Mountainous roadbed settlement simulation method and system based on long-term load action

Abstract

The application provides a mountainous roadbed settlement simulation method and system based on long-term load action, and the method comprises the following steps: acquiring regional layered settlement monitoring data and performing standardization pretreatment, and constructing a background settlement depth gradient distribution model; extracting soil layer layered parameters of a to-be-simulated roadbed settlement calculation model, and distributing the background settlement amount to each soil layer according to the depth; superimposing the layered background settlement amount of each soil layer and the roadbed additional settlement amount, and obtaining the total settlement distribution of the full depth. The method corrects the depth direction calculation deviation caused by the rigid body translation assumption of the background settlement under the premise of not expanding the calculation domain, improves the accuracy of the long-term settlement simulation of the mountainous roadbed, and meets the demand of the long-term settlement analysis of the mountainous highway roadbed.

Description

Technical Field

[0001] This application belongs to the field of geotechnical engineering testing technology, and in particular relates to a method and system for simulating settlement of roadbeds in mountainous areas based on long-term load. Background Technology

[0002] In the field of long-term settlement simulation of roadbeds in mountainous areas, existing technologies mainly fall into two categories: one is to incorporate the roadbed and surrounding mountains into the same numerical model for coupled calculation. While this method can consider the coupling effect of mountain deformation, it has a large computational domain, a large number of elements, and a long calculation cycle for a single working condition, making it unsuitable for rapid comparison and dynamic design of engineering schemes. The other is to use the background settlement superposition method, which directly superimposes the regional mountain settlement as rigid body displacement onto the roadbed settlement results. This method has high computational efficiency, but it assumes that the background settlement is uniform across the entire depth range, ignoring the objective law of the decay of soil and rock creep with depth. This results in large deviations in deep settlement calculations, especially in mountainous areas with obvious red bed weathering zones, where the settlement prediction error is difficult to meet engineering accuracy requirements. In addition, existing superposition methods cannot reproduce the time evolution characteristics of deep creep lag, and the simulation accuracy of the entire settlement process is insufficient, making it difficult to adapt to the needs of long-term settlement analysis under complex geological conditions in mountainous areas. Summary of the Invention

[0003] To address the issue of how to correct the depth direction calculation deviation caused by the rigid body translation assumption of background settlement in long-term mountain roadbed settlement simulation without expanding the computational domain or increasing computational overhead, and to improve the accuracy of long-term mountain roadbed settlement simulation, this application provides a method and system for simulating mountain roadbed settlement based on long-term load action.

[0004] This application first provides a method for simulating settlement of roadbed in mountainous areas based on long-term load, the method comprising: Regional stratified settlement monitoring data were acquired and standardized preprocessed to construct a background settlement depth gradient distribution model; the background settlement depth gradient distribution model is a distribution model that characterizes the attenuation of background settlement as soil depth increases. Extract the soil layer parameters of the roadbed settlement calculation model to be simulated, and according to the background settlement depth gradient distribution model, distribute the background settlement amount to each soil layer according to the depth to obtain the layered background settlement amount of each soil layer. The background settlement of each soil layer is superimposed with the additional settlement of the roadbed in the corresponding soil layer to obtain the total settlement distribution at full depth, thus completing the long-term settlement simulation of the roadbed in the mountainous area.

[0005] Optionally, constructing the background settlement depth gradient distribution model includes: Nonlinear fitting was performed on the preprocessed stratified settlement monitoring data to obtain the depth attenuation coefficient and the surface benchmark settlement. A continuous distribution function of background settlement along depth is generated based on the depth attenuation coefficient and the surface reference settlement. The goodness-of-fit of the continuous distribution function is checked, and the background settlement depth gradient distribution model is obtained after the check passes.

[0006] Optionally, the step of distributing the background settlement amount to each soil layer according to depth to obtain the layered background settlement amount for each soil layer includes: Determine the top and bottom depths of each soil layer based on the soil layer stratification parameters; Substituting the top and bottom depths of the layer into the background settlement depth gradient distribution model, respectively, yields the background settlement values ​​at the top and bottom of the layer. The difference between the background settlement value at the top of the layer and the background settlement value at the bottom of the layer is calculated to obtain the layered background settlement of the corresponding soil layer.

[0007] Optionally, the background settlement of each soil layer and the additional subgrade settlement of the corresponding soil layer are superimposed layer by layer to obtain the total settlement distribution across the entire depth, including: Extract the additional compression of each soil layer from the subgrade settlement calculation model; The total compression of the soil layer is obtained by adding the additional compression of the same soil layer to the background settlement of the layer. The total compression of all soil layers is accumulated from top to bottom to obtain the total settlement of the roadbed surface and the settlement distribution across the entire depth.

[0008] Optionally, the step of performing nonlinear fitting on the preprocessed stratified settlement monitoring data to obtain the depth attenuation coefficient and the surface reference settlement includes: Long-term subsidence sequences at each monitoring depth were extracted, and the time evolution parameters of surface subsidence were obtained by fitting. Calculate the surface baseline settlement at the current time based on the current calculation time and time evolution parameters; The depth attenuation coefficient is obtained by fitting the ratio of the settlement at each depth to the surface reference settlement.

[0009] Optionally, the goodness-of-fit verification of the continuous distribution function, and the obtaining of the background subsidence depth gradient distribution model after the verification passes, includes: Calculate the coefficient of determination between the continuous distribution function and the monitoring data; Determine whether the determination coefficient reaches a preset threshold; if it does, the verification passes. If the target is not met, additional monitoring samples are added and the model is refitted until the verification is passed, at which point the background settlement depth gradient distribution model is output.

[0010] Optionally, substituting the top and bottom depths of the layer into the background settlement depth gradient distribution model to obtain the background settlement value at the top and bottom of the layer includes: Determine whether the soil depth exceeds the maximum monitoring depth; If the value does not exceed the limit, directly substitute it into the model to calculate the background settlement value at the corresponding depth; If the value exceeds the limit, the settlement value of the deepest monitoring point will be extrapolated according to the gradient law, and the extrapolation depth will not exceed the preset ratio of the maximum monitoring depth.

[0011] Optionally, the calculation of the difference between the background settlement value at the top of the layer and the background settlement value at the bottom of the layer to obtain the layered background settlement of the corresponding soil layer includes: Multiple settlement zones are divided along the cross section of the roadbed; Match the corresponding background settlement depth gradient distribution model to each partition; Calculate the background settlement of each soil layer in each zone.

[0012] Optionally, the step of adding the additional compression of the same soil layer to the background settlement of the layers to obtain the total compression of the soil layer includes: Calculate the ratio of the additional settlement rate to the background settlement rate for the same soil layer; The nonlinear superposition correction coefficient is determined based on the rate ratio; The total compression of the soil layer is obtained by multiplying the background settlement of the layer by the correction factor and then adding it to the additional compression.

[0013] This application also provides a mountain roadbed settlement simulation system based on long-term load action, the system comprising: The data processing module is used to acquire regional stratified settlement monitoring data and perform standardized preprocessing to construct a background settlement depth gradient distribution model; the background settlement depth gradient distribution model is a distribution model that characterizes the attenuation of background settlement as the soil layer depth increases. The layered allocation module is used to extract the soil layering parameters of the roadbed settlement calculation model to be simulated, and to allocate the background settlement amount to each soil layer according to the background settlement depth gradient distribution model to obtain the layered background settlement amount of each soil layer. The settlement overlay module is used to overlay the background settlement of each soil layer with the additional settlement of the roadbed in the corresponding soil layer to obtain the total settlement distribution at full depth and complete the long-term settlement simulation of the roadbed in mountainous areas.

[0014] In the embodiments provided in this application, the method solves the total settlement by decomposing it into additional roadbed settlement and regional background settlement separately. This eliminates the need to construct a large-scale mountain calculation model, fundamentally controlling the computational domain size and maintaining the computational efficiency of the superposition method. Based on this, a background settlement depth gradient distribution model is constructed to restore the true law of background settlement attenuation with depth, replacing the traditional rigid body translation assumption and correcting the systematic errors caused by uniform settlement across the entire depth. Furthermore, through a layered mapping allocation method, the gradient-distributed background settlement is accurately matched to each soil layer of the roadbed model, achieving same-level superposition with the layered additional settlement calculation. This ensures spatial consistency of the superposition calculation. Without increasing computational overhead or modifying the original roadbed settlement model, it effectively reduces the settlement calculation deviation in the depth direction, improving the accuracy of long-term settlement simulation of mountain roadbeds. Simultaneously, it retains the advantages of the original method—lightweight and easily adaptable—and can directly interface with various roadbed settlement calculation models, adapting to the engineering application needs under complex geological conditions in mountainous areas. Attached Figure Description

[0015] To more clearly illustrate the technical solutions in the embodiments of this application 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 some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0016] Figure 1 This is a general flowchart of the method for simulating settlement of mountain roadbed based on long-term load in the embodiments of this application; Figure 2 This is a sub-flowchart of constructing a background settlement depth gradient distribution model in an embodiment of this application; Figure 3 This is a sub-flowchart illustrating the distribution of background settlement to each soil layer by depth in an embodiment of this application. Figure 4 This is a sub-flowchart illustrating the layered superposition of background settlement and additional subgrade settlement in an embodiment of this application. Figure 5 This is a sub-flowchart of nonlinear fitting of stratified settlement monitoring data in an embodiment of this application; Figure 6 This is a sub-flowchart for verifying the goodness of fit of a continuous distribution function in an embodiment of this application; Figure 7 This is a sub-flowchart of substituting depth into the background settlement depth gradient distribution model in an embodiment of this application; Figure 8 This is a sub-flowchart for calculating the stratified background settlement in an embodiment of this application; Figure 9This is a sub-flowchart in an embodiment of this application that superimposes the additional compression amount with the stratified background settlement amount; Figure 10 This is a schematic diagram of a mountain roadbed settlement simulation system based on long-term load in an embodiment of this application. Detailed Implementation

[0017] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not limiting, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application can also be implemented in other embodiments without such specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods are omitted so as not to obscure the description of this application with unnecessary detail.

