Calculation method of reinforcement force of end-wrapped reinforced soil roadbed

Abstract

The present invention discloses a method for calculating the force of the reinforcement of an end-turned reinforced soil roadbed, which has simple and reasonable modeling and algorithm operations and high calculation efficiency. The force of the reinforcement includes the surface shear stress and the cross-sectional axial force of the reinforcement, and the calculation method includes the following steps: Step 100, calculating the tension of the turn-up end of the i-th layer of reinforcement at the roadbed slope surface in the reinforced soil roadbed, i is the number of each layer of reinforcement from top to bottom in the reinforced soil roadbed; Step 200, calculating the tension of the i-th layer of reinforcement at the sliding rupture surface of the reinforced soil roadbed; Step 300, calculating the inclination angle of the sliding rupture surface of the reinforced soil roadbed corresponding to the limit state; Step 400, calculating and determining the free section length and anchor section length of the i-th layer of reinforcement; tep500, based on the basic equilibrium equation of the free section of the i-th layer of reinforcement, calculating the surface shear stress and cross-sectional axial force at any point of the free section of the reinforcement; Step 600, based on the basic equilibrium equation of the anchor section of the i-th layer of reinforcement, calculating the surface shear stress and cross-sectional axial force at any point of the anchor section of the reinforcement.

Description

Technical Field

[0001] The invention relates to the field of reinforced soil foundation engineering, and in particular to a method for calculating the force of reinforcement bars in an end-turned reinforced soil roadbed. Background Art

[0002] Reinforced soil roadbed is an engineering structure that adds reinforcement materials (usually geosynthetics) to the soil to improve its overall mechanical properties. In particular, the wrapped reinforced soil roadbed is to reversely wrap the ends of the reinforcement at the slope of the roadbed to form a local reverse end, which resists lateral sliding of the soil and can better improve the bearing capacity of the reinforced soil roadbed. Compared with the traditional pure soil roadbed, the reinforced soil roadbed is particularly suitable for road projects that need to cope with conditions such as large road loads, uneven foundation settlement, and high seismic resistance requirements. However, the accurate analysis and design calculation of the mechanical behavior of reinforced soil roadbeds still face a series of challenges.

[0003] The reinforcement has a decisive influence on the mechanical behavior of reinforced soil roadbed. At present, the computational analysis of the role of reinforcement in reinforced soil roadbed mainly relies on traditional soil mechanics theory and finite element numerical simulation methods. Although these methods are feasible, there are several problems in actual operation: (1) Complex modeling operation: The traditional finite element simulation method requires detailed modeling of the physical properties of soil and reinforcement, which involves a large number of engineering parameter measurements, resulting in a cumbersome modeling process and easy to be affected by subjective factors. (2) Time-consuming and laborious calculation: Finite element analysis requires a lot of computing time. For engineering designers, the operation is cumbersome and the time cost is high, which is not conducive to completing the design task quickly and effectively. (3) Lack of simple and easy-to-operate algorithms: Although the current calculation methods are feasible in theory, there is a lack of a simple and easy-to-operate algorithm in practical applications, which enables engineering designers to more conveniently perform mechanical behavior analysis and design calculations of reinforced soil roadbeds. Summary of the invention

[0004] The purpose of the present invention is to overcome the above-mentioned deficiencies in the prior art and to provide a method for calculating the force of reinforcement of an end-wrapped reinforced soil roadbed with simple and reasonable modeling and algorithm operations and high calculation efficiency.

[0005] In order to achieve the above-mentioned object of the invention, the present invention provides the following technical solutions:

[0006] A method for calculating the stress of the reinforcement of an end-wrapped reinforced soil roadbed, wherein the stress of the reinforcement includes the surface shear stress and the cross-sectional axial force of the reinforcement, and the calculation method comprises the following steps:

[0007] Step 100, calculating the tension on the reverse end of the i-th layer of reinforcement in the reinforced soil roadbed at the roadbed slope, where i is the number of each layer of reinforcement from top to bottom in the reinforced soil roadbed;

[0008] Step 200, calculate the tension of the i-th layer of reinforcement at the sliding fracture surface of the reinforced soil roadbed;

[0009] Step 300, calculating the inclination angle of the sliding rupture surface of the reinforced soil roadbed corresponding to the limit state;

[0010] Step 400, for the i-th layer of reinforcement, calculate and determine its free section length and anchor section length;

[0011] Step 500, for the i-th layer of reinforcement, based on the basic equilibrium equation of the free section of the reinforcement, calculate the surface shear stress and cross-sectional axial force at any point of the free section of the reinforcement;

[0012] Step 600, for the i-th layer of reinforcement, based on the basic equilibrium equation of the reinforcement anchorage section, calculate the surface shear stress and cross-sectional axial force at any point of the reinforcement anchorage section.

