CN110633541B - Group tension action spherical crown type slope stability evaluation method based on Janbu method - Google Patents

Group tension action spherical crown type slope stability evaluation method based on Janbu method Download PDF

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CN110633541B
CN110633541B CN201910908418.5A CN201910908418A CN110633541B CN 110633541 B CN110633541 B CN 110633541B CN 201910908418 A CN201910908418 A CN 201910908418A CN 110633541 B CN110633541 B CN 110633541B
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spherical crown
crown type
sector
janbu
slope
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CN110633541A (en
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沈志平
宋二祥
徐�明
陈德茂
朱军
付君宜
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Zhengye Engineering & Investment Inc Ltd
Tsinghua University
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Tsinghua University
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Abstract

The invention discloses a group tension action spherical crown type slope stability evaluation method based on a Janbu method, which comprises the following implementation processes of: dividing the spherical crown type slope into a plurality of annular strips, and acquiring the radius of each annular stripr i (ii) a Selecting included angle as deltaψObtaining each sectoriHeight of (2)h i Length of bottom surfacel i Bottom surface and horizontal plane inclination angleθ i (ii) a The slope safety factor is calculated iteratively by the following formulaF s . The improved Janbu method can be used for evaluating the stability of the group tension acting on the spherical crown type side slope, the calculation process is simple, and a method with a more reasonable calculation result is provided for the stability evaluation of the group tension acting on the spherical crown type side slope.

Description

Group tension action spherical crown type slope stability evaluation method based on Janbu method
Technical Field
The invention relates to a slope stability evaluation method, in particular to a group tension action spherical crown type slope stability evaluation method based on a Janbu 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 the actual situation, a two-dimensional limit balance method is generally adopted for evaluating slope stability in engineering, the calculation precision of the method is still good for a linear slope, but the calculation result of the slope with the obvious space effect for a spherical crown type slope is too conservative, and meanwhile, the method does not consider the situation that the slope is under the action of group tension. How to analyze the stability of the spherical crown type slope under the action of group tension is a problem to be solved in slope stability evaluation.
The method is based on a two-dimensional limit balance analysis method Janbu method commonly used in the current engineering, corrects the Janbu method by considering the arch effect of the spherical crown type side slope to be suitable for the three-dimensional spherical crown type side slope, and simultaneously considers the condition that the slope surface is under the action of group tension, so that the calculation result is more in line with the actual condition.
Disclosure of Invention
Aiming at the problems, the invention aims to provide a method for evaluating the stability of a group tension acting spherical crown type slope based on a Janbu method so as to solve the problem that the existing two-dimensional limit balance method is insufficient in evaluating the stability of a group tension acting three-dimensional spherical crown type slope.
The technical scheme adopted by the invention is as follows: the group tension action spherical crown type slope stability evaluation method based on the Janbu method comprises the following implementation processes:
the method comprises the following steps: divide the spherical crown type slope into a plurality of ringsThe radius r of each annular strip is obtainedi；
Step two: selecting a plurality of segments with the included angle delta phi and obtaining the height h of each segment iiLength of bottom surface liBottom surface and horizontal plane inclination angle thetai；
Step three: iteratively calculating slope safety factor F by the following formulas；
Figure GDA0002760228590000021
Figure GDA0002760228590000022
Figure GDA0002760228590000023
In the formula, c1iThe slip surface cohesive force of the ith sector;
Figure GDA0002760228590000024
the sliding surface internal friction angle of the ith sector; c. C2iThe cohesive force of the soil body of the ith sector is shown;
Figure GDA0002760228590000025
the inner friction angle of the ith sector soil body; gamma rayiThe volume weight of the soil body of the ith sector; fxiThe sum of the component force of all the pulling forces of the ith annular strip block on the horizontal plane; fyiThe sum of the vertical component of all the pulling forces of the ith annular strip block is obtained; riThe anti-sliding force generated by the axial pressure of the ith sector.
Wherein, in the second step, the angle phi is selected to be less than 20 degrees.
Wherein, the formula in step three is based on the Janbu method and considers the contribution of the axial pressure of the fan to the anti-slip force, and in addition to the basic assumption of the Janbu method, 2 new assumptions are introduced: (1) neglecting the sectorTangential force therebetween; (2) anti-slip force R generated by axial pressure of i-th sectoriThe point of action of which is located at the centre of gravity of the sector.
In the third step, the direction of each pulling force is directed to the symmetry axis.
The invention has the beneficial effects that: the improved Janbu method can be used for evaluating the stability of the group tension acting on the spherical crown type side slope, the calculation process is simple, and a method with a more reasonable calculation result is provided for the stability evaluation of the group tension acting on the spherical crown type side slope.
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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 sector i in an embodiment of the present invention;
FIG. 2 is a diagram illustrating an analysis of the axial force of the sector i according to the embodiment of the present invention;
FIG. 3 is a Janbu method force analysis diagram of sector i in the embodiment of the present invention;
fig. 4 is a three-dimensional model calculation parameter diagram of a spherical crown type slope under the action of group tension in the embodiment of the 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.
A group tension action spherical crown type slope stability evaluation method based on a Janbu method is specifically implemented as follows: a quadrant i of fig. 4 with an angle Δ ψ is shown in fig. 1.
Unconfined compressive strength sigma of soil bodyciObtaining the axial compressive resistance F of the sector i soil bodyNiThe calculation formula is as shown in the formulas (1) and (2)Shown in the figure.
FNi＝σcihilicosθi (1)
Figure GDA0002760228590000031
When delta psi is small, the axial compressive resistance F of the soil body of the sector iNiWill generate a sliding resistance Ri，RiOriented horizontally and away from the axis of symmetry as shown in FIG. 2, RiThe calculation formula is shown in formula (3).
Ri＝FNi·Δψ (3)
Introducing a safety factor, and substituting the formulas (1) and (2) into the formula (3) to obtain a formula (4).
Figure GDA0002760228590000041
Due to the anti-slip force R of the sector iiThe safety coefficient of the spherical crown type side slope is higher than that of a long straight side slope. R is to beiThe Janbu method is introduced, and a sector i is taken as a study object, and an external force applied to the sector i is projected onto a cross section where the center of gravity is located, as shown in fig. 3.
For sector i, from a vertical resultant force ∑ FzEquation (5) is obtained when 0.
Figure GDA0002760228590000042
In the formula, NiIs the normal force of sector i on the sliding surface, TiIs the anti-slip force of the sector i on the sliding surface.
For sector i, from the horizontal resultant force ∑ FxEquation (6) is obtained when 0.
ΔPi＝Pi+1-Pi＝Ti cosθi+Ri-Ni sinθi-FxiΔψ/2π (6)
In the formula, PiIs the normal force between the soil strips.
Substituting equation (5) into equation (6) yields equation (7).
ΔPi＝Ti(cosθi+sinθi tanθi)-(γiriΔψhili cosθi-FyiΔψ/2π)tanθi+Ri-FxiΔψ/2π (7)
By the molar coulomb strength criterion and introducing a safety factor FsAvailable TiAs shown in equation (8).
Figure GDA0002760228590000043
Substituting the formula (5) into the formula (8) to obtain the formula (9).
Figure GDA0002760228590000051
Substituting equation (9) into equation (7) yields equation (10).
Figure GDA0002760228590000052
By sigma delta PiWhen the value is 0, the value is reduced by Δ ψ to obtain formula (11).
Figure GDA0002760228590000053
Figure GDA0002760228590000054
Figure GDA0002760228590000055
Example (b): the method comprises the following steps: the group tension action spherical crown type slope is divided into 11 annular strips, and parameters are calculated: gamma rayiAre all 25kN/m3；c1iAre all at the pressure of 100kPa,
Figure GDA0002760228590000057
are all 45 degrees; c. C2iAre all at the pressure of 100kPa,
Figure GDA0002760228590000058
are all 45 degrees; r isiAs shown in table 1; fxiAnd FyiAs shown in table 2.
TABLE 1 circular bar radius ri
Figure GDA0002760228590000056
TABLE 2 annular bars FxiAnd Fyi
Number of bar 1 2 3 4 5 6 7 8 9 10 11
Fxi(kN) 2000 1800 1600 1400 1200 800 600 400 200 100 0
Fyi(kN) 2000 1800 1600 1400 1200 800 600 400 200 100 0
Step two: selecting a plurality of segments, h, having an included angle delta phii、li、θiAs shown in table 3.
TABLE 3 quadrant hi、li、θi
Figure GDA0002760228590000061
Figure GDA0002760228590000062
Figure GDA0002760228590000063
Figure GDA0002760228590000064
The number of iterations is 7, and the results of each iteration are 1.318, 1.442, 1.485, 1.499, 1.504, 1.506 and 1.506 respectively. Through iterative calculation, the final safety factor F is obtaineds＝1.506。
The improved Janbu method can be used for evaluating the stability of the spherical crown type side slope under the action of the group tension, the calculation process is simple, and a method with a more reasonable calculation result is provided for the stability evaluation of the spherical crown type side slope under the action of the group tension.
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 (4)

