A method for predicting the undrained shear strength of clay based on equivalent clay content
By defining equivalent clay content and analytical function model, the problem of soil property transition and continuity in the prediction of undrained shear strength of cohesive soil in the existing technology is solved, realizing efficient and accurate full-profile strength prediction, which is applicable to marine geotechnical engineering design.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- OCEAN UNIV OF CHINA
- Filing Date
- 2026-06-02
- Publication Date
- 2026-07-03
Smart Images
Figure CN122334033A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of data processing, and specifically to a method for predicting the undrained shear strength of cohesive soil based on equivalent clay content. Background Technology
[0002] Undrained shear strength (S) u Sa is one of the key mechanical parameters in marine geotechnical engineering investigation and design, and its accuracy directly affects the safety and economy of engineering structures such as offshore wind power, oil and gas platforms, and subsea pipelines. In the calculation of pile foundation bearing capacity, both side skin resistance and end bearing capacity are determined by Sa. u Directly determined; slope stability analysis, foundation pull-out capacity evaluation, and strength weakening assessment under cyclic loading are also based on S. u As the core input parameter, any deviation in its value will lead to an overly conservative basic design, significantly increasing project costs, or creating safety hazards that could cause structural failure.
[0003] Currently, the main methods for calculating the undrained shear strength of cohesive soils include: laboratory testing, vane shear testing, pore pressure static cone penetration testing (CPTU), and machine learning-based CPTU interpretation methods. Among these, laboratory testing (triaxial unconsolidated undrained test and unconfined compressive strength test) offers high accuracy, but is limited by high sampling costs and large disturbances, and can only obtain strength values at discrete depths, making it difficult to reflect continuous changes in the formation. While vane shear testing allows for in-situ testing, its slow testing speed also fails to meet the needs of continuous and efficient exploration. In contrast, pore pressure static cone penetration testing (CPTU), based on empirical formulas, can quickly and continuously obtain formation strength profiles, greatly improving exploration efficiency. However, this method relies on the empirical conic coefficient (N... kt The value of the coefficient is closely related to the soil composition (such as clay content and plasticity index), which makes the interpretation results highly dependent on regional experience and limits its universality in areas lacking calibration data. Although machine learning-based CPTU interpretation methods (such as random forests and neural networks) attempt to overcome the limitations of empirical coefficients, they often focus on mapping single-point data and ignore the stratigraphic continuity between adjacent depths. In terms of multidimensional information utilization, some models still rely too much on cone tip resistance or simply perform feature splicing on data such as pore pressure and friction ratio, failing to deeply explore the intrinsic correlation between multi-source data. In addition, the models have poor interpretability and weak extrapolation ability, making it difficult to embed physical constraints.
[0004] In summary, although CPTU has become the mainstream exploration method, both traditional interpretation based on empirical formulas and emerging data-driven methods still have limitations in obtaining undrained shear strength (Si). u The following shortcomings still exist: 1. Existing methods lack a unified physical model to characterize soil property transitions, making it difficult to continuously characterize the transition properties of cohesive soils from silty clay to highly plastic clay, and failing to establish a unified physical model for N. kt The explicit physical functional relationship between the clay content and the plasticity index.
[0005] 2. Existing methods are inadequate for determining the empirical conic coefficient N. kt There is significant subjectivity and ambiguity involved, and fixed values (such as N) are usually selected based on regional experience. kt =15), or interpolate within a broad range (10-20) based on soil type, ignoring N. kt With the continuous changes in soil composition, stress state, and drainage conditions.
[0006] 3. Existing methods typically treat CPTU data at each depth point as independent samples, ignoring the physical correlation between adjacent depths and the gradual changes in formation, and mainly relying on tip drag q. t It failed to effectively integrate pore pressure u2 and friction ratio F r Other CPTU parameters, which contain rich information about soil response, lead to insufficient utilization of multidimensional information.
[0007] Therefore, there is an urgent need for a method that integrates multidimensional CPTU features and establishes N kt A method for predicting shear strength that is explicitly physically correlated with soil properties and takes into account the continuity of strata is proposed to break away from the dependence on empirical coefficients and deeply explore the intrinsic correlation of multi-source data, thereby achieving continuous, accurate and physically interpretable interpretation of cohesive soil strength. Summary of the Invention
[0008] To address the aforementioned technical problems, this invention proposes a method for predicting the undrained shear strength of cohesive soil based on equivalent clay content. This method solves the technical problems existing in the prediction methods for the undrained shear strength of cohesive soil, such as subjective ambiguity in the determination of empirical conic coefficient, lack of a unified physical model to characterize soil property transition, neglect of the physical continuity of strata, and insufficient utilization of multidimensional CPTU information.
