Slope stability simplified analysis method considering actual seismic response

Abstract

The invention discloses a slope stability simplified analysis method considering actual seismic response, which comprises the following steps: establishing a simplified analysis model, and performing finite element mesh generation on a slope section through the simplified analysis model; performing finite element time-history response analysis on the finite element grid to obtain the maximum dynamic pore water pressure of each node in the finite element grid and the maximum absolute value of the acceleration with non-uniform spatial distribution; performing vertical strip division on the stability analysis simplified model, and dividing a soil strip into a plurality of soil strip units; calculating and determining the dynamic pore water pressure of the middle point of the bottom of the soil strip and the acceleration of the center of each soil strip unit, and calculating the seismic inertia force and the horizontal seismic moment of the soil strip; the dynamic pore water pressure, the seismic inertia force and the seismic moment of each soil strip are obtained, and finally the anti-sliding stability safety coefficient is obtained through calculation. According to the method, more accurate slope dynamic response can be simply and conveniently reflected in a traditional quasi-static stability analysis method, and the requirement of slope stability analysis can be efficiently and more accurately developed.

Description

Technical Field

[0001] The invention relates to the technical field of water conservancy project slope stability analysis, and in particular to a simplified slope stability analysis method taking actual earthquake response into consideration. Background Art

[0002] At present, the quasi-static method and finite element dynamic time-history analysis are commonly used in slope stability analysis. Among them, the quasi-static method has played a great role in the seismic design of slopes in my country and has accumulated rich experience. The traditional quasi-static method uses deterministic seismic inertia force to describe random seismic loads, and treats the seismic inertia force as a static force acting on each point of the slope. In addition, the seismic inertia force is determined based on the seismic intensity and slope elevation with reference to the inertia force distribution coefficient recommended by the code. Obviously, the seismic inertia force in the traditional quasi-static analysis is only an approximate consideration, which cannot reflect the reciprocating characteristics of seismic loads, the dynamic nonlinear characteristics of materials, and the overall dynamic response characteristics of slope engineering.

[0003] In addition, the pseudo-static method cannot take into account the dynamic pore water pressure, and often uses dynamic strength instead of effective stress intensity to consider the influence of dynamic pore water pressure. However, it cannot simulate the real mechanism by which dynamic pore water pressure reduces effective stress and is detrimental to slope stability. This often overestimates the impact of dynamic pore water pressure, and potential dangerous sliding arcs often deviate. Summary of the invention

[0004] In order to solve the above problems, the present invention provides a simplified slope stability analysis method taking into account actual earthquake response.

[0005] To achieve the above purpose, the technical solution adopted by the present invention is as follows:

[0006] A simplified slope stability analysis method considering actual earthquake response includes:

[0007] Establishing a simplified analysis model according to the material dividing lines and the contour lines, and performing finite element meshing on the slope section by using the simplified analysis model;

[0008] Finite element numerical static and dynamic time history response analysis is performed on the finite element mesh to obtain the maximum dynamic pore water pressure at each node in the finite element mesh and the maximum absolute value of the spatially unevenly distributed acceleration;

[0009] The center coordinates and the sliding arc radius are set to determine the potential sliding body, and the potential sliding body is superimposed on the finite element mesh. The superimposed part is divided into T soil strips in the horizontal direction, and each soil strip is divided into N soil strip units in the vertical direction.

