A method for predicting bearing behavior of a permafrost foundation in cooperation with multiple pile lengths

Abstract

The present application belongs to the technical field of frozen ground foundation engineering, and in particular to a frozen ground foundation bearing behavior prediction method with multi-pile length cooperation. A three-dimensional geological-temperature database of the frozen ground foundation is constructed, stratum distribution, water content, fine particle content and geothermal gradient data are integrated, frozen layers and unfrozen layers are divided, and high, medium and low frost heaving sensitive zones are identified. Based on the sensitive zone distribution, a three-level differentiated pile type of "short pile-medium pile-long pile" is designed, a coupling relationship between pile length and frost heaving sensitivity is established, a group pile soil resistance correction model considering pile length difference is constructed by introducing a multi-pile length cooperation effect coefficient, and a frozen layer rigid shell effect correction model and an unfrozen layer bearing decay model are integrated. Through the differentiated pile type design and the cooperation effect model, the problem that the traditional method cannot handle the spatial variability of frozen soil, resulting in inaccurate bearing behavior prediction, is solved, and the present application has the advantages of accurate prediction, optimized design, improved safety and economy.

Description

Technical Field

[0001] This invention relates to the field of frozen soil foundation engineering technology, specifically to a method for predicting the bearing behavior of frozen soil foundations with multi-pile length coordination. Background Technology

[0002] In engineering construction in permafrost and seasonally frozen soil regions, pile foundations are widely used as a key supporting structure. Permafrost exhibits significant temperature sensitivity; its strength and deformation characteristics are dynamically affected by parameters such as geothermal gradient, water content, and fine particle content, and undergo repeated freeze-thaw cycles with the seasons, resulting in highly time-varying and spatially heterogeneous physical and mechanical properties. Traditional pile foundation design generally adopts a uniform pile length scheme, failing to identify the non-uniform distribution characteristics of permafrost foundations in the horizontal and vertical directions, such as the differences between high, medium, and low frost-susceptible zones, the spatial distribution variations of ice-containing layers, and regional fluctuations in geothermal gradients. This design flaw easily leads to insufficient bearing capacity of pile foundations in highly frost-susceptible areas, causing excessive pile uplift or differential settlement, while in low-sensitivity areas, over-design occurs, resulting in a waste of materials and economic resources.

[0003] Existing technologies for predicting the bearing capacity of frozen soil foundations largely focus on simplified models of single pile lengths or idealized homogeneous frozen soil conditions, lacking in-depth analysis of the coupling mechanism between pile length differentiation and the spatial variability of frozen soil. The "rigid shell effect" formed after the frozen soil layer freezes significantly increases strength but also increases brittleness, while the unfrozen layer exhibits creep and strength decay over time. The coexistence of these two factors complicates the load transfer path in pile group systems. Especially when pile lengths differ, the mechanical responses of adjacent piles mutually constrain each other, making it difficult for traditional prediction methods to accurately quantify the impact of pile length variations on soil resistance distribution, stress field coordination, and long-term deformation behavior. Current technologies have not yet established a comprehensive prediction framework that integrates dynamic geological-temperature data throughout the freeze-thaw cycle, pile length synergy effects, and the interaction between frozen and unfrozen layers, making it difficult to achieve a reasonable balance between safety and economy in pile foundation design in frozen soil regions.

[0004] Therefore, we propose a multi-pile length collaborative method for predicting the bearing behavior of frozen soil foundations to solve the above problems. Summary of the Invention

[0005] (a) Technical problems to be solved To address the shortcomings of existing technologies, this invention provides a method for predicting the bearing behavior of permafrost foundations using a multi-pile-length collaborative approach. This method has the advantages of accurately predicting the bearing behavior of permafrost foundations, optimizing pile foundation design, and improving engineering safety and economy, thus solving the problems mentioned in the background section.

[0006] (II) Technical Solution To achieve the above objectives, the present invention specifically adopts the following technical solution: A method for predicting the bearing behavior of multi-pile long-coordinated permafrost foundations includes the following steps: S1. Construct a three-dimensional geological-temperature database for permafrost foundations, integrate data on stratigraphic distribution, water content, fine particle content, and geothermal gradient, divide the frozen layer into the unfrozen layer, and identify high, medium, and low frost heave sensitive areas; S2. Based on the distribution of sensitive areas, design three levels of differentiated pile types: "short pile - medium pile - long pile" to establish the coupling relationship between pile length and frost heave sensitivity; S3. Introduce a synergistic effect coefficient for multiple pile lengths to construct a group pile soil resistance correction model that considers the differences in pile lengths. The synergistic effect coefficient reflects the mechanical response correlation between different pile lengths. S4. Integrate the frozen layer rigid shell effect correction model and the unfrozen layer bearing capacity attenuation model to establish a total bearing capacity behavior prediction model with multi-pile length coordination; S5. Through on-site static load tests and numerical simulation verification, output the predicted results of pile top displacement, pile bending moment and ultimate bearing capacity of frozen soil foundation.

[0007] Furthermore, in step S1, when constructing the three-dimensional geothermal database of the permafrost foundation, a triple data acquisition system of "ground exploration + borehole coring + distributed optical fiber monitoring" is adopted: ground exploration uses ground-penetrating radar to detect the distribution range of the frozen layer, and borehole coring intervals do not exceed 5m to obtain the physical and mechanical parameters of soil layers at various depths; distributed optical fibers are deployed along the entire borehole, with a monitoring accuracy of ±0.1℃, and continuously collect geothermal data for more than 12 months to ensure that the database covers the dynamic changes in geothermal temperature throughout the entire freeze-thaw cycle, thus solving the problem of data partiality caused by a single acquisition method.

