CN116628801A - Nonlinear earthquake motion damage analysis method for reinforced concrete sluice-foundation-water system - Google Patents

Abstract

The invention discloses a nonlinear ground motion damage analysis method for a reinforced concrete sluice-foundation-water body system. According to the structural characteristics of a sluice chamber, a structure including a foundation, a water body, a gate pier, a gate floor, a steel gate, and an upper hoist room is established. And the three-dimensional finite element model of the sluice chamber structure of the steel bar, using the finite element numerical simulation technology, based on the viscoelastic artificial boundary conditions, considering the radiation damping effect of the infinite foundation, the dynamic damage of the concrete, the bond-slip effect of the reinforced concrete, and the water body and the sluice structure Based on the fluid-solid coupling effect of the sluice chamber structure, the nonlinear seismic damage analysis is carried out. The invention effectively makes up for the defects existing in the anti-seismic analysis process of the sluice chamber structure at the present stage, and improves the accuracy of the seismic damage analysis of the sluice structure.

Description

Nonlinear earthquake damage analysis of reinforced concrete sluice-foundation-water system method

technical field

The invention relates to anti-seismic safety analysis, in particular to a non-linear earthquake damage analysis method for a reinforced concrete sluice-foundation-water system.

Background technique

Sluices have dual functions of retaining water and releasing water, and are widely used in water conservancy projects. Seismic analysis of sluice structures is one of the important contents of the safety review of sluice structures. In recent years, a lot of research has been done on the seismic analysis of sluice structures at home and abroad. Initially, the research on the seismic analysis of the lock chamber structure was mainly done by manual calculation, and a lot of simplification work was done, a simplified model was established, and rough calculations were performed. With the rapid development of the finite element method and the wide application of computers, the analysis method of lock chamber structure has also made a qualitative leap. In recent years, the use of finite element numerical simulation technology to carry out seismic analysis and research on lock chamber structures has become a key technical means to solve the seismic problems of lock chamber structures. At present, scholars at home and abroad mainly use the quasi-static method, mode decomposition response spectrum method and time-history analysis method to study the seismic performance of the sluice structure. However, the existing research on the seismic analysis of the sluice structure mainly focuses on the linear elastic concrete structure. Considering the dynamic damage of concrete and the bond-slip effect of reinforced concrete, no one has been involved in the research on the seismic analysis of sluice structures. As we all know, the sluice chamber section is generally a reinforced concrete structure, and reinforced concrete is a very complex building material, which has complex mechanical behaviors such as plasticity, crushing, and cracking. In three-dimensional space, these extremely complex mechanical behaviors It is more difficult to determine the change, and it is biased to only analyze the linear elasticity of the concrete structure for the sluice structure. At the same time, the thin-walled structure of the sluice chamber is prone to penetrating cracks under strong earthquakes. At present, domestic scholars have little research on the possible failure modes of sluice structures under earthquakes, and there are few studies on the nonlinear seismic damage mechanism of sluice structures. Not much.

In addition, the existing research results all use the additional mass method to convert the seismic shock pressure of the sluice. In fact, the additional mass method mainly studies the hydrodynamic pressure problem of the infinite water body in front of the dam on the rigid dam surface, while for the sluice structure, the vibration of the water body in the lock chamber section and the infinite water area of the gravity dam, arch dam, etc. The vibration of the water body is different, both sides of the gate pier bear the action of water pressure, and the influence of the dynamic water pressure is more significant. Therefore, it is inappropriate to use the additional mass method to simulate the seismic shock hydraulic pressure acting on the sluice.

In summary, the existing analysis methods basically adopt the linear elastic analysis method, which does not consider the nonlinear damage of concrete materials, nor the interaction of reinforced concrete, which leads to inaccurate analysis of earthquake damage of sluices.

Contents of the invention

Purpose of the invention: the purpose of this invention is to provide a kind of reinforced concrete sluice-foundation-water body system nonlinear ground motion damage analysis method, solve existing analysis method and adopt linear elastic analysis method basically, do not consider the material nonlinear damage of concrete, also do not Considering the interaction of reinforced concrete, the seismic damage analysis of sluices is not accurate.

