Gravity dam anti-seismic capacity analysis method considering reinforcing effect of anti-seismic steel bars

Abstract

The invention provides a gravity dam anti-seismic capacity analysis method considering an anti-seismic reinforcement reinforcement effect. The gravity dam anti-seismic capacity analysis method comprises the steps that a gravity dam cross-joint reinforcement reinforcement model is constructed; the gravity dam joint-crossing reinforcing steel bar model comprises a dam body concrete structure, a crack structure and reinforcing steel bars penetrating through the crack structure to be reinforced. Determining the optimal value of the physical and mechanical parameters of the dam body concrete structure by using an inverse analysis method and combining an iterative optimization algorithm; the optimal values of the physical and mechanical parameters of the dam body concrete structure serve as initial parameters of the gravity dam cross-joint reinforcing steel bar model; and seismic acceleration is applied to the gravity dam joint-crossing reinforcing steel bar model, the multiple of the seismic acceleration is gradually increased, and anti-seismic simulation analysis is carried out. According to the gravity dam anti-seismic capacity analysis method considering the anti-seismic reinforcement reinforcement effect, the anti-seismic capacity of the gravity dam with cracks after anti-seismic reinforcement reinforcement can be accurately analyzed.

Description

Technical Field

[0001] The present invention belongs to the field of water conservancy and hydropower engineering, and particularly relates to a method for analyzing the seismic resistance capacity of a gravity dam considering the reinforcement effect of anti-seismic steel bars. Background Art

[0002] The gravity dam is one of the most common types of dams in water conservancy and hydropower engineering, and its seismic performance is directly related to the safety and reliability of the project. In actual projects, in order to improve the seismic performance of the gravity dam, steel bars are often used for reinforcement at the parts where cracks appear in the dam body.

[0003] The existing methods for seismic analysis of gravity dams have the following deficiencies: it is difficult to accurately reflect the cooperative working mechanism between the reinforcement steel bars and concrete; the simulation of the stress and strain characteristics in the crack area is not precise enough. Therefore, there is an urgent need to establish a method for analyzing the seismic resistance capacity of a gravity dam that can accurately consider the reinforcement effect of anti-seismic steel bars, so as to provide more powerful technical support for the seismic assessment, seismic design, and reinforcement and transformation of gravity dams. Summary of the Invention

[0004] In view of the defects existing in the prior art, the present invention provides a method for analyzing the seismic resistance capacity of a gravity dam considering the reinforcement effect of anti-seismic steel bars, which can effectively solve the above problems.

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

[0006] The present invention provides a method for analyzing the seismic resistance capacity of a gravity dam considering the reinforcement effect of anti-seismic steel bars, including the following steps:

[0007] S1: Construct a model of the cross-crack reinforcement steel bars of the gravity dam; the model of the cross-crack reinforcement steel bars of the gravity dam includes the dam body concrete structure, the crack structure, and the steel bars for reinforcement passing through the crack structure;

[0008] S2: Determine the optimal values of the physical and mechanical parameters of the dam body concrete structure by using the back-analysis method in combination with the iterative optimization algorithm;

[0009] S3: Take the optimal values of the physical and mechanical parameters of the dam body concrete structure as the initial parameters of the model of the cross-crack reinforcement steel bars of the gravity dam; apply the seismic ground acceleration to the model of the cross-crack reinforcement steel bars of the gravity dam, and gradually increase the multiple of the seismic ground acceleration, and carry out seismic simulation analysis;

[0010] S4: Record the peak value of the seismic ground acceleration when the steel bars reach the ultimate state, and record the displacement and stress distributions of the dam body concrete structure and the crack structure under the corresponding conditions to obtain the seismic simulation results; according to the seismic simulation results, analyze and evaluate the seismic resistance capacity of the dam body concrete structure after being cross-crack reinforced by the steel bars.

[0011] Preferably, S2 is specifically:

[0012] S2.1. Obtain the physical and mechanical parameters of the dam concrete structure by the back-analysis method;

[0013] S2.2. Take the obtained physical and mechanical parameters of the dam concrete structure as the initial physical and mechanical parameters of the dam concrete structure in the gravity dam cross-seam reinforcement steel bar model;

[0014] Then, apply the historical ground motion load to the gravity dam cross-seam reinforcement steel bar model for simulation calculation to obtain the calculated values of the dam concrete structure characteristics;

[0015] S2.3. Search for historical data to obtain the measured values of the dam concrete structure characteristics when the dam concrete structure is subjected to the historical ground motion load;

[0016] S2.4. Compare the deviation between the calculated values of the dam concrete structure characteristics and the measured values of the dam concrete characteristics, and use the iterative optimization algorithm to dynamically update the physical and mechanical parameters of the dam concrete structure, and return to S2.2, and cycle continuously like this until the error converges within the allowable range to obtain the optimal values of the physical and mechanical parameters of the dam concrete structure.

