CN110689970A - Arc-shaped concave slope stability evaluation method based on simplified Bishop method - Google Patents
Arc-shaped concave slope stability evaluation method based on simplified Bishop method Download PDFInfo
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Abstract
The invention discloses a simplified Bishop method-based stability evaluation method for an arc-shaped concave slope, wherein the two sides of the simplified Bishop method have arc-passing central axes and can provide constraint planes for normal rigid constraint and tangential friction. The implementation process is as follows: dividing the arc concave slope into a plurality of arc strips to obtain the gravity of each arc stripW i Area of sliding surfaceA i1(ii) a Obtaining the contact surface area of each arc-shaped strip block on the contact surface of the arc-shaped concave slope and the constraint planeA i2Inclination of sliding surfaceθ i (ii) a The slope safety factor is calculated iteratively by the following formulaF s (ii) a The simplified Bishop method is improved by considering the arch effect of the arc-shaped concave slope and the friction between the side slope and the constraints on two sides, can be used for evaluating the stability of the arc-shaped concave slope, is simple in calculation process, and provides a method with a more reasonable calculation result for evaluating the stability of the arc-shaped concave slope.
Description
Technical Field
The invention relates to a slope stability evaluation method, in particular to a simplified Bishop method-based arc concave slope stability evaluation method.
Background
In the mountain engineering construction, the slope stability analysis is inevitable, and the slope has various forms, and can be divided into convex, concave and linear shapes according to the shape in a horizontal plane. For a long straight slope in a straight line shape, a transverse sectioning unit of the long straight slope conforms to the plane strain hypothesis, and the stability of the long straight slope is reasonably analyzed by adopting a two-dimensional limit balance method in the existing specification. For the side slope with the convex and concave shape in the plane, the horizontal space shape of the side slope is changed, the assumption of plane strain is not completely met any more, and the stability of the side slope is not reasonable by directly adopting a two-dimensional limit balance method for analyzing. For a side slope with a remarkable space effect, namely an arc-shaped concave slope, a reasonable evaluation method is selected to solve the problem in the evaluation of the stability of the side slope.
The simplified Bishop method is corrected to be suitable for the three-dimensional arc concave slope by taking the arch effect of the arc concave slope and the friction between the slope and the constraints on two sides into consideration on the basis of the simplified Bishop method which is a commonly used two-dimensional limit balance analysis method 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 solve the problems that: the method for evaluating the stability of the arc-shaped concave slope based on the simplified Bishop method is provided, and the defects of the existing two-dimensional limit balancing method in the stability of the arc-shaped concave slope are overcome.
The method for evaluating the stability of the arc-shaped concave slope based on the simplified Bishop method comprises the following implementation processes:
the method comprises the following steps: dividing the arc-shaped concave slope into a plurality of arc-shaped strip blocks to obtainTaking the gravity W of each arc-shaped bariArea A of sliding surface1i；
Step two: obtaining the contact surface area A of each arc-shaped strip block on the contact surface of the arc-shaped concave slope and the constraint plane2iAngle of inclination theta of sliding surfacei；
Step two: iteratively calculating slope safety factor F by the following formulas；
In the formula, c1iThe cohesive force of the ith arc-shaped strip soil body;the inner friction angle of the ith arc-shaped strip soil body; c. C2iThe cohesive force of the contact surface of the ith arc-shaped strip block and the constraint planes on the two sides is provided;
the inner friction angle of the contact surface of the ith arc-shaped strip block and the constraint planes on the two sides is set; sigmaciOn the intensity molar coulomb envelope curve of the ith arc-shaped strip soil body, when the small principal stress is 0, the large principal stress in the soil body crushed by the axial direction is the compressive strength of the sliding body; t isiThe anti-sliding force is generated for the axial force of the ith arc-shaped strip block; riAnti-sliding force T generated for axial force of ith arc-shaped strip blockiMoment to the center of the arc sliding surface; t isiNAnti-skid shear generated by constrained friction between ith arc-shaped strip and side surfaceForce; riNThe anti-sliding force T generated by the constraint of the ith arc-shaped sliding block and the side surfaceiNMoment to the center of the arc sliding surface; r is the radius of the arc sliding surface; alpha is the arc center angle corresponding to the arc slope and is expressed by radian.
The formula in the third step is based on a simplified Bishop method, and the axial force of the arc-shaped strip and the contribution of the friction of the side slope and the constraints on the two sides to the anti-slip force are considered, and besides the basic assumption of the simplified Bishop method, 2 assumptions are newly introduced: (1) anti-sliding force T generated by axial force of ith arc-shaped strip blockiThe action point is positioned on the gravity center of the arc-shaped strip block; (2) frictional force T between ith arc-shaped strip and two-side constraintiNThe action point is positioned on the gravity center of the arc-shaped strip block.
Wherein, the two sides of the arc concave slope are provided with constraint planes passing through the arc center axis, and normal rigid constraint and tangential friction are provided.
The invention has the beneficial effects that: the improved simplified Bishop method can be used for stability of the arc-shaped concave slope, the calculation process is simple, and a method with more reasonable calculation results is provided for stability evaluation of the arc-shaped concave slope.