Technical solution: The non-linear earthquake damage analysis method for reinforced concrete sluice-foundation-water system of the present invention comprises the following steps:

(1) According to the structural size and reinforcement of the sluice chamber, establish a three-dimensional sluice chamber structure finite element model. The model includes foundation, water body, gate floor, gate pier, steel gate, traffic bridge, upper hoist room structure and concrete Inner reinforcement;

(2) Based on finite element analysis, considering the infinite foundation radiation damping effect, concrete dynamic damage, bond-slip effect of reinforced concrete, and fluid-solid coupling effect of water body and sluice structure, input preset material parameters, boundary conditions and different Non-linear ground motion damage calculation is carried out to obtain the dynamic response of each part of the lock chamber structure under the earthquake load;

(3) Based on the calculation results of step (2), select the feature points in the area with the largest displacement, stress and damage value, and draw the change curve of displacement, stress and damage value at the feature point with the earthquake duration.

(4) According to the change curve of the damage value with the earthquake duration, the proportion of the cross-sectional area of the damaged area is determined, and the structural damage level of the lock chamber is determined according to the proportion of the cross-sectional area of the damaged area.

Wherein, the scope of the foundation unit in the step (1) is based on the upstream, downstream, left, right and bottom elevations of the sluice floor, respectively extending to the upstream, downstream, left bank, right bank and vertically downward twice the height of the sluice chamber , the height of the lock chamber is the difference between the elevation of the top of the hoist room and the bottom of the gate floor; the upstream and downstream water body unit nodes are shared with the gate piers and steel gate nodes; In the spring coupling element method, the normal displacement of the steel bar node is calculated according to the following formula, and the specific formula is as follows:

In the formula, _is the displacement value of the i-th dimension of the reinforcement node in the local coordinate system; n is the model dimension; r _ij is the interpolation coefficient, that is, the element of the coordinate transformation matrix;

During the finite element calculation in the step (2), the concrete adopts a four-parameter dynamic damage constitutive model, and its failure criterion is:

In the formula: ε ^* is equivalent strain; A, B, C, D are four test constants, which can be obtained through uniaxial tensile test, uniaxial compression test, biaxial isostatic test and triaxial compression test; I′ ₁ = (ε ₁ +ε ₂ +ε ₃ )/3 is the first invariant of the strain tensor; is the maximum principal strain; /> is the second invariant of strain deviation; /> J′ ₃ ＝ε ₁ ε ₂ ε ₃ is the third invariant of strain deviation; ε ₁ , ε ₂ , ε ₃ are three-dimensional principal strains; ε _m is the strain under spherical stress.

Under the action of earthquake load, the unloading and reloading process of the softened section of concrete is inevitable. The following formula is used for the calculation of residual strain in this simulation:

In the formula, ε _p is the residual strain value; ε ₀ = f _t /E is the ultimate strain under the tensile strength of concrete, f _t is the tensile strength of concrete, E is the modulus of elasticity of concrete; ε _un is the strain value at the unloading point ;

The interaction between steel bar and concrete is simulated by the single spring coupling element method based on the hybrid coordinate system, where the interaction equation between steel bar and concrete is as follows:

In the formula, Δu, Δu ^* and ΔF, ΔF ^* are the displacement vector increment and load vector increment in the Oxyz and O ^* x ^* y ^* z ^* coordinate system respectively; k and k ^* are Oxyz and O ^* x ^* y respectively ^* z ^* The stiffness matrix in the coordinate system; k _s and r are the coordinate transformation matrix; r ^T is the transposition matrix of the coordinate transformation matrix.

The potential fluid element is used to simulate the fluid-solid coupling between the water body before and after the gate, the gate pier and the steel gate under the earthquake, and the governing equation is as follows:

In the formula, P represents the hydrodynamic pressure, c is the sound wave velocity in water, is the Laplacian operator, /> is the second derivative of hydrodynamic pressure with respect to time;

The fluid-solid coupling boundary is set between the water body and the gate pier, the gate floor and the steel gate to simulate the energy transfer between the water body and the steel gate, as follows:

In the formula, n is the outer normal direction of the fluid domain on the fluid-solid interface surface; is the absolute acceleration along the normal direction on the fluid-solid interface surface, and ρ is the water body density;

Based on the standard design response spectrum, two seismic acceleration time-history curves are generated by triangular series expansion method, and the velocity and displacement time-history curves are generated by integration. In the calculation process, based on viscoelastic artificial boundary conditions, the velocity wave and displacement wave.

