CN114428987B - Method for analyzing stress of concrete gravity dam body under action of multiple physical fields - Google Patents
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Abstract
The method for analyzing the stress of the dam body of the concrete gravity dam under the action of multiple physical fields comprises the following steps: step one, simplifying the geometric model and network division of a concrete gravity dam; step two, geometrically constructing a dam body stress analysis model under the action of a temperature field and a seepage field with a network dividing unit, and calculating the dam body stress analysis model to obtain the concrete temperature and the seepage coefficient; and thirdly, establishing a seepage field, a temperature field and a stress field coupling analysis equation through a stress analysis model, and obtaining stress distribution of the gravity dam through coupling analysis by the method, so that the stress condition and the deformation rule of the dam body of the dam under the action of different physical fields can be mastered, and an important basis is provided for further evaluating the safety of the dam body structure.
Description
Technical Field
The invention belongs to the technical field of hydroelectric engineering, and relates to a method for analyzing the stress of a concrete gravity dam body under the action of multiple physical fields.
Background
The gravity dam has the advantages of safe and reliable structure, convenient construction, suitability for most of terrain and geological environments and the like, and is widely applied to hydropower engineering. The gravity dam has larger water retention capacity, but once the dam body is deformed and destroyed, serious consequences can be brought about by the accident of breaking. The concrete is a typical porous medium, the wet and heat coupling transmission and deformation numerical simulation calculation of the concrete are carried out according to the heat and mass transfer principle of the porous medium, then the analysis of the dam body temperature field and the stress field is carried out, and the evolution rule of the dam body stress at different temperatures can be mastered. Therefore, the method can accurately analyze the gravity dam in multiple physical fields, adopts reasonable seepage control measures, and plays an important role in the stability and safety of the dam. The seepage field and the stress field in the gravity dam have coupling effect. The seepage influences the stress distribution of the dam body by applying the seepage pressure on a certain acting surface and the seepage volume force distributed in the seepage area; the stress influences the permeability parameters of the dam body by changing the volume strain and the porosity of the dam body, thereby influencing the seepage field of the dam body.
Disclosure of Invention
The invention aims to provide a method for analyzing the stress of a concrete gravity dam under the action of multiple physical fields, by using the method, the stress condition and the deformation rule of the dam under the action of different physical fields can be mastered, thereby providing an important basis for further evaluating the safety of the dam structure.
The technical scheme adopted by the invention is as follows:
the method for analyzing the stress of the dam body of the concrete gravity dam under the action of multiple physical fields comprises the following steps:
Step one, simplifying the geometric model and network division of a concrete gravity dam;
Step two, constructing a dam body stress analysis model under the action of a temperature field and a seepage field in the geometry of the network dividing unit, and calculating the dam body stress analysis model to obtain the concrete temperature and the seepage coefficient;
and thirdly, establishing a seepage field, a temperature field and a stress field coupling analysis equation through a stress analysis model, and obtaining stress distribution of the gravity dam through coupling analysis.
The invention is also characterized in that:
The first step is specifically as follows: simplifying the middle part of the dam crest and the dam bottom into simple geometric surfaces according to the structural plan of the gravity dam; and splitting the whole dam section two-dimensional model by using a free four-side grid by adopting a regional splitting method.
The second specific steps are as follows: the dam stress analysis model comprises a heat conduction equation and a saturated-unsaturated seepage model.
The heat conduction equation is:
Wherein: α is the coefficient of thermal conductivity of the concrete, α=λ/cρ, λ is the coefficient of thermal conductivity of the concrete, c is the specific heat of the concrete, ρ is the density of the concrete, θ is the adiabatic temperature rise (deg.c) of the concrete;
the three boundary constraints of the above heat conduction equation are:
The first type of boundary condition is that the surface temperature T of the concrete is a known function;
The second type of boundary condition is that the heat flux of the dam concrete surface is a known function as a function of time:
Third class of boundary conditions: the heat flow rate of the surface of the dam concrete, the surface temperature T of the dam concrete and the air temperature T α contacted with the concrete are in a proportional relation, and beta is 0.9:
And solving a heat conduction equation through boundary constraint conditions, and finally obtaining the concrete temperature.
