An earth-rock dam overtopping breaching analysis method based on material point method

Abstract

The application discloses a kind of earth-rock dam overtopping breaching analysis method based on material point method, belong to civil and water conservancy numerical simulation technical field.The steps are:S1, read each partition material point information, background grid information, material constitutive model and parameter of material point, load information and relevant calculation parameters of material point;S2, based on material point adaptive mapping technology, in each time step, update material point position, momentum;S3, the equivalent plastic strain of material point is calculated, the fluid-structure conversion of dam body area material point is considered by strength reduction method, and the stress of material point is updated according to the constitutive model of each partition material point;S4, cycle S2 and S3 until the calculation of all time steps is completed, and the deformation condition and reservoir water level elevation change result in the overtopping breaching process of earth-rock dam are output.The application uses adaptive mapping to improve the calculation efficiency of large-scale problem, effectively reflects the scouring effect of reservoir water on dam slope in overtopping process, and reasonably reproduces the evolution process of earth-rock dam overtopping breaching.

Description

Technical Field

[0001] This invention belongs to the field of numerical simulation technology in civil engineering and hydraulic engineering, and relates to a method for analyzing the overtopping failure of homogeneous dams based on the material point method. Background Technology

[0002] Under the influence of factors such as heavy rainfall, reservoir dams are prone to overtopping and collapse, causing incalculable losses. The dam failure process involves the impact of reservoir water on the dam body and the transformation of the dam body into a mud-fluid state. Traditional numerical finite element simulation methods often face problems such as mesh distortion and difficulties in simulating state transitions when dealing with such problems.

[0003] The Material Point Method (MPM) employs both the Eulerian and Lagrangian methods for description. Material points carry all material information and can move freely between background meshes, facilitating the tracking of material interfaces and effectively avoiding mesh distortion problems. This gives it a natural advantage in dam-break simulation. The origins of MPM can be traced back to the Material Point Mesh Method (PIC). In 1955, Harlow proposed a machine computation method to solve fluid dynamics problems. Later, Sulsky et al. improved PIC and extended it to the field of solid mechanics, enabling the simulation of materials with deformation histories. This marked the birth of the Material Point Method, which has been successfully applied to practical engineering problems such as slope sliding failure, fluid impact, foundation penetration, and structural collapse. When simulating dam break problems, MPM needs to consider the following issues: 1) The model is huge, with dimensions of hundreds of meters in each direction, resulting in millions of material points, which seriously affects computational efficiency. How can we efficiently conduct overtopping dam break analysis? 2) The simulation area involves reservoir water, dam, mud, and bedrock. How can we simulate multiple material properties under a unified solution framework? 3) The dam break process involves reservoir water impacting the dam body, which leads to the gradual transformation of the dam body into mud. How can we reasonably capture this phenomenon?

[0004] To address the aforementioned problems of the material point method in dam break simulation, numerous scholars have conducted related research. For example, Chinese invention patent N201910640947.1 discloses a numerical simulation method for overtopping and breaching floods of earth-rock dams that includes a reservoir area. This method incorporates the reservoir area into the entire computational domain, unifying the simulation of the outflow process at the breach with the simulation of flood evolution in the reservoir area and downstream inundation zone, thus expanding the applicability of the dam break model. However, it does not consider the transformation of the dam body into mud after being scoured by reservoir water. Chinese invention patent CN202311042624.5 discloses a simulation method for overtopping and breaching of earth-rock dams based on the SPH-DEM algorithm. This method establishes an SPH-DEM dam break simulation calculation model based on the combined effects of seepage and overflow by coupling the smoothed particle fluid dynamics method with the discrete element method. It achieves the simulation of different material properties under a unified solution framework, but its computational load is enormous, making it difficult to apply to the numerical simulation of overtopping and breaching of large earth-rock dams.

[0005] Therefore, it is necessary to propose a material point method for analyzing the overtopping failure of earth-rock dams, so as to more realistically and effectively simulate the evolution process of overtopping failure of earth-rock dams. Summary of the Invention

[0006] To address the challenges of large deformation phenomena, large-scale calculations, and fluid-solid state transitions involved in the numerical simulation of overtopping failure of earth-rock dams, this invention provides a method for analyzing overtopping failure of homogeneous dams based on the material point method. It fully leverages the advantages of the material point method in large deformation simulation, improves the computational efficiency of large-scale problems through adaptive material point mapping, proposes a practical dam-mud fluid-solid transformation scheme, and reasonably reproduces the evolution process of overtopping failure of earth-rock dams. This method is of great significance for the numerical simulation of overtopping failure of earth-rock dams.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0008] A method for analyzing the overtopping failure of earth-rock dams based on the material point method, comprising the following steps:

[0009] S1 reads in the material point information for each partition, background mesh information, material constitutive models and parameters for the material points, load information for the material points, and related calculation parameters. Specifically:

[0010] S1.1, Read in the material point information of each partition, including the material point number, material point material number, material point mass, material point initial momentum and material point coordinates; at the same time, read in the background mesh information, including the background mesh range and background mesh size;

[0011] Furthermore, each zone in S1.1 includes the dam area, reservoir water area, river valley area, and mud area;

[0012] S1.2, Read in the material constitutive model and parameters of the material points, including the linear elastic model, the DP elastoplastic constitutive model, and the Mie-Grüineisen equation of state model;

[0013] S1.3, Read in the load information of the material point, including: self-weight and seismic load;

[0014] S1.4, read in the relevant calculation parameters, including: calculation time step and total number of calculation time steps.

[0015] S2, based on S1, uses adaptive mapping technology for matter points to update the position and momentum of matter points at each time step. Specifically:

[0016] S2.1, determine the background grid where the material point is located, and map the mass, momentum, and load of each material point to the nodes of the background grid in sequence, as shown in formula (1):

[0017] (1)

[0018] In the formula, , , These represent the mass vector, momentum vector, and load vector of the background mesh node, respectively. , , Let these represent the mass vector, momentum vector, and load vector of the material point, respectively. n Indicates the first n One material point; n p Indicates the total number of material points within the background grid; subscript t Indicates the first t Time step; The mapping function from material points to background mesh nodes is used in this invention, which employs a linear interpolation function consistent with the finite element method.

[0019] S2.2, calculate the acceleration of the background mesh nodes and update the node momentum, see formula (2):

[0020] (2)

[0021] In the formula, , These represent the acceleration vector and the updated momentum vector of the background mesh node, respectively. Indicates the time step, subscript t Indicates the first t Time step.

[0022] S2.3 maps the calculation results on the background mesh nodes back to the material points to update the position and momentum of the material points.

[0023] Since the bidirectional mapping between material points and background grid nodes increases the computational burden significantly, this invention uses the mapping function from material points to background grid nodes as the criterion to determine whether a material point needs to undergo a mapping process, as shown in formula (3). If a material point does not require a mapping process, its first... t+ The displacement and momentum of the material point at time step 1 are calculated according to formula (4); otherwise, they are calculated according to formula (5); the formulas (3), (4), and (5) are as follows:

[0024] (3)

[0025] In the formula, Indicates the first t The mapping function from time step material points to background mesh nodes; Indicates the first tThe mapping function from the material point to the background mesh node at time step +1; H This indicates the set threshold. H The value range is 0.01 to 0.05.

[0026] (4)

[0027] In the formula, , , , These represent the position vector, mass vector, momentum vector, and load vector of each material point, respectively. Indicates the time step, subscript t Indicates the first t Time step, subscript t+ 1 indicates the first t+ 1 time step.

[0028] (5)

[0029] In the formula, , Represents the mass vector and momentum vector of each background mesh node, with subscripts. l Indicates the first l One background grid node, Indicates the total number of background grid nodes; Indicates the time step, subscript t Indicates the first t Time step, subscript t+ 1 indicates the first t+ 1 time step; The function representing the mapping from background mesh nodes to material points is used in this invention, which employs a linear interpolation function consistent with the finite element method.

[0030] S3 calculates the equivalent plastic strain of the material points based on the updated momentum of the material points in S2, and then considers the fluid-solid transformation of the material points in the dam area using the strength reduction method. Finally, it updates the stress of the material points based on the constitutive model of each zone. Specifically:

[0031] S3.1, the updated material point momentum is remapped to the background mesh node using formula (1), and the strain increment and spinor increment of the material point are calculated to update the equivalent plastic strain of the material point;

[0032] S3.2, based on the equivalent plastic strain of the material points updated in S3.1, the mechanical parameters such as cohesion and internal friction angle of the material points in the dam area are reduced by the strength reduction method to take into account the softening effect of the dam body after being scoured by the reservoir water, as shown in formula (6):

[0033] (6)

[0034] In the formula, , , These represent the current cohesion, internal friction angle, and equivalent plastic strain of the material point, respectively. , , These represent the peak cohesion, peak internal friction angle, and their corresponding equivalent plastic strain, respectively. , , These represent residual cohesion, residual internal friction angle, and residual cohesion, internal friction angle, and their corresponding equivalent plastic strain, respectively.

