CN114722474A - Method for analyzing stability of prestressed anchor cable reinforced crack-containing bentonite slope - Google Patents
Method for analyzing stability of prestressed anchor cable reinforced crack-containing bentonite slope Download PDFInfo
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Abstract
The invention discloses a method for analyzing the stability of a prestressed anchor cable reinforced fracture-containing bentonite slope, and provides a rotation-translation combined mechanism for evaluating the stability of the fracture-containing bentonite slope, wherein a translation mechanism is adopted to simulate a fracture sliding surface, and a rotation mechanism is adopted to simulate an arc sliding surface. Aiming at the characteristic that the unit weight of the bentonite is in nonlinear change along the depth of the soil layer, a sliding soil body is dispersed into a series of soil units, the power of the gravity of the bentonite is calculated by adopting a layering sum method and a rotating volume integral method, and the total power of the gravity is obtained by accumulation. And obtaining a safety coefficient expression of the bentonite slope according to a volume weight increasing principle, and searching the minimum safety coefficient of the slope based on an enumeration method to obtain a corresponding critical sliding surface. The method can effectively combine the bentonite strength theory and the limit analysis method, reasonably explains the suction effect of the side slope and the action mechanism of the anchor cable, and has important academic value and practical significance for guiding the design, construction and reinforcement of the side slope.
Description
Technical Field
The invention relates to a slope stability analysis method, in particular to a slope stability analysis method for prestressed anchor cables and reinforced fissure-containing bentonite.
Background
At present, the analysis and research on the stability of the engineering slope is mainly developed based on the plane strain problem, the consideration on the suction effect is not sufficient, the research method mainly focuses on the research aspects of a limit balance method and a finite element method, the research on the aspect of the limit analysis method is relatively less, and particularly, the research aspects of the stability and the reinforcement mechanism of the crack-containing bentonite slope are realized.
The bottleneck problems of slope stability analysis research include: the research method is not sufficient in consideration of the side slope suction effect, mainly focuses on the research of a limit balance method and a finite element method, and relatively few researches on the limit analysis method. The main difficulty of the crack-containing bentonite slope stability limit analytical method research is as follows: firstly, a static force permitted stress field and a motion permitted speed field in the heterogeneous material are difficult to construct; secondly, due to the space-time variability of the substrate suction force, a slope energy balance equation is difficult to construct to seek upper and lower limit solutions.
In addition, the existing soil slope stability analysis does not aim at the prestressed anchor cable to reinforce the crack-containing bentonite slope, and the simulation of the sliding surface in the analysis process is not accurate enough, so that the final analysis result is not accurate.
Disclosure of Invention
The purpose of the invention is as follows: the invention aims to provide a stability analysis method for a prestressed anchor cable reinforced fissure-containing bentonite slope, which is high in accuracy and reliability.
The technical scheme is as follows: the invention relates to a method for analyzing the stability of a prestressed anchor cable reinforced crack-containing bentonite slope, which evaluates the stability of the crack-containing bentonite slope by a rotation-translation combined mechanism, adopts a translation mechanism to simulate a crack sliding surface, adopts a rotation mechanism to simulate an arc sliding surface, disperses a landslide body into a series of soil units aiming at the characteristic that the heavy weight of the bentonite shows nonlinear change along the depth of a soil layer, calculates the external power of the gravity of the bentonite by adopting a layering total sum method and a rotation volume integration method, and accumulates to obtain the total power of the gravity; obtaining a safety coefficient expression of the bentonite side slope according to a volume weight increasing principle, and searching a global minimum safety coefficient of the side slope based on an enumeration method to obtain a corresponding critical sliding surface;
the method specifically comprises the following steps:
s1, controlling a most dangerous sliding surface of a bentonite slope by a crack surface, simulating a crack sliding surface by adopting a translation mechanism, simulating an arc sliding surface by adopting a rotating mechanism, and dividing a sliding soil body into an upper soil body and a lower soil body by taking an intersection point of the translation mechanism and the rotating mechanism as a boundary;
s2, calculating the external power of the gravity of the bentonite slope, wherein the external power is the sum of the external power of the gravity of the upper soil body and the external power of the gravity of the lower soil body; for the upper soil body, dividing the sliding soil body into a plurality of individual volume infinitesimal elements by corresponding polar angles by taking the rotating shaft as a polar point, and accumulating the external power made by the gravity of all the volume infinitesimal soil bodies to obtain the external power made by the gravity of the upper soil body; dividing the lower soil body into a plurality of discrete soil layer units along the horizontal direction, and accumulating the power made by the gravity of all the soil layer units to obtain the external power made by the gravity of the lower soil body;
s3, calculating the energy dissipation rate caused by the apparent cohesive force of the bentonite, and integrating the energy dissipation rate on the whole speed discontinuous surface by using the product of the area of the infinitesimal speed discontinuous surface and the capillary cohesive force and tangential speed component of the infinitesimal speed discontinuous surface;
s4, calculating the energy dissipation rate of the anchoring force of a single pre-stressed anchor cable, and accumulating to obtain the total energy dissipation rate caused by all anchor cables;
s5, calculating external power of the bentonite slope top loading;
s6, obtaining a safety coefficient expression of the bentonite side slope according to a volume weight increasing principle, and expressing the safety coefficient expression as a ratio of total energy dissipation rate caused by apparent cohesive force and anchoring force of the whole sliding soil body to the gravity of the sliding soil body and the power made by slope top stacking;
s7, searching the global minimum safety coefficient of the side slope based on an enumeration method, and giving a corresponding critical sliding surface.
