CN111651900A - Simulated dynamic upper limit method for calculating rock slope stability of Xigeda stratum - Google Patents

Simulated dynamic upper limit method for calculating rock slope stability of Xigeda stratum Download PDF

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CN111651900A
CN111651900A CN202010610993.XA CN202010610993A CN111651900A CN 111651900 A CN111651900 A CN 111651900A CN 202010610993 A CN202010610993 A CN 202010610993A CN 111651900 A CN111651900 A CN 111651900A
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xigeda
rock
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刘文连
李泽
眭素刚
李江龙
陆得志
许汉华
唐果
宁飞
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China Nonferrous Metals Industry Kunming Survey And Design Institute Co ltd
Kunming University of Science and Technology
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Abstract

The invention discloses a pseudo-dynamic upper limit method for calculating the stability of a Xigeda stratum rock slope, which takes the Xigeda stratum rock slope as a research object, adopts a finite element to disperse the Xigeda stratum rock slope, assumes seismic waves as simple harmonic waves, calculates the seismic acceleration of the finite element by using a pseudo-dynamic method principle, and establishes a pseudo-dynamic upper limit method nonlinear mathematical programming model for the stability of the Xigeda stratum rock slope under the action of an earthquake according to the upper limit method principle; and circularly solving the nonlinear mathematical programming model of the Xigeda stratum rock slope stability by using an 'interior point algorithm' to obtain a relation curve of the safety coefficient of the rock slope stability and time under the action of an earthquake. The method is rigorous in theory, high in calculation efficiency and simple and convenient in engineering application, and can be applied to the field of calculation of the stability of Xigeda stratum rock slopes under the action of earthquakes.

Description

Simulated dynamic upper limit method for calculating rock slope stability of Xigeda stratum
Technical Field
The invention relates to a pseudo-dynamic upper limit method for calculating the stability of a rock slope of a Xigeda stratum, belonging to the technical field of slope stability analysis.
Background
The Xigeda stratum is a sedimentary stratum of a river or a lake, is mainly formed between the late renewal world and the third family, and is widely distributed in the Panzhihua area of China. The Xigeda stratum is half-finished rock of siltstone and claystone interbedded, and the Xigeda stratum rock is low in compression strength, tensile strength and shear strength, is easy to soften when meeting water and belongs to extremely soft rock. The earthquakes in Panzhihua and Wenchang areas in Sichuan are frequent, the earthquake intensity reaches more than 7 ℃, and the earthquake intensity reaches 9 ℃ in individual areas. Landslide disasters often occur on a rock slope formed by Xigeda stratum under the action of an earthquake, and challenges are brought to the safe construction and operation of engineering.
Seismic effects are a significant cause of instability of the Xigeda formation lithologic slope. The stability evolution law of the Xigeda stratum lithologic slope is a comprehensive subject related to the interdisciplinary multidisciplinary project of geological engineering, seismic engineering, geotechnical dynamics, computational mechanics and the like. Generally, the instability of the side slope under the action of the earthquake is mainly caused by that the inertia force of the earthquake increases the downward slip force of the side slope, so that the overall safety degree of the side slope is reduced. The method is characterized in that a plurality of scholars develop fruitful research work on the aspects of a slope earthquake load calculation method under the earthquake action, a slope dynamic response rule, a instability mechanism, stability evaluation and the like, and research methods such as a quasi-static method, a quasi-dynamic method, a dynamic time course analysis method and the like are formed aiming at the slope stability research under the earthquake action.
The slope stability under the earthquake action specified in the technical Specification of building slope engineering (GB 50330-2013) in China is mainly calculated by adopting a quasi-static method. The quasi-static method simplifies the earthquake action into the static earthquake inertia force acting on the mass center of the rock-soil body, thereby simplifying the earthquake dynamic effect into the static effect and solving the stability safety coefficient of the side slope based on the limit balance principle. However, the quasi-static method simplifies the seismic effect into the static effect, does not consider the space-time effect of seismic wave propagation, does not consider the amplitude and frequency of the earthquake and the dynamic and damping characteristics of rock-soil materials, and has a great difference between the calculation result and the actual effect of the earthquake.
Disclosure of Invention
The invention provides a simulated dynamic upper limit method for calculating the stability of a Xigeda stratum rock slope, which is used for obtaining a safety coefficient distribution rule of the stability of the Xigeda stratum rock slope through the upper limit method.
The technical scheme of the invention is as follows: a pseudo-dynamic upper limit method for calculating the stability of a Xigeda stratum rock slope is characterized in that the Xigeda stratum rock slope is taken as a research object, a finite element discrete Xigeda stratum rock slope is adopted, seismic waves are assumed to be simple harmonic waves, the seismic acceleration of the Xigeda stratum rock slope finite element is calculated by using a pseudo-dynamic method principle, a target function, a plastic flow constraint condition of the finite element under the action of an earthquake, a plastic flow constraint condition of a common edge of the finite element, a finite element boundary condition and a function balance constraint condition are established according to the upper limit method principle, and then a pseudo-dynamic upper limit method nonlinear programming mathematical model of the Xigeda stratum rock slope stability under the action of the earthquake is established; and solving a nonlinear mathematical programming model of the Xigeda stratum rock slope stability.
The method comprises the following specific steps:
step one, simulating parameters for calculating the stability of the Xigeda formation rock slope;
step two, adopting a finite element discrete Xigeda stratum rock slope and calculating geometric characteristic parameters of the finite element;
step three, calculating the earthquake acceleration of the Xigeda stratum rock slope finite unit according to the principle of a pseudo-dynamic method;
step four, establishing a pseudo-dynamic upper limit method nonlinear mathematical programming model of rock slope stability of the Xigeda stratum under the action of the earthquake according to an upper limit method principle by combining the earthquake acceleration;
and step five, circularly solving the simulated dynamic upper limit method nonlinear mathematical programming model of the rock slope stability of the Xigeda stratum under the earthquake action by using an interior point algorithm to obtain a relation curve of the safety coefficient and the time of the rock slope stability under the earthquake action.
The parameters for calculating the stability of the pseudo-Xigeda formation rock slope comprise: firstly, determining geometric parameters of Xigeda stratum rock slope; determining the distribution conditions of the siltstone stratum and the claystone stratum in the Xigeda stratum; determining physical and mechanical parameters of the Xigeda stratum rock mass material; and fourthly, determining seismic parameters of the Xigeda stratum rock slope.
