CN112182731A - Non-extreme state two-dimensional slope stability evaluation method - Google Patents
Non-extreme state two-dimensional slope stability evaluation method Download PDFInfo
- Publication number
- 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
- Authority
- CN
- China
- Prior art keywords
- slope
- search
- calculation unit
- dimensional
- value calculation
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
- 238000011156 evaluation Methods 0.000 title claims abstract description 17
- 238000004364 calculation method Methods 0.000 claims abstract description 122
- 238000000034 method Methods 0.000 claims abstract description 68
- 230000006378 damage Effects 0.000 claims abstract description 25
- 239000002689 soil Substances 0.000 claims description 28
- 230000008569 process Effects 0.000 claims description 9
- 238000005192 partition Methods 0.000 claims description 4
- 238000010008 shearing Methods 0.000 claims description 3
- 238000004445 quantitative analysis Methods 0.000 abstract description 3
- 238000011158 quantitative evaluation Methods 0.000 abstract description 3
- 231100000817 safety factor Toxicity 0.000 description 17
- 238000004458 analytical method Methods 0.000 description 11
- 230000008901 benefit Effects 0.000 description 5
- 238000010586 diagram Methods 0.000 description 4
- 230000002787 reinforcement Effects 0.000 description 4
- 230000007547 defect Effects 0.000 description 3
- 238000005457 optimization Methods 0.000 description 3
- 239000011435 rock Substances 0.000 description 3
- 238000012360 testing method Methods 0.000 description 3
- 241000282414 Homo sapiens Species 0.000 description 2
- 238000009412 basement excavation Methods 0.000 description 2
- 238000013461 design Methods 0.000 description 2
- 230000002068 genetic effect Effects 0.000 description 2
- 238000012544 monitoring process Methods 0.000 description 2
- 101000760716 Homo sapiens Short-chain specific acyl-CoA dehydrogenase, mitochondrial Proteins 0.000 description 1
- 102100024639 Short-chain specific acyl-CoA dehydrogenase, mitochondrial Human genes 0.000 description 1
- 230000009471 action Effects 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 238000010835 comparative analysis Methods 0.000 description 1
- 238000010276 construction Methods 0.000 description 1
- 238000011161 development Methods 0.000 description 1
- 238000009826 distribution Methods 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
- 230000002650 habitual effect Effects 0.000 description 1
- 238000004519 manufacturing process Methods 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 230000002265 prevention Effects 0.000 description 1
- 238000004886 process control Methods 0.000 description 1
- 230000009467 reduction Effects 0.000 description 1
- 238000011160 research Methods 0.000 description 1
- 230000003068 static effect Effects 0.000 description 1
Images
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/10—Geometric CAD
- G06F30/13—Architectural design, e.g. computer-aided architectural design [CAAD] related to design of buildings, bridges, landscapes, production plants or roads
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
- G06F2119/02—Reliability analysis or reliability optimisation; Failure analysis, e.g. worst case scenario performance, failure mode and effects analysis [FMEA]
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Geometry (AREA)
- Theoretical Computer Science (AREA)
- Computer Hardware Design (AREA)
- General Physics & Mathematics (AREA)
- Evolutionary Computation (AREA)
- General Engineering & Computer Science (AREA)
- Architecture (AREA)
- Civil Engineering (AREA)
- Structural Engineering (AREA)
- Computational Mathematics (AREA)
- Mathematical Analysis (AREA)
- Mathematical Optimization (AREA)
- Pure & Applied Mathematics (AREA)
- Pit Excavations, Shoring, Fill Or Stabilisation Of Slopes (AREA)
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
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],
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;
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.
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, 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;
the friction angle of the soil body;
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;
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],
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;
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.
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;
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;
the friction angle of the soil body;
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;
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
(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 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
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 non-extreme state two-dimensional slope stability evaluation method is characterized by comprising 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;
let V be the four vertices of the numerical calculation unit i of the search grid 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;
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;
①f≤[f],
②p≥[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;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;
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 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 related to the slope;
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;
the friction angle of the soil body;
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;
the friction angle of the soil body.