[0010] The dynamic pore water pressure at the midpoint of the bottom of the soil strip is calculated and determined by the position of the midpoint of the bottom of the soil strip in the finite element grid;

[0011] The acceleration of the center of the soil strip unit is calculated and determined by the position of the center of the soil strip unit in the finite element grid;

[0012] The seismic inertia force of the soil strip unit is calculated and determined by the acceleration of the center of the soil strip unit, and the seismic inertia force of N soil strip units is accumulated to obtain the seismic inertia force of the soil strip; the seismic inertia force moment is calculated and determined by the seismic inertia force of the soil strip unit, and the seismic inertia force moment of N soil strip units is accumulated to obtain the seismic inertia force moment of the soil strip;

[0013] Circulate T soil strips, calculate the dynamic pore water pressure, seismic inertia force and seismic inertia force moment of each soil strip, and calculate the safety factor corresponding to the sliding arc according to the safety factor calculation formula of the pseudo-static method;

[0014] All set circle centers and all radii of each circle center are cycled to obtain a series of safety factors, among which the sliding arc with the smallest safety factor is the most potentially dangerous sliding body.

[0015] Further: the calculating and determining the dynamic pore water pressure at the midpoint of the bottom of the soil strip by the position of the midpoint of the bottom of the soil strip in the finite element grid comprises:

[0016] Determine the finite element grid unit A where the bottom midpoint p is located, and according to the coordinates of the bottom midpoint p of the soil strip (x pj ,y pj ), the coordinates of the four nodes a, b, c, and d of the finite element mesh unit A (x 1i ,y 1i ) and the quadrilateral isoparametric element shape function N expressed in local coordinates (ξ,η) i Calculate the local coordinates (ξ pj ,η pj ); According to the local coordinates, shape function N i And the maximum dynamic pore water pressure u at the four nodes a, b, c, and d obtained by dynamic time-history response analysis i , interpolation calculation to obtain the dynamic pore water pressure u at the bottom midpoint p of the soil strip pj , the calculation formula is:

[0017]

[0018] Further: the step of calculating and determining the acceleration of the center of the soil strip unit by the position of the center of the soil strip unit in the finite element grid comprises:

[0019] Determine the finite element mesh unit B where the center C of the soil strip unit is located, and according to the coordinates of the center C of the soil strip unit (x cj ,y cj ), the coordinates of the four nodes m, n, p, q of the finite element mesh unit B (x 2i ,y2i ) and the quadrilateral isoparametric element shape function N expressed in local coordinates (ξ,η) i Calculate the local coordinates (ξ cj ,η cj ); According to the local coordinates, shape function N i And the maximum absolute value of acceleration (a) of the four nodes m, n, p, and q obtained by dynamic time-history response analysis xci ,a yci ), and the acceleration of the center C of the soil strip unit is obtained by interpolation calculation (a xcj ,a ycj ), the calculation formula is:

[0020]

[0021] Further: the calculation and determination of the seismic inertia force of the soil strip unit by the acceleration of the center of the soil strip unit, and the accumulation of the seismic inertia forces of N soil strip units to obtain the seismic inertia force of the soil strip include:

[0022] According to the width b of the soil strip when divided in the horizontal direction and the height h of the soil strip unit when divided in the vertical direction j And the density of soil strips ρ j , calculate and determine the mass m of the soil strip unit j , according to the acceleration of the soil strip unit center C (a xcj ,a ycj ), we can get the seismic inertial force F of the soil strip unit xcj 、F ycj , accumulate the seismic inertia forces of N soil strip units to obtain the seismic inertia force of the soil strip, the formula is as follows:

[0023] m j =b*h j *ρ j

[0024] F xcj =m j *a xcj

[0025] F ycj =m j *a ycj

[0026]

[0027] Further: the calculation and determination of the seismic inertia moment by the seismic inertia force of the soil strip unit, and the accumulation of the seismic inertia moment of N soil strip units to obtain the seismic inertia moment of the soil strip include:

[0028] According to the coordinates of the center C of the soil strip unit (xcj ,y cj ), the center O coordinate (x O ,y O ), determine the vertical distance L between the center of the soil strip unit and the center of the circle j , combined with the seismic inertia force F of the soil strip unit xcj , calculate and determine the horizontal seismic inertia moment M of each soil strip unit j , accumulate the seismic inertia moments of N soil strip units to obtain the seismic inertia moment of the soil strip, the formula is as follows:

[0029] M j =F xcj L j

[0030]