Further, in step S1, the anchor cables in the pre-stressed anchor cable reinforcement may be the same or different in laying angle, height, anchoring force and spacing, and are all anchored in the soil body below the sliding surface; the side slope in the crack-containing bentonite side slope is under a one-dimensional vertical stable seepage condition and is a single-order regular side slope with only one slope angle; the most dangerous sliding surface of the bentonite side slope passes through the toe and is intersected with the top of the slope, and the underground water surface is positioned below the toe and is not intersected with the sliding surface; the translation mechanism is a linear sliding mechanism, and the rotating mechanism is a logarithmic spiral sliding mechanism.
Further, in step S2, in the external power generated by the gravity of the infinitesimal soil body, the gravity at the centroid of the unit body is used as the representative value of the volume unit, and the assumption is that the calculation accuracy for the gentle slope and the weak non-linear problem is higher, and the calculation accuracy for the steep slope and the strong non-linear problem is slightly lower, but the calculation accuracy still meets the practical application; if thetah>θBThe power made by the gravity of the upper soil body
The formula of (1) is as follows:
in the formula: theta0At initial angle of sliding surface, thetahIs the slip surface end angle, θBIs the corresponding polar angle of the shoulder0The diameter of the pole corresponding to the initial angle (i.e., the length of the OA line segment), gamma' is the unit weight of the bentonite, which can be obtained from the three-phase proportional relation of the soil by using Fredlund-Xing model, z1And z2The vertical distances from the centroid of the corresponding unit body of the rotating mechanism to the ground are respectively, and phi' is an effective internal friction angle. Wherein z is1And z2Can be respectively represented as
In the formula: h is the height of the bentonite side slope;
if thetah≤θBThe power made by the gravity of the upper soil body
The formula is as follows:
further, in step S2, if θ is equal toh>θBThe power made by the gravity of the lower soil body is the power made by the FED and ECD of the soil block
And
and the formula of the sum is as follows:
in the formula: omega is angular velocity, hdHeight of the fracture surface, hiLaying anchor cables at a height, wherein beta is a slope inclination angle, delta is a crack surface inclination angle, and m is the number of soil units; z is a radical ofiAnd zjRespectively the vertical distance z from the centroid of the soil layer corresponding to the unit of the translation mechanism to the groundiAnd zjCan be represented as:
if thetah≤θBThe power made by the gravity of the lower soil body is the power made by the BEDF and ECD of the soil blocks
And
and the formula of the sum is as follows:
power W made by gravity of bentonite slopeγ'The formula of (1) is:
further, in step S3, the energy dissipation rate of the bentonite due to apparent cohesion is determined
The formula is as follows:
in the formula: c. CcapThe specific expression of the apparent cohesive force of the bentonite can be obtained by adopting generalized Mohr-Coulomb destruction criterion according to a Fredlund-Xing model, dl is the infinitesimal length of a speed discontinuous surface, and z is3And z4The vertical distance, z, from the micro-element speed discontinuous surface of the rotating mechanism and the translation mechanism to the ground3And z4Can be respectively represented as
z3＝hd+z0+r0exp(θh-θ0)tanφ′sinθh-r0exp(θ-θ0)tanφ′sinθ (13)
z4＝l+z0 (14)
Further, in step S4, the total energy dissipation rate W of the prestressed anchorage cable anchoring forceTThe formula of (1) is:
in the formula: t isiFor the anchoring force of anchor cable i, /)iIs the polar diameter, theta, of the anchor cable i at the slopeiThe polar angle of the anchor cable at the slope surface is shown, and xi is the arrangement angle of the anchor cable.
