A method for analyzing the seismic capacity of gravity dams considering the effect of seismic steel reinforcement

Abstract

The present invention provides a method for analyzing the seismic capacity of a gravity dam that takes into account the effects of seismic steel reinforcement, including: constructing a gravity dam cross-seam reinforcement steel bar model; the gravity dam cross-seam reinforcement steel bar model includes a dam body concrete structure, a crack structure, and steel bars that penetrate the crack structure for reinforcement; using an inverse analysis method combined with an iterative optimization algorithm to determine the optimal values ​​of the physical and mechanical parameters of the dam body concrete structure; using the optimal values ​​of the physical and mechanical parameters of the dam body concrete structure as the initial parameters of the gravity dam cross-seam reinforcement steel bar model; applying earthquake acceleration to the gravity dam cross-seam reinforcement steel bar model, and gradually increasing the earthquake acceleration multiple to conduct seismic simulation analysis. The method for analyzing the seismic capacity of a gravity dam that takes into account the effects of seismic steel reinforcement provided by the present invention can accurately analyze the seismic capacity of a gravity dam with cracks after being reinforced with earthquake-resistant steel bars.

Description

Technical Field

[0001] The present invention belongs to the field of water conservancy and hydropower engineering, and in particular relates to a method for analyzing the seismic capacity of a gravity dam taking into account the reinforcement effect of seismic steel bars. Background Art

[0002] Gravity dams are one of the most common types of dams used in water conservancy and hydropower projects. Their seismic performance is directly related to the safety and reliability of the project. In actual projects, to improve the seismic performance of gravity dams, steel reinforcement is often used in areas where cracks appear in the dam body.

[0003] Existing seismic analysis methods for gravity dams suffer from the following deficiencies: They struggle to accurately reflect the synergistic effect between reinforcement steel and concrete, and they inaccurately simulate stress and strain characteristics in cracked areas. Therefore, there is an urgent need to develop a seismic capacity analysis method for gravity dams that accurately accounts for the effects of seismic reinforcement steel. This would provide stronger technical support for seismic assessment, design, and retrofitting of gravity dams. Summary of the Invention

[0004] In view of the defects of the existing technology, the present invention provides a method for analyzing the seismic capacity of a gravity dam taking into account the reinforcement effect of seismic steel bars, which can effectively solve the above problems.

[0005] The technical solution adopted in the present invention is as follows:

[0006] The present invention provides a method for analyzing the seismic capacity of a gravity dam taking into account the effect of seismic steel reinforcement, comprising the following steps:

[0007] S1: Constructing a gravity dam cross-crack reinforcement steel bar model; the gravity dam cross-crack reinforcement steel bar model includes a dam body concrete structure, a crack structure, and steel bars that cross the crack structure for reinforcement;

[0008] S2: using an inverse analysis method combined with an iterative optimization algorithm to determine the optimal values ​​of the physical and mechanical parameters of the dam concrete structure;

[0009] S3: using the optimal values ​​of the physical and mechanical parameters of the dam body concrete structure as initial parameters of the gravity dam span joint reinforcement steel bar model; applying seismic acceleration to the gravity dam span joint reinforcement steel bar model, and gradually increasing the seismic acceleration multiple to conduct seismic simulation analysis;

[0010] S4: Recording the peak value of the earthquake acceleration when the steel bar reaches the limit state, and recording the displacement and stress distribution of the dam concrete structure and the crack structure under corresponding conditions, to obtain seismic simulation results; based on the seismic simulation results, analyzing and evaluating the seismic capacity of the dam concrete structure after cross-crack reinforcement with the steel bar.

[0011] Preferably, S2 is specifically:

[0012] S2.1, obtaining the physical and mechanical parameters of the dam concrete structure using an inverse analysis method;

[0013] S2.2, using the obtained physical and mechanical parameters of the dam body concrete structure as the initial physical and mechanical parameters of the dam body concrete structure of the gravity dam joint reinforcement steel bar model;

[0014] Then, applying historical earthquake loads to the gravity dam joint reinforcement steel bar model to perform simulation calculations to obtain calculated values ​​of the dam body concrete structure characteristics;

[0015] S2.3, searching historical data to obtain measured values ​​of the dam concrete structure characteristics when the dam concrete structure is subjected to the historical earthquake load;

[0016] S2.4, compare the deviation between the calculated value of the dam body concrete structure characteristic and the measured value of the dam body concrete characteristic, dynamically update the physical and mechanical parameters of the dam body concrete structure using an iterative optimization algorithm, return to S2.2, and repeat this cycle until the error converges to an allowable range, thereby obtaining the optimal value of the physical and mechanical parameters of the dam body concrete structure.

[0017] Preferably, the physical and mechanical parameter of the dam body concrete structure is the dynamic elastic modulus; and the characteristic of the dam body concrete structure is the modal frequency of the dam body concrete structure.

[0018] Preferably, the iterative optimization algorithm is a double annealing optimization algorithm.

[0019] Preferably, S3 is specifically:

[0020] S3.1: The dam body concrete structure is simulated using isoparametric elements, which are divided into a plurality of concrete elements; the steel bars are simulated using rod elements, which are divided into a plurality of steel bar elements; the bonding area between the steel bars and the dam body concrete structure has a plurality of bonding elements;

[0021] S3.2: At the current time step t during the seismic simulation analysis, applying earthquake acceleration to the gravity dam joint reinforcement steel bar model;

[0022] S3.3: Inputting the earthquake acceleration into a pre-established crack contact model to determine the contact force of the crack contact interface and the crack contact state; wherein the crack contact state includes open, closed, or slip;

[0023] S3.4: Based on the crack contact state determined in S3.3, update the gravity dam cross-crack reinforcement steel bar model; based on the updated gravity dam cross-crack reinforcement steel bar model, further analyze the bond-slip relationship between the steel bar and the dam concrete structure, and evaluate the slip degree of the steel bar-concrete contact interface;

[0024] S3.5: Set time step t=t+1; apply the design multiple of earthquake acceleration to the gravity dam joint reinforcement steel bar model; return to S3.3; and repeat this cycle until the steel bar reaches the limit state.

