CN110245429B - Annular convex slope stability evaluation method based on simplified Bishop method - Google Patents
Annular convex slope stability evaluation method based on simplified Bishop method Download PDFInfo
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Abstract
The invention discloses a simplified Bishop method-based annular convex slope stability evaluation method, which comprises the following implementation processes of: dividing the annular convex slope into a plurality of annular strips, and acquiring the gravity of each annular stripW i Area of sliding surfaceA i1(ii) a Drawing the annular convex slope in any direction symmetrically and axially to form a section, forming a section on the section by each annular bar block, and acquiring the section area of each annular bar block on the sectionA i2Inclination of sliding surfaceθ i (ii) a The slope safety factor is calculated iteratively by the following formulaF s (ii) a The improved simplified Bishop method can be used for evaluating the stability of the annular convex slope, the calculation process is simple, and a method with more reasonable calculation results is provided for stability evaluation of the annular convex slope.
Description
Technical Field
The invention relates to a slope stability evaluation method, in particular to a simplified Bishop method-based annular convex slope stability evaluation method.
Background
In the mountain engineering construction and landslide hazard prediction analysis, slopes of various shapes can be encountered, for example, the shape of the slope in the horizontal plane is considered, the slope can be divided into a convex shape, a concave shape and a linear shape, and the stability of the slope is undoubtedly influenced by the spatial shape of the slope. Strictly speaking, slope stability analysis belongs to a space problem, a three-dimensional analysis method is more suitable for practical situations, a two-dimensional limit balance method is generally adopted for evaluating slope stability in engineering, the method has good calculation precision for a linear slope, but the method has a large error in a slope calculation result with a significant space effect of an annular convex slope. How to analyze the stability of the annular convex slope is a problem to be solved in slope stability evaluation.
The simplified Bishop method is corrected to be suitable for the annular convex slope by taking the contribution of axial tension of each annular strip block of the annular convex slope to the anti-slip force into consideration on the basis of the simplified Bishop method of the two-dimensional limit balance analysis method commonly used in the current engineering, so that the calculation result is more in line with the actual situation.
Disclosure of Invention
Aiming at the problems, the invention aims to provide a method for evaluating the stability of the annular convex slope based on a simplified Bishop method, so as to solve the problem that the existing two-dimensional limit balancing method is insufficient in evaluating the stability of the annular convex slope.
The technical scheme adopted by the invention is as follows: the method for evaluating the stability of the annular convex slope based on the simplified Bishop method comprises the following implementation processes:
the method comprises the following steps: dividing the annular convex slope into a plurality of annular strips, and acquiring the gravity W of each annular stripiArea A of sliding surface1i；
Step two: drawing the annular convex slope in any direction symmetrically and axially to form a section, forming a section on the section by each annular bar block, and acquiring the section area A of each annular bar block on the section2iAngle of inclination theta of sliding surfacei；
Step three: iteratively calculating slope safety factor F by the following formulas；
In the formula, ciThe cohesive force of the sliding surface of the ith annular strip block;
the sliding surface internal friction angle of the ith annular strip block; sigmaLai iThe tensile strength of the ith annular bar block soil body is obtained; t isiThe anti-sliding force is generated for the axial tension of the ith annular strip block; riAnti-slip force T generated for axial tension of ith annular stripiMoment to the center of the arc sliding surface; r is the radius of the arc sliding surface.
The formula in the third step is based on a simplified Bishop method and considers the contribution of the axial tension of the annular strip block to the anti-sliding force, and besides the basic assumption of the simplified Bishop method, 1 assumption is newly introduced: anti-slip force T generated by axial tension of ith annular strip blockiThe point of action is located at the center of gravity of the annular bar.
The invention has the beneficial effects that: the improved simplified Bishop method can be used for evaluating the stability of the annular convex slope, the calculation process is simple, and a method with more reasonable calculation results is provided for stability evaluation of the annular convex slope.
Drawings
For ease of illustration, the invention is described in detail by the following detailed description and the accompanying drawings.