[0008] Furthermore, the specific adaptation standards for the three differentiated pile types of "short pile - medium pile - long pile" in step S2 are as follows: Short piles are suitable for low frost heave sensitive areas, with the pile length only penetrating the surface seasonal frozen layer and the pile tip located on the upper part of the stable unfrozen layer; Medium piles are suitable for medium frost heave sensitive areas, with the pile length penetrating the seasonal frozen layer and part of the weakly weathered section of the perennial frozen layer, and the pile tip embedded in the strongly weathered section of the perennial frozen layer for no less than 1.5m; Long piles are suitable for high frost heave sensitive areas and areas with ice-containing layers, with the pile length needing to penetrate the entire frozen layer, and the pile tip embedded in the underlying stable bedrock or dense unfrozen soil layer for no less than 3m. In addition, long piles adopt an enlarged base pile design, with the enlarged base diameter being 1.8-2.5 times the pile body diameter, thereby improving the synergistic bearing capacity of tensile and compressive strength through pile structure optimization.

[0009] Furthermore, in step S2, the target pile length is determined through a multi-level pile length design function, the function expression of which is: in: Let m be the design pile length for the m-th engineering area; As a safety factor, the value ranges from 1.1 to 1.3, and is used to amplify the control depth of the sensitive layer; Let be the empirical weighting coefficient of the k-th soil layer, satisfying The soil layer weight in highly sensitive areas shall not be less than 0.4; The freezing sensitivity factor of the k-th soil layer is calculated by coupling the geothermal gradient, water content, and fine particle content. Let be the thickness of the k-th soil layer; This function represents the set of frost heave risk layers contained in the m-th region; it enables the quantitative mapping of geological parameters to pile length dimensions, ensuring accurate matching between pile type and frost heave risk.

[0010] Furthermore, in step S3, the synergistic effect coefficient of multiple pile lengths is optimized through an adjacent pile length difference control model, the model expression of which is: in: The difference in pile length between adjacent piles i and j; These are the design pile lengths of two adjacent piles; This is a transition control factor, and its value should not exceed 0.25; This represents the average pile length in the current pile group area; This model reduces stress concentration and enhances the collaborative bearing capacity of pile groups by limiting the amplitude of sudden changes in pile length.

[0011] Furthermore, in step S4, the frozen layer rigid shell effect correction model introduces a drag reduction coefficient that varies with depth. ,satisfy =0.3-0.5 ( (The depth of the frozen-unfrozen interface) increases monotonically to 1.0 with increasing depth, and is used to correct the degree of exertion of the resistance of the unfrozen soil.

[0012] Furthermore, in step S4, the unfrozen layer bearing capacity attenuation model considers the influence of temperature gradient and describes the recovery law of bearing capacity as the freezing depth increases by establishing a negative exponential relationship between the soil's elastic modulus and depth.

[0013] Furthermore, the negative exponential relationship between the elastic modulus of the unfrozen soil and its depth is as follows: in: Let z be the elastic modulus of the unfrozen soil at depth z; Frozen / Unfrozen Interface The elastic modulus of the unfrozen soil at point ( ) was measured by indoor triaxial tests; k is the attenuation coefficient, ranging from 0.002 to 0.005 m. -1 Adjust according to the formation porosity (the higher the porosity, the higher the k value); To calculate depth ( ); This relationship accurately describes the nonlinear recovery law of the bearing capacity of the unfrozen layer with depth, improving the prediction accuracy of the model.

[0014] Furthermore, the method also includes a real-time correction step: adjusting the synergistic effect coefficient in reverse using data monitored by the pile stress sensor to achieve dynamic prediction and updating of the bearing behavior; The real-time correction step employs an adaptive Kalman filter algorithm, specifically including: ① Using the monitoring data of the pile stress sensor as the observed value and the synergistic effect coefficient as the state variable, establish the state equation and the observation equation; ② Calculate the filter gain matrix and dynamically adjust the weights of the state variables based on the observation error; ③ Output the corrected synergy coefficient and update the overall prediction model; ④ Set a convergence threshold (error less than 3%). Stop iterating when the correction result meets the threshold requirement; otherwise, repeat steps ①-③. This algorithm enables dynamic coupling between monitoring data and prediction models, improving the method's adaptability to changes in geological conditions.

[0015] Furthermore, the prediction results output in step S5 are presented in a multi-dimensional format of "numerical table + 3D cloud map + trend curve": the numerical table accurately presents the maximum value of pile top displacement, the extreme value of pile body bending moment and the specific value of ultimate bearing capacity at different pile locations; the 3D cloud map intuitively reflects the spatial distribution characteristics of the stress field and displacement field of the pile group, and marks the stress concentration area and the displacement exceeding the limit; the trend curve shows the variation law of bearing performance under different freeze-thaw cycles and different load levels, and also includes the error range of the prediction results (confidence level 95%), providing engineering designers with a full-dimensional reference from quantitative data to qualitative analysis.