[0018] In this embodiment, the settlement simulation method is applied to the long-term settlement analysis of highway subgrades in mountainous areas. It is adaptable to the settlement calculation needs of subgrades under different terrain and geological conditions, and can be applied to multiple engineering stages, including scheme comparison in the subgrade design phase, dynamic optimization in the construction phase, and settlement prediction in the operation phase. This method is based on the idea of ​​settlement field decoupling, eliminating the need for large-scale solid modeling of the surrounding mountains. It can improve the accuracy of settlement calculation results while maintaining high computational efficiency.

[0019] This application provides a method for simulating settlement of roadbeds in mountainous areas based on long-term loads, such as... Figure 1 As shown, the method includes: S100: Acquire regional stratified settlement monitoring data and perform standardized preprocessing to construct a background settlement depth gradient distribution model; the background settlement depth gradient distribution model is a distribution model that characterizes the attenuation of background settlement as soil depth increases.

[0020] S200: Extract the soil layer parameters of the roadbed settlement calculation model to be simulated, and distribute the background settlement amount to each soil layer according to the background settlement depth gradient distribution model to obtain the layered background settlement amount of each soil layer.

[0021] S300: The background settlement of each soil layer is superimposed with the additional settlement of the roadbed in the corresponding soil layer to obtain the total settlement distribution at full depth, thus completing the long-term settlement simulation of the roadbed in the mountainous area.

[0022] Specifically, the implementation process first involves acquiring regional stratified settlement monitoring data and performing standardized preprocessing to construct a background settlement depth gradient distribution model. This model characterizes the attenuation of background settlement with increasing soil depth.

[0023] It should be noted that regional stratified settlement monitoring data refers to time-series data containing vertical deformation information of soil at different depths, collected by various monitoring facilities within the project's influence area. Data acquisition channels can be selected based on actual project conditions. Common sources include existing geological monitoring boreholes within the project area, stratified settlement monitoring facilities deployed in adjacent construction projects, depth settlement profiles obtained through a combination of surface remote sensing and deep exploration, and long-term deformation observation data accumulated from regional geological surveys. Monitoring data from different sources have different characteristics. During implementation, data from a single source can be selected based on data availability and accuracy requirements, or multiple sources can be integrated to combine the advantages of different data sources and improve the comprehensiveness and reliability of the data.

[0024] Among these, data collected from geological monitoring wells are of high precision and have good temporal continuity. They can directly obtain settlement values ​​at different depths, making them the primary source of stratified settlement data. The deployment of geological monitoring wells is usually integrated with regional geological surveys and geological hazard monitoring. Most mountainous engineering projects have existing monitoring well resources nearby, allowing for the direct reuse of existing monitoring results. This eliminates the need for separate monitoring facilities for this settlement simulation, reducing upfront investment costs. When using geological monitoring well data, priority should be given to selecting monitoring points with geological conditions consistent with the road section to be simulated, including consistency in rock type, weathering degree, and structural conditions. This ensures that the creep characteristics of the soil and rock reflected in the monitoring data match the target area. The distance between the monitoring well and the road section to be simulated can be determined based on the homogeneity of the regional geology. In areas with homogeneous geological conditions, slightly farther monitoring wells can be selected; in areas with significant variations in geological conditions, closer monitoring wells should be selected to ensure data representativeness.

[0025] Depth settlement profiles obtained through inversion using a combination of remote sensing and deep exploration have a wide coverage area, providing information on settlement distribution over large regions. This makes them suitable for use on large road sections with relatively flat terrain and geological changes. While the depth resolution of this type of data is lower than that of borehole monitoring data, its spatial coverage is stronger, compensating for the lack of borehole locations and aiding in determining the spatial distribution trend of settlement. When using this type of data, it is necessary to first verify its accuracy by comparing it with known borehole monitoring data and correcting for systematic biases before using it for model fitting.

[0026] Layered settlement monitoring data from adjacent construction projects typically have a construction timeline close to that of the target project, resulting in good data timeliness. Furthermore, the engineering geological conditions in the same area are highly similar, making the data highly reusable. When using this type of data, it is crucial to consider the differences in load conditions and construction timelines between the two projects, exclude additional settlement caused by artificial loads, and extract background settlement data solely due to the creep of the mountain itself to avoid parameter deviations caused by load factors.

[0027] Monitoring data must cover at least three different depth levels and have continuous time series records. The time span can be selected based on the stability of regional geological activity, ensuring it reflects the basic laws of rock mass creep. The longer the time span, the higher the reliability of the parameters obtained from subsequent fitting, and the better the stability of long-term settlement prediction. If the monitoring time is short, auxiliary corrections can be made using regional geological experience parameters to ensure the rationality of the fitting results.

[0028] After obtaining the raw monitoring data, the first step is to perform data cleaning to remove outliers from the data sequence. Outliers refer to abrupt changes in data that deviate from the normal creep pattern of the rock mass. These are usually caused by factors such as construction disturbance, equipment failure, extreme weather, or human contact. They do not reflect the normal creep pattern of the rock mass, and retaining them in the data sequence will lead to deviations in the fitting parameters. Therefore, they need to be removed in advance.

[0029] There are several methods for identifying outliers, and the appropriate method can be chosen based on data quality and computational conditions. One implementation method is the three-standard-deviation method. This method is based on the statistical assumption of a normal distribution. It first calculates the mean and standard deviation of the settlement rate sequence, and then identifies data points that exceed the mean plus or minus three standard deviations as outliers. The three-standard-deviation method is simple to calculate, can complete the identification process, does not require manual judgment of each data point, has high processing efficiency, and is suitable for scenarios with large amounts of data. The implementation steps of this method are as follows: first, calculate the settlement rate at adjacent monitoring times to form a settlement rate sequence; second, calculate the arithmetic mean and sample standard deviation of the rate sequence; finally, compare each rate value with a threshold point by point, and mark the points that exceed the threshold range as outliers, and remove the settlement data for the corresponding time period.

[0030] Another implementation method is the sliding window method. A fixed-length sliding window is set, and the average settlement rate within the window is calculated. Data deviating from the window average by more than a set threshold is identified as outliers. The sliding window method can adapt to slow rate changes, avoiding misjudging normal rate changes as anomalies, and is suitable for long-term time-series data where creep rate changes continuously over time. The window duration can be set according to the monitoring frequency and data fluctuations. A window that is too short is easily affected by random fluctuations, while a window that is too long reduces sensitivity to outliers; an appropriate window size must be selected based on the data characteristics. The threshold can be determined based on the normal fluctuation range of the data, typically two to three times the standard deviation of the rate within the window, ensuring that obvious anomalies are identified without mistakenly deleting normal fluctuation data.

[0031] Another implementation method is the trend line fitting method. First, a trend curve is fitted to the settlement time series to obtain the trend curve of settlement changing over time. Then, the residual between each measured point and the trend curve is calculated, and points with residuals exceeding a set threshold are identified as outliers. The trend line fitting method can better preserve the overall trend of settlement change and eliminate abrupt changes that deviate from the trend, making it suitable for monitoring sequences with relatively clear settlement trends. Trend fitting can use various forms such as polynomials and power functions, and the appropriate function form can be selected based on the data's changing patterns.

[0032] For missing data in the sequence, interpolation is used to complete it, ensuring the continuity and completeness of the time series for each depth point, thus providing a continuous data foundation for subsequent fitting calculations. Missing data completion methods include spatial interpolation of adjacent monitoring points at the same depth, and temporal interpolation of adjacent times at the same point; the appropriate method can be selected based on the extent of the missing data.