2. The non-extreme state two-dimensional slope stability evaluation method according to claim 1, wherein the step (1) is specifically as follows:
(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.
3. The non-extreme state two-dimensional slope stability evaluation method according to claim 2, wherein all the partitions are uniform partitions.
4. The method for evaluating the stability of the non-extreme state two-dimensional slope according to claim 1, wherein in the step (1), the number of numerical calculation units in each search grid is 1-25.
5. The method for evaluating the stability of a non-extreme state two-dimensional 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 non-extreme state two-dimensional 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' GB50330-2013 and 'building foundation pit support technical Specification' JGJ 120-2012.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202011166672.1A CN112182731A (en) | 2020-10-27 | 2020-10-27 | Non-extreme state two-dimensional slope stability evaluation method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202011166672.1A CN112182731A (en) | 2020-10-27 | 2020-10-27 | Non-extreme state two-dimensional slope stability evaluation method |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN112182731A true CN112182731A (en) | 2021-01-05 |
Family
ID=73922856
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202011166672.1A Pending CN112182731A (en) | 2020-10-27 | 2020-10-27 | Non-extreme state two-dimensional slope stability evaluation method |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN112182731A (en) |
Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112900410A (en) * | 2021-01-18 | 2021-06-04 | 汕头大学 | Method for determining ultimate bearing capacity of strip foundation |
| CN113591191A (en) * | 2021-07-29 | 2021-11-02 | 中国科学院武汉岩土力学研究所 | Two-dimensional slope stability vector sum analysis method and system based on integral gliding direction |
| CN114996809A (en) * | 2022-06-03 | 2022-09-02 | 兰州大学 | Nonlinear slope type slope stability evaluation method based on internal and external power ratio |
| CN117688780A (en) * | 2024-01-30 | 2024-03-12 | 中交一航局第三工程有限公司 | Method for calculating local and global safety coefficients of two-dimensional multistage stacking slope |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105224742A (en) * | 2015-09-29 | 2016-01-06 | 鞍钢集团矿业公司 | A kind of blast action of analyzing is got out of a predicament or an embarrassing situation the method for slope stability |
| CN105654550A (en) * | 2015-09-24 | 2016-06-08 | 中国电建集团昆明勘测设计研究院有限公司 | Three-dimensional geological display method for hydropower engineering side slope |
| KR102156832B1 (en) * | 2019-10-10 | 2020-09-16 | (주)지트 | System and method for survey slope area using drone |
-
2020
- 2020-10-27 CN CN202011166672.1A patent/CN112182731A/en active Pending
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105654550A (en) * | 2015-09-24 | 2016-06-08 | 中国电建集团昆明勘测设计研究院有限公司 | Three-dimensional geological display method for hydropower engineering side slope |
| CN105224742A (en) * | 2015-09-29 | 2016-01-06 | 鞍钢集团矿业公司 | A kind of blast action of analyzing is got out of a predicament or an embarrassing situation the method for slope stability |
| KR102156832B1 (en) * | 2019-10-10 | 2020-09-16 | (주)지트 | System and method for survey slope area using drone |
Non-Patent Citations (4)
| Title |
|---|
| 于继光等: "《北京钢铁学院研究生硕士学位论文摘要汇编1982年度》", 31 July 1982 * |
| 朱思哲等: "《三轴试验原理与应用技术》", 30 June 2003 * |
| 李博: "基于应力状态的边坡空间滑移面模型及其稳定性评价方法研究", 《兰州理工大学工程硕士学位论文》 * |
| 牛键: "基于加速度的地下洞室稳定性分析方法的改进与应用", 《中国优秀博硕士学位论文全文数据库(硕士)基础科学辑》 * |
Cited By (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112900410A (en) * | 2021-01-18 | 2021-06-04 | 汕头大学 | Method for determining ultimate bearing capacity of strip foundation |
| CN112900410B (en) * | 2021-01-18 | 2022-08-16 | 汕头大学 | Method for determining ultimate bearing capacity of strip foundation |
