CN116628801A - Nonlinear earthquake motion damage analysis method for reinforced concrete sluice-foundation-water system - Google Patents
Nonlinear earthquake motion damage analysis method for reinforced concrete sluice-foundation-water system Download PDFInfo
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Abstract
The invention discloses a method for analyzing nonlinear earthquake damages of a reinforced concrete sluice-foundation-water system, which establishes a three-dimensional finite element model of a sluice chamber structure comprising a foundation, a water body, a sluice pier, a sluice bottom plate, a steel sluice gate, an upper opening and closing machine room structure and steel bars according to the structural characteristics of the sluice chamber, adopts a finite element numerical simulation technology, and considers infinite foundation radiation damping effect, concrete dynamic damage, bonding sliding effect of reinforced concrete and fluid-solid coupling effect of the water body and the sluice structure based on viscoelastic artificial boundary conditions to analyze nonlinear earthquake damages of the sluice chamber structure. The method effectively overcomes the defects in the earthquake-resistant analysis process of the sluice chamber structure at the present stage, and improves the accuracy of earthquake damage analysis of the sluice structure.
Description
Technical Field
The invention relates to earthquake-proof safety analysis, in particular to a method for analyzing nonlinear earthquake damage of a reinforced concrete sluice-foundation-water system.
Background
The sluice has the dual functions of water retaining and water draining, and is widely applied in hydraulic engineering. The earthquake-proof analysis research of the sluice structure is one of important contents of the sluice structure safety review, and in recent years, a great deal of researches are carried out on the earthquake-proof analysis research of the sluice structure at home and abroad. Initially, the earthquake-resistant analysis and research of the sluice chamber structure is mainly performed by manual calculation, a great deal of simplification work is performed, a simplified model is built, and rough calculation is performed. With the rapid development of the finite element method and the wide application of computers, the analysis method of the gate chamber structure has a qualitative leap. In recent years, the research of earthquake-resistant analysis on the sluice chamber structure by utilizing a finite element numerical simulation technology has become a key technical means for solving the earthquake-resistant problem of the sluice chamber structure. At present, students at home and abroad mainly study the earthquake resistance of a sluice structure through a quasi-static force method, a vibration mode decomposition reaction spectrum method and a time-course analysis method, however, the existing study on earthquake resistance analysis of a sluice structure mainly aims at a linear elastic concrete structure, and the study on earthquake resistance analysis of the sluice structure by considering dynamic damage of concrete and bonding and sliding action of reinforced concrete is not involved at present. It is known that sluice chamber segments are generally reinforced concrete structures, and reinforced concrete is a very complex building material which has complex mechanical behaviors such as plasticity, crushing, cracking and the like, and in three-dimensional space, the extremely complex mechanical behaviors become more difficult to determine, and only the analysis of the elasticity of concrete structure lines of the sluice structures is deviated. Meanwhile, penetration cracks are easy to occur in the thin-wall structure of the sluice chamber under the action of strong earthquake, so that the research on possible damage modes of the sluice structure under the action of earthquake is less for domestic scholars at present, and the research on nonlinear earthquake damage mechanism of the sluice structure is also quite rare.
In addition, the existing research results all adopt an additional mass method to convert the earthquake water pressure of the sluice. In fact, the additional mass method mainly researches the problem of dynamic water pressure of the water body of the infinite domain in front of the dam on the rigid dam surface, and for the sluice structure, the vibration of the water body in the sluice chamber section is different from the vibration of the water body of infinite water areas of the reservoir water such as the gravity dam, the arch dam and the like, and the two sides of the sluice pier bear the action of the water pressure, so that the influence of the dynamic water pressure is more remarkable. Therefore, the additional mass method is adopted to simulate the lack of earthquake motion water pressure acting on the sluice.
In summary, the existing analysis method basically adopts a linear elastic analysis method, and does not consider the nonlinear damage of the concrete material or the interaction of reinforced concrete, so that the analysis of the earthquake damage of the sluice is inaccurate.
Disclosure of Invention
The invention aims to: the invention aims to provide a method for analyzing nonlinear earthquake vibration damage of a reinforced concrete sluice-foundation-water system, which solves the problems that the existing analysis method basically adopts a linear elastic analysis method, does not consider nonlinear damage of concrete materials and interaction of reinforced concrete, and is inaccurate in analysis of earthquake damage of the sluice.
The technical scheme is as follows: the invention relates to a method for analyzing nonlinear earthquake motion damage of a reinforced concrete sluice-foundation-water system, which comprises 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.
