CN110263423A - Group's pulling force effect ball crown type Slope Stability Evaluation method based on Janbu method - Google Patents
Group's pulling force effect ball crown type Slope Stability Evaluation method based on Janbu method Download PDFInfo
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Abstract
The invention discloses group's pulling force effect ball crown type Slope Stability Evaluation method based on Janbu method, implementation process is as follows: ball crown type side slope being divided into several annular sticks, obtains the gravity of each annular stickW i , sliding surface areaA 1i ；By ball crown type side slope, symmetrically any one axial direction stretches to form a section, and each annular stick forms a section on section, obtains each annular stick cross-sectional area on sectionA 2i , sliding surface inclination angleθ i ；Side Slope Safety Coefficient is iterated to calculate by following equationF s ；The arching for considering ball crown type side slope introduces new hypothesis to Janbu method and improves, group's pulling force is added in formula simultaneously, improved Janbu method can be used for evaluating group stability of pulling force effect ball crown type side slope, and calculating process is simple, the estimation of stability for group's pulling force effect ball crown type side slope provides a kind of method that calculated result is more reasonable.
Description
Technical field
The present invention relates to Slope Stability Evaluation methods, more particularly to group's pulling force effect ball crown type side based on Janbu method
Slope Stability Evaluation method.
Background technique
In mountain area engineering construction and landslide disaster forecast analysis, side slope of various shapes can be encountered, side slope is such as investigated and exists
Shape in horizontal plane, can be classified as convex, spill and linear, and the spatial form of side slope undoubtedly has shadow to its stability
It rings.Strictly speaking, Analysis of Slope Stability belongs to space problem, is more tallied with the actual situation using three dimensional analysis method, and engineering
The evaluation of upper Slope Stability, it is general using two-dimentional limit equilibrium method, such methods for linear side slope computational accuracy still
Can, but the significant side slope calculated result of three-dimensional effect this for ball crown type side slope can be overly conservative, while such methods are not yet
Consider the case where slope surface is by group's pulling force effect.How to analyze group stability of pulling force effect ball crown type side slope is slope stability
Problem to be solved in evaluation.
The present invention is based on two dimension limit equilibrium analysis method Janbu method common in current engineering, by considering ball
Janbu method is modified to be suitable for three-dimensional ball crown type side slope, while considering slope surface and being drawn by group by the arching of crown type side slope
The case where power acts on, makes calculated result more tally with the actual situation.
Summary of the invention
In view of the above-mentioned problems, the technical problem to be solved in the present invention is to provide group's pulling force effect spherical crowns based on Janbu method
Type Slope Stability Evaluation method, it is steady in evaluation group's pulling force effect three-dimensional ball crown type side slope to solve existing two-dimentional limit equilibrium method
The deficiency of qualitative aspect.
The technical solution adopted by the present invention are as follows: group's pulling force effect ball crown type Slope Stability Evaluation side based on Janbu method
Method, implementation process are as follows:
Step 1: ball crown type side slope is divided into several annular sticks, obtains the gravity W of each annular sticki, sliding surface area
A1i；
Step 2: by ball crown type side slope, symmetrically any one axial direction stretches to form a section, each annular stick
A section is formed on section, obtains each annular stick cross-sectional area A on section2i, sliding surface inclination angle thetai；
Step 3: Side Slope Safety Coefficient F is iterated to calculate by following equations；
In formula, c1iFor the sliding surface cohesive strength of i-th of annular stick；It rubs in sliding surface for i-th of annular stick
Angle；c2iFor the gliding mass cohesive strength of i-th of annular stick；For the gliding mass internal friction angle of i-th of annular stick；FxiFor i-th of ring
The summation of all pulling force of shape stick component size in the horizontal plane；FyiFor i-th of annular all pulling force of stick vertically component
The summation of size；RiThe antiskid shearing generated for i-th of annular stick axial force.