[0031] Compared with the prior art, the present invention has the following technical advances:

[0032] The finite element dynamic time history response analysis combined with the dynamic time history response analysis can not only consider the changing process of the state of each point in the slope during an earthquake, but also reflect the nonlinear characteristics of the slope soil strip material, which is significantly better than the pseudo-static method in terms of the accuracy of the stability analysis results. However, the finite element dynamic time history analysis needs to calculate the stability safety factor and deformation of the slope at each moment. The amount of calculation is generally greater than the dynamic time history response analysis, far exceeding the pseudo-static stability analysis, and the calculation efficiency is low, which is not convenient for engineers to quickly complete the dynamic stability analysis of slope projects such as earth-rock dam projects and nuclear power plant geotechnical structures on site. Therefore, the uncertain true acceleration peak value obtained by the finite element dynamic time history response analysis is used to replace the deterministic acceleration distribution coefficient recommended by the specification, and the dynamic pore water pressure combined with the effective stress intensity index obtained by the finite element dynamic time history response analysis can significantly improve the accuracy of the traditional pseudo-static method in both mechanism simulation and analysis result accuracy, and reduce calculation errors.

[0033] In the quasi-static analysis, the seismic inertia force is only an approximate consideration, and the dynamic pore water pressure cannot be considered. It cannot reflect the reciprocating characteristics of the seismic load, the dynamic nonlinear characteristics of the material, and the dynamic response characteristics of the slope as a whole. Substituting the dynamic pore water pressure and acceleration obtained by the finite element dynamic time-history response analysis into the simplified analysis model and using the effective stress strength of the soil strip, more reasonable calculation results can be obtained.

[0034] The calculation process of finite element dynamic time-history analysis is complicated and tedious and requires a lot of calculation time. This method is based on the quasi-static calculation method and obtains the safety factor through the traditional quasi-static calculation equation, which simplifies the stable calculation process.

[0035] This application uses the results of finite element dynamic time-history response analysis to obtain dynamic pore water pressure and acceleration, taking actual earthquake conditions into consideration. Therefore, this application can consider more actual earthquake conditions to meet the needs of actual engineering projects. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] The accompanying drawings are used to provide further understanding of the present invention and constitute a part of the specification. They are used to explain the present invention together with the embodiments of the present invention and do not constitute a limitation of the present invention.

[0037] In the attached picture:

[0038] Figure 1 It is a calculation flow chart of the present invention;

[0039] Figure 2 It is a schematic diagram of the finite element mesh of the present invention;

[0040] Figure 3 It is a cloud diagram of acceleration results obtained by the finite element numerical static and dynamic time-history response analysis of the present invention;

[0041] Figure 4 This is a schematic diagram of the potential sliding body of the simplified model of the present invention divided along the x-direction;

[0042] Figure 5 It is a schematic diagram of merging the finite element mesh and the simplified model mesh of the present invention;

[0043] Figure 6 This is a schematic diagram of dividing the soil strip into soil strip units along the y direction according to the present invention;

[0044] Figure 7 It is a schematic diagram of the interpolation calculation process of the dynamic pore water pressure of soil strips of the present invention;

[0045] Figure 8 It is a schematic diagram of the soil strip unit acceleration interpolation calculation process of the present invention;

[0046] Fig. 9 It is a schematic diagram of the calculation process of the seismic inertial force of the soil strip and the soil strip unit of the present invention;

[0047] Fig.10 It is a schematic diagram of the calculation process of the seismic inertia moment of the soil strip unit of the present invention. DETAILED DESCRIPTION

[0048] The following specific embodiments may be combined with each other, and the same or similar concepts or processes may not be described in detail in some embodiments. The embodiments of the present invention will be described below in conjunction with the accompanying drawings.

[0049] like Figure 1 As shown, the present invention discloses a simplified slope stability analysis method considering actual earthquake response, comprising the following steps:

[0050] Step 1: A simplified analysis model is established according to material dividing lines and contour lines, and finite element meshing is performed on the slope section through the simplified analysis model.

