Railway foundation bed mattress layer rib deformation analysis method

Abstract

The invention provides a railway bed mattress layer rib deformation analysis method, and belongs to the technical field of civil engineering design. According to the technical scheme, the method comprises the following steps that S1, in stress calculation, adverse conditions are considered, the sharing effect of the soil arching effect on overlying loads is ignored, calculation analysis is conducted according to the dead weight of all soil overlying geogrids and the adverse working conditions of train loads, and a basic assumption is made; s2, carrying out stress deformation calculation and solution on the upper-layer geogrid; and S3, calculating and solving the stress deformation of the bottom geogrid. The method has the beneficial effects that the blank of a calculation method of the double-layer geogrid under the condition of the local suspended section is filled up, and a scientific basis is provided for the design of the double-layer geogrid reinforced cushion layer of the railroad bed.

Description

Technical Field

[0001] The invention relates to the technical field of civil engineering design, and in particular to a method for analyzing deformation of reinforcement materials of a railway bed cushion layer. Background Art

[0002] For a long time, in the survey and design of railway subgrade engineering, when faced with artificial cave groups, mineral resource mining disturbance areas and other foundations, it is usually "tried to avoid"; when it is necessary to cross them, bridge crossing or grouting reinforcement are required. The former not only requires the lower foundation to have strong stability, but also has a high actual engineering cost. The latter is easily restricted by geological conditions such as groundwater, connectivity of voids between broken rocks and soil, etc., and the slurry is difficult to fill completely, resulting in a large number of voids that may be missed inside the foundation. These missed voids may be activated under the deadweight of the engineering structure and the vibration load, causing uneven settlement of the foundation, thereby posing potential risks to the stability and safety of the engineering structure.

[0003] In order to reduce the impact of uneven foundation settlement, geosynthetics (geotextiles, geogrids, etc.) and crushed stones are usually laid on the foundation surface to form a crushed stone cushion layer to reduce the impact of the lower differential settlement on the surface engineering structures. However, the deformation calculation method of the cushion layer under the condition of local settlement of the roadbed base currently used is mainly the deformation force calculation of a single-layer geogrid under the condition of complete suspension at the bottom, and there is a lack of force and deformation calculation method for each layer of geogrid in a double-layer geogrid under the condition of local collapse and suspension of the base. It can be seen that the theoretical calculation in this field is not perfect, and it is urgent to propose a force and deformation calculation method for a double-layer reinforced crushed stone cushion geogrid under the condition of local suspension of the low roadbed base. Summary of the invention

[0004] The technical problem to be solved by the present invention is to provide a method for calculating the stress and deformation of a double-layer reinforced crushed stone cushion geogrid under the condition of a partially suspended section of a low roadbed base, so as to provide a basis for the design of a low roadbed geogrid reinforced cushion layer and meet engineering needs.

[0005] In order to achieve the above-mentioned invention object, the technical solution adopted by the present invention is specifically: a method for analyzing the deformation of reinforcement materials of a railway bed cushion layer, comprising the following steps:

[0006] S1. In the force calculation, the sharing effect of soil arching effect on the overlying load is ignored, and the calculation and analysis are carried out based on the deadweight of all the soil overlying the geogrid and the unfavorable working conditions of train load, and basic assumptions are made;

[0007] S2. Calculation and solution of stress and deformation of upper geogrid (5);

[0008] S2.1, the stress-deformation differential equation of the upper geogrid (5) is established;

[0009] S2.2, solving differential equations;

[0010] S3. Calculation and solution of the stress and deformation of the bottom geogrid (6).

[0011] Preferably, in step S1, the method for making the basic assumption is:

[0012] S1.1. The suspended section of the geogrid is an axisymmetric figure with the center of the roadbed as the axis of symmetry. The deformation functions of the suspended sections of the upper and lower geogrids are different, and the stress-deformation analysis should be performed separately. The relationship between the geogrid and the gravel satisfies the Mohr-Coulomb model.

[0013] S1.2. The embankment height-span ratio H / B has an impact on the soil arch effect. B is the width of the local suspended section, and H is the height of the subgrade above the local suspended section. When the thickness of the soil above the horizontal reinforced body is greater than 3 times the width of the local suspended section, the soil arch effect is obvious, and the load above the reinforced body needs to consider the influence of the soil arch effect. When the fill height is too low, the soil arch cannot be formed and the soil arch effect cannot be caused. Therefore, in the low fill embankment, the soil above the horizontal reinforced body and the train load will be fully transferred to the bottom horizontal reinforced body, and the corresponding load is calculated by the strip method integration.

[0014] S1.3. Assume that the sliding surface of the low roadbed is a vertical sliding surface and the relative sliding effect between the soil strips is not considered. The sliding surface of the embankment directly above the local suspended section is a vertical sliding surface. There is no suspended part between the geogrid and the middle filler. Considering the unfavorable conditions and the sliding of the fillers at different positions, it is assumed that the equal settlement surface of the gravel cushion layer above the geogrid and above is a horizontal surface.

[0015] S1.4. Assume that the lower filling of the bottom geogrid of the suspended section of the roadbed base is completely collapsed, and ignore the support and friction effect of gravel and soil in the local suspended section on the horizontal reinforcement.

[0016] Preferably, in step S2.1, the differential equation is established as follows:

[0017] Assume that the uniformly distributed load of the train and the track is converted to the height h0 of the converted soil column (1), the height of the roadbed fill (2) is h1, the thickness of the upper layer (3) of the crushed stone cushion and the middle layer (4) of the crushed stone cushion are both h2, and the soil overlying the upper geogrid (5) is differentiated. A strip of soil block (7) of the upper filling of the upper geogrid (5) is taken for force analysis. The force on the strip is the self-weight of the soil block G 1i And gravel weight G 2i , soil density is γ1, gravel density is γ2, normal stress N 1i ', tangential stress T s1i ', from the balance of forces, we know that the following equation holds true:

[0018]

[0019] Assume that the upper geogrid (5) is subjected to a tangential reaction force T s1i , Normal reaction force N i The supporting force of the intermediate layer (4) of the crushed stone cushion layer is q s (x)dx, the support force of the middle layer (4) of the crushed stone cushion is the same as the foundation reaction force of the crushed stone cushion, that is, q s (x) = k s y2, where k s is the foundation reaction coefficient of the crushed stone cushion layer, and the tensions at both ends of the upper geogrid (5) are (T x1 , T y1 )、(T x1 +dT x1 , T y1 +dT y1 ), the tangential reaction force T s1i and the normal reaction force N 1i Decompose the force in the x and y directions respectively and list the force equilibrium equations as follows:

[0020]

[0021] Simplified:

[0022]

[0023] Integrating equation ③ yields:

[0024]

[0025] Among them, T1 is the integral constant, which is also the value of the lateral tension of the geogrid. When 0≤x≤D / 2, for T y1 Simplified:

[0026] T y1 =γ1(h0+h1)x+2γ2h2x-(γ2+k s )∫Z2(x)dx⑤

[0027] The boundary condition of the flexural deformation function Z2(x) of the upper geogrid (5) is:

[0028]

[0029] In the above formula, Z1 is the maximum deflection of the center of the upper geogrid (5), so:

[0030]

[0031] The tensile force of the reinforced body of the local suspended section is expressed as:

[0032]

[0033] According to equations ④, ⑤, ⑥, and ⑦, the flexural deformation function Z(x) of the upper geogrid (5) is obtained as the horizontal force T of the geogrid changes. x1 The relationship between them is simplified as follows:

[0034] Z2'(x)T1=γ1(h0+h1)x+2γ2h2x-(γ1+k s )∫Z2(x)dx⑨

[0035] Preferably, in step S2.2, the differential equation solving method is as follows:

[0036] Let F(x) = ∫Z2(x)dx, and set parameters a, b, c, m, t. All parameters are greater than zero. The meanings of the parameters are as follows:

[0037]

[0038] Then formula ⑩ is: mF(x)”=(a+b)x-cF(x), and the characteristic equation mλ is constructed 2 +cλ=0, considering that the parameters m and c are both greater than zero, the two roots λ of the characteristic equation 1,2 And the solution of the homogeneous equation They are:

[0039]

[0040] Using the constant variation method to solve the differential equation, the following equation is established:

[0041]

[0042] Among them, C(x) and C1(x) are unknown functions, and the following equations are established:

[0043]

[0044] In-style Under the condition of Use Cramer's rule to solve C(x) and C1(x).

[0045]

[0046] Substituting C(x) and C1(x) into the formula In the above equation, we can find the F(x) function and simplify it as follows:

[0047]

[0048] Pair Integrate and substitute into the boundary condition ⑥ to obtain the deflection function of the upper geogrid (5):

[0049]

[0050] Among them, C3 and C0 are integral constants, satisfying the following equation:

[0051]

[0052] Under theoretical conditions, the geogrid flexural deformation function is an axisymmetric figure. Therefore, when -D / 2≤x≤0 is the same as Z2(x), under the condition of partial suspension in the middle of the lower part of the roadbed, the flexural deformation function of the upper geogrid should conform to the flexural deformation form of the parabola plus or minus a cosine function, that is:

[0053]

[0054] In the formula, A, B, C, and D are parameters related to the roadbed size and filler properties, as follows:

[0055]

[0056] C=t

[0057] D=C0

[0058] Preferably, in step S3, the calculation method and solution method of the stress deformation of the bottom geogrid (6) are as follows:

[0059] According to the method in step S2, the force analysis and calculation are performed without considering the soil arch effect. At this time, the force on the strip block is the gravel deadweight G 3i and the crushed stone reaction force q s (x)dx, normal stress N 2i ', tangential stress T s2i ', from the balance of forces, we know that the following formula holds true:

[0060]

[0061] The force analysis of the micro-end of the geogrid shows that the bottom of the bottom geogrid (6) is no longer affected by the supporting force, and its force equation is:

[0062]

[0063] Pair Points can be obtained:

[0064]

[0065] Among them, T1 is the integral constant, which is also the value of the lateral tension of the geogrid. When 0<x≤D / 2, T y1 Simplified:

[0066]

[0067] Among them, the boundary condition of the geogrid deflection function z when 0<x≤D / 2 is:

[0068]

[0069] General Substitution In the solution, the analytical function of Z2(x) when 0<x≤D / 2 is as follows:

[0070]

[0071] In the formula, A, B, C, and D have the same meanings as in the formula The same, the meanings of the other parameters are: q = γ2 + k s , p=T2, k=γ2, C1, C0, Cp are integral constants respectively; the boundary conditions Substitution The integral constant is solved, and then the analytical function of Z1(x) is obtained when 0<x≤D / 2. When -D / 2≤x≤0, its deflection function can be solved according to the symmetric property of the suspended section geogrid function about the center of the roadbed.

[0072] Compared with the prior art, the present invention has the following beneficial effects:

[0073] 1. This calculation method takes into account the different stress conditions of different layers of the double-layer geogrid in the cushion layer of the railway subgrade when the base is partially suspended, gives the deformation function of different layers of geogrid under actual stress conditions, and uses numerical analysis results to compare and verify the theoretical function. The verification shows that the function has higher calculation accuracy; through more accurate stress-deformation calculation, it can provide a more reasonable scientific basis for the anchoring design of multi-layer geogrids in locally suspended sections, making up for the shortcomings of existing calculation methods.

[0074] 2. The railway subgrade cushion reinforcement deformation analysis method provided by the present invention fills the gap in the calculation method of double-layer geogrids under local suspension conditions, and provides a scientific basis for the design of double-layer geogrid reinforced cushions for railway subgrades. BRIEF DESCRIPTION OF THE DRAWINGS

[0075] The accompanying drawings are used to provide further understanding of the present invention and constitute a part of the specification. They are used to explain the present invention together with the embodiments of the present invention and do not constitute a limitation of the present invention.

[0076] Figure 1 It is a schematic diagram of the calculation model of the local suspended segment;

[0077] Figure 2 It is a schematic diagram of the force on the upper strips of the upper geogrid;

[0078] Figure 3 It is the micro-end force analysis of the upper geogrid;

[0079] Figure 4 It is the stress analysis of the soil overlying the bottom geogrid and the micro-end of the grid;

[0080] Figure 5 This is a comparison chart of the fitting results of different calculation methods.

[0081] Among them, the figure markings are: 1. converted soil column; 2. roadbed fill; 3. upper layer of crushed stone cushion; 4. middle layer of crushed stone cushion; 5. upper geogrid; 6. bottom geogrid; 7. strip soil blocks. DETAILED DESCRIPTION

[0082] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. Of course, the specific embodiments described here are only used to explain the present invention and are not used to limit the present invention.

[0083] Example: Figure 1-Figure 5 As shown, this embodiment provides a method for analyzing the deformation of reinforcement materials of a railway bed cushion layer.

[0084] 1. The specific steps include:

[0085] I. Basic assumptions: In the actual roadbed during the operation of the train, the fill on both sides of the local suspended section of the roadbed base will gradually move toward the center of the suspension under the influence of the train vibration load, and the soil arch effect is difficult to be fully formed. With the increase of the fill height, the differential settlement of the center and both ends of the local suspended section gradually decreases and tends to be consistent. Therefore, when performing the stress analysis in the present invention, the sharing effect of the soil arch effect on the overlying load is ignored, and the calculation and analysis are performed under the most unfavorable working conditions of the deadweight of all the soil covered by the geogrid and the train load; the following basic assumptions are made:

[0086] (1) Under the condition of local collapse of the base of the reinforced cushion layer of the railway embankment, the suspended section of the geogrid is an axisymmetric figure with the center of the embankment as the symmetry axis. The relationship between the geogrid and the gravel satisfies the Mohr-Coulomb model, that is, the linear elastic-total plastic model.

[0087] (2) The height-to-span ratio of the railway subgrade is H / B ≤ 2 (B is the width of the local suspended section, and H is the height of the subgrade above the collapsed local suspended section). The deadweight of the soil above the geogrid in the cushion layer and the train load are all transferred to the bottom horizontal reinforcement body, and the corresponding load is calculated by the strip method.

[0088] (3) When the base of the railway embankment is suspended, the upper soil and gradation are vertical along the vertical slip surface at any time, and the relative slip between the soil strips is not considered to restrict each other.

[0089] Ⅱ. Calculation and solution of stress and deformation of geogrid on upper layer of railway subgrade cushion:

[0090] (1) The stress and deformation calculation equation of the upper geogrid 5 without considering the soil arching effect is established: Figure 1 The schematic diagram of the geogrid stress model when the part is suspended in the air is shown in Figure 1. The uniformly distributed load of the train and the track is converted into the converted soil column height h0. The height of the roadbed fill 2 is h1. The thickness of the upper layer 3 of the crushed stone cushion and the middle layer 4 of the crushed stone cushion are both h2. The soil overlying the upper geogrid 5 is differentiated, and a strip of soil block 7 of the upper filling of the upper geogrid 5 is taken for stress analysis. The stress schematic diagram of the strip is shown in Figure 11. Figure 2 As shown, the force on the strip is the weight of the soil block G 1i And gravel weight G 2i The soil density is γ1, the gravel density is γ2, and the normal stress N 1i ', tangential stress T s1i ', from the balance of forces, we know that the following formula holds true:

[0091]

[0092] Figure 3 is the schematic diagram of the micro-end force of the upper geogrid. Figure 3 It can be seen that the upper geogrid 5 is subjected to a tangential reaction force T si , Normal reaction force N i , gravel cushion middle layer 4 support force q s (x)dx, the supporting force of the middle layer 4 of the crushed stone cushion is the same as the foundation reaction force of the crushed stone cushion, that is, q s (x) = k s y2, where k s is the foundation reaction coefficient of the crushed stone cushion layer, and the tensions at both ends of the upper geogrid 5 are (T x1 , T y1 )、(T x1 +dT x1 , T y1 +dT y1 ). The tangential reaction force T s1i and the normal reaction force N 1i Decomposing in the x and y directions respectively, the force equilibrium equation can be listed as follows:

[0093]

[0094] Simplifying, we get:

[0095]

[0096] Integrating equation ③ yields:

[0097]

[0098] Where T1 is the integral constant, which is also the value of the lateral tension of the geogrid; when 0≤x≤D / 2, for T y1 Simplifying, we get:

[0099] T y1 =γ1(h0+h1)x+2γ2h2x-(γ2+k s )∫Z2(x)dx⑤

[0100] The boundary condition of the flexural deformation function Z2(x) of the upper geogrid 5 is:

[0101]

[0102] In the above formula, Z1 is the maximum deflection of the center of the upper geogrid 5, which is given by Figure 3 It can be seen that:

[0103]

[0104] The tensile force of the reinforced body of the local suspended section can be expressed as:

[0105]

[0106] According to equations ④, ⑤, ⑥, and ⑦, the flexural deformation function Z(x) of the upper geogrid 5 can be solved as the horizontal force T of the geogrid. x1 The relationship between them is simplified as follows:

[0107] Z2'(x)T1=γ1(h0+h1)x+2γ2h2x-(γ1+k s )∫Z2(x)dx⑨

[0108] (2) Solving differential equations:

[0109] To facilitate the calculation and solution of the differential equation of formula ⑨, let F(x) = ∫Z2(x)dx, and set the parameters a, b, c, m, t, all of which are greater than zero. The meanings of the parameters are as follows:

[0110]

[0111] Then equation ⑩ can be written as: mF(x)”=(a+b)x-cF(x), and the characteristic equation mλ is constructed 2 +cλ=0, considering that the parameters m and c are both greater than zero, the two roots λ of the characteristic equation 1,2 And the solution of the homogeneous equation They are:

[0112]

[0113] Using the constant variation method to solve the differential equation, the following equation is established:

[0114]

[0115] Among them, C(x) and C1(x) are unknown functions, and the following equations are established:

[0116]

[0117] In-style Under the condition of Use Cramer's rule to solve C(x) and C1(x).

[0118]

[0119] Substituting C(x) and C1(x) into the formula In the above equation, we can find the F(x) function and simplify it as follows:

[0120]

[0121] Pair By integrating and substituting into the boundary condition ⑥, the deflection function of the upper geogrid 5 can be obtained as:

[0122]

[0123] Among them, C3 and C0 are integral constants, satisfying the following equation:

[0124]

[0125] Under theoretical conditions, the geogrid flexural deformation function is an axisymmetric graph, so when -D / 2≤x≤0, it is the same as Z2(x). Under the condition of the local suspended section in the middle of the lower part of the roadbed, the flexural function of the upper geogrid is:

[0126]

[0127] In the formula, A, B, C, and D are parameters related to the roadbed size, filler properties, etc., as follows:

[0128]

[0129] Ⅲ Calculation and solution of stress and deformation of bottom geogrid:

[0130] The stress analysis of the bottom geogrid 6 is similar to that of the upper geogrid 5. However, the difference between the bottom geogrid 6 and the upper geogrid 5 is that the bottom geogrid 6 does not consider the bottom support force in the stress analysis due to the influence of the local suspended section. The soil strip stress model and geogrid micro-segment calculation model are as follows: Figure 4 shown.

[0131] According to the method in step II, the force analysis and calculation are carried out without considering the soil arch effect. At this time, the force on the strip is the gravel deadweight G 3i and the crushed stone reaction force q s (x)dx, normal stress N 2i ', tangential stress T s2i ', from the balance of forces, we know that the following formula holds true:

[0132]

[0133] The same method is used to analyze the stress of the micro-end of the geogrid. Different from the upper geogrid 5, the bottom of the bottom geogrid 6 is no longer affected by the supporting force, and its stress equation can be written as:

[0134]

[0135] Pair Points can be obtained:

[0136]

[0137] Where T1 is the integral constant, which is also the value of the lateral tension of the geogrid. When 0<x≤D / 2, the same method is used to calculate T y1 Simplifying, we get:

[0138]

[0139] Among them, the boundary condition of the geogrid deflection function z when 0<x≤D / 2 is:

[0140]

[0141] General Substitution In the above example, the differential equation solution process is the same as above, and the analytical function of Z2(x) when 0<x≤D / 2 is as follows:

[0142]

[0143] In the formula, A, B, C, and D have the same meanings as in the formula The same, the meanings of the other parameters are: q = γ2 + k s , p=T2, k=γ2, C1, C0, Cp are integral constants respectively; the boundary conditions Substituting the integral constant into the above formula, we can solve for the analytical function of Z1(x) when 0<x≤D / 2; when -D / 2≤x≤0, its deflection function can be solved based on the symmetric property of the suspended section geogrid function about the center of the roadbed.

[0144] In summary, the calculation and solution of the stress and deformation of the upper geogrid 5 are as follows: differentiate the soil overlying the upper geogrid 5, take one of the strip soil blocks 7 for stress analysis, and perform stress analysis on the micro-end of the reinforced body under the soil strip. Assume that the deformation function of the upper geogrid is y2, the width of the local suspended section is D, and the supporting force of the gravel cushion layer in the middle is q s (x)dx, where q s (x) = k s y2, k s is the foundation reaction coefficient of the crushed stone cushion layer, and a group of differential equilibrium equations about the geogrid deformation function y2 at the end of the upper geogrid is established when 0≤x≤D / 2. The deformation function of the upper geogrid 5 when 0≤x≤D / 2 is solved using the geogrid deformation boundary condition, and the deformation function when -D / 2≤x≤0 is obtained based on the symmetry.

[0145] The calculation and solution of the stress and deformation of the bottom geogrid 6 are as follows: when analyzing the stress of the bottom geogrid 6, the influence of the local suspended section is taken into account, and it is assumed that there is no supporting force at the bottom. The stress and deformation equation of the bottom geogrid 6 is y1. According to the method in step II, a group of differential equilibrium equations about the geogrid deformation function y1 at the micro-end of the bottom geogrid 6 when 0≤x≤D / 2 is established. The deformation function of the bottom geogrid 6 when 0≤x≤D / 2 is solved using the geogrid deformation boundary condition, and the deformation function when -D / 2≤x≤0 is obtained based on symmetry.

[0146] 2. Comparative test of fitting results of different deformation functions of upper geogrid:

[0147] The parabola and catenary commonly used in the current geogrid deformation function theory are selected and compared with the function derived from the theory in step II through numerical simulation results. Figure 5 The figure is a comparison chart of the fitting results of three fitting functions. From the fitting results, it can be seen that the upper geogrid flexural deformation function using the parabola plus minus cosine function calculation method has a higher fitting degree than the other two common deformation functions, that is, the formula The deformation calculation of the local suspended section of the geogrid is more accurate, and the fitting effect is greatly improved compared with the calculation using only the quadratic function parabola.

[0148] The railway subgrade cushion reinforcement deformation analysis method provided by the present invention fills the gap in the calculation method of double-layer geogrid under local suspension conditions, and provides a scientific basis for the design of railway subgrade double-layer geogrid reinforced cushion.

[0149] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A railway bed cushion reinforcement deformation analysis method, characterized in that: The following steps are involved: S1. In the force calculation, the sharing effect of soil arching effect on the overlying load is ignored, and the calculation and analysis are carried out based on the deadweight of all the soil overlying the geogrid and the unfavorable working conditions of train load, and basic assumptions are made; S2. Calculation and solution of stress and deformation of upper geogrid (5); S2.1, the stress-deformation differential equation of the upper geogrid (5) is established; S2.2, solving differential equations; S3. Calculation and solution of the stress and deformation of the bottom geogrid (6).

2. The railway bed cushion reinforcement material deformation analysis method according to claim 1 is characterized in that: In step S1, the method of making the basic assumption is: S1.

1. The suspended section of the geogrid is an axisymmetric figure with the center of the roadbed as the axis of symmetry. The deformation functions of the suspended sections of the upper and lower geogrids are different, and the stress-deformation analysis should be performed separately. The relationship between the geogrid and the gravel satisfies the Mohr-Coulomb model. S1.

2. The embankment height-span ratio H / B has an impact on the soil arch effect. B is the width of the local suspended section, and H is the height of the subgrade above the local suspended section. When the thickness of the soil above the horizontal reinforced body is greater than 3 times the width of the local suspended section, the soil arch effect is obvious, and the load above the reinforced body needs to consider the influence of the soil arch effect. When the fill height is too low, the soil arch cannot be formed and the soil arch effect cannot be caused. Therefore, in the low fill embankment, the soil above the horizontal reinforced body and the train load will be fully transferred to the bottom horizontal reinforced body, and the corresponding load is calculated by the strip method integration. S1.

3. Assume that the sliding surface of the low roadbed is a vertical sliding surface and the relative sliding effect between the soil strips is not considered. The sliding surface of the embankment directly above the local suspended section is a vertical sliding surface. There is no suspended part between the geogrid and the middle filler. Considering the unfavorable conditions and the sliding of the fillers at different positions, it is assumed that the equal settlement surface of the gravel cushion layer above the geogrid and above is a horizontal surface. S1.

4. Assume that the filler below the bottom geogrid of the suspended section is completely collapsed, and ignore the support and friction effect of the gravel and soil in the local suspended section on the horizontal reinforcement.

3. The railway bed cushion reinforcement material deformation analysis method according to claim 2 is characterized in that: In step S2.1, the differential equation is established as follows: Assume that the uniformly distributed load of the train and the track is converted to the height h0 of the converted soil column (1), the height of the roadbed fill (2) is h1, the thickness of the upper layer (3) of the crushed stone cushion and the middle layer (4) of the crushed stone cushion are both h2, and the soil overlying the upper geogrid (5) is differentiated. A strip of soil block (7) of the upper filling of the upper geogrid (5) is taken for force analysis. The force on the strip is the self-weight of the soil block G 1i And gravel weight G 2i , soil density is γ1, gravel density is γ2, normal stress N 1i ', tangential stress T s1i ', from the balance of forces, we know that the following equation holds true: Assume that the upper geogrid (5) is subjected to a tangential reaction force T s1i , Normal reaction force N i The supporting force of the intermediate layer (4) of the crushed stone cushion layer is q s (x)dx, the support force of the middle layer (4) of the crushed stone cushion is the same as the foundation reaction force of the crushed stone cushion, that is, q s (x) = k s y2, where k s is the foundation reaction coefficient of the crushed stone cushion layer, and the tensions at both ends of the upper geogrid (5) are (T x1 , T y1 )、(T x1 +dT x1 , T y1 +dT y1 ), the tangential reaction force T s1i and the normal reaction force N 1i Decompose the force in the x and y directions respectively and list the force equilibrium equations as follows: Simplified: Integrating equation ③ yields: Among them, T1 is the integral constant, which is also the value of the lateral tension of the geogrid. When 0≤x≤D / 2, for T y1 Simplified: T y1 =γ1(h0+h1)x+2γ2h2x-(γ2+k s )∫Z2(x)dx⑤ The boundary condition of the flexural deformation function Z2(x) of the upper geogrid (5) is: In the above formula, Z1 is the maximum deflection of the center of the upper geogrid (5), so: The tensile force of the reinforced body of the local suspended section is expressed as: According to equations ④, ⑤, ⑥, and ⑦, the flexural deformation function Z(x) of the upper geogrid (5) is obtained as the horizontal force T of the geogrid changes. x1 The relationship between them is simplified as follows: Z2'(x)T1=γ1(h0+h1)x+2γ2h2x-(γ1+k s )∫Z2(x)dx⑨。 4. The railway bed cushion reinforcement material deformation analysis method according to claim 3 is characterized in that: In step S2.2, the differential equation is solved as follows: Let F(x) = ∫Z2(x)dx, and set parameters a, b, c, m, t. All parameters are greater than zero. The meanings of the parameters are as follows: Then formula ⑩ is: mF(x)”=(a+b)x-cF(x), and the characteristic equation mλ is constructed 2 +cλ=0, considering that the parameters m and c are both greater than zero, the two roots λ of the characteristic equation 1,2 And the solution of the homogeneous equation They are: Using the constant variation method to solve the differential equation, the following equation is established: Among them, C(x) and C1(x) are unknown functions, and the following equations are established: In-style Under the condition of Use Cramer's rule to solve C(x) and C1(x). Substituting C(x) and C1(x) into the formula In the above equation, we can find the F(x) function and simplify it as follows: Pair Integrate and substitute into the boundary condition ⑥ to obtain the deflection function of the upper geogrid (5): Among them, C3 and C0 are integral constants, satisfying the following equation: Under theoretical conditions, the geogrid deflection function is an axisymmetric graph, so when -D / 2≤x≤0, it is the same as Z2(x). Under the condition that the lower middle part of the roadbed is partially suspended, the deflection function of the upper geogrid (5) is: Z2(x)=Ax 2 +Bcos(Cx)+D In the formula, A, B, C, and D are parameters related to the roadbed size and filler properties, as follows: C=t;D=C 0。 5. The railway bed mattress reinforcement material deformation analysis method according to claim 4 is characterized in that: In step S3, the calculation method and solution method of the stress deformation of the bottom geogrid (6) are as follows: According to the method in step S2, the force analysis and calculation are performed without considering the soil arch effect. At this time, the force on the strip block is the gravel deadweight G 3i and the crushed stone reaction force q s (x)dx, normal stress N 2i ', tangential stress T s2i ', from the balance of forces, we know that the following formula holds true: The force analysis of the micro-end of the geogrid shows that the bottom of the bottom geogrid (6) is no longer affected by the supporting force, and its force equation is: Pair Points can be obtained: Among them, T1 is the integral constant, which is also the value of the lateral tension of the geogrid. When 0<x≤D / 2, T y1 Simplified: T2Z1'(x)=(γ2+k s )Z2(x)+γ2∫Z1(x)dx Among them, the boundary condition of the geogrid deflection function z when 0<x≤D / 2 is: General Substitution In the solution, the analytical function of Z2(x) when 0<x≤D / 2 is as follows: In the formula, A, B, C, and D have the same meanings as in the formula The same, the meanings of the other parameters are: q = γ2 + k s , p=T2, k=γ2, C1, C0, Cp are integral constants respectively; the boundary conditions Substitution The integral constant is solved, and then the analytical function of Z1(x) is obtained when 0<x≤D / 2. When -D / 2≤x≤0, its deflection function can be solved according to the symmetric property of the suspended section geogrid function about the center of the roadbed.

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