[0033] Missing data in the temporal dimension can be filled using methods such as linear interpolation and spline interpolation. Linear interpolation is simple to calculate and suitable for short-term missing data, directly using the values ​​from two consecutive time points to linearly extrapolate the missing value. Spline interpolation generates a smooth transition curve, suitable for longer-term missing data, and provides better continuity in the completed sequence, better conforming to the continuous change patterns of creep. Missing data in the spatial dimension can be filled using methods such as inverse distance weighted interpolation and kriging interpolation, using data from surrounding monitoring points at the same depth to extrapolate the value of the target point. This is suitable for scenarios where local data is missing from a particular monitoring well, but other monitoring wells exist nearby.

[0034] After data cleaning, standardization processing is performed to eliminate benchmark differences between different data sources, ensuring benchmark consistency for subsequent fitting and calculations and avoiding systematic errors caused by benchmark inconsistencies. Standardization processing includes three aspects: unification of depth benchmarks, unification of time benchmarks, and unification of settlement direction.

[0035] The depth datum is uniformly set with the original surface of the roadbed as the zero point, and the downward direction as positive. Depth data from all monitoring points are converted to this datum system. The specific conversion process is as follows: first, the elevation of each monitoring borehole opening is unified to the roadbed design elevation datum through elevation system conversion; then, the corresponding elevation is calculated based on the borehole depth at each measuring point; finally, the depth value for each measuring point is calculated using the original roadbed surface elevation as the datum. During the conversion process, attention must be paid to the datum system of the borehole opening elevation. Different monitoring boreholes may use different elevation datums; they must be unified to the same datum before conversion to avoid depth errors caused by datum misalignment.

[0036] The time reference point is uniformly set as the commencement time of the roadbed project to be simulated. All time series of monitoring data are converted to this time reference to ensure that the starting point of settlement calculations is consistent with the project progress. During the conversion, the timestamps of each monitoring data point are extracted and uniformly converted to the duration since the commencement time. The unit can be selected according to calculation needs, such as year, month, or day, to ensure a consistent calculation time scale. Monitoring data before commencement is converted to negative time values ​​to fit the initial creep trend; monitoring data after commencement corresponds to positive time values ​​for settlement calculations and verification during the project phase.

[0037] The settlement direction is uniformly defined with downward settlement as the positive direction. All settlement values ​​in the monitoring data are standardized according to this rule to avoid sign errors caused by differences in direction definitions. Different monitoring devices may use different direction definitions, with some devices using upward displacement as positive and others using downward displacement as positive. These must be uniformly converted to the rule of downward positive to ensure consistency of signs in subsequent calculations.

[0038] After standardized preprocessing, a background settlement depth gradient distribution model is constructed based on the processed monitoring data. The weathering degree of mountain rock mass typically decreases gradually with increasing depth. Surface rock mass exhibits high weathering degree, large porosity, loose structure, and active creep, resulting in relatively large settlement. Deep rock mass has low weathering degree, dense structure, good integrity, weak creep, and relatively small settlement. Therefore, background settlement exhibits a gradual decrease with increasing soil depth, rather than being uniform across the entire depth range. This application uses a gradient distribution model to reconstruct this spatial distribution pattern, replacing the assumption of uniform settlement across the entire depth.

[0039] In alternative implementations, such as Figure 2 As shown, the construction of the background subsidence depth gradient distribution model includes: S201: Nonlinear fitting is performed on the preprocessed stratified settlement monitoring data to obtain the depth attenuation coefficient and the surface benchmark settlement.

[0040] S202: Generate a continuous distribution function of background settlement along the depth based on the depth attenuation coefficient and the surface reference settlement.

[0041] S203: Perform a goodness-of-fit check on the continuous distribution function. Once the check passes, the background settlement depth gradient distribution model is obtained.

[0042] Specifically, the nonlinear fitting method selects settlement monitoring values ​​at different depths at the same time as sample data and uses the nonlinear least squares method for fitting calculations. The fitting process aims to minimize the sum of squared residuals between the monitored values ​​and the calculated values ​​from the model, and iteratively solves to obtain the relevant parameters of the model. The selected sample time can be determined based on the data situation. Usually, the time when the data in the monitoring sequence is complete and there are no abnormal disturbances is selected as the fitting reference time to ensure the reliability of the sample data. Data from a single time can be selected for fitting, or data from multiple time points can be fitted separately and then averaged to improve the stability of the parameters.

[0043] There are various algorithms for solving nonlinear least squares problems, and the appropriate one can be chosen based on the computational conditions. One such algorithm is the Gauss-Newton method, which iteratively approximates the optimal solution, resulting in a relatively fast convergence speed. This method is suitable for scenarios where the initial values ​​are relatively accurate. In practice, initial parameter values ​​are given, the model values ​​and residuals under the current parameters are calculated, then the parameter correction is calculated using the Jacobian matrix. After updating the parameters, the residuals are recalculated, and this iteration is repeated until the sum of squared residuals meets the convergence requirement.

[0044] Another method is the Levenberg-Marquardt method, which combines the advantages of gradient descent and Gauss-Newton's method. It has relatively lower requirements for initial values, better convergence stability, and is suitable for fitting calculations in engineering scenarios. When the parameters are far from the optimal solution, the algorithm tends towards gradient descent to ensure the correct convergence direction; when the parameters are close to the optimal solution, the algorithm tends towards Gauss-Newton's method to accelerate convergence. This method effectively avoids iterative divergence problems and is suitable for unattended computing scenarios.

[0045] During the fitting process, a reasonable iteration convergence threshold is set. When the change in parameters at each iteration step is less than the threshold, or the change in the sum of squared residuals is less than the threshold, convergence is determined, and the final fitted parameters are output. The convergence threshold can be set according to the accuracy requirements. The smaller the threshold, the more iterations are needed, and the higher the calculation accuracy, but the calculation time will also increase accordingly. An appropriate threshold should be selected based on the engineering requirements.

[0046] The basic function used for fitting is in the form of exponential decay, and the corresponding expression is: (1) In this formula, Indicates depth at reference time Background settlement at the location, expressed in units of length. This represents the background subsidence at the Earth's surface at a reference time, i.e., the reference surface subsidence, expressed in units of length. This represents the background settlement depth attenuation coefficient, expressed as the reciprocal of length, reflecting the rate at which settlement decreases with depth. Indicates soil depth, in units of length. It is a natural constant.

[0047] The physical meaning of this formula is that background settlement decreases exponentially with increasing soil depth, with the largest settlement at the surface. Settlement gradually decreases with increasing depth, and the rate of decrease is determined by the depth attenuation coefficient. A larger attenuation coefficient indicates a more significant difference in settlement between the surface and deeper layers, corresponding to more pronounced weathering zoning of the rock mass. A smaller attenuation coefficient indicates a more gradual change in settlement along depth, corresponding to better homogeneity of the rock mass. When the depth attenuation coefficient is zero, the formula degenerates into a uniform settlement form, meaning that background settlement does not change with depth. This is consistent with the calculation form of existing uniform settlement assumptions, indicating that the scheme in this application is compatible with the application scenarios of existing methods and has a wider range of applications.

[0048] The exponential decay model was chosen as the fundamental function because it conforms to the general law of stress and deformation decaying with depth in soil and rock masses, has fewer parameters, clear physical meanings, and good extrapolation stability. A linear decay model would overestimate deep settlement, contradicting actual decay patterns; a high-order polynomial model would have many parameters, be prone to overfitting, and have poor extrapolation stability, making it unsuitable for engineering applications; and a logarithmic decay model would show excessively rapid deep settlement decay, inconsistent with the creep characteristics of most rock masses. The exponential decay model has a wide application base in geotechnical engineering, with clearly defined physical meanings for its parameters, making it easy for engineers to understand and use.

[0049] After obtaining the depth attenuation coefficient and the surface baseline settlement, a continuous distribution function of background settlement along the depth can be generated. This continuous distribution function can output the background settlement at any depth, unrestricted by the depth of the monitoring points, and can match the depth of any soil layer in the subgrade model. Using a continuous function avoids errors caused by interpolation of discrete monitoring points, and the calculation process is simple, requiring no storage of large amounts of discrete data, resulting in high computational efficiency. The effective depth range of the continuous distribution function covers the entire depth range of the monitoring data, as well as the allowable extrapolation depth range. Within the effective range, the function can be directly called to calculate the settlement value at the corresponding depth, making it convenient to use.

[0050] After generating the continuous distribution function, a goodness-of-fit check is required to verify the degree of agreement between the function and the monitoring data, ensuring the reliability of subsequent calculations. The coefficient of determination (COD) is used as the evaluation metric. The COD reflects the degree to which the model's calculated values ​​explain the measured data; the closer the value is to one, the better the agreement.

[0051] In alternative implementations, such as Figure 3 As shown, the goodness-of-fit test of the continuous distribution function, after passing the test, yields the background subsidence depth gradient distribution model, including: S301: Calculate the coefficient of determination of the continuous distribution function and the monitoring data.

