Calculation method for simulating negative frictional resistance of ground fissure site pile foundation in collapsible loess area

Abstract

The invention discloses a calculation method for simulating negative friction of a ground fracture field pile foundation in a collapsible loess area, which comprises the following steps: firstly, preparing loess samples with different gradient water contents, carrying out a one-dimensional consolidation test, and fitting a collapsible loess equivalent formula; the hydraulic equivalent parameters are substituted into a Taisha foundation one-dimensional consolidation theory, and a settlement formula at different thicknesses under the loess collapsing effect is obtained; basic parameters of a ground fracture site are obtained, a numerical model is established, and a stratum differential settlement curve is output; substituting the settlement curve of each stratum into the error function to obtain the settlement deformation of the soil layer with the specific depth and a simplified difference function expression; based on a single-pile load transfer model, pile foundation deep displacement and pile-soil relative displacement expressions are deduced, and pile foundation negative friction is calculated in combination with soil layer displacement. According to the method, the double influences of loess collapsibility and ground fissure activity are considered, the calculation accuracy of the negative friction resistance of the pile foundation is improved, and a reliable theoretical basis and a calculation method are provided for design of the ground fissure site pile foundation in the collapsible loess area.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of civil engineering, and particularly relates to a method for calculating negative friction resistance of pile foundation in ground fissure field in collapsible loess area, and belongs to the technical field of pile foundation engineering design. BACKGROUND

[0002] Ground fissure can cause zonal rupture of ground surface, vertical differential settlement and normal fault shear deformation, and its activity can cause differential settlement of stratum soil. When the displacement amount of soil layer around pile foundation in ground fissure field is greater than the displacement amount of pile foundation, downward friction force, i.e. negative friction resistance, is generated on the surface of pile foundation, which cannot bear the upper load and causes a certain degree of harm to the upper building. The negative friction resistance of pile foundation has obvious difference between the upper and lower plates of ground fissure, and the research on the influence of such differential settlement on pile foundation is less. In collapsible loess area, the coupling effect of differential settlement caused by collapsible loess after water and ground fissure activity significantly aggravates the spatiotemporal evolution complexity of negative friction resistance at pile-soil interface. The existing research has proposed a calculation method for negative friction resistance of pile foundation under single environment. However, the calculation method for negative friction resistance of pile foundation under single factor is difficult to calculate the negative friction resistance of pile foundation under the action of differential deformation between the upper and lower plates caused by loess collapsibility and ground fissure activity. The current calculation method for negative friction resistance considering the double effects of ground fissure activity and loess collapsibility is extremely inaccurate, which poses a great challenge to pile foundation engineering construction in collapsible loess area, and an urgent need for a calculation method to provide a basis for the reduction measures of pile foundation negative friction resistance.

[0003] The existing calculation method for negative friction resistance of pile foundation mainly considers the influence of single factor. For example: Chinese patent application CN113849892A proposes a calculation method for negative friction resistance of single pile in hydraulic fill soil considering secondary consolidation effect, aiming to solve the deviation problem of pile foundation negative friction resistance calculation in hydraulic fill soil caused by ignoring secondary consolidation effect. One-dimensional secondary consolidation test is performed by improving the consolidation instrument to obtain the pore ratio-time logarithm (e-lgt) curve, determine the main-secondary consolidation demarcation point and secondary consolidation parameters (such as secondary consolidation coefficient, fitting constant, etc.), and then calculate the total deformation of hydraulic fill soil; the position of neutral point of negative friction resistance is determined based on the relationship between total deformation and pile settlement, and the negative friction resistance of pile side is calculated by integrating soil mechanics parameters. This method quantifies the time-varying characteristics of secondary consolidation effect, improves the calculation accuracy of negative friction resistance, and provides a more reliable theoretical basis for pile foundation design in hydraulic fill soil.

[0004] The Chinese patent application CN111382516A proposes a method for analyzing the negative friction resistance of an ultra-long pile foundation under the action of a stack load, which solves the problem of negative friction resistance caused by the settlement difference between the pile and the soil due to the stack load. By establishing a negative friction resistance analytical model considering the three-dimensional consolidation settlement of the soil around the pile and a nonlinear numerical model of the interaction between the pile and the soil, and combining with engineering example analysis and actual measurement verification, the development law of the negative friction resistance is obtained, providing a basis for the design of an ultra-long pile foundation.

