A method for determining the suitable length of slope rate transition section for treatment of slope collapse disaster

Abstract

The present application relates to a kind of slope collapse disaster treatment's slope rate transition section suitable length determination method, comprising: obtaining the geological parameter of highway slope;Design the design slope rate of collapse slope;Design the three-dimensional geometric parameter of slope;Establish the two-dimensional plane model corresponding to three-dimensional entity;Establish highway slope safety and economic multi-objective optimization nonlinear mathematical programming model;Solve highway slope safety and economic multi-objective optimization nonlinear mathematical programming model, obtain the slope rate transition section length of optimal economy under acceptable safety condition.The present application can quickly obtain the length of slope rate transition section, both can guarantee slope safety, also can achieve economic saving, bring greater convenience for highway slope collapse treatment design and construction.

Description

Technical Field

[0001] This invention belongs to the field of highway slope collapse disaster treatment, specifically relating to a method for determining the appropriate length of the slope transition section in slope collapse disaster treatment. Background Technology

[0002] In recent years, with the increase in the total length of highways open to traffic nationwide, the problem of slope collapse disasters has become increasingly prominent, especially in the mountainous areas of Yunnan, where high slopes are particularly numerous and the problem of high slope disasters is becoming increasingly significant. Whether it is a newly built highway or an existing highway, slope collapse disasters are always unavoidable. After a slope collapse disaster occurs, it is generally necessary to clear the debris and re-install protective measures. After clearing the loose material from the collapse, the normal slope is relatively steep, while the slope of the collapsed section is relatively gentler, resulting in a gradual change in slope ratio between the collapsed section and the normal (steeper) slope.

[0003] Currently, the handling of gradual slope changes often relies on design or construction experience, providing a transition section of 20 or 30 meters without systematic research and calculation based on geology, slope height, and slope difference. Due to inconsistent experience, the transition section length given based on experience is often either too long or too short. If the transition section is too long, a significant amount of abandoned, intact sections of protection need to be removed, resulting in inefficiency, waste, and increased land occupation. If the transition section is too short, the slope change is rapid, leading to local slope instability and the continued risk of slope collapse. If not handled properly, secondary collapse accidents are highly likely.

[0004] Therefore, given that the specific geological conditions, slope height, and slope collapse range are all determined, we can try to determine a more reasonable slope transition section length that can both ensure slope safety and achieve economic savings. Summary of the Invention

[0005] To address the aforementioned problems, this invention provides a method for determining the appropriate length of the slope transition section in the treatment of slope collapse disasters. This method can quickly obtain the length of the slope transition section, ensuring slope safety while achieving economic efficiency, thus greatly facilitating the design and construction of highway slope collapse treatment.

[0006] The specific technical solution of the present invention is as follows:

[0007] A method for determining the appropriate length of the slope transition section in the treatment of slope collapse disasters includes the following steps:

[0008] Step (1) Obtain the geological parameters of the highway slope;

[0009] Step (2) Determine the design slope ratio of the collapse slope; the proposed design slope ratio of the collapse slope is 1:n1; n1 is the design slope ratio of the collapse slope;

[0010] Step (3) Determine the three-dimensional geometric parameters of the slope;

[0011] The proposed three-dimensional geometric parameters include the slope ratio of a normal, intact slope (1:n2), slope height H, and the length of the slope transition section L; n2 is the slope ratio of a normal, intact slope.

[0012] Step (4) Establish a two-dimensional planar model corresponding to the three-dimensional entity;

[0013] The contour line method is used to convert the three-dimensional entity into a two-dimensional plane, and a two-dimensional plane model corresponding to the three-dimensional entity is established.

[0014] Step (5) Establish a multi-objective optimization nonlinear mathematical programming model for highway slope safety and economy;

[0015] The equilibrium equation constraints are established using the principle that the tangent values ​​of similar right triangles are equal in a two-dimensional plane model.

[0016] Step (6) Solve the multi-objective optimization nonlinear mathematical programming model for the safety and economy of highway slopes to obtain the optimal slope transition section length under acceptable safety conditions, i.e., the appropriate length of the slope transition section.

[0017] In this process, the multi-objective optimization nonlinear mathematical programming model of highway slope safety and economy is transformed into a single-objective optimization nonlinear mathematical programming model of highway slope economy by adopting a proposed safety acceptability R.

[0018] Furthermore, in step (1), the geological parameters of the highway slope obtained include stratum lithology, stratum occurrence, geological structure, weathering degree, basic allowable value of bearing capacity, and standard value of frictional resistance.

[0019] Furthermore, in step (4), the contour interval of the contour lines is 1 meter.

[0020] Furthermore, in step (5), the equilibrium equation constraints are as follows:

[0021] Max: A; (Indicates finding the maximum safety factor)

[0022] Max: J; (indicates finding the maximum economic coefficient)

[0023] Subject to: Max:A=Max:n m (This indicates that the maximum safety factor corresponds to the steepest and gentlest slope.)