[0051] Combination Figure 2 As shown, the calculated engineering section is divided into finite element meshes according to the material partition lines and contour lines. For the finite element mesh and the simplified stability analysis model, the characteristic point positions of the two meshes are the same, the material partitions are the same, and the positions of the meshes and soil strips can be different. The corresponding positions of the finite element model and the simplified stability analysis model are determined by the same characteristic points to ensure the accuracy of the calculation.

[0052] Step 2: Perform finite element numerical static and dynamic time history response analysis on the finite element mesh to obtain the maximum dynamic pore water pressure at each node in the finite element mesh and the maximum absolute value of the spatially unevenly distributed acceleration.

[0053] Combination Figure 3 As shown in the figure, the dynamic pore water pressure calculated by finite element method is the residual pore pressure at the end of the earthquake or the maximum pore pressure in the earthquake time history. The acceleration distribution obtained by finite element dynamic time history response analysis replaces the acceleration distribution recommended by the code. The distribution curve is no longer used, so a more accurate actual dynamic response of the slope can be obtained.

[0054] Step 3: Set the coordinates of the center of the circle and the radius of the sliding arc to determine the potential sliding body, superimpose the potential sliding body with the finite element mesh, divide the superimposed part into T soil strips along the horizontal direction, and divide each soil strip into N soil strip units along the vertical direction.

[0055] Specific combination Figure 4 and Figure 5 As shown, this application only establishes a simplified model based on the contour line and material partition line, and according to the set circle center O coordinate (x O ,y O ) and the sliding arc radius R to determine the potential sliding body, and superimpose the potential sliding body and the finite element mesh according to the upstream slope foot feature point A to determine the position of the potential sliding body in the finite element mesh. The superimposed part is divided into T soil strips along the horizontal direction. Figure 6 As shown, the coordinates of the top midpoint q and the bottom midpoint p of the soil strip are determined, and each soil strip is divided into N equal soil strip units along the vertical y direction. The coordinates of the center C of each soil strip unit are calculated and each soil strip is divided into N soil strip units along the vertical direction. The traditional quasi-static calculation does not consider the vertical acceleration change of the soil strip. The introduction of the concept of soil strip units can better consider the acceleration distribution, making the calculation results more realistic and more in line with reality.

[0056] Step 4: Calculate and determine the dynamic pore water pressure at the midpoint of the bottom of the soil strip based on the position of the midpoint of the bottom of the soil strip in the finite element grid.

[0057] Combination Figure 7 As shown in the figure, determine the finite element grid unit A where the bottom midpoint p is located, according to the coordinates of the bottom midpoint p of the soil strip (x pj ,y pj ), the coordinates of the four nodes a, b, c, and d of the finite element mesh unit A (x 1i ,y 1i ) and the quadrilateral isoparametric element shape function N expressed in local coordinates (ξ,η) i Calculate the local coordinates (ξ pj ,η pj ); According to the local coordinates, shape function N i And the maximum dynamic pore water pressure u at the four nodes a, b, c, and d obtained by dynamic time-history response analysis i , interpolation calculation to obtain the dynamic pore water pressure u at the bottom midpoint p of the soil strip pj , the calculation formula is:

[0058]

[0059] Step 5: Calculate and determine the acceleration of the center of the soil strip unit through the position of the center of the soil strip unit in the finite element grid.