[0052] S302: Determine whether the coefficient of determination has reached the preset threshold. If it has, the verification is successful.

[0053] S303: If the target is not met, supplement the monitoring samples and refit until the verification is passed, then output the background settlement depth gradient distribution model.

[0054] The coefficient of determination is calculated based on the ratio of the total sum of squares to the residual sum of squares. The total sum of squares is the sum of squares of the differences between the settlement values ​​at each monitoring point and the mean settlement value, reflecting the overall dispersion of the measured data. The residual sum of squares is the sum of squares of the differences between the measured values ​​at each monitoring point and the values ​​calculated by the model, reflecting the degree of deviation between the calculated values ​​and the measured values. The coefficient of determination is equal to one minus the ratio of the residual sum of squares to the total sum of squares, and its value ranges from zero to one. The closer the value is to one, the stronger the model's explanatory power for the data and the better the fit.

[0055] The preset threshold is set according to the accuracy requirements of the engineering calculations, and is usually set to no less than 0.9 to ensure that the fit results and monitoring data meet the needs of engineering applications. For road sections with high engineering importance, such as high embankment sections, soft soil sections, and bridge approach sections, where settlement control requirements are high, the threshold requirement can be appropriately increased to further ensure the accuracy of the fitting model. For the preliminary scheme comparison stage, where the accuracy requirements are relatively low, the threshold can be appropriately reduced to improve the fitting pass rate and speed up the calculation.

[0056] If the calculated coefficient of determination reaches the preset threshold, it indicates that the fitted continuous distribution function accurately reflects the depth distribution pattern of the regional background settlement, and the verification is successful. This function can then be used as the background settlement depth gradient distribution model for subsequent calculations. If the coefficient of determination does not reach the preset threshold, it indicates that the number or representativeness of the existing monitoring samples is insufficient to support accurate fitting calculations. In this case, more monitoring samples need to be added, including increasing monitoring points, extending monitoring time, and supplementing monitoring data from other sources. After adding samples, the fitting calculation is repeated until the coefficient of determination meets the threshold requirement. This verification process ensures the reliability of the gradient model and avoids systematic errors in subsequent settlement calculations due to model bias.

[0057] After constructing the background settlement depth gradient distribution model, the soil layer parameters of the roadbed settlement calculation model to be simulated are extracted. According to the background settlement depth gradient distribution model, the background settlement is distributed to each soil layer according to depth to obtain the layered background settlement of each soil layer.

[0058] It should be noted that the roadbed settlement calculation model to be simulated is an existing roadbed settlement calculation model, which can be calculated using different methods such as the layered summation method, the finite element method, and the finite difference method. This application does not modify the core structure of the original roadbed model, but only reuses its soil layer parameters and additional settlement calculation results. Therefore, it can be adapted to different types of roadbed settlement calculation models, without the need for remodeling, and the implementation cost is low.

[0059] For the layered summation method model, the soil layer division itself is based on geological stratification, and the top and bottom depths of each layer are clearly defined and can be directly read and used. The layered summation method is the most commonly used method in roadbed settlement calculation. The calculation process is simple, the physical meaning of the parameters is clear, and it has wide engineering applications. This method can directly interface with the calculation results of the layered summation method without the need for additional data conversion.

[0060] For finite element method (FEM) or finite difference method (FD) models, the element mesh may be finer than the geological stratification. In this case, all elements within the same geological stratum can be merged, the overall additional compression of the stratum can be calculated, and then superimposed with the corresponding background settlement of the stratum to ensure the consistency of soil stratification. When merging elements, the additional compression of the entire stratum can be calculated using a volume-weighted average method, or the settlement between the top and bottom of the stratum can be calculated using the nodal displacement difference, and then the compression within the stratum can be calculated. By merging elements, finite element models with different element sizes can be adapted without modifying the finite element mesh, making implementation easier.

[0061] Soil stratification parameters include the top and bottom depths of each foundation soil layer. Soil stratification is usually based on geological survey results and generally corresponds to the weathering zoning of the rock mass, thus effectively matching the depth gradient variation of background settlement. Soil layers are numbered sequentially from top to bottom for easy subsequent cumulative calculations.

[0062] In alternative implementations, such as Figure 4 As shown, the process of distributing background settlement to each soil layer according to depth to obtain the layered background settlement of each soil layer includes: S401: Determine the top and bottom depths of each soil layer based on the soil layering parameters.

[0063] S402: Substitute the top and bottom depths of the layer into the background settlement depth gradient distribution model to obtain the background settlement values ​​at the top and bottom of the layer.

[0064] S403: Calculate the difference between the background settlement value at the top of the layer and the background settlement value at the bottom of the layer to obtain the layered background settlement amount of the corresponding soil layer.

[0065] Specifically, soil layers are numbered sequentially from top to bottom, and the top and bottom depths of each layer are read in turn to form a sequence of soil layer depth parameters. The top depth is the depth value of the upper interface of the soil layer, and the bottom depth is the depth value of the lower interface of the soil layer. The bottom depth of the same soil layer is equal to the top depth of the next soil layer, ensuring the continuity of soil layer division without overlap or omission. When reading soil layer parameters, the geological properties and mechanical parameters of the soil layers must be verified to ensure consistency with geological survey data and avoid calculation errors caused by parameter mismatches. For road sections with complex geological conditions such as lenses and interlayers, lenses can be treated as a separate soil layer to improve the accuracy of the calculation; alternatively, they can be merged into the main soil layer and calculated using equivalent parameters to simplify the calculation process.

[0066] After obtaining the top and bottom depths of each soil layer, the two depth values ​​are substituted into the background settlement depth gradient distribution model to calculate the background settlement value at the corresponding depth. During the calculation, the depth values ​​are kept consistent with the model's depth reference, both using the original ground surface as the zero point and downwards as positive, ensuring a unified calculation reference.

[0067] In alternative implementations, such as Figure 5 As shown, substituting the layer top depth and layer bottom depth into the background settlement depth gradient distribution model to obtain the layer top background settlement value and layer bottom background settlement value includes: S501: Determine whether the soil depth exceeds the maximum monitoring depth; S502: If the value is not exceeded, directly substitute it into the model to calculate the background settlement value at the corresponding depth; S503: If the value exceeds the limit, the settlement value of the deepest monitoring point shall be extrapolated according to the gradient law, and the extrapolation depth shall not exceed the preset ratio of the maximum monitoring depth.

[0068] The maximum depth of monitoring data is determined by the number of monitoring boreholes in the area, and there are usually certain depth limitations. However, the depth range for calculating roadbed settlement may exceed the maximum monitoring depth, so extrapolation is required for the excess portion. Extrapolation follows the exponential decay gradient law, starting with the settlement value and depth of the deepest monitoring point, and continuing to extrapolate downwards according to the existing attenuation coefficient to ensure the continuity of settlement distribution. Using the existing attenuation coefficient for extrapolation is based on the assumption that the degree of rock weathering changes continuously with depth. This assumption holds true within a certain depth range, and the extrapolation error is controllable.

[0069] Simultaneously, the extrapolation depth is limited, not exceeding a preset percentage of the maximum monitoring depth. This percentage can be set according to engineering accuracy requirements, typically not exceeding 30%, to avoid error accumulation caused by excessive extrapolation distance and ensure the reliability of the calculation results. The basis for setting the extrapolation percentage is that the reliability of monitoring data decreases with depth. When the extrapolation distance is too large, the error of the attenuation coefficient will be amplified, leading to increased deviation in the calculation results. According to engineering experience, when controlled within 30%, the error introduced by extrapolation is within the acceptable range for engineering. If the roadbed calculation depth exceeds the allowable extrapolation range, deeper monitoring data needs to be supplemented; blind extrapolation should be avoided to ensure the reliability of the calculation results. Through limited extrapolation, the depth range of roadbed calculation can be covered while controlling the error introduced by extrapolation, balancing applicability and accuracy.

[0070] For areas with complex geological conditions, such as those with multiple layers of different lithologies, a segmented attenuation method can be used for extrapolation. Based on geological survey data, the lithological variations of deep rock masses are determined, and the attenuation coefficient is adjusted accordingly to improve the accuracy of the extrapolation. The parameters for segmented attenuation can be selected with reference to regional geological data or determined by referring to data from other monitoring wells with similar geological conditions.

[0071] After obtaining the background settlement values ​​at the top and bottom of the layer, the difference between them is calculated. This difference represents the compressive deformation of the soil layer caused by the background settlement, also known as the layered background settlement. Subtracting the bottom settlement from the top settlement yields the compressibility of the soil layer itself. This calculation method conforms to the basic definition of settlement deformation, which states that the compressibility of a soil layer is equal to the absolute settlement at the top surface minus the absolute settlement at the bottom surface.