[0025] Preferably, S3.3 specifically includes:

[0026] S3.3.1, using the crack as the boundary, divide the dam concrete structure into an upper concrete area and a lower concrete area;

[0027] S3.3.2, the steel bar passing through the crack contacts the upper concrete region and the lower concrete region, respectively; the concrete contact interfaces on both sides of the crack are referred to as the first concrete contact interface and the second concrete contact interface, respectively;

[0028] S3.3.3. Establish a local coordinate system ξηζ for the crack contact boundary; where ξ is the normal direction of the first concrete contact interface and the second concrete contact interface, and the normal directions of the first concrete contact interface and the second concrete contact interface are assumed to be the same; η is the tangent direction of the first concrete contact interface; ζ is the tangent direction of the second concrete contact interface;

[0029] S3.3.4, there are a number of contact point pairs between the first concrete contact interface and the second concrete contact interface;

[0030] S3.3.5, for each contact point pair j, including contact point j1 and contact point j2, the normal gap of contact point pair j at the current time step t is obtained by formula (1):

[0031]

[0032] in: represents the normal gap between contact point j1 and contact point j2 at time step t-1; and, the initial normal gap between contact point j1 and contact point j2 is a known value; represents the normal unit vector; represents the displacement of the contact point j1 at the current time step t; represents the displacement of contact point j2 at the current time step t;

[0033] Preliminary determination of the contact force exerted on contact point j1 from contact point j2 And the contact force on contact point j2 from contact point j1 in, Moreover, they all have components along the normal direction ξ, the tangential direction η, and the tangential direction ζ;

[0034] S3.3.6, determine the contact state of contact point pair j:

[0035] Open state: If δ t j >0, Then, at this time, the crack between the contact point pair j opens, and no contact force is transmitted;

[0036] Closed state: If Then, at this time, the crack between the contact point pair j is closed, but no slip occurs;

[0037] Slip state: If Then, the crack between the contact point pair j is closed and slip occurs;

[0038] Where: f ξ,t 、f η,t and f ζ,t , are the components of the contact force along the normal direction ξ, tangent direction η, and tangent direction ζ on any contact point in the contact point pair j; is the tensile strength between the contact point pair j; A is the control area of ​​the contact point pair j; μ is the friction coefficient between the first concrete contact interface and the second concrete contact interface; c is the cohesion between the first concrete contact interface and the second concrete contact interface;

[0039] S3.3.7, according to the crack flexibility equation shown in formula (2), the contact force f for all contact point pairs between the first concrete contact interface and the second concrete contact interface is obtained t j Array of contact force increments relative to the previous time step

[0040]

[0041] Where: [C] is the flexibility matrix of the contact boundary between the first concrete contact interface and the second concrete contact interface; β2 is the integral coefficient of the displacement equation; Δt is the time step; is the actual displacement increment of each contact point on the first concrete contact interface relative to the previous time step;

[0042] is the actual displacement increment of each contact point on the second concrete contact interface relative to the previous time step;

[0043] is the displacement increment of each contact point on the first concrete contact interface relative to the previous time step when only the external load is considered;

[0044] is the displacement increment of each contact point on the second concrete contact interface relative to the previous time step when only the external load is considered;

[0045] f t j , represents the contact force f between the first concrete contact interface and the second concrete contact interface at the contact point j t j , specifically the contact force received by any contact point in the contact point pair j from another contact point;

[0046] S3.3.8. At the current time step t, determine whether all contact point pairs between the first concrete contact interface and the second concrete contact interface satisfy the finite element equilibrium equation shown in formula (3):

[0047]

[0048] in:

[0049] [M] is the mass matrix of the dam concrete structure; [D] is the damping matrix between the first concrete contact interface and the second concrete contact interface; [K] is the overall stiffness matrix of the dam concrete structure;

[0050] and{u t}, are respectively the acceleration array, velocity array and displacement array of all contact point pairs between the first concrete contact interface and the second concrete contact interface at the current time step t; {F t} is the external load vector caused by the earthquake acceleration applied at the current time step t; is the contact force matrix of all contact point pairs at the previous time step;

[0051] S3.3.9: If the finite element equilibrium equation shown in formula (3) is satisfied, the contact forces of all contact point pairs between the first concrete contact interface and the second concrete contact interface at the current time step t are output; if not satisfied, return to S3.3.5 and adjust the contact forces of each contact point pair; this cycle is repeated until the contact forces of all contact point pairs that satisfy the finite element equilibrium equation are obtained, and based on the contact forces of all contact point pairs finally determined, the crack state between the first concrete contact interface and the second concrete contact interface is determined.

[0052] Preferably, in S3.4, the bond-slip relationship between the steel bar and the dam concrete structure is analyzed to evaluate the slip degree of the steel bar-concrete contact interface, specifically:

[0053] S3.4.1, based on the updated gravity dam joint reinforcement steel bar model, determine a bonding area between the steel bar and the dam body concrete structure; each bonding unit included in the bonding area is denoted as bonding unit i; bonding unit i is the bonding location between steel bar unit i and concrete unit i;

[0054] S3.4.2, construct the bond-slip relationship equation between the steel element and the concrete element shown in equation (4):

[0055]

[0056] in:

[0057] A reinforcement stiffness matrix formed by the stiffness of each reinforcement unit i having a bonding relationship with the dam concrete structure;

[0058] is the tangential stiffness matrix corresponding to the shear force exerted by concrete unit i on steel unit i at each bond unit i;

[0059] The flexibility matrix formed by the flexibility of concrete unit i at each bond unit i position;

[0060] {Δq i} is the slip increment array formed by the slip increment between the concrete unit i and the steel unit i at each bonding unit i;

[0061] [I] is the identity matrix;

[0062] is the array formed by the initial bonding force of steel bar unit i from concrete unit i at each bonding unit i;

[0063] is the array formed by the displacement of each concrete unit i caused only by the external load;

[0064] is the array formed by the initial slip between steel unit i and concrete unit i at each bonding unit i;

[0065] S3.4.3, at each time step t, solve for the following parameters that satisfy the bond-slip relationship equation between the steel element and the concrete element shown in Equation (4): the slip increment between the steel element i and the concrete element i at each bond element i, and then evaluate the degree of slip at the steel-concrete contact interface at each time step t.