[0013] The outstanding advantages of the method for calculating the force of the reinforcement of the end-turned reinforced soil roadbed of the present invention are:

[0014] First, the present invention calculates the free section and the anchoring section of each layer of reinforcement in the end-wrapped reinforced soil roadbed respectively, so as to determine the distribution of the reinforcement surface shear stress and the cross-sectional axial force along the entire reinforcement length direction.

[0015] Second, the present invention adopts the static equilibrium method based on the general pattern of stress on the reinforcement of each layer, and conducts a theoretical analysis on the stress on the reinforcement of the end-wrapped reinforced soil roadbed. While maintaining the basic characteristics of the mechanical properties of the soil and the reinforcement, the model is simplified to improve the calculation efficiency. The operation and solution process are simple, and the introduced mathematical expressions are simple and reasonable in form, which converts the complex internal mechanical behavior of the reinforced soil roadbed into a form that is easy to understand and calculate.

[0016] Third, the present invention can further discuss the relevant parameters that affect the stress of the reinforcement, and can analyze the parameter sensitivity of the maximum axial force of each layer of reinforcement, the maximum shear stress on the reinforcement surface and its position, providing a quick and effective method and scientific basis for the design, calculation and analysis of reinforced soil roadbed.

[0017] It can be seen that, unlike previous complex simulation methods, the present invention focuses on simplicity and practicality, making the engineering design of reinforced earth roadbed more intuitive and efficient. It does not require time-consuming, labor-intensive, and costly experiments to estimate and determine the surface shear stress and cross-sectional axial force of each layer of reinforcement in the end-wrapped reinforced earth roadbed, allowing engineering designers to more easily analyze and design the structural performance of the reinforced earth roadbed, providing a scientific basis and effective means for the design of actual reinforced earth roadbed projects, and has important technical significance and engineering application value.

[0018] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments. Additional aspects and advantages of the present invention will be partially given in the following description, partially become apparent from the following description, or be learned through the practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] The drawings constituting a part of the present invention are used to assist in understanding the present invention. The contents provided in the drawings and their related descriptions in the present invention can be used to explain the present invention, but do not constitute improper limitations on the present invention. In the drawings:

[0020] Figure 1 It is a schematic diagram of the plane sliding failure mode approximately adopted by the end-wrapped reinforced soil roadbed of the present invention.

[0021] Figure 2 The invention discloses a stress analysis model for a sliding soil wedge in a reinforced soil roadbed.

[0022] Figure 3 It is the full-length force analysis model of the i-th layer of reinforcement in the reinforced soil roadbed of the present invention.

[0023] Figure 4 It is the stress analysis model of the free section of the i-th layer of reinforcement in the reinforced soil roadbed of the present invention.

[0024] Figure 5 It is the stress analysis model of the i-th layer of reinforcement anchoring section in the reinforced soil roadbed of the present invention.

[0025] Figure 6 It is a schematic diagram of the cross section of the physical test model of the end-wrapped reinforced soil roadbed of Example 1 of the present invention.

[0026] Figure 7 1 is a comparison chart of the calculated results and the test results of the surface shear stress of the third layer of reinforcement in Example 1 of the present invention.

[0027] Figure 8 It is a comparison chart of the calculated results and the test results of the cross-sectional axial force of the third layer of reinforcement in Example 1 of the present invention.

[0028] Fig. 9 It is a schematic diagram of the cross section of the physical test model of the end-wrapped reinforced soil roadbed of Example 2 of the present invention.

[0029] Fig.10 This is a diagram showing the calculation results of the surface shear stress of the seventh layer of reinforcement in Example 2 of the present invention.

[0030] Fig.11 This is a diagram showing the calculation results of the cross-sectional axial force of the seventh layer of reinforcement in Example 2 of the present invention.