[0016] (III) Beneficial Effects Compared with existing technologies, this invention provides a method for predicting the bearing behavior of permafrost foundations based on multi-pile length coordination, which has the following beneficial effects: This application constructs a three-dimensional geo-temperature database for frozen soil foundations, integrating data on strata distribution, water content, fine particle content, and geothermal gradient to delineate frozen and unfrozen layers and identify high, medium, and low frost heave sensitive zones. Based on the distribution of sensitive zones, it designs three levels of differentiated pile types—short piles, medium piles, and long piles—and establishes the coupling relationship between pile length and frost heave sensitivity. It introduces a multi-pile length synergy effect coefficient to construct a pile group soil resistance correction model considering pile length differences; the synergy effect coefficient reflects the mechanical response correlation between different pile lengths. It integrates the frozen layer rigid shell effect correction model and the unfrozen layer bearing capacity attenuation model to establish a comprehensive model for predicting the bearing behavior of multiple pile lengths. Through field static load tests and numerical simulations, it outputs predicted results for pile top displacement, pile bending moment, and ultimate bearing capacity of frozen soil foundations.

[0017] By using differentiated pile design and synergistic effect model, the problem of inaccurate prediction of bearing behavior caused by the spatial variability of permafrost, which traditional methods have failed to address, is solved. It has the advantages of accurate prediction, optimized design, and improved safety and economy. Attached Figure Description

[0018] Figure 1 This is a schematic diagram of the process of the present invention. Detailed Implementation

[0019] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0020] Example Traditional pile foundation designs in permafrost regions often employ uniform pile lengths, neglecting the horizontal and vertical heterogeneity of permafrost foundations, such as differences in frost heave sensitivity, ice content variations, and geothermal gradients. This leads to inaccurate pile bearing capacity predictions, excessive differential settlement, or overly conservative designs. Existing prediction methods largely focus on single pile lengths or homogeneous permafrost conditions, failing to fully consider the coupling relationship between pile length differentiation and the spatial variability of permafrost. Furthermore, the coexistence of the rigid crust effect of the permafrost layer and the creep characteristics of the unfrozen layer makes the load sharing and deformation coordination behavior of pile groups complex, making it difficult to accurately predict long-term bearing behavior.

[0021] In this regard, such as Figure 1 As shown, an embodiment of the present invention proposes a method for predicting the bearing behavior of permafrost foundations with multi-pile length coordination, comprising the following steps: S1. Construct a three-dimensional geological-temperature database for permafrost foundations, integrate data on stratigraphic distribution, water content, fine particle content, and geothermal gradient, divide the frozen layer into the unfrozen layer, and identify high, medium, and low frost heave sensitive areas; S2. Based on the distribution of sensitive areas, design three levels of differentiated pile types: "short pile - medium pile - long pile" to establish the coupling relationship between pile length and frost heave sensitivity; S3. Introduce a synergistic effect coefficient for multiple pile lengths to construct a group pile soil resistance correction model that considers the differences in pile lengths. The synergistic effect coefficient reflects the mechanical response correlation between different pile lengths. S4. Integrate the frozen layer rigid shell effect correction model and the unfrozen layer bearing capacity attenuation model to establish a total bearing capacity behavior prediction model with multi-pile length coordination; S5. Through on-site static load tests and numerical simulation verification, output the predicted results of pile top displacement, pile bending moment and ultimate bearing capacity of frozen soil foundation.

[0022] For ease of understanding, the following explains some key terms in this embodiment: A three-dimensional geo-temperature database for permafrost foundations refers to a three-dimensional information system that reflects the spatial geological structure and dynamic changes in the temperature field of permafrost foundations by collecting and integrating data such as stratigraphic distribution, water content, fine particle content, and geothermal gradient in permafrost regions. This database provides fundamental data support for subsequent identification of frost-sensitive areas and pile type design.

[0023] The terms "frozen layer" and "unfrozen layer" refer to the classification of permafrost foundations based on ground temperature data. Frozen soil layers have temperatures below freezing and contain ice, while unfrozen soil layers have temperatures above freezing or below freezing but do not contain ice. This classification forms the basis for understanding the mechanical behavior and bearing capacity of permafrost.

[0024] Frost heave sensitive zones refer to areas classified as high, medium, or low in terms of their tendency to expand in volume during freezing, based on factors such as soil type, moisture content, fine particle content, and geothermal gradient. Identifying these zones helps in the targeted design of pile foundations.

[0025] The "short pile - medium pile - long pile" three-tier differentiated pile type refers to the design of pile foundations with different lengths and potentially different structural forms based on the frost heave sensitivity and geological conditions of different regions of frozen soil foundations. This differentiated design aims to optimize the bearing capacity and economy of the pile foundation.

[0026] The coupling relationship between pile length and frost heave sensitivity refers to the interrelationship and influence mechanism established between the design length of the pile foundation and the frost heave sensitivity of the soil in the area. Through this relationship, it can be ensured that the pile length can effectively cope with different frost heave risks.

[0027] The multi-pile length synergy effect coefficient is a quantitative indicator of the impact of the interaction between piles of different lengths on the overall bearing capacity of a pile group foundation. This coefficient is used to correct for the soil resistance of each pile in the pile group, reflecting the mechanical response correlation between different pile lengths.

[0028] The corrected model for soil resistance in pile groups is a mathematical model that considers the interaction between piles and the influence of pile length differences on soil resistance when calculating the bearing capacity of pile group foundations. This model introduces correction coefficients to make the calculation results more consistent with actual conditions.