Displacement in the described step (3) includes displacement along the river, displacement along the river and vertical displacement, and stress includes the first principal stress and the third principal stress; the displacement and stress curves at the characteristic points of the drawing take the earthquake duration as horizontal axis, with the displacement or stress response as the vertical axis; the plotted damage value versus earthquake duration curve has the earthquake duration as the horizontal axis, and the damage value as the vertical axis.

In the step (4), the different damage levels of the lock chamber structure are determined by using the ratio of the area of the concrete damaged area of the lock chamber structure under the earthquake, and the specific judgment criteria are as follows:

Criterion

Beneficial effects: according to the structural characteristics of the sluice chamber, the present invention establishes a three-dimensional finite element model of the sluice chamber structure including foundation, water body, gate pier, gate floor, steel gate, upper hoist room structure and steel bars, and adopts finite element numerical simulation , based on viscoelastic artificial boundary conditions, considering the infinite foundation radiation damping effect, concrete dynamic damage, bond-slip effect of reinforced concrete, and fluid-solid coupling between water body and sluice structure, a nonlinear seismic analysis of the sluice chamber structure is established. The method of dynamic damage analysis can effectively make up for the defects in the seismic analysis process of the sluice chamber structure at the present stage, and improve the accuracy of the seismic damage analysis of the sluice structure.

Description of drawings

Fig. 1 is the overall finite element model of the flood control sluice chamber structure;

Figure 2 is the finite element model of the flood control gate chamber structure;

Fig. 3 is the finite element model of the pier and the bottom plate of the flood control gate;

Fig. 4 The finite element model of the flood gate steel gate;

Fig. 5 Finite element model of hoist machine room for flood control gate

Fig. 6 is the finite element model of the reinforcement finite element model in the bent column of the hoist room of the flood control gate;

Fig. 7 is the finite element model of the flood control highway bridge;

Figure 8 is the finite element model of the steel gate of the flood control gate and the water body in front of the gate;

Fig. 9 is a standard design response spectrum;

Fig. 10 is the time-history curve of acceleration in x direction;

Fig. 11 is the y direction acceleration time history curve;

Fig. 12 is x direction velocity time history curve;

Fig. 13 is y direction velocity time history curve;

Fig. 14 is the time-history curve of displacement in x direction;

Fig. 15 is the y direction displacement time history curve;

Figure 16 Schematic diagram of the location of structural feature points in the sluice chamber;

Figure 17 is the time-history curve of the displacement along the river at the characteristic point A;

Fig. 18 is the time-history curve of the first principal stress at the characteristic point B;

Figure 19 is a comparison of the calculation results of the lateral displacement at the structural feature point A of the mesopore sluice chamber under different calculation methods;

Figure 20 is a comparison of the calculation results of the first principal stress at the structural feature point B of the mesopore lock chamber under different calculation methods;

Fig. 21 is the time history curve of the damage value at the characteristic point B;

Figure 22 is a schematic diagram of structural damage of the mesoporous lock chamber at 0.50s;

Figure 23 is a schematic diagram of structural damage of the mesoporous lock chamber at 2.60s;

Figure 24 is a schematic diagram of structural damage of the mesoporous lock chamber at 6.85s;

Fig. 25 is a schematic diagram of structural damage of the mesoporous lock chamber at 14.85s.

Detailed ways

The present invention will be further described below in conjunction with the accompanying drawings and specific examples.

The seismic intensity of the area where a flood control gate project is located is VIII degree. The flood control gate has a total of 6 holes, each with a width of 6m, and 2 holes in a row, making a total of three holes. In this calculation, the nonlinear seismic damage analysis is mainly performed on the structure of the middle-hole-coupled lock chamber. According to the structural characteristics of the flood control gate, a three-dimensional finite element model including foundation, water body, gate floor, gate pier, steel gate, highway bridge, upper hoist room and steel bars is established. The specific model is shown in Figure 1-8 of the manual. Among them, the scope of the foundation unit is based on the upstream, downstream, left, right and bottom elevations of the gate floor, respectively extending to the upstream, downstream, left bank, right bank and vertically downward twice the height of the lock chamber, where the height of the lock chamber is The difference between the elevation of the top of the closed machine room and the elevation of the bottom of the gate floor. At the same time, in order to facilitate the establishment of the model, the upstream and downstream water body unit nodes are shared with the pier and steel gate nodes; the steel bar unit nodes are not shared with the concrete unit nodes, and the interpolation method is used for calculation. In the single spring coupling element method, the steel bar is calculated according to the following formula The normal displacement of the node, the specific formula is as follows:

In the formula, _is the displacement value of the i-th dimension of the reinforcement node in the local coordinate system; n is the model dimension; r _ij is the interpolation coefficient, that is, the element of the coordinate transformation matrix;

Table 1 shows the water level in front of the gate and behind the gate under the normal water storage level condition of the middle-hole lock chamber structure.

Table 1 Water depth table before and after the structural gate of the flood control gate chamber

In this calculation process, the concrete adopts a four-parameter dynamic damage constitutive model, and its failure criterion is:

In the formula: ε ^* is equivalent strain; A, B, C, D are four test constants, which can be obtained through uniaxial tensile test, uniaxial compression test, biaxial isostatic test and triaxial compression test; I′ ₁ = (ε ₁ +ε ₂ +ε ₃ )/3 is the first invariant of the strain tensor; is the maximum principal strain; /> is the second invariant of strain deviation; /> J′ ₃ =ε ₁ ε ₂ ε ₃ is the third invariant of strain deviation; ε ₁ , ε ₂ , ε ₃ are three-dimensional principal strains; ε _m is the strain under spherical stress.

Under the action of earthquake load, the unloading and reloading process of the softened section of concrete is inevitable. The following formula is used for the calculation of residual strain in this simulation:

In the formula, ε _p is the residual strain value; ε ₀ = f _t /E is the ultimate strain under the tensile strength of concrete, f _t is the tensile strength of concrete, E is the modulus of elasticity of concrete; ε _un is the strain value at the unloading point .

The interaction between steel bar and concrete is simulated by the single spring coupling element method based on the hybrid coordinate system, where the interaction equation between steel bar and concrete is

In the formula, Δu, Δu ^* and ΔF, ΔF ^* are the displacement vector increment and load vector increment in the Oxyz and O ^* x ^* y ^* z ^* coordinate system respectively; k and k ^* are Oxyz and O ^* x ^* y respectively ^* z ^* The stiffness matrix in the coordinate system; k _s ; r is the coordinate transformation matrix; r ^T is the transposition matrix of the coordinate transformation matrix.

The potential fluid element is used to simulate the fluid-solid coupling between the water body before and after the gate, the gate pier and the steel gate under the earthquake, and the governing equation is as follows:

In the formula, P represents the hydrodynamic pressure, c is the sound wave velocity in water, is the Laplacian operator, /> is the second derivative of hydrodynamic pressure with respect to time.

The fluid-solid coupling boundary is set between the water body and the gate pier, the gate floor and the steel gate to simulate the energy transfer between the water body and the steel gate, as follows:

In the formula, n is the outer normal direction of the fluid domain on the fluid-solid interface surface; is the absolute acceleration along the normal direction on the fluid-solid interface surface, and ρ is the water body density.

The structural material parameters of the flood control sluice chamber are shown in Table 2.

Table 2 Concrete material parameters of the chamber structure of the middle hole chamber structure of the flood control gate

It should be pointed out that according to the "Standards for Seismic Design of Hydraulic Structures" (GB 51247-2018), the elastic modulus of concrete materials is increased by 50% on the basis of the static elastic modulus, and the standard value of the dynamic compressive strength of concrete is higher than the standard value of the static compressive strength 20%, the standard value of concrete dynamic tensile strength is 10% of the standard value of dynamic compressive strength. In addition, the density of the water body is 1000kg/m ³ and the bulk modulus is 2.3GPa during the numerical simulation calculation process.