The foundation unit range in the step (1) is based on the upstream, downstream, left side, right side and bottom elevation of the gate bottom plate, and extends to the upstream, downstream, left bank, right bank and vertically downwards by 2 times of gate chamber height, wherein the gate chamber height is the difference between the top elevation of the opening and closing machine room and the bottom elevation of the gate bottom plate; 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.
In the step (2), during finite element calculation, the concrete adopts a four-parameter dynamic damage constitutive model, and the failure 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>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 the external normal direction of the fluid domain on the fluid-solid coupling surface;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.
The displacement in the step (3) comprises a river-direction displacement, a transverse river-direction displacement and a vertical displacement, and the stress comprises a first main stress and a third main 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.
In the step (4), different damage levels of the sluice chamber structure are judged by using the sectional area of the concrete damaged area of the sluice chamber structure under the action of earthquake, and specific judgment standards are as follows:
discriminant criterion
The beneficial effects are that: according to the characteristics of the sluice chamber structure, the three-dimensional finite element model of the sluice chamber structure comprising a foundation, a water body, a sluice pier, a sluice bottom plate, a steel gate, an upper opening and closing machine room structure and steel bars is established, the method for analyzing the nonlinear vibration damage of the sluice chamber structure is established by adopting finite element numerical simulation and considering infinite foundation radiation damping effect, concrete dynamic damage, bonding sliding action of reinforced concrete and fluid-solid coupling action of the water body and the sluice structure based on viscoelastic artificial boundary conditions, defects in the earthquake damage analysis process of the sluice chamber structure at the present stage are effectively overcome, and the accuracy of earthquake damage analysis of the sluice structure is improved.
Drawings
FIG. 1 is a diagram of a monolithic finite element model of a floodgate mesojunction housing structure;
FIG. 2 is a finite element model of a structure of a central opening chamber of a flood gate;
FIG. 3 is a finite element model of a flood gate pier and gate base;
FIG. 4 is a finite element model of a floodgate steel gate;
figure 5 finite element model of flood gate opening and closing machine room
FIG. 6 is a finite element model of a reinforcement finite element model in a frame column of a flood gate hoist room;
FIG. 7 is a finite element model of a flood gate highway bridge;
FIG. 8 is a finite element model of a flood gate steel gate and a pre-gate body of water;
FIG. 9 is a standard design response spectrum;
FIG. 10 is an x-direction acceleration time course curve;
FIG. 11 is a y-direction acceleration time course curve;
FIG. 12 is an x-direction velocity time course curve;
FIG. 13 is a y-direction velocity time course curve;
FIG. 14 is an x-displacement time course curve;
FIG. 15 is a y-displacement time course curve;
FIG. 16 is a schematic view of the structural feature points of the cell;
FIG. 17 is a river-going displacement time course curve at feature point A;
FIG. 18 is a first principal stress time-course plot at feature point B;
FIG. 19 is a comparison of calculation results of lateral river displacement at a characteristic point A of a mesoporous lock chamber structure under different calculation methods;
FIG. 20 is a comparison of the results of a first principal stress calculation at a characteristic point B of the mesoporous chamber structure under different calculation methods;
FIG. 21 is a graph of damage value time course at feature point B;
FIG. 22 is a schematic diagram of a structural damage of the mesoporous chamber at a time of 0.50 s;
FIG. 23 is a schematic diagram of a structural damage of the mesoporous lock chamber at the moment of 2.60 s;
FIG. 24 is a schematic illustration of structural damage to the mesoporous chamber at time 6.85 s;
fig. 25 is a schematic diagram of structural damage to the mesoporous chamber at time 14.85 s.
Detailed Description
The invention will be further described with reference to the accompanying drawings and specific examples.
The earthquake intensity of the area where a flood gate project is located is VIII degrees, the total number of the flood gates is 6 holes, the width of each hole is 6m, and the total number of the holes is 2. The calculation is mainly used for nonlinear earthquake motion damage analysis of the medium-hole one-connected brake chamber structure. According to the structural characteristics of the flood gate, a three-dimensional finite element model comprising a foundation, a water body, a gate bottom plate, a gate pier, a steel gate, a highway bridge, an upper opening and closing machine room and steel bars is established, wherein the concrete model is shown in the accompanying drawings 1-8 of the specification. The foundation unit ranges are respectively extended to 2 times of gate chamber heights up to the upstream, down to the downstream, left bank, right bank and vertically downwards based on the heights of the upper part, the down stream, the left side, the right side and the bottom of the gate bottom plate, wherein the gate chamber height is the difference between the top height of the opening and closing machine room and the bottom height of the gate bottom plate. Meanwhile, in order to facilitate the establishment of a model, the nodes of the upstream and downstream water units are shared with the gate pier and the steel gate node; 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.