Wherein, the formula in the step three based on simple cloth Janbu method and considers the axial force of annular stick to antiskid
The contribution of power, it is new to introduce 5 hypothesis: (1) to ignore the tangential force between annular stick other than the basic assumption of simple cloth Janbu method；
(2) axial force that the horizontal component of annular stick gravity generates only is considered when annular stick Axial Force Calculating；(3) when i-th of ring
Shape stick sliding surface inclination angle thetaiWhen≤0, the antiskid for enabling annular stick axial force generate shears Ri=0；(4) i-th of annular stick are axial
The antiskid that power generates shears Ri, direction is located in the annular stick center of gravity with the annular stick glide direction on the contrary, position；
(5) ignore the equalising torque of annular stick.
Wherein, in the step three, the direction of each pulling force will be directed toward symmetry axis.
Beneficial effects of the present invention: considering that the arching of ball crown type side slope introduces new hypothesis to Janbu method and improves,
Group's pulling force is added in formula simultaneously, improved Janbu method can be used for evaluating the steady of group pulling force effect ball crown type side slope
It is qualitative, and calculating process is simple, a kind of calculated result is provided more for the estimation of stability of group's pulling force effect ball crown type side slope
Reasonable method.
Detailed description of the invention
Detailed description will be given by the following detailed implementation and drawings by the present invention for ease of explanation,.
Fig. 1 is the structural schematic diagram of annular stick i in embodiment of the present invention；
Fig. 2 is annular stick section force analysis figure in embodiment of the present invention；
Fig. 3 is the structural schematic diagram of annular stick and equivalent annular stick in embodiment of the present invention；
Fig. 4 is equivalent annular bar block Janbu method force analysis figure in embodiment of the present invention；
Fig. 5 is group's pulling force effect ball crown type side slope three-dimensional model calculating parameter figure in the embodiment of the present invention；
Fig. 6 is ball crown type slope discontinuity calculating parameter figure in the embodiment of the present invention.
Specific embodiment
Technical solution of the present invention is clearly and completely described below in conjunction in the embodiment of the present invention, it is clear that retouched
The embodiment stated is only a part of the embodiment of the present invention, instead of all the embodiments.Based on the embodiments of the present invention, originally
Field those of ordinary skill every other embodiment obtained without making creative work, belongs to the present invention
The range of protection.
Group pulling force effect ball crown type Slope Stability Evaluation method of the present embodiment based on Janbu method is implemented
Process is as follows: taking the annular stick i of any one in Fig. 5, as shown in Figure 1.
Its arbitrary section is taken as shown in Fig. 2, by annular stick gravity WiBy decomposing to obtain its horizontal component W twiceix, Wix
Shown in calculation formula such as formula (1).
Wix=Wisinθicosθi (1)
Gravity horizontal component WixAn annular can be formed on annular stick be evenly distributed with line load qi, evenly load qiAlso it is
Horizontal direction is simultaneously directed toward symmetry axis, qiShown in calculation formula such as formula (2).
In formula, riFor the gravity W of annular stick iiTo the distance of symmetry axis.
The uniformly distributed line load q of annulariAxial compressive force F can be generated inside annular stickNi, FNiCalculation formula such as formula (3) institute
Show.
FNi=qiri (3)
Formula (1) and formula (2) are substituted into formula (3) arrangement to obtain formula (4), the physical significance of formula (4) is in weight
Power acts on lower annular stick i to axial compressive force F when symmetry axis sliding, generated inside annular stick iNi。
Compared with conventional strip stick, annular stick is in gravity WiEffect is lower to generate additional axial compressive force FNi。
The strip stick that a section is identical as annular stick and length is equal with annular stick perimeter is now established, is named as
Imitate annular stick i, and by axial compressive force FNiThe two sides of equivalent annular stick i are applied to as shown in figure 3, later by equivalent annular
Stick i is as research object.
By mole coulomb criterion of strength and introduce safety coefficient Fs, the antiskid on equivalent annular two sides stick i can be obtained
Shear Ri, RiShown in calculation formula such as formula (5).
Formula (4) substitution formula (5) is obtained into formula (6).
Since equivalent annular stick i side antiskid shears RiPresence so that the safety coefficient of ball crown type side slope is longer straight
Side slope can more Gao Yidian.By RiIt is introduced into Janbu method, is rounded an equivalent annular stick i as research object, suffered by it
External force projects on the section where center of gravity as shown in Figure 4.
