A dynamic search complex stratum slip surface profile segmentation preprocessing method based on integral analysis method

Abstract

The application provides a dynamic search complex stratum slip surface profile division pretreatment method based on a whole analysis method, and aims to overcome the phenomenon that the area of the irregular polygon produced after the geological boundary line cuts the slip body unit cannot be accurately described due to the uncertainty of the dynamic slip surface shape in the slip surface dynamic search process when the stability analysis of the existing whole analysis method is performed, and the influence of the gravity and pore water pressure and other body force parameters cannot be considered. The application proposes a scheme for replacing the corresponding nodes by the new node numbering of the irregular polygon slip body unit in different positions after cutting based on the initial slip body unit node numbering and the intersection points of the geological boundary line, instead of renumbering. Since only the new node numbering after cutting is replaced and the uncut node numbering is retained, the programming implementation is facilitated and the storage space of the calculation is reduced. Further, the geometric parameters of the slip body unit after cutting and the physical and mechanical parameters of the corresponding stratum unit body are obtained, so as to provide parameter support for subsequent calculation.

Description

Technical Field

[0001] This invention belongs to the fields of geotechnical engineering and slope engineering technology, specifically relating to a dynamic search method for preprocessing of complex strata slip surface segmentation based on the overall analysis method. Background Technology

[0002] Landslides are a frequent geological hazard, ranking alongside earthquakes and volcanoes as one of the three major natural disasters affecting human survival and development. They not only threaten people's lives and property but also cause severe damage to the natural environment and resources. Research on landslide disasters and disaster prevention and mitigation are crucial topics in slope engineering, and reasonable landslide prevention measures depend on the correct evaluation and analysis of landslide stability. Therefore, research on landslide stability analysis methods has significant theoretical and practical implications. In engineering design and industry standards, the limit equilibrium method holds a dominant position. In the limit equilibrium method, compared to the traditional slice method, the overall analysis method does not rely on the assumption of inter-slice forces. It can use a three-force rectangular equilibrium condition instead of the commonly used basic form to establish the overall equilibrium equations of the sliding body, making the equation set simpler and more calibrated. It can be directly solved using Newton's method without further calibration.

[0003] Existing global analysis methods for slope stability analysis are convenient for considering different geological conditions because mechanical parameters such as cohesion and internal friction angle are only related to the slip surface. However, for volumetric parameters such as unit weight and pore water pressure, the area of ​​the slip body needs to be considered in the calculation. During the dynamic search of the slip surface, the slip surface and geological boundaries cut the slip body elements, forming irregular polygons. Solving for the area of ​​these polygons is difficult, making it challenging to directly and accurately apply geological volumetric parameters. Global analysis methods for complex geological formations with varying unit weights and pore water pressures are rarely used. Existing techniques for cutting slip body elements with fixed slip surface coordinates are relatively easy to implement using existing MATLAB programs. However, during dynamic slip surface searches, the slip surface coordinates change in real time, and the different ways the slip surface and geological boundaries cut the slip body elements can easily lead to irregular polygonal slip body elements. Using a single element numbering scheme makes it difficult to accurately calculate the area of ​​these irregular polygonal slip bodies. Summary of the Invention:

[0004] The purpose of this invention is to overcome the aforementioned shortcomings of existing global analysis preprocessing methods and propose a dynamic search method for complex strata slip surface segmentation preprocessing based on global analysis. During the dynamic search of the slip surface, the slip surface is divided into n initial slip body units according to the x-coordinate n. Based on the relative positions of the cut slip body units (i.e., upper, middle, and lower slip body units), and based on the numbers of the uncut initial slip body units, the corresponding nodes of the irregular polygonal slip body units at different positions after cutting are replaced, rather than renumbered. Slip body units at different positions within the same layer after cutting (middle and first / last slip body units) are processed using different schemes according to the number of geological boundaries cut. This is more conducive to considering the cutting of geological boundaries by different slip surfaces during the dynamic search process and also facilitates programming implementation. Because the shape of the slip surface is uncertain during the dynamic search process, and the number and sides of the irregular polygons formed after the slip surface is cut by the geological boundary line are also uncertain, the difficulty of this invention lies in accurately determining the location and number of nodes of the irregular polygonal slip surface units that need to be replaced during the dynamic changes of the slip surface. Then, the geometric parameters of these slip surface units (intersection number, slip surface unit number to which the intersection belongs, unit area, and centroid coordinates, etc.) are obtained. By summarizing the cut slip surface units according to the strata, the slip surface units of each stratum are assigned stratum physical and mechanical parameters (unit weight, cohesion, friction angle, and pore water pressure, etc.) to the slip surface units. This ensures the accurate application of stratum parameters, and the images of the cut nodes and slip surface units are plotted using MATLAB to facilitate checking the correctness of the program and provide parameter support for subsequent calculations using the overall analysis method.

[0005] The above-mentioned objective of this invention is achieved through the following technical solution:

[0006] A preprocessing method for dynamic searching of complex strata slip surfaces based on global analysis includes the following steps:

[0007] Step 1: Input the coordinates of the boundary nodes of the solution domain and the coordinates of the exit and entry nodes of the sliding surface dynamic search;

[0008] Step 1.1: Input the coordinates of the boundary nodes of the solution domain (x_boundary) i y_boundary i (i = 1, 2, ..., boundary), where i represents the node number of the solution domain boundary, and boundary represents the total number of boundary nodes in the solution domain, x_boundary i Let y_boundary represent the x-coordinate of the i-th solution domain boundary node. i This represents the x-coordinate of the i-th boundary node of the solution domain; where the coordinates of the slope crest node (x_e) are... e ,y_e e(e = 1, 2, ..., up), where e is the node number at the top of the slope and up is the number of nodes at the top of the slope;

[0009] Step 1.2: Set the exit coordinates of the sliding surface search (x_a) a ,y_a a (a = 1, 2, ..., exit), where a represents the exit node number of the sliding surface search, exit represents the total number of exit nodes in the sliding surface search, and x_a a Let y_a represent the x-coordinate of the exit node of the a-th sliding surface search. a This represents the ordinate of the exit node of the a-th sliding surface search; it sets the entry coordinate of the sliding surface search (x_b). b ,y_b b (b = 1, 2, ..., entry), where b represents the entry node number of the sliding surface search, entry represents the total number of entry nodes in the sliding surface search, and x_b b Let y_b represent the x-coordinate of the b-th sliding surface search entry node. b This represents the ordinate of the b-th sliding surface search entry node; the sliding surface exit point a and the entry point b determine the range of the sliding surface dynamic search.

[0010] Step 2: Divide the sliding surface from a single search into n equal segments based on its x-coordinate length, and number each segment counterclockwise. The more segments n are, the higher the calculation accuracy but the lower the efficiency. Dividing the total x-coordinate of the sliding surface into n equal segments, the x-coordinate length of a single sliding surface segment is... The initial sliding body element number and node number are expressed as follows:

[0011] Step 2.1: The nodes of the lower layer of the sliding surface of the sliding element are numbered c (c = 1, 2, ..., n+1), where n+1 represents the initial number of sliding elements n plus 1. The x-coordinate of the nodes of the lower layer of the sliding surface of the sliding element is x_c. c =x_b b +x_element·(c-1). The ordinate of the sliding surface nodes in the lower layer of the sliding body element. Where point o is a point on the perpendicular bisector of line segment ab, and its x-coordinate is... (Used to adjust the tilt of the sliding surface), ordinate y_o = k a-b ·(x_o-x_m)+y_m; Distance between point o and point a Mean slope k of the slip surface a-b =-(x_a a -x_b b ) / (y_a a -y_b b ); Average length of the sliding surface x_m = (x_a) a +x_b b ) / 2; Average length of the sliding surface ordinate y_m=(y_aa +y_b b ) / 2;

[0012] Step 2.2: The nodes of the upper layer of the sliding body unit are numbered as d (d = n+2, n+3, ..., 2n+1), where 2n+1 represents the initial number of sliding body units n multiplied by 2 and then added by 1. The x-coordinate of the nodes of the lower layer of the sliding body unit is x_d. d =x_b b +x_element·(d-1), y_d, the ordinate of the uniformly distributed slope node in the lower layer of the sliding body element. d =y_b b +(y_e e -y_b b ) / (x_e e -x_b b )·(x_d d -x_b b );

[0013] Step 2.3: The initial sliding body element number is n_element_s p =p (p = 1, 2, ..., n), where p is the value of the sliding element number. The first and last sliding elements need to have their shapes determined and can be simply referred to as the first and last elements. The remaining elements in the middle are referred to as the middle elements, and the middle elements are quadrilaterals. Numbering starts from the bottom left node counterclockwise. The first two points are sliding surface points located below the quadrilateral, and the last two are slope surface nodes located above the quadrilateral. The "above" and "below" mentioned later have the same orientation as here. Therefore, the initial middle element number of the sliding element is n_element_s. pp For: n_element_s pp =pp(pp=2,…,n-1), where pp is the value of the intermediate sliding element number, and n-1 represents the initial number of sliding elements n minus 1, and its node number num_element_s pp For: num_element_s pp =[c pp ,c pp+1 ,d pp+1 ,d pp ], pp+1 is the value of the intermediate sliding body unit number, which is pp plus 1. pp =pp represents the node number of the evenly distributed sliding surface in the lower layer of the pp-th sliding body element, d pp =pp represents the node number of the evenly distributed slope surface on the upper layer of the pp-th sliding body unit, [c pp ,c pp+1 ,d pp+1 ,d pp ] indicates from node c ppBegin arranging the four nodes in a counter-clockwise order. The initial sliding body elements are numbered n_element_s. ppp =ppp(ppp=1,n), where ppp is the set of first and last sliding body element numbers with values ​​of 1 and n. If n_element_s ppp If it is a quadrilateral element, then the node number of the first and last sliding body elements is num_element_s ppp For: num_element_s ppp =[c ppp ,c ppp+1 ,d ppp+1 ,d ppp If n_element_s ppp If it is a triangular element, then the node number is num_element_s ppp For: num_element_s ppp =[c ppp ,c ppp+1 ,d ppp ];

[0014] Step 3: Number the stratigraphic boundary line n_formation ii For: n_formation ii =ii (ii = 1, 2, ..., nn), where ii is the stratigraphic boundary number and nn is the total number of stratigraphic boundaries; the groundwater level is n_water. The two endpoints of the stratigraphic boundary are numbered as: nf_1 ii With nf_2 ii Its coordinates can be represented as: (xnf_1) ii ynf_1 ii ) and (xnf_2 ii ynf_2 ii ), xnf_1 ii ynf_1 represents the x-coordinate of the first endpoint of the boundary line of the ii-th stratigraphic layer. ii xnf_2 represents the ordinate of the first endpoint of the boundary line of the ii-th stratigraphic layer. ii ynf_2 represents the x-coordinate of the second endpoint of the boundary line of the ii-th stratigraphic layer. iiThe first endpoint of the stratum boundary of layer ii is represented by the ordinate of the second endpoint. The two endpoints of the groundwater level are numbered nw_1 and nw_2, and their coordinates can be represented as (xnw_1, ynw_1) and (xnw_2, ynw_2), where xnw_1 represents the x-coordinate of the first endpoint of the groundwater level, ynw_2 represents the x-coordinate of the second endpoint of the groundwater level, and ynw_2 represents the ordinate of the second endpoint of the groundwater level. The intersection points of the line segments with the sliding body elements are solved using MATLAB programming. The number of intersection points of the stratum boundary of layer ii is n_intersection. ii The number of intersections of the groundwater level lines is n_intersection water Following the top-to-bottom order of the vertical coordinates of the stratigraphic boundaries and groundwater levels, the coordinates of the intersection points of the stratigraphic boundaries and groundwater levels are numbered. To facilitate subsequent classification of stratigraphic units, the vertical slip surface node numbers and slope surface node numbers corresponding to the intersection points need to be stored. These numbers can be obtained using the MATLAB intersection point calculation program. The groundwater level is located above the stratigraphic boundaries. Therefore:

[0015] (1) Intersection number of groundwater level lines for:

[0016]

[0017] In the formula, jj represents the number of groundwater level intersections.