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

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

[0019] Preferably, S3 is specifically:

[0020] S3.1: The dam concrete structure is simulated by isoparametric elements, and the dam concrete structure is divided into several concrete elements; the steel bars are simulated by bar elements, and the steel bars are divided into several steel bar elements; there are several bonding elements in the bonding area between the steel bars and the dam concrete structure;

[0021] S3.2: At the current time step t during the seismic simulation analysis, apply the ground motion acceleration to the gravity dam cross-seam reinforcement steel bar model;

[0022] S3.3: Input the ground motion acceleration into the pre-established crack contact model to determine the contact force and crack contact state of the crack contact interface; wherein, the crack contact state includes opening, closing or slipping;

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

[0024] S3.5: Let the time step \(t = t + 1\); apply the seismic acceleration of the designed multiple to the cross-crack reinforcement steel bar model of the gravity dam; return to S3.3; and loop continuously until the steel bars reach the ultimate state.

[0025] Preferably, S3.3 is specifically as follows:

[0026] S3.3.1: Divide the dam body concrete structure into an upper concrete area and a lower concrete area with the crack as the boundary;

[0027] S3.3.2: The steel bars passing through the crack are in contact with the upper concrete area and the lower concrete area respectively; the concrete contact interfaces on both sides of the crack are respectively called the first concrete contact interface and the second concrete contact interface;

[0028] S3.3.3: Establish a local coordinate system \(\xi\eta\zeta\) of the crack contact boundary; where \(\xi\) is the normal direction of the first concrete contact interface and the second concrete contact interface, and it is assumed that the normal directions of the first concrete contact interface and the second concrete contact interface are the same; \(\eta\) is the tangent direction of the first concrete contact interface; \(\zeta\) is the tangent direction of the second concrete contact interface;

[0029] S3.3.4: There are several pairs of contact point pairs between the first concrete contact interface and the second concrete contact interface;

[0030] S3.3.5: For each pair of contact point pairs \(j\), including contact point \(j1\) and contact point \(j2\), obtain the normal gap of the contact point pair \(j\) at the current time step \(t\) through formula (1)

[0031]

[0032] Where: 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 \(j1\) at the current time step \(t\); represents the displacement of contact point \(j2\) at the current time step \(t\);

[0033] Preliminarily determine the contact force received by contact point j1 from contact point j2 and the contact force received by contact point j2 from contact point j1 wherein, moreover, both have components along the normal direction ξ, the tangential direction η, and the tangential direction ζ;

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

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

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

[0037] Slip state: If then the crack between contact point pair j is closed and slip occurs at this time;

[0038] where: f ξ,t , f η,t and f ζ,t are respectively the components of the contact force received by any one contact point in contact point pair j along the normal direction ξ, the tangential direction η, and the tangential direction ζ; is the tensile strength between contact point pair j; A is the control area of 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 compliance equation shown in formula (2), obtain the contact force f t j of all contact point pairs between the first concrete contact interface and the second concrete contact interface

[0040]

[0041] where: [C] is the compliance 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 considering the action of external loads;

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

[0045] f t j , representing the contact force f of the contact point pair j between the first concrete contact interface and the second concrete contact interface t j , specifically the contact force received by any contact point in the contact point pair j from the other 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] where:

[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 the acceleration column matrix, velocity column matrix, and displacement column matrix of all contact point pairs between the first concrete contact interface and the second concrete contact interface at the current time step t, respectively; {F t} is the external load vector caused by the seismic acceleration applied at the current time step t; is the contact force column 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, output 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; if not, return to S3.3.5 to adjust the contact forces of each contact point pair; and so on, until the contact forces of all contact point pairs that satisfy the finite element equilibrium equation are obtained, and based on the finally determined contact forces of all contact point pairs, determine the crack state between the first concrete contact interface and the second concrete contact interface.

