A method for estimating the value of a foundation level resistance coefficient proportionality coefficient m

Abstract

This invention discloses a method for estimating the proportionality coefficient m of the foundation horizontal resistance coefficient, comprising the following steps: determining the foundation parameters of the pile foundation and the foundation parameters of the soil layer; establishing a calculation expression for the proportionality coefficient m of the foundation horizontal resistance coefficient; providing an initial value for the proportionality coefficient m of the foundation horizontal resistance coefficient; calculating the dimensionless coefficient of the horizontal displacement at the pile top and the horizontal deformation coefficient at the pile top; obtaining the data set of the depth along the pile body below the ground and the corresponding horizontal displacement; determining the horizontal displacement x at the depth l0 of the first zero point of the deflection curve and the depth z1 = l0 / 2. z1 ; with z1 and x z1 Substitute the values ​​into the calculation expression to obtain the calculated value of m, denoted as m. c1 ; for the obtained m c1 Perform error analysis on the value; if the error condition is met, then take m. c1 As the final result; if the error condition is not met, the initial value m0 of the proportional coefficient m of the foundation horizontal resistance coefficient is adjusted, and the above calculation is repeated until the error condition is met. This method can directly calculate the m value of the foundation soil from the shear strength parameter.

Description

Technical Field

[0001] This invention belongs to the field of geotechnical engineering technology, and in particular relates to a method for estimating the proportional coefficient m of the foundation horizontal resistance coefficient. Background Technology

[0002] my country's coastal areas are widely covered by soft soils characterized by high compressibility, medium-to-high sensitivity, and low strength. Soft soil foundations are characterized by low bearing capacity and long settlement times. This region is economically developed, with significant demand for infrastructure construction such as railways. Due to the advantages of pile foundations in controlling deformation and improving bearing capacity, they are widely used as foundations for bridges and buildings. Common analytical methods for the internal forces and deformations of horizontally loaded piles include the m-method, k-method, c-method, and py-curve method. Currently, the m-method is the most commonly used in my country's railway, highway, port, and construction industries. The core calculation parameter of this method is the proportionality coefficient m-value (hereinafter referred to as "m-value") of the foundation's horizontal resistance coefficient. The rationality of its value directly affects the accuracy of the m-method calculation results, the economy of pile foundation design, and the safety of bridge and other superstructures.

[0003] Based on research of actual cases, it was found that due to the strict deformation control of high-speed railway bridges, the value of m is subject to "subjective" reduction in the design of pile foundations for high-speed railway bridges in soft soil areas along the coast of China. Although practice has proven that using a conservative reduced value of m for pile foundation design in soft soil areas provides sufficient stiffness to meet the safety requirements of high-speed railway operation, the significant reduction of the m design value and the unclear basis for it, while meeting the horizontal stiffness requirements, inevitably increases the number and diameter of piles, thus leading to uneconomical results.

[0004] As is well known, shear strength parameters (c, φ) are the most common soil property testing parameters, and relatively easy to obtain, whether in geological exploration, in-situ testing, or laboratory experiments. Therefore, obtaining a formula to directly determine the value of m from c and φ would undoubtedly be very convenient for engineering applications. Summary of the Invention

[0005] The main objective of this invention is to provide a method for estimating the proportional coefficient m of the foundation horizontal resistance coefficient. This method is based on Rankine's passive earth pressure theory and the mechanical principle of the "m" method for pile side soil resistance. It derives the expression for calculating the proportional coefficient of the foundation reaction coefficient, which can directly calculate the m value from the shear strength parameter, providing a reference for the design of high-speed railway bridge pile foundations in deep soft soil areas.

