Two-dimensional meso-analysis method for reinforced cage wrapped gravel slope

Abstract

The application discloses a kind of steel reinforcement cage package egg gravel side slope two-dimensional mesoscopic analysis method, it is related to hydraulic geotechnical engineering technical field.The specific includes: determining the steel reinforcement cage package egg gravel side slope to be measured, establishes the range line of side slope;Minimum distance measurement circle is generated;All edges are converted into wall, and wall is used as the partition boundary of each steel reinforcement cage unit;Through operation to initial equilibrium, ensure that the grouping of particles is not in suspension;Delete the wall of each steel reinforcement cage unit, set the connection effect of bond strength simulation steel bar;Restrict steel reinforcement cage particle, according to the distance of steel reinforcement cage unit distance side slope surface to calculate the size of internal stress;Remove the constraint of side slope top, apply side slope dead weight, form the stress state of natural steel reinforcement cage side slope;The peak value of curve is divided by the area of bearing plate to obtain bearing capacity value.The application can estimate macroscopic equivalent medium mechanical parameter, and provide design basis for the determination of mechanical parameter of egg gravel composite medium using steel reinforcement cage package.

Description

Technical Field

[0001] This invention belongs to the field of hydraulic and geotechnical engineering technology, and particularly relates to a two-dimensional microscopic analysis method for reinforced cage-encased gravel slopes. Background Technology

[0002] Gabion mesh has become a popular ecological revetment technology in riverbank protection projects in recent years. It consists of a rectangular cage made of woven steel bars, filled with readily available pebbles and gravel from the riverbed, creating a composite soil-rock material that possesses both strength and the ability to withstand some deformation. This material is then constructed by layering and connecting the gabions to form a flexible revetment slope, accommodating uneven settlement to some extent. This process is collectively referred to as reinforced gabion mesh with pebbles and gravel.

[0003] For gabion-encased composite slopes, the stress characteristics and bearing capacity are much higher than those of granular materials due to the inclusion effect of the steel cage, thus significantly increasing the slope stability. However, due to the complexity of composite materials, it is extremely difficult to study the mechanical characteristics of gabion-encased composite slopes through field or laboratory tests. In such cases, various numerical simulation methods are often used to simulate the mechanical response characteristics of real materials and the stability of slopes. Conventional continuous numerical simulation methods, such as the finite element method and the finite difference method, have limitations in analyzing and interpreting large deformations and soil failure problems. Therefore, the study of the deformation and strength properties of gabion-integrated composite slopes can only be carried out using the particle flow discrete element method.

[0004] However, when using discrete element method (DEM) numerical simulation to study the stability and mechanical properties of cage-enclosed gravel slopes, constructing a realistic micro-scale numerical model of the particles is a key technical challenge. For the reinforcing cage, flexible deformation must be allowed while conforming to its mesh-like distribution characteristics. For the internal particles, a suitable contact constitutive model needs to be established, and numerical simulation experiments should be conducted using a loading system. Only in this way can the strength and deformation properties of the system be evaluated, and the bearing capacity of the macroscopic medium estimated, providing a basis for the design of engineering revetment structures.

[0005] Therefore, proposing a two-dimensional microscopic analysis method for reinforced cage-encased gravel slopes to address the difficulties in existing technologies is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0006] This invention addresses the shortcomings of existing technologies by providing a two-dimensional microscopic analysis method for reinforced cage-encased gravel slopes.

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

[0008] A two-dimensional microscopic analysis method for a reinforced cage-encased gravel slope includes the following steps:

[0009] S1: Determine the slope of the reinforced cage containing gravel to be measured, establish the slope boundary line, divide the grid according to the size and side length of the reinforced cage, establish a two-dimensional continuous numerical grid, locate the grid points and grid composition, retrieve the model boundary coordinates, and regard each continuous grid as a reinforced cage unit.

[0010] S2: By searching the grid, retain the edges of each steel cage unit, and use each edge as a side edge of the steel cage. Generate a measurement circle with the radius as the minimum distance from the center to each edge at the centroid of each unit.

[0011] S3: Transform all edges into walls, and use the walls as the dividing boundaries of each steel cage unit;

[0012] S4: By calculating to the initial equilibrium, for units outside the preset stress threshold range, the particle size is adjusted to give them a certain internal stress, ensuring that the particles in this group are not suspended.

[0013] S5: Delete the walls of each rebar cage unit, set the size of the rebar cage particles, generate rebar cage particles connected end to end along the boundary of each rebar cage unit, use the contact bonding model to bond the rebar cage particles together, and set the bonding strength to simulate the connection of the rebar.

[0014] S6: Constrain the reinforcing cage particles. Calculate the internal stress based on the distance between the reinforcing cage unit and the slope surface. Use the particle internal adjustment method to adjust the stress level of the reinforcing cage particle system in the current reinforcing cage unit. When the unbalanced force of the model is less than the preset threshold, gradually remove the constraints of the reinforcing cage particles to bring the system into balance.

[0015] S7: Remove the constraint at the top of the slope, apply the slope's self-weight, and gradually bring the slope into self-weight equilibrium, forming the stress state of a natural reinforced cage slope.

[0016] S8: Set a bearing plate at the top of the slope, apply a vertical downward velocity, and record the curve of the force on the bearing plate changing with time or load step. Divide the peak value of the curve by the area of ​​the bearing plate to obtain the bearing capacity value.