[0060] Combination Figure 8 As shown in the figure, determine the finite element mesh unit B where the center C of the soil strip unit is located, and according to the coordinates (x cj ,y cj ), the coordinates of the four nodes m, n, p, q of the finite element mesh unit B (x 2i ,y 2i ) and the quadrilateral isoparametric element shape function N expressed in local coordinates (ξ,η) i Calculate the local coordinates (ξ cj ,η cj ); According to the local coordinates, shape function N i And the maximum absolute value of acceleration (a) of the four nodes m, n, p, and q obtained by dynamic time-history response analysis xci ,a yci ), and the acceleration of the center C of the soil strip unit is obtained by interpolation calculation (a xcj ,a ycj ), the calculation formula is:

[0061]

[0062] Step 6: Calculate and determine the seismic inertia force of the soil strip unit through the acceleration of the center of the soil strip unit, accumulate the seismic inertia forces of N soil strip units to obtain the seismic inertia force of the soil strip; calculate and determine the seismic inertia force moment through the seismic inertia force of the soil strip unit, accumulate the seismic inertia force moments of N soil strip units to obtain the seismic inertia force moment of the soil strip.

[0063] Combination Fig. 9 As shown, according to the soil strip width b when divided along the horizontal direction and the soil strip unit height h when divided along the vertical direction j And the density of soil strips ρ j , calculate and determine the mass m of the soil strip unit j , according to the acceleration of the soil strip unit center C (a xcj ,a ycj ), we can get the seismic inertial force F of the soil strip unit xcj 、F ycj , accumulate the seismic inertia forces of N soil strip units to obtain the seismic inertia force of the soil strip, the formula is as follows:

[0064] m j =b*h j *ρ j

[0065] F xcj =m j *a xcj

[0066] F ycj =m j *a ycj

[0067]

[0068] Combination Fig.10 As shown, according to the coordinates of the center C of the soil strip unit (x cj ,y cj ), the center O coordinate (x O ,y O ), determine the vertical distance L between the center of the soil strip unit and the center of the circle j , combined with the seismic inertia force F of the soil strip unit xcj , calculate and determine the horizontal seismic inertia moment M of each soil strip unit j , accumulate the seismic inertia moments of N soil strip units to obtain the seismic inertia moment of the soil strip, the formula is as follows:

[0069] M j =F xcj L j

[0070]

[0071] Step 7: Circulate T soil strips, calculate the dynamic pore water pressure, seismic inertia force and seismic inertia force moment of each soil strip, and calculate the safety factor corresponding to the sliding arc according to the traditional pseudo-static method safety factor calculation formula.

[0072] Step 8: Loop through all set circle centers and all radii of each circle center to obtain a series of safety factors, where the sliding arc with the smallest safety factor is the most potentially dangerous sliding body.

[0073] Finally, it should be noted that the above is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art can still modify the technical solutions described in the aforementioned embodiments or replace some of the technical features therein with equivalents. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the scope of protection of the claims of the present invention.

Claims

1. A simplified slope stability analysis method considering actual earthquake response, characterized in that: include: Establishing a simplified analysis model according to the material dividing lines and the contour lines, and performing finite element meshing on the slope section by using the simplified analysis model; Finite element numerical static and dynamic time history response analysis is performed on the finite element mesh to obtain the maximum dynamic pore water pressure at each node in the finite element mesh and the maximum absolute value of the spatially unevenly distributed acceleration; The center coordinates and the sliding arc radius are set to determine the potential sliding body, and the potential sliding body is superimposed on the finite element mesh. The superimposed part is divided into T soil strips in the horizontal direction, and each soil strip is divided into N soil strip units in the vertical direction. The dynamic pore water pressure at the midpoint of the bottom of the soil strip is calculated and determined by the position of the midpoint of the bottom of the soil strip in the finite element grid; The acceleration of the center of the soil strip unit is calculated and determined by the position of the center of the soil strip unit in the finite element grid; The seismic inertia force of the soil strip unit is calculated and determined by the acceleration of the center of the soil strip unit, and the seismic inertia force of N soil strip units is accumulated to obtain the seismic inertia force of the soil strip; the seismic inertia force moment is calculated and determined by the seismic inertia force of the soil strip unit, and the seismic inertia force moment of N soil strip units is accumulated to obtain the seismic inertia force moment of the soil strip; Circulate T soil strips, calculate the dynamic pore water pressure, seismic inertia force and seismic inertia force moment of each soil strip, and calculate the safety factor corresponding to the sliding arc according to the safety factor calculation formula of the pseudo-static method; All set circle centers and all radii of each circle center are cycled to obtain a series of safety factors, among which the sliding arc with the smallest safety factor is the most potentially dangerous sliding body.