[0006] Therefore, the present invention provides a method for estimating the proportionality coefficient m of the foundation horizontal resistance coefficient, comprising the following steps:

[0007] S1. Determine the foundation parameters of the pile foundation and the foundation parameters of the soil layer;

[0008] S2. Establish the calculation expression for the proportional coefficient m of the foundation horizontal resistance coefficient;

[0009] S3, the initial value of m0 for the given foundation horizontal resistance coefficient proportionality coefficient m;

[0010] S4. Calculate the dimensionless coefficient A of the horizontal displacement at the pile top. x and the horizontal deformation coefficient α at the pile top;

[0011] S5. Based on the deflection curve equation of the horizontally loaded pile in the relevant technical specifications, obtain the data set (z,x) of the depth along the pile body below the ground and the corresponding horizontal displacement.

[0012] S6. Determine the horizontal displacement x at the depth l0 of the first zero point of the deflection curve and the depth z1 = l0 / 2. z1 ;

[0013] S7, combine z1 and x z1 Substitute the values ​​into the calculation expression to obtain the calculated value of m, denoted as m. c1 ;

[0014] S8, regarding the obtained m c1 Perform error analysis on the values;

[0015] S9. If the error condition is met, then take m. c1 As the final result; if the error condition is not met, adjust the initial value m0 of the proportional coefficient m of the foundation horizontal resistance coefficient and repeat the above calculation until the error condition is met.

[0016] Specifically, using Rankine's passive earth pressure theory, the formula for calculating the proportionality coefficient m of the foundation horizontal resistance coefficient is as follows:

[0017]

[0018] In the formula, m is the proportional coefficient of the foundation horizontal resistance coefficient; b is the converted width of the retaining wall, taken as the diameter or width of the pile; b0 is the calculated width of the pile; x is the horizontal displacement of the pile at a certain depth z; γ is the unit weight of the soil around the pile; K p is Rankine's passive earth pressure coefficient; c is the cohesion of the soil around the pile.

[0019] Specifically, the derivation process of the expression for calculating the value of m based on Rankine's passive earth pressure theory is as follows:

[0020] Simplifying the soil around the pile as a nonlinearly discretely distributed spring, neglecting the adhesion and skin friction between the pile and the soil. Assuming the tensile strength of the soil is zero, i.e., the spring is only under compression and not tension, it can be concluded that the horizontal soil resistance p at any depth z along the pile side below the ground is proportional to the horizontal displacement x at that point, i.e.:

[0021] p=k(z)xb0 (2)

[0022] In the formula, k(z) is the horizontal foundation reaction coefficient of the pile. Currently, the most commonly used method to express k(z) is the m-method, and k(z) is shown in equation (3):

[0023] k(z)=mz (3)

[0024] Substituting equation (3) into equation (2), we get:

[0025] p=mzxb0 (4)

[0026] According to the current relevant technical specifications, b0 can be determined according to formula (5):

[0027] b0 = K f K0Kb (5)

[0028] In the formula, b is the width (or diameter) of the pile on a plane perpendicular to the direction of the external force H; K f K is the shape conversion factor; K0 is the stress conversion factor (i.e., the correction factor given when the soil on the side of the pile is actually subjected to a spatial stress problem when bearing a horizontal load, and simplified to a planar stress problem); K is the mutual influence factor between piles.

[0029] Since it is assumed that there is no friction between the wall and the soil, σ z σ x These are the major (minor) and minor (major) principal stresses, where σ z =γz,σ x This refers to earth pressure. During the process where the wall rotates towards the soil due to some force, causing displacement and compressing the soil, σ... x As it grows larger, the horizontal σ reaches a state of limiting equilibrium. x >Vertical pressure σ z , σ x Transformed into major principal stress σ1, vertical compressive stress σ z For minor principal stress σ3, when they reach limit equilibrium, they satisfy the limit equilibrium condition equation, that is:

[0030]

[0031] This gives us the passive earth pressure P of Rankine. p The calculation formula is as follows:

[0032]

[0033] c represents the cohesion of the soil layer. Let be the internal friction angle of the soil layer. Then we have:

[0034]

[0035] Combining equations (4) and (8), we obtain the expression for calculating the proportional coefficient m of the foundation horizontal resistance coefficient:

[0036]

[0037] After sorting, we can obtain c, The expression for calculating m is:

[0038]

[0039] Specifically, the arbitrary given initial m0 value is determined in combination with the geological data of the pile's location and relevant technical specifications.

