parameter range. After removing invalid samples, valid parameter combinations were formed. The valid parameter combinations were input into the one-dimensional nonlinear consolidation control equation to calculate the settlement-time curve samples. These samples were then standardized and divided into a training set (80%), a validation set (10%), and a test set (10%).

[0098] Machine learning model building and training: Several machine learning algorithms were selected for comparison, including decision trees, support vector machines, random forests, and neural networks. Each model was trained using K-fold cross-validation to evaluate its performance, and the best-performing model was selected. Grid search was used to adjust the model's hyperparameters to improve prediction accuracy.

[0099] The model was trained using a CNN-BiLSTM-Attention neural network. The CNN part uses one-dimensional convolutional layers to extract local features of the sedimentation-time curve; BiLSTM layers capture the dependencies between time series data; The Attention layer weights the output of BiLSTM to highlight the features of key time steps; Fully connected layer outputs penetration model parameters , , The predicted value; The loss function is mean squared error (MSE), and the Adam optimizer is used for training.

[0100] The selected best machine learning model is trained using the training set, and the model error is monitored in real time during the training process to avoid overfitting. The model's hyperparameters are optimized and tuned using the validation set to prevent overfitting and pursue the best generalization ability. The performance of the trained model is evaluated using a reserved test set.

[0101] The model's generalization ability is improved through five-fold cross-validation and hyperparameter optimization (such as the number of convolutional kernels, the number of LSTM units, and the learning rate). During training, the validation set loss is monitored, and an early stopping strategy is used to prevent overfitting.

[0102] Model evaluation and validation: The performance of the trained model is evaluated using a test set, with metrics including the coefficient of determination, root mean square error (RMSE), and mean absolute percentage error (MAPE). For example, in this embodiment, the model performs as follows on the test set: Coefficient of determination: 0.98 RMSE for 0.05 MAPE: <5% Compare the model's predictions with those of traditional empirical models (such as...) The traditional model is compared with the model to verify its superiority. The prediction results of the traditional model are expressed by formula (11) as follows: ; In formula (11), The permeability coefficient predicted by the traditional empirical model. The first empirical coefficient of the traditional model, The second empirical coefficient of the traditional model, This is the third empirical coefficient in the traditional model; Calculate the model's accuracy and root mean square error, and adjust the training strategy based on the evaluation metrics.

[0103] Engineering applications: The easily measurable physical parameters and current stress state of the soil to be back-calculated are input into the trained final machine learning model, and the model automatically outputs the corresponding predicted permeability coefficient value. No iterative calculations or additional experimental calibrations are required.

[0104] The newly acquired soil parameters are input into the trained model, which outputs the corresponding permeability coefficients. A visualization tool is provided to display dynamic charts showing the changes in permeability coefficients, facilitating user analysis and decision-making. At the same time, a report is generated, which includes the parameters on which the model is based, the prediction results, and relevant engineering recommendations.

[0105] System Implementation: Secondly, the present invention also provides a machine learning-based permeability coefficient inversion system for highly compressible soft soil, used to implement the above method, comprising: The data storage module is used to store sample data and trained models; The feature processing module is used to receive the raw parameters input by the user and to construct and scale the features; The model computation module loads the pre-trained machine learning model and performs forward propagation computation. The results output module outputs the predicted value of the permeability coefficient and the possible confidence interval.

[0106] Model maintenance and continuous optimization: In practice, the differences between the penetration coefficient predicted by the model and the field measurement value are collected and analyzed; new measured data are labeled for regular updates and training of the model to improve the accuracy of future predictions.

[0107] Through the above-described embodiments, the present invention achieves rapid and accurate inversion of the permeability coefficient of highly compressible soft soil, and has strong engineering applicability and a high degree of automation.

[0108] By adopting the above technical solutions, this invention differs from existing technologies and possesses the following beneficial effects: By combining a nonlinear consolidation control equation with a CNN-BiLSTM-Attention hybrid neural network model, rapid and accurate inversion of the permeability coefficient of highly compressible soft soil is achieved. This method effectively captures the complex nonlinear relationship between the permeability coefficient and multi-source soil parameters, significantly improving prediction accuracy and overcoming the limitations of traditional empirical models that rely on specific assumptions and parameter fitting. A high-quality training sample set is constructed through Latin hypercube sampling and physical rationality screening, combined with five-fold cross-validation and composite loss function optimization, ensuring the model's generalization ability and engineering applicability. After model training, instantaneous inversion from measured settlement-time curves to permeability coefficients can be achieved, greatly improving engineering efficiency and reducing reliance on time-consuming and expensive indoor permeability tests. The above technical solutions are applicable to various types of highly compressible soft soil and have strong engineering practical value and promising application prospects.