[0024] Max: J = Min: L; (This means the maximum economic coefficient corresponds to the shortest transition period)

[0025] ;

[0026] In the formula: Max represents finding the maximum, and Min represents finding the minimum; A is the safety factor for highway slope treatment; J is the economic factor for highway slope treatment; n m is the steepest slope rate of the transition section slope, and the larger the value of n m the safer it is; L is the length of the slope rate transition section, and the smaller the value of L, the more economical it is; a is the angle between n2 and n m which is equivalent to the angle between the contour line at the top of the transition section slope and the horizontal line.

[0027] Further, in step (6), the solution process is as follows:

[0028] Max: J; (represents finding the maximum economic factor)

[0029] Subject to: Max: J = Min: L; (represents that the maximum economic factor is the shortest for the transition section)

[0030] n m = R * n2;

[0031] ;

[0032] In the formula: R is the acceptable degree of safety, and the specific value of the acceptable degree is determined according to the geological parameters of the highway slope obtained in step (1).

[0033] Further, the value range of R is 0.7 < R < 1, and the larger the value of R, the safer the slope.

[0034] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0035] The present invention takes the length of the transition section between the collapsed slope and the normal slope as the research object, establishes a transition design model between the normal section slope and the collapsed section slope. The model uses contour lines to convert the model into a plane, and geometric methods are used to solve the model on the plane. By determining the steepest slope rate (that is, determining the acceptable degree value R), the appropriate length of the slope rate transition section can be solved.

[0036] The method of the present invention is different from the traditional design or construction experience of similar projects. The model combines theory with practice. Through the method of the present invention, the length of the slope rate transition section can be quickly obtained, which can not only ensure the safety of the slope but also achieve economy and savings, bringing great convenience to the design and construction of highway slope collapse treatment.

[0037] The present invention is applicable to determining the appropriate length of the slope rate transition section that comprehensively considers the safety and economy of highway slope collapse treatment, and has the characteristics of simple method, fast calculation, and strong engineering practicability. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 is a schematic diagram of the slope collapse model of the embodiment of the present invention;

[0039] Figure 2 for Figure 1 Detailed diagram of the geometric relationship of position I. Detailed Implementation

[0040] The technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.

[0041] Unless otherwise defined, the technical or scientific terms used in the embodiments of this application shall have the ordinary meaning as understood by one of ordinary skill in the art. Words such as "comprising" or "including" mean that the element or object preceding the word covers the element or object listed after the word and its equivalents, but does not exclude other elements or objects.

[0042] Example 1

[0043] This embodiment focuses on the slope of an interchange ramp of a highway. The slope soil is red clay with local mixed kiln mud, and the soil is in a saturated state.

[0044] For the aforementioned highway interchange ramp slopes, this embodiment presents a method for determining the appropriate length of the slope transition section in slope collapse disaster treatment. The method includes:

[0045] Step (1) Obtain the geological parameters of the highway slope.

[0046] This includes specific stratigraphic lithology, stratum occurrence, geological structure, weathering degree, basic allowable bearing capacity, and standard value of frictional resistance.

[0047] Step (2) Determine the design slope ratio of the collapsed slope.

[0048] The original design of the ramp was a 1:1 cut slope with a relatively flat farmland top. The slope was protected by cast-in-place concrete arched grids, and all construction has been completed. It is required to preserve as much of the undamaged concrete arched protection as possible and achieve a reasonable transition between the normal section and the collapsed section.

[0049] Due to the impact of heavy rainfall, a section of the ramp slope collapsed. After clearing the collapsed section and taking into account geological parameters, the design slope ratio of the collapsed slope is proposed to be 1:2, with n1 being 2.

[0050] Step (3) Determine the three-dimensional geometric parameters of the slope.

[0051] Based on the actual collapse at the site, the three-dimensional geometric parameters of the slope are proposed. The slope ratio of the normal section is 1:1, n2 is 1, the slope height H is 16 meters, and the length L of the slope transition section is unknown, but is tentatively set at 20 meters.

[0052] Step (4) Establish a two-dimensional plane model corresponding to the three-dimensional entity.

[0053] like Figure 1 As shown, the contour line method is used to convert the three-dimensional entity into a two-dimensional plane and establish a two-dimensional plane model corresponding to the three-dimensional entity. The contour interval of the contour lines in the model is 2 meters, the plane spacing of the contour lines of the normal slope is 2 meters, and the plane spacing of the contour lines of the collapsed slope is 4 meters.

[0054] Step (5) Establish a multi-objective optimization nonlinear mathematical programming model for highway slope safety and economy;

[0055] like Figure 2 At position I, using the principle that the tangent values ​​of similar right triangles are equal in a two-dimensional plane model, equilibrium equations and constraints are established. A multi-objective optimization nonlinear mathematical programming model for highway slope safety and economy is then established, as follows:

[0056] Objective 1: Maximum safety factor: Max: A;

[0057] Objective 2: Maximum economic coefficient: Max: J;

[0058] Constraints:

[0059] The maximum safety factor is the steepest slope with the gentlest gradient: Max:A = Max:n m ;

[0060] The maximum economic coefficient is the shortest transition period: Max:J = Min:L;

[0061] ;

[0062] Where: A is the safety factor for highway slope treatment; J is the economic factor for highway slope treatment; n m n represents the steepest slope rate of the transition section slope. m The larger the value, the safer it is; L is the length of the slope transition section, and the smaller the value of L, the more economical it is; a is the ratio of n² to n. m The angle between the contour line and the horizontal line at the top of the transition section slope is the same as the angle between the contour line and the horizontal line at the top of the transition section slope.

