CN109583135B - Limit balance analysis method for slope stability of S-shaped groove filling site - Google Patents
Limit balance analysis method for slope stability of S-shaped groove filling site Download PDFInfo
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Abstract
The invention belongs to the technical field of slope stability analysis, and discloses a limit balance analysis method for slope stability of an S-shaped groove filling site; dividing the landslide body into straight sliding sections with different main sliding directions according to the terrain features of the S-shaped groove filling site, and arranging turning sections in the middle for connection conversion; determining a slope stability calculation parameter according to site investigation data; and carrying out iterative computation to obtain the overall stability coefficient of the side slope. According to the invention, turning sections between adjacent straight sliding sections are discretized into quadrangular columns and triangular column unit strips, according to the angular point coordinate values of all the unit strips, the bottom sliding surfaces of the turning sections are fitted into a plane by a least square method, the boundary effect of a slope body is considered, the static balance analysis of the turning sections is carried out according to the geometric characteristics of the bottom sliding surfaces of the strips, the downward sliding force of the upper straight sliding section is transferred to the lower straight sliding section after the direction conversion is realized, and the stability coefficient of the whole slope is calculated by an unbalanced thrust method; the method has strong engineering practicability.
Description
Technical Field
The invention belongs to the technical field of slope stability analysis, and particularly relates to a limit balance analysis method for slope stability of an S-shaped groove filling site.
Background
Currently, the current state of the art commonly used in the industry is as follows:
According to the research current situation of the slope stability analysis method, the existing slope stability analysis method is mainly based on the assumption that the landslide body is the whole body with only one sliding direction, is suitable for the slope which is symmetrical in space, and is not suitable for the slope of the S-shaped groove filling site with the sliding direction changed in different landslide sections; the S-shaped landslide has different sliding directions in different sliding sections, the existing calculation method mainly aims at the whole landslide which is only in one sliding direction, namely is not laterally constrained, the problem of conversion of the landslide sections in different sliding directions at turning sections is not considered, a large gap is reserved between the S-shaped landslide and the actual condition of the landslide of the S-shaped groove filling site, and the problem of how to uniformly analyze stability of a plurality of landslide sections in different sliding directions is solved.
In summary, the problems of the prior art are:
The S-shaped landslide has different sliding directions in different sliding sections, the existing calculation method mainly aims at the whole landslide which is only in one sliding direction, namely is not laterally constrained, the problem of conversion of the landslide sections in different sliding directions at turning sections is not considered, a large gap is reserved between the S-shaped landslide and the actual condition of the landslide of the S-shaped groove filling site, and the problem of how to uniformly analyze stability of a plurality of landslide sections in different sliding directions is solved.
Disclosure of Invention
Aiming at the problems existing in the prior art, the invention provides a limit balance analysis method for the stability of the side slope of an S-shaped groove filling site.
The invention discloses a limit balance analysis method for slope stability of an S-shaped groove filling site, which comprises the following steps:
Step one: dividing a landslide body into a plurality of straight sliding sections with different main sliding directions according to the topography characteristics of an S-shaped groove filling site, and arranging turning sections in the middle for connection conversion;
Step two: carrying out stress analysis on the straight sliding section bar block and the turning section to obtain stress condition of the bar block and force transmission direction conversion of the turning section;
Step three: determining slope stability calculation parameters according to site survey data, and establishing a sliding force balance equation of the bar block;
Step four: and substituting the obtained geometric parameters, soil parameters and the like into a sliding force balance equation of the strip block based on that all landslide sections meet the static force balance condition, and performing iterative calculation to obtain the overall stability coefficient of the side slope.
In the first step, the slope is divided into a plurality of straight sliding sections according to different sliding directions and precision requirements, and a turning section is arranged between every two adjacent straight sliding sections.
In the first step, the straight sliding section is divided into different strips according to the folding lines at the bottom of the slope, and the turning section is fitted into a triangular prism according to the topography at the bottom of the slope.