[0017] The above method, optionally, includes the following specific components in S1:

[0018] A numerical model was established based on the dimensional range of the engineering reinforcement cage slope. Using AutoCAD and ANSYS tools, the side length (size) of the reinforcement cage was set, and the side length (size) controlled the division of a two-dimensional continuous numerical mesh. The mesh consisted of n mesh nodes. p Number of units n e Determining grid point coordinates and element composition parameters;

[0019] Traverse n pTo retrieve the model's boundaries using n nodes: First, set initial values ​​for the model's left, right, lower, and upper boundaries, then iterate through n nodes. p Given the coordinates of node i, if the coordinate value of node i is x i y i Satisfy x i <x min Then x min Replace with x i ; satisfy x i >x max Then x max Replace with x i ; satisfy y i <y min , then y min Replace with y i ; satisfy y i >y max , then y max Replace with y i After the traversal is complete, then x = x min That is, the left boundary of the model, x = x max As the right boundary, y = y min Let y be the lower boundary, then y = y max This is the upper boundary.

[0020] The above method, optionally, includes the following in S2: Given the node coordinates, traverse n... e Search for cell edges in each cell; traverse n cells. e For each unit, first extract the edges of that unit, then calculate the centroid (x) of that unit. c ,y c ):

[0021] The centroid of a quadrilateral is calculated as follows:

[0022] x c = (x1+x2+x3+x4) / 4

[0023] y c = (y1+y2+y3+y4) / 4

[0024] The centroid of the triangle is calculated as follows:

[0025] x c = (x1+x2+x3) / 3

[0026] y c = (y1+y2+y3) / 3

[0027] With the centroid of the unit (x) c ,y c Find the circle with center N. b Minimum distance D of the edgemin ;

[0028] With the center (x) c ,y c ), radius D min Generate a measurement circle.

[0029] The above method, optionally, includes the following specific components in S3:

[0030] Using the geometry to rigid wall command in the PFC6.0 platform, the edges of all steel cage elements are converted into walls that divide each steel cage element, and then labeled with names.

[0031] Traverse n e For each i-th rebar cage element, a geometry set named "linshi" is set to control the boundary geometry of the i-th rebar cage element. A disk is generated using the ball distribute command or an rblock is generated using the rblockdistribute command, and the porosity is controlled between 0.15 and 0.20. The generated rebar cage particles are grouped according to the rebar cage element number, and then the current geometry set is deleted.

[0032] After traversing n e After each rebar cage unit, each rebar cage unit is filled with fine particles. The default contact is set to linear contact with parameters emod=1.0e8, kratio=1.0, fric=0.5.

[0033] The above method, optionally, includes the following specific components in S4:

[0034] Calculate 50,000 steps to initial equilibrium using the PFC 6.0 platform;

[0035] Set the initial control stress value tao. Iterate through each rebar cage unit, check the measured circular stress sigxx and sigyy within the current rebar cage unit, and take their average value stress = 0.5(sigxx + sigyy). If stress is less than tao, increase the radius of all particles within the current rebar cage unit by 0.00001 times. If stress is greater than tao, decrease the radius of all particles within the current rebar cage unit by 0.00001 times. After iterating through all rebar cage units, iterate 5000 times. Repeat the above steps until the stress in each unit group is close to the design stress tao. When the error error = abs(tao - stress) / tao is less than 0.05, it is considered to meet the requirements.

[0036] The above method, optionally, includes the following specific features in S5:

[0037] Remove the walls that control the boundaries of each gabion unit;

[0038] Set the diameter d of the gabion mesh particles. c traverse n p For each node, use the ball create command to generate a ball with radius r. i =d c / 2.0, coordinates are (x i ,y i ) spherical particles; record the total number of particles n. b =n p Then iterate through n l Let the i-th edge have endpoints numbered j and k, respectively. Then its coordinates are (x, y). i ,y i ) and (x k ,y k );

[0039] Calculate the side length:

[0040]

[0041] Estimate the number of steel cage particles n needed to be added on the i-th side. i :

[0042] n i =int((dd c ) / d c +0.5)

[0043] int is the integer function, and 0.5 is for rounding to the nearest integer.

[0044] To balance n i The spacing between the steel cage particles, therefore for n i The radius of each steel cage particle is taken as:

[0045] r i =(dd c ) / n i

[0046] Using the ball create command, n are generated sequentially along the i-th edge and the j-th node. i The specific steps for making one ball are as follows:

[0047] Calculate the direction vector of the current edge using the coordinates of point j and point k:

[0048]

[0049] Without loss of generality, the center coordinates of the m-th rebar cage particle on the i-th edge are:

[0050]

[0051] Simultaneously accumulate the total number of balls n b =n b +n i , waiting for n l After traversing all edges, n b This refers to the number of steel bars used in the reinforcing cage.

[0052] The above method, optionally, includes the following specific components in S6:

[0053] In x = x min -d c Construct a rectangular wall at position / 2, which serves as the left boundary wall of the model; at x = x max +d c Construct a rectangular wall at position / 2, which will serve as the right boundary wall of the model; at y = y min -d c Construct a rectangular wall at position / 2 as the lower boundary wall of the model, serving as the boundary constraint for the slope model; constrain all the reinforcing cage particles, retrieve the positions of the reinforcing cage particles, and find the slope surface geometry;

[0054] Traverse n e Let there be 3 measuring circles, without loss of generality, with the center coordinates of the i-th measuring circle being (x, y). i ,y i Draw a straight line from this point to the slope surface using geometry, and find its intersection point (x). i ,y i top); then measure the design stress T of the circle. i =(y i top-y c )*γ, where γ is the average unit weight; after traversal, the design stress on all measurement circles is different, simulating the stress state of steel cages at different depths.

[0055] The above method, optionally, includes the following specific components in S7:

[0056] All walls outside the left, right, and bottom boundaries of the slope are deleted. Then, the displacement, velocity, and internal force of the steel cage particles are reset to zero every 10 iterations, for a total of more than 50,000 iterations.

