CN114925603B - Non-circular slope sliding surface searching method based on improved wolf algorithm - Google Patents
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Abstract
The invention discloses a non-circular slope sliding surface searching method based on an improved wolf algorithm, which comprises the following steps: establishing a numerical model and extracting basic information of the numerical model; classifying the unit cells according to the unit material numbers, and drawing the slope images in a layered manner; setting a region of the slope surface in a certain range of the slope top and the slope toe in the slope image as a possible movable range of the head wolf and the parent wolf; the head wolves, the mother wolves and the exploring wolves walk in a fixed step length to form a wolf group combination together, and stress information of each point on the path is determined; and calculating the sliding force and the anti-sliding force between two adjacent wolves according to the stress information, defining the fitness of the wolves as the reciprocal of the safety coefficient, and taking the spline curve with the largest fitness value as the optimized spline curve. The non-circular arc slope sliding surface searching method based on the improved wolf algorithm provided by the invention can make up for the defect that the circular arc sliding surface assumption is inconsistent with the actual situation, quickly and accurately determine the position of the slope sliding surface and calculate the safety coefficient.
Description
Technical Field
The invention relates to a non-circular arc slope sliding surface searching method based on an improved wolf's group algorithm, belonging to the technical field of geotechnical engineering slopes,
background
The side slope plays an important role in human engineering and economic activities, not only can cause casualties and property loss, but also can possibly induce other disasters directly or indirectly. Deformation and damage of a side slope are one of important subjects of research of geotechnical mechanics by experts and scholars, and are engineering problems which are necessary to be faced in infrastructure construction of civil engineering, water conservancy, mines, traffic and the like, determination of the most dangerous sliding surface and calculation of the minimum safety coefficient are key problems of side slope stability analysis, the existing side slope sliding surface searching method mostly assumes that the sliding surface is a circular arc sliding surface, and the calculating is performed by adopting a stripe method and the like. By assuming the circle center position and the radius, the anti-slip force and the sliding force on the smooth sliding surface are continuously tried to be calculated, and the minimum stability coefficient is found out. The arc-shaped assumption is only for convenience in calculation, and does not represent that the sliding surface in the actual engineering is arc-shaped, and the arc-shaped sliding surface in the actual engineering is not consistent with the actual sliding surface, so that the arc-shaped sliding surface cannot be guaranteed to be the most dangerous, and the problem to be solved in the current urgent need is how to quickly and accurately determine the position of the slope sliding surface and calculate the safety coefficient.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a non-circular arc slope sliding surface searching method based on an improved wolf's cluster algorithm, which can make up for the defect that the circular arc sliding surface assumption is inconsistent with the actual situation, rapidly and accurately determine the position of the slope sliding surface and calculate the safety coefficient.
In order to solve the technical problems, the invention adopts the following technical scheme:
a non-circular slope sliding surface searching method based on an improved wolf's swarm algorithm comprises the following steps:
establishing a numerical model, extracting basic information of the numerical model, including the number n of nodes p Number of cells n e Cell material number, node number in the cell, each grid node coordinate, stress component size at the node, and shear strength parameters for each material;
classifying the cells according to the serial numbers of the cell materials, displaying the cells of different types of materials with different colors, and layering and drawing the slope image;
setting a region of the slope surface in a certain range of the slope top and the slope toe in the slope image as a possible movable range of the head wolves and the parent wolves, namely a sliding-out and sliding-in point of the slope, and taking the possible movable range as the initial position of the head wolves and the parent wolves of the wolf swarm algorithm;
the method comprises the steps that a head wolf, a parent wolf and a exploring wolf walk in a fixed step length to form a wolf group combination together, the head wolf and the parent wolf are equally divided according to the abscissa of the head wolf, the longitudinal line of each equally divided point is set to be the active position of the exploring wolf, a spline curve equation is determined by the walk in the fixed step length, the head wolf executes calling behaviors, the coordinates of each point on a path are determined, then the slashing wolf executes enclosing behaviors, and stress information of each point on the path is determined;
calculating sliding force and anti-sliding force between two adjacent wolves according to stress information, wherein the safety coefficient is the sum of the sliding force and the anti-sliding force, defining the fitness of the wolves as the reciprocal of the safety coefficient, eliminating unsuitable wolves according to the fitness, and finally taking a spline curve with the maximum fitness value as an optimized spline curve.
Numerical model extractionThe specific process of the type basic information is as follows: the numerical model is composed of a series of polygonal standard units, each polygonal standard unit is composed of nodes and edges, the node numbers and the unit numbers in each polygonal unit start from 1, the numerical model is analyzed, and the number n of the unit cells of the numerical model is extracted e Each of the unit materials is numbered, for n e A plurality of unit cells for respectively extracting the number n of nodes p Three-component node coordinates (x, y, z) and stress component magnitude at node (σ) xx ，σ yy ，τ xy ) Cycle n e And (5) obtaining the coordinates and stress values of each node and the cell material numbers after the circulation is completed.
The polygon standard units comprise triangle units or quadrilateral units, each polygon standard unit is composed of 4 nodes, the quadrilateral units are written into (1, 2,3, 4), and the triangle units are written into (1, 2, 3).