In the third step, the stability calculation parameters are the geometric parameters of the straight sliding section and the turning section, and the geometric parameters of the straight sliding section are the inclination angle of the bottom sliding surface of the straight sliding section bar with the horizontal plane and the length of the sliding surface.
In summary, the invention has the advantages and positive effects that:
The invention expands the thought that the stability of a side slope is calculated by a traditional three-dimensional limit balance method and only considers one sliding direction, aiming at the characteristics of an S-shaped groove filling site, the S-shaped groove is divided into a plurality of straight sliding sections with different main sliding directions, turning sections between adjacent straight sliding sections are discretized into quadrangular and triangular prism unit strips, the bottom sliding surface of the turning sections is fitted into a plane by a least square method according to the corner coordinate values of all the unit strips, the boundary effect of a slope body is considered, the static balance analysis of the turning sections is carried out according to the geometric characteristics of the bottom sliding surface of the strips, the direction of the lower sliding force of the upper straight sliding section is converted and then is transmitted to the lower straight sliding section, and finally the stability coefficient of the whole side slope is calculated by iteration through an unbalanced thrust method; the method has strong engineering practicability.
Drawings
Fig. 1 is a schematic diagram of a limit balance analysis method for slope stability of an S-shaped trench fill site according to an embodiment of the present invention.
Fig. 2 is a schematic diagram of landslide engineering provided by an embodiment of the invention.
Fig. 3 is a schematic diagram of a landslide engineering dividing straight sliding section and a turning section according to an embodiment of the present invention.
Fig. 4 is a schematic diagram of corner points of a unit cell after the bottom sliding surface of the turning section is discretized into the unit cell according to the embodiment of the present invention.
Fig. 5 is a schematic diagram of a corner point scatter of a corner sliding surface of a turning segment according to an embodiment of the present invention.
Fig. 6 is a schematic plan view of a plane on which the bottom sliding surface of the turning section is fitted according to an embodiment of the present invention.
Fig. 7 is a schematic diagram of three projection points formed by projecting the projection to the bottom sliding surface fitting plane of the turning section according to the embodiment of the present invention.
Fig. 8 is a schematic view of a bottom sliding surface of a break-over section after fitting according to an embodiment of the present invention.
Fig. 9 is a schematic diagram of a stress analysis of a triangular prism according to an embodiment of the present invention.
Fig. 10 is a schematic diagram of the whole landslide section dividing straight sliding section provided by the embodiment of the invention.
Fig. 11 is a schematic diagram of a bar block divided by the inclination angle variation of the bottom sliding surface of the landslide section according to the embodiment of the invention.
Fig. 12 is a force analysis chart of m pieces of an nth landslide section provided by the embodiment of the invention.
Fig. 13 is a diagram of analysis of the stress of a turning section landslide body according to an embodiment of the present invention.
Fig. 14 is a view of an engineering field plane provided by an embodiment of the present invention.
FIG. 15 is a graph of a landslide surface including formation and terrain information using midasGTSNX soft-generative methods provided by embodiments of the present invention.
Fig. 16 is a schematic diagram of meshing a turning section landslide body by using midasGTSNX software according to an embodiment of the present invention.
Fig. 17 is a schematic cross-sectional view of different landslide sections divided according to the main sliding direction provided by the embodiment of the invention.
Fig. 18 is a scatter diagram of cell corners after the bottom sliding surface of the turning section 1 is discretized according to the embodiment of the present invention.
Fig. 19 is a schematic plan view of a fitting of the bottom sliding surface of the turning section 1 according to the embodiment of the present invention.
FIG. 20 is a computational flow diagram provided by an embodiment of the present invention.
Fig. 21 is a schematic diagram of a three-dimensional limit balance analysis method for stability of an S-shaped groove filling side slope according to an embodiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the following examples in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
In order to solve the problems in the prior art, the invention provides a limit balance analysis method for the stability of the side slope of an S-shaped groove filling site.