The geometrical parameters of the Xigeda formation rock slope comprise: the height H of the rock slope, the width of the rock slope and the coordinates of the control points of the geometrical shape of the slope; the distribution of the formation includes: the thickness of each layer of the siltstone and claystone stratum and the inclination angle of the interface of the siltstone and claystone; the physical mechanical parameters include: the unit weight of the siltstone and the claystone, the internal friction angle and the cohesion of the siltstone, and the internal friction angle and the cohesion of the claystone; the seismic parameters include: earthquake vibration period T and earthquake amplification coefficient fsShear wave velocity V of slope rock masssLongitudinal wave velocity V of slope rock masspHorizontal seismic acceleration coefficient khVertical seismic acceleration coefficient kv。
The method for dispersing Xigeda stratum rock slope by adopting the finite element specifically comprises the following steps:
(1) establishing a coordinate system of the Xigeda stratum rock slope, taking a slope toe of the slope as an origin of coordinates, taking a horizontal axis as an x-axis of the coordinate system, taking a horizontal right axis as a positive axis of the x-axis, taking a vertical axis as a y-axis of the coordinate system, and taking a vertical upward axis as a positive axis of the y-axis;
(2) using the finite element discrete Xigeda formation rock slope, any finite element i has three nodes, and the kth node of the ith finite element has horizontal velocity
Figure BDA0002560919150000031
And vertical velocity
Figure BDA0002560919150000032
Wherein i ═ 1, …, Ne)，k＝(1,2,3)，NeIs the number of finite elements in the Xigeda formation lithologic slope; common edge between adjacent finite elements: each common edge has four nodes, the h node of the g common edge has horizontal speed
Figure BDA0002560919150000033
And vertical velocity
Figure BDA0002560919150000034
Wherein g ═ 1, …, Ng)，h＝(1,2,3，4)，NgIs the number of finite element common edges in the Xigeda stratigraphic rock slope; the volume weight, the internal friction angle and the cohesion of the limited unit of the siltstone area are taken according to the physical mechanical parameters of the siltstone material, and the volume weight, the internal friction angle and the cohesion of the limited unit of the claystone area are taken according to the physical mechanical parameters of the claystone material;
(3) calculating geometric feature parameters of the finite elements, including: the centroid of the finite element to the vertical height of the slope toe of the slope, the area of the finite element:
the vertical height from the centroid of the finite element to the toe of the slope is calculated according to the following formula:
Figure BDA0002560919150000035
in the formula: hiIs the centroid to side slope of the ith finite elementThe vertical height of the toe;
Figure BDA0002560919150000036
is the y coordinate of the 1 st node of the ith triangle element,
Figure BDA0002560919150000037
is the y coordinate of the 2 nd node of the ith triangle element,
Figure BDA0002560919150000038
is the y coordinate of the 3 rd node of the ith triangular unit;
the area of the finite element is calculated as:
Figure BDA0002560919150000039
in the formula: siIs the area of the ith finite element;
Figure BDA00025609191500000310
is the x-coordinate of the 1 st node of the ith triangle element,
Figure BDA00025609191500000311
is the x-coordinate of the 2 nd node of the ith triangle element,
Figure BDA00025609191500000312
is the x coordinate of the 3 rd node of the ith triangle element.
The method for calculating the seismic acceleration of the Xigeda stratum rock slope finite unit according to the principle of the pseudo-dynamic method specifically comprises the following steps:
(1) calculating the seismic acceleration of the finite element in the horizontal direction according to the principle of a pseudo-dynamic method:
Figure BDA00025609191500000313
in the formula:
Figure BDA00025609191500000314
the seismic acceleration of the ith finite element of the jth time-step Xigeda stratum rock slope along the horizontal direction; i ═ 1, …, Ne)，NeIs the number of finite elements in the Xigeda formation lithologic slope; j ═ 1, …, Nt)，NtIs the number of time steps in the seismic oscillation period; t is the earthquake vibration period; k is a radical ofhIs the seismic acceleration coefficient in the horizontal direction; hiIs the vertical height from the centroid of the ith finite element to the toe of the side slope; h is the height of the Xigeda formation rock slope; f. ofsThe seismic amplification factor of the slope rock mass; pi is the circumference ratio; vsIs the shear wave velocity of the slope rock mass;
(2) calculating the earthquake acceleration of the limited unit in the vertical direction according to the principle of a pseudo-dynamic method:
Figure BDA0002560919150000041
in the formula:
Figure BDA0002560919150000042
the seismic acceleration of the ith finite element of the jth time-step Xigeda stratum rock slope along the vertical direction; k is a radical ofvIs the seismic acceleration coefficient in the vertical direction; vpIs the longitudinal wave velocity of the slope rock mass.
The establishment of the pseudo-dynamic upper limit method nonlinear mathematical programming model of the Xigeda stratum rock slope stability under the action of the earthquake specifically comprises the following steps:
(1) establishing an objective function:
taking the safety coefficient of the Xigeda stratum rock slope stability as an objective function, and solving the minimum value of the safety coefficient, wherein the minimum value is as follows:
Minimize:Kj
in the formula: j ═ 1, …, Nt)，NtIs the number of time steps in the seismic oscillation period; kjThe safety factor of the rock slope of the jth time step Xigeda stratum under the action of the earthquake is shown; minimize denotes "Minimize";
(2) establishing a limited unit plastic flow constraint condition:
Figure BDA0002560919150000043
in the formula:
Figure BDA0002560919150000044
is the geometrical compatibility constraint matrix of the ith finite element,
Figure BDA0002560919150000045
a plastic flow constraint matrix that is the ith finite element; i ═ 1, …, Ne)，NeIs the number of finite elements in the Xigeda formation lithologic slope; siIs the area of the ith finite element;
Figure BDA0002560919150000046
6 shape function coefficients of the ith finite element respectively;
Figure BDA0002560919150000047
m-is (1, 2.., 8) the 1 st to 8 th plastic flow matrix coefficients of the finite element, respectively,
Figure BDA0002560919150000051
m-is (1,2,. said., 8) the 9 th to 16 th plastic flow matrix coefficients, C, of the finite element, respectivelym+162sin (2 pi m/8), m (1,2,.., 8), which are the 17 th to 24 th plastic flow matrix coefficients of the finite element, respectively;
Figure BDA0002560919150000052
is the internal friction angle: in siltstone formation
Figure BDA0002560919150000053
Taking the internal friction angle of the siltstone when the siltstone is positioned in the claystone stratum
Figure BDA0002560919150000054
Taking an internal friction angle of claystone;
Figure BDA0002560919150000055
is the velocity vector of the ith finite element,
Figure BDA0002560919150000056
is the plastic multiplier vector of the ith finite element;
Figure BDA0002560919150000057
the horizontal velocity of the kth node of the ith finite element, k being (1,2, 3);
Figure BDA0002560919150000058
is the vertical velocity of the kth node of the ith finite element, k ═ 1,2, 3;
Figure BDA0002560919150000059
