CN110489935A - Group's pulling force effect ball crown type Slope Stability Evaluation method based on Bishop approach - Google Patents

Abstract

The invention discloses a method for evaluating the stability of a spherical crown slope based on a simplified Bishop method, the implementation process of which is as follows: the spherical crown slope is divided into several ring blocks, and the radius r _i of each ring block is obtained ; Select multiple sectors with an included angle of Δψ, and obtain the height h _i , the length of the bottom surface l _i , and the inclination angle θ _i between the bottom surface and the horizontal plane of each sector i ; iteratively calculate the slope safety factor F _s through the following formula. Considering the arching effect of the spherical crown slope, the simplified Bishop method is improved by introducing new assumptions, and the group tension is added to the formula. The improved simplified Bishop method can be used to evaluate the stability of the spherical crown slope under the group tension. And the calculation process is simple, which provides a more reasonable calculation method for the stability evaluation of the spherical crown slope under the action of group tension.

Description

Stability Evaluation Method for Spherical Crown Slope Under Group Tensile Force Based on Simplified Bishop Method

technical field

The invention relates to a slope stability evaluation method, in particular to a spherical crown type slope stability evaluation method based on a simplified Bishop method.

Background technique

In mountain engineering construction and landslide disaster prediction and analysis, slopes of various shapes will be encountered. For example, the shape of the slope in the horizontal plane can be divided into convex, concave and linear. The spatial shape of the slope It will undoubtedly affect its stability. Strictly speaking, slope stability analysis is a spatial problem, and the three-dimensional analysis method is more in line with the actual situation. In engineering, the evaluation of slope stability generally adopts the two-dimensional limit equilibrium method. This method is suitable for linear slope calculations. The accuracy is acceptable, but the calculation results of spherical crown slopes with significant spatial effects will be too conservative, and this method does not consider the situation that the slope is subjected to group tension. How to analyze the stability of the spherical crown slope under the action of group tension is a problem to be solved in the slope stability evaluation.

The present invention is based on the simplified Bishop method, which is a two-dimensional limit equilibrium analysis method commonly used in current engineering, and by considering the arch effect of the spherical crown slope, the simplified Bishop method is modified to be suitable for the three-dimensional spherical crown slope, and at the same time, the The fact that the slope is subjected to group tension makes the calculated results more in line with the actual situation.

Contents of the invention

In view of the above problems, the problem to be solved in the present invention is to provide a method for evaluating the stability of spherical crown slopes with group tension based on the simplified Bishop method, so as to solve the problem of the existing two-dimensional limit equilibrium method in evaluating the three-dimensional spherical crown slope with group tension. Insufficient slope stability.

Based on the simplified Bishop method, the method for evaluating the stability of spherical crown slopes under the action of group tension is implemented as follows:

Step 1: Divide the spherical slope into several circular blocks, and obtain the radius r _i of each circular block;

Step 2: Select multiple sectors with an included angle of Δψ, and obtain the height h _i , the length of the bottom surface l _i , and the inclination angle θ i between the bottom surface and the horizontal plane of each sector _i ;

Step 3: Calculate slope safety factor F _s iteratively through the following formula;

In the formula, c _1i is the sliding surface cohesion of the ith sector; is the sliding surface internal friction angle of the i-th sector; c _2i is the cohesion of the i-th sector soil; is the internal friction angle of the i-th segment soil; γ _i is the soil bulk density of the i-th segment; F _xi is the sum of all the tension components of the i-th ring bar on the horizontal plane; F _yi is the The sum of all the vertical components of the tensile force of the i ring bar; T _i is the anti-sliding force generated by the axial pressure of the i segment; R _i is the T _i of the i segment to the center of the arc sliding surface R is the radius of the arc sliding surface; R _i0 is the moment from the resultant force of F _xi on the ith sector to the arc sliding surface.

Wherein, the angle Δψ in the second step can usually be chosen to be less than 20°.

