Calculation method for design limit of lateral horizontal displacement of top of road shoulder retaining wall

Abstract

The invention relates to the technical field of roadbed engineering and building slope engineering, and discloses a calculation method for the design limit of the lateral horizontal displacement of the top of a shoulder retaining wall, which includes the following steps: using an earth pressure extreme value search method to calculate the vertical inclination of the potential sliding surface of the soil behind the wall, and then determining the range of the potential sliding soil wedge and its length at the top surface of the soil when the soil behind the wall is in an active limit equilibrium state; based on the differential settlement limit value of the top surface of the backfill of the shoulder retaining wall, according to the deformation coordination of the wall and soil, the design limit of the lateral horizontal displacement of the top of the wall is calculated. Based on the sliding instability mode of the soil behind the wall, the invention simply calculates the design limit of the lateral horizontal displacement of the top of the wall by considering the differential settlement limit value requirements of the top surface of the roadbed soil behind the wall and the deformation coordination of the soil behind the wall, thereby improving the calculation efficiency, and further analyzing the influence characteristics of the main factors affecting the displacement design limit, and can analyze the gravity retaining wall and the cantilever retaining wall.

Description

Technical Field

[0001] The present invention relates to the technical field of subgrade engineering and building slope engineering. Specifically, it relates to a calculation method for the design limit of the lateral horizontal displacement at the top of a shoulder retaining wall. Background Art

[0002] A shoulder retaining wall is a commonly used structure for retaining subgrade fill in railway and highway projects, used to slope the subgrade and reduce the land occupation area. The stability and deformation problems of the shoulder retaining wall affect the safety, stability and normal usability of related road projects. In current engineering practice, the stability of the wall is mainly the key control link. In fact, the lateral horizontal displacement of the wall directly affects the settlement deformation of the road surface and is also an important link.

[0003] However, there is no clear regulation in the current code for the calculation method of the lateral horizontal displacement of the shoulder retaining wall, making the design calculation of the lateral horizontal displacement of the shoulder retaining wall in actual projects lack a theoretical method reference and mainly rely on experience, with blindness in design. In particular, in high-speed railway and highway projects, there are relatively strict limit requirements for the differential settlement deformation of the subgrade. Correspondingly, for the shoulder retaining walls in such projects, since the lateral displacement of the wall will cause vertical differential settlement of the soil behind the wall, it is necessary to simultaneously put forward a limit on the lateral horizontal displacement at the top of the shoulder retaining wall, that is, it is necessary to determine the design limit of the lateral horizontal displacement at the top of the shoulder retaining wall in the relevant engineering design.

[0004] At present, for the calculation and analysis of the design limit of the lateral horizontal displacement at the top of the shoulder retaining wall, there is a lack of a conceptually simple and practically easy-to-operate method. Generally speaking, numerical simulation methods can be used to approximately simulate and analyze this problem, such as the finite element method, the finite difference method, etc. Although these methods are feasible, there are the following problems in the specific operation of actual engineering design: (1) Complex numerical model establishment operation: Numerical simulation methods require detailed modeling of the physical and mechanical properties of the soil, the wall, and the soil-wall contact interface, which involves a large number of engineering parameter measurements. Among them, it is difficult to determine the deformation parameters, soil-wall interface parameters, etc., resulting in a cumbersome numerical modeling process and being easily affected by subjective factors. (2) Time-consuming and laborious calculation: Numerical simulation analysis requires a large amount of calculation time. For engineering designers, the operation is cumbersome and the time cost is high, which is not conducive to quickly and effectively completing the design task.

[0005] Therefore, although the current related calculation methods are feasible at the theoretical level, there is a lack of a simple and easy-to-operate algorithm in actual application, enabling engineering designers to more conveniently and quickly perform the calculation and analysis of the design limit of the lateral horizontal displacement at the top of the shoulder retaining wall. Summary of the Invention

[0006] The main object of the present invention is to provide a calculation method for the design limit of the lateral horizontal displacement at the top of the shoulder retaining wall, so as to solve the technical problem of complex and difficult operation existing in the existing calculation methods.

[0007] In order to achieve the above object, the present invention provides a calculation method for the design limit of the lateral horizontal displacement at the top of the shoulder retaining wall, and the technical solution is as follows:

[0008] The calculation method for the design limit of the lateral horizontal displacement at the top of the shoulder retaining wall includes the following steps:

[0009] Adopt the extreme earth pressure search method to calculate the vertical inclination angle of the potential slip surface of the soil mass behind the wall, and then determine the range of the potential sliding soil wedge when the soil mass behind the wall is in the active ultimate equilibrium state and the length of its position on the top surface of the soil mass.