[0057] Apply self-weight acceleration to all reinforcing cage particles, with a design acceleration of 9.8, vertically downwards, according to N. S Step by step, that is, 9.8 divided into N S Each step increases by 9.8 of 1 / N. S The slope particle system is allowed to accumulate under its own weight until the unbalanced force of the model is less than a preset threshold.

[0058] The above method, optionally, includes the following specific features in S8:

[0059] A wall-like load-bearing plate with a width of w is placed horizontally at the top of the slope, slightly in contact with the particles. A slow application speed v is applied vertically downwards. The variation of the contact force on the load-bearing plate with loading time or time step is recorded.

[0060] Find the peak loading force F by analyzing the contact force variation diagram. max If this value is divided by w, then the magnitude of the ultimate bearing capacity of the gabion slope is obtained.

[0061] As can be seen from the above technical solution, compared with the prior art, the present invention provides a two-dimensional microscopic analysis method for reinforced cage-encased gravel slopes, which has the following beneficial effects:

[0062] (1) This application addresses the difficulty of eliminating internal forces in the microscopic model of a composite medium slope with a reinforced cage wrapped in gravel. It aims to use the microscopic numerical simulation method of particle flow to construct microparticles to simulate the reinforced cage, and discs or rigid blocks to simulate the gravel. Different microscopic mechanical parameters are set respectively. The load-time curve of the composite medium can be obtained by using the bearing plate test, thereby determining the ultimate bearing capacity of the reinforced cage slope.

[0063] (2) In this application, a sphere is used to simulate the steel cage, and the internal stress is adjusted by changing the particle size. This not only ensures the microscopic characteristics of the composite medium, but also reflects the flexibility of the gabion mesh. The obtained ultimate bearing capacity is reliable, and the simulation results are more realistic and effective. Attached Figure Description

[0064] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0065] Figure 1 This is a flowchart of a two-dimensional microscopic analysis method for a reinforced cage-encased gravel slope disclosed in this invention;

[0066] Figure 2 This is a typical steel cage slope grid diagram disclosed in an embodiment of the present invention;

[0067] Figure 3 This is a diagram showing the edge and node of the reinforcing cage as disclosed in an embodiment of the present invention;

[0068] Figure 4 This is a diagram showing the distribution of measurement circles within a steel cage unit as disclosed in an embodiment of the present invention.

[0069] Figure 5 This is a microscopic media grouping diagram at initial equilibrium disclosed in an embodiment of the present invention;

[0070] Figure 6 This is a diagram of the microscopic particle structure disclosed in an embodiment of the present invention;

[0071] Figure 7 This is the internal force diagram at initial equilibrium disclosed in the embodiments of the present invention;

[0072] Figure 8 This is the internal stress iterative equilibrium curve disclosed in the embodiments of the present invention;

[0073] Figure 9 This is a diagram of the internal stress of the reinforced steel cage slope after equilibrium, as disclosed in an embodiment of the present invention.

[0074] Figure 10 This is a diagram showing the placement of the slope bearing plate according to an embodiment of the present invention;

[0075] Figure 11 This is a deformation diagram of the slope ballast process disclosed in an embodiment of the present invention;

[0076] Figure 12 This is a graph showing the load-time variation of the bearing plate disclosed in an embodiment of the present invention.

[0077] Figure 13 This is a schematic diagram illustrating the contact force variation law disclosed in an embodiment of the present invention. Detailed Implementation

[0078] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0079] In this application, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. The terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0080] Reference Figure 1 As shown, a two-dimensional microscopic analysis method for a reinforced cage-encased gravel slope includes the following steps:

[0081] S1: Determine the slope of the reinforced cage containing gravel to be measured, establish the slope boundary line using tools such as AutoCAD or ANSYS, divide the grid according to the side length of the reinforced cage, establish a two-dimensional continuous numerical grid, locate the grid points and grid composition, retrieve the model boundary coordinates, and regard each continuous grid as a reinforced cage element.

[0082] S2: By searching the grid, retain the edges of each steel cage unit, and use each edge as a side edge of the steel cage. Generate a measurement circle with the radius as the minimum distance from the center to each edge at the centroid of each unit.

[0083] S3: Transform all edges into walls, using the walls as the dividing boundaries of each steel cage unit. Each unit uses four or three edges as a geometric boundary. Using this boundary, spheres or rigid blocks (rblocks) are generated within the unit to simulate the micro-medium, such as gravel, boulders, and pebbles, and the micro-medium is grouped separately.

[0084] S4: By calculating to the initial equilibrium, for units outside the preset stress threshold range, the particle size is adjusted to give them a certain internal stress, ensuring that the particles in this group are not suspended.

[0085] S5: Delete the walls of each rebar cage unit, set the size of the rebar cage particles, generate rebar cage particles connected end to end along the boundary of each rebar cage unit, use the contact bonding model to bond the rebar cage particles together, and set the bonding strength to simulate the connection of the rebar.

[0086] S6: Constrain the reinforcing cage particles. Calculate the internal stress based on the distance between the reinforcing cage unit and the slope surface. Use the particle internal adjustment method to adjust the stress level of the reinforcing cage particle system in the current reinforcing cage unit. After the model reaches the point where the unbalanced force is less than the preset threshold, gradually remove the constraints on the reinforcing cage particles to bring the system into equilibrium.

[0087] S7: Remove the constraint at the top of the slope, apply the slope's self-weight, and gradually bring the slope into self-weight equilibrium, forming the stress state of a natural reinforced cage slope.

[0088] S8: Set a bearing plate at the top of the slope, apply a vertical downward velocity, and record the curve of the force on the bearing plate changing with time or load step. Divide the peak value of the curve by the area of ​​the bearing plate to obtain the bearing capacity value.