[0040] Specifically, the basic parameters of the pile foundation include pile length, pile diameter, elastic modulus, and bending stiffness, while the basic parameters of the soil layer include soil unit weight, internal friction angle, cohesion, and Rankine passive earth pressure coefficient.

[0041] Specifically, the formula for calculating the horizontal deformation coefficient α at the pile top is:

[0042]

[0043] In the formula, EI is the bending stiffness of the pile.

[0044] Ax is the deformation calculation constant for the pile, and it is a dimensionless coefficient. This refers to Ax in the "Technical Specification for Building Pile Foundations JGJ 94-2008". x Fitting the data set with the αz dataset yields A x The fitting relationship between αz (α×z) and αz is as follows:

[0045] A x =0.0052(αz) 5 -0.0653(αz) 4 +0.2523(αz) 3 -0.0545(αz) 2 -1.6078(αz)+2.4404(11)

[0046] The square of the similarity coefficient R 2 =0.9999.

[0047] Specifically, the expression for calculating the horizontal displacement of the pile interface at any depth z along the pile body is as follows:

[0048]

[0049] In the formula, H0 is the critical load of the pile, EI is the bending stiffness of the pile, E is the elastic modulus of the pile, and I is the equivalent section spacing of the pile. The critical load of the pile can be calculated according to formula (13).

[0050]

[0051] In the formula, x0 is the allowable displacement at the pile top, and v x This is the horizontal displacement coefficient.

[0052] Specifically, by setting equation (12) to 0, the depth l0 of the first zero point of the deflection curve can be calculated, and the horizontal displacement x at z1 = l0 / 2 can be calculated accordingly. z1 .

[0053] Specifically, the (z1, x) obtained in step S6 z1 Substituting into equation (1), we obtain the calculated value of m, denoted as m. c1 .

[0054] Specifically, for m c1 Error analysis is performed, and the allowable relative calculation error is |(m) c1 -m0) / m0×100%︱<2%. If m c1 If it is close to m0 or within the acceptable error range, then m0 or m can be considered. c1 Alternatively, the arithmetic mean of the two can be used as the proportionality coefficient of the foundation reaction coefficient at this work site. If the error is not met, the initial m value needs to be adjusted and steps S5, S6, S7, and S8 need to be repeated.

[0055] Specifically, regarding the principle for readjusting the initial value of m, if m = 0... <m c1 If m0 > m c1 If so, reduce m0 appropriately and then calculate; or directly take m0 and m c1 The arithmetic mean is used as the initial value of m before calculation.

[0056] Compared with existing technologies, this invention has the following beneficial effects: Based on Rankine's passive earth pressure theory and the mechanical principle of the "m" method for pile side soil resistance, this invention also considers the rationality of using soil shear strength parameters to predict the value of m, overcoming the "subjectivity" reduction in the traditional method of determining the value of m, and avoiding the complex and lengthy process of determining the value of m in the traditional method. By directly predicting the value of m using easily obtainable soil shear strength parameters in actual engineering, it can provide a reliable reference for determining the value of the proportional coefficient of the foundation reaction coefficient m in deep soft soil, and provide theoretical support for the design of high-speed railway bridge pile foundations in deep soft soil areas. It can also provide theoretical methods for determining the value of m in the design of railway and highway bridge pile foundations and provide a reference for the revision of relevant technical specifications. Attached Figure Description

[0057] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0058] Figure 1 This is a flowchart of the estimation method provided in the embodiments of the present invention;

[0059] Figure 2 This is a schematic diagram showing the distribution and shape of pile side resistance and passive earth pressure in an embodiment of the present invention. Detailed Implementation

[0060] 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.