Among them, the formula in the third step is based on the simplified Bishop method and considers the contribution of the axial pressure of the sectors to the anti-sliding force. In addition to the basic assumptions of the simplified Bishop method, a new assumption is introduced: the i-th sector axial The point of action of the anti-sliding force T _i generated by the pressure is located on the center of gravity of the fan-shaped body.

Wherein, in the third step, the direction of each pulling force must point to the axis of symmetry.

Beneficial effect of the present invention: considering the arch effect of the spherical crown slope, the simplified Bishop method is improved by introducing a new assumption, and the group tension is added to the formula, and the improved simplified Bishop method can be used to evaluate the group tension effect of the spherical crown type The stability of the slope, and the calculation process is simple, which provides a more reasonable calculation method for the stability evaluation of the spherical crown slope under the action of group tension.

Description of drawings

Fig. 1 is the schematic structural view of sector i in the embodiment of the present invention;

Fig. 2 is an analysis diagram of the axial force of sector i in the embodiment of the present invention;

Fig. 3 is the simplified Bishop method stress analysis diagram of sector i in the embodiment of the present invention;

Fig. 4 is a calculation parameter diagram of a three-dimensional model of a spherical crown slope under group tension in an embodiment of the present invention.

Detailed ways

The technical solutions of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention. Apparently, the described embodiments are only some of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without making creative efforts belong to the protection scope of the present invention.

Based on the simplified Bishop method, the method for evaluating the stability of a spherical crown slope under the action of group tension is implemented as follows: Take a sector i with an included angle of Δψ in Figure 4, as shown in Figure 1.

From the unconfined compressive strength σ _ci of the soil, the axial compressive force F _Ni of the sector i soil can be obtained, and the calculation formulas are shown in formulas (1) and (2).

F _Ni ＝σ _ci h _i l _i cosθ _i (1)

When Δψ is small, the axial compressive force F _Ni of sector i soil will generate an anti-sliding force T _i , the direction of T _i is horizontal and away from the axis of symmetry as shown in Figure 2, and the calculation formula of T _i is shown in formula (3) .

Introduce the safety factor, put formulas (1) and (2) into (3) to get formula (4).

Due to the existence of the anti-sliding force T _i of the fan-shaped body i, the safety factor of the spherical crown slope is higher than that of the straight slope. Introduce T _i into the simplified Bishop method, take fan-shaped body i as the research object, and take the section where its center of gravity is located for force analysis, as shown in Figure 3, where O is the center of the arc sliding surface.

Formula (5) is obtained from the resultant vertical force ΣF _z =0.

In the formula, N _i is the normal force of sector i on the sliding surface, and T _i0 is the anti-sliding force of sector i on the sliding surface.

Formula (6) is obtained from the moment summation ΣM _O =0.

∑(γ _i r _i Δψh _i l _i cosθ _i -F _yi Δψ/2π)Rsinθ _i ＝∑T _i0 R+∑T _i R _i -∑F _xi R _i0 Δψ/2π (6)

T _i0 can be obtained from the Molar Coulomb intensity criterion and the safety factor F _s , as shown in formula (7).

Substitute formula (5) into formula (7) to get formula (8).

Substitute formula (8) into formula (6) and subtract Δψ to get formula (9).

Embodiment: Step 1: The spherical crown slope under the action of group tension is divided into 8 ring-shaped blocks, and the calculation parameters are: γ _i is 25kN/m ³ ; c _1i is 100kPa, Both are 45°; c _2i are both 100kPa, Both are 45°; R is 152.5m; r _i is shown in Table 1; F _xi and F _yi are shown in Table 2.