The saturated-unsaturated percolation model is:
Wherein ρ is the fluid density; c m is water holding capacity; g is gravity acceleration; s e is saturation; s is a water storage coefficient; p is the pressure; kappa s is saturation permeability; η is the fluid viscosity; kr is the relative permeability; d is a position water head; q m is the liquid source sink.
The constraints of the saturated-unsaturated percolation model are:
wherein n is the external normal direction of the boundary surface; z is an axis coordinate; n 0 is the inward flux; r b is the external conductivity; h b＝zb+pbρg is the external total head; z b is the external elevation; p b is the external pressure; h=z+pρ g is the total head. The mixed boundary condition of formula (6) becomes a second class boundary condition when R b =0; becomes a first type of boundary condition when R b = infinity. Dividing the boundary conditions by the conditions in the formula (6), pb=0, zb=z, the exit plane N 0 =n, and the boundary N 0 =0 above the exit plane; when p is more than or equal to 0 and R b(Hb -H) is less than 0, R b is = infinity, otherwise R b =0;
And solving the saturated-unsaturated seepage model by using the constraint condition of the saturated-unsaturated seepage model, and finally obtaining the permeability coefficient.
In the third step, the seepage field, the temperature field and the stress field are coupled and analyzed according to the equation:
Wherein u is stress at T moment, ρ is concrete density, S is unit stress, F v is model stress vector sum, ε p is T moment permeability coefficient, k is hydraulic conductivity, μ is dynamic viscosity, p is head pressure, C is concrete specific heat, T is concrete temperature, C p is specific heat capacity of water, Q is calculated heat, and Q ted is residual heat energy at T moment. And carrying out coupling analysis on the seepage field, the temperature field and the stress field coupling analysis equation in COMSOL Multiphysics software to obtain stress distribution.
The beneficial effects of the invention are as follows:
(1) Because the elastic modulus of concrete has great difference compared with that of stone masonry, the layered abnormal elastic modulus problem of the dam body has obvious influence on the stress of the dam heel, and even cracks can be caused, in addition, the gaps between the gravity dams are filled with materials, and the dam bodies are also provided with interaction forces, which cause great difficulty in building a three-dimensional model and meshing, therefore, the self-braiding finite element meshing method is adopted, and the problems are well treated.
(2) By comparing three conditions of three-field coupling, no consideration of a temperature field and no consideration of a seepage field, the temperature field can cause the whole gravity dam to receive larger horizontal tensile stress in the construction period. The maximum tensile stress value of the first main stress of the dam body is reduced by about 5% after the temperature field is not considered; the z-direction maximum tensile stress is reduced by about 0.5% without considering the seepage field. Under the three conditions, the stress variation trend of the representative points of the same dam body is basically the same, but the stress values are different and are close to the actual conditions.
Drawings
FIG. 1 is a flow chart of a method for analyzing the stress of a concrete gravity dam under the action of multiple physical fields;
FIG. 2 is a cross-sectional view of an embodiment of a dam;
FIG. 3 is a graph of the results of the unit cell temperature calculations;
FIG. 4 is a graph of the results of calculation of the cell permeability coefficients;
FIG. 5 is a graph of the stress distribution of a concrete gravity dam under the action of multiple physical fields.
Detailed Description
The invention will be described in detail below with reference to the drawings and the detailed description.
The method for analyzing the stress of the dam body of the concrete gravity dam under the action of multiple physical fields comprises the following steps:
Step one, simplifying the geometric model and network division of a concrete gravity dam;
Step two, constructing a dam body stress analysis model under the action of a temperature field and a seepage field in the geometry of the network dividing unit, and respectively calculating the dam body stress analysis model to obtain a seepage coefficient and a concrete temperature;
and thirdly, establishing a seepage field, a temperature field and a stress field coupling analysis equation through a stress analysis model, and obtaining stress distribution of the gravity dam through coupling analysis.
The first step is specifically as follows: simplifying the middle part of the dam crest and the dam bottom into simple geometric surfaces according to the structural plan of the gravity dam; and splitting the whole dam section two-dimensional model by using a free four-side grid by adopting a regional splitting method.
And the dam stress analysis model in the second step comprises a heat conduction equation and a saturated-unsaturated seepage model.