Further, in step S5, the power W for the bentonite slope top loadingQComprises the following steps:
WQ＝QωLAB(r0cosθ0-0.5LAB) (16)
in the formula: q is top load of slope, LABThe distance from the sliding surface at the top of the slope to the shoulder of the slope can be expressed as
Further, in step S6, regarding the feature that the unit weight of the bentonite slope changes nonlinearly along the soil depth and height, the sliding soil is dispersed into a plurality of soil cells, the unit weight in the soil cells is regarded as a fixed value, the power of the weight in the cells is calculated, and all the soil cells are accumulated to obtain the external power of the gravity of the whole sliding soil, so as to obtain a slope safety coefficient expression, and the method for searching the global minimum safety coefficient of the slope based on the enumeration method is as follows:
s601, developing an optimization program based on Mathemica software, taking the geometric parameters of the sliding soil body as independent variables, calculating the slope safety coefficient, comparing the slope safety coefficient with a preset value, and storing a smaller safety coefficient;
s602, changing the independent variables in sequence, changing each independent variable in sequence according to the size of the designated increment in a single calculation cycle, repeating the steps S1-S6 to obtain a new safety coefficient, comparing the new safety coefficient with a stored value, repeating the steps until the minimum value is searched, and finally outputting the minimum safety coefficient and the corresponding sliding soil body geometric parameters to obtain a critical sliding surface.
Further, according to the limit analysis upper limit theorem, the energy dissipation rate of the sliding soil body is certainly larger than or equal to the external power made by the gravity of the soil body, and in the process of searching the global minimum safety coefficient, when the safety coefficient is smaller than 1, the search can be automatically stopped.
Further, a slope safety factor expression is obtained based on a volume weight increasing principle, an optimization method based on an enumeration method is adopted, and in the searching process, searching is stopped when the increment of the initial and end angles corresponding to the sliding mass reaches one percent.
The method for analyzing the stability of the prestressed anchor cable reinforced crack-containing bentonite slope can effectively consider the influence rule of the unit weight of the soil body on the slope stability, reveal the suction force of the slope and the action mechanism of the prestressed anchor cable, search the optimized layout scheme of the prestressed anchor cable and provide theoretical guidance and empirical reference for the design, construction and reinforcement of the engineering slope.
Has the advantages that: compared with the prior art, the invention has the following remarkable advantages:
(1) the influence of the suction effect on the slope stability analysis result can be effectively considered, the calculation result is more consistent with the actual engineering situation, the analysis result is more reasonable, the slope safety and the slope safety reserve can be more accurately judged, and the life and property safety of people is guaranteed;
(2) the influence of environmental factors such as water content change in soil mass and external evaporation and infiltration on the slope stability can be effectively considered, the nonlinear problem of geotechnical materials is effectively solved, a slope stability analysis result closer to the actual situation is obtained, and theoretical guidance and reference are provided for slope engineering design and construction;
(3) the strengthening mechanism of the suction effect in the bentonite side slope can be effectively revealed, and the method has higher academic value and theoretical significance;
(4) the method has the advantages of simple calculation principle, high operability, no need of iterative calculation, high calculation efficiency and high calculation precision, and a large number of comparative analysis results show that the semi-analytic calculation result and the theoretical analysis result have high consistency by adopting a method for optimally designing the stability problem of the slope by adopting an enumeration method based on the volume weight increase principle;
(5) for the side slope needing to take reinforcement measures, the analysis result of the method is closer to the actual situation, the consumption amount and the engineering amount of the retaining structure are less, the side slope supporting cost is more reasonable, and the double-carbon target is better met.