The specific steps of slope image layering drawing are as follows: traversing all the cells, judging the types of the cell materials, classifying the cells according to the material types, finding out the coordinates of points corresponding to the node numbers of the cells in each material, connecting the coordinates in the order of 1-2, 2-3, 3-4, 4-1 or 1-2, 2-3, 3-3 and 3-1 to form a quadrangle or triangle, and drawing the cells of different materials with different colors in turn to obtain a two-dimensional slope image.
The initial position of the first wolf female wolf is determined by the following specific steps: given the sliding-out point abscissa range (X tl1 ，X tl2 ) And a sliding-in point abscissa range (X ml1 ，X ml2 ) Let x=x be the abscissa of the given initial slide-out point tl1 The initial slide-in point has an abscissa of x=x tl2 Traversing all nodes, calculating each node to a straight line x=x tl1 Distance d of (2) 1 ＝|x-X tl1 I, to straight line x=x ml1 Distance d of (2) 2 ＝|x-X ml1 The coordinates of K points with the smallest distance are respectively screened out, then the maximum value of the ordinate is selected from the K coordinates, the ordinate of the point corresponding to the moment is the ordinate of the sliding-out point, and the initial positions of the first wolf and the female wolf are the momentIs determined to be (X) tl1 ，Y tl1 ) And (X) ml1 ，Y ml1 ). Trisecting the abscissa of the first wolf and the female wolf, respectively denoted as X t1 ＝X tl1 +(X ml1 -X tl1 )/3，X t2 ＝X tl1 +2*(X ml1 -X tl1 ) 3, the initial exploring wolves are respectively a head wolf female wolf connecting line and x=x t1 X=x t2 The intersection point, i.e. the initial wolf coordinate is (X t1 ， (X t2 ， The initial probe wolf walks downstream by p and q steps with fixed steps x _ d3 and x _ d4 respectively, wherein x_d3= (y) max1 -y min1 )/p、x_d4＝(y max2 -y min2 ) Q), where y max1 And y max2 The upper limit of the walking area of each detected wolf, namely the initial wolf detection position, y min1 And y min2 The lower limit of each wolf-detecting wandering area, namely the lowest limit of the side slope, is respectively used as four control nodes of a cubic spline curve to calculate the expression of the spline curve.
The spline curve expression specifically solves the following steps:
the intervals of interest [ a, b ]]Divided into n intervals [ (x) 0 ，x 1 )，(x 1 ，x 2 )……(x n-1 ，x n )]N+1 points in total, and the end points are x respectively 0 ＝a，x n =b, cubic spline curve definition:
(1) Between each segmented cell [ x ] i ，x i+1 ]On, S (x) =s i (x) Are all a cubic equation, then at [ x ] i ，x i+1 ]Three of the positionsThe expansion of the secondary spline function is: s is S i (x)＝d i (x-x i ) 3 +c i (x-x i ) 2 +b i (x-x i )+a i ，x i ≤x≤x i+1 (1)，
(2) S (x), S' (x) are all continuous over [ a, b ],
(3) S (x) satisfies the difference condition S (x) i )＝y i ，i＝0，1，2……n，
And (3) making: y is i ＝f(x i )，h i ＝x i+1 -x i ，S i '(x i )＝m i I=0, 1,2 … … n is defined according to definition (1) (2) (3), at [ x i ，x i+1 ]The intervals are as follows:
(a) Interpolation continuity: s is S i (x i )＝y i 、S i (x i+1 )＝y i+1 Wherein i=0, 1,2, … …, n-1 is defined by S i (x i )＝y i Obtainable a i ＝y i
From S i (x i+1 )＝y i+1 Obtainable d i h i 3 +c i h i 2 +b i h i +a i ＝y i+1
(b) Differential continuity: s is S i ′(x i+1 )＝S i+1 ′(x i+1 )、S i ″(x i+1 )＝S i+1 ″(x i+1 ) Where i=0, 1,2, … …, n-1
From S i ′(x i+1 )＝S i+1 ′(x i+1 ) Namely:
S i ′(x i+1 )＝3d i (x i+1 -x i ) 2 +2c i (x i+1 -x i )+b i ＝3d i h i 2 +2c i h i +b i
S i+1 ′(x i+1 )＝3d i+1 (x i+1 -x i+1 ) 2 +2c i+1 (x i+1 -x i+1 )+b i+1 ＝b i+1
obtaining b i +3d i h i 2 +2c i h i -b i+1 ＝0
From S i ″(x i+1 )＝S i+1 ″(x i+1 ) Obtain 2c i +6d i h i -2c i+1 ＝0
(c) Differential formula of spline curve: s is S i (x)＝d i (x-x i ) 3 +c i (x-x i ) 2 +b i (x-x i )+a i
S i ′(x)＝3d i (x-x i ) 2 +2c i (x-x i )+b i
S i ″(x)＝6d i (x-x i )+2c i (x-x i )
Let m be i ＝S i ″(x i )＝2c i+1 Then 2c i +6d i h i -2c i+1 =0 can be written as m i +6d i h i -m i+1 ＝0，
Can be pushed outWill d i 、c i Substitution into y i +b i h i +2c i h i +d i h i 3 ＝y i+1 Is available in the form of
Will d i 、c i 、b i Substitution into
b i +3d i h i 2 +2c i h i -b i+1 ＝0
The method can obtain:
under the free boundary, i.e. S "=0, where m 0 ＝0，m n ＝0
According to the above formula, a matrix of the following formula (3) can be constructed:
in the formula (3), f i ＝6(p i+1 -p i ),i＝1,2,3……n-1
Under the fixed boundary, since differential values of the end-to-end points are specified, assuming A, B respectively, then S 0 ′(x 0 ) =a can be obtained:from S n-1 ′(x n ) =b can be obtained:
in the non-kinking boundary condition: s is S 0 ″′(x 0 )＝S 1 ″′(x 1 )、S n-2 ″′(x n-2 )＝S n-1 ″′(x n-1 )
Due to S i ″′(x)＝6d i Whereind 0 ＝d 1 ,d n-2 ＝d n-1 I.e. h 1 (m 1 -m 0 )＝h 0 (m 2 -m 1 )，h n-1 (m n-1 -m n-2 )＝h n-2 (m n -m n-1 )