[0005] The ground fissure site in the collapsible loess area has special geological conditions. The existence of the ground fissure can cause uneven settlement, dislocation, and stress concentration of the soil, and there is a very obvious differential settlement in each area of the upper and lower plates. In actual ground fissure sites, the displacement direction and size of the soil on both sides of the ground fissure are significantly different, which can cause the negative friction resistance of different parts of the pile to be different in size and direction. The above calculation methods cannot be universally applied to the ground fissure site in the collapsible loess area, and do not consider that the ground fissure activity can cause local stress concentration of the pile, thereby changing the size and distribution of the negative friction resistance.

[0006] At present, a calculation method for simulating the negative friction resistance of a pile foundation in a ground fissure site in a collapsible loess area is proposed, which not only perfects the design requirements of the pile foundation in the ground fissure site in the collapsible loess area, but also has urgent practical significance for ensuring the safety of infrastructure in the whole life cycle of the area. SUMMARY

[0007] To overcome the problems of the prior art, a calculation method for simulating the negative friction resistance of a pile foundation in a ground fissure site in a collapsible loess area is proposed, which can accurately calculate the differential settlement of the ground fissure activity and the loess collapse, and then deduce the negative friction resistance of the pile foundation in the complex site caused by the deformation of the soil layer.

[0008] To achieve the above-mentioned purpose, the technical scheme adopted by the present application is as follows: A calculation method for simulating the negative friction resistance of a pile foundation in a ground fissure site in a collapsible loess area, the steps are as follows: Step 1.1, prepare loess samples with different moisture content gradients, perform one-dimensional consolidation test on samples with different initial dry density and moisture content, apply load step by step after the sample is stable, draw P-S curve (vertical pressure-soil vertical compression curve), obtain the wetting deformation Δs1 and equivalent pressure Δp of the loess sample with different moisture content w1 and dry density under the initial pressure P0 through the indoor compression test, determine the model parameters by fitting the equivalent formula (1) of the collapsible loess based on the hydraulic equivalent principle ɑ and β : (1), Where α and β are parameters of the calculation model, ΔP is the humidification equivalent effect, w1 is the moisture content after humidification, w0 is the initial moisture content, and w p P0 is the soil's plastic limit water content, and P0 is the initial pressure exerted on the soil.

[0009] Step 1.2, substituting the hydraulic equivalent parameters α and β into Terzaghi's one-dimensional consolidation theory, we can obtain the calculation formula for the settlement of loess at different thicknesses under the hydraulic equivalent model, and the calculation formula (2) is as follows: (2), Where z1 is the settlement depth required for loess subsidence. H It refers to the thickness of the soil layer; E s The compression modulus of the soil layer; T v As a time factor, Tv = C v t / H 2 , Cv Here, t is the consolidation coefficient, and t is the consolidation time. M = Π ( 2m +1) / 2, where m is a non-negative integer.

[0010] Compression modulus in step 1.2 E s The coefficient of consolidation Cv is usually calculated by measuring the deformation of undisturbed soil samples through indoor compression tests in the "Standard for Geotechnical Testing Methods" GB / T 50123-2019, by applying different pressures. The coefficient of consolidation Cv is calculated by indoor lateral consolidation tests based on the square root time method.

[0011] Step 2.1: Obtain basic parameters of the ground fissure site and establish a numerical model through on-site investigation and literature review. The specific implementation method is as follows: First, drill holes to obtain soil samples at different depths to determine the soil profile parameters; second, use a geological compass to directly measure the dip angle of the ground fissure and arrange core drilling along the direction of the ground fissure to determine its underground extension depth; at the same time, measure the force and displacement in the normal and shear directions through direct shear tests, and calculate the interface strength parameters based on the slope of the force-displacement curve.

[0012] Soil profile parameters were obtained by analyzing the thickness, composition, and structure of each soil layer through borehole sampling. Compression, direct shear, and triaxial tests were used to determine the soil's elastic modulus E, Poisson's ratio μ, unit weight γ, cohesion c, and internal friction angle φ. The dip angle of ground fissures was directly measured using a geological compass, and the concealed depth was determined by core sampling along the fissure direction. The interface normal stiffness Kn and shear stiffness Kt were calculated from the slope of the force-displacement curve in the direct shear test.