[0089] Furthermore, S1 specifically includes the following:

[0090] A numerical model was established based on the dimensional range of the engineering reinforcement cage slope. Using AutoCAD and ANSYS tools, the side length (size) of the reinforcement cage was set, and the side length (size) controlled the division of a two-dimensional continuous numerical mesh. The mesh consisted of n mesh nodes. p Number of units n e Determining grid point coordinates and element composition parameters;

[0091] Traverse n p To retrieve the model's boundaries using n nodes: First, set initial values ​​for the model's left, right, lower, and upper boundaries, then iterate through n nodes. p Given the coordinates of node i, if the coordinate value of node i is x i y i Satisfy x i <x min Then x min Replace with x i ; satisfy x i >x max Then x max Replace with x i ; satisfy y i <y min , then y min Replace with y i ; satisfy y i >y max , then y max Replace with y i After the traversal is complete, then x = x min That is, the left boundary of the model, x = x max As the right boundary, y = y min Let y be the lower boundary, then y = y max This is the upper boundary.

[0092] Specifically, taking a quadrilateral element as an example, for any element (numbered ii), assuming it consists of four nodes i, k, m, and n, we need to examine four edges: ik, km, mn, and ni. For edges that have not been recorded, assign them a number and record the edge (its two endpoints). For edges that have already been recorded, discard them. Finally, find the total number of unique edges, n. l Record the node numbers corresponding to the two endpoints of each edge to ensure that the edge is unique. Also record the numbers of all edges enclosed by each cell (4 edges for quadrilaterals and 3 edges for triangles).

[0093] Furthermore, S2 specifically includes the following: given the node coordinates, traverse n... e Search for cell edges in each cell; traverse n cells. e For each unit, first extract the edges of that unit, then calculate the centroid (x) of that unit. c ,y c ):

[0094] The centroid of a quadrilateral is calculated as follows:

[0095] x c = (x1+x2+x3+x4) / 4

[0096] y c = (y1+y2+y3+y4) / 4

[0097] The centroid of the triangle is calculated as follows:

[0098] x c = (x1+x2+x3) / 3

[0099] y c = (y1+y2+y3) / 3

[0100] With the centroid of the unit (x) c ,y c Find the circle with center N. b Minimum distance D of the edge min ;

[0101] With the center (x) c ,y c ), radius D min Generate a measurement circle.

[0102] Specifically, traverse Nb edges. Without loss of generality, let the i-th edge have two endpoints with coordinates (x1, y1) and (x2, y2) respectively. Calculate the direction vector (v) of the line containing this edge. x ,v y ):

[0103]

[0104] v x =(x2-x1) / d

[0105] v y =(y2-y1) / d

[0106] The equation of the line is:

[0107]

[0108] Calculate (x) c ,y c The distance d from the line containing the i-th side i :

[0109] di = abs(v y ×x c -v x ×y c -vy x1+v x ×y1)

[0110] abs is the absolute value function; from N b Find the edge d with the minimum distance among the edges. min D min =min(d i (i = 1, 2, 3, ..., Nb), min is the minimum function.

[0111] Specifically, traverse N e After a certain number of units, a measurement circle appears on all units. To ensure the number of contacts within the measurement circle, if D... min The size of the particles differs significantly, such as D. min If the particle radius is less than 3 times, then take D. min = 3.0 times the minimum particle radius.

[0112] Furthermore, S3 specifically includes the following:

[0113] Using the geometry to rigid wall command in the PFC6.0 platform, the edges of all steel cage elements are converted into walls that divide each steel cage element, and then labeled with names.

[0114] Traverse n e For each i-th rebar cage element, a geometry set named linshi is set to control the boundary geometry of the i-th rebar cage element. A disk is generated using the ball distribute command or an rblock is generated using the rblockdistribute command, and the porosity is controlled between 0.15 and 0.20. The generated rebar cage particles are grouped according to the rebar cage element number, such as grouping the i-th element as zone_i. Then the current geometry set is deleted.

[0115] After traversing n e After each rebar cage unit, each rebar cage unit is filled with fine particles. The default contact is set to linear contact with parameters emod=1.0e8, kratio=1.0, fric=0.5.

[0116] Furthermore, S4 specifically includes the following:

[0117] Calculate 50,000 steps to initial equilibrium using the PFC 6.0 platform;

[0118] Set the initial control stress value tao. Iterate through each rebar cage unit, check the measured circular stress sigxx and sigyy within the current rebar cage unit, and take their average value stress = 0.5(sigxx + sigyy). If stress is less than tao, increase the radius of all particles within the current rebar cage unit by 0.00001 times. If stress is greater than tao, decrease the radius of all particles within the current rebar cage unit by 0.00001 times. After iterating through all rebar cage units, iterate 5000 times. Repeat the above steps until the stress in each unit group is close to the design stress tao. When the error error = abs(tao - stress) / tao is less than 0.05, it is considered to meet the requirements.

[0119] Furthermore, S5 specifically includes the following:

[0120] Remove the walls that control the boundaries of each gabion unit;

[0121] Set the diameter d of the gabion mesh particles. c traverse n p For each node, use the ball create command to generate a ball with radius r. i =d c / 2.0, coordinates are (x i ,y i ) spherical particles; record the total number of particles n. b =n p Then iterate through n l Let the i-th edge have endpoints numbered j and k, respectively. Then its coordinates are (x, y). i ,y i ) and (x k ,y k );

[0122] Calculate the side length:

[0123]

[0124] Estimate the number of steel cage particles n needed to be added on the i-th side. i :

[0125] n i =int((dd c ) / d c +0.5)

[0126] int is the integer function, and 0.5 is for rounding to the nearest integer.