A sufficient requirement for a unique solution from a non-homogeneous system of z unknowns ux=q is that R (U) =r (Q) =z, knowing that the matrix equation has a unique solution in all three cases,
the three matrix equations can be solved to obtain m by adopting a Gaussian column principal component elimination method i
Finally, substitution into equation (1) yields:
after each coefficient is calculated, the spline curve equation can be obtained, the first wolf moves m steps with a fixed step length x_d1, the second wolf moves t steps with a fixed step length x_d2, m groups of wolves with t groups of p groups of wolves are generated, each group of different combinations of the first wolf, the second wolf and the second wolf can be used for calculating a different spline curve result, and then curves which do not accord with the characteristics of the sliding surface of the side slope are screened according to the characteristics of the sliding surface of the side slope.
Before the stress information is determined, the odor concentration of the wolf on the path needs to be determined, and the specific determination mode is as follows: the machine learning method is used for taking the abscissa, the ordinate and the stress value at each cell node as a data set, taking the soil layer type as a label, classifying soil layers, taking the stress value at each point in each soil layer as a characteristic of the point, taking one part of the data set as a training set, learning the data in the training set according to the distribution rule of the stress value in the horizontal direction and the vertical direction in each soil layer, verifying the rule in the rest of the data set, comparing the prediction result with the actual result of the training data, and continuously adjusting the prediction model until the prediction result of the model reaches an expected accuracy.
The specific calculation process of the fitness D comprises the following steps:
if the sliding direction is rightward and counterclockwise, the shear strength τ on one section is equal to the positive sliding force f And the tangential stress τ is calculated as follows:
τ α ＝0.5(σ yy -σ xx )sin2α+τ xy cos2α (5)
σ α ＝0.5(σ xx +σ yy )-0.5(σ xx -σ yy )cos2α-τ xy sin2α (6)
average sliding force of the i th segment:
average slip resistance of section i:
wherein: sigma (sigma) xx ，σ yy ，τ xy Respectively, the positive stress of the unit centroid along the x direction, the positive stress of the unit centroid along the y direction and the tangential stress, alpha is the included angle between the inclined plane and the horizontal plane, and sigma α Is the normal stress of the inclined plane, τ α Is the tangential stress of the inclined section,and c is the internal friction angle and cohesion of the material, respectively; calculating the sliding force and the anti-sliding force on each section, and then calculating the safety coefficient on the corresponding sliding surface, wherein the safety coefficient is defined as:
wolf population fitness D is defined as:
in the formula (10): a and B are the starting point and the end point of the slope, w is the number of sections passed by the sliding surface, τ is the shear stress along the sliding direction of the sliding surface, τ f For shear strength, dL is the length increment, τ, of each segment along the sliding surface i From the i-1 st node to the i-th node the shear stress on the path of the individual nodes,for shear strength on the path from section i-1 to section i Δd i Is the length of the path from stage i-1 to stage i.
The invention has the beneficial effects that: according to the non-circular arc slope sliding surface searching method based on the improved wolf's algorithm, on the basis of the stress field obtained by calculation of the existing numerical model, information such as unit node coordinates and stress is obtained, the shape of the slope sliding surface is optimized by the improved wolf's algorithm, the sum of the anti-slip force and the sliding force on the spline curve approximation sliding surface generated by each iteration is calculated, the safety coefficient is used as an adaptive value to obtain a global optimal solution, so that the most dangerous non-circular sliding surface and the minimum safety coefficient of the slope are determined, the defect that the assumption of the circular arc sliding surface is inconsistent with the actual can be overcome, the position of the slope sliding surface is rapidly and accurately determined, and the safety coefficient is calculated.
Drawings
FIG. 1 is a diagram of a quadrilateral cell provided in the present invention;
FIG. 2 is a triangular cell diagram provided in the present invention;
FIG. 3 is a schematic representation of a spline provided in the present invention;
FIG. 4 is a force diagram and cell stress diagram provided in the present invention;
FIG. 5 is a side slope image of an embodiment of the present invention;
FIG. 6 is a sliding surface view of the natural working condition in the embodiment of the invention.