an mth finite element plastic multiplier that is an ith finite element;
(3) establishing a plastic flow constraint condition of a common edge of a limited unit:
Figure BDA00025609191500000510
in the formula:
Figure BDA00025609191500000511
is a geometric compatibility constraint matrix of the common edge of the g-th finite element,
Figure BDA00025609191500000512
is the plastic flow constraint matrix of the common edge of the g-th finite element; g ═ 1, …, Ng)，NgIs the number of finite element common edges in the Xigeda stratigraphic rock slope;
Figure BDA00025609191500000513
θgis the inclination angle of the common side of the g-th finite element, θgTaking the anticlockwise direction as positive;
Figure BDA00025609191500000514
is the velocity vector of the common edge of the g-th finite element,
Figure BDA00025609191500000515
is the plastic multiplier vector of the common edge of the g-th finite element;
Figure BDA00025609191500000516
the horizontal speed of the h node of the common edge of the g finite element is h ═ 1,2,3 and 4;
Figure BDA00025609191500000517
the vertical speed of the h-th node of the common edge of the g-th finite element is h ═ 1,2,3 and 4;
Figure BDA00025609191500000518
is the nth common edge plastic multiplier of the g finite element common edge, n is (1, …, 4);
(4) establishing a finite element boundary condition:
Abub＝0
in the formula: a. thebIs a coordinate transformation matrix of a finite element b on the boundary in the Xigeda stratigraphic rock slope; u. ofbIs the velocity vector of the finite element b on the boundary in the Xigeda stratigraphic rock slope; b ═ 1, …, Nb)，NbIs the number of finite elements in the Xigeda formation rock slope where the velocity at the boundary equals 0;
(5) establishing a function balance constraint condition of a limited unit:
Figure BDA0002560919150000061
in the formula: γ is the volume weight: when the reservoir is positioned in a siltstone stratum, the volume weight of the siltstone is taken as gamma, and when the reservoir is positioned in a claystone stratum, the volume weight of the claystone is taken as gamma;
Figure BDA0002560919150000062
is the seismic acceleration of the ith finite element of the jth time-step Xigeda stratum rock slope along the horizontal direction；
Figure BDA0002560919150000063
The seismic acceleration of the ith finite element of the jth time-step Xigeda stratum rock slope along the vertical direction; c. CsIs the cohesion: in siltstone formation csTaking the cohesive force of siltstone and locating in claystone stratum csTaking the cohesive force of claystone; lgIs the length of the common edge of the g-th finite element, g ═ 1, …, Ng)，NgIs the number of finite element common edges in the Xigeda stratigraphic rock slope;
(6) establishing a pseudo-dynamic upper limit method nonlinear mathematical programming model of rock slope stability of Xigeda stratum under the action of earthquake:
integrating the objective function, the limited unit plastic flow constraint condition, the limited unit common edge plastic flow constraint condition, the limited unit boundary condition, the function balance constraint condition and the earthquake acceleration equation to obtain the pseudo dynamic upper limit method nonlinear mathematical programming model of the Xigeda stratum rock slope stability under the earthquake action as follows:
Figure BDA0002560919150000071
in the formula: t is the earthquake vibration period; k is a radical ofhIs the seismic acceleration coefficient in the horizontal direction; hiIs the vertical height from the centroid of the ith finite element to the toe of the side slope; h is the height of the Xigeda formation rock slope; f. ofsThe seismic amplification factor of the slope rock mass; pi is the circumference ratio; vsIs the shear wave velocity of the slope rock mass; k is a radical ofvIs the seismic acceleration coefficient in the vertical direction; vpIs the longitudinal wave velocity of the slope rock mass.
The simulated dynamic upper limit method nonlinear mathematical programming model for solving the rock slope stability of the Xigeda stratum under the action of the earthquake specifically comprises the following steps: known parameters are changed from j-1 to j-NtCircularly bringing in a pseudo-dynamic upper limit method nonlinear mathematical programming model formula of Xigeda stratum rock slope stability under earthquake action, and solving Xigeda stratum rock slope stability under earthquake action by using an' interior point algorithmSolving to obtain N by a simulated dynamic upper limit method nonlinear mathematical programming model of the Geda stratum rock slope stabilitytSafety coefficient K of rock slope stability of individual Xigeda stratumj(ii) a Then, taking the safety factor as a vertical axis and time as a horizontal axis, and drawing the safety factor K of the Xigeda stratum rock slope stability under the action of earthquakejAnd time jT/NtThe relationship curve of (1); wherein j is (1, …, N)t)，NtIs the number of time steps in the seismic oscillation period; and T is the seismic vibration period.
The invention has the beneficial effects that: the method takes the Xigeda stratum lithologic slope as a research object, adopts a finite element to disperse the Xigeda stratum lithologic slope, assumes seismic waves as simple harmonic waves, calculates the seismic acceleration of the finite element by using a pseudo-dynamic method principle, and establishes a pseudo-dynamic upper limit method nonlinear mathematical programming model of the Xigeda stratum lithologic slope stability under the action of an earthquake according to an upper limit method principle; and circularly solving the nonlinear mathematical programming model of the Xigeda stratum rock slope stability by using an 'interior point algorithm' to obtain a relation curve of the safety coefficient of the rock slope stability and time under the action of an earthquake. The method is rigorous in theory, high in calculation efficiency and simple and convenient in engineering application, and can be applied to the field of calculation of the stability of Xigeda stratum rock slopes under the action of earthquakes.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a schematic diagram of finite elements of a Xigeda formation rock slope;
FIG. 3 is a schematic view of a common edge of adjacent finite elements of a Xigeda stratigraphic rock slope;
FIG. 4 is a schematic representation of the geometry of a rock slope of an example Xigeda formation (in m);
FIG. 5 is a schematic diagram of discrete finite elements of a rock slope of the Xigeda formation and numbering of the finite elements of the embodiment;
FIG. 6 is a plot of seismic acceleration versus time along the horizontal direction for the 86 th finite element of the example Xigeda stratigraphic rock slope;
FIG. 7 is a plot of seismic acceleration versus time for the 86 th finite element of the example Xigeda formation lithologic slope in the vertical direction;
FIG. 8 is a plot of seismic acceleration versus time for the 74 th finite element of the example Xigeda formation lithologic slope in the horizontal direction;
FIG. 9 is a plot of seismic acceleration versus time for the 74 th finite element of the example Xigeda formation lithologic slope in the vertical direction;
FIG. 10 is a plot of seismic acceleration versus time along the horizontal direction for the 12 th finite element of the example Xigeda stratigraphic rock slope;
FIG. 11 is a plot of seismic acceleration versus time for the 12 th finite element of the example Xigeda formation rock slope in the vertical direction;
FIG. 12 is a graph of safety factor versus time for a rock slope of an example Xigeda formation under the action of an earthquake.