The application principle of the invention is further described in detail below with reference to the attached drawings;
As shown in fig. 1, the limit balance analysis method for the slope stability of the S-shaped trench filling site provided by the embodiment of the invention specifically includes the following steps:
S101: dividing a landslide body into a plurality of straight sliding sections with different main sliding directions according to the topography characteristics of an S-shaped groove filling site, and arranging turning sections in the middle for connection conversion;
S102: carrying out stress analysis on the straight sliding section bar block and the turning section to obtain stress condition of the bar block and force transmission direction conversion of the turning section;
s103: determining slope stability calculation parameters according to site survey data, and establishing a sliding force balance equation of the bar block;
s104: and substituting the obtained geometric parameters, soil parameters and the like into a sliding force balance equation of the strip block based on that all landslide sections meet the static force balance condition, and performing iterative calculation to obtain the overall stability coefficient of the side slope.
In step S101, according to the sliding direction difference and the precision requirement provided by the embodiment of the present invention, the slope is divided into a plurality of straight sliding sections, and a turning section is arranged between every two adjacent straight sliding sections.
In step S101, the straight sliding section provided by the embodiment of the invention is divided into different strips according to the folding line at the bottom of the slope, and the turning section is fitted into a triangular prism according to the topography at the bottom of the slope.
In step S103, the stability calculation parameters provided by the embodiment of the present invention are the geometric parameters of the straight sliding section and the turning section, and the geometric parameters of the straight sliding section are the inclination angle of the bottom sliding surface of the straight sliding section bar with respect to the horizontal plane and the length of the sliding surface.
As shown in FIG. 2, the landslide engineering sketch provided by the embodiment of the invention.
The landslide engineering sketch applied by the limit balance analysis method for the slope stability of the S-shaped groove filling site.
The application principle of the present invention will be described in further detail with reference to specific embodiments;
Example 1;
The three-dimensional limit balance analysis method for the stability of the S-shaped groove filling side slope provided by the embodiment of the invention specifically comprises the following steps:
(1) Dividing the straight sliding section and the turning section. Dividing the side slope into a plurality of straight sliding sections according to different sliding directions and precision requirements, wherein a turning section is arranged between every two adjacent straight sliding sections;
as shown in fig. 3, the landslide engineering provided by the embodiment of the invention is divided into a straight sliding section and a turning section.
(2) And determining geometric parameters of the straight sliding section and the turning section. The geometrical parameters of the straight sliding section are the inclination angle of the bottom sliding surface of the straight sliding section bar block and the horizontal plane and the length of the sliding surface, and can be obtained according to geological section diagrams in survey data; a coordinate system is established at each turning section, so that the positive direction of the x-axis is consistent with the main sliding direction of the upper straight sliding section, the positive direction of the z-axis is opposite to the gravity direction, the positive direction of the y-axis is determined according to the right-hand spiral rule, and the origin of coordinates is the point of connection between the upper straight sliding section and the lower straight sliding section; the bottom sliding surface of the turning section is approximately a triangular curved surface as shown in fig. 2, and is discretized into a plurality of grid cells by adopting a plumb surface as shown in fig. 4, so as to obtain the corner coordinate value of each grid cell as shown in fig. 5; obtaining coordinate values of corner points for each discrete small cell grid on the bottom sliding surface at each turning section; fitting the bottom sliding surface of the turning section into a plane according to all angular point coordinate values of the bottom sliding surface of the current turning section by adopting a least square method, wherein the fitting principle is that the square sum of the distances of all the bottom angular points of the strip blocks from the fitting plane is minimum, and as shown in fig. 6, the normal vector of the plane is the normal vector of the bottom sliding surface of the turning section; the vertical surface of the upper and lower straight sliding sections connected with the turning section, the side sliding surface of the turning section and the bottom sliding surface of the turning section are projected to the fitting plane of the bottom sliding surface of the turning section to form three projection points, as shown in fig. 7, and the triangle formed by the three projection points is the fitted bottom sliding surface of the turning section, as shown in fig. 8.