[0109] Furthermore, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0110] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) or processor to execute all or part of the steps of the methods of various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0111] The above description is only a part of the embodiments of the present invention and does not limit the scope of protection of the present invention. Any equivalent device or equivalent process transformation made based on the content of the present invention specification and drawings, or direct or indirect application in other related technical fields, are similarly included within the patent protection scope of the present invention.

Claims

1. A machine learning-based method for inverting the permeability coefficient of highly compressible soft soil, characterized in that, include: Obtain multi-source soil and rock parameters of highly compressible soft soil, including initial void ratio, liquid limit void ratio, liquid limit water content, initial water content, and current effective stress; Based on the aforementioned multi-source soil and rock parameters, a nonlinear consolidation control equation is constructed, and the finite difference method is used to numerically solve the nonlinear consolidation control equation, generating a sample dataset containing settlement-time curves and permeability model parameters. The sample dataset is standardized, and the Latin hypercube sampling method is used to select effective parameter combinations that meet the preset permeability coefficient range to form a training sample set. A CNN-BiLSTM-Attention hybrid neural network model is constructed, in which a convolutional neural network is used to extract local features of the sedimentation-time curve, a bidirectional long short-term memory network is used to capture long-term dependencies of the time series, and an attention mechanism is used to enhance the feature weights of key time steps. The hybrid neural network model is trained using the training sample set, the model parameters of the hybrid neural network model are optimized using the adaptive moment estimation algorithm, and the generalization ability of the model is improved by the five-fold cross-validation method. The measured settlement-time curve of the soil to be inverted is input into the trained hybrid neural network model, which outputs the optimal combination of the corresponding permeability model parameters. Based on the optimal combination of the permeability model parameters, the permeability coefficient of the soil to be inverted is obtained by inversion through the nonlinear consolidation control equation.

2. The method for inverting the permeability coefficient of highly compressible soft soil based on machine learning according to claim 1, characterized in that, Based on the aforementioned multi-source soil and rock parameters, a nonlinear consolidation control equation was constructed. The finite difference method was then used to numerically solve the nonlinear consolidation control equation, generating a sample dataset containing settlement-time curves and permeability model parameters, including: A nonlinear relationship model between the permeability coefficient and the void ratio is established, and the nonlinear relationship model includes multiple undetermined permeability model parameters; A compression curve model considering stress history is established, wherein the compression curve model represents the evolution relationship between porosity and effective stress through multiple compression model parameters; The nonlinear relationship model and the compression curve model are coupled into the Terzaghi one-dimensional consolidation theory framework to derive the nonlinear partial differential control equation with excess pore water pressure as the variable. The nonlinear partial differential control equations are discretized in time and space using the Crank-Nicolson difference scheme to construct the corresponding set of difference equations. A closed solution system is established by setting predefined boundary conditions and initial conditions. The difference equations are solved by matrix iteration algorithm to obtain the distribution of ultrastatic pore water pressure at different spatiotemporal nodes. Based on the effective stress principle and the compression curve model, the porosity evolution process under the corresponding working conditions is calculated. Based on the porosity evolution process, integral calculations are performed to generate sedimentation-time curve samples corresponding to each combination of permeability model parameters; The parameters of the permeability model are matched and correlated with the corresponding sedimentation-time curves to generate a sample dataset for training machine learning models.