[0063] Step (6) Solve the nonlinear mathematical programming model for multi-objective optimization of highway slope safety and economy to obtain the optimal slope transition section length under acceptable safety conditions, i.e., the suitable length of the slope transition section.

[0064] The "nonlinear mathematical programming model for multi-objective optimization of highway slope safety and economy" is converted into the "nonlinear mathematical programming model for single-objective optimization of highway slope economy" by using the proposed safety acceptability R for solution as follows:

[0065] Objective of solution: Maximum economic coefficient: Max: J;

[0066] Constraints:

[0067] The maximum economic coefficient is that the transition section is the shortest: Max: J = Min: L;

[0068] n m = R * n2

[0069] ;

[0070] In the formula: R is the safety acceptability. Generally, 0.7 < R < 1. The larger the R value, the safer the slope. The specific value of the acceptability is determined according to the geological parameters of the highway slope. The minimum acceptable value of R is taken as 0.9.

[0071] The specific value of R defines the safety of the highway slope within an acceptable range. The maximum safety is the minimum acceptable value corresponding to the steepest slope rate, that is, the minimum acceptable degree corresponding to R. According to the above solution idea, we can get

[0072] ;

[0073] The appropriate length of the slope rate transition section of L is about 33 meters, which is the shortest slope rate transition section under acceptable safety conditions.

[0074] The above is only the preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for determining the appropriate length of the slope transition section in the treatment of slope collapse disasters, characterized in that: It includes the following steps: Step (1): Obtain the geological parameters of the highway slope; Step (2): Determine the designed slope ratio of the collapsed slope; the designed slope ratio of the collapsed slope is 1:n1; n1 is the designed slope ratio of the collapsed slope; Step (3): Determine the three-dimensional geometric parameters of the slope; Determine that the three-dimensional geometric parameters include the slope ratio of the normal intact slope 1:n2, the slope height H, and the length L of the slope ratio transition section; n2 is the slope ratio of the normal intact slope; Step (4): Establish a two-dimensional plane model corresponding to the three-dimensional entity; Use the contour line method to convert the three-dimensional entity into a two-dimensional plane and establish a two-dimensional plane model corresponding to the three-dimensional entity; Step (5): Establish a multi-objective optimization non-linear mathematical programming model for the safety and economy of the highway slope; Use the principle that the tangent values of similar right triangles in the two-dimensional plane model are equal to establish the equilibrium equation constraint conditions; The equilibrium equation constraint conditions are as follows: Solve objective 1: Maximum safety factor: Max: A; Solve objective 2: Maximum economic factor: Max: J; Constraint conditions: The maximum safety factor is the steepest slope with the gentlest gradient: Max:A = Max:n m ; The maximum economic factor is that the transition section is the shortest: Max: J = Min: L; ； In the formula: Max represents finding the maximum, Min represents finding the minimum; A is the safety factor for highway slope treatment; J is the economic factor for highway slope treatment; n m n represents the steepest slope rate of the transition section slope. m The larger the value, the safer it is; L is the length of the slope transition section, and the smaller the value of L, the more economical it is; a is the ratio of n² to n. m The angle between the contour line and the horizontal line at the top of the transition section slope is equal to the angle between the contour line and the horizontal line. Step (6): Solve the multi-objective optimization non-linear mathematical programming model for the safety and economy of the highway slope, and obtain the length of the slope ratio transition section with the optimal economy under the acceptable safety conditions, that is, the appropriate length of the slope ratio transition section; The solution process is as follows: Solve objective: Find the maximum economic factor: Max: J; Constraint conditions: The maximum economic factor is that the transition section is the shortest: Max: J = Min: L; n m =R*n2; ； In the formula: R is the acceptable degree of safety, and the specific value of the acceptable degree is determined according to the geological parameters of the highway slope obtained in step (1); Among them, the multi-objective optimization non-linear mathematical programming model for the safety and economy of the highway slope is converted into a single-objective optimization non-linear mathematical programming model for the economy of the highway slope by using the proposed acceptable degree of safety R for solution.

2. The method according to claim 1, characterized in that: In step (1), the obtaining of the geological parameters of the highway slope includes formation lithology, rock stratum occurrence, geological structure, weathering degree, basic allowable value of bearing capacity, and standard value of frictional resistance.

3. The method according to claim 1, characterized in that: In step (4), the contour interval of the contour line is 1 meter.

4. The method according to claim 1, characterized in that: In the solution process of step (6), the value range of R is 0.7 < R < 1, and the larger the R value, the safer the slope.

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