Detailed Description
The invention will be further described with reference to the following figures and examples, without however restricting the scope of the invention thereto.
Example 1: as shown in fig. 1-12, a pseudo-dynamic upper limit method for calculating the rock slope stability of the Xigeda stratum is characterized in that a Xigeda stratum rock slope is taken as a research object, a finite element is adopted to disperse the Xigeda stratum rock slope, seismic waves are assumed to be simple harmonic waves, the seismic acceleration of the Xigeda stratum rock slope finite element is calculated by using a pseudo-dynamic method principle, and an objective function, a plastic flow constraint condition of the finite element under the action of an earthquake, a plastic flow constraint condition of a common edge of the finite element, a boundary condition of the finite element and a functional balance constraint condition are established according to the upper limit method principle, so that a pseudo-dynamic upper limit method nonlinear mathematical programming model for calculating the rock slope stability of the Xigeda stratum under the action of the earthquake is established; and solving a nonlinear mathematical programming model of the Xigeda stratum rock slope stability. The process of the invention is shown in figure 1.
Further, the method may be configured to include the specific steps of:
step one, simulating parameters for calculating the stability of the Xigeda formation rock slope;
step two, adopting a finite element discrete Xigeda stratum rock slope and calculating geometric characteristic parameters of the finite element;
step three, calculating the earthquake acceleration of the Xigeda stratum rock slope finite unit according to the principle of a pseudo-dynamic method;
step four, establishing a pseudo-dynamic upper limit method nonlinear mathematical programming model of rock slope stability of the Xigeda stratum under the action of the earthquake according to an upper limit method principle by combining the earthquake acceleration;
and step five, circularly solving the simulated dynamic upper limit method nonlinear mathematical programming model of the rock slope stability of the Xigeda stratum under the earthquake action by using an interior point algorithm to obtain a relation curve of the safety coefficient and the time of the rock slope stability under the earthquake action.
Further, the invention combines the specific steps to give the following process:
step one, simulating parameters for calculating the rock slope stability of the Xigeda stratum.
According to the actual situation of the Xigeda stratum rock slope, stability calculation parameters are drawn up, and the method specifically comprises the following steps:
the method includes the following steps that geometric parameters of the Xigeda stratum rock slope are determined, and the geometric shape of the slope is shown in FIG. 4 and includes the following steps: the height H of the side slope is 30m, and the width of the side slope is 50 m; the coordinates of the slope geometric shape control points are as follows: coordinates (0,0) of point O, coordinates (50,0) of point a, coordinates (50,30) of point B, and coordinates (17.32,30) of point C;
determining the distribution conditions of the siltstone stratum and the claystone stratum in the Xigeda stratum, wherein the distribution conditions comprise the following steps: as shown in fig. 4, the slope stratum of the example is divided into 5 layers, which are siltstone, claystone, and siltstone from top to bottom, the corresponding thicknesses are 4.87m, 10m, and 6.13m, respectively, and the inclination angle of the interface between the siltstone and claystone is 25 °;
③ determining physical and mechanical parameters of Xigeda stratum rock mass material, including volume weight of siltstone 2550kN/m3The volume weight of claystone is 2450kN/m3(ii) a The internal friction angle of the siltstone is 26 degrees, and the siltstone is coagulatedForce 120 kPa; the internal friction angle of the claystone is 24 degrees, and the cohesive force of the claystone is 180 kPa.
④ determining seismic parameters of Xigeda stratum rock slope, including seismic vibration period T of 0.2s and seismic amplification factor fs1.1 as the ratio; shear wave velocity V of slope rock masss3275 m/s; longitudinal wave velocity V of slope rock massp5925 m/s; seismic acceleration coefficient k in horizontal directionh0.15, vertical seismic acceleration coefficient kv＝0.075。
Step two, adopting a finite element discrete Xigeda stratum rock slope and calculating geometric characteristic parameters of the finite element, wherein the method specifically comprises the following steps:
(1) establishing a coordinate system of the Xigeda stratum rock slope, taking the slope toe of the slope as the origin of coordinates, taking the horizontal axis as the x axis of the coordinate system, taking the horizontal right axis as the positive, taking the vertical axis as the y axis of the coordinate system, taking the vertical upward axis as the positive, and establishing the coordinate system as shown by xoy in figure 4.
(2) The Xigeda stratum rock slope is obtained by using a finite element discrete embodiment, a Xigeda stratum rock slope finite element discrete schematic diagram and finite elements are numbered as shown in FIG. 5, and the slope is divided into 232 finite elements 696 common edges. Any finite element i has three nodes, the k node of the ith finite element has horizontal speed
Figure BDA0002560919150000101
And vertical velocity
Figure BDA0002560919150000102
Wherein i ═ 1, …, Ne)，k＝(1,2,3)，NeIs the number of finite elements, N, in the Xigeda formation rock slope e232 percent; the common edges between adjacent finite elements are shown in FIG. 3, each common edge has four nodes, and the h node of the g common edge has horizontal velocity
Figure BDA0002560919150000103
And vertical velocity
Figure BDA0002560919150000104
Wherein g ═ 1, …, Ng)，h＝(1,2,3，4)，NgIs the number of finite element common edges in the Xigeda stratigraphic rock slope, Ng696. The volume weight, the internal friction angle and the cohesion of the limited unit of the siltstone area are taken according to the physical mechanical parameters of the siltstone material, and the volume weight, the internal friction angle and the cohesion of the limited unit of the claystone area are taken according to the physical mechanical parameters of the claystone material;
(3) calculating geometric feature parameters of the finite elements, including: the centroid of the limited unit to the vertical height of the slope toe of the side slope and the area of the limited unit.
The vertical height from the centroid of the finite element to the toe of the slope is calculated according to the following formula:
Figure BDA0002560919150000105
in the formula: i ═ 1, …, Ne)，NeIs the number of finite elements, N, in the Xigeda formation rock slopee＝232；HiIs the vertical height from the centroid of the ith finite element to the toe of the side slope;
Figure BDA0002560919150000106
is the y coordinate of the 1 st node of the ith triangle element,
Figure BDA0002560919150000107
is the y coordinate of the 2 nd node of the ith triangle element,
Figure BDA0002560919150000108
is the y coordinate of the 3 rd node of the ith triangular unit;
the area of the finite element is calculated as:
Figure BDA0002560919150000109
in the formula: i ═ 1, …, Ne)，NeIs in Xigeda stratum lithologic slopeNumber of finite elements, Ne＝232；SiIs the area of the ith finite element;
Figure BDA0002560919150000111
is the x-coordinate of the 1 st node of the ith triangle element,
Figure BDA0002560919150000112
is the x-coordinate of the 2 nd node of the ith triangle element,
Figure BDA0002560919150000113
is the x-coordinate of the 3 rd node of the ith triangle element,
Figure BDA0002560919150000114
is the y coordinate of the 1 st node of the ith triangle element,
Figure BDA0002560919150000115
is the y coordinate of the 2 nd node of the ith triangle element,
Figure BDA0002560919150000116
is the y coordinate of the 3 rd node of the ith triangle element.