[0018] (2) The vertical node number corresponding to the jjth intersection point of the groundwater level line in the sliding surface direction is denoted as: n_slide_water jj

[0019] (3) The vertical node number corresponding to the jjth intersection point of the groundwater level line in the slope direction is denoted as: n_slope_water jj

[0020] (4) The coordinates of the jjth intersection point of the groundwater level lines are:

[0021] In the formula, This represents the x-coordinate of the intersection of the j-th groundwater level lines. This represents the ordinate of the intersection point of the jj-th groundwater level line.

[0022] (5) Stratigraphic boundary of layer ii, layer kk ii Intersection number for:

[0023]

[0024]

[0025] (kk ii =1,2,…,n_intersection ii ), kk ii Number the number of intersection points of the stratigraphic boundary line of layer ii.

[0026] (6) Stratigraphic boundary of the iith layer, kkth layer ii The vertical direction corresponding to the sliding surface node number of the intersection point is denoted as:

[0027] (7) Stratigraphic boundary of layer ii, kk ii The vertical node numbers corresponding to the intersection points on the slope are denoted as follows:

[0028] (8) Stratigraphic boundary of layer ii, layer kk ii The coordinates of the intersection points can be represented as:

[0029] In the formula, This represents the boundary line of the ii-th stratigraphic layer, kk-th. ii The x-coordinates of the intersection points This represents the boundary line of the ii-th stratigraphic layer, kk-th. ii The ordinates of the intersection points.

[0030] (9) Store the intersection numbers of each stratum, slip surface nodes, and slope surface nodes together as a total node number point_num, which can be represented as:

[0031] (10) The coordinates corresponding to the summary point number are stored as point_xy, which can be represented as:

[0032]

[0033] Step 4: Based on the relative positions of the cut sliding body units (i.e., upper-layer sliding body units, intermediate-layer sliding body units, and lower-layer sliding body units), where the upper-layer sliding body unit refers to the sliding body unit located after the uppermost geological boundary line is cut, the lower-layer sliding body unit refers to the sliding body unit located after the lowermost geological boundary line is cut, and the remaining cut units located in the intermediate layer are all called intermediate-layer sliding body units. Based on the initial uncut sliding body unit numbering, the corresponding nodes of the irregular polygonal sliding body units located in different positions after cutting are replaced, rather than renumbered.

[0034] Step 4.1: Replacement scheme for lower-level sliding body unit numbering and node numbering:

[0035] (1) Replacement scheme for the numbering of the lower sliding body unit:

[0036] The lower sliding body unit number is represented as The number of the sliding mass unit when the uncut unit is retained, where end indicates that the cut sliding mass unit is located below the lowermost geological boundary (lower-layer sliding mass unit), and rr represents the value of the cut sliding mass unit, can be expressed as:

[0037]

[0038] In the formula, ynf_1 end and ynf_2 end respectively represent the ordinates of the two endpoints of the lowermost stratum boundary, max{ynf_1 end ,ynf_2 end} represents the maximum ordinate value among the two endpoints of the lowermost stratum boundary; ynw_1 and ynw_2 respectively represent the ordinates of the two endpoints of the groundwater level line, and max{ynw_1,ynw_2} represents the maximum ordinate value among the two endpoints of the groundwater level line. max{ynf_1 end ,ynf_2 end}>max{ynw_1,ynw_2} indicates that the maximum ordinate value among the two endpoints of the lowermost stratum boundary is greater than the maximum ordinate value among the two endpoints of the groundwater level line, which means the lowermost stratum boundary is higher than the groundwater level line, and the number of the lower-layer sliding mass unit is the value rr of the cut sliding mass unit, and the value of the cut sliding mass unit is rr=1,2,…,n_intersection water -1, n_intersection water represents the number of intersection points of the groundwater level line, and n_intersection water -1 represents the number of intersection points of the groundwater level line minus 1. Conversely, (max{ynf_1 end ,ynf_2 end}<max{ynw_1,ynw_2}) indicates that the maximum ordinate value among the two endpoints of the lowermost stratum boundary is less than the maximum ordinate value among the two endpoints of the groundwater level line, the value of the cut sliding mass unit rr=1,2,…,n_intersection end -1, n_intersection end represents the number of intersection points of the lowermost stratum boundary, and n_intersection end -1 represents the number of intersection points of the lowermost stratum boundary minus 1.

[0039] (2) Node number replacement scheme for the lower-layer intermediate sliding mass unit:

[0040] Similar to step 2, the shapes of the first and last units of the lower-layer sliding mass unit need to be determined, and the intermediate sliding mass unit is a quadrilateral. The node numbers of the intermediate sliding mass unit of the lower-layer sliding mass unit are expressed as where end indicates that the cut sliding mass element is located below the lowermost geological boundary (lower-layer sliding mass element), and rrr represents the value of the number of the cut intermediate sliding mass element. The node replacement idea is that part of the node numbers of the sliding mass element are changed from slope surface nodes to the intersection node numbers of the lowermost geological boundary, then is:

[0041]

[0042] In the formula, when max{ynf_1 end ,ynf_2 end}>max{ynw_1,ynw_2}, that is, the lowermost stratum boundary is higher than the groundwater level line, at this time the value of the number of the cut intermediate sliding mass element is expressed as rrr=2,…n_intersection water -2, where n_intersection water represents the number of intersections of the groundwater level line, and n_intersection water -2 represents the number of intersections of the groundwater level line minus 2. The number of the slope surface node located above the cut intermediate sliding mass element is replaced with the intersection number of the groundwater level line, that is from [c rrr ,c rrr+1 ,d rrr+1 ,d rrr becomes where, rrr+1 is the value obtained by adding 1 to the value rrr of the intermediate sliding mass element number, c rrr =rrr represents the node number of the equally divided sliding surface at the lower layer of the rrr-th sliding mass element, d rrr =rrr represents the node number of the equally divided slope surface at the upper layer of the rrr-th sliding mass element, [c rrr ,c rrr+1 ,d rrr+1 ,d rrr represents the arrangement of four nodes of the initial intermediate sliding mass element in counter-clockwise order starting from node c rrr . represents the rrr-th intersection number of the groundwater level line, represents the arrangement of four nodes of the intermediate sliding mass element of the replaced lower-layer sliding mass element in counter-clockwise order starting from node c rrr . Conversely, when max{ynf_1 end ,ynf_2 end}<max{ynw_1,ynw_2}, that is, the lowermost stratum boundary is lower than the groundwater level line, at this time the value of the number of the cut intermediate sliding mass element is expressed as rrr=2,…n_intersection end -2, where n_intersectionend n_intersection represents the number of intersections of the lowest stratigraphic boundary. end -2 indicates that the number of intersections of the lowest stratigraphic boundary line is reduced by 2. Then, the node numbers of the intermediate sliding body units located above are replaced with the intersection numbers of the lowest stratigraphic boundary line, i.e. By [c rrr ,c rrr+1 ,d rrr+1 ,d rrr ] becomes in, This indicates the number of the intersection point of the rrr-th lowest stratigraphic boundary line. This indicates that the intermediate sliding body element of the lower-level sliding body element after replacement originates from node c. rrr Begin arranging the four nodes in a counter-clockwise order.

[0043] (3) Replacement scheme for node numbers of the lower-level first and last sliding body units:

[0044] The node numbers of the first and last elements of the lower sliding body element are represented as follows: rrrr represents the value of the first and last sliding body unit number. If the first and last units of the lower sliding body unit are quadrilaterals, the replacement method is the same as that of the middle unit. If they are triangular, the upper slope nodes of the first and last units are changed to the intersection of the corresponding lowest geological boundary line. The node numbers contained in the triangular units of the first and last sliding bodies of the lower layer after cutting are... Represented as:

[0045]

[0046] In the formula, if max{ynf_1 end ynf_2 end}>max{ynw_1,ynw_2} indicates that the boundary of the lowest stratum is higher than the groundwater level. In this case, the values ​​of the first and last sliding body unit numbers after cutting are represented as rrrr=1,n_intersection water -1, where n_intersection water The number of intersections of groundwater levels, n_intersection water -1 indicates that the number of intersections of the groundwater level lines is reduced by 1. Number the first and last unit nodes. The slope node number d located above rrrr+1 ,d rrrr Replace with the intersection number of the groundwater level line The sliding surface node number c located below rrrr+1 Deletion, i.e., the first and last unit node numbers. The initial sliding body element node number [c rrrr ,c rrrr+1 ,d rrrr+1,d rrrr is replaced with where rrrr+1 is the value obtained by adding 1 to the base value rrrr of the intermediate sliding mass unit number, c rrrr =rrrr represents the number of the equally divided sliding surface node at the lower layer of the rrrr-th sliding mass unit, d rrrr =rrrr represents the number of the equally divided slope surface node at the upper layer of the rrrr-th sliding mass unit, [c rrrr ,c rrrr+1 ,d rrrr+1 ,d rrrr represents the arrangement of four nodes of the initial first and last sliding mass units in counter-clockwise order starting from node c rrrr , represents the number of the rrrr-th intersection point of the groundwater level line. Conversely, max{ynf_1 end ,ynf_2 end}<max{ynw_1,ynw_2}, which means that the lowermost stratum boundary line is lower than the groundwater level line. At this time, the values of the numbers of the first and last sliding mass units after cutting are expressed as rrrr=1,n_intersection end -1, where n_intersection end represents the number of intersection points of the lowermost stratum boundary line, and n_intersection end -1 represents the number of intersection points of the lowermost stratum boundary line minus 1. Then, the node numbers of the first and last sliding mass units the numbers of the slope surface nodes located above d rrrr+1 ,d rrrr are replaced with the numbers of the intersection points of the lowermost stratum boundary line , that is from [c rrrr ,c rrrr+1 ,d rrrr+1 ,d rrrr to

[0047] The numbers of the lower-layer sliding mass units after cutting and the numbers of the nodes contained therein have been updated completely.

[0048] Step 4.2: Replacement scheme for the numbers of upper-layer sliding mass units and node numbers:

[0049] The difference from step 4.1 is that the sliding mass units in this layer consist of two parts. The first part is the uncut units, that is, the original unit numbers and the node numbers contained therein are retained; the second part is the units cut by the geological boundary line. Only the corresponding numbers of the cut units and the node numbers contained therein need to be replaced and updated. Through such classified processing, in the dynamic search process of the sliding surface, it can adapt to the cutting of upper-layer units by different sliding surfaces, which also maximizes the improvement of cutting efficiency and facilitates the realization of programming.