[0013] Step 2.2: Establish a finite element model to simulate ground fissure activity and obtain the ground settlement curve. Assuming that shape parameter B is inversely proportional to the distance between the soil and the bedrock interface, and shape parameter C is inversely proportional to the dip angle of the bedrock fault plane, the settlement deformation of the soil layer at a specific depth and distance from the ground fissure can be obtained. The calculation formula (3) is as follows: ( B z2 >0) (3), Where: dz2 is the vertical displacement at depth z2 during ground fissure activity, h is the vertical displacement of the hanging wall of the bedrock, and H is the soil layer thickness. δ B is the displacement angle of the rigid body. Z2 Z is the shape coefficient that does not change with depth, X is the horizontal distance coordinate, and z2 is the depth of the ground fissure site settlement to be determined.

[0014] Step 3.1, based on the soil settlement prediction curve of the ground fissure site in the collapsible loess area established in Step 2.2, the expression for the relative displacement of the pile and soil at depth z (4) is: (4), Where, ∆ s (z) is the relative displacement between the pile and the soil at depth z. S s (z) The relative displacement of the soil layer at depth z under loess collapse and ground fissure activity.

[0015] Step 3.2, take any segment in the single pile load transfer model for stress analysis, and the displacement expression (5) at the z-depth of the pile foundation can be obtained as follows: (5), in, S p (z) is the displacement at point z of the pile foundation. S (0) is the pile top displacement. P (z) is the axial force at depth z. EA It refers to the axial stiffness of the pile.

[0016] Step 3.3: After determining the expression for the relative displacement between the pile and the soil at depth z, the axial force and side friction of the pile in the ground fissure site of the collapsible loess area can be calculated. The expression (6) is as follows: (6), in, E It is the elastic modulus of the pile. A It is the cross-sectional area of ​​the pile. For a circular pile, A = Π ( D / 2 ) 2 , DIt is the diameter of the pile, ∆ s (z) is the pile-soil relative displacement at depth z. This indicates that the second-order differential is performed at depth z to describe the pile-soil relative displacement ∆. s (z) Curvature characteristics as a function of depth z.

[0017] Step 3.4: Differentiate and simplify the displacement expression to obtain the second derivative calculated by Terzaghi consolidation theory based on the water-mechanical equivalence principle. The expression (7) is as follows: (7), in, α β and w1 are parameters of the calculation model, w1 is the moisture content after humidification, w0 is the initial moisture content, and w1 is the initial moisture content. p denoted as the soil's plastic limit water content, p0 as the initial pressure exerted on the soil, and z1 as the settlement depth to be calculated when the loess collapses. H It refers to the thickness of the soil layer; E s The compression modulus of the soil layer; Tv As a time factor, Tv = C v t / H 2 , Cv d is the consolidation coefficient, t is the consolidation time; dz1 is the vertical displacement at depth z1; S s 湿陷 The soil settlement prediction curve is represented by Terzaghi's consolidation theory based on the principle of water-mechanical equivalence. This represents the second-order differential with respect to depth z1; S s 地裂缝 This represents the differential settlement curve of ground fissures based on the error function. This represents the second-order derivative with respect to depth z2, used to describe the curvature characteristics of the soil settlement prediction curve as a function of depth z2.

[0018] The second derivative of the differential settlement curve of ground fissures based on the error function is given by equation (8): (8), Where: z2 is the desired settlement depth. d z2 represents the vertical displacement at depth z2, h represents the vertical displacement of the hanging wall of the bedrock, and H represents the soil layer thickness. δ B is the displacement angle of the rigid body. Z2 The shape factor is independent of depth, X is the horizontal distance coordinate, and S is the depth coefficient. s 地裂缝 This represents the differential settlement curve of ground fissures based on the error function. This represents the second-order derivative with respect to depth z2, used to describe the curvature characteristics of the soil settlement prediction curve as a function of depth z2.

[0019] The beneficial effects of this invention are as follows: By preparing loess samples and conducting one-dimensional consolidation tests, and combining the hydraulic equivalence principle to fit an equivalent formula for collapsible loess to determine model parameters, a calculation formula for settlement under collapsibility is obtained by incorporating Terzaghi's one-dimensional consolidation theory. Simultaneously, by obtaining site parameters of ground fissures through field investigation and testing, numerical and finite element models are established to simulate ground fissure activity and obtain ground settlement curves. Furthermore, expressions for pile-soil relative displacement, pile foundation displacement, and negative skin friction are derived. This method accurately couples the dual effects of collapsible loess deformation and ground fissure activity, improving the accuracy of parameter acquisition and the reliability of calculations, ensuring the safety of pile foundation design, optimizing project costs and construction period, improving the calculation theory of negative skin friction of pile foundations, and achieving precise mechanical analysis of pile foundations in complex sites, providing strong support for pile foundation engineering in special geological areas. Attached Figure Description