The heat conduction equation in the second step is:
Wherein: α is the coefficient of thermal conductivity of the concrete, α=λ/cρ, λ is the coefficient of thermal conductivity of the concrete, c is the specific heat of the concrete, ρ is the density of the concrete, θ is the adiabatic temperature rise (deg.c) of the concrete;
The boundary constraint conditions of the above heat conduction equation are:
Wherein the first type of boundary condition is that the surface temperature T of the concrete is a known function.
The second type of boundary condition is that the heat flux of the dam concrete surface is a known function as a function of time:
In calculating the internal temperature of dam concrete, the surface is assumed to be thermally insulated, and then the concrete is provided with
Where there is a portion of the surface of the calculated dam concrete that is in contact with air, the heat flow through the surface of the dam concrete can be expressed as:
Third class of boundary conditions: the heat flow rate of the surface of the dam concrete, the surface temperature T of the dam concrete and the air temperature T α contacted with the concrete are in a proportional relation, and beta is 0.9:
only the heat dissipation of the layer surface in the process of pouring the large-volume concrete is considered in the calculation. If the running water curing condition is considered, the layer heat dissipation coefficient can be set to be a relatively large value, and the external temperature can be considered as the average value of curing water and air temperature.
The saturated-unsaturated percolation model is built by the richard equation describing the fluid flow in a saturated-unsaturated porous medium as follows:
Wherein ρ is the fluid density; c m is water holding capacity; g is gravity acceleration; s e is saturation; s is a water storage coefficient; p is the pressure; kappa s is saturation permeability; η is the fluid viscosity; kr is the relative permeability; d is a position water head; q m is the liquid source sink.
The constraints of the saturated-unsaturated percolation model are:
wherein n is the external normal direction of the boundary surface; z is an axis coordinate; n 0 is the inward flux; r b is the external conductivity; h b＝zb+pbρg is the external total head; z b is the external elevation; p b is the external pressure; h=z+pρ g is the total head. The mixed boundary condition of formula (6) becomes a second class boundary condition when R b =0; becomes a first type of boundary condition when R b = infinity. Dividing the boundary conditions by the conditions in the formula (6), pb=0, zb=z, the exit plane N 0 =n, and the boundary N 0 =0 above the exit plane; when p is more than or equal to 0 and R b(Hb -H) is less than 0, R b is = infinity, otherwise R b =0;
Simplifying assumption is made on the dam: ① Considering the elastic homogeneous material of the dam body structure according to the line, the seepage motion of water accords with Darcy's law; ② Taking one dam segment for independent calculation, and not considering the influence of the adjacent dam segments; ③ The total strain of the material is the sum of the stress-induced strain and the strain caused by the water pressure; ④ In the basic calculation range, the bottom is considered to be fixed, and the dam foundation is a water impermeable layer. Thus, a two-dimensional stress balance equation of the gravity dam is obtained:
wherein σ x、σy、τxy、τyx is stress; x, Y is the physical strength in the x and y directions. According to the effective stress principle and the elastic constitutive relation, a balance equation which is rewritten as a displacement component and a pore water pressure representation is as follows:
Wherein E is the elastic modulus of the dam concrete 23GPa; mu is the Poisson's ratio of the dam concrete of 0.167; x 0、Y0 is the equivalent physical force caused by the initial strain; e is the volumetric strain, obtained by the following formula:
In the formula (8) The gradient calculation factor for the x, y direction is obtained by the following formula:
The total water head h is used for representing the pore water pressure p, and a formula (11) can be obtained according to the relation between h and p. Wherein, gamma w is the volume weight of water:
-p＝γw(h-y) (11)
For convenience, gamma wh is denoted as h, that is, the unit of total water head is the same as the unit of stress, and the constitutive equation expressed by displacement and water head is obtained by substituting formula (11) into formula (8):
According to the law of conservation of mass and Darcy law, a continuous equation of fluid is obtained:
wherein the permeability coefficient k(s):
wherein k x、ky is the permeability coefficient in x and y directions; θ is the porosity of the dam concrete; beta is the volume compression coefficient of water, which is equal to the reciprocal of the elastic modulus of water, and is generally 1.0; h d is the intake suction; n is a shape factor, m= (l+1) n+2; and l is a pore curvature factor, and 2 is taken.
And solving the saturated-unsaturated seepage model through the calculation, and finally obtaining the seepage coefficient k(s).