According to the "Zoning Map of Seismic Motion Parameters in China" (GB18306-2015), the seismic fortification intensity of the flood control gate project area is VIII degree, and the characteristic period T _g of the foundation response spectrum of this project is taken as 0.35s. According to the values stipulated in the "Standards for Seismic Design of Hydraulic Structures" (GB 51247-2018), the representative value of the horizontal design acceleration of the flood gate chamber structure α _h =0.2g. At the same time, according to Table 4.3.3 of the "Standards for Seismic Design of Hydraulic Structures" (GB 51247-2018), the representative value β _max of the maximum response spectrum of the sluice structure is taken as 2.25, and the sluice should consider both the direction along the river and the direction perpendicular to the river. horizontal seismic action.

Attached Figure 9 is a schematic diagram of the design response spectrum used in this calculation. According to this design response spectrum, two seismic acceleration time histories are generated using the method of triangular series expansion, and the two seismic acceleration time history curves are shown in Figures 10-11 , the velocity and displacement time-history curves are shown in Figures 12-13 and 14-15, respectively. The calculation process is based on viscoelastic artificial boundary conditions, and the velocity wave and displacement wave are input vertically from the bottom of the foundation.

Based on the above material parameters and load parameters, the nonlinear seismic damage analysis of the flood control sluice chamber structure is carried out. In order to facilitate the analysis of the response results of displacement, acceleration, stress, and damage distribution of the reinforced concrete lock chamber structure under earthquake action, a certain number of feature points are selected in the middle hole lock chamber structure of the flood control gate, and the positions of the feature points are shown in Figure 16.

Taking the displacement along the river as an example, Figure 17 shows the time-history curves of displacement in the cross-river direction and along the river direction at the characteristic point A of the mid-hole sluice chamber structure based on the reinforced concrete dynamic damage time-history analysis method. It can be seen that under the earthquake, the displacement along the river at the feature point A reciprocates with the seismic load, and due to the consideration of the nonlinearity of the concrete material, there is a residual displacement at the feature point A at the end of the seismic load. In addition, the maximum (absolute value) displacement along the river at feature point A is 12.98mm, which occurs at 12.58s. In addition, it should be pointed out that, from the displacement curve along the river at the characteristic point A, the displacement change law shows a divergent trend, which is mainly because the bent columns of the middle hole lock chamber structure of the flood control sluice appeared under the action of a magnitude VIII earthquake. damage damage.

Taking the first principal stress as an example, Fig. 18 shows the time history curve of the first principal stress at the characteristic point B of the sluice chamber structure based on the reinforced concrete dynamic damage time history analysis method. It can also be seen that the sum of the first principal stress at the characteristic point B under the earthquake is constantly changing with time, and the first principal stress at B has a maximum value at 1.22s, which is 2.26MPa.

In order to verify the correctness of the calculation results, the linear elastic mode decomposition response spectrum method, the linear elastic time-history analysis method, and the dynamic damage time-history analysis method based on concrete were used to perform dynamic calculations on the structure of the mesopore lock chamber. The comparison of the calculation results is as follows.

Figure 19 shows the comparison of the calculation results of the displacement along the river direction at the structural feature point A of the lower middle hole sluice chamber by different methods. It can be seen from the figure that the calculation result of the lateral displacement at the characteristic point A of the sluice chamber structure based on the linear elastic time history analysis method is smaller than the calculation result based on the linear elastic mode decomposition response spectrum method, which conforms to the general law. At the same time, after considering the interaction of reinforced concrete, the calculation results based on the time-history analysis method based on damaged reinforced concrete are obviously smaller than those based on the time-history analysis method based on damaged concrete. This is mainly because the existence of steel bars reduces the Dynamic response under earthquake action. In addition, the calculation results based on the time-history analysis method of damaged reinforced concrete and the time-history analysis method based on damaged concrete are larger than those based on the linear elastic mode decomposition response spectrum method. The bent columns of the room structure have different degrees of earthquake damage, and the calculation results show a divergent trend.

Figure 20 shows the comparison of the calculation results of the first principal stress at the structural characteristic point B of the lower middle hole lock chamber calculated by different methods. It can be seen that the calculation result of the first principal stress at the characteristic point B of the sluice chamber structure based on the linear elastic time history analysis method is smaller than the calculation result based on the linear elastic mode decomposition response spectrum method, which conforms to the general law. At the same time, after considering the concrete damage, the calculation result of the first principal stress at the feature point B is obviously smaller than the calculation result based on the linear elastic time history analysis method, which is mainly because the damage cracking of concrete has a certain degree of influence on the stress release, reducing the stress response of the mesoporous lock chamber structure.