Detailed Description
The present invention will be further described with reference to the accompanying drawings, wherein the following examples are provided for more clearly illustrating the technical aspects of the present invention, and are not to be construed as limiting the scope of the present invention,
the invention discloses a non-circular arc side slope sliding surface searching method based on an improved wolf's swarm algorithm, which aims to solve the problems that most of the existing side slope sliding surface searching methods assume circular arc sliding surfaces, the obtained sliding surfaces are circular arc, and the actual side slope sliding surfaces are non-circular, and specifically comprises the following steps:
step one, a numerical model is established, a numerical model of a typical geological slope is shown in fig. 5, and basic information of the numerical model is extracted, wherein the basic information comprises the number n of nodes p Number of cells n e Cell material number, node number in the cell, node coordinates of each grid, stress component size at the node, and shear strength parameters of each material. The specific process for extracting the basic information of the numerical model is as follows: the numerical model is composed of a series of polygonal standard units, each polygonal standard unit is composed of nodes and edges, the node numbers and the unit numbers in each polygonal unit start from 1, the numerical model is analyzed, and the number n of the unit cells of the numerical model is extracted e Each unit material number, for n e A plurality of unit cells for respectively extracting the number n of nodes p Three-component node coordinates (x, y, z) and stress component magnitude at node (σ) xx ，σ yy ，τ xy ) Cycle n e And (5) obtaining the coordinates and stress values of each node and the cell material numbers after the circulation is completed. The adhesive force and the internal friction angle of the slope material are sequentially set from small to large: phi=0.045 gpa, c=22°; phi=0.05 gpa, c=26.5 °; phi=0.08 gpa, c=33°;c＝15°；/>c＝36°；/>c＝45°；/>c＝26.5°；c＝22°；/>c＝22°；/>c＝15°；c＝36°。
the polygon standard units comprise triangle units or quadrilateral units, each polygon standard unit is composed of 4 nodes, the quadrilateral units are written into (1, 2,3, 4) as shown in fig. 1, and the triangle units are written into (1, 2, 3) as shown in fig. 2.
Classifying the cells according to the serial numbers of the cell materials, dividing the data into 9 types, displaying the cells of different types of materials with different colors, and layering and drawing the slope image. The specific steps of slope image layering drawing are as follows: traversing all the cells, judging the types of the cell materials, classifying the cells according to the material types, finding out the coordinates of points corresponding to the node numbers of the cells in each material, connecting the coordinates in the order of 1-2, 2-3, 3-4, 4-1 or 1-2, 2-3, 3-3 and 3-1 to form a quadrangle or triangle, and drawing the cells of different materials with different colors in turn to obtain a two-dimensional slope image.
And thirdly, setting the area of the slope surface in a certain range of the slope top and the slope toe in the slope image as the possible movable range of the head wolf and the parent wolf, namely the sliding-out sliding-in point of the slope, and taking the possible movable range as the initial position of the head wolf and the parent wolf of the wolf swarm algorithm. The initial position of the first wolf female wolf is determined by the following specific steps: given the sliding-out point abscissa range (X tl1 ，X tl2 ) And a sliding-in point abscissa range (X ml1 ，X ml2 ) In this embodiment, the slide-in point slides in the abscissa ranges 482-512m and 703-705m, respectively. Let x=x be the abscissa of the given initial slide-out point tl1 The initial slide-in point has an abscissa of x=x tl2 Traversing all nodes, calculating each node to a straight line x=x tl1 Distance d of (2) 1 ＝|x-X tl1 I, to straight line x=x ml1 Distance d of (2) 2 ＝|x-X ml1 And (3) respectively screening out coordinates of K points with minimum distances, for example: k=np/100-np/50, then selecting the maximum value of the ordinate among the K coordinates, the ordinate of the corresponding point at this time is the ordinate of the slide-out slide-in point, at this time, the initial head wolf and parent wolf positions are determined and set as (X tl1 ，Y tl1 ) And (X) ml1 ，Y ml1 )。
Fourthly, the head wolf, the mother wolf and the exploring wolf walk in a fixed step length to form a wolf group combination, the head wolf and the mother wolf are equally divided according to the abscissa of the head wolf, the longitudinal line of each equally divided point is set to be the active position of the exploring wolf, a spline curve equation is determined by the walking in the fixed step length, the head wolf executes calling behaviors, the coordinates of each point on a path are determined, then the slapping wolf executes enclosing behaviors, and stress information of each point on the path is determined. Trisecting the abscissa of the first wolf and the female wolf as the active positions of the exploring wolves, respectively marked as X t1 ＝X tl1 +(X ml1 -X tl1 )/3，X t2 ＝X tl1 +2*(X ml1 -X tl1 ) 3, the initial exploring wolves are respectively a head wolf female wolf connecting line and x=x t1 X=x t2 The intersection point, i.e. the initial wolf coordinate is (X t1 ，(X t2 ，/>The initial probe wolf is stepped downstream by p and q steps, respectively, with fixed steps x_d3 and x_d4, e.g., x_d3= (y) max1 -y min1 )/30、x_d4＝(y max2 -y min2 ) /20), wherein x_d3= (y) max1 -y min1 )/p、x_d4＝(y max2 -y min2 ) Q), where y max1 And y max2 The upper limit of the walking area of each detected wolf, namely the initial wolf detection position, y min1 And y min2 The lower limit of each wolf-detecting wander area, namely the lowest limit of the side slope, is respectively shown in figure 3, and the wolf-detecting, the head wolf and the parent wolf at the moment are used as cubic spline curvesTo find the expression of the spline curve.