[0010] Based on the differential settlement limit value of the top surface of the backfill soil behind the shoulder retaining wall, calculate the design limit of the lateral horizontal displacement at the top of the wall according to the deformation coordination between the wall and the soil.

[0011] The prominent advantages of the calculation method for the design limit of the lateral horizontal displacement at the top of the shoulder retaining wall of the present invention are as follows: Based on the sliding instability mode of the soil mass behind the wall, by considering the differential settlement limit value requirement of the top surface of the subgrade soil mass behind the wall and the deformation coordination of the soil mass behind the wall, simply calculate the design limit of the lateral horizontal displacement at the top of the wall, improve the calculation efficiency, and can further analyze the influence characteristics of the main factors affecting the displacement design limit. It can analyze gravity retaining walls and cantilever retaining walls, and has the unity of various common wall types.

[0012] It can be seen that the present invention overcomes the deficiencies of the traditional method. By introducing a simplified mathematical expression, the analysis of the design limit of the lateral horizontal displacement at the top of the shoulder retaining wall is transformed into a form that is easy to understand and calculate. Different from the previous numerical simulation methods with complex operations, this algorithm focuses on simplicity and practicability, making the engineering design more intuitive and efficient, enabling engineering designers to more easily analyze and design the lateral horizontal displacement limit at the top of the shoulder retaining wall, providing a fast and effective method and scientific basis for the deformation control design calculation and analysis of the shoulder retaining wall, and having important technical method significance and engineering application value.

[0013] The following further describes the present invention in conjunction with the drawings and specific embodiments. The additional aspects and advantages of the present invention will be partially given in the following description, partially become obvious from the following description, or be understood through the practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] The drawings constituting a part of the present invention are used to assist in understanding the present invention. The content provided in the drawings and the related descriptions in the present invention can be used to explain the present invention, but do not constitute an improper limitation to the present invention. In the drawings:

[0015] Figure 1 This is an analysis pattern diagram of the potential sliding soil wedge at the rear side when the retaining wall of the present invention is a gravity retaining wall.

[0016] Figure 2 This is an analysis pattern diagram of the potential sliding soil wedge at the rear side when the retaining wall of the present invention is a cantilever wall.

[0017] Figure 3 This is a schematic diagram of the gravity retaining wall supporting the soil mass in Embodiment 1 of the present invention.

[0018] Figure 4 This is the analysis result of the range of the potential sliding soil wedge at the rear side of the wall under normal working conditions in Embodiment 1 of the present invention.

[0019] Figure 5 This is the analysis result of the range of the potential sliding soil wedge at the rear side of the wall under seismic working conditions in Embodiment 1 of the present invention.

[0020] Figure 6 This is a schematic diagram of the cantilever wall supporting the soil mass in Embodiment 2 of the present invention.

[0021] Figure 7 This is the analysis result of the range of the potential sliding soil wedge at the rear side of the wall under normal working conditions in Embodiment 2 of the present invention.

[0022] Figure 8 This is the analysis result of the range of the potential sliding soil wedge at the rear side of the wall under seismic working conditions in Embodiment 2 of the present invention.

[0023] The relevant markings in the above-mentioned drawings are as follows:

[0024] 100 - retaining wall, 110 - vertical arm, 120 - heel slab, 130 - wall top, 210 - top surface of the soil mass behind the wall, 220 - potential sliding soil wedge. Detailed implementation manners

[0025] The present invention will be described clearly and completely below with reference to the drawings. Those of ordinary skill in the art will be able to implement the present invention based on these descriptions. Before describing the present invention with reference to the drawings, it should be particularly noted that:

[0026] The technical solutions and technical features provided in each part including the following description in the present invention can be combined with each other without conflict.

[0027] In addition, the embodiments of the present invention involved in the following description are usually only some embodiments of the present invention, rather than all embodiments. Therefore, all other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts should fall within the protection scope of the present invention.

[0028] Regarding the terms and units in the present invention. The terms "comprising", "having" and any variations thereof in the description, claims and relevant parts of the present invention are intended to cover non-exclusive inclusion.

