CN112182731A  Nonextreme state twodimensional slope stability evaluation method  Google Patents
Nonextreme state twodimensional slope stability evaluation method Download PDFInfo
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Abstract
The invention relates to a nonextreme state twodimensional slope stability evaluation method, firstly, dispersing a minimum rectangle surrounded by twodimensional 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 twodimensional 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
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 nonextreme state twodimensional slope stability evaluation method.
Background
The problem of slope stability analysis and reinforcement management is a longhistory 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 multipopulation 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 nonextreme state twodimensional slope stability evaluation method.
The overall thought of the invention is as follows: firstly, establishing a twodimensional rectangular coordinate system according to the geometric dimension of a solved twodimensional side slope, dispersing a minimum rectangle surrounded by the width and the height of the twodimensional 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 twodimensional 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 twodimensional slope, and calculating the local area or the whole safety coefficient of the twodimensional 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 nonextreme state twodimensional slope stability evaluation method comprises the following steps:
(1) establishing a search grid;
establishing a twodimensional rectangular coordinate system xy with an x axis parallel to the width of the twodimensional side slope and a y axis parallel to the height of the twodimensional side slope, dispersing a minimum rectangle surrounded by the width and the height of the twodimensional 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 V_{i1}、V_{i2}、V_{i3}、V_{i4}The coordinate of the center point of the search grid j is I_{j}(x_{j},y_{j}) 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;
①x_{min}＜x_{j}＜x_{max},y_{min}＜y_{j}＜y_{max}；
②A_{i}＝A_{i12}+A_{i23}+A_{i34}+A_{i41}；
wherein x is_{min}、x_{max}、y_{min}、y_{max}Respectively correspond to V_{i1}、V_{i2}、V_{i3}、V_{i4}Minimum x coordinate, maximum x coordinate, minimum y coordinate, maximum y coordinate; a. the_{i}Represents the area of the numerical calculation unit i; a. the_{i12}Is represented by point I_{j}、V_{i1}、V_{i2}The area of a triangle is enclosed; a. the_{i23}Is represented by point I_{j}、V_{i2}、V_{i3}The area of a triangle is enclosed; a. the_{i34}Is represented by point I_{j}、V_{i3}、V_{i4}The area of a triangle is enclosed; a. the_{i41}Is represented by point I_{j}、V_{i4}、V_{i1}The 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;
②_{p}≥[_{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;the friction angle of the soil body; tau represents the shearing stress corresponding to the target numerical value calculation unit;_{p}representing 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 01%_{pmax}In the abovementioned manner,_{pmax}representing the maximum plastic strain value of the side slope;
τ、σ、_{p}、_{pmax}all the stress strains are obtained by numerical calculation in advance (or obtained by field monitoring); C.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;
in the formula, K_{W}Representing the integral safety coefficient of the side slope; d represents the total number of potentially corrupted units; k is a radical of_{v}Representing a factor of safety for the vth potentially damaging element; sigma_{v}Representing a corresponding positive stress of the vth potential failure unit; tau is_{v}Representing the corresponding shear stress of the vth potential failure unit; c is the cohesive force of the soil body;the friction angle of the soil body;
in the formula, K_{L}Representing 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 of_{g}Representing the gth potential contained in the local area to be solvedA safety factor that destroys the cell; sigma_{g}Representing the positive stress corresponding to the gth potential failure unit contained in the local area needing to be solved; tau is_{g}Representing the shear stress corresponding to the gth potential failure unit contained in the local area needing to be solved; c is the cohesive force of the soil body;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 nonextreme state twodimensional slope stability evaluation method comprises the following steps of (1):
(1.1) establishing a twodimensional rectangular coordinate system xy according to the geometric dimension of the twodimensional slope, wherein the width of the twodimensional slope is parallel to an x axis, and the height of the twodimensional slope is parallel to a y axis;
(1.2) dividing a minimum rectangle surrounded by the width and the height of the twodimensional 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 twodimensional 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 nonextreme state twodimensional slope stability evaluation method, all the partitions are uniform partitions; all search grids are equal in size.
