CN112182731A - Non-extreme state two-dimensional slope stability evaluation method - Google Patents

Non-extreme state two-dimensional slope stability evaluation method Download PDF

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CN112182731A
CN112182731A CN202011166672.1A CN202011166672A CN112182731A CN 112182731 A CN112182731 A CN 112182731A CN 202011166672 A CN202011166672 A CN 202011166672A CN 112182731 A CN112182731 A CN 112182731A
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李忠
于开贞
赵俊杰
倪嘉卿
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Shanghai University of Engineering Science
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Abstract

The invention relates to a non-extreme state two-dimensional slope stability evaluation method, firstly, dispersing a minimum rectangle surrounded by two-dimensional slope width and height into a plurality of rectangular search grids, wherein each search grid comprises more than one numerical calculation unit, and the search grids are horizontally arranged in rows and vertically arranged in columns and are sequentially marked; then, determining a unique corresponding numerical calculation unit in each search grid, and taking the numerical calculation unit as a target numerical calculation unit; then, judging a target numerical value calculation unit which is most likely to reach the yield condition in each row of search grids, determining potential damage units according to the target numerical value calculation unit, and sequentially searching out the potential damage units of all the rows; and finally, obtaining the most dangerous slip surface by all the potential damage units, and simultaneously calculating the local area or the whole safety coefficient of the two-dimensional slope. The method provided by the invention can be suitable for quantitative evaluation and analysis of slope stability under any stress state condition, and the calculation result is closer to the real stress condition of the slope.

Description

Non-extreme state two-dimensional slope stability evaluation method
Technical Field
The invention belongs to the technical field of rock and soil mass slope stability analysis and disaster prevention and reduction, and relates to a non-extreme state two-dimensional slope stability evaluation method.
Background
The problem of slope stability analysis and reinforcement management is a long-history and energetic scientific branch, and the struggle between human beings and landslide disasters has not been interrupted since the time of human production. For a long time, analysis methods for slope stability have been developed, and various methods have appeared. Such as a striping method, a numerical analysis method, a plasticity limit method, a reliability method, a fuzzy mathematic method, a geological comparison method and the like.
Slope stability analysis is usually dominated by the limit balance method and the finite element method. The limit balance method is to consider the problem of slope stability as the problem of rigid body balance, i.e. the rock and soil bodies constituting the landslide body are regarded as rigid bodies in a complex state. Many scholars assume the direction, distribution and action positions of the acting force on the contact surface between the rock and soil blocks, and then derive various different types of extreme balance methods. However, these methods have many assumptions, especially the shape of the slip plane, which greatly limits the application range of the extreme equilibrium method. In recent years, along with the development of computers, a method combining a finite element method and a computer is gradually used for slope stability analysis at home and abroad, so that a slip surface can be better determined, and the slope stability is more accurately analyzed. Some researchers have made some researches, such as analyzing slope stability by searching a slip plane closer to the actual situation by using an ant algorithm on the basis of establishing a stress field by finite element analysis, but the ant algorithm has the defects of slow convergence and easy falling into local optimization. In addition, under the condition of a known stress field, a fitness function is constructed by using a multi-population genetic algorithm to search the most dangerous slip surface, so that the purpose of slope stability analysis is achieved, but the algorithm has the defects that the programming process is complex, and parameters such as the crossing rate and the variation rate generally need to be selected by experience, and is not easy to popularize and apply.
Disclosure of Invention
The invention aims to solve the problems in the prior art and provides a non-extreme state two-dimensional slope stability evaluation method.