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

[0053] S3.4.1, based on the updated cross-seam reinforced steel bar model of the gravity dam, determine the bond area between the steel bars and the dam concrete structure; each bond unit included in the bond area is represented as bond unit i; bond unit i is the bonding position of steel bar unit i and concrete unit i;

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

[0055]

[0056] Where:

[0057] is the steel bar stiffness matrix formed by the stiffnesses of each steel bar unit i having a bond relationship with the dam concrete structure;

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

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

[0060] {Δq i} is the slip increment column matrix formed by the slip increments between concrete unit i and steel bar unit i at each bond unit i;

[0061] [I] is the identity matrix;

[0062] is the column matrix formed by the initial bond forces received by steel bar unit i from concrete unit i at each bond unit i;

[0063] is the column matrix formed by the displacements generated by external loads only in each concrete unit i;

[0064] is the column matrix formed by the initial slip amounts between steel bar unit i and concrete unit i at each bond unit i;

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

[0066] Preferably, when solving the bond-slip relationship equation between the steel bar element and the concrete element, the following constraint conditions need to be satisfied:

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

[0068]

[0069] Where:

[0070] is the displacement column matrix formed by the displacements of each concrete element i;

[0071] is the column matrix formed by the loads transferred from the steel bar element i received by the concrete element i;

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

[0073]

[0074] Where:

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

[0076] is the column matrix formed by the loads transferred from the concrete element i received by the steel bar element i;

[0077]

[0078] The expression of is as shown in Formula (7):

[0079]

[0080] Where:

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

[0082] is the bond force received by the steel bar element i from the concrete element i at the bond element i;

[0083] and The expressions are respectively as shown in Formula (8) and Formula (9):

[0084]

[0085] Wherein:

[0086] is the initial bonding force received by the concrete element i at the bonding element i from the steel bar element i;

[0087] is the bonding force received by the concrete element i at the bonding element i from the steel bar element i;

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

[0089]

[0090] Wherein: is the initial slip amount between the steel bar element i and the concrete element i at the bonding element i;

[0091] Constraint condition 3: In the matrix satisfies the following constraint of Formula (11):

[0092]

[0093] Wherein: d is the diameter of the steel bar; l i is the length of the steel bar controlled by the bonding element i; is the uniform shear stress received by the steel bar element i from the concrete element i within the length range controlled by the bonding element i.

[0094] Preferably, when carrying out the seismic simulation analysis by applying the seismic ground acceleration to the cross - joint reinforced steel bar model of the gravity dam, the initial value of the applied seismic ground acceleration is the seismic ground acceleration value corresponding to the design intensity of the gravity dam.

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

[0096] The method for analyzing the seismic capacity of a gravity dam considering the seismic reinforcement effect of steel bars provided by the present invention can accurately analyze the seismic capacity of a gravity dam with cracks after seismic reinforcement with steel bars. Description of the Drawings

[0097] Figure 1 ​Overall schematic diagram of the gravity dam's cross - joint reinforcement steel bar model according to the embodiment of the present invention;

[0098] Figure 2 Schematic diagram of the crack damage and the bond - slip relationship between steel bars and reinforced concrete of the gravity dam's cross - joint reinforcement steel bar model according to the embodiment of the present invention;

[0099] Figure 3 Graph of the relationship between the peak ground acceleration and the stress of the earthquake - resistant steel bars according to the embodiment of the present invention;

[0100] Figure 4 Flow chart of an analysis method for the seismic capacity of a gravity dam considering the reinforcement effect of earthquake - resistant steel bars. Detailed implementation manners

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

[0102] Refer to Figures 1 to 4 , the present invention provides an analysis method for the seismic capacity of a gravity dam considering the reinforcement effect of earthquake - resistant steel bars, including the following steps:

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

[0104] S2: Use the 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;

[0105] S3: Take the optimal values of the physical and mechanical parameters of the dam body concrete structure as the initial parameters of the gravity dam cross - joint reinforcement steel bar model; apply ground motion acceleration to the gravity dam cross - joint reinforcement steel bar model, and gradually increase the multiple of the ground motion acceleration to carry out seismic simulation analysis;

[0106] S4: Record the peak value of the ground motion acceleration when the steel bars reach the limit state, and record the displacement and stress distributions of the dam body concrete structure and the crack structure under corresponding conditions to obtain the seismic simulation results; according to the seismic simulation results, analyze and evaluate the seismic capacity of the dam body concrete structure after being cross - joint reinforced by the steel bars.

[0107] The following is a detailed introduction to each step:

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

[0109] S2: Using the back-analysis method in combination with an iterative optimization algorithm, determine the optimal values of the physical and mechanical parameters of the dam concrete structure;

[0110] Specifically, this step is as follows:

[0111] S2.1, Use the back-analysis method to obtain the physical and mechanical parameters of the dam concrete structure; for example, the physical and mechanical parameter of the dam concrete structure is the dynamic elastic modulus;

[0112] S2.2, Take the obtained physical and mechanical parameters of the dam concrete structure as the initial physical and mechanical parameters of the dam concrete structure in the gravity dam cross-seam reinforcement steel bar model;

[0113] Then, apply historical ground motion loads to the gravity dam cross-seam reinforcement steel bar model for simulation calculation to obtain the calculated values of the dam concrete structure characteristics; among them, the dam concrete structure characteristics can be the modal frequencies of the dam concrete structure.