2. A simplified slope stability analysis method considering actual earthquake response according to claim 1, characterized in that: The calculation and determination of the dynamic pore water pressure at the midpoint of the bottom of the soil strip by the position of the midpoint of the bottom of the soil strip in the finite element grid comprises: Determine the finite element grid unit A where the bottom midpoint p is located, and according to the coordinates of the bottom midpoint p of the soil strip (x pj ,y pj ), the coordinates of the four nodes a, b, c, and d of the finite element mesh unit A (x 1i ,y 1i ) and the quadrilateral isoparametric element shape function N expressed in local coordinates (ξ,η) i Calculate the local coordinates (ξ pj ,η pj ); According to the local coordinates, shape function N i And the maximum dynamic pore water pressure u at the four nodes a, b, c, and d obtained by dynamic time-history response analysis i , interpolation calculation to obtain the dynamic pore water pressure u at the bottom midpoint p of the soil strip pj , the calculation formula is:

3. A simplified slope stability analysis method considering actual earthquake response according to claim 2, characterized in that: The step of calculating and determining the acceleration of the center of the soil strip unit by the position of the center of the soil strip unit in the finite element grid comprises: Determine the finite element mesh unit B where the center C of the soil strip unit is located, and according to the coordinates of the center C of the soil strip unit (x cj ,y cj ), the coordinates of the four nodes m, n, p, q of the finite element mesh unit B (x 2i ,y 2i ) and the quadrilateral isoparametric element shape function N expressed in local coordinates (ξ,η) i Calculate the local coordinates (ξ cj ,η cj ); According to the local coordinates, shape function N i And the maximum absolute value of acceleration (a) of the four nodes m, n, p, and q obtained by dynamic time-history response analysis xci ,a yci ), and the acceleration of the center C of the soil strip unit is obtained by interpolation calculation (a xcj ,a ycj ), the calculation formula is:

4. A simplified slope stability analysis method considering actual earthquake response according to claim 3, characterized in that: The calculation and determination of the seismic inertia force of the soil strip unit by the acceleration of the center of the soil strip unit, and the accumulation of the seismic inertia forces of N soil strip units to obtain the seismic inertia force of the soil strip include: According to the width b of the soil strip when divided in the horizontal direction and the height h of the soil strip unit when divided in the vertical direction j And the density of soil strip ρ j , calculate and determine the mass m of the soil strip unit j , according to the acceleration of the soil strip unit center C (a xcj ,a ycj ), we can get the seismic inertial force F of the soil strip unit xcj 、F ycj , accumulate the seismic inertia forces of N soil strip units to obtain the seismic inertia force of the soil strip, the formula is as follows: m j =b*h j *r j F xcj =m j *a xcj F ycj =m j *a ycj 5. A simplified slope stability analysis method considering actual earthquake response according to claim 4, characterized in that: The method of calculating and determining the seismic inertia moment of the soil strip unit by using the seismic inertia force of the soil strip unit, and accumulating the seismic inertia moment of N soil strip units to obtain the seismic inertia moment of the soil strip includes: According to the coordinates of the center C of the soil strip unit (x cj ,y cj ), the center O coordinate (x O ,y O ), determine the vertical distance L between the center of the soil strip unit and the center of the circle j , combined with the seismic inertia force F of the soil strip unit xcj , calculate and determine the horizontal seismic inertia moment M of each soil strip unit j , accumulate the seismic inertia moments of N soil strip units to obtain the seismic inertia moment of the soil strip, the formula is as follows: M j =F xcj L j

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