The overall thought of the invention is as follows: firstly, establishing a two-dimensional rectangular coordinate system according to the geometric dimension of a solved two-dimensional side slope, dispersing a minimum rectangle surrounded by the width and the height of the two-dimensional side slope into a plurality of search grids, wherein each search grid can contain one or more original numerical calculation units, and the search grids are horizontally arranged in lines and vertically arranged in lines and are sequentially marked; then, determining a unique corresponding numerical calculation unit in each search grid through a two-dimensional slope stress strain field obtained based on numerical calculation, and taking the numerical calculation unit as a target numerical calculation unit; secondly, judging a target numerical value calculation unit which is most likely to reach a yield condition according to numerical calculation stress and strain numerical values from bottom to top or from top to bottom in each row of search grids, marking the search grid where the target numerical value calculation unit is located as a potential damage unit, recording the position coordinate of the search grid where the target numerical value calculation unit is located and the stress and strain value of the search grid, and sequentially searching out potential damage units in all rows; and finally, connecting all the potential damage units in a plane to obtain the most dangerous slip surface of the two-dimensional slope, and calculating the local area or the whole safety coefficient of the two-dimensional slope according to the safety coefficient expression based on the coordinate position and the stress state of the generated most dangerous slip surface.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
a non-extreme state two-dimensional slope stability evaluation method comprises the following steps:
(1) establishing a search grid;
establishing a two-dimensional rectangular coordinate system x-y with an x axis parallel to the width of the two-dimensional side slope and a y axis parallel to the height of the two-dimensional side slope, dispersing a minimum rectangle surrounded by the width and the height of the two-dimensional side slope into n multiplied by m rectangular search grids, and numbering each search grid to complete the establishment of the search grids;
m is the row number parallel to the x axis formed by all the search grid arrangements, n is the column number parallel to the y axis formed by all the search grid arrangements, and the values of n and m satisfy: each search grid comprises more than one numerical calculation unit;
(2) a search target value calculation unit;
setting the search grid jThe four vertexes of the numerical calculation unit i are Vi1、Vi2、Vi3、Vi4The coordinate of the center point of the search grid j is Ij(xj,yj) Searching a numerical value calculation unit which simultaneously meets the following two conditions, namely a target numerical value calculation unit of the search grid j;
①xmin＜xj＜xmax,ymin＜yj＜ymax；
②Ai＝Ai12+Ai23+Ai34+Ai41；
wherein x ismin、xmax、ymin、ymaxRespectively correspond to Vi1、Vi2、Vi3、Vi4Minimum x coordinate, maximum x coordinate, minimum y coordinate, maximum y coordinate; a. theiRepresents the area of the numerical calculation unit i; a. thei12Is represented by point Ij、Vi1、Vi2The area of a triangle is enclosed; a. thei23Is represented by point Ij、Vi2、Vi3The area of a triangle is enclosed; a. thei34Is represented by point Ij、Vi3、Vi4The area of a triangle is enclosed; a. thei41Is represented by point Ij、Vi4、Vi1The area of a triangle is enclosed; (Note that the areas of the above triangles are scalar quantities, and when the area is calculated by using the vector, if the area is negative, the absolute value is taken)
According to the method, sequentially determining target numerical value calculation units corresponding to n multiplied by m rectangular search grids;
if the search grid does not contain the target numerical value calculation unit, the search grid is an invalid grid, and the search grid is marked according to zero in the calculation process and does not participate in the calculation process;
(3) searching for potentially damaging units;
searching target numerical value calculation units which simultaneously meet the following two conditions in the target numerical value calculation units corresponding to the m search grids in each row, wherein the search grids corresponding to the target numerical value calculation units are potential destruction units of the row; when the potential damage unit is judged, the side slope is in any stress state;
①f≤[f],
Figure BDA0002746021030000031
②p≥[p]；
wherein f represents a safety factor of the target value calculation unit; [ f ] of]Representing a safety factor allowable value which can be taken according to a relevant standard (the safety factor allowable value is a value given by a national standard); c is the cohesive force of the soil body; sigma represents the corresponding positive stress of the target numerical calculation unit;
Figure BDA0002746021030000036
the friction angle of the soil body; tau represents the shearing stress corresponding to the target numerical value calculation unit;prepresenting the plastic strain corresponding to the target numerical calculation unit; [p]The plastic strain value allowed in the slip plane search is represented, the value is determined according to the requirements of slope safety control, and the value range is 0-1%pmaxIn the above-mentioned manner,pmaxrepresenting the maximum plastic strain value of the side slope;
τ、σ、p、pmaxall the stress strains are obtained by numerical calculation in advance (or obtained by field monitoring); C.
Figure BDA0002746021030000037
the soil body inherent physical parameters are obtained through tests;
if a plurality of target numerical value calculation units meet the two conditions, taking the search grid corresponding to the target numerical value calculation unit with the minimum f value as a potential destruction unit; if the target numerical value calculation unit does not meet the two conditions, taking the search grid which contains the target numerical value calculation unit and is closest to the top of the column as a potential damage unit;
according to the method, n columns of potential damage units are determined in sequence;
(4) the central points of all potential failure units are sequentially connected into a line, namely a position line of a most dangerous slip surface in a plane is formed (the slip surface is a relatively weak slip band formed in a slope body when the slope is broken, and the slope body is sheared and broken along the slip surface soil body, so that the slope slides and is unstable;
Figure BDA0002746021030000032
Figure BDA0002746021030000033
in the formula, KWRepresenting the integral safety coefficient of the side slope; d represents the total number of potentially corrupted units; k is a radical ofvRepresenting a factor of safety for the vth potentially damaging element; sigmavRepresenting a corresponding positive stress of the v-th potential failure unit; tau isvRepresenting the corresponding shear stress of the v-th potential failure unit; c is the cohesive force of the soil body;
Figure BDA0002746021030000038
the friction angle of the soil body;
Figure BDA0002746021030000034
Figure BDA0002746021030000035
in the formula, KLRepresenting a local area safety factor; e represents the total number of potential damage units contained in the local area needing to be solved; k is a radical ofgRepresenting the g-th potential contained in the local area to be solvedA safety factor that destroys the cell; sigmagRepresenting the positive stress corresponding to the g-th potential failure unit contained in the local area needing to be solved; tau isgRepresenting the shear stress corresponding to the g-th potential failure unit contained in the local area needing to be solved; c is the cohesive force of the soil body;
Figure BDA0002746021030000041
the friction angle of the soil body.