As shown in fig. 4, the corner points of the turning section are shown after the bottom sliding surface of the turning section is discretized into the cells.
As shown in fig. 5, the embodiment of the invention provides a schematic diagram of the scattering points of the cell corners of the bottom sliding surface of the turning section.
As shown in fig. 6, a schematic plan view of a plane where the bottom sliding surface of the turning section is fitted is provided in the embodiment of the present invention.
As shown in fig. 7, the projection to the bottom sliding surface fitting plane of the turning section provided by the embodiment of the invention forms three projection point diagrams.
As shown in fig. 8, the embodiment of the invention provides a schematic diagram of the bottom sliding surface of the turning segment after fitting.
(3) And analyzing the stress of the straight sliding section bar and the turning section. Considering the straight sliding section bar according to a classical folding line method, the turning section converts the whole turning section into a triangular prism according to the turning section bottom sliding surface formed by fitting in the second step for stress analysis, as shown in fig. 9; and solving according to the space three-dimensional static balance condition to obtain the sliding force of the last bar block of the upper straight sliding section, and transmitting the sliding force to the sliding force of the first bar block of the lower straight sliding section after passing through the turning section.
As shown in fig. 9, the triangular prism stress analysis schematic diagram provided by the embodiment of the invention.
(4) And sequentially establishing a sliding force balance equation of the bar blocks. The bar block is assumed to be a rigid body, the stability coefficient is the ratio of the shear strength of the sliding surface to the actual shear stress, and the whole sliding surface is assumed to be in a limit balance state and meets the mole-coulomb strength criterion.
(5) Substituting the obtained geometric parameters, soil parameters and the like into a sliding force balance equation of the strip block, and solving the overall stability coefficient of the side slope under the condition that the sliding force of the last strip block is zero.
Step (2) specifically includes, assuming that each straight slide segment slides linearly along the main slide direction, dividing the entire slide segment into n straight slide segments as shown in fig. 10.
As shown in fig. 10, the whole landslide section provided by the embodiment of the invention is divided into a straight sliding section schematic diagram.
As shown in FIG. 11, the embodiment of the invention provides a schematic block diagram for dividing the inclination angle change of the bottom sliding surface of a landslide section.
The straight slide section may be subdivided into m pieces according to the inclination angle of the bottom slide as shown in fig. 11. Taking fig. 10 as an example, the first straight sliding section can be divided into two strips according to the inclination angle of the bottom sliding surface, the second straight sliding section is divided into three strips, and the third straight sliding section is divided into 3 strips.
A coordinate system is established at each turning section, so that the positive direction of the x-axis is consistent with the main sliding direction of the upper straight sliding section, the positive direction of the z-axis is opposite to the gravity direction, the positive direction of the y-axis is determined according to the right-hand spiral rule, and the origin of coordinates is the point of connection between the upper straight sliding section and the lower straight sliding section; the turning section bottom slip surface equation can be expressed as
Ax+By+z+D＝0
From the above formula, it is possible to obtain:
z＝-Ax-By-D
And (3) recording:
a0＝-A,a1＝-b,a2＝-D
z＝a0x+a1y+a2
Plane fitting is performed according to the basic principle of the least square method, i.e. the sum of squares of the distances of the 4 corner points of the bar from the fitting plane is smallest, even if the values of the following equations are smallest:
And using a least square method to the coordinate values of all the angular points of the current turning segment, namely, solving the partial derivative of a 0,a1,a2 by using the equation to obtain the value equal to 0, wherein the equation is as follows:
∑2(a0xi+a1yi+a2-z)xi＝0
∑2(a0xi+a1yi+a2-z)yi＝0
∑2(a0xi+a1yi+a2-z)＝0
Thus, it is possible to obtain:
And solving the equation to obtain a coefficient a 0,a1,a2, thereby determining A, B direction parameters and the value of a constant D, and further determining the bottom sliding surface equation of the turning section sliding mass. The vertical surface of the upper and lower straight sliding sections connected with the turning section, and the three corner points of the turning section side sliding surface intersected with the turning section bottom sliding surface are projected to the fitting plane of the turning section bottom sliding surface to form three projection points, and the triangle formed by the three projection points is the fitted turning section bottom sliding surface as shown in figure 7.