[0114] S2.3, Search for historical data to obtain the measured values of the dam concrete structure characteristics when the dam concrete structure is subjected to the historical ground motion loads;

[0115] S2.4, Compare the deviation between the calculated values of the dam concrete structure characteristics and the measured values of the dam concrete characteristics, and use the iterative optimization algorithm to dynamically update the physical and mechanical parameters of the dam concrete structure, and return to S2.2. Keep cycling like this until the error converges within the allowable range to obtain the optimal values of the physical and mechanical parameters of the dam concrete structure.

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

[0117] S3: Take the optimal values of the physical and mechanical parameters of the dam concrete structure as the initial parameters of the gravity dam cross-seam reinforcement steel bar model; apply ground motion acceleration to the gravity dam cross-seam reinforcement steel bar model and gradually increase the multiple of the ground motion acceleration to carry out seismic simulation analysis;

[0118] Specifically, this step is as follows:

[0119] S3.1: The dam concrete structure is simulated by isoparametric elements, and the dam concrete structure is divided into several concrete elements; the steel bars are simulated by bar elements, and the steel bars are divided into several steel bar elements; there are several bond elements in the bond area between the steel bars and the dam concrete structure;

[0120] S3.2: At the current time step t during the seismic simulation analysis, apply the ground motion acceleration to the gravity dam's cross-crack reinforcement steel bar model; among them, the initial value of the applied ground motion acceleration can be the ground motion acceleration value corresponding to the design intensity of the gravity dam.

[0121] S3.3: Input the ground motion acceleration into the pre-established crack contact model to determine the contact force and crack contact state at the crack contact interface; among them, the crack contact state includes opening, closing, or slipping.

[0122] Specifically, S3.3 is as follows:

[0123] S3.3.1: Divide the dam body concrete structure into an upper concrete area and a lower concrete area with the crack as the boundary.

[0124] S3.3.2: The steel bars passing through the crack are in contact with the upper concrete area and the lower concrete area respectively; the concrete contact interfaces on both sides of the crack are respectively called the first concrete contact interface and the second concrete contact interface.

[0125] S3.3.3: Establish a local coordinate system ξηζ at the crack contact boundary; where ξ is the normal direction of the first concrete contact interface and the second concrete contact interface, and it is assumed that the normal directions of the first concrete contact interface and the second concrete contact interface are 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 several pairs of contact point pairs between the first concrete contact interface and the second concrete contact interface.

[0127] S3.3.5: For each pair of contact point pairs j, including contact point j1 and contact point j2, obtain the normal gap of contact point pair j at the current time step t through formula (1).

[0128]

[0129] Among them: 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 j1 at the current time step t; represents the displacement of contact point j2 at the current time step t;

[0130] Preliminarily determine the contact force received by contact point j1 from contact point j2 and the contact force received by contact point j2 from contact point j1 wherein, and 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 the crack between contact point pair j is open at this time, and no contact force is transmitted;

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

[0134] Slip state: If then the crack between contact point pair j is closed and slip occurs at this time;

[0135] where: f ξ,t , f η,t and f ζ,t are respectively the components of the contact force received by any one contact point in contact point pair j along the normal direction ξ, the tangential direction η, and the tangential direction ζ; is the tensile strength between contact point pair j; A is the control area of 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 compliance equation shown in formula (2), obtain the contact force f t j of all contact point pairs between the first concrete contact interface and the second concrete contact interface

[0137]

[0138] where: [C] is the compliance 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: considering comprehensive factors such as contact force, steel bar restraint, structural restraint, etc., to obtain the actual displacement increment that conforms to the actual stress situation.

[0140] is the displacement increment of each contact point on the first concrete contact interface relative to the previous time step when only external loads are considered; here, considering only external loads means: assuming that there are no contact constraints on the crack surface and it is in a state of completely free deformation under external loads.