In addition, it should be noted that, as explained above, the potential failure unit calculates the search grid corresponding to the unit for a specific target value, and the stress and strain of the search grid are equal to the stress and strain of the unit for calculating the target value corresponding to the center point of the search grid, the method considers that the stress and strain values of all points in each search grid are the same, so that the stress and strain values are expressed by the stress and strain values of the center point of the search grid, so that the accuracy is higher when the grid division is finer.
As a preferred technical scheme:
the non-extreme state two-dimensional slope stability evaluation method comprises the following steps of (1):
(1.1) establishing a two-dimensional rectangular coordinate system x-y according to the geometric dimension of the two-dimensional slope, wherein the width of the two-dimensional slope is parallel to an x axis, and the height of the two-dimensional slope is parallel to a y axis;
(1.2) dividing a minimum rectangle surrounded by the width and the height of the two-dimensional slope into n vertical bars which are sequentially arranged along the x axis;
(1.3) dividing each vertical bar into m transverse bars which are sequentially arranged along the y axis, so that the minimum rectangle surrounded by the width and the height of the two-dimensional slope is dispersed into n multiplied by m rectangular search grids;
and (1.4) numbering each search grid, namely finishing the establishment of the search grids.
According to the non-extreme state two-dimensional slope stability evaluation method, all the partitions are uniform partitions; all search grids are equal in size.
According to the non-extreme state two-dimensional slope stability evaluation method, in the step (1), the number of the numerical calculation units in each search grid is 1-25, the calculation precision is higher as the number of the numerical calculation units is larger, but the calculation time is increased, and the number of the numerical calculation units in each search grid is 1-25 in comprehensive consideration.
In the non-extreme state two-dimensional slope stability evaluation method, in the step (3), when target value calculation units which simultaneously satisfy the following two conditions among the target value calculation units corresponding to the m search grids in each row are searched, the target value calculation units are arranged in the order from bottom to top or from top to bottom.
In the non-extreme state two-dimensional slope stability evaluation method, in the step (4), the national and local regulations related to the slope include "building slope engineering technical specification" GB50330-2013 and "building foundation pit support technical specification" JGJ 120-2012.
In addition, it should be noted that the units of symbols in all formulas in the present invention are only required to be prepared according to unified international units, wherein the safety factor and the strain are dimensionless units.
Has the advantages that:
(1) compared with a limit balance method, the method is not limited to the traditional limit stress state hypothesis and slip surface shape hypothesis any more, can be suitable for quantitative evaluation and analysis of slope stability under any stress state condition, and the calculation result is closer to the real stress condition of the slope;
(2) the method is simple in algorithm, high in calculation efficiency, suitable for computer programming, closely combined with national specifications, convenient for quantitative analysis and evaluation of slope stability based on commercial numerical analysis software, and easy to popularize and apply, and compared with an analysis method combining other optimization technologies such as a finite element method and a genetic algorithm, the method overcomes the defects that some existing complex algorithms are slow in convergence, easy to fall into local optimization, low in calculation efficiency and difficult to popularize and apply;
(3) the method can adapt to more working conditions, has stronger applicability to the stability of the non-extreme side slope in the side slope reinforcement construction process, has a calculation result closer to the real stress condition of the side slope, is beneficial to improving the accuracy and safety of the evaluation of the stability of the side slope, and has better social benefit and economic benefit.
Drawings
FIG. 1 is a schematic diagram of a search grid;
FIG. 2 is a diagram illustrating a correspondence relationship between a search grid j and a numerical calculation unit i;
FIG. 3 is a schematic diagram of a two-dimensional slope finite element calculation model;
FIG. 4 is a schematic diagram showing the comparison of slip plane position and shape in two methods.