[0050] (1) Upper sliding mass element number replacement scheme:

[0051] Since only the case of elements that are cut is considered, the numbers of uncut elements and the contained node numbers remain unchanged, and the number of the new upper element generated after cutting is expressed as rr represents the number range of new sliding mass elements after cutting, and 1 indicates that the sliding mass element after cutting is located above the first geological boundary (upper sliding mass element). is:

[0052]

[0053] In the formula, ynf_11 and ynf_21 respectively represent the ordinates of the two endpoints of the first stratum boundary, max{ynf_11,ynf_21} represents the maximum ordinate among the two endpoints of the first stratum boundary; max{ynw_1,ynw_2} represents the maximum ordinate among the two endpoints of the groundwater level line. max{ynf_11,ynf_21}<max{ynw_1,ynw_2} means that the maximum ordinate among the two endpoints of the first stratum boundary is less than the maximum ordinate among the two endpoints of the groundwater level line, which indicates that the first stratum boundary is lower than the groundwater level line, and at this time, the number range of new sliding mass elements after cutting is rr=1,2,…,n_intersection water -1, n_intersection water represents the number of intersection points of the groundwater level line, n_intersection water -1 represents the number of intersection points of the groundwater level line minus 1. The number of the new upper sliding mass element after cutting is the sum of the initial number of sliding mass elements n and the new sliding mass element number range rr, that is, n+rr. On the contrary, when max{ynf_11,ynf_21}>max{ynw_1,ynw_2}, it means that the maximum ordinate among the two endpoints of the first stratum boundary is greater than the maximum ordinate among the two endpoints of the groundwater level line, at this time, the number range of new sliding mass elements after cutting is rr=1,2,…,n_intersection1-1, n_intersection1 represents the number of intersection points of the first stratum boundary, and n_intersection1-1 represents the number of intersection points of the first stratum boundary minus 1.

[0054] (2) Upper intermediate sliding mass element node number replacement scheme:

[0055] When the upper sliding mass unit is not cut, the upper node is a slope surface node and the lower node is a sliding surface node, the node numbers of the uncut unit remain unchanged, and after cutting, the lower sliding surface node needs to be changed to the intersection number of the first geological boundary line. Similar to step 2, it is necessary to determine the shape of the first and last sliding mass units, while the middle sliding mass unit is a quadrilateral, and the node numbers contained in the new middle sliding mass unit after cutting where 1 indicates that the cut sliding mass unit is located above the first geological boundary line (upper sliding mass unit), and rrr represents the value of the number of the middle sliding mass unit after cutting. is:

[0056]

[0057] In the formula, max{ynf_11,ynf_21}<max{ynw_1,ynw_2} indicates that the first stratum boundary line is lower than the groundwater level line, at this time the node number range rrr of the new sliding mass unit after cutting is rrr=2,…,n_intersection water -2, the sliding surface node number below the new middle sliding mass unit after cutting is replaced with the intersection number of the groundwater level line, that is, the node numbers contained in the middle sliding mass unit change from [c rrr ,c rrr+1 ,d rrr+1 ,d rrr to Conversely, max{ynf_11,ynf_21}>max{ynw_1,ynw_2} indicates that the first stratum boundary line is higher than the groundwater level line, at this time the number range of the new sliding mass unit after cutting is rrr=2,…n_intersection1-2, then the node numbers contained in the middle sliding mass unit change from [c rrr ,c rrr+1 ,d rrr+1 ,d rrr to represents the rrr-th intersection number of the first stratum boundary line.

[0058] (3) Replacement scheme for node numbers of the first and last upper sliding mass units:

[0059] If the first and last units of the upper sliding mass unit are quadrilaterals, the representation method is consistent with that of the middle unit. The difference from step 4.1 here is that the sliding surface is generally not a horizontal straight line, but is composed of short line segments with a certain angle. Therefore, after being cut by the geological boundary line, the first and last units are not regular triangles, but irregular polygons, and the node numbers contained in the first and last units of the upper sliding mass unit where 1 indicates that the cut sliding mass element is located above the first geological boundary (upper-layer sliding mass element), and rrrr represents the value range of the numbers of the first and last sliding mass elements. is expressed as:

[0060]

[0061] wherein, if max{ynf_11, ynf_21} > max{ynw_1, ynw_2}, it indicates that the first stratum boundary is higher than the groundwater level line. When the number rrrr of the first element of the upper-layer sliding mass element is equal to 1, the sliding surface node number is replaced with the number of the intersection point of the first stratum boundary, that is is replaced by [c rrrr ,c rrrr+1 ,d rrrr+1 ,d rrrr to which represents the number of the rrr-th intersection point of the first stratum boundary. When the number rrrr of the last element of the upper-layer sliding mass element is equal to n_intersection1-1, the sliding mass element is cut into a pentagon, and the sliding surface node number is replaced with the number of the intersection point of the first stratum boundary, that is is replaced by [c rrrr ,c rrrr+1 ,d rrrr+1 ,d rrrr to Conversely, when max{ynf_11, ynf_21} < max{ynw_1, ynw_2}, it indicates that the first stratum boundary is lower than the groundwater level line. When the number rrrr of the first element of the upper-layer sliding mass element is equal to 1, the sliding surface node number is replaced with the number of the intersection point of the groundwater level line, that is is replaced by [c rrrr ,c rrrr+1 ,d rrrr+1 ,d rrrr to When the number rrrr of the last element of the upper-layer sliding mass element is equal to n_intersection1-1, the sliding mass element is cut into a pentagon, and the sliding surface node number is replaced with the number of the intersection point of the groundwater level line, that is is replaced by [c rrrr ,c rrrr+1 ,d rrrr+1 ,d rrrr to

[0062] The update of the number of the upper-layer cut elements and the numbers of the nodes contained therein is completed.

[0063] Step 4.3: Scheme for replacing the number of the middle-layer sliding mass element and the node number:

[0064] Similar to step 4.2, the intermediate layer of sliding body units consists of two parts: the first part consists of sliding body units cut by only one geological boundary line, and the second part consists of sliding body units cut by two or more geological boundary lines. The replacement method for the first part is similar to that in step 4.2. However, the second part involves multiple geological boundary lines cutting the sliding body units, and it requires numbering the newly generated irregular polygons. As the sliding surface is dynamically searched, the relative relationship between the sliding body units and the geological boundary lines changes continuously, and the cutting situation also changes. This is the key challenge of the replacement. This invention, based on the node numbers of the uncut sliding body units, replaces the corresponding intersection points of the cutting units sequentially according to steps 4.1 and 4.2, following the order of the stratigraphic boundary lines and groundwater levels intersecting the sliding body units from top to bottom. Because the replacement is performed step-by-step based on the intersection points of the cutting units, the node numbers of the irregular polygons can be obtained even when the sliding surface node situation is constantly changing during dynamic searching.

[0065] (1) Replacement scheme for intermediate layer sliding body unit numbering:

[0066] For the first part of the sliding body elements in the intermediate layer, retain the initial element number. For the second part of the sliding body elements, new sliding body numbers need to be added. The new sliding body element numbers are as follows: ii = 2, 3, ..., nn-1 represents the geological boundary numbers from top to bottom, excluding the middle section between the uppermost and lowermost layers. nn is the total number of stratigraphic boundaries, nn-1 is the total number of stratigraphic boundaries minus 1, and rr represents the range of newly added sliding body unit numbers after cutting. Represented as:

[0067]

[0068] In the formula, n represents the initial total number of uncut units, ynf_1 ii With ynf_2 ii Represent the ordinates of the two endpoints of the boundary line of the ii-th stratigraphic layer, respectively, max{ynf_1 ii ynf_2 ii} represents the maximum ordinate value between the two endpoints of the boundary line of the ii-th stratum; max{ynw_1,ynw_2} represents the maximum ordinate value between the two endpoints of the groundwater level line. If max{ynw_1,ynw_2} ii ynf_2 ii}>max{ynw_1,ynw_2} indicates that the maximum ordinate value between the two endpoints of the ii-th stratum boundary is greater than the maximum ordinate value between the two endpoints of the groundwater level, meaning the ii-th stratum boundary is higher than the groundwater level. In this case, the newly added sliding body element numbering range after cutting is rr=1,2,…,n_intersection ii -1, n_intersectionii represents the number of intersection points of the stratum boundary line of the ii-th layer, n_intersection ii -1 represents the number of intersection points of the stratum boundary line of the ii-th layer minus 1. The number of the newly added unit after cutting is the sum of the total number of uncut units n and the intersection point number of the stratum boundary line of the iii-th layer and rr, that is Conversely, if the maximum ordinate value among the two endpoints of the stratum boundary line of the ii-th layer is less than the maximum ordinate value among the two endpoints of the groundwater level line, it indicates that the stratum boundary line of the ii-th layer is below the groundwater level line, that is, max{ynf_1 ii ,ynf_2 ii}<max{ynw_1,ynw_2}. At this time, the number range rr of the newly added sliding mass unit after cutting is rr=1,2,…,n_intersection water -1, n_intersection water represents the number of intersection points of the groundwater level line, n_intersection water -1 represents the number of intersection points of the groundwater level line minus 1.

[0069] (2) Node number replacement scheme for intermediate sliding mass units in the intermediate layer:

[0070] For the node numbers of the first part of sliding mass units in the intermediate layer, the corresponding nodes can be replaced with reference to step 4.1; the node numbers of the second part of sliding mass units are replaced layer by layer according to the top-to-bottom order of the geological boundary lines, which is similar to step 4.2. If the second part of intermediate sliding mass unit in the intermediate layer is a quadrilateral, the node numbers included in the intermediate sliding mass unit of the intermediate layer ii=2,3,…nn-1 represents the number of the stratum boundary line in the middle part excluding the uppermost layer and the lowermost layer from top to bottom of the geological boundary lines, and rrr represents the value of the number of the intermediate sliding mass unit after cutting. is expressed as:

[0071]

[0072] In the formula, ii=2,3,…nn-1 represents the number of the stratum boundary line in the middle part excluding the uppermost layer and the lowermost layer from top to bottom of the stratum boundary lines, nn represents the total number of stratum boundary lines, nn-1 represents the total number of stratum boundary lines nn minus 1 in quantity. ii-1 represents the stratum boundary line of the layer immediately above the stratum boundary line of the ii-th layer, ynf_1 ii-1 and ynf_2 ii-1 respectively represent the ordinates of the two endpoints of the stratum boundary line of the ii-1-th layer, max{ynf_1 ii-1 ,ynf_2 ii-1} represents the maximum ordinate value among the two endpoints of the stratum boundary line of the ii-1-th layer. max{ynf_1ii-1 ,ynf_2 ii-1}>max{ynw_1,ynw_2} means that the maximum ordinate value among the two endpoints of the stratum boundary line of the ii-1th layer is greater than the maximum ordinate value among the two endpoints of the groundwater level line, that is, the stratum boundary line of the ii-1th layer is above the groundwater level line, max{ynf_1 ii-1 ,ynf_2 ii-1}<max{ynw_1,ynw_2} means that the stratum boundary line of the ii-1th layer is below the groundwater level line, max{ynf_1 ii ,ynf_2 ii}>max{ynw_1,ynw_2} means that the stratum boundary line of the iith layer is above the groundwater level line, max{ynf_1 ii ,ynf_2 ii}<max{ynw_1,ynw_2} means that the stratum boundary line of the iith layer is below the groundwater level line. (max{ynf_1 ii ,ynf_2 ii}>max{ynw_1,ynw_2} and max{ynf_1 ii-1 ,ynf_2 ii-1}>max{ynw_1,ynw_2}) means that the groundwater level line is above the stratum boundary lines of the iith layer and the ii-1th layer; (max{ynf_1 ii ,ynf_2 ii}<max{ynw_1,ynw_2} and max{ynf_1 ii-1 ,ynf_2 ii-1}<max{ynw_1,ynw_2}) means that the groundwater level line is below the stratum boundary lines of the iith layer and the ii-1th layer; at this time, the value of the number of the middle sliding mass unit after cutting is rrr=2,…,n_intersection ii -2, n_intersection ii represents the number of intersection points of the stratum boundary line of the iith layer, n_intersection ii -2 represents the number of intersection points of the stratum boundary line of the iith layer minus 2. The node numbers included in the middle sliding mass unit of the middle layer are replaced by [[c rrr ,c rrr+1 ,d rrr+1 ,d rrr represents the number of the rrr-th intersection point of the stratum boundary line of the iith layer, represents the number of the rrr+1-th intersection point of the stratum boundary line of the iith layer, ​represents the number of the rrr-th intersection point of the stratum boundary line of the ii-1-th layer, represents the number of the (rrr+1)-th intersection point of the stratum boundary line of the ii-1-th layer. (max{ynf_1 ii ,ynf_2 ii}>max{ynw_1,ynw_2} and max{ynf_1 ii-1 ,ynf_2 ii-1}<max{ynw_1,ynw_2}) indicates that the groundwater level line is above the stratum boundary line of the ii-th layer and below the stratum boundary line of the ii-1-th layer. In this case, the value of the number of the cut intermediate sliding mass unit is rrr=2,…,n_intersection water -2, n_intersection water represents the number of intersection points of the groundwater level line, n_intersection water -2 represents the number of intersection points of the groundwater level line minus 2. The node numbers contained in the intermediate sliding mass unit of the intermediate layer are replaced by [[c rrr ,c rrr+1 ,d rrr+1 ,d rrr represents the number of the rrr-th intersection point of the groundwater level line, represents the number of the (rrr+1)-th intersection point of the groundwater level line.