[0035] S3.3 When the equivalent plastic strain of the material points in the dam body exceeds the equivalent plastic strain corresponding to the residual cohesion and the internal friction angle (predetermined value), the material points in the dam body are transformed into material points in the mud zone.

[0036] S3.4, based on the strain increment and spinor increment in S3.1, update the stress at the material point according to the material constitutive model of each partition.

[0037] S4, repeats S2 and S3 until all time steps are calculated, outputting the deformation and reservoir water level changes at typical moments during the overtopping failure of the earth-rock dam. Specifically:

[0038] S4.1, repeat S2 and S3 until all time steps are calculated, thus completing an analysis of the overtopping failure of an earth-rock dam based on the material point method;

[0039] S4.2, based on the displacement of material points at each time step obtained in S2, outputs the deformation at each typical moment during the flood overflow process. At the same time, based on the maximum vertical coordinate of the material points in the reservoir area, outputs the result of the change in reservoir water level elevation.

[0040] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0041] (1) This invention proposes an adaptive mapping technique based on the change value of the shape function as the criterion, and combines it with a parallel solution strategy to improve the computational scale and efficiency of the dam-break problem;

[0042] (2) This invention proposes a practical fluid-solid transformation scheme based on strength reduction, which effectively reflects the softening effect of the dam body after being scourd by reservoir water during the overtopping process;

[0043] (3) This invention reasonably simulates the evolution process of the overtopping failure of earth-rock dams and can provide a time history curve of the maximum reservoir water level, which can provide important support for the risk assessment of the overtopping failure of earth-rock dams.

[0044] In summary, this invention employs adaptive mapping to improve the computational efficiency of large-scale problems, ensuring that the simulation scale of material points reaches the million level. At the same time, it proposes a practical fluid-solid transformation scheme based on the strength reduction method, which effectively reflects the scouring effect of reservoir water on the dam slope during the overtopping process, and finally reasonably reproduces the evolution process of the overtopping failure of an earth-rock dam. Attached Figure Description

[0045] Figure 1 This is a schematic diagram of the main process of the method of the present invention;

[0046] Figure 2 This is a schematic diagram of the material point method solution;

[0047] Figure 3 This is a schematic diagram of a material point flow-solid transformation scheme;

[0048] Figure 4 Material point model diagram and downstream dimension diagram of the Abu Mansur Dam; Figure 4 (a) in the diagram is a material point model of the computational domain of the Abu Mansur Dam; Figure 4 (b) in the diagram shows the dimensions of the Abu Mansur Dam in the direction of water flow;

[0049] Figure 5 for t Deformation diagram of material points at 0 min;

[0050] Figure 6 for t Deformation diagram of material points at 10 min;

[0051] Figure 7 for t Deformation diagram of material points at 20 min;

[0052] Figure 8 for t Deformation diagram of material points at 40 min;

[0053] Figure 9 for t Deformation diagram of material points at 60 min;

[0054] Figure 10 A comparison chart of time history curves for maximum water level height;

[0055] In the diagram: 1. Reservoir; 2. Dam; 3. Valley; L1=244m, L2=160m, L3=42m. Detailed Implementation

[0056] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but the scope of protection of the present invention is not limited thereto.

[0057] A method for analyzing the overtopping failure of earth-rock dams based on the material point method includes the following steps:

[0058] S1, read in the material point information of each partition, background mesh information, material constitutive model and parameters of the material points, load information of the material points and related calculation parameters;

[0059] S2, based on S1, uses the material point adaptive mapping technology to update the position and momentum of the material point in each time step;

[0060] S3 calculates the equivalent plastic strain of the material point based on the updated momentum of the material point in S2, and considers the fluid-solid transformation of the material point in the dam area through the strength reduction method. Finally, the stress of the material point is updated according to the constitutive model of the material point in each zone.

[0061] S4, repeat S2 and S3 until all time steps are calculated, output the deformation and reservoir water level changes at typical moments during the overtopping failure of the earth-rock dam.

[0062] Example 1: Numerical simulation of the overtopping failure of the Abu Mansour Dam in Libya;

[0063] A method for analyzing the overtopping failure of earth-rock dams based on the material point method, the flowchart of which is shown below. Figure 1 As shown, the method for analyzing the overtopping failure of an earth-rock dam includes the following steps:

[0064] S1 reads in the material point information for each partition, background mesh information, material constitutive models and parameters for the material points, load information for the material points, and related calculation parameters. Specifically:

[0065] S1.1, refer to Figure 4 ,in Figure 4 (a) Material point model of the computational domain of the Abu Mansur Dam and Figure 4 (b) shows the dimensions of the Abu Mansur Dam along the river flow direction. Material point information for each zone (including the dam body zone, reservoir water zone, river valley zone, and mud zone) is read in. Simultaneously, background grid information, including the background grid range and size, is also read in. The Abu Mansur Dam has a length of 294m along the river, a reservoir upstream water level of 47m, a dam height of 42m, a dam crest width of 10m, and a river valley slope ratio of 1:1. The number of material points in the dam body is 933,816, in the reservoir water is 2,072,670, and in the river valley is 1,121,504. The spacing between material points is 0.25m, and the background grid size is 1m.

[0066] S1.2, Read in the material constitutive model and parameters of the material points. The linear elastic model is used in the valley area, the DP elastoplastic constitutive model is used in the dam area, the Newtonian fluid Mie-Gruneisen equation of state model is used in the fluid area, and the non-Newtonian fluid Mie-Gruneisen equation of state model is used in the mud area. Detailed material parameters are shown in Tables 1 to 4.

[0067] Table 1: Parameters of the Valley Linear Elastic Body Model

[0068]

[0069] Table 2: Parameters of the DP Elastoplastic Constitutive Model of the Dam Body

[0070]

[0071] Table 3: Parameters of the Mie-Gruneisen Equation of State for Newtonian Fluids in Reservoirs

[0072]

[0073] Table 4: Parameters of the Mie-Gruneisen Equation of State for Non-Newtonian Fluids in Mud

[0074]

[0075] S1.3, Read in the load information of the material point. In this implementation case, only the gravity of the material point is considered.

[0076] S1.4, Read in the relevant calculation parameters, including the calculation time step and the total number of calculation time steps. In this implementation case, the time step is 0.0001s, the total number of time steps is 36,000,000, and the total calculation time is 60min.

[0077] S2, based on S1, uses the matter point adaptive mapping technique to update the matter point position and momentum at each time step. A schematic diagram of the matter point method solution is shown below. Figure 2 As shown, specifically:

[0078] S2.1, determine the background grid where the material point is located, and map the mass, momentum, and load of each material point to the background grid node in turn, as shown in formula (1):

[0079] (1)

[0080] In the formula, , , These represent the mass vector, momentum vector, and load vector of the background mesh node, respectively. , , Let these represent the mass vector, momentum vector, and load vector of the material point, respectively. n Indicates the first n One material point; n p Indicates the total number of material points within the background grid; subscript t Indicates the first t Time step; The mapping function from material points to background mesh nodes is used in this invention, which employs a linear interpolation function consistent with the finite element method.

[0081] S2.2, calculate the acceleration of the background mesh nodes and update the node momentum, see formula (2):

[0082] (2)

[0083] In the formula, , These represent the acceleration vector and the updated momentum vector of the background mesh node, respectively. Indicates the time step, subscript t Indicates the first t Time step.

[0084] S2.3 maps the calculation results on the background mesh nodes back to the material points to update the position and momentum of the material points.

[0085] Since the bidirectional mapping between material points and background grid nodes increases the computational burden significantly, this implementation uses the mapping function from material points to background grid nodes as the criterion to determine whether a material point needs to undergo a mapping process, as shown in formula (3). If a material point does not require a mapping process, its first... t+ The displacement and momentum of the material point at time step 1 are calculated according to formula (4); otherwise, they are calculated according to formula (5); the formulas (3), (4), and (5) are as follows:

[0086] (3)

[0087] In the formula, Indicates the first t The mapping function from time step material points to background mesh nodes; Indicates the first t The mapping function from the material point to the background mesh node at time step +1; H This indicates the set threshold. H The value range is as described in this embodiment. H =0.02.

[0088] (4)

[0089] In the formula, , , , These represent the position vector, mass vector, momentum vector, and load vector of each material point, respectively. Indicates the time step, subscript t Indicates the first t Time step, subscript t+ 1 indicates the first t+ 1 time step.

[0090] (5)

[0091] In the formula, , Represents the mass vector and momentum vector of each background mesh node, with subscripts. l Indicates the first l One background grid node, Indicates the total number of background grid nodes; Indicates the time step, subscript t Indicates the first t Time step, subscript t+ 1 indicates the first t+ 1 time step; The function representing the mapping from background mesh nodes to material points is used in this invention, which employs a linear interpolation function consistent with the finite element method.

[0092] S3 calculates the equivalent plastic strain of the material points based on the updated momentum of the material points in S2, and then considers the fluid-solid transformation of the material points in the dam area using the strength reduction method. Finally, it updates the stress of the material points based on the constitutive model of each zone. Specifically:

[0093] S3.1, the updated material point momentum is remapped to the background mesh node using formula (1), and the strain increment and spinor increment of the material point are calculated to update the equivalent plastic strain of the material point;

[0094] S3.2, based on the equivalent plastic strain of the material points updated in S3.1, the mechanical parameters such as cohesion and internal friction angle of the material points in the dam area are reduced by the strength reduction method to take into account the softening effect of the dam body after being scoured by the reservoir water, as shown in formula (6):

[0095] (6)

[0096] In the formula, , , These represent the current cohesion, internal friction angle, and equivalent plastic strain of the material point, respectively. , , These represent the peak cohesion, peak internal friction angle, and their corresponding equivalent plastic strain, respectively. , , These represent residual cohesion, residual internal friction angle, and residual cohesion, internal friction angle, and their corresponding equivalent plastic strain, respectively. In this implementation case... .

[0097] S3.3, when the equivalent plastic strain of the material points in the dam body exceeds the equivalent plastic strain corresponding to the residual cohesion and the internal friction angle (predetermined value), the material points in the dam body are transformed into material points in the mud zone, as shown in formula (7). The schematic diagram of the material point flow-solid transformation scheme is as follows: Figure 3 As shown;

[0098] (7)

[0099] In the formula, This represents the current equivalent plastic strain. This represents the equivalent plastic strain corresponding to the residual cohesion / internal friction angle.

[0100] The material points in the dam area are modeled using the DP elastoplastic constitutive model. Analogous to the Tresca and Mises yield conditions, the DP model provides a yield function that is both smooth and considers the influence of hydrostatic pressure, which is used to determine whether the material undergoes plastic deformation, i.e., equation (8):

[0101] (8)

[0102] In the formula: Represents the yield function; For equivalent shear stress, It is the second invariant of the deviatoric stress tensor. Represents the deviatoric stress tensor; For spherical stress, It is the first invariant of the stress tensor. Represents the stress tensor; The yield stress under pure shear conditions; It is the coefficient of friction, which controls the degree of influence of pressure on the yield strength. The above equation represents a smooth conical surface in principal stress space. It is a circle on a plane.

[0103] The above material parameters and Due to the cohesive force of the material c and the angle of friction Confirmed, see formula (9):

[0104] (9)

[0105] By selecting parameters, the DP yield surface can be... πThe Mohr-Coulomb (MC) yield surface is either circumscribed or inscribed in the plane (where the minus sign in the denominator corresponds to circumscription, and the plus sign corresponds to inscription). In this embodiment, the DP yield surface is selected. π Inscribed in the plane at the MC yield surface, see formula (10):

[0106] (10)

[0107] S3.4, based on the strain increment and spinor increment in S3.1, update the stress at the material point according to the material constitutive model of each partition material point;

[0108] In this implementation case, the bedrock adopts a linear elastic model, the dam body adopts a DP elastoplastic constitutive model, and the reservoir water adopts a model based on the Mie-Grüineisen equation of state, as shown in formula (11):

[0109] (11)

[0110] in, and For the pressure and internal energy per unit mass at a point on the Hugoniot curve; The compressibility coefficient of the material. Indicates the current density of the material. Indicates the initial density of the material; Indicates the speed of sound; Represents an empirical constant; and It is Grüneisen's constant; This represents the internal energy of a potential mass.

[0111] The mud is modeled based on the Mie-Grüineisen equation of state and takes into account the viscosity of non-Newtonian fluids, as shown in equation (12):

[0112] (12)

[0113] In the formula, This represents the shear stress at the current material point. This represents the shear strain at the current material point. u Indicates the viscosity coefficient. n This represents the power parameter, which is set to 2 in this implementation example.

[0114] S4, repeats S2 and S3 until all time steps are calculated, outputting the deformation and reservoir water level changes at typical moments during the overtopping failure of the earth-rock dam. Specifically:

[0115] S4.1, with a time step of 0.0001s, repeat S2 and S3 until 36,000,000 calculation steps are completed (cumulative 60 minutes). During the iteration process, the equivalent plastic strain development of the material points in the dam body under the combined action of reservoir water scouring and gravity is tracked in real time. The movement trajectory of the material points in the reservoir water area is monitored simultaneously to obtain the dynamic change process of water level. This enables dynamic simulation of the entire process of earth-rock dam from initiation to final failure, and thus completes an analysis of overtopping failure of earth-rock dam based on the material point method.

[0116] S4.2 outputs the displacement and strain deformation results of all material points at each time step, and calculates the maximum vertical coordinate of each time step based on the spatial coordinates of the material points in the reservoir area, outputting the process of reservoir water level elevation change. To improve the simulation efficiency of this invention, a dynamic selective output strategy is adopted. That is, based on the spatial location and dynamic participation of the material points, the output of material points with minimal impact on dam break evolution is automatically filtered out during the simulation process. For example, water body material points with slight movement in the middle of the reservoir area will no longer be output after the reservoir water level drops. Thus, while ensuring the integrity of key physical processes, the efficiency of large-scale material point numerical simulation is significantly improved.

[0117] Through the above steps, the spatiotemporal evolution of the dam's overtopping failure was reconstructed. To visually demonstrate the dam erosion and fluid-structure interaction-transformation process, deformation results at different moments during the dam failure simulation were selected for display, such as... Figures 5-9 As shown, it presents the deformation of the dam at various typical moments during the 0-60 minute period.

[0118] During the dam break simulation, the longitudinal coordinates of reservoir water material points were monitored in real time, and the maximum upstream water level was recorded at each moment in the model. This data was then compared with the measured time-history data of the maximum water level within 60 minutes of a dam break. The comparison results are as follows: Figure 10 As can be seen, the two sets of data are basically similar and the error is controllable, indicating that the present invention matches the measured results well and has high accuracy, which can provide scientific guidance for the safety management, emergency plan formulation and downstream risk assessment of similar dam projects.

[0119] The above description describes a more feasible specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions, improvements, or adaptive adjustments made within the technical concept and core principles disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for analyzing the overtopping failure of earth-rock dams based on the material point method, characterized in that, The aforementioned method for analyzing the overtopping failure of earth-rock dams includes the following steps: S1, read in the material point information of each partition, background mesh information, material constitutive model and parameters of the material points, load information of the material points and related calculation parameters; S2, based on S1, uses adaptive mapping technology for matter points to update the position and momentum of matter points at each time step; specifically: S2.1, determine the background grid where the material point is located, and map the mass, momentum, and load of each material point to the nodes of the background grid in sequence; S2.2, calculate the acceleration of the background mesh nodes and update the node momentum; S2.3, map the calculation results on the background mesh nodes back to the material points to update the position and momentum of the material points; The mapping function from the material point to the background grid node is used as the criterion to determine whether the material point needs to undergo a mapping process. If no mapping process is needed, the position and momentum of the material point in the next time step are calculated according to the load, momentum and mass of the material point in the current time step; otherwise, the calculation results on the background grid node are mapped to the material point to update its position and momentum. S3 calculates the equivalent plastic strain of the material point based on the updated momentum of the material point in S2, and considers the fluid-solid transformation of the material point in the dam area through the strength reduction method. Finally, the stress of the material point is updated according to the constitutive model of the material point in each zone. S4, repeat S2 and S3 until all time steps are calculated, output the deformation and reservoir water level changes at typical moments during the overtopping failure of the earth-rock dam.

2. The method for analyzing the overtopping failure of earth-rock dams based on the material point method according to claim 1, characterized in that, Specifically, S1 refers to: S1.1, Read in the material point information of each partition, including the material point number, material point material number, material point mass, material point initial momentum and material point coordinates; at the same time, read in the background mesh information, including the background mesh range and background mesh size; S1.2, Read in the material constitutive model and parameters of the material points, including the linear elastic model, the DP elastoplastic constitutive model, and the Mie-Grüineisen equation of state model; S1.3, Read in the load information of the material point, including: self-weight and seismic load; S1.4, read in the relevant calculation parameters, including: calculation time step and total number of calculation time steps.

3. The method for analyzing the overtopping failure of earth-rock dams based on the material point method according to claim 2, characterized in that, In S1.1, each zone includes the dam area, reservoir area, river valley area, and mud area.

4. The method for analyzing the overtopping failure of earth-rock dams based on the material point method according to claim 3, characterized in that, Specifically, S2 is: S2.1 is as described in formula (1): （1） In the formula, , , These represent the mass vector, momentum vector, and load vector of the background mesh node, respectively. , , Let these represent the mass vector, momentum vector, and load vector of the material point, respectively. n Indicates the first n One material point; n p Indicates the total number of material points within the background grid; subscript t Indicates the first t Time step; The mapping function from material points to background mesh nodes; S2.2 is as described in formula (2): （2） In the formula, , These represent the acceleration vector and the updated momentum vector of the background mesh node, respectively. Indicates the time step, subscript t Indicates the first t Time step; S2.3, using the mapping function from the material point to the background grid node as the criterion, determine whether the material point needs to undergo a mapping process, as shown in formula (3). If a material point does not need a mapping process, its first... t+ The displacement and momentum of the material point at time step 1 are calculated according to formula (4); otherwise, they are calculated according to formula (5); the formulas (3), (4), and (5) are as follows: （3） In the formula, Indicates the first t The mapping function from time step material points to background mesh nodes; Indicates the first t The mapping function from the material point to the background mesh node at time step +1; H This indicates the set threshold. （4） In the formula, , , , These represent the position vector, mass vector, momentum vector, and load vector of each material point, respectively. Indicates the time step, subscript t Indicates the first t Time step, subscript t+ 1 indicates the first t+ 1 time step; （5） In the formula, , Represents the mass vector and momentum vector of each background mesh node, with subscripts. l Indicates the first l One background grid node, Indicates the total number of background grid nodes; Indicates the time step, subscript t Indicates the first t Time step, subscript t+ 1 indicates the first t+ 1 time step; This represents the mapping function from background mesh nodes to material points.

5. The method for analyzing the overtopping failure of earth-rock dams based on the material point method according to claim 4, characterized in that, In S2.1 and S2.3, the mapping function A linear interpolation function consistent with the finite element method is selected.

6. The method for analyzing the overtopping failure of earth-rock dams based on the material point method according to claim 4, characterized in that, In S2.3, the threshold H The value range is 0.01 to 0.

05.

7. The method for analyzing the overtopping failure of earth-rock dams based on the material point method according to claim 4, characterized in that, Specifically, S3 is: S3.1, the updated material point momentum is remapped to the background mesh node using formula (1), and the strain increment and spinor increment of the material point are calculated to update the equivalent plastic strain of the material point; S3.2, based on the equivalent plastic strain updated by the material points in S3.1, the mechanical parameters of the material points in the dam area are reduced by the strength reduction method, as shown in formula (6): （6） In the formula, , , These represent the current cohesion, internal friction angle, and equivalent plastic strain of the material point, respectively. , , These represent the peak cohesion, peak internal friction angle, and their corresponding equivalent plastic strain, respectively. , , These represent residual cohesion, residual internal friction angle, and residual cohesion, internal friction angle, and their corresponding equivalent plastic strain, respectively. S3.3 When the equivalent plastic strain of the material points in the dam body exceeds the equivalent plastic strain corresponding to the residual cohesion and internal friction angle, the material points in the dam body are transformed into material points in the mud zone. S3.4, based on the strain increment and spinor increment in S3.1, update the stress at the material point according to the material constitutive model of each partition.

8. The method for analyzing the overtopping failure of earth-rock dams based on the material point method according to claim 7, characterized in that, Specifically, S4 is: S4.1, repeat S2 and S3 until all time steps are calculated, thus completing an analysis of the overtopping failure of an earth-rock dam based on the material point method; S4.2, based on the displacement of material points at each time step obtained in S2, outputs the deformation at each typical moment during the flood overflow process. At the same time, based on the maximum vertical coordinate of the material points in the reservoir area, outputs the result of the change in reservoir water level elevation.

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