Drawings
Fig. 1 is a schematic structural view of an arc-shaped bar block i according to an embodiment of the present invention;
FIG. 2 is a schematic structural diagram of an arc-shaped bar according to an embodiment of the present invention;
FIG. 3 is a schematic structural diagram of an equivalent circular arc-shaped bar in an embodiment of the present invention;
FIG. 4 is a top view of a dome of a circular arc in accordance with an embodiment of the present invention;
FIG. 5 is a simplified Bishop method stress analysis diagram of an equivalent circular arc-shaped bar in the embodiment of the present invention;
FIG. 6 is a schematic diagram of a three-dimensional model of a circular arc-shaped concave slope in the embodiment of the invention;
FIG. 7 is a parameter diagram of a three-dimensional model of a circular arc-shaped concave slope according to an embodiment of the present invention;
fig. 8 is a calculation parameter diagram of a circular arc concave slope section in the 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 arc-shaped concave slope based on the simplified Bishop method comprises the following specific implementation processes: any one of the arc-shaped blocks i in fig. 6 is taken, as shown in fig. 1.
Compressive strength sigma of soil body single axisciObtaining the axial compressive resistance F of the arc-shaped strip soil bodyNiThe calculation formula is shown in formula (1).
FNi＝σciA2i(1)
Axial compressive resistance F of arc-shaped bar soil bodyNiWill generate an arc-shaped uniform distribution line to resist the load qi，qiOriented horizontally and away from the arc axis, qiThe calculation formula is shown in formula (2).
In the formula, riThe distance from the gravity center of the vertical section of the arc-shaped strip block i to the arc-shaped central axis.
Substituting equation (1) into equation (2) yields equation (3).
Establishing a long strip-shaped bar with the same section, length and mass as the arc-shaped bar, naming the long strip-shaped bar as an equivalent arc-shaped bar i, and loading the arc-shaped uniform distribution line qiThe result is applied to the arc-equivalent bar i as shown in fig. 3, and then the arc-equivalent bar i is set as a study object.
Introducing a safety factor FsEquivalent sliding resistance T of arc-shaped strip block 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 arc-shaped strip block iiThe safety coefficient of the arc-shaped convex slope is higher than that of the long straight slope. Will TiThe method is introduced into a simplified Bishop method, the whole equivalent arc-shaped strip i is taken as a research object, the external force borne by the equivalent arc-shaped strip i is projected to a section where the center of gravity is located, as shown in figure 4, and O is the center of a circular arc sliding surface.
And resists the pressure force F in the axial directionNiUnder the action of the action, the arc-shaped strip block and the side surface restrain friction can generate an anti-sliding force T opposite to the sliding directioniNAssuming the shearing strength between the arc-shaped strip block and the side surface boundary to be combined with the molar coulomb strength criterion, and introducing a safety coefficient FsObtaining TiNThe calculation formula of (a) is as follows:
aiming at the whole equivalent arc-shaped strip block i, the vertical resultant force sigma FzEquation (5) is obtained when 0.
In the formula, NiIs a normal force on the sliding surface of an equivalent circular arc-shaped bar i, Ti0The sliding resistance and the shearing force of the equivalent arc-shaped strip block i on the sliding surface are achieved.
For the whole equivalent arc-shaped strip block i, summing sigma M by momentOEquation (6) is obtained when 0.
∑WiRsinθi＝∑Ti0R+∑TiRi+∑TiNR (6)
According to the molar coulomb strength criterion and introducing ampereCoefficient of total 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 comprises the following steps: the circular arc concave slope three-dimensional model calculation parameter diagram is shown in FIG. 5 and is totally divided into 10 circular arc strips, and the sliding volume weight of all the circular arc strips is 25kN/m3The arc center angle alpha is 90 deg. Soil mass cohesive force c of all circular arc-shaped bars1iAll 20kPa, internal friction angle
All are 30 degrees; slip surface cohesive force c of contact surface of all circular arc-shaped strips and side constraint2iAll 20kPa, internal friction angle
Are all 30 degrees. Gravity W of 10 arc-shaped barsiAnd the area A of the sliding surface1iAs shown in table 1.
TABLE 1 gravity W of circular arc-shaped barsiAnd the area A of the sliding surface1i
Step two: the circular arc concave slope section calculation parameter diagram is shown in FIG. 6, and the contact surface area A of each circular arc strip and the side surface constraint surface2iAngle of inclination theta of sliding surfaceiAs shown in table 2.