Fifthly, calculating the sliding force and the anti-sliding force between two adjacent wolves according to the stress information, the safety coefficient is the sum of sliding force and anti-sliding force, and the fitness of the wolf group is defined as the reciprocal of the safety coefficient. The spline curve expression specifically solves the following steps: the intervals of interest [ a, b ]]Divided into n intervals [ (x) 0 ，x 1 )，(x 1 ，x 2 )……(x n-1 ，x n )]N+1 points in total, and the end points are x respectively 0 ＝a，x n =b, cubic spline curve definition:
(1) Between each segmented cell [ x ] i ，x i+1 ]On, S (x) =s i (x) Are all a cubic equation, then at [ x ] i ，x i+1 ]The expansion of the cubic spline function at this point is: s is S i (x)＝d i (x-x i ) 3 +c i (x-x i ) 2 +b i (x-x i )+a i ，x i ≤x≤x i+1 (1)，
(2) S (x), S' (x) are all continuous over [ a, b ],
(3) S (x) satisfies the difference condition S (x) i )＝y i ，i＝0，1，2……n，
And (3) making: y is i ＝f(x i )，h i ＝x i+1 -x i ，S i '(x i )＝m i I=0, 1,2 … … n is defined according to definition (1) (2) (3), at [ x i ，x i+1 ]The intervals are as follows:
(a) Interpolation continuity: s is S i (x i )＝y i 、S i (x i+1 )＝y i+1 Where i=0, 1,2, … …, n-1
From the following components S is S i (x i )＝y i Obtainable a i ＝y i
From S i (x i+1 )＝y i+1 Obtainable d i h i 3 +c i h i 2 +b i h i +a i ＝y i+1
(b) Differential continuity: s is S i ′(x i+1 )＝S i+1 ′(x i+1 )、S i ″(x i+1 )＝S i+1 ″(x i+1 ) Where i=0, 1,2, … …, n-1
From S i ′(x i+1 )＝S i+1 ′(x i+1 ) Namely:
S i ′(x i+1 )＝3d i (x i+1 -x i ) 2 +2c i (x i+1 -x i )+b i ＝3d i h i 2 +2c i h i +b i
S i+1 ′(x i+1 )＝3d i+1 (x i+1 -x i+1 ) 2 +2c i+1 (x i+1 -x i+1 )+b i+1 ＝b i+1
obtaining b i +3d i h i 2 +2c i h i -b i+1 ＝0
From S i ″(x i+1 )＝S i+1 ″(x i+1 ) Obtain 2c i +6d i h i -2c i+1 ＝0
(c) Differential formula of spline curve: s is S i (x)＝d i (x-x i ) 3 +c i (x-x i ) 2 +b i (x-x i )+a i
S i ′(x)＝3d i (x-x i ) 2 +2c i (x-x i )+b i
S i ″(x)＝6d i (x-x i )+2c i (x-x i )
Let m be i ＝S i ″(x i )＝2c i+1 Then 2c i +6d i h i -2c i+1 =0 can be written as m i +6d i h i -m i+1 =0, can be pushed outWill d i 、c i Substitution into y i +b i h i +2c i h i +d i h i 3 ＝y i+1 Available->Will d i 、c i 、b i Substitution b i +3d i h i 2 +2c i h i -b i+1 ＝0
The method can obtain:under the free boundary, i.e. S "=0, where m 0 ＝0，m n ＝0
According to the above formula, a matrix of the following formula (3) can be constructed:
in the formula (3), f i ＝6(p i+1 -p i ),i＝1,2,3……n-1
Under the fixed boundary, since differential values of the end-to-end points are specified, assuming A, B respectively, then S 0 ′(x 0 ) =a can be obtained:from S n-1 ′(x n ) =b can be obtained:
in the non-kinking boundary condition: s is S 0 ″′(x 0 )＝S 1 ″′(x 1 )、S n-2 ″′(x n-2 )＝S n-1 ″′(x n-1 )
Due to S i ″′(x)＝6d i Whereind 0 ＝d 1 ,d n-2 ＝d n-1 I.e. h 1 (m 1 -m 0 )＝h 0 (m 2 -m 1 )，h n-1 (m n-1 -m n-2 )＝h n-2 (m n -m n-1 )
A sufficient requirement for a unique solution from a non-homogeneous system of z unknowns ux=q is that R (U) =r (Q) =z, knowing that the matrix equation has a unique solution in all three cases,
the three matrix equations can be solved to obtain m by adopting a Gaussian column principal component elimination method i
Finally, substitution into equation (1) yields:
after each coefficient is solved, the spline curve equation can be obtained, the first wolf moves m steps with a fixed step length x_d1, the second wolf moves t steps with a fixed step length x_d2, and m, t, p and q groups of wolves are generated. In this embodiment, the sliding-out point and the sliding-in point are respectively walked by steps of 5m and 1m to generate 18 groups of head wolves and mother wolves, three equal division points of the abscissa of the head wolves and the mother wolves are selected as the active positions of the detection wolves, the intersection point of the connecting line of the sliding-out point and the abscissa of the mother wolves is regarded as the upper limit, the lower limit is the lowest point of the side slope, the highest and lowest points 30 and 20 are equally divided, respectively regarded as the positions of the detection wolves, the head wolves, the mother wolves and the two detection wolves are regarded as four nodes of a spline curve, and the spline curve (wolf group) is constructed together as 18×20x30=10800 groups. Each group of different head wolves, mother wolves and exploring wolves can calculate different spline curve results, and then the curve which does not accord with the characteristics of the sliding surface of the side slope is screened according to the characteristics of the sliding surface of the side slope. Specifically, the spline curve is eliminated as a concave function (the second order derivative is not more than 0) and the first two sections are not monotonically decreased (the first order derivative is not more than 0).