[0127] To balance n i The spacing between the steel cage particles, therefore for n iThe radius of each steel cage particle is taken as:

[0128] r i =(dd c ) / n i

[0129] Using the ball create command, n are generated sequentially along the i-th edge and the j-th node. i The specific steps for making one ball are as follows:

[0130] Calculate the direction vector of the current edge using the coordinates of point j and point k:

[0131]

[0132] Without loss of generality, the center coordinates of the m-th rebar cage particle on the i-th edge are:

[0133]

[0134] Simultaneously accumulate the total number of balls n b =n b +n i , waiting for n l After traversing all edges, n b This refers to the number of steel bars used in the reinforcing cage.

[0135] Furthermore, S6 specifically includes the following:

[0136] In x = x min -d c Construct a rectangular wall at position / 2, which serves as the left boundary wall of the model; at x = x max +d c Construct a rectangular wall at position / 2, which will serve as the right boundary wall of the model; at y = y min -d c Construct a rectangular wall at position / 2 as the lower boundary wall of the model, serving as the boundary constraint for the slope model; constrain all the reinforcing cage particles, retrieve the positions of the reinforcing cage particles, and find the slope surface geometry;

[0137] Specifically, iterate through all the particles, according to x min -x max The range is divided into 100 segments, totaling 101 points. Therefore, the length of each segment is dx = (x...). max -x min () / 100. Without loss of generality, counting from left to right, for the i-th point, its x-coordinate is x. i =x min +(i-1)*dxlength, at this point, we traverse all (number n) ball ) particles in [x i-0.5*dxlength,x i For particles with a length of +0.5*dxlength, let y i Initial value = -10000. If the particle's coordinates plus its radius exceed y... i , then y i Replace it with the particle coordinates + particle radius, and the final y-coordinate is obtained. i These are the geometric points of the slope surface. Connecting these 101 points from left to right forms the slope geometry.

[0138] Traverse n e Let there be 3 measuring circles, without loss of generality, with the center coordinates of the i-th measuring circle being (x, y). i ,y i Draw a straight line from this point to the slope surface using geometry, and find its intersection point (x). i ,y i top); then measure the design stress T of the circle. i =(y i top-y c )*γ, where γ is the average unit weight; after traversal, the design stress on all measurement circles is different, simulating the stress state of steel cages at different depths.

[0139] Furthermore, S7 specifically includes the following:

[0140] All walls outside the left, right, and bottom boundaries of the slope are deleted. Then, the displacement, velocity, and internal force of the steel cage particles are reset to zero every 10 iterations, for a total of more than 50,000 iterations.

[0141] Specifically, the stress level of the granular system within the reinforcing cage is adjusted using an internal particle adjustment method. This involves traversing each unit and checking the measured circular stress within that unit, sigyy=T. i If the stress is less than sigyy, increase the radius of all particles within that element by 0.00001; if the stress is greater than sigyy, decrease the radius of all particles within that element by 0.00001. After iterating through all elements, repeat the process for 5000 steps. Continue this process until the stress within each element group is close to the design stress T. i When error = abs(T) i -stress) / T iA value less than 0.05 is considered satisfactory. For the reinforcing cage composed of spheres, the contact between adjacent particles is set as a linear contact bonding model, where the effective modulus (emod) is 1.0e9, the stiffness ratio is 3.0, and the normal and tangential bond strengths are 1.0e10 MPa. The constraints on the reinforcing cage particles are removed, and the particle velocity, displacement, and contact force are reset to zero every 10 iterations. After running for more than 50,000 iterations, the system is brought to basic equilibrium.

[0142] Apply self-weight acceleration to all reinforcing cage particles, with a design acceleration of 9.8, vertically downwards, according to N. S Step by step, that is, 9.8 divided into N S Each step increases by 9.8 of 1 / N. S The slope particle system is allowed to accumulate under its own weight until the unbalanced force is less than the preset threshold (0.00001).

[0143] Furthermore, S8 specifically includes the following:

[0144] A wall-like load-bearing plate with a width of w is placed horizontally at the top of the slope, slightly in contact with the particles. A slow application speed v is applied vertically downwards. The variation of the contact force on the load-bearing plate with loading time or time step is recorded.

[0145] Find the peak loading force F by analyzing the contact force variation diagram. max If this value is divided by w, then the magnitude of the ultimate bearing capacity of the gabion slope is obtained.

[0146] In a specific embodiment of the present invention, a bank protection project uses gabion mesh to wrap gravel, with dimensions of 20m*15m and a slope of 45 degrees. The gravel used on site is filled with 10cm to 20cm of material. Because this is a plane strain problem, it can be simplified to a two-dimensional analysis. However, since gravel is a loose structure, its mechanical properties are difficult to estimate after being wrapped with gabion mesh to construct the slope, making it very difficult to determine the stability during design and construction. This invention utilizes a two-dimensional microscopic analysis method for reinforced cage-wrapped gravel slopes to estimate the ultimate bearing capacity. The steps are as follows:

[0147] (1) Construct slope meshes using AutoCAD or ANSYS, referring to... Figure 2 As shown, the gabion on site is 1m*1m*1m, therefore the slope uses a boundary size of 1m to control the mesh division. The number of elements is n. e =207, number of nodes n p =240 units, and the x and y coordinates of each point. Among them, there are 206 quadrilateral units and 1 triangular unit.

[0148] Traverse n p=240 nodes, retrieving the model boundary. First, set the initial value x for the left boundary of the model. min =1000.0, initial value of the right boundary x max = -1000.0, initial value of the front boundary y min =1000.0, initial value of the back boundary y max = -1000.0, initial value of the upper boundary z max = -1000.0, initial value of lower boundary z min =1000.0, iterate through n p The coordinates of the i-th node are given, without loss of generality, if the coordinate value of the i-th node is x... i y i z i Satisfy x i <x min Then x min Replace with x i ; satisfy x i >x max Then x max Replace with x i ; satisfy y i <y min , then y min Replace with y i ; satisfy y i >y max , then y max Replace with y i Finally, the left boundary x is obtained. min =0.0, right boundary x max =20.0, lower boundary y min =0.0, upper boundary y max =15.0.