[0029] The specific implementation manner of the calculation method for the design limit value of the lateral horizontal displacement at the top of the shoulder retaining wall of the present invention includes the following steps: Step 10, using the extreme earth pressure search method, calculate the vertical inclination angle of the potential slip surface of the soil mass behind the wall, and then determine the range of the potential sliding soil wedge when the soil mass behind the wall is in the active ultimate equilibrium state and the length of the potential sliding soil wedge at the position of the top surface of the soil mass; Step 20, based on the differential settlement limit value of the backfill top surface behind the shoulder retaining wall, calculate the design limit value of the lateral horizontal displacement at the top of the wall according to the deformation coordination between the wall and the soil.

[0030] In Step 10, for the action of seismic force, the pseudo-static method is used for analysis; the potential slip surface of the soil mass behind the wall includes a first slip surface relatively far from the wall and a second slip surface relatively close to the wall in the soil mass behind the wall, and there is a common intersection point between the first slip surface and the second slip surface. When the retaining wall 100 is a gravity retaining wall, the analysis mode of the corresponding potential sliding soil wedge 220 behind the retaining wall is as Figure 1 shown. The first slip surface AB is the slip surface to be calculated and determined, the second slip surface AD is the back surface of the wall, and the intersection point A is located at the rear end of the wall bottom in contact with the soil mass behind the wall; when the retaining wall 100 is a cantilever wall, the analysis mode of the corresponding potential sliding soil wedge 220 behind the retaining wall is as Figure 2 shown. Both the first slip surface AB and the second slip surface AD are the slip surfaces to be calculated and determined, and the intersection point A is located in the local soil mass behind the wall at the rear of the wall bottom end.

[0031] Adopt the plane sliding mode for the soil mass behind the wall. According to the principle of ultimate equilibrium, use the extreme earth pressure search method to calculate the vertical inclination angles of the first slip surface AB and the second slip surface AD, and then determine the range ABD of the potential sliding soil wedge 220 when the soil mass behind the wall is in the active ultimate equilibrium state. The length of its BD is the length of the potential sliding soil wedge 220 behind the wall at the position of the top surface 210 of the soil mass behind the wall.

[0032] The calculation expression of the extreme earth pressure search method with the vertical inclination angles of the first slip surface AB and the second slip surface AD as variables is:

[0033]

[0034] In the formula, E a is the active earth pressure acting on the second slip surface AD;

[0035] X 1 、X 2 、X 3They are all intermediate calculation variables, and their expressions are as follows:

[0036]

[0037] In the formula, k h is the horizontal seismic influence coefficient, with the direction from the backfill soil side to the retaining wall being positive; k v is the vertical seismic influence coefficient, with the vertical downward direction being positive; q is the uniformly distributed vertical load acting on the top surface 210 of the backfill soil; c is the cohesion of the backfill soil; is the internal friction angle of the backfill soil; β is the vertical inclination angle of the first slip surface AB; α is the vertical inclination angle of the second slip surface AD; δ is the external friction angle of the second slip surface AD; l is the length of the first slip surface AB; L 0 is the length of the potential sliding soil wedge 220 behind the retaining wall at the position of the top surface 210 of the backfill soil; G is the gravity value of the potential sliding soil wedge 220 behind the retaining wall;

[0038] l, L 0 and G are calculated by the following expressions respectively:

[0039]

[0040] In the formula, H is the height of the retaining wall 100; η is the horizontal inclination angle of the top surface 210 of the backfill soil; γ is the unit weight of the backfill soil.

[0041] In step 20, the calculation expression for the design limit value of the lateral horizontal displacement at the top of the wall 130 is:

[0042]

[0043] In the formula, u is the design limit value of the lateral horizontal displacement at the top of the wall 130; ω is the differential settlement limit value of the top surface 210 of the backfill soil.

[0044] The beneficial effects of the present invention will be described below through specific embodiments.

[0045] Embodiment 1

[0046] Figure 3 is a schematic diagram of the gravity retaining wall retaining soil in this embodiment. As Figure 3 shown, the back of the gravity retaining wall is vertical, the wall height H is 10 m, and the uniformly distributed vertical load q acting on the top surface 210 of the backfill soil is 70 kPa. The cohesion c of the backfill soil is 5 kPa, the internal friction angle is 35°, the unit weight γ of the soil is 20 kN / m 3 , and the external friction angle δ of the back of the wall is taken as the internal friction angle of the soil Half of it. The horizontal inclination angle η of the top surface 210 of the soil mass behind the wall is 10°, and the vertical inclination angle α of the second slip surface AD is 0°. The differential settlement limit value ω of the top surface 210 of the soil mass behind the wall is 80 mm. Then, the design limits of the lateral horizontal displacement of the wall top 130 under the general working condition without considering earthquakes and the earthquake working condition are calculated as follows:

[0047] General working condition (k h = k v = 0):

[0048] According to Step 10, substitute the relevant calculation parameters into Equations (1) to (3). Through mathematical calculations, it can be obtained that: As Figure 4 shown, the vertical inclination angle β of the first slip surface AB is 31.19°, and the width L of the potential sliding soil wedge 220 behind the wall at the position of the top surface 210 of the soil mass behind the wall 0 = 6.88 m.

[0049] According to Step 20, substitute the relevant calculation parameters into Equation (4) and calculate to obtain:

[0050]

[0051] Therefore, the design limit value u of the lateral horizontal displacement of the wall top 130 under the general working condition is 55.3 mm.

[0052] Earthquake working condition (k h = 0.1, k v = 0.06):

[0053] According to Step 10, substitute the relevant calculation parameters into Equations (1) to (3). Through mathematical calculations, it can be obtained that: As Figure 5 shown, the vertical inclination angle β of the first slip surface AB is 39.87°, and the width L of the potential sliding soil wedge 220 behind the wall at the position of the top surface 210 of the soil mass behind the wall 0 = 9.95 m.

[0054] According to Step 20, substitute the relevant calculation parameters into Equation (4) and calculate to obtain:

[0055]

[0056] Therefore, the design limit value u of the lateral horizontal displacement of the wall top 130 under the earthquake working condition is 80.0 mm.

[0057] Table 1 presents the comparison between the calculation results of the method of the present invention in Example 1 and the numerical simulation results of FLAC3D. It can be seen that for the design limit value u of the horizontal displacement at the top of the wall 130, under normal conditions and seismic conditions, the numerical simulation results of FLAC3D are 60.2 mm and 89.1 mm respectively, and the absolute values of the deviation of the method of the present invention relative to FLAC3D are 8.1% and 10.2% respectively. The two are relatively consistent, and the results of the method of the present invention are on the small side, that is, relatively conservative for engineering design, indicating that the method of the present invention has good rationality.

[0058] Table 1

[0059] Working condition The method of the present invention FLAC3D numerical simulation Absolute value of relative deviation (%) General working condition 55.3 60.2 8.1 Seismic working condition 80.0 89.1 10.2

[0060] Example 2

[0061] Figure 6 is a schematic diagram of the cantilever wall retaining the soil body for this example. As Figure 6 shown, the back of the cantilever wall is vertical, the wall height H is 6 m, the height of the vertical arm 110 is 5.5 m, the width of the heel plate 120 is 4 m, the thickness of the heel plate 120 is 0.5 m, and the uniformly distributed vertical load q acting on the top surface 210 of the soil body behind the wall is 20 kPa. The cohesion c of the soil body behind the wall is 5 kPa, the internal friction angle is 34°, the unit weight γ of the soil is 19 kN / m 3 , and the external friction angle δ on the back of the wall is taken to be equal to the internal friction angle of the soil body . The horizontal inclination angle η of the top surface 210 of the soil body behind the wall is 5°. The differential settlement limit value ω of the top surface 210 of the soil body behind the wall is 100 mm. Then, the design limit values of the lateral horizontal displacement of the top of the wall 130 under normal conditions without considering earthquakes and seismic conditions are calculated as follows:

[0062] Normal conditions (k h =k v =0):

[0063] According to step 10, substituting the relevant calculation parameters into equations (1) to (3), through mathematical calculations, it can be obtained that: as Figure 7 shown, the vertical inclination angle β of the first slip surface AB is 26.93°, the vertical inclination angle α of the second slip surface AD is 36.03°, and the width L of the potential sliding soil wedge 220 behind the wall at the position of the top surface 210 of the soil body behind the wall 0 = 7.79 m.

[0064] According to step 20, substituting the relevant calculation parameters into equation (4), the calculation result is:

[0065]

[0066] Thus, the design limit value u of the lateral horizontal displacement of the top of the wall 130 under normal conditions is 130.9 mm.