[0073] (3) Node number replacement scheme for the head and tail sliding mass units of the intermediate layer:

[0074] If the head and tail sliding mass units of the intermediate layer are quadrilaterals, the representation method is consistent with that of the intermediate units. The difference from step 4.1 here is that the sliding surface is composed of line segments with a certain angle, and the changing sliding surface and geological boundary line will cut off irregular polygons, most of which are pentagons, and quadrilaterals or triangles may also appear. The node numbers contained in the last sliding mass unit of the intermediate layer ii=2,3,…nn-1 represents the numbers of the stratum boundary lines in the middle part excluding the uppermost layer and the lowermost layer from top to bottom, and rrrr represents the value of the number of the head and tail sliding mass units.

[0075] is expressed as:

[0076]

[0077] When the groundwater level line is above the stratum boundary lines of the ii-th layer and the ii-1-th layer, that is, (max{ynf_1 ii ,ynf_2 ii ​}>max{ynw_1, ynw_2} and max{ynf_1 ii-1 , ynf_2 ii-1}>max{ynw_1, ynw_2}), or the groundwater level line is below the stratum boundary between the ii-th layer and the (ii-1)-th layer, i.e. (max{ynf_1 ii , ynf_2 ii}<max{ynw_1, ynw_2} and max{ynf_1 ii-1 , ynf_2 ii-1}<max{ynw_1, ynw_2}); in this case, the value of the number of the head and tail sliding mass units after cutting is rrr = 1, n_intersection ii -1, where n_intersection ii -1 represents the number of intersection points of the stratum boundary of the ii-th layer minus 1. When the head and tail sliding mass units of the middle layer are triangular, the contained node numbers are composed of [c rrr , c rrr+1 , d rrr+1 , d rrr are replaced by When they are quadrilateral, the contained node numbers are composed of [c rrr , c rrr+1 , d rrr+1 , d rrr are replaced by When they are pentagonal, the contained node numbers are composed of [c rrr , c rrr+1 , d rrr+1 , d rrr are replaced by When the groundwater level line is above the stratum boundary of the ii-th layer and below the stratum boundary of the (ii-1)-th layer, i.e. (max{ynf_1 ii , ynf_2 ii}>max{ynw_1, ynw_2} and max{ynf_1 ii-1 , ynf_2 ii-1}<max{ynw_1, ynw_2}), in this case, the value of the number of the head and tail sliding mass units after cutting is rrrr = 1, n_intersection water -1, where n_intersection water -1 represents the number of intersection points of the groundwater level line minus 1. When the head and tail sliding mass units of the middle layer are triangular, the contained node numbers are composed of [c rrr , c rrr+1 , d rrr+1 , d rrrReplace with When it is a quadrilateral, the node numbers it contains are... By [c rrr ,c rrr+1 ,d rrr+1 ,d rrr Replace with When it is a pentagon, the node numbers it contains By [c rrr ,c rrr+1 ,d rrr+1 ,d rrr Replace with

[0078] The unit numbers and node numbers of the intermediate layer have been updated after the intermediate layer is cut.

[0079] Step 4.4: Summarize the updated sliding body element node numbers

[0080] The updated included node number num_element after cutting the sliding body element num Represented as:

[0081]

[0082]

[0083] In the formula, This indicates the node number of the intermediate sliding body element in the upper sliding body element. Indicates the node numbers of the first and last elements of the upper sliding body element; This indicates the node number of the intermediate sliding body unit in the middle layer of the stratigraphic boundary of layer ii. Indicates the node numbers of the first and last units of the sliding body unit in the middle layer of the stratigraphic boundary of layer ii; This indicates the node number of the intermediate sliding body element in the lower-level sliding body element. `n_element_s` represents the node numbers of the first and last elements of the lower-level sliding body element. `rrr` represents the value of the middle sliding body element number after cutting, and `rrrr` represents the value of the first and last sliding body element numbers. Specific values ​​are given in steps 4.1 to 4.3. ttrepresents that the middle element of the upper sliding mass element is not cut and retains the initial element node number; tt represents the value range of the element number of the middle element of the upper sliding mass element that is not cut and retains the initial element node number. When the first stratum boundary line is lower than the groundwater level line, that is, max{ynf_11,ynf_21}<max{ynw_1,ynw_2}, the value of tt is expressed as tt=n_intersection1,…,n-1, where n_intersection1 represents the number of intersection points of the first stratum boundary line, and n-1 represents the initial sliding mass element number n minus 1; when the first stratum boundary line is higher than the groundwater level line, that is, max{ynf_11,ynf_21}>max{ynw_1,ynw_2}, the value of tt is expressed as tt=n_intersection water ,…,n-1, n_intersection water represents the number of intersection points of the groundwater level line. n_element_s ttt represents that the last element of the upper sliding mass element is not cut and retains the initial element node number; ttt represents the value range of the element number of the last element of the upper sliding mass element that is not cut and retains the initial element node number, and ttt=n.

[0084] Step 5: Use MATLAB to solve and store the element centroid centroid_element and area area_element of the new elements after cutting;

[0085] Step 6: Group the element numbers contained in each stratum to prepare for subsequently assigning corresponding physical and mechanical parameters of elements to each stratum.

[0086] (1) The element numbers of the lower sliding mass remain unchanged and retain the initial sliding mass numbers, and the element numbers of the lower stratum sliding mass element_stratum end can be expressed as:

[0087]

[0088] wherein, represents the element number of the lower sliding mass; rr represents the number range of new sliding mass elements added after cutting, and the specific values have been given in Step 4.1 to Step 4.3.

[0089] (2) The element numbers of the upper sliding mass consist of two parts, that is, the first part is the initial uncut elements that are retained, and the second part is the numbers of new sliding mass elements added after cutting. Therefore, the sliding mass element numbers contained in the upper stratum can be expressed as element_stratum 1 :

[0090]

[0091] In the formula, if max{ynf_11,ynf_21}>max{ynw_1,ynw_2}, it indicates that the first stratum boundary line is higher than the groundwater level line, represents the number of the newly added upper unit after cutting; represents the number of the last intersection point of the first stratum boundary line, end denotes the last one, and n is the number of equally divided units of the sliding surface, represents from increasing by 1 to n at intervals, which is used to represent the number of the uncut unit, represents the sliding mass unit of the upper stratum comprising the number of the sliding mass unit. When the first stratum boundary line is lower than the groundwater level line, that is, max{ynf_11,ynf_21}<max{ynw_1,ynw_2}, represents the number of the last intersection point of the groundwater level line, and n is the number of equally divided units of the sliding surface, represents from increasing by 1 to n at intervals, which is used to represent the number of the uncut unit, represents the sliding mass unit of the upper stratum comprising the number of the sliding mass unit.

[0092] (3) The number of the middle sliding mass unit consists of two parts, that is, the number of the new sliding mass unit added after being cut by multiple geological boundary lines and the number of the initial uncut unit that is only cut by one geological boundary line and retained. Therefore, the number of the sliding mass unit comprised in the middle stratum sliding mass unit can be expressed as element_stratum ii :

[0093]

[0094] In the formula, when (max{ynf_1 ii ,ynf_2 ii}>max{ynw_1,ynw_2} and max{ynf_1 ii-1 ,ynf_2 ii-1}>max{ynw_1,ynw_2}), it indicates that the groundwater level line is above the ii-th and (ii-1)-th stratum boundary lines; (max{ynf_1 ii ,ynf_2 ii}<max{ynw_1,ynw_2} and max{ynf_1 ii-1 ,ynf_2 ii-1}<max{ynw_1,ynw_2}) indicates that the groundwater level line is below the ii-th and (ii-1)-th stratum boundary lines; in this case, represents the number of the last intersection point of the ii-th stratum boundary line, represents the number of the last intersection point of the stratum boundary of the ii-1-th layer, represents from incrementing by 1 to is used to represent the number of a unit that is only cut by one geological boundary but retains the initial uncut state, represents the landslide mass unit of the intermediate stratum contains the number of the landslide mass unit. When (max{ynf_1 ii ,ynf_2 ii}>max{ynw_1,ynw_2} and max{ynf_1 ii-1 ,ynf_2 ii-1}<max{ynw_1,ynw_2}) it means the groundwater level line is above the stratum boundary of the ii-th layer and below the stratum boundary of the ii-1-th layer, at this time, represents from incrementing by 1 to represents the number of a unit that is only cut by one geological boundary but retains the initial uncut state, represents the landslide mass unit of the intermediate stratum contains the number of the landslide mass unit.

[0095] (4) The general form of the number of landslide mass units contained in each stratum is expressed as follows:

[0096]

[0097] where w represents the number of each stratum, with a value range of w=1,2,…,nn.

[0098] Step 7: Summarize the node numbers contained in each layer of landslide mass units, and assign physical and mechanical parameters to each layer of landslide mass units to provide calculation parameters for subsequent solution.

[0099] (1) Summarize the node numbers contained in each layer of landslide mass units:

[0100] According to the numbers of landslide masses contained in each stratum obtained in step 6 obtain the contained landslide mass node numbers which are expressed as:

[0101]

[0102] where, represents the number of landslide masses contained in each stratum, num_element num represents the updated contained node number of the cut landslide mass unit, represents the node number contained in the landslide mass unit of the layer stratum boundary, w represents the number of each stratum, with a value range of w=1,2,…,nn.

[0103] (2) Assign physical and mechanical parameters to the corresponding sliding body units of each stratum, expressed as:

[0104] ①Unit density:

[0105] In the formula, This represents the number of the sliding body unit contained in each stratum, and w represents the stratum number, with a value range of w = 1, 2, ..., n. Indicates the first Unit weight of the sliding body at the boundary of the stratigraphic layers.

[0106] ②Unit cohesion:

[0107] In the formula, Indicates the first Cohesion of sliding body units at the stratigraphic boundary.

[0108] ③Internal friction angle of the unit:

[0109] In the formula, Indicates the first The friction angle within the sliding body unit at the boundary between strata.

[0110] ④ Unit pore water pressure:

[0111] In the formula, Indicates the first Pore ​​water pressure of sliding body units at the strata boundary.

[0112] Step 8: Using MATLAB, plot the total node positions according to the coordinates point_xy corresponding to the total node number, and label the total node number point_num; plot the nodes according to the node numbers num_element contained in the cut sliding body elements. num Draw the cut elements and the centroid_element position of the new elements. Mark the updated total number n_element of the cut sliding body elements at the centroid position. num ; and the stratigraphic boundary n_formation ii Draw the graph along the groundwater level n_water. Use the visualization results to verify the correctness of the node numbering and sliding body elements after cutting.