[0066] Preferably, when solving the bond-slip relationship equation between the steel bar unit and the concrete unit, the following constraints need to be met:

[0067] Constraint 1: The equilibrium equation of concrete element i in contact with steel element i:

[0068]

[0069] in:

[0070] is the displacement array formed by the displacement of each concrete unit i;

[0071] is the array formed by the load transferred from steel bar unit i to concrete unit i;

[0072] Constraint 2: The equilibrium equation of the steel bar element i in contact with the concrete element i:

[0073]

[0074] in:

[0075] is the displacement matrix formed by the displacement of each steel bar element i;

[0076] is the array formed by the load transferred from concrete element i to steel element i;

[0077]

[0078] The expression of is as follows:

[0079]

[0080] in:

[0081] q i represents the slip between steel element i and concrete element i at each bond element i;

[0082] is the bonding force exerted on steel bar unit i from concrete unit i at bonding unit i;

[0083] and The expressions are as follows:

[0084]

[0085] in:

[0086] is the initial bond force exerted on concrete unit i from steel unit i at bond unit i;

[0087] is the bonding force exerted on concrete unit i by steel unit i at bonding unit i;

[0088] According to the interaction relationship between steel bar unit i and concrete unit i, and The difference satisfies formula (10):

[0089]

[0090] in: is the initial slip between steel unit i and concrete unit i at bond unit i;

[0091] Constraint 3: Matrix middle, Satisfy the following constraints of formula (11):

[0092]

[0093] Where: d is the diameter of the steel bar; l i is the length of the reinforcement controlled by the bonding unit i; The uniform shear stress on steel bar unit i from concrete unit i within the control length of bond unit i.

[0094] Preferably, when applying seismic acceleration to the gravity dam seam reinforcement steel bar model to carry out seismic simulation analysis, the initial value of the applied seismic acceleration is the seismic acceleration value corresponding to the design intensity of the gravity dam.

[0095] The seismic capacity analysis method of a gravity dam considering the seismic reinforcement effect of seismic steel bars provided by the present invention has the following advantages:

[0096] The present invention provides a method for analyzing the seismic capacity of a gravity dam taking into account the effect of seismic steel reinforcement, which can accurately analyze the seismic capacity of a gravity dam with cracks after seismic steel reinforcement. BRIEF DESCRIPTION OF THE DRAWINGS

[0097] Figure 1Schematic diagram of the overall structure of the reinforcement steel bar model for the seam reinforcement of a gravity dam according to an embodiment of the present invention;

[0098] Figure 2 Schematic diagram of the relationship between crack damage and reinforced concrete bond slip in a gravity dam span joint reinforcement steel bar model according to an embodiment of the present invention;

[0099] Figure 3 This is a diagram showing the relationship between earthquake peak acceleration and seismic steel bar stress according to an embodiment of the present invention;

[0100] Figure 4 This is a flow chart of a method for analyzing the seismic capacity of a gravity dam taking into account the effect of seismic steel reinforcement. DETAILED DESCRIPTION

[0101] In order to make the technical problems, technical solutions and beneficial effects solved by the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0102] See Figures 1 to 4 The present invention provides a method for analyzing the seismic capacity of a gravity dam taking into account the effect of seismic steel reinforcement, comprising the following steps:

[0103] S1: Constructing a gravity dam cross-crack reinforcement steel bar model; the gravity dam cross-crack reinforcement steel bar model includes a dam body concrete structure, a crack structure, and steel bars that cross the crack structure for reinforcement;

[0104] S2: using an inverse analysis method combined with an iterative optimization algorithm to determine the optimal values ​​of the physical and mechanical parameters of the dam concrete structure;

[0105] S3: using the optimal values ​​of the physical and mechanical parameters of the dam body concrete structure as initial parameters of the gravity dam span joint reinforcement steel bar model; applying seismic acceleration to the gravity dam span joint reinforcement steel bar model, and gradually increasing the seismic acceleration multiple to conduct seismic simulation analysis;

[0106] S4: Recording the peak value of the earthquake acceleration when the steel bar reaches the limit state, and recording the displacement and stress distribution of the dam concrete structure and the crack structure under corresponding conditions, to obtain seismic simulation results; based on the seismic simulation results, analyzing and evaluating the seismic capacity of the dam concrete structure after cross-crack reinforcement with the steel bar.

[0107] The following is a detailed description of each step:

[0108] S1: Constructing a gravity dam cross-crack reinforcement steel bar model; the gravity dam cross-crack reinforcement steel bar model includes a dam body concrete structure, a crack structure, and steel bars that cross the crack structure for reinforcement;

[0109] S2: using an inverse analysis method combined with an iterative optimization algorithm to determine the optimal values ​​of the physical and mechanical parameters of the dam concrete structure;

[0110] This step is specifically as follows:

[0111] S2.1, obtaining the physical and mechanical parameters of the dam concrete structure using an inverse analysis method; for example, the physical and mechanical parameters of the dam concrete structure are dynamic elastic modulus;

[0112] S2.2, using the obtained physical and mechanical parameters of the dam body concrete structure as the initial physical and mechanical parameters of the dam body concrete structure of the gravity dam joint reinforcement steel bar model;

[0113] Then, historical earthquake loads are applied to the gravity dam joint reinforcement steel bar model to perform simulation calculations to obtain calculated values ​​of dam body concrete structure characteristics; wherein the dam body concrete structure characteristics may be modal frequencies of the dam body concrete structure.

[0114] S2.3, searching historical data to obtain measured values ​​of the dam concrete structure characteristics when the dam concrete structure is subjected to the historical earthquake load;

[0115] S2.4, compare the deviation between the calculated value of the dam body concrete structure characteristic and the measured value of the dam body concrete characteristic, dynamically update the physical and mechanical parameters of the dam body concrete structure using an iterative optimization algorithm, return to S2.2, and repeat this cycle until the error converges to an allowable range, thereby obtaining the optimal value of the physical and mechanical parameters of the dam body concrete structure.

[0116] In this step, the iterative optimization algorithm may adopt a double annealing optimization algorithm.