[0020] Figure 1 This is a schematic diagram of the process of this invention; Figure 2 This is a schematic diagram of the hydraulic equivalence obtained from consolidation tests of loess with different moisture contents; Figure 3 The original numerical analysis model unit mesh diagram for the established ground fissure site; Figure 4 This is a schematic diagram of the negative skin friction of the pile foundation at different distances from the ground fissure, calculated according to the present invention. Detailed Implementation

[0021] The following description is only a preferred embodiment of the present invention and does not limit the scope of protection of the present invention. The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0022] like Figures 1-4 As shown, a method for calculating the negative skin friction of pile foundations in a ground-fissure area of ​​collapsible loess is implemented according to the following steps: Step 1.1: Prepare loess samples with different moisture contents. Following the consolidation test requirements, conduct one-dimensional consolidation tests on samples with different initial dry densities and moisture contents. After the samples stabilize, gradually apply larger loads. Plot the test data as a PS curve (vertical pressure - vertical compression curve of soil sample), and the moisture gain Δw under the initial pressure P0 can be obtained. i Humidification deformation Δs i And the humidification equivalent pressure ΔP, taking the humidification deformation and humidification equivalent pressure under multiple sets of tests, based on the hydraulic equivalent schematic diagram Figure 2 The equivalent formula for the collapsible loess of this site (1) is obtained by fitting: (1), Where α and β are parameters of the calculation model, ΔP is the humidification equivalent effect, w1 is the moisture content after humidification, w0 is the initial moisture content, and wp P0 is the soil's plastic limit water content, and P0 is the initial pressure exerted on the soil.

[0023] Step 1.2: After determining the hydraulically equivalent parameters, substitute them into Terzaghi's one-dimensional consolidation theory to obtain the settlement of loess at different thicknesses under the hydraulically equivalent model. The settlement of loess at different thicknesses under the action of loess collapse is calculated, and the formula (2) is as follows: (2), Where z1 is the settlement depth required for loess subsidence. H It refers to the thickness of the soil layer; E s The compression modulus of the soil layer; T v As a time factor, Tv = C v t / H 2 , Cv Here, t is the consolidation coefficient, and t is the consolidation time. M = Π ( 2m +1) / 2, where m is a non-negative integer.

[0024] Compression modulus in step 1.2 E s The coefficient of consolidation Cv is usually calculated by measuring the deformation of undisturbed soil samples through indoor compression tests in the "Standard for Geotechnical Testing Methods" GB / T 50123-2019, by applying different pressures. The coefficient of consolidation Cv is calculated by indoor lateral consolidation tests based on the square root time method.

[0025] Step 2.1: Obtain basic parameters of the ground fissure site and establish a numerical model through on-site investigation and literature review. The specific implementation method is as follows: First, drill holes to obtain soil samples at different depths to determine the soil profile parameters; second, use a geological compass to directly measure the dip angle of the ground fissure and arrange core drilling along the direction of the ground fissure to determine its underground extension depth; at the same time, measure the force and displacement in the normal and shear directions through direct shear tests, and calculate the interface strength parameters based on the slope of the force-displacement curve.

[0026] A numerical model is established based on the above parameters, as follows: Figure 3As shown, the ground fissure dip angle is selected as 80°, stratum 1 is plain fill, stratum 2 is loess, stratum 3 is paleosol, and bottom layer 4 is silt interbedded soil. A ground fissure differential settlement motion model is carried out, and after outputting the stratum differential settlement curve, the settlement data of each stratum are substituted into the error function. Assuming that the shape parameter B is inversely proportional to the distance between the soil and the bedrock interface, and the shape parameter C is inversely proportional to the dip angle of the bedrock fault plane, the settlement deformation of the soil layer at a specific depth and distance from the ground fissure is calculated by the formula. The simplified expression of the error function (3) is as follows: ( B z2 >0) (3), Where: dz2 is the vertical displacement at depth z2 during ground fissure activity, h is the vertical displacement of the hanging wall of the bedrock, and H is the soil layer thickness. δ B is the displacement angle of the rigid body. Z2 Z is the shape coefficient that does not change with depth, X is the horizontal distance coordinate, and z2 is the depth of the ground fissure site settlement to be determined.