[0113] Compared with the prior art, the present invention has the following advantages:

[0114] This invention proposes a preprocessing method for dynamic searching of complex strata slip surface subdivision based on a global analysis approach. Existing preprocessing methods based on the global analysis approach do not consider the cutting of slip surface units by geological boundaries, making it difficult to account for the influence of structural parameters such as unit weight and pore water pressure of different strata on the slip surface safety factor. While existing technologies can easily implement slip surface unit cutting using existing MATLAB programs for fixed slip surface coordinates, they are less effective for dynamic slip surface searches where slip surface coordinates change in real time. Different situations arise where the slip surface and geological boundaries cut slip surface units, easily resulting in irregular polygonal slip surface units. A single unit numbering scheme is insufficient to address these irregular polygonal slip surface units, making it impossible to accurately calculate their area and consequently, calculate the influence of structural parameters such as unit weight and pore water pressure between different strata on the slip surface safety factor. Therefore, the challenge of this invention lies in accurately determining the location and number of nodes of the irregular polygonal slip surface units that need to be replaced, thereby accurately calculating the area of ​​the slip surface units. This invention proposes to replace the corresponding nodes of irregular polygonal sliding units at different positions after cutting (i.e., upper, middle, and lower sliding units) based on the initial uncut sliding unit number, rather than re-numbering them. It also proposes to process sliding units at different positions within the same layer after cutting (middle and first / last sliding units) according to the number of stratigraphic boundaries cut. This approach is more conducive to considering the cutting of geological boundaries by different sliding surfaces during dynamic search and is also easier to implement in programming. Attached image description:

[0115] Figure 1 The flowchart of this invention

[0116] Figure 2 This is a geological diagram of the foundation pit in this invention.

[0117] Figure 3 Schematic diagram of the smooth surface entrance / exit

[0118] Figure 4 The search process involved cutting through units using four geological boundary lines and groundwater level lines.

[0119] Figure 5 The search process involved cutting through the unit using three geological boundary lines. Detailed implementation method:

[0120] To facilitate understanding and implementation of the present invention by those skilled in the art, the present invention will be further described in detail below with reference to specific embodiments. It should be understood that the embodiments described herein are for illustrative and explanatory purposes only, and all technologies implemented based on the content of this invention fall within the scope of this invention.

[0121] Example 1:

[0122] This case study involves a more complex geological formation compared to the scenarios described above. The excavation pit comprises four geological strata. Specific dimensions of the excavation pit are as follows: Figure 2 As shown in Table 1, the formation physical and mechanical parameters are as follows:

[0123] Step 1: Input the coordinates of the solution domain boundary nodes and the entry / exit coordinates of the sliding surface search.

[0124] (1) Input the coordinates of the boundary nodes of the solution domain:

[0125]

[0126] In the formula, i represents the solution domain boundary node number, i = 1, 2, ..., boundary, and boundary represents the total number of solution domain boundary nodes, boundary = 6.

[0127] (2) Coordinates of the slope top node:

[0128] (x_e e ,y_e e = [10, 23]

[0129] In the formula, e is the node number at the top of the slope, e = 1, 2, ..., up, and up is the number of nodes at the top of the slope, up = 1.

[0130] (3) Set the coordinates of the sliding surface search entry point:

[0131]

[0132] In the formula, a represents the exit node number of the sliding surface search, a = 1, 2, ..., exit, and exit represents the total number of exit nodes of the sliding surface search, exit = 7.

[0133] (4) Coordinates of the exit point for the sliding surface search:

[0134]

[0135] In the formula, b represents the entry node number of the sliding surface search, b = 1, 2, ..., entry, and entry represents the total number of entry nodes of the sliding surface search, entry = 7.

[0136] The entry point a and exit point b of the sliding surface determine the range of the dynamic search of the sliding surface. Figure 2 This is a schematic diagram of the coordinates of the entrance and exit of the sliding surface.

[0137] Step 2: Initial number of sliding body elements, initial sliding body element numbers, and node numbers:

[0138] (1) Set the initial sliding surface with the number of segments n = 40, the inlet coordinates (x_a2; y_a2) = (8, 12), and the outlet coordinates (x_b6; y_b6) = (23, 23) for analysis.

[0139] (2) The length of the horizontal coordinate of each segment of the sliding body element is...

[0140] (3) Point c, the point where the sliding surface is evenly divided c The coordinates of (c = 1, 2, ..., 41) can be represented as: (x_c) c ,y_c c ); The x-coordinate of the evenly distributed sliding surface node in the lower layer of the sliding body element is x_c c =x_b6 + x_element·(c-1) = 23 + 0.375·(c-1); Point o is a point on the perpendicular bisector of line segment ab, and its x-coordinate is... Mean slope k of the slip surface a-b =-(x_a2-x_b6) / (y_a2-y_b6)=15 / 11=1.36; Average length of the sliding surface x_m on the horizontal axis=(x_a2+x_b6) / 2=15.5; Average length of the sliding surface y_m on the vertical axis=(y_a2+y_b6) / 2=17.5, Vertical axis y_o=k a-b ·(x_o-x_m)+y_m=1.36·(30-15.5)+17.5=37.22, the distance between point o and point a The ordinates of the sliding surface nodes in the lower layer of the sliding body element are evenly distributed.

[0141] (4) The point d of the slope is the even division point d The coordinates of (d = 41, 42, ..., 81) can be represented as: (x_d) d ,y_d d ); x_d, the abscissa of the uniformly distributed slope node in the lower layer of the sliding body element. d =x_b6 + x_element·(d-1) = 23 + 0.375·(d-1). The ordinate y_d of the evenly distributed slope node in the lower layer of the sliding body element. d =y_b6+(y_e e -y_b6) / (x_e e -x_b6)·(x_d d -x_b6)=23+0=23.

[0142] (5) Initial sliding element number n_element_s p (p = 1, 2, ..., 40), the intermediate element number of the initial sliding body element is: n_element_s pp=pp(pp=2,…,39), the first and last elements of the initial sliding body element are numbered n_element_s ppp =ppp(ppp=1,40);

[0143] (6) The node number of the intermediate element of the initial sliding body element, num_element_s pp (pp=2,…,39), taking the second element as an example (pp=2): num_element_s2=[c2,c3,d3,d2]=[2,3,43,42]; the initial sliding body element's first and last element node numbers num_element_s ppp (ppp=1,40), the first unit is a triangle (ppp=1): num_element_s1=[c1,c2,d1]=[1,2,42].

[0144] Step 3: Storage of geological boundary intersection information:

[0145] (1) Stratigraphic boundary n_formation ii (ii=1,2,…,5), groundwater level n_water, nn=5.

[0146] (2) The two endpoints of the stratigraphic boundary are numbered as: nf_1 ii With nf_2 ii (ii = 1, 2, ..., 5), its coordinates can be represented as:

[0147]

[0148]

[0149] (3) The two endpoints of the groundwater level line are numbered as nw_1 and nw_2, and their coordinates can be represented as:

[0150] (xnw_1,ynw_1)=(10,13)

[0151] (xnw_2,ynw_2)=(30,13)

[0152] (4) The number of intersections of the boundary lines of each stratigraphic layer is: n_intersection ii =[7; 27; 2; 19; 0](ii = 1, 2, ..., 5), the number of intersections of the groundwater level lines is: n_intersection water =16.

[0153] (5) The intersection points of groundwater levels can be represented as:

[0154]

[0155] The vertical node number corresponding to the jjth intersection point of the groundwater level lines is denoted as:

[0156] n_slide_water jj =[6~21]

[0157] The vertical node number corresponding to the jjth intersection point of the groundwater level lines in the slope direction is denoted as:

[0158] n_slope_water jj =[47~62]

[0159] (6) Stratigraphic boundary of the iith layer, kkth layer ii The intersection point numbers can be represented as:

[0160]

[0161] Stratigraphic boundary of layer ii, kk ii The vertical direction corresponding to the sliding surface node number of the intersection point is denoted as:

[0162]

[0163] Stratigraphic boundary of layer ii, kk ii The vertical node numbers corresponding to the intersection points on the slope are denoted as follows:

[0164]

[0165] (7) Store the intersection numbers of each stratum, slip surface nodes, and slope surface nodes together as a total node number, point_num, represented as:

[0166]

[0167] The coordinates corresponding to the summary point number are stored as point_xy as follows:

[0168]

[0169] Step 4: Update the numbers of the cut sliding body units and their included nodes based on the coordinates of the intersection points of the geological boundary lines. Then:

[0170] Step 4.1: Replacement scheme for lower-level sliding body unit numbering and node numbering:

[0171] The groundwater level is at the lowest layer, i.e., max{ynf_1 end ynf_2 end}>max{ynw_1,ynw_2}, Element node numbering replacement scheme: The lower sliding body element is divided into two parts. One part is not cut by the waterline, and the element number and the number of its contained nodes remain unchanged. The other part retains the unit numbers, but the node numbers need to be modified. Here The unit contains nodes For example, the change is: [7,8,49,48]→[7,8,139,138].

[0172] Step 4.2: Replacement scheme for upper-layer sliding body unit numbering and node numbering:

[0173] The upper sliding body unit is cut by three stratigraphic boundaries, n_formation 1～3 The upper-level unit numbering replacement scheme is as follows: the first stratigraphic boundary line is higher than the groundwater level, i.e., max{ynf_11,ynf_21}>max{ynw_1,ynw_2}; the second stratigraphic boundary line is higher than the groundwater level, i.e., max{ynf_12,ynf_22}>max{ynw_1,ynw_2}; and the third stratigraphic boundary line is higher than the groundwater level, i.e., max{ynf_13,ynf_23}>max{ynw_1,ynw_2}.

[0174] The first stratigraphic boundary line n_formation1 contains element numbers:

[0175] The second stratigraphic boundary line n_formation2 includes element numbers:

[0176] The third stratigraphic boundary line n_formation3 includes element numbers:

[0177] Here The unit contains nodes For example, the change is: [13,14,55,54] → [90,91,55,54]

[0178] Step 4.3: Replacement scheme for intermediate layer sliding body element numbering and node numbering:

[0179] The intermediate layer has two parts, n_formation 2～4 Inter-stratigraphic units and n_formation 1,4The strata and groundwater level n_water inter-unit numbering replacement scheme: the second and third strata boundary lines are higher than the groundwater level, i.e., max{ynf_12,ynf_22}>max{ynw_1,ynw_2} and max{ynf_13,ynf_23}>max{ynw_1,ynw_2}. The third and fourth strata boundary lines are higher than the groundwater level, i.e., max{ynf_12,ynf_22}>max{ynw_1,ynw_2}. _13,ynf_23}>max{ynw_1,ynw_2} and max{ynf_14,ynf_24}>max{ynw_1,ynw_2}, the first and fourth stratigraphic boundaries are higher than the groundwater level, that is, max{ynf_11,ynf_21}>max{ynw_1,ynw_2} and max{ynf_14,ynf_24}>max{ynw_1,ynw_2}:

[0180] n_formation 2～4 Interstratal units include unit numbers:

[0181] n_formation 1,4 Stratigraphy and groundwater level n_water inter-strata elements include element numbers:

[0182]

[0183] Here The unit contains nodes For example, the change is: [13,14,55,54] → [119,120,91,90]

[0184] Here The unit contains nodes For example, the change is: [13,14,55,54] → [144,145,120,119]

[0185] Step 4.4: Summarize the element numbers and node numbers after cutting:

[0186] (1) Update the total number of the cut sliding body unit to:

[0187] n_element num =[n_element 1～5 n_element end ;n_element_s]

[0188] (2) The nodes of the cut sliding body element are numbered as follows:

[0189] num_elementnum =[num_element 1～5 ;num_element end ;num_element_s]