| CN113591191A (en) * | 2021-07-29 | 2021-11-02 | 中国科学院武汉岩土力学研究所 | Two-dimensional slope stability vector sum analysis method and system based on integral gliding direction |
| CN113591191B (en) * | 2021-07-29 | 2024-04-23 | 中国科学院武汉岩土力学研究所 | Two-dimensional side slope stability vector sum analysis method and system based on integral sliding direction |
| CN114996809A (en) * | 2022-06-03 | 2022-09-02 | 兰州大学 | Nonlinear slope type slope stability evaluation method based on internal and external power ratio |
| CN117688780A (en) * | 2024-01-30 | 2024-03-12 | 中交一航局第三工程有限公司 | Method for calculating local and global safety coefficients of two-dimensional multistage stacking slope |
| CN117688780B (en) * | 2024-01-30 | 2024-04-12 | 中交一航局第三工程有限公司 | Method for calculating local and global safety coefficients of two-dimensional multistage stacking slope |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN112182731A (en) | Non-extreme state two-dimensional slope stability evaluation method | |
| CN112214921B (en) | Three-dimensional slope stability evaluation method based on stress vector | |
| CN105260575B (en) | A kind of deformation of the surrounding rock in tunnel prediction technique neural network based | |
| CN110889588A (en) | Method for evaluating risk level of shield tunnel construction adjacent building by using factor judgment matrix | |
| CN110210776B (en) | Tunnel construction dynamic risk assessment method based on monitoring measurement | |
| CN110162932B (en) | Calculation method for automatically monitoring slope stability based on finite element division | |
| CN108256141A (en) | A kind of main aftershock joint vulnerability analysis method based on Copula theories | |
| CN115659729A (en) | Dam safety monitoring analysis method and system based on structural simulation calculation | |
| WO2023241472A1 (en) | Geotechnical engineering structure modal prediction and analysis method and system | |
| CN106952000A (en) | A kind of Karst Regional landslide disaster risk dynamic assessment method | |
| CN110348074A (en) | The method and device of climate change risk partition | |
| CN117763895A (en) | Dynamic response sensitivity analysis method and system for concrete gravity dam | |
| CN115238553A (en) | Method and system for dividing dangerous area of buried pipeline leakage erosion | |
| CN111339602A (en) | Method for determining earthquake resistance evaluation index of underground vertical wall vault tunnel structure | |
| CN113221399B (en) | Decision method for dividing scheme of railway tunnel fabricated lining components | |
| CN110555598A (en) | Fuzzy comprehensive evaluation method for stability of karst foundation | |
| CN113153348B (en) | Underground cavern group arrangement scheme comparison and selection method under high ground stress condition | |
| Alkroosh et al. | Soft computing for modeling punching shear of reinforced concrete flat slabs | |
| CN116595890A (en) | Stability modeling method for layered rock slope | |
| CN117195363A (en) | Complex surrounding rock aging stability analysis method based on joint shearing damage area range | |
| CN106709199A (en) | Robustness method based on storey drift | |
| Delalibera et al. | Numerical analysis of two pile caps with sockets embedded, subject the eccentric compression load | |
| CN114492206A (en) | Calculation method for determining tunnel excavation footage based on fractured rock mass joint model | |
| CN110598349B (en) | Goaf dangerous pillar identification method | |
| CN112487712A (en) | Underground suspended pipeline working condition parameter intelligent identification method based on genetic algorithm and multidimensional dynamic time warping |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| RJ01 | Rejection of invention patent application after publication | ||
| RJ01 | Rejection of invention patent application after publication |
Application publication date: 20210105 |