Detailed Description
The invention will be further illustrated with reference to specific embodiments. It should be understood that these examples are for illustrative purposes only and are not intended to limit the scope of the present invention. Further, it should be understood that various changes or modifications of the present invention may be made by those skilled in the art after reading the teaching of the present invention, and such equivalents may fall within the scope of the present invention as defined in the appended claims.
A non-extreme state two-dimensional slope stability evaluation method comprises the following steps:
(1) establishing a search grid;
establishing a two-dimensional rectangular coordinate system x-y with an x axis parallel to the width of the two-dimensional side slope and a y axis parallel to the height of the two-dimensional side slope, dispersing a minimum rectangle surrounded by the width and the height of the two-dimensional side slope into n multiplied by m rectangular search grids with equal size as shown in figure 1, numbering each search grid to realize search process control, namely completing the establishment of the search grids; m is the row number parallel to the x axis formed by all the search grid arrangements, n is the column number parallel to the y axis formed by all the search grid arrangements, and the values of n and m satisfy: each search grid comprises more than one numerical calculation unit (preferably 1-25 numerical calculation units), wherein the numerical calculation units are divided when a numerical model is built; the method comprises the following specific steps:
(1.1) establishing a two-dimensional rectangular coordinate system x-y according to the geometric dimension of the two-dimensional slope, wherein the width of the two-dimensional slope is parallel to an x axis, and the height of the two-dimensional slope is parallel to a y axis;
(1.2) uniformly dividing a minimum rectangle surrounded by the width and the height of the two-dimensional slope into n vertical bars which are sequentially arranged along the x axis;
(1.3) uniformly dividing each vertical bar into m transverse bars which are sequentially arranged along the y axis, so that the minimum rectangle surrounded by the width and the height of the two-dimensional slope is dispersed into n multiplied by m rectangular search grids with equal size;
(1.4) numbering each search grid, namely completing the establishment of the search grids;
(2) a search target value calculation unit;
as shown in FIG. 2, let V be the four vertices of the numerical calculation unit i of the search mesh ji1、Vi2、Vi3、Vi4The coordinate of the center point of the search grid j is Ij(xj,yj) Searching a numerical value calculation unit which simultaneously meets the following two conditions, namely a target numerical value calculation unit of the search grid j;
①xmin＜xj＜xmax,ymin＜yj＜ymax；
②Ai＝Ai12+Ai23+Ai34+Ai41；
wherein x ismin、xmax、ymin、ymaxRespectively correspond to Vi1、Vi2、Vi3、Vi4Minimum x coordinate, maximum x coordinate, minimum y coordinate, maximum y coordinate; a. theiRepresents the area of the numerical calculation unit i; a. thei12Is represented by point Ij、Vi1、Vi2The area of a triangle is enclosed; a. thei23Is represented by point Ij、Vi2、Vi3The area of a triangle is enclosed; a. thei34Is represented by point Ij、Vi3、Vi4The area of a triangle is enclosed; a. thei41Is represented by point Ij、Vi4、Vi1The area of a triangle is enclosed; (Note that the areas of the above triangles are scalar quantities, and when the area is calculated by using the vector, if the area is negative, the absolute value is taken)
According to the method, sequentially determining target numerical value calculation units corresponding to n multiplied by m rectangular search grids;
if the search grid does not contain the target numerical value calculation unit, the search grid is an invalid grid, and the search grid is marked according to zero in the calculation process and does not participate in the calculation process;
(3) searching for potentially damaging units;
searching target numerical value calculation units which simultaneously meet the following two conditions in the target numerical value calculation units corresponding to the m search grids in each row according to the sequence from bottom to top or from top to bottom, wherein the search grids corresponding to the target numerical value calculation units are potential damage units of the row;
①f≤[f],
Figure BDA0002746021030000061
②p≥[p]；
wherein f represents a safety factor of the target value calculation unit; [ f ] of]Representing a safety factor allowable value which can be taken according to a relevant standard (the safety factor allowable value is a value given by a national standard); c is the cohesive force of the soil body; sigma represents the corresponding positive stress of the target numerical calculation unit;
Figure BDA0002746021030000062
the friction angle of the soil body; tau represents the shearing stress corresponding to the target numerical value calculation unit;prepresenting the plastic strain corresponding to the target numerical calculation unit; [p]The plastic strain value allowed in the slip plane search is represented, the value is determined according to the requirements of slope safety control, and the value range is 0-1%pmaxIn the above-mentioned manner,pmaxrepresenting the maximum plastic strain value of the side slope;
τ、σ、p、pmaxall the stress strains are obtained by numerical calculation in advance (or obtained by field monitoring); C.