[0031] The relevant marks in the above-mentioned drawings are: 100-reinforcement, 200-turned-up end, 300-sliding rupture surface, 400-reinforcement free section, 500-reinforcement anchoring section, 600-roadbed center line, 700-roadbed slope. DETAILED DESCRIPTION

[0032] The present invention is described clearly and completely below in conjunction with the accompanying drawings. A person skilled in the art will be able to implement the present invention based on these descriptions. Before describing the present invention in conjunction with the accompanying drawings, it should be particularly noted that:

[0033] The technical solutions and technical features provided in each part of the present invention, including the following description, may be combined with each other if there is no conflict.

[0034] In addition, the embodiments of the present invention involved in the following description are generally only a part of the embodiments of the present invention, rather than all the embodiments. Therefore, based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0035] About the terms and units in the present invention: The terms "include", "have" and any variations thereof in the description and claims of the present invention and related parts are intended to cover non-exclusive inclusions.

[0036] Figure 1 The schematic diagram is a planar sliding failure mode approximately adopted by the end-wrapped reinforced soil roadbed of the present invention. The geogrid reinforcement 100 is laid horizontally, the length of the reinforcement 100 increases from top to bottom, the reinforcement 100 is arranged vertically at equal intervals, the surface where the AB segment is located is the roadbed slope surface 700, the surface where the AC segment is located is the sliding rupture surface 300, and the soil body surrounded by the surface where the AB segment is located, the surface where the AC segment is located, and the surface where the BC segment is located is a sliding soil wedge.

[0037] Figure 2 The force analysis model of the sliding soil wedge in the reinforced soil roadbed of the present invention is shown in FIG. 1 , wherein Q is the resultant force of the surface load on the top of the roadbed acting on the sliding soil wedge, S and N are the tangential force and the normal force acting on the sliding fracture surface 300, respectively, and T is the total tension of each layer of the reinforcement 100 at the sliding fracture surface 300.

[0038] Figure 3 It is the full-length force analysis model of the i-th layer of reinforcement 100 in the reinforced soil roadbed of the present invention. Figure 4 It is a stress analysis model of the free section 400 of the i-th layer of reinforcement in the reinforced soil roadbed of the present invention. Figure 5It is a stress analysis model of the anchoring section of the i-th layer of reinforcement in the reinforced soil roadbed of the present invention. Under the roadbed sliding limit state, the sliding fracture surface 300 divides the reinforcement 100 into a free section 400 outside the sliding fracture surface 300 (i.e., the i-th layer of reinforcement 100 located between the sliding fracture surface 300 and the turn-up end 200) and an anchoring section 500 inside the sliding fracture surface 300 (i.e., the i-th layer of reinforcement 100 located between the sliding fracture surface 300 and the roadbed centerline 600). In the free section 400 and the anchoring section 500, the reinforcement 100 slides and deforms toward the inside and outside of the roadbed relative to the roadbed soil, respectively.

[0039] based on Figure 1-5 The specific implementation of the method for calculating the force of the reinforcement of the end-wrapped reinforced soil roadbed of the present invention is used to calculate the surface shear stress and cross-sectional axial force of the reinforcement 100. The calculation method includes the following steps Step 100-Step 600:

[0040] Step 100, calculate the tension of the i-th layer of reinforcement 100 at the turn-up end 200 at the roadbed slope 700 in the reinforced soil roadbed, where i is the number of each layer of reinforcement 100 from top to bottom in the reinforced soil roadbed; the details are as follows:

[0041] The tensile force N on the reverse end 200 of the i-th layer of reinforcement 100 at the roadbed slope 700 is r (0) can be expressed by the sum of the active earth pressure at the end 200 of the reinforcing bar 100 and the lateral pressure generated by the roadbed top surface load at the position of the layer, that is:

[0042] N r (0)=(σ h1i +σ h2i )h (1)

[0043] In the formula, σ h1i , σ h2i They are respectively the active earth pressure generated by the soil behind the inverted end 200 of the i-th layer of reinforcement 100 and the lateral pressure generated by the surface load on the top of the roadbed at this layer, which can be determined by the relevant formula in Article 9.2.3 of "TB 10025-2019 Code for Design of Railway Roadbed Support Structures"; h is the vertical spacing between two adjacent layers of reinforcement 100.