[0061] like Figure 1 As shown, the method for predicting the proportional coefficient m of the foundation horizontal resistance coefficient provided in this embodiment of the invention includes the following steps:

[0062] S1. Determine the foundation parameters of the pile foundation and the foundation parameters of the soil layer; among which, the foundation parameters of the pile foundation include pile length, pile diameter, elastic modulus, and bending stiffness, and the foundation parameters of the soil layer include soil unit weight, internal friction angle, cohesion, and Rankine passive earth pressure coefficient.

[0063] S2. Establish the calculation expression for the proportionality coefficient m of the foundation horizontal resistance coefficient; using Rankine's passive earth pressure theory, the calculation expression for the proportionality coefficient m of the foundation horizontal resistance coefficient is as follows:

[0064]

[0065] In the formula, m is the proportional coefficient of the foundation horizontal resistance coefficient; b is the converted width of the retaining wall, taken as the diameter or width of the pile; b0 is the calculated width of the pile; x is the horizontal displacement of the pile at a certain depth z; γ is the unit weight of the soil around the pile; K p is Rankine's passive earth pressure coefficient; c is the cohesion of the soil around the pile.

[0066] The specific derivation process of the calculation expression for the proportionality coefficient m of the foundation horizontal resistance coefficient is as follows, based on Rankine's passive earth pressure theory:

[0067] Simplifying the soil around the pile as a nonlinearly discretely distributed spring, neglecting the adhesion and skin friction between the pile and the soil. Assuming the tensile strength of the soil is zero, i.e., the spring is only under compression and not tension, it can be concluded that the horizontal soil resistance p at any depth z along the pile side below the ground is proportional to the horizontal displacement x at that point, i.e.:

[0068] p=k(z)xb0 (2)

[0069] In the formula, k(z) is the horizontal foundation reaction coefficient of the pile. Currently, the most commonly used method to express k(z) is the m-method, and k(z) is shown in equation (3):

[0070] k(z)=mz (3)

[0071] Substituting equation (3) into equation (2), we get:

[0072] p=mzxb0 (4)

[0073] According to the current relevant technical specifications, b0 can be determined according to formula (5):

[0074] b0 = K f K0Kb (5)

[0075] In the formula, b is the width (or diameter) of the pile on a plane perpendicular to the direction of the external force H; K f K is the shape conversion factor; K0 is the stress conversion factor (i.e., the correction factor given when the soil on the side of the pile is actually subjected to a spatial stress problem when bearing a horizontal load, and simplified to a planar stress problem); K is the mutual influence factor between piles.

[0076] Since it is assumed that there is no friction between the wall and the soil, σ z σ x These are the major (minor) and minor (major) principal stresses, where σ z =γz,σ x This refers to earth pressure. During the process where the wall rotates towards the soil due to some force, causing displacement and compressing the soil, σ... x As it grows larger, the horizontal σ reaches a state of limiting equilibrium. x >Vertical pressure σ z , σ x Transformed into major principal stress σ1, vertical compressive stress σ z For minor principal stress σ3, when they reach limit equilibrium, they satisfy the limit equilibrium condition equation, that is:

[0077]

[0078] This gives us the passive earth pressure P of Rankine. p The calculation formula is as follows:

[0079]

[0080] c represents the cohesion of the soil layer. Let be the internal friction angle of the soil layer. Then we have:

[0081]

[0082] Combining equations (4) and (8), we obtain the expression for calculating the proportional coefficient m of the foundation horizontal resistance coefficient:

[0083]

[0084] After sorting, we can obtain c, The expression for calculating m is as follows:

[0085]

[0086] S3. The initial value of the proportional coefficient m for the foundation horizontal resistance coefficient is given; the initial value of m0 is determined by combining the geological data of the pile location and relevant technical specifications.

[0087] S4. Calculate the dimensionless coefficient A of the horizontal displacement at the pile top. x And the horizontal deformation coefficient α at the pile top; the expression for calculating the horizontal deformation coefficient α at the pile top is:

[0088]

[0089] In the formula, EI is the bending stiffness of the pile.

[0090] A x Let be the deformation calculation constant for the pile, and be a dimensionless coefficient. This applies to section A of the "Technical Specification for Building Pile Foundations JGJ 94-2008". x Fitting the data set with the αz dataset yields A x The fitting relationship between αz and αz is:

[0091] A x =0.0052(αz) 5 -0.0653(αz) 4 +0.2523(αz) 3 -0.0545(αz) 2 -1.6078(αz)+2.4404(11)

[0092] The square of the similarity coefficient R 2 =0.9999.

[0093] S5. Based on the deflection curve equation of a horizontally loaded pile in the relevant technical specifications, obtain the data set (z, x) of the depth along the pile body below the ground and the corresponding horizontal displacement; the expression for calculating the horizontal displacement of the pile body interface at any depth z along the pile body is as follows:

[0094]

[0095] In the formula, H0 is the critical load of the pile, EI is the bending stiffness of the pile, E is the elastic modulus of the pile, and I is the equivalent section spacing of the pile. The critical load of the pile can be calculated according to formula (13).

[0096]

[0097] In the formula, x0 is the allowable displacement at the pile top, and v x This is the horizontal displacement coefficient.

[0098] S6. Determine the horizontal displacement x at the depth l0 of the first zero point of the deflection curve and the depth z1 = l0 / 2. z1 ; By setting x(z) in equation (12) to 0, the depth l0 of the first zero point of the deflection curve is calculated, and the horizontal displacement x at z1 = l0 / 2 is calculated accordingly. z1 .

[0099] S7. Based on the proposed formula for calculating the proportional coefficient m of the horizontal resistance coefficient, calculate (z1, x z1 ) of m c1 Value; the (z1, x) obtained in step S6 z1 Substituting into equation (1), we obtain the calculated value of m, denoted as m. c1 .

[0100] S8, regarding the obtained m c1 Perform error analysis on the value; for m c1 Error analysis is performed, and the allowable relative calculation error is |(m) c1 -m0) / m0×100%︱<2%. If m c1 If it is close to m0 or within the acceptable error range, then m0 or m can be considered. c1 Alternatively, the arithmetic mean of the two can be used as the proportionality coefficient of the foundation reaction coefficient at this work site. If the error is not met, the initial m value needs to be adjusted and steps S5, S6, S7, and S8 need to be repeated.

[0101] S9. Adjust the initial value m0 of the proportional coefficient m for the foundation horizontal resistance coefficient. The principle for readjusting the initial value of m is that if m0... <m c1 If m0 > m c1 If so, reduce m0 appropriately and then calculate; or directly take m0 and m c1 The arithmetic mean is used as the initial value of m before calculation.

[0102] Compared with existing methods, this application has the following advantages:

[0103] This invention is based on Rankine's passive earth pressure theory and the mechanical principle of the "m" method for pile side soil resistance. It also considers the rationality of using soil shear strength parameters to estimate the value of m, overcomes the "subjectivity" reduction of the m value in traditional methods, and avoids the complex and lengthy process of determining the m value in traditional methods. By directly estimating the m value using soil shear strength parameters that are readily available in actual engineering, it can provide a reliable reference for determining the m value of the foundation reaction coefficient proportionality coefficient in deep soft soil, and at the same time provide theoretical support for the design of high-speed railway bridge pile foundations in deep soft soil areas.

[0104] This invention, based on a derived expression for calculating the proportional coefficient m of the foundation reaction coefficient, enables the direct calculation of the m value from the soil's shear strength parameters. This will facilitate the reasonable and convenient selection of the m value in high-speed railway bridge pile foundation engineering. Combining Rankine's passive earth pressure theory, this invention establishes a calculation expression for directly calculating the m value from the soil's shear strength parameters, avoiding the shortcomings of traditional static load testing methods such as long test cycles, high test costs, and the reduction due to "subjectivity," thus improving calculation efficiency and providing high prediction accuracy. This method can provide theoretical support for the design of high-speed railway bridge pile foundations in deep soft soil areas.

[0105] Engineering Cases

[0106] Project Background: The Jinyong Railway is a railway line connecting Jinhua and Ningbo, primarily a Class I double-track railway for both passenger and freight transport. The design speed is 160 km / h, with provisions for future upgrades to 200 km / h. The line passes through the deep soft soil region of Ningbo. The Ningbo area is located on an alluvial plain, with flat and open terrain and widespread distribution of soft soil (mainly silty clay), characterized by its large thickness (25-39m), high water content, high compressibility, and poor permeability. Its unfavorable engineering geological characteristics are mainly manifested in its thixotropy, high compressibility, high sensitivity, and low strength, resulting in low horizontal resistance of the foundation and complex pile-soil interactions. This places more stringent requirements on the horizontal bearing capacity and deformation control of bridge foundations. This test site was selected near pier #16 of the Yinfeng Grand Bridge on the Jinyong Railway for relevant experimental research.

[0107] The terrain of the Yinfeng Grand Bridge site, from DK0+699.05 to DK6+391.84, is a flat alluvial plain. The strata at the site of the selected pier No. 16 (DK001+127.290) are silty clay. According to the engineering geological survey report, the specific soil layers are described as follows:

[0108] Silty clay (Q4) m Gray, fluid-plastic, containing organic matter and humus, with local thin layers of silt and silt. Distributed throughout the site, with a layer thickness of 25.2–39.0 m, and the average measured SPT blow count is [missing information]. The natural moisture content W = 48.49% (range: 33.7%–72.0%), the natural porosity e = 1.384 (range: 1.01–2.096), and the liquidity index I... L =1.08 (range: 0.76~1.40), mean elastic modulus E s =2.22MPa (range: 1.24-3.61MPa).

[0109] S1. Determine the foundation parameters for the pile foundation and the foundation parameters for the deep soft soil. The basic parameters for the pile are: pile length l = 60m, pile diameter b = 1m, and C40 concrete is used. For a circular single pile with a diameter of 1m, K f =0.9. When the pile diameter d ≥ 1m, K0 = (d + 1) / d = 2m. For the horizontal static load test of a single pile, K = 1. Therefore, its calculated width b0 = 1.8m, elastic modulus E = 34GPa, and equivalent section moment I = 0.0427m. 4 The bending stiffness of the pile section is EI = 0.8E·I = 1161113 kN·m 2 The shear strength parameters and Rankine passive earth pressure coefficient of the soft soil layer are cohesion c = 8.78 kPa and internal friction angle, respectively. Soil weight γ = 17.2 kN / cm 3 The passive earth pressure coefficient K of Rankine was calculated. p =1.14.

[0110] S2. Using Rankine's passive earth pressure theory, the calculation expression for the proportional coefficient m of the foundation horizontal resistance coefficient is established as shown in equation (1):

[0111]

[0112] In the formula, m is the proportional coefficient of the soil's horizontal resistance coefficient; b is the converted width of the retaining wall, taken as the diameter or width of the pile; b0 is the calculated width of the pile; x is the horizontal displacement of the pile at a certain depth z; γ is the unit weight of the soil surrounding the pile; K p is Rankine's passive earth pressure coefficient; c is the cohesion of the soil around the pile.

[0113] S3. Since the silty clay layer at this work site is 37.1m thick and the pile length is 60m, it can be preliminarily determined that the proportional coefficient of the pile side subgrade coefficient under horizontal working loads only needs to consider the silty clay layer. Therefore, the initial value of m can be set based on the properties of the silty clay at this work site and combined with the empirical values ​​of m for soft soil (silt, silty soil, and fluid plastic clay) in the main technical specifications of various industries in China. The recommended value of 3000-5000 kN / m is referenced from railway and highway specifications. 4In this case study, the initial value of the foundation coefficient ratio was taken as the median value of 4000 kN / m. 4 .

[0114] S4. According to equation (10), the horizontal deformation coefficient α at the pile top is calculated to be 0.3618m. -1 A at different depths z x Then calculate according to equation (11), or refer to the relevant technical specifications ("Technical Specification for Building Pile Foundations JGJ94-2008"). The horizontal critical load of the pile foundation is determined according to equation (13), where the allowable displacement x0 at the pile top is 6mm, and the horizontal displacement coefficient v x We take 2.441. Therefore, we calculate H0 = 135.19 kN.

[0115] S5. According to equation (12), the horizontal displacement x at any depth z along the pile can be obtained. z .

[0116] S6, such as Figure 2 As shown, we can set the left side of equation (10) to 0 and calculate z = 0 (discarded) or 6.67m, i.e., l0 = 6.67. From this, we get z1 = l0 / 2 = 3.37m. Substituting z1 = 3.37 into equation (12), we can calculate x. z1 =1.82mm.

[0117] S7. Substituting (3.37, 1.82) into equation (1), we can calculate m. c1 =7572kN / m 4 .

[0118] S8, At this point, the relative calculation error |(m) c1 -m0) / m0×100%︱=89.3%. The error condition is not met, and the initial m0 needs to be readjusted.

[0119] S9. Take m0 = 5000, 6000, 6500, 7000, 7500, 7600, and 7700 kN / m respectively. 4 ,count

[0120] The calculated m c1 The values ​​are 7650, 7716, 7746, 7774, 7780, 7805, and 7810 kN / m, respectively. 4 The relative calculation errors were 53%, 28.6%, 19.2%, 11.1%, 3.7%, 2.7%, and 1.4%, respectively. Considering an allowable relative calculation error of <2%, m would then be between 7700 and 7810 kN / m. 4 Between these two values ​​(where the error is only about 1%), the average of the two values ​​is taken as the final result, and the value of m is 7755.1 kN / m. 4 .

[0121] The static load test of a single pile at the site of the railway bridge pile foundation project at this construction site showed that the m value when the horizontal displacement of the pile top was 6mm was 6416~9160kN / m. 4 The average value is 7788 kN / m 4 As can be seen, the calculation results obtained from the formula derived in this paper are very close to the field measurements. This demonstrates the reliability of the formula derived in this paper.

[0122] The above embodiments are merely illustrative examples to clearly illustrate the present invention and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all embodiments here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A method for estimating the proportionality coefficient m of the foundation horizontal resistance coefficient, characterized in that, Includes the following steps: S1. Determine the foundation parameters of the pile foundation and the foundation parameters of the soil layer; S2. Based on Rankine's passive earth pressure theory, establish a calculation expression for the proportional coefficient m of the foundation horizontal resistance coefficient; S3, the initial value of m0 for the given foundation horizontal resistance coefficient proportionality coefficient m; S4. Calculate the dimensionless coefficient A of the horizontal displacement at the pile top. x and the horizontal deformation coefficient α at the pile top; S5. Based on the deflection curve equation of the horizontally loaded pile, obtain the data set (z, x) of the depth z along the pile body below the ground and the corresponding horizontal displacement x. S6. Determine the depth l0 of the first zero point of the deflection curve and the horizontal displacement x at the depth z1 = l0 / 2. z1 ; S7, combine z1 and x z1 Substitute the values ​​into the calculation expression to obtain the calculated value of m, denoted as m. c1 ; S8, regarding the obtained m c1 Perform error analysis on the values; S9. If the error condition is met, then take m. c1 As a final result; If the error condition is not met, adjust the initial value m0 of the proportional coefficient m of the foundation horizontal resistance coefficient and repeat the above calculation until the error condition is met. The formula for calculating the proportionality coefficient m of the foundation horizontal resistance coefficient is: （1）； In the formula, m is the proportional coefficient of the foundation horizontal resistance coefficient; b is the converted width of the retaining wall, taken as the diameter or width of the pile; b0 is the calculated width of the pile; x is the horizontal displacement of the pile at a certain depth z; γ is the unit weight of the soil around the pile; K p is Rankine's passive earth pressure coefficient; c is the cohesion of the soil around the pile; The specific derivation process of the expression for calculating the proportional coefficient m of the foundation horizontal resistance coefficient is as follows: Simplifying the soil around the pile as a nonlinearly discretely distributed spring, neglecting the adhesion and skin friction between the pile and the soil, and assuming the tensile strength of the soil is zero (i.e., the spring is only under compression and not tension), we find that the horizontal soil resistance p at any depth z along the pile side below the ground is proportional to the horizontal displacement x at that point, i.e.: （2）； In the formula, k(z) is the horizontal foundation reaction coefficient of the pile, and the expression of k(z) is shown in equation (3): （3）； Substituting equation (3) into equation (2), we get: （4）； According to current relevant technical specifications, b0 is determined by the following formula: （5）； In the formula, b is the width or diameter of the pile on a plane perpendicular to the direction of the external force H; K f K is the shape conversion factor; K0 is the stress conversion factor; K is the mutual influence factor between piles; Since it is assumed that there is no friction between the wall and the soil, σ z =γz,σ x As earth pressure, during the process where the wall rotates towards the soil due to some force, causing displacement and compressing the soil, σ x As it grows larger, the horizontal σ reaches a state of limiting equilibrium. x Greater than vertical stress σ z , σ x Transformed into major principal stress σ1 and vertical stress σ z For minor principal stress σ3, when they reach limit equilibrium, they satisfy the limit equilibrium condition equation, that is: （6）； This gives us the passive earth pressure p of Rankine. p The calculation formula is as follows: （7）； Where φ is the internal friction angle of the soil layer, let K p =tan 2 (45°+φ / 2), then we have: （8）； Combining equations (4) and (8), we obtain the expression for calculating the proportional coefficient m of the foundation horizontal resistance coefficient: （9）； The expression for calculating m, expressed in terms of c and φ, can be obtained as follows: （1）。 2. The prediction method according to claim 1, characterized in that: The formula for calculating the horizontal deformation coefficient α at the pile top is: （10）； In the formula, EI is the bending stiffness of the pile.