According to the nonextreme state twodimensional slope stability evaluation method, in the step (1), the number of the numerical calculation units in each search grid is 125, 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 125 in comprehensive consideration.
In the nonextreme state twodimensional 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 nonextreme state twodimensional slope stability evaluation method, in the step (4), the national and local regulations related to the slope include "building slope engineering technical specification" GB503302013 and "building foundation pit support technical specification" JGJ 1202012.
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 nonextreme 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 twodimensional 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 nonextreme state twodimensional slope stability evaluation method comprises the following steps:
(1) establishing a search grid;
establishing a twodimensional rectangular coordinate system xy with an x axis parallel to the width of the twodimensional side slope and a y axis parallel to the height of the twodimensional side slope, dispersing a minimum rectangle surrounded by the width and the height of the twodimensional 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 125 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 twodimensional rectangular coordinate system xy according to the geometric dimension of the twodimensional slope, wherein the width of the twodimensional slope is parallel to an x axis, and the height of the twodimensional slope is parallel to a y axis;
(1.2) uniformly dividing a minimum rectangle surrounded by the width and the height of the twodimensional 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 twodimensional 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 j_{i1}、V_{i2}、V_{i3}、V_{i4}The coordinate of the center point of the search grid j is I_{j}(x_{j},y_{j}) 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;
①x_{min}＜x_{j}＜x_{max},y_{min}＜y_{j}＜y_{max}；
②A_{i}＝A_{i12}+A_{i23}+A_{i34}+A_{i41}；
wherein x is_{min}、x_{max}、y_{min}、y_{max}Respectively correspond to V_{i1}、V_{i2}、V_{i3}、V_{i4}Minimum x coordinate, maximum x coordinate, minimum y coordinate, maximum y coordinate; a. the_{i}Represents the area of the numerical calculation unit i; a. the_{i12}Is represented by point I_{j}、V_{i1}、V_{i2}The area of a triangle is enclosed; a. the_{i23}Is represented by point I_{j}、V_{i2}、V_{i3}The area of a triangle is enclosed; a. the_{i34}Is represented by point I_{j}、V_{i3}、V_{i4}The area of a triangle is enclosed; a. the_{i41}Is represented by point I_{j}、V_{i4}、V_{i1}The 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;
②_{p}≥[_{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;the friction angle of the soil body; tau represents the shearing stress corresponding to the target numerical value calculation unit;_{p}representing 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 01%_{pmax}In the abovementioned manner,_{pmax}representing the maximum plastic strain value of the side slope;
τ、σ、_{p}、_{pmax}all the stress strains are obtained by numerical calculation in advance (or obtained by field monitoring); C.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 twodimensional calculation, and is a line which is generated in a geometric sense, but is threedimensional 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 twodimensional 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 GB503302013 and building foundation pit support technical specification JGJ1202012) related to the slope;
in the formula, K_{W}Representing the integral safety coefficient of the side slope; d represents the total number of potentially corrupted units; k is a radical of_{v}Representing a factor of safety for the vth potentially damaging element; sigma_{v}Representing a corresponding positive stress of the vth potential failure unit; tau is_{v}Representing the corresponding shear stress of the vth potential failure unit; c is the cohesive force of the soil body;the friction angle of the soil body;
in the formula, K_{L}Representing 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 of_{g}Representing the safety factor of the gth potential damage unit contained in the local area needing to be solved; sigma_{g}Representing the positive stress corresponding to the gth potential failure unit contained in the local area needing to be solved; tau is_{g}Representing the shear stress corresponding to the gth potential failure unit contained in the local area needing to be solved; c is the cohesive force of the soil body;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 twodimensional 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
(the parameters in the above table are all required for numerical calculations, C,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 twodimensional 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 nonextreme 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
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. A nonextreme state twodimensional slope stability evaluation method is characterized by comprising the following steps:
(1) establishing a search grid;
establishing a twodimensional rectangular coordinate system xy with an x axis parallel to the width of the twodimensional side slope and a y axis parallel to the height of the twodimensional side slope, dispersing a minimum rectangle surrounded by the width and the height of the twodimensional 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;
let V be the four vertices of the numerical calculation unit i of the search grid j_{i1}、V_{i2}、V_{i3}、V_{i4}The coordinate of the center point of the search grid j is I_{j}(x_{j},y_{j}) 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;
①x_{min}＜x_{j}＜x_{max},y_{min}＜y_{j}＜y_{max}；
②A_{i}＝A_{i12}+A_{i23}+A_{i34}+A_{i41}；
wherein x is_{min}、x_{max}、y_{min}、y_{max}Respectively correspond to V_{i1}、V_{i2}、V_{i3}、V_{i4}Minimum x coordinate, maximum x coordinate, minimum y coordinate, maximum y coordinate; a. the_{i}Represents the area of the numerical calculation unit i; a. the_{i12}Is represented by point I_{j}、V_{i1}、V_{i2}The area of a triangle is enclosed; a. the_{i23}Is represented by point I_{j}、V_{i2}、V_{i3}The area of a triangle is enclosed; a. the_{i34}Is represented by point I_{j}、V_{i3}、V_{i4}The area of a triangle is enclosed; a. the_{i41}Is represented by point I_{j}、V_{i4}、V_{i1}The area of a triangle is enclosed;
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;
②_{p}≥[_{p}]；
wherein f represents a safety factor of the target value calculation unit; [ f ] of]Representing a safety factor allowable value; c is the cohesive force of the soil body; sigma represents the corresponding positive stress of the target numerical calculation unit;the friction angle of the soil body; tau represents the shearing stress corresponding to the target numerical value calculation unit;_{p}representing 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 01%_{pmax}In the abovementioned manner,_{pmax}representing the maximum plastic strain value of the side slope;
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) sequentially connecting the central points of all the potential damage units into a line, namely forming a position line of the most dangerous slip plane in a plane, simultaneously calculating the safety coefficient of the twodimensional 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 related to the slope;
in the formula, K_{W}Representing the integral safety coefficient of the side slope; d represents the total number of potentially corrupted units; k is a radical of_{v}Representing a factor of safety for the vth potentially damaging element; sigma_{v}Representing a corresponding positive stress of the vth potential failure unit; tau is_{v}Representing the corresponding shear stress of the vth potential failure unit; c is the cohesive force of the soil body;the friction angle of the soil body;
in the formula, K_{L}Representing 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 of_{g}Representing the safety factor of the gth potential damage unit contained in the local area needing to be solved; sigma_{g}Representing the positive stress corresponding to the gth potential failure unit contained in the local area needing to be solved; tau is_{g}Representing the shear stress corresponding to the gth potential failure unit contained in the local area needing to be solved; c is the cohesive force of the soil body;the friction angle of the soil body.
2. The nonextreme state twodimensional slope stability evaluation method according to claim 1, wherein the step (1) is specifically as follows:
(1.1) establishing a twodimensional rectangular coordinate system xy according to the geometric dimension of the twodimensional slope, wherein the width of the twodimensional slope is parallel to an x axis, and the height of the twodimensional slope is parallel to a y axis;
(1.2) dividing a minimum rectangle surrounded by the width and the height of the twodimensional 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 twodimensional 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.
3. The nonextreme state twodimensional slope stability evaluation method according to claim 2, wherein all the partitions are uniform partitions.
4. The method for evaluating the stability of the nonextreme state twodimensional slope according to claim 1, wherein in the step (1), the number of numerical calculation units in each search grid is 125.
5. The method for evaluating the stability of a nonextreme state twodimensional slope according to claim 1, wherein in the step (3), when target value calculation units meeting the following two conditions simultaneously among the target value calculation units corresponding to the m search grids in each column are searched, the target value calculation units are arranged in a sequence from bottom to top or from top to bottom.
6. The method for evaluating the stability of the nonextreme state twodimensional slope according to claim 1, wherein in the step (4), the national and local regulations related to the slope comprise 'building slope engineering technical Specification' GB503302013 and 'building foundation pit support technical Specification' JGJ 1202012.
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