[0044] Step 200, calculate the tension of the i-th layer of reinforcement 100 at the sliding fracture surface 300 of the reinforced soil roadbed; the details are as follows:

[0045] Since the tie rod 100 can be regarded as a linear elastic body, there is a positive proportional relationship between the tension on the tie rod 100 and its axial displacement. Therefore, the tension N on the i-th layer of tie rod 100 at the sliding fracture surface 300 is r (l a ) is:

[0046]

[0047] In the formula, S i is the lateral horizontal displacement of the i-th layer of reinforcement 100 at the end 200 of the turn-up, which is a dimensionless quantity obtained by dividing 1000 times the actual displacement by the total height H of the roadbed; S max is the maximum lateral horizontal displacement of the reinforcement 100 in each layer at the turned-up end 200, that is, S i The maximum value of T max The designed ultimate tensile force of the reinforcement 100 that produces the maximum lateral horizontal displacement.

[0048] For the lateral horizontal displacement of the i-th layer of reinforcement 100 at the reversed end 200, according to the large-scale model test of the end reversed reinforced soil roadbed, the displacement is obtained along the roadbed height in a parabolic curve distribution mode with large displacement in the middle and small displacement at the upper and lower ends. The general expression is:

[0049] S i =7.665y i 3 -17.188y i 2 +9.520y i +0.100 (3)

[0050] In the formula, y i It is the height of the turned-up end 200 of the i-th layer of reinforcement 100 from the subgrade surface divided by the total subgrade height.

[0051] Step 300, calculating the inclination angle of the sliding fracture surface 300 of the reinforced soil roadbed corresponding to the limit state; the details are as follows:

[0052] According to the limit equilibrium and geometric conditions of the sliding soil wedge of the reinforced soil roadbed, the overall stability factor F of the sliding soil wedge can be derived: s The relationship between the inclination angle θ of the sliding fracture surface 300 is expressed as:

[0053]

[0054] Where c is the cohesion of the roadbed soil; is the internal friction angle of the roadbed soil; q is the surface load on the top of the roadbed; L t is the horizontal distance from the intersection of the sliding rupture surface 300 and the top surface of the roadbed to the shoulder, a is the horizontal clear distance from the shoulder to the top surface of the roadbed; if L t -a is negative, then take L t -a is zero; L is the length of the sliding fracture surface 300; G is the deadweight of the sliding soil wedge; T is the total tension of the reinforcement 100 of each layer at the sliding fracture surface 300;

[0055] L, G, T, L t The calculation expressions are:

[0056]

[0057]

[0058]

[0059]

[0060] Among them, H is the total height of the reinforced soil roadbed; γ is the weight of the roadbed soil; β is the inclination angle of the roadbed slope 700; n is the total number of horizontally laid reinforcement 100 layers in the roadbed.

[0061] For the sliding limit state of reinforced soil roadbed, its overall stability coefficient should obtain the minimum value, so it can be obtained:

[0062]

[0063] Therefore, according to formula (5), the calculated value θ of the inclination angle θ of the sliding fracture surface 300 of the reinforced soil roadbed corresponding to the sliding limit state can be determined: c , and substituting it into formula (4) can obtain the corresponding overall stability coefficient.

[0064] Step 400, for the i-th layer of reinforcement 100, calculate and determine the length of the free section 400 and the length of the anchoring section 500; specifically, as follows:

[0065] For the i-th layer of reinforcing bar 100, the length l of its free section 400 can be determined by geometric relationship. a The calculation expression is:

[0066]

[0067] The length of the anchoring section of the i-th layer of reinforcement is 500 b The calculation expression is:

[0068] l b =wl a (6b)

[0069] In the formula, θ c is the calculated value of the inclination angle θ of the sliding fracture surface 300; L c is the length occupied by the turned-up end 200 of the i-th layer of reinforcement 100 along the length direction of the reinforcement 100; w is the horizontal distance between the turned-up end 200 of the i-th layer of reinforcement 100 and the center line 600 of the roadbed.

[0070] Step 500, for the i-th layer of the reinforcement 100, based on the basic equilibrium equation of the reinforcement free section 400, the surface shear stress and the cross-sectional axial force at any point of the reinforcement free section 400 are calculated; specifically, as follows:

[0071] According to the general distribution characteristics of the shear stress on the surface of the tie rod 100 along the length of the tie rod 100 and the boundary conditions of the free section 400 of the tie rod that need to be satisfied, that is, x = 0 at the end 200 of the turn-up and x = l at the sliding rupture surface 300 a The surface shear stress of the tie rod 100 is 0, and the calculation expression of the surface shear stress τ1(x) at any point of the free section 400 of the tie rod can be constructed as follows:

[0072]

[0073] Where x is the horizontal distance from any point on the free section 400 of the tie rod to the end 200 of the turn-up, x≤l a ; m′ is the shape correction coefficient of the shear resistance of the free section 400 of the i-th layer of reinforcement toward the outside of the roadbed, and its value is 2 to 3; τ0 is the reference shear stress on the surface of the free section 400 of the reinforcement; e is the natural index.