The step (3) specifically comprises the following steps:
1) The side shearing force is ignored between the bars, and it is assumed that the acting direction of the sliding pushing force between the bars is parallel to the sliding surface of the corresponding bars, and the acting point is located at the midpoint of the dividing surface between the bars.
As shown in fig. 12, the stress analysis chart of the m pieces of the nth landslide section is provided in the embodiment of the invention.
Wherein P is the inter-strip force, the direction of the inter-strip force P is parallel to the bottom sliding surface, alpha is the included angle between the direction of the bottom sliding surface and the horizontal plane, W is the gravity of the strip section sliding body, S is the friction force provided by the bottom sliding surface, N is the normal force of the bottom sliding surface, l is the length of the bottom sliding surface of the strip block, c and phi are soil body strength indexes, and phi is the transmission coefficient between the strip blocks. The forces are projected onto the slip plane with the equilibrium equations as follows:
2) As shown in fig. 13, the turning section landslide body stress analysis chart provided by the embodiment of the invention.
For the turning section, only the direction conversion and transmission problem of the turning section is considered, and the safety coefficient is not considered in the calculation of the turning section. The obtained downward sliding force of the last strip block of the upper straight sliding section is converted into a form of concentrated force according to the width of the last strip block of the straight sliding section, the size is P X1, the direction is the sliding direction (alpha 1,β1,γ1) of the last strip block of the upper sliding section, the acting force of the lower straight sliding section to the sliding body of the turning section is considered as a concentrated force form, the size is P X2, the direction is opposite to the main sliding direction of the first strip block of the lower straight sliding section, the direction is (alpha 2,β2,γ2), the normal force of the side sliding to the turning section and the normal force of the bottom sliding surface are both considered as concentrated forces, the sizes are P X3 and N respectively, and the directions are (alpha 3,β3,γ3)、(α4,β4,γ4); according to the mole-coulomb law, the magnitudes of shearing resistance T R1 on the bottom sliding surface and the sliding resistance T R2 on the side surface of the sliding section are Ntan phi+cA 1、PX3tanφ+cA2 respectively, c and phi are soil body strength indexes, A 1、A2 is the area of the side sliding surface, W is the gravity of the turning section, the direction of T R1、TR2 is parallel to the intersection line of the side sliding surface and the bottom sliding surface, the direction is (alpha 5,β5,γ5), the geometric parameters are known, and the balance equation of X, Y, Z directions can be established:
the combination is simplified as follows:
When P X1 is known, the unknown quantity is totally three of P X2、PX3 and N, the values of P X2、PX3 and N can be obtained by solving an equation group, and then the unknown quantity can be brought into a stress balance equation of the first strip block of the next straight sliding section after P X2 is converted into unit width distribution force according to the width of the first strip block of the next straight sliding section.
The step (4) is specifically as follows:
When the method is used for calculation, an initial F S value can be firstly assumed, the unbalanced sliding force P 1,1 (when P 1,1 is calculated, the term is 0) is calculated from the first block at the top of the slope, namely the thrust between the first block and the second block, Then calculating the unbalanced sliding force P 1,2 between the second bar and the third bar, when the last bar P 1,m of the straight sliding section 1 is calculated, obtaining the unbalanced sliding force P 2,1 of the first bar of the second sliding section by P 1,m in the equation set, repeating the steps until the unbalanced sliding force P n,m corresponding to the last bar block of the last landslide section is calculated, and if P n,m =0, assuming the initial F S is the calculated stability coefficient; If P n,m is greater than 0, then decreasing F s is recalculated in accordance with the procedure described above; if P n,m is less than 0, then increase F s is recalculated as described above until the condition of P n,m =0 is met. The whole calculation process can also be directly carried out by utilizing the univariate solving function of excel, P n,m =0 is taken as a condition cell, F S is taken as a variable cell, and finally, the univariate solving key is clicked to directly obtain the F S value.