[0027] The soil profile parameters mentioned in step 2.1 include the structural composition of each layer, the burial depth Hi, and the elastic modulus E, Poisson's ratio μ, unit weight γ, cohesion c, and internal friction angle φ measured by compression tests, direct shear tests, and triaxial compression tests; the interface strength parameters include normal stiffness Kn, shear stiffness Kt, cohesion c, and internal friction angle φ. Step 3.1, take any segment in the single pile load transfer model for stress analysis, and the displacement expression (4) at the z-depth of the pile foundation can be obtained as follows: (4), in, S p (z) is the displacement at point z of the pile foundation. S (0) is the pile top displacement. P (z) is the axial force at depth z. EA It refers to the axial stiffness of the pile.

[0028] The expression for the relative displacement between the pile and the soil at depth h (5) is then: (5), Where, ∆ s (z) is the relative displacement between the pile and the soil at depth z. S s (z) The relative displacement of the soil layer at depth z under loess collapse and ground fissure activity.

[0029] Step 3.2, after determining the displacement expression of the pile foundation at depth h, the negative skin friction of the pile foundation under the action of loess collapsibility and ground fissure at a specific depth can be calculated by the pile-soil relative displacement. Finally, the pile side skin friction of the ground fissure site in the collapsible loess area can be calculated. The expression (6) is as follows: (6), in, E It is the elastic modulus of the pile. A It is the cross-sectional area of ​​the pile. For a circular pile, A = Π ( D / 2 ) 2 , D It is the diameter of the pile, ∆ s (z) is the pile-soil relative displacement at depth z. This represents the second-order differential with respect to depth z, used to describe the pile-soil relative displacement ∆. s (z) Curvature characteristics as a function of depth z.

[0030] in The second derivative calculated based on Terzaghi's consolidation theory using the hydro-mechanical equivalence principle and simplified is as follows: (7), in, α β and w1 are parameters of the calculation model, w1 is the moisture content after humidification, w0 is the initial moisture content, and w1 is the initial moisture content. p denoted as the soil's plastic limit water content, p0 as the initial pressure exerted on the soil, and z1 as the settlement depth to be calculated when the loess collapses. H It refers to the thickness of the soil layer; E s The compression modulus of the soil layer; Tv As a time factor, Tv = C v t / H 2 , Cv d is the consolidation coefficient, t is the consolidation time; dz1 is the vertical displacement at depth z1; S s 湿陷 The soil settlement prediction curve is represented by Terzaghi's consolidation theory based on the principle of water-mechanical equivalence. This represents the second-order differential with respect to depth z1; S s 地裂缝 This represents the differential settlement curve of ground fissures based on the error function. This represents the second-order derivative with respect to depth z2, used to describe the curvature characteristics of the soil settlement prediction curve as a function of depth z2.

[0031] The second derivative of the differential settlement curve of ground fissures based on the error function is: (8), Where: z2 is the desired settlement depth. d z2 represents the vertical displacement at depth z2, h represents the vertical displacement of the hanging wall of the bedrock, and H represents the soil layer thickness. δ B is the displacement angle of the rigid body. Z2 The shape factor is independent of depth, X is the horizontal distance coordinate, and S is the depth coefficient. s 地裂缝 This represents the differential settlement curve of ground fissures based on the error function. This represents the second-order derivative with respect to depth z2, used to describe the curvature characteristics of the soil settlement prediction curve as a function of depth z2.

[0032] Step 3.3, by repeating the calculation, the negative skin friction of the pile foundation at various distances from the ground fissure can be obtained as follows: Figure 4 As shown, by Figure 4 It was found that when the pile foundation is located in the main deformation zone of the upper plate, the negative skin friction of the pile foundation is relatively large. Example

[0033] The project site is located in a collapsible loess area, and ground fissures exist within the site. Geological investigation revealed that the dip angle of the ground fissures is 70°. The parameters of each soil layer and the ground fissures are defined as follows: Plain fill layer (S1): elastic modulus 26.0 GPa, unit weight 18.0 kN / m³, Poisson's ratio 0.35, cohesion 20 kPa, internal friction angle 15°, and layer thickness 8.6 m.

[0034] Loess layer (S2): elastic modulus 28.0 GPa, unit weight 18.5 kN / m³, Poisson's ratio 0.30, cohesion 40 kPa, internal friction angle 20°, and stratum thickness 41.2 m.

[0035] Paleosol layer (S3): elastic modulus 41.7 GPa, unit weight 18.6 kN / m³, Poisson's ratio 0.28, cohesion 40 kPa, internal friction angle 21°, and stratum thickness 19.5 m.

