CN110689969B - Arc-shaped concave slope stability evaluation method based on simple plane sliding method - Google Patents
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Abstract
本发明公开了基于简单平面滑动法的圆弧型凹坡稳定性评价方法，其实施过程如下：获取圆弧型滑体的重力W和滑面面积A 1；考虑圆弧型凹坡两侧过弧心轴且可提供法向刚性约束和切向摩擦的约束边界，获取圆弧型滑体与约束边界的接触面面积A 2、滑面倾角θ；通过下列公式计算边坡安全系数F s ；考虑圆弧型凹坡的拱效应及两侧约束边界的摩擦，对简单平面滑动法引入新的假定进行改进，经过改进的简单平面滑动法可以用于评价圆弧型凹坡的稳定性，且计算过程简单，为圆弧型凹坡的稳定性评价提供了一种计算结果更为合理的方法。
The invention discloses a method for evaluating the stability of a circular arc concave slope based on a simple plane sliding method. The arc axis can provide the normal rigid constraint and the constraint boundary of tangential friction, obtain the contact surface area A 2 of the arc-shaped sliding body and the constraint boundary, and the inclination angle θ of the sliding surface; calculate the slope safety factor F s by the following formula; Considering the arching effect of the arc-shaped concave slope and the friction of the constraint boundary on both sides, the simple plane sliding method is improved by introducing new assumptions. The improved simple plane sliding method can be used to evaluate the stability of the arc-shaped concave slope, and The calculation process is simple, and a more reasonable calculation method is provided for the stability evaluation of circular arc concave slopes.
Description
Technical Field
The invention relates to a slope stability evaluation method, in particular to a method for evaluating the stability of an arc-shaped concave slope based on a simple plane sliding 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 invention is based on a two-dimensional limit balance analysis method which is commonly used in the current engineering, namely a simple plane sliding method, and corrects the simple plane sliding method by considering the arch effect of the arc-shaped concave slope and the friction between the concave slope and the constraints at two sides so as to be suitable for the three-dimensional arc-shaped concave slope, so that the calculation result is more in line with the actual situation.
Disclosure of Invention
In view of the above problems, the technical problem to be solved by the present invention is to provide a method for evaluating stability of an arc-shaped concave slope based on a simple plane sliding method, so as to solve the problem of the existing two-dimensional limit balancing method in evaluating stability of an arc-shaped concave slope.
The technical scheme adopted by the invention is as follows: the method for evaluating the stability of the arc-shaped concave slope based on the simple plane sliding method comprises the following implementation processes:
the method comprises the following steps: obtaining the gravity W and the sliding of the arc-shaped sliding bodyArea of surface A1；
Step two: considering the arc-shaped central axis passing through two sides of the arc-shaped concave slope and providing a constraint boundary of normal rigid constraint and tangential friction, obtaining the contact surface area A of the arc-shaped sliding body and the constraint boundary2A sliding surface inclination angle theta;
step three: calculating the slope safety factor F by the following formulas。
R1＝ασcA2
In the formula, c1The adhesive force of the sliding surface of the arc-shaped sliding body;
the inner friction angle of the sliding surface of the arc-shaped sliding body; c. C2The cohesive force of the contact surface between the arc-shaped sliding body and the constraint boundaries at the two sides is adopted;
the inner friction angle of the contact surface between the arc-shaped sliding body and the two sides of the constraint is formed; sigmacOn an arc-shaped sliding body molar coulomb strength envelope line, when the small principal stress is 0, the large principal stress in the soil body crushed by axial compression is the compressive strength of the sliding body; alpha is an arc center angle corresponding to the arc concave slope and is expressed by radian; r1The sliding resistance force is generated by the axial pressure of the arc-shaped sliding body; r2The anti-sliding force is generated by the restriction of the arc-shaped sliding body and the two sides of the arc-shaped sliding body.