Before the stress information is determined, the odor concentration of the wolf on the path needs to be determined, and the specific determination mode is as follows: dividing the first segment 30, the second segment 20 and the third segment 15 of the filtered spline curve equally according to different path lengths, using a machine learning method to take the abscissa, the ordinate and the stress value at each cell node as a data set, classifying soil layers by taking the soil layer type as a label, taking the stress value at each point in each soil layer as a characteristic of the point, taking 80% of the data set as a training set, learning the data in the training set according to the distribution rule of the stress value in the horizontal direction and the vertical direction in each soil layer, verifying the rule in the rest 20% of the data set, comparing the prediction result with the actual result of the training data, and continuously adjusting the prediction model until the prediction result of the model reaches an expected accuracy. From this, the positive stress σ at the desired node can be predicted α Shear stress τ α 。
The specific calculation process of the fitness D comprises the following steps: as shown in FIG. 4, if the sliding direction is rightward and counterclockwise, and the sliding force is positive, the shear strength τ on one section is high f And the tangential stress τ is calculated as follows:
τ α ＝0.5(σ yy -σ xx )sin2α+τ xy cos2α (5)
σ α ＝0.5(σ xx +σ yy )-0.5(σ xx -σ yy )cos2α-τ xy sin2α (6)
average sliding force of the i th segment:
average slip resistance of section i:
wherein: sigma (sigma) xx ，σ yy ，τ xy Respectively, the positive stress of the unit centroid along the x direction, the positive stress of the unit centroid along the y direction and the tangential stress, alpha is the included angle between the inclined plane and the horizontal plane, and sigma α Is the normal stress of the inclined plane, tau α Is the tangential stress of the inclined section,and c is the internal friction angle and cohesion of the material, respectively; calculating the sliding force and the anti-sliding force on each section, and then calculating the safety coefficient on the corresponding sliding surface, wherein the safety coefficient is defined as:
wolf group fitness D is defined as:
as shown in fig. 6, the fitness of the wolves of all the satisfactory combinations is calculated, respectively, in the formula (10): a and B are the starting point and the end point of the slope, w is the number of sections passed by the sliding surface, τ is the shear stress along the sliding direction of the sliding surface, τ f For shear strength, dL is the length increment, τ, of each segment along the sliding surface i To shear stress on the path from the i-1 st node to the i-th node,for shear strength on the path from section i-1 to section i Δd i Is the length of the path from stage i-1 to stage i.
And finally, eliminating unsuitable wolf clusters according to the fitness, and finally taking the spline curve with the largest fitness value as an optimized spline curve.
The foregoing is only a preferred embodiment of the present invention, it should be noted that: it will be apparent to those skilled in the art that various modifications and adaptations can be made without departing from the principles of the present invention, and such modifications and adaptations are intended to be comprehended within the scope of the invention.