In COMSOL Multiphysics software, performing coupling analysis on the seepage field, the temperature field and the stress field, and establishing a three-field coupling analysis equation of the concrete gravity dam section two-dimensional seepage field, the temperature field and the stress field based on a partial differential equation set:
Wherein u is stress at T, ρ is concrete density, S is unit stress, F v is model stress vector sum, ε p is time permeability coefficient, k is hydraulic conductivity, μ is dynamic viscosity, p is head pressure, C is concrete specific heat, T is concrete temperature, C p is specific heat capacity of water, Q is calculated heat, and Q ted is residual heat energy at T.
And carrying out coupling analysis on the seepage field, the temperature field and the stress field coupling analysis equation in COMSOL Multiphysics software to obtain stress distribution.
Examples
The actual structure of the gravity dam body of the embodiment is shown as a sectional view of the dam body in fig. 2, and stress analysis is performed on the upper dam body in fig. 2:
step one, dividing a dam into two parts according to an actual structure: the dam comprises a dam body and a dam top, wherein the dam body is hexahedral, the cross section of the dam body is rectangular trapezoid, and the dam top is cuboid.
Network partitioning of profile models
And splitting the whole dam section two-dimensional model by using a free tetrahedral mesh by adopting a zonal splitting method. Maximum unit 11.2m, minimum unit 0.11m, maximum unit growth rate 1.3, curvature factor 0.2, narrow region resolution 1. The method comprises the steps of encrypting grids aiming at the dam crest area and the water retaining dam bottom position in the model, wherein the maximum unit is 1m, the minimum unit is 0.01m, the maximum unit growth rate is 1.3, the curvature factor is 0.2 and the resolution of a narrow area is 1. Because of the smaller geometry and higher density of structures, the partial stress field and temperature gradient distribution are larger. A mesh is generated dividing the model into 2043 nodes, 3888 cells. The boundary conditions of the model are considered to be three types of seepage boundary conditions, stress boundary conditions and displacement boundary conditions. In normal water storage conditions, the percolation boundary conditions include head boundary, flow boundary and mixing boundary:
(1) The water head boundary is the part below the water level lines of the upstream surface and the downstream surface of the dam body;
(2) The flow boundary is a contact surface between the dam bottom and the dam foundation, and the dam bottom is a watertight boundary;
(3) The mixed boundary is an overflow boundary and a seepage free surface, the displacement boundary condition is the bottom surface complete displacement constraint, and the stress boundary is the self-weight load and the seepage pressure.
And because of calculation requirement, carrying out detail adjustment on the built dam body, namely removing details, wherein the details to be removed comprise continuously tangent vertexes, short sides, facets, strip faces, narrow side areas and thin domains. The total of 3 vertexes, 3 edges and a collapse domain are ignored, and in the selection of parameters, the detail size is selected to be automatic, and the continuous tangent tolerance is 5deg.
Executing the second step
Establishing a heat conduction equation according to formula (1), T being a known function, i.e. T (τ) =37 ℃, c being 880[ j/(kg×k) ]; ρ is 2300[ kg/m 3]; θ was 45.38 ℃.
The temperature distribution diagram of the unit cell is calculated as shown in fig. 3. Establishing a seepage equation according to a formula (5), wherein ρ is the fluid density of 1000[ kg/m≡3]; c m is water holding capacity; g is gravity acceleration; s e is saturation 1; s is water storage coefficient 0.5; p is the pressure of 1MPa; kappa s is the saturation permeability 0.5; η is the fluid viscosity 0.6; kr is the relative permeability of 0.1; d is a position water head 10M; q m is water sink 1.
The percolation coefficient and the directional distribution diagram of the unit cell were calculated as shown in fig. 4.
And step three, establishing a seepage field, a temperature field and a stress field coupling analysis equation, substituting parameters into a formula (15) according to an embodiment model, and obtaining the following components:
And (3) carrying out two-dimensional geometric dam stress deformation and analysis based on comsol, substituting a multi-physical field equation to calculate dam planing surface stress distribution, and finally loading to obtain a stable dam stress presentation rule. The comprehensive research overall operation result of the seepage, temperature and stress field of the concrete dam model of the hydropower station is shown in figure 5, the overall stress is about 0.6MPa, the overall stress accords with the design specification required 0.5-0.7 MPa, and the whole gravity dam stress analysis method has practical reference value and provides theoretical guidance for subsequent maintenance and monitoring.