[0009] To achieve the above objectives, the present invention provides a method for predicting the undrained shear strength of cohesive soil based on equivalent clay content, specifically comprising the following steps: S1: Acquire indoor test data and CPTU data, and perform deep matching between the two to obtain paired datasets; S2: Based on the formula for the undrained shear strength of cohesive soil, using discrete depth points Indoor test of undrained shear strength Inverse calculation of each discrete depth point The true conic coefficient at the location ; S3: Obtain discrete depth points using the paired dataset in S1 clay content at the location With plasticity index Based on clay content With plasticity index Define equivalent clay content And calculate each discrete depth point Equivalent clay content at the location ; S4: Establish the true conic coefficients With equivalent clay content The analytical function model between them; S5: Using discrete depth points The true conic coefficient at the location With equivalent clay content By calibrating the unknown parameters in the above analytical function model, a site-specific analytical function model is obtained. S6: Constructing clay content based on CPTU parameters With plasticity index An empirical regression model was developed, and the paired dataset in S1 was used for regression fitting to determine the regression coefficients. Then, the CPTU parameters of the entire profile were substituted into this empirical regression model to calculate the clay content at continuous depths. and plasticity index And combined with the equivalent clay content defined in S3 The calculation formula is used to determine the equivalent clay content across the entire cross-section. ; S7: The equivalent clay content obtained from the full profile in S6. Substituting the site-specific analytical function model obtained from S5, the conic coefficient of the continuous cross-section is solved. Therefore, this should be substituted into consideration of clay content. With plasticity index Formula for predicting the undrained shear strength of cohesive soil affected by the influence of the soil, calculate and output the undrained shear strength of the entire profile. .
[0010] The beneficial effects of this invention are:
[0011] To address the difficulty of characterizing soil property transitions using existing methods, this invention proposes for the first time an "equivalent clay content" index that couples clay content with the plasticity index. This index overcomes the limitations of traditional "clay / silty clay" binarization, and can continuously and uniquely characterize the complete spectrum of clays from low to high plasticity, providing a solid physical foundation for establishing a unified strength prediction formula model.
[0012] against To address the problem of ambiguous values, this invention abandons traditional fixed-value or black-box machine learning approaches and, based on the theory of circular hole expansion, derives... An analytical function that decays exponentially with equivalent clay content eliminates the over-reliance on regional experience and has a clear physical mechanism and interpretability.
[0013] To address the problem that traditional methods neglect the physical continuity of formations, this invention introduces a continuity function. For N kt Dynamic characterization is performed. This method effectively solves the problem of non-physical jumps in the predicted undrained shear strength at the formation interface, ensuring the continuity and smoothness of the shear strength profile as it gradually changes with formation characteristics.
[0014] This invention significantly reduces exploration costs and time, requiring only 5-10 conventional indoor test points (clay content, liquid limit, plastic limit, triaxial UU or unconfined compressive strength) to complete function calibration, reducing sampling and testing workload by 30%-50%, and establishing an exploration model dominated by efficient CPTU in-situ testing; ultimately outputting continuous, physically self-consistent data at full depth. The cross-section can be directly used for pile foundation bearing capacity calculation, slope stability analysis, and foundation pull-out and cyclic load assessment. Attached Figure Description
[0015] Figure 1 This is the overall flowchart of the method proposed in this invention; Figure 2 This is a scatter plot and a fitted curve of the equivalent clay content and conic coefficient of the present invention; Figure 3 This is a curve comparing the fitting results of the clay content of this invention with the measured results; Figure 4 This is a curve comparing the fitting result of the plasticity index of this invention with the measured result; Figure 5 This is a comparison chart of the final curve predicted by the full profile of this invention and the discrete points of the indoor test. Detailed Implementation
[0016] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.
[0017] like Figure 1 As shown, a method for predicting the undrained shear strength of cohesive soil based on equivalent clay content includes the following specific implementation steps: S1: Obtain indoor test data and corresponding CPTU data at discrete borehole depths.
[0018] In-situ CPTU penetration tests were conducted at the target site to obtain the modified cone tip drag at continuous depths. Side wall friction pore water pressure The total overburden stress was calculated using the following formulas. Normalized cone tip resistance Normalized friction ratio and pore pressure ratio .
[0019] ; ; ; in, This indicates hydrostatic pressure.
[0020] Sampling was conducted in the same borehole to perform indoor geotechnical tests and determine the discrete depth. clay content at the location Liquid limit Plastic Limit Calculate the plasticity index Undrained shear strength .
[0021] The indoor test sites were aligned with the CPTU data depth (with an allowable deviation of ≤0.1m) to form a paired dataset.
[0022] S2: Back-calculated true conic coefficient at discrete borehole depths
[0023] Based on the formula for the undrained shear strength of cohesive soil, and utilizing indoor tests... Inverse calculation of each sampling depth The true conic coefficient at the location The specific calculation formula is as follows: ; in, Indicates the sampling depth; The cone tip resistance at the sampling depth is expressed in MPa. This represents the total overburden stress at the sampling depth; This indicates the undrained shear strength at the sampling depth in indoor geotechnical tests.
[0024] S3: Define the equivalent clay content and calculate the discrete values.
[0025] Equivalent clay content The weighted coupling function for clay content and plasticity index is defined by the following formula: ; in, The measured clay content (%) is given. Plasticity index For reference, the plasticity index is taken as 20% (the dividing value between typical silty clay and clay). This is a weighting coefficient, ranging from 0.5 to 2.0, reflecting the contribution of plasticity to the equivalent clay particles. The initial value is... .
[0026] For each sampling depth, substitute the measured clay content. and plasticity index The equivalent clay content at this depth was calculated. .
[0027] S4: Establish an analytical function model between the true conic coefficient and the equivalent clay content; Establish and The analytical function model between them is adopted, which takes the form of an exponential function, and the specific expression is as follows: ; in, The conic section limit for silty soil (low clay content) is 20~30. The conic section limit for highly plastic clay (high clay content) is 8 to 15. This is the decay rate parameter; This represents the equivalent clay content.
[0028] The physical mechanism of this model is based on the theory of circular hole expansion: when the clay content is extremely low, the soil exhibits partial drainage during penetration, resulting in relatively high cone tip resistance. The soil has a relatively high pore water pressure; as the clay content increases, a clay network gradually forms within the soil, exhibiting completely undrained characteristics. This high pore water pressure inhibits the growth of cone tip resistance, while the undrained shear strength of the soil... Significantly increased, leading to a conicity coefficient It decreases and eventually tends to a constant; within this transition range, the conicity coefficient decreases exponentially with the increase of the equivalent clay content.
[0029] S5: Employ the least squares method to calibrate function parameters using discrete data.
[0030] The nonlinear least squares method is used, utilizing the true conic coefficients. With equivalent clay content Unknown parameter in the discrete data calibration function model: decay rate The limit value of the conic section of silty soil The limit value of the conic section of highly plastic clay ; After calibration, the site-specific analytical function is obtained. .
[0031] S6: Establish an empirical regression model and solve for the equivalent clay content of the entire profile. Constructing clay content based on CPTU parameters With plasticity index The empirical regression model is expressed as follows: ; ; in, Indicates clay content, and Represents the regression coefficient. This represents the normalized cone tip resistance. This represents the normalized friction ratio. Indicates the pore pressure ratio. It represents the plasticity index.
[0032] Using the paired dataset obtained in S1, the above model is fitted with regression to determine the regression coefficients. and Substituting the continuous CPTU parameters across the entire profile into the above regression equation, the clay content at continuous depths was calculated. and plasticity index Then, calculate the equivalent clay content of the entire profile according to the S3 definition. .
[0033] S7: Solve for the conicity coefficient based on the continuous equivalent clay content of the entire profile, and calculate the undrained shear strength of the entire profile.
[0034] The equivalent clay content obtained from the full profile in S6 By substituting each point into the calibrated analytical function model in S5, the conic coefficient of the continuous cross-section can be calculated. Then, substituting the clay content into the equation... With plasticity index Formula for predicting the undrained shear strength of cohesive soil affected by the influence of the soil, calculate and output the undrained shear strength of the entire profile. .
