Method for evaluating stability of pile-supported embankment based on additional stress theory

Abstract

This invention discloses a stability evaluation method for pile-supported embankments based on the theory of additional stress, comprising: S1, calculating the trapezoidal embankment load shared by the pile tops; S2, obtaining the initial potential slip surface center, radius, and stability coefficient; S3, decomposing the trapezoidal embankment load into rectangular and triangular loads, and determining the distribution of net horizontal earth pressure on the pile sides; S4, determining the maximum net horizontal thrust that each pile can resist based on the current slip surface center and radius, identifying critical piles and calculating the net horizontal thrust of non-critical piles, characterizing the true progressive failure characteristics of the pile body; S5, calculating the anti-slip moment provided by each pile; S6, converting the anti-slip moment into a comprehensive anti-slip force, and calculating the new potential slip surface center, radius, and stability coefficient; S7, determining whether the difference in stability coefficients calculated in two adjacent iterations is less than a preset threshold. If so, a reasonable evaluation of the overall stability of the pile-supported embankment is performed based on the current stability coefficient; if not, the iteration count is incremented by one, and the process returns to S4.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of road and railway engineering, and particularly relates to a pile-supported embankment stability evaluation method based on additional stress theory. BACKGROUND

[0002] With the rapid development of high-speed railways and highways in soft soil foundations and complex geological conditions, pile-supported embankments are widely used due to their ability to effectively reduce settlement, improve bearing capacity and stability. Pile-supported composite foundations rely on the combined action of piles, inter-pile soil and reinforced mats to resist instability caused by embankment loads, but the problem of lateral anti-sliding stability has not been completely solved.

[0003] Existing composite foundation stability evaluation methods mainly include the BS8006 specification method, composite shear strength method, equivalent shear strength method and the simplified method recommended by the specification. These methods mostly determine the anti-sliding moment through equivalent soil strength or pile ultimate bearing capacity, and fail to systematically consider the combined action of pile top load, pile side soil pressure and reinforcement restraint force. The assumed pile failure mode is usually shear failure, but in actual roadbed engineering, the commonly used rigid pile material has weak tensile capacity and is usually dominated by bending failure. In addition, due to the uneven characteristics of embankment loads, the stress states of each pile under the embankment are different, and their ability to resist external loads is also different, so the pile failure does not occur simultaneously, but has a progressive failure characteristic. If it is assumed that the pile failure occurs simultaneously, the stability will be overestimated. Therefore, the current methods often overestimate the stability of composite foundations.

[0004] On this basis, existing research has proposed a calculation method that combines pile bending resistance and pile top load sharing, such as patent CN115982848B, which proposes an evaluation method based on pile-supported horizontal net thrust coefficient. This method can reflect the progressive failure characteristics of piles at different positions to some extent, but the key parameter—pile-supported horizontal net thrust coefficient is an empirical treatment and lacks a clear physical meaning, making it difficult to accurately describe the influence of soil pressure differences on both sides of the pile on the stress and failure process of the pile.

[0005] In fact, the inter-pile soil under the action of embankment loads will generate unbalanced horizontal soil pressure on both sides of the pile, which is the main reason for the bending failure of the pile. Due to differences in axial force, displacement and stress environment, the failure of piles at different positions does not occur simultaneously, but shows a progressive failure process that gradually expands from the toe pile to the internal pile. How to accurately calculate the net horizontal soil pressure on both sides of the pile from a physical perspective and determine the key pile failure in combination with the bending and axial force conditions of the pile is of great significance for establishing a reasonable stability evaluation method.

[0006] Therefore, there is an urgent need for a pile side net horizontal soil pressure calculation method with clear physical meaning, which can reflect the ultimate bending capacity and progressive failure characteristics of the pile body, and reasonably evaluate the overall stability of the pile-supported embankment. SUMMARY

[0007] In view of the above problems in the prior art, the pile-supported embankment stability evaluation method based on the additional stress theory provided by the present application directly obtains the net horizontal soil pressure on both sides of the pile by calculating the additional stress distribution under the trapezoidal load of the embankment through the Bousinessq solution, and determines the key pile in combination with the bending capacity of the pile body and the axial force condition, thereby realizing reasonable evaluation of the overall stability of the pile-supported embankment, and solving the problems of the existing pile-supported embankment stability evaluation method, i.e., the calculation of the soil pressure on the pile side depends on the empirical coefficient, lacks clear physical meaning, and is difficult to accurately reflect the progressive failure process of the pile body.

[0008] To achieve the above-mentioned purposes, the technical scheme adopted by the present application is as follows: the pile-supported embankment stability evaluation method based on the additional stress theory comprises the following steps:

[0009] S1, obtaining the physical and mechanical indexes of the strength and modulus of the embankment and the foundation, the pile body and the tendon belt, and calculating the trapezoidal embankment load shared by the pile top;

[0010] S2, obtaining the initial potential sliding surface center, radius and stability coefficient when only the tendon belt is set through the circular arc strip method based on the limit equilibrium theory, and initializing the iteration number;

[0011] S3, decomposing the trapezoidal embankment load into rectangular load and triangular load by using the Bousinessq solution, calculating the horizontal additional stress of any point in the foundation, and obtaining the horizontal additional stress difference on both sides of the pile according to the superposition principle, thereby determining the net horizontal soil pressure distribution on the pile side;

[0012] S4, determining the maximum net horizontal thrust that each pile can resist according to the current sliding surface center and radius in combination with the bending strength of the pile section and the axial force condition at the pile top, and taking the maximum net horizontal thrust as the basis to calculate the amplification coefficient under the unit trapezoidal load, thereby determining the key pile, and calculating the net horizontal thrust of the non-key pile according to the amplification coefficient, which represents the real progressive failure characteristics of the pile body;

[0013] S5, based on the net horizontal soil pressure distribution on the pile side, substituting the net horizontal thrust received by each pile and the trapezoidal embankment load shared by the pile top into the pile body anti-sliding moment calculation formula, to obtain the anti-sliding moment provided by each pile;

[0014] S6, converting the anti-sliding moment into comprehensive anti-sliding force according to the shear strength equivalence principle, thereby assigning the equivalent shear strength to the pile element, and calculating the new potential sliding surface center, radius and stability coefficient according to the circular arc strip method of the limit equilibrium theory;

[0015] S7. Determine whether the difference between the current stability coefficient and the new stability coefficient is less than the preset threshold. If yes, complete a reasonable evaluation of the overall stability of the pile-supported embankment based on the current stability coefficient. If no, increment the iteration count by one, use the new potential slip surface center, radius, and stability coefficient as the current potential slip surface center, radius, and stability coefficient, and return to S4.

[0016] Furthermore, S3 includes the following sub-steps:

[0017] S31. Equivalently transform any trapezoidal embankment load into the product of a unit trapezoidal load with a fixed geometric boundary and an amplification factor, and decompose the unit trapezoidal load into a rectangular load and two triangular loads.

[0018] S32. Calculate the horizontal additional stress at any point in the foundation under rectangular load, and calculate the horizontal additional stress at any point in the foundation under triangular load.

[0019] S33. The calculated horizontal additional stress is superimposed according to the superposition principle to obtain the horizontal additional stress at any point in the foundation under the trapezoidal embankment load.

[0020] S34. Subtract the horizontal additional stresses on the left and right sides of the pile to obtain the net horizontal earth pressure distribution on the pile side.

[0021] Furthermore: In S32, calculate the additional horizontal stress at any point in the foundation under a rectangular load. The specific expression is:

[0022]

[0023] In the formula, B The width of the roadbed surface of a full-section trapezoidal embankment. x and z Each point in the foundation is calculated as a separate point. M Distance from the centerline of the embankment and the foundation surface;

[0024] Calculate the horizontal additional stress at any point in the foundation under the first triangular load. The specific expression is:

[0025]

[0026] In the formula, H The height of the embankment, m The slope of the left side of the embankment;

[0027] Calculate the horizontal additional stress at any point in the foundation under the second triangular load. The specific expression is:

[0028]

[0029] In the formula, n The slope of the right side of the embankment;

[0030] In S33, the horizontal additional stress at any point in the foundation under the trapezoidal embankment load is obtained. The specific expression is:

[0031] .

[0032] Furthermore: In S4, calculate the maximum net horizontal thrust that any pile can resist. The specific expression is:

[0033]

[0034] In the formula, M i,max This is the maximum bending moment that the pile can resist under the action of a vertical axial force. This represents the difference in tensile force exerted by the reinforcing bars on the pile top within the longitudinal influence width. This is the lever arm of the tension force of the reinforcing band at the depth of the sliding surface. The height coefficient of the point of application of the net horizontal thrust;

[0035]

[0036] In the formula, W For the section modulus of the pile, f tk The tensile strength of the pile material. A c The cross-sectional area of ​​the pile is... The trapezoidal embankment load shared by the pile top.

[0037] Furthermore: In S4, calculate the amplification factor under a unit trapezoidal load. K The specific expression is:

[0038]

[0039] In the formula, F hk,1 The net horizontal thrust on the side of the critical pile under unit load. F hk,max The maximum net horizontal thrust that the key pile can withstand. F hi,1 The net horizontal thrust at any side of the pile under a unit load; F hi,max This represents the maximum net horizontal thrust that any pile can withstand.

[0040] Furthermore: In S4, the method for calculating the net horizontal earth pressure on non-critical piles is as follows:

[0041] When the critical pile reaches the ultimate limit state, calculate the net horizontal thrust of any pile in the non-ultimate state. ;

[0042] .

[0043] Furthermore: In S5, the anti-sliding moment provided by each pile is calculated. The specific expression is:

[0044]

[0045] In the formula, N i The trapezoidal embankment load distributed at the pile top, R Let be the radius of the sliding surface. α ci Let be the horizontal inclination angle of the tangent to the pile at the slip surface. l T This is the height of the center of the sliding surface from the ground surface.

[0046] Furthermore, in S6, based on the principle of equivalent shear strength, the anti-slip moment is converted into a comprehensive anti-slip force. ;

[0047] .

[0048] The beneficial effects of this invention are as follows:

[0049] (1) Based on the theory of additional stress, this invention directly calculates the difference of horizontal additional stress on both sides of the pile under the load of the trapezoidal embankment through the Businsk solution, avoiding the introduction of empirical coefficients and having a clear physical meaning.

[0050] (2) By introducing a method for determining key piles and amplification factors, this invention can reflect the differences in pile stress and progressive failure characteristics, and achieve a reasonable analysis of the instability process of pile-supported embankments.

[0051] (3) This invention combines the calculation of net horizontal earth pressure on the pile side with the anti-sliding moment of the pile body and the circular arc strip method to form a complete stability evaluation method, which can more reasonably evaluate the stability of pile-supported embankments.

[0052] (4) The calculation steps of the method of the present invention are clear and the formulas are well-defined. It can be implemented in conjunction with common numerical calculation software (such as the Slide series), and has good engineering applicability and promotion value. Attached Figure Description

[0053] Figure 1 This is a flowchart of the stability evaluation method for pile-supported embankments based on the additional stress theory of the present invention.

[0054] Figure 2 This is a schematic diagram of the stability analysis of the pile-supported embankment of the present invention.

[0055] Figure 3 This diagram illustrates the calculation of additional stress at any point in the foundation under a unit trapezoidal strip load according to the present invention.

[0056] Figure 4 The horizontal additional stress coefficient on the pile side under a unit trapezoidal strip load according to the present invention.

[0057] Figure 5 The difference in the horizontal additional stress coefficient on the pile side under the unit trapezoidal distributed strip load of the present invention. Detailed Implementation

[0058] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0059] like Figure 1 As shown, in one embodiment of the present invention, the stability evaluation method for pile-supported embankments based on the theory of additional stress includes the following steps:

[0060] S1. Obtain the physical and mechanical properties of the embankment and foundation, piles and reinforcement strips, and calculate the trapezoidal embankment load shared by the pile top.

[0061] S2. Using the circular arc strip method based on limit equilibrium theory, obtain the initial potential sliding surface center, radius, and stability coefficient when only rib constraints are set, and initialize the number of iterations;

[0062] S3. The trapezoidal embankment load is decomposed into rectangular and triangular loads using the Businsk solution. The horizontal additional stress at any point in the foundation is calculated, and the difference in horizontal additional stress on both sides of the pile is obtained according to the superposition principle, thereby determining the distribution of net horizontal earth pressure on the pile side.

[0063] S4. Based on the current center and radius of the slip surface, combined with the bending strength of the pile section and the axial force at the pile top, determine the maximum net horizontal thrust that each pile can resist, and use this as a benchmark to calculate the amplification factor under the unit trapezoidal load, thereby determining the critical piles, and calculating the net horizontal thrust of the non-critical piles based on the amplification factor, thus characterizing the true progressive failure characteristics of the pile body.

[0064] S5. Based on the distribution of net horizontal earth pressure on the pile side, the net horizontal thrust on each pile and the trapezoidal embankment load shared by the pile top are substituted into the calculation formula of the anti-sliding moment of the pile body to obtain the anti-sliding moment provided by each pile.

[0065] S6. Based on the principle of equivalent shear strength, the anti-slip moment is converted into a comprehensive anti-slip force, which is then assigned the equivalent shear strength of the pile element. The center, radius, and stability coefficient of the new potential sliding surface are calculated using the circular arc slice method of the limit equilibrium theory.

[0066] S7. Determine whether the difference between the current stability coefficient and the new stability coefficient is less than the preset threshold. If yes, complete a reasonable evaluation of the overall stability of the pile-supported embankment based on the current stability coefficient. If no, increment the iteration count by one, use the new potential slip surface center, radius, and stability coefficient as the current potential slip surface center, radius, and stability coefficient, and return to S4.

[0067] S3 includes the following steps:

[0068] S31. Equivalent to any trapezoidal embankment load as a unit trapezoidal load with a fixed geometric boundary and an amplification factor. K The product of the units and the unit trapezoidal load is decomposed into a rectangular load and two triangular loads;

[0069] S32. Calculate the horizontal additional stress at any point in the foundation under rectangular load, and calculate the horizontal additional stress at any point in the foundation under triangular load.

[0070] S33. The calculated horizontal additional stress is superimposed according to the superposition principle to obtain the horizontal additional stress at any point in the foundation under the trapezoidal embankment load.

[0071] S34. Subtract the horizontal additional stresses on the left and right sides (the plane where the sliding surface is located) of the pile body to obtain the net horizontal earth pressure distribution on the pile side.

[0072] In S32, calculate any point in the foundation under rectangular load. M Horizontal additional stress The specific expression is:

[0073]

[0074] In the formula, B The width of the roadbed surface of a full-section trapezoidal embankment. x and z Each point in the foundation is calculated as a separate point. M Distance from the centerline of the embankment and the foundation surface;

[0075] Calculate the horizontal additional stress at any point in the foundation under the first triangular load. The specific expression is:

[0076]

[0077] In the formula, H The height of the embankment, m The slope of the left side of the embankment;

[0078] Calculate the horizontal additional stress at any point in the foundation under the second triangular load. The specific expression is:

[0079]

[0080] In the formula, n The slope of the right side of the embankment;

[0081] In S33, the horizontal additional stress at any point in the foundation under the trapezoidal embankment load is obtained. The specific expression is:

[0082]

[0083] In this embodiment, the calculated horizontal additional stress is superimposed according to the superposition principle to obtain the horizontal additional stress at any point under the trapezoidal load, and then the net horizontal earth pressure distribution on both sides of the pile can be obtained.

[0084] In S4, calculate the maximum net horizontal thrust that any pile can resist. The specific expression is:

[0085]

[0086] In the formula, M i,max This is the maximum bending moment that the pile can resist under the action of a vertical axial force. This represents the difference in tensile force exerted by the reinforcing bars on the pile top within the longitudinal influence width. This is the lever arm of the tension force of the reinforcing band at the depth of the sliding surface. Net horizontal thrust After determining the slip surface depth by the height coefficient of the point of application, the distribution of net horizontal earth pressure on the pile side is simplified to a trapezoid and calculated according to the height of the centroid of the trapezoid.

[0087]

[0088] In the formula, W For the section modulus of the pile, f tk The tensile strength of the pile material. A c The cross-sectional area of ​​the pile is... The trapezoidal embankment load shared by the pile top.

[0089] In S4, calculate the magnification factor under a unit trapezoidal load. K The specific expression is:

[0090]

[0091] In the formula, F hk,1 The net horizontal thrust on the side of the critical pile under unit load. F hk,max The maximum net horizontal thrust that the key pile can withstand. F hi,1 The net horizontal thrust at any side of the pile under a unit load; F hi,max This represents the maximum net horizontal thrust that any pile can withstand.

[0092] According to the above formula, the pile that first reaches its own resistance limit is the key pile.

[0093] In S4, the specific method for calculating the net horizontal earth pressure on non-critical piles is as follows:

[0094] When the critical pile reaches the ultimate limit state, calculate the net horizontal thrust of any pile in the non-ultimate state. ;

[0095] .

[0096] In S5, the anti-sliding moment provided by each pile is calculated. The specific expression is:

[0097]

[0098] In the formula, N i The trapezoidal embankment load distributed at the pile top was calculated using various soil arch models, such as Hewlett & Randolph. R Let be the radius of the sliding surface. α ci Let be the horizontal inclination angle of the tangent to the pile at the slip surface. l T This is the height of the center of the sliding surface from the ground surface.

[0099] In S6, based on the principle of equivalent shear strength, the anti-slip moment is converted into a comprehensive anti-slip force. ;

[0100] .

[0101] In this embodiment, The equivalent shear strength of the pile element is assigned, and the center, radius, and stability coefficient of the new potential slip surface are calculated using the circular arc slice method based on the limit equilibrium theory.

[0102] In S7, the preset threshold is set to 0.01, and the stability coefficient is repeatedly calculated iteratively until the convergence condition is met, and the overall stability coefficient of the embankment is output.

[0103] To verify the effectiveness of the method of the present invention, this embodiment provides an experimental case, as follows:

[0104] Taking the centrifuge model test results of a certain embankment project as an example, this paper illustrates the calculation of net horizontal earth pressure on the pile side and the stability assessment of pile-supported embankments. The model test scale is 1:60, and the model embankment height is... H =77.2 mm, roadbed width B =532mm (tested at half width 266mm), slope m = n =1:1.725. The foundation uses CFG piles with a diameter of 8.33 mm and a length of 250 mm, with a pile spacing of 41.6 mm, arranged in a square pattern. The embankment stability analysis is shown below. Figure 2 As shown.

[0105] Step 1: Decompose the trapezoidal embankment load into a rectangular load AEFD and two triangular loads ABE and DFC, as follows: Figure 3 As shown.

[0106] Step 2: Based on the Buschinsk solution and the superposition principle, calculate the additional horizontal stress between the two piles under rectangular and triangular loads, such as... Figure 4 As shown.

[0107] Step 3: Calculate the difference in horizontal additional stress on both sides of the pile, as shown in Table 1. Based on this, the distribution of net horizontal earth pressure on the pile side is obtained, as shown in Table 1. Figure 5 As shown.

[0108] Table 1. Difference in horizontal additional stress coefficients along pile sides under unit trapezoidal strip load.

[0109]

[0110] Among them, pile #1 is located near the toe of the slope.

[0111] Step 4: Calculate the maximum net horizontal thrust that the critical pile can withstand based on the tensile strength of the material and the axial force of the pile. The ratio of the maximum net horizontal thrust that the critical pile can withstand to the net horizontal thrust on the side of the critical pile under unit load is the amplification factor under unit trapezoidal load. K The first pile to reach its own resistance limit is the key pile. KThe minimum value is calculated using the following formula: the maximum net horizontal thrust that the key pile can resist.

[0112]

[0113] Step 5: Determine the key pile and its corresponding amplification factor when it enters the limit state. K In this example, the key pile is pile number 2, calculated in the last iteration. K The value is 4.044, representing the net horizontal thrust of the remaining non-critical piles under this amplification factor. F hi Calculated by the following formula

[0114]

[0115] Step 6: Substitute the net horizontal earth pressure on each pile side and the embankment load shared by the pile top into the calculation formula for the anti-sliding moment of the pile body to obtain the anti-sliding moment provided by each pile. M RCi As shown in the following formula:

[0116]

[0117] Step 7: Based on the principle of equivalent shear strength, convert the anti-slip moment into a comprehensive anti-slip force. T τi As shown in the following formula:

[0118]

[0119] Step 8: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation would require the full T τi The equivalent shear strength of the pile element is assigned, and the center, radius, and stability coefficient of the new potential slip surface are calculated using the circular arc slice method based on the limit equilibrium theory.

[0120] Step 9: Determine if the difference between two adjacent iterations is less than the threshold (0.01). If yes, output the overall stability coefficient of the embankment. If no, return to S4 and repeat the iteration until the convergence condition is met. The comprehensive anti-sliding force of the piles after the last iteration is shown in Table 2.

[0121] Table 2. Comprehensive anti-sliding force of the piles obtained from the last iteration calculation.

[0122]

[0123] The calculated stability coefficient was 1.042, which is in good agreement with the critical state (failure of the key pile) observed in the experiment.

[0124] In the description of this invention, it should be understood that the terms "center," "thickness," "upper," "lower," "horizontal," "top," "bottom," "inner," "outer," and "radial," etc., indicating orientation or positional relationships based on the orientation or positional relationships shown in the accompanying drawings, are only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying the relative importance or the number of technical features implicitly specified. Therefore, a feature defined by "first," "second," and "third" may explicitly or implicitly include one or more of that feature.

Claims

1. A stability evaluation method for pile-supported embankments based on the theory of additional stress, characterized in that, Includes the following steps: S1. Obtain the physical and mechanical properties of the embankment and foundation, piles and reinforcement strips, and calculate the trapezoidal embankment load shared by the pile top. S2. Using the circular arc strip method based on limit equilibrium theory, obtain the initial potential sliding surface center, radius, and stability coefficient when only rib constraints are set, and initialize the number of iterations; S3. The trapezoidal embankment load is decomposed into rectangular and triangular loads using the Businsk solution. The horizontal additional stress at any point in the foundation is calculated, and the difference in horizontal additional stress on both sides of the pile is obtained according to the superposition principle, thereby determining the distribution of net horizontal earth pressure on the pile side. S4. Based on the current center and radius of the slip surface, combined with the bending strength of the pile section and the axial force at the pile top, determine the maximum net horizontal thrust that each pile can resist, and use this as a benchmark to calculate the amplification factor under the unit trapezoidal load, thereby determining the critical piles, and calculating the net horizontal thrust of the non-critical piles based on the amplification factor, thus characterizing the true progressive failure characteristics of the pile body. S5. Based on the distribution of net horizontal earth pressure on the pile side, the net horizontal thrust on each pile and the trapezoidal embankment load shared by the pile top are substituted into the calculation formula of the anti-sliding moment of the pile body to obtain the anti-sliding moment provided by each pile. S6. Based on the principle of equivalent shear strength, the anti-slip moment is converted into a comprehensive anti-slip force, which is then assigned the equivalent shear strength of the pile element. The center, radius, and stability coefficient of the new potential sliding surface are calculated using the circular arc slice method of the limit equilibrium theory. S7. Determine whether the difference between the current stability coefficient and the new stability coefficient is less than the preset threshold. If yes, complete a reasonable evaluation of the overall stability of the pile-supported embankment based on the current stability coefficient. If no, increment the iteration count by one, use the new potential slip surface center, radius, and stability coefficient as the current potential slip surface center, radius, and stability coefficient, and return to S4.