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

[0142] f t j , represents the contact force f of contact point pair j between the first concrete contact interface and the second concrete contact interface t j , specifically, it is the contact force received by any contact point in contact point pair j from the other 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] where:

[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 the acceleration column matrix, velocity column matrix, and displacement column matrix of all contact point pairs between the first concrete contact interface and the second concrete contact interface at the current time step t respectively; {F t} is the external load vector caused by the ground motion acceleration applied at the current time step t; is the contact force column 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, output 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; if not, return to S3.3.5 to adjust the contact forces of each contact point pair; and so on in a loop until the contact forces of all contact point pairs that satisfy the finite element equilibrium equation are obtained, and based on the finally determined contact forces of all contact point pairs, determine the crack state between the first concrete contact interface and the second concrete contact interface.

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

[0150] In this step, analyzing the bond - slip relationship between the steel bars and the dam body concrete structure and evaluating the slip degree of the steel bar - concrete contact interface specifically includes:

[0151] S3.4.1: Based on the updated cross - crack reinforcement steel bar model of the gravity dam, determine the bond area between the steel bars and the dam body concrete structure; Each bond unit included in the bond area is represented as bond unit i; Bond unit i is the bonding position of steel bar unit i and concrete unit i;

[0152] S3.4.2: Construct the bond - slip relationship equation between the steel bar unit and the concrete unit shown in formula (4):

[0153]

[0154] Where:

[0155] is the steel bar stiffness matrix formed by the stiffnesses of each steel bar unit i having a bond relationship with the dam body concrete structure;

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

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

[0158] {Δq i} is the slip increment column matrix formed by the slip increments between concrete unit i and steel bar unit i at each bond unit i;

[0159] [I] is the identity matrix;

[0160] is the column matrix formed by the initial bond forces received by steel bar unit i from concrete unit i at each bond unit i;

[0161] is the column matrix formed by the displacements generated by external loads only in each concrete unit i;

[0162] is the column matrix formed by the initial slip amounts between steel bar unit i and concrete unit i at each bond unit i;

[0163] It also has the following constraint conditions:

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

[0165]

[0166] Where:

[0167] is the displacement column matrix formed by the displacements of each concrete element i;

[0168] is the column matrix formed by the loads transferred from steel bar element i to concrete element i;

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

[0170]

[0171] Where:

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

[0173] is the column matrix formed by the loads transferred from concrete element i to steel bar element i;

[0174]

[0175] The expression of is as shown in formula (7):

[0176]

[0177] Where:

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

[0179] is the bonding force of steel bar element i from concrete element i at bonding element i;

[0180] and The expressions are as shown in formula (8) and formula (9) respectively:

[0181]

[0182] Where:

[0183] is the initial bonding force exerted on concrete element i at bonding element i by steel bar element i;

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

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

[0186]

[0187] Where: is the initial slip amount between steel bar element i and concrete element i at bonding element i;

[0188] Constraint condition 3: Matrix In Satisfies the following formula (11) constraint:

[0189]

[0190] Where: d is the diameter of the steel bar; l i is the length of the steel bar controlled by bonding element i; is the uniform shear stress exerted on steel bar element i by concrete element i within the length controlled by bonding element i.

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

[0192] S3.5: Let the time step t = t + 1; Apply the seismic acceleration of the design multiple to the cross-joint reinforced steel bar model of the gravity dam; Return to S3.3; Repeat this process continuously until the steel bar reaches the ultimate state.

[0193] S4: Record the peak value of the seismic acceleration when the steel bar reaches the ultimate state, and record the displacement and stress distributions of the dam body concrete structure and the crack structure under the corresponding conditions to obtain the seismic simulation results; According to the seismic simulation results, analyze and evaluate the seismic capacity of the dam body concrete structure after being cross-joint reinforced by the steel bar.

[0194] The analysis method for the seismic capacity of a gravity dam considering the seismic reinforcement effect of seismic-resistant steel bars provided by the present invention can be mainly described as follows:

[0195] S1: Construct a gravity dam cross - joint reinforcement steel bar model based on the actual engineering dimensions. Among them, accurately simulate the dam body concrete structure, crack damage, and cross - joint steel bars in sequence through three - dimensional finite - element meshes;

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

[0197] Specifically, establish a crack contact model according to the contact simulation of the cross - joint steel bars passing through the cracks with the dam head and the dam body concrete; simulate the bond - slip relationship between the steel bars and the dam body concrete as the basis for subsequent seismic simulation calculations;

[0198] S3: Use historical earthquake monitoring data to invert the physical and mechanical parameters of the dam body;

[0199] Specifically, back - analyze the physical and mechanical parameters of the dam body concrete. For the initially obtained physical and mechanical parameters, use them as the initial parameters of the gravity dam cross - joint reinforcement steel bar model. Through applying dynamic loads to the model for simulation calculations, compare the deviation between the calculated value and the measured value of the dam modal frequency, and use the iterative optimization algorithm to dynamically update the parameters until the error converges within the allowable range to obtain the optimal physical and mechanical parameters;

[0200] S4: Carry out seismic capacity simulation calculations based on the gravity dam cross - joint reinforcement steel bar model and the physical and mechanical parameters obtained from the back - analysis. Conduct seismic capacity simulation by applying artificial seismic waves, and analyze the displacement and stress distributions and possible failure modes of the overall dam body and the reinforced parts under the influence of each artificial seismic wave. Finally, analyze and evaluate the seismic capacity of the dam after being reinforced with seismic reinforcement bars.