And step three, calculating the seismic acceleration of the Xigeda stratum rock slope finite unit according to the principle of a pseudo-dynamic method.
The invention assumes the seismic wave as simple harmonic wave, and adopts the principle of a pseudo-dynamic method to calculate the seismic acceleration of the Xigeda stratum rock slope finite unit, which comprises the following concrete steps:
(1) and calculating the seismic acceleration of the finite element in the horizontal direction according to the principle of the pseudo-dynamic method.
Figure BDA0002560919150000117
In the formula: i ═ 1, …, Ne)，NeIs the number of finite elements, N, in the Xigeda formation rock slopee＝232；j＝(1,…,Nt)，NtIs the number of time steps in the seismic oscillation period, NtGet 20(ii) a T is the earthquake vibration period, and T is 0.2 s; Δ T ═ T/NtThe time length of the time step is shown, and delta t is 0.01 s;
Figure BDA0002560919150000118
the seismic acceleration of the ith finite element of the jth time-step Xigeda stratum rock slope along the horizontal direction; hiIs the vertical height from the centroid of the ith finite element to the toe of the side slope; h is the height of the Xigeda stratum rock slope, and H is 30 m; f. ofsIs the seismic amplification factor of the slope rock mass, fs＝1.1；khIs the seismic acceleration coefficient, k, in the horizontal directionh0.15; pi is the circumferential rate, and pi is 3.14; vsIs the shear wave velocity, V, of the rock mass of the side slopes＝3275m/s；
According to the formula, the seismic acceleration of all finite elements of the rock slope of the Xigeda stratum in the embodiment along the horizontal direction at all time steps is calculated
Figure BDA0002560919150000119
The seismic accelerations in the horizontal direction of the 86 th, 74 th and 12 th finite elements are shown in fig. 6, 8 and 10 respectively.
(2) And calculating the seismic acceleration of the finite element in the vertical direction according to the principle of the pseudo-dynamic method.
Figure BDA00025609191500001110
In the formula: i ═ 1, …, Ne)，NeIs the number of finite elements, N, in the Xigeda formation rock slopee＝232；j＝(1,…,Nt)，NtIs the number of time steps in the seismic oscillation period, NtTaking 20; t is the vibration period of the earthquake, and T is 0.2 s;
Figure BDA0002560919150000121
the seismic acceleration of the ith finite element of the jth time-step Xigeda stratum rock slope along the vertical direction; hiIs the vertical height from the centroid of the ith finite element to the toe of the side slope; h is Xigeda formationThe height of the rock slope is H equal to 30 m; f. ofsIs the seismic amplification factor of the slope rock mass, fs＝1.1；kvIs the seismic acceleration coefficient in the vertical direction, kv0.075; 9.81 is the acceleration of gravity in m/s2(ii) a Pi is the circumferential rate, and pi is 3.14; vpIs the longitudinal wave velocity, V, of the rock mass on the side slopep＝5925m/s。
The seismic acceleration in the vertical direction of all finite elements of the rock slope of the Xigeda stratum of the embodiment at all time steps is calculated according to the formula
Figure BDA0002560919150000122
The seismic accelerations in the vertical direction of the 86 th, 74 th and 12 th finite elements are shown in fig. 7, 9 and 11, respectively.
And step four, establishing a pseudo-dynamic nonlinear mathematical programming model of the Xigeda stratum rock slope stability under the action of the earthquake according to the upper limit method principle.
The method comprises the following specific steps:
(1) and establishing an objective function. According to the upper limit method theory, the safety coefficient of the Xigeda stratum rock slope stability is taken as an objective function, and the minimum value of the safety coefficient is solved. The method comprises the following specific steps:
Minimize:Kj(5)
in the formula: j ═ 1, …, Nt)，NtIs the number of time steps in the seismic oscillation period, NtTaking 20; kjThe safety factor of the rock slope of the jth time step Xigeda stratum under the action of the earthquake is shown; minimize denotes "Minimize".
(2) Establishing a limited unit plastic flow constraint condition:
Figure BDA0002560919150000123
in the formula:
Figure BDA0002560919150000124
is the geometrical compatibility constraint matrix of the ith finite element,
Figure BDA0002560919150000125
a plastic flow constraint matrix that is the ith finite element; i ═ 1, …, Ne)，NeIs the number of finite elements in the Xigeda formation lithologic slope; siIs the area of the ith finite element;
Figure BDA0002560919150000126
6 shape function coefficients of the ith finite element respectively;
Figure BDA0002560919150000127
m-is (1, 2.., 8) the 1 st to 8 th plastic flow matrix coefficients of the finite element, respectively,
Figure BDA0002560919150000131
m-is (1,2,. said., 8) the 9 th to 16 th plastic flow matrix coefficients, C, of the finite element, respectivelym+162sin (2 pi m/8), m (1,2,.., 8), which are the 17 th to 24 th plastic flow matrix coefficients of the finite element, respectively;
Figure BDA0002560919150000132
is the internal friction angle of the finite element, when the finite element is in the siltstone formation
Figure BDA0002560919150000133
Taking the internal friction angle of the siltstone and locating the finite element in the claystone stratum
Figure BDA0002560919150000134
Taking an internal friction angle of claystone;
Figure BDA0002560919150000135
is the velocity vector of the ith finite element,
Figure BDA0002560919150000136
is the plastic multiplier vector of the ith finite element;
Figure BDA0002560919150000137
the horizontal velocity of the kth node of the ith finite element, k being (1,2, 3);
Figure BDA0002560919150000138
is the vertical velocity of the kth node of the ith finite element, k ═ 1,2, 3;
Figure BDA0002560919150000139
an mth finite element plastic multiplier that is an ith finite element;
(3) establishing a plastic flow constraint condition of a common edge of a limited unit:
Figure BDA00025609191500001310
in the formula: in the formula:
Figure BDA00025609191500001311
is a geometric compatibility constraint matrix of the common edge of the g-th finite element,
Figure BDA00025609191500001312
is the plastic flow constraint matrix of the common edge of the g-th finite element; g ═ 1, …, Ng)，NgIs the number of finite element common edges in the Xigeda stratigraphic rock slope, Ng＝696；
Figure BDA00025609191500001313
θgIs the inclination angle of the common side of the g-th finite element, θgTaking the anticlockwise direction as positive;
Figure BDA00025609191500001314
is the velocity vector of the common edge of the g-th finite element,
Figure BDA00025609191500001315
is the plastic multiplier vector of the common edge of the g-th finite element;
Figure BDA00025609191500001316
the horizontal speed of the h node of the common edge of the g finite element is h ═ 1,2,3 and 4;
Figure BDA00025609191500001317
the vertical speed of the h-th node of the common edge of the g-th finite element is h ═ 1,2,3 and 4;
Figure BDA00025609191500001318
is the nth common edge plastic multiplier of the g finite element common edge, n is (1, …, 4);
Figure BDA00025609191500001319
the internal friction angle of the rock mass is 26 degrees, and the internal friction angle of the siltstone is 24 degrees.