3. The machine learning-based permeability coefficient inversion method for highly compressible soft soil according to claim 2, characterized in that, The nonlinear relationship model is represented by formula (1), which is as follows: ； In formula (1), Permeability coefficient, These are the parameters for the first penetration model. These are the parameters for the second penetration model. These are the parameters for the third penetration model. Porosity Liquid limit porosity; The compression curve model is represented by formula (2), which is as follows: ； In formula (2), The initial void ratio, For effective stress, These are the parameters for the first compression model. These are the parameters for the second compression model. These are the parameters for the third compression model; The nonlinear partial differential control equation is expressed by formula (3), which is as follows: ； In formula (3), The symbol is for partial differentials. The pressure of the superstatic pore water. For depth coordinates, For time, Indicates excess pore water pressure Second-order partial derivative along the depth direction, Indicates excess pore water pressure Over time rate of change, This represents the gradient of excess pore water pressure along the depth direction. The square of, The first coefficient related to soil parameters, The second coefficient is related to soil parameters. This can be expressed by formula (4). Equation (5) expresses the following: Equation (4) is as follows: ； In formula (4), For the specific gravity of water, This represents the current porosity. The formula (5) is as follows: 。 4. The machine learning-based permeability coefficient inversion method for highly compressible soft soil according to claim 1, characterized in that, The sample dataset is standardized, and effective parameter combinations that meet the preset permeability coefficient range are selected using the Latin hypercube sampling method to form a training sample set, including: The sedimentation-time curves in the sample dataset are preprocessed by normalization to obtain standardized sedimentation-time curves; Determine a reasonable range of values ​​for the permeability model parameters, the range of values ​​being determined based on the typical physical and mechanical properties of highly compressible soft soil; The Latin hypercube sampling method is used to generate uniformly distributed sample points in the multidimensional parameter space within the range of values. The permeability model parameters corresponding to each sample point are input into the nonlinear consolidation control equation to calculate the corresponding permeability coefficient value. Establish screening criteria based on a reasonable range of penetration coefficients, and automatically eliminate invalid parameter combinations that exceed the preset screening threshold range; Cluster analysis was performed on the selected effective parameter combinations to ensure the uniformity and representativeness of the sample distribution in the parameter space; The selected effective parameter combinations are paired with the corresponding standardized sedimentation-time curves to construct a training sample set for neural network training.

5. The machine learning-based permeability coefficient inversion method for highly compressible soft soil according to claim 4, characterized in that, The preset screening threshold range is determined by the physical rationality of the permeability coefficient, which satisfies formula (6), as follows: ； Parameter combinations that exceed the preset screening threshold range are determined to be invalid samples and are removed.

6. The method for inverting the permeability coefficient of highly compressible soft soil based on machine learning according to claim 1, characterized in that, A CNN-BiLSTM-Attention hybrid neural network model is constructed, in which a convolutional neural network is used to extract local features of the sedimentation-time curve, a bidirectional long short-term memory network is used to capture long-term dependencies in the time series, and an attention mechanism is used to enhance the feature weights at key time steps, including: A one-dimensional convolutional neural network module is constructed. By setting multiple layers of convolutional kernels of different scales, multi-level feature extraction is performed on the input sedimentation-time curve to obtain a high-dimensional feature vector containing local fluctuation patterns and trend changes. A bidirectional long short-term memory network module is constructed to process the high-dimensional feature vector through both forward and backward channels, capturing the forward causal dependence and backward correlation characteristics of the sedimentation development process, and fusing them to generate a hidden state sequence containing complete temporal context information. An attention mechanism module is constructed, which calculates the weight coefficients of each time step in the hidden state sequence through a trainable parameter matrix, and performs a weighted summation of the hidden states based on the weight coefficients to highlight the characteristic contributions of the consolidation inflection point and the key stage of rate change during the settlement process. Construct a fully connected regression module to map the attention-weighted feature representations to the penetration model parameter space and output the optimal combination of penetration model parameters; A residual connection mechanism is introduced into the hybrid neural network model to alleviate the gradient vanishing problem during deep network training. A hierarchical regularization strategy is adopted, and Dropout operations are applied to the convolutional layer and the recurrent layer respectively to suppress the overfitting tendency of the model, so as to obtain the hybrid neural network model to be trained.