[0029] The frozen layer rigid shell effect correction model is a mathematical model used to describe the characteristics of frozen soil layers, which show a significant increase in strength but also an increase in brittleness after freezing, and to correct the bearing behavior of pile foundations in frozen layers. This model considers the special contribution of the frozen layer to the side resistance and end resistance of the pile.

[0030] The unfrozen layer bearing capacity attenuation model is a mathematical model used to describe the attenuation of the bearing capacity of unfrozen soil layers below or around frozen layers due to factors such as temperature gradients and creep. This model aims to more accurately assess the contribution of the unfrozen layer to the bearing capacity of pile foundations.

[0031] The overall model for predicting the bearing behavior of multi-pile length synergy refers to a comprehensive mathematical model that integrates multiple factors such as pile length differences, group pile synergy effect, frozen layer rigid shell effect, and unfrozen layer bearing capacity attenuation, and is used to comprehensively predict the long-term bearing performance of multi-pile group foundations in frozen soil foundations.

[0032] Pile top displacement, pile body bending moment, and ultimate bearing capacity refer to the vertical or horizontal displacement of the pile top, the bending moment generated inside the pile body, and the maximum load that the pile foundation can withstand under load. These are key indicators for evaluating pile foundation performance.

[0033] Implementing this method first requires constructing a three-dimensional geothermal database for permafrost foundations. Data acquisition can employ traditional geological exploration methods, such as manual borehole sampling for soil layer identification and physical and mechanical parameter testing, followed by ground temperature measurement using conventional thermometers. This data is then entered into the database, and the distribution of strata, water content, fine particle content, and ground temperature gradient are integrated through manual analysis or basic geographic information system software. The division between frozen and unfrozen layers can be based on empirical judgment or simple temperature thresholds. Identification of frost heave-sensitive zones can be initially determined by consulting standards or empirical charts based on basic parameters such as soil type and water content.

[0034] Furthermore, based on the identified distribution of sensitive areas, a three-tiered differentiated pile type—short pile, medium pile, and long pile—was designed, and a coupling relationship between pile length and frost heave sensitivity was established. After identifying frost heave-sensitive areas, different pile lengths can be selected empirically based on the degree of frost heave sensitivity in different areas. For example, relatively short piles can be designed in areas with low frost heave sensitivity, while relatively long piles can be designed in areas with high frost heave sensitivity. The coupling relationship between pile length and frost heave sensitivity can be established through simple correspondence rules; for example, high-sensitivity areas correspond to long piles, medium-sensitivity areas to medium piles, and low-sensitivity areas to short piles. Conventional equal-diameter piles can be used for pile design.

[0035] Based on this, a synergistic effect coefficient for multiple pile lengths is introduced to construct a corrected model for the soil resistance of pile groups that considers differences in pile lengths. The introduction of the synergistic effect coefficient can be achieved by simply modifying existing theories of pile group effects. For example, based on the calculation method for pile group effect coefficients in homogeneous soil layers, the coefficient can be empirically adjusted to roughly reflect the influence of different pile lengths on the overall bearing capacity of the pile group. The corrected model for the soil resistance of pile groups can be constructed by superimposing the bearing capacity of individual piles and multiplying it by an empirical correction coefficient, which considers the average influence of pile length differences on the soil resistance.

[0036] Subsequently, the frozen layer rigid shell effect correction model and the unfrozen layer bearing capacity attenuation model were integrated to establish a comprehensive bearing capacity prediction model based on the synergistic effect of multiple pile lengths. The frozen layer rigid shell effect correction model can be constructed using simplified elastic theory or empirical formulas. For example, the frozen layer can be considered a homogeneous layer with high stiffness, and the pile side resistance can be empirically amplified based on its thickness. The unfrozen layer bearing capacity attenuation model can be described using linear attenuation or piecewise constant attenuation. For example, it can be assumed that the bearing capacity of the unfrozen layer attenuates at a fixed ratio within a certain depth range below the frozen-unfrozen interface. Therefore, these simplified correction models are combined with the multi-pile length synergistic effect coefficients, and a comprehensive bearing capacity prediction model is established using simple mechanical equilibrium equations or finite element analysis software.

[0037] Finally, through on-site static load tests and numerical simulations, the predicted results of pile top displacement, pile bending moment, and ultimate bearing capacity for frozen soil foundations are output. On-site static load tests can be performed by applying loads to selected pile locations and measuring the pile top displacement. Numerical simulations can be conducted using commercial finite element software, with simplified geological parameters and a pile foundation model as input. The verification process includes comparing the predicted results with the experimental results, for example, through visual inspection or by calculating the average error. The predicted results can be presented in a simple numerical table, listing the calculated values ​​of pile top displacement, pile bending moment, and ultimate bearing capacity.

[0038] This method constructs a three-dimensional geo-temperature database for permafrost foundations, enabling a comprehensive understanding of the dynamic changes in geology and temperature within permafrost regions, laying the foundation for accurate identification of frost-heave sensitive areas. By designing differentiated pile types based on the distribution of sensitive areas and establishing a coupling relationship between pile length and frost-heave sensitivity, it effectively avoids insufficient bearing capacity or economic waste caused by traditional uniform pile length design. The introduction of a multi-pile-length synergistic effect coefficient and a correction model improves the accuracy of predicting the bearing behavior of pile groups. Integrating the frozen layer rigid shell effect and the unfrozen layer bearing capacity attenuation model allows the overall prediction model to more comprehensively reflect the complex mechanical properties of permafrost. Finally, experimental and simulation verification ensures the reliability of the prediction results, thus solving the prediction challenges caused by the heterogeneity of permafrost foundations and optimizing pile foundation design.