Example 2;
Case verification for a certain engineering case:
And according to the actual condition of the field, the natural working condition is selected to analyze the overall stability of the side slope. Under the natural working condition, only the slope body dead weight is considered.
According to the physical and mechanical test data of the field rock and soil layer, the parameters of the rock and soil body are determined as follows:
As shown in fig. 14, an engineering field plan is provided in an embodiment of the present invention.
The actual calculation process comprises the following steps:
1. Dividing the straight sliding section and the turning section
(1) Extraction of elevation point coordinates from CAD topographic plan
In the survey plan, three-dimensional coordinate information of the contour lines and contour points of the slope is provided. The number of elevation lines and elevation points is enough to approximate the slope surface morphology of the side slope. And extracting three-dimensional coordinate values of elevation points of the original ground of the side slope by utilizing a data extraction function in CAD software, and generating an excel file.
(2) Geometric model creation using midas software
MidasGTSNX software can generate curved surfaces from the coordinate data containing formation and topography information, as shown in the following figures. To segment an entity using a formation face, a face slightly larger than the entity needs to be generated. Therefore, the extracted three-dimensional information is selected, and the slope surface and the sliding surface are generated by midasGTSNX software. A box entity representing a landslide is then generated and cut using the ground surface and the sliding surface as in fig. 15.
As shown in fig. 15, the embodiment of the present invention provides a landslide body curved surface map containing stratum and topography information generated by using midasGTSNX soft codes.
(3) Establishment of landslide body and division of straight sliding section and turning section
According to the filling scheme, a plurality of planes are respectively generated according to the elevation and slope rate of the filling body, and the intersection of the planes and the ground surface is the part of the filling body, and the schematic diagram of the filling body is shown in the following figure 16. Meshing of the turning segments using midasGTSNX software is shown in fig. 16.
As shown in fig. 16, the embodiment of the present invention provides a schematic diagram of meshing a turning section landslide body by using midasGTSNX software.
As shown in fig. 17, the cross-sectional schematic view of different landslide sections divided according to the main sliding direction is provided in the embodiment of the invention.
2. Fitting the bottom sliding surface of the turning section
All three-dimensional coordinates of the bottom sliding surface of the turning section after grid division are shown in fig. 18, matlab software is input for programming treatment to obtain a plane equation of the bottom sliding surface, three angular points of a vertical surface, a turning section side sliding surface and a turning section bottom sliding surface, which are connected with the upper straight sliding section and the lower straight sliding section, are projected to a turning section bottom sliding surface fitting plane to form three projection points, and a triangle formed by the three projection points is the turning section bottom sliding surface after fitting, and the turning section 1 is taken as an example for fitting to obtain the bottom sliding surface of the turning section as shown in fig. 19.
As shown in fig. 18, the embodiment of the invention provides a scatter diagram of cell corners after the bottom sliding surface of the turning section 1 is discrete.
As shown in fig. 19, the embodiment of the present invention provides a schematic plan view of the bottom sliding surface of the turning section 1.
3. Establishing static equilibrium equation of bar
And extracting coordinate information of the angular points of the split prism by using a node information extraction function of midasGTSNX software, generating a text file, wherein the file extension name is txt, reading the three-dimensional coordinate information, calculating the weight of the prism, the area of the bottom sliding surface, the inclination angle of the bottom sliding surface on a xoz plane and the x axis, the inclination angle of the bottom sliding surface on a yoz plane and the y axis, the unit normal vector of the bottom sliding surface and other geometric parameters. Substituting the sliding force P X1 of the last bar block of the upper straight sliding section, the soil parameters and the extracted geometric parameters into the following equation set can solve the residual sliding force P X2 suffered by the first bar block of the lower straight sliding section, and the whole equation set can be calculated by excel.