[0117] S3: using the optimal values ​​of the physical and mechanical parameters of the dam body concrete structure as initial parameters of the gravity dam span joint reinforcement steel bar model; applying seismic acceleration to the gravity dam span joint reinforcement steel bar model, and gradually increasing the seismic acceleration multiple to conduct seismic simulation analysis;

[0118] This step is specifically as follows:

[0119] S3.1: The dam body concrete structure is simulated using isoparametric elements, which are divided into a plurality of concrete elements; the steel bars are simulated using rod elements, which are divided into a plurality of steel bar elements; the bonding area between the steel bars and the dam body concrete structure has a plurality of bonding elements;

[0120] S3.2: At the current time step t during the seismic simulation analysis, seismic acceleration is applied to the gravity dam seam reinforcement steel bar model; wherein the initial value of the applied seismic acceleration may be the seismic acceleration value corresponding to the design intensity of the gravity dam.

[0121] S3.3: Inputting the earthquake acceleration into a pre-established crack contact model to determine the contact force of the crack contact interface and the crack contact state; wherein the crack contact state includes open, closed, or slip;

[0122] S3.3 specifically reads:

[0123] S3.3.1, using the crack as the boundary, divide the dam concrete structure into an upper concrete area and a lower concrete area;

[0124] S3.3.2, the steel bar passing through the crack contacts the upper concrete region and the lower concrete region, respectively; the concrete contact interfaces on both sides of the crack are referred to as the first concrete contact interface and the second concrete contact interface, respectively;

[0125] S3.3.3. Establish a local coordinate system ξηζ for the crack contact boundary; where ξ is the normal direction of the first concrete contact interface and the second concrete contact interface, and the normal directions of the first concrete contact interface and the second concrete contact interface are assumed to be the same; η is the tangent direction of the first concrete contact interface; ζ is the tangent direction of the second concrete contact interface;

[0126] S3.3.4, there are a number of contact point pairs between the first concrete contact interface and the second concrete contact interface;

[0127] S3.3.5, for each contact point pair j, including contact point j1 and contact point j2, the normal gap of contact point pair j at the current time step t is obtained by formula (1):

[0128]

[0129] in: represents the normal gap between contact point j1 and contact point j2 at time step t-1; and, the initial normal gap between contact point j1 and contact point j2 is a known value; represents the normal unit vector; represents the displacement of the contact point j1 at the current time step t; represents the displacement of contact point j2 at the current time step t;

[0130] Preliminary determination of the contact force exerted on contact point j1 from contact point j2 And the contact force on contact point j2 from contact point j1 in, Moreover, they all have components along the normal direction ξ, the tangential direction η, and the tangential direction ζ;

[0131] S3.3.6, determine the contact state of contact point pair j:

[0132] Open state: If Then, at this time, the crack between the contact point pair j opens, and no contact force is transmitted;

[0133] Closed state: If Then, at this time, the crack between the contact point pair j is closed, but no slip occurs;

[0134] Slip state: If Then, the crack between the contact point pair j is closed and slip occurs;

[0135] Where: f ξ,t 、f η,t and f ζ,t , are the components of the contact force along the normal direction ξ, tangent direction η, and tangent direction ζ on any contact point in the contact point pair j; is the tensile strength between the contact point pair j; A is the control area of ​​the contact point pair j; μ is the friction coefficient between the first concrete contact interface and the second concrete contact interface; c is the cohesion between the first concrete contact interface and the second concrete contact interface;

[0136] S3.3.7, according to the crack flexibility equation shown in formula (2), the contact force f for all contact point pairs between the first concrete contact interface and the second concrete contact interface is obtained t j Array of contact force increments relative to the previous time step

[0137]

[0138] Where: [C] is the flexibility matrix of the contact boundary between the first concrete contact interface and the second concrete contact interface; β2 is the integral coefficient of the displacement equation; Δt is the time step; is the actual displacement increment of each contact point on the first concrete contact interface relative to the previous time step;

[0139] is the actual displacement increment of each contact point on the second concrete contact interface relative to the previous time step. Here, the actual displacement increment refers to the actual displacement increment that conforms to the actual stress conditions, taking into account comprehensive factors such as contact force, reinforcement constraint, and structural constraint.

[0140] It is the displacement increment of each contact point of the first concrete contact interface relative to the previous time step when only the external load is considered. Here, considering only the external load means: assuming that the crack surface has no contact constraints and is completely free to deform under the external load.

[0141] is the displacement increment of each contact point on the second concrete contact interface relative to the previous time step when only the external load is considered;

[0142] f t j , represents the contact force f between the first concrete contact interface and the second concrete contact interface at the contact point j t j , specifically the contact force received by any contact point in the contact point pair j from another contact point;

[0143] S3.3.8. At the current time step t, determine whether all contact point pairs between the first concrete contact interface and the second concrete contact interface satisfy the finite element equilibrium equation shown in formula (3):

[0144]

[0145] in:

[0146] [M] is the mass matrix of the dam concrete structure; [D] is the damping matrix between the first concrete contact interface and the second concrete contact interface; [K] is the overall stiffness matrix of the dam concrete structure;

[0147] and{u t}, are respectively the acceleration array, velocity array and displacement array of all contact point pairs between the first concrete contact interface and the second concrete contact interface at the current time step t; {F t} is the external load vector caused by the earthquake acceleration applied at the current time step t; is the contact force matrix of all contact point pairs at the previous time step;

[0148] S3.3.9: If the finite element equilibrium equation shown in formula (3) is satisfied, the contact forces of all contact point pairs between the first concrete contact interface and the second concrete contact interface at the current time step t are output; if not satisfied, return to S3.3.5 and adjust the contact forces of each contact point pair; this cycle is repeated until the contact forces of all contact point pairs that satisfy the finite element equilibrium equation are obtained, and based on the contact forces of all contact point pairs finally determined, the crack state between the first concrete contact interface and the second concrete contact interface is determined.