Drawings
FIG. 1 is a schematic view of the calculation of a bentonite slope according to the invention;
FIG. 2 is a simplified diagram of the calculation of the power and apparent cohesive force energy dissipation rate by the gravity of the bentonite slope of the present invention, wherein (a) the polar diameter of the sliding surface end point intersects with the slope surface (theta)h>θB) And (b) the intersection of the sliding surface end point pole diameter and the slope top (theta)h≤θB)；
Fig. 3 shows the influence of cracks in the bentonite slope stability analysis according to the present invention, (a) is 0 °, (b) is 5 °;
fig. 4 shows the effect of suction effect in the analysis of the slope stability of bentonite according to the invention, (a) is 0 °, (b) is 5 °;
FIG. 5 shows the reinforcing effect of the anchor cable in the bentonite slope stability analysis of the present invention, wherein (a) is h2-h 12m, (b) is h2-h1＝4m。
Detailed Description
The technical scheme of the invention is further explained by combining the attached drawings.
A three-dimensional stability analysis model of a prestressed anchor cable anchored crack-containing bentonite slope is shown in the embodiment mode of figures 1-2, the height of the bentonite slope is H, and the slope surface inclinesThe angle is beta, the top of the slope is loaded with Q, the side slope is in static condition, the underground water line is below the ground z0The soil bodies are distributed horizontally and divided into saturated areas and unsaturated areas; the initial angle and the final angle of the arc sliding surface are respectively theta0And thetah，θhAnd theta0In a logarithmic spiral relationship, i.e. the sliding surface is a logarithmic spiral. A plurality of prestressed anchor cables are adopted to reinforce the side slope, the arrangement angles of the anchor cables are xi, and the arrangement height is hiAnchoring force of Ti(in this description, it is assumed that the anchoring force and the anchor cable spacing are the same for all anchor cables), all anchor cables are anchored in the soil body below the sliding surface, and the polar diameter and polar angle of each anchor cable at the slope surface are liAnd thetai(ii) a The angle of the fracture surface is delta and the height is hdThe strength of the bentonite is described by adopting a generalized Mohr-Coulomb failure criterion, the strength indexes are effective internal cohesion c 'and an effective internal friction angle phi', and the influence of the suction force of the bentonite on the slope stability can be reflected by regarding the suction force of the bentonite as apparent cohesion.
Specifically, fig. 1 is a model for analyzing the stability of a prestressed anchor cable reinforced crack-containing bentonite slope, wherein the height and slope angle of an engineering typical bentonite slope are known, cracks are mainly gentle dip angles, underground water lines are located below the ground and are distributed horizontally, and a soil body is ideally divided into a bentonite layer and a saturated soil layer; the strength characteristic of the bentonite is described according to generalized Mohr-Coulomb destruction criterion by adopting effective strength index; the invention provides a rotation-translation combined mechanism for simulating the stability of a crack-containing bentonite slope, wherein a translation mechanism is adopted for simulating a crack sliding surface, and a rotation mechanism is adopted for simulating an arc sliding surface.
Specifically, the prestressed anchor cable reinforced crack-containing bentonite slope stability analysis model comprises the following steps:
s1, controlling the most dangerous sliding surface of the bentonite slope by a crack surface, and aiming at the stability problem, simulating the sliding surface by using a rotation-translation combined mechanism, simulating the crack sliding surface by using a translation mechanism, and simulating an arc sliding surface by using a rotation mechanism;
s2 calculating the power W of the gravity of the moist soil slopeγ'See in particular fig. 2. With the intersection point of the two mechanisms as a boundary, willThe sliding soil body is divided into two parts;
s201, regarding an upper soil body, taking a rotating shaft as a pole, dividing a polar angle corresponding to a sliding soil body into a plurality of volume infinitesimals, neglecting the characteristic of local nonlinear change of the soil unit gravity in the volume infinitesimals, expressing the power made by the soil body gravity in the infinitesimals as the product of the gravity of the infinitesimals and the gravity direction speed at the centroid, expressing the gravity of the infinitesimals by the product of the volume of the infinitesimals and the corresponding gravity at the centroid, and accumulating the external power made by the soil body gravity of all the volume infinitesimals to obtain the power made by the upper soil body gravity. When theta ish>θBThe power made by the ABFD gravity of the soil mass is expressed as
In the formula: omega is angular velocity, theta0Initial angle of logarithmic spiral sliding surface, thetahIs the logarithmic spiral sliding surface end angle, thetaBIs the corresponding polar angle of the shoulder0The specific expression can be obtained by using Fredlund-Xing model according to the three-phase proportional relation of soil, and z is1And z2Respectively the vertical distance from the centroid of the corresponding unit body of the rotating mechanism to the ground, z1And z2Can be respectively represented as