[0149] (2) Given the node coordinates, traverse n e = 207 cell edges are searched. Without loss of generality, taking a quadrilateral cell as an example, for any cell (numbered ii), assuming it consists of four nodes i, k, m, and n, then we need to examine four edges: ik, km, mn, and ni. For edges that have not been recorded, assign them numbers and record the edge (both endpoints); for edges that have already been recorded, discard them at the current stage. The final number of unique edges found is n. l =447, and record the node numbers corresponding to the two endpoints of each edge to ensure that the edge is unique. Also record the numbers of all edges enclosed by each cell (4 edges for quadrilaterals, 3 edges for triangles). The relationship between each node and edge is as follows: Figure 3 As shown.

[0150] Traverse n e For each cell, first extract the edges of that cell (the number of edges in a cell is N). bThis indicates that there are 4 quadrilaterals Nb and 4 triangles N. b =3 items) numbered. Based on radius D min A measurement circle is generated at the center position. Traverse N e After a certain number of units, a measurement circle appears on all units. To ensure the number of contacts within the measurement circle, if D... min The size of the particles differs significantly, such as D. min If the particle radius is less than 3 times, then take D. min =3.0 times the minimum particle radius. The final measured circle is as follows: Figure 4 As shown.

[0151] (3) Using the geometry to rigid wall command in the PFC6.0 platform, convert all element edges into walls. These serve as the walls that divide each gabion element, and are labeled with names (name is "inner_wall"). Iterate through n e For each element, without loss of generality, a geometry set named "linshi" is set for the i-th element to control its boundary geometry. Disks are generated using the `ball distribute` command, or rblocks are generated using the `rblock distribute` command, with porosity controlled between 0.15 and 0.20. The generated particles are grouped according to their element numbers; for example, the i-th element is grouped as `zone_i`. Then, the current geometry set "set" is deleted. After traversing *n* elements, each element is filled with microparticles. The default contact is set to linear contact with parameters emod = 1.0e8, kratio = 1.0, and fric = 0.5. The grouped particles are as follows: Figure 5 As shown.

[0152] (4) Calculate 50,000 steps to initial equilibrium using the PFC2D6.0 platform (unbalanced force less than 0.00001), such as Figure 6 As shown.

[0153] Set the initial control stress value tao = 10 kPa. Iterate through each element, checking the measured circular stresses sigxx and sigyy within that element, and taking their average stress = 0.5(sigxx + sigyy). If stress is less than tao, increase the radius of all particles within that element by 0.00001 times; if stress is greater than tao, decrease the radius of all particles within that element by 0.00001 times. After iterating through all elements, perform 5000 iterations. Repeat the above steps until the stress within each element group is close to the design stress tao. The requirement is considered met when the error error = abs(tao - stress) / tao is less than 0.05. The internal force diagram at initial equilibrium is shown below. Figure 7As shown in the figure, there are significant differences in stress levels within different elements. The stress error changes with time step after the iterative process is as follows: Figure 8 As shown, the force chain after iteration is as follows Figure 9 As shown.

[0154] (5) The initial model has been generated, and the wall is no longer needed to constrain the particles. Therefore, the wall that controls the boundary of each gabion unit is deleted.

[0155] Set the diameter d of the gabion mesh particles. c traverse n p For each node, use the ball create command to generate a ball with radius r. i =d c / 2.0, coordinates are (x i ,y i ) spherical particles. Record the total number of particles n. b =n p Then iterate through n l Let the i-th edge, without loss of generality, have its two endpoints numbered j and k, then its coordinates are (x, y, k). j ,y j ) and (x k ,y k ).

[0156] Calculate the side length:

[0157]

[0158] Estimate the number of particles n that need to be added to the i-th edge. i :

[0159] n i =int((dd c ) / d c +0.5)

[0160] Where int is the integer function, 0.5 is for rounding, and d c To design the particle diameter.

[0161] To balance n i The spacing between the particles, therefore for n i The radius of each particle is taken as:

[0162] r i =(dd c ) / n i

[0163] Using the ball create command, n are generated sequentially along the i-th edge and the j-th node. i The specific steps for making one ball are as follows:

[0164] Calculate the direction vector of the side using the coordinates of point j and point k:

[0165]

[0166] Without loss of generality, the center coordinates of the m-th particle on the i-th edge are:

[0167]

[0168] Simultaneously accumulate the total number of balls n b =n b +n i , waiting for n l After traversing all edges, n b This refers to the number of steel bars used in the reinforcing cage.

[0169] The velocity of the reinforcing steel spheres is constrained to prevent deformation of the reinforcing cage due to imbalance in the sphere system. For the reinforcing cage composed of spheres, the contact between adjacent spheres is set as a linear contact bond model, where the effective modulus (emod) is 1.0e9, the stiffness ratio is 3.0, and the normal bond strength and tangential bond strength are 1.0e10 MPa.

[0170] (6) Using the `wall generate` command on the PFC2D6.0 platform, in x = x min -d c Construct a rectangular wall at position / 2, which serves as the left boundary wall of the model; at x = x max +d c Construct a rectangular wall at position / 2, which serves as the right boundary wall of the model; at y = y min -d c Construct a rectangular wall at position / 2 as the lower boundary wall of the model, serving as a boundary constraint for the slope model. This constrains all the reinforcing cage particles to prevent deformation and failure due to excessive internal forces during subsequent equilibration. Retrieve particle positions to determine the slope surface geometry. Specifically, iterate through all particles, following the x-axis... min -x max The range is divided into 100 segments, totaling 101 points. Then, for each segment d... xlength =(x max -x min () / 100. Without loss of generality, counting from left to right, for the i-th point, its x-coordinate is x. i =x min +(i-1)*d xlength At this point, traversing all (number of n balls) particles in the [x] position... i -0.5*d xlength ,xi+0.5*d xlength Let y be the particle.i Initial value = -10000. If the particle's coordinates plus its radius exceed y... i , then y i Replace it with the particle coordinates + particle radius, and the final y-coordinate is obtained. i These are the geometric points of the slope surface. Connecting these 101 points from left to right forms the slope geometry.