[0072] By using a layered calculation method, the background settlement contribution corresponding to each soil layer can be obtained, rather than adding all background settlement as a rigid displacement to the surface. This accurately reflects the deformation differences at different depths and is more consistent with the actual deformation patterns of soil and rock masses. The results obtained from layered calculations can be directly superimposed with the additional settlement of the same layer, ensuring a perfect spatial scale match and avoiding depth misalignment errors caused by overall superposition. The overall superposition method attributes all background settlement to the surface, essentially assuming that deep rock masses do not undergo self-compression, which is inconsistent with reality and overestimates the absolute settlement of deep layers, leading to biases in differential settlement calculations. The layered superposition method corrects this bias, ensuring that deformation at different depths corresponds to the corresponding soil layers, resulting in a more rigorous calculation logic and more realistic results.

[0073] In alternative implementations, such as Figure 6 As shown, the difference between the background settlement value at the top of the layer and the background settlement value at the bottom of the layer is used to obtain the layered background settlement of the corresponding soil layer, including: S601: Divide the roadbed cross section into multiple settlement zones.

[0074] S602: Match the corresponding background settlement depth gradient distribution model for each partition.

[0075] S603: Calculate the background settlement of each soil layer in each zone.

[0076] Mountain roadbeds are often situated in complex terrain conditions such as slopes, valleys, and partial fill / cut sections. Geological conditions vary at different locations along the cross-section, and using a uniform gradient model can introduce computational bias. By dividing the cross-section into settlement zones based on differences in topographic and geological conditions, and matching each zone with a gradient model tailored to its specific geological conditions, layered settlement calculations can be performed. This improves the accuracy of calculating differential settlement across the cross-section and better meets the settlement simulation needs of complex mountainous terrain.

[0077] The number of zones is determined based on the complexity of the cross-section. The more varied the geological conditions, the more zones can be added. Zone boundaries are set at transitional locations where geological conditions change to ensure relative uniformity of geological conditions within each zone. Zone width can be adjusted according to the severity of topographic changes. Zones with drastic topographic changes should have smaller widths, while those with gentle topography should have larger widths. The number of zones should be controlled while ensuring computational accuracy to avoid excessive computational burden.

[0078] For a semi-cut / semi-fill section, it can be divided into three zones: the cut zone, the transition zone, and the fill zone. Below the cut zone is the original rock mass, whose structure remains undisturbed and whose creep characteristics are natural; a gradient model corresponding to the original rock mass is used. Below the fill zone is the compacted fill material and the underlying rock mass. The compressibility characteristics of the fill material differ from the original rock mass, and the filling load has an additional impact on the underlying rock mass; a gradient model corresponding to the fill section is used. The transition zone is located between the two, where geological conditions gradually change; interpolated gradient parameters are used to ensure the continuity of settlement distribution. The width of the transition zone can be determined based on the slope of the semi-cut / semi-fill section; the steeper the slope, the narrower the transition zone, and the gentler the slope, the wider the transition zone.

[0079] For gully fill sections, they can be divided laterally into the core area and the slope area. The core area has a larger fill thickness, a thicker underlying weak layer, and higher base stress. Its background settlement pattern differs from that of the slope area. Therefore, corresponding parameters are used for calculations to improve the accuracy of cross-sectional settlement distribution calculations. The attenuation coefficient of the core area is relatively small, and the settlement influence depth is greater; the attenuation coefficient of the slope area is relatively large, and settlement is mainly concentrated in the surface layer.

[0080] The boundaries of the zones can be determined based on geological survey data, and should coincide with geological boundary lines as much as possible to ensure the uniformity of geological conditions within the zones. Settlement transitions between zones can be handled using linear interpolation to ensure the continuity of the cross-sectional settlement curves and avoid abrupt changes in elevation.

[0081] After obtaining the background settlement of each soil layer, the background settlement of each soil layer is superimposed with the additional settlement of the subgrade of the corresponding soil layer to obtain the total settlement distribution at full depth, thus completing the long-term settlement simulation of the subgrade in the mountainous area.

[0082] It should be noted that the additional settlement of the roadbed is the soil compression deformation caused by artificial loads such as roadbed filling load and vehicle traffic load. It is calculated independently by the existing roadbed settlement calculation model. The calculation range only includes the roadbed and the foundation at a certain depth below it. It does not need to include the surrounding large-scale mountains. Therefore, the calculation domain is small and the calculation efficiency is high.

[0083] Additional settlement is also calculated layer by layer, yielding the additional compression of each soil layer. This corresponds one-to-one with the layered background settlement, providing a consistent spatial scale for layered superposition. The calculation of additional settlement includes settlement during construction and long-term settlement during operation, corresponding to different calculation points to achieve full life-cycle settlement simulation. The calculation of additional settlement considers the consolidation process and creep characteristics of the soil, reflecting the changes in settlement rate at different times. It matches the time evolution model of background settlement, and the two can be superimposed at the same time point to obtain the total settlement at that time.

[0084] In alternative implementations, such as Figure 7 As shown, the background settlement of each soil layer and the additional subgrade settlement of the corresponding soil layer are superimposed layer by layer to obtain the total settlement distribution at full depth, including: S701: Extract the additional compression of each soil layer from the subgrade settlement calculation model.

[0085] S702: The additional compression of the same soil layer is added to the background settlement of the layer to obtain the total compression of the soil layer.

[0086] S703: The total compression of all soil layers is accumulated from top to bottom to obtain the total settlement of the roadbed surface and the settlement distribution at all depths.

[0087] Specifically, from the output of the existing roadbed settlement calculation model, the additional compression of each soil layer is extracted sequentially according to the soil layer number. When extracting, attention should be paid to the correspondence between the soil layer number and the depth to ensure that the soil layer division is completely consistent with the background settlement of the layer and to avoid superposition errors caused by soil layer misalignment.

[0088] Additional compression is the compressive deformation of soil under additional stress. The calculation takes into account the long-term deformation characteristics of the soil, such as consolidation and creep, and reflects the long-term settlement process under load. When extracting additional compression, it is necessary to correspond to a specific calculation time to ensure consistency with the calculation time of the background settlement, achieving superposition calculation of the same time section. For different calculation times, the corresponding additional compression can be extracted separately and then superimposed with the background settlement at the same moment to obtain the total settlement results for different periods.

[0089] After extracting the additional compression of each soil layer, the additional compression of the same soil layer is added to the background settlement of the layer to obtain the total compression of that soil layer. By using a layered superposition method, the deformation of each layer is superimposed separately, rather than the total background settlement is directly added to the surface. This can accurately reflect the total deformation at different depths and avoid the calculation deviation of deep deformation caused by overall superposition.

[0090] The spatial scale of the layered superposition is consistent with that of the original subgrade model. The superposition process does not disrupt the computational logic of the original model; it only adds values ​​at the result level and is non-intrusive to the original model. This superposition method can be applied to any type of subgrade settlement calculation model. As long as the model can output layered compression, this method can be used to superimpose and correct background settlement, demonstrating strong adaptability.

[0091] In alternative implementations, such as Figure 8 As shown, the step of adding the additional compression of the same soil layer to the background settlement of the layers to obtain the total compression of the soil layer includes: S801: Calculate the ratio of the additional settlement rate to the background settlement rate of the same soil layer.

[0092] S802: Determine the nonlinear superposition correction coefficient based on the rate ratio.

[0093] S803: Multiply the background settlement of the layer by the correction factor and add it to the additional compression to obtain the total compression of the soil layer.

[0094] Soil creep deformation is a nonlinear process. When two creep deformations in the same direction are superimposed, the total strain rate is not a simple algebraic sum of the two rates. Energy dissipation within the soil and structural damage will have a certain coupling effect, leading to a difference between the total deformation rate and the linear superposition result. Therefore, introducing a nonlinear superposition correction coefficient to adjust the superposition result can more accurately reflect the nonlinear characteristics of soil creep and improve the accuracy of settlement calculation.

[0095] The nonlinear superposition correction coefficient is related to the ratio of settlement rate, and the corresponding expression is: (2) in: (3) In this formula, This represents the nonlinear superposition correction coefficient, which is a dimensionless parameter. This is a nonlinear influence coefficient, a dimensionless parameter determined based on the creep characteristics of the regional soil, with a value ranging from greater than zero to less than one. This represents the ratio of settlement rates, and is a dimensionless parameter. This represents the rate of background settlement, expressed in length per unit time. This indicates the rate of additional settlement, expressed in units of length per unit time.

[0096] When the background settlement rate and the additional settlement rate are equal, the rate ratio is equal to one, the correction coefficient reaches its minimum value, and the nonlinear correction effect is strongest. As the difference between the two rates gradually increases, the rate ratio deviates from one, the correction coefficient gradually increases and approaches one, the nonlinear correction effect gradually weakens, and the superposition method degenerates into linear superposition. This correction law conforms to the nonlinear characteristics of soil creep; that is, when the two deformation rates are similar, the coupling effect is more obvious, and the nonlinear correction effect is stronger; when the difference between the two rates is large, the coupling effect is weaker, and linear superposition can meet the accuracy requirements.