Wherein, two sides of the arc concave slope are provided with constraint planes passing through the arc center axis, and the constraint planes provide normal rigid constraint and tangential friction; the formula in the third step is based on a simple plane sliding method and considers the contribution of the axial pressure of the arc-shaped sliding body and the friction force restrained at two sides to the anti-sliding force, except for the contribution of the simple plane slidingBesides the basic assumptions of law, 2 assumptions were newly introduced: (1) anti-sliding force R generated by axial pressure of arc-shaped sliding body1The action point is positioned on the gravity center of the arc-shaped sliding body; (2) anti-sliding force R generated by side surface constraint boundary of arc-shaped sliding body2The action point is positioned on the gravity center of the arc-shaped sliding body.
The invention has the beneficial effects that: the method has the advantages that a new assumption is introduced into the simple plane sliding method to improve by considering the arch effect of the arc-shaped concave slope and the friction force generated by side constraint, the improved simple plane sliding method can be used for evaluating the stability of the arc-shaped concave slope, the calculation process is simple, and a method with a more reasonable calculation result is provided for evaluating the stability of the arc-shaped concave slope.
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FIG. 1 is a schematic structural view of an arc slider according to an embodiment of the present invention;
FIG. 2 is a schematic structural diagram of an equivalent arc slider according to an embodiment of the present invention;
FIG. 3 is a force analysis diagram of the simple planar sliding method of the equivalent circular arc slider in the embodiment of the present invention;
FIG. 4 is a top view of a circular arc-shaped concave slope in an embodiment of the present invention;
FIG. 5 is a bottom oblique view of the arc-shaped concave slope in an embodiment of the present invention;
FIG. 6 is a three-dimensional model calculation parameter map of a circular arc-shaped recess in an embodiment of the present invention;
FIG. 7 is a cross-sectional parameter chart of the arc-shaped recess 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 embodiment of the invention relates to a stability evaluation method of an arc-shaped concave slope based on a simple plane sliding method, which comprises the following implementation processes:
taking the arc-shaped sliding body in the figure 6, and taking the large principal stress inside the soil body crushed by the axial direction as the compression strength sigma of the sliding body when the small principal stress is 0 on the molar coulomb strength envelope curve of the sliding bodycAnd accordingly obtaining the axial compressive resistance F of the arc-shaped sliding body soil bodyNThe calculation formula is shown in formula (1).
FN＝σcA2 (1)
Arc-shaped sliding body soil body axial compressive resistance FNAn even wiring load q is generated, the direction of the q is horizontal and deviates from the arc center axis, and the q calculation formula is shown as a formula (2).
In the formula, r is the radius of the arc-shaped sliding body.
Substituting equation (1) into equation (2) yields equation (3):
a strip-shaped sliding body with the same section as the arc-shaped sliding body, the same length as the arc length of the arc-shaped sliding body and the same mass as the arc-shaped sliding body is established, named as an equivalent arc-shaped sliding body, and a uniform linear load q is applied to the equivalent arc-shaped sliding body as shown in fig. 2, and then the equivalent arc-shaped sliding body is taken as a research object.
Introducing a safety factor FsEquivalent arc-shaped sliding body axial force generated anti-sliding force R1The calculation formula is shown in formula (4), R1The direction is horizontal and directed into the slope, and the angle alpha is shown in fig. 3.
R1＝ασcA2 (4)
Due to equivalent arc-shaped sliding body R1The safety coefficient of the arc-shaped concave slope is higher than that of the long straight slope. At the same time, resisting the pressure force F in the axial directionNUnder the action of the force, the arc-shaped sliding body and the radial boundaryCan generate an anti-sliding force R opposite to the sliding direction2Assuming that the shear strength between the arc-shaped sliding body and the radial boundary meets the molar coulomb strength criterion, R can be obtained2The calculation formula of (a) is as follows:
also, since R2The safety coefficient of the arc-shaped concave slope is higher than that of the long straight slope, and the arc-shaped concave slope is introduced into the equivalent arc-shaped sliding body as shown in figure 2; and the force received by the equivalent arc-shaped sliding body is projected on the section where the center of gravity is located, as shown in FIG. 3, by the resultant force Σ FN0 yields equation (6):
N＝Wcosθ+R1 sinθ (6)
in the formula, N is the normal force of the equivalent arc-shaped sliding body on the sliding surface.