[0149] S3.4: Based on the crack contact state determined in S3.3, update the gravity dam cross-crack reinforcement steel bar model; based on the updated gravity dam cross-crack reinforcement steel bar model, further analyze the bond-slip relationship between the steel bar and the dam concrete structure, and evaluate the slip degree of the steel bar-concrete contact interface;

[0150] In this step, the bond-slip relationship between the steel bars and the dam concrete structure is analyzed to evaluate the slip degree of the steel bar-concrete contact interface, specifically:

[0151] S3.4.1, based on the updated gravity dam joint reinforcement steel bar model, determine a bonding area between the steel bar and the dam body concrete structure; each bonding unit included in the bonding area is denoted as bonding unit i; bonding unit i is the bonding location between steel bar unit i and concrete unit i;

[0152] S3.4.2, construct the bond-slip relationship equation between the steel element and the concrete element shown in equation (4):

[0153]

[0154] in:

[0155] A reinforcement stiffness matrix formed by the stiffness of each reinforcement unit i having a bonding relationship with the dam concrete structure;

[0156] is the tangential stiffness matrix corresponding to the shear force exerted by concrete unit i on steel unit i at each bond unit i;

[0157] The flexibility matrix formed by the flexibility of concrete unit i at each bond unit i position;

[0158] {Δq i} is the slip increment array formed by the slip increment between the concrete unit i and the steel unit i at each bonding unit i;

[0159] [I] is the identity matrix;

[0160] is the array formed by the initial bonding force of steel bar unit i from concrete unit i at each bonding unit i;

[0161] is the array formed by the displacement of each concrete unit i caused only by the external load;

[0162] is the array formed by the initial slip between steel unit i and concrete unit i at each bonding unit i;

[0163] The following constraints also apply:

[0164] Constraint 1: The equilibrium equation of concrete element i in contact with steel element i:

[0165]

[0166] in:

[0167] is the displacement array formed by the displacement of each concrete unit i;

[0168] is the array formed by the load transferred from steel bar unit i to concrete unit i;

[0169] Constraint 2: The equilibrium equation of the steel bar element i in contact with the concrete element i:

[0170]

[0171] in:

[0172] is the displacement matrix formed by the displacement of each steel bar element i;

[0173] is the array formed by the load transferred from concrete element i to steel element i;

[0174]

[0175] The expression of is as follows:

[0176]

[0177] in:

[0178] q i represents the slip between steel element i and concrete element i at each bond element i;

[0179] is the bonding force exerted on steel bar unit i from concrete unit i at bonding unit i;

[0180] and The expressions are as follows:

[0181]

[0182] in:

[0183] is the initial bond force exerted on concrete unit i from steel unit i at bond unit i;

[0184] is the bonding force exerted on concrete unit i by steel unit i at bonding unit i;

[0185] According to the interaction relationship between steel bar unit i and concrete unit i, and The difference satisfies formula (10):

[0186]

[0187] in: is the initial slip between steel unit i and concrete unit i at bond unit i;

[0188] Constraint 3: Matrix middle, Satisfy the following constraints of formula (11):

[0189]

[0190] Where: d is the diameter of the steel bar; l i is the length of the reinforcement controlled by the bonding unit i; The uniform shear stress on steel bar unit i from concrete unit i within the control length of bond unit i.

[0191] S3.4.3, at each time step t, solve for the following parameters that satisfy the bond-slip relationship equation between the steel element and the concrete element shown in Equation (4): the slip increment between the steel element i and the concrete element i at each bond element i, and then evaluate the degree of slip at the steel-concrete contact interface at each time step t.

[0192] S3.5: Set time step t=t+1; apply the design multiple of earthquake acceleration to the gravity dam joint reinforcement steel bar model; return to S3.3; and repeat this cycle until the steel bar reaches the limit state.

[0193] S4: Recording the peak value of the earthquake acceleration when the steel bar reaches the limit state, and recording the displacement and stress distribution of the dam concrete structure and the crack structure under corresponding conditions, to obtain seismic simulation results; based on the seismic simulation results, analyzing and evaluating the seismic capacity of the dam concrete structure after cross-crack reinforcement with the steel bar.

[0194] The main idea of ​​the gravity dam seismic capacity analysis method considering the seismic reinforcement effect of seismic steel bars provided by the present invention can be described as follows:

[0195] S1: A gravity dam cross-joint reinforcement steel bar model was constructed based on the actual project dimensions. The dam concrete structure, crack damage, and cross-joint reinforcement were accurately simulated using a 3D finite element mesh.

[0196] S2: Simulate crack damage, establish a crack contact model, and simulate the bond-slip relationship between seismic reinforcement and dam concrete;

[0197] Specifically, a crack contact model was established based on the contact simulation between the cross-crack reinforcement and the dam head and dam body concrete. The bond-slip relationship between the reinforcement and the dam body concrete was simulated to serve as the basis for subsequent seismic simulation calculations.

[0198] S3: Inverse the physical and mechanical parameters of the dam using historical earthquake monitoring data;

[0199] Specifically, the physical and mechanical parameters of the dam concrete are reverse-analyzed. The initially obtained physical and mechanical parameters are used as the initial parameters of the gravity dam joint reinforcement steel bar model. Dynamic loads are applied to the model for simulation calculations. The deviation between the calculated and measured modal frequencies of the dam is compared. The parameters are dynamically updated using an iterative optimization algorithm until the error converges to the allowable range, thereby obtaining the optimal physical and mechanical parameters.

[0200] S4: Conduct seismic capacity simulations based on the gravity dam joint reinforcement steel reinforcement model and the physical and mechanical parameters derived from back analysis. Simulating the seismic capacity by applying artificial seismic waves, the authors analyze and calculate the displacement and stress distribution of the dam body and reinforced areas, as well as the potential failure modes, under the influence of each artificial seismic wave. Finally, the seismic capacity of the dam after reinforcement with seismic-resistant steel reinforcement is evaluated.

[0201] Specifically, the physical and mechanical parameters obtained from the back analysis are assigned to the reinforcement steel bar model of the gravity dam joint as the initial material parameters for the seismic simulation calculation. The design seismic acceleration is applied to the model, and the seismic acceleration multiple is gradually increased to carry out the seismic simulation calculation. In actual application, the corresponding seismic acceleration is determined according to the design intensity of the dam, and the seismic acceleration multiple is gradually increased.

[0202] Record the peak earthquake acceleration when the seismic reinforcement reaches the limit state, and record the displacement and stress distribution, failure mode, etc. of the dam body and cracks under corresponding conditions; analyze and evaluate the seismic resistance of the gravity dam based on the calculation results of the seismic simulation.

[0203] The present invention proposes a method for evaluating the seismic capacity of a gravity dam reinforced with seismic steel bars, which can effectively address the limitations of current seismic analysis and evaluation methods.