[0097] The nonlinear influence coefficient can be determined through indoor triaxial creep tests. Creep tests are conducted on soil samples under different stress level combinations to obtain the total creep rate at different rate ratios, from which the nonlinear influence coefficient can be calculated. During the test, soil samples consistent with the engineering area are selected, and multiple different stress level combinations are set up. The creep rate under single stress and under dual stress is tested separately. By comparing the results, the degree of nonlinear coupling influence is obtained, and the value of the nonlinear influence coefficient is determined.

[0098] The nonlinear influence coefficient can also be obtained through inversion from field monitoring data. For road sections with clear geological conditions and sufficient monitoring data, the appropriate nonlinear influence coefficient for the region is derived by inverting the total settlement monitoring data. During the inversion, a linear superposition is first used to obtain the calculated value, which is then compared with the measured value. An optimization algorithm is used to adjust the nonlinear influence coefficient to minimize the deviation between the calculated and measured values. The resulting coefficient is the applicable value for the region.

[0099] By introducing dynamically changing correction coefficients, the impact of nonlinear coupling effects can be considered without altering the original calculation framework, further improving the accuracy of the calculations. This correction is an optional module, and its activation can be chosen based on accuracy requirements. In the scheme comparison stage with lower accuracy requirements, linear superposition can be used directly to improve calculation speed; in the construction drawing design stage with higher accuracy requirements, nonlinear correction can be enabled to improve calculation accuracy.

[0100] After obtaining the total compression of each soil layer, the total compression of all soil layers is accumulated sequentially from top to bottom to obtain the total settlement of the roadbed surface. The physical meaning of the accumulation is that the absolute settlement of the ground surface is equal to the sum of the compression deformation of all the soil layers below, which conforms to the basic principle of settlement calculation.

[0101] Meanwhile, by summing the results of each layer, the total absolute settlement at any depth can be obtained, thus forming a settlement distribution across the entire depth. This can be used to analyze deformation at different depths, calculate differential settlement between layers, and evaluate the deformation compatibility of the subgrade, providing comprehensive data support for subgrade deformation control. The settlement distribution across the entire depth can also be used to determine the thickness of the compressible layer of the foundation and analyze the contribution ratio of deep deformation, providing a basis for the design of foundation treatment schemes.

[0102] After calculating the total settlement distribution across the entire depth, the simulation process for the long-term settlement of the entire mountainous roadbed is complete. The output settlement results can be used for engineering applications such as roadbed design scheme comparison, deformation control measure optimization, and long-term settlement prediction. The output result format can be set according to needs, including settlement numerical tables, settlement depth curves, settlement cross-sectional distribution maps, and settlement time curves, to meet different analysis requirements.

[0103] It should be noted that the background subsidence is not constant, but evolves over time. The creep of the mountain rock mass is a long-term dynamic process, and the subsidence rate gradually decreases over time. Therefore, it is necessary to consider the time evolution characteristics of background subsidence to achieve dynamic subsidence simulation.

[0104] In alternative implementations, such as Figure 9 As shown, the nonlinear fitting of the preprocessed stratified settlement monitoring data to obtain the depth attenuation coefficient and the surface reference settlement includes: S901: Extract long-term subsidence sequences at each monitoring depth and fit them to obtain the time evolution parameters of surface subsidence.

[0105] S902: Calculate the surface baseline settlement at the current time based on the current calculation time and time evolution parameters.

[0106] S903: The depth attenuation coefficient is obtained by fitting the ratio of the settlement at each depth to the surface reference settlement.

[0107] Long-term settlement sequences at each monitoring depth were extracted, and settlement sequences from surface monitoring points were selected for time evolution parameter fitting. A power-law creep model was used for fitting, which can well reflect the long-term deceleration creep variation law of soil and rock.

[0108] The time evolution expression for surface subsidence is: (4) In this formula, express Background subsidence of the Earth's surface at any given time, expressed in units of length. This represents the surface creep coefficient, expressed in units of length. It is related to factors such as regional rock mass properties, geological structure, and stress conditions, and is obtained by fitting monitoring data. The creep time exponent is a dimensionless parameter, ranging from zero to one. It reflects the characteristic of creep rate decaying over time; the smaller the time exponent, the faster the rate decays. This indicates the calculation time, expressed in time units.

[0109] This formula conforms to the changing law of the long-term creep deceleration stage of rock and soil masses. As time goes by, the settlement rate gradually decreases, and the settlement gradually tends to stabilize, which can accurately reflect the long-term evolution process of background settlement of the mountain. The power-law model is mainly applicable to the deceleration creep stage, which is the main stage of mountain creep. Most long-term creep of mountain rock masses is in this stage, so this model has good applicability. If the project operation cycle is extremely long and enters the steady-state creep stage, the time evolution model can be adjusted to adopt a linear evolution form to ensure the calculation accuracy of different stages.

[0110] After obtaining the time evolution parameters, substituting them into the current calculation time allows for the calculation of the corresponding surface baseline settlement. Different calculation times correspond to different surface settlement amounts, enabling dynamic updates of background settlement over time, rather than linearly allocating it using a fixed final settlement value. This more accurately reflects changes in settlement rate at different times, restores the time evolution characteristics of deep creep lagging behind the surface, and improves the simulation accuracy of the entire settlement process.

[0111] Fitting time-evolution parameters requires a sufficiently long monitoring sequence. The longer the monitoring period, the more accurate the fitted parameters and the higher the reliability of long-term predictions. If the monitoring period is short, empirical values ​​can be selected as initial parameters based on regional geological data, and then gradually corrected as monitoring data accumulates. A nonlinear least squares method can be used for fitting, consistent with the method used for depth gradient parameters, to ensure consistency in parameter fitting.

[0112] After calculating the current baseline settlement, the settlement at each depth monitoring point is divided by the baseline settlement to obtain the settlement ratio for each depth. Then, a depth attenuation coefficient is fitted based on these settlement ratios. Since the settlement ratio eliminates the influence of time and only reflects the depth distribution pattern, the depth attenuation coefficient does not change with time and is only related to the depth distribution characteristics of the regional rock mass. This parameter decomposition method separates the temporal evolution characteristics from the depth distribution characteristics, resulting in clear physical meaning of the parameters, a simple fitting process, and the ability to achieve comprehensive simulation across the spatiotemporal dimensions.

[0113] By combining the time evolution model with the depth gradient model, a spatiotemporally unified expression for background settlement distribution can be obtained. This expression can output the background settlement at any time and any depth, providing a computational basis for full-cycle, full-depth settlement simulation. All parameters of this expression are obtained by fitting monitoring data, have clear physical meanings, and the calculation process is concise, making it suitable for engineering applications.

[0114] In this application embodiment, a mountain roadbed settlement simulation system based on long-term load is also provided, such as... Figure 10 As shown, the system includes: The data processing module is used to acquire regional stratified settlement monitoring data and perform standardized preprocessing to construct a background settlement depth gradient distribution model; the background settlement depth gradient distribution model is a distribution model that characterizes the attenuation of background settlement as the soil layer depth increases. The layered allocation module is used to extract the soil layering parameters of the roadbed settlement calculation model to be simulated, and to allocate the background settlement amount to each soil layer according to the background settlement depth gradient distribution model to obtain the layered background settlement amount of each soil layer. The settlement overlay module is used to overlay the background settlement of each soil layer with the additional settlement of the roadbed in the corresponding soil layer to obtain the total settlement distribution at full depth and complete the long-term settlement simulation of the roadbed in mountainous areas.

[0115] The data processing module is used to acquire regional stratified settlement monitoring data and perform standardized preprocessing to construct a background settlement depth gradient distribution model. The module has data access capabilities, allowing access to monitoring data from various sources, including locally stored monitoring files and real-time data transmitted from online monitoring platforms. It also has data preprocessing capabilities, performing standardization processes such as outlier removal, missing data completion, and benchmark unification. Finally, it has model fitting capabilities, calculating gradient model parameters based on the processed data, verifying the goodness of fit, and outputting a qualified background settlement depth gradient distribution model.

[0116] The data processing module supports batch data import and can process data from multiple monitoring wells simultaneously. It performs data quality evaluation and filtering, and outputs data quality reports to help users understand the data situation. The module includes multiple preset fitting algorithms and validation rules, allowing users to select the appropriate processing method based on data characteristics. Users can also manually adjust parameters to suit different application needs. The module has a built-in parameter library that can store fitting parameters for different regions, facilitating direct access in subsequent similar projects and reducing redundant calculations.