3. The prediction method according to claim 2, characterized in that: Regarding section A of the "Technical Specification for Building Pile Foundations JGJ 94-2008" x Fitting the data set with the αz dataset yields A x The fitting relationship between αz and αz is: （11）； The square of the similarity coefficient R 2 =0.9999.

4. The prediction method according to claim 3, characterized in that: Horizontal displacement of the pile interface at any depth z along the pile: （12）； In the formula, H0 is the critical load of the pile, EI is the bending stiffness of the pile, E is the elastic modulus of the pile, and I is the equivalent section spacing of the pile. The critical load of the pile is calculated according to formula (13): （13）； In the formula, x0 is the allowable displacement at the pile top, and v x This is the horizontal displacement coefficient.

5. The prediction method according to claim 4, characterized in that: Setting equation (12) to 0, the depth l0 of the first zero point of the deflection curve is calculated, and the horizontal displacement x at z1 = l0 / 2 is calculated based on this. z1 The calculated z1 and x z1 Substituting into equation (1), we obtain the calculated value of m, denoted as m. c1 .

6. The estimation method according to any one of claims 1-5, characterized in that: For m c1 Error analysis is performed, and the allowable relative calculation error is |(m) c1 -m0) / m0×100%︱<2%, if m c1 If it is close to m0 or within the acceptable error range, then m0 or m can be considered. c1 Alternatively, the arithmetic mean of the two can be used as the proportional coefficient of the foundation reaction coefficient at this work site. If the error is not met, the initial m0 value should be adjusted and steps S5-S8 should be repeated.

7. The prediction method according to claim 6, characterized in that: The principle for readjusting the initial value of m is that if m = 0... <m c1 If m0 > m c1 If so, reduce m0 appropriately and then calculate; or directly take m0 and m c1 The arithmetic mean is used as the initial value of m before calculation.

8. The prediction method according to claim 7, characterized in that: The foundation parameters of a pile foundation include pile length, pile diameter, elasticity, and bending stiffness. The strength parameters of the soil layer include the unit weight, internal friction angle, cohesion, and Rankine passive earth pressure coefficient.

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