Table 1 Radius r _i of the annular bar

bar number 1 2 3 4 5 6 7 8 r_i(m) 125.9 113.6 102.6 92.6 83.6 74.6 64.6 55.6

Table 2 Ring bars F _xi and F _yi

bar number 1 2 3 4 5 6 7 8 F_xi(kN) 2000 1800 1600 1400 1200 800 600 400 F_yi(kN) 2000 1800 1600 1400 1200 800 600 400

Step 2: Select multiple fan-shaped bodies with an included angle of Δψ, h _i , l _i , θ _i , R _i , and R _i0 are shown in Table 3.

Table 3 sectors h _i , l _i , θ _i , R _i , R _i0

sector number 1 2 3 4 5 6 7 8 h_i(m) 18.5 44.8 49.4 43.3 36.1 27.4 16.8 5.4 l_i(m) 35.3 24.3 17.0 11.6 12.4 11.1 12.9 9.9 θ_i(°) 68 57 49 44 39 35 30 26 R_i(m) 52.6 63.6 75.6 88.6 100.6 111.6 122.6 132.6 R_i0(m) 41.5 41.5 50.9 67.3 82.3 98.0 115.0 131.8

Step 3: Iteratively calculate the safety factor F _s through the formula,

A total of 9 iterations were performed, and the results of each iteration were 1.278, 1.43, 1.50, 1.53, 1.542, 1.547, 1.549, 1.55, and 1.55. Through iterative calculation, the final safety factor F _s =1.55 is obtained.

The present invention considers the arching effect of the spherical crown slope and improves the simplified Bishop method by introducing a new assumption, and at the same time adds the group tension to the formula, and the improved simplified Bishop method can be used to evaluate the stability of the spherical crown slope under the action of the group tension and the calculation process is simple, which provides a method with more reasonable calculation results for the stability evaluation of spherical crown slopes under the action of group tension.

Although the embodiments of the present invention have been shown and described, those skilled in the art can understand that various changes, modifications and substitutions can be made to these embodiments without departing from the principle and spirit of the present invention. and modifications, the scope of the invention is defined by the appended claims and their equivalents.

Claims (4)

1. group's pulling force effect ball crown type Slope Stability Evaluation method based on Bishop approach, it is characterised in that: it is implemented Process is as follows:

Step 1: ball crown type side slope is divided into several annular sticks, obtains the radius r of each annular stick_i；

Step 2: multiple segments that angle is Δ ψ are chosen, the height h of each segment i is obtained_i, base length l_i, bottom surface with Horizontal plane inclination angle theta_i；

Step 3: Side Slope Safety Coefficient F is iterated to calculate by following equation_s；

In formula, c_1iFor the sliding surface cohesive strength of i-th of segment；For the sliding surface internal friction angle of i-th of segment；c_2iIt is i-th The cohesive strength of a segment soil body；For the internal friction angle of i-th of segment soil body；γ_iHold for the soil body of i-th of segment Weight；F_xiFor the summation of i-th of annular all pulling force of stick component size in the horizontal plane；F_yiFor i-th of all drawing of annular stick The summation of power vertically component size；T_iThe skid resistance generated for i-th of segment axial compressive force；R_iFor i-th segment T_iTo the torque in the circular surface center of circle；R is circular surface radius；R_i0For the F in i-th of segment_xiResultant force arrives circular surface Torque.

2. group's pulling force effect ball crown type Slope Stability Evaluation side according to claim 1 based on Bishop approach Method, it is characterised in that: Δ ψ can usually choose the angle less than 20 ° in the step two.

3. group's pulling force effect ball crown type Slope Stability Evaluation side according to claim 1 based on Bishop approach Method, it is characterised in that: the formula in the step three based on Bishop approach and considers that the axial compressive force of segment is fought The contribution of sliding power, other than the basic assumption of Bishop approach, new to introduce 1 hypothesis: i-th of segment axial compressive force is generated Skid resistance T_i, position is located in the center of gravity of the segment.

4. group's pulling force effect ball crown type Slope Stability Evaluation side according to claim 1 based on Bishop approach Method, it is characterised in that: in the step three, the direction of each pulling force will be directed toward symmetry axis.