When theta ish≤θBThe power made by the soil mass AFD gravity is expressed as
S202, dividing a lower soil body into a plurality of discrete soil layer units along the horizontal direction, wherein the thickness of each soil layer unit can be represented as the ratio of the height of a crack surface to the number of the soil layer units, the gravity of each soil layer unit can be represented by a numerical value at the centroid, the power of the gravity of each soil layer unit can be represented as the product of the gravity and the speed of the gravity at the centroid, the gravity of each soil layer unit can be represented by the product of the volume of the gravity and the corresponding gravity at the centroid, and the power of the gravity of all the soil layer units is accumulated to obtain the power of the gravity of the lower soil body; when theta ish>θBThe power of the gravity of the earth mass FED and ECD can be respectively expressed as
In the formula: m is the number of divided units, ziAnd zjRespectively the vertical distance z from the centroid of the soil layer corresponding to the unit of the translation mechanism to the groundiAnd zjCan be respectively represented as
When theta ish≤θBThe power made by the gravity of the soil blocks BEDF and ECD can be expressed as
S203, obtaining the total power made by the gravity of the sliding soil body according to the angle thetahAngle theta withBRelation between, power W by gravityγ'Can be expressed as
S3, obtaining a safety coefficient expression of the bentonite side slope according to a volume weight increasing principle, and expressing the safety coefficient expression as a ratio of total energy dissipation rate caused by the apparent cohesive force of the whole sliding soil body and the anchoring force of the prestressed anchor cables to the power made by the gravity of the sliding soil body and the top loading of the slope;
s301, calculating the energy dissipation rate caused by the apparent cohesive force of the bentonite, and integrating the product of the area of the infinitesimal velocity discontinuous surface and the capillary cohesive force and tangential velocity component of the infinitesimal velocity discontinuous surface on the whole velocity discontinuous surface, namely obtaining the integral of the infinitesimal velocity discontinuous surface
In the formula: c. CcapThe specific expression for the apparent cohesive force of the bentonite can be obtained by adopting generalized Mohr-Coulomb destruction criterion according to Fredlund-Xing model, z3And z4The vertical distance, z, from the micro-element speed discontinuous surface of the rotating mechanism and the translation mechanism to the ground3And z4Can be respectively represented as
z3＝hd+z0+r0exp(θh-θ0)tanφ′sinθh-r0exp(θ-θ0)tanφ′sinθ (13)
z4＝l+z0 (14)
S302, calculating the energy dissipation rate of the anchoring force of the single pre-stressed anchor cable, and accumulating to obtain all mTTotal energy dissipation rate due to anchor lines, i.e. root line
S303, calculating the power of the bentonite slope top loading, namely
WQ＝QωLAB(r0cosθ0-0.5LAB) (16)
In the formula: l isABThe distance from the sliding surface at the top of the slope to the shoulder of the slope can be expressed as
S4, searching for a global minimum safety Factor (FOS) of the side slope based on an enumeration method, and giving a corresponding critical sliding surface of the FOS. An optimization program is developed based on Mathemica software, the geometric parameters of the sliding soil body are taken as independent variables, the slope safety coefficient is calculated and compared with a preset value, and a smaller safety coefficient is stored; and (3) sequentially changing the independent variables, sequentially changing each independent variable according to the size of a designated increment in a single calculation cycle, repeating the steps of S1-S3 to obtain a new safety coefficient, comparing the new safety coefficient with a stored value, repeating the steps until the minimum value is searched, and finally outputting the minimum safety coefficient and corresponding sliding soil body geometric parameters to obtain a critical sliding surface.
Specifically, in an optimization enumeration method based on a volume weight increase principle, in a searching process, the increment of an initial angle and an end angle corresponding to a sliding mass is one percent, and the searching is stopped when the increment of an initial vector ratio of a rotating body reaches one thousandth. Tables 1-2 show that the results of the calculation according to the invention, compared with other methods, show a higher consistency of the results of the settlement according to the invention with other calculation methods and theoretical calculation results, illustrating the rationality of the calculation according to the invention, where comparative example 1 in table 2 uses the literature
O.,Pula,W.,&Wolny,A.(2005).On the variational solution ofa limiting equilibrium problem involving an anchored wall.Computers and Geotechnics,32(2), 107-; comparative example 2 uses the reference Xiao, s.g.,&guo, W.D, (2017), Limit analysis of ground and color forces, proceedings of the organization of Civil Engineers-Geotechnical Engineering,170(2),175 and 185. Fig. 3, fig. 4 and fig. 5 are partial analysis results, which reveal the influence mechanism of cracks, suction effect and anchor rope reinforcement measures on the stability of the bentonite slope.