Figure BDA0002746021030000075
the soil body inherent physical parameters are obtained through tests;
if a plurality of target numerical value calculation units meet the two conditions, taking the search grid corresponding to the target numerical value calculation unit with the minimum f value as a potential destruction unit; if the target numerical value calculation unit does not meet the two conditions, taking the search grid which contains the target numerical value calculation unit and is closest to the top of the column as a potential damage unit;
according to the method, n columns of potential damage units are determined in sequence;
(4) connecting the central points of all the potential failure units in sequence to form a line, namely forming a position line of the most dangerous slip plane in a plane (the slip plane is a relatively weak slip band formed in a slope body when the slope is broken, and the slope body is sheared and broken along the slip plane soil body, so that the slope slides and is unstable; in actual engineering, the slope is mostly simplified into two-dimensional calculation, and is a line which is generated in a geometric sense, but is three-dimensional in practice, and is called as the most dangerous slip plane by a person skilled in the art, which is a habitual statement in the field), meanwhile, calculating the safety coefficient of the two-dimensional slope according to the following formula, comparing the safety coefficient with a reference value, and quantitatively evaluating the stability of the slope, wherein the reference value is an allowable safety coefficient value specified by national and local specifications (including building slope engineering technical specification GB50330-2013 and building foundation pit support technical specification JGJ120-2012) related to the slope;
Figure BDA0002746021030000071
Figure BDA0002746021030000072
in the formula, KWRepresenting the integral safety coefficient of the side slope; d represents the total number of potentially corrupted units; k is a radical ofvRepresenting a factor of safety for the vth potentially damaging element; sigmavRepresenting a corresponding positive stress of the v-th potential failure unit; tau isvRepresenting the corresponding shear stress of the v-th potential failure unit; c is the cohesive force of the soil body;
Figure BDA0002746021030000076
the friction angle of the soil body;
Figure BDA0002746021030000073
Figure BDA0002746021030000074
in the formula, KLRepresenting a local area safety factor; e represents the total number of potential damage units contained in the local area needing to be solved; k is a radical ofgRepresenting the safety factor of the g-th potential damage unit contained in the local area needing to be solved; sigmagRepresenting the positive stress corresponding to the g-th potential failure unit contained in the local area needing to be solved; tau isgRepresenting the shear stress corresponding to the g-th potential failure unit contained in the local area needing to be solved; c is the cohesive force of the soil body;
Figure BDA0002746021030000077
the friction angle of the soil body;
in addition, it should be noted that, as explained above, the potential failure unit calculates the search grid corresponding to the unit for a specific target value, and the stress and strain of the search grid are equal to the stress and strain of the unit for calculating the target value corresponding to the center point of the search grid, the method considers that the stress and strain values of all points in each search grid are the same, so that the stress and strain values are expressed by the stress and strain values of the center point of the search grid, so that the accuracy is higher when the grid division is finer.
The method can obtain the safety coefficient value of a local area besides the whole safety coefficient value, can provide scientific calculation basis for the local or subarea excavation and reinforcement design of the side slope, has stronger applicability and calculation advantages compared with the traditional method, and is explained by combining with specific cases, specifically as follows:
1. establishing finite element calculation model and obtaining stress strain field
Taking the examination questions provided by the Australian Computer Association (ACADS) as an example, the slope is a homogeneous slope, the slope ratio is 1:2, the example is usually used by domestic and foreign scholars to test the feasibility of a two-dimensional slope numerical calculation model, the specific conditions of the size, boundary conditions and the like of the example slope are shown in fig. 3, and the detailed soil layer parameters are shown in table 1.
TABLE 1
Figure BDA0002746021030000081
(the parameters in the above table are all required for numerical calculations, C,
Figure BDA0002746021030000082
Is also used in the method, E, gamma and mu are only used in numerical calculation, which is equivalent to early calculation, and the method is later calculation)
As shown in fig. 3, a two-dimensional slope numerical calculation model (there are many numerical calculation methods, a finite element method is a common one of them, and the method is also applicable to other numerical calculation methods as long as a stress strain field can be obtained, in this example, a finite element method is used, so the finite element calculation model is written) built by using commercial finite element software has a width direction of 40m and a height direction of 20m, the model load only considers dead weight, and the boundary constraint conditions are as follows: the upper boundary is free without constraint condition, the left and right boundaries are horizontally constrained, and the lower boundary is horizontally and vertically constrained. And calculating to obtain the stress field and the strain field of the side slope by adopting nonlinear static analysis.