The water level of the front gate and the rear gate of the medium-hole gate chamber structure under the working condition of normal water storage level is shown in table 1.
TABLE 1 flood control gate chamber structure gate front and rear depth of water meter
In the calculation process, 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 that
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 The method comprises the steps of carrying out a first treatment on the surface of the 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 the external normal direction of the fluid domain on the fluid-solid coupling surface;the absolute acceleration along the normal direction on the fluid-solid coupling surface is represented by ρ, which is the water density.
The parameters of the structural materials of the medium-hole lock chamber of the flood-gate are shown in Table 2.
Table 2 parameters of concrete materials for the cell structure of the flood gate
It should be pointed out that according to the "engineering standard for earthquake resistance of hydraulic construction" (GB 51247-2018), the elastic modulus of concrete material is improved by 50% on the basis of static elastic modulus, the standard value of dynamic compressive strength of concrete is improved by 20% compared with the standard value of static compressive strength, and the standard value of dynamic tensile strength of concrete is 10% of the standard value of dynamic compressive strength. In addition, the water density in the numerical simulation calculation process is 1000kg/m 3 The bulk modulus was 2.3GPa.
As known from the Chinese earthquake motion parameter demarcation graph (GB 18306-2015), the earthquake fortification intensity of the flood gate junction engineering area is VIII DEG, and the characteristic period T of the foundation reaction spectrum of the local engineering g Take 0.35s. According to the specification of the engineering standard for earthquake resistance of hydraulic buildings (GB 51247-2018), the horizontal design acceleration representative value alpha of the sluice chamber structure of the floodgate h =0.2 g. Meanwhile, according to the specification in the "engineering standards for earthquake resistance of Water works construction" (GB 51247-2018) table 4.3.3, the representative value beta of the maximum value of the response spectrum of the sluice structure max Taking 2.25, the sluice should consider the horizontal earthquake action along the river direction and the vertical river direction at the same time.
FIG. 9 is a schematic diagram of a design response spectrum adopted in the calculation, 2 seismic acceleration time courses are generated according to the design response spectrum by adopting a triangle series expansion method, 2 seismic acceleration time course curves are shown in FIGS. 10-11, velocity and displacement time course curves are shown in FIGS. 12-13 and 14-15 respectively, and velocity waves and displacement waves are vertically input from the bottom of a foundation based on viscoelastic artificial boundary conditions in the calculation process.
Based on the material parameters and the load parameters, nonlinear earthquake motion damage analysis is performed on the sluice chamber structure of the flood control sluice. In order to facilitate analysis of the response results of displacement, acceleration, stress, damage distribution and the like under the earthquake action of the reinforced concrete sluice chamber structure, a certain number of characteristic points are selected from the sluice chamber structure of the flood control sluice, and the positions of the characteristic points are shown in a figure 16.
Taking the forward displacement as an example, fig. 17 shows the transverse river displacement time course curve and the forward displacement time course curve at the structural feature point A of the pore lock chamber in the reinforced concrete dynamic damage time course analysis method. It can be seen that under the action of the earthquake, the river-direction displacement at the characteristic point A oscillates reciprocally along with the earthquake load, and the residual displacement exists at the characteristic point A when the earthquake load is finished due to the fact that the nonlinearity of the concrete material is considered. In addition, the maximum value (absolute value) of the river displacement at the characteristic point a is 12.98mm, and occurs at 12.58 s. In addition, it should be pointed out that, from the characteristic point A along the river displacement curve, the displacement change rule is divergent, mainly because the bent column of the sluice chamber structure in the floodgate is damaged under the action of VIII degree earthquake.
Taking the first principal stress as an example, fig. 18 shows a first principal stress time-course curve at a structural feature point B of the cell in a reinforced concrete dynamic damage time-course analysis method. It can also be seen that the sum of the first principal stresses at the characteristic point B under the action of the earthquake varies continuously with time, wherein the first principal stress at the point B has a maximum value of 2.26MPa at the moment of 1.22 s.
In order to verify the correctness of the calculation results, a linear elastic vibration mode decomposition reaction spectrum method, a linear elastic time-course analysis method and a dynamic damage time-course analysis method based on concrete are respectively adopted to carry out dynamic calculation on the structure of the central hole lock chamber, and the calculation results are compared as follows.