[0204] An embodiment is described below:

[0205] Reference Figure 1In an embodiment of the present invention, a model of reinforcement steel bars for cross-seam reinforcement of a gravity dam is constructed. The prototype is a section of a buttress gravity dam. Under the action of an earthquake, a through-crack developed at the angle where the dam head and dam body meet, and steel bars were subsequently used for seismic reinforcement. The model of reinforcement steel bars for cross-seam reinforcement of a gravity dam includes the dam body concrete structure, the crack structure, and reinforcement steel bars that penetrate the crack structure for reinforcement. The model of reinforcement steel bars for cross-seam reinforcement of a gravity dam is a three-dimensional finite element mesh model. It uses isoparametric elements to simulate the dam body concrete structure, cross-seam reinforcement bar elements to simulate the existing reinforcement steel bars, and bonding elements to connect the steel bars to the dam body concrete structure.

[0206] Reference Figure 2 , which is a schematic diagram of the bond-slip relationship between reinforced concrete and crack damage in the reinforcement model of the gravity dam cross-seam reinforcement according to an embodiment of the present invention. In this embodiment, after drilling holes in the crack site, seismic reinforcement bundles are added, arranged horizontally in a staggered manner, and grouted and anchored. In this embodiment, the established crack contact model includes crack contact conditions, finite element equilibrium equations under multiple load steps, and crack flexibility equations. In this embodiment, the through crack generated at the corner where the dam head and the dam body are connected divides the dam body concrete structure into upper and lower regions. The seismic reinforcement passing through the crack surface contacts the dam head and dam body concrete respectively. The functional relationship between the bond unit shear stress and the relative slip amount at the bond between the seismic reinforcement and the dam body concrete in each region satisfies the bond-slip relationship equation shown in formula (4) and the constraints shown in formulas (5) to (10).

[0207] Reference Figure 3 , which is a relationship diagram between the peak value of earthquake acceleration and the stress of seismic steel bars in an embodiment of the present invention. In this embodiment, as the earthquake acceleration continues to increase, the stress of the seismic steel bars increases significantly. When the peak value of the earthquake acceleration reaches 0.38g, the tensile stress of the steel bars reaches the yield strength of the steel bars (335MPa), indicating that the seismic steel bars have failed; then the stress on the seismic steel bars increases further, which may cause the steel bars to pull out, and ultimately greatly reduce the overall stability of the dam head, making it prone to slippage and leading to overall structural damage.

[0208] Reference Figure 4 , is a flow chart of a method for analyzing the seismic capacity of a gravity dam taking into account the effect of seismic steel reinforcement. The specific process of this method is as follows:

[0209] S1: Construct a model of the reinforcement bars for the cross-joint reinforcement of a gravity dam. Using a three-dimensional finite element mesh, the dam concrete structure, crack damage, and cross-joint reinforcement are accurately simulated in sequence. The dam concrete structure is simulated using isoparametric elements, while the cross-joint reinforcement is simulated using rod elements. Bonded elements are used between the reinforcement and the dam concrete structure.

[0210] S2: Based on the contact simulation between the cross-crack reinforcement and the dam head and dam body concrete, a crack contact model is established, as well as the bond-slip relationship equations and related constraints between the reinforcement unit and the concrete unit. The bond-slip relationship between the cross-crack reinforcement and the dam body concrete structure is simulated, which serves as the basis for subsequent seismic simulation calculations.

[0211] S3: Inversely analyze the physical and mechanical parameters of the dam concrete structure; use the initially obtained physical and mechanical parameters as the initial parameters of the gravity dam span joint reinforcement steel bar model, apply dynamic loads to the gravity dam span joint reinforcement steel bar model for simulation calculation, and obtain the calculated values ​​of the dam concrete structure characteristics; compare the deviations between the calculated values ​​of the dam concrete structure characteristics and the measured values ​​of the dam concrete structure characteristics, and dynamically update the physical and mechanical parameters using an iterative optimization algorithm until the error converges to the allowable range, thereby obtaining the optimal physical and mechanical parameters of the dam concrete structure;

[0212] In this embodiment, the physical and mechanical parameters of the dam concrete obtained by back analysis are the dynamic elastic modulus of the concrete. Based on the historical earthquake observation data during the operation of the dam, the self-power spectrum function identification method is used to perform modal analysis of the dam body to obtain the measured frequencies and vibration modes of the dam body. The optimization process adopts a double annealing algorithm, with the square difference between the simulated modal characteristics and the measured modal characteristics as the objective function. The specific steps are as follows: substitute the initial dynamic elastic modulus into the gravity dam span reinforcement steel bar model; apply historical seismic loads and calculate the current modal characteristics, including frequency and vibration mode; compare the calculated modal characteristics with the measured values, and update the physical and mechanical parameters of the concrete through the optimization algorithm; repeat the calculation until the frequency error is minimized, and obtain the current dynamic elastic modulus as the result of the back analysis.

[0213] S4: Assign the physical and mechanical parameters obtained from the back analysis to the gravity dam span joint reinforcement steel bar model as the initial material parameters for seismic simulation; apply the design seismic acceleration to the gravity dam span joint reinforcement steel bar model, and gradually increase the seismic acceleration multiple to carry out seismic simulation calculations;

[0214] In this embodiment, the design earthquake acceleration applied to the reinforcement steel bar model of the gravity dam seam in the earthquake simulation calculation is selected based on the provisions of the design intensity of the dam in the "Code for Seismic Design of Hydropower Projects" (NB 35057-2015). The pier gravity dam in this embodiment belongs to the large (1) type project, the water retaining dam level is level 1, and the seismic category of the water retaining dam is Class A. According to the code, the design intensity should be increased by 1 degree on the basis of the basic intensity, that is, the design intensity of the dam is 8 degrees, and the corresponding earthquake acceleration peak is 0.20g. In order to analyze and evaluate its earthquake resistance, the earthquake simulation calculation needs to gradually increase the earthquake acceleration multiple, and take it as 1.5, 2.0, 2.5, and 3.0 times the design earthquake acceleration respectively. The earthquake resistance of the dam in the event of an extreme earthquake is analyzed by the time history method.