7. The machine learning-based permeability coefficient inversion method for highly compressible soft soil according to claim 1, characterized in that, The hybrid neural network model is trained using the training sample set, and the model parameters are optimized using an adaptive moment estimation algorithm. The generalization ability of the model is improved through five-fold cross-validation, including: The training sample set is randomly divided into five non-overlapping subsets. A rotational validation strategy is adopted, in which one subset is used as the validation set and the other four subsets are used as the training set, and five rounds of model training and validation are performed. In each training round, the learning rate of the model parameters is dynamically adjusted using an adaptive moment estimation algorithm. The adaptive update of the model parameters is achieved by calculating the first-order moment estimate and the second-order moment estimate of the gradient. A composite loss function based on mean square error is established, which simultaneously considers the prediction accuracy of the permeability model parameters and the reconstruction error of the settlement-time curve. An early stopping strategy is implemented during training. Training is automatically terminated when the validation set loss function no longer decreases over several consecutive training cycles to prevent model overfitting. Gradient clipping is used to limit the range of gradient values ​​during backpropagation, ensuring numerical stability during training. After each round of training, model performance evaluation metrics are calculated based on the validation set, including the coefficient of determination, root mean square error, and mean absolute percentage error. By integrating the optimal model parameters from five rounds of cross-validation, a final model with the best generalization ability is obtained. The final model is then optimized using hyperparameters. A Bayesian optimization algorithm is used to search for the optimal combination of the number of convolutional kernels, the number of long short-term memory units, and the attention dimension.

8. The machine learning-based permeability coefficient inversion method for highly compressible soft soil according to claim 7, characterized in that, The composite loss function is expressed by formula (7), which is as follows: ； In formula (7), For composite loss function, This represents the mean square error between the predicted values ​​and the actual values ​​of the permeability model parameters. These are the predicted values ​​of the permeability model parameters. These are the true values ​​of the penetration model parameters. This represents the mean square error between the reconstructed settlement-time curve and the measured settlement-time curve. To reconstruct the settlement-time curve, For the measured settlement-time curve, As the first weighting coefficient, This is the second weighting coefficient. .

9. The method for inverting the permeability coefficient of highly compressible soft soil based on machine learning according to claim 1, characterized in that, The measured settlement-time curve of the soil to be inverted is input into the trained hybrid neural network model, which outputs the optimal combination of corresponding permeability model parameters, including: The measured settlement-time curves are subjected to standardized preprocessing consistent with the training sample set; The preprocessed measured settlement-time curve is input into the trained hybrid neural network model, and the feature extraction and fusion process is carried out sequentially through the convolutional neural network module, the bidirectional long short-term memory network module, and the attention mechanism module through forward propagation calculation. In the attention mechanism module, key feature weights corresponding to the turning point of the primary consolidation stage and the starting point of the secondary consolidation stage in the measured settlement-time curve are automatically identified and enhanced. The fully connected regression module maps the attention-weighted feature representations to the initial predicted values ​​of the penetration model parameters. Based on the initial predicted values ​​of the permeability model parameters, the corresponding settlement-time curve is reconstructed using the nonlinear consolidation control equation, and is denoted as the reconstructed settlement-time curve. Calculate the similarity index between the reconstructed settlement-time curve and the measured settlement-time curve. When the similarity index does not reach a preset threshold, use an iterative optimization algorithm to fine-tune the initial predicted values ​​of the permeability model parameters. Repeat the reconstruction and fine-tuning process until the similarity index reaches the preset requirements, and output the current penetration model parameters as the optimal combination; The physical rationality of the optimal combination is verified to ensure that the permeability model parameters are within the typical range of highly compressible soft soil. The optimal combination that passes the physical rationality check is denoted as the final optimal combination of permeation model parameters.

10. The machine learning-based permeability coefficient inversion method for highly compressible soft soil according to claim 1, characterized in that, Based on the optimal combination of the permeability model parameters, the permeability coefficient of the soil to be inverted is obtained through the inversion of the nonlinear consolidation control equation, including: The optimal combination of the permeability model parameters is substituted into the preset permeability coefficient mathematical model to establish a quantitative relationship expression between the porosity and the permeability coefficient. Based on the measured physical state parameters of the soil to be inverted, determine the initial void ratio and current effective stress conditions required for the calculation. By inputting the initial void ratio and the current effective stress into the quantitative relationship expression, the current permeability coefficient of the soil to be inverted can be directly calculated. The nonlinear consolidation control equation is used to simulate the consolidation development process of soil under load, and the void ratio change sequence at different consolidation stages is obtained. Based on the porosity change sequence, the corresponding permeability coefficient sequence is continuously calculated using the quantitative relationship expression to obtain the permeability coefficient change law with time. A verification mechanism for the permeability coefficient inversion results is established. The calculated permeability coefficient is substituted into the nonlinear consolidation control equation to verify its matching degree with the measured settlement-time curve. When the verification result meets the preset accuracy requirements, the current permeability coefficient value of the soil to be inverted is output as the final permeability coefficient of the soil to be inverted.

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