[0039] In some of the embodiments described above in this application, a three-dimensional geo-temperature database for permafrost foundations is proposed to divide the frozen layer and the unfrozen layer and identify high, medium and low frost heave sensitive areas. However, in its implementation, a single data acquisition method cannot fully cover the dynamic changes in geo-temperature throughout the entire freeze-thaw cycle, resulting in the partiality of the database data and affecting the accuracy of subsequent prediction models.

[0040] like Figure 1 As shown, in some embodiments, when constructing the three-dimensional geothermal database of permafrost foundation in step S1, a triple data acquisition system of "ground exploration + borehole coring + distributed optical fiber monitoring" is adopted: ground exploration uses ground-penetrating radar to detect the distribution range of the permafrost layer, and borehole coring intervals do not exceed 5m to obtain the physical and mechanical parameters of soil layers at various depths; distributed optical fibers are deployed along the entire borehole, with a monitoring accuracy of ±0.1℃, and continuously collect geothermal data for more than 12 months to ensure that the database covers the dynamic changes in geothermal temperature throughout the entire freeze-thaw cycle, thus solving the problem of data partiality caused by a single acquisition method.

[0041] Specifically, the triple data acquisition system of "surface exploration + core drilling + distributed fiber optic monitoring" is a comprehensive data acquisition strategy designed to overcome the limitations of a single data source. This system integrates data of different scales and types to achieve a comprehensive and accurate characterization of the geological and temperature features of permafrost foundations. In addition to ground-penetrating radar, core drilling, and distributed fiber optic monitoring, this system can be further combined with other geophysical exploration methods (such as electrical resistivity tomography and seismic exploration) or remote sensing technologies to obtain more macroscopic or specific regional geological information, thus forming a more complete data acquisition network. Through the above technical solution, this application effectively solves the problem of data partiality caused by a single data acquisition method. Surface exploration provides macroscopic spatial distribution information of the permafrost layer, core drilling provides detailed physical and mechanical parameters of the soil layers, and distributed fiber optic monitoring provides dynamic data on geothermal changes throughout the freeze-thaw cycle. The synergistic effect of this triple data acquisition system enables the constructed three-dimensional geothermal database of permafrost foundations to comprehensively and accurately reflect the complex spatial and temporal variability of permafrost foundations, including key information such as stratigraphic distribution, water content, fine particle content, and geothermal gradient. This provides a solid data foundation for the subsequent step S2, which designs three levels of differentiated pile types—short piles, medium piles, and long piles—based on the distribution of sensitive areas, ensuring a precise match between pile type design and frost heave risk. Simultaneously, it provides accurate input parameters and verification basis for introducing the multi-pile length synergy effect coefficient in step S3 and integrating the frozen layer rigid shell effect correction model and the unfrozen layer bearing capacity attenuation model in step S4. This significantly improves the accuracy and reliability of the overall model for predicting the bearing behavior of multi-pile length synergy, ultimately making the output prediction results of pile top displacement, pile body bending moment, and ultimate bearing capacity closer to actual engineering conditions, providing a more scientific and reliable basis for the design of frozen soil foundation engineering.

[0042] In some of the above-mentioned schemes in this application, a three-level differentiated pile design is proposed to optimize the pile bearing behavior of frozen soil foundations. However, in its implementation, the lack of specific adaptation standards may lead to inaccurate matching of pile types with different frost heave sensitive areas, affecting the accuracy of bearing behavior prediction and engineering application effects.

[0043] like Figure 1As shown, in some embodiments, the specific adaptation standards for the three-level differentiated pile types of "short pile-medium pile-long pile" in step S2 are as follows: short piles are suitable for low frost heave sensitive areas, with the pile length only penetrating the surface seasonal frozen layer and the pile tip located on the upper part of the stable unfrozen layer; medium piles are suitable for medium frost heave sensitive areas, with the pile length penetrating the seasonal frozen layer and part of the weakly weathered section of the perennial frozen layer, and the pile tip embedded in the strongly weathered section of the perennial frozen layer for no less than 1.5m; long piles are suitable for high frost heave sensitive areas and areas with ice-containing layers, with the pile length needing to penetrate the entire frozen layer, and the pile tip embedded in the underlying stable bedrock or dense unfrozen soil layer for no less than 3m. In addition, long piles adopt an enlarged base pile design, with the enlarged base diameter being 1.8-2.5 times the pile body diameter, thereby improving the synergistic bearing capacity of tensile and compressive strength through pile structure optimization.

[0044] This adaptation standard aims to provide clear guiding principles for pile foundation design based on the varying degrees of frost heave sensitivity in permafrost foundations. Its purpose is to ensure that pile type selection accurately matches geological conditions, avoiding engineering risks or resource waste caused by inappropriate pile lengths. For example, preliminary pile type selection can be made based on the high, medium, and low frost heave sensitivity zones identified in S1, combined with data such as soil layer distribution and frost depth from the geological survey report. Another approach is to establish a frost heave sensitivity zone database based on a Geographic Information System (GIS) and combine it with preset pile type selection rules to achieve automated or semi-automated pile type adaptation recommendations.