To sum up, through the comparative analysis of different calculation results, the correctness of the reinforced concrete dynamic damage model adopted this time can also be verified.

In order to analyze the non-linear earthquake damage mechanism of the lock chamber structure, Figure 21 shows the time history curve of the damage value at the characteristic point B of the lock chamber structure based on the reinforced concrete dynamic damage time history analysis method. Combined with the time-history curve of the first principal stress at feature point B, it can be seen that a large first principal stress appears at feature point B at 1s, and its maximum tensile stress value (2.26MPa) has exceeded the dynamic tensile strength of plain concrete. Damage and destruction began to appear, and its damage value reached 0.48, and with the increase of the earthquake duration, a larger first principal stress appeared at 2s and 3s, although the value of the first principal stress did not exceed the dynamic tensile strength of plain concrete at this time , but because the concrete has been damaged to a certain extent at this time, its damage value continues to increase under the action of the tensile stress, and its final damage value reaches 0.64.

In order to further reveal the nonlinear seismic damage accumulation process of the flood control sluice, Figures 22-25 respectively show structural damage diagrams of the flood control sluice mid-hole sluice chamber based on the dynamic damage time history analysis method of reinforced concrete at different times. It can be seen that at the initial stage of the earthquake, the overall structure of the lock chamber was not damaged. As the duration of the earthquake increased, the structure of the lock chamber began to be damaged gradually at the part with the larger first principal stress, and the damage value and damage area increased with the increase of the earthquake load. Continue to gradually increase until the end of the seismic load. In addition, it can be seen from the figure that after 2.6s, the damage value of each corner of the bent column on the first floor of the flood control sluice structure has exceeded 0.5, and the damage area has a tendency to run through the entire cross section of the bent column. This trend becomes more and more obvious until the final damage occurs.

In order to determine the different damage levels of the gate chamber structure, according to the damage value time history curve in Figure 21, it is calculated that at the end of the earthquake, the proportion of the cross-sectional area of the damaged area of the concrete bent column of the hoist room structure has reached 82%.

Based on the above calculation results, the ratio of the cross-sectional area of the concrete damage area of the lock chamber structure under earthquake action is used to determine the different damage levels of the lock chamber structure. The specific criteria are as follows:

Criterion

Claims (5)

1. A method for analyzing nonlinear earthquake motion damage of a reinforced concrete sluice-foundation-water system is characterized by comprising the following steps:

(1) According to the structural size and reinforcement condition of the sluice gate chamber, a three-dimensional sluice gate chamber structure finite element model is established, wherein the three-dimensional sluice gate chamber structure finite element model comprises a foundation, a water body, a gate bottom plate, a gate pier, a steel gate, a traffic bridge, an upper opening and closing machine room structure and reinforcement in concrete;

(2) Based on finite element analysis, taking infinite foundation radiation damping effect, concrete dynamic damage, bonding sliding action of reinforced concrete and fluid-solid coupling action of a water body and a sluice structure into consideration, inputting preset material parameters, boundary conditions and different loads to perform nonlinear earthquake damage calculation, and obtaining dynamic response of each part of a sluice chamber structure under the action of earthquake load;

(3) And (3) selecting the characteristic points of the area with the maximum displacement, stress and damage values based on the calculation result in the step (2), and drawing the change curve of the displacement, stress and damage values along with the earthquake duration at the characteristic points.

(4) And determining the sectional area occupation ratio of the damaged area according to the change curve of the damage value along with the earthquake duration, and judging the structural damage level of the lock chamber according to the sectional area occupation ratio of the damaged area.

2. The method for analyzing nonlinear earthquake motion damage of a reinforced concrete sluice-foundation-water system according to claim 1, wherein in the step (1), foundation unit ranges are based on upstream, downstream, left side, right side and bottom elevations of a sluice bottom plate, and the sluice chamber heights are respectively 2 times of the sluice chamber heights which are the difference between the top elevation of a start-stop machine room and the bottom elevation of the sluice bottom plate, wherein the sluice chamber heights are respectively upstream, downstream, left bank, right bank and vertically downward; the upstream and downstream water body unit nodes are shared with gate piers and steel gate nodes; in the single spring coupling unit method, the normal displacement of the steel bar nodes is calculated according to the following formula, and the concrete formula is as follows:

in the method, in the process of the invention,the displacement value is the displacement value of the ith dimension of the steel bar node under the local coordinate system; n is the model dimension; r is (r) _ij Is an interpolation coefficient, namely a coordinate transformation matrix element; u (u) _j And the displacement value is the j-th dimension displacement value of the concrete node under the integral coordinate system.