[0215] S5: Record the peak seismic acceleration when the seismic reinforcement reaches the limit state, and record the displacement and stress distribution of the dam body and cracks under the corresponding conditions; analyze and evaluate the seismic resistance of the gravity dam based on the seismic simulation results.

[0216] In this example, when the seismic reinforcement reaches its ultimate limit, it is considered an extreme earthquake condition. The corresponding ground acceleration at this point is the ultimate seismic capacity of the dam under these calculation conditions. Further analysis of the displacement and stress distribution of the dam body and cracks includes: dam body longitudinal and vertical displacement, dam body primary principal stress, vertical stress; time-history changes in reinforcement stress; crack surface stress and opening displacement. Further analysis of failure modes includes concrete cracking or fracture, reinforcement yielding or pullout, dam head slippage, and overall structural failure.

[0217] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for analyzing the seismic capacity of a gravity dam considering the effect of seismic steel reinforcement, characterized in that: The following steps are involved: S1: Constructing a gravity dam cross-crack reinforcement steel bar model; the gravity dam cross-crack reinforcement steel bar model includes a dam body concrete structure, a crack structure, and steel bars that cross the crack structure for reinforcement; S2: using an inverse analysis method combined with an iterative optimization algorithm to determine the optimal values ​​of the physical and mechanical parameters of the dam concrete structure; S3: using the optimal values ​​of the physical and mechanical parameters of the dam body concrete structure as initial parameters of the gravity dam span joint reinforcement steel bar model; applying seismic acceleration to the gravity dam span joint reinforcement steel bar model, and gradually increasing the seismic acceleration multiple to conduct seismic simulation analysis; S3 specifically: S3.1: The dam body concrete structure is simulated using isoparametric elements, which are divided into a plurality of concrete elements; the steel bars are simulated using rod elements, which are divided into a plurality of steel bar elements; the bonding area between the steel bars and the dam body concrete structure has a plurality of bonding elements; S3.2: At the current time step t during the seismic simulation analysis, applying earthquake acceleration to the gravity dam joint reinforcement steel bar model; S3.3: Inputting the earthquake acceleration into a pre-established crack contact model to determine the contact force of the crack contact interface and the crack contact state; wherein the crack contact state includes open, closed, or slip; S3.4: Based on the crack contact state determined in S3.3, update the gravity dam cross-crack reinforcement steel bar model; based on the updated gravity dam cross-crack reinforcement steel bar model, further analyze the bond-slip relationship between the steel bar and the dam concrete structure, and evaluate the slip degree of the steel bar-concrete contact interface; S3.5: Set time step t = t + 1; apply a design multiple of earthquake acceleration to the gravity dam joint reinforcement steel bar model; return to S3.3; and repeat this process until the steel bar reaches the ultimate limit state. S4: Recording the peak value of the earthquake acceleration when the steel bar reaches the limit state, and recording the displacement and stress distribution of the dam concrete structure and the crack structure under corresponding conditions, to obtain seismic simulation results; based on the seismic simulation results, analyzing and evaluating the seismic capacity of the dam concrete structure after cross-crack reinforcement with the steel bar.

2. The method for analyzing the seismic capacity of a gravity dam considering the reinforcement effect of seismic steel bars according to claim 1, characterized in that: S2 is specifically: S2.1, obtaining the physical and mechanical parameters of the dam concrete structure using an inverse analysis method; S2.2, using the obtained physical and mechanical parameters of the dam body concrete structure as the initial physical and mechanical parameters of the dam body concrete structure of the gravity dam joint reinforcement steel bar model; Then, applying historical earthquake loads to the gravity dam joint reinforcement steel bar model to perform simulation calculations to obtain calculated values ​​of the dam body concrete structure characteristics; S2.3, searching historical data to obtain measured values ​​of the dam concrete structure characteristics when the dam concrete structure is subjected to the historical earthquake load; S2.4, compare the deviation between the calculated value of the dam body concrete structure characteristic and the measured value of the dam body concrete structure characteristic, dynamically update the physical and mechanical parameters of the dam body concrete structure using an iterative optimization algorithm, return to S2.2, and repeat this cycle until the error converges to an allowable range, thereby obtaining the optimal values ​​of the physical and mechanical parameters of the dam body concrete structure.

3. The method for analyzing the seismic capacity of a gravity dam considering the reinforcement effect of seismic steel bars according to claim 2, characterized in that: The physical and mechanical parameter of the dam body concrete structure is the dynamic elastic modulus; the characteristic of the dam body concrete structure is the modal frequency of the dam body concrete structure.

4. The method for analyzing the seismic capacity of a gravity dam considering the reinforcement effect of seismic steel bars according to claim 2, characterized in that: The iterative optimization algorithm is a double annealing optimization algorithm.

5. The method for analyzing the seismic capacity of a gravity dam considering the reinforcement effect of seismic steel bars according to claim 1, characterized in that: S3.3 specifically reads: S3.3.1, using the crack as the boundary, divide the dam concrete structure into an upper concrete area and a lower concrete area; S3.3.2, the steel bar passing through the crack contacts the upper concrete region and the lower concrete region, respectively; the concrete contact interfaces on both sides of the crack are referred to as the first concrete contact interface and the second concrete contact interface, respectively; S3.3.

