Method for determining slope slip plane with gently-inclined soft interlayer

Abstract

The disclosure provides a method for determining a slope slip plane with a gently-inclined soft interlayer, including: S1, determining a curve formed with a slip arc of a trailing edge tearing plane, a soft interlayer plane and a slip arc of a leading edge shear opening as a slope slip plane; S2, calculating a slip plane stability coefficient; S3, determination of a position of the gently-inclined soft interlayer plane: if the slip plane stability coefficient is less than 1 but close to 1, determining that the position of the slope slip plane is accurate; otherwise, moving the position of the soft interlayer plane and repeating steps S1 and S2, until the slip plane stability coefficient is less than 1 and close to 1. The method is simple, and has a high accuracy for determining a non-circular slip plane with a soft interlayer as a bottom slip plane.

Claims

1. A method for determining a slope slip plane with a gently-inclined soft interlayer, comprising following steps of: S1. determination of the slope slip plane by a computer: S1.1. determination of a slip arc of a trailing edge tearing plane: in a case of assuming that a soft interlayer plane is at a certain depth, selecting a starting point A and an ending point B of a slip deformation produced at the trailing edge of the slip plane, drawing an arc tangent to the soft interlayer plane through the two points A and B to get a tangent point C, and taking an arc ABC as the slip arc of the trailing edge tearing plane; S1.2. determination of a slip arc of a leading edge shear opening: selecting a leading edge shear point D of the slip plane, and in a case of assuming that the leading edge of the slip plane is sheared horizontally, drawing an arc tangent to both a horizontal line and the soft interlayer plane through the point D according to a tangent length theorem, to get a tangent point E between the arc and the soft interlayer plane; and taking an arc ED as the slip arc of the leading edge shear opening; wherein a curve formed with the slip arc of the trailing edge tearing plane, the soft interlayer plane and the slip arc of the leading edge shear opening is taken as the slope slip plane; S2. calculating a slip plane stability coefficient with a limit equilibrium method by the computer; S3. determination of a position of the gently-inclined soft interlayer plane by the computer: if the slip plane stability coefficient calculated in step S2 is less than 1 but close to 1, determining that the position of the slope slip plane is accurate; otherwise, moving the position of the soft interlayer plane and repeating steps S1 and S2, until the slip plane stability coefficient is less than 1 and close to 1; and S4. designing a landslide treatment scheme for a slope with the gently-inclined soft interlayer based on the position of the gently-inclined soft interlayer plane.

2. The method for determining the slope slip plane with the gently-inclined soft interlayer according to claim 1, wherein the limit equilibrium method in step S2 is a Morgenstern-Price method or an imbalance thrust force method suitable for a non-circular slip.

3. The method for determining the slope slip plane with the gently-inclined soft interlayer according to claim 1, wherein a stratum of the trailing edge of the slip plane in step S1.1 is a quaternary soil layer.

4. The method for determining the slope slip plane with the gently-inclined soft interlayer according to claim 1, wherein a stratum of the leading edge of the slip plane in step S1.2 is gravelly soil.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is an overall flow chart of the disclosure.

(2) FIG. 2 is a schematic diagram of determining a slip arc of a trailing edge tearing plane.

(3) FIG. 3 is a schematic diagram of determining a slip arc of a leading edge shear opening.

(4) FIG. 4 is a schematic diagram of a slip plane determined by an embodiment of the disclosure.

(5) FIG. 5 is a slope geological model diagram according to an embodiment of the disclosure.

(6) In the figures: 1. slip arc of trailing edge tearing plane; 2. soft interlayer plane; 3. produced slip rock; 4. slip arc of leading edge shear opening; 5. slope slip plane; 6. quaternary soil; 7. gravelly soil; 8. limestone.

DETAILED DESCRIPTION OF THE EMBODIMENTS

(7) The disclosure will be further described below with reference to the drawings and embodiments.

(8) As shown in FIG. 1, the method for determining the slope slip plane with the gently-inclined soft interlayer provided by this embodiment includes steps S1-S3:

(9) S1. determination of the slope slip plane:

(10) S1.1. determination of a slip arc of a trailing edge tearing plane 1: in a case of assuming that the soft interlayer plane 2 is an inclined plane at a certain depth, a starting point A and an ending point B of a slip deformation produced at the trailing edge of the slip plane of the produced slip rock 3 are selected, as shown in FIG. 2; an arc tangent to the soft interlayer plane through the two points A and B is drawn to get a tangent point C, and the arc ABC is taken as the slip arc of the trailing edge tearing plane 1;