[0190] Step 5: Use MATLAB to solve for and store the centroid_element and area_element of the new element after cutting:

[0191] (1) The centroid of the new element after cutting is: centroid_element

[0192] (2) The area of ​​the new element after cutting is: area_element;

[0193] Step 6: Group the unit numbers contained in each stratum:

[0194] (1) Numbering of the lowest layer of sliding body unit:

[0195] (2) From the first stratigraphic boundary to the third stratigraphic boundary (n_formation) 1～3 If all are above the groundwater level (n_water), then the upper stratum sliding body unit number is:

[0196]

[0197] (3) From the second stratigraphic boundary to the fourth stratigraphic boundary (n_formation) 2～4 All are above the groundwater level (n_water). The second stratum sliding body unit number is:

[0198]

[0199] (4) From the third stratigraphic boundary to the fourth stratigraphic boundary (n_formation) 3～4 All are above the groundwater level (n_water), and the third stratum sliding body unit number is:

[0200]

[0201] (5) General form of the numbering of sliding body units contained in each stratum for:

[0202]

[0203] Step 7: Assign physical and mechanical parameters to the corresponding sliding body elements in each stratum:

[0204] (1) Based on the number of the sliding bodies contained in each stratum obtained in step 6 Find the node numbers of the included sliding bodies. Represented as:

[0205]

[0206] (2) Bulk density of each stratigraphic unit:

[0207] (3) Cohesion of each stratigraphic unit:

[0208] (4) Internal friction angle of each stratigraphic unit:

[0209] (5) Pore water pressure in each stratum unit:

[0210] Step 8: Draw the diagram showing the element numbers and node numbers of the sliding body after the first search surface cut:

[0211] Figure 4 The cutting element partition diagram obtained by analyzing the initial slip surface in the example above, with inlet coordinates (x_a2; y_a2) = (8, 12) and outlet coordinates (x_b6; y_b6) = (23, 23), shows the centroid position of the new slip surface after the initial slip surface is cut by the geological boundary line. It can be seen that the centroid position changes as the area of ​​the slip surface changes after cutting, demonstrating the correctness of this invention. To illustrate the results of the replacement of element numbers during the search process, two representative element partition diagrams are selected for display. Figure 5 This is a diagram showing the segmentation of the unit cut by three geological boundary lines during the search process.

[0212] Table 1. Physical and mechanical parameters of the foundation pit strata

[0213]

Claims

1. A preprocessing method for dynamic searching and profiling of slip surfaces in complex formations based on a global analysis approach, characterized in that, Includes the following steps: Step 1: Set the exit and entry coordinates of the sliding surface search, which determines the range of the sliding surface dynamic search; Step 2: Divide the surface from a single search into equal parts according to the length of the x-axis. Each sliding body element is assigned a number, and the nodes of the sliding body elements are numbered in a counterclockwise direction. Step 3: Find the intersection points of the geological boundary line and the initial sliding body unit, and number the intersection points in order from top to bottom according to the vertical coordinate of the geological boundary line; the geological boundary line includes the stratigraphic boundary line and the groundwater level line; Step 4: Based on the relative positions of the sliding body units after being cut by the geological boundary line, i.e., the upper, middle and lower layers, and based on the initial sliding body unit numbering before cutting, replace the corresponding nodes of the irregular polygonal sliding body units in different positions after cutting, instead of re-numbering them; Step 4.1: Replacement scheme for the lower-level sliding body unit number and the included node number: The lower-level unit retains the unit number of the uncut initial unit, and the slope node number of this unit is replaced with the number of the intersection of the geological boundary line located at the lowest level in the vertical coordinate; Step 4.2: Replacement scheme for upper-layer sliding body unit number and its included node number: The difference from Step 4.1 is that this layer of units consists of two parts. The first part is the part not cut by the geological boundary line, which uses the initial sliding body unit number and its included node number. The second part is the newly added sliding body unit after being cut by the geological boundary line. Its unit number is added based on the unit number of the first part. The sliding surface node number of the initial sliding body unit is replaced with the intersection point number of the geological boundary line at the top layer on the vertical coordinate. Step 4.3: Replacement scheme for intermediate layer unit number and included node number: This layer unit consists of two parts: the part not cut by the geological boundary line and the newly added sliding body unit after being cut by the geological boundary line. The replacement method is the same as in Step 4.

2. Step 4.4: Summarize the node numbers of the new sliding body elements after cutting and the nodes contained in the sliding body elements; Step 5: Use MATLAB to solve and store the centroid coordinates and area of ​​the new sliding body element after cutting; Step 6: Group the sliding body units contained in each stratum according to the stratum number to prepare for assigning physical and mechanical parameters to the corresponding units of each stratum in the future; Step 7: For each stratum containing a sliding body number obtained in Step 6, assign physical and mechanical parameters to the corresponding sliding body unit of each stratum. The parameters include unit weight, cohesion, internal friction angle and pore water pressure. Step 8: Use MATLAB to draw the element numbering and node numbering diagram of the cut sliding body.