(4) Establishing a finite element boundary condition:
Abub＝0 (8)
in the formula: a. thebIs a coordinate transformation matrix of finite elements b on the boundary in the Xigeda stratigraphic rock slope, ubIs the velocity vector of the finite element b on the boundary in the Xigeda stratigraphic rock slope; b ═ 1, …, Nb)，NbIs the number of finite elements in the Xigeda formation rock slope with a velocity equal to 0 at the boundary, Nb＝54。
(5) Establishing a function balance constraint condition of a limited unit:
Figure BDA0002560919150000141
in the formula: i ═ 1, …, Ne)，NeIs the number of finite elements, N, in the Xigeda formation rock slopee＝232；j＝(1,…,Nt)，NtIs the number of time steps in the seismic oscillation period, NtTaking 20; n is a radical ofgIs the number of finite element common edges in the Xigeda stratigraphic rock slope, Ng＝696；KjThe safety factor of the rock slope of the jth time step Xigeda stratum under the action of the earthquake is shown; siIs the ith limitThe area of the cell;
Figure BDA0002560919150000142
the seismic acceleration of the ith finite element of the jth time-step Xigeda stratum rock slope along the horizontal direction;
Figure BDA0002560919150000143
the seismic acceleration of the ith finite element of the jth time-step Xigeda stratum rock slope along the vertical direction;
Figure BDA0002560919150000144
the horizontal velocity of the kth node of the ith finite element, k being (1,2, 3);
Figure BDA0002560919150000145
is the vertical velocity of the kth node of the ith finite element, k ═ 1,2, 3; lgIs the length of the common edge of the g-th finite element, g ═ 1, …, Ng)，NgIs the number of finite element common edges in the Xigeda stratigraphic rock slope;
Figure BDA0002560919150000146
is the mth finite element plastic multiplier of the ith finite element, with m ═ (1, …, 8);
Figure BDA0002560919150000147
is the nth common edge plastic multiplier of the g finite element common edge, n is (1, …, 4); gamma is the volume weight of the finite element, when the finite element is positioned in the siltstone stratum, the volume weight of the siltstone is taken from gamma, and when the finite element is positioned in the claystone stratum, the volume weight of the claystone is taken from gamma;
Figure BDA0002560919150000148
is the internal friction angle of the finite element, when the finite element is in the siltstone formation
Figure BDA0002560919150000149
Taking the internal friction angle of the siltstone and locating the finite element in the claystone stratum
Figure BDA0002560919150000151
Taking an internal friction angle of claystone; c. CsIs the cohesive force of finite elements, c when finite elements are in siltstone formationssTaking out the cohesive force of siltstone, when a finite element is in the claystone formation csTaking the cohesive force of claystone; the volume weight of the siltstone is 2550kN/m3The volume weight of claystone is 2450kN/m3(ii) a The internal friction angle of the siltstone is 26 degrees, and the cohesive force of the siltstone is 120 kPa; the internal friction angle of the claystone is 24 degrees, and the cohesive force of the claystone is 180 kPa.
(6) And establishing a pseudo-dynamic upper limit method nonlinear mathematical programming model of rock slope stability of the Xigeda stratum under the action of the earthquake. Integrating the objective function, the limited unit plastic flow constraint condition, the limited unit common edge plastic flow constraint condition, the limited unit boundary condition and the function balance constraint condition, and obtaining the pseudo dynamic upper limit method nonlinear mathematical programming model of Xigeda stratum rock slope stability under the action of earthquake as follows:
Figure BDA0002560919150000152
in the formula: i ═ 1, …, Ne)，NeIs the number of finite elements, N, in the Xigeda formation rock slopee＝232；g＝(1,…,Ng)，NgIs the number of finite element common edges in the Xigeda stratigraphic rock slope, Ng＝696；j＝(1,…,Nt)，NtIs the number of time steps in the seismic oscillation period, NtTaking 20;
and step five, circularly and iteratively solving the simulated dynamic upper limit method nonlinear mathematical programming model of the Xigeda stratum rock slope stability under the earthquake action by using an inner point algorithm to obtain the safety coefficient of the slope stability under the earthquake action.
The method specifically comprises the following steps: known parameters are changed from j-1 to j-NtThe simulation dynamic upper limit method nonlinear mathematical programming model formula (10) of Xigeda stratum rock slope stability under the action of earthquake is carried out by 20 cycles, and an interior point algorithm is used for solving the problem under the action of earthquakeThe simulated dynamic upper limit method nonlinear mathematical programming model of Xigeda stratum rock slope stability is solved to obtain NtFactor of safety for rock slope stability of Cigeda formation, where j ═ 1, …, Nt)，NtIs the number of time steps in the seismic oscillation period, N t20; the safety factors for solving and obtaining the Xigeda stratum rock slope stability under the action of 20 earthquakes are shown in table 1, and the safety factor K for the Xigeda stratum rock slope stability under the action of the earthquakes is drawnjThe time dependence is shown in fig. 12.
TABLE 1 factor of safety for Xigeda formation rock slope dynamic stability
Figure BDA0002560919150000161
While the present invention has been described in detail with reference to the embodiments shown in the drawings, the present invention is not limited to the embodiments, and various changes can be made without departing from the spirit of the present invention within the knowledge of those skilled in the art.

Claims (8)

1. A simulated dynamic upper limit method for calculating the rock slope stability of Xigeda stratum is characterized by comprising the following steps: taking the Xigeda stratum lithologic slope as a research object, adopting a finite element to disperse the Xigeda stratum lithologic slope, assuming seismic waves as simple harmonic waves, calculating the seismic acceleration of the finite element of the Xigeda stratum lithologic slope by using a pseudo-dynamic method principle, establishing a target function, a plastic flow constraint condition of the finite element under the action of an earthquake, a plastic flow constraint condition of a common edge of the finite element, a boundary condition of the finite element and a functional balance constraint condition according to an upper limit method principle, and further establishing a pseudo-dynamic upper limit method nonlinear mathematical programming model of the Xigeda stratum lithologic slope stability under the action of the earthquake; and solving a nonlinear mathematical programming model of the Xigeda stratum rock slope stability.