[0074] According to the axial static equilibrium condition of the free section 400 of the tie rod, the basic equilibrium equation of the free section 400 of the tie rod is obtained as follows:

[0075]

[0076] Substituting formula (7) into formula (8), we can obtain:

[0077]

[0078] Thus, the reference shear stress τ0 on the surface of the free section 400 of the tie rod can be determined by equation (9), and thus the specific expression of τ1(x) can be determined. Therefore, according to the static equilibrium condition of the free section 400 of the tie rod, it can be obtained that 0≤x≤l a The cross-sectional axial force at any point of the free section of the tie rod is N r1 The calculation expression of (x) is:

[0079]

[0080] Step 600, for the i-th layer of reinforcement 100, based on the basic equilibrium equation of the anchoring section 500, the surface shear stress and the cross-sectional axial force at any point of the anchoring section 500 are calculated; specifically, as follows:

[0081] According to the general distribution characteristics of the surface shear stress of the reinforcing bar 100 along the length of the reinforcing bar 100 and the boundary conditions of the anchoring section 500 that need to be satisfied, that is, at x=l a and x = l a +lb The surface shear stress of the reinforcement 100 is 0, and the calculation expression of the surface shear stress τ2(x) at any point of the anchoring section 500 can be constructed as follows:

[0082]

[0083] Wherein, τ0′ is the reference shear stress on the surface of the anchoring section 500; x is the horizontal distance from any point on the anchoring section 500 to the end of the turn-up 200, l a ≤x≤l a +l b ; n′ is the shape correction coefficient of the shear resistance of the i-th layer reinforcement anchor section 500 toward the inner side of the roadbed, which is 2 to 3 and is smaller than the shape correction coefficient of the shear resistance of the i-th layer reinforcement free section 400 toward the outer side of the roadbed; e is the natural index.

[0084] According to the axial static equilibrium condition of the anchoring section 500, the basic equilibrium equation of the free section 400 of the reinforcement can be obtained as follows:

[0085]

[0086] Where N r (l a +l b ) is the 600th position of the roadbed centerline x=l a +l b The tension on the reinforcement 100 is approximately the sum of the static earth pressure generated by the soil at the position of the layer at the center line 600 of the roadbed and the horizontal earth pressure generated by the surface load on the top of the roadbed at the layer, because there is almost no lateral horizontal displacement at the center line 600 of the roadbed, that is:

[0087] N r (l a +l b )=K0(γih+σ vi )h (12a)

[0088] Where K0 is the static earth pressure coefficient, which can be taken as σ vi It is the vertical compressive stress generated by the surface load on the top of the roadbed in the middle of the i-th layer of reinforcement 100. The specific calculation can be based on the relevant formula in Article 9.2.3 of "TB 10025-2019 Code for Design of Railway Roadbed Support Structures".

[0089] Substituting formula (11) into formula (12), we get:

[0090]

[0091] Thus, the reference shear stress τ0' on the surface of the reinforcing bar anchoring section 500 can be determined by equation (13), and thus the specific expression of τ2(x) can be determined. Therefore, according to the static equilibrium condition of the anchoring section 500, we can get a ≤x≤l a +l b The cross-sectional axial force N at any point of the anchoring section 500 r2 The calculation expression of (x) is:

[0092]

[0093] The beneficial effects of the present invention are described below through specific embodiments.

[0094] Example 1

[0095] Figure 6 It is a schematic diagram of the cross section of the physical test model of the end-wrapped reinforced soil roadbed of Example 1 of the present invention.

[0096] Figure 6 The model size and soil parameters of the physical test model of the end-upturned reinforced soil roadbed (half width) shown in Table 1 are shown in Table 1. Among them, the total height H is 1.8m, the angle β between the roadbed slope 700 and the horizontal direction is 87°, the roadbed top surface width is 2.9m, the roadbed bottom surface width is 3.0m, the spacing h of the reinforcement 100 is 0.3m, and the length L occupied by the upturned end 200 of the reinforcement 100 along the length direction of the reinforcement 100 c The cohesion c of the roadbed soil is 5 kPa, and the internal friction angle is The angle is 35° and the gamma is 20 kN / m 3 , the maximum lateral displacement of the tie rod is 100, and the design limit tension is T max =12kN / m, the surface load q on the top of the roadbed is 60kPa, the width of action on the top of the half-width roadbed is 2m (the total width b of the surface load on the top of the roadbed is 4.0m), and the net distance a from the shoulder is 0.9m. Then, according to the above calculation method, take m'=3 and n'=2 to calculate the surface shear stress and cross-sectional axial force of the third layer of reinforcement (i=3).