2. The method according to claim 1, characterized in that: Step 1: Input the coordinates of the boundary nodes of the solution domain and the coordinates of the exit and entry nodes of the sliding surface dynamic search; Step 1.1: Input the coordinates of the boundary nodes of the solution domain , , This indicates the node number of the solution domain boundary. This represents the total number of boundary nodes of the solution domain. Indicates the first x-coordinates of the boundary nodes of the solution domain Indicates the first The x-coordinates of the boundary nodes of the solution domain; where the coordinates of the slope top node are included. , ; Number the nodes at the top of the slope. This refers to the number of nodes at the top of the slope. Step 1.2: Set the exit coordinates for the sliding surface search , , Indicates the exit node number for the slip surface search. This indicates the total number of exit nodes in the smooth surface search. Indicates the first The x-coordinate of the exit node for each smooth surface search Indicates the first The vertical coordinate of the exit node for each sliding surface search; Set the coordinates of the slip surface search entry point. , , Indicates the entry node number for the smooth surface search. This indicates the total number of entry nodes for the smooth surface search. Indicates the first The x-coordinate of the entry node for the smooth surface search. Indicates the first The ordinate of the entry node for the surface search; the exit point of the surface. With the entrance point This determines the range of the dynamic search for the smooth surface; Step 2: Divide the surface from a single search into equal parts according to the length of the x-axis. Each unit is numbered in a counter-clockwise direction. The more data points there are, the higher the calculation accuracy but the lower the efficiency; the total abscissa of the sliding surface is divided equally. If the segment is a single sliding body element, then the x-coordinate length is... The initial sliding body element number and node number are expressed as follows: Step 2.1: The nodes of the lower layer of the sliding surface of the sliding body element are numbered as follows: , , Indicates the initial number of sliding body units Increment the quantity by 1, and evenly distribute the x-coordinates of the sliding surface nodes in the lower layer of the sliding body unit. ; The ordinates of the sliding surface nodes in the lower layer of the sliding body element are evenly distributed. ;in, A point is a line segment A point on the perpendicular bisector has the following x-coordinate and y-coordinate: ;point With point distance Mean slope of the slip surface Average length of the horizontal axis of the sliding surface ; Average length of the sliding surface (ordinate) ; Step 2.2: The node numbers of the upper layer of the sliding body unit's uniformly distributed slope surface are as follows: , , Indicates the initial number of sliding body units Multiply the quantity by 2 and add 1 to get the x-coordinate of the slope node in the lower layer of the sliding body unit. The ordinate of the lower layer of the sliding body unit's uniformly distributed slope surface nodes ; Step 2.3: The initial sliding body unit number is , , Assign values ​​to the sliding body elements; the first and last sliding body elements need to have their shapes determined, and can be referred to as the first and last elements. The remaining elements in the middle are referred to as the middle elements, which are quadrilaterals. Numbering starts counter-clockwise from the bottom left node. The first two points are sliding surface points located below the quadrilateral, and the last two are slope surface nodes located above the quadrilateral. The "above" and "below" mentioned later refer to the same orientation here. Therefore, the initial sliding body elements are numbered as follows: for: , , Assign values ​​to the intermediate sliding body unit numbers. Indicates the initial number of sliding body units Decrease by 1, its node number for: , Assign values ​​to intermediate sliding body unit numbers The value is increased by 1 from the base value. Indicates the first Each sliding body unit has its lower layer evenly divided sliding surface node numbered. Indicates the first Each sliding body unit has its upper layer slope node numbered evenly. Indicates from node The initial arrangement of the four nodes is counter-clockwise; the first and last elements of the initial sliding body are numbered as follows: , , The values ​​for the first and last sliding body unit numbers are: and The set; if If it is a quadrilateral element, then the node numbers of the first and last sliding body elements are... for: ;like If it is a triangular element, then the node number is... for: ; Step 3: Numbering of stratigraphic boundaries for: , , Numbering of stratigraphic boundaries The total number of stratigraphic boundaries; groundwater level. The two endpoints of the stratigraphic boundary are numbered as follows: and Its coordinates are represented as: and , Indicates the first The x-coordinate of the first endpoint of the stratigraphic boundary line. Indicates the first The ordinate of the first endpoint of the stratigraphic boundary. Indicates the first The x-coordinate of the second endpoint of the stratigraphic boundary line Indicates the first The ordinate of the second endpoint of the stratigraphic boundary; The two endpoints of the groundwater level are numbered as follows: and Its coordinates are represented as: and , This represents the x-coordinate of the first endpoint of the groundwater level. This represents the ordinate of the first endpoint of the groundwater level. This represents the x-coordinate of the second endpoint of the groundwater level. The vertical coordinate of the second endpoint of the groundwater level line is represented; the intersection of the line segment and the sliding body element is solved using MATLAB programming. The number of intersections of the stratigraphic boundaries is The number of intersections of the groundwater level lines is Following the top-to-bottom order of the vertical coordinates of the stratigraphic boundary and the groundwater level, number the coordinates of the intersection points of the stratigraphic boundary and the groundwater level. To facilitate subsequent classification of stratigraphic units, it is necessary to store the vertical slip surface node number and slope surface node number corresponding to the intersection points. The specific numbers can be obtained using the MATLAB intersection point calculation program. The groundwater level is located above the stratigraphic boundary. Therefore: (1) Intersection number of groundwater level lines for: ； ； In the formula, This refers to the number of intersections of groundwater levels; (2) Groundwater level The vertical direction corresponding to the sliding surface node number of the intersection point is denoted as: ; (3) Groundwater level The vertical node numbers corresponding to the intersection points on the slope are denoted as follows: ; (4) Groundwater level The coordinates of the intersection points are: ; In the formula, Indicates the first The x-coordinate of the intersection of the groundwater level lines Indicates the first The vertical coordinate of the intersection of the groundwater level lines; (5) No. Stratigraphic boundary line Intersection number for: ; ;, For the first Number of intersections of stratigraphic boundaries; (6) No. Stratigraphic boundary line The vertical direction corresponding to the sliding surface node number of the intersection point is denoted as: ; (7) No. Stratigraphic boundary line The vertical node numbers corresponding to the intersection points on the slope are denoted as follows: ; (8) No. Stratigraphic boundary line The coordinates of the intersection points are represented as follows: ; In the formula, Indicates the first Stratigraphic boundary line The x-coordinates of the intersection points Indicates the first Stratigraphic boundary line The ordinates of the intersection points; (9) Store the intersection numbers of each stratum, slip surface nodes, and slope surface nodes together as the total node number. , is represented as: ; (10) Store the coordinates corresponding to the summary point number as , is represented as: ； Step 4: Based on the relative positions of the cut landslide units, namely the upper landslide unit, the middle landslide unit, and the lower landslide unit, the upper landslide unit refers to the landslide unit located after the uppermost geological boundary line is cut, the lower landslide unit refers to the landslide unit located after the lowermost geological boundary line is cut, and the remaining units located in the middle layer after being cut are all called the middle landslide units. Instead of renumbering, the corresponding nodes of irregular polygonal sliding body elements in different positions after cutting are replaced based on the initial uncut sliding body element number. Step 4.1: Replacement scheme for lower-level sliding body unit numbering and node numbering: (1) Replacement scheme for the numbering of the lower sliding body unit: The lower sliding body unit number is represented as Retain the sliding body number when the unit is not cut, where This indicates that the cut landmass unit is located below the lowest geological boundary, i.e., the lower landmass unit. This indicates the value of the sliding body element after cutting. Represented as: ； In the formula, and These represent the ordinates of the two endpoints of the boundary line of the lowest stratum. This represents the maximum value of the ordinate between the two endpoints of the boundary line of the lowest stratum; and These represent the ordinates of the two endpoints of the groundwater level line. This represents the maximum value of the ordinate between the two endpoints of the groundwater level line; If the maximum ordinate value between the two endpoints of the lowest stratum boundary is greater than the maximum ordinate value between the two endpoints of the groundwater level, then the lowest stratum boundary is higher than the groundwater level. The lower sliding body unit number... The values ​​of the sliding body elements after cutting The values ​​of the sliding body elements after cutting , Indicates the number of intersections of groundwater levels. This indicates that the number of intersections of the groundwater level lines is reduced by 1; conversely, This indicates that the maximum value of the ordinate at both ends of the boundary line of the lowest stratum is less than the maximum value of the ordinate at both ends of the groundwater level line, and the values ​​of the sliding body elements after cutting... , This indicates the number of intersections of the boundary lines of the lowest strata. This indicates that the number of intersections of the lowest stratum boundary lines is reduced by 1. (2) Replacement scheme for node numbers of the lower intermediate sliding body unit: Similar to step 2, the shapes of the first and last elements of the lower-level sliding body element need to be determined, and the middle sliding body element is a quadrilateral; the node number of the middle sliding body element of the lower-level sliding body element is represented as follows. ,in This indicates that the cut landmass unit is located below the lowest geological boundary, i.e., the lower landmass unit. This indicates the value of the intermediate sliding body unit number after cutting; the node replacement approach is to change the node numbers of some sliding body units from slope surface nodes to the intersection points of the lowest geological boundary lines. for: ； In the formula, when When the boundary of the lowest stratum is higher than the groundwater level, the value of the intermediate sliding body unit number after cutting is represented as follows: ,in Indicates the number of intersections of groundwater levels. This indicates that the number of intersections of the groundwater level lines is reduced by 2; the slope node numbers of the intermediate sliding body units located above after cutting are replaced with the groundwater level line intersection numbers, i.e. Depend on Become ,in, Assign values ​​to intermediate sliding body unit numbers The value is increased by 1 from the base value. Indicates the first Each sliding body unit has its lower layer evenly divided sliding surface node numbered. Indicates the first Each sliding body unit has its upper layer slope node numbered evenly. Indicates the initial intermediate sliding body element from node Begin arranging the four nodes in a counter-clockwise order; Indicates the first Numbering of the intersection points of the groundwater level lines This indicates that the intermediate sliding body element of the lower sliding body element after replacement is from node [node name missing]. Start by arranging the four nodes in a counter-clockwise order; conversely, when... When the boundary of the lowest stratum is below the groundwater level, the value of the intermediate sliding body unit number after cutting is represented as follows: ,in This indicates the number of intersections of the boundary lines of the lowest strata. Subtracting 2 from the number of intersections of the lowest stratigraphic boundary line indicates that the node number of the intermediate sliding body unit located above it is replaced with the intersection number of the lowest stratigraphic boundary line. Depend on Become ,in, Indicates the first Numbering of the intersection of the lowest stratigraphic boundary lines This indicates that the intermediate sliding body element of the lower sliding body element after replacement is from node [node name missing]. Begin arranging the four nodes in a counter-clockwise order; (3) Replacement scheme for node numbers of the lower-level first and last sliding body units: The node numbers of the first and last elements of the lower sliding body element are represented as follows: , This indicates the value of the first and last sliding body unit number; if the first and last units of the lower sliding body unit are quadrilaterals, the replacement method is the same as that of the middle unit; if they are triangular, the upper slope nodes of the first and last units are changed to the intersection of the corresponding lowest geological boundary line, and the node numbers contained in the lower first and last sliding body triangular units after cutting are... Represented as: ； In the formula, if This means that the boundary line of the lowest stratum is higher than the groundwater level. In this case, the values ​​for the numbers of the first and last sliding body units after cutting are represented as follows: ,in Indicates the number of intersections of groundwater levels. The number of intersections of the groundwater level lines is reduced by 1; the first and last unit nodes are numbered. Slope node number located above Replace with the intersection number of the groundwater level line The sliding surface node number located below Deletion, i.e., the first and last unit node numbers. Numbered by the initial sliding body element nodes Replace with ;in, Assign values ​​to intermediate sliding body unit numbers The value is increased by 1 from the base value. Indicates the first Each sliding body unit has its lower layer evenly divided sliding surface node numbered. Indicates the first Each sliding body unit has its upper layer slope node numbered evenly. Indicates the initial head and tail sliding body elements from node Begin arranging the four nodes in a counter-clockwise order. Indicates the first Numbering of the intersection points of the groundwater level lines; on the contrary, This means that the boundary line of the lowest stratum is below the groundwater level; at this time, the values ​​of the first and last sliding body unit numbers after cutting are represented as follows: ,in This indicates the number of intersections of the boundary lines of the lowest strata. Subtract 1 from the number of intersections of the lowest stratigraphic boundary; then number the nodes of the first and last sliding body units. Slope node number located above Replace with the intersection number of the lowest stratigraphic boundary line ,Right now Depend on Become ; The numbering of the lower sliding body unit and the numbering of its contained nodes have been updated after the cutting. Step 4.2: Replacement scheme for upper-layer sliding body unit numbering and node numbering: The sliding body unit consists of two parts: the first part is the uncut unit, which retains the original unit number and the node number it contains; the second part is the unit cut by the geological boundary line; only the corresponding number of the cut unit and the node number it contains need to be replaced and updated. (1) Replacement scheme for the numbering of the upper sliding body unit: Since only the cut elements are considered, the numbers of the uncut elements and the containing node numbers remain unchanged. Therefore, the number of the newly added upper-level element after cutting is represented as follows: , This indicates the range of newly added sliding body unit numbers after cutting. This indicates that the cut sliding body unit is located above the first geological boundary line; for: ； In the formula, and These represent the ordinates of the two endpoints of the first stratigraphic boundary line. This represents the maximum value of the ordinate between the two endpoints of the first stratigraphic boundary line; This represents the maximum value of the ordinate between the two endpoints of the groundwater level line; If the maximum ordinate value between the two endpoints of the first stratum boundary is less than the maximum ordinate value between the two endpoints of the groundwater level, it indicates that the first stratum boundary is below the groundwater level. In this case, the range of newly added sliding body unit numbers after cutting is determined. , Indicates the number of intersections of groundwater levels. This indicates the number of intersections of the groundwater level lines minus 1; the number of newly added sliding body units in the upper layer after cutting. Initial number of sliding body units With the range of newly added sliding body unit numbers The sum of Conversely, when This indicates that the maximum value of the ordinate at both ends of the first stratigraphic boundary line is greater than the maximum value of the ordinate at both ends of the groundwater level line. Therefore, the range of newly added sliding body unit numbers after cutting is [not specified]. , This indicates the number of intersections of the first-layer stratigraphic boundary lines. This indicates that the number of intersections of the first stratigraphic boundary line is reduced by 1; (2) Replacement scheme for the node number of the upper intermediate sliding body unit: When the upper sliding body unit is not cut, the upper nodes are slope nodes and the lower nodes are sliding surface nodes. The node numbers of the uncut units remain unchanged. After cutting, the lower sliding surface nodes need to be changed to the intersection numbers of the first geological boundary line. Similar to step 2, the shapes of the first and last sliding body units need to be determined. Since the middle sliding body unit is a quadrilateral, the node numbers of the middle sliding body unit are added after cutting. ,in This indicates that the cut landmass unit is located above the first geological boundary line, i.e., the upper landmass unit. This indicates the value of the intermediate sliding body unit number after cutting; for: ； In the formula, This indicates that the first stratum boundary is below the groundwater level. In this case, the newly added sliding body unit after cutting includes the range of node numbers. After cutting, the node numbers of the sliding surface below the newly added intermediate sliding body unit are replaced with the intersection numbers of the groundwater level lines, that is, the node numbers contained in the intermediate sliding body unit. Depend on Become ;on the contrary, This indicates that the boundary of the first stratigraphic layer is higher than the groundwater level, and the range of newly added sliding body unit numbers after cutting is determined by this. The node numbers contained in the intermediate sliding body element are... Depend on Become , Indicates the first Numbering of the intersection points of the first-layer stratigraphic boundary lines; (3) Replacement scheme for node numbers of the upper-level first and last sliding body units: If the first and last units of the upper sliding body unit are quadrilaterals, the representation method is the same as that of the middle unit. The difference here from step 4.1 is that the sliding surface is generally not a horizontal straight line, but is composed of short line segments with a certain angle. Therefore, after being cut by the geological boundary line, the first and last units are not regular triangles, but irregular polygons. The node numbers contained in the first and last units of the upper sliding body unit are... ,in This indicates that the cut landmass unit is located above the first geological boundary line (upper landmass unit). The values ​​representing the unit numbers of the first and last sliding bodies; Represented as: ； In the formula, if This indicates that the boundary of the first stratum is higher than the groundwater level, and the first unit of the upper sliding body unit is... At that time, the slip surface node number is replaced with the intersection number of the first stratigraphic boundary line, i.e. Depend on Replace with , Indicates the first Numbering of the intersection points of the first-layer stratigraphic boundary lines; the last unit of the upper-layer sliding body unit. At that time, the sliding body unit was cut into pentagons, and the sliding surface node numbers were replaced with the intersection numbers of the first stratigraphic boundary lines, i.e. Depend on Replace with Conversely, when This indicates that the boundary of the first stratum is lower than the groundwater level, and the first unit of the upper sliding body unit... At that time, the slip surface node number will be replaced with the groundwater level intersection number, i.e. Depend on Replace with The last unit of the upper sliding body unit. At that time, the sliding body element was cut into pentagons, and the sliding surface node numbers were replaced with the groundwater level intersection numbers, i.e. Depend on Replace with ; The unit numbers and their constituent node numbers after the upper layer was cut have been updated; Step 4.3: Replacement scheme for intermediate layer sliding body element numbering and node numbering: This layer unit consists of two parts: the first part is a sliding body unit cut by only one geological boundary line, and the second part is a sliding body unit cut by two or more geological boundary lines. Based on the node number of the uncut sliding body unit, the corresponding intersection points of the cutting units are replaced in order from top to bottom according to the stratigraphic boundary line and groundwater level line intersecting with the sliding body unit. Since the replacement is carried out step by step according to the intersection points of the cutting units, the node number of the irregular polygon can be obtained even for the constantly changing sliding surface node situation in the dynamic search of the sliding surface. (1) Replacement scheme for intermediate layer sliding body unit numbering: For the first part of the sliding body elements in the intermediate layer, retain the initial element number. For the second part of the sliding body elements, new sliding body numbers need to be added. The new sliding body element numbers are as follows: , The geological boundary number indicates the section between the uppermost and lowermost stratigraphic layers from top to bottom. The total number of stratigraphic boundaries. Total number of stratigraphic boundaries Decrease the quantity by 1. This indicates the range of newly added sliding body unit numbers after cutting. Represented as: ； In the formula, This represents the initial total number of uncut units. and They represent the first The ordinates of the two ends of the stratigraphic boundary line Indicates the first The maximum value of the ordinate between the two endpoints of the stratigraphic boundary line; This represents the maximum value of the ordinate between the two endpoints of the groundwater level line; if , indicating the first If the maximum ordinate value between the two endpoints of the stratigraphic boundary line is greater than the maximum ordinate value between the two endpoints of the groundwater level line, then it indicates that the stratum boundary line is... The strata boundary is higher than the groundwater level; at this point, the newly added sliding body unit numbering range after cutting... , Indicates the first Number of intersections of stratigraphic boundaries Indicates the first The number of intersections of stratigraphic boundaries is reduced by 1; New unit number after cutting The total number of uncut units , No. The sum of the intersection numbers of the stratigraphic boundaries and The sum of Conversely, the first If the maximum ordinate value between the two endpoints of the stratigraphic boundary line is less than the maximum ordinate value between the two endpoints of the groundwater level line, then it indicates that the strata boundary line is... The strata boundary line is lower than the groundwater level, that is... At this point, the range of newly added sliding body unit numbers after cutting. , Indicates the number of intersections of groundwater levels. This indicates that the number of intersections of groundwater levels has been reduced by 1. (2) Replacement scheme for the node number of the intermediate sliding body unit in the intermediate layer: For the node numbers of the first part of the intermediate layer sliding body unit, refer to step 4.1 to replace the corresponding nodes. For the node numbers of the second part of the sliding body unit, replace them layer by layer according to the geological boundary line from top to bottom, similar to step 4.