[0067] Seismic condition (k h = 0.15, k v = 0.10):

[0068] According to step 10, substitute the relevant calculation parameters into equations (1) to (3), and through mathematical calculations, it can be obtained that: as Figure 8 shown, the vertical inclination angle β of the first slip surface AB is 44.96°, the vertical inclination angle α of the second slip surface AD is 36.03°, and the width L of the potential sliding soil wedge 220 behind the wall at the top surface 210 of the soil behind the wall 0 = 11.39 m.

[0069] According to step 20, substitute the relevant calculation parameters into equation (4), and the calculation result is as follows:

[0070]

[0071] Thus, the design limit value u of the lateral horizontal displacement at the top 130 of the wall under the seismic condition is 191.6 mm.

[0072] Table 2 gives the comparison between the calculation results of the method of the present invention in Example 2 and the FLAC3D numerical simulation results. It can be seen that for the design limit value u of the horizontal displacement at the top 130 of the wall, under the normal condition and the seismic condition, the FLAC3D numerical simulation results are 143.5 mm and 209.2 mm respectively, and the absolute values of the deviation of the method of the present invention relative to FLAC3D are 8.8% and 8.4% respectively. The two are relatively consistent, and the result of the method of the present invention is smaller, that is, it is relatively conservative for engineering design, which also shows that the method of the present invention has good rationality.

[0073] Table 2

[0074] Working condition The method of the present invention FLAC3D numerical simulation Absolute value of relative deviation (%) General working condition 130.9 143.5 8.8 Seismic working condition 191.6 209.2 8.4

[0075] The above describes the relevant content of the present invention. Those of ordinary skill in the art will be able to implement the present invention based on these descriptions. Based on the above content of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

Claims

1. The calculation method of the design limit of the lateral horizontal displacement of the top of the shoulder retaining wall is characterized by: The following steps are involved: The soil pressure extreme value search method is used to calculate the vertical inclination of the potential sliding surface of the soil behind the wall, and then determine the range of the potential sliding soil wedge and its length at the top surface of the soil when the soil behind the wall is in an active limit equilibrium state; the potential sliding surface of the soil behind the wall includes the first sliding surface relatively far away from the wall and the second sliding surface relatively close to the wall in the soil behind the wall, and the first sliding surface and the second sliding surface have a common intersection; Based on the differential settlement limit of the top surface of the fill behind the shoulder retaining wall and the coordination of wall-soil deformation, the design limit of the lateral horizontal displacement of the top of the wall is calculated; Among them, the calculation expression of the earth pressure extreme value search method is: ； In the formula, E a is the active earth pressure acting on the second sliding surface; X 1. X 2. X 3 are all intermediate calculation variables, and their expressions are: ； The calculation expression of the design limit of the lateral horizontal displacement of the wall top is: ； In the formula, k h is the horizontal earthquake influence coefficient, with the coefficient pointing from the soil behind the wall to the wall as positive; k v is the vertical earthquake influence coefficient, with vertical downward being positive; q is the full vertical load acting on the top surface of the soil behind the wall; c is the cohesion of the soil behind the wall; φ is the internal friction angle of the soil behind the wall; β is the vertical inclination of the first slip surface; α is the vertical inclination of the second slip surface; δ is the external friction angle of the second sliding surface; l is the length of the first slip surface; L 0 is the length of the potential sliding soil wedge behind the wall at the top surface of the soil behind the wall; G is the gravity value of the potential sliding soil wedge behind the wall; u is the design limit of the lateral horizontal displacement of the wall top; ω is the differential settlement limit value of the top surface of the soil behind the wall; H is the height of the retaining wall.

2. The method for calculating the design limit of the lateral horizontal displacement of the top of the shoulder retaining wall according to claim 1, characterized in that: The retaining wall is a gravity retaining wall or a cantilever wall.

3. The method for calculating the design limit of the lateral horizontal displacement of the top of the shoulder retaining wall according to claim 2, characterized in that: When the retaining wall is a gravity retaining wall, the first sliding surface is the sliding surface to be determined by calculation, the second sliding surface is the back of the wall, and the intersection is located at the rear end of the wall bottom in contact with the soil behind the wall; When the retaining wall is a cantilever wall, the first sliding surface and the second sliding surface are both sliding surfaces to be determined by calculation, and the intersection is located in the rear side local wall rear soil at the rear end of the wall bottom.

4. The method for calculating the design limit of the lateral horizontal displacement of the top of the shoulder retaining wall according to claim 1, characterized in that: l , L 0. G The calculation expressions are: ； In the formula, η is the horizontal inclination angle of the top surface of the soil behind the wall; γ It is the weight of the soil behind the wall.

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