(11) S1.2. determination of the slip arc of the leading edge shear opening 4: as shown in FIG. 3, a leading edge shear point D of a slip plane of the produced slip rock 3 is selected; assuming that the leading edge of the slip plane is sheared horizontally, an intersection point between the horizontally sheared line and the soft interlayer plane is F; and an arc tangent to both the horizontal line and the soft interlayer plane 2 through the point D is drawn according to the tangent length theorem to get a tangent point E between the arc and the soft interlayer plane, and the arc ED is taken as the slip arc of the leading edge shear opening 4;

(12) as shown in FIG. 4, a curve formed with the slip arc of the trailing edge tearing plane 1, the soft interlayer plane 2 and the slip arc of the leading edge shear opening 4 is taken as the slope slip plane 5;

(13) S2. calculation of the slip plane stability coefficient with the limit equilibrium method: the slip plane stability coefficient is calculated by using the Morgenstern-Price method or the imbalance thrust force method suitable for a non-circular slip;

(14) wherein, the imbalance thrust force method is:

(15) $F=\frac{\underset{i=1}{\overset{n-1}{.Math.}}\left(R_i\underset{{j=i+1}^{}}{\overset{n}{.Math.}}{\psi }_j\right)+R_n}{\underset{i=1}{\overset{n-1}{.Math.}}\left(T_i\underset{j=1+1}{\overset{n}{.Math.}}{\psi }_j\right)+T_n};$

(16) the Morgenstern-Price method is:

(17) $M_n\left(F,\lambda \right)={\int }_a^b\left(X-E\frac{\mathrm{dy}}{\mathrm{dx}}\right)\mathrm{dx}-{\int }_a^b\frac{\mathrm{dQ}}{\mathrm{dx}}{h}_e\mathrm{dx}=0.$

(18) S3. determination of a position of the gently-inclined soft interlayer plane: if the slip plane stability coefficient F calculated in step S2 is less than 1 but close to 1, the position of the slope slip plane is determined to be accurate; otherwise, the position of the soft interlayer plane is moved and steps S1 and S2 are repeated, until the slip plane stability coefficient F is less than 1 and close to 1.

(19) The slope model with gently-inclined soft interlayer in this embodiment is shown in FIG. 5, which includes limestone 8, a soft interlayer 2, gravel soil 7, and quaternary soil 6. An accuracy of the position of the slip plane is simulated with a rainfall conditions and a stability coefficient of 1.0. Wherein, the slope rock parameters of the gently-inclined soft interlayer arc shown in Table 1, and the slip plane stability coefficients at different depths of the soft interlayer calculated by the limit equilibrium method are shown in Table 2. The calculation shows that the depths of the slip plane of the soft interlayer are between 23-26 m, and a more specific depth of the slip plane of the soft interlayer can be determined by further calculations. In this embodiment, Slide limit equilibrium analysis software is used to perform calculations. Computer-aided calculation makes the calculation process more convenient, faster, and more accurate.

(20) TABLE-US-00001 TABLE 1 slope rock parameters of the gently-inclined soft interlayer lithology c(MPa) φ(°) E(GPa) σ.sub.t(MPa) μ ρ(g/cm.sup.3) soft interlayer 0.010 22.00 0.67 0.008 0.3 2.020 limestone 1.030 31.01 1.5 1.200 0.24 2.680 Q.sub.4 0.015 16.00 0.04 0 0.37 2.004 Wherein, c is cohesion, φ is internal friction angle, E is elastic modulus, σ.sub.t is tensile strength, μ is Poisson’s ratio, and ρ is density.

(21) TABLE-US-00002 TABLE 2 slip plane stability coefficients at different depths of the soft interlayer stability coefficient depth/m (rainfall condition) 17 0.964 20 0.971 23 0.984 26 1.001 29 1.014

(22) The above-mentioned specific embodiments are merely explanations of the disclosure, not a limitation of the disclosure. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the disclosure shall fall into the protection scope of the disclosure.

(23) In the method for determining the slope slip plane with the gently-inclined soft interlayer of the disclosure, the most important step is to determine a depth position of the soft interlayer. Herein, the slip plane stability coefficient is calculated through the limit equilibrium method, the stability coefficient is used to determine whether the position of the soft interlayer is accurate, and after the position of the soft interlayer is determined, the slope slip plane with the gently-inclined soft interlayer is formed with the position of the soft interlayer, the slip arc of the trailing edge tearing plane and the slip arc of the leading edge shear opening. This method is simple and reliable, and can determine the position of the slip plane under the condition of satisfying a certain accuracy, which provides a basis for the design of the landslide treatment scheme for the slope with the gently-inclined soft interlayer.