[0171] Traverse n e Let there be 3 measuring circles, without loss of generality, with the center coordinates of the i-th measuring circle being (x, y). i ,y i Draw a straight line from this point to the slope surface using geometry, and find its intersection point (x). i ,y itop The design stress T of the measured circle is then determined. i =(y itop -y c )*γ, where γ is the average unit weight. After traversal, the design stress on all measurement circles is different, which can simulate the stress state of gabion mesh at different depths.

[0172] The stress level of the granular system within the reinforcing cage is adjusted using an internal granular adjustment method. This involves traversing each unit and checking the measured circular stress within that unit, sigyy=T. i If the stress is less than sigyy, increase the radius of all particles within that element by 0.00001; if the stress is greater than sigyy, decrease the radius of all particles within that element by 0.00001. After iterating through all elements, repeat the process for 5000 steps. Continue this process until the stress within each element group is close to the design stress T. i When error = abs(T) i -stress) / T i A value less than 0.05 is considered to meet the requirements.

[0173] Remove the constraints on the steel cage particles, and reset the particle velocity, displacement, and contact force to zero every 10 iterations. Run more than 50,000 iterations to bring the system into basic equilibrium.

[0174] (7) Delete all walls outside the left, right, and bottom boundaries of the slope. Then, reset the displacement, velocity, and internal force of the particles to zero every 10 iterations, for a total of 50,000 iterations. Apply gravity acceleration to all particles, with a designed acceleration of 9.8, vertically downwards, applied according to NS = 10 steps, that is, divide 9.8 into 10 parts, increasing by 1 / N of 9.8 in each step. S The slope particle system is allowed to accumulate under its own weight until the unbalanced force is less than 0.00001. The force chain after equilibrium is as follows: Figure 10 As shown.

[0175] (8) Place a wall-like simulated bearing plate at the top of the slope, slightly in contact with the particles. The wall has a width of w = 2m. Apply a slow application speed v, vertically downwards. Figure 11 As shown. Deformation and failure during loading are as follows. Figure 12 As shown, the variation of the contact force on the bearing plate with loading time or time step is recorded. Figure 13 As shown. The peak loading force F is found through the contact force variation diagram. max =556kN, then dividing this value by w=2m gives the magnitude of the ultimate bearing capacity of the gabion slope, which is 278kPa.

[0176] The various embodiments in this specification are described in a progressive manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, for system or system embodiments, since they are basically similar to the method embodiments, the description is relatively simple; relevant parts can be referred to the descriptions of the method embodiments.

[0177] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A two-dimensional microscopic analysis method for a reinforced cage-encased gravel slope, characterized in that, Includes the following steps: S1: Determine the slope of the reinforced cage containing gravel to be measured, establish the slope boundary line, divide the grid according to the size and side length of the reinforced cage, establish a two-dimensional continuous numerical grid, locate the grid points and grid composition, retrieve the model boundary coordinates, and regard each continuous grid as a reinforced cage unit. S2: By searching the grid, retain the edges of each steel cage unit, and use each edge as a side edge of the steel cage. Generate a measurement circle with the radius as the minimum distance from the center to each edge at the centroid of each unit. S3: Transform all edges into walls, and use the walls as the dividing boundaries of each steel cage unit; S4: By calculating to the initial equilibrium, for units outside the preset stress threshold range, the particle size is adjusted to give them a certain internal stress, ensuring that the particles in this group are not suspended. S5: Delete the walls of each rebar cage unit, set the size of the rebar cage particles, generate rebar cage particles connected end to end along the boundary of each rebar cage unit, use the contact bonding model to bond the rebar cage particles together, and set the bonding strength to simulate the connection effect of the rebar. S6: Constrain the reinforcing cage particles. Calculate the internal stress based on the distance between the reinforcing cage unit and the slope surface. Use the particle internal adjustment method to adjust the stress level of the reinforcing cage particle system in the current reinforcing cage unit. When the unbalanced force of the model is less than the preset threshold, gradually remove the constraints of the reinforcing cage particles to bring the system into balance. S7: Remove the constraint at the top of the slope, apply the slope's self-weight, and gradually bring the slope into self-weight equilibrium, forming the stress state of a natural reinforced cage slope. S8: Set a bearing plate at the top of the slope, apply a vertical downward velocity, record the curve of the force on the bearing plate changing with time or load step, and divide the peak value of the curve by the area of ​​the bearing plate to obtain the bearing capacity value. S3 specifically includes the following: Using the geometry to rigid wall command in the PFC6.0 platform, the edges of all steel cage elements are converted into walls that divide each steel cage element, and then labeled with names. Traversal n e The first steel cage unit, for the first... i The first rebar cage unit is assigned a geometry set named linshi to control the first... i The boundary geometry of each rebar cage element is generated by using the ball distribute command to create a disk or the rblock distribute command to create an rblock, controlling the porosity between 0.15 and 0.20; the generated rebar cage particles are grouped according to the rebar cage element number, and then the current geometry set is deleted. Traversal complete n e After each rebar cage unit, each rebar cage unit is filled with fine particles. The default contact is set to linear contact with parameters emod=1.0e8, kratio=1.0, and fric=0.

5.

