Simulation Method and System for the Damage Process of Retaining Dams under Debris Flow Impact

Abstract

The present invention belongs to the technical field of geological disaster simulation, and relates to a method and system for simulating the damage process of a retaining dam under debris flow impact. The method includes: constructing a depth-averaged two-phase flow model of debris flow; discretizing the depth-averaged two-phase flow model of debris flow by using the second-order finite volume method; describing the impact events by using a Poisson counting process to obtain the time distribution of impact boulders; calculating the impact load including the elastoplastic deformation stage to obtain the strength distribution of impact boulders; and calculating the cumulative damage index according to the time distribution and strength distribution of the impact events, and updating the geometric parameters of the retaining dam. The present invention integrates a depth-averaged two-phase model, a random probability model of impact boulders and an impact load model to describe the conditions of debris flow propagation and the retaining dam during the flow process, and can quantitatively describe the debris flow propagation process and the change of dam body damage caused by boulder impact, improving the accuracy of simulation results.

Description

Technical Field

[0001] The present invention belongs to the technical field of geological disaster simulation. Specifically, it relates to a method and system for simulating the damage process of a retaining dam under debris flow impact. Background Art

[0002] Retaining dams are widely used as key engineering measures to mitigate debris flow risks. Debris flow is a fast gravity-driven mixture composed of water, sediment, and stones, posing a significant threat to downstream infrastructure and communities. However, retaining dams are often subjected to extreme dynamic loads generated by debris flow impacts, especially the impacts of large stones entrained in the debris flow, resulting in severe structural damage.

[0003] Traditional models (such as the vertical jet model and the momentum jump model) mainly target fine-grained debris flows and do not fully reflect the high kinetic energy impact characteristics of boulders in stone-rich debris flows. The kinetic energy of boulders dominates, and their impact stress is likely to exceed the local bearing capacity limit of the dam body. However, existing formulas do not quantify the influence of the randomness of boulder size, quantity, and impact sequence on the load, resulting in significant load estimation deviations. Existing research is mostly based on single impact event simulations, and the finite element analysis or Euler-Lagrange method is used to only evaluate the instantaneous stress distribution and failure mode, without considering the cumulative damage (such as material fatigue and microcrack propagation) under repeated debris flow impacts. In actual scenarios, the dam body needs to withstand multiple impacts, and progressive damage will accelerate the structural degradation, but relevant long-term performance research is lacking.

[0004] Traditional techniques study the structural response and debris flow dynamics separately and do not couple the interaction between the heterogeneous fluid characteristics (such as the mixed movement of slurry and boulders) and the dynamic damage of the dam body, which leads to the inability to accurately evaluate the continuous impact of the dam body damage on the debris flow regulation ability (such as flow velocity reduction and sediment interception) after boulder impact. Existing risk assessments assume that the dam body structure is intact and ignore the functional attenuation caused by actual damage. This static assumption overestimates the dam body's effectiveness and may mislead downstream disaster management decisions.

[0005] Although current numerical techniques can simulate single impact events, they lack dynamic modeling of the evolution of material damage (such as crack coalescence and stress redistribution) under multiple impacts and are difficult to quantify the law of the attenuation of the bearing capacity of the dam body during long-term service. Debris flow is heterogeneous, and it is necessary to combine structural engineering and fluid dynamics for more comprehensive research to accurately evaluate the long-term durability of retaining dams. Summary of the Invention

[0006] To solve the above technical problems, the present invention provides a method and system for simulating the damage process of a retaining dam under debris flow impact.

[0007] In a first aspect, the present invention provides a method for simulating the damage process of a retaining dam under debris flow impact, including:

[0008] Considering the interaction between the solid phase and the fluid phase, a depth-averaged two-phase flow model for debris flow is constructed based on the flow field parameters; the depth-averaged two-phase flow model for debris flow includes the mass conservation equations of the solid phase and the fluid phase, the momentum conservation equation of the fluid phase, and the momentum conservation equation of the solid phase;

[0009] The depth-averaged two-phase flow model for debris flow is discretized using the second-order finite volume method, and the flow field parameters are updated using the HLLC Riemann solver;

[0010] The Poisson counting process is used to describe the impact events, a stochastic probability model for impact boulders is constructed, and the time distribution of impact boulders is obtained;

[0011] Based on the velocity of the impact boulders, the Hertz contact theory is used to calculate the impact load including the elastic-plastic deformation stage, and the strength distribution of the impact boulders is obtained;

[0012] Based on the time distribution and strength distribution of the impact events, the cumulative damage index is calculated based on the ratio of the plastic zone diameter to the residual thickness, and the geometric parameters of the retaining dam are updated.