2. Comparative analysis of calculation results
Based on the calculation example, firstly, a limit balance method is adopted to calculate the most dangerous slip surface and the safety coefficient, and then the technical method provided by the invention is adopted to analyze the slope stability to obtain the most dangerous slip surface and the safety coefficient. The calculation results and the difference of the two methods are obtained by comparing and analyzing the position, the shape and the safety coefficient of the slip surface, and the specific process is not described. The results of comparing the slip plane position, shape and safety factor for both methods are shown in fig. 4 and table 2.
The extreme balance method and the slip plane position and shape obtained by the method of the invention are plotted in fig. 4, respectively. The extreme balance method usually assumes that a slip surface is a circular arc curve and has a regular shape, the position of the slip surface is determined by the circle center and the radius, and assumes that soil bodies of the necessary slip surface are all in an extreme stress state, and only the whole safety coefficient can be obtained by calculation. The method does not make assumptions on the shape of the slip surface, does not assume that soil bodies of the slip surface are in the ultimate stress state, can obtain the slip surface in any shape through calculation, and can obtain local safety factors and overall safety factors in different areas. The slip surface shape in fig. 4 shows that the method is suitable for slope stability analysis in a non-extreme stress state, and the obtained slip surface shape is closer to the reality.
Table 2 shows the results of the ultimate balance method and the calculation of the safety factor obtained by the method of the present invention.
TABLE 2
Figure BDA0002746021030000091
From table 2, it can be seen that the overall safety factor of the slope stability evaluation calculated by the method of the present invention is not much different from the answer of the classical example of the ultimate balance method, the overall safety factor is less than 1.0, and the slope is in an unstable state. The results calculated by the limit balance method are relatively small, because the results are conservative due to various assumptions of the limit balance method. However, the method can obtain the safety coefficient value of a local area besides the whole safety coefficient value, and can provide scientific calculation basis for slope local or subarea excavation and reinforcement design. Therefore, compared with the traditional limit balance method, the method has stronger applicability and calculation advantages.

Claims (6)

1.一种非极限状态二维边坡稳定性评价方法，其特征在于，步骤如下：1. a non-limit state two-dimensional slope stability evaluation method, is characterized in that, step is as follows: (1)建立搜索网格；(1) Establish a search grid; 建立x轴平行于二维边坡宽且y轴平行于二维边坡高的二维直角坐标系x-y，将二维边坡宽和高所围成的最小矩形离散成n×m个矩形搜索网格，对每个搜索网格进行编号，即完成搜索网格的建立；Establish a two-dimensional Cartesian coordinate system x-y with the x-axis parallel to the two-dimensional slope width and the y-axis parallel to the two-dimensional slope height, and discretize the minimum rectangle enclosed by the two-dimensional slope width and height into n × m rectangles for search Grid, number each search grid, that is, complete the establishment of the search grid; m为所有的搜索网格排列形成的平行于x轴的行数，n为所有的搜索网格排列形成的平行于y轴的列数，n、m的取值满足：各搜索网格内包含一个以上数值计算单元；m is the number of rows parallel to the x-axis formed by all the search grid arrangements, n is the number of columns parallel to the y-axis formed by all the search grid arrangements, and the values of n and m satisfy: each search grid contains More than one numerical calculation unit; (2)搜索目标数值计算单元；(2) Searching the target numerical calculation unit; 设搜索网格j的数值计算单元i的四个顶点为Vi1、Vi2、Vi3、Vi4，搜索网格j的中心点坐标为Ij(xj,yj)，搜索同时满足以下两个条件的数值计算单元，即为搜索网格j的目标数值计算单元；Let the four vertices of the numerical calculation unit i of the search grid j be V i1 , V i2 , V i3 , and V i4 , and the coordinates of the center point of the search grid j be I j (x j , y j ), and the search