Fig. 19 shows comparison of calculation results of the forward river displacement at the structural feature point A of the mesopore gate chamber under calculation by different methods. The graph shows that the calculation result of the horizontal river displacement at the characteristic point A of the pore gate chamber structure in the linear elastic time-course analysis method is smaller than the calculation result based on the linear elastic vibration mode decomposition reaction spectrum method, and accords with the general rule. Meanwhile, after the interaction of reinforced concrete is considered, the calculation result based on the damaged reinforced concrete time-course analysis method is obviously smaller than the calculation result based on the damaged concrete time-course analysis method, and the dynamic response of the mesoporous lock chamber structure under the earthquake action is reduced mainly because of the existence of the reinforcing steel bars. In addition, the calculation results based on the damaged reinforced concrete time-course analysis method and the calculation results based on the damaged concrete time-course analysis method are larger than those based on the linear elastic vibration mode decomposition reaction method, because after the damage of the concrete is considered under the VIII degree earthquake action, the bent frame columns of the lock chamber structure are damaged in different degrees, and the calculation results are in a divergent trend.
FIG. 20 shows a comparison of the results of the first principal stress calculation at the structural feature point B of the mesoporous chamber under calculation by different methods. It can be seen that the calculation result of the first principal stress at the structural feature point B of the pore lock chamber in the linear elastic time-course analysis method is smaller than the calculation result based on the linear elastic vibration mode decomposition reaction spectrum method, and accords with the general rule. Meanwhile, after the damage of the concrete is considered, the calculation result of the first main stress at the characteristic point B is obviously smaller than the calculation result based on the linear elasticity time-course analysis method, mainly because the damage and cracking of the concrete release the stress to a certain extent under the action of the earthquake load, and the stress response of the medium-pore lock chamber structure is reduced.
In summary, the correctness of the dynamic damage model of the reinforced concrete adopted at the present time can be verified through the comparative analysis of different calculation results.
In order to analyze the nonlinear earthquake damage mechanism of the sluice chamber structure, a damage value time curve at a characteristic point B of the pore sluice chamber structure in a reinforced concrete-based dynamic damage time analysis method is shown in the figure 21. As can be seen by combining the first principal stress time course curve at the characteristic point B, the larger first principal stress appears at the characteristic point B for 1s, the maximum tensile stress value (2.26 MPa) of the first principal stress exceeds the dynamic tensile strength of plain concrete, the damage value reaches 0.48 at the moment, the larger first principal stress appears at the moment for 2s and 3s along with the increase of the earthquake duration, and the damage value continuously increases under the action of the tensile stress because the concrete has damaged to a certain extent, and the final damage value reaches 0.64 although the first principal stress value does not exceed the dynamic tensile strength of plain concrete.
In order to further disclose the nonlinear earthquake damage accumulation process of the floodgate, the structural damage schematic diagrams of the floodgate middle-hole gate chamber based on the reinforced concrete dynamic damage time course analysis method at different times are respectively shown in the attached figures 22-25. It can be seen that the whole sluice chamber structure is not damaged at the beginning of the earthquake, the sluice chamber structure starts to be damaged gradually at the position with larger first main stress along with the increase of the duration of the earthquake, and the damage value and the damage area gradually increase along with the continuation of the earthquake load until the earthquake load is ended. In addition, as shown in the figure, the damage value of each bent angle part of the Kong Zhashi structure first layer bent column in the flood control gate after 2.6s is more than 0.5, and the damage area has a trend of penetrating the cross section of the whole bent column, and the trend is gradually obvious along with the increase of the earthquake duration until the damage and the destruction finally occur.
In order to judge different damage levels of the lock chamber structure, according to the damage value time curve of fig. 21, the area occupation ratio of the cross section damage area of the cross section of the concrete bent column of the open and close machine room structure reaches 82% after the earthquake is calculated.
Based on the calculation result, the different damage levels of the sluice chamber structure are judged by adopting the sectional area of the concrete damaged area of the sluice chamber structure under the action of earthquake, and specific judgment standards are as follows:
discriminant 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:
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN117973117A (en) * | 2024-01-12 | 2024-05-03 | 三峡金沙江云川水电开发有限公司 | Non-uniform main aftershock sequence earthquake motion input method and device suitable for dynamic analysis of high arch dam |
| CN118095020A (en) * | 2024-04-28 | 2024-05-28 | 湖南百舸水利建设股份有限公司 | Construction method of porous flood diversion gate |
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117973117A (en) * | 2024-01-12 | 2024-05-03 | 三峡金沙江云川水电开发有限公司 | Non-uniform main aftershock sequence earthquake motion input method and device suitable for dynamic analysis of high arch dam |
| CN118095020A (en) * | 2024-04-28 | 2024-05-28 | 湖南百舸水利建设股份有限公司 | Construction method of porous flood diversion gate |
| CN118095020B (en) * | 2024-04-28 | 2024-07-12 | 湖南百舸水利建设股份有限公司 | Construction method of porous flood diversion gate |
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