3. The method for analyzing nonlinear earthquake motion damage of a reinforced concrete sluice-foundation-water system according to claim 1, wherein in the step (2), the concrete adopts a four-parameter dynamic damage constitutive model, and the damage criterion is as follows:

wherein: epsilon ^* Is equivalent strain; A. b, C, D is four test constants, which can be obtained by combining a uniaxial tensile test, a uniaxial compression test, a biaxial isostatic test and a triaxial compression test; i' ₁ ＝(ε ₁ +ε ₂ +ε ₃ ) 3 is the first invariant of the strain tensor;is the maximum principal strain; />The second invariant is the strain offset; />J′ ₃ ＝ε ₁ ε ₂ ε ₃ The third invariant is the strain offset; epsilon ₁ ,ε ₂ ,ε ₃ Three-way main strain is respectively adopted; epsilon _m Indicating strain under ball stress.

Under the action of earthquake load, the concrete inevitably has unloading and reloading processes of a softening section, and the residual strain calculation in the simulation adopts the following formula:

wherein ε _p Is the residual strain value; epsilon ₀ ＝f _t and/E is the ultimate strain under the tensile strength of the concrete, f _t The tensile strength of the concrete is that E is the elastic modulus of the concrete; epsilon _un Is the strain value at the unloading point.

The interaction between the steel bar and the concrete is simulated by a single spring coupling unit method based on a mixed coordinate system, wherein the interaction equation between the steel bar and the concrete is as follows:

wherein Deltau, deltau ^* And DeltaF, deltaF ^* Oxyz and O, respectively ^* x ^* y ^* z ^* Displacement vector increment and load vector increment in a coordinate system; k and k ^* Oxyz and O, respectively ^* x ^* y ^* z ^* A stiffness matrix in a coordinate system; k (k) _s And r is a coordinate transformation matrix; r is (r) ^T Is the transpose of the coordinate transformation matrix.

The potential fluid unit is adopted to simulate the fluid-solid coupling effect between the front and rear water bodies of the gate and the gate pier and the steel gate under the action of earthquake, and the control equation is as follows:

wherein P represents dynamic water pressure, c represents underwater acoustic wave velocity,for Laplace operator>Is the second derivative of hydrodynamic pressure with time.

The fluid-solid coupling boundary is arranged between the water body and the gate pier, the gate bottom plate and the steel gate, so that the energy transfer between the water body and the steel gate is simulated, and the method is concretely as follows:

wherein n is a fluid-solid couplingThe external normal direction of the fluid domain on the joint surface;the absolute acceleration along the normal direction on the fluid-solid coupling surface is represented by ρ, which is the water density.

2 seismic acceleration time-course curves are generated by adopting a triangle series expansion method based on a standard design reaction spectrum, and the velocity and displacement time-course curves are generated through integration, wherein velocity waves and displacement waves are vertically input from the bottom of the foundation based on viscoelastic artificial boundary conditions in the calculation process.

4. The method for analyzing nonlinear earthquake motion damage of a reinforced concrete sluice-foundation-water system according to claim 1, wherein the displacement in the step (3) includes a forward displacement, a lateral displacement and a vertical displacement, and the stress includes a first principal stress and a third principal stress; the displacement and stress curve at the drawn characteristic points takes the duration of the earthquake as a horizontal axis and takes the displacement or stress response as a vertical axis; the curve of the damage value plotted with the earthquake duration is plotted with the earthquake duration as the horizontal axis and the damage value as the vertical axis.

5. The method for analyzing nonlinear earthquake motion damage of a reinforced concrete sluice-foundation-water system according to claim 1, wherein in the step (4), different damage levels of the sluice chamber structure are determined by using the sectional area of the concrete damage area of the sluice chamber structure under the action of earthquake, and specific determination criteria are as follows: