Method for evaluating anti-overturning capacity of gravity-type shoulder retaining wall of ballastless track under rock foundation

Abstract

This invention discloses a method for assessing the overturning resistance of gravity shoulder retaining walls for ballastless track under rock foundations, comprising the following steps: S1: obtaining embankment parameters supported by gravity retaining walls; S2: calculating the overturning stability coefficient of the retaining wall; S3: calculating the limit value of the overturning stability coefficient of the retaining wall; S4: comparing the overturning stability coefficient of the retaining wall with the limit value of the overturning stability coefficient to assess the overturning resistance of the retaining wall. This invention is beneficial for controlling the dynamic deformation of the ballastless track subgrade surface under gravity shoulder retaining wall support conditions, improving train operation conditions, ensuring the long-term stability of the subgrade under train loads, and the overturning stability coefficient of the retaining wall involved is widely used in engineering. The limit value of the overturning stability coefficient of the retaining wall is only related to the wall back inclination angle, and the assessment process is simple and convenient. It is a supplement and improvement to the construction assessment technology of gravity shoulder retaining walls for high-speed railway ballastless track subgrades under rock foundation conditions.

Description

Technical Field

[0001] This invention belongs to the field of railway engineering technology, specifically relating to a method for assessing the overturning resistance of gravity shoulder retaining walls for ballastless tracks under rock foundations. Background Technology

[0002] Embankment structures supported by retaining walls have advantages such as small footprint and are widely used in railway subgrade engineering. Gravity retaining walls mainly resist the earth pressure behind the wall through their own weight, restraining the soil behind the wall to prevent collapse and lateral slippage. Under train loads, the dynamic deformation of the subgrade surface of gravity shoulder retaining wall-supported embankment structures is closely related to the stability of the retaining wall. A more stable wall has a stronger restraining effect on the subgrade fill, which is beneficial for controlling the dynamic deformation of the subgrade surface.

[0003] High-speed railways operate at high speeds, and the requirements for dynamic deformation of ballastless track subgrades are stringent. For high-speed railway ballastless track subgrades supported by gravity shoulder retaining walls, the stability of the retaining walls needs to be improved to control the dynamic deformation of the subgrade surface. Under the most unfavorable conditions, the constraint of the retaining wall on the embankment structure should be no weaker than that of the standard cross-section embankment slope soil, so that the dynamic deformation ω of the subgrade surface under retaining wall support conditions is no greater than the corresponding value δ of the standard cross-section embankment structure, that is, the dynamic deformation index of the subgrade surface R=δ / ω≥1.0.

[0004] Retaining walls on rock foundations exhibit rotation around their toes as the dominant displacement mode, and their resistance to rotational displacement can be characterized by an overturning stability coefficient, K0. Using the subgrade surface dynamic deformation index R ≥ 1.0 as a constraint, a limit value for the overturning stability coefficient [K0] is determined. By comparing the relationship between K0 and [K0], the overturning resistance of shoulder retaining walls based on subgrade surface dynamic deformation control is assessed. This is of great significance for improving the construction and evaluation of gravity shoulder retaining walls for ballastless track subgrades under rock foundation conditions. Summary of the Invention

[0005] Based on the above scheme, this invention proposes a method for evaluating the overturning resistance of gravity shoulder retaining walls for ballastless tracks under rock foundations.

[0006] The technical solution of this invention is: a method for assessing the overturning resistance of a gravity shoulder retaining wall for ballastless track under rock foundation, comprising the following steps:

[0007] S1: Obtain parameters for gravity retaining wall-supported embankments;

[0008] S2: Calculate the overturning stability coefficient of the retaining wall based on the parameters of the gravity retaining wall-supported embankment;

[0009] S3: Calculate the overturning stability coefficient limit of the retaining wall based on the parameters of the gravity retaining wall-supported embankment;

[0010] S4: Compare the overturning stability coefficient of the retaining wall with the overturning stability coefficient limit to evaluate the overturning capacity of the retaining wall.

[0011] Furthermore, in step S1, the parameters of the gravity retaining wall supported embankment include geometric parameters, material physical parameters, and loads above the roadbed surface;

[0012] The geometric parameters of the retaining wall support embankment include wall height H, wall breast slope 1:n, wall back inclination angle α, wall top width b, and distance d between the top of the wall back and the center of the track near the wall.

[0013] The physical parameters of the materials for retaining wall-supported embankments include the unit weight of the embankment soil behind the wall and the comprehensive internal friction angle, as well as the wall-soil friction angle and the unit weight of the wall material.

[0014] The loads above the roadbed surface include the uniformly distributed load of the track structure's self-weight and the uniformly distributed load of the train.

[0015] Furthermore, in step S2, the self-weight G of the retaining wall is determined based on the parameters of the gravity retaining wall supporting the embankment. w The lever arm Z of the moment of the wall's self-weight about the wall toe w The horizontal component of the active earth pressure borne by the back of the wall, E x The vertical component of the active earth pressure borne by the back of the wall, E y The lever arm Z of the horizontal component of the active earth pressure borne by the back of the wall about the toe moment of the wall. x The lever arm Z of the vertical component of the active earth pressure borne by the back of the wall about the toe of the wall. y The formula for calculating the overturning stability coefficient K0 of the retaining wall is as follows:

[0016] K0=(G w Z w +E y Z y ) / (E x Z x ).

[0017] Furthermore, in step S3, the formula for calculating the overturning stability coefficient limit [K0] of the retaining wall is as follows:

[0018]

[0019] In the formula, L = -2.062tanα - 0.188 represents the first function of the wall back inclination angle α; M = 7.086tanα + 0.839 represents the second function of the wall back inclination angle α; N = 0.268(tanα) 2 -5.371tanα-0.803 represents the third function of the wall back slope angle α. -0.20 <tanα<0.20。

[0020] Furthermore, in step S4, the specific method for evaluating the overturning resistance of the retaining wall is as follows: if K0≥[K0], the overturning resistance of the retaining wall is qualified; if K0<[K0], the overturning resistance of the retaining wall is unqualified, and the retaining wall is reinforced; where K0 represents the overturning stability coefficient of the retaining wall, and [K0] represents the limit value of the overturning stability coefficient of the retaining wall.

[0021] The beneficial effects of this invention are as follows: Based on the premise that the dynamic deformation of the roadbed surface under retaining wall support conditions is not greater than the corresponding value of the standard cross-section embankment structure, this invention establishes an estimation formula for the overturning stability coefficient limit [K0] of gravity shoulder retaining walls for ballastless track under rock foundation conditions. By comparing the overturning stability coefficient K0 and the overturning stability coefficient limit [K0], it is determined whether the overturning resistance of the wall meets the requirements. If K0 ≥ [K0], the overturning resistance meets the requirements; if K0 < [K0], the retaining wall needs to be reinforced to improve the overturning resistance. This method is beneficial for controlling the dynamic deformation of the roadbed surface under retaining wall support conditions, improving train operation conditions, ensuring the long-term stability of the roadbed under train loads, and the K0 involved is widely used in engineering. [K0] is only related to the wall back inclination angle, and the evaluation process is simple and convenient. This invention supplements and improves the construction evaluation technology of gravity shoulder retaining walls for high-speed railway ballastless track under rock foundation conditions. Attached Figure Description

[0022] Figure 1 A flowchart for assessing the overturning resistance of gravity shoulder retaining walls for ballastless track under rock foundations;

[0023] Figure 2 Cross-sectional views of gravity shoulder retaining wall supported embankments and standard section embankments;

[0024] Figure 3 The graph shows the relationship between the overturning stability coefficient limit [K0] of a gravity shoulder retaining wall and the wall back tilt angle α. Detailed Implementation

[0025] The embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0026] like Figure 1 As shown, this invention provides a method for assessing the overturning resistance of gravity shoulder retaining walls for ballastless tracks under rock foundations, characterized by comprising the following steps:

[0027] S1: Obtain parameters for gravity retaining wall-supported embankments;

[0028] S2: Calculate the overturning stability coefficient of the retaining wall based on the parameters of the gravity retaining wall-supported embankment;

[0029] S3: Calculate the overturning stability coefficient limit of the retaining wall based on the parameters of the gravity retaining wall-supported embankment;

[0030] S4: Compare the overturning stability coefficient of the retaining wall with the overturning stability coefficient limit to evaluate the overturning capacity of the retaining wall.

[0031] In this embodiment of the invention, in step S1, the parameters of the gravity retaining wall supported embankment include geometric parameters, material physical parameters, and loads above the roadbed surface.

[0032] The geometric parameters of the retaining wall support embankment include wall height H, wall breast slope 1:n, wall back inclination angle α, wall top width b, and distance d between the top of the wall back and the center of the track near the wall.

[0033] The physical parameters of the materials for retaining wall-supported embankments include the unit weight of the embankment soil behind the wall and the comprehensive internal friction angle, as well as the wall-soil friction angle and the unit weight of the wall material.

[0034] The loads above the roadbed surface include the uniformly distributed load of the track structure's self-weight and the uniformly distributed load of the train.

[0035] In this embodiment of the invention, in step S2, the self-weight G of the wall is determined based on the parameters of the gravity retaining wall supporting the embankment. w The lever arm Z of the moment of the wall's self-weight about the wall toe w The horizontal component of the active earth pressure borne by the back of the wall, E x The vertical component of the active earth pressure borne by the back of the wall, E y The lever arm Z of the horizontal component of the active earth pressure borne by the back of the wall about the toe moment of the wall. x The lever arm Z of the vertical component of the active earth pressure borne by the back of the wall about the toe of the wall. y The formula for calculating the overturning stability coefficient K0 of the retaining wall is as follows:

[0036] K0=(G w Z w +E y Z y ) / (E x Z x ).

[0037] The active earth pressure borne by the back of the wall is calculated based on Coulomb's earth pressure theory.

[0038] In this embodiment of the invention, the formula for calculating the overturning stability coefficient limit [K0] of the retaining wall in step S3 is as follows:

[0039]

[0040] In the formula, L = -2.062tanα - 0.188 represents the first function of the wall back inclination angle α; M = 7.086tanα + 0.839 represents the second function of the wall back inclination angle α; N = 0.268(tanα) 2-5.371tanα-0.803 represents the third function of the wall back slope angle α. -0.20 <tanα<0.20。

[0041] In this embodiment of the invention, the specific method for evaluating the overturning resistance in step S4 is as follows: if K0≥[K0], the overturning resistance of the retaining wall is qualified; if K0<[K0], the overturning resistance of the retaining wall is unqualified, and it is recommended to reinforce the retaining wall; where K0 represents the overturning stability coefficient of the retaining wall, and [K0] represents the limit value of the overturning stability coefficient of the retaining wall.

[0042] The present invention will now be described with reference to specific embodiments.

[0043] Example 1

[0044] Step S1: Determine the parameters of the gravity retaining wall supported embankment. Specifically, the parameters of the gravity retaining wall supported embankment include geometric parameters, material physical parameters, and loads above the subgrade surface.

[0045] The geometric parameters of the retaining wall-supported embankment include the wall height H, the wall breast slope 1:n, the wall back inclination angle α, the wall top width b, and the distance d between the top of the wall back and the center of the track near the wall. Figure 2 As shown in the figure, the roadbed below the shoulder edge is a standard cross-section embankment with a slope. The top shoulder of the roadbed is 4.3m from the center of the track on the side closest to the slope. Therefore, for Figure 2 For embankment structures supported by retaining walls, when d≤4.3m, the top of the wall should be at the same height as the roadbed surface; when d>4.3m, a low slope with a gradient of 1:1.5 should be provided above the top of the wall, with a height h'=(d-4.3m) / 1.5.

[0046] The physical parameters of the retaining wall supporting the embankment include the unit weight of the embankment soil behind the wall, the combined internal friction angle, the wall-soil friction angle, and the unit weight of the wall material. Based on experience, the unit weight of the soil behind the wall can be taken as 20.5 kN / m³. 3 The overall internal friction angle is 35°, and the wall-soil friction angle is 0.5 times the overall internal friction angle of the soil. For a C30 concrete retaining wall, the material density is taken as 23 kN / m³. 3 .

[0047] The load above the roadbed surface refers to the design load above the roadbed surface, including the uniformly distributed load of the track structure's self-weight and the uniformly distributed load of the train (ZK load). The track and train loads above the roadbed surface are considered based on CRTSⅢ type slab track, and the uniformly distributed load of the track structure's self-weight can be taken as q1 = 13.7 kN / m. 2 The uniformly distributed load on the train is q2 = 40.4 kN / m. 2 The load distribution width is 3.1m.

[0048] Step S2: Determine the self-weight G of the retaining wall based on the parameters of the gravity retaining wall supporting the embankment. w The lever arm Z of the moment of the wall's self-weight about the wall toew 1. The horizontal component E of the active earth pressure borne by the wall back x 2. The vertical component E of the active earth pressure borne by the wall back y 3. The lever arm Z of the moment of the horizontal component of the active earth pressure borne by the wall back about the wall toe x 4. The lever arm Z of the moment of the vertical component of the active earth pressure borne by the wall back about the wall toe y , to calculate the anti-overturning stability coefficient K0 of the retaining wall = (G w Z w + E y Z y ) / (E x Z x ).

[0049] Step S3: Determine the limit value [K0] of the anti-overturning stability coefficient of the retaining wall. Specifically, it can be calculated according to the inclination angle α of the wall back where L = -2.062tanα - 0.188, M = 7.086tanα + 0.839, N = 0.268(tanα) 2 - 5.371tanα - 0.803, and it should satisfy -0.20 < tanα < 0.20. The corresponding relationship between [K0] and tanα is as Figure 3 shown.

[0050] Step S4: Evaluate the anti-overturning ability of the ballastless track gravity shoulder retaining wall under rock foundation conditions. Specifically, compare the magnitudes of K0 and [K0]. If K0 ≥ [K0], it is evaluated that the anti-overturning ability of the retaining wall meets the requirements, and it can ensure that the maximum dynamic deformation of the subgrade surface under the retaining wall support condition is not greater than the corresponding value of the standard cross-section embankment structure; if K0 < [K0], the retaining wall needs to be strengthened to improve the anti-overturning ability.

[0051] Example 2

[0052] In the embodiment of the present invention, the method in Example 1 is used to evaluate the anti-overturning ability of the gravity shoulder retaining wall of the CRTS III type slab ballastless track subgrade.

[0053] Construction site 1: The wall height H = 6.0m, the wall breast is vertical, the inclination angle α of the wall back corresponds to tanα = 0.2, and the top width b of the wall = 1.28m. The spatial position of the retaining wall, that is, the distance d between the top of the wall back and the center of the near-wall side line = 4.3m. The track and train loads above the subgrade surface are considered according to the CRTS III type slab ballastless track. The calculated anti-overturning stability coefficient K0 of the retaining wall = 1.60, and the limit value [K0] of the anti-overturning stability coefficient = 1.23. K0 > [K0], the anti-overturning ability of the retaining wall meets the requirements, and it can ensure that the maximum dynamic deformation of the subgrade surface under the wall support condition is not greater than the corresponding value of the standard cross-section embankment structure.

[0054] Site 2: Wall height H = 10m, wall breast slope 1:n = 1:0.2, wall back inclination angle α corresponding to tanα = -0.2, wall top width b = 2.31m, distance between the top of the wall back and the center of the track near the wall d = 4.3m, using CRTSⅢ type slab track. The calculated overturning stability coefficient K0 = 1.70, and the overturning stability coefficient limit [K0] = 1.92. K0 < [K0], the overturning resistance of the retaining wall does not meet the requirements, and it is difficult to ensure that the maximum dynamic deformation of the roadbed surface under the wall support condition does not exceed the corresponding value of the standard cross-section embankment structure. The retaining wall needs to be reinforced to improve its overturning resistance.

[0055] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A method for assessing the overturning resistance of gravity shoulder retaining walls for ballastless track under rock foundations, characterized in that... Includes the following steps: S1: Obtain parameters for gravity retaining wall-supported embankments; S2: Calculate the overturning stability coefficient of the retaining wall based on the parameters of the gravity retaining wall-supported embankment; S3: Calculate the overturning stability coefficient limit of the retaining wall based on the parameters of the gravity retaining wall-supported embankment; Limit value of overturning stability coefficient of retaining wall [ K The formula for calculating 0] is: In the formula, L = -2.062tan α - 0.188 indicates the wall back slope angle. α The first function; M = 7.086tan α +0.839 indicates the wall back slope angle. α The second function; N = 0.268(tan α ) 2 -5.371tan α -0.803 indicates the wall back slope angle. α The third function, where, in representing the wall back slope angle α In the first, second, and third functions, -0.20 < tan α < 0.20; S4: Compare the overturning stability coefficient of the retaining wall with the overturning stability coefficient limit to evaluate the overturning capacity of the retaining wall.

2. The method for assessing the overturning resistance of gravity shoulder retaining walls for ballastless track under rock foundations according to claim 1, characterized in that, In step S1, the parameters of the gravity retaining wall supported embankment include geometric parameters, material physical parameters, and loads above the roadbed surface. The geometric parameters of retaining wall-supported embankments include the wall height. H , Wall slope 1: n Wall back slope angle α Wall top width b and the distance between the top of the wall back and the center of the track near the wall d ; The physical parameters of the retaining wall support for the embankment include the unit weight of the embankment soil behind the wall and the comprehensive internal friction angle, as well as the wall-soil friction angle and the unit weight of the wall material. The loads above the roadbed surface include the uniformly distributed load of the track structure's self-weight and the uniformly distributed load of the train.

3. The method for assessing the overturning resistance of gravity shoulder retaining walls for ballastless track under rock foundations according to claim 1, characterized in that, In step S2, the self-weight of the retaining wall is determined based on the parameters of the gravity retaining wall supporting the embankment. G w The lever arm of the moment of the wall's self-weight about the wall toe Z w Horizontal component of active earth pressure borne by the back of the wall E x Vertical component of active earth pressure borne by the back of the wall E y The lever arm of the horizontal component of the active earth pressure borne by the back of the wall about the toe moment. Z x The lever arm of the vertical component of the active earth pressure borne by the back of the wall about the toe moment of the wall. Z y Calculate the overturning stability coefficient of the retaining wall K 0, its calculation formula is: 。 4. The method for assessing the overturning resistance of gravity shoulder retaining walls for ballastless tracks under rock foundations according to claim 1, characterized in that, In step S4, the specific method for assessing the overturning resistance of the retaining wall is as follows: If K 0 ≥ [ K If 0], then the retaining wall's overturning resistance is qualified; if K 0 < [ K If the value is 0, then the retaining wall's overturning resistance is substandard, and the retaining wall needs to be reinforced; among which, K 0 indicates the overturning stability coefficient of the retaining wall. K 0] indicates the limit value of the overturning stability coefficient of the retaining wall.

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