2. The upper limit method for simulated dynamics of slope stability calculation of Xigeda formation rock according to claim 1, wherein: the method comprises the following specific steps:
step one, simulating parameters for calculating the stability of the Xigeda formation rock slope;
step two, adopting a finite element discrete Xigeda stratum rock slope and calculating geometric characteristic parameters of the finite element;
step three, calculating the earthquake acceleration of the Xigeda stratum rock slope finite unit according to the principle of a pseudo-dynamic method;
step four, establishing a pseudo-dynamic upper limit method nonlinear mathematical programming model of rock slope stability of the Xigeda stratum under the action of the earthquake according to an upper limit method principle by combining the earthquake acceleration;
and step five, circularly solving the simulated dynamic upper limit method nonlinear mathematical programming model of the rock slope stability of the Xigeda stratum under the earthquake action by using an interior point algorithm to obtain a relation curve of the safety coefficient and the time of the rock slope stability under the earthquake action.
3. The upper limit method for simulated dynamics of slope stability calculation of Xigeda formation rock according to claim 2, wherein: the parameters for calculating the stability of the pseudo-Xigeda formation rock slope comprise: firstly, determining geometric parameters of Xigeda stratum rock slope; determining the distribution conditions of the siltstone stratum and the claystone stratum in the Xigeda stratum; determining physical and mechanical parameters of the Xigeda stratum rock mass material; and fourthly, determining seismic parameters of the Xigeda stratum rock slope.
4. The upper limit method for simulated dynamics of slope stability calculation of Xigeda formation rock according to claim 3, wherein: the geometrical parameters of the Xigeda formation rock slope comprise: the height H of the rock slope, the width of the rock slope and the coordinates of the control points of the geometrical shape of the slope; the distribution of the formation includes: the thickness of each layer of the siltstone and claystone stratum and the inclination angle of the interface of the siltstone and claystone; the physical mechanical parameters include: the unit weight of the siltstone and the claystone, the internal friction angle and the cohesion of the siltstone, and the internal friction angle and the cohesion of the claystone; the seismic parameters include: seismic vibrationsPeriod T, seismic amplification factor fsShear wave velocity V of slope rock masssLongitudinal wave velocity V of slope rock masspHorizontal seismic acceleration coefficient khVertical seismic acceleration coefficient kv。
5. The upper limit method for simulated dynamics of slope stability calculation of Xigeda formation rock according to claim 1 or 2, wherein: the method for dispersing Xigeda stratum rock slope by adopting the finite element specifically comprises the following steps:
(1) establishing a coordinate system of the Xigeda stratum rock slope, taking a slope toe of the slope as an origin of coordinates, taking a horizontal axis as an x-axis of the coordinate system, taking a horizontal right axis as a positive axis of the x-axis, taking a vertical axis as a y-axis of the coordinate system, and taking a vertical upward axis as a positive axis of the y-axis;
(2) using the finite element discrete Xigeda formation rock slope, any finite element i has three nodes, and the kth node of the ith finite element has horizontal velocity
Figure FDA0002560919140000021
And vertical velocity
Figure FDA0002560919140000022
Wherein i ═ 1, …, Ne)，k＝(1,2,3)，NeIs the number of finite elements in the Xigeda formation lithologic slope; common edge between adjacent finite elements: each common edge has four nodes, the h node of the g common edge has horizontal speed
Figure FDA0002560919140000023
And vertical velocity
Figure FDA0002560919140000024
Wherein g ═ 1, …, Ng)，h＝(1,2,3，4)，NgIs the number of finite element common edges in the Xigeda stratigraphic rock slope; the volume weight, the internal friction angle and the cohesion of the finite unit of the siltstone area are valued according to the physical and mechanical parameters of the siltstone material, and the siltstone material is stickyThe volume weight, the internal friction angle and the cohesion of the limited unit of the soil-rock area are valued according to the physical and mechanical parameters of the claystone material;
(3) calculating geometric feature parameters of the finite elements, including: the centroid of the finite element to the vertical height of the slope toe of the slope, the area of the finite element:
the vertical height from the centroid of the finite element to the toe of the slope is calculated according to the following formula:
Figure FDA0002560919140000025
in the formula: hiIs the vertical height from the centroid of the ith finite element to the toe of the side slope;
Figure FDA0002560919140000026
is the y coordinate of the 1 st node of the ith triangle element,
Figure FDA0002560919140000027
is the y coordinate of the 2 nd node of the ith triangle element,
Figure FDA0002560919140000028
is the y coordinate of the 3 rd node of the ith triangular unit;
the area of the finite element is calculated as:
Figure FDA0002560919140000029
in the formula: siIs the area of the ith finite element;
Figure FDA00025609191400000210
is the x-coordinate of the 1 st node of the ith triangle element,
Figure FDA00025609191400000211
is the x-coordinate of the 2 nd node of the ith triangle element,
Figure FDA00025609191400000212
is the x coordinate of the 3 rd node of the ith triangle element.
6. The upper limit method for simulated dynamics of slope stability calculation of Xigeda formation rock according to claim 1 or 2, wherein: the method for calculating the seismic acceleration of the Xigeda stratum rock slope finite unit according to the principle of the pseudo-dynamic method specifically comprises the following steps:
(1) calculating the seismic acceleration of the finite element in the horizontal direction according to the principle of a pseudo-dynamic method:
Figure FDA0002560919140000031
in the formula:
Figure FDA0002560919140000032
the seismic acceleration of the ith finite element of the jth time-step Xigeda stratum rock slope along the horizontal direction; i ═ 1,. Ne)，NeIs the number of finite elements in the Xigeda formation lithologic slope; j ═ 1, …, Nt)，NtIs the number of time steps in the seismic oscillation period; t is the earthquake vibration period; k is a radical ofhIs the seismic acceleration coefficient in the horizontal direction; hiIs the vertical height from the centroid of the ith finite element to the toe of the side slope; h is the height of the Xigeda formation rock slope; f. ofsThe seismic amplification factor of the slope rock mass; pi is the circumference ratio; vsIs the shear wave velocity of the slope rock mass;
(2) calculating the earthquake acceleration of the limited unit in the vertical direction according to the principle of a pseudo-dynamic method:
Figure FDA0002560919140000033
in the formula:
Figure FDA0002560919140000034
is the jth time frameThe seismic acceleration of the ith finite unit of the formation rock slope along the vertical direction is reached; k is a radical ofvIs the seismic acceleration coefficient in the vertical direction; vpIs the longitudinal wave velocity of the slope rock mass.