[0201] Specifically, assign the physical and mechanical parameters obtained from the back - analysis to the gravity dam cross - joint reinforcement steel bar model as the initial material parameters for seismic simulation calculations; apply the design ground motion acceleration to the model and gradually increase the multiple of the ground motion acceleration to carry out seismic simulation calculations; in practical applications, determine the corresponding ground motion acceleration according to the design intensity of the dam and gradually increase the multiple of the ground motion acceleration;

[0202] Record the peak value of the ground motion acceleration when the seismic reinforcement bars reach the ultimate state, and record the displacement, stress distribution, failure mode, etc. of the dam body and the crack part under the corresponding conditions; analyze and evaluate the seismic capacity of the gravity dam according to 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 reinforcement bars, which can effectively solve the limitations of current seismic analysis and evaluation methods.

[0204] The following introduces an embodiment:

[0205] Refer to Figure 1, in the embodiment of the present invention, a model of the gravity dam's cross - joint reinforcement steel bars is constructed. The prototype is a certain dam section of a buttress gravity dam, which once had a penetrating crack at the connection corner between the dam head and the dam body under earthquake action and was later seismically reinforced with steel bars. The model of the gravity dam's cross - joint reinforcement steel bars includes the dam body concrete structure, the crack structure, and the steel bars that penetrate the crack structure for reinforcement; the model of the gravity dam's cross - joint reinforcement steel bars belongs to a three - dimensional finite - element mesh model. The dam body concrete structure is simulated by isoparametric elements, the cross - joint steel bar elements are used to simulate the existing reinforced steel bars, and the connection between the steel bars and the dam body concrete structure is realized through bonding elements.

[0206] Refer to Figure 2 , which is a schematic diagram of the bond - slip relationship between steel bars and concrete and crack damage of the gravity dam's cross - joint reinforcement steel bar model in the embodiment of the present invention. In this embodiment, after drilling holes at the crack part, additional seismic steel bar bundles are added, arranged horizontally and staggeredly, and grouted and anchored. In this embodiment, the established crack contact model includes crack contact conditions, the finite - element equilibrium equation under multiple load steps, and the crack flexibility equation. In this embodiment, the penetrating crack generated at the connection corner between the dam head and the dam body divides the dam body concrete structure into upper and lower regions. The seismic steel bars passing through the crack surface are in contact with the dam head and the dam body concrete respectively. The functional relationship between the shear stress and the relative slip amount of the bonding elements at the bonding parts between the seismic steel bars 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] Refer to Figure 3 , which is a relationship diagram between the peak value of ground motion acceleration and the stress of seismic steel bars in the embodiment of the present invention. In this embodiment, as the ground motion acceleration continuously increases, the stress of the seismic steel bars all increases significantly. When the peak value of ground motion acceleration reaches 0.38g, the tensile stress of the steel bars reaches the yield strength of the steel bars (335 MPa), indicating that the seismic steel bars fail; then the stress borne by the seismic steel bars further increases, which may lead to the pulling out of the steel bars, ultimately greatly reducing the overall stability of the dam head, prone to slip phenomenon, and resulting in the overall failure of the structure.

[0208] Refer to Figure 4 , which is a flow chart of a method for analyzing the seismic capacity of a gravity dam considering the reinforcement effect of seismic steel bars. The specific process of this method is as follows:

[0209] S1: Construct a model of the gravity dam's cross - joint reinforcement steel bars, and accurately simulate the dam body concrete structure, crack damage, and cross - joint steel bars in sequence through three - dimensional finite - element meshes; the dam body concrete structure is simulated by isoparametric elements, the cross - joint steel bars are simulated by bar elements, and the connection between the steel bars and the dam body concrete structure is composed of bonding elements;

[0210] S2: Establish a crack contact model based on the contact simulation of the cross-crack steel bars passing through the cracks with the concrete of the dam head and the dam body, as well as the bond-slip relationship equation and related constraint conditions between the steel bar elements and the concrete elements, to simulate the bond-slip relationship between the cross-crack steel bars and the dam body concrete structure, which serves as the basis for subsequent seismic simulation calculations.