FIG. 1 is a schematic structural diagram of a ring-shaped bar block i in an embodiment of the present invention;
FIG. 2 is a schematic structural view of a ring bar and an equivalent ring bar in an embodiment of the present invention;
FIG. 3 is a simplified Bishop method force analysis diagram of an equivalent annular bar in accordance with an embodiment of the present invention;
FIG. 4 is a parameter diagram of the annular convex slope three-dimensional model calculation in the embodiment of the present invention;
FIG. 5 is a cross-sectional view of an annular convex slope according to an embodiment of the present invention.
Detailed Description
The technical solutions of the present invention will be described clearly and completely in the following embodiments of the present invention, and it should be understood that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The method for evaluating the stability of the annular convex slope based on the simplified Bishop method comprises the following implementation processes: take any one of the annular blocks i in fig. 4, as shown in fig. 1.
From the tensile strength sigma of the soilLai iObtaining the axial tensile resistance F of the annular bar-block soil bodyNiThe calculation formula is shown in formula (1).
FNi＝σLai iA2i(1)
Annular bar soil body axial tensile resistance FNiWill generate an annular uniform distribution line load qi，qiOriented horizontally and pointing towards the axis of symmetry, qiThe calculation formula is shown in formula (2).
In the formula, riIs the weight W of the ith annular bariDistance to the axis of symmetry.
Substituting equation (1) into equation (2) yields equation (3).
Establishing a long strip-shaped bar with the same cross section as the annular bar and the same length as the circumference of the annular bar, naming the long strip-shaped bar as an equivalent annular bar i, and distributing loads q on the annular bariApplied to the equivalent annular bar i as shown in fig. 2, and then the equivalent annular bar i is used as the study object.
Introducing a safety factor FsEquivalent slip resistance T of the annular bar iiThe calculation formula is shown as formula (4), TiThe direction is horizontal and points into the slope.
Due to the sliding resistance T of the equivalent annular bar iiThe safety coefficient of the annular convex slope is higher than that of the long straight slope. Will TiThe method is introduced into a simplified Bishop method, the whole equivalent annular block i is taken as a research object, the external force borne by the equivalent annular block i is projected to a section where the center of gravity is located, as shown in figure 3, and O is the center of a circular arc sliding surface.
For the whole equivalent annular bar i, by a vertical resultant force ∑ FzEquation (5) is obtained when 0.
In the formula, NiSliding surface A of equivalent annular strip block i1iUpper normal force, Ti0For equivalent annular strip block i on sliding surface A1iAnd anti-skid and anti-shearing force.
For the entire equivalent annular bar i, ∑ M by moment summationOEquation (6) is obtained when 0.
∑WiRsinθi＝∑Ti0R+∑TiRi(6)
By the molar coulomb strength criterion and introducing a safety factor FsAvailable Ti0As shown in equation (7).
Substituting the formula (5) into the formula (7) and arranging to obtain the formula (8).
Substituting the formula (8) into the formula (6) to obtain the formula (9).
Example (b): the method for evaluating the stability of the annular convex slope based on the simplified Bishop method comprises the following steps: the method comprises the following steps: the annular convex slope three-dimensional model calculation parameter map is shown in FIG. 4 and is totally divided into 10 annular strips, and the volume weight of the sliding mass of all the annular strips is 25kN/m3. Slip surface cohesive force c of all annular stripsiAll 33kPa, internal friction angle
All are 35 degrees, and the tensile strength sigma of all soil bodiesLai iAll at 32 kPa. Gravity W of 10 annular barsiAnd the area A of the sliding surface1iAs shown in table 1.
TABLE 1 gravity W of annular barsiAnd the area A of the sliding surface1i
| Number of bar | 1 | 2 | 3 | 4 | 5 |
| Wi(kN) | 46125 | 100475 | 141125 | 102275 | 204125 |
| Number of |
6 | 7 | 8 | 9 | 10 |
| Wi(kN) | 194400 | 192525 | 166150 | 161325 | 117925 |
| Number of bar | 1 | 2 | 3 | 4 | 5 |
| A1i(m2) | 1084 | 884 | 848 | 512 | 912 |
| Number of |
6 | 7 | 8 | 9 | 10 |
| A1i(m2) | 816 | 828 | 800 | 1008 | 2572 |
Step two: the annular convex slope section calculation parameter diagram is shown in FIG. 5, and the section area A of each annular strip block2iAngle of inclination theta of sliding surfaceiAs shown in table 2.