3. Establish a local coordinate system ξηζ for the crack contact boundary; where ξ is the normal direction of the first concrete contact interface and the second concrete contact interface, and the normal directions of the first concrete contact interface and the second concrete contact interface are assumed to be the same; η is the tangent direction of the first concrete contact interface; ζ is the tangent direction of the second concrete contact interface; S3.3.4, there are a number of contact point pairs between the first concrete contact interface and the second concrete contact interface; S3.3.5, for each contact point pair j, including contact point j1 and contact point j2, the normal gap of contact point pair j at the current time step t is obtained by formula (1): in: represents the normal gap between contact point j1 and contact point j2 at time step t-1; and, the initial normal gap between contact point j1 and contact point j2 is a known value; represents the normal unit vector; represents the displacement of contact point j 1 at the current time step t; represents the displacement of contact point j2 at the current time step t; Preliminary determination of the contact force received by contact point j1 from contact point j2 And the contact force on contact point j2 from contact point j1 in, Moreover, they all have components along the normal direction ξ, the tangential direction η, and the tangential direction ζ; S3.3.6, determine the contact state of contact point pair j: Open state: If Then, at this time, the crack between the contact point pair j opens, and no contact force is transmitted; Closed state: If Then, at this time, the crack between the contact point pair j is closed, but no slip occurs; Slip state: If Then, the crack between the contact point pair j is closed and slip occurs; Where: f ξ,t 、f η,t and f ζ,t , are the components of the contact force along the normal direction ξ, tangent direction η, and tangent direction ζ on any contact point in the contact point pair j; is the tensile strength between the contact point pair j; A is the control area of ​​the contact point pair j; μ is the friction coefficient between the first concrete contact interface and the second concrete contact interface; c is the cohesion between the first concrete contact interface and the second concrete contact interface; S3.3.7, according to the crack flexibility equation shown in formula (2), the contact force f for all contact point pairs between the first concrete contact interface and the second concrete contact interface is obtained t j Array of contact force increments relative to the previous time step Where: [C] is the flexibility matrix of the contact boundary between the first concrete contact interface and the second concrete contact interface; β2 is the integral coefficient of the displacement equation; Δt is the time step; is the actual displacement increment of each contact point on the first concrete contact interface relative to the previous time step; is the actual displacement increment of each contact point on the second concrete contact interface relative to the previous time step; is the displacement increment of each contact point on the first concrete contact interface relative to the previous time step when only the external load is considered; is the displacement increment of each contact point on the second concrete contact interface relative to the previous time step when only the external load is considered; f t j , represents the contact force f between the first concrete contact interface and the second concrete contact interface at the contact point j t j , specifically the contact force received by any contact point in the contact point pair j from another contact point; S3.3.

8. At the current time step t, determine whether all contact point pairs between the first concrete contact interface and the second concrete contact interface satisfy the finite element equilibrium equation shown in formula (3): in: [M] is the mass matrix of the dam concrete structure; [D] is the damping matrix between the first concrete contact interface and the second concrete contact interface; [K] is the overall stiffness matrix of the dam concrete structure; and{u t }, are respectively the acceleration array, velocity array and displacement array of all contact point pairs between the first concrete contact interface and the second concrete contact interface at the current time step t; {F t } is the external load vector caused by the earthquake acceleration applied at the current time step t; is the contact force matrix of all contact point pairs at the previous time step; S3.3.9: If the finite element equilibrium equation shown in formula (3) is satisfied, the contact forces of all contact point pairs between the first concrete contact interface and the second concrete contact interface at the current time step t are output; if not satisfied, return to S3.3.5 and adjust the contact forces of each contact point pair; this cycle is repeated until the contact forces of all contact point pairs that satisfy the finite element equilibrium equation are obtained, and based on the contact forces of all contact point pairs finally determined, the crack state between the first concrete contact interface and the second concrete contact interface is determined.

6. The method for analyzing the seismic capacity of a gravity dam considering the effect of seismic steel reinforcement according to claim 5, characterized in that: In S3.4, the bond-slip relationship between the steel bars and the dam concrete structure is analyzed to evaluate the degree of slip at the steel bar-concrete contact interface, specifically: S3.4.1, based on the updated gravity dam joint reinforcement steel bar model, determine a bonding area between the steel bar and the dam body concrete structure; each bonding unit included in the bonding area is denoted as bonding unit i; bonding unit i is the bonding location between steel bar unit i and concrete unit i; S3.4.2, construct the bond-slip relationship equation between the steel element and the concrete element shown in equation (4): in: A reinforcement stiffness matrix formed by the stiffness of each reinforcement unit i having a bonding relationship with the dam concrete structure; is the tangential stiffness matrix corresponding to the shear force exerted by concrete unit i on steel unit i at each bond unit i; The flexibility matrix formed by the flexibility of concrete unit i at each bond unit i position; {Δq i } is the slip increment array formed by the slip increment between the concrete unit i and the steel unit i at each bonding unit i; [I] is the identity matrix; is the array formed by the initial bonding force of steel bar unit i from concrete unit i at each bonding unit i; is the array formed by the displacement of each concrete unit i caused only by the external load; is the array formed by the initial slip between steel unit i and concrete unit i at each bonding unit i; S3.4.3, at each time step t, solve for the following parameters that satisfy the bond-slip relationship equation between the steel element and the concrete element shown in Equation (4): the slip increment between the steel element i and the concrete element i at each bond element i, and then evaluate the degree of slip at the steel-concrete contact interface at each time step t.

7. The method for analyzing the seismic capacity of a gravity dam considering the reinforcement effect of seismic steel bars according to claim 6, characterized in that: When solving the bond-slip relationship equation between the steel bar unit and the concrete unit, the following constraints must also be met: Constraint 1: The equilibrium equation of concrete element i in contact with steel element i: in: is the displacement array formed by the displacement of each concrete unit i; is the array formed by the load transferred from steel bar unit i to concrete unit i; Constraint 2: The equilibrium equation of the steel bar element i in contact with the concrete element i: in: is the displacement matrix formed by the displacement of each steel bar element i; is the array formed by the load transferred from concrete element i to steel element i; The expression of is as follows: in: q i represents the slip between steel element i and concrete element i at each bond element i; is the bonding force exerted on steel bar unit i from concrete unit i at bonding unit i; and The expressions are as follows: in: is the initial bond force exerted on concrete unit i from steel unit i at bond unit i; is the bonding force exerted on concrete unit i by steel unit i at bonding unit i; According to the interaction relationship between steel bar unit i and concrete unit i, and The difference satisfies formula (10): in: is the initial slip between steel unit i and concrete unit i at bond unit i; Constraint 3: Matrix middle, Satisfy the following constraints of formula (11): Where: d is the diameter of the steel bar; l i is the length of the reinforcement controlled by the bonding unit i; The uniform shear stress on steel bar unit i from concrete unit i within the control length of bond unit i.

8. The method for analyzing the seismic capacity of a gravity dam considering the reinforcement effect of seismic steel bars according to claim 1, characterized in that: When applying earthquake acceleration to the gravity dam seam reinforcement steel bar model to carry out seismic simulation analysis, the initial value of the applied earthquake acceleration is the earthquake acceleration value corresponding to the design intensity of the gravity dam.

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