For entire equivalent annular stick i, by vertical resultant force ∑ Fz=0 obtains formula (7).
In formula, NiIt is equivalent annular stick i in sliding surface A1iOn normal force, TiIt is equivalent annular stick i in sliding surface A1i
On antiskid shearing.
For entire equivalent annular stick i, by horizontal resultant ∑ Fx=0 obtains formula (8).
ΔPi=Pi+1-Pi=(Ti+Ri)cosθi-Nisinθi-Fxi (8)
In formula, PiThe normal force between native item.
Formula (7) brings formula (8) into and obtains formula (9).
ΔPi=Ti(cosθi+sinθitanθi)-(Wi-Fyi)tanθi+secθiRi-Fxi (9)
By mole coulomb criterion of strength and introduce safety coefficient FsT can be obtainedi, as shown in formula (10).
Formula (7) brings formula (10) arrangement into and obtains formula (11).
It brings formula (11) into formula (9) and obtains formula (12).
By ∑ Δ Pi=0 arrangement obtains formula (13)~(15).
Embodiment: step 1: group's pulling force effect ball crown type side slope three-dimensional model calculating parameter figure is as shown in figure 5, be divided into
The gliding mass bulk density of 10 annular sticks, all annular sticks is 25kN/m3.The sliding surface cohesive strength c of all annular sticks1iIt is
33kPa, internal friction angleIt is 35 °；The gliding mass cohesive strength c of all annular sticks2iIt is equally 33kPa, internal friction angle
It is equally 35 °.The gravity W of 10 annular sticksiWith sliding surface area A1i, as shown in table 1；The annular each pulling force of stick is in level
On face and vertically upper component is 50kN, the summation F of all pulling force of each annular stick component size in the horizontal planexiWith it is vertical
The summation F of upper component sizeyiAs shown in table 2.
The gravity W of the annular stick of table 1iWith sliding surface area A1i
| Block number | 1 | 2 | 3 | 4 | 5 |
| Wi(kN) | 15117.5 | 34959 | 59216.75 | 93444.5 | 128684.25 |
| Block number | 6 | 7 | 8 | 9 | 10 |
| Wi(kN) | 159992.5 | 182100 | 191273.8 | 173358.5 | 83665.25 |
| Block number | 1 | 2 | 3 | 4 | 5 |
| A1i(m2) | 389.68 | 447.36 | 547.92 | 648.48 | 778.08 |
| Block number | 6 | 7 | 8 | 9 | 10 |
| A1i(m2) | 931.76 | 1125.92 | 1403.6 | 1880.24 | 2843.04 |
The annular stick F of table 2xiAnd Fyi
| Block number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Fxi(kN) | 400 | 600 | 800 | 1200 | 1400 | 1600 | 1800 | 2000 | 2200 | 2400 |
| Fyi(kN) | 400 | 600 | 800 | 1200 | 1400 | 1600 | 1800 | 2000 | 2200 | 2400 |
Step 2: ball crown type slope discontinuity calculating parameter figure is as shown in fig. 6, each annular stick cross-sectional area A2i, sliding surface
Inclination angle thetai, as shown in table 3.
The annular stick cross-sectional area A of table 32iWith sliding surface inclination angle thetai
Step 3: it is iterated by formula and calculates safety coefficient Fs,
Iteration 8 times altogether, each iteration result is respectively 1.783,1.959,2.01,2.018,1.998,1.995,1.994,
1.994.By iterative calculation, final safety coefficient F is obtaineds=1.994.
The present invention considers that the arching of ball crown type side slope introduces new hypothesis to Janbu method and improves, while in formula
Middle addition group's pulling force, improved Janbu method can be used for evaluating group stability of pulling force effect ball crown type side slope, and calculate
Process is simple, and the estimation of stability for group's pulling force effect ball crown type side slope provides a kind of method that calculated result is more reasonable.
It although an embodiment of the present invention has been shown and described, for the ordinary skill in the art, can be with
A variety of variations, modification, replacement can be carried out to these embodiments without departing from the principles and spirit of the present invention by understanding
And modification, the scope of the present invention is defined by the appended.