[0097] First, the calculated value θ of the inclination angle θ of the sliding fracture surface 300 of the reinforced soil roadbed corresponding to the limit state is calculated by formula (5): c =36.39°.

[0098] Furthermore, taking the third layer of reinforcement as an example, we can calculate l by using equations (6a) and (6b): a =0.974m,l b =1.773m.

[0099] Furthermore, the force calculation results of points at different horizontal distances of 200 from the end of the turn-up along the length direction of the third layer of reinforcement are shown in Table 1.

[0100] Table 1

[0101]

[0102] Figure 7 3 is a comparison chart of the calculated results and the test results of the surface shear stress of the third layer of reinforcement in Example 1 of the present invention, wherein the negative value represents the shear stress of the anchoring section 500 .

[0103] like Figure 7 As shown, the maximum value of the surface shear stress within the free section 400 of the third layer of the reinforcement calculated by the calculation method of the present invention is 6.35 kPa, and the curvature of the surface shear stress distribution curve is relatively large; the maximum value of the surface shear stress within the third layer of the anchoring section 500 is 1.31 kPa, and the curvature of the surface shear stress distribution curve becomes smaller. According to the test results, the maximum surface shear stresses of the free section 400 of the reinforcement and the anchoring section 500 are 7.08 kPa and 1.51 kPa, respectively. It can be calculated that the relative errors of the calculation method of the present invention and the test results are 10.3% and 13.2%, respectively.

[0104] Figure 8 It is a comparison chart of the calculated results and the test results of the cross-sectional axial force of the third layer of reinforcement in Example 1 of the present invention.

[0105] like Figure 8 As shown, the distribution patterns of the cross-sectional axial forces of the calculated results and the test results are similar, both showing a single-peak curve distribution, wherein the maximum cross-sectional axial force of the reinforcement 100 obtained by the calculation method of the present invention is 11.08 kN / m, and the maximum cross-sectional axial force of the reinforcement 100 obtained by the test is 11.85 kN / m, and the error between the two is about 6.5%.

[0106] It can be seen that the error between the calculation result of the present invention and the test result is relatively small, and the change characteristics of the distribution curve are consistent, which shows that the calculation method of the present invention has good rationality.

[0107] Example 2

[0108] Fig. 9 It is a schematic diagram of the cross section of the physical test model of the end-wrapped reinforced soil roadbed of Example 2 of the present invention.

[0109] Fig. 9The model size and soil parameters of the physical test model of the end-upturned reinforced soil roadbed (full width) shown in Table 2 are shown in Table 2. Among them, the total height H is 6.0m, the angle β between the roadbed slope 700 and the horizontal direction is 87°, the roadbed top surface width is 10.6m, the roadbed bottom surface width is 11.2m, the spacing h of the reinforcement 100 is 0.5m, and the length L occupied by the upturned end 200 of the reinforcement 100 along the length direction of the reinforcement 100 c is 0.3m. The cohesion c of the roadbed soil is 0kPa, and the internal friction angle is is 34°, and the heavy gamma is 20kN / m 3 , the maximum lateral displacement of the tie rod is 100, and the design limit tension is T max =35kN / m, the top surface load q of the roadbed is 70kPa, the total width b of the top surface load of the roadbed is 3.7m, and the net distance a from the shoulder is 3.45m. Then, according to the above calculation method, take m'=3 and n'=2 to calculate the surface shear stress and cross-sectional axial force of the 7th layer of reinforcement (i=7).

[0110] First, the calculated value θ of the inclination angle θ of the sliding fracture surface 300 of the reinforced soil roadbed corresponding to the limit state is calculated by formula (5): c =39.61°.

[0111] Furthermore, taking the third layer of reinforcement as an example, we can calculate l by using equations (6a) and (6b): a =2.589m,l b =2.594m.

[0112] Furthermore, the force calculation results of points at different horizontal distances of 200 from the end of the turn-up along the length direction of the 7th layer of reinforcement are shown in Table 2.