Claims (3)
1. A non-circular slope sliding surface searching method based on an improved wolf's swarm algorithm is characterized in that: the method comprises the following steps:
extracting basic information of the numerical model based on a pre-established numerical model, wherein the basic information comprises the number n of nodes p Number of cells n e Cell material number, node number in the cell, each grid node coordinate, stress component size at the node, and shear strength parameters for each material;
classifying the cells according to the serial numbers of the cell materials, displaying the cells of different types of materials with different colors, and layering and drawing the slope image;
setting a region of the slope surface in a certain range of the slope top and the slope toe in the slope image as a possible movable range of the head wolves and the parent wolves, namely a sliding-out and sliding-in point of the slope, and taking the possible movable range as the initial position of the head wolves and the parent wolves of the wolf swarm algorithm;
the method comprises the steps that a head wolf, a parent wolf and a exploring wolf walk in a fixed step length to form a wolf group combination together, the head wolf and the parent wolf are equally divided according to the abscissa of the head wolf, the longitudinal line of each equally divided point is set to be the active position of the exploring wolf, a spline curve equation is determined by the walk in the fixed step length, the head wolf executes calling behaviors, the coordinates of each point on a path are determined, then the slashing wolf executes enclosing behaviors, and stress information of each point on the path is determined;
calculating sliding force and anti-sliding force between two adjacent wolves according to stress information, defining the fitness of the wolves as the reciprocal of the safety coefficient, eliminating unsuitable wolves according to the fitness, taking a spline curve with the maximum fitness value as an optimized spline curve,
extraction ofThe specific process of the basic information of the numerical model is as follows: the numerical model is composed of a series of polygonal standard units, each polygonal standard unit is composed of nodes and edges, the node numbers and the unit numbers in each polygonal unit start from 1, the numerical model is analyzed, and the number n of the unit cells of the numerical model is extracted e Each unit material number, for n e A plurality of unit cells for respectively extracting the number n of nodes p Three-component node coordinates (x, y, z) and stress component magnitude at node (σ) xx ，σ yy ，τ xy ) Cycle n e And each cell, after the circulation is completed, obtaining the coordinate and stress value of each node and the cell material number,
the polygon standard units comprise triangle units or quadrilateral units, each polygon standard unit is composed of 4 nodes, the quadrilateral units are written into (1, 2,3, 4), and the triangle units are written into (1, 2, 3);
the specific steps of slope image layering drawing are as follows: traversing all the cells, judging the types of cell materials, classifying the cells according to the material types, finding out the coordinates of points corresponding to the node numbers of the cells in each material, connecting the coordinates in the order of 1-2, 2-3, 3-4, 4-1 or 1-2, 2-3, 3-3 and 3-1 to form a quadrangle or triangle, and drawing the cells of different materials with different colors in turn to obtain a two-dimensional slope image;
the initial position of the first wolf female wolf is determined by the following specific steps: given the sliding-out point abscissa range (X tl1 ，X tl2 ) And a sliding-in point abscissa range (X ml1 ，X ml2 ) Let x=x be the abscissa of the given initial slide-out point tl1 The initial slide-in point has an abscissa of x=x tl2 Traversing all nodes, calculating each node to a straight line x=x tl1 Distance d of (2) 1 ＝|x-X tl1 I, to straight line x=x ml1 Distance d of (2) 2 ＝|x-X ml1 The coordinates of K points with the smallest distance are respectively screened out, then the maximum value of the ordinate is selected from the K coordinates, the ordinate of the point corresponding to the moment is the ordinate of the sliding-out point, and the initial head wolf and the parent wolf are positioned at the momentThe positions are determined to be (X) tl1 ，Y tl1 ) And (X) ml1 ，Y ml1 )；
Trisecting the abscissa of the first wolf and the female wolf, respectively denoted as X t1 ＝X tl1 +(X ml1 -X tl1 )/3，X t2 ＝X tl1 +2*(X ml1 -X tl1 ) 3, the initial exploring wolves are respectively a head wolf female wolf connecting line and x=x t1 X=x t2 The intersection point, i.e. the initial wolf coordinate is The initial probe wolf is stepped downstream by p and q steps with fixed steps x_d3 and x_d4, respectively, where x_d3= (y) max1 -y min1 )/p、x_d4＝(y max2 -y min2 ) Q), where y max1 And y max2 The upper limit of the walking area of each detected wolf, namely the initial wolf detection position, y min1 And y min2 The lower limit of each penetrating wolf wander area, namely the lowest limit of the side slope, is respectively used as four control nodes of a cubic spline curve to calculate the expression of the spline curve;
the spline curve expression specifically solves the following steps:
the intervals of interest [ a, b ]]Divided into n intervals [ (x) 0 ，x 1 )，(x 1 ，x 2 )……(x n-1 ，x n )]N+1 points in total, and the end points are x respectively 0 ＝a，x n =b, cubic spline curve definition:
(1) between each segmented cell [ x ] i ，x i+1 ]On, S (x) =s i (x) Are all a cubic equation, then at [ x ] i ，x i+1 ]The expansion of the cubic spline function at this point is:
S i (x)＝d i (x-x i ) 3 +c i (x-x i ) 2 +b i (x-x i )+a i ，x i ≤x≤x i+1 (1)，
(2) s (x), S' (x) are all continuous over [ a, b ],