[0036] Silt-sand interbedded layer (S4): elastic modulus 46.0 GPa, unit weight 19.5 kN / m³, Poisson's ratio 0.31, cohesion 40 kPa, internal friction angle 24°, formation thickness 10.7 m.

[0037] Ground fissure (F): Both normal stiffness and shear stiffness are 6.75 × 10⁻⁶. 4 kPa, cohesion 10kPa, internal friction angle 12°.

[0038] Step 1.1 Calculation of loess collapsibility: Loess samples with different moisture contents were prepared (initial moisture content w0 was approximated to 12% based on the natural moisture content of loess, and the moisture contents after moistening were 15%, 18%, and 20%, respectively). The plastic limit moisture content of the soil was determined to be 22%. The soil was initially subjected to the original site load, P0, which was taken as 120 kPa. One-dimensional consolidation tests were conducted on the loess samples with different moisture contents. Based on the data fitting, the hydraulic equivalent formula parameters α=0.6 and β=1.2 were obtained. The final hydraulic equivalent formula is as follows: .

[0039] Taking loess as an example, with a soil layer thickness H=41.2m, when the moisture content is 18% after moistening, according to the hydraulic equivalence principle, it is equivalent to a uniformly distributed load on the soil surface: .

[0040] Step 1.2: After determining the hydraulically equivalent parameters, substitute them into Terzaghi's one-dimensional consolidation theory to obtain the settlement of loess at different thicknesses under the hydraulically equivalent model. The settlement of loess at different thicknesses under the action of loess collapse is calculated, and the formula (1) is as follows: (1), Where z1 is the settlement depth required for loess subsidence. H It refers to the thickness of the soil layer; E s The compression modulus of the soil layer; Tv As a time factor, Tv = C v t / H 2 , Cv Here, t is the consolidation coefficient, and t is the consolidation time. M = Π ( 2m +1) / 2, where m is a non-negative integer.

[0041] Step 2.1, differential settlement calculation of ground fissures: Detailed parameters of ground fissure activity were obtained through on-site borehole exploration. The ground fissure dip angle was measured to be 70°, and the maximum dislocation h was determined to be 300 mm based on monitoring data. A numerical model was established based on the on-site environment, and the differential settlement curve of the strata was extracted and substituted into the simplified error function expression (2). ( B z2 >0) (2), Where: dz2 is the vertical displacement at depth z2 during ground fissure activity, h is the vertical displacement of the hanging wall of the bedrock, and H is the soil layer thickness. δ B is the displacement angle of the rigid body. z2Z is the shape coefficient that does not change with depth, X is the horizontal distance coordinate, and z2 is the depth of the ground fissure site settlement to be determined.

[0042] The expression (3) at depth z in the site can be obtained as follows: ( B z2 >0) (3), Step 3.1: After determining the displacement expression for the pile foundation at depth h, the negative skin friction of the pile foundation under the action of loess collapsibility and ground fissures at a specific depth can be calculated by the pile-soil relative displacement. Finally, the pile side skin friction of the ground fissure site in the collapsible loess area can be calculated. The expression (4) is as follows: (4), in, E It is the elastic modulus of the pile. A It is the cross-sectional area of ​​the pile. For a circular pile, A = Π ( D / 2 ) 2 , D It is the diameter of the pile, ∆ s (z) is the pile-soil relative displacement at depth z.

[0043] Step 3.2, for the formula The parameters in the model are derived and simplified to obtain the second derivative calculated by Terzaghi's consolidation theory based on the hydro-mechanical equivalence principle: (5), in, α β and w1 are parameters of the calculation model, w1 is the moisture content after humidification, w0 is the initial moisture content, and w1 is the initial moisture content. p denoted as the soil's plastic limit water content, p0 as the initial pressure exerted on the soil, and z1 as the settlement depth to be calculated when the loess collapses. H It refers to the thickness of the soil layer; E s The compression modulus of the soil layer; Tv As a time factor, Tv = C v t / H 2 , Cv d is the consolidation coefficient, t is the consolidation time; dz1 is the vertical displacement at depth z1; S s 湿陷 The soil settlement prediction curve is represented by Terzaghi's consolidation theory based on the principle of water-mechanical equivalence. This represents the second-order differential with respect to depth z1; S s 地裂缝This represents the differential settlement curve of ground fissures based on the error function. This represents the second-order derivative with respect to depth z2, used to describe the curvature characteristics of the soil settlement prediction curve as a function of depth z2.