[0045] The design philosophy of short piles prioritizes economy and effectiveness. In low-frost-heave sensitive areas, frost heave forces are primarily concentrated in the surface seasonally frozen layer, with relatively small frost deformation. Therefore, the pile length of short piles is limited to penetrate only this surface layer, allowing the pile tip to rest on top of a stable, unfrozen layer unaffected by seasonal freeze-thaw cycles. This can be achieved by accurately determining the depth of the seasonally frozen layer and the location of the top surface of the unfrozen layer through precise geological surveys. Another approach is to dynamically adjust the minimum penetration depth of the short piles based on long-term geothermal monitoring data to accommodate interannual variations in the depth of the seasonally frozen layer.

[0046] The design of the center pile is intended to address the more complex permafrost conditions in areas with moderate frost heave sensitivity. These areas may contain deep seasonally frozen layers, and even parts of the perennial frozen layer exhibit some frost heave sensitivity. Therefore, the center pile must not only penetrate the seasonally frozen layer but also penetrate a portion of the weakly weathered section of the perennial frozen layer, embedding the pile tip into the more mechanically stable, strongly weathered section of the perennial frozen layer, with an embedment depth of no less than 1.5m. This ensures that the pile foundation can effectively resist the frost heave force from the overlying permafrost layer and obtain sufficient bearing capacity. In practice, the required embedment depth can be accurately calculated based on the weathering degree classification of the perennial frozen layer in the geotechnical investigation report, combined with soil strength parameters determined by indoor geotechnical tests.

[0047] Long piles are designed for areas highly sensitive to frost heave and areas with ice-containing layers. These areas have high frost heave forces and complex geological conditions, requiring extremely high stability from the pile foundation. The design goal of long piles is to completely penetrate all frozen layers, placing the pile tip in deep, stable strata unaffected by freeze-thaw cycles, such as bedrock or dense unfrozen soil, with an embedment depth of at least 3 meters. This ensures that the pile foundation completely avoids the effects of frost heave forces and obtains reliable bearing support. Achieving this goal requires detailed drilling and geophysical exploration to accurately determine the depth of all frozen layers, ice content, and the nature and depth of the underlying stable strata. In step S2, the target pile length is determined using a multi-level pile length design function, the function expression of which is: in: Let m be the design pile length for the m-th engineering area; As a safety factor, the value ranges from 1.1 to 1.3, and is used to amplify the control depth of the sensitive layer; Let be the empirical weighting coefficient of the k-th soil layer, satisfying The soil layer weight in highly sensitive areas shall not be less than 0.4; The freezing sensitivity factor of the k-th soil layer is calculated by coupling the geothermal gradient, water content, and fine particle content. Let be the thickness of the k-th soil layer; This function represents the set of frost heave risk layers contained in the m-th region; it enables the quantitative mapping of geological parameters to pile length dimensions, ensuring accurate matching between pile type and frost heave risk.

[0048] Specifically, the multi-level pile length design function is a mathematical model or algorithm whose core lies in calculating the optimal pile length for different regions or pile locations based on a series of input parameters, such as geological conditions, frost heave sensitivity, and safety requirements. The function's role is to transform complex engineering geological information into specific pile length design parameters, thereby achieving quantitative and refined pile length design. In practical applications, this function can be implemented in various ways. For example, it can be based on fitting of numerous empirical formulas and field test data, establishing the relationship between parameters through regression analysis; alternatively, it can be combined with finite element analysis or numerical simulation techniques, using iterative optimization algorithms to solve for pile lengths that meet specific bearing and deformation requirements.

[0049] like Figure 1 As shown, in some embodiments, in step S3, the synergistic effect coefficient of multiple pile lengths is optimized through an adjacent pile length difference control model, the model expression of which is: in: The difference in pile length between adjacent piles i and j; These are the design pile lengths of two adjacent piles; This is a transition control factor, and its value should not exceed 0.25; This represents the average pile length in the current pile group area; This model reduces stress concentration and enhances the collaborative bearing capacity of pile groups by limiting the amplitude of sudden changes in pile length.

[0050] Specifically, in permafrost foundations, due to the complexity of geological conditions and spatial differences in frost heave sensitivity, pile foundation design often employs differentiated pile lengths. The multi-pile length synergy coefficient aims to quantify the interaction and load distribution mechanism between piles of different lengths. However, if the difference between adjacent pile lengths is too large, it may lead to uneven stress distribution within the pile body, or even local stress concentration, thereby affecting the overall bearing capacity of the pile group and the accuracy of the prediction model. Therefore, optimizing the synergy coefficient through an adjacent pile length difference control model can ensure that the pile length difference is within a reasonable range, thus more accurately reflecting the actual mechanical response of the pile group and improving the reliability of the prediction model. This optimization process can be carried out during the pile foundation design stage. For example, after initially determining the design pile length for each pile location, the control model can be used to check the difference between adjacent pile lengths. If the requirements are not met, the pile lengths can be fine-tuned until the control conditions are met to ensure the synergistic performance of the pile group. Furthermore, this optimization can also be performed during the prediction model iteration process. For example, after calculating the synergistic effect coefficient based on the initial pile length, if it is found that there is a large deviation between the prediction result and the actual monitoring data, the difference control model can be used to correct the synergistic effect coefficient so that it is more in line with the pile interaction under actual engineering conditions.