[0113] Table 2

[0114]

[0115] Fig.10 4 is a diagram showing the calculation results of the surface shear stress of the seventh layer of reinforcement in Example 2 of the present invention, wherein the negative value represents the shear stress of the anchoring section 500 .

[0116] like Fig.10 As shown, the maximum value of the surface shear stress within the free section 400 of the 7th layer of reinforcement calculated by the calculation method of the present invention is 11.82 kPa, and the curvature of the surface shear stress distribution curve is relatively large; the maximum value of the surface shear stress within the anchoring section 500 of the 7th layer is 6.85 kPa, and the curvature of the surface shear stress distribution curve becomes smaller.

[0117] Fig.11 This is a diagram showing the calculation results of the cross-sectional axial force of the seventh layer of reinforcement in Example 2 of the present invention.

[0118] like Fig.11 As shown, the cross-sectional axial force of the seventh layer of reinforcement is distributed in a single-peak curve along the length direction of the reinforcement 100, and the maximum axial force of the reinforcement 100 is 34.78 kN / m.

[0119] The above is a description of the relevant contents of the present invention. A person skilled in the art will be able to implement the present invention based on these descriptions. Based on the above contents of the present invention, all other embodiments obtained by a person skilled in the art without making any creative work shall fall within the scope of protection of the present invention.

Claims

1. A method for calculating the stress of the reinforcement of the end-wrapped reinforced soil roadbed, wherein the stress of the reinforcement includes the surface shear stress and the cross-sectional axial force of the reinforcement, and is characterized in that: The calculation method includes the following steps: Step 100, calculating the tension on the reverse end of the i-th layer of reinforcement in the reinforced soil roadbed at the roadbed slope, where i is the number of each layer of reinforcement from top to bottom in the reinforced soil roadbed; Step 200, calculate the tension of the i-th layer of reinforcement at the sliding fracture surface of the reinforced soil roadbed; Step 300, calculating the inclination angle of the sliding rupture surface of the reinforced soil roadbed corresponding to the limit state; Step 400, for the i-th layer of reinforcement, calculate and determine its free section length and anchor section length; Step 500, for the i-th layer of reinforcement, based on the basic equilibrium equation of the free section of the reinforcement, calculate the surface shear stress and cross-sectional axial force at any point of the free section of the reinforcement; Step 600, for the i-th layer of reinforcement, based on the basic equilibrium equation of the reinforcement anchoring section, calculate the surface shear stress and cross-sectional axial force at any point of the reinforcement anchoring section; Among them, the calculation expression of the free section length of the i-th layer of reinforcement is: The calculation expression of the length of the anchorage section of the i-th layer of reinforcement is: l b ＝w-l a In the formula, l a is the length of the free section of the i-th layer of reinforcement, and the free section is the i-th layer of reinforcement located between the sliding rupture surface and the end of the reverse package; H is the total height of the reinforced soil roadbed; h is the vertical spacing between two adjacent layers of reinforcement; β is the inclination angle of the roadbed slope; θ is the inclination angle of the sliding rupture surface, θ c Calculate the value for it; L c is the length of the turned-up end of the i-th layer of reinforcement along the length direction of the reinforcement; l b is the length of the anchoring section of the i-th layer of reinforcement, where the anchoring section is the i-th layer of reinforcement located between the sliding rupture surface and the center line of the roadbed; w is the horizontal distance between the turned-up end of the i-th layer of reinforcement and the center line of the roadbed; The calculation expression of the surface shear stress at any point of the free section of the reinforcement is: The calculation expression of the cross-sectional axial force at any point of the free section of the reinforcement is: Where τ1(x) is the surface shear stress at any point on the free segment of the reinforcement, x is the horizontal distance from any point on the free segment of the reinforcement to the end of the turn-up, and x≤l a ; τ0 is the reference shear stress on the free section of the reinforcement surface; m′ is the shape correction coefficient of the shear resistance of the free section of the i-th layer of reinforcement toward the outside of the roadbed, with a value of 2 to 3; e is the natural index; N r1 (x) is the cross-sectional axial force at any point of the free section of the reinforcement; N r (0) is the tension on the end of the i-th layer of reinforcement at the roadbed slope; The calculation expression of the surface shear stress at any point of the reinforcement anchor section is: The calculation expression of the cross-sectional axial force at any point of the reinforcement anchor section is: Where τ2(x) is the surface shear stress at any point of the reinforcement anchorage segment, x is the horizontal distance from any point on the reinforcement anchorage segment to the end of the turn-up, and l a ≤x≤l a +l b ; τ0′ is the reference shear stress on the surface of the reinforcement anchorage section; n′ is the shape correction coefficient of the shear resistance to the inner side of the roadbed of the i-th layer reinforcement anchorage section, which is 2 to 3 and is smaller than the shape correction coefficient of the shear resistance to the outer side of the roadbed of the i-th layer reinforcement free section; e is the natural index; N r2 (x) is the cross-sectional axial force at any point of the reinforcement anchorage section; N r (l a ) is the tensile force on the i-th layer of reinforcement at the sliding rupture surface.