1. A group tension action spherical crown type slope stability evaluation method based on a Janbu method is characterized by comprising the following steps: the implementation process is as follows:
the method comprises the following steps: dividing the spherical crown type slope into a plurality of annular strips, and obtaining each stripRadius r of the annular stripi；
Step two: selecting a plurality of segments with the included angle delta phi and obtaining the height h of each segment iiLength of bottom surface liBottom surface and horizontal plane inclination angle thetai；
Step three: iteratively calculating slope safety factor F by the following formulas；
Figure FDA0002760228580000011
Figure FDA0002760228580000012
Figure FDA0002760228580000013
In the formula, c1iThe slip surface cohesive force of the ith sector;
Figure FDA0002760228580000014
the sliding surface internal friction angle of the ith sector; c. C2iThe cohesive force of the soil body of the ith sector is shown;
Figure FDA0002760228580000015
the inner friction angle of the ith sector soil body; gamma rayiThe volume weight of the soil body of the ith sector; fxiThe sum of the component force of all the pulling forces of the ith annular strip block on the horizontal plane; fyiThe sum of the vertical component of all the pulling forces of the ith annular strip block is obtained; riThe anti-sliding force generated by the axial pressure of the ith sector.
2. The method for evaluating the stability of the group tension action spherical crown type slope based on the Janbu method according to claim 1, which is characterized in that: in the second step, the angle delta psi is selected to be less than 20 degrees.
3. The method for evaluating the stability of the group tension action spherical crown type slope based on the Janbu method according to claim 1, which is characterized in that: the formula in step three is based on the Janbu method and considers the contribution of the axial pressure of the fan body to the anti-slip force, and in addition to the basic assumption of the Janbu method, 2 new assumptions are introduced: (1) ignoring tangential forces between the segments; (2) anti-slip force R generated by axial pressure of i-th sectoriThe point of action of which is located at the centre of gravity of the sector.
4. The method for evaluating the stability of the group tension action spherical crown type slope based on the Janbu method according to claim 1, which is characterized in that: in the third step, the direction of each pulling force is directed to the symmetry axis.
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CN111898067B (en) * 2020-07-06 2023-07-21 河海大学 Strip block removing Janbu strip dividing method for optimizing thrust between landslide strips

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CN106855637A (en) * 2016-12-10 2017-06-16 国家海洋局第二海洋研究所 Underwater Slope method for analyzing stability
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