2. The stability evaluation method for pile-supported embankments based on the additional stress theory according to claim 1, characterized in that, S3 includes the following steps: S31. Equivalently transform any trapezoidal embankment load into the product of a unit trapezoidal load with a fixed geometric boundary and an amplification factor, and decompose the unit trapezoidal load into a rectangular load and two triangular loads. S32. Calculate the horizontal additional stress at any point in the foundation under rectangular load, and calculate the horizontal additional stress at any point in the foundation under triangular load. S33. The calculated horizontal additional stress is superimposed according to the superposition principle to obtain the horizontal additional stress at any point in the foundation under the trapezoidal embankment load. S34. Subtract the horizontal additional stresses on the left and right sides of the pile to obtain the net horizontal earth pressure distribution on the pile side.

3. The stability evaluation method for pile-supported embankments based on the additional stress theory according to claim 2, characterized in that, In S32, calculate the horizontal additional stress at any point in the foundation under a rectangular load. The specific expression is: In the formula, B The width of the roadbed surface of a full-section trapezoidal embankment. x and z Each point in the foundation is calculated as a separate point. M Distance from the centerline of the embankment and the foundation surface; Calculate the horizontal additional stress at any point in the foundation under the first triangular load. The specific expression is: In the formula, H The height of the embankment, m The slope of the left side of the embankment; Calculate the horizontal additional stress at any point in the foundation under the second triangular load. The specific expression is: In the formula, n The slope of the right side of the embankment; In S33, the horizontal additional stress at any point in the foundation under the trapezoidal embankment load is obtained. The specific expression is: 。 4. The stability evaluation method for pile-supported embankments based on the additional stress theory according to claim 1, characterized in that, In S4, calculate the maximum net horizontal thrust that any pile can resist. The specific expression is: In the formula, M i,max This is the maximum bending moment that the pile can resist under the action of a vertical axial force. This represents the difference in tensile force exerted by the reinforcing bars on the pile top within the longitudinal influence width. This is the lever arm of the tension force of the reinforcing band at the depth of the sliding surface. The height coefficient of the point of application of the net horizontal thrust; In the formula, W For the section modulus of the pile, f tk The tensile strength of the pile material. A c The cross-sectional area of ​​the pile is... The trapezoidal embankment load shared by the pile top.

5. The stability evaluation method for pile-supported embankments based on the additional stress theory according to claim 4, characterized in that, In S4, calculate the magnification factor under a unit trapezoidal load. K The specific expression is: In the formula, F hk,1 The net horizontal thrust on the side of the critical pile under unit load. F hk,max The maximum net horizontal thrust that the key pile can withstand. F hi,1 The net horizontal thrust at any side of the pile under a unit load; F hi,max This represents the maximum net horizontal thrust that any pile can withstand.

6. The stability evaluation method for pile-supported embankments based on the additional stress theory according to claim 5, characterized in that, In S4, the specific method for calculating the net horizontal earth pressure on non-critical piles is as follows: When the critical pile reaches the ultimate limit state, calculate the net horizontal thrust of any pile in the non-ultimate state. ; 。 7. The stability evaluation method for pile-supported embankments based on the theory of additional stress according to claim 5, characterized in that, In S5, the anti-sliding moment provided by each pile is calculated. The specific expression is: In the formula, N i The trapezoidal embankment load distributed at the pile top, R Let be the radius of the sliding surface. α ci Let be the horizontal inclination angle of the tangent to the pile at the slip surface. l T This is the height of the center of the sliding surface from the ground surface.

8. The stability evaluation method for pile-supported embankments based on the theory of additional stress according to claim 7, characterized in that, In S6, based on the principle of equivalent shear strength, the anti-slip moment is converted into a comprehensive anti-slip force. ; 。

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