4. Solving for the overall stability coefficient
When solving F S, inputting the formula corresponding to the variable into excel, and starting iterative calculation of the unbalanced thrust method. The whole calculation process can be carried out by utilizing a single variable solving function of excel, the sliding force P of the last bar block 4.4 of the whole landslide section is taken as 0 as a target value, the whole stability coefficient F S is a variable cell, and the whole stability coefficient value of the slope is directly obtained and is 1.7091. The whole calculation flow is as shown in fig. 19.
As shown in fig. 20, a calculation flowchart is provided in an embodiment of the present invention.
The calculation result is more consistent with the actual situation on site.
As shown in fig. 21, a schematic diagram of a three-dimensional limit balance analysis method for stability of an S-shaped groove filling side slope is provided in an embodiment of the present invention.
The foregoing description of the preferred embodiments of the invention is not intended to be limiting, but rather is intended to cover all modifications, equivalents, and alternatives falling within the spirit and principles of the invention.
Claims (7)
1. The limit balance analysis method for the stability of the side slope of the S-shaped groove filling site is characterized by comprising the following steps of:
Step one: dividing a landslide body into a plurality of straight sliding sections with different main sliding directions according to the topography characteristics of an S-shaped groove filling site, and arranging turning sections in the middle for connection conversion;
Step two: carrying out stress analysis on the straight sliding section bar block and the turning section to obtain stress condition of the bar block and force transmission direction conversion of the turning section;
Step three: determining slope stability calculation parameters according to site survey data, and establishing a sliding force balance equation of the bar block;
Step four: based on that all landslide sections meet static balance conditions, substituting the obtained geometric parameters and soil parameters into a sliding force balance equation of the strip block, and performing iterative calculation to obtain a slope overall stability coefficient;
The third step specifically comprises the following steps:
1) Neglecting side shearing force among the strips, wherein the acting direction of the sliding pushing force among the strips is parallel to the sliding surface of each corresponding strip, and the acting point is positioned at the midpoint of the dividing surface among the strips; wherein P is an inter-strip force, the direction of the inter-strip force P is parallel to a bottom sliding surface, alpha is an included angle between the direction of the bottom sliding surface and a horizontal plane, W is the gravity of a strip block sliding body, S is the friction force provided by the bottom sliding surface, N is the normal force of the bottom sliding surface, l is the length of the bottom sliding surface of the strip block, c and phi are soil body strength indexes, and phi is the transmission coefficient between the strip blocks; the forces are projected onto the slip plane with the equilibrium equations as follows:
2) Analyzing the stress of the turning section sliding body, namely converting the obtained downward sliding force of the last strip block of the upper straight sliding section into a concentrated force form according to the width of the last strip block of the straight sliding section, wherein the size is P X1, the direction is the sliding direction (alpha 1,β1,γ1) of the last strip block of the upper sliding section, the acting force of the lower straight sliding section on the turning section sliding body is considered as a concentrated force form, the size is P X2, the direction is opposite to the main sliding direction of the first strip block of the lower straight sliding section, the normal force of the side sliding on the turning section and the normal force of the bottom sliding surface are considered as concentrated forces, and the sizes are P X3 and N respectively (alpha 3,β3,γ3)、(α4,β4,γ4); according to the mole-coulomb law, the magnitudes of shearing resistance T R1 on the bottom sliding surface and the sliding resistance T R2 on the side surface of the sliding section are Ntan phi+cA 1、PX3tanφ+cA2 respectively, c and phi are soil body strength indexes, A 1、A2 is the area of the side sliding surface, W is the gravity of the turning section, the direction of T R1、TR2 is parallel to the intersection line of the bottom sliding surface and the side sliding surface, the direction is (alpha 5,β5,γ5), and the equilibrium equation of X, Y, Z three directions is established:
the combination is simplified as follows:
When P X1 is known, the unknown quantity is totally three of P X2、PX3 and N, the values of P X2、PX3 and N can be obtained by solving an equation group, and the unknown quantity is brought into a stress balance equation of the first bar block of the next straight sliding section after P X2 is converted into a unit width distribution force according to the width of the first bar block of the next straight sliding section.