[0211] S3: Back-analyze the physical and mechanical parameters of the dam body concrete structure; for the initially obtained physical and mechanical parameters, use them as the initial parameters of the gravity dam cross-crack reinforcement steel bar model, conduct simulation calculations by applying dynamic loads to the gravity dam cross-crack reinforcement steel bar model, and obtain the calculated values of the dam body concrete structure characteristics; compare the deviation between the calculated values of the dam body concrete structure characteristics and the measured values of the dam body concrete structure characteristics, and use the iterative optimization algorithm to dynamically update the physical and mechanical parameters until the error converges within the allowable range to obtain the optimal physical and mechanical parameters of the dam body concrete structure.

[0212] In this embodiment, the physical and mechanical parameters of the dam body 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 auto-power spectrum function identification method is used for the modal analysis of the dam body to obtain the measured frequencies and vibration modes of each order of the dam body. The double annealing algorithm is adopted in the optimization process, and the sum of squared differences between the simulated modal characteristics and the measured modal characteristics is used as the objective function. The specific steps are as follows: substitute the initial dynamic elastic modulus into the gravity dam cross-crack reinforcement steel bar model; apply the historical ground motion load and calculate the current modal characteristics, including frequencies and vibration modes; compare the calculated values of the 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 by back-analysis to the gravity dam cross-crack reinforcement steel bar model as the initial material parameters for seismic simulation; apply the design ground motion acceleration to the gravity dam cross-crack reinforcement steel bar model, and gradually increase the multiple of the ground motion acceleration to carry out seismic simulation calculations.

[0214] In this embodiment, the design ground motion acceleration applied to the model of the cross-joint reinforcement steel bars of the gravity dam in the seismic simulation calculation is selected according to the provisions of the Design Code for Seismic Design of Hydropower Projects (NB 35057-2015) regarding the design seismic intensity of the dam. The buttress gravity dam in this embodiment belongs to a large (1)-type project, the water retaining dam level is Class 1, and the seismic category of the water retaining dam is Class A. According to the code, the design seismic intensity should be increased by 1 degree on the basis of the basic seismic intensity, that is, the design seismic intensity of the dam is 8 degrees, and the corresponding peak ground motion acceleration is 0.20g. To analyze and evaluate its seismic capacity, the seismic simulation calculation needs to gradually increase the ground motion acceleration multiple, which are taken as 1.5, 2.0, 2.5, and 3.0 times the design ground motion acceleration amplification factors respectively, and analyze its seismic capacity in the case of encountering the extreme earthquake by the time history method.

[0215] S5: Record the peak ground motion acceleration when the seismic reinforcement reaches the limit state, and record the displacement and stress distributions of the dam body and the crack location under the corresponding conditions; according to the seismic simulation results, analyze and evaluate the seismic capacity of the gravity dam.

[0216] In this embodiment, when the seismic reinforcement reaches the limit state, it can be regarded as the extreme earthquake situation, and the corresponding ground motion acceleration at this time is the ultimate seismic capacity of the dam under this calculation condition. The further analyzed displacement and stress distributions of the dam body and the crack location include: the longitudinal displacement and vertical displacement of the dam body, the first principal stress of the dam body, the vertical stress; the time history change of the steel bar stress; the stress and opening displacement of the crack surface, etc. The further analyzed failure modes include concrete cracking or fracture, steel bar yielding or pulling out, dam head sliding, and overall structural failure, etc.

[0217] The above are only the preferred embodiments of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present invention.

Claims

1. A method for analyzing the seismic capacity of a gravity dam considering the seismic reinforcement effect of seismic steel bars, 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: taking 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 joint reinforcement steel bar model, and gradually increasing the earthquake acceleration multiples, to carry out earthquake simulation analysis; S4: Record the peak value of the earthquake acceleration when the steel bar reaches the limit state, and record 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, analyze and evaluate the seismic capacity of the dam concrete structure after the cross-crack reinforcement by the steel bar.

2. The method for analyzing the seismic capacity of a gravity dam considering the seismic reinforcement effect of seismic steel bars according to claim 1 is characterized in that: S2 is specifically: S2.1, using an inverse analysis method to obtain the physical and mechanical parameters of the dam concrete structure; 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 cross-seam 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 dam body concrete structure characteristics; S2.3, searching historical data to obtain measured values ​​of characteristics of the dam body concrete structure when the dam body 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 characteristic, dynamically update the physical and mechanical parameters of the dam body concrete structure by 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.