For the whole equivalent arc-shaped sliding body, the downward sliding force F on the sliding surfaceLower slideThe calculation formula is shown in formula (7):
Flower slide＝Wsinθ (7)
The anti-sliding force F on the sliding surface of the whole equivalent arc-shaped sliding body is obtained by the formula (6) and the molar coulomb intensity criterionAnti-skidThe calculation formula is shown as formula (8):
in the formula, T is the sliding resistance on the sliding surface of the equivalent arc-shaped sliding body.
The safety factor F is obtained from the formula (7) and the formula (8)sThe calculation formulas are shown in formulas (9) to (11).
R1＝ασcA2 (10)
Example (b): the method comprises the following steps: the circular arc type concave slope three-dimensional model calculation parameter diagram is shown in FIG. 6, and the volume weight of the sliding mass is 25kN/m3(ii) a Arc-shaped sliding surface cohesive force c of sliding body110kPa, internal friction angle
Is 20 degrees; cohesive force c between side surface of arc-shaped sliding body and constraint boundaries at two sides210kPa, internal friction angle
Is 20 degrees; uniaxial compressive strength sigma of arc-shaped sliding mass soil bodyc28.57 kPa; the weight W of the sliding body is 13123.25 kN; the sliding surface area A shown in FIG. 41＝203m2(ii) a As shown in fig. 4, α is 60 °.
Step two: FIG. 7 is a parameter diagram of a circular arc concave slope section, showing the contact surface area A of the slider and the constraint boundary2＝33m2The slip surface inclination angle θ is 34 °.
Step three: calculating the safety factor F by a formulas，
R1＝ασcA2
Calculating to obtain a safety factor Fs＝1.132。
The invention takes the arch effect of the arc-shaped concave slope into consideration to introduce a new assumption for the simple plane sliding method for improvement, the improved simple plane sliding 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 result is provided for evaluating the stability of the arc-shaped concave 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 (1)
1. The method for evaluating the stability of the arc-shaped concave slope based on the simple plane sliding method is characterized by comprising the following steps of:
constraint planes passing through the arc center axis exist on two sides of the arc concave slope, and the constraint planes provide normal rigid constraint and tangential friction;
the implementation process of the circular arc concave slope stability evaluation method is as follows:
the method comprises the following steps: obtaining the gravity W and the sliding surface area A of the arc-shaped sliding body1；
Step two: considering the arc-shaped central axis passing through two sides of the arc-shaped concave slope and providing a constraint boundary of normal rigid constraint and tangential friction, obtaining the contact surface area A of the arc-shaped sliding body and the constraint boundary2A sliding surface inclination angle theta;
step three: calculating the slope safety factor F by the following formulas；
R1＝ασcA2
In the formula, c1The adhesive force of the sliding surface of the arc-shaped sliding body;
is a circular arcThe sliding surface internal friction angle of the profile sliding body; c. C2The cohesive force of the contact surface between the arc-shaped sliding body and the constraint boundaries at the two sides is adopted;
the inner friction angle of the contact surface between the arc-shaped sliding body and the two sides of the constraint is formed; sigmacOn an arc-shaped sliding body molar coulomb strength envelope line, when the small principal stress is 0, the large principal stress in the soil body crushed by axial compression is the compressive strength of the sliding body; alpha is an arc center angle corresponding to the arc concave slope and is expressed by radian; r1The sliding resistance force is generated by the axial pressure of the arc-shaped sliding body; r2The sliding resistance force is generated by the restriction of the arc-shaped sliding body and the two sides of the arc-shaped sliding body; fNThe soil body is an arc-shaped sliding body and resists pressure axially;
and in the formula, in addition to the basic assumption of the simple plane sliding method, 2 assumptions are newly introduced: (1) anti-sliding force R generated by axial pressure of arc-shaped sliding body1The action point is positioned on the gravity center of the arc-shaped sliding body; (2) anti-sliding force R generated by side surface constraint boundary of arc-shaped sliding body2The action point is positioned on the gravity center of the arc-shaped sliding body.
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