TABLE 2 area of the cross-section of the annular bar2iAnd slip plane inclination angle thetai
| Number of bar | 1 | 2 | 3 | 4 | 5 |
| A2i(m2) | 5.9 | 13.7 | 20.4 | 15.6 | 33 |
| Number of |
6 | 7 | 8 | 9 | 10 |
| A2i(m2) | 34 | 36.4 | 34 | 39 | 29.2 |
| Number of bar | 1 | 2 | 3 | 4 | 5 |
| θi(°) | 10 | 16 | 21 | 27 | 30 |
| Number of |
6 | 7 | 8 | 9 | 10 |
| θi(°) | 36 | 42 | 49 | 55 | 65 |
Step three: iterative calculation of the safety factor F by means of a formulas，
The number of iterations is 7, and the results of each iteration are 1.290, 1.399, 1.432, 1.441, 1.444, 1.445 and 1.445 respectively. Through iterative calculation, the final safety factor F is obtaineds＝1.445。
The improved simplified Bishop method can be used for evaluating the stability of the annular convex slope, is simple in calculation process, and provides a method with a more reasonable calculation result for evaluating the stability of the annular convex slope.
Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.
Claims (2)
1. The annular convex slope stability evaluation method based on the simplified Bishop method is characterized by comprising the following steps: the implementation process is as follows:
the method comprises the following steps: dividing the annular convex slope into a plurality of annular strips, and acquiring the gravity W of each annular stripiArea A of sliding surface1i；
Step two: drawing the annular convex slope in any direction symmetrically and axially to form a section, forming a section on the section by each annular bar block, and acquiring the section area A of each annular bar block on the section2iAngle of inclination theta of sliding surfacei；
Step three: iteratively calculating slope safety factor F by the following formulas；
In the formula, ciThe cohesive force of the sliding surface of the ith annular strip block;
the sliding surface internal friction angle of the ith annular strip block; sigmaLai iThe tensile strength of the ith annular bar block soil body is obtained; t isiThe anti-sliding force is generated for the axial tension of the ith annular strip block; riAnti-slip force T generated for axial tension of ith annular stripiMoment to the center of the arc sliding surface; r is the radius of the arc sliding surface.
2. The method for evaluating the stability of the annular convex slope based on the simplified Bishop method according to claim 1, wherein: the formula in step three is based on a simplified Bishop method and considers the contribution of the axial tension of the annular bar block to the anti-sliding force, and besides the basic assumption of the simplified Bishop method,newly introduced 1 hypothesis: anti-slip force T generated by axial tension of ith annular strip blockiThe point of action is located at the center of gravity of the annular bar.
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| CN110489935B (en) * | 2019-06-18 | 2021-01-15 | 贵州正业工程技术投资有限公司 | Stability evaluation method of spherical cap slope under group tension based on simplified Bishop method |
| CN110263422A (en) * | 2019-06-18 | 2019-09-20 | 贵州正业工程技术投资有限公司 | Convex annular Slope Stability Evaluation method based on simple flat surface sliding scale |
| CN110674550B (en) * | 2019-09-25 | 2021-03-26 | 贵州正业工程技术投资有限公司 | Stability evaluation method of circular arc concave slope based on transfer coefficient method |
| CN110689969B (en) * | 2019-09-25 | 2021-03-26 | 贵州正业工程技术投资有限公司 | Arc-shaped concave slope stability evaluation method based on simple plane sliding method |
| CN110598354B (en) * | 2019-09-25 | 2021-04-02 | 贵州正业工程技术投资有限公司 | Stability evaluation method of circular arc concave slope based on Janbu method |
| CN111368458B (en) * | 2020-03-23 | 2021-04-02 | 青岛理工大学 | A method for calculating the safety factor of a foundation pit excavation slope |
| CN112597569B (en) * | 2020-12-17 | 2023-05-16 | 贵州正业工程技术投资有限公司 | Composite foundation filling slope stability evaluation method based on simplified PicoPu method |
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