2. The intermediate sliding body unit of the second part of the intermediate layer is quadrilateral, therefore the node numbers contained in the intermediate sliding body unit of the intermediate layer are... , The geological boundary line is indicated by its number, representing the stratigraphic boundary line between the uppermost and lowermost layers from top to bottom. This indicates the value of the intermediate sliding body unit number after cutting; Represented as: ； In the formula, The stratigraphic boundary number indicates the stratigraphic boundary line from top to bottom, excluding the section between the uppermost and lowermost layers. This indicates the total number of stratigraphic boundaries. Indicates the total number of stratigraphic boundaries Decrease the quantity by 1; Indicates the first The stratigraphic boundary of the layer above the stratigraphic boundary. and They represent the first The ordinates of the two ends of the stratigraphic boundary line Indicates the first The maximum value of the ordinate between the two endpoints of the stratigraphic boundary line; Indicates the first The maximum value of the ordinate at both ends of the stratigraphic boundary line is greater than the maximum value of the ordinate at both ends of the groundwater level line, i.e., the th stratigraphic boundary line. The strata boundary line is above the groundwater level. Indicates the first The strata boundary is below the groundwater level. Indicates the first The strata boundary line is above the groundwater level. Indicates the first The strata boundary is below the groundwater level. and Indicates the groundwater level at the 1st Layer and first Above the stratigraphic boundary; and Indicates the groundwater level at the 1st Layer and first Below the stratigraphic boundary; at this point, the value of the intermediate sliding body unit number after cutting. , Indicates the first Number of intersections of stratigraphic boundaries Indicates the first The number of intersections of stratigraphic boundaries is reduced by 2; The intermediate sliding body element contains the node numbering. Depend on Replace with , Indicates the first Stratigraphic boundary line The intersection point number, Indicates the first Stratigraphic boundary line The intersection point number, Indicates the first Stratigraphic boundary line The intersection point number, Indicates the first Stratigraphic boundary line Numbering of each intersection point; and Indicates the groundwater level at the 1st Above the stratigraphic boundary and the first Below the stratigraphic boundary, at this point, the value of the intermediate sliding body unit number after cutting is determined. , Indicates the number of intersections of groundwater levels. This indicates that the number of intersections of groundwater levels is reduced by 2; The intermediate sliding body element contains the node numbering. Depend on Replace with , Indicates the groundwater level line. The intersection point number, Indicates the groundwater level line. Numbering of each intersection point; (3) Replacement scheme for node numbers of the first and last sliding body units in the intermediate layer: If the first and last sliding body units of the intermediate layer are quadrilaterals, the representation method is the same as that of the intermediate units. The difference from step 4.1 is that the slip surface is composed of line segments with a certain angle. During the search process, the changing slip surface and geological boundary will cut off irregular polygons, mostly pentagons, but quadrilaterals or triangles may also appear; the node number contained in the last sliding body unit of the intermediate layer. , The stratigraphic boundary number indicates the stratigraphic boundary line from top to bottom, excluding the section between the uppermost and lowermost layers. The values ​​representing the unit numbers of the first and last sliding bodies; Represented as: ； When the groundwater level is at the Layer and first Above the stratigraphic boundary, that is and Or the groundwater level at the Layer and first Below the stratigraphic boundary line, that is and ; At this point, the values ​​of the unit numbers of the first and last sliding bodies after cutting are... , Indicates the first The number of intersections of stratigraphic boundaries is reduced by 1; When the first and last sliding body elements in the middle layer are triangular, the included node numbers are... Depend on Replace with When it is a quadrilateral, the number of the included nodes. Depend on Replace with When it is a pentagon, the node numbers it contains are... Depend on Replace with When the groundwater level is at the Above the stratigraphic boundary and the first Below the stratigraphic boundary line, that is and At this point, the values ​​of the first and last sliding body unit numbers after cutting are determined. , This indicates that the number of intersections of groundwater levels has been reduced by 1. When the first and last sliding body elements in the middle layer are triangular, the included node numbers are... Depend on Replace with When it is a quadrilateral, the number of the included nodes. Depend on Replace with When it is a pentagon, the node numbers it contains are... Depend on Replace with ; The unit numbers and node numbers of the intermediate layer have been updated after the intermediate layer has been cut. Step 4.4: Summarize the updated sliding body element node numbers Updated node numbers of the sliding body element after cutting Represented as: ； In the formula, This indicates the node number of the intermediate sliding body element in the upper sliding body element. Indicates the node numbers of the first and last elements of the upper sliding body element; Indicates the first Intermediate sliding body unit node numbering of the middle sliding body unit in the stratigraphic boundary. Indicates the first The node numbers of the first and last units of the sliding body unit in the middle layer of the stratigraphic boundary; This indicates the node number of the intermediate sliding body element in the lower-level sliding body element. This indicates the node numbers of the first and last elements of the lower sliding body element. This indicates the value of the intermediate sliding body unit number after cutting. The values ​​for the first and last sliding body unit numbers are given in steps 4.1 to 4.

3. This indicates that the intermediate elements of the upper sliding body element were not cut and the initial element node number was retained; This indicates the range of element numbers for the intermediate elements of the upper sliding body unit that were not cut but retained their initial element node numbers. This range applies when the first stratum boundary is below the groundwater level. , The value of is represented as , This indicates the number of intersections of the first-layer stratigraphic boundary lines. Indicates the initial number of sliding body units Subtract 1; when the boundary line of the first stratum is higher than the groundwater level, i.e. , The value of is represented as , Indicates the number of intersections of groundwater level lines; This indicates that the last element of the upper sliding body element was not cut and the initial element node number was retained; This indicates the range of element numbers for the last element of the upper sliding body element that was not cut and retained its initial element node number. ; Step 5: Use MATLAB to solve for and store the centroids of the new elements after cutting. and area ; Step 6: Group the unit numbers contained in each stratum to prepare for assigning physical and mechanical parameters to the corresponding units of each stratum in the future; (1) The lower-level sliding body unit number remains unchanged. The initial sliding body number is retained. The lower-level stratum sliding body unit number is... , is represented as: ； In the formula, Indicates the lower sliding body unit number; This indicates the range of numbers for the newly added sliding body units after cutting; specific values ​​are given in steps 4.1 to 4.

3. (2) The upper-layer sliding body unit number consists of two parts: the first part is the number of the initially uncut units and the second part is the number of the newly added sliding body units after cutting; therefore, the upper-layer stratum sliding body unit includes the sliding body unit number as follows: : ； In the formula, if This indicates that the boundary of the first stratum is higher than the groundwater level. This indicates the number of the newly added upper-level unit after the cut; This indicates the number of the last intersection point of the first stratigraphic boundary line. Indicates the last one. The number of evenly divided units on the smooth surface. Indicates from Increase every 1 to This is used to indicate the unit number that has not been cut. This indicates that the upper strata sliding body unit includes the sliding body unit number; when the boundary line of the first stratum is lower than the groundwater level, i.e. , This indicates the number of the last intersection of the groundwater level lines. The number of evenly divided units on the smooth surface. Indicates from Increase every 1 to This is used to indicate the unit number that has not been cut. This indicates that the upper stratum sliding body unit includes the sliding body unit number; (3) The intermediate sliding body unit number consists of two parts: the newly added sliding body unit number after being cut by multiple geological boundaries, and the unit number of the initially uncut unit that was only cut by one geological boundary; therefore, the intermediate stratum sliding body unit containing the sliding body unit number is represented as follows: : ； In the formula, when and Indicates the groundwater level at the 1st Layer and first Above the stratigraphic boundary; and Indicates the groundwater level at the 1st Layer and first Below the stratigraphic boundary; at this point... Indicates the first The last intersection point of the stratigraphic boundary is numbered. Indicates the first The last intersection point of the stratigraphic boundary is numbered. Indicates from Increase every 1 to This is used to indicate the unit number that is cut by only one geological boundary line but retains its original uncut state. This indicates that the intermediate strata sliding body unit contains sliding body unit numbers; when and Indicates the groundwater level at the 1st Above the stratigraphic boundary and the first Below the stratigraphic boundary, at this point... Indicates from Increase every 1 to This indicates that the unit is cut by only one geological boundary line but retains the initial uncut unit number. This indicates that the intermediate stratum sliding body unit contains sliding body unit numbers; (4) General form of the numbering of the sliding body units contained in each stratum for: ； ； In the formula, This represents the stratigraphic number, with a value range of [value range missing]. ; Step 7: Summarize the node numbers of each layer of sliding body elements and assign physical and mechanical parameters to each layer of sliding body elements to provide calculation parameters for subsequent solutions; (1) Summarize the node numbers included in each layer of sliding body element: Based on the landslide numbers contained in each stratum obtained in step 6 Find the node numbers of the included sliding bodies. , is represented as: ； In the formula, This indicates the number of the sliding body contained in each stratum. This indicates the updated included node number of the sliding body element after cutting. Indicates the first The node numbers contained in the sliding body units of the stratigraphic boundary. This represents the stratigraphic number, with a value range of [value range missing]. ; (2) Assign physical and mechanical parameters to the corresponding sliding body units of each stratum, expressed as: ①Unit density: ; In the formula, This indicates the number of the sliding body unit contained in each stratum. This represents the stratigraphic number, with a value range of [value range missing]. , Indicates the first Unit weight of the sliding body at the stratigraphic boundary; ②Unit cohesion: ; In the formula, Indicates the first Cohesion of sliding body units at the stratigraphic boundary; ③Internal friction angle of the unit: ; In the formula, Indicates the first The internal friction angle of the sliding body unit at the stratigraphic boundary; ④ Unit pore water pressure: ; In the formula, Indicates the first Pore ​​water pressure of sliding body units at the stratigraphic boundary; Step 8: Use MATLAB to determine the coordinates corresponding to the total node number. Draw the total node positions and label the total node numbers. According to the node numbers included in the cut sliding body element. Draw the cut elements and the centroid of the new elements. The location point is marked with the updated total number of the sliding body element after cutting at the centroid location point. ; and the stratigraphic boundary line With groundwater level Draw it.

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