7. The upper limit method for simulated dynamics of slope stability calculation of Xigeda formation rock according to claim 1 or 2, wherein: the establishment of the pseudo-dynamic upper limit method nonlinear mathematical programming model of the Xigeda stratum rock slope stability under the action of the earthquake specifically comprises the following steps:
(1) establishing an objective function:
taking the safety coefficient of the Xigeda stratum rock slope stability as an objective function, and solving the minimum value of the safety coefficient, wherein the minimum value is as follows:
Minimize:Kj
in the formula: j ═ 1, …, Nt)，NtIs the number of time steps in the seismic oscillation period; kjThe safety factor of the rock slope of the jth time step Xigeda stratum under the action of the earthquake is shown; minimize denotes "Minimize";
(2) establishing a limited unit plastic flow constraint condition:
Figure FDA0002560919140000035
in the formula:
Figure FDA0002560919140000041
is the geometrical compatibility constraint matrix of the ith finite element,
Figure FDA0002560919140000042
a plastic flow constraint matrix that is the ith finite element; i ═ 1, …, Ne)，NeIs the number of finite elements in the Xigeda formation lithologic slope; siIs the area of the ith finite element;
Figure FDA0002560919140000043
6 shape functions of i-th finite elementA number coefficient;
Figure FDA0002560919140000044
m-is (1, 2.., 8) the 1 st to 8 th plastic flow matrix coefficients of the finite element, respectively,
Figure FDA0002560919140000045
m-is (1,2,. said., 8) the 9 th to 16 th plastic flow matrix coefficients, C, of the finite element, respectivelym+162sin (2 pi m/8), m (1,2, …,8), which are the 17 th to 24 th plastic flow matrix coefficients of the finite element, respectively;
Figure FDA0002560919140000046
is the internal friction angle: in siltstone formation
Figure FDA0002560919140000047
Taking the internal friction angle of the siltstone when the siltstone is positioned in the claystone stratum
Figure FDA0002560919140000048
Taking an internal friction angle of claystone;
Figure FDA0002560919140000049
is the velocity vector of the ith finite element,
Figure FDA00025609191400000410
is the plastic multiplier vector of the ith finite element;
Figure FDA00025609191400000411
the horizontal velocity of the kth node of the ith finite element, k being (1,2, 3);
Figure FDA00025609191400000412
is the vertical velocity of the kth node of the ith finite element, k ═ 1,2, 3;
Figure FDA00025609191400000413
an mth finite element plastic multiplier that is an ith finite element;
(3) establishing a plastic flow constraint condition of a common edge of a limited unit:
Figure FDA00025609191400000414
in the formula:
Figure FDA00025609191400000415
is a geometric compatibility constraint matrix of the common edge of the g-th finite element,
Figure FDA00025609191400000416
is the plastic flow constraint matrix of the common edge of the g-th finite element; g ═ 1, …, Ng)，NgIs the number of finite element common edges in the Xigeda stratigraphic rock slope;
Figure FDA0002560919140000051
θgis the inclination angle of the common side of the g-th finite element, θgTaking the anticlockwise direction as positive;
Figure FDA0002560919140000052
is the velocity vector of the common edge of the g-th finite element,
Figure FDA0002560919140000053
is the plastic multiplier vector of the common edge of the g-th finite element;
Figure FDA0002560919140000054
the horizontal speed of the h node of the common edge of the g finite element is h ═ 1,2,3 and 4;
Figure FDA0002560919140000055
is the h-th node of the g-th finite element common edgeVertical velocity of the point, h ═ (1,2,3, 4);
Figure FDA0002560919140000056
is the nth common edge plastic multiplier of the g finite element common edge, n is (1, …, 4);
(4) establishing a finite element boundary condition:
Abub＝0
in the formula: a. thebIs a coordinate transformation matrix of a finite element b on the boundary in the Xigeda stratigraphic rock slope; u. ofbIs the velocity vector of the finite element b on the boundary in the Xigeda stratigraphic rock slope; b ═ 1, …, Nb)，NbIs the number of finite elements in the Xigeda formation rock slope where the velocity at the boundary equals 0;
(5) establishing a function balance constraint condition of a limited unit:
Figure FDA0002560919140000057
in the formula: γ is the volume weight: when the reservoir is positioned in a siltstone stratum, the volume weight of the siltstone is taken as gamma, and when the reservoir is positioned in a claystone stratum, the volume weight of the claystone is taken as gamma;
Figure FDA0002560919140000058
the seismic acceleration of the ith finite element of the jth time-step Xigeda stratum rock slope along the horizontal direction;
Figure FDA0002560919140000059
the seismic acceleration of the ith finite element of the jth time-step Xigeda stratum rock slope along the vertical direction; c. CsIs the cohesion: in siltstone formation csTaking the cohesive force of siltstone and locating in claystone stratum csTaking the cohesive force of claystone; lgIs the length of the common edge of the g-th finite element, g ═ 1, …, Ng)，NgIs the number of finite element common edges in the Xigeda stratigraphic rock slope;
(6) establishing a pseudo-dynamic upper limit method nonlinear mathematical programming model of rock slope stability of Xigeda stratum under the action of earthquake:
integrating the objective function, the limited unit plastic flow constraint condition, the limited unit common edge plastic flow constraint condition, the limited unit boundary condition, the function balance constraint condition and the earthquake acceleration equation to obtain the pseudo dynamic upper limit method nonlinear mathematical programming model of the Xigeda stratum rock slope stability under the earthquake action as follows:
Figure FDA0002560919140000061
in the formula: t is the earthquake vibration period; k is a radical ofhIs the seismic acceleration coefficient in the horizontal direction; hiIs the vertical height from the centroid of the ith finite element to the toe of the side slope; h is the height of the Xigeda formation rock slope; f. ofsThe seismic amplification factor of the slope rock mass; pi is the circumference ratio; vsIs the shear wave velocity of the slope rock mass; k is a radical ofvIs the seismic acceleration coefficient in the vertical direction; vpIs the longitudinal wave velocity of the slope rock mass.
8. The upper limit method for simulated dynamics of slope stability calculation of Xigeda formation rock according to claim 1 or 2, wherein: the simulated dynamic upper limit method nonlinear mathematical programming model for solving the rock slope stability of the Xigeda stratum under the action of the earthquake specifically comprises the following steps: known parameters are changed from j-1 to j-NtCircularly bringing the simulated dynamic upper limit method nonlinear mathematical programming model formula of Xigeda stratum rock slope stability under the action of earthquake, solving the simulated dynamic upper limit method nonlinear mathematical programming model of Xigeda stratum rock slope stability under the action of earthquake by using an 'interior point algorithm', and solving to obtain NtSafety coefficient K of rock slope stability of individual Xigeda stratumj(ii) a Then, taking the safety factor as a vertical axis and time as a horizontal axis, and drawing the safety factor K of the Xigeda stratum rock slope stability under the action of earthquakejAnd time jT/NtThe relationship curve of (1); wherein j is (1, …, N)t)，NtIs the number of time steps in the seismic oscillation period; t isIs the seismic oscillation period.
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