2. The two-dimensional microscopic analysis method for a reinforced cage-encased gravel slope according to claim 1, characterized in that, Specific in S1 Includes the following: A numerical model was established based on the dimensional range of the engineering reinforcement cage slope. Using AutoCAD and ANSYS tools, the side length of the reinforcement cage was set, and the side length controlled the division of a two-dimensional continuous numerical mesh. The mesh consisted of the number of mesh nodes. n p Number of units n e Determine the grid point coordinates and element composition parameters; Traversal n p Each node retrieves the model's boundaries: First, set initial values ​​for the model's left, right, lower, and upper boundaries, then iterate through the nodes. n p The coordinates of the nth node, if the nth node... i Node coordinates x i , y i satisfy x i < x min ,but x min Replace with x i ;satisfy x i > x max ,but x max Replace with x i ;satisfy y i < y min ,but y min Replace with y i ;satisfy y i > y max ,but y max Replace with y i After the traversal is complete, then x = x min That is, the left boundary of the model. x = x max The right boundary y = y min The lower boundary is... y = y max This is the upper boundary.

3. The two-dimensional microscopic analysis method for a reinforced cage-encased gravel slope according to claim 2, characterized in that, S2 specifically includes the following: Given the node coordinates, traverse n e Search for cell edges in each cell; traverse n e For each unit, first extract the edges of that unit and then calculate its centroid. : The centroid of a quadrilateral is calculated as follows: The centroid of the triangle is calculated as follows: With unit centroid Find the center of the circle and the circle with the center of the circle. N b Minimum distance of the strip edge D min ; With the center ,radius D min Generate a measurement circle.

4. The two-dimensional microscopic analysis method for a reinforced cage-encased gravel slope according to claim 1, characterized in that, S4 specifically includes the following: Calculate 50,000 steps to initial equilibrium using the PFC 6.0 platform; Set the initial control stress value tao, traverse each rebar cage unit, check the measured circular stress sigxx and sigyy in the current rebar cage unit, and take their average value stress=0.5(sigxx+sigyy); if stress is less than tao, then increase the radius of all particles in the current rebar cage unit by 0.00001 times; if stress is greater than tao, then decrease the radius of all particles in the current rebar cage unit by 0.00001 times. After traversing all the steel cage elements, iterate 5000 times; repeat the above steps until the stress in each element group is close to the design stress tao. When the error = abs(tao - stress) / tao is less than 0.05, it is considered to meet the requirements.

5. A two-dimensional microscopic analysis method for a reinforced cage-encased gravel slope according to claim 4, characterized in that, S5 specifically includes the following: Remove the walls that control the boundaries of each gabion unit; Set the gabion mesh particle diameter d c traversal n p For each node, use the ball create command to generate a ball with a radius of [missing value]. r i = d c / 2.0, coordinates are ( x i , y i ) spherical particles; record the total number of particles. n b = n p Then iterate through n l Let the edge be the first one. i An edge, whose two endpoints correspond to the node numbers as follows: j , k Then its coordinates are ( x i , y i )and( x k , y k ); Calculate the side length: Estimate the first i The number of steel reinforcement cage particles that need to be added to the side n i : int is the integer function, and 0.5 is for rounding to the nearest integer. In order to balance n i The spacing between the individual steel cage particles, therefore for n i The radius of each steel cage particle is taken as: Using the ball create command along the line i The edge of the first j Nodes are generated sequentially n i The specific steps for making one ball are as follows: use j Point and k Point coordinates, calculate the direction vector of the current edge: Without loss of generality, for the first i The first edge m The center coordinates of each steel cage particle are: Simultaneously accumulate the total number of balls n b = n b + n i ,treat n l After traversing all edges, n b This refers to the number of steel bars used in the reinforcing cage.

6. A two-dimensional microscopic analysis method for a reinforced cage-encased gravel slope according to claim 1, characterized in that, S6 specifically includes the following: exist x = x min - d c Construct a rectangular wall at position / 2, which will serve as the left boundary wall of the model; x = x max + d c Construct a rectangular wall at position / 2, which will serve as the right boundary wall of the model; y = y min - d c Construct a rectangular wall at position / 2 as the lower boundary wall of the model, serving as the boundary constraint for the slope model; constrain all the reinforcing cage particles, retrieve the positions of the reinforcing cage particles, and find the slope surface geometry; Traversal n e A measuring circle, without loss of generality, assumes the first... i A measuring circle, with center coordinates ( ). x i , y i Draw a straight line from this point to the slope surface to find its intersection point. x i , y i top Then measure the design stress of the circle. ,in The average density is used; after the traversal is completed, the design stress on all the measuring circles is different, simulating the stress state of the steel cage at different depths.

7. A two-dimensional microscopic analysis method for a reinforced cage-encased gravel slope according to claim 6, characterized in that, S7 specifically includes the following: All walls outside the left, right, and bottom boundaries of the slope are deleted. Then, the displacement, velocity, and internal force of the steel cage particles are reset to zero every 10 iterations, for a total of more than 50,000 iterations. Apply self-weight acceleration to all reinforcing cage particles, with a design acceleration of 9.8, vertically downwards, according to... N S Step by step, it will be 9.8 points. N S Each step increases by 9.8 by 1 / 3 N S The slope particle system is allowed to accumulate under its own weight until the unbalanced force of the model is less than a preset threshold.

8. A two-dimensional microscopic analysis method for a reinforced cage-encased gravel slope according to claim 1, characterized in that, S8 specifically includes the following: A wall-like load-bearing plate is placed horizontally at the top of the slope, slightly in contact with the particles, with a width of [missing information]. w Apply a slower application speed. v The direction is vertically downward; record the variation of the contact force on the bearing plate with the loading time or time step; Find the peak loading force by analyzing the contact force variation diagram. F max Then divide the value by w This refers to the magnitude of the ultimate bearing capacity of the gabion slope.

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