[0044] The second derivative of the differential settlement curve of ground fissures based on the error function is: (6), Where: z2 is the desired settlement depth. d z2 represents the vertical displacement at depth z2, h represents the vertical displacement of the hanging wall of the bedrock, and H represents the soil layer thickness. δ B is the displacement angle of the rigid body. z2 The shape factor is independent of depth, X is the horizontal distance coordinate, and S is the depth coefficient. s 地裂缝 This represents the differential settlement curve of ground fissures based on the error function. This represents the second-order derivative with respect to depth z2, used to describe the curvature characteristics of the soil settlement prediction curve as a function of depth z2.

[0045] Step 3.3: Finally, the pile side friction resistance of the ground fissure in the collapsible loess area, 5m away from the ground fissure and 20m deep, can be calculated. The expression (7) is as follows: (7).

[0046] The structures, proportions, and sizes illustrated in the accompanying drawings are merely for illustrative purposes and to aid those skilled in the art in understanding and reading the invention. They are not intended to limit the scope of the invention and therefore have no substantial technical significance. Any modifications to the structure, changes in proportions, or adjustments to size, without affecting the effectiveness and purpose of the invention, should still fall within the scope of the technical content disclosed herein. Furthermore, the terms "upper," "lower," "left," "right," "middle," and "one" used in this specification are merely for clarity and not intended to limit the scope of the invention. Changes or adjustments to their relative relationships, without substantially altering the technical content, should also be considered within the scope of the invention.

Claims

1. A method for calculating the negative skin friction of pile foundations in simulated ground fissure areas of collapsible loess regions, characterized in that, Includes the following steps: Step 1.1: Prepare loess samples with different gradient moisture contents. Conduct one-dimensional consolidation tests on samples with different initial dry densities and moisture contents. After the samples stabilize, apply loads step by step and plot the PS curve (vertical pressure-soil sample vertical compression curve). Obtain the humidification deformation Δs1 and the humidification equivalent pressure ΔP under the initial pressure P0 and humidification Δw1. Fit the equivalent formula of collapsible loess based on the hydraulic equivalence principle. Step 1.2: Substitute the hydraulic equivalent parameters α and β into Terzaghi's one-dimensional consolidation theory to obtain the formula for the settlement of loess at different thicknesses under the hydraulic equivalent model. Step 1.3: Obtain the basic parameters of the ground fissure site and establish a finite element model. Simulate the differential settlement movement of the ground fissure through the finite element model and obtain the differential settlement curve of the strata. Step 1.4: Substitute the settlement curves of each stratum obtained in Step 1.3 into the error function to calculate the settlement deformation of the soil layer at a specific depth and distance from the ground fissure. Assume that the shape parameter B is inversely proportional to the distance between the soil and the bedrock interface, and the shape parameter C is inversely proportional to the dip angle of the bedrock fault plane, and obtain a simplified expression for the error function. Step 1.5: Based on the single pile load transfer model, derive the displacement expression at the z-depth of the pile foundation and the pile-soil relative displacement expression. Combined with the soil layer displacement under loess collapsibility and ground fissure activity, calculate the expression for the negative skin friction of the pile foundation. Step 1.6: Repeat the calculation to obtain the negative skin friction of the pile foundation at various distances from the ground fissure.

2. The method for calculating the negative skin friction of pile foundations in simulated collapsible loess areas with ground fissures, as described in claim 1, is characterized in that... The equivalent formula in step 1.1 is: （1） Where α and β are parameters of the calculation model, ΔP is the humidification equivalent effect, w1 is the moisture content after humidification, w0 is the initial moisture content, and w p P0 is the soil's plastic limit water content, and P0 is the initial pressure exerted on the soil.

3. The method for calculating the negative skin friction of pile foundations in simulated collapsible loess areas with ground fissures, as described in claim 1, is characterized in that... The settlement formula in step 1.2 is as follows: （2） Where z1 is the settlement depth calculated for loess collapse, α and β are parameters of the calculation model, w1 is the moisture content after humidification, w0 is the initial moisture content, and w p P0 is the plastic limit water content of the soil, and P0 is the initial pressure exerted on the soil. H It refers to the thickness of the soil layer; E s The compression modulus of the soil layer; T v As a time factor, Tv=C v t / H 2 , Cv Here, t is the consolidation coefficient, and t is the consolidation time. M = Π ( 2m +1) / 2, where m is a non-negative integer.

4. The method for calculating the negative skin friction of pile foundations in simulated collapsible loess areas with ground fissures, as described in claim 3, is characterized in that... The compression modulus Es of the soil layer was determined by indoor compression test in the "Standard for Geotechnical Testing Methods" GB / T 50123-2019, and the consolidation coefficient Cv was calculated based on the square root time method by indoor lateral confinement test.

5. The method for calculating the negative skin friction of pile foundations in simulated collapsible loess areas with ground fissures, as described in claim 1, is characterized in that... The error function expression in step 1.4 is as follows: ( B z2 ＞0) （3） in: d z2 The depth z during ground fissure activity 2 The vertical displacement at point H is the vertical displacement of the hanging wall of the bedrock, and H is the soil layer thickness. δ B is the displacement angle of the rigid body. z2 Z is the shape coefficient that does not change with depth, X is the horizontal distance coordinate, and z2 is the depth of the ground fissure site settlement to be determined.

6. The method for calculating the negative skin friction of pile foundations in simulated collapsible loess areas with ground fissures, as described in claim 5, is characterized in that... In step 1.4, the second derivative of the differential settlement curve of the ground fissure based on the error function is: （4） Where z2 is the desired settlement depth. d z2 represents the vertical displacement at depth z2, h represents the vertical displacement of the hanging wall of the bedrock, and H represents the soil layer thickness. δ B is the displacement angle of the rigid body. z2 The shape factor is independent of depth, X is the horizontal distance coordinate, and S is the depth coefficient. s 地裂缝 This represents the differential settlement curve of ground fissures based on the error function. This represents the second-order derivative with respect to depth z2, used to describe the curvature characteristics of the soil settlement prediction curve as a function of depth z2.

7. The method for calculating the negative skin friction of pile foundations in simulated collapsible loess areas with ground fissures, as described in claim 1, is characterized in that... The displacement expression for the pile foundation at depth z in step 1.5 is as follows: （5） in, S p (z) is the displacement at point z of the pile foundation. S (0) is the pile top displacement. P (z) is the axial force at depth z. EA It refers to the axial stiffness of the pile.

8. The method for calculating the negative skin friction of pile foundations in simulated collapsible loess areas with ground fissures, as described in claim 1, is characterized in that... The expression for the pile-soil relative displacement in step 1.5 is as follows: （6） Where, ∆ s (z) is the relative displacement between the pile and the soil at depth z. S s (z) The relative displacement of the soil layer at depth z under loess collapse and ground fissure activity.

9. The method for calculating the negative skin friction of pile foundations in simulated collapsible loess areas with ground fissures, as described in claim 1, is characterized in that... The expression for the negative skin friction of the pile foundation in step 1.5 is as follows: （7） in, E It is the elastic modulus of the pile. A It is the cross-sectional area of ​​the pile. For a circular pile, A = Π ( D / 2 ) 2 , D It is the diameter of the pile, ∆ s (z) is the pile-soil relative displacement at depth z. This represents the second-order differential with respect to depth z, used to describe the pile-soil relative displacement ∆. s (z) Curvature characteristics as a function of depth z.

10. The method for calculating the negative skin friction of pile foundations in simulated collapsible loess areas with ground fissures, as described in claim 3, is characterized in that... Differentiating and simplifying the displacement expression (2) at point z of the pile foundation, we obtain the second derivative calculated by Terzaghi's consolidation theory based on the principle of water-mechanical equivalence, as shown in the following formula: （8） in, α β and w1 are parameters of the calculation model, w1 is the moisture content after humidification, w0 is the initial moisture content, and w1 is the initial moisture content. p denoted as the soil's plastic limit water content, p0 as the initial pressure exerted on the soil, and z1 as the settlement depth to be calculated when the loess collapses. H It refers to the thickness of the soil layer; E s The compression modulus of the soil layer; TV As a time factor, Tv=C v t / H 2 t is the consolidation time. C v is the consolidation coefficient; dz1 is the vertical displacement at depth z1; S s 湿陷 The soil settlement prediction curve is represented by Terzaghi's consolidation theory based on the principle of water-mechanical equivalence. This represents the second-order differential at depth z1; S s 地裂缝 This represents the differential settlement curve of ground fissures based on the error function. This represents the second-order derivative with respect to depth z2, used to describe the curvature characteristics of the soil settlement prediction curve as a function of depth z2.

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