2. The method for analyzing the limit balance of the slope stability of an S-shaped trench filling site according to claim 1, wherein in the first step, the slope is divided into a plurality of straight sliding sections according to the sliding direction and the accuracy requirement, and a turning section is arranged between every two adjacent straight sliding sections.
3. The method for analyzing the limit balance of the slope stability of an S-shaped trench filling site according to claim 1, wherein in the first step, the straight sliding section is divided into different bars according to the folding line of the slope bottom, and the turning section is fitted into a triangular prism according to the topography of the slope bottom.
4. The method for analyzing the limit balance of the slope stability of an S-shaped trench filling site according to claim 1, wherein in the third step, the stability calculation parameters are the geometric parameters of the straight sliding section and the turning section, and the geometric parameters of the straight sliding section are the inclination angle of the bottom sliding surface of the straight sliding section bar with respect to the horizontal plane and the length of the sliding surface.
5. The limit balance analysis method for slope stability of an S-shaped trench fill site according to claim 1, wherein the stripes divided by the inclination angle change of the bottom sliding surface of the sliding section divide the straight sliding section into m stripes according to the inclination angle of the bottom sliding surface, the first straight sliding section is divided into two stripes according to the inclination angle of the bottom sliding surface, the second straight sliding section is divided into three stripes, and the third straight sliding section is divided into 3 stripes; a coordinate system is established at each turning section, so that the positive direction of the x-axis is consistent with the main sliding direction of the upper straight sliding section, the positive direction of the z-axis is opposite to the gravity direction, the positive direction of the y-axis is determined according to the right-hand spiral rule, and the origin of coordinates is the point of connection between the upper straight sliding section and the lower straight sliding section; the turning segment bottom slip equation is expressed as:
Ax+By+z+D＝0
From the above formula, we obtain:
z＝-Ax-By-D
And (3) recording:
a0＝-A,a1＝-B,a2＝-D,
z＝a0x+α1y+a2
Plane fitting is performed according to the basic principle of the least square method, i.e. the sum of squares of the distances of the 4 corner points of the bar from the fitting plane is smallest, even if the values of the following equations are smallest:
And using a least square method to the coordinate values of all the angular points of the current turning segment, namely, solving the partial derivative of a 0,a1,a2 by using the equation to obtain the value equal to 0, wherein the equation is as follows:
∑2(a0xi+a1yi+a2-z)xi＝0
∑2(a0xi+a1yi+a2-z)yi＝0
∑2(a0xi+a1yi+a2-z)＝0
Obtaining:
Solving the equation to obtain a coefficient a 0,a1,a2, thereby determining A, B direction parameters and a constant D value, and determining a bottom sliding surface equation of the turning section landslide body; and projecting three corner points, which are the vertical surfaces of the upper and lower straight sliding sections connected with the turning section and the side sliding surfaces of the turning section and the bottom sliding surface of the turning section, onto a fitting plane of the bottom sliding surface of the turning section to form three projection points.
6. The limit balance analysis method for the slope stability of the S-shaped trench fill site according to claim 1, wherein the step four is characterized in that an initial F S value is calculated from a first block at the top of the slope to obtain an unbalanced sliding force P 1,1, which is the thrust between the first block and a second block, and then an unbalanced sliding force P 1,2 between the second block and a third block is calculated, when the final block P 1,m of the straight sliding section 1 is calculated, an unbalanced sliding force P 2,1 of the first block of the second sliding section is obtained from a P 1,m person equation set, and is repeated until an unbalanced sliding force P n,m corresponding to the final block of the final sliding section is calculated, and if P n,m =0, the initial F S is the required stability coefficient; if P n,m is greater than 0, then reducing F s to recalculate in steps; if P n,m is less than 0, then increase F s is recalculated in steps until the condition of P n,m =0 is met.
7. A slope stability analysis platform applying the limit balance analysis method for slope stability of an S-shaped trench fill site according to any one of claims 1 to 6.
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