TABLE 2 area A of contact surface between the arc-shaped bar and the side constraint surface2iAnd slip plane inclination angle thetai
| Number of bar | 1 | 2 | 3 | 4 | 5 |
| A2i(m2) | 4.76 | 13.69 | 21.69 | 28.72 | 34.7 |
| Number of bar | 6 | 7 | 8 | 9 | 10 |
| A2i(m2) | 39.48 | 41.7 | 34.75 | 24.08 | 9.48 |
| Number of bar | 1 | 2 | 3 | 4 | 5 |
| θi(°) | 4 | 8 | 14 | 19 | 25 |
| Number of bar | 6 | 7 | 8 | 9 | 10 |
| θi(°) | 30 | 37 | 43 | 51 | 59 |
TABLE 3 ith circleAnti-slip force T generated by axial force of arc-shaped stripiMoment R to the center of circular arc sliding surfacei
| Number of bar | 1 | 2 | 3 | 4 | 5 |
| Ri(m) | 33.19 | 31.63 | 29.79 | 27.78 | 25.59 |
| Number of bar | 6 | 7 | 8 | 9 | 10 |
| Ri(m) | 23.204 | 20.80 | 19.30 | 17.63 | 15.65 |
TABLE 4 anti-skid shear force T generated by the i-th arc-shaped bar and the side surface constraint frictioniNMoment R to the center of circular arc sliding surfaceiN
| Number of bar | 1 | 2 | 3 | 4 | 5 |
| RiN(m) | 33.27 | 32.03 | 30.86 | 29.22 | 29.90 |
| Number of bar | 6 | 7 | 8 | 9 | 10 |
| RiN(m) | 28.79 | 28.93 | 30.17 | 31.77 | 33.24 |
Step three: iterative calculation of the safety factor F by means of a formulas，
The number of iterations is 6, and the results of each iteration are 1.429, 1.543, 1.566, 1.570, 1.571, 1.571 and 1.571 respectively. Through iterative calculation, the final safety factor F is obtaineds＝1.571。
The improved simplified Bishop method can be used for evaluating the stability of the arc-shaped concave slope, the calculation process is simple, and a method with more reasonable calculation results is provided for evaluating the stability of the arc-shaped concave slope under the action of 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 (3)
1. The method for evaluating the stability of the arc concave slope 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 arc-shaped concave slope into a plurality of arc-shaped strips, and acquiring the gravity W of each arc-shaped stripiArea A of sliding surface1i；
Step two: obtaining the contact surface area A of each arc-shaped strip block on the contact surface of the arc-shaped concave slope and the constraint plane2iAngle of inclination theta of sliding surfacei；
Step three: iteratively calculating slope safety factor F by the following formulas；
In the formula, c1iThe cohesive force of the ith arc-shaped strip soil body;
the inner friction angle of the ith arc-shaped strip soil body; c. C2iThe cohesive force of the contact surface of the ith arc-shaped strip block and the constraint planes on the two sides is provided;
the inner friction angle of the contact surface of the ith arc-shaped strip block and the constraint planes on the two sides is set; sigmaciOn the intensity molar coulomb envelope curve of the ith arc-shaped bar soil body, when the small principal stress is 0, the large principal stress in the soil body crushed by the axial direction isCompressive strength of the slider; t isiThe anti-sliding force is generated for the axial force of the ith arc-shaped strip block; riAnti-sliding force T generated for axial force of ith arc-shaped strip blockiMoment to the center of the arc sliding surface; t isiNThe anti-skid shear force is generated by the constrained friction between the ith arc-shaped strip block and the side surface; riNThe anti-sliding force T generated by the constraint of the ith arc-shaped sliding block and the side surfaceiNMoment to the center of the arc sliding surface; r is the radius of the arc sliding surface; alpha is the arc center angle corresponding to the arc slope and is expressed by radian.
2. The method for evaluating the stability of the arc-shaped concave slope based on the group tension effect of the simplified Bishop method according to claim 1, wherein the method comprises the following steps: the formula in the third step is based on a simplified Bishop method, and the axial force of the arc-shaped strip and the contribution of the friction of the side slope and the constraints on two sides to the sliding force are considered, and besides the basic assumption of the simplified Bishop method, 2 assumptions are newly introduced: (1) anti-sliding force T generated by axial force of ith arc-shaped strip blockiThe action point is positioned on the gravity center of the arc-shaped strip block; (2) frictional force T between ith arc-shaped strip and two-side constraintiNThe action point is positioned on the gravity center of the arc-shaped strip block.
3. The simplified Bishop method-based arc-shaped concave slope stability evaluation method according to claim 1, wherein the simplified Bishop method comprises the following steps: and the two sides of the arc concave slope are provided with constraint planes passing through the arc center shaft, so that normal rigid constraint and tangential friction are provided.
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| US20120025522A1 (en) * | 2009-04-17 | 2012-02-02 | Sumitomo Metal Industries, Ltd. | Tubular component for drilling and operating hydrocarbon wells, and resulting threaded connection |
| CN106428197A (en) * | 2016-11-15 | 2017-02-22 | 南京航空航天大学 | Controller and control method based on multi-mode steering system auxiliary power coupler |
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| US20120025522A1 (en) * | 2009-04-17 | 2012-02-02 | Sumitomo Metal Industries, Ltd. | Tubular component for drilling and operating hydrocarbon wells, and resulting threaded connection |
| CN102009598A (en) * | 2010-10-22 | 2011-04-13 | 张文 | Introduction of normalized traffic servo system |
| CN106428197A (en) * | 2016-11-15 | 2017-02-22 | 南京航空航天大学 | Controller and control method based on multi-mode steering system auxiliary power coupler |
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