Table 1 shows the comparison of the results of the calculation of the method of the present invention with those of other methods
Table 2 shows the comparison of the method of the present invention with other theoretical calculation results
In conclusion, the invention creatively provides a three-dimensional stability analysis model of the prestressed anchor cable anchored crack-containing bentonite side slope, combines the advantages of a limit analysis analytical method and a limit analysis finite element method, effectively combines a bentonite strength theory and the limit analysis method, can reasonably explain the action mechanism of the suction effect of the side slope, and has important academic value and practical significance for guiding the design, construction and reinforcement of the side slope under complex conditions.
The above examples are merely illustrative for clearly explaining the present invention and do not limit the embodiments. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. Nor is it necessary or exhaustive for all embodiments. And obvious variations or modifications are intended to be within the scope of the present invention.
Claims (10)
1. A method for analyzing the stability of a prestressed anchor cable reinforced crack-containing bentonite slope is characterized by comprising the following steps:
s1, controlling a most dangerous sliding surface of a bentonite slope by a crack surface, simulating a crack sliding surface by adopting a translation mechanism, simulating an arc sliding surface by adopting a rotating mechanism, and dividing a sliding soil body into an upper soil body and a lower soil body by taking an intersection point of the translation mechanism and the rotating mechanism as a boundary;
s2, calculating the external power of the gravity of the bentonite slope, wherein the external power is the sum of the external power of the gravity of the upper soil body and the external power of the gravity of the lower soil body; for the upper soil body, dividing the sliding soil body into a plurality of individual volume infinitesimal elements by using the rotating shaft as a pole and the corresponding polar angle of the sliding soil body, and accumulating the external power made by the gravity of all the volume infinitesimal soil bodies to obtain the external power made by the gravity of the upper soil body; dividing the lower soil body into a plurality of discrete soil layer units along the horizontal direction, and accumulating the power made by the gravity of all the soil layer units to obtain the external power made by the gravity of the lower soil body;
s3, calculating the energy dissipation rate caused by the apparent cohesive force of the bentonite, and integrating the energy dissipation rate on the whole speed discontinuous surface by using the product of the area of the infinitesimal speed discontinuous surface and the capillary cohesive force and tangential speed component of the infinitesimal speed discontinuous surface;
s4, calculating the energy dissipation rate of the anchoring force of a single pre-stressed anchor cable, and accumulating to obtain the energy dissipation rate caused by all anchor cables;
s5, calculating external power of the bentonite slope top loading;
s6, obtaining a safety coefficient expression of the bentonite side slope according to a volume weight increasing principle, and expressing the safety coefficient expression as a ratio of total energy dissipation rate caused by apparent cohesive force and anchoring force of the whole sliding soil body to power made by gravity of the sliding soil body and slope top stacking;
and S7, searching the global minimum safety factor of the side slope based on an enumeration method, and giving a corresponding critical sliding surface.
2. The method for analyzing the stability of the prestressed anchor cable-reinforced fissure-containing bentonite slope according to claim 1, wherein in step S1, the prestressed anchor cable has the same or different laying angle, height, anchoring force and spacing, and the anchor cables are anchored in the soil body under the sliding surface; the crack-containing bentonite side slope is under a one-dimensional vertical stable seepage condition and is a single-order regular side slope with only one slope angle; the most dangerous sliding surface of the bentonite side slope passes through the toe and is intersected with the top of the slope, and the underground water surface is positioned below the toe and is not intersected with the sliding surface; the translation mechanism is a linear sliding mechanism, and the rotating mechanism is a logarithmic spiral sliding mechanism.