simultaneously satisfies the following The numerical calculation unit of the two conditions is the target numerical calculation unit of the search grid j; ①xmin＜xj＜xmax,ymin＜yj＜ymax；①x min <x j <x max , y min <y j <y max ; ②Ai＝Ai12+Ai23+Ai34+Ai41；②A i =A i12 +A i23 +A i34 +A i41 ; 其中，xmin、xmax、ymin、ymax分别对应为Vi1、Vi2、Vi3、Vi4中的最小x坐标、最大x坐标、最小y坐标、最大y坐标；Ai表示数值计算单元i的面积；Ai12表示由点Ij、Vi1、Vi2围成的三角形面积；Ai23表示由点Ij、Vi2、Vi3围成的三角形面积；Ai34表示由点Ij、Vi3、Vi4围成的三角形面积；Ai41表示由点Ij、Vi4、Vi1围成的三角形面积；Among them, x min , x max , y min , and y max correspond to the minimum x coordinate, maximum x coordinate, minimum y coordinate, and maximum y coordinate in Vi1 , Vi2 , Vi3 , and Vi4 respectively; A i represents numerical calculation The area of the unit i; A i12 represents the area of the triangle enclosed by the points I j , V i1 , and V i2 ; A i23 represents the area of the triangle enclosed by the points I j , V i2 , and V i3 ; A i34 represents the area of the triangle enclosed by the points I j , V i3 , V i4 enclosed triangle area; A i41 represents the triangle area enclosed by points I j , V i4 , V i1 ; 按此方法，依次确定n×m个矩形搜索网格对应的目标数值计算单元；According to this method, sequentially determine the target numerical calculation units corresponding to the n×m rectangular search grids; 若搜索网格内不包含目标数值计算单元，则该搜索网格为无效网格，在计算过程中按零标记，不参与计算过程；If the search grid does not contain the target numerical calculation unit, the search grid is an invalid grid, which is marked as zero in the calculation process and does not participate in the calculation process; (3)搜索潜在破坏单元；(3) Search for potentially damaging units; 搜索每列的m个搜索网格对应的目标数值计算单元中同时满足以下两个条件的目标数值计算单元，该目标数值计算单元对应的搜索网格即为该列的潜在破坏单元；Search the target numerical calculation units corresponding to the m search grids in each column that satisfy the following two conditions at the same time, and the search grid corresponding to the target numerical calculation unit is the potential damage unit of the column; ①f≤[f],
Figure FDA0002746021020000011
①f≤[f],
Figure FDA0002746021020000011
 ②εp≥[εp]；②ε p ≥[ε p ]; 其中，f表示目标数值计算单元的安全系数；[f]表示安全系数允许值；C为土体的粘聚力；σ表示目标数值计算单元对应的正应力；
Figure FDA0002746021020000012
为土体的摩擦角；τ表示目标数值计算单元对应的剪应力；εp表示目标数值计算单元对应的塑性应变；[εp]表示滑移面搜索时允许的塑性应变值，取值大小根据边坡安全控制要求确定，取值范围介于0～1％εpmax之间，εpmax表示边坡最大塑性应变值；Among them, f represents the safety factor of the target numerical calculation unit; [f] represents the allowable value of the safety factor; C is the cohesion of the soil; σ represents the normal stress corresponding to the target numerical calculation unit;
Figure FDA0002746021020000012
is the friction angle of the soil body; τ represents the shear stress corresponding to the target numerical calculation unit; ε p represents the plastic strain corresponding to the target numerical calculation unit; The slope safety control requirements are determined, and the value range is between 0 and 1% ε pmax , where ε pmax represents the maximum plastic strain value of the slope; 如果存在多个目标数值计算单元满足以上两个条件，则将f值最小的目标数值计算单元对应的搜索网格作为潜在破坏单元；如果不存在目标数值计算单元满足以上两个条件，则以包含目标数值计算单元且最靠近该列顶部的搜索网格作为潜在破坏单元；If there are multiple target numerical calculation units that satisfy the above two conditions, the search grid corresponding to the target numerical calculation unit with the smallest f value is used as the potential damage unit; The target numerical calculation unit and the search grid closest to the top of the column are used as potential damage units; 按此方法，依次确定n列的潜在破坏单元；According to this method, the potential damage units of n columns are determined in turn; (4)将所有潜在破坏单元的中心点顺序连接成线，即形成最危险滑移面在平面内位置线，同时，按以下公式计算二维边坡安全系数，并将其与参考值进行比较，定量评价边坡稳定性，参考值为与边坡相关的国家及地方规范规定的允许安全系数值；(4) Sequentially connect the center points of all potential damage units into a line, that is, form the position line of the most dangerous slip surface in the plane, at the same time, calculate the two-dimensional slope safety factor according to the following formula, and compare it with the reference value , quantitatively evaluate the slope stability, the reference value is the allowable safety factor value stipulated by the national and local codes related to the slope;
Figure FDA0002746021020000021
Figure FDA0002746021020000021
Figure FDA0002746021020000022