[0051] like Figure 1 As shown, in some embodiments, in step S4, the frozen layer rigid shell effect correction model introduces a drag reduction coefficient that varies with depth. ,satisfy =0.3-0.5 ( (The depth of the frozen-unfrozen interface) increases monotonically to 1.0 with increasing depth, and is used to correct the degree of exertion of the resistance of the unfrozen soil.

[0052] In step S4, the unfrozen layer bearing capacity attenuation model takes into account the influence of temperature gradient and describes the recovery law of bearing capacity as the freezing depth increases by establishing a negative exponential relationship between the elastic modulus of the soil and the depth.

[0053] The specific negative exponential relationship between the elastic modulus of the unfrozen soil and its depth is as follows: in: Let z be the elastic modulus of the unfrozen soil at depth z; Frozen / Unfrozen Interface The elastic modulus of the unfrozen soil at point ( ) was measured by indoor triaxial tests; k is the attenuation coefficient, ranging from 0.002 to 0.005 m.-1 Adjust according to the formation porosity (the higher the porosity, the higher the k value); To calculate depth ( ); This relationship accurately describes the nonlinear recovery law of the bearing capacity of the unfrozen layer with depth, improving the prediction accuracy of the model.

[0054] like Figure 1 As shown, in some embodiments, the prediction results output in step S5 are presented in a multi-dimensional format of "numerical table + three-dimensional cloud map + trend curve": the numerical table accurately presents the maximum value of pile top displacement, the extreme value of pile body bending moment and the specific value of ultimate bearing capacity at different pile locations; the three-dimensional cloud map intuitively reflects the spatial distribution characteristics of the stress field and displacement field of the pile group, and marks the stress concentration area and the displacement exceeding the limit; the trend curve shows the change law of bearing performance under different freeze-thaw cycles and different load levels, and also includes the error range of the prediction results (confidence level 95%), providing engineering designers with a full-dimensional reference from quantitative data to qualitative analysis.

[0055] like Figure 1 As shown, in some embodiments, the method further includes a real-time correction step: adjusting the synergistic effect coefficient in reverse using data monitored by pile stress sensors to achieve dynamic prediction and updating of bearing behavior; The real-time correction step employs an adaptive Kalman filter algorithm, specifically including: ① Using the monitoring data of the pile stress sensor as the observed value and the synergistic effect coefficient as the state variable, establish the state equation and the observation equation; ② Calculate the filter gain matrix and dynamically adjust the weights of the state variables based on the observation error; ③ Output the corrected synergy coefficient and update the overall prediction model; ④ Set a convergence threshold (error less than 3%). Stop iterating when the correction result meets the threshold requirement; otherwise, repeat steps ①-③. This algorithm enables dynamic coupling between monitoring data and prediction models, improving the method's adaptability to changes in geological conditions.

[0056] In summary, this application constructs a three-dimensional geo-temperature database for frozen soil foundations, integrating data on strata distribution, water content, fine particle content, and geothermal gradient to delineate frozen and unfrozen layers and identify high, medium, and low frost heave sensitive zones. Based on the distribution of sensitive zones, it designs three levels of differentiated pile types—short piles, medium piles, and long piles—and establishes the coupling relationship between pile length and frost heave sensitivity. It introduces a multi-pile length synergy effect coefficient to construct a pile group soil resistance correction model considering pile length differences; the synergy effect coefficient reflects the mechanical response correlation between different pile lengths. It integrates the frozen layer rigid shell effect correction model and the unfrozen layer bearing capacity attenuation model to establish a comprehensive model for predicting the bearing behavior of multiple pile lengths. Through field static load tests and numerical simulations, it outputs predicted results for pile top displacement, pile bending moment, and ultimate bearing capacity of frozen soil foundations.

[0057] By using differentiated pile design and synergistic effect model, the problem of inaccurate prediction of bearing behavior caused by the spatial variability of permafrost, which traditional methods have failed to address, is solved. It has the advantages of accurate prediction, optimized design, and improved safety and economy.

[0058] Finally, it should be noted that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for predicting the bearing behavior of permafrost foundations with multi-pile length coordination, characterized in that: Includes the following steps: S1. Construct a three-dimensional geological-temperature database for permafrost foundations, integrate data on stratigraphic distribution, water content, fine particle content, and geothermal gradient, divide the frozen layer into the unfrozen layer, and identify high, medium, and low frost heave sensitive areas; S2. Based on the distribution of sensitive areas, design three levels of differentiated pile types: "short pile - medium pile - long pile" to establish the coupling relationship between pile length and frost heave sensitivity; S3. Introduce a synergistic effect coefficient for multiple pile lengths to construct a group pile soil resistance correction model that considers the differences in pile lengths. The synergistic effect coefficient reflects the mechanical response correlation between different pile lengths. S4. Integrate the frozen layer rigid shell effect correction model and the unfrozen layer bearing capacity attenuation model to establish a total bearing capacity behavior prediction model with multi-pile length coordination; S5. Through on-site static load tests and numerical simulation verification, output the predicted results of pile top displacement, pile bending moment and ultimate bearing capacity of frozen soil foundation.