[0117] The layered allocation module extracts the soil layer parameters from the subgrade settlement calculation model to be simulated. Based on the background settlement depth gradient distribution model, it allocates the background settlement amount to each soil layer according to depth, obtaining the layered background settlement amount for each soil layer. The layered allocation module can read the soil layer parameters of the existing subgrade calculation model and identify the top and bottom depths of the soil layers; it has depth judgment and extrapolation functions, which can identify soil layers exceeding the monitoring depth and complete gradient extrapolation; it has a zone calculation function, which can calculate the layered background settlement amount of different zones according to the cross-sectional zoning settings and output the background settlement calculation results for each soil layer.

[0118] The layered allocation module supports custom soil layer division, allowing for adjustments to the layering scheme to flexibly adapt to different calculation models. For fine-grained finite element models, the module can complete the merging mapping from elements to soil layers, eliminating the need for manual soil layer parameter processing and improving processing efficiency. The module supports batch import of soil layer parameters, enabling the processing of soil layer data from multiple cross-sections at once and generating layered background settlement results in batches, thus improving the efficiency of multi-section calculations.

[0119] The settlement overlay module is used to overlay the background settlement of each soil layer with the corresponding additional settlement of the subgrade, obtaining the total settlement distribution across the entire depth, and completing the long-term settlement simulation of the subgrade in mountainous areas. The settlement overlay module can read the additional settlement data output from the subgrade model and complete the matching overlay with the same soil layer; it has a nonlinear correction function, which can calculate the correction coefficient based on the settlement rate to complete the nonlinear overlay correction; and it has a result summarization function, which can accumulate the total surface settlement and the settlement distribution across the entire depth, outputting the final settlement simulation result.

[0120] The settlement overlay module supports batch calculations under multiple load conditions, enabling simultaneous calculation of settlement results for multiple load schemes and multiple time points. It outputs comparative analysis tables for easy scheme selection. The module can also generate settlement curves, differential settlement distribution maps, and other charts to visually display the calculation results and improve readability. The module supports result export, allowing calculation results to be exported to common file formats for easier report preparation and application.

[0121] During system operation, after the data processing module completes model construction, it transmits the background settlement depth gradient distribution model to the layer allocation module. The layer allocation module, combined with the read soil layer parameters, calculates the background settlement of each soil layer and transmits the results to the settlement overlay module. The settlement overlay module, combined with the read roadbed additional settlement data, completes the overlay calculation and outputs the final result. These three modules are sequentially connected, with a clear data flow, enabling end-to-end processing from data input to result output, reducing manual operations and improving computational efficiency.

[0122] This system can be deployed on different hardware platforms according to usage requirements. It can be deployed on a local computer for standalone computing or on a cloud server for network access, adapting to different application scenarios. The system's input and output interfaces can be customized according to engineering needs, connecting to different roadbed calculation software and monitoring data platforms, demonstrating good adaptability and scalability. The system can set different user permissions, distinguishing between administrators and ordinary users, ensuring data security and parameter stability.

[0123] For example, a high-fill section of a mountain highway in a valley needs to undergo long-term settlement simulation. The roadbed filling height of this section is relatively large, and the weathering zoning of the rock mass within the foundation area is obvious. From top to bottom, it is divided into three layers: strongly weathered layer, moderately weathered layer, and slightly weathered layer. There are existing geological monitoring wells in the area, which have long-term settlement monitoring data at multiple depths. The geological conditions at the location of the monitoring wells are consistent with those of the road section to be simulated.

[0124] The implementation process begins with collecting stratified settlement data from monitoring wells. This data includes continuous settlement records from the surface and multiple deep monitoring points, with a time span sufficient for data fitting. The collected data is then cleaned, using a three-standard-deviation method to remove abnormal data caused by disturbances during construction. Missing data is supplemented using linear interpolation to ensure the continuity of the data sequence. Subsequently, standardization is performed, unifying the depth benchmark to the original roadbed surface, the time benchmark to the start of construction, and the settlement direction to downwards as positive, thus completing the entire preprocessing procedure.

[0125] Based on the preprocessed monitoring data, a long-term subsidence sequence of surface monitoring points is first extracted, and the temporal evolution parameters of surface subsidence are fitted to obtain the corresponding creep coefficient and time exponent. Subsidence values ​​at various depths at a reference time are selected, and depth attenuation coefficients are fitted to generate a continuous distribution function of background subsidence along depth. The coefficient of determination of this distribution function is calculated, and after verifying that the goodness of fit meets the preset requirements, a background subsidence depth gradient distribution model for the region is obtained.

[0126] Next, the soil layer parameters of the roadbed settlement calculation model to be simulated are extracted to obtain the top and bottom depths of the three rock layers. The depth of each soil layer is then checked to see if it falls within the monitoring depth range. The depths of the strongly weathered and moderately weathered layers are within the monitoring range, and are directly substituted into the gradient model to calculate the background settlement values ​​at the top and bottom of the layers. The lower depth of the bottom slightly weathered layer exceeds the maximum monitoring depth, and is extrapolated to a limited extent according to the gradient law. The extrapolation depth is controlled within the allowable range to ensure that the calculation error is controllable.

[0127] The difference between the top and bottom settlements of each soil layer is calculated to obtain the layered background settlement of each soil layer. Since the road section has a semi-cut and semi-fill section, the cross-section is divided into two zones: a cut zone and a fill zone. Gradient models corresponding to the geological conditions are matched for each zone, and the layered background settlement within each zone is calculated separately.

[0128] After obtaining the layered background settlement, the additional compression of each soil layer at the corresponding calculation time is extracted from the existing roadbed settlement calculation model. Based on the additional settlement rate and background settlement rate at that time, the ratio of the calculated rates and the nonlinear superposition correction coefficient, the layered background settlement is multiplied by the correction coefficient and then added to the additional compression of the corresponding soil layer to obtain the total compression of each soil layer.

[0129] By summing the total compression of all soil layers in a top-down order, the total settlement of the roadbed surface is obtained, along with the settlement distribution curve at full depth, thus completing the long-term settlement simulation of this road section. The output results include the total surface settlement value, the compression of each soil layer, the settlement distribution at full depth, and the differential settlement distribution across the cross section, which can be directly used for the evaluation and optimization of roadbed schemes.

[0130] This method of settlement simulation eliminates the need to construct a large-scale numerical model that includes the surrounding mountains, maintaining the computational domain at the size of the original roadbed model, resulting in high computational efficiency. Furthermore, it considers the attenuation law of background settlement along depth, correcting the deep deformation deviation caused by the assumption of uniform settlement, thus improving the accuracy of settlement calculations. The method is simple to implement, requires minimal modification to the original calculation model, and can be quickly applied to the comparison and optimization of engineering schemes, adapting to the settlement analysis needs under complex geological conditions in mountainous areas.

[0131] It should be noted that the current technical approaches for simulating long-term settlement of roadbeds in mountainous areas mainly fall into two categories. One category involves incorporating the roadbed and surrounding mountains into the same numerical model for coupled calculation. This approach can simultaneously consider the interaction between the additional deformation of the roadbed and the deformation of the mountain itself, providing a more comprehensive consideration of the deformation mechanism. However, because the computational domain needs to cover a large area of ​​mountains, the number of elements is large, the model size is large, and the calculation cycle for a single working condition is long, it is difficult to meet the timeliness requirements for rapid comparison and dynamic design of engineering solutions. Furthermore, the modeling is difficult, and the requirements for computing hardware and personnel capabilities are high, making it difficult to promote and apply on a large scale in engineering.

[0132] Another approach is to use background settlement overlay, directly superimposing the mountain settlement as a whole onto the roadbed settlement results. This method is simple to calculate and highly efficient, as it does not require building a mountain model. However, it assumes that the background settlement is uniform across the entire depth range, treating the mountain as an undeformable rigid body. This contradicts the actual law of creep decay along depth in soil and rock, especially in mountainous areas with distinct weathering zones, where the calculation of deep settlement has a large deviation, making it difficult to meet the requirements of high-precision settlement analysis. Existing overlay methods mostly focus on the total value of background settlement, paying less attention to the distribution of settlement along depth, and rarely overlay the background settlement in layers with the layered settlement of the roadbed. Deformation differences in the depth dimension are not taken into account in the calculation.

[0133] The approach adopted in this application first decomposes the total settlement into two parts: additional subgrade settlement and regional background settlement, which are solved separately. This retains the advantages of the superposition method, such as a small computational domain and high computational efficiency, while avoiding the computational overhead caused by large-scale mountain models. Based on this, the depth gradient distribution law of background settlement is introduced to reconstruct the spatial distribution of background settlement, restoring the actual characteristics of settlement attenuation with depth. This replaces the assumption of uniform rigid body translation across the entire depth, correcting the systematic errors of existing superposition methods from a spatial distribution perspective. Simultaneously, a layered allocation method is adopted, corresponding the gradient-distributed background settlement to the soil layers of the subgrade model one-to-one, achieving layered superposition at the same scale. This ensures spatial consistency in the superposition calculation and avoids depth misalignment errors caused by overall superposition. These three aspects are interconnected, improving the accuracy of settlement calculation without expanding the computational domain, increasing computational overhead, or modifying the original subgrade model, achieving a better balance between computational efficiency and accuracy.

