Method for calculating design limit value of lateral horizontal displacement of wall 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 of a road shoulder retaining wall top lateral horizontal displacement design limit value, which comprises the following steps of: calculating a vertical inclination angle of a potential slip crack surface of a soil body behind a wall by adopting a soil pressure extreme value search method; further determining a potential sliding soil wedge body range when the soil body behind the wall is in an active limit equilibrium state and the length of the potential sliding soil wedge body on the top surface of the soil body; and calculating the design limit value of the lateral horizontal displacement of the wall top according to the differential settlement limit value of the filling top surface of the rear side of the road shoulder retaining wall and the wall soil deformation coordination. Based on the sliding instability mode of the soil body behind the wall, the lateral horizontal displacement design limit value of the wall top is simply calculated by considering the differential settlement limit value requirement of the top surface of the roadbed soil body behind the wall and the deformation coordination of the soil body behind the wall, the calculation efficiency is improved, and the calculation cost is reduced. The influence characteristics of main factors influencing the displacement design limit value can be further analyzed, and a gravity retaining wall and a cantilever retaining wall can be analyzed.

Description

Technical Field

[0001] The invention relates to the technical field of roadbed engineering and building slope engineering, and in particular to a method for calculating a design limit value of lateral horizontal displacement of a top of a shoulder retaining wall. Background Art

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

[0003] However, there is no clear provision for the calculation method of the lateral horizontal displacement of the shoulder retaining wall in the current specifications, which makes the design and calculation of the lateral horizontal displacement of the shoulder retaining wall in actual projects lack theoretical reference and are mostly based on experience, which is blind in design. In particular, in high-speed railway and highway projects, there are relatively strict restrictions on the differential settlement deformation of the roadbed. Accordingly, for the shoulder retaining wall 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 limit the lateral horizontal displacement of the top of the shoulder retaining wall, that is, the design limit of the lateral horizontal displacement of the top of the shoulder retaining wall needs to be determined in the relevant engineering design.

[0004] At present, there is a lack of a simple and practical method for the calculation and analysis of the design limit of the lateral horizontal displacement of the top of the shoulder retaining wall. From a general perspective, numerical simulation methods can be used to approximate the simulation and analysis of this problem, such as the finite element method and the finite difference method. Although these methods are feasible, there are several problems in the specific operation of actual engineering design: (1) Complex numerical model establishment operation: The numerical simulation method requires detailed modeling of the physical and mechanical properties of the soil, wall, and the wall-soil contact interface, which involves a large number of engineering parameter measurements. Among them, the determination of deformation parameters and wall-soil interface parameters is difficult, resulting in a cumbersome numerical modeling process and easy to be affected by subjective factors. (2) Time-consuming and laborious calculation: Numerical simulation analysis requires a lot of calculation 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.

[0005] Therefore, although the current relevant calculation methods are feasible at the theoretical level, they lack a simple and easy-to-operate algorithm in practical applications, which enables engineering designers to more conveniently and quickly calculate and analyze the design limit of the lateral horizontal displacement of the top of the shoulder retaining wall. Summary of the invention

[0006] The main purpose of the present invention is to provide a calculation method for the design limit of the lateral horizontal displacement of the top of the shoulder retaining wall, so as to solve the technical problems of the calculation methods in the prior art that are complicated and difficult to operate.

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

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

[0009] 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.

[0010] Based on the differential settlement limit value of the top surface of the fill behind the shoulder retaining wall and the coordination of wall-soil deformation, the design limit value of the lateral horizontal displacement of the wall top is calculated.

[0011] The outstanding advantages of the calculation method of the lateral horizontal displacement design limit of the top of the shoulder retaining wall of the present invention are: based on the sliding instability mode of the soil behind 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, the lateral horizontal displacement design limit of the top of the wall is simply calculated, the calculation efficiency is improved, and the influence characteristics of the main factors affecting the displacement design limit can be further analyzed. Gravity retaining walls and cantilever retaining walls can be analyzed, and it has the unity of multiple common wall types.

[0012] It can be seen that the present invention overcomes the shortcomings of traditional methods. By introducing simplified mathematical expressions, the analysis of the design limit of the lateral horizontal displacement of the top of the shoulder retaining wall is converted into a form that is easy to understand and calculate. Unlike the previous complex numerical simulation methods, this algorithm focuses on simplicity and practicality, making engineering design more intuitive and efficient, and enabling engineering designers to more easily analyze and design the lateral horizontal displacement limit of the top of the shoulder retaining wall, providing a quick and effective method and scientific basis for the deformation control design calculation and analysis of the shoulder retaining wall, which has important technical method significance and engineering application value.

[0013] 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

[0014] 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:

[0015] Figure 1 This is an analysis model 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 model 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 Schematic diagram of a gravity retaining wall supporting a soil body according to Example 1 of the present invention.

[0018] Figure 4 This is the analysis result of the potential sliding soil wedge range behind the wall under the general working condition of Example 1 of the present invention.

[0019] Figure 5 This is the analysis result of the potential sliding soil wedge range behind the wall under the earthquake condition of Example 1 of the present invention.

[0020] Figure 6 Schematic diagram of a cantilever wall retaining body according to Example 2 of the present invention.

[0021] Figure 7 This is the analysis result of the potential sliding soil wedge range behind the wall under the general working condition of Example 2 of the present invention.

[0022] Figure 8 This is the analysis result of the potential sliding soil wedge range behind the wall under the earthquake condition of Example 2 of the present invention.

[0023] The relevant marks in the above drawings are:

[0024] 100-retaining wall, 110-vertical arm, 120-heel plate, 130-top of wall, 210-top surface of soil behind the wall, 220-potential sliding soil wedge. DETAILED DESCRIPTION

[0025] 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:

[0026] 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.

[0027] 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.

[0028] 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.

[0029] The specific implementation method of the method for calculating the design limit of the lateral horizontal displacement of the top of the shoulder retaining wall of the present invention includes the following steps: Step 10, using the soil pressure extreme value search method to calculate the vertical inclination angle 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; Step 20, based on the differential settlement limit value of the top surface of the fill on the rear side of the shoulder retaining wall, according to the coordination of wall-soil deformation, calculate the design limit of the lateral horizontal displacement of the top of the wall.

[0030] In step 10, the quasi-static method is used to analyze the earthquake force. The potential sliding surface of the soil behind the wall includes a first sliding surface relatively far from the wall and a second sliding surface relatively close to the wall in the soil behind the wall. The first sliding surface and the second sliding surface have a common intersection. When the retaining wall 100 is a gravity retaining wall, the analysis mode of the potential sliding soil wedge 220 behind the retaining wall is as follows: Figure 1 As shown, the first sliding surface AB is the sliding surface to be determined by calculation, the second sliding surface AD ​​is the back of the wall, and the intersection A is located at the rear end of the wall bottom in contact with the soil behind the wall; when the retaining wall 100 is a cantilever wall, the corresponding analysis mode of the potential sliding soil wedge 220 on the rear side of the retaining wall is as follows Figure 2 As shown, the first sliding surface AB and the second sliding surface AD ​​are both sliding surfaces to be determined by calculation, and the intersection A is located in the rear side local wall back soil at the rear end of the wall bottom.

[0031] A plane sliding mode is adopted for the soil behind the wall. According to the limit equilibrium principle, the soil pressure extreme value search method is used to calculate the vertical inclination angles of the first sliding surface AB and the second sliding surface AD, and then the range ABD of the potential sliding soil wedge 220 when the soil behind the wall is in an active limit equilibrium state is determined. The BD length is the length of the potential sliding soil wedge 220 behind the wall at the top surface 210 of the soil behind the wall.

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

[0033]

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

[0035] X1, X2, and X3 are all intermediate calculation variables, and their expressions are:

[0036]

[0037] In the formula, k h k is the horizontal earthquake influence coefficient, with the value from the side of the soil behind the wall pointing to the wall as positive; v is the vertical earthquake influence coefficient, with vertical downward being positive; q is the full vertical load acting on the top surface 210 of the soil behind the wall; c is the cohesion of the soil behind the wall; is the internal friction angle of the soil behind the wall; β is the vertical inclination angle of the first sliding surface AB; α is the vertical inclination angle of the second sliding surface AD; δ is the external friction angle of the second sliding surface AD; l is the length of the first sliding surface AB; L0 is the length of the potential sliding soil wedge 220 behind the wall at the top surface 210 of the soil behind the wall; G is the gravity value of the potential sliding soil wedge 220 behind the wall;

[0038] The calculation expressions of l, L0, and G are:

[0039]

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

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

[0042]

[0043] Where u is the design limit of the lateral horizontal displacement of the wall top 130°; ω is the limit value of the differential settlement of the top surface 210° of the soil behind the wall.

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

[0045] Example 1

[0046] Figure 3 FIG. 1 is a schematic diagram of the gravity retaining wall supporting the soil body of this embodiment. Figure 3 As shown in the figure, the back of the gravity retaining wall is vertical, the wall height H is 10m, and the full vertical load q acting on the top surface 210 of the soil behind the wall is 70kPa. The cohesion c of the soil behind the wall is 5kPa, and the internal friction angle is is 35°, soil weight γ is 20kN / m 3 The external friction angle δ on the back of the wall is taken as the internal friction angle of the soil The horizontal inclination angle η of the top surface 210 of the soil behind the wall is 10°, and the vertical inclination angle α of the second sliding surface AD ​​is 0°. The differential settlement limit value ω of the top surface 210 of the soil behind the wall is 80 mm. Then the design limit of the lateral horizontal displacement of the top 130 of the wall under the general working condition without considering the earthquake and the earthquake working condition is calculated as follows:

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

[0048] According to step 10, the relevant calculation parameters are substituted into equations (1) to (3), and after mathematical calculation, the following is obtained: Figure 4 As shown, the vertical inclination angle β of the first sliding surface AB is 31.19°, and the width L0 of the potential sliding soil wedge 220 behind the wall at the top surface 210 of the soil behind the wall is 6.88 m.

[0049] According to step 20, the relevant calculation parameters are substituted into formula (4) to obtain:

[0050]

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

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

[0053] According to step 10, the relevant calculation parameters are substituted into equations (1) to (3), and after mathematical calculation, the following is obtained: Figure 5 As shown, the vertical inclination angle β of the first sliding surface AB is 39.87°, and the width L0 of the potential sliding soil wedge 220 behind the wall at the top surface 210 of the soil behind the wall is 9.95m.

[0054] According to step 20, the relevant calculation parameters are substituted into formula (4) to obtain:

[0055]

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

[0057] Table 1 shows the comparison between the calculation results of the method of the present invention and the FLAC3D numerical simulation results of Example 1. It can be seen that for the design limit u of the horizontal displacement of the top of the wall 130, under normal working conditions and earthquake working conditions, the FLAC3D numerical simulation results are 60.2 mm and 89.1 mm respectively, and the absolute values ​​of the deviations of the method of the present invention relative to FLAC3D are 8.1% and 10.2% respectively, which are relatively consistent, and the results of the method of the present invention are smaller, that is, relatively conservative for engineering design, which shows that the method of the present invention has good rationality.

[0058] Table 1

[0059] Working conditions Method of the present invention FLAC3D numerical simulation Absolute value of relative deviation (%) General working conditions 55.3 60.2 8.1 Earthquake conditions 80.0 89.1 10.2

[0060] Example 2

[0061] Figure 6 FIG. 2 is a schematic diagram of the cantilever wall retaining body of this embodiment. Figure 6 As shown, the back of the cantilever wall is vertical, the wall height H is 6m, the height of the vertical arm 110 is 5.5m, the width of the heel plate 120 is 4m, the thickness of the heel plate 120 is 0.5m, and the full vertical load q acting on the top surface 210 of the soil behind the wall is 20kPa. The cohesion c of the soil behind the wall is 5kPa, and the internal friction angle is 34°, and the soil weight γ is 19kN / m 3 The external friction angle δ on the back of the wall is taken as the internal friction angle with the soil The horizontal inclination angle η of the top surface 210 of the soil behind the wall is 5°. The differential settlement limit value ω of the top surface 210 of the soil behind the wall is 100 mm. Then the design limit of the lateral horizontal displacement of the top 130 of the wall under the general working condition without considering the earthquake and the earthquake working condition is calculated as follows:

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

[0063] According to step 10, the relevant calculation parameters are substituted into equations (1) to (3), and after mathematical calculation, the following is obtained: Figure 7 As shown, the vertical inclination angle β of the first sliding surface AB is 26.93°, the vertical inclination angle α of the second sliding surface AD ​​is 36.03°, and the width L0 of the potential sliding soil wedge 220 behind the wall at the top surface 210 of the soil behind the wall is 7.79 m.

[0064] According to step 20, the relevant calculation parameters are substituted into formula (4) to obtain:

[0065]

[0066] Therefore, the design limit value of the lateral horizontal displacement of the wall top 130 under general working conditions is u=130.9 mm.

[0067] Earthquake conditions (k h =0.15, k v =0.10):

[0068] According to step 10, the relevant calculation parameters are substituted into equations (1) to (3), and after mathematical calculation, the following is obtained: Figure 8 As shown, the vertical inclination angle β of the first sliding surface AB is 44.96°, the vertical inclination angle α of the second sliding surface AD ​​is 36.03°, and the width L0 of the potential sliding soil wedge 220 behind the wall at the top surface 210 of the soil behind the wall is 11.39 m.

[0069] According to step 20, the relevant calculation parameters are substituted into formula (4) to obtain:

[0070]

[0071] Therefore, the design limit value of the lateral horizontal displacement of the wall top 130 under earthquake conditions is u=191.6 mm.

[0072] Table 2 shows the comparison between the calculation results of the method of the present invention and the FLAC3D numerical simulation results of Example 2. It can be seen that for the design limit u of the horizontal displacement of the top of the wall 130, under normal working conditions and earthquake working conditions, the FLAC3D numerical simulation results are 143.5 mm and 209.2 mm respectively, and the absolute values ​​of the deviations of the method of the present invention relative to FLAC3D are 8.8% and 8.4% respectively, which are relatively consistent, and the results of the method of the present invention are smaller, that is, relatively conservative for engineering design, which also shows that the method of the present invention has good rationality.

[0073] Table 2

[0074] Working conditions Method of the present invention FLAC3D numerical simulation Absolute value of relative deviation (%) General working conditions 130.9 143.5 8.8 Earthquake conditions 191.6 209.2 8.4

[0075] 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 creative work shall fall within the scope of protection 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. 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 wall top is calculated.

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: The potential sliding surface of the soil behind the wall includes a first sliding surface relatively far from the wall and a 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.

4. The method for calculating the design limit of the lateral horizontal displacement of the top of the shoulder retaining wall according to claim 3 is 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.

5. 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: 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; X1, X2, and X3 are all intermediate calculation variables, and their expressions are: In the formula, k h k is the horizontal earthquake influence coefficient, with the value from the side of the soil behind the wall pointing to the wall as positive; 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; is the internal friction angle of the soil behind the wall; β is the vertical inclination angle of the first sliding surface; α is the vertical inclination angle of the second sliding surface; δ is the external friction angle of the second sliding surface; l is the length of the first sliding surface; L0 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.

6. The method for calculating the design limit of the lateral horizontal displacement of the top of the shoulder retaining wall according to claim 5, characterized in that: The calculation expressions of l, L0, and G are: Where H is the height of the retaining wall; η is the horizontal inclination angle of the top surface of the soil behind the wall; γ is the weight of the soil behind the wall.

7. The method for calculating the design limit of the lateral horizontal displacement of the top of the shoulder retaining wall according to claim 5, characterized in that: The calculation expression of the design limit of the lateral horizontal displacement of the wall top is: Where u is the design limit of the lateral horizontal displacement of the wall top; ω is the limit of differential settlement of the top surface of the soil behind the wall.

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