Claims (3)
1. group's pulling force effect ball crown type Slope Stability Evaluation method based on Janbu method, it is characterised in that: its implementation process is such as
Under:
Step 1: ball crown type side slope is divided into several annular sticks, obtains the gravity W of each annular sticki, sliding surface area A1i；
Step 2: by ball crown type side slope, symmetrically any one axial direction stretches to form a section, and each annular stick is cuing open
A section is formed on face, obtains each annular stick cross-sectional area A on section2i, sliding surface inclination angle thetai；
Step 3: Side Slope Safety Coefficient F is iterated to calculate by following equations；
In formula, c1iFor the sliding surface cohesive strength of i-th of annular stick；For the sliding surface internal friction angle of i-th of annular stick；c2i
For the gliding mass cohesive strength of i-th of annular stick；For the gliding mass internal friction angle of i-th of annular stick；FxiFor i-th of annular bar
The summation of all pulling force of block component size in the horizontal plane；FyiFor i-th of annular all pulling force of stick vertically component size
Summation；RiThe antiskid shearing generated for i-th of annular stick axial force.
2. group's pulling force effect ball crown type Slope Stability Evaluation method according to claim 1 based on Janbu method, special
Sign is: formula in the step three is based on simple cloth Janbu method and considers tribute of the axial force to skid resistance of annular stick
It offers, it is new to introduce 5 hypothesis: (1) to ignore the tangential force between annular stick other than the basic assumption of simple cloth Janbu method；(2) ring
The axial force that the horizontal component of annular stick gravity generates only is considered when shape stick Axial Force Calculating；(3) when i-th of annular stick
Sliding surface inclination angle thetaiWhen≤0, the antiskid for enabling annular stick axial force generate shears Ri=0；(4) i-th of annular stick axial force generate
Antiskid shear Ri, direction is located in the annular stick center of gravity with the annular stick glide direction on the contrary, position；(5) it neglects
The equalising torque of slightly annular stick.
3. group's pulling force effect ball crown type Slope Stability Evaluation method according to claim 1 based on Janbu method, special
Sign is: in the step three, the direction of each pulling force will be directed toward symmetry axis.
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| CN201910908418.5A CN110633541B (en) | 2019-06-18 | 2019-09-25 | Group tension action spherical crown type slope stability evaluation method based on Janbu method |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN110689969A (en) * | 2019-09-25 | 2020-01-14 | 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 |
| CN111898067A (en) * | 2020-07-06 | 2020-11-06 | 河海大学 | Strip removing block Janbu strip dividing method for optimizing thrust between landslide strips |
| CN110598354B (en) * | 2019-09-25 | 2021-04-02 | 贵州正业工程技术投资有限公司 | Arc-shaped concave slope stability evaluation method based on Janbu method |
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| US6607332B2 (en) * | 2001-08-30 | 2003-08-19 | Soo-Yong Kang | Method of reinforcing slope reverse analysis technique |
| CN101514553B (en) * | 2009-04-03 | 2012-05-30 | 重庆交通大学 | Soil slope stability analysis method based on limit equilibrium theory and stress analysis |
| CN104268380B (en) * | 2014-09-16 | 2017-02-08 | 重庆大学 | Long-term stability prediction method for three-dimensional creep slope |
| 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 |
| CN107067333B (en) * | 2017-01-16 | 2022-12-20 | 长沙矿山研究院有限责任公司 | Method for monitoring stability of high-altitude and steep slope at high cold altitude |
| CN109598013A (en) * | 2018-09-30 | 2019-04-09 | 青岛理工大学 | Method for determining most dangerous sliding surface of push type landslide and optimal pile position of slide-resistant pile |
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Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110689969A (en) * | 2019-09-25 | 2020-01-14 | 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 |
| 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 | Arc-shaped concave slope stability evaluation method based on Janbu method |
| CN111898067A (en) * | 2020-07-06 | 2020-11-06 | 河海大学 | Strip removing block Janbu strip dividing method for optimizing thrust between landslide strips |
| 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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