(3) s (x) satisfies the difference condition S (x) i )＝y i ，i＝0，1，2……n，
And (3) making: y is i ＝f(x i )，h i ＝x i+1 -x i ，S i '(x i )＝m i I=0, 1,2 … … n is defined according to definition (1) (2) (3), at [ x i ，x i+1 ]The intervals are as follows:
(a) Interpolation continuity: s is S i (x i )＝y i 、S i (x i+1 )＝y i+1 Where i=0, 1,2, … …, n-1
From S i (x i )＝y i Obtainable a i ＝y i
From S i (x i+1 )＝y i+1 Obtainable d i h i 3 +c i h i 2 +b i h i +a i ＝y i+1
(b) Differential continuity: s is S i ′(x i+1 )＝S i+1 ′(x i+1 )、S i ″(x i+1 )＝S i+1 ″(x i+1 ) Where i=0, 1,2, … …, n-1
From S i ′(x i+1 )＝S i+1 ′(x i+1 ) Namely:
S i ′(x i+1 )＝3d i (x i+1 -x i ) 2 +2c i (x i+1 -x i )+b i ＝3d i h i 2 +2c i h i +b i
S i+1 ′(x i+1 )＝3d i+1 (x i+1 -x i+1 ) 2 +2c i+1 (x i+1 -x i+1 )+b i+1 ＝b i+1
obtaining b i +3d i h i 2 +2c i h i -b i+1 ＝0
From S i ″(x i+1 )＝S i+1 ″(x i+1 ) Obtain 2c i +6d i h i -2c i+1 ＝0
(c) Differential formula of spline curve: s is S i (x)＝d i (x-x i ) 3 +c i (x-x i ) 2 +b i (x-x i )+a i
S i ′(x)＝3d i (x-x i ) 2 +2c i (x-x i )+b i
S i ″(x)＝6d i (x-x i )+2c i (x-x i )
Let m be i ＝S i ″(x i )＝2c i+1 Then 2c i +6d i h i -2c i+1 =0 can be written as m i +6d i h i -m i+1 =0, can be pushed outWill d i 、c i Substitution into y i +b i h i +2c i h i +d i h i 3 ＝y i+1 Available->Will d i 、c i 、b i Substitution b i +3d i h i 2 +2c i h i -b i+1 ＝0
The method can obtain:under the free boundary, i.e. S "=0, where m 0 ＝0，m n ＝0
According to the above formula, a matrix of the following formula (3) can be constructed:
in the formula (3), f i ＝6(p i+1 -p i ),i＝1,2,3……n-1
Under the fixed boundary, since differential values of the end-to-end points are specified, assuming A, B respectively, then S 0 ′(x 0 ) =a can be obtained:
from S n-1 ′(x n ) =b can be obtained:
in the non-kinking boundary condition: s is S 0 ″′(x 0 )＝S 1 ″′(x 1 )、S n-2 ″′(x n-2 )＝S n-1 ″′(x n-1 )
Due to S i ″′(x)＝6d i Whereind 0 ＝d 1 ,d n-2 ＝d n-1 I.e. h 1 (m 1 -m 0 )＝h 0 (m 2 -m 1 )，h n-1 (m n-1 -m n-2 )＝h n-2 (m n -m n-1 )
From zThe sufficient requirement that the non-homogeneous equation set Ux=Q with unknown numbers has a unique solution is R (U) =R (Q) =z, and the matrix equations can be solved by adopting a Gaussian column principal component elimination method to obtain m i
Finally, substitution into equation (1) yields:
after each coefficient is calculated, the spline curve equation can be obtained, the first wolf moves m steps with a fixed step length x_d1, the second wolf moves t steps with a fixed step length x_d2, m groups of wolves with t groups of p groups of wolves are generated, each group of different combinations of the first wolf, the second wolf and the second wolf can be used for calculating a different spline curve result, and then curves which do not accord with the characteristics of the sliding surface of the side slope are screened according to the characteristics of the sliding surface of the side slope.
2. The non-circular slope sliding surface searching method based on the improved wolf's algorithm of claim 1, which is characterized in that: before the stress information is determined, the odor concentration of the wolf on the path needs to be determined, and the specific determination mode is as follows: the machine learning method is used for taking the abscissa, the ordinate and the stress value at each cell node as a data set, taking the soil layer type as a label, classifying soil layers, taking the stress value at each point in each soil layer as a characteristic of the point, taking one part of the data set as a training set, learning the data in the training set according to the distribution rule of the stress value in the horizontal direction and the vertical direction in each soil layer, verifying the rule in the rest of the data set, comparing the prediction result with the actual result of the training data, and continuously adjusting the prediction model until the prediction result of the model reaches an expected accuracy.
3. The non-circular slope sliding surface searching method based on the improved wolf's algorithm of claim 2, which is characterized in that: the specific calculation process of the fitness D comprises the following steps:
if the sliding direction is rightward and counterclockwise, the shear strength τ on one section is equal to the positive sliding force f And the tangential stress τ is calculated as follows:
τ α ＝0.5(σ yy -σ xx )sin2α+τ xy cos2α (5)
σ α ＝0.5(σ xx +σ yy )-0.5(σ xx -σ yy )cos2α-τ xy sin2α (6)
average sliding force of the i th segment:
average slip resistance of section i:
wherein: sigma (sigma) xx ，σ yy ，τ xy Respectively, the positive stress of the unit centroid along the x direction, the positive stress of the unit centroid along the y direction and the tangential stress, alpha is the included angle between the inclined plane and the horizontal plane, and sigma α Is the normal stress of the inclined plane, tau α Is the tangential stress of the inclined section,and c is the internal friction angle and cohesion of the material, respectively;
calculating the sliding force and the anti-sliding force on each section, and then calculating the safety coefficient on the corresponding sliding surface, wherein the safety coefficient is defined as:
wolf population fitness D is defined as:
in the formula (10): a and B are the starting point and the end point of the slope, w is the number of sections passed by the sliding surface, τ is the shear stress along the sliding direction of the sliding surface, τ f For shear strength, dL is the length increment, τ, of each segment along the sliding surface i To shear stress on the path from the i-1 st node to the i-th node,for shear strength on the path from section i-1 to section i Δd i Is the length of the path from stage i-1 to stage i.
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