[0013] In a second aspect, the present invention provides a simulation system for the damage process of a retaining dam under debris flow impact, including a model construction unit, a parameter update unit, a time distribution processing unit, a strength distribution processing unit, and a damage calculation and parameter update unit;

[0014] The model construction unit is used to consider the interaction between the solid phase and the fluid phase and construct a depth-averaged two-phase flow model for debris flow based on the flow field parameters; the depth-averaged two-phase flow model for debris flow includes the mass conservation equations of the solid phase and the fluid phase, the momentum conservation equation of the fluid phase, and the momentum conservation equation of the solid phase;

[0015] The parameter update unit is used to discretize the depth-averaged two-phase flow model for debris flow using the second-order finite volume method and update the flow field parameters using the HLLC Riemann solver;

[0016] The time distribution processing unit is used to describe the impact events using the Poisson counting process, construct a stochastic probability model for impact boulders, and obtain the time distribution of impact boulders;

[0017] The strength distribution processing unit is used to calculate the impact load including the elastic-plastic deformation stage based on the velocity of the impact boulders using the Hertz contact theory, and obtain the strength distribution of the impact boulders;

[0018] The damage calculation and parameter update unit is used to calculate the cumulative damage index based on the ratio of the plastic zone diameter to the residual thickness according to the time distribution and strength distribution of the impact events, and update the geometric parameters of the retaining dam until the retaining dam fails.

[0019] Based on the above technical solutions, the present invention can also be improved as follows.

[0020] Furthermore, let the direction of debris flow movement along the slope be axis, and the direction perpendicular to the slope of debris flow movement be axis, be the time, be the volume fraction of the fluid phase, be the volume fraction of the solid phase, be the flow depth, be the flow velocity of the fluid phase along the direction, be the flow velocity of the solid phase along the direction, be the flow velocity of the liquid phase, be the component of the gravitational acceleration in the direction, be the component of the gravitational acceleration in the direction, be the riverbed elevation, be the velocity vector of the fluid phase, be the gravitational acceleration, be the component of the phase resistance in the direction, be the component of the phase resistance in the direction, be the flow velocity of the solid phase along the direction, be the Euler's constant, be the basal friction angle of the solid phase, be the velocity vector of the solid phase, be the Manning friction coefficient of the fluid phase, be the earth pressure coefficient describing the stress state in the direction during the deformation of the material element, be the earth pressure coefficient describing the stress state in the direction during the deformation of the material element. Then:

[0021] The mass conservation equation of the solid phase is:

[0022] ;

[0023] The mass conservation equation of the fluid phase is:

[0024] ;

[0025] The momentum conservation equation of the fluid phase in the direction is:

[0026] ;

[0027] The momentum conservation equation of the fluid phase in the direction is:

[0028] ;

[0029] The momentum conservation equation of the solid phase in direction is:

[0030] ;

[0031] The momentum conservation equation of the solid phase in direction is:

[0032] .

[0033] Furthermore, let be the resistance correction factor describing the influence of particle concentration, be the resistance coefficient, be the density of the fluid phase, be the volume fraction of the solid phase, be the particle diameter, be the particle viscosity, be the fluid viscosity, and the resistance considering the change of phase volume fraction is , then:

[0034] .

[0035] Furthermore, according to the time distribution and intensity distribution of impact events, a Poisson counting process is used to describe the impact events, and a stochastic probability model of impact boulders is constructed to obtain the time distribution of impact boulders, including: Let be the time, represent the th occurring event, represent the boulder impact probability correction factor affected by the density of surrounding particles, be the average rate of event occurrence per unit time, represent the number of discrete boulder impact events within a given time interval , represent the probability of the number of discrete boulder impact events, obtained from the Poisson distribution:

[0036] ;

[0037] Let be the The waiting time before a boulder impact event, and the cumulative distribution function is , the event occurrence time follows a gamma distribution, and the cumulative distribution function is expressed as:

[0038] ;

[0039] Let the boulder radius be , and are empirical parameters of the radius distribution, and the extreme value distribution function is , is the probability function of the boulder radius, following an extreme value distribution:

[0040] .

[0041] Furthermore, according to the velocity of the boulder impact, the Hertz contact theory is used to calculate the impact load including the elastic-plastic deformation stage, and the strength distribution of the boulder impact is obtained, including: is the impact pressure of the debris flow mud on the retaining dam. Let be the static component linearly and uniformly distributed along the flow depth, be the dynamic component linearly and uniformly distributed along the flow depth, be the gravitational acceleration, be the mud flow depth, be the mud flow velocity, be the density of the two-phase mud. Then the impact pressure of the debris flow mud on the retaining dam is expressed as:

[0042] .

[0043] Furthermore, the velocity of the boulder impact is determined according to the mud viscosity; let the velocity of the boulder impact be , the boulder radius be , the mud viscosity be , be the coefficient related to the mud properties. When the fluid viscosity is greater than the set threshold, , when the fluid viscosity is less than or equal to the set threshold, .

[0044] Furthermore, the impact pressure of the debris flow mud on the dam body includes static water pressure and dynamic water pressure; let be the contact stiffness, be the boulder radius, be the time, be the equivalent elastic modulus, , be the contact displacement during the contact process between the boulder impact and the dam body. The boulder impact load is , and the boulder impact load is calculated based on the Hertz contact theory:

[0045] 。

[0046] Furthermore, calculate the cumulative damage index based on the ratio of the plastic zone diameter to the residual thickness, including: Let be the length of the plastic zone diameter, be the permanent indentation depth generated by the th impact, and the remaining thickness of the dam body impact section is ; be the remaining thickness of the th impact section, be the cumulative damage index, and the cumulative damage index of the first impact is ; be the length of the plastic zone diameter, be the remaining thickness of the first impact section, ; be the th cumulative damage degree of the impact retaining dam, then:

[0047] ;

[0048] 。

[0049] Furthermore, update the geometric parameters of the retaining dam until the cumulative damage degree of the retaining dam reaches the set threshold or the number of impacts reaches the set reference value.

[0050] The beneficial effects of the present invention are: The present invention proposes a new numerical method to evaluate the damage evolution of the interception dam under the impact of debris flow rich in boulders. This method integrates the depth-averaged two-phase model, the stochastic probability model of impact boulders, and the impact load model to describe the debris flow propagation and the conditions of the retaining dam during the flow process. By applying the finite volume method, it is possible to capture the dynamics of debris flow propagation and dam body damage while ensuring the calculation efficiency. The present invention can quantitatively describe the debris flow propagation process and the change of dam body damage caused by boulder impact, improving the accuracy of the simulation results. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 is the schematic diagram of the method for simulating the damage process of the retaining dam under debris flow impact provided in Embodiment 1 of the present invention;

[0052] Figure 2 is the schematic diagram of the system for simulating the damage process of the retaining dam under debris flow impact provided in Embodiment 2 of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0053] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. The components of the embodiments of the present invention usually described and illustrated in the drawings here can be arranged and designed in various different configurations.

[0054] Embodiment 1

[0055] As an embodiment, as shown in the appendix Figure 1 To solve the above technical problems, this embodiment provides a method for simulating the damage process of a retaining dam under debris flow impact, including:

[0056] Considering the interaction between the solid phase and the fluid phase, a depth-averaged two-phase flow model of debris flow is constructed according to the flow field parameters; the depth-averaged two-phase flow model of debris flow includes the mass conservation equations of the solid phase and the fluid phase, the momentum conservation equation of the fluid phase, and the momentum conservation equation of the solid phase;

[0057] The depth-averaged two-phase flow model of debris flow is discretized using the second-order finite volume method, and the flow field parameters are updated using the HLLC Riemann solver;

[0058] The Poisson counting process is used to describe the impact events, and a stochastic probability model of impact boulders is constructed to obtain the time distribution of impact boulders;

[0059] According to the velocity of the impact boulders, the impact load including the elastic-plastic deformation stage is calculated using the Hertz contact theory to obtain the strength distribution of the impact boulders;

[0060] According to the time distribution and strength distribution of the impact events, the cumulative damage index is calculated based on the ratio of the plastic zone diameter to the residual thickness, and the geometric parameters of the retaining dam are updated.

[0061] To describe the damage evolution of a retaining dam under debris flow impact rich in boulders, it is necessary to accurately describe the damage evolution of a retaining dam under debris flow impact rich in boulders, which requires describing debris flow dynamics, determining the characteristics of impact boulders, and estimating the damage of the dam body under impact loads. The present invention proposes a depth-averaged two-phase flow model of debris flow for describing fluid dynamics, a stochastic probability model of impact boulders for determining the random characteristics of boulders, and an impact load model for describing the damage of the dam body.

[0062] Optionally, let the debris flow movement direction along the slope be the axis, and the debris flow movement direction perpendicular to the slope be the axis, be the time, be the volume fraction of the fluid phase, be the volume fraction of the solid phase, be the flow depth, is the flow velocity of the fluid phase along direction, is the flow velocity of the solid phase along direction, is the flow velocity of the liquid phase, is the component of the acceleration due to gravity in direction, is the component of the acceleration due to gravity in direction, is the riverbed elevation, is the fluid phase velocity vector, is the acceleration due to gravity, is the component of the phase drag force in direction, is the component of the phase drag force in direction, is the flow velocity of the solid phase along direction, is the Euler's constant, is the basal friction angle of the solid phase, is the solid phase velocity vector, is the Manning's friction coefficient of the fluid phase, is the coefficient of earth pressure describing the stress state during the deformation of the material element in direction, is the coefficient of earth pressure describing the stress state during the deformation of the material element in direction, then:

[0063] The mass conservation equation of the solid phase is:

[0064] ;

[0065] The mass conservation equation of the fluid phase is:

[0066] ;

[0067] The momentum conservation equation of the fluid phase in direction is:

[0068] ;

[0069] The momentum conservation equation of the fluid phase in direction is:

[0070] ;

[0071] The momentum conservation equation of the solid phase in direction is:

[0072] ;

[0073] Solid phase The momentum conservation equation in the direction is:

[0074] .

[0075] Debris flow is a typical solid-liquid two-phase flow, and the depth-averaged two-phase flow model of debris flow can effectively capture the typical characteristics. The right side of the momentum conservation equation represents the influence of gravity, fluid pressure gradient, riverbed topography, resistance and friction loss on the debris flow, and the terms on the right side of the solid phase momentum conservation equation represent the influence of gravity, solid phase stress, riverbed topography, resistance and friction loss on the debris flow.

[0076] Optional, set is the resistance correction factor describing the effect of particle concentration, is the drag coefficient, is the density of the fluid phase, is the volume fraction of the solid phase, is the particle diameter, is the particle viscosity, is the fluid viscosity, and the resistance to the change of phase volume fraction is ,but:

[0077] .

[0078] Debris flows are characterized by the rapid mixing movement of water and heterogeneous particles, occasionally interspersed with boulders of different sizes. During the movement of debris flows, coarse and fine particles interact with each other to form a fluid structure different from that of traditional Newtonian fluids, which can be described by a two-phase model with variable viscosity. However, large boulders do not participate in the fluid structure, but form a lattice structure that supports, superimposes, and inlays with the mud. Debris flows with different viscosity coefficients usually present different movement patterns, among which viscous debris flows show more obvious surge characteristics. Consider a debris flow event in the time domain, and regard the mud surge sequence and boulder appearance as discrete events. The time of mud surge sequence and boulder appearance is random. The discrete impact event of boulders can be described by a Poisson counting process, in which the time of event occurrence is a random variable. The number of discrete boulder impact events in a given time interval is obtained by Poisson distribution.

[0079] The application of the Poisson distribution is based on the following assumptions: the number of discrete boulder impact events at the initial moment is 0; there is no overlap between events; the probability of an event occurring within any time increment is asymptotically proportional to the time increment, which means the process has stationary increments; the occurrences of events in different time increments are independent. Therefore, the Poisson counting process is a Markov process with discrete states in continuous time.

[0080] Optionally, according to the time distribution and intensity distribution of the impact events, the Poisson counting process is used to describe the impact events, and a randomness probability model of the impact boulders is constructed to obtain the time distribution of the impact boulders, including: Let be the time, represent the th occurring event, represent the correction coefficient of the boulder impact probability affected by the density of surrounding particles, be the average rate of event occurrence per unit time, represent the number of discrete boulder impact events within a given time interval , represent the probability of the number of discrete boulder impact events, obtained from the Poisson distribution:

[0081] ;

[0082] Let be the waiting time before the th boulder impact event occurs, and the cumulative distribution function is , and the event occurrence time follows a gamma distribution, and the cumulative distribution function is expressed as:

[0083] ;

[0084] Let the boulder radius be , and be the empirical parameters of the radius distribution, and the extreme value distribution function is , be the probability function of the boulder radius, following the extreme value distribution:

[0085] .

[0086] Hydrodynamic numerical models have difficulties in simulating the occurrence, movement, and interaction of boulders in mud. Therefore, the present invention uses a combination of impact loads to characterize the combined action of mud and impact boulders on the retaining dam. Experimental evidence shows that the impact pressure of debris flow mud on a rigid barrier is proportional to the hydrostatic pressure on the structure, and the proportionality coefficient ranges from 2.5 to 11.

[0087] Optionally, the Hertz contact theory is used to calculate the impact load including the elastic-plastic deformation stage based on the velocity of the impact boulder, and the strength distribution of the impact boulder is obtained, including: is the impact pressure of the debris flow mud on the retaining dam. Let be the static component linearly and uniformly distributed along the flow depth, be the dynamic component linearly and uniformly distributed along the flow depth, be the acceleration due to gravity, be the flow depth of the mud, be the flow velocity of the mud, be the density of the two-phase mud. Then the impact pressure of the debris flow mud on the retaining dam is expressed as:

[0088] .

[0089] Optionally, the velocity of the impact boulder is determined according to the mud viscosity; let the velocity of the impact boulder be , the radius of the boulder be , the mud viscosity be , be the coefficient related to the mud properties. When the fluid viscosity is greater than the set threshold, , when the fluid viscosity is less than or equal to the set threshold, .

[0090] Optionally, the impact pressure of the debris flow mud on the dam body includes static water pressure and dynamic water pressure; let be the contact stiffness, be the radius of the boulder, be the time, be the equivalent elastic modulus, , be the contact displacement during the contact process between the impact boulder and the dam body. The boulder impact load is . Based on the Hertz contact theory, the boulder impact load is calculated as:

[0091] .

[0092] Optionally, the cumulative damage index is calculated based on the ratio of the plastic zone diameter to the residual thickness, including: Let be the length of the plastic zone diameter, be the th permanent indentation depth generated by the impact, and the remaining thickness of the dam body impact section is , be the th remaining thickness of the impact section, be the cumulative damage index, and the cumulative damage index of the first impact is , be the length of the plastic zone diameter, be the remaining thickness of the first impact section, , For the cumulative damage degree of the secondary impact retaining dam, then:

[0093] ;

[0094] .

[0095] Optionally, update the geometric parameters of the retaining dam until the cumulative damage degree of the retaining dam reaches the set threshold or the number of impacts reaches the set reference value.

[0096] By comparing the numerical results with the results of debris flow flume experiments and debris flow impact pier experiments, the effectiveness of the proposed method is verified. The simulation results show that the propagation process of debris flow and the change of dam damage caused by boulder impact can be quantitatively described.

[0097] The present invention proposes a new numerical method to evaluate the damage evolution of an interception dam under the impact of debris flow rich in boulders. This method integrates a depth-averaged two-phase model, a stochastic probability model of impact boulders, and an impact load model to describe the conditions of debris flow propagation and the interception dam during the flow process. By applying the finite volume method, it can capture the dynamics of debris flow propagation and dam damage while ensuring computational efficiency. The verification results show that this method can quantitatively describe the debris flow propagation process and the change of dam damage caused by boulder impact, improving the accuracy of the simulation results.

[0098] Embodiment 2

[0099] Based on the same principle as the method shown in Embodiment 1 of the present invention, as shown in the appendix Figure 2 The present invention also provides a simulation system for the damage process of a retaining dam under debris flow impact, including a model construction unit, a parameter update unit, a time distribution processing unit, an intensity distribution processing unit, and a damage calculation and parameter update unit;

[0100] The model construction unit is used to consider the interaction between the solid phase and the fluid phase and construct a depth-averaged two-phase flow model of debris flow according to the flow field parameters; the depth-averaged two-phase flow model of debris flow includes the mass conservation equation of the solid phase and the fluid phase, the momentum conservation equation of the fluid phase, and the momentum conservation equation of the solid phase;

[0101] The parameter update unit is used to discretize the depth-averaged two-phase flow model of debris flow by using the second-order finite volume method and update the flow field parameters by using the HLLC Riemann solver;

[0102] The time distribution processing unit is used to describe the impact event by using the Poisson counting process, construct a stochastic probability model of impact boulders, and obtain the time distribution of impact boulders;

[0103] The strength distribution processing unit is used to calculate the impact load including the elastic-plastic deformation stage according to the speed of the impacting boulder by using the Hertz contact theory, and obtain the strength distribution of the impacting boulder.

[0104] The damage calculation and parameter update unit is used to calculate the cumulative damage index based on the ratio of the plastic zone diameter to the residual thickness according to the time distribution and strength distribution of the impact events, and update the geometric parameters of the retaining dam until the retaining dam fails.

[0105] Optionally, let the direction of debris flow movement along the slope be axis, and the direction perpendicular to the slope of debris flow movement be axis, be the time, be the volume fraction of the fluid phase, be the volume fraction of the solid phase, be the flow depth, be the flow velocity of the fluid phase along the direction, be the flow velocity of the solid phase along the direction, be the flow velocity of the liquid phase, be the component of the gravitational acceleration in the direction, be the component of the gravitational acceleration in the direction, be the riverbed elevation, be the velocity vector of the fluid phase, be the gravitational acceleration, be the component of the phase resistance in the direction, be the component of the phase resistance in the direction, be the flow velocity of the solid phase along the direction, be the Euler constant, be the basal friction angle of the solid phase, be the velocity vector of the solid phase, be the Manning friction coefficient of the fluid phase, be the earth pressure coefficient describing the stress state in the direction during the deformation of the material element, be the earth pressure coefficient describing the stress state in the direction during the deformation of the material element, then:

[0106] The mass conservation equation of the solid phase is:

[0107] ;

[0108] The mass conservation equation of the fluid phase is:

[0109] ;

[0110] The momentum conservation equation of the fluid phase in the direction is:

[0111] ;

[0112] The momentum conservation equation of the fluid phase in the direction is:

[0113] ;

[0114] The momentum conservation equation of the solid phase in the direction is:

[0115] ;

[0116] The momentum conservation equation of the solid phase in the direction is:

[0117] .

[0118] Optionally, let be the resistance correction factor describing the influence of particle concentration, be the drag coefficient, be the density of the fluid phase, be the volume fraction of the solid phase, be the particle diameter, be the particle viscosity, be the fluid viscosity, and the drag force considering the change of phase volume fraction is , then:

[0119] .

[0120] Optionally, according to the time distribution and intensity distribution of the impact events, a Poisson counting process is used to describe the impact events, and a stochastic probability model of impact boulders is constructed to obtain the time distribution of impact boulders, including: Let be the time, represent the th occurring event, represent the boulder impact probability correction factor affected by the density of surrounding particles, be the average rate of event occurrence per unit time, Indicates the number of discrete boulder impact events within a given time interval The number of discrete boulder impact events The probability of the number of discrete boulder impact events, obtained from the Poisson distribution:

[0121] ;

[0122] Let be the waiting time before the th boulder impact event occurs, and the cumulative distribution function is , and the event occurrence time follows a gamma distribution, and the cumulative distribution function is expressed as:

[0123] ;

[0124] Let the boulder radius be , and be the empirical parameters of the radius distribution, and the extreme value distribution function is , is the probability function of the boulder radius, following the extreme value distribution:

[0125] .

[0126] Optionally, according to the velocity of the impacting boulder, the Hertz contact theory is used to calculate the impact load including the elastic-plastic deformation stage, and the strength distribution of the impacting boulder is obtained, including: is the impact pressure of the debris flow slurry on the retaining dam. Let be the static component linearly and uniformly distributed along the flow depth, be the dynamic component linearly and uniformly distributed along the flow depth, be the acceleration due to gravity, be the flow depth of the slurry, be the flow velocity of the slurry, be the density of the two-phase slurry, then the impact pressure of the debris flow slurry on the retaining dam is expressed as:

[0127] .

[0128] Optionally, the velocity of the impacting boulder is determined according to the slurry viscosity; let the velocity of the impacting boulder be , the boulder radius be , the slurry viscosity be , be the coefficient related to the slurry characteristics. When the fluid viscosity is greater than the set threshold, , when the fluid viscosity is less than or equal to the set threshold, .

[0129] Optionally, the impact pressure of the debris flow slurry on the dam body includes hydrostatic pressure and dynamic hydrostatic pressure; let is the contact stiffness, is the boulder radius, is the time, is the equivalent elastic modulus, , is the contact displacement during the contact process between the impacting boulder and the dam body, and the boulder impact load is . Based on the Hertz contact theory, the boulder impact load is calculated as follows:

[0130] .

[0131] Optionally, the cumulative damage index is calculated based on the ratio of the plastic zone diameter to the residual thickness, including: Let be the length of the plastic zone diameter, be the th permanent indentation depth generated by the impact, and the remaining thickness of the dam body impact section is , be the th remaining thickness of the impact section, be the cumulative damage index, and the cumulative damage index of the first impact is , be the length of the plastic zone diameter, be the remaining thickness of the first impact section, , be th cumulative damage degree of the impact retaining dam, then:

[0132] ;

[0133] .

[0134] Optionally, update the geometric parameters of the retaining dam until the cumulative damage degree of the retaining dam reaches the set threshold or the number of impacts reaches the set reference value.

[0135] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention can have various changes and modifications. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A method for simulating the damage process of a retaining dam under the impact of debris flow, characterized in that: include: Considering the interaction between solid and fluid phases, a depth-averaged two-phase flow model of debris flow is constructed based on flow field parameters. The depth-averaged two-phase flow model of debris flow includes the mass conservation equations of the solid phase and the fluid phase, the momentum conservation equation of the fluid phase, and the momentum conservation equation of the solid phase. Assume that the direction of the debris flow movement along the slope is Axis, the debris flow moves perpendicular to the slope axis, For time, is the volume fraction of the fluid phase, is the volume fraction of the solid phase, For the flow to be deep, For fluid phase Directional flow rate, For the solid phase Directional flow rate, is the liquid phase flow rate, is the gravitational acceleration The direction of the component, is the gravitational acceleration The direction of the component, is the riverbed elevation, is the fluid phase velocity vector, is the acceleration due to gravity, The relative resistance is The direction of the component, The relative resistance is The direction of the component, For the solid phase Directional flow rate, is Euler's constant, is the base friction angle of the solid phase, is the solid phase velocity vector, is the Manning friction coefficient of the fluid phase, To describe the stress state when the material unit is deformed Earth pressure coefficient in the direction, To describe the stress state when the material unit is deformed The earth pressure coefficient in the direction is: The mass conservation equation for the solid phase is: ； The fluid phase mass conservation equation is: ； Fluid phase The momentum conservation equation in the direction is: ； Fluid phase The momentum conservation equation in the direction is: ； Solid phase The momentum conservation equation in the direction is: ； Solid phase The momentum conservation equation in the direction is: ； The second-order finite volume method is used to discretize the depth-averaged two-phase flow model of debris flow, and the HLLC Riemann solver is used to update the flow field parameters. The Poisson counting process is used to describe the impact event, and the random probability model of the impact boulder is constructed to obtain the time distribution of the impact boulder. For time, Indicates events that occurred, The boulder impact probability correction factor that represents the influence of the surrounding particle density. is the average rate of events occurring per unit time, Indicates that at a given time interval The number of discrete megalithic impact events within The probability representing the number of discrete boulder impact events is obtained from the Poisson distribution: ； set up For the The waiting time before the impact boulder event occurs, and the cumulative distribution function is , the event time follows the gamma distribution, and the cumulative distribution function is expressed as: ； Assume the radius of the boulder is , and is the empirical parameter of radius distribution, and the extreme value distribution function is , is the probability function of the boulder radius, which follows an extreme value distribution: ； According to the speed of the impact boulder, the Hertz contact theory is used to calculate the impact load in the elastic-plastic deformation stage, and the strength distribution of the impact boulder is obtained; is the impact pressure of debris flow mud on the retaining dam, is the static component that is linearly and uniformly distributed along the flow depth, is the dynamic component that is linearly and uniformly distributed along the flow depth, is the acceleration due to gravity, For the mud flows deep, is the mud flow rate, is the density of the two-phase mud, then the impact pressure of the debris flow mud on the retaining dam is expressed as: ； The impact pressure of debris flow mud on the dam body includes static water pressure and dynamic water pressure. is the contact stiffness, is the boulder radius, For time, is the equivalent elastic modulus, , is the contact displacement between the impact boulder and the dam body, and the boulder impact load is , calculate the boulder impact load based on Hertz contact theory: ; According to the time distribution and intensity distribution of the impact event, the cumulative damage index is calculated based on the ratio of the plastic zone length to the residual thickness, and the geometric parameters of the retaining dam are updated; is the diameter length of the plastic zone, For the The depth of the permanent indentation caused by the impact is the residual thickness of the impact section of the dam body. , For the The residual thickness of the secondary impact section, is the cumulative damage index, and the cumulative damage index of the first impact is , is the diameter length of the plastic zone, is the remaining thickness of the first impact section, , for The cumulative damage degree of the secondary impact barrier dam is: ； 。 2. The method for simulating the damage process of a retaining dam under the impact of debris flow according to claim 1 is characterized in that: set up is the resistance correction factor describing the effect of particle concentration, is the drag coefficient, is the density of the fluid phase, is the volume fraction of the solid phase, is the particle diameter, is the particle viscosity, is the fluid viscosity, and the resistance to the change of phase volume fraction is ,but: 。 3. The method for simulating the damage process of a retaining dam under the impact of debris flow according to claim 1 is characterized in that: The speed of impacting the boulder is determined according to the viscosity of the mud; let the speed of impacting the boulder be , the boulder radius is The mud viscosity is , is a coefficient related to mud properties. When the fluid viscosity is greater than the set threshold, , when the fluid viscosity is less than or equal to the set threshold, .

4. The method for simulating the damage process of a retaining dam under the impact of debris flow according to claim 1 is characterized in that: The geometric parameters of the retaining dam are updated until the cumulative damage degree of the retaining dam reaches the set threshold or the number of impacts reaches the set reference value.

5. The simulation system of the damage process of the retaining dam under the impact of debris flow is characterized by: It includes a model building unit, a parameter updating unit, a time distribution processing unit, an intensity distribution processing unit, and a damage calculation and parameter updating unit; The model building unit is used to consider the interaction between the solid phase and the fluid phase and to build a depth-averaged two-phase flow model of debris flow according to the flow field parameters; the depth-averaged two-phase flow model of debris flow includes the mass conservation equations of the solid phase and the fluid phase, the momentum conservation equation of the fluid phase and the momentum conservation equation of the solid phase; assuming that the direction of the debris flow movement along the slope is Axis, the debris flow moves perpendicular to the slope axis, For time, is the volume fraction of the fluid phase, is the volume fraction of the solid phase, For the flow to be deep, For fluid phase Directional flow rate, For the solid phase Directional flow rate, is the liquid phase flow rate, is the gravitational acceleration The direction of the component, is the gravitational acceleration The direction of the component, is the riverbed elevation, is the fluid phase velocity vector, is the acceleration due to gravity, The relative resistance is The direction of the component, The relative resistance is The direction of the component, For the solid phase Directional flow rate, is Euler's constant, is the base friction angle of the solid phase, is the solid phase velocity vector, is the Manning friction coefficient of the fluid phase, To describe the stress state when the material unit is deformed Earth pressure coefficient in the direction, To describe the stress state when the material unit is deformed The earth pressure coefficient in the direction is: The mass conservation equation for the solid phase is: ； The fluid phase mass conservation equation is: ； Fluid phase The momentum conservation equation in the direction is: ； Fluid phase The momentum conservation equation in the direction is: ； Solid phase The momentum conservation equation in the direction is: ； Solid phase The momentum conservation equation in the direction is: ； The parameter updating unit is used to discretize the depth-averaged two-phase flow model of debris flow using the second-order finite volume method and update the flow field parameters using the HLLC Riemann solver; For time, Indicates events that occurred, The boulder impact probability correction factor that represents the influence of the surrounding particle density. is the average rate of events occurring per unit time, Indicates that at a given time interval The number of discrete boulder impact events within The probability representing the number of discrete boulder impact events is obtained from the Poisson distribution: ； set up For the The waiting time before the impact boulder event occurs, and the cumulative distribution function is , the event time follows the gamma distribution, and the cumulative distribution function is expressed as: ； Assume the radius of the boulder is , and is the empirical parameter of radius distribution, and the extreme value distribution function is , is the probability function of the boulder radius, which follows an extreme value distribution: ； The time distribution processing unit is used to describe the impact event using the Poisson counting process, build a random probability model of the impact boulder, and obtain the time distribution of the impact boulder; For time, Indicates events that occurred, The boulder impact probability correction factor that represents the influence of the surrounding particle density. is the average rate of events occurring per unit time, Indicates that at a given time interval The number of discrete boulder impact events within The probability representing the number of discrete boulder impact events is obtained from the Poisson distribution: ； set up For the The waiting time before the impact boulder event occurs, and the cumulative distribution function is , the event time follows the gamma distribution, and the cumulative distribution function is expressed as: ； Assume the radius of the boulder is , and is the empirical parameter of radius distribution, and the extreme value distribution function is , is the probability function of the boulder radius, which follows an extreme value distribution: ； The strength distribution processing unit is used to calculate the impact load including the elastic-plastic deformation stage according to the speed of the impact boulder using the Hertz contact theory to obtain the strength distribution of the impact boulder; is the impact pressure of debris flow mud on the retaining dam, is the static component that is linearly and uniformly distributed along the flow depth, is the dynamic component that is linearly and uniformly distributed along the flow depth, is the acceleration due to gravity, For the mud flows deep, is the mud flow rate, is the density of the two-phase mud, then the impact pressure of the debris flow mud on the retaining dam is expressed as: ； The impact pressure of debris flow mud on the dam body includes static water pressure and dynamic water pressure. is the contact stiffness, is the boulder radius, For time, is the equivalent elastic modulus, , is the contact displacement between the impact boulder and the dam body, and the boulder impact load is , calculate the boulder impact load based on Hertz contact theory: ； The damage calculation and parameter updating unit is used to calculate the cumulative damage index based on the ratio of the plastic zone diameter to the residual thickness according to the time distribution and intensity distribution of the impact event, and update the geometric parameters of the retaining dam until the retaining dam fails; is the diameter length of the plastic zone, For the The depth of the permanent indentation caused by the impact is the residual thickness of the impact section of the dam body. , For the The residual thickness of the secondary impact section, is the cumulative damage index, and the cumulative damage index of the first impact is , is the diameter length of the plastic zone, is the remaining thickness of the first impact section, , for The cumulative damage degree of the secondary impact barrier dam is: ； 。

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