[0035] The formula for predicting the undrained shear strength of cohesive soil, taking into account the influence of clay content and plasticity index, is as follows: ; in, The full-section undrained shear strength; z represents the continuous depth variable; The cone tip resistance at the sampling depth; This represents the total overburden stress at the sampling depth; This is the minimum value of the conic coefficient; This represents the maximum value of the conic coefficient; This is the decay rate parameter; This represents the measured clay content; These are the weighting coefficients; Indicates the plasticity index; This indicates the reference plasticity index, taken as 20%.
[0036] Example 1: An offshore wind farm 1. Site and Data Overview The drilling depth was 0-10m, and the CPTU sampling interval was 0.02 m. Samples were taken at depths of 1m, 3m, 5m, 7m, and 9m, and indoor tests were conducted. The test results for each parameter are detailed in Table 1. Table 1: Test results of soil parameters 2. Calculation of equivalent clay content and inverse calculation of true conic coefficient
[0037] Pick , =20, calculate the equivalent clay content. = Based on the formula for the undrained shear strength of cohesive soil, the true conic coefficient at each sampling depth was calculated using the measured values from indoor tests. The results are shown in Table 2: Table 2: True Conic Factors at Different Sampling Depths 3. Construction and parameter calibration of an analytical model for the true conic coefficient and equivalent clay content
[0038] Establish and Analytical function model between: ; Nonlinear least squares fitting is employed, utilizing the true conic coefficients of discrete data. With equivalent clay content The unknown parameters in the above calculation model are obtained from the discrete data. =22.5, =9, =0.019, the coefficient of determination R is 0.019. 2 =0.94. The model fitting results are as follows: Figure 2 As shown.
[0039] 4. Establish CPTU parameters and measured clay content Plasticity index regression model
[0040] An empirical regression model incorporating CPTU parameters is constructed, and its expression is as follows: ; ;
[0041] Five discrete depth points from the indoor experimental data (as shown in Table 3) were selected as calibration samples for the regression model.
[0042] Table 3: Calibration Samples of Regression Model Based on Indoor Experiments The comparison results between the actual and fitted values of the calibrated model are as follows: Figure 3 and Figure 4 As shown. Figure 3 and Figure 4 This demonstrates the equivalent clay content obtained based on CPTU parameter regression. With plasticity index The comparison between the predicted values and the measured values from the indoor tests showed that the coefficients of determination were as high as 0.99 and 0.98, respectively. This indicates that the established empirical regression model has extremely high fitting accuracy and can accurately invert soil properties using continuous CPTU data, providing a reliable basis for the continuous calculation of equivalent clay content across the entire profile.
[0043] Based on CPTU full profile clay content Multiple linear regression was used to... , , The fitting coefficients are shown in Table 4, with as the independent variable: Table 4: Calibration coefficients of the equivalent clay content prediction formula based on CPTU characteristic parameters ; Coefficient of determination R 2 =0.99.
[0044] Predicting the full-section plasticity index of CPTU At that time, the multiple linear regression method was used to... , The fitting coefficients obtained are shown in Table 5, with as the independent variable: Table 5: Calibration coefficients of the plasticity index prediction formula based on CPTU characteristic parameters ; Coefficient of determination R 2 =0.98.
[0045] Each depth point , Substituting into the above formula, we can obtain the continuous... and , and then calculate .
[0046] 5. Calculate the full profile of CPTU The result is as follows Figure 5 As shown.
[0047] For each depth ,Depend on Calculate the full profile of CPTU Substitute The calculation formula yields the full profile of CPTU. And draw the full cross section. The curve. Compared with the indoor test points, the maximum relative error is less than 10%. As shown in Table 6.
[0048] Table 6: Actual vs. Forecast Comparison results This invention provides an innovative method for continuously predicting the undrained shear strength of cohesive soils in geotechnical engineering investigation. It couples the quantity of clay particles with plasticity by proposing the concept of "equivalent clay content," and establishes a conic coefficient based on the theory of pore expansion. An analytical function model with exponential decay of equivalent clay content was used. The function parameters could be calibrated using a small number (5) of conventional indoor test points. Then, combined with CPTU in-situ test data, the equivalent clay content of the entire profile was obtained. Finally, the physically self-consistent and continuously smooth undrained shear strength S was calculated. u Profile. This method completely eliminates the limitations of black-box machine learning and empirical constants, and has outstanding advantages such as clear physical mechanism, strong interpretability, no need for a large amount of training data, excellent extrapolation ability, and simple calculation. It significantly reduces the cost and cycle of exploration and provides efficient and reliable data support for marine geotechnical engineering design.