[0134] This technological approach does not involve simple parameter adjustments to existing superposition methods. Instead, it starts with the spatial distribution patterns of mountain creep, modifies the assumptions about the distribution of background settlement, and then achieves accurate superposition with the additional settlement of the roadbed through layered matching. Existing technologies often aim to improve the accuracy of settlement simulation by expanding the computational domain, increasing model complexity, and introducing more refined constitutive models—essentially trading increased computational cost for improved accuracy. However, this application's approach improves accuracy within the framework of existing superposition methods by optimizing the distribution and superposition method of background settlement. This does not require increasing the computational scale or altering the core structure of the original model, making it a lightweight accuracy improvement solution.

[0135] Furthermore, this application can further introduce a time evolution model and a nonlinear correction mechanism to further optimize the accuracy of the calculation from the perspectives of time dimension and nonlinear coupling. All optimizations are performed within the original decoupled superposition framework, without adding additional computational burden or compromising the lightweight characteristics of the original method. The solution is highly scalable, allowing for different configurations to be selected based on engineering accuracy requirements. For lower accuracy requirements, a basic gradient layer superposition scheme can be used; for higher accuracy requirements, time dynamics and nonlinear correction modules can be added, flexibly adapting to different application scenarios.

[0136] The introduction of a time-evolution model transforms background settlement from a static final value into a dynamic process that changes over time. This model accurately reflects the decay characteristics of creep rates, matching the time evolution of additional subgrade settlement and further improving the accuracy of full-cycle settlement simulation. The introduction of a nonlinear correction mechanism considers the nonlinear coupling effect of soil creep, making the superposition calculation more consistent with the actual mechanical properties of the soil and avoiding biases caused by the linear superposition assumption. All extended functions are modularly designed and can be activated as needed without affecting the operation of the foundation scheme. Users can flexibly select functions according to their actual requirements.

Claims

1. A method for simulating settlement of roadbed in mountainous areas based on long-term load, characterized in that, The method includes: Regional stratified settlement monitoring data were acquired and standardized preprocessed to construct a background settlement depth gradient distribution model; the background settlement depth gradient distribution model is a distribution model that characterizes the attenuation of background settlement as soil depth increases. Extract the soil layer parameters of the roadbed settlement calculation model to be simulated, and according to the background settlement depth gradient distribution model, distribute the background settlement amount to each soil layer according to the depth to obtain the layered background settlement amount of each soil layer. The background settlement of each soil layer and the additional settlement of the roadbed in the corresponding soil layer are superimposed to obtain the total settlement distribution at the full depth, thus completing the long-term settlement simulation of the roadbed in the mountainous area. The construction of the background subsidence depth gradient distribution model includes: Nonlinear fitting was performed on the preprocessed stratified settlement monitoring data to obtain the depth attenuation coefficient and the surface benchmark settlement. A continuous distribution function of background settlement along depth is generated based on the depth attenuation coefficient and the surface reference settlement. The goodness-of-fit of the continuous distribution function is checked, and the background settlement depth gradient distribution model is obtained after the check passes. The process of distributing background settlement to each soil layer according to depth to obtain the layered background settlement of each soil layer includes: Determine the top and bottom depths of each soil layer based on the soil layer stratification parameters; Substituting the top and bottom depths of the layer into the background settlement depth gradient distribution model, respectively, yields the background settlement values ​​at the top and bottom of the layer. Calculate the difference between the background settlement value at the top of the layer and the background settlement value at the bottom of the layer to obtain the layered background settlement of the corresponding soil layer; The process of performing nonlinear fitting on the preprocessed stratified settlement monitoring data to obtain the depth attenuation coefficient and the surface baseline settlement includes: Long-term subsidence sequences at each monitoring depth were extracted, and the time evolution parameters of surface subsidence were obtained by fitting. Calculate the surface baseline settlement at the current time based on the current calculation time and time evolution parameters; The depth attenuation coefficient is obtained by fitting the ratio of the settlement at each depth to the surface reference settlement.

2. The method for simulating settlement of mountain roadbeds based on long-term load as described in claim 1, characterized in that, The background settlement of each soil layer is superimposed with the additional subgrade settlement of the corresponding soil layer to obtain the total settlement distribution across the entire depth, including: Extract the additional compression of each soil layer from the subgrade settlement calculation model; The total compression of the soil layer is obtained by adding the additional compression of the same soil layer to the background settlement of the layer. The total compression of all soil layers is accumulated from top to bottom to obtain the total settlement of the roadbed surface and the total settlement distribution across the entire depth.

3. The method for simulating settlement of mountain roadbeds based on long-term load as described in claim 1, characterized in that, The goodness-of-fit test of the continuous distribution function, after passing the test, yields the background subsidence depth gradient distribution model, including: Calculate the coefficient of determination of the continuous distribution function with respect to the stratified settlement monitoring data; Determine whether the determination coefficient reaches a preset threshold; if it does, the verification passes. If the target is not met, additional monitoring samples are added and the model is refitted until the verification is passed, at which point the background settlement depth gradient distribution model is output.

4. The method for simulating settlement of mountain roadbeds based on long-term load as described in claim 1, characterized in that, The step of substituting the top and bottom depths of the layer into the background settlement depth gradient distribution model to obtain the background settlement values ​​at the top and bottom of the layer includes: Determine whether the soil depth exceeds the maximum monitoring depth; If the value does not exceed the limit, directly substitute it into the background settlement depth gradient distribution model to calculate the background settlement value at the corresponding depth. If the value exceeds the limit, the settlement value of the deepest monitoring point will be extrapolated according to the gradient law, and the extrapolation depth will not exceed the preset ratio of the maximum monitoring depth.

5. The method for simulating settlement of mountain roadbeds based on long-term load as described in claim 1, characterized in that, The difference between the background settlement value at the top of the calculated layer and the background settlement value at the bottom of the calculated layer is used to obtain the layered background settlement of the corresponding soil layer, including: Multiple settlement zones are divided along the cross section of the roadbed; Match the corresponding background settlement depth gradient distribution model to each partition; Calculate the background settlement of each soil layer in each zone.

6. The method for simulating settlement of mountain roadbeds based on long-term load according to claim 2, characterized in that, The method of adding the additional compression of the same soil layer to the background settlement of the layers to obtain the total compression of the soil layer includes: Calculate the ratio of the additional settlement rate to the background settlement rate for the same soil layer; The nonlinear superposition correction coefficient is determined based on the ratio of the additional settlement rate to the background settlement rate. The total compression of the soil layer is obtained by multiplying the layered background settlement by the nonlinear superposition correction coefficient and then adding it to the additional compression.

7. A settlement simulation system for mountain roadbeds based on long-term load, characterized in that, The system includes: The data processing module is used to acquire regional stratified settlement monitoring data and perform standardized preprocessing to construct a background settlement depth gradient distribution model; the background settlement depth gradient distribution model is a distribution model that characterizes the attenuation of background settlement as the soil layer depth increases. The construction of the background subsidence depth gradient distribution model includes: Nonlinear fitting was performed on the preprocessed stratified settlement monitoring data to obtain the depth attenuation coefficient and the surface benchmark settlement. A continuous distribution function of background settlement along depth is generated based on the depth attenuation coefficient and the surface reference settlement. The goodness-of-fit of the continuous distribution function is checked, and the background settlement depth gradient distribution model is obtained after the check passes. The process of performing nonlinear fitting on the preprocessed stratified settlement monitoring data to obtain the depth attenuation coefficient and the surface baseline settlement includes: Long-term subsidence sequences at each monitoring depth were extracted, and the time evolution parameters of surface subsidence were obtained by fitting. Calculate the surface baseline settlement at the current time based on the current calculation time and time evolution parameters; Based on the ratio of settlement at each depth to the surface baseline settlement, the depth attenuation coefficient is obtained by fitting. The layered allocation module is used to extract the soil layering parameters of the roadbed settlement calculation model to be simulated, and to allocate the background settlement amount to each soil layer according to the background settlement depth gradient distribution model to obtain the layered background settlement amount of each soil layer. The process of distributing background settlement to each soil layer according to depth to obtain the layered background settlement of each soil layer includes: Determine the top and bottom depths of each soil layer based on the soil layer stratification parameters; Substituting the top and bottom depths of the layer into the background settlement depth gradient distribution model, respectively, yields the background settlement values ​​at the top and bottom of the layer. Calculate the difference between the background settlement value at the top of the layer and the background settlement value at the bottom of the layer to obtain the layered background settlement of the corresponding soil layer; The settlement overlay module is used to overlay the background settlement of each soil layer with the additional settlement of the roadbed in the corresponding soil layer to obtain the total settlement distribution at full depth and complete the long-term settlement simulation of the roadbed in mountainous areas.

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