Claims (6)
1. The method for analyzing the stress of the dam body of the concrete gravity dam under the action of multiple physical fields is characterized by comprising the following steps:
Step one, simplifying the geometric model and network division of a concrete gravity dam;
step two, constructing a dam body stress analysis model under the action of a temperature field and a seepage field in the geometry of a network dividing unit, and calculating the dam body stress analysis model to obtain the temperature and the seepage coefficient of the concrete;
and thirdly, establishing a seepage field, a temperature field and a stress field coupling analysis equation through a stress analysis model, and obtaining stress distribution of the gravity dam through coupling analysis.
2. The method for analyzing the stress of the dam body of the concrete gravity dam under the action of multiple physical fields as set forth in claim 1, wherein the first step is specifically as follows: simplifying the middle part of the dam crest and the dam bottom into simple geometric surfaces according to the structural plan of the gravity dam; and splitting the whole dam section two-dimensional model by using a free four-side grid by adopting a regional splitting method.
3. The method for analyzing the stress of the dam body of the concrete gravity dam under the action of multiple physical fields as set forth in claim 1, wherein the steps two include: the dam stress analysis model comprises a heat conduction equation and a saturated-unsaturated seepage model.
4. The method for analyzing the stress of the dam body of the concrete gravity dam under the action of multiple physical fields as claimed in claim 3, wherein the heat conduction equation is as follows:
Wherein: α is the coefficient of thermal conductivity of the concrete, α=λ/cρ, λ is the coefficient of thermal conductivity of the concrete, c is the specific heat of the concrete, ρ is the density of the concrete, θ is the adiabatic temperature rise (deg.c) of the concrete;
Three boundary constraints of the thermal conduction equation are:
The first type of boundary condition is that the surface temperature T of the concrete is a known function;
The second type of boundary condition is that the heat flux of the dam concrete surface is a known function as a function of time:
Third class of boundary conditions: the heat flow rate of the surface of the dam concrete, the surface temperature T of the dam concrete and the air temperature T α contacted with the concrete are in a proportional relation, and beta is 0.9:
And solving a heat conduction equation through boundary constraint conditions, and finally obtaining the concrete temperature.
5. The method for analyzing the stress of a concrete gravity dam body under the action of multiple physical fields according to claim 3, wherein the saturated-unsaturated seepage model is as follows:
Wherein ρ is the fluid density; c m is water holding capacity; g is gravity acceleration; s e is saturation; s is a water storage coefficient; p is the pressure; kappa s is saturation permeability; η is the fluid viscosity; kr is the relative permeability; d is a position water head; q m is a liquid source sink;
The constraint conditions of the saturated-unsaturated seepage model are as follows:
Wherein n is the external normal direction of the boundary surface; z is an axis coordinate; n 0 is the inward flux; r b is the external conductivity; h b＝zb+pbρg is the external total head; z b is the external elevation; p b is the external pressure; h=z+pρ g is the total head; the mixed boundary condition of formula (10) becomes a second class boundary condition when R b =0; becomes a first type boundary condition when R b = infinity; dividing the boundary conditions by the conditions in the formula (10), pb=0, zb=z, the exit plane N 0 =n, and the boundary N 0 =0 above the exit plane; when p is more than or equal to 0 and R b(Hb -H) is less than 0, R b is = infinity, otherwise R b =0;
And solving the saturated-unsaturated seepage model by using the constraint condition of the saturated-unsaturated seepage model, and finally obtaining the permeability coefficient.
6. The method for analyzing the stress of the concrete gravity dam body under the action of multiple physical fields according to claim 1, wherein the seepage field, the temperature field and the stress field coupling analysis equation are as follows:
Wherein u is stress at T, ρ is concrete density, S is unit stress, F v is model stress vector sum, ε p is time permeability coefficient, k is hydraulic conductivity, μ is dynamic viscosity, p is head pressure, C is concrete specific heat, T is concrete temperature, C p is specific heat capacity of water, Q is calculated heat, and Q ted is residual heat energy at T;
and carrying out coupling analysis on the seepage field, the temperature field and the stress field coupling analysis equation in COMSOL Multiphysics software to obtain stress distribution.
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| Title |
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| 西非高温干旱地区混凝土重力坝仿真研究;崔延龙等;《海河水利》;20230430;第124-128页 * |
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| CN114428987A (en) | 2022-05-03 |
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