2. The method for calculating the force of the reinforcement of the end-turned reinforced soil roadbed according to claim 1 is characterized in that: In step 100: the calculation expression of the tension on the reversed end of the i-th layer of reinforcement at the roadbed slope is: N r (0)=(σ h1i +s h2i )h In the formula, σ h1i , σ h2i They are respectively the active earth pressure generated by the soil behind the reversed end of the i-th layer of reinforcement and the lateral pressure generated by the surface load on the top of the roadbed at this layer.

3. The method for calculating the force of the reinforcement of the end-wrapped reinforced soil roadbed according to claim 2 is characterized in that: In step 200: the calculation expression of the tension of the i-th layer of reinforcement at the sliding fracture surface is: In the formula, S i is the lateral horizontal displacement of the i-th layer of reinforcement at the end of the turn-up; S max is the maximum lateral horizontal displacement of the reinforcement in each layer at the end of the turnup, that is, S i The maximum value of T max The design ultimate tensile force of the reinforcement that produces the maximum lateral horizontal displacement.

4. The method for calculating the force of the reinforcement of the end-turned reinforced soil roadbed according to claim 3 is characterized in that: In step 200: the calculation expression of the lateral horizontal displacement is: Si=7.665yi 3 -17.188yi 2 +9.520yi+0.100 In the formula, y i It is the height from the end of the i-th layer of reinforcement to the subgrade surface divided by the total subgrade height.

5. The method for calculating the force of the reinforcement of the end-turned reinforced soil roadbed according to claim 3 is characterized in that: In step 300: the relationship between the overall stability coefficient of the sliding soil wedge and the inclination angle of the sliding fracture surface is expressed as: In the formula, F s is the overall stability coefficient of the sliding soil wedge; c is the cohesion of the roadbed soil; is the internal friction angle of the roadbed soil; q is the surface load on the top of the roadbed; L t is the horizontal distance from the intersection of the sliding fracture surface and the top surface of the roadbed to the shoulder, a is the horizontal clear distance from the shoulder to the top of the roadbed surface load. t -a is negative, then take L t -a is zero; L is the length of the sliding fracture surface, G is the deadweight of the sliding soil wedge, γ is the weight of the roadbed soil; T is the total tension of the reinforcement in each layer at the sliding rupture surface, n is the total number of horizontally laid reinforcement layers in the reinforced soil roadbed.

6. The method for calculating the force of the reinforcement of the end-turned reinforced soil roadbed according to claim 5 is characterized in that: In step 300: for the sliding limit state of the reinforced soil roadbed, the overall stability coefficient of the sliding soil wedge should obtain a minimum value, that is, Thus, the inclination angle of the sliding rupture surface of the reinforced soil roadbed corresponding to the sliding limit state can be obtained, and then the overall stability coefficient of the sliding soil wedge can be obtained.

7. The method for calculating the force of the reinforcement of the end-turned reinforced soil roadbed according to claim 6 is characterized in that: In step 500: the axial static equilibrium condition of the free section of the tie rod, the basic equilibrium equation of the free section of the tie rod is:

8. The method for calculating the force of the reinforcement of the end-turned reinforced soil roadbed according to claim 6 is characterized in that: In step 600: according to the axial static equilibrium condition of the reinforcement anchoring section, the basic equilibrium equation of the reinforcement anchoring section can be obtained as follows: Where Nr(la+lb) is the tension on the reinforcement at x=la+lb at the centerline of the roadbed, N r (l a +l b )=K0(γih+σ vi )h, K0 is the static earth pressure coefficient, take σ vi It is the vertical compressive stress generated in the middle of the i-th layer of reinforcement by the surface load on the top of the roadbed.

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