Figure FDA0002746021020000022
 式中，KW表示边坡整体安全系数；d表示潜在破坏单元的总数；kv表示第v个潜在破坏单元的安全系数；σv表示第v个潜在破坏单元对应的正应力；τv表示第v个潜在破坏单元对应的剪应力；C为土体的粘聚力；
Figure FDA0002746021020000023
为土体的摩擦角；In the formula, K W represents the overall safety factor of the slope; d represents the total number of potential failure units; k v represents the safety factor of the v-th potential failure unit; σ v represents the normal stress corresponding to the v-th potential failure unit; τ v represents The shear stress corresponding to the vth potential failure element; C is the cohesion of the soil;
Figure FDA0002746021020000023
is the friction angle of the soil;
Figure FDA0002746021020000024
Figure FDA0002746021020000024
Figure FDA0002746021020000025
Figure FDA0002746021020000025
 式中，KL表示局部区域安全系数；e表示需要求解的局部区域所包含的潜在破坏单元的总数；kg表示需要求解的局部区域所包含的第g个潜在破坏单元的安全系数；σg表示需要求解的局部区域所包含的第g个潜在破坏单元对应的正应力；τg表示需要求解的局部区域所包含的第g个潜在破坏单元对应的剪应力；C为土体的粘聚力；
Figure FDA0002746021020000026
为土体的摩擦角。In the formula, K L represents the safety factor of the local area; e represents the total number of potential damage units contained in the local area to be solved; k g represents the safety factor of the gth potential damage unit contained in the local area to be solved; σ g represents the normal stress corresponding to the g-th potential failure element contained in the local region to be solved; τ g represents the shear stress corresponding to the g-th potential failure element contained in the local region to be solved; C is the cohesion of the soil ;
Figure FDA0002746021020000026
is the friction angle of the soil. 2.根据权利要求1所述的一种非极限状态二维边坡稳定性评价方法，其特征在于，步骤(1)具体如下：2. a kind of non-limit state two-dimensional slope stability evaluation method according to claim 1, is characterized in that, step (1) is specifically as follows: (1.1)根据二维边坡的几何尺寸建立二维直角坐标系x-y，二维边坡宽平行于x轴，二维边坡高平行于y轴；(1.1) Establish a two-dimensional rectangular coordinate system x-y according to the geometric dimensions of the two-dimensional slope, the two-dimensional slope width is parallel to the x-axis, and the two-dimensional slope height is parallel to the y-axis; (1.2)将二维边坡宽和高所围成的最小矩形划分为沿x轴依次排列的n个竖条；(1.2) Divide the minimum rectangle enclosed by the width and height of the two-dimensional side slope into n vertical bars arranged in sequence along the x-axis; (1.3)将每个竖条划分为沿y轴依次排列的m个横条，至此，二维边坡宽和高所围成的最小矩形离散成n×m个矩形搜索网格；(1.3) Divide each vertical bar into m horizontal bars arranged in sequence along the y-axis, so far, the smallest rectangle enclosed by the width and height of the two-dimensional slope is discrete into n×m rectangular search grids; (1.4)对每个搜索网格进行编号，即完成搜索网格的建立。(1.4) Number each search grid, that is, complete the establishment of the search grid. 3.根据权利要求2所述的一种非极限状态二维边坡稳定性评价方法，其特征在于，所有的划分都为均匀划分。3 . The non-limit state two-dimensional slope stability evaluation method according to claim 2 , wherein all divisions are uniform divisions. 4 . 4.根据权利要求1所述的一种非极限状态二维边坡稳定性评价方法，其特征在于，步骤(1)中，各搜索网格内数值计算单元的个数为1～25。4 . The non-limit state two-dimensional slope stability evaluation method according to claim 1 , wherein in step (1), the number of numerical calculation units in each search grid is 1-25. 5 . 5.根据权利要求1所述的一种非极限状态二维边坡稳定性评价方法，其特征在于，步骤(3)中，搜索每列的m个搜索网格对应的目标数值计算单元中同时满足以下两个条件的目标数值计算单元时，按从下往上或从上往下的顺序。5. a kind of non-limit state two-dimensional slope stability evaluation method according to claim 1, is characterized in that, in step (3), search in the target numerical calculation unit corresponding to m search grids of each column at the same time. When the target numerical calculation unit meets the following two conditions, the order is from bottom to top or top to bottom. 6.根据权利要求1所述的一种非极限状态二维边坡稳定性评价方法，其特征在于，步骤(4)中，与边坡相关的国家及地方规范包括《建筑边坡工程技术规范》GB50330-2013和《建筑基坑支护技术规程》JGJ120-2012。6. a kind of non-limit state two-dimensional slope stability evaluation method according to claim 1, is characterized in that, in step (4), the national and local norms relevant to side slope comprise "Construction side slope engineering technical specification" "GB50330-2013 and "Technical Regulations for Building Foundation Pit Support" JGJ120-2012.
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