2. The method for predicting the bearing behavior of permafrost foundations with multi-pile length coordination according to claim 1, characterized in that: In step S1, when constructing the three-dimensional geo-temperature database of permafrost foundation, a triple data acquisition system of "ground exploration + borehole coring + distributed optical fiber monitoring" is adopted: ground exploration uses ground-penetrating radar to detect the distribution range of the permafrost layer, and borehole coring intervals do not exceed 5m to obtain the physical and mechanical parameters of soil layers at each depth; distributed optical fiber is deployed along the entire borehole, with a monitoring accuracy of ±0.1℃, and continuously collects geothermal data for more than 12 months.

3. The method for predicting the bearing behavior of permafrost foundations with multi-pile length coordination according to claim 1, characterized in that: The specific adaptation standards for the three-level differentiated pile types of "short pile-medium pile-long pile" in step S2 are as follows: short piles are suitable for low frost heave sensitive areas, the pile length only penetrates the surface seasonal freezing layer, and the pile end is located on the upper part of the stable unfrozen layer. Medium-sized piles are suitable for areas with moderate frost heave sensitivity. The pile length penetrates the seasonally frozen layer and part of the weakly weathered section of the perennial frozen layer, and the pile tip is embedded in the strongly weathered section of the perennial frozen layer for no less than 1.5m. Long piles are suitable for areas with high frost heave sensitivity and areas with ice-containing layers. The pile length must penetrate the entire frozen layer, and the pile tip must be embedded in the underlying stable bedrock or dense unfrozen soil layer for no less than 3m. Long piles adopt an enlarged base pile design, and the enlarged base diameter is 1.8-2.5 times the pile body diameter.

4. The method for predicting the bearing behavior of permafrost foundations with multi-pile length coordination according to claim 1, characterized in that: In step S2, the target pile length is determined using a multi-level pile length design function, the function expression of which is: in: Let m be the design pile length for the m-th engineering area; As a safety factor, the value ranges from 1.1 to 1.3, and is used to amplify the control depth of the sensitive layer; Let be the empirical weighting coefficient of the k-th soil layer, satisfying The soil layer weight in highly sensitive areas shall not be less than 0.4; The freezing sensitivity factor of the k-th soil layer is calculated by coupling the geothermal gradient, water content, and fine particle content. Let be the thickness of the k-th soil layer; Let m be the set of frost heave risk layers contained in the m-th region.

5. The method for predicting the bearing behavior of permafrost foundations with multi-pile length coordination according to claim 1, characterized in that: In step S3, the synergistic effect coefficient of multiple pile lengths is optimized through the adjacent pile length difference control model, and the model expression is: in: The difference in pile length between adjacent piles i and j; These are the design pile lengths of two adjacent piles; This is a transition control factor, and its value should not exceed 0.

25. This represents the average pile length in the current pile group area.

6. The method for predicting the bearing behavior of permafrost foundations with multi-pile length coordination according to claim 1, characterized in that: In step S4, the frozen layer rigid shell effect correction model introduces a drag reduction coefficient that varies with depth. ,satisfy =0.3-0.5, monotonically increasing to 1.0 with increasing depth, used to correct the degree of exertion of resistance in unfrozen soil.

7. The method for predicting the bearing behavior of permafrost foundations with multi-pile length coordination according to claim 1, characterized in that: In step S4, the unfrozen layer bearing capacity attenuation model takes into account the influence of temperature gradient and describes the recovery law of bearing capacity as the freezing depth increases by establishing a negative exponential relationship between the elastic modulus of the soil and the depth.

8. The method for predicting the bearing behavior of permafrost foundations with multi-pile length coordination according to claim 7, characterized in that: The specific negative exponential relationship between the elastic modulus of the unfrozen soil and its depth is as follows: in: Let z be the elastic modulus of the unfrozen soil at depth z; Frozen / Unfrozen Interface The elastic modulus of the unfrozen soil at point ( ) was measured by indoor triaxial tests; k is the attenuation coefficient, ranging from 0.002 to 0.005 m. -1 Adjust according to the formation porosity (the higher the porosity, the higher the k value); To calculate depth ( ).

9. The method for predicting the bearing behavior of permafrost foundations with multi-pile length coordination according to claim 1, characterized in that: The method also includes a real-time correction step: adjusting the synergistic effect coefficient in reverse using data monitored by pile stress sensors to achieve dynamic prediction and updating of bearing behavior; The real-time correction step employs an adaptive Kalman filter algorithm, specifically including: ① Using the monitoring data of the pile stress sensor as the observed value and the synergistic effect coefficient as the state variable, establish the state equation and the observation equation; ② Calculate the filter gain matrix and dynamically adjust the weights of the state variables based on the observation error; ③ Output the corrected synergy coefficient and update the overall prediction model; ④ Set a convergence threshold. Stop iterating when the correction result meets the threshold requirement; otherwise, repeat steps ①-③.

10. The method for predicting the bearing behavior of permafrost foundations with multi-pile length coordination according to claim 1, characterized in that: The prediction results output in step S5 are displayed in a multi-dimensional format of "numerical table + 3D cloud map + trend curve": the numerical table accurately presents the maximum value of pile top displacement, the extreme value of pile body bending moment and the specific value of ultimate bearing capacity at different pile locations; the 3D cloud map intuitively reflects the spatial distribution characteristics of the stress field and displacement field of the pile group, and marks the stress concentration area and the displacement exceeding the limit; the trend curve shows the change law of bearing performance under different freeze-thaw cycles and different load levels, and also includes the error range of the prediction results.

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