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

5. The method for analyzing the seismic capacity of a gravity dam considering the seismic reinforcement effect of seismic steel bars according to claim 1, characterized in that: S3 is specifically: S3.1: The dam body concrete structure is simulated by isoparametric units, and the dam body concrete structure is divided into a plurality of concrete units; the steel bars are simulated by bar units, and the steel bars are divided into a plurality of steel bar units; the bonding area between the steel bars and the dam body concrete structure has a plurality of bonding units; S3.2: at the current time step t in the seismic simulation analysis process, 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 opening, closing or slipping; S3.4: updating the reinforcement steel bar model of the gravity dam cross-crack reinforcement according to the crack contact state determined in S3.3; further analyzing the bond-slip relationship between the reinforcement steel bar and the dam body concrete structure based on the updated reinforcement steel bar model of the gravity dam cross-crack reinforcement, and evaluating the slip degree of the reinforcement-concrete contact interface; S3.5: Let time step t=t+1; apply the seismic acceleration of the design multiple 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.

6. A method for analyzing the seismic capacity of a gravity dam considering the seismic reinforcement effect of seismic steel bars according to claim 5, characterized in that: S3.3 specifically states: S3.3.1, the dam concrete structure is divided into an upper concrete area and a lower concrete area with the crack as the boundary; S3.3.2, the steel bar passing through the crack comes into contact with the upper concrete region and the lower concrete region respectively; the concrete contact interfaces on both sides of the crack are respectively referred to as the first concrete contact interface and the second concrete contact interface; S3.3.3, establish a local coordinate system ξηζ of the crack contact boundary; wherein 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 δ of contact point pair j at the current time step t is obtained by formula (1): t j : 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 the contact point j2 at the current time step t; Preliminary determination of the contact force on contact point j1 from contact point j2 And the contact force on contact point j2 from contact point j1 in, And, they all have components along the normal direction ξ, the tangent direction η, and the tangent direction ζ; S3.3.6, determine the contact state of contact point pair j: 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; 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, at this time, 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 respectively; 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 of all contact point pairs between the first concrete contact interface and the second concrete contact interface is obtained: t j The contact force increment array {Δf t j }: 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 of the first concrete contact interface relative to the previous time step; is the actual displacement increment of each contact point of the second concrete contact interface relative to the previous time step; 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; is the displacement increment of each contact point of 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; [L] 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 in 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 to 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.

7. A method for analyzing the seismic capacity of a gravity dam considering the seismic reinforcement effect of seismic steel bars according to claim 6, characterized in that: 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: S3.4.1, based on the updated reinforcement steel bar model of the gravity dam, determining the bonding area between the reinforcement steel bar and the dam body concrete structure; each bonding unit included in the bonding area is represented as bonding unit i; bonding unit i is the bonding position between the reinforcement steel bar unit i and the concrete unit i; S3.4.2, construct the bond-slip relationship equation between the steel bar unit and the concrete unit 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 body concrete structure; is the tangential stiffness matrix corresponding to the shear force applied by concrete unit i to steel unit i at each bonding unit i; The flexibility matrix formed by the flexibility of concrete unit i at each bonding 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 received by the steel bar unit i from the 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 the steel bar unit i and the 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 bar unit and the concrete unit shown in equation (4): the slip increment between the steel bar unit i and the concrete unit i at each bond unit i position, and then evaluate the slip degree of the steel bar-concrete contact interface at each time step t.

8. The method for analyzing the seismic capacity of a gravity dam considering the seismic reinforcement effect of seismic steel bars according to claim 7, characterized in that: When solving the bond-slip relationship equation between the steel bar unit and the concrete unit, the following constraints need to 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 loads on concrete element i transferred from steel element i; Constraint 2: The equilibrium equation of the steel bar element i in contact with the concrete element i: in: is the displacement array formed by the displacement of each steel bar unit i; is the array formed by the loads transferred from concrete unit i to steel unit i; The expression of is as follows: in: q i represents the slip between steel bar unit i and concrete unit i at each bonding unit i; is the bonding force exerted on the steel bar unit i from the concrete unit i at the bonding unit i; and The expressions are as follows: in: is the initial bonding force exerted on concrete unit i from steel unit i at bonding unit i; is the bonding force exerted on concrete unit i from 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, The following formula (11) constraints are satisfied: 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 range of bonding unit i.

9. The method for analyzing the seismic capacity of a gravity dam considering the seismic reinforcement effect of seismic steel bars according to claim 1, characterized in that: When applying seismic acceleration to the gravity dam seam reinforcement steel bar model for 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.

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