[0049] The foregoing has provided a detailed description of one embodiment of the present invention, but this description is merely a preferred embodiment and should not be construed as limiting the scope of the invention. All equivalent variations and modifications made within the scope of the claims of this invention should still fall within the patent coverage of this invention.
Claims
1. A method for predicting the undrained shear strength of a clayey soil based on equivalent clay content, characterized in that, Includes the following steps: S1: Acquire indoor test data and CPTU data, and perform deep matching between the two to obtain paired datasets; S2: Based on the undrained shear strength formula of cohesive soil, the undrained shear strength of each discrete depth point is calculated by using the indoor test undrained shear strength of each discrete depth point ; S3: Obtain discrete depth points using the paired data set in S1 Plasticity Index Plasticity Index Plasticity Index Plasticity Index Plasticity Index Plasticity Index Plasticity Index Plasticity Index S4: Establishing the real cone coefficient with the equivalent clay content analytical function model between them; S5: Using discrete depth points The true conic coefficient at the location With equivalent clay content By calibrating the unknown parameters in the above analytical function model, a site-specific analytical function model is obtained. S6: Constructing clay content based on CPTU parameters With plasticity index An empirical regression model was developed, and the paired dataset in S1 was used for regression fitting to determine the regression coefficients. Then, the CPTU parameters of the entire profile were substituted into this empirical regression model to calculate the clay content at continuous depths. and plasticity index And combined with the equivalent clay content defined in S3 The calculation formula is used to determine the equivalent clay content across the entire cross-section. ; S7: The equivalent clay content obtained from the full profile in S6. Substituting the site-specific analytical function model obtained from S5, the conic coefficient of the continuous cross-section is solved. Therefore, this should be substituted into consideration of clay content. With plasticity index Formula for predicting the undrained shear strength of cohesive soil affected by the influence of the soil, calculate and output the undrained shear strength of the entire profile. .
2. The method for predicting the undrained shear strength of cohesive soil based on equivalent clay content according to claim 1, characterized in that, The formula for the undrained shear strength of the cohesive soil in S2 is as follows: ； in, This represents the true conic coefficient at each sampling depth. This represents the depth of the i-th discrete sampling point; The cone tip resistance, expressed as sampling depth, is measured in MPa. The total overburden stress represents the sampling depth; This indicates the undrained shear strength at the sampling depth in indoor geotechnical tests.
3. The method for predicting the undrained shear strength of cohesive soil based on equivalent clay content according to claim 1, characterized in that, The S3 equivalent clay particles Content is defined as clay content With plasticity index The weighted coupling function is defined by the following formula: ； in, The measured clay content is expressed in % (%). Plasticity index; For reference, the plasticity index; These are the weighting coefficients.
4. The method for predicting the undrained shear strength of cohesive soil based on equivalent clay content according to claim 1, characterized in that, The true conic coefficient in S4 With equivalent clay content The analytical function model expression between them is: ； in, This represents the limit value of the conic section coefficient for silty soil. This represents the limit value of the conic section coefficient for highly plastic clay. This is the decay rate parameter.
5. The method for predicting the undrained shear strength of cohesive soil based on equivalent clay content according to claim 1, characterized in that, The unknown parameter in S5 refers to the limit value of the conic section coefficient of silty soil. The limit value of the conic section of highly plastic clay With decay rate .
6. The method for predicting the undrained shear strength of cohesive soil based on equivalent clay content according to claim 1, characterized in that, The clay content based on the CPTU parameter in S6 With plasticity index The empirical regression model expressions are as follows: ； ； in, , , , , , and Represents the regression coefficient. This represents the normalized cone tip resistance. This represents the normalized friction ratio. This indicates the pore pressure ratio.
7. The method for predicting the undrained shear strength of cohesive soil based on equivalent clay content according to claim 1, characterized in that, The formula for predicting the undrained shear strength of cohesive soil in S7 is as follows: ； in, The full-section undrained shear strength; z represents the continuous depth variable; The cone tip resistance at the sampling depth; This represents the total overburden stress at the sampling depth; This is the minimum value of the conic coefficient; This represents the maximum value of the conic coefficient; This is the decay rate parameter; This represents the measured clay content; These are the weighting coefficients; Indicates the plasticity index; This indicates the reference plasticity index.