3. The method for analyzing the stability of the prestressed anchor cable-reinforced fissure-containing bentonite slope as claimed in claim 1, wherein in step S2, if θ is θh>θBThe power made by the gravity of the upper soil body
The formula of (1) is:
in the formula: omega is angular velocity, theta0Is the initial angle of logarithmic spiral sliding surface, thetahIs the logarithmic spiral sliding surface end angle, thetaBIs the corresponding polar angle of the shoulder, r0The diameter of the pole corresponding to the initial angle, gamma' is the unit weight of the bentonite, and z1And z2The vertical distances from the centroids of the corresponding unit bodies of the rotating mechanism to the ground are respectively, and phi' is an effective internal friction angle;
wherein z is1And z2Can be respectively represented as
In the formula: h is the height of the bentonite side slope;
if thetah≤θBThe power made by the gravity of the upper soil body
The formula is as follows:
4. the method for analyzing the stability of the prestressed anchor cable-reinforced fissure-containing bentonite slope as claimed in claim 3, wherein in step S2, if θ is θh>θBThe power made by the gravity of the lower soil body is the power made by the FED and ECD of the soil block
And
and the formula of the sum is as follows:
in the formula: h isdHeight of the fracture surface, hiLaying anchor cables at a height, wherein beta is a slope inclination angle, delta is a crack surface inclination angle, and m is the number of soil units; z is a radical ofiAnd zjRespectively the vertical distance z from the centroid of the soil layer corresponding to the unit of the translation mechanism to the groundiAnd zjCan be respectively represented as
If thetah≤θBThe power made by the gravity of the lower soil body is the power made by the BEDF and ECD
And
and the formula of the sum is as follows:
power W made by gravity of bentonite slopeγ'The formula of (1) is:
5. the method for analyzing the stability of the prestressed anchor cable-reinforced fissure-containing bentonite slope as claimed in claim 1, wherein in step S3, the energy dissipation rate caused by the apparent cohesion of the bentonite is
The formula is as follows:
in the formula: c. CcapThe apparent cohesive force of the bentonite, dl is the infinitesimal length of a speed discontinuous surface, and z3And z4The vertical distance, z, from the micro-element speed discontinuous surface of the rotating mechanism and the translation mechanism to the ground3And z4Can be respectively represented as
z3＝hd+z0+r0exp(θh-θ0)tanφ′sinθh-r0exp(θ-θ0)tanφ′sinθ (13)
z4＝l+z0 (14)
6. The method for analyzing the stability of the prestressed anchor cable-reinforced fissure-containing bentonite slope according to claim 1, wherein in step S4, the total energy dissipation rate W of the prestressed anchor cable anchoring forceTThe formula of (1) is:
in the formula: t isiFor the anchoring force of anchor cable i, /)iIs the polar diameter, theta, of the anchor cable i at the slopeiThe polar angle of the anchor cable at the slope surface is shown, and xi is the arrangement angle of the anchor cable.
7. The method for analyzing the stability of the prestressed anchor cable reinforced fissure-containing bentonite slope according to claim 1, wherein in step S5, the power W for the top loading of the bentonite slope is WQComprises the following steps:
WQ＝QωLAB(r0cosθ0-0.5LAB) (16)
in the formula: q is top load of slope, LABThe distance from the sliding surface at the top of the slope to the shoulder of the slope can be expressed as
8. The method for analyzing the stability of the prestressed anchor cable reinforced fracture-containing bentonite slope according to claim 1, wherein in step S7, the method for searching the global minimum safety factor of the slope based on an enumeration method comprises:
an optimization program is developed based on Mathemica software, the geometric parameters of the sliding soil body are taken as independent variables, the slope safety coefficient is calculated and compared with a preset value, and a smaller safety coefficient is stored; and (3) sequentially changing the independent variables, sequentially changing each independent variable according to the size of a designated increment in a single calculation cycle, repeating the steps S1-S6 to obtain a new safety coefficient, comparing the new safety coefficient with a stored value, repeating the steps until the minimum value is searched, and finally outputting the minimum safety coefficient and the corresponding sliding soil body geometric parameters to obtain a critical sliding surface.
9. The method for analyzing the stability of the prestressed anchor cable reinforced fracture-containing bentonite slope according to claim 8, wherein in the process of searching the global minimum safety factor, when the safety factor is less than 1, the search can be automatically stopped.
10. The method for analyzing the stability of the prestressed anchor cable reinforced fracture-containing bentonite slope according to claim 8, wherein a slope safety coefficient expression is obtained based on a volume weight increase principle, and an optimization method based on an enumeration method is adopted, and in the searching process, the searching is stopped when the increment of the initial and end angles corresponding to the landslide body reaches one percent.
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